Answer:
(4x + 3)(2x + 5)
4x(2x + 5) +3(2x + 5)
8x^2 +20x +6x + 15
8x^2 +26x + 15
so, g(h(x))=8x^2 +26x +15
again
(4x + 3)(2x +5).0
0
so, g(h(0))=0
HELP ME FIND X AND Y
<EOG =90° AS INDICATED IN THE DIAGRAM
<EOF+<FOG=<EOG(THEY MAKE THE ANGLE)
[tex]27 + 3y = 90 \\ 3y = 90 - 27 \\ 3y = 63 \\ \frac{3y}{3} = \frac{63}{3} \\ y= 21[/tex]
<AOB =180°( STRAIGHT LINE )
<AOE+EOF+<FOG+<GOB=<AOB(THWY MAKE THE ANGLE)
[tex]x + 27 + 3(21) + 8x + 18 = 180[/tex]
[tex]x + 27 + 63 + 8x + 18 = 180 \\ x + 8x + 27 + 63 + 18 = 180 \\ 9x - + 108 = 180 \\ 9x = 180 - 108 \\ 9x =72 \\ \frac{9x}{9} = \frac{72}{8} \\ x = 9[/tex]
ATTACHED IS THE SOLUTION
sarah has 85 and 89 on her first two math 23 tests. what must she get on the third test to have at least 90% test average?Assume three tests and represent the problem with an inequality
The value that Sarah must she get on the third test to have at least 90% test average is represented by the inequality x ≥ 96.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤.
In this case, Sarah has 85 and 89 on her first two math 23 tests.
Let the third test be represented as x. This will be illustrated as:
(85 + 89 + x) / 3 ≥ 90
Cross multiply
85 + 89 + x ≥ 90 × 3
174 + x ≥ 270
Collect like terms
x ≥ 270 - 174
x ≥ 96
The value is x ≥ 96.
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what’s is the expression that is equivalent (x^2-3x)(4x^2+2x-9)?
4x^4-10x^3-15x^2+27x
(use foiling)
PLEASE HELP 20−(2)(−7)+(−9)÷(−3)
Answer:
37
Step-by-step explanation:
Use PEMDAS, in this case, start with multiplication: (2)(-7), don't forget there is a minus sign in front of the two which is important later, then move on to dividing (-9) by (-3). Then you are left with 20-(-14)+3, which is the same as 20+14+3, which equals 37.
Tom has 13 new magazines to read. Let M be the number of magazines he would have left to Read after reading R of them. Write an equation relating to M to R. Then graph your equation using the axis below
The equation that relates M to R is M = 13 - R
How to determine the equation that relates M to R?From the question, we have the following parameters:
Total number of new magazines = 13Number of magazines read = RNumber of magazines left = MThe total number of new magazines is the sum of the number of magazines read and the number of magazines left
This is represented as
Total number of new magazines = Number of magazines read + Number of magazines left
Substitute the known values in the above equation
13 = R +M
Make M the subject
M = 13 - R
Hence, the equation is M = 13 - R
See attachment for the graph
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Consider the line y = = 8 x-4. Find the equation of the line that is parallel to this line and passes through the point (7, -2). Find the equation of the line that is perpendicular to this line and passes through the point (7, -2).
Answer: y=8x-58
Step-by-step explanation:
1. find the slope
Since the new line is parallel to the first one that means the slope of 8x will remain the same.
2. plug it into the point slope formula y-y1=m(x-x1)
which would look like
y-(-2)=8(x-7)
3. solve for y
y-(-2)=8(x-7)
y+2=8x-56
y=8x-58
find the 41st term 11, 16, 21…
Answer:
You can add up to 5 each time, so we just need to multiply 5 by 40 although we already have the first three terms.
A: 40*5 = 200
Step-by-step explanation:
21 + 200 = 221
bradley consumes an energy drink that contains caffeine. after consuming the energy drink, the amount of caffeine in bradley's body decreases exponentially. the 10-hour decay factor for the number of mg of caffeine in bradley's body is 0.2722. what is the 5-hour growth/decay factor for the number of mg of caffeine in bradley's body?
The 5-hour growth/decay factor for the number of mg of caffeine in Bradley's body is 0.521
In mathematics, the term "exponential decay" refers to the process of a constant percentage rate decline in a value over time. Exponential decay differs from linear decay in that the decay factor depends on a percentage of the initial sum, meaning that the amount by which the original sum may be lowered will fluctuate over time as opposed to a linear function, which reduces the original sum by the same amount each time.
Given,
10 hour decay factor = 0.2722
Let us calculate the one-hour decay factor first,
One-hour decay factor = (10 hour decay factor)^1/10 = (0.2722)^1/10 = 0.8779
Now, Calculating the 5-hour decay factor,
5 hour decay factor = ( 1 hour decay factor )^5 = (0.8779)^5 = 0.521
Hence, the 5-hour growth/decay factor for the number of mg of caffeine in Bradley's body is 0.521
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find x and y intercepts of x+4y=8
Answer: You could assume that X=8 and y=0
Step-by-step explanation:
Answer:
Solutions below.
Step-by-step explanation:
This Question involves the concept of intercepts of a graph.
InterceptsIntercepts of a graph are namely the x-intercept and y-intercept.
x-intercept is when y = 0. Example: (3,0)
y-intercept is when x = 0. Example: (0,9)
ApplicationWe are given the equation: x + 4y = 8
To find x-intercept, we can substitute y = 0 into the equation to obtain the value of x.
x + 4(0) = 8
x + 0 = 8
x = 8
Coordinates: (8, 0)
To fins y-intercept, we can substitute x = 0 into the equation to obtain the value of y.
0 + 4y = 8
4y = 8
y = 8 ÷ 4
y = 2
Coordinates: (0, 2)
Rectangle A measures 12 cm by 3 cm.Rectangle B is a scaled copy of rectangle A.Select all the measurement pairs that could be the dimensions of rectangle B.
The measurement pairs that could be the dimensions of rectangle B include:
A. 6cm by 1.5cm
D. 18cm by 4.5vm
F. 80cm by 20cm
How to illustrate the information?From the information, Rectangle A measures 12 cm by 3cm. Therefore, it should be noted that the scale factor is:
= 12/3
= 4/1
Therefore, the options should also have that same constant of 4:1
In this case, 6cm by 1.5cm, 18cm by 4.5cm, and 80cm by 20cm all possess this. This illustrates the concept of equivalent dimensions since they all have a ratio of 4:1.
The complete question is written below.
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Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A. Select all of the measurement pairs that could be the dimensions of Rectangle B.
A. 6 cm by 1.5 cm
B.10 cm by 2 cm
C. 13 cm by 4 cm
D.18 cm by 4.5 cm
E.80 cm by 20 cm
In an examination, Sarah obtained 87.5% by gaining 105 marks. How
many marks did she lose?
Answer: 14
Step-by-step explanation:
87.5% of 105 is 91.875 (91)
105-91=14
explain why the solution to the equation |x-2|-1=x+3 is 1
[tex]|x-2|-1=x+3\rightarrow|1-2|-1=1+3\rightarrow1-1=4\rightarrow0=4[/tex]
Given segments AB and CD intersect at E.
A(1, 2), B(4, 5), C(2, 4), D(2, 1), E(2, 3)
What is the midpoint of cd?
Answer: (2, 5/2)
Step-by-step explanation:
CD=(2, 4),(2, 1)
((2+2)/2, (4+1)/2)=
(4/2, 5/2)=(2, 5/2)
Find the volume of a cone with a base diameter of 6 m and a height of 10 m.
Use the value 3.14 for , and do not do any rounding.
Be sure to include the correct unit in your answer.
ANSWER:
94.2m^3
STEP BY STEP:
V = 1/3 x PI x R^2 x h = 1/3 x 3.14 x 3^2 x 10 =94.2^3
Answer:
V = 94.25m³
I don't have enough time to show work because I have to go, but I hope this helped.
A pole 5 feet tall is used to support guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Zoe measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire to the nearest foot
The length of the guy wire to the nearest foot is 42 feet.
How to find the length of the guy wire?The pole 5 ft tall is used to support the guy wire for the tower, which runs from the tower to a metal stake in the ground.
The situations forms a right angle triangle.
Therefore, the length of the guy wire can be found as follows:
Using trigonometric ratios, we can find the angle the guy wire made with the ground.
tan ∅ = opposite / adjacent
tan ∅ = 5 / 15
∅ = tan ⁻¹ 1 / 3
∅ = 18.4349488057
∅ = 18.43°
Therefore, let's find the length of the guy wire using the angle.
cos 18.43° = adjacent / hypotenuse
0.94871060813 = 40 / h
h = 40 / 0.94871060813
h = 42.162488395
Therefore,
length of the guy wire = 42 feet
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Answer the following. Where necessary, round your answers to 2 decimal places
In a work survey, it was found that:
28 employees preferred tea
45 employees preferred coffee
32 didn't like either
A) Express the number of employees that prefer coffee using a simplified fraction.
B) What percentage of employees don't like either tea or coffee?
C) Express the number of employees that preferred tea using a simplified fraction.
a) Number of employees that prefer coffee are [tex]\frac{3}{7}[/tex].
b) Percentage of employees don't like either tea or coffee is 30.4%
c) Number of employees that prefer tea are [tex]\frac{28}{105}[/tex]
Define fraction.The numerical numbers that make up a fraction of the whole are called fractions. A whole can be a single item or a collection of items. When anything or a number is divided into equal parts, each piece represents a portion of the total. A fraction is represented as a/b, where a and b are the numerator and denominator, respectively. A fraction only informs us of the number of parts that make up the whole. The slash that is inserted between the two numbers identifies a fraction. The numerator is the highest number, and the denominator is the lowest number. [tex]\frac{1}{2}[/tex], for instance, is a fraction.
Given Data
In a work survey, it was found that:
28 employees preferred tea
45 employees preferred coffee
32 didn't like either
a) Number of employees that prefer coffee
= 45
Fraction:
= [tex]\frac{45}{105}[/tex]
= [tex]\frac{3}{7}[/tex]
b) Percentage of employees don't like either tea or coffee
= [tex]\frac{32}{105}[/tex] × 100
= 30.4%
c) Number of employees that prefer tea.
= 28
= [tex]\frac{28}{105}[/tex]
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the quotient of 21 and a equals 30
The resulting value for the quotient of 21 and a equals 30 is 7/10.
Quotient of two numbersThe result of dividing two numbers is known as the quotient. Six divided by two results in the number three.
Latin's "how many times" is the meaning of the word "quotient." That is really logical. For instance, the quotient of a and b is a/b
Given the statement "the quotient of 21 and a equals 30", this can be written mathematically as;
21/a = 30
Cross multiply
30a = 21
Divide both sides by 30
30a/30 = 21/30
a = 21/30
a = 7/10
Hence the value of a from the equivalent expression is 7/10.
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please help!!!!
Submit a picture of your work :
Prove: All right angles are congruent. Use the definition of a right angle and the definition of congruent angles to prove
All right angles are congruent which is determined by the definitions of a right angle and congruent angles.
What are congruent angles?Congruent angles are two or more angles that are identical to each other. As a result, the measurements of these angles are equivalent.
Given that ∠1 and ∠2 are right angles.
By the definition of right angles i.e. right angle is one that is exactly 90 degrees. It is precisely one-quarter of a circle. When a pie is divided into four equal pieces, the tip of each slice forms a straight angle.
⇒ m ∠1 =90° ; m ∠2 = 90°
By the substitution to get
⇒ m ∠1 = m ∠2
Therefore, ∠1 ≅ ∠2
Hence, all right angles are congruent which is determined by the definitions of a right angle and congruent angles.
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Please help me I have 5 minutes left!!!
A proportion is an equation in which two ratios are set equal to each other. No option is satisfying the proportion
What is Ratio and Proportion?Ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
A proportion is an equation in which two ratios are set equal to each other.
In the given question, rayon drove 320 miles in 5 hours to complete the first part of his trip. 12 hours to drive 768 miles.
we can write this
320miles/5 = 768 miles/12
320miles/768 miles=5/12
In option d the values are not given in a correct way. It doesnot hold for the proportion.
Hence no option is correct.
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The cost (in dollars) of a basic music streaming service for m months
is represented by B(m) = 5m. The cost of the premium service is represented by
P(m) 10m. Describe the transformation from the graph of B to the graph of P.
The transformation from the graph of B to the graph of P is a vertical stretch by a scale factor of 2
How to determine the transformation?From the question, the function definitions are given as
B(m) = 5m
P(m) = 10m
Rewrite the function P(m) as follows
P(m) = 2 x 5m
Substitute B(m) = 5m in the equation P(m) = 2 x 5m
P(m) = 2 x B(m)
When a function is represented as
f(x) = kg(x), then the transformation is a vertical stretch by k
Hence. the transformation a vertical stretch by 2
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which of the following graphs could be the graph of g (x)= (x+1) (x-2) (x+5)
D
1) Taking the function g(x)= (x+1) (x-2) (x+5), as we can see this a 3rd degree ploynomial
g (x)= (x+1) (x-2) (x+5)
g(x) =x³+4x²-7x-10
As the coefficient is positive, then we'll have
Examining the options, we have as the roots S={-5,-1,2} So the answer is D
A Ford F-150 truck is considered a half-ton truck because that is how much it can haul. How many pounds can the truck haul?
The truck can haul 1102 pounds.
According to the question,
We have the following information:
A Ford F-150 truck is considered a half-ton truck because that is how much it can haul.
(We will not directly convert ton into pounds. We will follow the following steps.)
Now, we know that 1 ton is equal to 1000 kilograms.
So, half ton makes 500 kg.
Now, to convert this into pounds, we will multiply 500 kg by 2.205 because we know that 1 kg is equal to 2.205 pounds.
1 kg = 2.205 pounds
500 kg = (500*2.205) pounds
500 kg = 1102.5 pounds
Hence, the truck can haul 1102.5 pounds.
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pls help meeeee xxxxxxxxx
t + 4 < 13 solve the inequality of t and simplify your answer as much as possible
Answer:
9
Step-by-step explanation:
t < 13 - 4
t < 9
again as far as it goes
Rewrite in exponential form: \log _3x=4
Answer:
x = 3⁴
Step-by-step explanation:
You want the exponential form of log₃(x) = 4.
LogarithmIt can be helpful to remember that a logarithm is an exponent of the base of the logarithm.
log₃(x) = 4 ⇔ x = 3⁴
The exponential form is x = 3⁴.
PLEASE HURRY
Which table represents a linear function?
The table that represents a linear function is Table 1. Thus, the correct option is A.
What is a linear equation?A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c.
Linear equation with two variables, when graphed on a cartesian plane with axes of those variables, give a straight line.
We know that, slope m= (y2-y1)/(x2-x1)
Table 1:
Put (x1, y1)=(1, 5) and (x2, y2)=(2, 9) in slope formula
That is, (9-5)/(2-1)
= 4
Similarly, the slope between last two points is (9-5)/(4-1)
=4
Table 2:
Put (x1, y1)=(1, -5) and (x2, y2)=(2, 10) in slope formula
That is, (10+5)/(2-1)
= 15
Similarly, slope between last two points (20+15)/(4-3)
=35
Hence, the table that represents a linear function is Table 1. Thus, the correct option is A.
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PLEASE HELP!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
2nd one
Hi thank you so for all your time and help
Hello there. To solve this question, we'll have to remember some properties about trigonometric functions and the right triangle.
We want to find x such that:
[tex]\tan (x)=\sqrt[]{3}[/tex]We'll use the second right triangle to show what we want.
First, given a triangle:
We know that the hypotenuse will be:
[tex]\sqrt[]{x^2+y^2}[/tex]But most importantly, the tangent of the angles α and β can be calculated by only using the legs of the triangle: it is the ratio between the opposite side and the adjacent side to an angle.
[tex]\tan (\alpha)=\frac{y}{x}[/tex]and
[tex]\tan (\beta)=\frac{x}{y}[/tex]Now look at the triangle we have:
We can easily check that:
[tex]\sqrt[]{3}=\frac{\sqrt[]{3}}{1}[/tex]So it would be good to find something that relates the ratio between those two numbers: the tangent of 60º!!
Therefore, we have:
[tex]\tan (60^{\circ})=\frac{\sqrt[]{3}}{1}=\sqrt[]{3}[/tex]And the solution to x is:
[tex]x=60^{\circ}[/tex]Someone please answer this I'm offering all my points.
What is the equation of the line that passes through the point (−6,−3) and has a slope of 0?
The equation of the line that passes through the point (-6,-3) and has a slope of 0 is y = -3
The line is passing through the point = (-6,-3)
The slope of the line = 0
The point slope form is
[tex](y-y_1)=m(x-x_1)[/tex]
Substitute the values in the equation
(y-(-3)) = 0×(x-(-6))
We have to convert this equation the slope intercept form
Slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
(y-(-3)) = 0×(x-(-6))
y+3 = 0×(x+6)
y+3 = 0
y = -3
Hence, the equation of the line that passes through the point (-6,-3) and has a slope of 0 is y = -3.
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