Step by step solution

Answer:

a.) r = 60ft

b.) ball_distance = 68ft

Step-by-step explanation:

Use Pythagorean theorem:

(r^2) + (32ft)^2 = (r + 8ft)^2

r^2 + 1024sqft = r^2 + (16ft)×r + 64sqft

960sqft = r×(16ft)

(960sqft) / (16ft) = r

r = 60ft

Radius is green. Ball is 8ft further than green. 68ft.

============================================

Explanation:

Since we have an isosceles right triangle, the the length of the hypotenuse (let's call it y) is equal to sqrt(2) times the leg length x.

In other words, [tex]y = x*\sqrt{2}[/tex]

If we replaced y with 3*sqrt(2), then we could say,

[tex]y = x*\sqrt{2}\\\\3\sqrt{2} = x*\sqrt{2}[/tex]

in which we can see that x = 3 must be the case. Or you could divide both sides of that last equation by sqrt(2) to find x = 3.

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

Another method:

We'll use the pythagorean theorem

[tex]a^2+b^2 = c^2\\\\x^2+x^2 = \left(3\sqrt{2}\right)^2\\\\2x^2 = 3^2*\left(\sqrt{2}\right)^2\\\\2x^2 = 9*2\\\\2x^2 = 18\\\\x^2 = 18/2\\\\x^2 = 9\\\\x = \sqrt{9}\\\\x = 3\\\\[/tex]

We get the same answer as before.

Answer:

The answers are options A and C.

They are (-2,0) and (0,0).

Step-by-step explanation:

x-intercept

(-2,0) and (0,0)

Answer:

8/x-6

Step-by-step explanation:

When it says a number fewer, that means to put it behind rather than in the front.

Hope this helps!!:)

Answer:

The expression to represent the phrase is 8/x - 6.

Answer:

i think (4,2)

Step-by-step explanation:

Given:

A line passes through the point (1,4) and is parallel to the x-axis.

To find:

The equation of the line.

Solution:

If a line is parallel to x-axis, then the line is a horizontal line. We know that the slope of a horizontal line is always 0. So, the slope of the required line is 0.

The point-slope form of a line is:

[tex]y-y_1=m(x-x_1)[/tex]

Where, m is the slope and [tex](x_1,y_1)[/tex] is the point.

The slope of the required line is 0 and it passes through the point (1,4). So, the equation of the line is:

[tex]y-4=0(x-1)[/tex]

[tex]y-4=0[/tex]

[tex]y-4+4=0+4[/tex]

[tex]y=4[/tex]

The required equation is [tex]y=4[/tex].

Therefore, the correct option is B.

Answer:

y=25

Step-by-step explanation:

150=8x+6y

150=8(0)+6y

150=6y

divided by 6 on both sides because what you do to one side you have to do to the other side.

then your left with y=25

Answer:

Simplifying

150 = 8x + 6y

Solving

150 = 8x + 6y

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-8x' to each side of the equation.

150 + -8x = 8x + -8x + 6y

Combine like terms: 8x + -8x = 0

150 + -8x = 0 + 6y

150 + -8x = 6y

Add '-150' to each side of the equation.

150 + -150 + -8x = -150 + 6y

Combine like terms: 150 + -150 = 0

0 + -8x = -150 + 6y

-8x = -150 + 6y

Divide each side by '-8'.

x = 18.75 + -0.75y

Simplifying

x = 18.75 + -0.75y

Step-by-step explanation:

Answer:

[tex]{ \tt{5a - 4b - 2{ (a - (2b + c))}}} \\ = { \tt{5a - 4b - 2a + 4b - 2c}} \\ { \tt{ = (5 - 2)a + ( - 4 + 4)b - 2c}} \\ { \tt{ = 3a - 2c}}[/tex]

Answer:

Step-by-step explanation:

5a - 4b -2[a - 2b + c] = 5a - 4b -2a + 4b - 2c     {Distributive property}

                                  = (5a - 2a) + (4b - 4b) - 2c   {Group like terms}

                                  = 3a - 2c

Answer:

Step-by-step explanation:

Answer:

Sin ? = 4/7

? = arcSin (4/7)

? = 35° (rounded to the nearest degree)

So the answer is 35°

Answered by GAUTHMATH

Step-by-step explanation:

second option is the correct answer

Answer:

The maximum  volume is 35316.4 in^3.

Step-by-step explanation:

Length + width + height is less than equal to 62 inches

Height = width = W

Let the length is L .

[tex]L + W + W = 62 \\\\L= 62 - 2 W\\\\Volume, V = L W H\\\\V = (62 - 2 W)\times W \times W\\\\V = 62 W^2 - 2 W^3\\\\\frac{dV}{dW}=124 W - 6 W^2\\\\So, \frac{dV}{dW} =0\\\\124 = 6 W\\\\W = 20.67 inches[/tex]

So, the maximum volume is

[tex]V =124\times 20.67\times 20.67 - 2 \times 20.67^3\\\\V =52978.86 - 17662.46 = 35316.4 inch^3[/tex]

Answer:

G = 9y

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

18y² = G(2y²)

Step 2: Solve for G

Option 1: Factor

Option 2: Isolate

Answer:

[tex]\boxed {\boxed {\sf G= 9y}}[/tex]

Step-by-step explanation:

We are given the following equation and asked to find the missing factor that makes the equality true.

[tex]18y^3=(G)(2y^2)[/tex]

Essentially, we need to solve for the variable G.

1. Factoring

One method we can use is factoring.

We could factor the expression 18y³ because we know one factor is 2y². Since this is one of the factors, the other must be 9y.

[tex]18y^3=(9y)(2y^2)[/tex]

If we compare this factored version of the expression with the original equation we see that 9y and G correspond, so they must be equal.

[tex]G=9y[/tex]

2. Solving

Another method we could use is solving.

We can solve the original equation for G by isolating the variable.

[tex]18y^3= (G)(2y^2)[/tex]

G is being multiplied by 2y³. The inverse of multiplication is division, so we divide both sides of the equation by 2y³.

[tex]\frac {18y^3}{2y^2}=\frac{(G)(2y^2)}{2y^2}[/tex]

[tex]\frac {18y^3}{2y^2}= G[/tex]

The coefficients are divided as usual and the exponents are subtracted.

[tex]9y= G[/tex]

Answer:

the second option : w should be 25 units

Step-by-step explanation:

the area of the rectangle is length×width = L×W

the perimeter of a rectangle = 2L + 2W

now, we know that the perimeter is 100 units.

and we have to find the best length of W, that will then define L (to keep the 100 units of perimeter) and maximizes the area of the rectangle.

in other words, what is the maximum area of a rectangle with perimeter of 100 (and what are the corresponding side lengths)?

now, w = 625 is impossible. that side alone would be bigger than the whole perimeter.

W = 0 would render the whole rectangle to a flat line with L = 50 because of

100 = 2L + 2W = 2L + 0 = 2L

L = 50

and A = L×W = 50×0 = 0

an area of 0 is for sure not the largest possible area.

w = 50 would cause L = 0

100 = 2L + 2W = 2L + 2×50 = 2L + 100

0 = 2L

L = 0

and with L = 0 the same thing happens as with W = 0 : a flat line with 0 area.

so, the only remaining useful answer is W = 25

100 = 2L + 2W = 2L + 2×25 = 2L + 50

50 = 2L

L = 25

A = L×W = 25×25 = 625 units²

and indeed, the maximum area for a given perimeter is achieved by arranging the sides to create a square.

Total amount she wants to raise = $3200

Amount she'll get for each kilometer = $35

So, number of kilometers she need to run

= Total amount she wants to raise/Amount she'll get for each kilometer

= $3200/$35

= 91.42....

Since her sponser is will donate only for whole kilometers she'll have to run 92 km.

w=-1.5

w=2

Answer:

Solution given:

[tex]\sqrt{2w²-19w+31}+2=7-2w[/tex]

again

keep square root alone

[tex]\sqrt{2w²-19w+31}=7-2w-2[/tex]

solve subtraction of 7-2

[tex]\sqrt{2w²-19w+31}=5-2w[/tex]

Squaring on both side

[tex](\sqrt{2w²-19w+31})²=(5-2w)²[/tex]

2w²-19w+31=5²-2*5*2w+4w²

take terms one side

2w²-19w+31-25+20w-4w²=0

-2w²+w+6=0

2w²-w-6=0

doing middle term factorisation

2w²-(4-3)w-6=0

2w²-4w+3w-6=0

take common from each two term

2w(w-2)+3(w-2)=0

(w-2)(2w+3)=0

either

w=2

or

W=-3/2=-1.5

Answer:

Volume=Area × height

=35×7

volume = {245} m³

OAmalOHopeO

Answer:

Since the area of the triangle(base) is known we now multiply it to the height so we can get the volume.

7 x 35 = 245 m3 is your answer

You can picture it too:

(sorry my drawing is bad with the marker)

Answer:

Below.

Step-by-step explanation:

4^(x+2)+4^(x+1)+4^x

= 4^x*4^2 + 4^x*4 + 4^4

= 4^x(16 + 4 + 1)

= 21*4^x.

As 21 is divisible by 7, 21*4^x is also divisible by 7  for all positive integers of x.

Thus the original expression must be also divisible by 7  for all positive integers of x.

Answer:

140 degrees

Step-by-step explanation:

(n-2) times 180

9-2 times 180

7 times 180

1260

1260/9 = 140

Interior angle sum of the given regular polygon of 9 sides is 1260°.

A regular polygon is a closed figure where all sides are equal. Interior angles of a regular polygon are the angles formed between the edges of the polygon. The formula for calculating the sum of interior angles of a regular polygon = (n-2) * 180

where, n is the number of sides of a regular polygon.

Number of sides in the regular polygon  = 9

n = 9

Sum of interior angle of the regular polygon =

(n-2) * 180 = (9-2) * 180 = 7 * 180 = 1260°

Learn more about polygon here

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Given:

x is a number between 8 and 12 exclusive.​

To find:

The value of x.

Solution:

It is given that x is a number between 8 and 12 exclusive.​ It means the value of x lies between 8 and 12 but 8 and 12 are not included.

[tex]8<x<12[/tex]

The whole numbers for [tex]8<x<12[/tex] range are 9, 10, 11.

Therefore, the values of x are 9, 10, 11 and the value of x in the form of inequality is [tex]8<x<12[/tex].

Answer:

QR=5.25 units

PR=5 units

PQ=6.25 units

Answer:

-1

Step-by-step explanation:

The only variable in this expression is y and it's coefficient, which is the number and it's sign before the term, is -1.

In the expression, 6 and 3 are constants. This is because they have a fixed value and they do not change.

However, the algebraic term y can have different values depending on the equation it is in and is thus known as a variable term.

Although the number '1' is not written, it is implied that the digit 1 (or in this case -1) is there. For example, instead of writing 1x, we can simply write x. The coefficient cannot be zero as if there is zero y, the y term would not exist in the first place.

Given:

Cost of 200 g of mixed nuts = $2.50.

To find:

The price of 450 g of nuts.

Solution:

We have,

Cost of 200 g of mixed nuts = 2.50 dollars

Cost of 1 g of mixed nuts = [tex]\dfrac{2.50}{200}[/tex] dollars

Cost of 450 g of mixed nuts = [tex]\dfrac{2.50}{200}\times 450[/tex] dollars

                                               = [tex]\dfrac{2.50}{4}\times 9[/tex] dollars

                                               = [tex]5.625[/tex] dollars

Therefore, the price of 450 g of nuts is $5.625.

One of the ways to graph this is to use plug in a few x-values and get an idea of the shape. Since the x values keep getting squared, there is an exponential increase on either side of the y-axis. You can see this by plugging in a few values:

When

x=0,f(x)=0

x=1,f(x)=1^2=1

x=2,f(x)=2^2=4

x=3,f(x)=3^2=9

x=4,f(x)=4^2=16

The same holds true for negative x-values to the left of the y-axis since a negative value squared is positive. For example,

x=−1,f(x)=(−1)2=1*−1=1

x=2,f(x)=(−2)2=−2*−2=4

The graph of f(x)=x^2 is called a "Parabola." It looks like this:

[tex]\large\sf \: x + \frac{3x}{2} = 35[/tex]

Find x

________________

[tex]\sf \: x + \frac{3x}{2} = 35 \\ \sf \: \frac{x}{1} + \frac{3x}{2} = 35 \: (take \: LCM \: = 2) \\ \sf \: \frac{2x}{2} + \frac{3x}{2} = 35 \\ \sf \: \frac{2x + 3x}{2} = 35 \\ \sf \: 2x + 3x = 35 \times 2 \\ \sf \: 5x = 70 \\ \sf \: x = \frac{70}{5} \\ \sf \: x = \boxed{ \underline{ 14}}[/tex]

_________________

Answer ⟶ [tex]\boxed{\bf{x= 14}}[/tex]

Answer:

20 degrees

Step-by-step explanation:

One angle is 70 degrees and the other is 90. Angles of a triangle add up to 180. 180 - 70 - 90 = 20. The final angle is 20 degrees.

Answer:

[tex]\angle ARU=40^{\circ}[/tex]

AU=20 units

[tex]m\angle QPA=35^{\circ}[/tex]

Step-by-step explanation:

We are given that

[tex]\angle ARQ=40^{\circ}[/tex]

AT=20 units

Point A is the incenter of triangle PQR.

Incenter is that point where three angle bisector of triangle meets.

AR is the bisector of angle R of triangle PQR.

Therefore, [tex]\angle ARQ=\angle ARU=40^{\circ}[/tex]

All right triangles are similar when two triangles are similar then the ratio of their corresponding sides are equal.

Right angled triangle ATP and Right triangle AUP are similar.

Therefore,

[tex]\frac{AT}{AU}=\frac{AP}{AP}=1[/tex]

[tex]\frac{20}{AU}=1[/tex]

[tex]AU=20[/tex]units

AP is the angle bisector  of angle P of triangle PQR

[tex]\angle APQ=\angle APU[/tex]

[tex]3x+2=4x-9[/tex]

[tex]2+9=4x-3x[/tex]

[tex]x=11[/tex]

Using the value of angle x

[tex]\angle APQ=3x+2=3(11)+2[/tex]

[tex]\angle APQ=35^{\circ}[/tex]

Hence, the measure of angle QPA=35 degree

The incenter of a triangle is the point of intersection of all the three interior angle bisectors of the triangle. This point is equidistant from the sides of a triangle.

Angle ARU = 40 degree

Length of AU = 20

Angle QPA = 35 degree

Here a figure is attached.

Since, AR is angle bisector of angle URK.

So,   ∠ARU = ∠ARK = 40 degree

Since, incenter point is equidistant from the sides of a triangle.

So, AT = AU = AK = 20

Since, PA is angle bisector of angle QPU.

So,  ∠QPA = ∠UPA

    3x + 2 = 4x - 9

    4x - 3x = 9 + 2

        x = 11

Substituting value of x in angle 3x + 2

We get,  ∠QPA = 3(11) + 2 = 35 degree

Learn more:

https://brainly.com/question/1620555

Answer:

8

Step-by-step explanation:

If the diagonal line passes through the origin, that means it is proportional. That means that for every point on the line y/x is constantly the same value. So we have k/2=32/k.

Cross multiply: k^2=64

Square root both sides: k=8

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Answer:

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