The shortest side of an isosceles triangle is 4x−2 inches long. The two longer sides are 5 inches longer than the shortest side. The perimeter of the triangle is 64 inches.

What is the length of the longer sides of the triangle?

Answer:

64

Step-by-step explanation:

Since 64 is a multiple of itself and of all the other numbers, the answer is 64.

1 minute = 60 seconds.

Multiply the speed per second by 60 to get speed per minute:

8 * 60 = 480 miles per minute.

Multiply speed per minute by number of minutes to get total miles traveled:

480 * 6 = 2,880 total miles.

Answer:

y = ln(x -5)

Step-by-step explanation:

The log function has a vertical asymptote at x=0 and goes through the point (1, 0). This looks like that function translated 5 units to the right. When f(x) is translated right 5 units, x is replaced by x-5. The graph seems to be of the function ...

... y = ln(x -5)

_____

The natural log function will go through the points (2.718, 1) and (7.389, 2), as this curve appears to do.

The numerator can be found by multiplying each of these fractions by 100. It can be helpful to reduce these fractions first.

Here, we calculate those numerators.

a) 15/60 · 100 = 1/4 · 100 = 100/4 = 25

b) 30/60 · 100 = 1/2 · 100 = 100/2 = 50

c) 25/75 · 100 = 1/3 · 100 = 100/3 = 33 1/3

Of course, the denominator is 100, so the fractions are ...

... 15/60 = 25/100

... 30/60 = 50/100

... 25/75 = (33 1/3)/100

_____

Comment on this solution

Effectively, we have multiplied each fraction by 1 = 100/100. That is ...

... fraction × (100/100) = (fraction × 100)/100

This changes the form, but not the value.

To find the x-intercept, set y=0 and solve.

... 0 = log(12x +7) -3

... 3 = log(12x +7) . . . . add 3

... 1000 = 12x +7 . . . . take the antilog. (10^3 = 1000)

... 993 = 12x . . . . . . . .subtract 7

... 82.75 = x . . . . . . . . divide by 12

To find the y-intercept, set x=0 and solve.

... y = log(12·0 +7) -3

... y = log(7) -3 . . . . . . simplify

... y ≈ 0.85 -3 = -2.15 . . . . use a calculator for the log function

Answer:

68

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you ...

... Tan = Opposite/Adjacent

For this geometry, this means ...

... tan(x°) = 5/2

Taking the inverse tangent, we can find x.

... x° = arctan(5/2) ≈ 68.199°

... x ≈ 68

Answer:

Step-by-step explanation:

A graphing calculator can show you the intercepts.

___

Or you can figure them out.

The y-intercept is where x=0, so is ...

  y = log(12·0 +7) -3 = log(7) -3 ≈ -2.1549 ≈ -2.15

___

The x-intercept is where y = 0, so is ...

  0 = log(12x +7) -3

  3 = log(12x +7) . . . . . . add 3

  10^3 = 12x +7 . . . . . . . take the antilog

  993 = 12x . . . . . . . . . . subtract 7

  993/12 = x = 82.75 . . . divide by the coefficient of x

Answer:

D) 15

Step-by-step explanation:

We know the formula for direct variation is  

y=kx

Substituting y=5 and x=4 we can calculate k

5=k4

Divide each side by 4

5/4 =k

Now y= 5/4 x

If x =12

y =5/4*12

y = 15

Answer:

14 years 7 months

Step-by-step explanation:

If the average age was increased by 2 months by adding a 7th child, the total age was increased by 2·7 months = 14 months more than the previous average. That is, the added child's age is 14 months more than the previous average, so is ...

... (13 years + 5 months) + (1 year + 2 months) = 14 years + 7 months

_____

For the non-believers:

The previous total of all ages was ...

... 6 × (13 years 5 months) = 80 years 6 months

The new total of all ages is ...

... 7 × (13 years 7 months) = 95 years 1 month

The amount added to the previous total is ...

... (95 1/12 - 80 6/12) years = 14 7/12 years = 14 years 7 months

To find the age of the seventh child, calculate the total age of the six children and the total age of all seven children.

To solve this problem, we can use the concept of the average. Step 1: Calculate the total age of the six children by multiplying the average age (13 years and 5 months) by the number of children (6). Step 2: Calculate the total age of all seven children by multiplying the new average age (13 years and 7 months) by the total number of children (7). Step 3: Subtract the total age of the six children from the total age of all seven children to find the age of the seventh child.

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3x = -4y

To solve for X, divide both sides by 3:

x = -4y / 3

The answer is D.

If you travel at a constant speed, you follow this equation:

[tex] d = st [/tex]

where d is the distance, s is the speed and t is the time.

In this example, you first travel 60 miles per hour for 45 minutes. Since 45 minutes are 3/4 of a hour, you will cover a distance of

[tex] d_1 = 60\cdot\dfrac{3}{4} = 45 [/tex]

In the second part, since 30 minutes is half a hour, you will cover a distance of

[tex] d_2 = 50\cdot\dfrac{1}{2}=25 [/tex]

So, in total, you travel

[tex] d=d_1+d_2=45+25 = 70 [/tex] miles

Answer:

C-70 miles

Hope this helped :)

See the attachment

In this context, "x" stands for "a number". Then 1/2x is "one-half of a number" and 3/4x is "three-fourths of a number."

3/4 - ( ) means "three-fourths minus ..."

( ) + 1/2 means "one-half more than ..." or "the sum of ... and one-half."

Putting these ideas together lets you choose the phrases as indicated below.

Answer:

y = 3x +8

Step-by-step explanation:

The slope of the given line is -1/3. The slope of a perpendicular line is the opposite of the reciprocal of that: -1/(-1/3) = 3.

Then, in point-slope form, the equation of the line is ...

... y - k = m(x - h) . . . . . for slope m through point (h, k)

... y - 5 = 3(x -(-1)) . . . . . for line of slope 3 through (-1, 5)

... y = 3x +8 . . . . . . . . . simplify

14.4

This is a special case of the situation where two secant lines intersect a circle. The product of the near distance to the circle and the far distance to the circle from their point of intersection is a constant. A tangent is a degenerate case, where the near and far intersection points with the circle are the same point.

So, ...

... x · x = 9 · (9+14)

... x = 3√23 ≈ 14.4 . . . . . taking the square root

_____

Additional note on the geometry

This rule for the product of segments of secant lines also applies when the secants intersect inside the circle.

Answer:

14.39

Step-by-step explanation:

Theorem 12-15 III

(y+z) y=t squared

(9+14)9=x squared

23•9=x squared

207 =x squared

Square root of 207 is 14.39

Answer:

4

Step-by-step explanation:

8 2/9 is close to 8

3 6/7 is close to 4

8 2/9 - 3 6/7  is close to 8-4 = 4

My estimate is 4

You want to determine the number of text messages students at your school send in a month. You randomly ask 10 students from each grade.

This is a random sampling method.

This sampling method is a basic sampling method where we select a group of subjects (a sample) for study from a larger group or  population. Each individual is chosen entirely by chance. Each member of the population has an equal chance of being included in the sample.

Answer:

answer is pretty much in the last sentance lol. random

Step-by-step explanation:

The polynomial function f(x) having roots [tex]-2 + \sqrt(8)[/tex] and 9 would have factors  [tex](x + 2 - 2\times \sqrt(2))[/tex] and (x - 9). These roots can be determined by setting the known values equal to x and subtracting from x.

In mathematics, specifically in polynomial functions, the roots of a function are values that make the function equal to zero. These roots correspond to the factors of the polynomial function. If a function f(x) has roots -2 + square root 8 and 9, then the factors of f(x) will be those values set equal to x and then subtracted from x.

Therefore, the corresponding factors would be  [tex]x - (-2 + \sqrt{8})[/tex] and (x - 9). When you simplify these, they become [tex](x + 2 - \sqrt(8))[/tex] and (x - 9). To further simplify, we know that  [tex]\sqrt(8) = 2\times \sqrt(2),[/tex] therefore we get  [tex](x + 2 - 2\times \sqrt(2))[/tex] and (x - 9).

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If a polynomial function has roots -2 + Square root 8 and 9, then x - (-2 + Square root 8) and x - 9 must be factors of the polynomial.

Polynomial functions are mathematical expressions comprising variables, coefficients, and non-negative integer exponents. They are used in various fields, including mathematics, physics, engineering, and computer science. They model relationships between variables, aiding in solving equations, analyzing data, and predicting outcomes in diverse applications.

If the polynomial function f(x) has roots -2 + Square root 8 and 9, then x - (-2 + Square root 8) and x - 9 must be factors of f(x). This is because if a number is a root of a polynomial, then the polynomial can be divided evenly by the corresponding linear factor.

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Answer:

1920 cm^3

Step-by-step explanation:

Divide into the rectangular prism on top, and the one on the bottom. Whole = sum of parts, so you find the volumes of those two separately and add them together to get the total.

V of rectangular prism = l x w x h (length x width x height)

Top:

l = 10

w = 8

h = 14 - 10 = 4

10 x 8 x 4 = 320

Bottom:

l = 10 + 10 = 20

w = 8

h = 10

20 x 8 x 10 = 1600

1600 + 320 = 1920

The volume of the rectangular prism together with subparts is 1920 cubic meters.

The volume of the rectangular prism is the product of the length, breadth, and height of the given prism.

Volume of rectangular prism = (length x width x height)

Divide into the rectangular prism on top, and the one on the bottom.

total volume = sum of parts, so we need to find the volumes of those two separately and add them together to get the total.

Top

l = 10

w = 8

h = 14 - 10 = 4

The volume of the rectangular prism = length x width x height

= 10 x 8 x 4 = 320

Bottom

l = 10 + 10 = 20

w = 8

h = 10

The volume of the rectangular prism = length x width x height

= 20 x 8 x 10 = 1600

The total volume of the shape = 1600 + 320 = 1920

Learn more about volume;

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Answer:

D. $5.37

Step-by-step explanation:

We need to figure out how much grapes cost per pound

Change the mixed number to an improper fraction

7 1/5 = (5*7+1) /5 = 36/5

$12.89 / 36/5

Copy dot flip

12.89 * 5/36 = 1.79 per lb

If we are purchasing 3 pounds, we will multiply by 3

3 lbs * $1.79 / lb = $5.37

Answer with explanation:

3.19 =There are two digits after decimals.

An integer is set of numbers which includes both positive natural number, Negative Natural number and Zero.

[tex]3.19=\frac{319}{100}[/tex]

Here, 319 and 100 , both are integers.

You can write equivalent form of

[tex]\frac{319}{100}=\frac{319 \times 2}{100 \times 2}=\frac{319 \times 3}{100 \times 3}=........[/tex]

The value 3.19 expressed as a ratio of two integers is :

[tex] \frac{319}{100} [/tex]

Given the decimal :

3.19 which can be expressed as an integer by multiplying with the Number of decimal places after the decimal Point.

To express 3.19 as a combination of two integer values, we divide 319 by 100

Hence, 3.19 = 319 ÷ 100

[tex] \frac{319}{100} [/tex]

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[tex]0.5x+\dfrac{7}{8}=5\qquad\text{multiply both sides by 8}\\\\4x+7=40\qquad\text{subtract 7 from both sides}\\\\4x=33\qquad\text{divide both sides by 4}\\\\\boxed{x=\dfrac{33}{4}\to x=8\dfrac{1}{4}}[/tex]

In 4 months, the total cost of Yoga Studio A would equal that of Yoga Studio B

The cost of Yoga Studio A at any given month can be represented as:

= Membership fee + (Monthly fee x Number of months)

Assuming number of months is x, the formula would be:

= 24 + (21.50 × x)

= 24 + 21.50x

Yoga Studio B would be:

= 41 + (17.25 × x)

= 41 + 17.25x

In order to find the month that these costs would be equal, equate both formulas:

24 + 21.50x = 41 + 17.25x

21.50x - 17.25x = 41 - 24

4.25x = 17

x = 17 / 4.25

x = 4 months

In conclusion, their costs would be the same in the 4th month.

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Answer:

P

Step-by-step explanation:

The distance doesn't change during segment Q, so that is when the cyclist is stopped. The segment before that is labeled P.

The question asks the label of the segment before the one where the cyclist was stopped, so the appropriate choice is P.

Answer:

it is Q

Step-by-step explanation:

Because it is stopped and its a strait line making it look like it is taking a brake.

Answer:

$9800

Step-by-step explanation:

commission = 5% × car price

20 × commission = 100% × car price . . . . . . multiply by 20

20 × $490 = car price = $9800 . . . . . . . . . . fill in given value of commission

The price of a car on which a salesperson earns a 5% commission of $490 is calculated by dividing the commission amount by the commission rate as a decimal (0.05), resulting in a car price of $9,800.

The question is asking to calculate the price of a car based on the commission earned by the salesperson. The salesperson receives a 5% commission on each sale and has earned $490 from the sale of one car.

To find the price of the car, we need to set up a simple equation. If 5% of the price results in a $490 commission, we need to divide the commission by the percentage rate expressed as a decimal.

The calculation will look as follows:

Convert the commission percentage to a decimal: 5% = 0.05.

Divide the commission earned by the decimal rate: $490 ÷ 0.05.

The result is the price of the car.

So, $490 ÷ 0.05 = $9,800.

Therefore, the price of the car is $9,800.

Answer:

the first selection (see below)

Step-by-step explanation:

The average rate of change (m) on the interval [x1, x2] is given by ...

... m = (g(x2) -g(x1))/(x2 -x1)

For g(x) = -x²-4x and (x1, x2) = (6, 8), the expression is the one attached.

Answer:

[tex]\frac{[-8^2 - 4(8)]- [-6^2 - 4(6)]}{8-6}[/tex]

Step-by-step explanation:

average rate of change of the function g(x) = -x^2 - 4x on the interval 6 ≤ x ≤ 8

To find average rate of change we use formula

Average =[tex]\frac{g(x_2)-g(x_1)}{x^2-x_1}[/tex]

use the given interval 6<=-x<=8

x2=8  and x1= 6

we replace the value in the given formula

g(x) = -x^2 - 4x

[tex]g(8) = -8^2 - 4(8)[/tex]

[tex]g(6) = -6^2 - 4(6)[/tex]

x2-x1 is 8-6

So equation becomes

[tex]\frac{[-8^2 - 4(8)]- [-6^2 - 4(6)]}{8-6}[/tex]

Answer:

"earn"

Step-by-step explanation:

He paid $9 for a box of 24 pens. Selling those 24 pens for $1 each, he sold them for $24. Thus he earned $24 -9 = $15 on each of the 8 boxes he bought.

C. None of the above

It appears to me the average times for Ravens backs are lower (< 4.44 s) than those of Chiefs backs (< 4.48 s), so the Ravens are faster on average.

The spread of Ravens times is 4.30–4.57 s, whereas the spread of Chiefs times is 4.42–4.56. The Ravens clearly show a greater variation.

The offered choices suggest the Chiefs are faster on average (not true) and that the Chiefs have a greater variation (not true). Since both of these choices are incorrect, the only remaining suitable choice is None of the above.

Answer:

x = 3

Step-by-step explanation:

f'(x) = 0 for x = 3 and x = 4 . . . . by the zero product rule.

The coefficient of x² in f'(x) is negative, so the parabola opens downward.

f''(x) is positive for x < 3.5, so the coordinate x = 3 represents a relative minimum.

First differences start at 1 and increase by 2.

Whenever analyzing any sort of sequence, it is usually helpful to look at the differences between terms. Here, they are ...

... 1, 3, 5, 7

This set of numbers clearly increases by 2 from one to the next. That is, second differences are 2.

_____

When 2nd differences are constant, the pattern can be described by a 2nd-degree polynomial. In this case, that is

... n² -2n +2 . . . . for n = 1, 2, 3, ...

Answer:

Quadratic sequence with

nth term = n^2 - 2n + 2.

Step-by-step explanation:

1,2,5,10,17

The differences between terms  are

1,3,5,7

and the second differences are

2,2,2

This is a quadratic sequence  with first term n^2  ( where n = sequence number).

List the original sequence and the values of n^2:-

1  2  5  10  17

1  4  9  16  25

If we subtract the first list from the second we get

0  2  4  6  8   which is arithmetic with common difference  2 and first term 0

The nth term of this is 2(n - 1)

So the explicit formula for the nth term of the original sequence is

n^2 - 2(n - 1)

= n^2 - 2n + 2

Answer:

$217.07

Step-by-step explanation:

Each year, the cost of the groceries was multiplied by 100% +2.7% = 1.027. Doing this multiplication for 5 years result in a multiplying facor of ...

... 1.027^5

so the cost of the groceries after 5 years is ...

... $190.00 × 1.027^5 ≈ $217.07