The total area of a picture and its frame can be represented by ^l + 2f h^w + 2f h, where l and w represent the length and width of the picture, respectively, and f represents the thickness of the frame.



a. Sketch a diagram to represent this scenario.



b. What binomial multiplication represents the area of an 8" # 12" picture and its frame?



c. Multiply the binomials from b., and combine like terms to simplify.



d. What is the total area of an 8" # 12" picture and its frame if the frame is 1.5" thick?

Angles on straight line = 180

180 - 115 = 65

So, angle above 4 in the top corner is 65.

Co-interior angles add up to 180.

(180-65=115)

Thus, the value of 4 is 115 degrees.

Hope this helps!

Answer:

The volume is

[tex]339.4 {yd}^{3} [/tex]

Step-by-step explanation:

The solution is in the image

The inverse function of f(x) = 4^(x + 3) -2 is f-1(x) = log₄(x + 2) - 3

The function is given as:

f(x) = 4^(x + 3) -2

Rewrite as:

y = 4^(x + 3) -2

Swap x and y

x = 4^(y + 3) -2

Add 2 to both sides

x + 2 = 4^(y + 3) -2 + 2

This gives

x + 2 = 4^(y + 3)

Take the logarithm of both sides

log(x  + 2)= log(4)^(y + 3)

Apply the base rule of logarithm

log(x  + 2)= (y + 3)log(4)

Divide both sides by log(4)

log(x + 2)/log(4) = y + 3

Apply the change of base rule of logarithm

log₄(x + 2) = y + 3

Subtract 3 from both sides

log₄(x + 2) - 3 = y + 3 - 3

Evaluate the difference

log₄(x + 2) - 3 = y

Rewrite as:

y = log₄(x + 2) - 3

Rewrite as:

f-1(x) = log₄(x + 2) - 3

Hence, the inverse function of f(x) = 4^(x + 3) -2 is f-1(x) = log₄(x + 2) - 3

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Answer:

1/4

Step-by-step explanation:

Given [tex]\displaystyle{s=\dfrac{1}{4}}[/tex] and we have to evaluate [tex]\displaystyle{4s^2}[/tex]. We can do by substituting the given value s = 1/4 in 4s² term:

[tex]\displaystyle{4\cdot \left(\dfrac{1}{4}\right)^2}\\\\\displaystyle{4\cdot \dfrac{1}{16}}\\\\\displaystyle{\dfrac{1}{4}}[/tex]

Therefore the value is 1/4

The sum of the ten terms to the nearest whole number is 50857.

Using geometric sequence formula,

nth term = arⁿ⁻¹

where

r = 20 / 8 = 5 / 2

a = 8

Hence,

s₁₀ = a(rⁿ - 1) / r - 1

s₁₀ = 8((5 / 2)¹⁰ - 1) / 5 / 2 - 1

s₁₀ = 8(9535.74316406) / 1.5

s₁₀ = 50857.296875

s₁₀ = 50857

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Answer:

y = 40

Step-by-step explanation:

y/8 = 5

———————————————————

Multiply both sides by 8:

8y/8 = 5 * 8

———————————————————

Simplify:

y = 40

Hope that helps! :)

Answer:

Y = 40

Step-by-step explanation:

Step 1:

y/8 = 5

Bring 8 to the right side changing its arithmetic sign to multiply.

Step 2:

y = 5 x 8

Now multiply 5 by 8 to get the answer.

Step 3:

y = 40

Therefore, y is equal to 40.

The  bottom cutoff for receiving an A grade is 88.

The bottom cutoff for receiving an A grade is found as follows:

The mean of the distribution = 75

The standard deviation = 9

The z-score for the 93% = 1.476

The score for an A grade, x = mean + z-score * standard deviation

Score for an A grade, x = 75 + 1.476 * 9

Score for an A grade, x = 88

In conclusion, the minimum score for an A grade is obtained from the mean, the z-score and the standard deviation.

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Answer: [tex]a=\frac{b}{zm-1}[/tex]

Step-by-step explanation:

Let's first multiply both sides by m to get rid of the denominator.

[tex]za=\frac{a+b}{m}\\zam=a+b[/tex]

Now, we have an a on both sides of the equation. It will be easier to solve if there is only one, so let's divide both sides by a.

[tex]\frac{zam}{a}=\frac{a+b}{a}\\zm=\frac{a}{a}+\frac{b}{a}\\zm=1+\frac{b}{a}[/tex]

The 1 on the right can be moved to the left to isolate the fraction.

[tex]zm-1=\frac{b}{a}[/tex]

We want to get a by itself, so let's multiply it on both sides to remove it from the denominator.

[tex]a(zm-1)=b[/tex]

Finally, we can divide zm-1 from both sides to get a by itself.

[tex]a=\frac{b}{zm-1}[/tex]

Okay, it's very simple, to solve this triangle you need to understand what the other angles are. We know that angle A is 90º, as it is represented as a square.

We now need to solve for angle B. angle B can be solved for by

Sin (x) = Opposite / Hypotenuse = 3 / 3√5 = 2.24ish
sin(x) = 2.24

x = [tex]sin^{-1}[/tex](2.24)

Use sin.

Answer:

Step-by-step explanation:

what's the answer

Based on the calculations, all of the numbers belong to this arithmetic sequence.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

[tex]a_n = a_1 +(n-1)d[/tex]

Where:

Next, we would determine the common difference as follows:

d = a₂ - a₁

d = 105 - 99 = 6.

d = a₃ - a₂

d = 111 - 105 = 6.

d = a₄ - a₃

d = 117 - 111 = 6.

Based on the calculations, all of the numbers belong to this arithmetic sequence.

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Complete Question:

What is the number that does not belong to this sequence 99, 105, 111, 117, 123, 129, 135, 141, 147, 153

In other words, 12 goes in the top box and 13 goes in the bottom. The fraction slash sign is not part of either box.

===========================================================

Explanation:

Cosine is the ratio of adjacent over hypotenuse.

cos(angle) = adjacent/hypotenuse

For the reference angle X, the adjacent leg is 36 units long. It's the leg closest or touching angle X.

The hypotenuse is always the longest side. It is always opposite the 90 degree angle. The hypotenuse in this case is 39 units.

Therefore,

cos(X) = 36/39 = (12*3)/(13*3) = 12/13

Answer:

144 boxes, 4 popsicles left over

Step-by-step explanation:

# of boxes and the remainder: 1148/8 = 143 boxes 4 popsicles left over

Since they need to buy full boxes we add 1 to 143 = 144 boxes

A full box is 8 and they only need 4 more so they have 4 left over.

64 decrease by twice the number then the algebraic expression be

64 - 2m.

The algebraic expression exists acquired by a finite number of the fundamental functions of algebra upon characters expressing numbers. Algebraic expressions contain at least one variable and at least one operation (addition, subtraction, multiplication, division).

From the given information, we get

Let, Matt's savings be denoted by the variable m.

Twice the number be 2m.

64 decrease by twice the digit then the algebraic expression be 64-2w.

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Step-by-step explanation:

(f+g)(x)=4x-1+2x²+3===> 2x²+4x+2

Answer: D.

Step-by-step explanation: First you find the common factor, which is 5x³y. Then you write in parenthesis what's left over from each term. So  the answer should look like: 5x³y(-3x⁵-4z+9).

Answer:

30624; 1514,6; a1,6.

Answer:

55

Step-by-step explanation:

61.621 rounded to the nearest whole number is 62. We know this by looking at the whole number "61" and rounding its last digit by the digit to the right of it, depending if its <5 or >5. In this case, the right ones digit is "6", being greater than 5 means we can round 61.621 to 62.

The same applies to 7.173, given that "1" is less than 5, we don't round down (because we are rounding up), instead we replace remaining digits with 0, leaving us with 7.

To find the difference means to subtract;

62-7 = 55.

Answer:

A card balance is the total amount of money that you currently owe on your credit card. The balance increases when purchases are made and decreases when payments are made. Purchases, balance transfers, foreign exchange, fees, and interest all factor into your credit card balance.

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Angle L: 70°

The trigonometric ratio used to solve for NM is the tangent ratio.

NM = 57.7 [nearest tenth]

Using the triangle sum theorem, find angle L.

Angle L = 180 - 90 - 20 = 70°

Using the tangent ratio, we can use  ∠M and LN to solve for NM

Tan 20 = 21/NM [tan ∅ = opposite/adjacent]

NM = 21/tan 20

NM = 57.7 [nearest tenth]

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Answer:

70, tangent, 57.7

Step-by-step explanation:

Answer: [tex]g(x)=\left(\frac{x}{5} \right)^2[/tex]

Step-by-step explanation:

See attached image.

Answer:

QO < OP < QP

Step-by-step explanation:

The third angle, angle Q, must measure 45° since angles in a triangle add to 180°.

So, OQ < OP < QP.

Answer:

PQ>OP>QO

Greater than symbol goes from largest to smallest

Due to length restrictions, we kindly invite to read the explanation of this question for further details about the table and graph of the function.

In this problem we must plot the graph of a function on a Cartesian plane. The procedure is summarized below:

After following the procedure, we have the following result:

Input, x             x + 4                Output, y             (x, y)

   - 2               - 2 + 4                     2                    (- 2, 2)

     0                 0 + 4                     4                     (0, 4)

     2                 2 + 4                     6                     (2, 6)

     4                 4 + 4                     8                      (4, 8)

     6                 6 + 4                    10                      (6, 10)

     8                 8 + 4                    12                      (8, 12)

Lastly, we plot the graph of the linear function.

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Answer:

Step-by-step explanation:

Hello : let A(0,-6) B(8,-8)

the slope is : (YB - YA)/(XB -XA)

(-8+6)/(8-0) = -2/8=-1/4

an equation is : y=ax+b a is a slope

y = (-1/4)x +b

the line through point A (0;-6) : -6 = (-1/4)(0)+b

b = -6            the equation is : y =(-1/)4x-6

Therefore, the bones were 6612.5 years old at the time they were discovered.

Given that the radioactive element​ carbon-14 has a​ half-life of 5750 years, and a scientist determined that the bones from a mastodon had lost 57.5​% of their​ carbon-14, to determine how old were the bones at the time they were discovered, the following calculation must be made:

Therefore, the bones were 6612.5 years old at the time they were discovered.

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Answer:Therefore, the bones were 6612.5 years old at the time they were discovered.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Shift right

f(x)=√x-4.7

f(x)=√x-25

f(x)=√x-11

Shift left

f(x)=√x+0.8

f(x)=√x+6

Answer:

iTS 6 2/3 OPTION 2.

Step-by-step explanation:

Because Area = L*B

SO L = A/b

L= 65/3 * 4/13(reciprocal and multiply)

L=20/3 = 6 2/3

Answer:

So answer is 6 2/3

because Look carefully

Area =length× width

length=Area÷ width

so

[tex]21 \frac{2}{3} \div 3 \frac{1}{4} = 6 \frac{2}{3} [/tex]

Using the z-distribution, the p-value would be given as follows:

b) 0.0086.

At the null hypothesis we test if the means are equal, hence:

[tex]H_0: \mu_D - \mu_C = 0[/tex]

At the alternative hypothesis, it is tested if they are different, hence:

[tex]H_1: \mu_D - \mu_C \neq 0[/tex]

For each sample, they are given as follows:

Hence, for the distribution of differences, they are given by:

The test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Hence:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

[tex]z = \frac{-2 - 0}{0.76}[/tex]

z = -2.63.

Using a z-distribution calculator, for a two-tailed test, with z = -2.63, the p-value is of 0.0086.

Hence option B is correct.

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Answer:

(x - 5) ^2 + (y -2)^2 = 1

Step-by-step explanation:

This is for a circle.

We need to complete the square

(x^2 -10x      ) + ( y^2 -4y       )  = -28

(x^2 - 10x +25) + (y^2 - 4y 2y) = -28 + 25 + 4

(x-5)^2 + (y-2)^2 = 1

The center of this circle would be (5,2)  with a radius of 1.