how do you solve 8/14 = 2/x

Answer:

∠ RST = 68°

Step-by-step explanation:

Since RT = ST then the triangle is isosceles with 2 base angles congruent

∠ RST = [tex]\frac{180-44}{2}[/tex] = [tex]\frac{136}{2}[/tex] = 68°

Answer:

18 ft

Step-by-step explanation:

Since the triangle is right angled ; we could use trigonometry ;

Using the angle , 40° ; adjacent side, = 14 feets ; hypotenus = x

Cos θ = Adjacent / hypotenus

Cos 40 = 14 / x

0.7660444 = 14 / x

0.7660444x = 14

x = 14 / 0.7660444

x = 18.27

= 18 ( nearest foot)

Answer:

a) 1650 m

b) 1677.05 m

Step-by-step explanation:

Hi there!

1) Determine what is required for the answers

For part A, we're asked for solve for the horizontal distance in which the road will rise 300 m. In other words, we're solving for the distance from point A to point C, point C being the third vertex of the triangle.

For part B, we're asked to solve for the length of the road, or the length of AB.

2) Prove similarity

In the diagram, we can see that there are two similar triangles: Triangle AXY and ABC (please refer to the image attached).

How do we know they're similar?

Therefore, the two triangles are similar because of AA~ (angle-angle similarity).

3) Solve for part A

Recall that we need to find the length of AC.

First, set up a proportion. XY corresponds to BC and AY corresponds to AC:

[tex]\frac{XY}{BC}=\frac{AY}{AC}[/tex]

Plug in known values

[tex]\frac{2}{300}=\frac{11}{AC}[/tex]

Cross-multiply

[tex]2AC=11*300\\2AC=3300\\AC=1650[/tex]

Therefore, the road will rise 300 m over a horizontal distance of 1650 m.

4) Solve for part B

To find the length of AB, we can use the Pythagorean theorem:

[tex]a^2+b^2=c^2[/tex] where c is the hypotenuse of a right triangle and a and b are the other sides

Plug in 300 and 1650 as the legs (we are solving for the longest side)

[tex]300^2+1650^2=c^2\\300^2+1650^2=c^2\\2812500=c^2\\1677.05=c[/tex]

Therefore, the length of the road is approximately 1677.05 m.

I hope this helps!

Answer:

= $1226.25

Step-by-step explanation:

There are 327 students

Each student lunch is $3.75

She needs 327 of these $3.75 lunches

So 327 times $3.75

= $1226.25

Answer:

624,600

Step-by-step explanation:

624,612

612 rounds to 600

624,600

Answer:

624,600

Step by step explanatiom:

cause math

Answer:

it's hypotenuse will be -8

Answer:

the ans has to be 6.........

Answer:

question one:

x = 6.018150231520483

adjacent angle = 7.986355100472928

Step-by-step explanation:

i have no links, but try to search triginometry calculator and pick carbide calculator for fast trigonometry calculations

it automaticly does sin, cos, and tan for you.

Answer:

yes

Step-by-step explanation:

Answer:

the anser is no.b that is 30°

Answer:

90°

Step-by-step explanation:

There's are supplementary angles at point C. These are two angles that add up to 180°. We know this because a straight line makes 180° on both sides. Since we know that the first angle is 150°, we can determine the angle a point C is 30°. This is shown by:

180-150=30

So now we know 1 angle and the other two angles are put into like terms (in this case, multiples of x). It is known that the sum of all angles in a triangle equates to 180°. Using this information we can set up a simple equation.

[tex]3x+2x+30=180[/tex]

Combining like terms, we get:

[tex]5x+30=180[/tex]

Isolating x, we get:

[tex]5x=150[/tex]

Dividing both sides by 5, we get:

[tex]x=30[/tex]

So now we can use this x-value to determine the angle that is being asked. It is shown that angle ABC is equal to 3x. Using the x value we just calculated, we get a final answer of:

[tex]3x=3(30)=90[/tex]

Therefore, the answer is 90°. Hope this helps!

Answer:

I think b

Step-by-step explanation:

Answer:

As x reaches negative infinity y reaches negative infinity

Step-by-step explanation:

So, first off, when looking at graphs, there will always be a infinite end behavior.

This is because either the x or y axis can be set to a infinitly large number.

We can instantly set up a 2 things for this graph.

We see that y NEVER reaches postive infinity. This is because both left and right sides of the graph have downwards slopes.

This removes our second answer, because it is postive infinity for y.

It also removes our first answer, since it is just 5 for y, notn negative infinity.

Finally, it removes our third answer, since it is just 7 for y, not negative infinity.

This leaves D.

D is correct since y reaches negative infinity when x reaches both postive and negative infinity.

D says x is negativly infinite, which fits this.

So D is our answer.

Hope this helps!

Answer:

(a) -1

(b) -2

Step-by-step explanation:

(a) Replace the a's with 1 and the b's with 3 to get 1*3 = 1-3+1 = -1

(b) We already figured out that (1*3) equals -1 so we just need to find -1*2. Using same strategy as part a, replace a and b with -1 and two, respectively. -1*2 = -1-2+1= -2. Hope this helps and sorry if I made a mistake. :)

Answer: [tex]100\ cm^3[/tex]

Step-by-step explanation:

Given

The ratio of mixture of sand and cement is 5:3

If the total volume of mixture is [tex]160\ cm^3[/tex]

Suppose there is 5x and 3x cubic centimeter of sand and cement respectively i.e.

[tex]\Rightarrow 5x+3x=160\\\Rightarrow 8x=160\\\Rightarrow x=20\ cm^3[/tex]

Sand [tex]5x=5\times 20=100\ cm^3[/tex]

So, there is [tex]100\ cm^3[/tex] of sand in the mixture

Step-by-step explanation:

answer is in photo above

Answer:

0.25

Step-by-step explanation:

f(1)=(1/4)^1

0.25

Answer:

Centre = (-1, 5)

radius = 8units

Explanation

The standard form of the equation of a circle is expressed as

x^2+y^2+2gx+2fy+C = 0

Center = (-g, -f)

radius = √g²+f²-C

Given the equation of a circle is x² + y²+ 2x - 10y - 38 = 0.

On comparing

2gx = 2x

2g = 2

g = 2/2

g = 1

2fy = -10y

2f =-10

f =-5

Centre = (-1, -(-5)) = (-1, 5)

radius  = √1²+5²-(-38)

radius = √1+25+38

radius = √64

radius = 8units

Answer:

{-2, -1 , 3}

Step-by-step explanation:

When we have a set like:

{x₁, x₂, x₃}

The mode is the value that appears the most, so if there is no mode, then each value appears just one time.

The median is the middle value, here we know that the median is -1, then we can rewrite the set as:

{x₁, -1 , x₃}

The mean is computed as:

Mean = (x₁ + x₂ + x₃)/3

in this case we know that the mean is 0, then:

0 =  (x₁ + x₂ + x₃)/3

then the numerator must be zero, so:

0 =  (x₁ + x₂ + x₃)

replacing the value of x₂ = -1 we get:

0 = (x₁ - 1 + x₃)

where:

-5 < x₁ < -1 < x₃ ≤ 3

Now we can select the values of x₁ and x₃ such that the sum is equal to zero, and it meets the wanted restrictions.

here we can choose x₃ to be equal to 3 (the maximum allowed value), I do this because I noticed that the other values that are larger than -1 will not work (just with quick math).

then:

0 = x₁ - 1 + 3

Now we can solve this for x₁

0 = x₁ + 2

-2 = x₁

Then the set is:

{-2, -1 , 3}

Answer:

65

Step-by-step explanation:

Since they drove for 2 hours at an average rate of 40 miles per hour, they've travelled [tex]40\cdot 2=80[/tex] miles so far. Therefore, they still have [tex]145-80=\boxed{65}[/tex] miles to go.

Answer:

65

Step-by-step explanation:

Since u traveled for 2 hours at 40 miles per hour, you have traveled for 80 miles. Then u subtract the total miles, 145 by 80

145-80

= 65 more miles

Answer:

4/27

Step-by-step explanation:

F(x) = 4(1/3)^x

Let x =3

F(3) = 4(1/3)^3

Exponents first

F(3) = 4 * 1/27

Then multiply

f(3) = 4/27

Answer:

4/27

Step-by-step explanation:

f(x) = 4(1/3)^x

f(3) = 4(1/3)^3

f(3) = 4(1/27)

f(3) = 4/27

hope that helps

Answer: c

Step-by-step explanation:

Answer:

The equation of the line is:

[tex]y = -\frac{3}{2}x - 2[/tex]

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

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

In which m is the slope and b is the y-intercept.

Slope:

We have two points, (-2,1) and (2,-5). The slope is given by the change in y divied by the change in x. So

Change in y: -5 - 1 = -6

Change in x: 2 - (-2) = 2 + 4 = 4

Slope: [tex]m = \frac{-6}{4} = -\frac{3}{2}[/tex]

So

[tex]y = -\frac{3}{2}x + b[/tex]

Passes through (-2, 1)

This means that when [tex]x = -2, y = 1[/tex]. We use this to find the y-intercept. So

[tex]y = -\frac{3}{2}x + b[/tex]

[tex]1 = -\frac{3}{2}(-2) + b[/tex]

[tex]1 = 3 + b[/tex]

[tex]b = -2[/tex]

So, the equation of the line is:

[tex]y = -\frac{3}{2}x - 2[/tex]

Answer:

469.875 square feet

Step-by-step explanation:

Find how many square feet she can cover by multiplying 125.3 by 3.75 (same as 3 3/4):

125.3(3.75)

= 469.875

So, she will be able to cover 469.875 square feet with soil

Answer:

61,70,79

Step-by-step explanation:

common difference=9

It is an arithmetic progression.

therefore next 3 terms of the sequence is 61,70,79

Answer:

61, 70,79

Step-by-step explanation:

34 - 25 = 9

43 - 34 = 9

52 - 43 = 9

52 + 9 =61

the pattern is plus 9

Answer:

[tex]5^{3}[/tex] · [tex]5^{8}[/tex] = [tex]5^{11}[/tex]

Step-by-step explanation:

when the bases are the same, add exponents

Given:

Renee has dimes and quarters in her wallet that total $1.60.

She has 2 more dimes than quarters.

To find:

The number of each type of coins.

Solution:

Let x be the number of dimes and y be the number of quarters.

She has 2 more dimes than quarters. So,

[tex]x=y+2[/tex]            ...(i)

We know that,

1 dime = $0.10

1 quarter = $0.25

Renee has dimes and quarters in her wallet that total $1.60. So,

[tex]0.10x+0.25y=1.60[/tex]              ...(ii)

From (i) and (ii), we get

[tex]0.10(y+2)+0.25y=1.60[/tex]

[tex]0.10y+0.20+0.25y=1.60[/tex]

[tex]0.35y=1.60-0.20[/tex]

[tex]0.35y=1.40[/tex]

Divide both sides by 0.35.

[tex]y=\dfrac{1.40}{0.35}[/tex]

[tex]y=4[/tex]

Substituting [tex]y=4[/tex] in (i), we get

[tex]x=4+2[/tex]

[tex]x=6[/tex]

Therefore, the number of dimes is 6 and the number of quarters is 4.

Answer:19

Step-by-step explanation: draw the tanks put 6 fish in each tank until you get all 115 in each tank

Answer:

20 km

Step-by-step explanation:

Circumference is given by

C = pi*d

20 pi = pi *d

Divide  each side by pi

20 =d

I dkabouthtisoneiuisrhihurg

Answer:

x=16

..................