Jack went to Disney World and bought 4 balloons for $8. How much will 6 dozen balloons coast?

Answer:B & E

Step-by-step explanation:

We can first rearrange the function to isolate y. Then, we can find the slope as the function is in the form y=mx+b.

[tex]3x-4y=7\\-4y=-3x+7\\y=\frac{3}{4}x-\frac{7}{4}[/tex]

Since parallel lines have the same slope, we can put the slope of 3/4 into the point slope form to get the answer.

For reference, the point-slope form is [tex]y-y_1=m(x-x_1)[/tex]

[tex]y+2=\frac{3}{4}(x+4)\\y+2=\frac{3}{4}x+3\\y=\frac{3}{4}x+1[/tex]

The first line is found in option E, so option E is one of the correct options.

We can also move the x to the other side, as two of the 5 options have both variables on the left (B and C).

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

If we multiply the whole equation by -4, we can get rid of the fraction.

[tex]-4(-\frac{3}{4}x+y)=-4(1)\\3x-4y=-4[/tex]

Hence, option B is also correct.

Each junior  receives 93 score on the test. It is also the average score of the juniors.

Given Information

It is given that 10% of the strength of the class consists of juniors and 90% consists of seniors.

Let us assume the total strength of the class is 100, then,

Number of seniors = 90

Number of juniors = 10

It is also given that the average score of the class = 84

And, average score of the seniors = 83

Another given information is that all the juniors all received the same score, which is their average score. Let it be x.

Average Score of Juniors

Total marks obtained by the seniors = Number of seniors × Average score of seniors

= 90 × 83

= 7470

Total marks obtained by the juniors = Number of juniors × Average score of juniors

= 10x

Average marks on the test = Total marks / Total number of students

⇒ 84 = (7470 + 10x)/100

⇒ 84 × 100 = 7470 + 10x

⇒ 10x + 7470 = 8400

⇒ 10x = 8400-7470

⇒ 10x = 930

⇒ x = 930/10

⇒  x = 93

Thus, each junior scores 93 on the test.

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Answer:

True

Step-by-step explanation:

The relation between the variables in the equation x^4/y=7 is (b) x^4 varies directly as y

The complete question is added as an attachment

From the attached figure, we have the following equation

x^4/y = 7

Multiply both sides of the equation by y

x^4 = 7y

The above represents a direct variation from x^4 to y.

Where 7 represents the variation constant

Hence, the relation between the variables in the equation x^4/y=7 is (b) x^4 varies directly as y

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The result of the evaluation of the equation given in the task content is; x =-2.

It follows from the task content that the equation given whose solution is to be determined is;

3[-x + (2 x +1)]=x-1

The equation can be solved as follows;

-3x + 6x +3 = x-1

2x = -4

x = -2

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Answer:

8(3j - 2).

Step-by-step explanation:

24j-16

GCF = 8

so the answer is

8(3j - 2).

Answer:

w = ±[tex]\sqrt{1/2}[/tex] or w= ±[tex]\sqrt{2}[/tex]

Step-by-step explanation:

if we say some variable y = w^2, we can rewrite the equation to:

2y^2 - 5y + 2 = 0

this can be factored into (2y-1)(y-2) = 0

putting w^2 back in the place of y, that's (2w^2 - 1)(w^2 - 2) = 0

The equation is a fourth degree polynomial, so there are four roots, or four values of w that will cause the equation to equal 0.

If 0 is multiplied by anything, the result is 0, so we set 2w^2 - 1 = 0 and solve for w, which is ±√1/2, then set w^2 - 2 = 0 to get w = ±√2 as our roots

the four solutions are ±√1/2 and ±√2

(because the positive counts as one solution and the negative another solution)

Answer:

y=0.75x+3.75

Step-by-step explanation:

The slope is

[tex] \frac{6 - 4.5}{3 - 1} = \frac{3}{4} [/tex]

Substituting into point-slope form,

y - 6 = 0.75(x - 3)

y - 6 = 0.75x - 2.25

y = 0.75x + 3.75

Answer:

3

Step-by-step explanation:

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (1 - 7)/(3 - 5)

slope = -6/(-2)

slope = 3

Parallel lines have equal slopes.

Answer: 3

Answer:

h(x) = 6x² - 10x - 4

Step-by-step explanation:

h(x) = f(x) g(x)

       = (2x - 4)(3x + 1)

each term in the second factor is multiplied by each term in the first factor, that is

2x(3x + 1) - 4(3x + 1) ← distribute parenthesis

= 6x² + 2x - 12x - 4 ← collect like terms

= 6x² - 10x - 4

that is h(x) = 6x² - 10x - 4

Using a system of equations, the weight of 5 apples, 2 oranges are 4 bananas is given as follows:

B. 1147 gm.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Considering the data given, the equations are:

From the first equation:

3x = 928 - 5y.

x = 309.33 - 1.667y.

From the second equation:

6z = 1088 - 4y

z = 181.33 - 0.667y

Replacing in the third equation:

5x + 3z = 799

5(309.33 - 1.667y) + 3(181.33 - 0.667y) = 799

10.336y = 12961.64

y = 1291.64/10.336

y = 125 gm.

The other weights are:

The weight of 5 apples, 2 oranges are 4 bananas is:

5x + 2y + 4z = 5 x 101 + 2 x 125 + 4 x 98 = 1147 gm, option B.

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Excel uses VAR function for determining the residual variance.

The variation of any error is known as residual variance, also known as unexplained variance or error variance.

Depending on the type of analysis you're doing, the precise definition will vary. For instance, random fluctuations in regression analysis produce volatility around the "actual" regression line.There are two components to a regression line's total variance: variation that can be explained and variance that cannot. Simply put, the residual variance after deducting the variation resulting from the regression from the total variance of the dependent variable is the residual variance.

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The number of times that Derrick batted last season is 188 times.

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentage is a measure of frequency. The sign used to denote percentage is %.

A percentage of 25% here means that twenty five times out of hundred times, Derrick hit the ball. In order to convert a percentage to a decimal, divide the percentage by 100.

Number of times Derrick bat last season = Number of hits last season / percentage of his batting average

47 / 25%

47 / 0.25 = 188

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Answer:

One side is 40 cm and the adjacent side is 50 cm

Step-by-step explanation:

We can use a rectangle because a rectangle is a parallelogram.  Draw a rectangle.  Write the width as x and the length as x + 10.  We find the perimeter by adding all 4 side lengths.

Two side lengths are x and two side lengths are x + 10.  If we add all of this together we get 180

x +x +x+10+x+10 = 180

4x + 20 = 180  Combine the like terms.  There are 4 x's and 10+10 is 20

4x = 160  Subtract 20 from both sides

x  = 40  Divide both sides by 4

So, two sides are 40 and two sides are 50, this will add up to 180

Answer:

40 cm & 50 cm

Step-by-step explanation:

one side = X cm (??)

the other side =X+10 cm

Solve

2(x+x+10)=180

x+x+10=90

2x=80

x = 80/2

x=40

therefore

x+10=50cm

The lateral and total surface areas of the given cone are 753.98 cm² and 1206.31 cm² respectively.

A cone has a height 'h', radius 'r', and slant height 'l'.

The slant height of the cone is obtained by the Pythagorean theorem. I.e.,

l² = h² + r²

Then,

Its lateral surface area(LSA) = πr([tex]\sqrt{h^2+r^2}[/tex]) square units and

Its total surface area(TSA) = πr(r + l) square units

It is given that,

A cone has a height h = 16 cm and radius r = 12 cm

Then, the slant height is calculated by

l² = h² + r²

l  = [tex]\sqrt{h^2+r^2}[/tex]

On substituting,

l = [tex]\sqrt{16^2+12^2}[/tex]

 = [tex]\sqrt{400}[/tex]

 = 20 cm

So,

LSA = πr([tex]\sqrt{h^2+r^2}[/tex])

       = π × 12 × ([tex]\sqrt{16^2+12^2}[/tex])

       = π × 12 × 20

       = 753.98 cm²

and

TSA = πr(r + l)

       = π × 12 × (12 + 20)

       = π × 12 × 32

       = 1206.37 cm²

Therefore, the lateral and total surface areas of the cone with a height of 16 cm and a radius of 12 cm are 753.98 cm² and 1206.37 cm².

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Answer: The lateral area is 240π square centimeters. The total surface area is 384π square centimeters.

Step-by-step explanation:

Answer:

  (c)  5y -17x +99 = 0

Step-by-step explanation:

The median of a triangle is the line through a vertex and the midpoint of the opposite side. The median of ΔXYZ from vertex Y will be the line through point Y and the midpoint of XZ.

The midpoint of XZ is the average of the coordinates of X and Z.

  M = (X +Z)/2

  M = ((1, -2) +(8, -7))/2 = (9, -9)/2 = (4.5, -4.5)

The slope of the median can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

The slope of line YM is ...

  m = (-4.5 -4)/(4.5 -7) = -8.5/-2.5 = 17/5

The point-slope form of the equation of a line is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

The line with slope 17/5 through point Y(7, 4) is ...

  y -4 = 17/5(x -7)

Subtracting the right side, and multiplying by 5 gives ...

  5(y -4) -17(x -7) = 0

  5y -17x +99 = 0 . . . . equation of the median through Y

The distance of the top of the building from a is 163m and that from b is 115m .

Calculating the Perpendicular Distance of the Top From Ground

It is given that the angle of elevations of the building top from a and b are 25° and 37° respectively.

ab = 57m

Let the top of the building be point c and the distance between the building and the point b be x. Then, from the figure, we can deduce the following,

In Δacd, tan 25° = cd/ad

⇒ 0.4663 = cd /(x+57)

⇒ cd = 0.4663(x+57)             ......................... (1)

In Δbcd, tan 37° = cd/x

⇒ 0.7536 = cd/x

⇒ x =cd / 0.7536                   .......................... (2)

Solving for the Distance cd

Substitute the value of in equation (2) to equation (1) to get,

cd = 0.4663 ((cd/0.7536)+57)

cd = 0.4663(cd+42.9552)/0.7536

0.7536cd = 0.4663cd + 20.03

0.7536cd - 0.4663cd = 20.03

0.2906cd = 20.03

cd = 20.03/0.2906

Thus, the distance cd ≈ 68.93m

Finding the Distance cb and Distance ca

In Δacd, sin25° = cd/ca

⇒ 0.4226 = 68.93/ca

ca = 68.93/0.4226

ca = 163.10

∴ The distance ca ≈ 163m

Similarly, in Δbcd, sin37° = cd/cb

⇒ 0.6018 = 68.93/cb

cb = 68.93/0.6018

cb =114.54m

∴ The distance cb ≈ 115m

Therefore, the points a and b are at a distance of 163m and 115m respectively from the top of the building.  

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Answer:

Step-by-step explanation:

(7x-3)(12x-7)

we are solving for x and we are multiplying.

we start with the x's 7x*12x=  84x

-3*-7=21

so now we have

84x+21=0

the 0 is a placer for answering the question

we minus 21 to both sides

84x=-21

now we divide

84/-21= -4

x=-4

Answer:

-500

Step-by-step explanation:

since 501 has a negative sign,add 1 to to the number,the next number will be -500

-501 +1 = -500

successor in this case means a number that succeeds another

Answer:

Step-by-step explanation:

      the answer is on the graph

Answer:

1) [tex]x_1=-1-2\sqrt{2},\ x_2=-1+2\sqrt{2}[/tex]

2) [tex]x_1=\dfrac{-5 - \sqrt{13}}{6},\ x_2=\dfrac{-5 + \sqrt{13}}{6}[/tex]

Step-by-step explanation:

[tex]{\large \textsf{ Quadratic Formula: }}x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\ \Bigg{\|}\ \textsf{when }ax^2+bx+c=0[/tex]

Given quadratic equations:

1. [tex]x^2+2x-7=0[/tex]

2. [tex]4x^2-3=x^2-5x-4[/tex]

1. x² + 2x - 7 = 0

[tex]\implies a=\textsf{1},b=\textsf{2},c=\textsf{-7}[/tex]

Step 1: Substitute the given values into the formula and simplify.

[tex]\begin{aligned}\implies x&=\dfrac{-(\textsf{2})\pm \sqrt{(\textsf{2})^2-4(\textsf{1})(\textsf{-7})}}{2(\textsf{1})}\\\implies x&=\dfrac{-2\pm \sqrt{4-4(-7)}}{2}\\\implies x&=\dfrac{-2\pm \sqrt{4+28}}{2}\\\implies x&=\dfrac{-2\pm \sqrt{32}}{2}\end{aligned}[/tex]

Step 2: Simplify the radicand (under the square root).

[tex]\begin{aligned}x&=\dfrac{-2\pm \sqrt{16\times2}}{2}\\x&=\dfrac{-2\pm 4\times\sqrt{2}}{2}\\x&=\dfrac{-2\pm 4\sqrt{2}}{2}\end{aligned}[/tex]

Step 3: Separate into two solutions and simplify them.

[tex]\implies x_1&=\dfrac{-2 - 4\sqrt{2}}{2},\ x_2&=\dfrac{-2 + 4\sqrt{2}}{2}[/tex]

[tex]\begin{aligned}\implies x_1&=\dfrac{-2}{2}+\dfrac{- 4\sqrt{2}}{2},\ x_2=\dfrac{-2 + 4\sqrt{2}}{2}\\\implies {x_1&=\boxed{-1-2\sqrt{2}},\ x_2=\boxed{-1+2\sqrt{2}} \end{aligned}[/tex]

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

2. 4x² - 3 = x² - 5x - 4

Step 1: Set the equation to zero (by moving the "x² - 5x - 4" to the left).

4x² - 3 - x² + 5x + 4 = 0 [ Combine like terms. ]

3x² + 5x + 4 = 0

[tex]\implies a=\textsf{3},b=\textsf{5},c=\textsf{1}[/tex]

Step 2: Substitute the given values into the formula and simplify.

[tex]\begin{aligned}\implies x&=\dfrac{-(\textsf{5})\pm \sqrt{(\textsf{5})^2-4(\textsf{3})(\textsf{1})}}{2(\textsf{3})}\\\implies x&=\dfrac{-5\pm \sqrt{25-12}}{6}\\\implies x&=\dfrac{-5\pm \sqrt{13}}{6}\end{aligned}[/tex]

Step 3: Separate into two solutions.

[tex]\implies x_1=\dfrac{-5 - \sqrt{13}}{6},\ x_2=\dfrac{-5 + \sqrt{13}}{6}[/tex]

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Answer:

C)  x = 3

Step-by-step explanation:

Given equation:

[tex]5^x=125[/tex]

Rewrite 125 with base 5:  125 = 5³

[tex]\implies 5^x=5^3[/tex]

[tex]\textsf{Apply the one-to-one property of exponents}: \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]

[tex]\implies x=3[/tex]

Answer:

y = |x + 8|

Explanation:

Please see the table attached below.

Answer:y=|x+8|

Step-by-step explanation:

Answer: [tex]110^{\circ}[/tex]

Step-by-step explanation:

[tex]m\angle 20=62^{\circ}[/tex] (linear pair)

[tex]m\angle 11=70^{\circ}[/tex] (angle sum in a triangle)

[tex]m\angle 12=110^{\circ}[/tex] (linear pair)

The expressions for the length and the width of the rectangular garden are 3x + 2 feet, and x + 5 feet respectively where x is the length of the square patch for tomatoes.

A square is a quadrilateral with all four sides equal, and all four angles at 90°, whereas a rectangle is a quadrilateral with opposite pair of sides equal, and all four angles at 90°.

In the question, we are informed that Melissa is planning a rectangular vegetable garden with a square patch for tomatoes.

The side of the square is given to be x feet.

We are asked to write expressions for the length and width of the rectangular garden.

For the length of the rectangle:-

We are informed that she wants the length of the garden to exceed three times the length of the tomato patch by 2 feet.

Thus, the length of the garden can be shown as the expression 3x + 2 feet.

For the width of the rectangle:-

We are informed that she also wants the garden's width to exceed the width of the tomato patch by 5 feet.

Thus, the width of the garden can be shown as the expression x + 5 feet.

Thus, the expressions for the length and the width of the rectangular garden are 3x + 2 feet, and x + 5 feet respectively where x is the length of the square patch for tomatoes.

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The provided question is incomplete. The complete question is:

"Melissa is planning a rectangular vegetable garden with a square patch for tomatoes. She wants the length of the garden to exceed three times the length of the tomato patch by 2 feet. She also wants the garden's width to exceed the width of the tomato patch by 5 feet.

Let x represent the length, in feet, of the square tomato patch.

Write expressions to represent the length and width of Melissa's vegetable garden in terms of x.

Enter the correct answer in the box."

Answer:  [tex]\frac{2}{9}[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt{4} }{3^{3} }[/tex]
The square root of 4 can be written as 2
3 to the third power can be written as 9

So, the answer is [tex]\frac{2}{9}[/tex]

8/9 = 0.888888....

7/18 = 0.388888888889

10/16 = 0.625

Ascending order - means going up, smallest to largest. (Imagine climbing a ladder, where you start of low, then, go higher up the ladder.)

Thus, answer is 7/18, 10/16, 8/9

Hope this helps!

By applying the transformation rules for horizontal and vertical translation, we find that the resulting function is g(x) = cos (x - 7) + 4.

Transformation rules are rules that makes changes on charateristics and behavior of a function to create a new one. Rigid transformations like horizontal and vertical translations are examples of transformation rules. In this question we must apply the following transformation rules to the parent cosine function f(x) = cos x:

Now we proceed to derive the resulting function by applying the rules defined above:

Horizontal translation

f'(x) = cos (x - 7)      (3)

Vertical translation

g(x) = cos (x - 7) + 4     (4)

By applying the transformation rules for horizontal and vertical translation, we find that the resulting function is g(x) = cos (x - 7) + 4.

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Answer:

222

Step-by-step explanation:

Hey there!

250 - {(135 + 34) ÷ (46 - 33)} - 15 

= 250 - 169/(46 - 44) - 15

= 250 - 169/13 - 15

= 250 - 13 - 15

= 237 - 15

= 222

Therefore, your answer should be:

222

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)