central school is hosting a "central has talent" show. they will award various prizes for the best acts in the show. first place wins the most money

Answer:

hello : x = - 4 or x = - 8

Step-by-step explanation:

x²+12x+32=0​

(x² +2(6)(x) +6²) - 6² +32 = 0....by completing the square

(x + 6 )²- 2² = 0

(x+6-2)(x+6+2)=0 by idetity : a² - b² = (a - b ) ( a + b )

(x+4)(x+8) =0

x+4=0 or x+8= 0

x = - 4 or x = - 8

Answer:

x = - 8, x = - 4

Step-by-step explanation:

Given

x² + 12x + 32 = 0 ( subtract 32 from both sides )

x² + 12x = - 32

To complete the square

add (half the coefficient of the x- term)² to both sides

x² + 2(6)x + 6² = - 32 + 6²

(x + 6)² = - 32 + 36 = 4

Take the square root of both sides

x + 6 = ± 2 ( subtract 6 from both sides )

x = - 6 ± 2

Hence

x = - 6 - 2 = - 8

x = - 6 + 2 = - 4

Answer:

Amount invested at 6 percent interest is $69,200

Amount invested at 9 percent interest is $34,600

Step-by-step explanation:

Let the amount invested (or principal) at 6 percent interest be $2x

The principal(P) (amount invested) at 9 percent interest will be $x

Amount(A) = P(1 + rt)

Time(t) = one year = 1

Amount at 6% interest = 2x(1 + 0.06) = $2.12x

Interest accumulated = Amount - Principal = $2.12x - $2x = $0.12x

Amount at 9% interest = x(1 + 0.09) = $1.09x

Interest accumulated = Amount - Principal = $1.09x - $x = $0.09x

Total interest = $7,266

So, $0.12x + $0.09x = $7,266

$0.21x = $7,266

x = [tex]\frac{7,266}{0.21}[/tex] = $34,600

The principal (amount invested) at 9 percent interest rate is $34,600

The principal (amount invested) at 6 percent interest rate is 2 × $34,600 = $69,200

Answer:

[tex]-2\frac{2}{3} y^{2} -1\frac{8}{9}y -3\frac{1}{9}[/tex]

Step-by-step explanation:

[tex]\bf \begin{cases} \boxed{y}=6x-11\\ \cline{1-1} -2x-3y=-7 \end{cases}\qquad \implies \stackrel{\textit{substituting \underline{y} in the 2nd equation}}{-2x-3\left( \boxed{6x-11} \right)=-7}[/tex]

[tex]\bf -2x-18x+33=-7\implies -20x+33=-7\implies -20x=-40 \\\\\\ x=\cfrac{-40}{-20}\implies \blacktriangleright x=2 \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that }}{y=6x-11}\implies y=6(2)-11\implies y=12-11\implies \blacktriangleright y=1 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (2,1)~\hfill[/tex]

Step 1: Plug 6x - 11 in for y in the equation -2x - 3y = -7

-2x - 3(6x-11) = -7

Step 2: Distribute -3 to the numbers inside the parentheses (6x -11)

-2x - 18x + 33 = -7

Step 3: Combine like terms

x's go with x's

-20x + 33 = -7

Step 4: Subtract 33 to both sides

-20x = -40

Step 5: Isolate x by dividing -20 to both sides

x =  2

Step 6: To solve for y plug 2 in for x in the equation y = 6x - 11

y = 6(2) - 11

y = 12 - 11

y = 1

(2, 1)

Check:

1 = 6(2) - 11

1 = 12 - 11

1 = 1

-2(2) - 3(1) = -7

-4 - 3 = -7

-7 = -7

Hope this helped!

ANSWER

[tex] \frac{1}{2} [/tex]

EXPLANATION

The given expression is;

[tex]2 {x}^{ - 4} y[/tex]

We want to find the value of this expression when x=2 and y=4.

We substitute to get,

[tex]2 {(2)}^{ - 4} (4) [/tex]

[tex]8 \times {2}^{ - 4} [/tex]

Recall that

[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]

This implies that,

[tex]8 \times {2}^{ - 4} = 8 \times \frac{1}{ {2}^{4} } [/tex]

[tex]8 \times {2}^{ - 4} = 8 \times \frac{1}{16 } = \frac{1}{2} [/tex]

Answer:

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

The distance between two points is found by

d = sqrt((y2-y1)^2 + (x2-x1)^2)

  = sqrt( (4-7)^2 + (6-2)^2)

  =sqrt( 3^2 +4^2)

  = sqrt(9+16)

  =sqrt(25)

  = 5

Answer:

False

Step-by-step explanation:

Because....

* Hopefully this helps:) Mark me the brainliest:)!!!

∞ 234483279c20∞

Answer:

h = 3πx

Step-by-step explanation:

The volume (V) of the cylinder is calculated using the formula

V = πr²h ( r is the radius and h the height )

V = π × x² × 3x = 3πx³

The volume of the cuboid therefore has volume of 3πx³, that is

x × x × h = 3πx³

x²h = 3πx³ ( divide both sides by x² )

h = 3πx³ ÷ x² = 3πx

Answer:

[tex]\large\boxed{A=25\pi}[/tex]

Step-by-step explanation:

The formula of an area of a circle:

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

r - radius

We have r = 5. Substitute:

[tex]A=\pi(5^2)=25\pi[/tex]

Answer:

the height is 20 inches

Step-by-step explanation:

Answer: 20 inches

Step-by-step explanation:

This is a triangular prism, we first need to find the area of the triangle!

A (triangle) = 1/2 x base of triangle x height of triangle

A = 1/2 x 3 x 5 = 7.5 square inches

Now lets work out the height of the prism, we can use the volume of the prism to do so.

V = Area of triangle x height

150 = 7.5 x height

Height = 150/7.5 = 20 inches

Answer:

Step-by-step explanation:

From the net:

S.A. = 2(25 in²) + 4(60 in²) = 50 in² + 240 in² = 290 in²

From the model:

The formula of a Surface Area of a rectangular prism:

S.A. = 2(lw + lh + wh)

l - length

w - width

h - height

We have l = 5 in, w = 5 in, and h = 12 in. Substitute:

S.A. = 2(5 · 5 + 5 · 12 + 5 · 12) = 2(25 + 60 + 60) = 2(145) = 290 in²

Answer: 290 in.^2

Step-by-step explanation: Just did on iready. Hope i helped! (:

Answer:

Q1: 11x - 8

Q2: 2x + 10

Q3: -3v + 12

Answer:

Q1: 11x + 8

Q2: 2x + 10

Q3: 3v - 12

So, input into distance formula to get ....

√(22-(-18))²+(0-9)²

√1600+81

√1681 is about 41.

Answer:

41 units

Step-by-step explanation:

Distance equation: Distance = √((x₁ - x₂)² + (y₁ - y₂)²), where (x₁, y₁) is one coordinate, and (x₂,y₂) is the other.

Plug in: √((-18 - 22)² + (9 - 0)²)

Add: √((-40)² + (9)²)

Exponents: √(1600 + 81)

Add: √1681

Square roots: ± 41

Domain: 41 units (negatives are not allowed)

Answer:

14

Step-by-step explanation:

Rewriting this as

-8      -7

----- · -----

 1         4

makes this problem a bit easier to do.  Reduce the -8/4 to -2:

-8      -7       -2(-7)

----- · ----- = ----------- = 14

 1         4           1

Answer:

Step-by-step explanation:

If AB is parallel to XY, then they have the same slope.

If the slope of AB is 2/3, then the slope of XY is 2/3 too.

Answer:

y = 192

Step-by-step explanation:

Given y varies directly as z and inversely as x then the equation relating them is

y = [tex]\frac{kx}{z}[/tex] ← k is the constant of variation

To find k use the condition y = 16 and z = 2 when x = 42

k = [tex]\frac{yx}{z}[/tex] = [tex]\frac{16(42)}{2}[/tex] = 336

y = [tex]\frac{336z}{x}[/tex] ← equation of variation

When x = 14 and z = 8, then

y = [tex]\frac{336(8)}{14}[/tex] = 192

Answer:

9 purple 10 green

Step-by-step explanation:

20 total- you have a 50 50 chance (50 percent) to get either color

Answer:

x =  0.35   or x = -11.35

Step-by-step explanation:

Points to remember

Solution of a quadratic equation ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/2a

It is given that,  x² = –11x + 4

x² + 11x - 4 = 0

To find the solution

Here a = 1, b = 11 and c = -4

x = [-b ± √(b² - 4ac)]/2a

x = [-11 ± √(11² - 4 * 1 * (-4))]/2*1

 =  [-11 ± √(121 + 16)]2

 = [-11 ± √137]/2

 = [-11 ± 11.70]/2

x = -11 + 11.70  or x = -11 - 11.70

x =  0.35   or x = -11.35

Final answer:

The expression (3x²y³) ³ is found by cubing the coefficient and multiplying each variable's exponent by 3, which results in 27x⁶y⁹.

Explanation:

When we deal with the cubing of exponentials, as in the expression (3x²y³) ³, both the numerical coefficient and the variables with their exponents are raised to the power of 3. The rules of exponents guide us to cube the number 3 and multiply the exponents of x and y by 3.

To cube the number 3, we would calculate 3³, which equals 27. For the variables, we apply the exponent to each exponent: x raised to the 2³ (which is 6) and y raised to the 3³ (which is 9). Hence, the expression (3x²y³) ³ simplifies to 27x⁶y⁹. This demonstrates that when cubing an exponential expression, we obtain a new exponent for each variable by multiplying the original exponent by 3, and we cube the numerical coefficient as well.

Answer:-5/6 -1/6 5/3

Answer:

-3

Step-by-step explanation:

The slope for two points is found by

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

   = (4--2)/(0-2)

  = (4+2)/(0-2)

  = (6/-2)

 =-3

Answer:

The slope is -3

Step-by-step explanation:

[tex]\frac{y}{x}[/tex]

You do the change in y over the change in x

[tex]\frac{-2 - 4}{2 - 0}[/tex]

which equals

[tex]\frac{-6}{2} = -3[/tex]

Answer:

If x = 20, then y = 12.5/20 = 0.625

Step-by-step explanation:

The pertinent relationship is y = k/x, where k is the constant of proportionality.

Subbing 5 for y and 2.5 for x yields 5 = k/2.5, so k = 12.5.

Then the specific relationship fit to this problem is y = 12.5/x.

If x = 20, then y = 12.5/20 = 0.625

ANSWER

The vertex of g(x) is (2,-5).

EXPLANATION

The given function is:

[tex]g(x) = 3 {x}^{2} - 12x + 7[/tex]

The vertex form of this function is:

[tex]g(x) = 3 {(x - 2)}^{2} -5[/tex]

This is of the form

[tex]g(x) = a {(x - h)}^{2} + k[/tex]

where (h,k) is the vertex.

When we to

[tex]g(x) = 3 {(x - 2)}^{2} -5[/tex]

h=2 and k=-5

The vertex of the parabola is (2,-5).

30 seconds/per burger

Answer:

30 seconds

Step-by-step explanation:

4 burgers in 2 mins

1 burger

= 2 ÷ 4

= 0.5 min

= 30 seconds

Answer:

(-7,-5)

Step-by-step explanation:

Converting the circle into the form (x-h)^2+(y-k)^2=r^2, we get

x^2+14x+49+y^2+10y+25=7+25+49

So we get

(X+7)^2+(y+5)^2=81

So the center of the circle is (-7,-5)

Answer:

centre = (- 7, - 5)

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Arrange the equation by placing the x and y terms together

x² + 14x + y² + 10y - 7 = 0 ( add 7 to both sides )

x² + 14x + y² + 10y = 7

Use the method of completing the square

add (half the coefficient of the x/y term)² to both sides

x² + 2(7)x + 7² + y² + 2(5)y + 5² = 7 + 7² + 5²

(x + 7)² + (y + 5)² = 7 + 49 + 25 = 81 ← in standard form

with (h, k) = (- 7, - 5) ← centre of circle

the square root is 13.7 hope this helps!

[tex] \sqrt{ - 188} = 13.7113092 \: i[/tex]

hope that helped you!

Answer:

False

Step-by-step explanation:

Continuous data is data that can take any value within a range, including non-whole number values.

Because the number of tickets sold can only take whole number values, it is not an example of continuous data.

False

I hope this helps you understand continuous data. Have a great day. :)

Answer: False

Step-by-step explanation: Continuous data is data that can be measured. The number of tickets that were sold would only be positive integers meaning that there can't be a fraction of a ticket sold. Since discrete data is data that can be counted, the number of tickets sold would be an example of data that is discrete.

Answer:

[tex]-6x^{2}-78x-252[/tex]  or  [tex]-(6x^{2}+78x+252)[/tex]

Step-by-step explanation:

we have

[tex]-6(x+6)(x+7)[/tex]

Applying distributive property

[tex]-6(x+6)(x+7)=-6[x^{2}+7x+6x+42]\\=-6[x^{2} +13x+42]\\=-6x^{2}-78x-252\\=-(6x^{2}+78x+252)[/tex]

Answer:

The answer is length: 9, width: 5

Step-by-step explanation:

5 x 9 = 45

5 x 4 = 20

20 - 11 = 9

Hope this helps :P

The length of a rectangle is 9 cm and width of the rectangle is 5 cm.

The area of Rectangle is length times of width.

Length of a rectangle is 11 centimeters less than four times its width.

Length=4W-11

Width=W

Area=45

Area=Length×Width

=(4w-11)w

45=4w²-11w

4w²-11w-45=0

After applying a =4, b=-11 and c=-45 in the quadratic formula

we get w=5

Plug in the value of w in length

Length=4W-11

=4(5)-11

=20-11

=9

Hence, the length of a rectangle is 9 cm and width of the rectangle is 5 cm.

To learn more on Rectangle click:

https://brainly.com/question/20693059

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the answer will beeeeeeeeeeeeeeeeee c

The answer to your question is b

ans:-7.54

do u understand

Answer:

-7.44

Step-by-step explanation:

Just do it out