The angle of elevation from a soccer ball on the ground to the top of the goal is 34. If the goal is 8 feet tall, What is the distance from he ball to the goal?

36 cm

Let s represent the side of the square in cm. Then s+3 and s-2 are the sides of the rectangle of interest.

The area of the rectangle is the product of its side lengths:

... rectange area = (s+3)(s-2) = s² +s -6

The area of the square is the product of its side lengths, both of which are s.

... square area = s²

The difference of these areas is 30 cm², so ...

... rectangle area - square area = 30

... (s² +s -6) -(s²) = 30

... s = 36 . . . . . . . . . . . . simplify, add 6

The side of the square is 36 cm.

_____

Check

The rectangle dimensions are 39 cm by 34 cm, so its area is

... (39 × 34) cm² = 1326 cm²

The area of the square is (36 cm)² = 1296 cm²

The difference in areas is (1326 -1296) cm² = 30 cm², as required.

Answer:

c. 12x − 24 = 60

Step-by-step explanation:

x is the number of boxes Krys bought.

12x is the number of pastries in those boxes. 2·12 = 24 is the number of pastries in the boxes Krys kept for herself. Then the number of pastries Krys brought to the party is ....

... 12x -24

We are told that number is 60, so we can use this equation to find x:

... 12x -24 = 60

Answer:

Option C : 12x − 24 =60

Step-by-step explanation:

Given :

Krys bought x boxes of pastries to bring to a party.

Each box contains 12 pastries.

She decides to keep two boxes for herself.

She brings 60 pastries to the party.

To Find : Equation can be used to find the number of boxes, x, Krys bought.

Solution :

Krys bought x boxes of pastries .

Each box contains 12 pastries.

So, total pastries she bought = 12 x

She decides to keep two boxes for herself.

Since 1 box contain 12 pastries .

Thus two box contains pastries = 12*2 =24 pastries

Now total pastries she bought is 12 x . Out of which she decides to keep 24 pastries . after keeping 24 pastries from 12 x pastries she bought 60 pastries to the party i.e.

⇒ 12 x - 24 = 60

Thus,Equation can be used to find the number of boxes, x, Krys bought:

12 x - 24 = 60

Hence Option C is correct .

Answer:

24 gallons

Step-by-step explanation:

18 divided by 3 is 6

6 x 4 = 24

so there are 24 gallons as a whole

You said . . . . . 18 = 3/4 g

Multiply each side by 4 . . . 72 = 3g

Divide each side by 3 . . . 24 = g

600 m

The slope between 1 minute and 2 minutes is ...

... (800 -500)/(2 -1) = 300 . . . . . . m/min

Thus in 20 seconds, 1/3 minute, Jason will fall ...

... (1/3 min)·(300 m/min) = 100 m

This distance is in addition to the 500 m he has already fallen in the first minute.

In 1 min 20 sec, Jason falls 500 m + 100 m = 600 m.

_____

Comment on the graph

We don't expect Jason's rate of fall to change dramatically at the 2-minute mark. We suspect the last point should be (2 2/3, 1000).

Answer:

Mean score for the students = 593.3

Step-by-step explanation:

Name    Score

Julia      650

Andrew 550

Jason    380

Cathy     720

Jessica   710

Robert    550

1) Mean Score = [tex]\frac{Sum of the scores}{Total number of students}[/tex]

= [tex]\frac{650+550+380+720+710+550}{6}[/tex]

= 593.33

2) Upon rounding off to the nearest tenth, we get

Mean Score = 593.3 (since the hundredth digit is lesser than 5, the tenth digit is not increased)

Answer:

593.3

Step-by-step explanation:

Assuming random sample, assuming "point estimate of mean score" means "estimate of mean score in points",

(650+550+380+720+710+550)/6 is 593.3

Sample size 6 population size 25 is irrelevant except to note estimate might not be very good.

B. mx−y=−b

Start with ...

... y = mx +b

Subtract mx.

... -mx +y = b

You want the leading coefficient positive, so multiply by -1.

... mx -y = -b . . . . matches selection B

Answer: B. mx−y=−b

Step-by-step explanation:

The equation of a line in standard form is given by :-

[tex]Ax+By=C[/tex]

, where A is a positive integer , B and C are integers.

The given equation : [tex]y = mx + b[/tex]

, where m is a positive integer.

The convert it into standard form , we subtract y and b from both sides , we get

[tex]y -y-b= mx + b-y-b[/tex]

Simplify,

[tex]-b= mx -y[/tex]

Or we can write it as [tex] mx -y=-b[/tex] → Standard form.

Thus , the equation of line in standard form = [tex] mx -y=-b[/tex] , where m is a positive integer.

Hence, the correct answer is B. mx−y=−b

Answer:

D) 15

Step-by-step explanation:

We know the formula for direct variation is

y=kx

Substituting y=5 and x=4 we can calculate k

5=k4

Divide each side by 4

5/4 =k

Now y= 5/4 x

If x =12

y =5/4*12

y = 15

Answer:

4^x+1

Step-by-step explanation:

because i got it wrong

Answer:

[tex]y= 4^{x+1}[/tex]

Step-by-step explanation:

Answer:

Show ΔBCD ≅ ΔGFE, so ∠C ≅ ∠F. Base angle of an isosceles triangle are congruent, so ΔACF is isosceles.

Step-by-step explanation:

Informally, subtract DE from CE and DF. This will show CD ≅ EF.

Then ΔBCD ≅ ΔGFE by the HL theorem for right triangles.

Corresponding parts of congruent triangles are congruent, namely the angles C and F.

Since base angles of ΔACF are congruent, it is isosceles.

Answer:

C. 1,-1

Step-by-step explanation:

The sum of the coefficient is 0 so x=1 is a root and (x-1) as a factor

so x^4+3x^3+3x^2-3X-4=(x-1)(x^3+4x^2+7x+4)

and the root of that is x=-1 and the factor is (x+1)

SO the answer is: x=1 and x=-1

Answer: -1, 1

Step-by-step explanation:

To solve the polynomial equation x^4 + 3x^3 + 3x^2 - 3x - 4 = 0, do a quick test of polynomials using 1 and -1 in place of x.

This gives the sum of coefficients as zero

Testing with 1: 1 + 3 + 3 - 3 - 4 = 0

Testing with -1: 1 + (-3) + 3 - (-3) - 4

= 1 - 3 + 3 + 3 - 4 = 0

This gives that both (x + 1) and (x - 1) are roots.

(x + 1)(x - 1) = x² - 1 {difference of two squares}

Dividing the polynomial x^4 + 3x^3 + 3x^2 - 3x - 4 by (x² - 1) results in x² - 3x + 4 as quotient. Factorizing this result would give complex roots.

Therefore, x² - 1 = 0

x² = 1

Taking square of both sides of the equation gives

x = ± 1

1 and -1 are the rational roots to the polynomial.

Answer:

132(X) + 64(2X) = $1040.00

Step-by-step explanation:

equations

solution

a. It usually works well to let a variable represent the quantity the problem statement is asking you to find. I like to choose variable names that help me remember what the variable stands for. (x and y rarely do that) So, let's choose "a" for the cost of an adult ticket, and "s" for the cost of a student ticket.

The equations express the relationships described by the problem statement. The first relationship expresses the total revenue in terms of the numbers of tickets sold. You know that multiplying the number of tickets by the cost of the ticket will give the revenue from sales of that ticket. So, the total revenue is ...

... 64a +132s = 1040

The problem statement also tells you the relationship between the costs. An adult ticket is twice the cost of a student ticket, so ...

... a = 2s

These equations are your system of linear equations.

_____

b. The solution can be found using substitution. Since the second equation gives an expression for "a", we can use that in the first equation.

... 64(2s) +132s = 1040

... 260s = 1040 . . . . . . . . simplify

... 1040/260 = s = 4

... a = 2s = 2·4 = 8

An adult ticket costs $8; a student ticket costs $4.

2.54 cm/in

In this context, "constant of proportionality" and "unit rate" mean the same thing.

Answer:

i think it is true and true

Step-by-step explanation:

Answer:

35. False

36. True

Step-by-step explanation:

35. [tex]-3\:<\:-2[/tex]

On the number line [tex]-3[/tex] is to the left of [tex]-2[/tex].

Therefore [tex]-3[/tex] is not greater than [tex]-2[/tex].

[tex]-3[/tex] is rather less than [tex]-2[/tex].

36. [tex]y\leq 3[/tex] includes three as a possible solution.

The reason is that, the inequality contains an equal sign in it, the boundary is also inclusive, therefore 3 is itself a possible solution.

In order words, the statement

[tex]3\leq3[/tex] is a truth statement.

Answer:

The correct option is A. The height of tree is 60 ft.

Step-by-step explanation:

From the given figure it is noticed that the building is creating a right angle triangle from a point and the tree divides the hypotenuse and base in two equal part.

According to midpoint theorem of triangle: In a triangle, if a line segment connecting the midpoints of two sides, then the line is parallel to third side. The length of line segment is half of the length of third side.

Using midpoint theorem of triangle, we can say that the length of tree is half of the building.

[tex]Tree=\frac{1}{2}\times Building[/tex]

[tex]Tree=\frac{1}{2}\times 120[/tex]

[tex]Tree=60[/tex]

Therefore correct option is A. The height of tree is 60 ft.

x² + y² = 50

The circle centered at (h, k) with radius r has equation ...

... (x -h)² + (y -k)² = r²

You have (h, k) = (0, 0), so all we need to do is find r². We can do that by choosing r² so that the equation is true at the given point.

... x² + y² = (5)² + (-5)² = 25 + 25 = 50

Your equation is x² + y² = 50.

-7 = 7d - 8

Add 8 to both sides.

1 = 7d

Divide both sides by 7.

Answer:

$3.46

Step-by-step explanation:

Unpaid February balance = $345.67

Annual Percentage Rate(APR) = 13.99 %

                                                  = [tex]\frac{13.99}{100}[/tex]

                                                  = 0.1399 (converted into decimal)

Periodic (monthly) interest rate = [tex]\frac{0.1399}{12}[/tex]  (since there are 12 months in a year)

                                                    = 0.01

Interest he owes on his unpaid February balance of $345.67

       = Periodic (monthly) interest rate * unpaid February balance

       = 0.01 * 345.67

       = 3.456

       = $3.46     (rounded off to the hundredth place)

Answer:

6/x weeks

Hope this helps

Answer:

6/x weeks

Step-by-step explanation:

This is the correct answer, credits to the other person who answered.

[tex]\bf \textit{exponential form of a logarithm} \\\\ log_a b=y \implies a^y= b\qquad\qquad a^y= b\implies log_a b=y \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ y=\log_4(0.25) ~\hfill 0.\underline{25}\implies \cfrac{025}{1\underline{00}}\implies \cfrac{1}{4}\implies 4^{-1} \\\\\\ y=\log_4\left( 4^{-1} \right)\implies 4^y=4^{-1}\implies y=-1[/tex]

Answer:

B) 6

Step-by-step explanation:

It is 45, 45, 90 degrees right triangle, the ratio of the triangle 1:1:√2

Hypotenuse = 3√2*√2

= 3*2

= 6

Thank you.

Answer:

6

Step-by-step explanation:

Hypotenuse is the side that is opposite of the 90 degree angle (the longest side as well).

As seen in the triangle, the side opposite of 45° angle is known AND we want to find the hypotenuse.

Which trigonometric ratio relates opposite with hypotenuse?

SINE

We can write:

[tex]sin(A)=\frac{opposite}{hypotenuse}\\sin(45)=\frac{3\sqrt{2}}{h}[/tex]

We let hypotenuse be [tex]h[/tex]. Also we know that [tex]sin(45)=\frac{1}{\sqrt{2}}[/tex]

Now we can solve for [tex]h[/tex]:

[tex]sin(45)=\frac{3\sqrt{2}}{h}\\h*sin(45)=3\sqrt{2}\\h=\frac{3\sqrt{2}}{sin(45)}\\h=\frac{3\sqrt{2}}{\frac{1}{\sqrt{2}}}\\h=3\sqrt{2}*\frac{\sqrt{2}}{1}\\h=6[/tex]

(we used the identity [tex](\sqrt{a})(\sqrt{a})=a[/tex])

2nd answer choice is right. Hypotenuse is 6.

Answer:

7x^2y(x +2xy^2 -y)

Step-by-step explanation:

7, x^2, and y are factors of every term, so we can start by factoring those out.

... = 7x^2y(x +2xy^2 -y)

The trinomial does not factor further, so this is it.

Answer:

7x^2y(x +2xy^2 -y)

Step-by-step explanation:

7x^3y +14x^2y^3 − 7x^2y^2

WE find out GCF

7x^3y= 7*x*x*x*y

14x^2y^3= 7*2*x*x*y*y*y

7x^2y^2 = 7 *x*x*y*y

GCF is 7x^2y

Factor out GCF from the given expression. when we factor out 7x^2y we divide each term by GCF. we put GCF 7x^2y outside

7x^2y(x +2xy^2 -y)

Answer:

a) [tex]-5x^{2}+3x+27[/tex]

b) [tex]-5x^{2}+3x+9[/tex]

Step-by-step explanation:

a) Let the required polynomial be p(x).

We have the relation, [tex]5x^{2}-3x-9[/tex] + p(x) = 18

i.e. p(x) = 18 [tex]-5x^{2}+3x+9[/tex]

i.e. p(x) = [tex]-5x^{2}+3x+27[/tex]

b) Let the required polynomial be q(x).

We have the relation, [tex]5x^{2}-3x-9[/tex] + q(x) = 0

i.e. q(x) = 0 [tex]-5x^{2}+3x+9[/tex]

i.e. q(x) = [tex]-5x^{2}+3x+9[/tex]

Answer:

(a) [tex]-5x^2+3x+27[/tex]

(b)  [tex]-5x^2+3x+9[/tex]

Step-by-step explanation:

(a)

Let the polynomial be Q(x).

Given polynomial P(x) = [tex]5x^2-3x-9[/tex]

As per the given statement: A polynomial(Q(x)) which, when added to the polynomial [tex]5x^2-3x-9[/tex], is equivalent to 18.

[tex]P(x)+Q(x) = 18[/tex]

[tex]5x^2-3x-9 +Q(x) = 18[/tex]

⇒[tex]Q(x) = 18 -(5x^2-3x-9)[/tex]

or

[tex]Q(x) = 18 -5x^2+3x+9[/tex]

Simplify:

[tex]Q(x) =-5x^2+3x+27[/tex]

Therefore, the polynomial is,  [tex]-5x^2+3x+27[/tex]

Check:

[tex]P(x)+Q(x)[/tex] = [tex]5x^2-3x-9 +(-5x^2+3x+27)[/tex]

                      = [tex]5x^2-3x-9 -5x^2 +3x+27[/tex]

                       = 18

(b)

Let the polynomial be Q(x).

Given polynomial P(x) = [tex]5x^2-3x-9[/tex]

As per the given statement: A polynomial(Q(x)) which, when added to the polynomial [tex]5x^2-3x-9[/tex], is equivalent to 0.

[tex]P(x)+Q(x) = 0[/tex]

[tex]P(x) = -Q(x)[/tex]

⇒[tex]Q(x) = -(5x^2-3x-9)[/tex]

or

[tex]Q(x) = -5x^2+3x+9[/tex]

Therefore, the polynomial is,  [tex]-5x^2+3x+9[/tex]

Check:

[tex]P(x)+Q(x)[/tex]=[tex]5x^2-3x-9 +(-5x^2+3x+9)[/tex]

                      = [tex]5x^2-3x-9-5x^2 +3x+9[/tex]

                       = 0

Answer:

∠ABC ≅ ∠XYZ

Step-by-step explanation:

Given: ΔABC is similar to ΔXYZ.

If two triangles are similar, then

1. the corresponding angles are congruent

2. the corresponding sides are proportional

From the options given,

AB ≅ XY is not applicable for similar triangles. Hence the option is wrong.

∠ABC ≅ ∠XYZ since  ΔABC ≅ ΔXYZ

Hence the answer is ∠ABC ≅ ∠XYZ

The equation 15x + 8y = 56 can be rewritten in slope-intercept form (y = mx + b) as y = -15/8x + 7, where -15/8 is the slope and 7 is the y-intercept.

To convert the equation 15x + 8y = 56 into slope-intercept form (y = mx + b), we want to isolate y. Here are the steps:

In this equation, -15/8 is the slope, and 7 is the y-intercept. This means the line intersects the y-axis at y = 7, and for every 8 units increase in x, there is a 15 unit decrease in y, as the slope is negative.

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Answer:

D -5/12

Step-by-step explanation:

2 1/2 = 2·(2/2) + 1/2 = 5/2

Dividing by 6 is the same as multiplying by 1/6.

... (-5/2)×(1/6) = -5·1/(2·6) = -5/12

Answer:

42.5

Step-by-step explanation:

76.8% × ? = 32.64

? =

32.64 ÷ 76.8% =

32.64 ÷ (76.8 ÷ 100) =

(100 × 32.64) ÷ 76.8 =

3,264 ÷ 76.8 =

42.5

To solve for the number that 76.8% of it equals 32.64, you can write an equation and solve for x: 0.768 * x = 32.64. Dividing both sides by 0.768 gives x = 42.5.

The question asks about a percentage of a number, which is a math concept. If 76.8% of a number equals 32.64, you can use basic algebra to find that number. Let's call it 'x'. You can write it as an equation: 0.768 * x = 32.64. Solving for x, divide both sides of the equation by 0.768.

x = 32.64 /0.768

When you perform this calculation, you'll find that x is approximately 42.5. So, 76.8% of 42.5 is approximately 32.64.

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Answer:

6 cm,12 cm,8 cm

Step-by-step explanation:

add the perimeter of the first triangle to get 65

then divide 65 by 26 to get 2.5

then divide all the side lengths by 2.5

15/2.5=6

20/2.5=8

30/2.5=12

The lengths of the sides of a similar triangle that has a perimeter of 26 cm are 6 cm, 8 cm, and 12 cm and this can be determined by using the given data.

Given :

The lengths of the sides of a triangle are 15 cm, 20 cm, 30 cm.

The following steps can be used in order to determine the lengths of the sides of a similar triangle that has a perimeter of 26 cm:

Step 1 - The formula of the perimeter of the triangle is given below:

[tex]\rm P = a + b + c[/tex]

where a, b, and c are the length of the sides of the triangle.

Step 2 - Now, determine the perimeter of the triangle whose sides are 15 cm, 20 cm, 30 cm.

P' = 15 + 20 + 30

P' = 65 cm

Step 3 - Now, divide both the perimeters of the triangles, that is:

[tex]=\dfrac{65}{26}[/tex]

= 2.5

Step 4 - So, the side length of the sides of a similar triangle is given below:

[tex]\rm \dfrac{15}{2.5} = 6\;cm[/tex]

[tex]\rm \dfrac{20}{2.5}=8 \;cm[/tex]

[tex]\rm \dfrac{30}{2.5}=12\;cm[/tex]

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Answer:

$51

Step-by-step explanation:

To solve this, we must divide the total amount of miles by the miles per gallon, and multiply that by the cost per gallon.

430 / 26 = 16.53

Because this is talking about gallons, we should round up to 17.

17 * 3 = 51

It costs $51 to drive 430 miles when gasoline costs $3 per gallon.

Answer:

$49.62

Step-by-step explanation:

We know that the car travels for 26 miles in 1 gallon. So we will find out the number of gallons it requires to travel for 430 miles by simple ratio method.

[tex]\frac{1 gallon}{x} =\frac{26 miles}{430}[/tex]

[tex]x=\frac{430}{26}[/tex]

[tex]x=16.54[/tex]

Now that we know that the car needs 16.54 gallons of gasoline to drive for 430 miles, we can simply multiply the number of gallons by the cost per gallon to find its total cost.

Total cost of gasoline to drive 430 miles = 16.54 x 3 = $49.62

Answer:

[tex]<\:3[/tex] is the angle of elevation from the boat to the lighthouse.

Step-by-step explanation:

From the boat, the angle through which you will raise your head to see the light house is the angle of elevation, which is [tex]<\:3[/tex].

See graph for the illustration.

The correct answer is A

Answer:

The angle of elevation from the boat to the lighthouse is:

First option: <3

Step-by-step explanation:

The angle of elevation from the boat to the lighthouse is the angle of the visual since the boat to the lighthouse with the horizontal, according with the graph this angle is <3 (First option)