Rationalize the denominator and simplify.
3 √6+5 √2/4 √6-3 √2

Answer:

true

Step-by-step explanation:

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+10}x\stackrel{\stackrel{c}{\downarrow }}{+24} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{10}{2(1)}~~,~~24-\cfrac{10^2}{4(1)} \right)\implies (-5~,~24-25)\implies (-5~,~-1)[/tex]

The vertex of the quadratic function y = x² + 10x + 24 is located at point B. (-5, -1). This is found by using the formula -b/2a for the x-coordinate and substituting the x coordinate into the function for the y-coordinate.

The vertex of a quadratic function (a function in the form of y=ax²+bx+c) is the point that represents the minimum or maximum of the function graph. In this case, we are looking to find the vertex of the function y = x² + 10x + 24. The formula to find the x-coordinate of the vertex of a quadratic function is -b/2a. In this function, a = 1 and b = 10, giving us -10/(2*1) = -5 for the x-coordinate of vertex. We then substitute -5 into the function for x to determine the y-coordinate, resulting in y = (-5)² + 10*-5 + 24 = -1. Therefore, the vertex of the function is (-5,-1). So, the correct choice is B. (-5, -1).

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Answer: [tex]80 in^2[/tex]

Step-by-step explanation:

The area of a parallelogram can be calculated with the following formula:

[tex]A=b*h[/tex]

Where "b" is the base and "h" is the height or altitude.

You know that the base of  this parallelogram  is 8 inches long and the altitude to the base is 10 inches, then:

[tex]b=8in\\h=10in[/tex]

You need to substutite these values into the formula.

Therefore, the area the parallelogram is:

[tex]A=(8in)(10in)\\\\A=80in^2[/tex]

Answer:

Option A)724 square centimeters

Step-by-step explanation:

we know that

The surface of the prism is equal to the area of its six rectangular faces

The surface area is equal to

[tex]SA=2B+PH[/tex]

where

B is the area of the base

P is the perimeter of the base

H is the height of the prism

we have

[tex]L=12\ cm[/tex]

[tex]W=11\ cm[/tex]

[tex]H=10\ cm[/tex]

Find the area of the base B

[tex]B=LW[/tex]

[tex]B=(12)(11)=132\ cm^{2}[/tex]

Find the perimeter of the base P

[tex]P=2(L+W)[/tex]

[tex]P=2(12+11)=46\ cm[/tex]

Find the surface area SA

[tex]SA=2(132)+(46)(10)=724\ cm^{2}[/tex]

Answer:

15,36,39

Step-by-step explanation:

primitive pythag: 5, 12, 13 *3

Answer:

The Answer is D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Angles (2x + 14)° and (x + 7)° are complementary angles.

If two angles are complementary, then they add up to 90°.

Therefore we have the equation:

(2x + 14) + (x + 7) = 90      combine like terms

(2x + x) + (14 + 7) = 90

3x + 21 = 90          subtract 21 from both sides

3x = 69          divide both sides by 3

x = 23

Answer:

From the looks of things, it seems to be 140 ft, the maximum height being 150 ft and the minimum height being 10 ft. Find the difference, and that should be your answer :)

Answer:C 140

Step-by-step explanation:

Answer: Area: 256 ft squared   Perimeter: 64 feet

Step-by-step explanation: If the scale is 1 cm to 8 ft then if you multiply 1 cm by 2 you get 2 cm. Then you multiply 8 by 2 to get 16 feet. Once you get 16 feet, you can do 16 times 16 to find the area and 16 times 4 to find the perimeter.

Answer:

[tex]n=5[/tex]

Step-by-step explanation:

We have the following expression [tex]\frac{2}{8} = \frac{n}{20}[/tex] and we must solve for variable n.

To solve the equation multiply by 20 on both sides of the equality and you will get the following

[tex]20*\frac{2}{8} = 20*\frac{n}{20}[/tex]

[tex]\frac{20*2}{8} = \frac{20n}{20}[/tex]

[tex]\frac{40}{8} = n[/tex]

[tex]n= \frac{40}{8}[/tex]

Finally we have that:

[tex]n=5[/tex]

Answer:

n=5

Step-by-step explanation:

2/8 = n/20

Using cross products

2 * 20 = 8*n

40 = 8n

Divide each side by 8

40/8 = 8n/8

5 =n

Answer:

Zero

Step-by-step explanation:

there is no solution the sides are uneven. if you solve for it 3x and 3x cancels out each other leaving you with -2=5

Answer:

Zero

Step-by-step explanation:

Periodt

Answer:

40 deg

Step-by-step explanation:

This is just m anglex=.5(58+22)=.5(80)=40

Answer:

x = 40

Step-by-step explanation:

When 2 chords intersect inside a circle then the measure of the angle formed is half the sum of the arcs intercepted by the angle and it's vertical angle, so

x = 0.5(58 + 22)° = 0.5 × 80° = 40°

Answer:

A = 10.9 cm^2

Step-by-step explanation:

If a circle has a radius of 13 and a sector defined by a 7.4 degree arc, the area, in cms, of the sector is 10.9 cm^2 or 10 cm^2 to the nearest tenth.

Answer:

25%

1/3

100%

5/4

2.5

Step-by-step explanation:

Convert all the values into decimals and order them from least to greatest.

Answer:

D) (the fourth one)

Step-by-step explanation:

The function will never go below 0 since the absolute of a negative number is a positive number, so C is out of the question.

The equation of an absolute function is f(x) = a|x-h|+k

h is the offset on the x axis, and the equation of this function is |x-(1)|, so that means the function is shifted one to the right, making it D.

Answer:

1/4

Step-by-step explanation:

Answer:

[tex]slope =\frac{1}{4}[/tex]

slope is undefined

Step-by-step explanation:

WE need to find the slope of two lines

to find out slope we use formula

[tex]slope =\frac{y_2-y_1}{x_2-x_1}[/tex]

To find slope we pick two points from the line

(-4,0) and (0,1) is (x1,y1) and (x2,y2)

[tex]slope =\frac{1-0}{0+4}=\frac{1}{4}[/tex]

[tex]slope =\frac{1}{4}[/tex]

To find slope we pick two points from the line

(1,0) and (1,1) is (x1,y1) and (x2,y2)

[tex]slope =\frac{1-0}{1-1}=\frac{1}{0}[/tex]

When denominator =0 then the slope is undefined

Answer:

Yes

Step-by-step explanation:

The more you jump, the higher your blood flow becomes, since your heart needs to pump more blood to the working areas. This really doesn't belong in math though.

Answer: yes

Step-by-step explanation: but i am not that sure how i can explain it, here look at the guys answer above. Also thank the guy above, not me.

Answer:

drag each result in the corresponding box according to the results

Step-by-step explanation:

Hello

The product of two or more powers of equal  base "a" is equal to the power of base  "a" with   exponent equal to the sum of the respective exponents.

[tex]a^{m}*a^{n} =a^{n+m}[/tex]

Step 1

[tex]d*2d^{2}\\[/tex]

[tex]d*2d^{2}=(2*1)d^{(2+1)}\\d*2d^{2}=2d^{3} \\[/tex]

Step 2

[tex]-9*2d^{2}\\[/tex]

[tex]-9*2d^{2}=(-9*2)d^{(2+0)}\\-9*2d^{2}=-18d^{2} \\[/tex]

Step 3

[tex]d*11d\\[/tex]

[tex]d*11d=(1*11)d^{(1+1)}\\11*d^{2}=11d^{2} \\[/tex]

Step 4

[tex]-9 * 11d\\[/tex]

[tex]-9 * 11d = (-9*11)d^{1+0}=-99 d[/tex]

Step 5

[tex]d*-4=-4d[/tex]

Step 6

[tex]-9*-4 = ( -*- ) (9*4)= 36[/tex]

Step 7

Now, drag each result in the corresponding box .

Have a great day

Answer:

Your welcome :)

Step-by-step explanation:

Answer: 4/5

Step-by-step explanation:

1. you need to know the formula which is m = y2-y1/x2-x1

2. you plug in the numbers which would be 9-5/3-(-2)

3. you get your answer as 4/5

4. the answer is 4/5

Answer:

○ b ⅘

Step-by-step explanation:

-y₁ + y₂\-x₁ + x₂ = m

[tex] \frac{4}{5} = \frac{ -5 + 9}{2 + 3}[/tex]

I am joyous to assist you anytime.

Answer:

xy(x+8)(x^2-6y)

Step-by-step explanation:

To long to explain, but you can just google it if you just need the answer

Answer:

xy(x^2 - 6y)(x + 8 ) .

Step-by-step explanation:

The Greatest Common Factor of this expression is:

 xy so dividing by this:

= xy(x^3 + 8x^2  - 6xy - 48y).

Factoring the expression in the parentheses by grouping:

= xy [ x^2( x + 8) - 6y (x + 8)]

= xy(x^2 - 6y)(x + 8 )  (answer).

Answer:

Simplified to -281250

Step-by-step explanation:

Answer:

A. 1/4

Step-by-step explanation:

The line is upwards so slope will be positive. (either A or C will be the answer)

Now to solve for slope to find out

Two coordinate points on graph (-3,-1) ad (5,1)

Slope = (y2 - y1)/(x2 - x1)

Slope = (1 + 1)/(5 + 3) = 2/8 = 1/4

Answer:

[tex]A.\frac{1}{4}[/tex]

Step-by-step explanation:

Hello, I think I can help you  with this

The slope is the inclination of the line with respect to the abscissa axis, if you know two points  it can be calculated using

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}\[/tex]

where

[tex]P1(x_{1},y_{1})\\P2(x_{2},y_{2})[/tex]

Step 1

put the values into the equation

Let

[tex]P1(-3,-1) \\P2(5,1)\\\\m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} } \\m=\frac{1-(-1)}{5-(-3) } \\m=\frac{1+1}{5+3} \\m=\frac{2}{8} \\m=\frac{1}{4}[/tex]

Have a great day

Final answer:

Jonathan's weekly income is determined by a linear function M(h) = 9.5h + 25, with the domain being 0 ≤ h ≤ 20 to reflect his work hour limitations. A sketch of this function would show a linear increase from an initial allowance of $25, rising by $9.50 for each hour worked up to 20 hours.

Explanation:

Jonathan makes a weekly allowance of $25 and earns $9.50 per hour at his job, with a maximum work limit of 20 hours per week.

a) Function for Jonathan's weekly earnings:

The function M(h) = 9.5h + 25 represents the amount of money Jonathan makes each week, where h is the number of hours he works.  

b) Domain of the function:

The domain of this function, considering Jonathan's work hour limitation, is 0 ≤ h ≤ 20. This range is because Jonathan cannot work more than 20 hours a week due to his age restrictions.

c) Sketch of the graph:

The graph would start at the point (0, 25), which represents Jonathan's weekly allowance without any worked hours. Then, it would rise linearly at a slope of $9.50 for each additional hour worked, up to the point (20, 215), which represents the maximum amount Jonathan can earn by working 20 hours plus his weekly allowance. Note: The actual graph is not displayed here but can easily be sketched using the described points and slope.

Answer:

Their point of intersection will always be on the line y = x.

Step-by-step explanation:

We have a function f(x) and its inverse is the function f⁻¹(x).

The domain and range of a function replaces each other for the inverse of that function.

So if f(x) and f⁻¹(x) are inverse of each other

and f(a) = b

then a = f⁻¹(b)

Another example to make it clear is that

f(5) = 25

f⁻¹(25) = 5

The function and its inverse will intersect each other at the point where f(x) = f⁻¹(x) which is only possible when a = b.

Hence, a function and its inverse will always intersect at a point on the line x=y.

Answer:

B. [tex]x=3,\ y=20,\ z=-14[/tex]

Step-by-step explanation:

Consider the system of three equations:

[tex]\left\{\begin{array}{l}2x+2y+3z=4\\5x+3y+5z=5\\3x+4y+6z=5\end{array}\right.[/tex]

Multiply the first equation by 5, the second equation by 2 and subtract them:

[tex]\left\{\begin{array}{r}2x+2y+3z=4\\4y+5z=10\\3x+4y+6z=5\end{array}\right.[/tex]

Multiply the first equation by 3, the second equation by 2 and subtract them:

[tex]\left\{\begin{array}{r}2x+2y+3z=4\\4y+5z=10\\-2y-3z=2\end{array}\right.[/tex]

Multiply the third equation by 2 and add the second and the third equations:

[tex]\left\{\begin{array}{r}2x+2y+3z=4\\4y+5z=10\\-z=14\end{array}\right.[/tex]

Fro mthe third equation

[tex]z=-14[/tex]

Substitute it into the second equation:

[tex]4y+5\cdot (-14)=10\\ \\4y=10+70\\ \\ 4y=80\\ \\y=20[/tex]

Substitute y=20 and z=-14 into the first equation:

[tex]2x+2\cdot 20+3\cdot (-14)=4\\ \\2x+40-42=4\\ \\2x-2=4\\ \\2x=6\\ \\x=3[/tex]

The solution is

[tex]x=3,\ y=20,\ z=-14[/tex]

Answer:

First car:  35 gallons

Second car: 15 gallons

Step-by-step explanation:

Assuming [tex] x [/tex] to be the gas consumed by 1st car and [tex] 50 - x [/tex] to be the gas consumed by 2nd car.

We know that:

Distance traveled = fuel efficiency × gas consumed

[tex]20x+35(50-x)=1225[/tex]

[tex]20x+1750-35x=1225[/tex]

[tex]35x-20x=1750-1225[/tex]

[tex]15x=525[/tex]

[tex]x=35[/tex]

So [tex]50 - x = 50-35=15 [/tex]

Therefore, first car consumed 35 gallons while second car consumed 15 gallons.

Answer:

First car: 35 gallons

Second car: 15 gallons

Step-by-step explanation:

Set up a system of equations.Let be "x" the number of gallons consumed by the first car and "y" the number of gallons consumed by the second car.

Then:

[tex]\left \{ {{x+y=50} \atop {20x+35y=1,225}} \right.[/tex]

Applying the Elimination method, multiply the first equation by -20, then  add both equations and solve for "y":

[tex]\left \{ {{-20x-20y=1,000} \atop {20x+35y=1,225}} \right. \\.......................\\15y=225\\y=15[/tex]

Substitute this value into the first equation and solve for "x":

[tex]x+15=50\\x=35[/tex]

Answer:

53

Step-by-step explanation:

Let's make some equations.

The number is two-digit, so let's make it [tex]xy[/tex]

Also, the two digits add up to 8, so [tex]x+y=8[/tex]

Now the value of [tex]xy=10x+y[/tex]

and the value of [tex]yx=10y+x[/tex]

Since we know that when we reverse the digits the number is less than the resulting number by 18, we can formulate an equation.

[tex]10y+x=10x+y+18[/tex]

Solve this equation.

[tex]9y-9x=18[/tex]

[tex]9(y-x)=18[/tex]

[tex]y-x=2[/tex]

Now let's use the equation we made earlier.

Change [tex]x+y=8[/tex] into [tex]y=8-x[/tex]

Solve the system of equations.

[tex]y-x=2[/tex]

[tex]y=8-x[/tex]

[tex]8-x-x=2[/tex]

[tex]8-2x=2[/tex]

[tex]-2x=-6[/tex]

[tex]x=3[/tex]

[tex]y-3=2[/tex]

[tex]y=5[/tex]

So the original number is 53.

Answer:

C

Step-by-step explanation:

Answer:

Pie: Pie is a dessert that has pastry from top to bottom and has filling in the middle.

Best type of pie: In my opinion: Key Lime Pie

Pie Emoji: No clue, you'll have to email Apple or Samsung (or whatever your phone provider is) and ask them to update or change the emoji.

Step-by-step explanation:

These are very important questions

The ratio of time on vacation to time working as a fraction in lowest terms when working 24 weeks and rewarded with 3 days of vacation is 1/56.

If you spent 24 weeks working on a project for your job and were rewarded with 3 days of vacation, the ratio of time on vacation to time working as a fraction in lowest terms can be calculated as follows: