A line passes through the points one, four and three, -4 which is the equation of the line

[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:

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:

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: 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.

−x = 4 − 3x + 6

Move the -3x to the other side and simplify 4+6.

2x= 10

Divide both sides by 2

x=5.

Answer: First option.

Step-by-step explanation:

Given the equation [tex]-x = 4- 3x + 6[/tex], you need to solve for the variable "x" to find its value.

Add the like terms on the right side of the equation:

 [tex]-x = 10-3x [/tex]

Now you need to subtract 10 from both sides of the equation:

 [tex]-x-10 = 10- 3x -10[/tex]

 [tex]-x-10 =- 3x[/tex]

 The next step is to add "x" to both sides of the equation:

  [tex]-x-10+x = - 3x +x[/tex]

   [tex]-10 = - 2x[/tex]

And finally, divide both side by -2:

[tex]\frac{-10}{-2}=\frac{-2x}{-2}\\\\x=5[/tex]

Final answer:

The ordered pair of M after rotating 90 degrees clockwise is (-6,5).

Explanation:

When a point undergoes a 90-degree clockwise rotation around the origin, a distinct transformation occurs. Specifically, the x-coordinate of the original point becomes the negative value of its original y-coordinate, and the y-coordinate takes on the positive value of the original x-coordinate. This geometric operation is fundamental in transforming coordinates.

Taking point M(5,6) as an example, after the 90-degree clockwise rotation, the new coordinates manifest as (-6,5). This rotation plays a crucial role in various mathematical and geometric applications, contributing to the understanding of spatial transformations and coordinate systems.

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:

true

Step-by-step explanation:

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:

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

The best way to describe a ratio is option c, which is 'A comparison of two numbers'.

A ratio shows us the number of times a number contains another number. therefore, it helps us to compare two numbers.

As we have already discussed the ratio is the comparison of two numbers for a particular.

Hence, the best way to describe a ratio is option c, which is 'A comparison of two numbers'.

Learn more about Ratio:

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Answer:

b) (-6, 0)

Step-by-step explanation:

The quickest method to use is to put "0" in for y, then figure out which term for x would make the equation authentic, or genuine.

Answer:

3/11 + 5 5/8 > 5 6/8

Step-by-step explanation:

find the LCD's for both sides of the comparison. After this, add fractions from the same side of the comparison. Then, you must compare the two and check your answer. Have a nice day!

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:

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:

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.

[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{4}{5}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{5}{4}}\qquad \stackrel{negative~reciprocal}{+\cfrac{5}{4}\implies \cfrac{5}{4}}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-0}{2-(-2)}\implies \cfrac{5}{2+2}\implies \cfrac{5}{4} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{9-(-1)}{10-2}\implies \cfrac{9+1}{8}\implies \cfrac{10}{8}\implies \cfrac{5}{4}[/tex]

Answer: Im pretty sure it answer options 1 and 5

Step-by-step explanation: 1) (-2,0) and (2,5)      5) (2,-1) and (10,9)

its on edg.

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: First Option

[tex]x= -3.396[/tex]

Step-by-step explanation:

We have the following expression

[tex]log_{\frac{3}{4}}25 = 3x -1[/tex]

To solve the equation add 1 to both sides of the equality

[tex]log_{\frac{3}{4}}25 +1= 3x -1+1[/tex]

[tex]log_{\frac{3}{4}}25 +1= 3x[/tex]

Divide between 3 to both sides of the equation

[tex]\frac{log_{\frac{3}{4}}25 +1}{3}= x[/tex]

[tex]x= \frac{-11.19 +1}{3}[/tex]

[tex]x= -3.396[/tex]

The answer is the first option

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:

{196, 256, 484}

Step-by-step explanation:

14² = 196;

16² = 256;

19² = 361;   390 lies between 361 and 400, and is thus NOT a perfect square;

20² = 400;

22² = 484

564 lies between the two perfect squares 23² and 24², but is itself NOT a perfect square.

Thus, the perfect squares are {196, 256, 484}

The perfect squares out of the numbers 196, 256, 390, 484, 564 are 196, 256, and 484. A perfect square is a number that can be expressed as an integer multiplied by itself.

The perfect squares from the list you provided are: 196, 256, and 484. A perfect square is a number that can be expressed as the product of an integer with itself. For example, 256 is a perfect square because it can be expressed as 16 times 16, or 16^2. Similarly, 196 and 484 are perfect squares as they can be expressed as 14^2 and 22^2, respectively. On the other hand, numbers 390 and 564 are not perfect squares as they cannot be expressed as the product of an integer with itself.

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Answer:

$7.63

Step-by-step explanation:

We are given:

r=9 icnhes

We have to find the area of the circular ornament first. The formula for area of circle is:

Area= πr^2

Putting the value of r

Area=3.14*(9)^2

=3.14*81

=254.34 Square inches

As the company pays $0.03 for 1 square inch, for 254.34 square inch the company will have to pay:

=254.34*0.03

=$7.6302

Rounding off to the nearest cent

The cost for one ornament = $7.63

Answer:

$30.52

Step-by-step explanation:

4 x 9^2 x 3.14 x 0.03 = around 30.52

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:

15,36,39

Step-by-step explanation:

primitive pythag: 5, 12, 13 *3

Answer:

The Answer is D

Step-by-step explanation:

Answer:

2x + 7

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x) - g(x) = 3x + 1 - (x - 6) = 3x + 1 - x + 6 = 2x + 7

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:

Last option: 7

Step-by-step explanation:

The Standard form of a quadratic equation is the following:

[tex]ax^{2}+bx+c=0[/tex]

Where "a" is the quadratic coefficient (This coefficient cannot be 0), "b" is the linear coefficient, "c" is the constant and "x" is the variable.

In this case you have the quadratic equation [tex]3x^2 + 5x + 7 = 0[/tex] which is written is Standarf form. Then, you can identify that:

[tex]a=3\\b=5\\c=7[/tex]

Therefore the value of "c" is 7.

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.