Using translation concepts, the equation of g(x) is:
D) [tex]\log_5{x + 3}[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Researching this problem on the internet, g(x) is a shift left of 3 units of [tex]f(x) = \log_5{x}[/tex], hence:
[tex]g(x) = f(x + 3) = \log_5{x + 3}[/tex], which means that option D is correct.
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find the measures of thr angles of a right triangle where one of the two acute angles measurres 8 times the other
The two angle of the right triangle are found as 30 degrees and 60 degrees.
Define the term acute angles?Less than 90 degrees is considered an acute angle. Right angles have a 90 degree angle. More than 90 degrees is found in obtuse angles.
Let one acute angle be 'x'.Then, the other actue angle will be '2x'One of the angle of right angles triangle is 90 degress.By using angle sum property of right angle triangle:
x + 2x + 90 = 180
3x = 90
x = 30 (one angle)
2x = 60 (Other angle)
Thus, the two acute angle of the right triangle are found as 30 degrees and 60 degrees.
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Who first used geometry?
Because he invented geometry, Euclid, a renowned mathematician, is frequently referred to as the father of geometry.
Constructions using a compass and a straightedge were a focus of classical geometry. Euclid, who brought mathematical rigour and the axiomatic technique still in use today, transformed geometry. Up until the middle of the 20th century, all educated people in the West were familiar with his book, The Elements, which is usually regarded as the most important textbook of all time.
Current geometric notions have undergone a high level of abstraction and complexity as well as calculus and abstract algebra techniques, resulting in several modern sections of the science that are hardly recognizably descended from early geometry.
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What is the area of 8 cm triangle?
The area of a (equilateral) triangle with side 8cm is 16√3cm^2.
What is a triangle and its types?
A figure which has a three-sided closed figure is called a triangle.
Types
Equilateral Triangle
A triangle where all the sides are the same is called an equilateral triangle.
Isosceles Triangle
When two of the sides of a triangle are the same it’s called an isosceles triangle. It’s a hard one to spell, but an easy one to recognize!
Scalene Triangle
In our last triangle, none of the sides have the same length, so this is called a scalene triangle.
Acute Triangle
when the largest angle in the triangle is less than 90, that is an acute triangle. Just remember that acute angles are less than 90 degrees.
Right Triangle
When the largest angle is exactly 90 degrees. You might remember that a 90-degree angle is a right angle, so this triangle is a right triangle.
Obtuse Triangle
When largest angle is more than 90 degrees, this is an obtuse angle, so we call this triangle an obtuse triangle.
Area of an equilateral triangle whose side is 8 cm is √3/4*a^2 where
a=8
= √3/4*8^2
= √3/4*64
= √3*16
Area=16√3
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please help Im not sure what I'm doing
The function rules for each table are given as follows:
7. y = 5x - 2.
8. y = x³.
9. y = x³ + 1.
How to obtain the function rules?For item 7, when x increases by one, y is increased by 5, hence the function is a linear function with slope 5, as follows:
y = 5x + b
When x = 6, y = 28, hence the intercept b is given as follows:
28 = 5(6) + b
b = 28 - 30
b = -2.
Hence the function is:
y = 5x - 2.
For item 8, the each term is cubed, hence the function is given as follows:
y = x³.
For item 9, the function is one added to the function in the previous problem, hence:
y = x³ + 1.
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What is the additive inverse of 2 /- 7?
The additive inverse of 2 /- 7 is -2 /+ 7.
An additive inverse is a number that when added to the number in question, the sum is equal to zero. This can be expressed by the formula x + (-x) = 0, where x is the number in question. In this case, x is 2 /- 7. So, when 2 /- 7 is added to its additive inverse, -2 /+ 7, the sum is 0. This can be expressed mathematically as 2 /- 7 + (-2 /+ 7) = 0. Calculating this equation, we get 2 /- 7 + (-2 /+ 7) = -2 /+ 7 + (-2 /+ 7) = -4 /+ 14 = 0. Therefore, the additive inverse of 2 /- 7 is -2 /+ 7.
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a/a+b is the same as
a/a+b is the same as a/(a+b). This is because the division of two numbers is represented by the symbol '/', and when a and b are being divided, it is written as a/b.
In this case, a and b are being divided by a+b, so it is written as a/(a+b). This is known as a fraction, which represents a ratio of two numbers. This fraction represents the proportion of a to the total of a+b. The numerator (a) represents the part of the total that you are interested in, and the denominator (a+b) represents the entire quantity.
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The following data points represent the number of points scored in the last basketball game by each player on the Dragons basketball team.
7, 5,8,11,7,5,?
If the mean of the data set is 8 points, find the missing number of points
The missing number of points scored in the last basketball game is 13.
What is the meaning of the data set?
A data set is a grouping of data. A data set refers to one or more database tables in the case of tabular data, where each column of a table represents a specific variable and each row corresponds to a specific record of the data set in question.
Given that,
the number of points scored in the last basketball game by each player on the Dragons basketball team are 7, 5,8,11,7,5,?.
Assume that the missing point is x.
The sum of points is 7+5+8+11+7+5+x = 43 + x.
The number of points is 7.
The mean is the sum of points/number of points
= (43+x)/7
Given that the mean of the data set is 8 points.
Therefore,
(43+x)/7 = 8
Multiply both sides by 7:
43+x = 8×7
43 + x = 56
x = 56 - 43
x = 13
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48 decreased by Craig’s savings is 16. Use the variable c to represent Craig’s savings.
Craig's savings is c-48=16
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given:
Let craig's savings be c then we have c-48=16
c=64
Hence, craig's savings is 64
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Without using a calculator, determine between which two integers the following surds lie (1)√5 (2) √1 (3)√107 (4)√3
Answer:
Step-by-step explanation:
Create two different explicit equations that describe the values in the table. Use a different point in the table for each of the equations you create. Choose one of the equations you created to produce an equivalent form that reveals the y intercept of the function within the equation.
Answer:
Step-by-step explanation:
if x were starting at 0, we would have
y = (x - 7)×7 = 7x - 49
but we start at x = 57. We need adjust for these extra 57 to get the above equation.
so, it
y = (x - 57 - 7)×7 = (x - 64)×7 = 7x - 448
so, for
y = (x - 64)×7
I choose x = 57
y = (57 - 64)×6 = -7×7 = -49
for
y = 7x - 448
I choose x = 58
y = 7×58 - 448 = 406 - 448 = -42
from this form we get the y-intercept (the y- value when x = 0) : -448
6(2+4)negative 1 dived by 2•3+1
Answer:
First you do what is in the parentheses.
2+4= 6
The equation is now:
6(6) -1 / 2 *3 + 1 =
Then you do the division:
-1 / 2 = -0.5
6(6) (-0.5) * 3 + 1 =
3 + 1 = 4
-0.5 * 4 = -2
The equation is now:
6 * 6 * -2
6 * 6 = 36
36 * -2 = -72
Is this proportional or nonproportional please tell me asap with right answer please
Answer:
Its proportional
Step-by-step explanation:
Answer:
Proportional
Step-by-step explanation:
36/3 = 12
60/5 = 12
96/8 = 12
Why quadratic equation is parabola?
A parabola is the form of a quadratic function's graph because the vertex of a parabola is the location where the axis of symmetry of the curve crosses.
f(x) = ax^2 + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the form of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form.
Regarding a line known as the axis of symmetry, all parabolas are symmetric. The vertex of a parabola is the location where the axis of symmetry of the curve crosses.
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Travis, Devon, and Ramon have 17, 20, and 26 trading cards, respectively. Every minute, one of the three boys gives away two of his trading cards such that the other two boys get one trading card each. What is the shortest amount of time, in minutes, that it could take for the three boys to each have an equal number of trading cards?
We can start solving this problem by using the concept of greatest common divisor (GCD). The GCD of 17, 20, and 26 is 1, which means that the three numbers are relatively prime to each other. This means that there is no common divisor of the three numbers other than 1.
Since the trading cards are given away in pairs, we need to divide the GCD by 2, which gives us 0.5. This means that it would take half a minute for the three boys to each have an equal number of trading cards.
However, half a minute is not possible as time cannot be measured in fractions of a minute. Therefore, it is not possible for the three boys to have an equal number of trading cards in the shortest amount of time, because the numbers are relatively prime.
Answer: 5 minutes. ✅
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Is 1 a polynomial or not?
Yes, 1 is a monomial, a unique type of polynomial.
You must first understand what a word is. A term is a real number multiplied by one or more variables, each of which has been raised to a power. Remember that a constant might appear in a phrase when a variable is multiplied by itself to the power of 0. (which is 1). A polynomial is just the sum of one or more terms that meet the criteria listed below:
1] There are no variables to split the words into.
The variables' exponents are whole numbers, e.g. 0, 1, 2, 3, etc.
Thus, 1 is just 1*(x0).
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auline's Print Store and Carla's Copy Shop charge different rates to make copies. There is a proportional relationship between the number of copies and the total cost.
Answer:
The cost at Pauline's print store can be described with the following equation, where y represents the cost in dollars of x copies:
y = 0.05x, because 1.25/25 = 2.75/55 = 90/4.50 = 0.05
Carla's Copy Shop charges a higher unit right
and it is $0.04 higher per copy
Step-by-step explanation:
Hope this helps. Much appreciated if Brainlisest.
At a certain restaurant, each table seats 5 people. How many tables will a group of 45 people need?
Determine whether the triangles are similar. If so, write a similarity statement and name the postulate or theorem you used
Answer:
I can't comment, but we can't see what we are supposwd to bw doing
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equations equivalent to 2.3p – 10.1 = 6.5p – 4 – 0.01p are;
2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – pThe correct answer is option B and C
How to determine equivalent equation?2.3p – 10.1 = 6.5p – 4 – 0.01p
collect like terms
2.3p - 6.5p + 0.01p = -4 + 10.1
-4.19p = 6.1
p = 6.1/-4.19
p = -1.46
2.3p – 10.1 = 6.5p – 4 – 0.01p
= 2.3p – 10.1 = 6.49p – 4
Given options:
2.3p – 10.1 = 6.4p – 4
False
2.3p – 10.1 = 6.49p – 4
True
230p – 1010 = 650p – 400 – p
divide through by 100
= 2.3p – 10.1 = 6.5p – 4 – 0.01p
True
23p – 101 = 65p – 40 – p
False
2.3p – 14.1 = 6.4p – 4
False
Therefore, 2.3p – 10.1 = 6.49p – 4; 230p – 1010 = 650p – 400 – p are equivalent to 2.3p – 10.1 = 6.5p – 4 – 0.01p.
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Is an exponential function a first order?
The integral rate law for a first-order reaction has the following exponential form: [A] = [tex][A]_{0}e^{-kt}[/tex]
If there are constants c, M > 0, and T > 0 such that |f(t)| ≤ Mect for all t>T, then a function f is said to be of exponential order c.
It is helpful to keep in mind the exponential's definition and characteristics since they serve as the foundation for the solution of first-order linear differential equations.
The Concentration of the Reactant Decreases Exponentially with Time in First-Order Reactions. A plot of the natural logarithm of the concentration is a linear function of time according to this form.
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Match each function formula with the corresponding transformation of the parent function y= - (x+ 2)^2
Answer:
Step-by-step explanation:
1-6
3-2
4-1
NEED HELP WITH BOTH. I WILL GIVE BRAINLIST
Find the missing length
Answer
2 =1
3=1.4
Step-by-step explanation:
hb=2A
b=2·5
10=1
hb=2A
b=2·14
20=1.4
Step-by-step explanation:
2 .) Using Pythagorean Theorem,
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]5^{2}+ 10^{2} = c^{2}[/tex]
[tex]25 + 100 = c^{2}[/tex]
[tex]125 = c^{2}[/tex]
[tex]\sqrt{125}= c[/tex]
[tex]11 . 18 = c[/tex]
3.) Using Pythagorean Theorem,
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]a^{2} + 14^{2} = 20^{2}[/tex]
[tex]a^{2}= 20^{2}- 14^{2}[/tex]
[tex]a^{2} = 400 - 196\\a^{2} = 204[/tex]
[tex]a = \sqrt{204}[/tex]
[tex]a = 14.28[/tex]
If A and B are mutually exclusive, then P(A\capB) = 0.
A and B are independent if and only if P(A\capB) = P(A)P(B)
If A and B are two events with P(A) = 0.4, P(B) = 0.2, and P(A B) = 0.5. Find the following:
(a) P(A\capB) (b) P(A?\capB) (c) P(A?\cupB?) (d) P(A|B)
If A and B are independent events with P(A) = 0.4 and P(B) = 0.2. Find the following:
Roll a die once. The event of getting a "2" and the event of getting a "5" are (a) independent;
(b) mutually exclusive;
(c) Neither
Roll a die twice. The event of getting a "2" on the first roll and the event of getting a "5" on the second roll are
(a) independent;
(b) mutually exclusive;
(c) Neither
The probability of both events occurring is P(A ∩ B) = P(A)P(B) = 0.16^2 = 0.0256.
The event of getting a "2" and the event of getting a "5" on the first roll of a die are mutually exclusive events because they cannot both occur in the same trial. The probability of either of these events occurring is P(A) = 0.16, and the probability of both events occurring at the same time is P(A ∩ B) = 0.00.
The event of getting a "2" on the first roll and the event of getting a "5" on the second roll of a die are independent events. This can be confirmed using the formula P(A ∩ B) = P(A)P(B). The probability of getting a "2" on the first roll is P(A) = 0.16 and the probability of getting a "5" on the second roll is P(B) = 0.16. Thus, the probability of both events occurring is P(A ∩ B) = P(A)P(B) = 0.16^2 = 0.0256.
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which angles are vertical angles ?
Answer:
<UVS and <WVX
Step-by-step explanation:
They are both supplementary to the same angle. (<SVW)
Otherwise, you could just see if they are across from each other.
Circumference question #1 if you are good at this I’ll be posting each question! 10 points per question
The triangles are similar. what is the value of x? enter your answer in the box. x = two right triangles. the larger triangle has a long leg of 36 units, a short leg of 15 units, and a hypotenuse of 39 units. the smaller triangle has a long leg of 12 units, short leg of 5 units, and the hypotenuse is labeled x minus 10.
For the above set of similar triangles, the value of x is 23 units.
What is similar triangles?Similar triangles have the same proportionate side lengths and related angle measurements. Two triangles are comparable if their corresponding angles and sides have the same ratio (or proportion). Similar triangles will have the same form but may or may not have the same size. Similar triangles are triangles that have the same shape but differ in size. Similar items include all equilateral triangles and squares with any side length. In other words, if two triangles are identical, their corresponding angles and sides are congruent and in equal proportion.
Here,
Two triangles are comparable if their corresponding angles and sides have the same ratio (or proportion).
x-10/39=12/36
x-10=13
x=23
The value of x for given set of similar triangles is 23 units.
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write and equation for the proportional relationship graphed below
Therefore ,In light of this, the answer to the above equation issue is
be 8.
What does equation mean?An equation must always include two equal members and one or more unknown members (the unknown variables). When multiplied by itself, what number, for example, results in 16. To express this maths equation mathematically, use the equation or expression.
Here,
Replace -3 with the following in the above quadratic equation.
(-3)² - 5(-3) + c = 0
measuring c:
c = -24
a quadratic equation that looks like this
x² - 5x - 24 = 0
x's value can be determined using the quadratic formula as follows:
x = [-b ±√(b² - 4(a)(c))]
/2a
x = [-(-5) ± √((-5)² - 4(1)(-24))] /2(1)
x = 8, -3
Therefore ,In light of this, the answer to the above equation issue is
be 8.
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In art class students are mixing black and white paint to make gray paint. Julian mixes 9 cups of black paint and 8 cups of white paint. Harper mixes 7 cups of black paint and 5 cups of white paint. Use Julian and Harper's percent of black paint to determine whose gray paint will be darker.
We calculate the percentage of black paint in each mix by dividing the amount of black paint by the total amount of paint and multiplying by 100. Julian's mix has a black paint percentage of 52.94% while Harper's mix has a black paint percentage of 58.33%. Therefore, Harper's gray paint will be darker.
Explanation:The first step to determine whose gray paint will be darker is to calculate the percentage of black paint each student has in their mix. To find this, one must know that the percentage is calculated by dividing the part (the quantity of black paint) by the whole (the total amount of paint) and then multiplying by 100.
Julian's percentage of black paint: (9 cups black / 17 total cups) * 100 = 52.94%
Harper's percentage of black paint: (7 cups black / 12 total cups) * 100 = 58.33%
Since the percentage of black paint correlates with the darkness of the gray paint, Harper's gray paint will be darker because it contains a higher percentage of black paint.
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4. Find the equation of opened downward parabola which contains the points (0,5), (2,5), and (-2,-5).
Equation of opened downward parabola is (x - 1) ²= - 4/5 (y - 25/4)
What is parabola?Parabola is a curve created by the intersection of a cone and a plane. Generally, parabola is U shaped and either open in downward or opened in upward direction.
What will be the equation of opened downward parabola contains the points given in question?
The formula for opened downward parabola is given by (x - h) ² = - 4p (y - k)
as the parabola contains the points (0, 5) (2, 5) and (- 2, -5)
so, the equation can be (0 -h) ² = - 4p(5 - k) [ put the value (0, 5)]
h² = - 20p+4pk ..... equation 1
while putting the value (2, 5) we have the equation of parabola.
(2 - h) ² = - 4p(5 - k)
4 - 4h + h ² = - 20p + 4pk .... equation 2
from the equation 1 and 2, the right-hand side is similar.
hence, 4 - 4h +h² = h²
4 = 4h
h = 1
put h =1 in the equation 1 we get, 1 = - 20p + 4pk .... equation 3
when we put the value ( -2, -5) in the formula.
(- 2- h) ² = - 4p ( -5 -k)
( -2 -1) ² = 20p +4pk
9 = 20p +4pk ....... equation 4
from equation 4 and equation 3
we get, 9 = 20p +4pk
1 = - 20p+ 4pk
- + -
solve by addition method and we get, 8 = 40p
p = 1/5
from h = 1 and p = 1/5 we get the value of k from equation 3
1 = - 20/5 + 4/5k
k = 25/4
now the equation of opened downward parabola will be.
(x - 1) ² = - 4/5 (y - 25/4)
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crying for help on this
For 16-19, graph each equation or inequality.
16. 2y – 4x < 8
17. -4y > -x + 12
18. | x + 3 |= y
19. |2x – 6| + 2 = y
The solution is the set of all points (x,y) that satisfy the inequalities:
y < 2x + 4, y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.
What is the graph of a function?
The graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of the function. In other words, it is a visual representation of the function's rule.
The graph of a function can take many different forms, depending on the function's rule. Linear functions, for example, will produce a straight line on the graph.
i) 2y - 4x < 8 can be solved by adding 4x to both sides and then dividing by 2, giving:
y < 2x + 4.
ii) -4y > -x + 12 can be solved by adding x to both sides and then dividing by -4, giving: y < x/4 - 3.
iii) | x + 3 | = y, you can split this into two cases:
i. x + 3 = y
ii. -(x + 3) = y
iv) |2x – 6| + 2 = y, you can split this into two cases:
i. 2x - 6 + 2 = y
ii. -(2x - 6) + 2 = y
We can use these equations to plot the graph on a coordinate plane.
Hence, the solution is the set of all points (x,y) that satisfy the inequalities:
y < 2x + 4, y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.
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