Modeling an Equation

Use the algebra tiles to model the equation
2x + 4 = 3x + (−1). Then complete the sentences.

To model 2x + 4, you need:


positive x-tiles to represent 2x.

positive unit tiles to represent 4.

To model 3x + (−1) you’ll need:

3
x-tiles to represent 3x.
1
unit tile to represent –1.

The Sine or Sin(θ) in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. The Height on the wall till which the ladder reaches is 21.148 ft.

The Sine or Sin(θ) in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,

Sin(θ) = Perpendicular/Hypotenuse

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The hypotenuse is the longest side of the triangle.

The height of the wall can be found by using the trigonometry ratios, therefore, the height of the wall can be determined as,

Sin(74°) = (Height on the wall)/(Length of the wall)

Sin(74°) = (Height on the wall)/22 ft

(Height on the wall) = 21.148 ft

Hence, the Height on the wall till which the ladder reaches is 21.148 ft.

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Answer:

21.15

Step-by-step explanation:

Answer:

Step-by-step explanation:

x + x + 36 = 180

2x + 36 = 180

2x = 144

x = 72

The quotient of the expressions (9.6 x 10⁻⁸) and (3.2 x 10⁴) is 3.0 × 10⁻¹². Then the correct option is D.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

The expressions are given below.

(9.6 x 10⁻⁸) and (3.2 x 10⁴)

Then the quotient of the expressions will be

⇒ (9.6 x 10⁻⁸) / (3.2 x 10⁴)

⇒ (3 x 10⁻⁸) / (10⁴)

⇒ 3 x 10⁻⁸ x 10⁻⁴

⇒ 3 x 10⁻⁸⁻⁴

⇒ 3 x 10⁻¹²

Then the correct option is D.

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Answer:

221.16

Step-by-step explanation:

Find the difference between each day. Add all the differences together, then divide that number by 6 (the number of differences) to find the mean.

Answer:

189.57 miles per day.

Step-by-step explanation:

I took the test

Answer + Step-by-step explanation:

» ABC ≅ DBE

» DE // AC  

(properties of the mid-segment of a triangle)

» Length of DE = 1/2 length of AC  

(properties of the mid-segment of a triangle)

» ∠BDE = ∠DAC

(Corresponding angles)

No it can't be factored , whenever there is addition between two squares , the expression can't be factored

The area of the target which earns 30 points on a throw.

[tex]\huge\boxed{Formula: a= \pi{r}^{2}}[/tex]

[tex]4+3[/tex]

[tex]=7[/tex]

Let's solve

We have to find the answer in terms of π so, we'll just have to multiply the radius by itself.

[tex]a={7}^{2}[/tex]

[tex]\large\boxed{a= 49 \pi\: {in}^{2}}[/tex]

Hence, the area of the target which earns 30 points on a throw is 49π square inches.

Answer= Option B

Answer:

by solving the divisions

Step-by-step explanation:

8/9 ÷ 3/10 = 8/9 × 10/3 = 80/27 = 2.96.

now from the solutions you can get the least to greatest

1.40 , 2.96, 5.28 and 23.75

After getting answer in decimal form change it to fraction like how they set the question

Answer:

B. x = 5/2

Step-by-step explanation:

-2x+14+ 10x=34

-2x+10x=34-14

8x=20

x=20/8 =5/2

Answer:

Step-by-step explanation:

Answer:

  C.  g(x) = 3·2^x +2

Step-by-step explanation:

The graph of g(x) appears to be a translation upward of the graph of f(x).

__

To find the equation of g(x), we can add 5 to f(x), since the translation appears to be 5 units. (The y-intercept of f(x) is 0; the y-intercept of g(x) is 5.)

  g(x) = f(x) +5

  g(x) = (3·2^x -3) +5

  g(x) = 3·2^x +2

__

You can also determine the correct choice by looking at the value at x=0:

  A. g(0) = 3 +6 = 9

  B. g(0) = 1 +3 = 4

 C. g(0) = 3 +2 = 5 . . . . matches g(0) on the given graph

  D. g(0) = 3

The total amount Sam will pay in all will be $2,400,000

From the question, we are to determine the interest Sam pays in all

Using the simple interest formula,

I = PRT

From the given information,

P = $2,000,000

R = 5% = 0.05

T = 4

Putting the parameters into the formula,

I = $2000000 × 0.05 × 4

I = $400000

The interest Sam will pay is $400,000

The total amount Sam will pay in all will be $2,000,000 + $400,000

= $2,400,000

Hence, the total amount Sam will pay in all will be $2,400,000

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Answer:

Step-by-step explanation:400000

Step-by-step explanation:

$79.99 - $64.99 = $15

(79.99 - 64.99)/|79.99| =15

15/79.99 =

15 ÷ 79.99 =

15 ÷ 79.99 × 100/100 =

(15 × 100 ÷ 79.99)/100 =

(1,500 ÷ 79.99)/100

≈18.752344043005/100 =

18.752344043005% ≈18.75%;

By using any two of the points in the table, we will see that the slope is -2.

A general linear relationship is:

y = a*x + b

Where a is the slope and b is the y-intercept.

Remember that if the line passes through (x₁, y₁) and (x₂, y₂), the slope is:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we can use the first two points on the table:

(-4, 11) and (2, -1), so the slope is:

[tex]a = \frac{11 - (-1)}{-4 - 2} = 12/-6 = -2[/tex]

Then the slope of the line is -2.

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Answer:

(4,0)

Step-by-step explanation:

The point where the line cuts the x-axis is called the x-intercept.

x-intercept is when y = 0.

So given y = 0,

3x+4(0) = 12

3x =  12

x = 12/3

x = 4

therefore the point is (4,0)

Answer:

c (2,0) and (-2,0) I hope ot helps

Answer:

7

Step-by-step explanation:

m=pendiente

por lo tanto:

pendiente=7

Hii!

__________________________________________________________

Answer:

Slope = 7! ^^

Step-by-step explanation:

Note that the equation is given to us in slope intercept form.

The slope intercept formula is y=mx+c.

m denotes the slope

c denotes the y intercept.

/--------------\

The slope of the line that we are working with is 7.

Remember how I said that the slope of the line y=mx+c is m?

Similarly, the slope of the line y=7x-3 is 7! ^^

--

Hope that this helped! Best wishes.

--

Solving the exponential function, it is found that the times that will take to have the desired measures are given by:

a) 3.6 hours.

b) 38.51 hours.

c) 56.98 hours.

The function is given by:

[tex]A(t) = 140(0.5)^{\frac{t}{19.255}}[/tex]

Solving for t, we have that:

[tex](0.5)^{\frac{t}{19.255}} = \frac{A(t)}{140}[/tex]

[tex]\log{(0.5)^{\frac{t}{19.255}}} = \log{\frac{A(t)}{140}}[/tex]

[tex]\frac{t}{19.255} = \frac{\log{\frac{A(t)}{140}}}{\log{0.5}}[/tex]

[tex]t = 19.255\frac{\log{\frac{A(t)}{140}}}{\log{0.5}}[/tex]

In item A, we have that A(t) = 123, hence:

[tex]t = 19.255\frac{\log{\frac{123}{140}}}{\log{0.5}}[/tex]

t = 3.6 hours.

In item B, we have that A(t) = 35, hence:

[tex]t = 19.255\frac{\log{\frac{35}{140}}}{\log{0.5}}[/tex]

t = 38.51 hours.

In item C, we have that A(t) = 18, hence:

[tex]t = 19.255\frac{\log{\frac{18}{140}}}{\log{0.5}}[/tex]

t = 56.98 hours.

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Answer:

y = -3x+4

Step-by-step explanation:

The slope intercept form of a line is given by

y = mx+b  where m is the slope and b is the y intercept

y = -3x+4

Step-by-step explanation:

We have,

We know that,

y = mx+c

y = -3x+4

Hence, option (D) is correct.

The series is a convergence series and the sum of the series is -8/3

The series is given as:

[tex]\sum\limits^{\infty}_{n = 1} -4(-\frac 12)^{n-1}[/tex]

The above series has the following properties:

Start by calculating the absolute value of the common ratio

Absolute value = |-1/2|

This gives

Absolute value = 1/2

The above value is less than 1.

It means that the series converges.

This is calculated using:

[tex]S_{\infty} = \frac{a}{1 -r}[/tex]

So, we have:

[tex]S_{\infty} = \frac{-4}{1 + \frac 12}[/tex]

Evaluate the sum

[tex]S_{\infty} = \frac{-4}{\frac 32}[/tex]

Evaluate the quotient

[tex]S_{\infty} = \frac{-8}{3}[/tex]

Hence, the sum of the series is -8/3

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Answer:

[tex]\displaystyle\frac{5}{36}[/tex]

Step-by-step explanation:

Probability is used to find how likely an outcome is to happen. Probability can be expressed as a fraction with the total outcomes as the denominator and the number of successful outcomes (what you want to happen) as the numerator.

Sample Size

The sample size is the number of possible outcomes. In this case, the sample size will be the total number of coins. To find the sample size we need to add together all of the coins.

This means that the sample size is 12. For this type of probability, the sample size will serve as the denominator for each probability.

Replacement

In the question, it is stated that coins are replaced. This means that the sample size will not change at any point. So, the denominator will be the same for every probability.

Creating Probability Fractions

We are looking for the probability of getting a quarter and nickel, so we need to find the fractions that represent both situations.

First, let's find the quarter. As stated in the first paragraph, the number of successful outcomes is the numerator. There are 4 quarters, so 4 is the number of successful outcomes. Therefore, 4 will be the numerator. Then, 12 will be the denominator because 12 is the sample size.

Next, we need to find the probability of a nickel. Since there are 5 nickels, there are 5 successful outcomes. Then, the sample size is still 12 because there is replacement.

Complex Probability

Now we have the probability of both a quarter and nickel alone. However, this question asks about the probability of both, so this is an example of complex probability. To find complex probability, you have to multiply each probability together.

To reach the final answer we have to simplify the answer.

This means that the probability of pulling a quarter and then a nickel is 5/36.

Answer:

Yes they are.

Step-by-step explanation:

By simply moving 2x from the LHS to the RHS we'll get it's equivalent to be 3x.

i.e 5x - 2x = 3x

The required total distance the ball travels, approximately, is 180 feet.

Let's denote the height of the first fall as a (initial height of 60 feet), and the distance covered during each rebound as r (two-thirds the distance of the previous fall).

The first fall distance (a) is 60 feet.

The first rebound distance (r) is (2/3) * 60 feet.

The total distance covered during the first fall and rebound cycle is:

60 + (2/3) * 60 = 60 + 40 = 100 feet.

Now, for the subsequent cycles, the ball will continue to fall and rebound in the same pattern:

Second fall distance = r * a
                                  = (2/3) * 60
                                  = 40 feet.

Second rebound distance = r*(2/3) * 60
                                            = (2/3) * 40
                                            = 80/3 feet.

The total distance covered during the second fall and rebound cycle is:

40 + (80/3) ≈ 66.67 feet.

The pattern will continue for the subsequent cycles.

To represent this as an infinite geometric series, we can write:

Total distance = [tex]a + (a * r) + (a * r^2) + (a * r^3) + ...[/tex]

Where:

a = 60 feet (height of the first fall)

r = 2/3 (rebound factor)

Using the formula for the sum of an infinite geometric series:

Total distance = a / (1 - r)

Total distance = 60 / (1 - 2/3)

Total distance = 60 / (1/3)

Total distance = 60 * 3

Total distance = 180 feet.

Therefore, the total distance the ball travels, approximately, is 180 feet.

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Answer:

the missing angle or the exterior angle is 120

Step-by-step explanation:

180-60=120

Answer:

90 degrees.

Step-by-step explanation:

The square symbol at the unlabeled angle means 90 degrees. Also, a triangle's interior angles equal 180. We already have 30 and 60, so 30+60=90. Now, subtract this from 180. 180-90=90. The answer is 90 degrees.

Hope this helps!

The equation that can be paired with x + 2y = 5 to create an inconsistent system is given by:

2x + 4y = 3.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

An inconsistent system is a system that has no solutions, and it happens when the coefficients of x and y are multiples, and the independent terms are not.

Hence:

x + 2y = 5.

2x + 4y = 3.

Is inconsistent, as the variables are each multiplied by 2, but the independent term is not.

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Answer:

A

Step-by-step explanation:

Edge.

Answer:

triagle

Step-by-step explanation:

it is tringle because because this pattern other is tall and other is short it gona be isocelese triagle

Answer:

X=1 and Y=4

By counting eacht vetmrtical divided units