MATHEMATICS HIGH SCHOOL

Solve the equation ; 4x-4=2x+10
Someone help?

Answers

Answer 1
Answer: 4x-4=2x+10
4x-2x=10+4
2x=14
x=14/2
x=7

hope this helps!

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When exercising Alison Berns 120 cal every 15 minutes how many calories does Allison burn during 75 minutes

Answers

120x75=9000

Hope this helps

A ladder is 95 inches tall. How tall is it in feet and inches

Answers

The answer is 7.91667 in feet but it is ninety five in inches.
 The ladder is about 7' 9''

What is the slope of the line 6x-2y=15?

a) -7.5
b) -3
c) 2.5
d) 3

Answers

What is the slope of the line 6x-2y=15?
 Rewrite the equation in the y = mx + b form
-2y = -6x+15
y = 3x + 15

m represents the slope.
So,
m = 3
the slope is m=3 in this case

A bag of fertilizer covers 3000 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 260 feet by 120 feet. *Round up to the nearest integer*

Answers

The number of bags of fertilizer should be purchased to cover a rectangular lawn 260 feet by 120 feet is 9.53 bags.

First step is to find the area of the lawn  

Area = 260 ft × 110 ft

Area = 28600 ft2

Second step is to calculate  how many bags of fertilizer

Number of bags=Area/3,000ft

Number of bags=28600 ft / 3000 ft

Number of bags= 9.53 bags

Inconclusion the number of bags of fertilizer should be purchased to cover a rectangular lawn 260 feet by 120 feet is 9.53 bags.

Learn more about area here:brainly.com/question/1631786
The first step is to find the area of the lawn. This can be done by multiplying its dimensions, so: 260 x 120. This equals 31,200.

Now to find how many bags of fertilizer are needed, divide 31,200 by 3000. This equals 10.4, but must be rounded up to 11bags of fertilizer.

The planets in our solar system do not travel in circular paths. Rather, their orbits are elliptical. The Sun is located at a focus of the ellipse. The perihelion is the point in a planet’s orbit that is closest to the Sun. So, it is the endpoint of the major axis that is closest to the Sun.

The aphelion is the point in the planet’s orbit that is furthest from the Sun. So, it is the endpoint of the major axis that is furthest from the Sun.

The closest Mercury comes to the Sun is about 46 million miles. The farthest Mercury travels from the Sun is about 70 million miles.


1. What is the distance between the perihelion and the aphelion?


2. What is the distance from the center of Mercury’s elliptical orbit and the Sun?


3. Write the equation of the elliptical orbit of Mercury, where the major axis runs horizontally. Allow a and b to be measured in millions of miles. Use the origin as the center of the

Answers

Answer:

(1) 83.764 million miles

(2) 52.766 million miles

(3) (x^2)/(4900)+(y^2)/(2116)=1.

Step-by-step explanation:

Let the origin C(0,0) be the center of the elliptical path as shown in the figure, where the location of the sun is at one of the two foci, say f.

The standard equation of the ellipse having the center at the origin is

(x^2)/(a^2)+(y^2)/(b^2)=1\;\cdots(i)

where a and b are the semi-axes of the ellipse along the x-axis and y-axis respectively.

Let the points P and A represent the points of perihelion (nearest to the sun) and the aphelion (farthest to the sun) of the closest planet Mercury.

Given that,

CP=46 million miles and

CA=70 million miles.

So, CP=b is the semi-minor axis and CA=a is the semi-major axis.

Let the distances on the axes are in millions of miles. So, the coordinates of the point P and A are P(0,46) and A(70,0) respectively.

(1) From the distance formula, the distance between the perihelion and the aphelion is

PA=√((0-70)^2+(46-0)^2)=83.764 million miles.

(2) Location of the Sun is at focus, f, of the elliptical path.

From the standard relation, the distance of the focus from the center of the ellipse, c, is

c=ae\;\cdots(ii)

where a and e are the semi-major axis and the eccentricity of the ellipse.

The eccentricity of the ellipse is

e=\sqrt{1-(b^2)/(a^2)}

\Rightarrow e=\sqrt{1-(46^2)/(70^2)}=0.7538.

Hence, from the equation (i) the distance of the Sun from the center of the elliptical path of the Mercury is

c=70*0.7538=52.766 million miles.

(3) From the equation (i), the equation of the elliptical orbit of Mercury is

(x^2)/(70^2)+(46^2)/(b^2)=1

\Rightarrow (x^2)/(4900)+(y^2)/(2116)=1.

In a sequence of numbers, each term except the first is 4 less than 4 times the previous term. If the fourth term in this sequence is 12, what is the first term?

Answers

First term is -1 because the common difference between each term 4n-4 where n is the term before. Therefore of you work backwards by taking 4 away from 12 then diving by 4 you should get 4 as third term. So you can keep going back till first term and you would get the following sequence

-1, 0, 4, 12...
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