Entercept word problems

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2. the water in nate's swimming pool is

currently 72 inches deep. however, nate

noticed a hole in the liner that is causing

water to leak out of the pool. the depth of

the water is decreasing at a rate of 2 inches

per hour. which equation relates the depth

(d) of the water in inches after h hours?

Answer:

50.24

Step-by-step explanation:

the formula to find a circle is radius times radius times pi, which equals 3.14.      The radius is 2 so radius times radius would be 4. Now u times it by pi so 4 times 3.14 equals 12.56. Do this times ur hight wich is times 4 and u come up with 50 .24

f

Answer:

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

Sometimes you give the solutions as just the x.

x = -1 and x = 1

Step-by-step explanation:

The two curvy pieces are f(x) and the straight line is g(x). The solutions are where the two graphs intersect. There are two points where this happens: (-1,-3) and (1,-1).

Sometimes your teacher, the text or the course just wants you to give the answer as the x where it happens. The graphs intersects where x=-1 and x=1

The best measure of the angle ∠XYZ is given by: Option B: 39.8°

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled (not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\\\[/tex]

The missing figure is attached below.

From the given figure, if we see from the angle x which is ∠XYZ, the hypotenuse is YZ, perpendicular = XZ with length 10 inches, and base XY with length 12 inches.

Since perpendicular and base are specified, we can directly use tangent ratio and then its inverse to find the measure of the ∠XYZ, as shown below:

[tex]\tan(\angle XYZ) = \dfrac{|XZ|}{|XY|} = \dfrac{10}{12}\\\\\angle XYZ = \tan^{-1}\left(\dfrac{10}{12}\right) \approx 39.8^\circ[/tex]

Thus, the best measure of the angle ∠XYZ is given by: Option B: 39.8°

Learn more about inverse trigonometric functions here:

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Answer:

b

Step-by-step explanation:

took the test

Answer:

36

Step-by-step explanation:

[tex]12p-20t=4(3p-5t)[/tex]

Substitute [tex]3p - 5t = 9[/tex] into the equation:

[tex]\implies 12p-20t=4(9)=36[/tex]

Any number greater than 3.

Step-by-step explanation:

To find the answers to this question, start by solving the inequality for x.

2x - 1 > x + 2

x - 1 > 2

x > 3

Using this, we now know that any number that is greater than 3 would work for this inequality.

Answer:

Step-by-step explanation:

.4

.5

The awnser is 60 because

It is a cube so it has the smae amout of sides

Answer:

1. b/c        4. c/b

2. a/c       5. c/a

3. b/a       6. a/b

Step-by-step explanation:

sin theta = opposite/hypotenuse    = b/c

cos theta = adjacent/hypotenuse   = a/c

tan theta= opposite/adjacent          = b/a

For the rest, you just flip it:

csc theta  = c/b

sec theta = c/a

cot theta = a/b

Answer:

29.02

Step-by-step explanation:

The area of traingle formula with two sides and one angle is:

[tex]A = ab\frac{siny}{2}[/tex]

When you put the values in, you can simplify it and put it into a calculator for sin. And, you then have your answer.

Hope it helps.

Do comment if you have any query.

Answer:

2 cups

Step-by-step explanation:

5/8 + 11/ 8 = 16/8 = 2

Answer:

18.15 cm

Step-by-step explanation:

.33    is 33% in decimal

.33 * 55 cm = 18.15 cm

Answer:

The correct answer is x = 32/9

Step-by-step explanation:

You must multiply the given numbers from left to right, resulting in:

x - 4 + x/2 = x + 12 - 3x - x

Then, by combining phrases on both sides that are similar, we get:

(3/2)x - 4 = -3x + 12

By adding 4 to both sides of the equation, it becomes:

(3/2)x = -3x + 16, or

3/2)x + (6/2)x = 16, which may be written as:

3x + 6x = 32, or 9x = 32

Therefore, the answer is x = 32/9

I hope this helps! ^-^

If Mr. Swift is traveling from his house to the history museum. The number of meters will he travel to the museum is 6,400 meters.

Given:

Distance=6.4 Kilometres

Hence:

1 kilometre= 1,000 meters

Number of meters=6.4 kilometres x 1,000 meters

Number of meters =6,400 meters

Therefore the number of meters will he travel to the museum is 6,400 meters.

Learn more about number of meters here:https://brainly.com/question/870330

Answer:

5

Step-by-step explanation:

Hope this helps! Have a great day!

Answer:

58

Step-by-step explanation:

Answer:

Quadrant III

Step-by-step explanation:

sin and cos are both less than zero thus negative

the x and y axis are both negative in QIII

sorry if the explaination is wrong but I know the answer is right bc I took the test

Hello! Mikosan here to help doll!

The Answer is: Quadrant 3

I hope this helps doll!

Have a great day love~

Answer:

x > 21/32

Step-by-step explanation:

I've used an app but for some reson it won't let me tell you.

Answer:

-8,6

Step-by-step explanation:

all of the other answers are within the highlighted area of tha graph and thus are solutions but -8,6 is outside the highlighted area

Answer:

I think it is 142 I'm not sure if it's right or wrong

Answer:

x = 20

B = 92°

C = 40°

Step-by-step explanation:

The sum of the interior angles of a triangle is 180°

⇒ A + B + C = 180°

⇒ 48 + (6x - 28) + 2x = 180

⇒ 48 + 6x - 28 + 2x = 180

⇒ 48 - 28 + 6x + 2x = 180

⇒ 20 + 8x = 180

⇒ 8x = 180 - 20

⇒ 8x = 160

⇒ x = 160 ÷ 8

⇒ x = 20

Now we have found x, simply substitute this into the expressions for angles B and C:

B = 6(20) - 28

   = 120 - 28

   = 92°

C = 2(20)

  = 40°

Answer:

x = 20

m<B = 92

m<C = 40

(m<A = 48)

Step-by-step explanation:

triangles are 180 degrees

add up the sides

48 + (6x-28) + 2x

8x + 20 = 180

8x = 160

x = 20

put 20 where the x is for B and C

B.

6(20)-28 =

120 - 28 =

92

C.

2(20) =

40

Answer:

Its a - Isosceles Right Triangle -

Step-by-step explanation:

It has two equal length sides and is a right triangle

The distance between Reeta and the school when the cyclists arrive the home for this case is found being 2 km

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

If the object is going linearly, and at constant speed, then the speed of that object is given by the distance it traveled to the time it took to travel that distance.

If the object traveled D distance in T units time, then that object's speed is

[tex]Speed = S = \dfrac{\: Distance \: traveled}{\: Time \: taken} = \dfrac{D}{T} \: \rm unit \: length/unit \: time[/tex]

Given that:

To find: Disance of Reeta from school when cyclist reach home.

Suppose at time 0 hours, all three people departed from school (on that monday).

After 't' hours, suppose the cycle gets punctured.

Then, as the cycle was going by 20 km / hour speed, so in 't' hours, it must have covered d kilometers (suppose),

then we get:
[tex]S = \dfrac{D}{T}\\\\20 = \dfrac{d}{t}\\\\d = 20 t \: \rm km[/tex]

This distance is measured from school. But we know that this distance is 4 km, so we get:

[tex]20t = 4\\t = \dfrac{4}{20} = 0.2 \: \rm hours[/tex]

The remaining 1 km (as home is 5 km away from school and 4 km is already traveled) is walked by Cyclists. And walking speed is 5 km / hour, so let they take T hours to travel that 1 km walking, then we get:
[tex]S = D/T\\\\5 = \dfrac{1}{T} \\\\T = 0.2 \: \rm hours[/tex]

So, total time cyclists took to reach home from school is: [tex]0.2 + 0.2 = 0.4 \: \rm hours[/tex]

Reeta is walking that whole 5 km.

The time the cyclist reached home, Reeta had walked for 0.4 hours as they had started at the same time, and it took cyclists 0.4 hours to reach home.

Thus, we have:

Time taken  0.4 hours, speed of Reeta = walking speed= 5 km/hour, then we get:

[tex]S = D/T\\D = ST\\D = 5 \times 0.4 = 2 \: \rm km[/tex]

So Reeta was 2 km away from school when cyclists reached home on that monday.

Thus, the distance between Reeta and the school when the cyclists arrive the home for this case is found being 2 km

Learn more about forming equations here:

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Answer:

42 degrees

Step-by-step explanation:

The measure of the indicated angle is 42 degree.

An isosceles triangle has two equal sides regardless of the direction the apex (or peak) of the triangle points. Some useful information regarding isosceles triangles is as follows:

We have a Triangle.

Then, using Isosceles Triangle Theorem

Angles opposite an isosceles triangle's equal sides are also equal.

According to the isosceles triangle theorem, if two sides of a triangle are congruent, then the angles opposite the congruent sides are likewise congruent.

So, x= 42 degree.

Learn more about Isosceles Triangle Theorem here:

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Answer:

[tex]\Longrightarrow: \boxed{\sf{26}}[/tex]

Step-by-step explanation:

Use the order of operations.

PEMDAS stands for:

First, solve parentheses.

(8-2)=6

Rewrite the problem down.

4+3*6+4

Multiply the numbers from left to right.

3*6=18

4+18+4

Add the numbers from left to right.

4+18=22

22+4=26

[tex]\Longrightarrow: \boxed{\sf{26}}[/tex]

I hope this helps! Let me know if you have any questions.

Answer:

so let's see buddy....

Step-by-step explanation:

look at that angle having 45, zed (Z) angles are equal, which means the bottom left inside the triangle is also 45°.

now sum of angles in a triangle is 180°...

so we add up all the angles and equal them to 180° but an angle is missing, let's name it Y°.

so...

96°+45°+Y°=180°

101°+Y°=180°

Y°=180°–101°

Y°=79°

to find x, sum of angles in a straight line is 90°

so we subtract 79 from 90

x°= 11

Answer:

n=3.3

Step-by-step explanation:

9n²-10=890    1. + 10 on both sides

9n² = 900

[tex]9n²[/tex]= 9n

[tex]900[/tex] = 30

9n=30  2. /9 on both sides

n=3.33

the 3's repeat

Step-by-step explanation:

Substitute y = 4 into the first equation:

[tex]4=2x^2+x-6[/tex]

Subtract 4 from both sides:

[tex]2x^2+x-10=0[/tex]

We can factor in order to find values of x.

Factor the equation:

[tex]2x^2+x-10=0[/tex]

Factors of 10 we'll use:

5 and 2.

[tex](2x+5)(x-2)=0[/tex]

Set the parentheses equal to 0 then find the values of x:

[tex](2x+5)=0[/tex]

[tex]x=-2\frac{1}{2}[/tex]

[tex](x-2)=0[/tex]

[tex]x=2[/tex]

[tex]x=2, \: or \: -2\frac{1}{2} .[/tex]

Check:

[tex]4=2(2)^2+2-6[/tex]

[tex]4=2(4)+2-6[/tex]

[tex]4=4 \: \checkmark[/tex]

[tex]4=2(-2\frac{1}{2} )^2-2\frac{1}{2} -6[/tex]

[tex]4=2(6\frac{1}{4})-2\frac{1}{2} -6[/tex]

[tex]4=12\frac{1}{2} -2\frac{1}{2} -6[/tex]

[tex]4=10-6[/tex]

[tex]4=4 \: \checkmark[/tex]

The statement which is true of the base, b of a logarithmic function is; b > 0 and b = 1.

When the base of a logarithmic function is set to a negative number, it follows that;

Such a logarithmic function wouldn't give us any real solutions.

So the base CAN NOT be negative.

Putting together all 3 conclusions, we can say that the base of a logarithm can only be positive numbers greater than 1.

Hence, the statement which is true of the base, b of a logarithmic function is; b > 0 and b = 1.

Read more on logarithmic functions;

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Answer:

b > 0 and b = 1.

Step-by-step explanation:

Answer:1

Step-by-step explanation:

Answer:

a₈ = 1

Step-by-step explanation:

substitute n = 8 into the nth term rule

a₈ = 25 - 3(8) = 25 - 24 = 1