Find missing length.
A trapezoid has a height of 8 meters, a base length of 12 meters, and an area of 64 square meters. What is the length of the other base?

Answer:

purple. (said with British ascent)

Answer:

option 3

Step-by-step explanation:

4x² - 100 = 0 ( add 100 to both sides )

4x² = 100 ( divide both sides by 4 )

x² = 25 ( take square root of both sides )

x = ± [tex]\sqrt{25}[/tex] = ± 5

then

x = - 5 , x = 5

Using linear functions, we have that:

a. Sara will have driven 2.25 hours when Pedro catches up with her.

b. They are 146.25 miles from home when Pedro catches up with Sara.

A linear function is modeled by:

y = mx + b

In which:

We have to consider the starting time as when Pedro leaves, when Sara will be at position 45 miles. Considering the velocities as the slope, the functions are:

Pedro will catch up with Sara when:

P(t) = S(t)

Hence:

65t = 45t + 45

20t = 45

t = 45/20

t = 2.25 hours.

Sara will have driven 2.25 hours when Pedro catches up with her.

The distance from home will be given by:

P(2.25) = S(2.25) = 65(2.25) = 45(2.25) + 45 = 146.25.

They are 146.25 miles from home when Pedro catches up with Sara.

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Answer:

1400

Step-by-step explanation:

10² is 100 so 100*14 is 1400

The factored expression of 21x^7y^7z^4 + 31x^4y^4 is  x^4y^4(21x^3y^3z^4 + 31)

The expression is given as

21x^7y^7z^4 + 31x^4y^4

Express the above expression as a product

So, we have

21x^7y^7z^4 + 31x^4y^4 = 21x^3y^3z^4 * x^4y^4 + 31 * x^4y^4

Factor out x^4y^4

So, we have

21x^7y^7z^4 + 31x^4y^4 =  x^4y^4(21x^3y^3z^4 + 31)

Hence, the factored expression of 21x^7y^7z^4 + 31x^4y^4 is  x^4y^4(21x^3y^3z^4 + 31)

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The linear function that gives the cost of spending h hours at the park is given by:

C(h) = 2 + mh.

In which m is the hourly rate.

Two separate but related concepts are referred to as linear functions in mathematics: A polynomial function of degree 0 or 1 is referred to as a linear function in calculus and related fields if its graph is a straight line.

A straight line makes up the graph of a linear function. The following expression describes a linear function. Y equals f(x) = a + bx. Both the independent and dependent variables of a linear function are one. X is an independent variable, whereas Y is a dependent variable.

The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.

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The answers are as follows -

(a) f(x) = 0.15 + 0.89x

(b) $ 10.83.

(c) 7 donuts

(a) Firstly, forming the function using given information. Let x be the number of donuts. Adding the one-time fee and cost per donut.

f(x) = 0.15 + 0.89x

(b) As per the known fact, 1 dozen = 12 quantities. Hence, there will be 12 donuts. Keeping the values in formula to find the price of box.

f(12) = 0.15 + 0.89 × 12

f(12) = 0.15 + 10.68

f(12) = 10.83

Thus, the price of box containing one dozen donuts is 10.83.

(c) Now, finding the value of x as per given cost.

6.38 = 0.15 + 0.89x

0.89x = 6.38 - 0.15

0.89x = 6.23

x = 6.23 ÷ 0.89

x = 7

Thus, a box costing $6.38 will contain 7 donuts.

Hence, (a) f(x) = 0.15 + 0.89x, (b) $ 10.83 and (c) 7 donuts.

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The Percent of Aileen's bi-weekly gross pay has been withheld for tax is 81 %.

A part of a whole expressed in hundredths a high percentage of students attended. Also the result obtained by multiplying a number by a percent the percentage equals the rate times the base.

Given:

Aileen's bi-weekly gross pay = $799.80

Deducted for taxes=$151.96

According to given question we have

Percent of Aileen's bi-weekly gross pay has been withheld for tax

[tex]\frac{799.80-151.96 }{799.80} *100\\\\=81 %[/tex]

Therefore, the Percent of Aileen's bi-weekly gross pay has been withheld for tax is 81 %.

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Answer: 19%

Step-by-step explanation: Just took the test. 799.80 x .19= 151.96

Factors estimate 5,897 times 67

The estimate product of the factors 5897 times 67 is 383500.

We have to use strategies to estimate the products.

We can round each factor to the greatest place value which is the place value farthest to the left.

we can use compatible numbers.

compatible numbers are friendly numbers they are easy to compute numbers.

Given 5897[tex]\times[/tex]67=395099

This is the actual factor

But the estimation product is

We use mental math and compatible numbers here.

step1: 5900[tex]\times\\[/tex]70=413000

step2:5900[tex]\times[/tex]65=383500

Both the step1 and step2 are reasonable because the factor are close to the actual factor.

But 5900[tex]\times[/tex]65=383500 is better because it is very close to the actual factor compared to 5900[tex]\times\\[/tex]70=413000.

Therefore, The estimate product of the factors 5897 times 67 is 383500.

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If Samantha works in a department store selling clothing and she makes a guaranteed salary of $500 per week but is paid a commission on top of her base salary equal to 25% of her total sales for the week, then Samantha would make $662.5 in a week in which she made $650 in sales and she would make 500 + 0.25 xx in a week in which she made xx dollars in sales.

The amount of money Samantha makes in a week can be given by an algebraic expression.

Amount of money Samantha makes in a week = Salary per week + 25% of her total sale

Amount of money Samantha makes in a week = 500 + 0.25 x

Here x is the sales Samantha made in a week

If she made $650 in sales in a week :

Amount of money Samantha makes in a week = 500 + 0.25(650)

Amount of money Samantha makes in a week = 500 + 162.5

Amount of money Samantha makes in a week = $662.5

If she made xx dollars in sales in a week :

Amount of money Samantha makes in a week = 500 + 0.25 x

Amount of money Samantha makes in a week = 500 + 0.25 xx

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Answer:

D has the coordinate 17

Step-by-step explanation:

Given

DE  has as the mid point H at 5

D > E

DE = 24

Find the coordinate of D

5 + (24/2) = 5+12 = 17

When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

Given,

The cost of Carpet per square foot = $4

Total cost of the carpet = $616

We know

Area of the rectangle = Length × Width

Length = 14 feet

Consider the width of the rectangular room as x

Then the area of the room = 14x

Total cost of carpet = Area of the rectangular room× Cost of carpet per foot

Substitute the values

14x×4=616

14x=154

x=11 feet

Hence, When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

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Graph the coordinates J(-2,-0.5) K(0,2) L(-4,-2) is attached.

Given that

Three points

To do

So, according the question

We have

Three points J,K AND .L

For Showing that all points in graph, We have to follow some points

So, from question

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Answer:

45mph

Step-by-step explanation:

Answer:

[tex]y = \frac{ac}{a - b - c} [/tex]

Finding the numeric value of the function, it is found that the car is worth $24,780 after 4 years.

This problem is incomplete, but researching it on a search engine, we have that:

The straight line depreciation equation for a car is y = -3680x + 39500.

It asks the value of the car after 4 years.

The numeric value of a function is found replacing each instance of x by the value that we want to find.

For this problem, means that the value of the car after x years is given by:

y = -3680x + 39500.

Hence, after 4 years, the value is:

y = -3680(4) + 39500 = $24,780.

The car is worth $24,780 after 4 years.

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35-25/7-5

10/2= 5

5 trees per hour

Take the difference in y coordinates and divide that by the difference in the x coordinates. That's the slope, sometimes called the "rise over run"  For a straight line or a linear function the slope is a constant

(6-10)(7,10) = 2/3 = slope

the line is

y-h = m(x-k) where m=2/3 and (k,h) = (10,10) or either point

to get y-10 = (2/3)(x-10)

3y -30 = 2x-20

2x-3y = -10

or use (k,h) as (7,8)

y-8 = (2/3)(x-7)

3y-24 = 2x-14

2x-3y = -10

or if you write it in y=mx + b form

it's y=(2/3)x + 10/3  where 10/3 is the y-intercept and 2/3 = slope

In this form, take the derivative of (2/3)x + 10/3

to get y' = 2/3,  the derivative is the slope

Answer:

0.000000072

Step-by-step explanation:

Assuming you mean Regular Notation, that's your answer.

Answer:720,000,000

Step-by-step explanation:

1. Convert to decimal notation

More Icon

The exponent is 8, making it 10 to the power of 8. As the exponent is positive, the solution is a number greater than the origin or base number. To find our answer, we move the decimal to the right 8 time(s):

7.2 -> 720,000,000

Answer:

B

Step-by-step explanation:

According to the given statement the first 13 words in this sequence add up to 260.

In mathematics, a sequence is an itemized group of elements where repeats are tolerated and order is significant. It has members, just like a set (also called elements, or terms). The length of the series is the number of items (potentially infinite). In contrast to a set, the same items might occur more than once in a sequence at various points, and unlike a set, the order is important. A sequence can be described formally as a function from natural numbers (the locations of the sequence's members) to the items at each of those positions. An indexed family, which is a function from an index set that may not be integers to another set of elements, can be thought of as a more extended version of a sequence.

We are informed that the order is2,5, 8, 11, ..... ..............(1)

The total of the first 13 terms must always be established.

Sum of n terms formula is

Sn (2a + (n − 1)d)

First term = a = 2 from

(1)The average difference is 3 (5-2=8-5=11-8=3).

via formula

S13 13 (2a +(13 – 1)d) 2S13 13

(2 x 2 + (13 - 1) 3) 213

(4+36)13 (40)

= 260

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Answer:

I already checked the question .I think it is correct

The counterweight lifted in each rotation of the drum is 18.85m.

The diameter of the drum is : d=6m

hlift=C=πd

C=[tex]\frac{22}{7}[/tex]×6

C=18.85 m

Any straight line segment that cuts through the center of a circle and has ends that are on the circle is considered a circle's diameter in geometry. It is also known as the circle's longest chord.

Diameter also refers to the length d of a diameter. As opposed to a diameter, which refers to the line segment itself, one uses the term "diameter" in this context since all diameters of a circle or sphere have the same length, which is equal to twice the radius r. The longest distance that may be generated between the tangents of two opposite parallel lines is referred to as the diameter for a convex shape in the plane.

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Answer:

12:1

Step-by-step explanation:

1 purple bead for every 12 pink beads

The proportion of the measurements lie in the interval is 0.9.

According to the given question.

Weigths of 10 young dogs.

W : 7, 5, 11, 8, 14, 19, 16, 15, 13, 27

As we know that mean si calculated by the formula

Mean = ΣW / n

Thereofre, the mean of the weights of 10 young dogs

= 7 + 5 + 11 + 8 + 14 + 19 + 16 + 15 + 13 + 27/ 10

= 13.5

And, Standard deviation (s) = 6.433

Proportion that lies in mean ± 2s

Lower = Mean - 2s

⇒ 13.5 - 2(6.433) = 0. 632

Also, Upper = Mean + 2s

⇒ 13.5 + 2(6.433) = 26.376

Mean ± 2(sd) = (0.632, 26.276)

The only digit from the data which falls outside the defined range = 27

Proportion within interval = 9 / n

Proportion which falls within interval = 9/10 = 0.9

Hence, the proportion of the measurements lie in the interval is 0.9.

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In Wednesday, the stock market had its biggest loss.

Over the course of a day, the stock market will fluctuate in value due to a number of factors. These include political news and economic data. Over the first four days of the week, this means that Monday through Thursday there is more volatility because these are typically the busiest trading days for stocks.

10.45 - (-18.75) = +29.2

-34.75 - (10.45) = -45.2

-40.89 - (-34.75) = -6.14

On Wednesday the stock value lost -45.2 of its value.

When the stock market loses value, it is usually because there are concerns about a company's future prospects. This can be due to changes in the business environment, new technologies that negatively impact the company's performance, or regulatory issues.

Hence, the stock market lost its most value on Wednesday .

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Answer:

x>=27

Step-by-step explanation:

You have to remove the -3 from the left side by adding 3 to both sides, 4x=108 then 108/4 to get x. x=27