HELP PLEASE?
Henry showed all the steps he took to solve the equation.
(picture)

Sammy tried to verify the solution by substituting x=5 back into the original equation. It did not result in a true statement. Which explains why Henry’s solution is incorrect?

Step 1 is wrong because the distributive property of equality was used incorrectly.
Step 2 is wrong because the addition property of equality was used incorrectly.
Step 3 is wrong because the subtraction property of equality was used incorrectly.
Step 4 is wrong because the division property was used incorrectly.

Answer:

Step-by-step explanation:

Answer:

x

=

π

3

,

2

π

3

,

4

π

3

,

5

π

3

Explanation:

(

sin

x

)

2

=

3

(

cos

x

)

2

(

sin

x

)

2

=

3

(

1

−

(

sin

x

)

2

)

(

sin

x

)

2

=

3

−

3

(

sin

x

)

2

4

(

sin

x

)

2

=

3

(

sin

x

)

2

=

3

4

sin

x

=

±

(

√

3

2

)

x

=

π

3

,

π

−

π

3

,

π

+

π

3

,

(

2

π

)

−

π

3

x

=

π

3

,

2

π

3

,

4

π

3

,

5

π

3

If this was in the region

0

≤

x

≤

2

π

[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin^2(x)=3cos^2(x)\implies sin^2(x)=3[1-sin^2(x)] \implies sin^2(x)=3-3sin^2(x) \\\\\\ sin^2(x)+3sin^2(x)=3\implies 4sin^2(x)=3\implies sin^2(x)=\cfrac{3}{4}[/tex]

[tex]\bf sin(x)=\pm\sqrt{\cfrac{3}{4}}\implies sin(x)=\pm\cfrac{\sqrt{3}}{\sqrt{4}}\implies sin(x)=\pm\cfrac{\sqrt{3}}{2} \\\\\\ sin^{-1}[sin(x)]=sin^{-1}\left( \pm\cfrac{\sqrt{3}}{2} \right)\implies x= \begin{cases} \frac{\pi }{3}\\\\ \frac{2\pi }{3}\\\\ \frac{4\pi }{3}\\\\ \frac{5\pi }{3} \end{cases}[/tex]

that is, on the interval [0, 2π].

The answer is the AREA of a figure is a measurement of the space inside it.

The answer is:

The correct option is:

c) [tex]f^{-1}(x)=\frac{e^{x}}{10}[/tex]

Inversing a function means switching the range and domain of the function. To inverse a function we need to rewrite the variable (x) with the function (f(x) or y), and rewrite the function (f(x) or y) with the variable (x), and then, isolate "y" or "f(x)".

Also, we need to remember how to isolate the variable from a logarithmic function.

[tex]ln(x)=a\\\\e^{a}=e^{ln(x)}\\\\e^{a}=x[/tex]

So, we are given the function:

[tex]f(x)=ln(10x)[/tex]

Which it's equal to write:

[tex]y=ln(10x)[/tex]

Then, inversing the function we have:

[tex]y=ln(10x)[/tex]

[tex]x=ln(10y)[/tex]

[tex]x=ln(10y)\\\\e^{x}=e^{ln(10y)} \\e^{x}=10y\\\\y=\frac{e^{x}}{10}[/tex]

Hence, we have that the correct answer is the option:

c) [tex]f^{-1}(x)=\frac{e^{x}}{10}[/tex]

Have a nice day!

[tex]f(x) = \ln(10x)\\ \\ f^{-1}\Big(f(x)\Big) =x \\ \\ f^{-1}\Big(\ln(10x)\Big) = x\\ \\ \ln(10x) = t \Rightarrow 10x = e^t \Rightarrow x = \dfrac{e^t}{10} \\ \\ \Rightarrow f^{-1}(t) = \dfrac{e^t}{10} \Rightarrow \boxed{f^{-1}(x) = \dfrac{e^x}{10}}[/tex]

Answer:

d may cause f

Step-by-step explanation:

Apex

The true statement is that the d may cause f. Correlation is a statistical measure used to measure the relationship that exists between two variables.

Correlation is a statistical measure used to measure the relationship that exists between two variables.

Here are the options

d must not cause f.

f must cause d.

d must cause f.

d may cause f.

1. Positive correlation: it means that the two variables move in the same direction. If one variable increases, the other variable also increases.

For example, there should be a positive correlation between quantity supplied and price

When there is a positive correlation, the graph of the variables is upward sloping

2. Negative correlation:  it means that the two variables move in a different direction. If one variable increases, the other variable decreases.

For example, there should be a negative correlation between quantity demanded and price

When there is a negative correlation, the graph of the variables is downward sloping

3. Zero correlation: there is no relationship between the variables

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Use sin because in relation to angle F, side 12 is the opposite and side 17 is the hypotenuse (soh-cah-toa) so that's why the answer is 45°

Answer:

A

Step-by-step explanation:

Calculate ∠F using the sine ratio

sinF = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{CF}[/tex] = [tex]\frac{12}{17}[/tex]

F = [tex]sin^{-1}[/tex] ([tex]\frac{12}{17}[/tex] ) ≈ 45° → A

Answer:true

Step-by-step explanation:

The statement given is true , Option A is the correct answer.

A cylinder is a three dimensional figure which has two parallel circular bases joint by a curved surface of fixed length.

A statement related to Cylinder is given and asked if it is true

Yes , the statement that a cylinder is made up of discs of same radius , this can be very well understood from the figure itself as the cylinder definition says that it has a curved surface of same radius and fixed height.

Therefore Option A is the correct answer.

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Answer:

x=4

Step-by-step explanation:

11x-4=5x+20

4x=16

x=4

Answer:

x = 4

Step-by-step explanation:

Note the equal sign, what you do to one side, you do to the other. Isolate the variable, x. First, subtract 5x and add 4 to both sides.

11x (-5x) - 4 (+4) = 5x (-5x) + 20 (+ 4)

11x - 5x = 20 + 4

Combine like terms. Simplify:

(11x - 5x) = (20 + 4)

6x = 24

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Divide 6 from both sides.

(6x)/6 = (24)/6

x = 24/6

x = 4

x = 4 is your answer.

~

Answer:

56

Step-by-step explanation:

First, do you know what a CD is? ;-)

Since you will pick 3 CDs out of 8, and the order of the CDs don't import (1,2,4 is the same as 2,1,4 and 4,2,1 for example),we'll calculate the Combinations (and not the permutations). The formula for Combinations is:

[tex]C(n,r) = \frac{n!}{(r!(n-r)!)}[/tex]

Where n is the number of elements (8 in our case) an n is the sample (3 in our case).

[tex]C(8,3) = \frac{8!}{(3!(8-3)!)} = \frac{40320}{6 * 120} = 56[/tex]

So, there are 56 random groups of 3 you can pick from your potential 8 CDs.

Answer:

Step-by-step explanation:LEVEL 1:   x + 1

LEVEL 2:  3x + 1 plus 2 bonus points

A)  3x - x + 2     =   2 + 2 = 4 more points earned on level 2

B) x + 1 + 3x + 1 + 2

    4x + 4

4x + 4 ÷ 2 = 2x + 2

To determine the ratios and averages of Travis's score, first the total points earned on each level were determined. From there, the larger total was divided by the smaller for part A, and the total points from both levels were averaged for part B. The calculations involve algebraic expressions and basic mathematical operations.

To solve this, first identify the total points earned on each level. On Level 1, Travis earned x + 1 points. On Level 2, he earned 3x + 1 points as well as 2 bonus points, meaning he earned a total of 3x + 3 points.

a) To find how many times more points Travis earned on the second level than the first, you'd calculate (3x + 3)/(x + 1).

b) To find the average number of points earned, add the total points from both levels and divide by 2: ((x + 1) + (3x + 3))/2.

c) Both calculations involve algebraic expressions relating to the specific number of points earned on each level, by using the operations of addition, multiplication and division.

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Answer:

I believe the answer is B.

Step-by-step explanation:

Because a proportional relationship is one where x is proportional (equal) to y, and Graph A does not fall into that category, and Graph B does, the answer should be B.

Answer:

The answer A

Step-by-step explanation:

Only graph A represents a proportional relationship.

Two quantities are proportional to each other if the graph is a straight line through the origin.

Answer:

Simple, 19 days.

Step-by-step explanation:

Divide the number of versus you want to read by the among of versus per day you want to read.

76 / 4 = 19

To learn 76 Bible verses at a pace of 4 verses per day, it will take 19 days.

This question demands basic understanding of mathematical operations in general and about basic understanding of word problems in general.

If you need to learn 76 Bible verses and you plan to learn 4 verses a day, you would do some quick math to determine how many days it will take to learn all the verses. By dividing the total number of verses by the number of verses you can learn a day, you get

76 ÷ 4 = 19 days.

So, it will take you 19 days to learn all 76 Bible verses, assuming that you maintain the consistent pace of learning 4 verses per day.

For this case we have that by definition, the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

A: It's the radio

h: It's the height

We have according to the data:

[tex]r = 4 \ in\\h = 15 \ in[/tex]

Substituting:

[tex]V = \pi * (4) ^ 2 * 15\\V = \pi * 16 * 15\\V = \pi * 240\\V = 753.6 \ in[/tex]

Thus, the volume of the paint can is 753.6 cubic inches.

Answer:

[tex]V = 753.6 \ in^3[/tex]

The answer is 753.6 inches.

Hope this helps!

Answer:

$1.45-$0.25=x

x=$1.20

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Stem            Leaf

6                   4 9

7

8                   8 8

9                   1  2 3 4 5 7 7

10                  0

Step-by-step explanation:

The stem-and-leaf plot is a semi-graph that allows presenting the distribution of a quantitative variable. It consists of separating each data in the last digit (which is called a leaf) and the remaining front numbers (which form the stem).

It is especially useful for medium-sized data sets and that your data is not grouped around a single stem. With it we can get the idea of ​​what distribution the data have, the asymmetry, etc.

The name of stem and leaves refers to the branch of a plant, with the front digits marking the stem where the number is located and the final digit of the leaf.

1. First at all, we have to sort the data from lowest to highest

64, 69, 88, 88, 91, 92, 93, 94, 95, 97, 97, and 100

2. Draw a table with two columns, the first column for the stem and the second for the leaves. Arrange all the stems in the first column in descending order. Each stem is written only once.

Stem            Leaf

3.  Record all the leaves in the second column, in increasing order, next to the corresponding stem.

Stem            Leaf

6                   4 9

7

8                   8 8

9                   1  2 3 4 5 7 7

10                  0

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

[tex]m = \frac {y2-y1} {x2-x1}[/tex]

We have the following points:[tex](x1, y1) :( 5,6)\\(x2, y2) :( 4,8)[/tex]

Substituting:

[tex]m = \frac {8-6} {4-5}\\m = \frac {2} {- 1}\\m = -2[/tex]

Then, the equation is:

[tex]y = -2x + b[/tex]

To find "b" we substitute one of the points:

[tex]8 = -2 (4) + b\\8 = -8 + b\\b = 8 + 8\\b = 16[/tex]

Finally, the equation is:

[tex]y = -2x + 16[/tex]

Answer:

Option B

Answer:

9

Step-by-step explanation:

multiply the 3 by 3

The answer is:

The value of "x" is 90.16

To solve the problem we need to use the trigonometric identity of the sine that establish that:

[tex]Sin(\alpha )=\frac{OppositeSide}{Hypotenuse}[/tex]

So, we are given the following information:

[tex]\alpha =48(degrees)\\\\OppositeSide=67[/tex]

Then, applying the trigonometric identity, we have:

[tex]Sin(48)=\frac{67}{Hypotenuse}[/tex]

[tex]Sin(48)=\frac{67}{Hypotenuse}\\\\Hypotenuse=\frac{67}{sin(48)}=90.157=90.16[/tex]

Hence, the value of "x" is (rounded to the nearest hundreth) 90.16.

Have a nice day!

Due To My Calculations, The Answer Is 90.16.

Answer:

A

Step-by-step explanation:

One side is 6 the other is 17. If you multiply 6 by 17 it equals 102(AREA). If you add up, 6+6+17+17=46(PERIMETER)

Answer:

Stepby-step explanation:

step 1: L+W =18

step 2: L*W =80

find a pair factors 80 with a sum of 18 eg.

step 3: 1*80

step 4: 2*40

step 5: 4*20 etc.

Answer:

1- exponential

2- constant multiplicative rate of change

Step-by-step explanation:

Answer:

Exponential

Constant multiplicative rate of change

Step-by-step explanation:

It is not a linear function because in order to be linear it should decrease or increase the same amount from one moment to another.

Nor is it a quadratic function, since to be quadratic it should have values that increase and then decrease (a point of return).

So the correct option is that it is an exponential function because the values do not change the same amount each time, they change constantly but by a multiplication factor.

So for the second of the options it will be: constant multiplicative rate of change

In summary:

The data in the table can best be described as exponential because there is a constant multiplicative rate of change.

Answer:

There are 28 more dogs than cats at the animal shelter.

Step-by-step explanation:

If the ratio of dogs to cats at an animal shelter is 3:1, that means there are 3 dogs for every 1 cat.

The way I think about it is I try multiplying every number by 3 and 1, kind of like process of elimination.

After using every number from 1-13, I finally got to 14. Now, 3 x 14 = 42 and 1 x 14 = 14. Add 42 + 14 and you will get 56.

So there are 42 dogs and 14 cats at the animal shelter.

However, it is asking for how many more dogs than cats there are, so you have to subtract 42 - 14 and the answer is 28 more dogs than cats.

Answer:

5a

Step-by-step explanation:

Just use the reflexive property / reflexive angles, 5a = x and 4a equals the remaining side.

Answer:

100

Step-by-step explanation:

5a+4a=9a

180/9=a

20=a

4a+x=180

(4 times 20)+x=180

80+x=180

x=100

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

f -----> the number of pounds of fertilizer

s ----> the number of pounds of seeds

we know that

The inequality that represent the situation is

[tex]2f+20s\leq 4,000[/tex]

using a graphing tool

see the attached figure

The solution is the triangular shaded area

Answer:

top right :D

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

The coefficient is the number in front of the variable.

The coefficient of the a² term in the expression -2a(a + b - 5) + 3(-5a + 2b) + b(6a + b - 8) is a² -2.

To find the coefficient of the a² term in the expression -2a(a + b - 5) + 3(-5a + 2b) + b(6a + b - 8) we proceed as follows

Since we have that expression  -2a(a + b - 5) + 3(-5a + 2b) + b(6a + b - 8) and we want to find the coeffiecient of the a², we need to determine which of the terms in the brackets would be multiplied to give a term in a².

To have a term in a², there must be at one a term outside the bracket and one a term in side the bracket.

Looking at the expression -2a(a + b - 5) + 3(-5a + 2b) + b(6a + b - 8) , the only bracket that has two a terms is the first bracket -2a(a + b - 5).

So, expanding the bracket, we have that -2a(a + b - 5) = -2a² - 2ab + 10.

Now, the coefficient of the a²,  -2a² is the number in front of the a² which is - 2

So,the coeffieient of the a² is - 2.

Answer: Just use the volume formula

Step-by-step explanation:

The volume formula for a rectangular prism is: V= L x W x H

The L is Length, the W is Width, the H is Height. If you had fractions for L, W, and H, you will just have to multiply them. (Example) V= 1/2 x 1/4 x 8/6

To calculate the volume of a rectangular prism with fractional dimensions, multiply the length, width, and height fractions together and simplify. This will yield the volume in cubic units.

Calculating the Volume of a Rectangular Prism Using Fractions :

To calculate the volume of a rectangular prism when the dimensions are given in fractions, you follow three main steps.

First, identify the length (L), width (W), and height (H) of the rectangular prism.

Second, multiply these three dimensions together: Volume = L × W × H. Finally, simplify the resulting fraction to get the volume of the prism.

For instance, if you have a prism with length 5/2 cm, width 3/4 cm, and height 2/3 cm, the volume would be (5/2) × (3/4) × (2/3) cm³.

When you multiply the numerators together and the denominators together, you get (5 × 3 × 2)/(2 × 4 × 3) cm³, which simplifies to 30/24 cm³.

This further simplifies to 5/4 cm³, which is the volume of the prism.

Answer:

1) 269

2) 122

Step-by-step explanation: use pemdas

Parenthesis

Exponents

Division

Multiplication

Addition

Subtraction

Answer: 13°

Step-by-step explanation: The correct answer is 13°. Since you know the opposite and adjacent you will use tangent tan x= 12/50

Final answer:

To find the angle of elevation between the diver and the diving board, we use the tangent function of a right triangle, which results in an angle of approximately 13 degrees. Thus, option B (13 degrees) is the correct answer.

Explanation:

The question is asking for the measure of the angle of elevation from the diver looking up to the top of the diving board. To calculate this, we can use trigonometry, specifically the tangent function, which relates the opposite side to the adjacent side of a right-angled triangle. We have a right triangle where the height of the diving board is the opposite side (12 feet), and the distance from the diver to the base of the diving board is the adjacent side (50 feet).

The tangent of the angle \heta is the ratio of the opposite side to the adjacent side:

tan(\ heta) = opposite / adjacent = 12/50

To find \ heta, we take the inverse tangent (arctan) of the ratio:

\heta = arctan(12/50)

Using a calculator, we find that:

\heta\approx 13.4\extdegree

Finally, we round to the nearest whole number:

\heta\approx 13\extdegree

Therefore, the angle of elevation is approximately 13 degrees, which corresponds to option B.

Answer:

[tex]y=2.5x-1[/tex]

Step-by-step explanation:

we know that

The equation of the line into slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

In this problem we have

[tex]15x-6y=6[/tex] ---> equation of the line in standard form

Convert to slope intercept form

Isolate the variable y

Subtract 15x both sides

[tex]-6y=-15x+6[/tex]

Divide by -6 both sides

[tex]y=(15/6)x-1[/tex]

[tex]y=2.5x-1[/tex] ----> equation of the line into slope intercept form

Step-by-step explanation:

A triangular prism has five faces in total. There are two triangular bases and three rectangular lateral faces. Few examples of triangular prism are - a camping tent, Toblerone chocolate shape. The base of a prism is also a face.

Here the given prism is a triangular prism which has triangular bases.

Therefore, the answer is option C triangle.

By critically observing the triangular prism shown in the image attached above, the base shape of this triangular prism is a: C. triangle.

A triangular prism can be defined as a geometric shape (figure) with five (5) faces in total. Generally, a triangular prism comprises two (2) triangular bases and three (3) rectangular lateral faces.

By critically observing the triangular prism shown in the image attached above, we can logically deduce that the base shape of this prism is a triangle.

In conclusion, the base shape of this triangular prism is a triangle.

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Answer:

130.07 Watts

Step-by-step explanation:

hope this helps

Answer:

130.1 W

Step-by-step explanation:

Power is work or energy divided by time, so power has the units of joules/second, which is called the watt.

Power = gravitational potential energy / time

Gravitational potential energy = m g h

here m = mass

        g = gravity die to acceleration = 9.81 m/s²

        h = height

1 Ib = 0.453592 kg

32 Ib = 14.5 kg

1 feet = 0.3048 m

12 feet = 3.6576 m

Plug value in the formula

(14.5) (9.81) (3.6576)

520.3 J

520.3 / 4

130.1 W