Which orderd pair is a solution of the equation-3x+5y = 2x + 3y

Answer:

[tex]\frac{(x-30)^{2}}{40^{2}} - \frac{(y+15)^{2}}{3^{2}} = 1[/tex]

Step-by-step explanation:

The equation of the horizontal hyperbola in standard form is:

[tex]\frac{(x-k)^{2}}{a^{2}} - \frac{(y-k)^{2}}{b^{2}} = 1[/tex]

The position of its center is:

[tex]C(x,y) = \left(\frac{-10 + 70}{2}, -15 \right)[/tex]

[tex]C(x, y) = (30,-15)[/tex]

The values for c and a are respectively:

[tex]a = 70 - 30[/tex]

[tex]a = 40[/tex]

[tex]c = 30 - (-11)[/tex]

[tex]c = 41[/tex]

The remaining variable is computed from the following Pythagorean identity:

[tex]c ^{2} = a^{2} + b^{2}[/tex]

[tex]b = \sqrt{c^{2}-a^{2}}[/tex]

[tex]b = \sqrt{41^{2}-40^{2}}[/tex]

[tex]b = 3[/tex]

Now, the equation of the hyperbola is:

[tex]\frac{(x-30)^{2}}{40^{2}} - \frac{(y+15)^{2}}{3^{2}} = 1[/tex]

Answer:

The above answer is correct but the 3 should be a 9

Step-by-step explanation:

Plato

Answer:

x=18.9

Step-by-step explanation:

Answer:

2625*0.2= $525 in profit

Pls brainliest!!

Answer:

  b1 = (28/h) -b2

Step-by-step explanation:

Filling in the given value for A, you have ...

  14 = (1/2)(b1 +b2)h

Multiply by 2/h:

  28/h = b1 +b2

Subtract b2:

  b1 = (28/h) -b2

Step-by-step explanation:

75 ÷ 2/3 = 12.5

This is the correct answer

Answer:

The answer is 225/2 or 112 1/2 or 112.5

Step-by-step explanation:

When a number is divided by a fraction, you have to convert it into multiply by making the fraction upside down :

[tex]75 \div \frac{2}{3} [/tex]

[tex] = 75 \times \frac{3}{2} [/tex]

[tex] = \frac{75 \times 3}{2} [/tex]

[tex] = \frac{225}{2} [/tex]

[tex] = 112 \frac{1}{2} \: or \: 112.5[/tex]

Answer:

8

Step-by-step explanation:

6/3 + 2 x 3

6/3 + 6

2 + 6=8

Answer:

[tex]2/3[/tex]

Step-by-step explanation:

[tex]\frac{6}{3x}[/tex]

[tex]\frac{6}{3(3)}[/tex]

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

Answer:

134 - 85 = a

a = 49

Step-by-step explanation:

The sum of the two angles is 134

a+ 85 = 134

134 - 85 = a

49 =a

Answer:

3 laps per minute

Step-by-step explanation:

Take the number of laps and divide by the minutes

18/6 = 3 laps per minute

Answer:

3 laps per min

Step-by-step explanation: divide 18 and 6

Answer:

167

Step-by-step explanation:

Answer:

The probability that at most three used the emergency room for a sample of 10 people is 0.8791.

Step-by-step explanation:

The random  variable X can be defined as the number of people in a community using the emergency room.

The probability that a person uses the emergency room is, p = 0.20.

A sample of n = 10 people are selected.

A person using the emergency room is independent of others.

The random variable X thus follows a Binomial distribution with parameters n = 10 and p = 0.20.

The probability mass function of X is provided as follows:

[tex]P(X=x)={10\choose x}\ (0.20)^{x}\ (1-0.20)^{10-x};\ x=0,1,2,3...[/tex]

Compute the probability that at most three used the emergency room as follows:

P (X ≤ 3) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)

             [tex]=\sum\limits^{3}_{x=0}{{10\choose x}\ (0.20)^{x}\ (1-0.20)^{10-x}}\\\\=0.10737+0.26844+0.30199+0.20133\\\\=0.87913\\\\\approx 0.8791[/tex]

Thus, the probability that at most three used the emergency room for a sample of 10 people is 0.8791.

Answer:

The net of a triangular pyramid with an equilateral triangle for the base consists of four triangles, and at least three of them are congruent to each other.

Step-by-step explanation:

Answer:

t = 3 seconds

Step-by-step explanation:

I took the test and i got it right.

The time the given ball traveled for is required.

The time the ball traveled was t = 3 seconds

The given equation is [tex]H(t)=-16t^2+48t[/tex]

The ball never leaves the ground so the height of the ball is 0.

[tex]0=-16t^2+48t[/tex]

Solving the equation we get

[tex]-48t=-16t^2[/tex]

Dividing the equation by [tex]t[/tex] on both sides

[tex]\Rightarrow 48=16t[/tex]

Dividing the equation by 16 on both sides

[tex]\Rightarrow t=\dfrac{48}{16}\\\Rightarrow t=3\ \text{s}[/tex]

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Answer:

  see below

Step-by-step explanation:

You don't even need to do any math for this one.

All of the other figures will fit inside the first figure with space left over. Obviously, the first figure has the greatest volume.

The Cube is the diagram with the greatest volume which is 64 inch³.

The volume of a solid body represents the space occupied by the body.

For example:

Volume of Cube = (side)³

Volume of Sphere = 4/3  π (radius)³

Volume of Cylinder = π (radius)² (height)

Volume of Cone = ⅓ pi (radius)² (height)

We will just put the value of radius, side, and height in the formula of the Volume of the corresponding diagrams.

Volume of the given Cube = (4)³ = 64 inch³

Volume of the given sphere = 4/3 π (2)³ = 8(4/3)π = 33.51  inch³

as the radius of the sphere is 2 inches, because the diameter of the sphere is 4 inches.

Volume of the given Cylinder =  π (2)² (4) =50.26 inch³

as the radius of the Cylinder is 2 inches, because the diameter of the Cylinder is 4 inches.

Volume of the given Cone = ⅓ π (2)² (4) = 16.76  inch³

as the radius of the Cone is 2 inches, because the diameter of the Cone is 4 inches.

Thus, we come to the conclusion that the Cube is the diagram with the greatest volume which is 64 inch³.

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Answer:

C. 271.44 [tex]mm^3[/tex]

Step-by-step explanation:

We need to first find the volume of the pipe, then find the volume of the hole and then subtract the volume of the hole from the volume of the pipe.

The diameter of the pipe is 8.4 mm. This means its radius is:

8.4/2 = 4.2 mm

The height of the pipe is 10 mm

The volume of a cylinder is given as:

[tex]V = \pi r^2h[/tex]

where r = radius

h - height

Therefore, the volume of the cylinder  without the hole is:

[tex]V = \pi * 4.2^2 * 10\\\\V = 554.18 mm^3[/tex]

The diameter of the hole is 6 mm. Its radius is:

6/2 = 3 mm

The volume of the hole is:

[tex]V = \pi * 3^2 * 10\\\\V = 282.74 mm^3[/tex]

The volume is:

554.18 - 282.74 = 271.44 [tex]mm^3[/tex]

Answer:

B. 271.3 [tex]mm^{3}[/tex]

Step-by-step explanation:

Volume of the outer cylinder minus the volume of the inner cylinder returns the volume of the metal outer ring that surrounds the hole.

Answer: y=-3x-4

Step-by-step explanation:

Since we know slope, we can plug it into slope-intercept form to find the y-intercept by using the given points,

y=-3x+b

8=-3(-4)+b

8=12+b

b=-4

Now that we know the y-intercept, we can complete the slope-intercept form.

y=-3x-4

Answer:

5.7

Step-by-step explanation:

The altitude of a right triangle divides it into two smaller triangles, all three of which are similar.

ΔABC ~ ΔADB ~ ΔBDC

Writing and solving a proportion:

AD / BD = BD / CD

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

(x + 3) (2x + 3) = 25

2x² + 9x + 9 = 25

2x² + 9x − 16 = 0

x = [ -9 ± √(81 − 4(2)(-16)) ] / 2(2)

x = [ -9 ± √(81 + 128) ] / 4

x = (-9 ± √209) / 4

x = -5.86 or 1.36

Since x can't be -5.86, x = 1.36.  So the length of CD is:

CD = 2(1.36) + 3

CD = 5.7

Answer:

She needs $6,949.65 in the account today.

Step-by-step explanation:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

In this question:

She needs $9,000 in 3 years, so [tex]t = 3, A(t) = A(3) = 9000[/tex]

9% annual interest, so [tex]r = 0.09[/tex]

1 compounding, so [tex]n = 1[/tex]

How much money needs to be in the account today so she will have enough to pay for the repairs

We need to find P.

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]9000 = P(1 + \frac{0.09}{1})^{1*3}[/tex]

[tex]P(1.09)^{3} = 9000[/tex]

[tex]P = \frac{9000}{(1.09)^{3}}[/tex]

[tex]P = 6949.65[/tex]

She needs $6,949.65 in the account today.

Answer:

4 answer

Step-by-step explanation:

The quotient 1 / (1 + √3) is (- 1 +√3) / 2.

Option D is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1 / (1 +√3)

Rationalize the denominator.

1 / (1 +√3) x (1 -√3) / (1 -√3)

{ a² - b² = (a + b) (a - b) ]

(1 -√3) / (1 - 3)

(1 -√3) / -2

-(1 -√3) / 2

(- 1 +√3) / 2

Thus,

The final expression is (- 1 +√3) / 2

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Answer:

D and F

Step-by-step explanation:

In the attached file

Answer:

C= -5.3

Hope this helps!

Brainliest?

Answer:

C = -5.3

Step-by-step explanation:

C+9=3.7

Subtract 9 from both sides

C+9-9=3.7-9

Simplify

C = -5.3

Answer:

6 feet.

Step-by-step explanation:

Dimensions of the Pool =80 feet long by 20 feet wide

Area of the walkway =1344 square feet.

If the width of the walkway=w

Area of the Walkway =Area of the Larger Rectangle - Area of the Pool

[tex]1344=(80+2w)(20+2w)-(80*20)\\1344=80*20+160w+40w+4w^2-80*20\\4w^2+200w=1344\\4w^2+200w-1344=0\\We factorize\\4(w^2+50w-336)=0\\4(w^2-6w+56w-336)=0\\w(w-6)+56(w-6)=0\\(w-6)(w+56)=0\\w-6=0$ or $ w+56=0\\w=6$ ft or $ w=-56$ \\Therefore, the width of the walkway , w=6 feet.[/tex]

The question is incomplete:

The cost of a parking permit consists of a one-time administration fee plus a monthly fee. A permit purchased for 12 months costs $660. A permit purchased for 15 months costs $810.

What is the administration fee?

Answer:

$60

Step-by-step explanation:

To calculate the administration fee, first you have to calculate the difference between the two permits and divide that by the month difference that is: 15-12= 3 to know the cost of the monthly fee:

$810-$660= 150

$150/3= $50

Now, you can multiply the monthly fee for 12 to know the total cost of the monthly fee for 12 months and then, subtract this from the cost of a permit purchased for 12 months to find the cost of the one-time administration fee:

$50*12= $600

$660-$600= $60

According to this, the administration fee is $60.

Answer:

AB = 4.41

Step-by-step explanation:

→You are given the adjacent side and need to find the hypotenuse. For this, we use cos.

→Set it up, like so:

[tex]cos25=\frac{4}{x}[/tex]

→To get rid of the x in the denominator, multiply everything by x:

[tex]x(cos25=\frac{4}{x})[/tex]

[tex]xcos25 = 4[/tex]

→Divide both sides by cos25:

x = 4.413

→Round to nearest hundredth:

x = 4.41

Answer:P(BBR) = 1/2 × 25/51 × 26/50 = 13/102 if cards are not replaced.

P(RBB) = 1/2 × 26/51 × 25/50 (simplified 1/2) = 13/102

P(BRB) = 1/2 × 26/51 ×25/50 (simplified 1/2) = 13/102

Step-by-step explanation: P(B) at first step is 26 cards out of a possible 52 therefore 26/52 (or simplified 1/2). We then have 25 black cards left out of a possible 51 therefore 25/51. The final card then has to be red to meet the criteria, we have 26 red cards still out of a possible 50 therefore 26/50.

This would be an example of binomial probability as at each step there are only 2 options R or B.

Answer:

72

Step-by-step explanation:

Answer:

cost = c*d

Step-by-step explanation:

Unless the cost is calculated by the time (hours) or mileage, we can use the number of days in the calculation.

Everyday is one unit of c, so c times the number of days it is used gives us the cost. Simply multiply the number of days by cost per day to get the total cost.

Answer:

Step-by-step explanation:

1 km= 1000m

1.5 km = 1 x 1000 + 500

1000 + 500

1500m

1500 m : 250 m

750 m : 125 m

150 m : 25 m

30 m : 5 m

6 m : 1m

0.0

Answer:x=-8

Step-by-step explanation:

Answer:

40% profit

Step by step Explanation:

Profit percentage

=( profit/cost price) * 100

0.2 = profit/cost

10+15+20+25+30= 100

Let's assume the cost price of the items is $1 each

Cost price total= $100

Profit made when buyer of 20 toffe didn't say was

0.2=profit/cost

0.2*100 =$20

If the$ 20 paid.

Total profit = $40

So percentage profit now

40/100 * 100 = 40%

The shopkeeper makes a loss of 40% and this can be determined by using the given data.

Given :

The following steps can be used in order to determine the profit or loss the shopkeeper makes:

Step 1 - The total number of toffees can be calculated as:

[tex]\rm Total \; Toffees = 10 +15 + 20+ 25+ 30\\\rm Total \; Toffees = 100\\[/tex]

Step 2 - Now, let the cost of 1 toffee be $1. So, the cost of 80 toffees is $80.

Step 3 - So, the value of 20% profit by selling 80 toffees be 'x'. So, the value of 'x' is:

[tex]x = \dfrac{20}{100}\times 80[/tex]

[tex]x = \$16[/tex]

Step 4 - Now, let the profit or loss be 'y'. So, the value of 'y' is:

[tex]y = \dfrac{20}{80}\times 16[/tex]

[tex]y = \$4[/tex]

Step 5 - So, the loss percentage is 40%.

Therefore, the correct option is C).

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