For 14a through 14d, tell which expressions require you to rename mixed numbers before you can subtract. Find each difference. Write each expression and the difference as an equation in the correct box PLEASE ANSWER

Answer:

24p

Step-by-step explanation:

This is the difference of 2 squares:-  a^2 - b^2 = (a + b)(a - b).

So here we have:-

(2p + 3)^2 - (2p - 3)^2

= (2p + 3 + (2p - 3))(2p + 3 - (2p - 3))

= (2p + 3 + 2p - 3)(2p + 3 - 2p + 3

= 4p * 6

= 24p   (answer)

Final answer:

To simplify the expression (2p+3)² - (2p-3)², apply the difference of squares formula to get ((2p+3) + (2p-3)) * ((2p+3) - (2p-3)), which simplifies to 24p.

Explanation:

To simplify the expression (2p+3)² - (2p-3)², we need to apply the difference of squares formula, which is

a² - b² = (a+b)(a-b).

Here, a is (2p+3) and b is (2p-3). The result will be the product of the sum and difference of a and b.

Let's perform the simplification step-by-step:

Simplify both products:
 (4p) * (6)

Finally, multiply the results to get the simplified expression:
24p

The simplified result of the expression (2p+3)² - (2p-3)² is 24p.

Answer:

14.

Unless your assignments tells you not to round to whole numbers or to round to the nearest decimal places, then 13.99. But, in most cases, you'd round to 14.

60%

The percent change can be found from ...

... ((new value)/(old value) -1) × 100%

... (1520/950 -1) × 100% . . . . . . filling in your numbers

... (1.6 - 1) × 100% = 60% . . . . . . simplify

Attendance this year was 60% higher than last year.

Answer:

See attached

Step-by-step explanation:

For each increase of 1 in the index, the function value doubles. The size of the function value rapidly exceeds the limit of any linear grid.

We've shown a few points plotted. Perhaps it will give you the idea of what you need to do.

Answer:

The index starts at 1, so the domain of the function is D = {1, 2, 3, 4, 5, 6, . . .}. The sequence is based on the add 3 rule. So, to get more terms of the sequence, add 3 to the last term to get the next one. The range values include the terms of the sequence, so the range is R = {1, 4, 7, 10, 13, 16, . . .}.

To graph the function of this sequence on a coordinate plane, pair the domain values with the corresponding range values to get {(1, 1), (2, 4), (3, 7), (4, 10), (5, 13), (6, 16), . . .}. Then plot these points on the graph.

Step-by-step explanation:

Answer:

HL Congruence Theorem

Step-by-step explanation:

Answer:

HL congruence theorem

Step-by-step explanation:

Given that WZX is an isosceles triangle with sides WX=WZ

Also given that WY is altitude on side XZ

Consider triangles WXY and WZY

WX=WZ             Given

WY=WY             REflexive property

Angle wyz =angle wyx     Right angle

Hence by HL congruence theorem, since one leg and hypotenuse are equal we get the two triangles to be congruent.

x-intercept: -4

y-intercept: +1

The x-axis is the horizontal line on the graph with "x" marked at the right end. It is also identified by the "0" among the numbers on the vertical scale at the left side of the graph.

You can consider the x-axis to be a number line. The numbers on that number line are those of the horizontal sequence of numbers at the bottom of the graph. (On many graphs, they're shown adjacent to the x-axis in the middle of the page. That's not the case here.) These numbers are the x-coordinate of any point with the corresponding horizontal position.

The x-intercept is where the blue line crosses the x-axis. It is marked with a dot on the vertical line that has -4 at the bottom. That -4 is the x-coordinate of the x-intercept, the value the problem is asking for.

___

The y-axis is the vertical line on the graph with "y" marked at the top end. It is also identified by the "0" among the numbers on the horizontal scale at the bottom of the graph.

You can consider the y-axis to be a number line. The numbers on that number line are those of the vertical sequence of numbers at the left side of the graph. (On many graphs, they're shown adjacent to the y-axis in the middle of the page. That's not the case here.) These numbers are the y-coordinate of any point with the corresponding vertical position.

The y-intercept is where the blue line crosses the y-axis. It is marked with a dot on the horizontal line that has 1 at the left side. That 1 is the y-coordinate of the y-intercept, the value the problem is asking for.

___

The (x, y) coordinates of the x-intercept are (-4, 0). The y-coordinate is always zero, because that is the definition of x-intercept: the x-coordinate of the point on the graph where y=0.

The (x, y) coordinates of the y-intercept are (0, 1). The x-coordinate is always zero, because that is the definition of y-intercept: the y-coordinate of the point on the graph where x=0.

Answer:

AC = √7 in

Step-by-step explanation:

ΔABC is isosceles, so ΔADC is a right triangle with AD = 2 in and CD = √3 in. The length of hypotenuse AC is found using the Pythagorean theorem.

... AC² = AD² +CD² = (2 in)² +(√3 in)² = (4 +3) in²

... AC = √7 in . . . . take the square root

Evan has the most in his beaker.

This is because:

0.75 < 0.8 < 1.05 < 1.2.

The problem is symmetrical, so proof for ΔCDG can serve as a model for proof for ΔCEH.

∠DGA ≅ ∠DCA ≅ 90° . . . . given

∠GAD ≅ ∠CAD . . . . definition of angle bisector AD

AD ≅ AD . . . . reflexive property

ΔDGA ≅ ΔDCA . . . . AAS congruence theorem

CD ≅ GD . . . . CPCTC

∴ ΔCDG is isosceles . . . . definition of isosceles triangle (2 sides congruent)

_____

To do the same for ΔCEH, replace "D" with "E", replace "G" with "H", and replace "A" with "B". The rest of the logic applies.

y = (9/8)(x +4)(x -2)

When the x-intercepts are "a" and "b", you know factors of the function are (x-a) and (x-b). So, we can write the function as ...

... y = k(x -(-4))(x -2) = k(x +4)(x -2) . . . . . for some scale factor k

We can find k using the given point.

... -9 = k(0 +4)(0 -2) = -8k

Dividing by -8 gives ...

... 9/8 = k

The desired function is ...

... y = (9/8)(x +4)(x -2)

... = (9/8)(x² +2x -8)

A. -59,048

The first pair of terms sums to -8; the second pair to -72. Each pair after that sums to a value 9 times the previous one. Then the sum of 10 terms is ...

... (-8) + (-72) + (-648) + (-5832) + (-52488)

Before you even add this up, you know the answer choice is A. The sum is ...

... -59, 048

_____

Using the formula

The formula for the sum of a geometric series is ...

... S = a1·(r^n -1)/(r -1) . . . . . where a1 = 4 is the initial term, r=-3 is the common ratio, and n=10 is the number of terms.

Filling in the values and doing the arithmetic, we have ...

... S = 4·((-3)^10 -1)/(-3-1) = 4·(59,049 -1)/(-4) = -59,048

Answer:

-59,048

Step-by-step explanation:

Answer:

[tex]\begin{array}{ccc}\text{Radius}&\text{Volume of sphere}&\text{Volume of cylinder}\\&&\\1&\dfrac{4}{3}\pi &2\pi \\&&\\2&\dfrac{32}{3}\pi &16\pi \\&&\\3&36\pi &54\pi \\&&\\4&\dfrac{256}{3}\pi &128\pi \\&&\\5&\dfrac{500}{3}\pi &250\pi\end{array}[/tex]

Step-by-step explanation:

Use formulas for the volumes:

[tex]V_{sphere}=\dfrac{4}{3}\pi r^3,\\ \\V_{cylinder}=\pi r^2h=\pi r^2\cdot 2r=2\pi r^3.[/tex]

1. When r=1,

[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 1^3=\dfrac{4}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 1^3=2\pi.[/tex]

2. When r=2,

[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 2^3=\dfrac{32}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 2^3=16\pi.[/tex]

3. When r=3,

[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 3^3=36\pi,\\ \\V_{cylinder}=2\pi \cdot 3^3=54\pi.[/tex]

4. When r=4,

[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 4^3=\dfrac{256}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 4^3=128\pi.[/tex]

5. When r=5,

[tex]V_{sphere}=\dfrac{4}{3}\pi\cdot 5^3=\dfrac{500}{3}\pi,\\ \\V_{cylinder}=2\pi \cdot 5^3=250\pi.[/tex]

Note that for all r,

[tex]\dfrac{V_{sphere}}{V_{cylinder}}=\dfrac{\frac{4}{3}\pi r^3}{2\pi r^3}=\dfrac{2}{3}.[/tex]

Answer:

Please, see the attached file.

Thanks.

Step-by-step explanation:

Please, see the attached file.

Thanks.

Answer:

1636.4 ft/min

Step-by-step explanation:

Multiply by the conversion factors that change the units you have to the units you want.

(200 yd)/(22 s) × (3 ft/yd) × (60 s/min) = 18000/11 ft/min ≈ 1636.4 ft/min

Answer:

14 bags

Step-by-step explanation:

If you earn $17, to find the number of bags substitute 17 for y in the equation y=0.50x+10. Then use inverse operations to solve for x.

17 = 0.50x+10               Subtract 10 from both sides.

17-10 = 0.50x

7=0.50x                        Divide both sides by 0.50

7/0.50 = x

14 =x

Answer:

15 ft²

Step-by-step explanation:

The volume of a cone is given in terms of the base area (B) and height (h) by the formula ...

... V = (1/3)Bh

Putting in the given numbers, you have ...

... 35 ft³ = (1/3)B(7 ft)

... B = (35·3/7) ft² = 15 ft² . . . . . . solve for B

The answer is C) 41 hope this helped

Answer:

speed = (3/8 mi)/(3/5 h)

Step-by-step explanation:

... speed = distance/time

Fill in the given values:

... speed = (3/8 mi)/(3/5 h)

_____

Comment on units

You can use the units to provide both guidance and assurance. You know speed is generally expressed in miles per hour. If you consider "per" to mean "divided by", this expression of units tells you speed is calculated by dividing miles by hours.

If you leave the units with the numbers, as we have above, they enter into the calculation the same way any variable might. You can do the arithemetic with the numbers, and you can indicate the arithmetic with the units (just as you would with any variables). Here, the result of evaluating the equation would be ...

[tex]\displaystyle\frac{\frac{3}{8}\,\text{mi}}{\frac{3}{5}\,\text{h}}=\frac{\frac{3}{8}}{\frac{3}{5}}\,\frac{\text{mi}}{\text{h}}=\frac{5}{8}\,\text{mi/h}[/tex]

The fact that the units come out mi/h (the units of speed) provides assurance that you probably did the math correctly.

Answer:

three eighths over three fifths = five eighths mile per hour

Step-by-step explanation:

Answer:

5 weeks

Step-by-step explanation:

John creates apps at the rate ...

... (3 apps)/(6 weeks) = 1/2 app/week

Ben creates apps at the rate ...

... (3 apps)/(2 weeks) = 3/2 app/week

Together, they create ...

... (1/2) app/week + (3/2) app/week = 2 app/week

So, the time for 10 apps is ...

... (10 app)/(2 app/week) = 5 week

_____

Comment on the problem

If the guys actually work at a uniform rate like this, the result after 5 weeks will be 9 completed apps and 2 half-completed apps. Their rate is 10 apps in 5 weeks, but their actual output in that time period may not be 10 completed apps.

One should beware of the "mythical man-month." Rates of job completion depend on many factors. Individual average rates cannot always be summed when folks "work together."

Answer:

y = ($0.5/ch) x + $10

Step-by-step explanation:

Let

x = number of chores

y = allowance

The relationship between y and x can be expressed in a linear equation in the slope-intercept form.

y = mx + b

where

m is the slope

b is the y-intercept

We have the ordered pairs (8, 14) and (12, 16). We can calculate the slope using the following expression.

m = Δy/Δx = $16-$14/12ch-8ch = $0.5/ch

The equation is

y = ($0.5/ch) x + b

We will replace the first point in the previous equation.

$14 = ($0.5/ch) 8ch + b

b = $10

The final equation is

y = ($0.5/ch) x + $10

This equation can be used to predict Hari's allowance for any number of chores. For example, if Hari does 10 chores, his allowance will be $12.50. The final equation is y = ($0.5/ch) x + $10.

We are given that Hari's allowance varies depending on the number of chores he does.

We are also given two points, (8, 14) and (12, 16), that represent the relationship between the number of chores and the allowance.

We can use these two points to find the slope of the line.

The slope is equal to rise over run, which in this case is equal to

$16 - $14 / 12 - 8 = 0.5/ch.

We can now plug the slope and one of the points into the slope-intercept form of the equation to find the value of b, the y-intercept.

We will use the point (8, 14).

y = mx + b

14 = ($0.5/ch) 8ch + b

14 = $4 + b

b = $10

The final equation is y = ($0.5/ch) x + $10.

This equation can be used to predict Hari's allowance for any number of chores. For example, if Hari does 10 chores, his allowance will be $12.50.

Learn more about slope-intercept form here:

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Answer:

1767 cm³

Step-by-step explanation:

We can use volume V = 4/3 π r³

We have diameter of 15 cm. To get radius, we need to divide diameter by 2.

r = 7.5 cm

So now plug in r = 7.5 then calculate V:

V = 4/3 π ( 7.5 )³

V =  4/3 π * 421.875 ≈ 1767.145 ≈ 1767

Hope this helps.

y = 10.29·0.7^x . . . . . selection c seems the closest

For most any exponential function, the exponential multiplier will be 1 when x=0, so the y-intercept is the overall multiplier for the function.

The values decrease as x increases, so the base of the exponential term must be less than 1.

These considerations narrow your choice to C.

... y = 10.29·0.7^x

_____

If you actually want to determine the equation, you can do it several ways. One is to make use of the exponential regression function of your graphing calculator. (See attached). Another is to take the logarithms of the y-values and find a best-fit line through them.

_____

Comment on the answer choices

You may notice that none of the offered answers appears to be anything but the product of two numbers. There are no x-variables involved, and no exponents indicated. Cutting and pasting answers like this does not work.

Answer:

c

Step-by-step explanation:

Answer:

The baseball team plays 25 games

Step-by-step explanation:

If they have lost 5 games and that is 20 %, we can make a ratio.

games/ total = 20/100

5              20

------ = -----------

total        100

Using cross products

5*100 = 20*total

500 = 20* total

Divide by 20 on each side

500/20 = 20/20 * total

25 = total

Answer:

its D which is also 25 games

Step-by-step explanation:

Answer:

Step-by-step explanation:

14 cows

46 turkeys

If all the animals were turkeys, there would be 120 legs. There are 28 more than that. Replacing a turkey with a cow adds 2 legs, so there must be 14 such replacements.

There are 14 cows and 46 turkeys.

_____

Check

14×4 + 46×2 = 56 + 92 = 148 . . . . legs

14 + 46 = 60 . . . . . . heads

Answer:

Step-by-step explanation:

I like to form the product of something like this by multiplying binomial pairs first. The distributive property applies for that (as does FOIL).

... (x^2 -3)(x^2 +2) = x^2·x^2 + x^2·2 + (-3)·x^2 + (-3)·2

... = x^4 -x^2 -6 . . . . . the two x^2 terms combine

Now, it is a simple matter to multiply each term by 2x:

... y = 2x^5 -2x^3 -12x

_____

The highest-degree term has degree 5. There are 3 terms. (All are odd-degree, so this is an odd function, symmetrical about the origin.)

As with any odd-degree function (with positive leading coefficient) the overall shape has a positive slope (/), tending toward -∞ for large negative values of x, and tending toward +∞ for large positive values of x.

Answer:

75.00

Step-by-step explanation:

Let x be unknown number. Then

x is 100% and

60 is 80%.

Write a proportion:

[tex]\dfrac{x}{60}=\dfrac{100}{80},\\ \\x=\dfrac{60\cdot 100}{80}=75=75.00.[/tex]

Answer: 41

Step-by-step explanation:

533÷41 = 533/41

Se photo for step -by-step of ling division

The answer to the long division of 533 by 41 is 13. This is reached by multiplying 13 by 41 which results in 533, the original dividend. The remainder is 0.

Let's perform a long division of 533 by 41. First, write the number 533, which is the dividend, inside the long division bracket and the number 41, the divisor, outside of it. Now we need to see how many times 41 fits into 533.

It fits 13 times because 13 times 41 equals 533. Therefore, write 13 above on your long division bracket.

When you multiply 13 (your answer) by 41 (your divisor), you get 533, which is your dividend. Subtract 533 from 533 and you get a remainder of 0. The answer of the long division of 533 by 41 is 13.

Done correctly, long division is a reliable method of dividing large numbers. The important thing is to ensure all steps are followed orderly and accurately.

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7 . . . . . inches per week

The average rate of change of height is ...

... (change in height)/(change in time)

The height changes from 41 inches to 83 inches when the time changes from 3 weeks to 9 weeks. Then the rate of change is ...

... (83 -41) inches/((9 -3) weeks) = (42/6) inches/week = 7 inches/week

It seems likely that the required answer will just be a number: 7.

Answer:

4 cm

Step-by-step explanation:

The midpoint segment has length ...

... L = AB/2 + BC + CD/2 = 16 cm

The entire segment has length ...

... AD = AB + BC + CD = 28 cm

If we subtract AD from 2L, we have ...

... 2L - AD - 2L = 2(AB/2 +BC + CD/2) - (AB +BC +CD) = 2(16 cm) -28 cm = 4 cm

... AB +2BC + CD -AB -BC -CD = 4 cm . . . . remove parentheses

... BC = 4 cm . . . . simplify

Answer:

≈10.99525 cm.

Step-by-step explanation:

1. The length of the circle is L=2πr, where π≈3.1415 and r- radius of the circle.

2. if the given arc is 45° and full circle is 360°, then the length of the arc is 45/360=0.125 of full circle, that is L(arc)=0.125L=0.25πr; ⇒ L(arc)≈0.25*3.1415*14=10.99525 (cm).

Answer:

10.99 ≈ 11cm

Step-by-step explanation:

To find the length of the arc, first we need to find the circumference of the circle, which we find with the following formula :

[tex]c=2\pi r[/tex]

where  [tex]r[/tex] is the radius which is indicated in the image: [tex]r=14cm[/tex].

so the circumference  is:

[tex]c=2\pi(14cm)\\c=87.96cm[/tex]

This is the measure of the entire perimeter of the circle, it is the measure of the 360 ° arc.

Because we only want 45 ° of those 360 °, we divide the value of the circumference by 360 and multiply po 45:

[tex]\frac{87.96cm(45)}{360}=\frac{3958.2}{360}=10.99cm[/tex]

which can be rounded to 11cm

The length of the arc is 11cm

Answer:

Answer - 160

Step-by-step explanation:

2L+2W = 430

L = 3W-5

2(3W-5)+2W = 430

6W-10+2W = 430

8W = 440

W = 55 and L = 3(55)-5 = 160

Answer:

Length = 160 and width = 55 yards

Step-by-step explanation:

Perimeter =  2L + 2W  where L = the length and W = the width.

L = 3W - 5   (given).

So substituting for L is the formula for the perimeter:-

2(3W - 5) + 2W = 430

6W - 10 + 2W = 430

8W = 440

W = 55 yards.

So the Length L = [430 - 2(55]) / 2  = 160 yards.