Find the value of x when a = 7/2, h = 10, k = 15, If

Answer:

Option C. [tex](x-8)^{2}=52[/tex]

Step-by-step explanation:

we have

[tex]x^{2}-16x+12=0[/tex]

Complete the square

[tex](x^{2}-16x+8^2)+12-8^2=0[/tex]

[tex](x^{2}-16x+64)+12-64=0[/tex]

[tex](x^{2}-16x+64)-52=0[/tex]

rewrite as perfect squares

[tex](x-8)^{2}-52=0[/tex]

Move the constant to the right side

[tex](x-8)^{2}=52[/tex]

Answer:

5 times

Step-by-step explanation:

$25 - $10 (fixed rate) = $15

$15 / $3 = 5 times.

Mia must watch her brother 5 times within the week to make the desired amount. Hope this helps :)

Answer:

0.33...acre

Step-by-step explanation:

1/4=0.25

3/4=0.75

-------------

0.25/0.75=x/1

cross product

0.75*x=0.25*1

0.75x=0.25

x=0.25/0.75

x=0.3

Answer:

1.5a - 0.5

Step-by-step explanation:

Add like terms

4.4 - 2.9 = 1.5

7.3 - 6.8 = 0.5

Final answer:

To find the sum of the two expressions -2.9a+6.8 and 4.4a-7.3, you need to combine the like terms. Simply add or subtract the coefficients of like terms while keeping the variable the same, the sum of the two expressions -2.9a+6.8 and 4.4a-7.3 is (4.4a - 2.9a) + (6.8 + (-7.3)). .

Explanation:

To find the sum of the two expressions -2.9a+6.8 and 4.4a-7.3, you need to combine the like terms. Like terms are terms that have the same variable raised to the same power. In this case, -2.9a and 4.4a are like terms because they both have the variable 'a' raised to the first power. Similarly, 6.8 and -7.3 are also like terms because they don't have any variables. To combine like terms, simply add or subtract their coefficients while keeping the variable the same.

So, -2.9a + 4.4a can be combined as (4.4a - 2.9a) and 6.8 - 7.3 can be combined as (6.8 + (-7.3)).

Therefore, the sum of the two expressions -2.9a+6.8 and 4.4a-7.3 is (4.4a - 2.9a) + (6.8 + (-7.3)).

Answer:

The answer is 123.

Step-by-step explanation:

Given that-

( [tex]x + \frac{1}{x}[/tex] ) = 3.....................(i)

To find -

( [tex]x^{5} + \frac{1 }{x^{5} }[/tex] ) = ?

Now squaring both sides of equation (i)-

( [tex]x^{2}  + \frac{1}{x^{2} } + 2[/tex] ) = 9

( [tex]x^{2} + \frac{1}{x^{2} }[/tex] ) = 7....................(ii)

On cubing equation (i) both sides-

( [tex]x^{3} + \frac{1}{x^{3} } + 3 ( x + \frac{1}{x} )[/tex] ) = 27

( [tex]x^{3} + \frac{1}{x^{3} } + 3 * 3[/tex] ) = 27

( [tex]x^{3} + \frac{1}{x^{3} }[/tex] ) = 27 - 9

( [tex]x^{3} + \frac{1}{x^{3} }[/tex] ) = 18.....................(iii)

Multiply equation (i)  and equation (ii)-

( [tex]x^{2} + \frac{1}{x^{2} }[/tex] )  ( [tex]x^{3} + \frac{1}{x^{3} }[/tex] ) = 7 × 18

( [tex]x^{5} + \frac{1}{x^{5} } )+ ( x + \frac{1}{x} )[/tex] = 126

( [tex]x^{5} + \frac{1}{x^{5} } ) = 126 - 3

( [tex]x^{5} + \frac{1}{x^{5} } ) = 123

Answer:

Step-by-step explanation:

36 + m = 54           subtract 36 from both sides

36 - 36 + m = 54 - 36

m = 54 - 36

m = 18

Answer:

m=18

Step-by-step explanation:

36+m=54

m=54-36

m=18

Answer:

So the values of x for which the function is positive are x ≥ -3 and x ≤ -9.

Step-by-step explanation:

We are given a function and we have to find the intervals in which the function has positive value.

y = [tex]x^{2} +12x+27[/tex]

y =(x + 3)(x + 9)

For the function to be positive , y ≥ 0

(x + 3)(x +  9) ≥ 0

Here there are two cases , either both should be positive or both should be negative.

If both are positive,

(x + 3)≥0 and (x + 9)≥0

So, x ≥ -3

If both are negative,

(x + 3)≤0 and (x + 9)≤0

So, x ≤ -9

So the values of x for which the function is positive are x ≥ -3 and x ≤ -9.

The intervals on which the function y = x² + 12x + 27 is positive are

x > -3 and x > -9

For the function given to be positive, it has to be greater than zero.

Since the expression is greater then zero, hence;

x² + 12x + 27 > 0

Factorize the resulting expression

x² + 3x + 9x + 27 > 0

x(x+3) + 9(x+3) > 0

(x+3) (x+9) > 0

x+3 > 0 and x + 9 > 0

x > -3 and x > -9

Hence the intervals on which the function y = x² + 12x + 27 is positive are

x > -3 and x > -9

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Answer:

100

Step-by-step explanation:

It will help in the future to memorize your time tables

10*10 is basically 10 plus 10, 10 times but in a easier form

10+10+10+10+10+10+10+10+10+10=100

10+10=20

20+10=30

30+10=40

40+10=50

50+10=60

60+10=70

70+10=80

80+10=90

90+10=100

Answer:

The point lie outside the circle

Step-by-step explanation:

step 1

Find the distance between the center of the circle and the given point

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

(0,0) and (-3,-7)

substitute the values

[tex]d=\sqrt{(-7-0)^{2}+(-3-0)^{2}}[/tex]

[tex]d=\sqrt{58}\ units[/tex]

step 2

Compare the distance with the radius

If d=r ----> the point lie on the circle

If d > r -----> the point lie outside the circle

If d < r -----> the point lie inside the circle

we have

[tex]d=\sqrt{58}\ units[/tex]

[tex]r=\sqrt{53}\ units[/tex]

so

[tex]\sqrt{58}\ units > \sqrt{53}\ units[/tex]

[tex]d > r[/tex]

therefore

The point lie outside the circle

Answer:

C outside the circle

Step-by-step explanation:

khan

Answer:

The thickness of 1 card  = 0.0025 inches

Step-by-step explanation:

Here, the total number of cards in the stack = 250 cards

The total height of the stack = 5/8 inch = 0.625 in.

[tex]\textrm{Thickness of one card} = \frac{\textrm{The total thickness of the stack}}{\textrm{The total cards in the stack}}[/tex]

[tex]\implies \textrm{Thickness of one card} =\frac{0.625}{250} = 0.0025[/tex]

Hence, the thickness of 1 card  = 0.0025 inches

Work is provided in the image attached.

Answer:

  x < 1

Step-by-step explanation:

Divide both sides of the inequality by 2:

  (2x)/2 < (2)/2

  x < 1 . . . . . . . . . . simplify

The solution is x < 1.

Answer:  4y + x - 22 = 0

Step-by-step explanation:

Recall that  for two lines to be perpendicular m1m2 = -1 ie, the product of their gradients must = -1

from the equation given, y - 3 = 4(x + 2), we need to rearrange it in the form

y = mx  + c in order for us to ascertain the gradient.

y -3 = 4x + 8

y = 4x + 8 + 3

y = 4x + 11

Therefore, m1 = 4 while m2 = -1/4

The coordinate of the line = (-2, 6) . We now use this to find the value of c.

6 = -1/4 x -2 + c

6 = 1/2 + c

multiply by 2

12 = 1 + 2c

12 - 1 = 2c

11 = 2c

c = 11/2

now to find the equation of the second line

y = -x/4 + 11/2

now multiply through by 4

4y = -x + 22

4y + x - 22 = 0 is the required equation

3 small boxes and 6 large boxes were sent to the retailer.

Step-by-step explanation:

Number of books held by small boxes = 30

Number of books held by large boxes = 40

Total books held by boxes = 330

Let,

x represent the number of small boxes

y represent the number of large boxes

According to given statement;

y = 2x     Eqn 1

30x+40y=330    Eqn 2

Putting value of y from Eqn 1 in Eqn 2

[tex]30x+40(2x)=330\\30x+80x=330\\110x=330[/tex]

Dividing both sides by 110

[tex]\frac{110x}{110}=\frac{330}{110}\\x=3[/tex]

Putting x=3 in Eqn 1

[tex]y=2(3)\\y=6[/tex]

3 small boxes and 6 large boxes were sent to the retailer.

Keywords: linear equation, substitution method

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Answer:

  [tex]32\text{ for }x=0.\overline{40}[/tex]

Step-by-step explanation:

It looks like you want the sum of digits of the product ...

  [tex]x = (0.\overline{6})(0.\overline{60})=\dfrac{2}{3}\cdot\dfrac{20}{33}=\dfrac{40}{99}=0.\overline{40}[/tex]

Since the decimal fraction starts off with 4 and has an even number of repeating digits, there will be 8 4's and 7 0's in the sum of the first 15 decimal digits:

  sum = 8×4 +7×0 = 32

The sum of the first 15 digits after the decimal point is 32.

Answer:

206

Step-by-step explanation:

197 + 3 + 6 = 206

To find Jack's starting weight before he started his diet, we need to add the pounds he lost in the first and the second week back to his current weight.
Jack's current weight is 197 pounds.
In the first week, he lost 3 pounds.
In the second week, he lost 6 pounds.
So the total weight lost over the two weeks is 3 pounds + 6 pounds = 9 pounds.
Now we just add these 9 pounds back to Jack's current weight to find his starting weight before the diet.
197 pounds (current weight) + 9 pounds (total weight lost) = 206 pounds.
Thus, Jack's starting weight was 206 pounds.

Answer:

here the coordinates given are incorrect but I have solved it anyway see the attachment for further information

Answer:

x = 3

Step-by-step explanation:

Two points are given.  The x-coordinates are one and the same.  This means that x does not change, and thus the line is a VERTICAL line:  x = 3.

Answer:

A) 8, 15, 17.

Step-by-step explanation:

Right triangle obey the Pythagorean theorem. Thus, we choose the two smaller numbers (being the cathetus) and if after applying the P. Theorem we get the biggest of each option  (the hypotenuse) that means that those numbers could be the sides of a right triangle.

The Pythagorean theorem states that: [tex]a^2+b^2=c^2[/tex]

Thus:

[tex]\sqrt{a^2+b^2}=c[/tex]

Option A:

[tex]\sqrt{8^2+15^2}=17[/tex] → 17 = 17 OK!

Option B:

[tex]\sqrt{6^2+8^2}  = 10[/tex] → 10 ≠ 12 NO

Option C:

[tex]\sqrt{9^2+11^2} = [tex]\sqrt{202}[/tex][/tex] → [tex]\sqrt{202}[/tex] ≠ 21 NO

Option D:

[tex]\sqrt{4^2+13^2} = \sqrt{185}[/tex] → [tex]\sqrt{185}[/tex] ≠ 16 NO

Answer:

add

Step-by-step explanation:

23456

Answer:

( 7, 5 )

Step-by-step explanation:

when reflected over the y axis they numbers are in quadrant 1 which means both numbers are positive.

Answer:

n=8

Step-by-step explanation:

3n-5=19

3n=19+5

3n=24

n=24/3

n=8

Answer:

Step-by-step explanation:

4 cm to 25 miles = 20 cm to x miles

4 / 25 = 20 / x

cross multiply

4x = (25)(20)

4x = 500

x = 500/4

x = 125 miles <=====

Answer:

The correct answer is that the actual distance in miles represented by a line that is 20 cm on map is 125 miles.

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Scale on a map: 4 cm = 25 miles

2.  What is the actual distance in miles represented by a line that is 20 cm on map ?

For calculating the distance in miles represented, we will use the following equation:

Actual distance in miles represented = Miles in the scale/Centimeters in the scale * 20

Replacing with the real values:

Actual distance in miles represented = 25/4 * 20 = 25 * 5 = 125

The correct answer is that the actual distance in miles represented by a line that is 20 cm on map is 125 miles.

Answer:

1.3889

Step-by-step explanation:

42*25.5=1,071

1,071/771.12=1.3889

Answer:

35.34 centimeters

Step-by-step explanation:

The amount of pizza is same as the area. The pizza is in a shape of a circle. The area of a circle is:

[tex]A=\pi r^2[/tex]

Where

r is the radius (half of diameter)

Area of one medium size pizza is (diameter 25 means radius is 25/2 = 12.5):

[tex]A=\pi r^2\\A=\pi (12.5)^2\\A=490.87[/tex]

So, area of two of these medium size pizzas is:

490.87 * 2 = 981.74

This should be the area of the large pizza. We can find the radius of that by substituting into formula. Shown below:

[tex]A=\pi r^2\\981.75=\pi r^2\\r=\sqrt{\frac{981.74}{\pi}} \\r=17.67[/tex]

Hence, the diameter would be around:

17.67 * 2 = 35.34 centimeters

Answer:

$150.

Step-by-step explanation:

$250 - 0.20 *250 = $200.

Final price = 200 - 0.25*200

= $150.

Money earned after working for 15 hours and making 8 deliveries is $ 534

Solution:

Given that pizza delivery person earns 30 per hour plus 10.50 for each delivery made

The expression used to find the earnings for him is given as:

30h + 10.50d

Where "h" is the number of hours and "d" is the number of deliveries

We have to find the money earned by him after working for 15 hours and making 8 deliveries

Therefore we get, h = 15 and d = 8

Substitute h = 15 and d = 8 in given expression

Money earned = 30(15) + 10.50(8)

Money earned = 450 + 84 = 534

Thus money earned after working for 15 hours and making 8 deliveries is $ 534

Answer:

Yes, Juanita is correct.

Step-by-step explanation:

Given:

The function given is:

[tex]f(x)=x^2+64[/tex]

The roots of a function means the values of 'x' for which the function intersects or touches the x-axis. Therefore, the roots are nothing but the x-intercepts of the function.

In order to find the roots of the above function, we should equate it to 0.

So, [tex]f(x)=0[/tex]

[tex]x^2+64=0\\\\x^2=-64[/tex]

We know that, square of any number is always a positive quantity. But here, the square of 'x' is -64 which is a negative number. This is not possible.

So, there is no real solution to the given function. In other words, we can say that the function doesn't intersect the x-axis.

Therefore, Juanita is correct in her argument.

Answer:

Graph A

Step-by-step explanation:

As we know, in 3 minutes he washes 18 dishes. Without even doing any math, you can see that this is the only graph that represents that. The others show that he washes two dishes in 12 minutes, which doesn’t make sense.

Ned's rate of washing dishes is 6 dishes per minute. The graph representing the number of dishes Ned can wash in any number of minutes would be an upward sloping line originating from the origin. The slope of this line, or the rate of change, signifies Ned's dish-washing rate.

This is a typical problem in Mathematics subject related to speed or rate, specifically, it involves a rate of washing dishes. Ned can hand-wash 18 dishes in 3 minutes. Thus, Ned's rate of washing is 18 dishes per 3 minutes, or 6 dishes per minute.

The relationship between the dishes and the minutes is a direct proportional relationship since the amount of dishes Ned can hand-wash increases directly as the time increases.

To reflect this in a graph, we would have a straight, upward sloping line originating from the graph's origin (0,0). The slope of this line, or the rate of change, signifies the rate at which Ned can wash dishes.

Given that Ned can wash 6 dishes per minute, each point on the line should increase by 6 dishes for each increment of 1 minute on the time axis. Hence the correct graph would be a straight line with a slope of 6.

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Answer:

The answer is B

Step-by-step explanation:

You just have to subtract the lowest temp by the highest temp

Answer:

2 cups of flour

Step-by-step explanation:

To make 5 batches of cookies, 10 cups of flour are required.

To make 1 batch of cookies:

10 cups ÷ 5 cups = 2 cups of flour.

To find out how many cups of flour are required for each batch of cookies, divide the total cups of flour (10 cups) by the number of batches (5 batches), which equals 2 cups of flour per batch.

To determine how many cups of flour are needed for each batch, we can set up a simple division equation where we divide the total amount of flour by the number of batches. The student is given that 10 cups of flour make 5 batches of cookies. Using this information, we calculate the amount of flour per batch as follows:

Amount of flour per batch = Total cups of flour ÷ Number of batches

Amount of flour per batch = 10 cups ÷ 5 batches

Thus, the amount of flour required for each batch is:

Amount of flour per batch = 2 cups