9. Evaluate 14(-6x +10) - 16x - 100x + 140 for x = -2.

Answer:

[tex](5d^4-8)^2[/tex]

Step-by-step explanation:

[tex]\textsf{Let }\:u=d^4[/tex]

[tex]\implies 25d^8-80d^4+64=25u^2-80u+64[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex],  find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex] :

[tex]\implies ac=25 \cdot 64=1600[/tex]

[tex]\implies b=-80[/tex]

Two numbers that multiply to 1600 and sum to -80 are:

-40 and -40

Rewrite b as the sum of these two numbers:

[tex]\implies 25u^2-40u-40u+64[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies 5u(5u-8)-8(5u-8)[/tex]

Factor out the common term (5u - 8):

[tex]\implies (5u-8)(5u-8)[/tex]

Simplify:

[tex]\implies (5u-8)^2[/tex]

Substitute back [tex]u=d^4[/tex]

[tex]\implies (5d^4-8)^2[/tex]

Therefore:

[tex]25d^8-80d^4+64=(5d^4-8)^2[/tex]

Let's see

Used formula

[tex]\sqrt{2^{2}+6^{2}}=\sqrt{4+36}=\sqrt{40}=\boxed{2\sqrt{10}}[/tex]

The cost to paint the walls and the ceiling is $855

First, we need to find the area that will be painted.

The area of two of the walls is:

A = 20ft*12ft = 240ft²

The area of the other two walls:

A' = 30ft*12ft = 360ft²

The area of the ceiling is:

A'' = 20ft*30ft = 600ft²

We also need to subtract the areas of the two doors and the 4 windows.

Each door is 7ft by 3ft, so the area of each door is:

a = 7ft*3ft = 21ft²

Each window is 4ft by 3ft:

a' = 4ft*3ft = 12ft²

Then the total area that will be painted is:

area = 2A + 2A' + A - 2a - 4a'

area = 2*( 240ft²) + 2*(360ft²) + 600ft² - 2*(21ft²) - 4*(12ft²)

area = 1,710 ft²

We know that we need two coats of paint to cover that area, and the cost per square foot of paint is $0.25, then the total cost is:

C = $0.25*2*(1,710) = $855

The cost to paint the walls and the ceiling is $855

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Hello !

We replace x by 3.

[tex]f(3) = {2}^{3} = 8[/tex]

Have a nice day ;)

[tex]\frak{Hi!}[/tex]

[tex]\orange\hspace{300pt}\above2[/tex]

                              We have the expression -:

                             [tex]\boldsymbol{\sf{f(x)=2^x}}[/tex], and we're asked to find

                             [tex]\boldsymbol{\sf{f(3)}}[/tex].

                             To do that we put in the value for x (3)-:

                             [tex]\boldsymbol{\sf{f(3)=2^3}}[/tex].

                             Evaluate-:

                             [tex]\boldsymbol{\sf{f(3)=2\times2\times2=8}}[/tex]

[tex]\orange\hspace{300pt}\above3[/tex]

Based on Diego's normal usage of his phone, if the battery is at 75%, the phone will not last the whole trip.

First find out how long each percentage of battery life lasts:

= 15 / 100

= 0.15 hours

If Diego is going on a 12 hour trip with 75%, the length of time it would last is:

= 0.15 x 75

= 11.25 hours

This is less than the 12 hours required so the phone will not last the whole trip.

Rest of question:

At 100%, the battery can go for 15 hours.

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The radius and height, in two decimal places are mathematically given as

r=10.60

Generally, the equation for the volume is mathematically given as

[tex]V=\pi r^{2} h+\frac{2}{3} \pi r^{3}[/tex]

Therefore

[tex]5000 &=\pi 0^{2} h+\frac{2}{3} \pi r^{3}[/tex]

[tex]V(r, h) &=\pi r^{2} h+\frac{2}{3} \pi r^{3}-5000 \\\nabla V &=\left\langle 2 \pi r h+2 \pi r^{2}, \pi r^{2}\right\rangle \\[/tex]

[tex]\cos t &=100\left(2 \pi r^{2}\right)+75(2 \pi r h) \\\\\cos t &=200 \pi r^{2}+150 \pi r h \\\\\nabla C(r, h) &=\langle 400 \pi r+150 \pi h, 150 \pi r\rangle[/tex]

Using Lagrange method

[tex]$\langle 400 \pi \gamma+150 \pi \gamma h, 150 \pi \gamma\rangle=\lambda\left\langle 2 \pi \gamma h+2 \pi \gamma^{2}, \pi r^{2}\right\rangle$[/tex]

[tex]$400 \pi r+150 \pi r=\left(2 \pi r h+2 \pi r^{2}\right) \lambda$[/tex]

[tex]$400 \pi \gamma+150 \pi h=300 \pi h+300 \pi r \\\\[/tex]

[tex]$400 \pi r-300 \pi r=150 \pi h$[/tex]

[tex]$160 \pi r=150 \pi h \quad \\\\\\[/tex]

with

[tex]h=\frac{2}{3} r $[/tex]

[tex]$\pi r^{2} h+\frac{2}{3} \pi r^{3}=5000$[/tex]

[tex]\pi r}\left(\frac{2}{3} r \right)+\frac{2}{3} \pi^{3}=5000$[/tex]

[tex]$\frac{4 \pi \gamma^{3}}{3}=5000 \quad[/tex]

[tex]r^{3}=\left(\frac{5000 \times 3}{4 \pi}\right)$[/tex]

r=10.60

In conclusion, the radius and height, in two decimal places is

r=10.60

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The surface area of the triangular pyramid shown is 94.6 in²

An equation is an expression that shows the relationship between two or more variables and numbers.

The surface area of the regular pyramid is given as:

Surface area = 3(0.5 * 4.3 * 13) + (0.5 * 4.3 * 5) = 94.6 in²

The surface area of the triangular pyramid shown is 94.6 in²

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The property that best matches the equation is the associative property.

It should be noted that the associative property simply implies that the way the factors are grouped in a multiplication problem doesn't change the product.

In this case, since it's illustrated that (5 × 3) × 2 = (2 × 3) × 5. They both will give a value of 40.

In this case, the associative property is illustrated.

The complete question is:

Write the property that best matches the following: (5 × 3) × 2 = (2 × 3) × 5.

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Answer:

Step-by-step explanation:

AAS and SAS

The congruence theorems or postulates could be given as reasons why ABC= ADEF are SAS, AAS the correct options are A and F.

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written matters.

For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]

(|AB| denotes length of line segment AB, and so on for others).

We are given that;

The diagram

Now,

Based on the information given in the diagram, we can use the following congruence theorems or postulates as reasons why ABC= ADEF:

SAS (Side-Angle-Side): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

We can use SAS to show that ABC and ADEF are congruent, since AB = AD, BC = DE, and the included angle BAC = the included angle EDF.

AAS (Angle-Angle-Side): If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

We can use AAS to show that ABC and ADEF are congruent, since the included angles BAC and EDF are congruent, angle ABC is congruent to angle ADE (since they are vertical angles), and side BC is congruent to side EF.

Therefore, by congruent triangles the answer will be SAS, AAS.

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Answer:

Sprinter #1

Step-by-step explanation:

Sprinter #1 is running at 96/12 feet per second: 8 feet per second

Sprinter  #2 is running at 475/60 feet per second: approximately 7.9 feet per second

Sprinter #1 covers more distance per second.

Answer:

1.   Cost per customer:  10 + x

     Average number of customers:  16 - 2x

[tex]\textsf{2.} \quad -2x^2-4x+160\geq 130[/tex]

3.    $10, $11, $12 and $13

Step-by-step explanation:

Given information:

Let x = the number of $1 increases in the cost of the buffet

Part 1

Cost per customer:  10 + x

Average number of customers:  16 - 2x

Part 2

The cost per customer multiplied by the number of customers needs to be at least $130.  Therefore, we can use the expressions found in part 1 to write the inequality:

[tex](10 + x)(16 - 2x)\geq 130[/tex]

[tex]\implies 160-20x+16x-2x^2\geq 130[/tex]

[tex]\implies -2x^2-4x+160\geq 130[/tex]

Part 3

To determine the possible buffet prices that Noah could charge and still maintain the restaurant owner's revenue requirements, solve the inequality:

[tex]\implies -2x^2-4x+160\geq 130[/tex]

[tex]\implies -2x^2-4x+30\geq 0[/tex]

[tex]\implies -2(x^2+2x-15)\geq 0[/tex]

[tex]\implies x^2+2x-15\leq 0[/tex]

[tex]\implies (x-3)(x+5)\leq 0[/tex]

Find the roots by equating to zero:

[tex]\implies (x-3)(x+5)=0[/tex]

[tex]x-3=0 \implies x=3[/tex]

[tex]x+5=0 \implies x=-5[/tex]

Therefore, the roots are x = 3 and x = -5.

Test the roots by choosing a value between the roots and substituting it into the original inequality:

[tex]\textsf{At }x=2: \quad -2(2)^2-4(2)+160=144[/tex]

As 144 ≥ 130, the solution to the inequality is between the roots:  

-5 ≤ x ≤ 3

To find the range of possible buffet prices Noah could charge and still maintain a minimum revenue of $130, substitute x = 0 and x = 3 into the expression for "cost per customer.  

[Please note that we cannot use the negative values of the possible values of x since the question only tells us information about the change in average customers per hour considering an increase in cost.  It does not confirm that if the cost is reduced (less than $10) the number of customers increases per hour.]

Cost per customer:  

[tex]x =0 \implies 10 + 0=\$10[/tex]

[tex]x=3 \implies 10+3=\$13[/tex]

Therefore, the possible buffet prices Noah could charge are:

$10, $11, $12 and $13.

Answer:

Step-by-step explanation:

To answer this, you also need to click the transversal pic above.

Answer:

Since the radius is 3.5, to figure out the length on the diameter/side of the triangle, we have to multiply it by 2:

3.5 x 2 = 7

Now we can use the Pythagorean theorem to figure out the length of the other side of the triangle.

a^2 + b^2 = c^2

7^2 + b^2 = 25^2

49 + b^2 = 625

b^2 = 576

b = 24cm

Now that we have all the lengths of the triangle, using the radius, we can calculate the arc of the semi circle using the following formula:

(π + 2)r

(π + 2)3.5

3.5π + 7 = 18cm

Now we can add all of the lengths excluding the diameter of the circle since we want to calculate the perimeter:

25 + 24 + 18 = 67cm

Therefore, the correct answer would be C.

Question 5

1) Given

2) Definition of congruent segments

3) Reflexive property of equality

4) Addition property of equality

5) Substitution

6) Commutative property of addition

7) Segment addition postulate

8) Substitution

9) Segments with equal measure are congruent

Question 6

1) Given

3) Segment addition postulate

4) Substitution

5) Subtraction property of equality

7) SSS

Answer:

-3/2

Step-by-step explanation:

gradient= y2-y1 over x2-x1

2-5 over 6-4

which equals to -3 over 2

Answer:

 -3/2.

Step-by-step explanation:

Slope of a line joining the points (x1, y1) and (x2, y2) is:

(y2 - y1) / (x2 - x1)  so here we have

Slope = (2 - 5)/(6 - 4)

          =  -3/2

Answer:

it is 3 i think

Step-by-step explanatplease mark brainlest

Answer: D. Cannot be determined

Step-by-step explanation: There are 3 postulates we can use for determining similar triangles.

There is Side Side Side (SSS) Postulate, which requires you have 2 sides of each triangle that are the same proportion as the other triangle. For example, in a triangle ABC, if 2 sides are 5 and 7, and in a triangle DEF, if 2 sides are 10 and 14, then the proportions 5/10 ( 1/2) and 7/14 (1/2) are equal. Thus these are similar triangles and the scale is 1/2.

There is Angle Angle (AA) postulate. If 2 angles are the same to another 2 angles in another triangle, then the two triangles are automatically similar.

The last is Side Angle Side (SAS), which requires you to have an angle that is congruent to another angle in a different triangle, and the angle is in between 2 sides that are proportionally equal to another triangle that also has the same angle in 2 sides. For example, if triangles ABC have angles A, B and C, and angle A is the same equal degrees to another angle in a triangle D, and both A and D are in between 2 sides (i.e DE and AB) that are proportionate (e.g DE and AB are proportionate.) The triangles are then similar.

None of these postulates can be applied to our given problem. Let's see why.

For Angle-Angle, we don't have 2 congruent angles. We have 2 right angles, but that's only 1 angle.

For Side Side Side, we don't have 2 sides given on each triangle, let alone proportionate ones.

For Side Angle Side, we don't even have 2 sides for each triangle given, so this cannot be used either.

Answer:

9 units and 12 units to nearest hundredth.

Step-by-step explanation:

Let one leg be x units long  then the other = x+3 units.

By Pythagoras:

x^2 + (x+3)^2 = 15^2 = 225

2x^2 + 6x + 9 = 225

2x^2 + 6x - 216 =0

x^2 + 3x - 108 = 0

(x - 9)(x + 12) = 0

x = 9

So the other 2 legs are 9 and 12.

Answer:

The dependent variables in most cases is output variable. That is a value that depends on some other input value and changes based on that input value.

Step-by-step explanation:

9/20 is the probability that Bob's password consists of an odd single-digit number followed by a letter and a positive single-digit number

It is given that bob's password consists of a non-negative single-digit number followed by a letter and another non-negative single-digit number (which could be the same as the first one).

P (odd single digit number )  =  ( 5 odd single digits / 10 non-negative single digits)  = (5/10)  = 1/2

P (positive single digit number ) =  (9 positive single digits / 10 non-negative single digits)  = 9/10

The total probability is   (1/2) (9/10)  =  9/20

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Answer:

y + 2 = -5(x - 4)

Step-by-step explanation:

Point-slope form is the following: [tex]y-y_{1}=m(x-x_{1})[/tex], where m is the slope of the line and [tex](x_{1}, y_{1} )[/tex] is a point on the line. We are already given all of the information we need, so all we have to do is write it out. We are told that the slope (m) is -5, and the point the question wants us to use is (4, -2), though either of the points given would work. If we plug in the quantities, we get that y - (-2) = -5(x - 4), or y + 2 = -5(x - 4)

Answer:

Step-by-step explanation:

Answer:

26.9 ft

Step-by-step explanation:

So this answer is going to require one of the trigonometric functions, which is the ratio of sides of a triangle. So I attached a diagram to my answer, which is depicting the given information and hopefully this should be able to help a bit.

Anyways, we know the hypotenuse, an angle, and the opposite side of the angle. There is a trigonometric function which is defined as: [tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]. We can use the sine function to solve for the opposite side. So let's plug in known values into this equation:

Known Values: theta=85 degrees, hypotenuse = 27 ft

[tex]sin(85)=\frac{opposite}{27 ft}[/tex]

Multiply both sides by 27 ft]

[tex]sin(85)*27ft=opposite[/tex]

Now you can approximate the value of sin(85) using your calculator, and make sure it's in degree mode not radian mode.

[tex]0.996194698*27ft\approx opposite[/tex]

Simplify

[tex]26.8973 ft\approx opposite[/tex]

Rounding this to one decimal place makes it

[tex]26.9 ft\approx opposite[/tex]

The equivalent expression of [tex]\frac{2^4}{\sqrt[3]{xy}}[/tex] is [tex]\frac{\sqrt[3]{\frac{2^{12}}{xy}}}[/tex]

The expression is given as:

[tex]\frac{2^4}{\sqrt[3]{xy}}[/tex]

Multiply 4 by 1

[tex]\frac{2^{4 * 1}}{\sqrt[3]{xy}}[/tex]

Express 1 as 3/3

[tex]\frac{2^{4 * 3/3}}{\sqrt[3]{xy}}[/tex]

Evaluate the product

[tex]\frac{2^{12 * 1/3}}{\sqrt[3]{xy}}[/tex]

Apply the following law of indices

[tex]a^\frac 1n = \sqrt[n]{a}[/tex]

So, we have:

[tex]\frac{\sqrt[3]{2}^{12}}{\sqrt[3]{xy}}[/tex]

The numerator and the denominator have the same root

So, we have:

[tex]\frac{\sqrt[3]{\frac{2^{12}}{xy}}}[/tex]

Hence, the equivalent expression of [tex]\frac{2^4}{\sqrt[3]{xy}}[/tex] is [tex]\frac{\sqrt[3]{\frac{2^{12}}{xy}}}[/tex]

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In order to get 97% confidence level, with confidence interval of

+/- 1%, and standard deviation of 0.5 our sample size should be 11,772 samples

A confidence interval for a population mean, when the population standard deviation is known based on the conclusion of the Central Limit Theorem that the sampling distribution of the sample means follow an approximately normal distribution.

Accordingly, the Necessary Sample Size is calculated as follows:

Necessary Sample Size = [tex](Z-score)^{2} . StdDev*(1-StdDev) / (Margin Of Error)^{2}[/tex]

Given:-

Substituting in the given formula we get

Necessary Sample Size =

= ((2.17)² x 0.5(0.5)) / (0.01)²

= (4.7089x 0.25) / .0001

= 1.177225 / 0.0001

= 11,772.25

Hence in order to get 97% confidence level, with confidence interval of

+/- 1%,  and standard deviation of 0.5 our sample size should be 11,772

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Answer:

c.) [tex]x^{3} -16x^{2} +75x-108[/tex]

Step-by-step explanation:

Check the attachment.

The answer is B.

the graph of x²+2 (quadratic) has domain values less than 1 because the circle in the graph is an open circle

The graph of -x+2 (linear) has domain values greater than or equal to 1 because the circle in the graph is a closed circle

Hope it helps!

Answer:

a,b,d

Step-by-step explanation:

When Shanti had crossed the finish line, she was a distance of 250 m ahead of Belle

We are given;

Length of Race = 1000 m

When nina crossed the finish line, she was 200 m ahead of Shanti and 400 m ahead of Belle.

Thus;

Shanti had run 4/5 of the race when Nina finished.

So, if Nina's time was x, then by variation, we can say that;

Time it took Shanti to finish the race = 5/4x

So, Belle had run 5/4 * 600 = 750 meters when Shanti finished.

Thus, means Shanti was; 1000 - 750 = 250m ahead of Belle.

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Answer:

for x = 0 ; we have f(x) = 0,5

We can eliminate the first and the last proposal because

f(x) = 0,2(0,5ˣ) ⇒ f(0) = 0,2(0,5⁰) = 0,2 × 1 = 0,2 ≠ 0,5

f(x) = 0,2(0,2ˣ) ⇒ f(0) = 0,2(0,2⁰) = 0,2 × 1 = 0,2 ≠ 0,5

Try for x = 1, we have f(x) = 0,1

f(x) = 0,5(5ˣ) ⇒ f(1) = 0,5 × 5 = 2,5 ≠ 0,1

f(x) = 0,2(0,5ˣ) ⇒ f(1) = 0,2(0,5) = 0,1 ⇒ ok

So the answer is f(x) = 0,2(0,5ˣ)

Answer:

Equation of a line passing through two point (a, 0) and (c, d) is given by [tex]$y=\frac{d}{c-a} x-\frac{a d}{c-a}$[/tex].

Step-by-step explanation:

In the question, it is given that a line passes through (a, 0) and (c, d).

It is asked to write the equation of line.

To do so, first find the values which are given in the question and put it in the formula of the equation of line passing through two points.

Step 1 of 2

Passing point of the line is (a, 0).

Hence, [tex]$x_{1}=a$[/tex] and

[tex]$$y_{1}=0 \text {. }$$[/tex]

Also, Passing point of the line is (c, d).

Hence, [tex]$x_{2}=c$[/tex] and

[tex]$$y_{2}=d \text {. }$$[/tex]

Step 2 of 2

Substitute the above values in the formula of equation of line passing through two point given by [tex]$y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\left(x-x_{1}\right)$[/tex].

[tex]y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\left(x-x_{1}\right)$$\\ $y-0=\frac{d-0}{c-a}(x-a)$\begin{aligned}&y=\frac{d}{c-a}(x-a) \\&y=\frac{d}{c-a} x-\frac{d a}{c-a}\end{aligned}$$[/tex]

Hence, [tex]$y=\frac{d}{c-a} x-\frac{d a}{c-a}$[/tex].