Which function is represented by the graph?

Answer: 674 ft

Step-by-step explanation:

[tex]\tan 12^{\circ}=\frac{y}{1315} \\ \\ 1315\tan 12^{\circ}=y[/tex]

[tex]\tan 8^{\circ}=\frac{y}{x+1315} \\ \\ (x+1315)\tan 8^{\circ}=y \\ \\ (x+1315)\tan 8^{\circ}=1315 \tan12^{\circ} \\ \\ x \tan 8^{\circ}+1315 \tan 8^{\circ}=1315 \tan 12^{\circ} \\ \\ x \tan 8^{\circ}=1315 \tan 12^{\circ}-1315 \tan 8^{\circ} \\ \\ x=\frac{1315 \tan 12^{\circ}-1315 \tan 8^{\circ}}{\tan 8^{\circ}} \approx \boxed{674 \text{ ft}}[/tex]

The number of each type of coin that Joan has are; 16 dimes and 3 quarters

We are told that Joan has a total of 19 coins.

Now, the worth of the coins is $2.35

Let dimes be d and let quarters be q. Thus;

10d + 25q = 235

d + q = 19

Substitute d = 19 - q in the 1st equation to get;

10(19 - q) + 25q = 235

190 - 10q + 25q = 235

15q = 45

q = 45/15

q = 3

Thus;

d = 19 - 3

d = 16

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We are given the equation for the height of the arrow. If you graph it, you see that it's a parabola and that the arrow kinda peaks and then falls back down. Another way of thinking about this problem is that you're looking for the time when the height is 0. You can see on the graph that there are two times that h=0. The first is obviously at t=0, when the arrow hasn't left the ground yet. The second is what we're looking for, when the arrow reaches the ground.

To solve this, let's set h=0. So 0=40t-5t^2. If you factor this, you get 5t(8-t) = 0. Continuing that leads to 5t=0 where t=0 which we already knew, and 8-t=0 where t=8. So that second time is when the arrow is back on the ground. Therefore your answer is 8 sec.

The conversion of 120 sq. inches is equivalent to 0.09264 sq. yd.

Conversion is the process of changing the value of one form to another for example inches to millimeters, or liters to gallons.

Here, we know that,

    1 square inches = 0.000772 sq yd

we have 120 sq. inches

so, 120 sq. inches = 120 X 0.000772 sq yd

                              = 0.09264 sq. yd.

Thus, the conversion of 120 sq. inches is equivalent to 0.09264 sq. yd.

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The average rates of change of f(x) and their corresponding intervals are given as:

Interval          Rate of Change

[-5, -1]                 -8

[-4, -1]                 -7

[-3, 1]                  -4

[-2, 1]                  -3.

Step 1 - See Table Attached

Step 2 - State the formula for rate of change

The formula for rate of change is given as:
= [change in f(x)] / [change in x]

a) For interval [5, -1] ⇒

Rate of Change - [ f(1) - f(-5) ] / [-1 - (-5)]  

= [-1 - 35] / [-1+5]

= -36 / 4

= - 8

b) For interval [-4, -1] ⇒

rate of change = [ f(-1) - f(-4) ] / [ -1 - (-4) ]

= [3 - 24] / [-1 + 4]

= -21/3

= - 7

c) interval [-3,1] ⇒

rate of change = [ f(1) - f(-3) ] / [ 1 - (-3) ]

= [-1 - 15] / [1 + 3]

= -16/4

= - 4

d) interval [-2,1] ⇒

rate of change = [f (1) - f(-2)] / [1 - (-2)]

= [ -1 - 8] / [1 + 2]

= -9/3

= -3

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Answer: (8, -4)

Step-by-step explanation:

-5x - 3y = -28
  x + 2y = 0

1. Multiply both sides of the bottom system by 5 to cancel the x out

   5(x+2y=0)

   5x + 10y = 0

2. rewrite

   -5x - 3y = -28

    5x + 10y = 0

3. add

   0x + 7y = -28

4. divide by 7

   7y = -28

5. y = -4

6. plug in -4 for y in one of the original equations

   x + 2(-4) = 0

7. simplify

   x = 8

9. solution is

   (8, -4)

The measures of BC will be 100°. Option D is correct.

It is a point locus drawn equidistant from the center. The radius of the circle is the distance from the center to the circumference.

The angle at the center is twice as large as the angle at the perimeter.

BC = 2 ×∠CDB

BC=2×50°

BC= 100°

Hence option D is correct.

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Answer:

Angle 1 = 90 degree

Angle 2 = 55 degree

Angle 3 = 35 degree

Step-by-step explanation:

A rhombus has four equal sides. Since the intersection angle of a rhombus is always 90 degree, angle 1 is 90 degree

Angle 3 = 180 degree - 90 degree - 55 degree = 35 degree

Angle 2 = 180 degree - 90 degree - 35 degree = 55 degree

Answer:

See below ~

Step-by-step explanation:

Classifying the triangles by sides and angles :

Triangle ABC

⇒ By Sides : Scalene (All sides are unequal)

⇒ By Angles : Right (There is a right angle = 90°)

============================================================

Triangle GHI

⇒ By Sides : Isosceles (2 sides are equal)

⇒ By Angles : Obtuse (One angle is greater than 90°)

============================================================

Triangle DEF

⇒ By Sides : Equilateral (All sides are equal)

⇒ By Angles : Acute (All angles are less than 90°)

The solution to the absolute value inequality is (-3,-2)

On the absolute value inequality, we have:

Interval = -3 to 2

The intervals are represented with open circles.

This means that -3 and 2 are exclusive of the values of the inequality.

So, we have:

-3 < x < 2

As an interval notation, we have:

(-3,-2)

Hence, the solution to the absolute value inequality is (-3,-2)

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Answer:

the measure of each angle is 75degrees

Answer + Step-by-step explanation:

Question 4 :

Construct the angle 0MN :

1) Draw a segment MO

2) Put the protractor so that it is in line with the segment MO

At the same time ,line up the points M with the little circle of the protractor.

3) Spot 40° on the protractor ,then draw a point.

4) Use the ruler to connect point M through that point

Construct the angle MON :

1) Put the protractor so that it is in line with the segment MO

At the same time ,line up the points O with the little circle of the protractor

2) Spot 70° on the protractor ,then draw a point.

3) Use the ruler to connect point O through that point.

Construct the point N :

N is the point of intersection of the lines that go (respectively) through M and O.

Question 6 :

1) Draw a segment XZ such that XZ = 2.

2) construct the angle ZXY = 25°.   (follow the steps described in the Previous question).

NOTE : ∠Z = 180 - (∠X + ∠Y) = 180 - (25 + 45) = 110°

3) construct the angle XZY = 110° .  (follow the steps described in the Previous question)

4) Y is the point of intersection of the lines that go (respectively) through X and Z.

Answer:

B) [tex]8\sqrt[4]{4}[/tex]

Step-by-step explanation:

[tex](2^{8} *2^{6} )^\frac{1}{4} = (2^{8+6} )^\frac{1}{4} =(2^{14} )^\frac{1}{4} =2^{\frac{7}{2} }=\sqrt{2^{7} } =2^{3} \sqrt{2} =8\sqrt{2} = 8\sqrt[4]{2^{2} } = 8\sqrt[4]{4}[/tex]

Answer:

Q = 40.6°

Explanation:

Given three sides: 9.6, 8.1, 6.3

Use the cosine rule:

c² = a² + b² - 2ab cos(C)

Insert following variables:

6.3² = 9.6² + 8.1² - 2(9.6)(8.1) cos(Q)

39.69 = 157.77 - 155.52 cos(Q)

cos(Q) = -118.08/-155.52

cos(Q) = 41/54

Q = cos⁻¹(41/54) = 40.6°

Answer:

360 degrees

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

[tex]\begin{array}{ccll} feet&seconds\\ \cline{1-2} 19 & 1\\ 600& x \end{array} \implies \cfrac{19}{600}~~=~~\cfrac{1}{x} \\\\\\ 19x=600\implies x=\cfrac{600}{19}\implies \stackrel{\textit{about half a minute}}{x\approx 31.58~seconds}[/tex]

Answer:

  10/19 min ≈ 0.5263 min

Step-by-step explanation:

The woman's sprinting speed is given in feet per second, and we are asked for it in minutes per 600 feet. To find the time, we can use the relation ...

  time = distance / speed

Using the given numbers will give a time in seconds, so we need to do a units conversion to find the answer in minutes.

__

  time = distance/speed

  time = (600 ft) / (19 ft/s) = (600/19) s

Converting the units gives ...

  time = (600/19) s × (1 min)/(60 s) = (600·1)/(19·60) min

The time it takes the woman to sprint 600 feet will be ...

  time = 600/(19·60) min = 10/19 min ≈ 0.5263 min

The length of the curve will be given by the definite integral

[tex]\displaystyle \int_0^1 \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} \, dt[/tex]

From the given parametric equations, we get derivatives

[tex]x(t) = 3t^2 + 5 \implies \dfrac{dx}{dt} = 6t[/tex]

[tex]y(t) = 2t^3 + 5 \implies \dfrac{dy}{dt} = 6t^2[/tex]

Then the arc length integral becomes

[tex]\displaystyle \int_0^1 \sqrt{\left(6t\right)^2 + \left(6t^2\right)^2} \, dt = \int_0^1 \sqrt{36t^2 + 36t^4} \, dt \\\\ = \int_0^1 6|t| \sqrt{1 + t^2} \, dt[/tex]

Since 0 ≤ t ≤ 1, we have |t| = t, so

[tex]\displaystyle \int_0^1 6|t| \sqrt{1 + t^2} \, dt = 6 \int_0^1 t \sqrt{1 + t^2} \, dt[/tex]

For the remaining integral, substitute [tex]u = 1 + t^2[/tex] and [tex]du = 2t \, dt[/tex]. Then

[tex]\displaystyle 6 \int_0^1 t \sqrt{1 + t^2} \, dt = 3 \int_1^2 \sqrt{u} \, du \\\\ = 3\times \frac23 u^{3/2} \bigg|_{u=1}^2 \\\\ = 2 \left(2^{3/2} - 1^{3/2}\right) = 2^{5/2} - 2 = \boxed{4\sqrt2-2}[/tex]

Step-by-step explanation:

quarter circle means that you just find the are and then divide it by 4.

hence,

(3.14 × 8²) ÷ 4 = answer

the answer is 50.24 cm²

hope this helps.

Answer: 6.28

Step-by-step explanation: In order to get your answer, the equation that you need to do is 8 X 3.14 / 4 to get your answer.

Answer: 1.125 pounds of blueberries or  [tex]1 \frac{1}{8}[/tex] or [tex]\frac{9}{8}[/tex]

Step-by-step explanation:

Since she will eat it for 9 days, just multiply or add the pounds.

Step-by-step explanation:

The wording is slightly confusing so I will just solve the equation.

2 (y + 6) = 4y

We expand the bracket

2y + 12 = 4y

We subtract 2y from both sides

12 = 2y

We divide both sides by 2

6 = y

Answer:

320 cents per pound

Step-by-step explanation:

so we do 9.60 divided by 3, which is 3.20. So, 3.20 for each pound. Now we need in cents. 3 dollars is 300 cents, plus another 20, so 320 cents. I hope this helped.

The perimeter of Rosalie's new rectangular mural is given by P = 21 feet

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P of rectangle = 2 ( Length + Width )

Given data ,

Let the perimeter of the rectangular mural be represented as P

Now , the equation will be

Let the initial length of the rectangular mural be L = 3.5 feet

Let the initial width of the rectangular mural be W = 5.5 feet

Now , the new mural is having an extra length of 1.5 feet

So , the new length of the rectangular mural is L₁ = 3.5 + 1.5 = 5 feet

Now , Perimeter P of rectangle = 2 ( Length + Width )

Substituting the values in the equation , we get

Perimeter of rectangular mural = 2 ( 5 + 5.5 )

On simplifying the equation , we get

Perimeter of rectangular mural P = 2 x 10.5

Perimeter of rectangular mural P = 21 feet

Hence , the perimeter of rectangular mural is 21 feet

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Answer:

1400

Step-by-step explanation:

The numbers that can be pulled based on the probability of the calls will be 90, 110, and 50.

From the information given, the bag has 9 blue cubes, 11 red cubes, and 5 green cubes and when one draws a cube and replace it in the bag 250 times, the number of blue balls that can be gotten will be:

= 9/(9+ 11 + 5) × 250

= 9/25 × 250

= 90

The number of red balls that can be gotten will be:

= 11/25 × 250

= 110

The number of green balls that can be gotten will be:

= 5/25 × 250

= 50

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By weighted average, we need 75 liters of 24 % iodine solution and 25 liters of 40 % iodine solution to obtain 100 liters of 28 % iodine solution.

Physically speaking, concentration is equal to the amount of solute divided by the volume of solution. We have two solutions with same solute and different concentration and can find the right proportion between the 24 % solution and the 40 % solution by concept of weighted average:

x · 24 + (1 - x) · 40 = 28

40 - 16 · x = 28

16 · x = 40 - 28

16 · x = 12

x = 3/4

By weighted average, we need 75 liters of 24 % iodine solution and 25 liters of 40 % iodine solution to obtain 100 liters of 28 % iodine solution.

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Answer:

z = 1/4

Step-by-step explanation:

See attached image

Answer:

z = 5

Step-by-step explanation:

simplify

5/(z-25) first

turning it into

((0 - 3/z) + 7/4z) - 5/(z - 25) = 0

then simplify 7/4z

((0 - 3/z) + 7/4z) - 5/(z-25) = 0

when the fractions denominator is 0 then the numerator must be 0

turning the equation into

-25  *  (z - 5)  = 0

solve

-25   =  0

something that is not zero cannot equal zero.

z - 5 = 0

5 - 5 = 0

z = 5

hope this helps:)

[tex]f(x) = 3(x+5)\\\\f(a+2) = 3(a+2 +5) \\\\~~~~~~~~~~~~=3(a+7)\\\\~~~~~~~~~~~~=3a+21[/tex]

Answer:

x = 11

Step-by-step explanation:

3/(3(2x-3)) = 2/(3x+5)

3(2x-3) = 6x - 9

3/(6x-9) = 2/(3x+5)

3(3x+5) = 2(6x-9)

9x + 15 = 12x - 18

12x - 9x = 15 + 18

3x = 33

x = 11

Answer:

[tex]\mathrm x= \dfrac{87}{10} \quad or \quad 8.7[/tex]

Explanation:

[tex]\longrightarrow \sf \dfrac{3}{4} (2x-3)=\:\dfrac{2}{3}\:x+5[/tex]

[tex]\longrightarrow \sf \dfrac{3}{2} x-\dfrac{9}{4} =\:\dfrac{2}{3}\:x+5[/tex]

[tex]\longrightarrow \sf \dfrac{3}{2} x-\dfrac{2}{3}x=5+\dfrac{9}{4}[/tex]

[tex]\longrightarrow \sf \dfrac{5}{6} x=\dfrac{29}{4}[/tex]

[tex]\longrightarrow \sf x=\dfrac{29(6)}{4(5)}[/tex]

[tex]\longrightarrow \sf x=\dfrac{87}{10} \quad or \quad 8.7[/tex]

Answer:

[tex]0.95*10^8[/tex]

Step-by-step explanation:

Hello!

Rules for scientific notation format:

[tex]\bold{0.95*10^8}[/tex]

There is a multiplication to a power of 10, but the other factor is less than 1.

This is NOT in Scientific Notation.

All the other options have a multiplication operation to a power of 10, and all the other factors are above 1 and less than 10.