The graph of y = 15x is a straight line passing through the origin (0, 0) with a slope of 15. The line extends infinitely in both directions and represents the relationship between the number of weeks and the number of new vocabulary words learned.
The given equation is:
y = 15x
where y represents the number of new vocabulary words learned after x weeks.
This equation is a linear equation with a slope of 15, which means that for each week, the number of new vocabulary words learned increases by 15.
To graph this equation, we can plot points on the coordinate plane, where the x-coordinate represents the number of weeks and the y-coordinate represents the number of new vocabulary words learned.
For example, if we plug in x = 0, we get y = 0, which means that at the beginning (0 weeks), we haven't learned any new vocabulary words. This gives us the point (0, 0) on the coordinate plane.
If we plug in x = 1, we get y = 15, which means that after 1 week, we have learned 15 new vocabulary words. This gives us the point (1, 15) on the coordinate plane.
Similarly, we can plug in other values of x to get more points on the graph. For instance, plugging in x=2, we get y = 30, which gives us the point (2,30).
Continuing this process, we can get more points and plot them on the coordinate plane. Once we have enough points, we can connect them with a straight line to get the graph of the equation.
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What does a scale factor of 1.5 mean?
Scale Factor. To create a scaled copy, we multiply all the lengths in the original figure by the same number.
What does the number 1.5 signify on a scale?A 1.5 GPA, or Grade Point Average, is comparable to a D+ letter grade on a scale of 4.0 GPA. This corresponds to a grade of around 69%. The Scale Factor. To make a scaled replica, multiply all of the original figure’s lengths by the same number. This figure is known as the scaling factor. The scale factor in this case is 1.5 since 4(1.5)=6, 5(1.5)=7.5, and 6(1.5)=9.
An Over 1.5 Goals bet is simply a betting on there being two or more goals scored in a given game. The scoreboard is irrelevant; as long as the two sides collaborated for at least two goals, your bet will win.
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A baker sells bread for $3 a loaf and rolls for $1 each. The baker needs to sell $27 worth of baked goods by
the end of the day.
Graph the linear equation 3b + r = 27, where b is the number of loaves of bread sold and r is the
number of rolls sold.
Answer:
4 loaves of bread
Step-by-step explanation:
Cost of 1 loaf of bread = $3
Cost of 1 roll = $1
The baker needs to sell both items and it should be worth $24.
To find the linear equation,
Suppose, the baker sells
x
loaves of bread and
y
rolls.
Then the total cost of the sales has to be $24.
So, the linear equation will be:
3
x
+
1
y
=
24
.......................(A)
Now, it is given that the baker sold 12 rolls and we need to know how many loaves he has to sell.
For that, replace the
y
in equation (A) with 12 as
y
represents number of rolls sold.
Then the new equation becomes:
3
x
+
1
×
12
=
24
0r
3
x
=
24
−
12
or
3
x
=
12
Solving for
x
,
x
=
12
3
=
4
loaves
Find an expression to present the perimeter of the rectangle below
An expression to represent the perimeter of the rectangle with 10/(x² + 11x +24) and (x+1)/(x+3) would be (x+12)(x+6)//(x+8)/(x+3).
What is the perimeter?
A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.
Here, we have
Given: Sides = 10/(x² + 11x +24) and (x+1)/(x+3)
The perimeter is when you add all the sides of a shape.
In a rectangle, two sides are the same, and so are the other two. therefore, if the two sides are 10/(x² + 11x +24) and (x+1)/(x+3) the expression will be:
= 2(10/(x² + 11x +24)) + 2(x+1)/(x+3)
= 20/(x² + 11x +24) + 2(x+1)/(x+3)
= 20/(x+8)/(x+3) + 2(x+1)/(x+3)
= {20 + 2(x+1)(x+8)}/(x+8)/(x+3)
= {20 + 2(x² + 9x + 8)}/(x+8)/(x+3)
= { 20 + 2x² + 18x + 16}/(x+8)/(x+3)
= {2x² + 18x + 36}/(x+8)/(x+3)
= (x+12)(x+6)//(x+8)/(x+3)
Hence, an expression to represent the perimeter of the rectangle with 10/(x² + 11x +24) and (x+1)/(x+3) would be (x+12)(x+6)//(x+8)/(x+3).
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How do I covert between VOLUME units??
We will convert between volume units by multiplication or division process depending on the standard metric units.
What is unit conversion?
Unit conversion is done either by multiplication or division process between numerical values. There are some standard metric units. By following the standard, we can convert one unit to another. As example we have a box that is 2 square feet area, now we want to know the area in inches. So, we will multiply it by 144 to convert in square inches.
How do we convert between volume units?
We convert between volume units either by multiplication or division process depending on the standard unit. If we find a volume in liter and we can convert it in cubic meter by multiplying the number by 0.001. Assume, we measured a volume in cubic feet, but someone want to know this volume in cubic meter that time we divide this value by 35.32 to convert in required unit.
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find the area of STUV.
T(d) is a function that relates the number of tickets sold for a movie to the number of days since the movie was released. The average rate of change in T(d) for the interval d = 4 and d = 10 is 0. Which statement must be true?
A: Fewer tickets were sold on the fourth day than on the tenth day.
B:No tickets were sold on the fourth day and tenth day.
C: The same number of tickets was sold on the fourth day and tenth day.
D: More tickets were sold on the fourth day than on the tenth day.
The statement that must be true since the average rate of change T(d) for the interval d = 4 and d = 10 is 0 is this:
C: The same number of tickets was sold on the fourth day and tenth day.
What is the average rate of change?The average rate of change is a measurement that shows how much the function of a unit changes over a given interval. In the above question, we can see that the average rate of change given the two intervals is zero and this means that there was no change among the variables.
Thus, we can conclude that the number of tickets that were sold on day 4 was also the number of tickets sold on day 10.
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Gabi is helping her friend Joaquin create a square tile design in his backyard. Joaquin has one large square tile that is no longer being manufactured. He also has eight rectangular tiles that have the same side length as the large tile, and one small square tile that has the same width as the rectangular tiles. Gabi gets her algebra tiles to model the situation. How many small square tiles does Joaquin need to buy to complete a square tile design? please help
Answer:
Step-by-step explanation:
15 tiles
What is 3X3X3X3X3 in exponential form?
3×3×3×3×3 in exponential form is 3⁵.
When we represent a number in the exponential form then we can say that its power has been raised by an exponent. The exponential form is an easier way of representing repeated multiplication involving base and exponents.
For example, If we have to write the exponential form of a×a×a×a×a, we can write it as a base and the number of a's as the power that is
a×a×a×a×a = a⁵
Where
a is the base
5 is the power of a
We can simply write 3×3×3×3×3 in exponential form by raising the power to the base 3,
3×3×3×3×3 = 3⁵
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decide if the absolute value inequality is an “and” compound inequality, an “or” compound inequality, or neither.
1. |5+m|<13
a. “and” b. “or” c. neither
2. 4|y + 6| ≥ 3
a. “and” b. “or” c. neither
3. Choose the answer to | g – 3 | = -2
a. g = 5 or -5
b. g = 1 or -1
c. null set
1. |5+m|<13 is an "or" compound inequality. 2. 4|y + 6| ≥ 3 is neither compound inequality. 3. null set.
1. The inequality is given in the question, is as follows:
|5+m| < 13
The absolute value of the expression "5+m" is less than 13.
To solve the inequality, we need to split the inequality in two separate inequalities: 5+m < 13 and -5-m < 13.
Thus, |5+m|<13 is an "or" compound inequality.
2. 4|y + 6| ≥ 3 is neither compound inequality because we have just one inequality.
3. The absolute value of a number is always positive, so it is impossible for |g - 3| = -2. So the answer is c. null set.
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A horizontal parabola centered on the origin opens to the left and has a directrix at x = 2. The focal width is 8. The vertex of the parabola is at [ Select ]. The focus of the parabola is at [ Select ] . The axis of symmetry of the parabola is [ Select ] .
The vertex of the parabola is at (0, 0), the focus of parabola is at (2, 0) and axis of symmetry of parabola is x-axis.
What is parabola?A parabola is an approximately U-shaped, mirror-symmetrical planar curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.
One definition of a parabola includes a line and a point (the focus) (the directrix). The directrix is not the main focus. The locus of points in that plane that are equally spaced apart from the directrix and the focus is known as the parabola.
Given a horizontal parabola centered on the origin opens to the left,
the equation for a horizontal parabola,
(y − b)² = 4p(x − a), p≠0
a and b are the vertex of parabola,
since the parabola is centered on the origin, a and b are (0, 0)
vertex of parabola is at (0, 0),
and for horizontal parabola axis of symmetry is the x-axis.
focus of parabola is at (a + p, b)
given p = 2
focus of parabola is at (0 + 2, 0) = (2, 0)
Hence vertex at (0, 0), focus at (2, 0), and symmetry with the x-axis.
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A ceiling fan has 19-inch blades(so the radius of the circular fan is 19 inches). Suppose the dan turns at a rate of 69 revolutions per minute.
a) Find angular speed of the fan in radians per minute
b) Find the linear speed of the tip of a blade in inches per minute
Angular speed of the fan in radians per minute is 421 (crad /min) , The linear speed of the tip of a blade in inches per minute is
What the linear speed and angular speed?Suppose the dan turns at a rate of 69 revolutions per minute.
Angular speed of the fan in radians per minute is
According to the problem
w = 2zn
(a) w = 2z * 67
= 134z
≈ 421 crad /min)
Angular speed of the fan in radians per minute is 421 (crad /min)
The linear speed of the tip of a blade in inches per minute is
(b) v = 2z * 19 * 67
{ v = 2zrn}
=2546z
7988(cin / m * in)
The linear speed of the tip of a blade in inches per minute is 7988(cin / m * in)
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For what value of A is x 4 a factor of 5x³ 7x² ax 28?
(x - 4) is a factor of the expression 5x³ − 7x² − ax − 28, when a = 28
Here we are given the expression 5x³ − 7x² − ax − 28
now we need to find a value of a for which (x - 4) is a factor of
5x³ − 7x² − ax − 28
This implies that 5x³ − 7x² − ax − 28.must be divisible by (x - 4)
On dividing 5x³ − 7x² − ax − 28. by x - 4 will give us
[tex]x-4) \overline{5x^{3}-7x^{2}-ax-28.}(5x^{2}+14x+(56-a)\\{\hspace{1cm} 5x^{3}-20x^{2}\\\\\hspace{2cm}\overline{14x^{2}-ax}\\{\hspace{2cm}14x^{2}-56x\\\\{\hspace{3cm} \overline{(56 - a)x - 28}\\{\hspace{3cm} (56-a)x-(56-a)\\{\hspace{5cm} \overline{28-a}[/tex]
Since (x - 4) is a factor of 5x³ − 7x² − ax − 28, there should not be any remainder left
Hence, 28 - a = 0
or, a = 28
Hence (x - 4) is a factor of 5x³ − 7x² − ax − 28, when a = 28
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Correct Question
Find the value of a such that (x−4) is a factor of 5x³ − 7x² − ax − 28.
I NEED HELP WITH 4 ,5, 6 and 7 PLEASE ???
The Wien Apetrol UC 20142000 was a unique and innovative venture that aimed to provide clean energy solutions to the people of Austria.
Solve for x ?x = -7
ma = 54
m23 = 54
The project was a collaboration between the Austrian government, private companies, and research institutions.It focused on developing and implementing renewable energy sources such as solar, wind, and hydropower, as well as energy storage systems. The project showcased the potential of renewable energy sources to provide a sustainable and affordable energy solution to citizens.It also promoted the use of energy efficiency measures to reduce energy consumption and costs. The project was a success, and it achieved its goal of providing reliable and affordable energy to the people of Austria.The project has been cited as a model for renewable energy projects around the world and has served as an example of how collaboration between different sectors can be successful.To learn more about Wien Apetrol refer to:
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Need help pls and thanks
You can tell if a table shows a proportional relationship by calculating the ratio of each pair of values.
The table depicts a proportionate relationship if all of those ratios are the same.
If all of the ratios of the variables are equal, then there is a proportional link between the two variables.
In proportional relationships, one variable is, in other words, always a constant value multiplied by the other variable. The proportionality constant is the name given to the constant value. A mathematical equation of the form y=kx, where k is the proportionality constant, can be used to model any proportional relationships. The unit rate is another name for the proportionality constant.
Dustin, for instance, spends $8 each month for a music streaming service. The total cost of the service, c, and the number of months Dustin pays for the streaming service, m, are proportionate.
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Challenge A family wants to rent a car to go on vacation Company A charges $30.50 and 10¢ per mile. Company B charges $75.50 and 16¢ per mile. How much more does Company B charge for x
miles than Company A?
For x miles, Company B charges dollars more than Company A
(Simplify your answer. Use integers or decimals for any numbers in the expression.)
A
Integers are a type of real number that just includes positive and negative whole numbers and natural numbers. Real numbers can include fractions due to rational and irrational numbers, but integers cannot include fractions.
How do you know if a number is integer or decimal?In this method, we will check the number by dividing it with 1, if it is completely divided by 1 then the function will return value as 0 and the number is a whole number. Otherwise, the number is a decimal point number.Fractions and decimals are not integers. All whole numbers are integers (and all natural numbers are integers), but not all integers are whole numbers or natural numbers. For example, -5 is an integer but not a whole number or a natural number.An integer, also called a "round number" or “whole number,” is any positive or negative number that does not include decimal parts or fractions. For example, 3, -10, and 1,025 are all integers, but 2.76 (decimal), 1.5 (decimal), and 3 ½ (fraction) are not.An integer is a number with no decimal or fractional part, from the set of negative and positive numbers, including zero.
$75.50 and 18 cents - $35.50 and 8 cents = $40.00 and 10 cents per mile. For x miles, we multiply $40.00 and 10 cents by x miles.
Also, we could convert dollars to cents by multiply it by 100 Since $1 =100 cents.
7568 - 3558 cents = 4010 cents. For x miles, 4010X cents.
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Multiply the first number by its reciprocal:
6
X
6
42
The result after multiplication = 6/X, 1, 1/ 7
What is reciprocal?When one is divided by a number or value it is called the reciprocal of that number or value. It is also said the inverse form of the value or number. As example, reciprocal of 12 is written as 1/12.
What is the result?
There are four values 6, X, 6 and 42.
multiply the first number by the reciprocal of others.
reciprocal of X = 1/X
reciprocal of 6 = 1/6
reciprocal of 42 = 1/42
now we multiply, 6×1/X = 6/X
6×1/ 6 = 1
6×1/ 42 = 1 /7
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What is the constant of Y 10x?
For y = 10x the constsnt of proportionality is 10
We know that the quantity m is proportional to quantity n if there is a constant p such that m = pn
Here, p is called as the constsnt of proportionality.
This means, the constsnt of proportionality is nothing but the ratio between two proportional quantities.
Two variables are proportonal to each others means, when the variable increase the other one would also increase at some rate and that rate is the constant of proportionality.
We have been given an equation y = 10x.
Comparing given equation y = 10x with y = kx (here k is the constsnt of proportionality)
we have k = 10
This means, the constsnt of proportionality is k = 10
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Use a trigonometric ratio to solve for c. Round to two decimal places as necessary!!
HELP, and can someone explain how to get the answer?
Given that the one side of a right-angled triangle is 12 and its angle is 19, the value of c is 36.85.
what is trigonometry ?Trigonometry, a branch of mathematics, studies how triangle side lengths and angles relate to one another. Around the third century BC, the use of geometry in astronomical study led to the first appearance of the area. The study of specific trigonometric functions and how they could be applied to calculations is a topic covered in the branch of mathematics known as precise techniques. Trigonometry includes six well-known trigonometric operations. The names and acronyms for each are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of triangle properties, specifically of right triangle properties. But geometry is the study of geometric figures and their features.
given
a/sinA = c / sinB
12 / sin19 = c / sin90
36.85 = c /1
c = 36.85
Given that the one side of a right-angled triangle is 12 and its angle is 19, the value of c is 36.85.
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Isabel chooses one ball from the bag at random. She wins 1 if the number 1 is selected, 2 if the number 2 is selected,5 if the number 3 is selected, 6 if the number 4 is selected 8 if the number 5 is selected and 10 if the number 6 is selected. She loses 16 if 7 or 8 is selected
The expected value of Isabel's game is given as follows:
E(X) = 0.
How to obtain the expected value of a discrete distribution?The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.
The game is composed by choosing eight balls, which are equally as likely to be chosen.
Then the probability distribution of earnings is given as follows:
P(X = 1) = 1/8.P(X = 2) = 1/8.P(X = 5) = 1/8.P(X = 6) = 1/8.P(X = 8) = 1/8.P(X = 10) = 1/8.P(X = -16) = 2/8.Hence the expected value of the price is given as follows:
E(X) = 1/8 x (1 + 2 + 5 + 6 + 8 + 10) - 16 x 2/8.
E(X) = 0.
Missing InformationThe problem asks for the expected earnings.
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hey free 100 points :) (not really) please help!
Complete the square in the quadratic function f given by
f(x) = 2x2 - 6x + 4
Answer: x = 2, 1
Step-by-step explanation:2x^2 - 6x + 4 = 0
Firstly, simplify. Divide by 2 to get
2(x^2-3x+2) = 0
Move the constant to the other side.
2(x^2-3x) = -2
Divide the x term by 2 and square it
-3/2^2 = 9/4
Add this result to both sides.
2(x^2-3x+9/4) = 1/4.
Put the perfect sq on both sides
2(x-3/2)^2=1/4
Then solve the equation:
take the sqrt of both sides and isolate x for each solution
x-3/2= +/-1/2
x = 3/2 + 1/2
x= 3/2-1/2
x= 2, 1
Circle A has circumference 2/2/3 m.Circle B has a diameter that is 1/1/2 times as long as Circle A's diameter.What is the circumference of circle B
The circumference of circle B is 14 m
What is the area and circumference of a circle?The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.
Given here: The circumference of circle A as 2²/₃ m and circumference of circle B as 1¹/2 times the diameter of circle A
let the radius of the circle A be r then we have
2πr=8/3
r=4/3×7/22
r=14/33 m
or diameter of the circle A= 28/33
Again let the circumference of the circle be x then we have
x=28/3 ×3/2
x=14
Hence, The circumference of circle B is 14 m
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A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 447 gram setting. Based on a 24 bag sample where the mean is 444 grams and the standard deviation is 10, is there sufficient evidence at the 0.1 level that the bags are underfilled or overfilled? Assume the population distribution is approximately normal.
Step 5 of 5: Make the decision to reject or fail to reject the null hypothesis.
The decision rule for is to reject null if critical value is higher than the test statistic, since there is insufficient evidence to show that the machines are underfilling the bag.
How to carry out the hypothesis testFirst we have to solve for the test statistic
t = x - u / s /√n
the variables are stated as:
where x = 444
u = 447
n = 24
s = 10
we would have the test statistic solved as :
444 - 447 / 10 / √24
-3 / 2.0412
= -1.4697
at 0.1 significance level, we would have:
degree of freedom
n - 1
= 24 - 1 = 23
the critical value is -1.3194.
Because the critical value is greater than the test statistic, we are going to reject the null.
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Line m passes through point (5, 8) and has a slope 3/5. What is the equation for the line
The equation for the line is y = 3/5x + 5.
What is equation ?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
y = mx + b
8 = 3/5(5) + b
8 = 15/5 + b
b = 5
∴ equation is y = 3/5x + 5
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The volume of a right cone is 4487 units³. If its height is 21 units, find its radius.
Answer:
Step-by-step explanation:
V=(1/3)hπr^2
<=> 4487 = 1/3x21πxr^2
<=> r^2 = 641/π
<=> r = squrt( 641/π)
Elena and Jada each make money by helping out their neighbor. Elena babyit. Her earning are given by the equation y=8. 40x, where x repreent how many hour he work and y repreent how much money he earn. Jada earn $7 per hour mowing her neighbor' lawn. How long would it take to make each peron 150$?
If Elena earn y = 8.40x dollars where x represent how many hours she work and Jada earn $7 per hour, it would take Elena approximately 17.86 hours and Jada approximately 21.43 hours to earn $150
To find out how many hours it would take for Elena to earn $150, we need to solve the equation:
y = 8.4x
150 = 8.4x
x = 150/8.4
x ≈ 17.86 hours
So it would take Elena approximately 17.86 hours to earn $150.
To find out how many hours it would take for Jada to earn $150, we divide 150 by her hourly rate:
= $150 /( $7/ hour)
≈ 21.43
So it would take Jada approximately 21.43 hours to earn $150.
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What additional information must be known to prove the triangles similar by SSS?
A)
The lengths of and
B)
∠F ≅ ∠K
C)
No additional information is needed.
D)
∠D ≅ ∠J
The angle also should be known to prove congruency.
What is congruence?It states that two triangles are said to be congruent if they are exact copies of one another and completely cover one another when superposed. In other words, two triangles are congruent if their corresponding sides and angles are equal to those of the first triangle.
A congruence theorem, is AAA?It is ineffective to only know angle-angle-angle (AAA), as this can result in triangles that are similar but not congruent. There are four short cuts that can be used to check whether two triangles are congruent.
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Which of the following angles are congruent to ∠5? Select all that apply.
Angle 5 is congruent to angle 8 by (vertically opposite angle )
Angle 5 is also Congruent to Angle 4 (alternate Angles)
Angle 5 is also Congruent to Angle 1 ( corresponding Angles )
What is Congruency ?When two figures or things are similar in size and shape, or when one is the mirror image of the other, they are said to be congruent.
It states that two triangles are considered to be congruent if they are identical duplicates of one another and completely cover one another when superposed. In other words, two triangles are congruent if their corresponding sides and angles are equivalent to those of the first triangle.
Two line segments are said to be congruent if their lengths are identical. In addition, two congruent line segments have the same length. Two angles are congruent if they have the same measure.
Angle 5 is congruent to angle 8 by (vertically opposite angle )
Angle 5 is also Congruent to Angle 4 (alternate Angles)
Angle 5 is also Congruent to Angle 1 ( corresponding Angles )
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Angle 5 is congruent to angle 8 by (vertically opposite angle )
Angle 5 is also Congruent to Angle 4 (alternate Angles)
Angle 5 is also Congruent to Angle 1 ( corresponding Angles )
What is Congruency ?When two figures or things are similar in size and shape, or when one is the mirror image of the other, they are said to be congruent.
It states that two triangles are considered to be congruent if they are identical duplicates of one another and completely cover one another when superposed. In other words, two triangles are congruent if their corresponding sides and angles are equivalent to those of the first triangle.
Two line segments are said to be congruent if their lengths are identical. In addition, two congruent line segments have the same length. Two angles are congruent if they have the same measure.
Angle 5 is congruent to angle 8 by (vertically opposite angle )
Angle 5 is also Congruent to Angle 4 (alternate Angles)
Angle 5 is also Congruent to Angle 1 ( corresponding Angles )
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analyze the two equations: 12y= -3x+8 and 6y =kx-5 for what value of k are the graphs equal
The value of k are the graphs (equations) equal is k = -3/2
What are equations?Equations are mathematical expressions that show the relationship between two variables.
How to find for what value of k are the graphs equal?Since we have the two equations 12y = -3x + 8 and 6y = kx -5, re-writing them, we have
12y = -3x + 8
3x + 12y - 8 = 0 (1)
Also, 6y = kx - 5
-kx + 6y + 5 = 0 (2)
Condition for equal (consistent) equations?For a pair of equations ax + bx + c = 0 (3) and a'x + b'x + c' = 0 (4) to be equal (or consistent), then
a/a' = b/b' = c/c'
Comparing with (1) and (2), with (3) and (4) above, we have that
a = 3, b = 12c = -8a' = -kb' = 6 andc' = 5So, using a/a' = b/b', we find k.
So, substituting the values of the variables into the equation, we have that
a/a' = b/b'
⇒ 3/-k = 12/6
Cross-multiplying, we have that
3 × 6 = -k × 12
k = -3 × 6/12
k = -3/2
So, the value of k = -3/2
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What is the height of a triangle if its base is 24 cm and its area is 216 cm2?
The height of a triangle if its base is 24 cm and its area is 216 cm² is 18 cm.
The area of triangle is calculated using the below mentioned formula -
Area = 1/2 × base × height. We will use the formula of area of triangle to calculate the height of triangle.
Keep the values in formula -
216 × 2 = 24 × height
Firstly multiplying the values given on Left Hand Side of the equation
height × 24 = 432
Shifting 24 to Right Hand Side of the equation
Height = 432/24
Now dividing the values
Height = 18 cm
Thus, the height of the triangle is 18 cm.
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Help please due by tonight
The table shows the temperature of a substance at the start of a science experiment which - 16.8°C and we were told that it changed by 3/4 of the value which therefore means that the final temperature at 2:35pm is - 29.4°C.
What is Temperature?This is referred to as the degree of hotness or coldness of a substance and it is measured in Celsius, kelvin etc.
In this scenario we were told that the temperature - 16.8°C changed by 3/4 of the value which means that:
3/4 × - 16.8°C = - 12.6°C
The temperature at 2:35pm will therefore be - 16.8°C - 12.6°C = - 29.4°C.
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