The side lengths of the base of this right triangular prism are 3 ft, 4 ft, and 5 ft. The height of the prism is 9 ft. What is the total surface area of the prism in square feet? Enter your answer in the box.

Answer:

y = |x+1.5|

Step-by-step explanation:

Start with the graph of y = |x|. To shift it left by 1.5 units, replace x with x+1.5.

General rules for shifting graphs:

Answer:

y=abs(x+1.5)

Step-by-step explanation:

Step-by-step explanation:

LaToya spend $14 each time she travels. the toll roads.

Answer:

Step-by-step explanation:

a.224-14(11)=70

b.A(t)=224-14t  solve it like linear equation  bring -14t to other side of equal sign and divide 224/14t=16

Answer: 7 is the 10% of 70

Step-by-step explanation:

1. write 10% as 10/100 as we convert in this form to find the percentage.

2. 10/100 x 70 = 7

therefore the answer is 7

As a backpack designer at a sportswear company, my team has been assigned the task of creating a smaller toddler size backpack and a larger teen size backpack based on our already popular kids model. In addition to designing these new backpacks, we will also create accessories that can be sold alongside them.

For the smaller toddler size backpack, our focus will be on ensuring a comfortable fit for young children while incorporating fun and age-appropriate designs. We will consider using lightweight and durable materials to make it easier for toddlers to carry. The backpack will have adjustable straps to accommodate their smaller frames and promote proper weight distribution. As for accessories, we can design detachable safety harnesses, featuring playful characters or animal shapes, to help parents keep their toddlers close in crowded places.

For the larger teen size backpack, we will prioritize functionality and style to cater to the needs and preferences of teenagers. The backpack will have ample storage compartments to accommodate textbooks, laptops, and other school essentials. We will also consider incorporating features like padded laptop sleeves, water bottle pockets, and headphone ports to enhance convenience and usability. To complement the backpack, we can design coordinating accessories such as pencil cases, lunch bags, and keychain attachments that match the overall design aesthetic.

Throughout the design process, we will ensure that both the toddler and teen size backpacks maintain the high quality and attention to detail that our brand is known for. Our team will carefully select fabrics, hardware, and zippers that are durable and long-lasting, considering the wear and tear expected in different age groups. We will also focus on ergonomic design principles to prioritize comfort and proper weight distribution for both the smaller and larger backpacks.

By expanding our backpack line to include smaller toddler and larger teen sizes, along with the accompanying accessories, we aim to provide functional, stylish, and age-appropriate options for a broader range of customers.

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The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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Step-by-step explanation:

Well, 40 - 8 = 32, since she had 8 remaining. Then divide 32 by 2, since she gave 2 to each of her friends. Therefore, she has 16 friends.

Answer:

Well so just divide 40÷8 = 5 that's the answer

Answer:

the answer is a. The population is all words in the book report and the sample is the random sample of 20 words.

Step-by-step explanation:

got it right on edge

Answer: a. The population is all words in the book report and the sample is the random sample of 20 words.

Step-by-step explanation:

The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.

To find the extreme values of V, we need to take the derivative of V and set it equal to zero. So, let's begin:

\(V(x) = x(10-2x)(16-2x)\)
Taking the derivative with respect to x:
\(V'(x) = 10x - 4x^2 - 32x + 12x^2 + 320 - 48x\)
Setting V'(x) = 0 and solving for x:
\(10x - 4x^2 - 32x + 12x^2 + 320 - 48x = 0\\8x^2 - 30x + 320 = 0\)
Solving for x using the quadratic formula:
\(x = (30 ± \sqrt{(30^2 - 4(8)(320))) / (2(8))\\x = (30 ± \sqrt{(1680)) / 16\\x = 0.93 or x =5.07\)
So, the extreme values of V occur at x ≈ 0.93 and x ≈ 5.07. To determine whether these are maximum or minimum values, we need to examine the second derivative of V. If the second derivative is positive, then the function has a minimum at that point. If the second derivative is negative, then the function has a maximum at that point. If the second derivative is zero, then we need to use a different method to determine whether it's a maximum or minimum.

Taking the second derivative of V:
V''(x) = 10 - 8x - 24x + 24x + 96
V''(x) = -8x + 106

Plugging in x = 0.93 and x = 5.07:
V''(0.93) ≈ 98.36 > 0, so V has a minimum at x ≈ 0.93.
V''(5.07) ≈ -56.56 < 0, so V has a maximum at x ≈ 5.07.

Now, to interpret these values in terms of the volume of the box, we need to remember that V(x) represents the volume of a box with length 2x, width 2x, and height x. So, the maximum value of V occurs at x ≈ 5.07, which means that the volume of the box is greatest when the height is about 5.07 units. The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.

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a) The extreme values of V are:

Minimum value: V(0) = 0

Relative maximum value: V(3) = 216

Absolute maximum value: V(4) = 128

b) The absolute maximum value of V at x = 4 represents the case where the box has a square base of side length 4 units, height 2 units, and width 8 units, which has a volume of 128 cubic units.

a) To find the extreme values of V, we first need to find the critical points of the function. This means we need to find where the derivative of the function equals zero or is undefined.

Taking the derivative of V(x), we get:

\(V'(x) = 48x - 36x^2 - 4x^3\)

Setting this equal to zero and solving for x, we get:

\(48x - 36x^2 - 4x^3 = 0\)
4x(4-x)(3-x) = 0

So the critical points are x = 0, x = 4, and x = 3.

We now need to test these critical points to see which ones correspond to maximum or minimum values of V.

We can use the second derivative test to do this. Taking the derivative of V'(x), we get:

\(V''(x) = 48 - 72x - 12x^2\)

Plugging in the critical points, we get:

V''(0) = 48 > 0 (so x = 0 corresponds to a minimum value of V)
V''(4) = -48 < 0 (so x = 4 corresponds to a maximum value of V)
V''(3) = 0 (so we need to do further testing to see what this critical point corresponds to)

To test the critical point x = 3, we can simply plug it into V(x) and compare it to the values at x = 0 and x = 4:

V(0) = 0
V(3) = 216
V(4) = 128

So x = 3 corresponds to a relative maximum value of V.
b) In terms of the volume of the box, the function V(x) represents the volume of a rectangular box with a square base of side length x and height (10-2x) and width (16-2x).
The minimum value of V at x = 0 represents the case where the box has no dimensions (i.e. it's a point), so the volume is zero.
The relative maximum value of V at x = 3 represents the case where the box is a cube with side length 3 units, which has a volume of 216 cubic units.
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Answer:

p = 8

Step-by-step explanation:

17 = 3 ( p - 5 ) + 8

Distribute

17 = 3p - 15 + 8

Simplify

17 = 3p - 7

Inverse operations

17 = 3p - 7

+7         +7

24 = 3p

/3    /3

8 = p

Answer:

\(p=8\)

Step-by-step explanation:

First you need to distribute the 3 with the values in the parentheses.

\(3*p= 3p\\3*-5=-15\)

\(17=3p-15+8\)

Then combine like terms...

\(17=3p-7\\17+7=3p-7+7\\24=3p\\\33p= 24\)

Divide by 3 to get the variable by itself.

\(\frac{3p}{3}=\frac{24}{3}\\p=8\)

Answer:

1.27 centimeters

Step-by-step explanation:

brainliest??

Answer:

The z-score for this data point is -1.5

Step-by-step explanation:

Mean = M = 150

Standard Deviation = S = 20

Value = x = 120

We find the z value,

\(z = (x-M)/S\\z = (120 - 150)/20\\z = (-30)/20\\z=-3/2\\z=-1.5\)

Hence the z value is z = -1.5

Answer:

Yes

Step-by-step explanation:

In mathematics rational means "ratio like." so a rational number is one that can be written as the ratio of two integers. 1 3/23 can be converted into 26/23, which is a ratio, therefore, 1 3/23 is a rational number.

Hope this helps!

Answer:

310

Step-by-step explanation:

Multiply the l/w/h x 2

Answer:

If he mows 3/20 in 1/6 of an hour he'll mow 18/20 or 9/10 in one hour

which means the ratios are equal

1/6:3/20 = 1:18/20 = 1:9/10

Therefore, Jerry will mow 90% of the lawn in one hour

Step-by-step explanation:

Hope this helps:)...if not then sorry for wasting your time and may GOd bless you

Answer:

3/2

Step-by-step explanation:

The total number of students in the four classes is 100 students.

From the information, the numbers of students in the four sixth-grade classes at Northside School are 26, 19, 34, and 21.

Therefore, the total number of students will be:

= 26 + 19 + 34 + 21

= 100

Therefore there are 100 students.

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Answer: Answer is D and B

Step-by-step explanation:

Answer:

Right and isosceles

Step-by-step explanation:

There is a marked right angle in the diagram of the triangle. Two side lengths are the same, meaning it is isosceles.

The line 2x +3y = 1 is tangent to 4x^2 -9y^2 = 19

:

Solve the linear equation for y

:

1) y = -2x/3 +1/3

:

substitute for y in the equation of the hyperbole

:

4x^2 -9(-2x/3 +1/3)^2 = 19

:

4x^2 -9(4x^2/9 -4x/9 +1/9) = 19

:

4x^2 -4x^2 +4x -1 = 19

:

4x -20 = 0

:

4x = 20

:

x = 5

:

use equation 1 to get the value of y

:

y = -2(5)/3 +1/3 = -3

:

******************************************************************

solution is x = 5, y = -3 which is the point (5, -3)

:

check the solution

:

hyperbole

:

4(5^2) -9(-3)^2 = 19

:

100 -81 = 19

:

19 = 19

:

Line

:

2(5) +3(-3) = 1

:

10 -9 = 1

:

1 = 1

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The 20th prize is $4400.

It is a sequence where the difference between each consecutive terms is the same.

Example:

2, 4, 6, 8 is an arithmetic sequence.

We have,

First prize = $12,000

Successive prize worth $400 less than the preceding prize.

Now,

We can make an arithmetic sequence.

12,000, 11,600, 11,200, ...

So,

a = 12,000

d = -400

The nth term of an arithmetic sequence.

= a + (n - 1)d

So,

The 20th prize.

= 12,000 + (20 -1)400

= 12,000 - 19 x 400

= 12,000 - 7600

= 4400

Thus,

20th prize = $4400

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Answer:

X+1=3

x = 3 - 1

x = 2

Check:

2 + 1 = 3

x-4=5

x = 5 + 4

x = 9

Check:

9 - 4 = 5

Answer:

1)x=2

2)x=9

Step-by-step explanation:

x+1=3

=>x=3-1

therefore

x=2

second question

x-4=5

=>x=5+4

therefore

x=9

The answer to questions are as follows- a)720 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used once. b)240 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used once, containing the block cd. c)120 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used once, that start with the letter f.d)4 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used once, that contain the blocks abc and ef.

a) To find the number of strings that can be formed using the letters a, b, c, d, e, f with each letter used formerly, we need to find the number of permutations of the letters. This can be set up using the formula for permutations of n objects taken r at a time, which is n!/( n- r)!.

In this case, we've 6 objects and we want to take all 6, so we have

6!/( 6- 6)! = 6! = 720

thus, there are 720 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly.

b) To find the number of strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly, that contain the block cd, we can treat the block cd as a single object and find the number of permutations of the performing 5 objects( alphabet, e, f, and the block cd). We also multiply this by the number of ways that cd can be arranged within the string( which is 2 since cd can be arranged as cd or dc).

So we have

5! * 2 = 240

thus, there are 240 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly, containing the block cd.

c) To find the number of strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly, that starts with the letter f, we can fix f as the first letter and also find the number of permutations of the remaining 5 objects. This can be set up using the formula for permutations of n objects taken r at a time, which is n!/( n- r)!.

In this case, we've 5 objects and we want to take all 5, so we have

5!/( 5- 5)! = 5! = 120

thus, there are 120 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly, that start with the letter f.

d) To find the number of strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly, that contain the blocks alphabet and ef, we can fix alphabet and ef as blocks and find the number of permutations of the remaining 2 objects( d and f). We also multiply this by the number of ways that the blocks can be arranged within the string( which is 2 since alphabet can be before ef or ef can be before the alphabet).

So we have

2 * 2! = 4

thus, there are 4 different strings that can be formed using the letters a, b, c, d, e, and f with each letter used formerly, that contain the blocks alphabet and ef.

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The correct questions are given below-

a)how many strings can be formed using the letters a, b, c, d, e, f, with each letter used once?

b) how many strings can be formed using the letters a, b, c, d, e, f, with each letter used once, that contain the block cd?

c)how many strings can be formed using the letters a, b, c, d, e, f, with each letter used once, that start with the letter f?

d)how many strings can be formed using the letters a, b, c, d, e, f, with each letter used once, that contain the blocks abc and ef?

Working is attached below with answers.

Answer:

the angles are the same but the lengths are now 15 feet

Step-by-step explanation:

similar shapes have the same angles and 1.5 x 10 is 15

Answer:

I got x=4/7

Step-by-step explanation:

hoped I helped:) please correct me if in wrong:)

Answer:

A

Step-by-step explanation:

A trinomial has 3 terms

This could be A , B or C

A leading coefficient of 3 is the coefficient of the term with the largest exponent in the expression.

This could be A or C

The constant term has no variable attached, that is purely numeric.

The only expression with a constant term of - 5 is A

The expression meeting all the given conditions is A

A quadratic equation is a polynomial equation of degree 2, which means the highest power of the variable is 2. It is generally written in the form: ax^2 + bx + c = 0. Option (d) x = -8, x = 8 is the correct answer.

The given equation is 15x^2 - 56 = 88 - 6x^2.

We need to find the values of x that are solutions to the given equation.

Solution: We are given an equation 15x² - 56 = 88 - 6x².

Rearrange the equation to form a quadratic equation in standard form as follows: 15x² + 6x² = 88 + 56  21x² = 144  

x² = 144/21 = 48/7

Therefore x = ±sqrt(48/7) = ±(4/7)*sqrt(21).

The values of x that are solutions to the given equation are x = -4/7 sqrt(21) and x = 4/7 sqrt(21).

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The given equation is 15x² - 56 = 88 - 6x². Values of x are solutions to the equation below 15x² - 56 = 88 - 6x² are x = -2.62, 2.62 or x ≈ -2.62, 2.62.

Firstly, let's add 6x² to both sides of the equation as shown below.

15x² - 56 + 6x² = 88

15x² + 6x² - 56 = 88

Simplify as shown below.

21x² = 88 + 56

21x² = 144

Now let's divide both sides by 21 as shown below.

x² = 144/21

x² = 6.86

Now we need to solve for x.

To solve for x we need to take the square root of both sides.

Therefore, x = ±√(6.86).

Therefore, the values of x are solutions to the equation below are x = -2.62, 2.62 or x ≈ -2.62, 2.62.

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Answer:

4 hours

Step-by-step explanation:

Distance / Velocity = Time

In this case, 8 / 2 = 4