In ΔPQR, the measure of ∠R=90°, the measure of ∠P=40°, and QR = 5.1 feet. Find the length of RP to the nearest tenth of a foot.

Answer:

4x^2 - 4x + 1

Step-by-step explanation:

Step-by-step explanation:

The Science of Thought is the book

Answer:

Step-by-step explanation:

A regular polygon is a polygon that is both equiangular and equilateral. All sides are equal length placed around a common center so that all angles between sides are also equal. When the number of sides, n, is equal to 3 it is an equilateral triangle and when n = 4 is is a square.

Answer:

Step-by-step explanation:

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards.  One rushed 4 times as many yards as the other.  Let x and y represent the number of yards each individual player rushed. this is the equation that was used

         x + y = 1550

         y  = 4x

Answer:

the coordinates of b if it is reflected over the x-axis (-2,5)

Answer:

I might be wrong but since ur in a rush: 173

Step-by-step explanation:

Answer:

287.25 miles in 5.75 hours

Step-by-step explanation:

so he was first driving at 48mph because 168/3.5=48

5 miles per hour faster than that is 53mph

53*2.25=119.25

then we add 119.25 and 168

Answer:

7/8

Step-by-step explanation:

U have to use the highest common factor and the lowest common denominator

Answer:

[tex] \frac{7}{8} = 0.875 [/tex]

Step-by-step explanation:

devide the numerator and denumerator by nine

Answer:

y = -1/5x -8/5

Step-by-step explanation:

(-3,-1) and (2,-2)

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

m = ( -2 + 1)/(2 + 3)

m = (-1)/(5)

m = -1/5

y - y1 = m(x - x1)

y + 1 = -1/5(x + 3)

y + 1 = -1/5x -3/5

y = -1/5x -8/5

For each t-shirt sold, which I'll call t, 8th grade makes $15.

For each hat sold, which I'll call h, 8th grades makes $5.

They want to raise $900

A: The equation to represent this situation is 15t+5h=900 because if 8th grade adds up all the profits from both hats and t-shirts, the goal is to make $900, so the total profit from shirts and hats should equal 900 dollars.

B: I'm just going to choose random numbers. Let's say nobody wanted to buy a hat from the 8th graders (h=0). You'd end up with

15t+5(0)=900

15t=900

t=60 - If they sold 0 hats they would have sold 60 shirts to raise $900

Now let's say it was the other way around - nobody wanted to buy t-shirts

15(0)=5h=900

5h=900

h=180 - If they sold 0 t-shirts they'd have to sell 180 hats to raise $900

Finally let's say they sold 30 t-shirts

15(30)+5h=900

450+5h=900

5h=450

h=90 - They'd have to sell 30 t-shirts and 90 hats to raise $900

Answer:

x=9, -9

Step-by-step explanation:

Use difference of squares to the denominator.

so

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

If you plug 9 or -9 for x, the denominator becomes 0, meaning that the value would be undefined. Thus, if would not be in the domain of g.

So, x=9, -9

Answer:

B .3 I m not sure about it but I think it's 3

Answer:

When x  =1, y = 3(1) + 4 = 7

When x = 2, y = 3(2) + 4 = 10

When x = 3, y = 3(3) + 4 = 13

Answer:

Maximum rate change |[tex]\nabla[/tex]f| = √65

Direction = ( 1, 8 ) / √65

i.e Maximum rate change is √65 and it occurs in a direction of ( 1, 8 )

Step-by-step explanation:

Given that;

f(x, y) = 4y √x, (4, 1)

{ x=4 and y=1 }

Maximum rate of change occurs with the gradient vector;

[tex]\nabla[/tex]f = [ df/dx, df/dy ] = [ 2y/√x, 4√x ]

we substitute in our value of x and y

[tex]\nabla[/tex]f =  2(1)/√4, 4√4

[tex]\nabla[/tex]f = 2/√4, 4√4

[tex]\nabla[/tex]f = ( 1, 8 )

Maximum rate change |[tex]\nabla[/tex]f| = | ( 1, 8 ) | = √( 1² + 8² ) = √(1 + 64)

Maximum rate change |[tex]\nabla[/tex]f| = √65

Direction = [tex]\nabla[/tex]f / |[tex]\nabla[/tex]f|

we substitute

Direction = ( 1, 8 ) / √65

i.e Maximum rate change is √65 and it occurs in a direction of ( 1, 8 )

Answer:

(-6, -6)

Step-by-step explanation:

Find the coordinates of the point where the lines with equations y=x and y=-6 intersect.

The lines intersect at y = y

Equating the right hand side of both expressions we have;

x  = -6

Since y = x, hence y = -6

The required coordinate where they intersect is at (-6, -6)

Answer:

$615.54

Step-by-step explanation:

Step 1

Write your problem.

577.98 x 6.5% = ?

Step 2

Convert the % to a decimal:

6.5% to 0.065

Step 3

Rewrite the problem with decimal replacing the percentage.

Now the problem looks like this:

577.98 x 0.065 = 37.56

This problem gives the amount of the tax.

Step 4

Add the original price with the tax amount:

577.98 + 37.56 = $615.54 (total cost)

Answer:

its blurry

Step-by-step explanation:

Step-by-step explanation:

7/10 in percentage form is 70%

70/100 in percentage form is 70%

Simple as that

It is proved that the given decimals are equivalent decimals.

Given are the fractions -

7/10 and 70/100

We have the following fractions -

A = (7/10) = 0.7

B = 70/100 = (7 x 10)/(10 x 10) = (7/10)

B = (7/10) = 0.7

It can be seen that fraction A equals to B.

Therefore, it is proved that the given decimals are equivalent decimals.

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Answer:

W + 5

Step-by-step explanation:

Given a number, W

An increase in W by a constant 5 ; can be expressed as ;

W plus the constant value increase

Hence,

Increase in W by 5 equals ;

W + 5

Answer:

1/6

Step-by-step explanation:

The die is rolled once, so it is 1 out of the total number on the die ie 6, as a die has only faces or sides so its obvious out of these 6 faces only one will show.

Answer:

The area of the triangle is 84.511 square units.

Step-by-step explanation:

First step, we need to calculate lengths of line segments AB, BC and AC by Pythagorean Theorem:

AB:

[tex]AB = \sqrt{(12-0)^{2}+(3-8)^{2}}[/tex]

[tex]AB = 13[/tex]

BC:

[tex]BC = \sqrt{(7-12)^{2}+(-9-3)^{2}}[/tex]

[tex]BC = 13[/tex]

AC:

[tex]AC = \sqrt{(7-0)^{2}+(-9-8)^{2}}[/tex]

[tex]AC \approx 18.385[/tex]

Now, we can determine the area of the triangle ([tex]A[/tex]) by Heron's formula:

[tex]A = \sqrt{s\cdot (s-AB)\cdot (s-BC)\cdot (s-AC)}[/tex] (1)

[tex]s = \frac{AB+BC+AC}{2}[/tex] (2)

Where [tex]s[/tex] is the semiperimeter of the triangle.

If we know that [tex]AB = 13[/tex], [tex]BC = 13[/tex] and [tex]AC \approx 18.385[/tex], then the area of the triangle is:

[tex]s = 22.193[/tex]

[tex]A = 84.511[/tex]

The area of the triangle is 84.511 square units.

Answer:

1440 different arrangements are possible.

Step-by-step explanation:

Number of arrangements of n elements:

The number of arrangements of n elements is given by:

[tex]A_{n} = n![/tex]

In this question:

6 couples, in which each can be positioned in 2 ways(him/her or her/him). So

[tex]T = 2A_{6} = 2*6! = 1440[/tex]

1440 different arrangements are possible.

Answer:Just multiply Step-by-step explanation:do 12x10x20=2,400

Answer:

x=27

Step-by-step explanation:

It’s a ratio:

9.9/11=x/30

cross multiply

11x=297

x=27

Answer:

R11 303

Step :

Find 11% of R12 700

R12 700 × 11/100

=R1 397

then substract the 11% from R12 700

R12 700 - R1 397

=R11 303

The sum of the measures of the interior angles of a 20-sided figure is 3240.

What are Interior angles ?

An interior angle of a polygon is an angle that is created between two of the polygon's adjacent sides. The interior angle of a polygon is also known as the angle measured at the interior of a polygon.

the number of sides of given polygon is 20.

we know that, sum of the measures of the interior angles can be found by using formula : (n-2) × 180

where n= no. of sides of given polygon

So, sum of the measures of the interior angles of 20 sided figure :

     = (n-2) × 180

     = (20-2) × 180

     = 18 × 180

     = 3240 .

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Answer:

$123.66

Step-by-step explanation:

53 divided by 3 is 17.66, which is how much one ticket will cost. 17.66 multiplied by 7 is 123.66