In simplest radical form, what are the solutions to the quadratic equation 6 = x2 – 10x?

Answer:

Distributive property.

For this case we have that by definition, the distributive property establishes that:

[tex]a (b + c) = ab + ac[/tex]

So, if we have:

[tex]5 (x-7) = 55[/tex]

When applying distributive property to the terms within the parenthesis we have:

[tex]5x-35 = 55[/tex]

The distributive property was used to write the second step.

Answer:

Distributive property

Answer:

Part 5) The roots are x=-3 and x=1.5

Part 6) The solution on a number line is the shading area below of the line y=-1/3 (close circle)

Step-by-step explanation:

Part 5) Find the roots of the parabola given by the following equation

[tex]2x^{2} +5x-9=2x[/tex]

we know that

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]2x^{2}+5x-2x-9=0[/tex]

[tex]2x^{2}+3x-9=0[/tex]

so

[tex]a=2\\b=3\\c=-9[/tex]

substitute in the formula

[tex]x=\frac{-3(+/-)\sqrt{3^{2}-4(2)(-9)}} {2(2)}[/tex]

[tex]x=\frac{-3(+/-)\sqrt{81}} {4}[/tex]

[tex]x=\frac{-3(+/-)9} {4}[/tex]

[tex]x=\frac{-3(+)9} {4}=1.5[/tex]

[tex]x=\frac{-3(-)9} {4}=-3[/tex]

therefore

The roots are x=-3 and x=1.5

Part 6) Solve the inequality and graph the solution on a number line.

[tex]-3(5y-4)\geq 17[/tex]

Solve for y

[tex]-15y+12\geq 17[/tex]

Subtract 12 both sides

[tex]-15y\geq 17-12[/tex]

[tex]-15y\geq 5[/tex]

Multiply by -1 both sides

[tex]15y\leq -5[/tex]

Divide by 15 both sides

[tex]y\leq -1/3[/tex]

The solution is the interval -----> (-∞, -1/3]

All  real numbers less than or equal to negative one third

The solution on a number line is the shading area below of the line y=-1/3 (close circle)

The graph in the attached figure

See the attached picture:

Answer:

y=3

Step-by-step explanation:

3 (3y - 9) = 0

Divide each side by 3

3/3 (3y - 9) = 0/3

3y -9 = 0

Add 9 to each side

3y -9+9 = 0+9

3y =9

Divide by 3

3y/3 = 9/3

y =3

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Answer:

The simplification of the given expression  (r3s2t)4 is:

r¹²s⁸t⁴

Step-by-step explanation:

Given expression:

(r³s²t)⁴

power of '4' on the whole term will be applied to individual terms after we open the brackets. In this case the power on the whole term will be multiplied to the power of each individual term:

= (r³)⁴(s²)⁴(t1)⁴

= r³ˣ⁴ s²ˣ⁴ t¹ˣ⁴

= r¹²s⁸t⁴

Answer: 1439

Step-by-step explanation:

Volume= Length* breadth* height

= 15*1312*112

= 1439

The center of the circle is (-3, -9/2) and the radius is sqrt(41)/2.

To find the coordinates of the center and length of the radius of the circle, we need to rewrite the equation of the circle in the standard form (x-h)^2 + (y-k)^2 = r^2. First, complete the square for the x and y terms by adding and subtracting the necessary constants:

x^2 + 6x + 4y = 23

x^2 + 6x + 9 + 4y + 9 = 23 + 9 + 9

(x + 3)^2 + (y + 9/2) = 41/4

Therefore, the center of the circle is (-3, -9/2) and the radius is sqrt(41/4), which simplifies to sqrt(41)/2.

Answer:True

Step-by-step explanation:

Answer:

The sum of the exterior angles of a polygon is always 180 degrees.

Step-by-step explanation:

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Answer:

An  equilateral triangle has all sides equal.  

If perimeter = 18y -6 then one side = (18y -6) / 3 =

6y -2

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

18y-6

y=18/6

y=3

18*3=54

Answer:

41°

Step-by-step explanation:

∠C is opposite of side c.

Using law of cosines:

c² = a² + b² − 2ab cos C

17.2² = 26² + 19² − 2(26)(19) cos C

cos C = 0.750

C ≈ 41°

Answer:

The answer is 41 degrees

F (- 12) = 2/3(-12)+7

F (- 12) = 2(-4) + 7

F(-12) = -8 + 7

F(-12) = -1

A transversal is a line that passes through two lines (as shown above) on the same plane.

N is the transversal since it passes through line L and M at two distinct points.

Answer:

A transversal is a line that passes through two lines (as shown above) on the same plane.

N is the transversal since it passes through line L and M at two distinct points.

Step-by-step explanation:

Well going off what I know (you don't have the equations up)

You have to isolate x

3/4x = 6

(4) 3/4x = 6 *multiplying by 4 cancels the fraction.

3x = 24

Divide by 3

X = 6

Answer:

[tex]x = 8[/tex]

Step-by-step explanation:

Let multiply each side by 4/3:

[tex]\frac{4}{3}\cdot \frac{3}{4} \cdot x = 6\cdot \frac{4}{3}[/tex]

[tex]x = 8[/tex]

Answer:

12

Step-by-step explanation:

First, multiply the length by two then, subtract the total by the sum, last divide by two.

(25 * 2)

(74 - 50)

(24/2)

Answer = 12

Answer:

w>/=12

Step-by-step explanation:

2(25)+2w>/= 74

50+2w>/=74

-50          -50

2w>/=24/2

w>/=12

Answer:

[tex]\boxed{\text{A. \$1.25; B. September by 4.7 \%}}[/tex]

Step-by-step explanation:

Part A. Price of flowers in September

Let x = price of flowers in September.

Then 1.2x = price of flowers in October

1.2x = $1.50

[tex]x = \dfrac{\$1.50 }{1.20} = \$1.25\\\\\text{The price of flowers in September was }\boxed{\textbf{\$1.25}}[/tex]

Part B. Seventh-grade class

40 % of September price = 0.40 × $1.25 = $0.50

    40 % of October price = 0.40 × $1.50 = $0.60

In September

[tex]\text{Earnings} = \text{900 flowers} \times \dfrac{\$0.50}{\text{1 flower} } = \$450[/tex]

In October,

[tex]\text{Earnings} = \text{700 flowers} \times \dfrac{\$0.60}{\text{1 flower} } = \$430\\\\\text{Difference} = \$450 - \$430 = \$20[/tex]

The class earned $20 more in September.

Compared with October earnings,

[tex]\text{\% Difference} = \dfrac{\text{Difference}}{\text{October earnings}} \times 100\%\\\\\text{\% Difference} = \dfrac{\$20}{\$430} \times 100\% = 4.7 \%\\\\\text{The class made more money in } \boxed{\textbf{September}} \text{ by } {\boxed{\mathbf{4.7 \%}}[/tex]

The answer above me deserves brainliest !! They did so well!!!

Answer:

I think the answer is B= 62  

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

38

Step-by-step explanation:

The 38-deg angle and and angle 6 are vertical angles, so they are congruent.

m<6 = 38 deg

Angles 6 and 4 are corresponding angles of parallel lines cut by a transversal, so they are congruent.

m<4 = m<6 = 38 deg

Answer:

38

Step-by-step explanation:

< 6 = 38  vertical angles

< 6 = <2  alternate interior angles

<2 = <4  vertical angles

<4 = 38

Answer:

(-5, 1)

Step-by-step explanation:

We are given a kite on the graph which is rotated 180° clockwise about the origin and then reflected over the Y axis followed by reflection over the X axis.

We are to find the coordinates of point A after the complete transformation.

A (-5, 1)

When a point is rotated 180° clockwise about the origin, the signs of its coordinates change.

A (-5, 1) ---> A' (5, -1) - after clockwise rotation of 180 degrees about origin

Then this point A' is reflected over the Y axis where the y coordinate remains the same but x coordinate changes its sign.

A' (5, -1) ---> A'' (-5, -1) - after reflection through y axis

Now this point A'' is reflected over the X axis where the x coordinate remains the same while y coordinates changes its sign.

A'' (-5, -1) ---> A''' (-5, 1) - after complete transformation

Answer:(-5, 1)

Step-by-step explanation:

Answer:

x = -4, 10

Step-by-step explanation:

We take the square root and use the fact of "plus-minus" and find two values of x. The process of solving this equation is shown below:

[tex](x-3)^2 = 49\\\sqrt{(x-3)^2}=\sqrt{49}\\  x-3=+-7\\x=3+7=10\\x=3-7=-4[/tex]

Hence the two values of x are -4 and 10

Note: both (-7)^2 and (7)^2 are 49 . So we took "plus-minus" values of [tex]\sqrt{49}[/tex]

Answer: -4 and 10

Step-by-step explanation:

b and c

the second and and the third option

the middle two

Answer:

The answer is 21%.

Step-by-step explanation:

1) divide 134 by 106

106/134 is about 0.79

2) Multiply by 100 to find the percentage

0.79(100)= 79%

3) Subtract 79% from 100% to find the percentage difference

100%-79%= 21%

Therefore, the percent of change between 134 and 106 is 21%.

Hope this helps!

Answer:

C

Step-by-step explanation:

Ok, so to do this, we are just going to plug in (0,0) and see it it checks out.

Let's take the first question. y[tex]y\geq x^{2} -4[/tex]

When we plug (0,0) into this, we get the following

[tex]0\leq 0^{2} -4[/tex]

[tex]0\leq 0-4[/tex]

[tex]0\leq -4[/tex]

This is false.

Let's check the other equation:

[tex]0>2(0)-1\\0>0-1\\0>-1[/tex]

This is true.

So the correct answer is C

Answer:

Yes,they will intersect at (0.686,3.941) and (2.914,-2.741)

Step-by-step explanation:

Given the values that represent the function g(x) you can plot them directly on a graph tool and plot the function y²+x²=16 then visualize

You can also determine the equation of the linear function as then graph both equations on the graph tool

Finding gradient m

Given (0,6) and (1,3)

m=change in value of y/change in value of x

[tex]m=\frac{3-6}{1-0} =\frac{-3}{1} =-3[/tex]

Finding the equation of the linear function

Taking points (2,0)   and (x,y)

[tex]m=\frac{y-0}{x-2} \\\\-3=\frac{y-0}{x-2} \\\\\\-3(x-2)=y-0\\\\\\-3x+6=y-0\\\\\\y=-3x+6[/tex]

From the graph,they intersect at

(0.686,3.941) and (2.914,-2.741)

Answer:

Yes, at positive x coordinates

Answer:

34/13

Step-by-step explanation:

The length-to-width ratio here is:

8.5 / 3.25

which can be reduced by dividing numerator and denominator both by 0.25:

8.5/0.25

--------------- = 34/13

3.25/0.25

Answer:

2[tex]\sqrt{34}[/tex]

Step-by-step explanation:

Calculate the distance (d) using the distance formula

d = √(x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 2, 4) and (x₂, y₂ ) = (4, - 6)

d = [tex]\sqrt{(4+2)^2+(-6-4)^2}[/tex]

  = [tex]\sqrt{6^2+(-10)^2}[/tex]

  = [tex]\sqrt{36+100}[/tex]

  = [tex]\sqrt{136}[/tex] = [tex]\sqrt{4(34)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{34}[/tex] = 2[tex]\sqrt{34}[/tex]

Answer:

4.75 is the answer

Step-by-step explanation:

The Gross sales were 393 million.

It is required to find the gross sales rounded to the nearest million

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Let gross sales = x millions

Returns = 1/80xmillions

x-1/80x=380

29x/30=380

x=380*30/29

x=393.10≈393

Therefore, the Gross sales were 393 million.

Learn more about arithmetic here:

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Answer:

1120

Step-by-step explanation:

8/50=x/7000

50x=56000

Divide 50 on both sides

1120

Answer:

1120

Step-by-step explanation:

8/50=x/7000

50x=56000

Divide 50 on both sides

1120

Since 25% of something is also 1/4 of something, multiply 25% by 4 to get the full value.

Since 75 is 25 percent, multiply 75 by 4.

75*4=300

The value is 300.

Hope this helps!

Answer: 495 degrees

Step-by-step explanation:

[tex]\frac{11\pi }{4}[/tex] · [tex]\frac{180}{\pi }[/tex]

[tex]\frac{1980}{4}[/tex]

495 degrees

[tex](x-1)(x+20)=x^2+20x-x-20=x^2+19x-20[/tex]