The sail on a boat is triangular and its area is 216 feet. If the length of the base of the sail is 18 feet, find its
height.

Answer:

7km

Step-by-step explanation:

[tex] \frac{1}{3} x + \frac{1}{4} x = \frac{4}{12} x + \frac{3}{12} x = \frac{7}{12} x \\ \\ \\ x - \frac{7}{12} x = \frac{12}{12} x - \frac{7}{12} x = \frac{5}{12} x \\ \\ \frac{5}{12} x = 5 - - - > x = 12[/tex]

[tex]12 \times \frac{7}{12} = 7[/tex]

Answer:

no (see below)

Step-by-step explanation:

Not all of the months have the same amount of days therefore Thomas does not work the same percentage of days each month.

Answer:

1/4.

Step-by-step explanation:

3/4 of 1/3

= 1/3 * 3/4

= 3/12

= 1/4

Answer:

C

Step-by-step explanation:

vertex form:

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

the negative sign in front of x^2 is also -1, which is the "a". A controls if the parabola will opek up or down, and the width of the function. In this problem, the parabola opens down. the -3 corresponds to "k" in vertex form. K is the vertical shift or the y coordinate of the vertex. If k is positive it moves up, and if it is negative it moves down. Because of the -3, the vertex of the parabola will move down 3 units on the y-axis.

Answer:

m = 7/6

Step-by-step explanation:

Find coordinates of two points:

(-2,3)

(-8,-4)

Slope formula =

y1 - y2 / x1 - x2

So...

-4-3 / -8 -- 2

-7 / -6

7/6

remember brainliest and have a great day!

#1

[tex]\\ \rm\Rrightarrow \dfrac{WX}{GH}=\dfrac{UY}{JI}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{8}{14}=\dfrac{UY}{28}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{8(28)}{14}=UY[/tex]

[tex]\\ \rm\Rrightarrow UY=8(2)=16[/tex]

#2

[tex]\\ \rm\Rrightarrow \dfrac{UV}{UY}=\dfrac{FJ}{JI}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{UV}{16}=\dfrac{21}{28}[/tex]

[tex]\\ \rm\Rrightarrow UV=\dfrac{3}{4}\times 16[/tex]

[tex]\\ \rm\Rrightarrow UV=3(4)=12[/tex]

#3

[tex]\\ \rm\Rrightarrow \dfrac{WX}{XY}=\dfrac{GH}{HI}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{8}{XY}=\dfrac{14}{35}=\dfrac{2}{5}[/tex]

[tex]\\ \rm\Rrightarrow 2XY=40[/tex]

[tex]\\ \rm\Rrightarrow XY=20[/tex]

Answer:

UY = 16

UV = 12

XY = 20

Step-by-step explanation:

If UVWXY ~ JFGHI

then:

UV~JF

VW~FG

WX~GH

XY~HI

UY~JI

The only pair of sides that both have measures is WX and GH:

WX = 8

GH = 14

⇒ GH/WX = 14/8 = 1.75

Therefore, JFGHI is and enlargement of UVWXY by scale factor 1.75

As IJ = 28

⇒ UY = 28 ÷ 1.75 = 16

As JF = 21

⇒ UV = 21 ÷ 1.75 = 12

As HI = 35

⇒ XY = 35 ÷ 1.75 = 20

[tex]y= f(x) = 3^x+1\\\\\text{Replace x with y and solve for y}\\ \\~~~~~~x=3^y+1\\\\\implies 3^y = x-1\\ \\\implies \ln(3^y) = \ln(x-1)\\\\\implies y \ln 3= \ln(x-1)\\\\\implies y= \dfrac{\ln(x-1)}{\ln 3}\\\\\implies f^{-1}(x) = \dfrac{\ln(x-1)}{\ln 3}[/tex]

The time it would take for Rudy to have the same number of each punch card is 1 week.

The number of punches on each card Rudy would have is 8 punches.

The equation that represents the number of punches on the tea punch card is: 1 + 7t

The equation that represents the number of punches on the coffee punch card is: 2 + 6t

Where t represents the number of weeks

When both cards would have the same amount of punches, the two above equations would be equal:

1 + 7t = 2 + 6t

To find the value of t, take the following steps:

Combine similar terms

7t - 6t = 2  - 1

t = 1 week

Number of punches on each card = 1 + 7(1) = 8 punches

To learn more about when the two different variables would have the same amount, please check: https://brainly.com/question/25711114

Answer:

$68

Step-by-step explanation:

Mrs. reynolds now has 68 dollars. 153-105=48. 48+20=68

Answer:

She has $68 dollars remaining

Step-by-step explanation:

(no bar diagram needed, lol jk.)

anyways she started off with 153, right?

She then buys a bike worth $105; thats -$105  which leaves here with $48 dollars

Then ooo its her lucky day, she finds a $20 dollar bill, you add it to $48 (+$20) , now she has $68 dollars in total.

<3

Answer:

x = 25/3; y = -5/3

Step-by-step explanation:

You did well so far by multiplying both sides of the first equation by 2.

Now notice that you have -2y in the new first equation and 2y in the second equation. -2y and 2y add to 0.

Now add the equations to eliminate y.

      2x - 2y = 20

(+)   4x + 2y = 30

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

      6x         = 50

6x/6 = 50/6

x = 50/6 = 25/3

2x - 2y = 20

2(25/3) - 2y = 20

50/3 - 2y = 60/3

-2y = 60/3 - 50/3

-2y = 10/3

-2y/2 = (10/3)/(-2)

y = -5/3

Solution: x = 25/3; y = -5/3

Answer:

4 inches

Step-by-step explanation:

The scale is 1:3 based on that info, x:12

There is a 4-factor increase, meaning x=4

The Zoo is 16 Inches from the school

Answer:

[tex]\frac{9}{x-3}[/tex]

Convert the problem into split up expressions.

[tex]\frac{18}{2}(x - 6)[/tex]

Take both 6 and 18's most common factor here, 2, and divide by 2 to simplify.

[tex]\frac{18}{2} = 9\\\\\frac{6}{2} = 3[/tex]

Cancel.

18 becomes 9

6 becomes 3

The equation turns into:

[tex]\frac{9}{x - 3}[/tex]

note that because we, "canceled" 2, that also means it does not appear in the simplified form since it was a factor.

1. At an annual interest rate of 17.11%, an average family needs 74 months to settle $7,942 at a $175 monthly payment.

2. The total interest is $4,932.10.

The monthly payment is the amount paid each month to settle the loan within its maturity period.

The monthly payment can be computed using an online finance calculator.

We can also determine the period of payment using the same online finance calculator as below.

I/Y (Interest per year) = 17.11%

PV (Present Value) = $7,942

PMT (Periodic Payment) = $-175

FV (Future Value) = $0

Results:

N = 73.566

Sum of all periodic payments = $12,874.10

Total Interest = $4,932.10

Thus, while it will take 74 months for the average American family to pay off the loan of $7,942 with a monthly payment of $175 at 17.11% interest, the total interest paid is $4,932.10.

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Answer:

19/100

Step-by-step explanation:

Answer:

19/100

Step-by-step explanation:

The answer is 19/100 because the percentage should be out of 100. Therefore, the fraction is 19/100.

Answer:

x = 0.75

Step-by-step explanation:

first make the x term the subject

-7 = 12x - 16

-7 + 16 = 12x

add the like terms

9 = 12x

solve for x

9÷ 12 = 12x ÷ 12

0.75 = x

Answer:

50 * 30 = 1500

Answer:

Actual Product =54*31= 1,674

Estimated Product = 50*30=1,500

Step-by-step explanation:

The new center is 5 units away from the original, hence we added 5 to the x-value.

If you notice the sides of the new triangle are twice the size of the original one, meaning that it was dilated by a scale factor of 2.

Answer:

A) 175π / 9 squared inches,

Step-by-step explanation:

Radius = 10 inches

AB = BD = 10 = radius

Triangle ABD is isosceles

Angle DAB = Angle BDA = 35 degrees,

Base angles theroem

35 + 35 + x = 180, angles in triangle

x = 180 - 70

x = 110 degrees

Angle DBC is supplementary with ABD

110 + x = 180

x = 70

70 degrees is angle for the sector

70 is 70/360, 7/36 of the circle

The area will also be 7/36 of the circle area

Area of circle = πr^2

Area =  100π

Area of sector = (100π * 7) / 36

Area of sector = 700π / 36

Simplified area = 175π / 9 squared inches

Using the unit circle, it is found that the terminal point of the angle 5pi/4 is given by:

A. [tex]\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)[/tex]

For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].

The angle 5pi/4 is in the third quadrant, as it is greater than pi and less than 1.5pi, in which both the sine and the cosine are negative. Hence, considering the reference angle, we have that:

[tex](\cos{(\left(\frac{5\pi}{4}\right)}, \sin{(\left(\frac{5\pi}{4}\right)}) = (-\cos{(\left(\frac{\pi}{4}\right)}, -\sin{(\left(\frac{\pi}{4}\right)}) = \left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)[/tex]

Hence option A is correct.

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Answer:

A

Step-by-step explanation:

Answer:

They gave her a $6.12 tip

Step-by-step explanation:

You have to multiply the total ($34) by the Percent (18% = 0.18), and then you will have your final answer.

Answer:

[tex]\boxed{8x+6 \: units= base}[/tex]

Step-by-step explanation:

Altitude = 3x

Area = 12x² + 9x

We know that

Area of right triangle = ½ × base × altitude

Then,

12x² + 9x = ½ × 3x × base

[tex]12x ^ { 2 } +9x= \frac{ 3x }{ 2 } \times \: base[/tex]

[tex]\frac{6x\left(4x+3\right)}{3x} = \frac{3x\times \: base}{3x}[/tex]

[tex]\frac{6x\left(4x+3\right)}{3x} = base[/tex]

[tex]\underline{\underline{8x+6 \: units= base}}[/tex]

________

Hope it helps ⚜

Answer:

7π/6, 11π/6

Step-by-step explanation:

2cscx + 17 = 15 + cscx

1. Subtract cscx and 17 from both sides ⇒ cscx = -2

2. cscx = 1/sinx ⇒ 1/sinx = -2

3. Multiply by sinx and divide by -2 ⇒ sinx = -1/2

When is sinx equal to -1/2? ⇒ 7π/6, 11π/6

The solution of the equation 2cosec x+17 = 15+cosec x is 7π/6 and 11π/6.

Given:

Find:

Solution:

2Cosec x + 17 = 15 + Cosec x

⇒ 2Cosec x - Cosec x = 15 - 17

⇒ Cosec x = -2

Now, 1/sinx = -2

   ⇒  sinx = -1/2

we know, sin 30° = 1/2

Since, sinx is negative,

x will be in 3rd and 4th quadrant.

value in 3rd quadrant = 180° + 30° = 210°

value in 4th quadrant = 360° - 30° = 330°

So, x = 210° = 210 * π/180 = 7π/6

Also, x = 330° = 330 * π/180 = 11π/6

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Answer:

  A"(1, -2)

Step-by-step explanation:

In addition to the translation transformation given, you are asked to transform the figure further by rotating it 180° about the origin. The translation for that is ...

  (x, y) ⇒ (-x, -y)

Then the composition of the two transformations is ...

  (x, y) ⇒ (-(x -5), -(y -1)) = (-x +5, -y +1)

__

Applied to the given point(s), we have ...

  (x, y) ⇒ (-x +5, -y +1)

  A(4, 3) ⇒ (-4 +5, -3 +1) = A"(1, -2)

  B(1, 1) ⇒ (-1 +5, -1 +1) = B"(4, 0)

The coordinates of A" after translation and rotation are (1, -2).

Answer:

0; 3.

Step-by-step explanation:

1) if to substitute x=1 into the given equation, it is possible to calculate the value of 'm':

1-m²-m+1=0; ⇔ m²+m-2=0; ⇒ m₁=-2; m₂=1;

2) if m=-2 and m=1, then the initial equation is:

x²-4x+3=0 or x²-x=0;

3) according to the item 3), the 2d root is:

x₂=3 or x₂=0.

Answer:

6

Step-by-step explanation:

once you replace the letters with numbers you get, 81/9-3 and 81/9 is equal to 9 and 9-3=6