subtract (9x+8) from the sum of (3x^2-2x-x^3+2) and (5x^2-8x-x^3+4)

Answer:

gfgfcvfvghcghccghcgcvchdcfgcfcfrtyc

Step-by-step explanation:

The length of the original square must be equal to 3 inches.

To find the length of the original square, we have to first assume the unknown length is equal x and then use formula of area of a square to determine it's length.

Since the new length is stretched by 5in, the new length would be.

\(l = (x + 5)in\)

The area of a square is given as

\(A = l^2\)

But the area is equal 64 squared inches; let's use substitute the value of l into the equation above.

\(A = l^2\\l = x + 5\\A = 64\\64 = (x+5)^2\\64 = x^2 + 10x + 25\\x^2 + 10x - 39 = 0\\\)

Solving the quadratic equation above;

\(x^2 + 10x - 39 = 0\\x = 3 or x = -13\)

Taking the positive root only, x = 3.

The side length of the original square is equal to 3 inches.

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a. The hypothesis to be tested are given as follows:

b. The p-value is of: 0.0047.

c. The decision is of: Reject the null hypothesis.

d. The conclusion is of: There is enough evidence to conclude that the mean rate is less for people who exercise regularly.

At the null hypothesis, it is tested if there is not enough evidence to conclude that the heart rate is less, than is, if the difference is not negative, hence:

\(H_0: \mu_d \leq 0\)

At the alternative hypothesis, it is tested if there is enough evidence to conclude that the heart rate is less, that is, if the difference is negative, hence:

\(H_1: \mu_d > 0\)

The parameters to the p-value are given as follows:

We have a left-tailed test, as we are testing if the mean is less than a value, hence, using a t-distribution calculator, the p-value is of:

0.0047.

Since the p-value is less than the critical value, the decision and the conclusion are given as follows:

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Rounded to the nearest tenth, the acceleration in inches per second squared is approximately 15222.8 in/s².

To convert the acceleration from meters per second squared (m/s²) to inches per second squared (in/s²), we need to use the conversion factor between the two units.

1 meter is equal to 39.37 inches.

To convert the units, we can set up the following conversion factor:

1 m/s² = (39.37 in/m)^2 = 1550.0031 in/s²

Now, we can multiply the given acceleration in m/s² by the conversion factor to obtain the acceleration in in/s²:

Acceleration in in/s² = 9.81 m/s² * 1550.0031 in/s²

Acceleration in in/s² ≈ 15222.7568 in/s²

Rounded to the nearest tenth, the acceleration in inches per second squared is approximately 15222.8 in/s².

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For this equation you simply have to graph it.

First, you have to remember that these equations follow a formula: y=mx+b. m is the slope of you line and b is the y-intercept.

Next, you need to graph it. First, graph your b, in this case 2. You would go up 2 on you graph (graph (0,2)). Then, you would graph your slope which is 3.

Now, remember that slope equals y/x, so think of the number 3 being like 3/1. You would start at (0,2) and go up 3 points in the graph, then over 1 point (graph where you end up). You repeat that from each new point you make until you have enough points to create a straight line.

Hope this helps a bit,

Answer:

It represents the total amount that Erin is going to spend at the store.

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

Answer:

uhhh

Step-by-step explanation:

The linear pair property and the trigonometric table indicates;

tan(∠QSR) = √3/3

A trigonometric table lists the value of trigonometric functions for standard angles.

The measure of the angles in the question indicates;

m∠QST = 150°

The linear pair property indicates that the angles ∠QST and ∠QSR are linear pair angles, therefore;

m∠QST + m∠QSR = 180°

The substitution property indicates that we get;

150° + m∠QSR = 180°

m∠QSR = 180° - 150° = 30°

Therefore; tan(∠QSR) = tan(30°)

The trigonometric table indicates that we get;

tan(30°) = 1/√3 = 1/√3 × (√3)/(√3) = √3/3

The correct option is therefore;

A. √3/3

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The total height of the three jumps is A = 20.744 feet

Given data ,

1st high jump score: 7.016 feet

2nd high jump score: 5.42 feet

3rd high jump score: 8.308 feet

On adding the scores , we get

7.016 + 5.42 + 8.308 = 20.744 feet

On simplifying the equation , we get

A = 20.744 feet

Hence , Oliver jumped a total of 20.744 feet in the three high jumps

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Answer:

3

Step-by-step explanation:

The answer is three because u need to simply the fractions

The hοle needs tο be 39 inches deeper.

A cοnversiοn factοr is a number used tο change οne set οf units tο anοther, by multiplying οr dividing. When a cοnversiοn is necessary, the apprοpriate cοnversiοn factοr tο an equal value must be used. Fοr example, tο cοnvert inches tο feet, the apprοpriate cοnversiοn value is 12 inches equals 1 fοοt.

The current depth οf the hοle is 2 feet 9 inches, which is the same as 2 + 9/12 = 2.75 feet (since there are 12 inches in 1 fοοt).

Tο find οut hοw much deeper the hοle needs tο be, we need tο subtract the current depth frοm the required depth:

6 feet - 2.75 feet = 3.25 feet

Hοwever, we are asked tο express the answer in inches, sο we need tο cοnvert the 3.25 feet tο inches using the given cοnversiοn factοr:

3.25 feet x 12 inches/1 fοοt = 39 inches

Therefοre, the hοle needs tο be 39 inches deeper.

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In this case value of x is 24 inches.

How can we explain this ?

In the given situation we can see that one angle is equal in both the triangles, reflex angles are going to be equal as per theorem of reflex angle. therefore when two angles are equal then in that case third angle of both the triangles are going to be equal.

As per given situation parallel sides of both the triangles are 5 and 15 simultaneously which means one side of larger triangle is 3's that of the smaller triangle. Keeping in mind this situation we can say that value of x will be 3*8=24 inches.

An equilateral triangle is a type of triangle in which all three sides are of equal length, and all three angles are also equal to 60 degrees.

In an equilateral triangle, the three angles are congruent, meaning they are all the same measure. They measure 60 degrees each.

Also, the three medians, angle bisectors, and altitudes of an equilateral triangle are concurrent at the centroid.

An equilateral triangle is also a regular polygon, which means all its sides are of equal length and all its angles are congruent.

It is also a special case of isosceles triangles.

It is symmetric, so the medians, altitudes, angle bisectors, and perpendicular bisectors all intersect at the same point, which is the centroid of the triangle.

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Answer:

$13.99

Step-by-step explanation:

that's the burger and pop and half the onion rings cost combined

The two types of frequency distributions are Discrete Frequency Distribution and Grouped Frequency Distribution

The two types of frequency distributions are;

When the data consists of discrete, separate values, this sort of distribution is used. It displays the frequency or number of occurrences of each value.

The data is often expressed in a table with two columns: one for distinct values and another for the frequencies of those values.

This distribution is utilized when the data is continuous and has a wide range of values. It entails categorizing the data into intervals or classes and then calculating the frequency of values that fall within each interval.

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using the law of sines the results are:

Angle B = 70°

Side a = 7.97 cm

Side c = 12.31 cm

To solve the triangle using the law of sines, we have the following information:

Angle A = 42°

Angle C = 68°

Side b = 12 cm

We want to find Angle B, side a, and side c.

First, we can find Angle B using the fact that the sum of the angles in a triangle is 180°:

Angle B = 180° - Angle A - Angle C

Angle B = 180° - 42° - 68°

Angle B = 70°

Next, we can use the law of sines to find side a and side c:

sin(A)/a = sin(B)/b = sin(C)/c

We know b = 12 cm and angles A, B, and C. Let's focus on finding side a:

sin(A)/a = sin(B)/b

We have:

sin(42°)/a = sin(70°)/12

To find side a, we rearrange the equation:

a = (sin(42°) × 12) / sin(70°)

a ≈ 7.97 cm

Now, let's find side c using the same law of sines equation:

sin(C)/c = sin(B)/b

We have:

sin(68°)/c = sin(70°)/12

Rearranging the equation, we can solve for side c:

c = (sin(68°) × 12) / sin(70°)

c = 12.31 cm

So, the results are:

Angle B = 70°

Side a = 7.97 cm

Side c = 12.31 cm

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if we  that Abby spent 50% of her time on School, 30% on Work, and 20% on Sleep, we can estimate that she spent:

100% - (50% + 30% + 20%) = 100% - 100% = 0% on Other.

If Abby divided her time into four categories (School, Work, Other, and Sleep), the percentage she spent on Other would be 100% less the sum of the percentages she spent on School, Work, and Sleep.

So, assuming Abby spending 50% of her time at school, 30% at work, and 20% sleeping, we can estimate she spent:

On Other, 100% - (50% + 30% + 20%) = 100% - 100% = 0%.

However, this is just a guess based on assumptions about how Abby spent her time. It's difficult to provide a more accurate estimate without more information.

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Answer:

Step-by-step explanation:Le quedo +10$

Ya que

-65 y le regalaron +10

The unknown angle measures are d = 76, c = 53, a = 51 and b = 76

From the question, we have the following parameters that can be used in our computation:

The lines

The sum of angles on a line is 180

So, we have

b = 180 - 51 - 53

b = 76

By vertical angle theorems, we have

d = 76

c = 53

a = 51

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By using the figure below, the value of line segment PT is equal to 54 units.

In Mathematics, the midpoint of a line segment with two endpoints can be calculated by adding each point on a line segment together and then divide by two (2).

Since T is the midpoint of PQ, we have the following:

Line segment PT = Line segment TQ

7x + 5 = 9x - 9

9x - 7x = 9 + 5

2x = 14

x = 14/2

x = 7.

Now, we can determine the value of PT:

PT = 7x + 5

PT = 7(7) + 5

PT = 54 units.

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Complete Question:

Use the figure to the right to find the value of PT. T is the midpoint of PQ PT=7x+9 and TQ=9x-5

The valid conclusion form the statement is

The value of y is

The length of KP is

The side y is solved using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

30² = y² + y²

900 = 2y²

450 =  y²

y = √450

y = 21.21

The length of KP is calculated by taking the ratios of the corresponding sides of the similar triangle

(x - 25) / (x - 9) = 2 / 10

10(x - 25) = 2(x - 9)

10x - 250 = 2x - 18

collecting like terms

10x - 2x = 250 - 18

8x = 232

x = 29

Length KP = x - 9 = 29 - 9 = 20

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Answer:

Raul's mistake was in step 2

Step-by-step explanation:

Step 1 ;

\(3+5-7\)

Step 2 :

\(3+2\)

This was where Raul made a mistake

5-7 = -2 not +2

So the correct workings are ;

\(3+5-7\\\\3-2\\\\=1\)

Answer:

25 milliliters of 25% solution and 75 milliliters of 5% solution should be used.

Step-by-step explanation:

Since the druggist has to prepare 100 ml of a 10% solution, but has only 5% and 25% solutions, to determine the proportion of each solution that he must use to prepare the solution with the desired percentage, it is necessary to perform the following calculation:

25 x 1 + 5 x 0 = 25

25 x 0.9 + 5 x 0.1 = 23

25 x 0.8 + 5 x 0.2 = 21

25 x 0.7 + 5 x 0.3 = 19

25 x 0.6 + 5 x 0.4 = 17

25 x 0.5 + 5 x 0.5 = 15

25 x 0.4 + 5 x 0.6 = 13

25 x 0.3 + 5 x 0.7 = 11

25 x 0.2 + 5 x 0.8 = 9

Therefore, the percentage that the druggist must use will be between 20% and 30% of the 25% solution, and between 70% and 80% of the 5% solution, that is:

25 x 0.25 + 5 x 0.75 = 10

Therefore, the druggist should use a 25% solution at 25%, and a 75% solution at 5%: Thus, since 100 x 0.25 is equal to 25, 25 milliliters of 25% solution and 75 milliliters of 5% solution should be used.

Answer:

65 x 160  / 100 = 104

Step-by-step explanation:

Answer: 854.775

Explanation: (19.65 x 40) + [(19.65/2)x7]

I had a little trouble understanding the way the question was worded, so let me know if I'm wrong.

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

The total surface area of the doghouse is 1452 ft²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The dog house has many surfaces including the roofs . The total surface area is the sum of all the area of the surfaces.

area of the roof part = 2( 13×11) + 2( 12× 10)×1/2

= 286 + 720

= 1006 ft²

surface area of the building

= 2( lb + lh + bh) -bh

= 2( 10× 11 + 10×8 + 11×8) - 10×11

= 2( 110+80+88)-110

= 2( 278) -110

= 556 -110

= 446ft²

The total surface area = 1006 + 446

= 1452 ft²

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The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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