The following graph shows a proportional relationship.

What is the constant of proportionality between y and x in the graph?

Answer:

The figure is not symmetrical

Answered by GAUTHMATH

the center is at the origin of a coordinate system and the foci are on the y-axis, then the foci are symmetric about the origin.

The hyperbola focus F1 is 46 feet above the vertex of the parabola and the hyperbola focus F2 is 6 ft above the parabola's vertex. Then the distance F1F2 is 46-6=40 ft.

In terms of hyperbola, F1F2=2c, c=20.

The vertex of the hyperba is 2 ft below focus F1, then in terms of hyperbola c-a=2 and a=c-2=18 ft.

Use formula c^2=a^2+b^2c

2

=a

2

+b

2

to find b:

\begin{gathered} (20)^2=(18)^2+b^2,\\ b^2=400-324=76 \end{gathered}

(20)

2

=(18)

2

+b

2

,

b

2

=400−324=76

.

The branches of hyperbola go in y-direction, so the equation of hyperbola is

\dfrac{y^2}{b^2}- \dfrac{x^2}{a^2}=1

b

2

y

2

−

a

2

x

2

=1 .

Substitute a and b:

\dfrac{y^2}{76}- \dfrac{x^2}{324}=1

76

y

2

−

324

x

2

=1 .

N is the midpoint of MO and NO is 5, so MN would also be 5

MP = MN + NP = 5 + 9 = 14

Answer:

6:21

Step-by-step explanation:

We want to find the ratio of squares to shapes

So simply count the squares

There are 6 squares

And then find the total number of shapes

There are a total of 21 shapes

So for every 6 squares there are 21 total shapes

In other words the ratio of squares to shapes is 6:21

Answer:

Step-by-step explanation:

Given,

Number of squares = 6

Total no. of shapes = 21

Therefore,

Unsimplified ratio of squares to total shapes

= 6:21 (Ans)

Answer:

x=15, y=2

Step-by-step explanation:

By AA similarity, the triangles are similar. Therefore, we can find the ratios of the side lengths.

9/3=3=ratio of the side length of a larger triangle to a smaller one.

3=6/y, y=2

3=x/5, x=15

Hope this helped,

~cloud

Answer:

true

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

A

[tex]\frac{12}{2\pi }[/tex]  ≈ 1.91 < 2

B

8 - π 8 - 3.14 = 4.86 < 5

C

10π ≈ 31.42 > 30 ← True

D

π + 4 = 3.14 + 4 = 7.14 > 7

Option C is a true inequality

Answer:

A = 0.46, B = 0.61 and C = 0.46

Step-by-step explanation:

From the number line given, we can see that the distance between 0.5 and the next value is by 0.01, hence to get B, we will add 0.01 to the value of 0.6 as shown;

B = 0.6 + 0.01

B = 0.61

To get A, we will add 0.03 to 0.5 as shown:

A = 0.5 + 0.03

A = 0.53

To get the value of C, we will subtract 0.04 from  0.5

as shown:

C = 0.5 - 0.04

C =0.46

Hence A = 0.46, B = 0.61 and C = 0.46

Answer:

both

Step-by-step explanation:

Congruent shapes have equal corresponding side lengths

The true statement is (c) both

To map the quadrilaterals on one another, then the sequence of transformation must be rigid transformation

The given sequence of transformations are both rigid, and they both would map quadrilaterals STUV and ABCD

Hence, the true statement is (c) both

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Answer:

a.) 1908.30

b.) 96373.15

c.)302491.15

unrounded answers below

Step-by-step explanation:

The amount that is to be loaned out is 380000-110000=270000

The effective montly rate is .07/12=.005833333

a.)

[tex]270000=x(\frac{1-(1+.005833333)^{-(25*12)}}{.005833333})=1908.303833[/tex]

b.)

use what is called the prospective method (the outstanding loan balance at time n is equal to the present value of the remaining payments)

[tex]1908.303833(\frac{1-(1+.005833333)^{-(25*12-20*12)}}{.005833333})=96373.14775[/tex]

c.)

total paid= 1908.303833*12*25=572491.1499

amount of loan: 270000

Total interest paid:

572491.1499-270000=302491.1499

Answer:

1/120

Step-by-step explanation:

For the first letter, you have a 1/5 chance of getting w

On the second you have a 1/4 chance to get the r

Then 1/3 and 1/2

Next you just multiply the bottom numbers

That gives you how many diffrent outcomes there can be. Put that over 1 and you have your answer.

Hope this helps <3

Answer:

10 gallons

Step-by-step explanation:

84 ÷ 6.5 =12.9(The unit rate.)

Seeing as one gallon can get you 12.9 miles;

126÷12.9=9.7

So the answers 9.7 gallons, but if you need to round, then 10 to get a whole number.

Answer:

9.75

Step-by-step explanation:

We can write a ratio to solve

84 miles          126 miles

--------------   = -------------------

6.5 gallons        x gallons

Using cross products

84 x = 6.5 * 126

84x=819

84x/84 = 819/84

x = 9.75

Answer:

The answer is "18".

Step-by-step explanation:

In the given graph by concluding we observe that  on the x-axis, one step is 2 units, and when we half each of the steps it will= 1 unit

[tex]\therefore\\\\CD = distance\ from\ -(8+1)\ to\ (8+1)\ = \text{distance between} -9 \ to\ 9\ = 18[/tex]

Answer:

[tex]\cos(\theta) = -\frac{\sqrt{17}}{6}[/tex]

Step-by-step explanation:

Given

[tex]\tan(\theta) = -\sqrt{\frac{19}{17}}[/tex]

Required

Determine [tex]\cos(\theta)[/tex]

We have:

[tex]\tan(\theta) = -\sqrt{\frac{19}{17}}[/tex]

Split

[tex]\tan(\theta) = -\frac{\sqrt{19}}{\sqrt{17}}[/tex]

tan is calculated as:

[tex]\tan(theta) = \frac{opposite}{adjacent}[/tex]

So:

[tex]Opposite = -\sqrt{19[/tex]

[tex]Adjacent = \sqrt{17[/tex]

And:

[tex]Hypotenuse^2 = Opposite^2 + Adjacent^2[/tex] --- Pythagoras theorem

[tex]Hypotenuse^2 = (-\sqrt{19})^2 + (\sqrt{17})^2[/tex]

[tex]Hypotenuse^2 = 19 + 17[/tex]

[tex]Hypotenuse^2 = 36[/tex]

Take square roots

[tex]Hypotenuse = 6[/tex]

[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

[tex]\cos(\theta) = \frac{\sqrt{17}}{6}[/tex]

Since it is in the second quadrant, then:

[tex]\cos(\theta) = -\frac{\sqrt{17}}{6}[/tex]

Answer:

y=-x+28

Step-by-step explanation:

The slope(rise/run) is -1, and because it starts at y=28, the answer is y=-x+28

Answer:

"C"

The slope is -2 !!! delta y = 20 delta x = 10

the y intercept is 28

Step-by-step explanation:

Answer:

General Educational Development (GED) tests

What do subject do you need help?

Step-by-step explanation:

The GED® exam is made up of 4 subjects, broken into separate exams: Mathematical Reasoning, Reasoning Through Language Arts, Social Studies, and Science.

Answer:

The expected total amount of time in minutes the operator will spend on the calls each day is of 174.8 minutes.

The standard deviation of the total amount of time in minutes the operator will spend on the calls each day is of 17.4356 minutes.

0.3085 = 30.85% approximate probability that the total time spent on the calls will be less than 166 minutes.

The value c such that the approximate probability that the total time spent on the calls each day is less than c is 0.95 is [tex]c = 203.4816[/tex]

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

n instances of a normally distributed variable:

For n instances of a normally distributed variable, the mean is:

[tex]M = n\mu[/tex]

The standard deviation is:

[tex]s = \sigma\sqrt{n}[/tex]

Calls to a customer service center last on average 2.3 minutes with a standard deviation of 2 minutes.

This means that [tex]\mu = 2.3, \sigma = 2[/tex]

An operator in the call center is required to answer 76 calls each day.

This means that [tex]n = 76[/tex]

What is the expected total amount of time in minutes the operator will spend on the calls each day?

[tex]M = n\mu = 76*2.3 = 174.8[/tex]

The expected total amount of time in minutes the operator will spend on the calls each day is of 174.8 minutes.

What is the standard deviation of the total amount of time in minutes the operator will spend on the calls each day?

[tex]s = \sigma\sqrt{n} = 2\sqrt{76} = 17.4356[/tex]

The standard deviation of the total amount of time in minutes the operator will spend on the calls each day is of 17.4356 minutes.

What is the approximate probability that the total time spent on the calls will be less than 166 minutes?

This is the p-value of Z when X = 166.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem:

[tex]Z = \frac{X - M}{s}[/tex]

[tex]Z = \frac{166 - 174.8}{17.4356}[/tex]

[tex]Z = 0.5[/tex]

[tex]Z = 0.5[/tex] has a p-value of 0.6915.

1 - 0.6915 = 0.3085.

0.3085 = 30.85% approximate probability that the total time spent on the calls will be less than 166 minutes.

What is the value c such that the approximate probability that the total time spent on the calls each day is less than c is 0.95?

This is X = c for which Z has a p-value of 0.95, so X = c when Z = 1.645. Then

[tex]Z = \frac{X - M}{s}[/tex]

[tex]1.645 = \frac{c - 174.8}{17.4356}[/tex]

[tex]c - 174.8 = 1.645*17.4356[/tex]

[tex]c = 203.4816[/tex]

The value c such that the approximate probability that the total time spent on the calls each day is less than c is 0.95 is [tex]c = 203.4816[/tex]

1) Seven less than twice a number, n, is 32.

ANS) B. 2n - 7 = 32

Answer:

1.

B. 2n - 7 = 32 is the right answer

Answer: 0, 5

Step-by-step explanation: a translation is just like sliding the object in this case a triangle/point on the triangle. so the point it is at now is -2, 5 because it is 2 to the left and 5 up. and if you go to the right 2. then you are adding 2 to the x value. so -2 +2 = 0. which is how you get 0, 5

Answer:

The student is completely incorrect because there is no solution to this inequality.

Answer:

D on edge

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

amount of water w

l liter of pure alcohol = 100% alcohol

solution is 45 % percent alcohol

total amount of fluid is w+l

(w+l)( .45) = l*.100

Distribute

.45w  + .45 l = 1l

.45 w = 1l - .45l

.45 w = .55l

w = .55l / .45

w =11/9 l

9514 1404 393

Answer:

  17.  25 mile per gallon

  18. Eduardo did should have divided by -4.

Step-by-step explanation:

17. The least mileage will be had when the most gas is used to go a given distance. For the given distance, the most gas that could have been used (without adding any) is 18 gallons. Then the least mileage is ...

  (450 mi)/(18 gal) = 25 mi/gal

__

18. The appropriate method for solving this inequality is ...

  -4x/(-4) < 120/(-4) . . . . divide both sides by -4 (and reverse the > symbol)

  x < -30

The step Eduardo took of adding 4 will give ...

  -4x +4 > 124 . . . . . puts him one step farther away from a solution

Eduardo chose an operation to perform that did not get him closer to a solution.

Answer:

The answer is "[tex]\frac{5 e^{5\sqrt{x} }}{2\sqrt{x}}[/tex]".

Step-by-step explanation:

Given:

[tex]y = e^{{\color{\red}5}\sqrt{x}}[/tex]

let

[tex]\to t= 5\sqrt{x}\\\\\frac{dt}{dx}= 5 \frac{1}{2\sqrt{x}}\\\\\frac{dt}{dx}= \frac{5}{2\sqrt{x}}\\\\[/tex]

and

[tex]\to y=e^t\\\\\to \frac{dy}{dt}=e^t\\[/tex]

[tex]\to \frac{dy}{dt}=e^{5\sqrt{x} }\\[/tex]

So,

[tex]\to \frac{dy}{dx}= \frac{dy}{dt} \times \frac{dt}{dx}[/tex]

         [tex]=e^{5\sqrt{x} }\times \frac{5}{2\sqrt{x}}\\\\= \frac{5 e^{5\sqrt{x} }}{2\sqrt{x}}[/tex]

OR

[tex]\to g(x) = 5\sqrt{x} \\\\\to f(x) = e^{(x)}\\\\[/tex]

Derivate:  

[tex]\to f''g' = \frac{e^{(5\sqrt{x})}5}{(2\sqrt{x})}[/tex]

Answer:

L(x)=-4x+9

L(2.1)=0.6

Step-by-step explanation:

It's asking us to find the tangent line to curve f(x) = 5−x^2 at x = 2.

Theb use this to estimate f(2.1).

To find slope of tangent line, we must differentiate and then plug in 2 for x.

f'(x)=0-2x by constant and power rule.

f'(x)=-2x

So the slope of the tangent line is -2(2)=-4.

A point on this tangent line shared by the curve is at x=2. We can find it's corresponding y-value using f(x)=5-x^2.

f(2)=5-(2)^2

f(2)=5-4

f(2)=1

So let's rephrase the question a little.

What's the equation for a line with slope -4 and goes through point (2,1).

Point-slope form y-y1=m(x-x1) where m is slope and (x1,y1) is a point on the line.

Plug in our information: y-1=-4(x-2).

Distribute: y-1=-4x+8

Add 1 on both sides: y=-4x+9

Let's call this equation L(x), an expression to approximate value for f near x=2.

L(x)=-4x+9

Now the appropriation at x=2.1:

L(2.1)=-4(2.1)+9

L(2.1)=-8.4+9

L(2.1)=0.6

If we did plug in 2.1 into given function we get 5-(2.1)^2=0.59 . This is pretty close to our approximation above.

Answer:

15/4

Step-by-step explanation:

sin60 =z/15

z=15sin60 =(15√3)/2

cos30 =b/z

b = zcos30 = (15√3)/2 * √3/2 = 45/4

a = 15-b = 15-45/4 = 15/4

The value of a is 15/4

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

According to the given figure,

Here is a right triangle

Let, The hypotenuse = 15

perpendicular = z and base = 15 = a + b

⇒ sin60 = perpendicular/hypotenuse = z/15

⇒ z = 15sin60 = (15√3)/2

⇒ cos30 = base/hypotenuse = b/z

⇒ b = zcos30 = (15√3)/2 * √3/2 = 45/4

⇒ a + b = 15

Substitute the value of b in the above equation,

⇒ a = 15-b = 15-45/4 = 15/4

Hence, the value of a is 15/4.

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Answer: 20.5

Step-by-step explanation:

Cos 43 = X/28

O.73 = x/28

(0.73)(28)=20.5

Answer:

Step-by-step explanation:

x3−x2+5x−12

x

≥0

Let's find the critical points of the inequality.

x3−x2+5x−12

x

=0

x3−x2+5x−12=0(Multiply both sides by x)

(Use cubic formula)

x=1.836169

Check possible critical points.

x=1.836169(Works in original equation)

Critical points:

x=1.836169(Makes both sides equal)

x=0(Makes left denominator equal to 0)

Check intervals in between critical points. (Test values in the intervals to see if they work.)

x<0(Works in original inequality)

0<x≤1.836169(Doesn't work in original inequality)

x≥1.836169(Works in original inequality)

Answer:

x<0 or x≥1.836169

Answer:

x=12,y=3

Step-by-step explanation:

x/6-y/3=1

x can equal 12 because 12/6 is equal to 2.

y can equal 3 because 3/3 equals 1

2-1=1

Answer:

1

5

=

8

2

−

1

4

15=8x^{2}-14x

15=8x2−14x

1

5

−

(

8

2

−

1

4

)

=

0

Step-by-step explanation:

=

−

3

4

=

5

2

The solution of equation is x =5/2  or  x= -3/4.

A number or other mathematical object is factored (or factorised, see variants in spelling in English) or factored when it is written as the product of numerous factors, typically smaller or simpler things of the same kind.

We have,

Equation: 15 = 8x² - 14x

Now, rearranging the equation as

8x² -14x -15 = 0

8x² - 20x + 6x -15=0

4x( 2x - 5) + 3 (2x-5)= 0

(2x-5)(4x +3)= 0

2x-5 =0  or 4x+ 3= 0

x =5/2  or  x= -3/4

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