B = (2a + 11)/5 is an expression for b when expressed in terms of a.
What exactly are slopes and lines?
We are aware that lines might have several kinds of equations; the typical form is
The equation of a line in slope-intercept form is Ax + By + c = 0, and
y = mx + b.
m is the slope, and b is the y-intercept.
The y-intercept, or (0,b), is the point where the line crosses the y-axis when x = 0. The slope represents the rate of change of the y-axis relative to the x-axis.
Given:
Coordinates of point Q = (2,3)
Coordinates of point R = (a,b)
The equation of the line is 5x + 2y = 9 ⇒ 2y = - 5x + 9
Therefore, y = (-5/2)x + 9/2.
We know slope m = (y2 - y1) / (x2 - x1)
∴ m = (b - 3)/(a - 2).
∴ (2/5) = (b - 3).(a - 2).
2(a - 2) = 5(b - 3).
2a - 4 = 5b - 15.
2a + 11 = 5b.
b = (2a + 11)/5.
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Can someone help me in number 3?
Answer:
1.5 kilograms
Step-by-step explanation:
You need to convert grams to kilograms, this means you must divide the mass value by 1000 to find your answer.
1,500/1,000 = 1.5
Answer:
For 1500 grams in kilogram we get 1.5 kg
Step-by-step explanation:
to convert a gram into a kilogram we have to divide the gram term by 1000
URGENT!! 60 POINTS!!!!! Based on the linear table of ordered pairs, what is the y intercept?
Answer:
The y-intercept is (0, 8)-----------------------------------
According the the table the slope is:
m = (12 - 4)/(1 - (-1)) = 8/2 = 4Use slope-intercept form:
y = mx + b, where b is the y-interceptAnd substitute one of the ordered pairs, to find the value of b:
4 = 4(-1) + b4 = - 4 + bb = 4 + 4b = 8The y-intercept is (0, 8).
Write the equation of the line that passes through (7, 6) and (-- 1, 2) in slope-intercept form.
○ y = − 1/x + 2/1/2
O y = 2x + 4
○ y = 1/x + 1/2/2
○ y = 1/x + 1/2
The equation of the line that passes through (7, 6) and (-1, 2) in slope-intercept form is, [tex]y=\frac{1}{2}x + \frac{5}{2}[/tex].
What is slope intercept form of the line?
Using a straight line's slope and the location of its y-axis intersection, the slope intercept equation can be used to determine the general equation of the line. y = mx + b is the equation in slope intercept form.
Given:
The line passes through the points (7, 6) and (- 1, 2).
We have to find the equation of the line that passes through (7, 6) and (-- 1, 2) in slope-intercept form.
First to find the slope of the line using the formula,
Slope = m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Here, [tex](x_1, y_1)= (7, 6), (x_2,y_2)=(-1, 2)[/tex]
Plug the values in the above formula.
[tex]m = \frac{2-6}{-1-7} = \frac{-4}{-8}=\frac{1}{2}[/tex]
Now consider the point slope form of the line,
[tex]y-y_1=m(x-x_1)\\y-6=\frac{1}{2}(x-7) \\y-6=\frac{1}{2}x-\frac{7}{2}\\ y=\frac{1}{2}x -\frac{7}{2}+6 \\y=\frac{1}{2}x+\frac{5}{2}[/tex]
Hence, the equation of the line that passes through (7, 6) and (-1, 2) in slope-intercept form is, [tex]y=\frac{1}{2}x + \frac{5}{2}[/tex].
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10. Jim estimates the width of his wall to be 7.5 feet. The actual wall measures 8.25 feet wide. What is
Jim's percent error?
Answer:
Below
Step-by-step explanation:
Error : (8.25 - 7.5)
% error : ( 8.25-7.5) / 8.25 * 100% = 9.1 %
Jim's percent error is 9.09%.
What is the percentage error?
The percentage error is given as the difference between the actual value and the estimated value divided by the actual value, multiplied by 100%.
The percentage error is a relative value that compares the actual value and the estimated value to explain any deviations.
Estimated width of wall = 7.5 feet
The actual width of the wall = 8.25 feet
The difference in estimate = (8.25 - 7.5) = 0.75 feet
Percentage Error = (0.75/8.25 x 100) = 9.09%
Thus, we can conclude that Jim made a percentage error of 9.09% in his estimate of the width of the wall.
Find the unit rate of the constant of proportionality for the following: $9.80 for 5 pounds.
Showing your work would be appreciated, so if you could, that’d be great. But it’s not needed, if you don’t want to. :)
Thank you in advance to anyone who answers!
The unit rate of constant means that for every 1 pound, the output is 1.96 dollar.
What is proportionality?Proportionality is a relationship between two variables in which their ratio is always equal to a constant value. In mathematical terms, it can be expressed as y = kx, where y and x are the two variables, and k is the constant of proportionality.
What is rate?A rate is a measure of how one quantity changes in relation to another quantity. It is usually expressed as a ratio and has units of measurement, such as miles per hour, dollars per pound, etc. A unit rate is a rate in which the second quantity is one unit of measurement.
The unit rate of the constant of proportionality is found by dividing the change in y (output) by the change in x (input).
In this case:
$9.8/5$ = $1.96$, so the unit rate of the constant of proportionality is 1.96 pounds/dollar.
It means that for every 1 pound, the output is 1.96 dollar.
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What is ordinate of a 3 4?
The coordinate of 3 4 indicates a point on a cartesian plane.
What is coordinates system?In mathematics, the coordinate system refers to the method in which a location of a point is identified in the plane or space.
There are two coordinate system, one is cartesian coordinate system and the other is polar coordinate system.
Each coordinate system has some reference lines called reference axis or reference direction or point called reference direction and point.
What do we mean by coordinate of 3 4?As per the definition of a cartesian coordinate system, a location of a point is identified by a pair of numerical terms. The first one indicates the X coordinate and the second one indicates the Y coordinate.
So, the above coordinate 3 4 refers to a point on the XY coordinate system where 3 is the X coordinate and the distance from Y axis and 4 is the Y coordinate and distance from the X axis.
ordinate refers to y point in (x, y)
in (3,4)
ordinate = 4
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What is the solution of 2x^2 5x 3 0?
The Given quadratic equation has two solutions: 1 and 3/2. A quadratic problem was solved by utilizing the factoring method.
A quadratic equation is defined.
At least one squared term must be present because a quadratic is a second-degree polynomial equation. It is also known as quadratic equations. ax^2 + b*x + c = 0 is the quadratic equation's general form.
where x is the unknown variable and a, b, and c are constant terms.
In this case, I'm solving a quadratic problem by factoring.
The following quadratic equation is
2x^2 - 5x + 3 = 0.
2x^2 - (3+2)x + 3 = 0
2x^2 -3x -2x + 3 = 0.
x(2x-3) -1(2x -3) = 0.
(2x-3)(x-1) = 0.
2x - 3 =0 or x -1 =0
x = 3/2 or x =1
So the solutions of a quadratic equation are 3/2 and 1.
Given Question is incomplete complete question here:
What are the solutions of the quadratic equation 2x^2-5x+3 = 0?
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The length of the rectangle is X units more than its
width. The width of the rectangle is 11 units and the
length of the wire that is used to make this rectangle
is a maximum of 57 units. Represent this situation
using an inequality.
Answer: [tex]2x+44 \le 57\\\\[/tex]
Explanation:
W = width
W = 11
L = length
L = width+x
L = 11+x
P = perimeter of the rectangle
P = 2L+2W
P = 2*(11+x)+2*11
P = 22+2x+22
P = 2x+44
The perimeter is at max 57 units because it is the length of wire used. Think of it like fencing around a piece of land. Be sure not to mix up the length of the wire with the rectangle length; those are two different things.
Anyways, because the perimeter maxes out at 57, this means either P = 57 or P < 57.
This leads to:
[tex]P \le 57\\\\2x+44 \le 57\\\\[/tex]
Forming Equations with a given variable
1. The ages of three cats are and. Their total age is
21. Determine.
The value of {a} in the given modelled statement equation is 5.
What are equations?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".
Given is that the ages of three cats are (a) , (a + 4) and (2a - 3). Their total age is 21.
We can model the given equation is -
(a) + (a + 4) + (2a - 3) = 21
a + a + 4 + 2a - 3 = 21
4a + 1 = 21
4a = 20
a = 5
Therefore, the value of {a} in the given modelled statement equation is 5.
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{
Complete question is given below -
The ages of three cats are a, a+4 and 2a-3. Their total age is 21. Determine a.
}
Please Simplify the phrase the first two and find the last one
Answer:
1) 23x + 6y
2) 8x - 4y
3) 4x - x² + 7
Step-by-step explanation:
Simplify:
Multiply each term of (3x + 6y) by 5 and multiply each term of (2x - 6y) by 4.
5(3x + 6y) + 4 (2x - 6y) = 5*3x + 5*6y + 4*2x - 4*6y
= 15x + 30y + 8x - 24y
Now, combine like terms. Like terms have same variable with same power.
= 15x + 8x + 30y - 24y
= 23x + 6y
2) 3(4x - 2y) - 2*(2x -y) = 3*4x + 3*(-2y) + (-2)* 2x + (-2)*(-y)
= 12x - 6y - 4x + 2y
= 12x - 4x - 6y + 2y
= 8x - 4y
3) f(x) = 3x + 2
To find f(x +1), replace x with (x +1)
f(x +1) = 3*(x + 1) + 2
= 3*x + 3*1 + 2
= 3x + 3 + 2
=3x + 5
f(2x) = 3*(2x) + 2
= 6x + 2
f(2x) + h(x) = 6x + 2 - x² - 2x + 5
= 6x - 2x - x² +2 + 5
= 4x - x² + 7
I AM GIVING 30 POINTS!!!!!!!! TO WHOEVER ANSWERS THIS!!!! PLEASEPedro loves to try new adventures. His most recent was jumping out of an airplane. His special watch tells him his altitude. He set a timer at the moment he opened his parachute. His altitude relative to sea level, A, in feet, which is a function of time, in minutes, is shown in the table below. A t 11,100 4 7200 8 3300 12 A function could be written to describe the decent: Blank 1 = (Blank 2 )t + Blank 3
Answer:Sorry cant find
Step-by-step explanation:
please help with this shapes question
Given the surface area of the sphere, and the formula for the surface area, the value of the radius is 11 cm
How to find the radius ?The radius of the sphere allows for the surface area of the sphere to be calculated, with the formula 4 πr².
Given that the surface area of the sphere is 484 π cm then the radius can be found to be :
484 π = 4 πr²
r ² = 484 π / 4 π
r ² = 121
The value of the radius would then be:
r ² = 121
r = √ 121
r = 11 cm
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What is an example of horizontal symmetry?
The examples of horizontal symmetry is B, C, H, E.
The term horizontal symmetry is defined as is a line about which the object is symmetric.
Here we know that the symmetry line or horizontal axis of a shape which divides the shape into two identical halves is known as horizontal line of symmetry.
Which defines that the axis here crosses across the shape to cut it into two equal parts.
Therefore, the English alphabets such as B, C, H, E, are the examples of horizontal symmetry.
In this case, here we have a horizontal line passing through the middle of the image and when the image is folded along this line, then we get the two halves overlapping and coinciding perfectly.
Therefore, this one is also an example for this could be a square or a rectangle or any other object that is symmetric horizontally.
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lines a and b are parallel. which angles is congruent to angle? 4
Answer:
ANGLE 5 IS CONGURENT TO ANGLE 4
PLEASE MARK BRAINLIEST
Equilateral triangle T is inscribed in circle A , which has radius 10 . Circle B with radius 3 is internally tangent to circle A at one vertex of T . Circles C and D , both with radius 2, are internally tangent to circle A at the other two vertices of T. Circles B, C , and D are all externally tangent to circle E, which has radius m/n , where m and nare relatively prime positive integers. Find m+n
For the given figure, where m and nare relatively prime positive integers. The value of m+n is 32.
Explain Law of Cosines.The law of cosines, also known as the law of cosines, relates all three sides of a triangle to one angle of the triangle. Most useful for searching for missing information in triangles. For example, if you know all three sides of a triangle, you can use the law of cosines to find the measure of the angle. Similarly, if you know two sides and the angle between them, you can find the length of the third side by the law of cosines.
Let X be the intersection of the circles with centers B and E, and Y be the intersection of the circles with centers C and E.
Since the radius of B is 3, AX = 4.
Assume AE = p.
Then EX and EY are radii of circle E and have length 4 + p.
AC = 8, and ∠CAE = 60° because we are given that triangle T is equilateral.
Using the Law of Cosines on Δ CAE, we obtain
(6+p)² =p² + 64 - 2(8)(p) cos 60
The 2 and the cos 60 terms cancel out:
p² + 12p + 36 = p² + 64 - 8p
12p+ 36 = 64 - 8p
p = 28/20
= 7/5
The radius of circle E is 4 + (7/5)
= 27/5,
So, the answer is 27 + 5 = 32
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The table provides information on road accidents reported to the police for the days in December.
Accidents reported l Frequency
3 - 7 l 17
8 - 12 l 1
13 - 18 l 1
19 - 25 l 12
Estimate the range.
The range of the accidents reported from the grouped frequency table is 22.
What is a range in a set of data?The range is the difference between the highest value and the lowest value of a given set of data.
We have,
The number of accidents reported from the grouped frequency table.
The largest number of accidents = (19 - 25)
The smallest number of accident = (3 - 7)
Now,
Range.
= 25 - 3
= 22
Thus,
The range of the reported accidents is 22.
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Select perpendicular lines from the given pair of lines :
Select one:
a.
y = − 3x + 7, y = 3x + 11
b.
y = 3x + 7, y = x / 3 + 11
c.
y = − 3x + 7, y = x / 3 + 11
d.
y = − 3x + 7, y = − x / 3 + 11
Answer:
The line pairs that are pendicular are shown in option c.
c. y = − 3x + 7, y = x / 3 + 11
Step-by-step explanation:
Perpendicular lines have slopes that are the negative inverse of each other. For example, a line with slope of 5 would have a line perpendicular to it if the second line has a slope of -(1/5) [the negative inverse of +5].
Cmpare the slopes of each pair of linear equations:
a. -3 and 3 The negative inverse of -3 would be (1/3), not 3. These lines are not perpendicular.
b. 3 and (1/3). The negative inverse of 3 would be -(1/3), not (1/3). These lines are not perpendicular.
c. -3 and (1/3). The negative inverse of -3 would be (1/3). These lines are perpendicular.
d. -3 and (-1/3). The negative inverse of - 3 would be (1/3). These lines are not perpendicular.
Bookwork code: E13 Work out the equation of the straight line shown below. Give your answer in the form y = mx + c, where m and care integers or fractions in their simplest forms. 7 4- 3. 2- 1- -6 -5 -4 -3 -2 -1.0 -1- --2- --3- -4- -5- Calculator not allowed T 2 3 4 5 6 X
Answer:
y = -5x +4
Step-by-step explanation:
You want the point-slope equation of the line with y-intercept +4 and through the point (1, -1).
SolutionThe graph shows you the line decreases 5 units from +4 to -1 as x increases 1 unit from 0 to 1. This tells you the slope is ...
m = rise/run = -5/1 = -5
The y-intercept is the value of y where the line crosses the y-axis:
b = 4
These values go into the point-slope equation:
y = mx +b . . . . . . line with slope m and y-intercept b
y = -5x +4 . . . . . . line with slope -5 and y-intercept 4
makayla runs 3/5 of a mile in 1/6 of an hour. How fast, in miles per hour, does she run
Answer:
3.6 miles
Step-by-step explanation:
SolutionGiven information from the question,
[tex]\frac{1}{6} \ hour = \frac{3}{5} \ miles\\ 1 \ hour = \frac{3}{5} / \frac{1}{6} \ miles\\1 \ hour = \frac{18}{5} \ or\ 3\frac{3}{5} \ or \ 3.6 miles[/tex]
Answer:
Velocity is the term to illustrate speed
Step-by-step explanation:
velocity = distance ÷ time
velocity = 3/5 ÷ 1/6
= 18/5 m/h
[tex]343^{-4/3}[/tex]simplify
The value of the expression [tex]343^{-4/3}[/tex] is 1/2401.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[tex]343^{-4/3}[/tex]
This can be written as,
1/[tex]343^{4/3}[/tex]
343 = 7³
= 1/[tex]7^{3\times4/3}[/tex]
= 1/[tex]7^4[/tex]
[tex]7^4[/tex] = 7 x 7 x 7 x 7 = 49 x 49 = 2401
= 1/2401
Thus,
The value of the expression is 1/2401.
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Complete the inequality below to describe the
domain of the graph shown.
Domain:
DONE
completo the inequality holow to dogorike the
On solving the provided inequality equation we cans ay that therefore, 60x + 45 <250 is the necessary inequality for the given situation.
Describe inequality.An inequality in mathematics shows how two values are related in an imbalanced algebraic expression. According to inequality signals, one of the two variables on either side of the inequality may be larger than, greater than or equal to, less than, or less than or equal to another value.
If the daily cost for each crew member is $60, the daily wage for crew members is $60, and the daily cost of operations is $45; the amount paid equals the total of the wages for each crew member plus the cost of operations. In this case, let x indicate the size of the crew.
= 60x + 45
Since the maximum daily payment is $250,
In other words, the total payment cannot be more than $250.
60x + 45 ≤ 250
Therefore , the required inequality for given problem is 60x + 45 ≤ 250.
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For what value of k the equation 4x2 2 K 1 )= 0 has real and equal roots?
The values of k are 3 and −1.
Note: The equation taken here is 4x^2 −2(k+1)x+(k+1)=0
Given: Equation 4X^2−2(k+1)x+(k+1)=0 has real and equal roots i.e., its discriminant is zero.
⇒b2−4ac=0
[An expression that can be produced from the square of a binomial equation is a perfect square trinomial. A perfect square trinomial is a formula that has the elements ax^2 + bx + c and satisfies the condition b^2 = 4ac. The roots of the quadratic equation ax2 + bx + c = 0 are real and equivalent if the discriminant is equal to zero (b2 - 4ac = 0), a, b, and c are real values, and a0.]
For given equation, a=4, b=2(k+1),c=(k+1)
(2(k+1))^2 −4.4(k+1)=0
⇒(2k+2)^2−16(k+1)=0
⇒4k2+8k+4−16k−16=0
⇒4k2−8k−12=0
⇒4(k2−2k−3)=0
⇒k2−2k−3=0
⇒k2−3k+k−3=0
⇒k(k−3)+1(k−3)=0
⇒(k−3)(k+1)=0
⇒k−3=0 and k+1=0
⇒k=3 and k=−1
So, the values of k are 3 and −1.
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x +96 > 12 solving inequalities
The solution to the inequality expression is x > -84
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
x +96 > 12
Subtract 96 from both sides of the inequality expression
So, we have the following representation
- 96 + x +96 > 12 - 96
Evaluate the like terms
x > -84
Hence, the solution is x > -84
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Finn leaned a 100-foot ladder against the side of a building. The base
of the ladder is 14 feet from the base of the building. The top of the
ladder is 11 feet from the top of the building. How tall is the building?
Provide an answer accurate to the nearest tenth of a foot.
The height of the Building is 110.01 feet.
What is the Pythagorean theorem?The square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides, according to Pythagoras' Theorem.
Given, Finn leaned a 100-foot ladder against the side of a building. The base of the ladder is 14 feet from the base of the building. The top of the ladder is 11 feet from the top of the building.
For the triangle made by ladder
hypotenuse = 100
base = 14
thus, from the Pythagorean theorem
hypotenuse² = base² + height²
100² = 14² + height²
height² = 10000 - 196
height = √9804
height = 99.01
total height of the wall = height of triangle + remaining height of the wall
Thus the total height of the wall = 99.01 + 11
the total height of the wall = 110.01
therefore, the building is 110.01 feet tall.
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Use the distributive property to simplify each expression.
-2(x - 2) + 5x
please help
Answer:
3x + 4
Step-by-step explanation:
Using the distributive property simply means that when there is a number in front of a pair of parentheses, every value inside the parentheses is multiplied by the co-efficient to expand the parentheses.
Here, the coefficient is -2, therefore we multiply both terms inside the parentheses (x and -2) by -2 to expand them:
-2(x - 2) + 5x
= (-2)(x) + (-2)(-2) + 5x
Now we simply evaluate and combine like terms to simplify:
= -2x +4 +5x
= 3x + 4
Andrew buy 8 pound of apple for $12. 0. He want to know and ue the unit rate of the cot per pound. True or Fale: Two pound of apple cot more than $3. 50
It is false that the cost of two pounds of apple cast is more than $ 3.50.
Finding the cost of a given quantity:Here to find the cost of the given quantity we need to find the cost of 1 unit i.e 1 pound in the given problem so that we can find the cost of given quantities. It is called a unitary method.
Given that
Andrew buy 8 pounds of apples for $ 12.00
Let 'x' be the cost of 1 pound of apples
By the given data,
=> 8x = $ 12
=> x = 12/8
=> x = 1.5
The cost of 1 pound of apples = $ 1.5
Cost of 2 pounds apples = 2 × 1.5 = 3
Therefore,
It is false that the cost of two pounds of apple cast is more than $ 3.50.
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What percent of left-handed people surveyed have artistic ability?
Answer:
65.6488549618 %
Step-by-step explanation:
total left = 131
left who have artistic ability = 86
proportion of left who have artistic ability = number of favorable outcomes/total outcomes = 86/131 = 0.65648854961
mutliply by 100 to convert to a percent
65.6488549618 %
Mei needs to cut a 12-inch loaf of bread into slices that are inch thick.
a. How many 2-inch thick slices can Mei cut from the 12-inch loaf of bread?
b. How many inches of bread would be left over?
a. The number of 2-inch thick slices that Mei can cut from the 12-inch loaf of bread is 6.
b. The inches of bread that would be left over is zero.
How to illustrate the expression?The information given an be solved by Illustratingnut with an expression. This is simply used to show the relationship between the variables that are provided or the data given regarding an information.
Since Mei needs to cut a 12-inch loaf of bread into slices that are inch thick, the number of 2-inch thick slices that Mei can cut from the 12-inch loaf of bread is:
= 12 / 2
= 6
There'll be no left over
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Help please with this maths
Answer:
9 cm
Step-by-step explanation:
You want the radius of the sphere that has a surface area of 324π cm².
AreaThe area of a sphere is given by the formula ...
A = 4πr²
Filling in the given values, we can solve for r:
324π = 4πr²
81 = r² . . . . . . . . . divide by 4π
9 = r . . . . . . . . . . . take the square root
The radius of the sphere is 9 cm.
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Boxplots are NOT recommended for use with which of the following types of? distributions?
Choose the correct answer below.
a. Symmetric
b. Unimodal
c. Skewed
d. Bimodal or any multimodal distribution
Due to the fact that they obscure bimodality or any multimodality, boxplots are best reserved for distributions with a single mode.
Which distributions are unimodal?The distribution is said to be symmetrical when the box's whiskers are roughly the same on both sides and the median is in the centre of the box. The distribution is positively skewed if the whisker is shorter on the lower end of the box and the median is closer to the bottom of the box (skewed right).
Due to the fact that they obscure bimodality or any multimodality, boxplots are best reserved for distributions with a single mode.
There is just one peak in a unimodal distribution, two peaks in a bimodal distribution, and three or more peaks in a multimodal distribution. If the data is skewed or symmetric, such information can also be used to characterise the histogram's structure.
Therefore, the correct answer is option b) Unimodal.
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The required correct option for the given question is uni-modal.
Which distributions are uni-modal?The distribution is said to be symmetrical when the box's whiskers are roughly the same on both sides and the median is in the center of the box. The distribution is positively skewed if the whisker is shorter on the lower end of the box and the median is closer to the bottom of the box (skewed right).
Due to the fact that they obscure bi-modality or any multi-modality, box-plots are best reserved for distributions with a single mode.
There is just one peak in a uni-modal distribution, two peaks in a bimodal distribution, and three or more peaks in a multi-modal distribution. If the data is skewed or symmetric, such information can also be used to characterize the histogram's structure.
Therefore, the correct answer is option b) Uni-modal.
To learn more about Uni-modal refer to:
brainly.com/question/30125628
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