Step-by-step explanation:
1. given,
4x = 13 + 5
= 4x= 8
= x = 8/4
there fore x = 2
2. given,
= a < 11- 8
= a < 3
3. given,
b< 2-15
= b < 13
write these symbolically
1. a + 5 is not equal 15
2. b - 8 > 3
3. 5 × c is not qual 4
The slope of the line that passes through (5, 4) and (-4,3) is ![\frac{1}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B9%7D)
<u>Solution:</u>
Given, two points are (5, 4) and (-4, 3)
We have to find the slope of a line that passes through the above given two points.
Slope of a line that pass through
is given as:
![m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
![\text { Here, in our problem, } x_{1}=-4, y_{1}=3 \text { and } x_{2}=5, y_{2}=4](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Here%2C%20in%20our%20problem%2C%20%7D%20x_%7B1%7D%3D-4%2C%20y_%7B1%7D%3D3%20%5Ctext%20%7B%20and%20%7D%20x_%7B2%7D%3D5%2C%20y_%7B2%7D%3D4)
![\text { slope } m=\frac{4-3}{5-(-4)}=\frac{1}{5+4}=\frac{1}{9}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20slope%20%7D%20m%3D%5Cfrac%7B4-3%7D%7B5-%28-4%29%7D%3D%5Cfrac%7B1%7D%7B5%2B4%7D%3D%5Cfrac%7B1%7D%7B9%7D)
Hence, the slope the line that passes through the given points is ![\frac{1}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B9%7D)
Answer:
a. 8
b. 2, 3, 4
Step-by-step explanation:
We have to:
Pedro's age = 14 years
Elisa's age = 3 years
The years to elapse = x
Pedro's age = 14 + x
Elisa's age = 3 + x
14 + x = 2 * (3 + x)
14 + x = 6 + 2 * x
14 - 6 = 2 * x - x
x = 8
Eight years must pass before Pedro's age is twice Elisa's
Now the second question:
Let x be the smallest number
Let x + 1 be the consecutive number
Let x + 2 be the consecutive number
x + (x + 1) + (x + 2) = 2 * (x + 2) +1
x + x +1 + x + 2 = 2 * x + 4 + 1
3 * x +3 = 2 * x + 5
3 * x -2 * x = 5 - 3
x = 2
So:
x = 2
x + 1 = 2 + 1 = 3
x + 2 = 2 + 2 = 4
Therefore the numbers are 2, 3, 4 are consecutive and equality is true
Choose the most appropriate unit to measure the weight of each.
Write oz., lb., or T.
#1. Car = T
#2. Computer = lb.
#3. Bowling Ball = lb.
#4. Onion = oz.
#5. Tyrannosaurus Rex = T.
#6. Vacuum Cleaner = lb.
#7. Q. A hippo weighs about 5,000 lb.. Does the same hippo weigh more or less than 5,000 oz.?
A. If one ounces is 0.0625 pounds then 5000 ounces are 312.5 pounds so the same hippo weighs more than 5,000 oz.
Hope I helped!
Answer:
The graph of the ellipse is shown in the attachment
vertices; ( -5,0) and (5,0)
co-vertices; (0, -2) and (0, 2)
foci; (
,0), (
,0)
Step-by-step explanation:
The vertices and co-vertices of the ellipse are on the graph. They represent the turning points of the ellipse.
To determine the foci of the ellipse we write the given equation in standard form by dividing both sides by 100 and then simplifying;
![\frac{x^{2} }{25}+\frac{y^{2} }{4}=1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E%7B2%7D%20%7D%7B25%7D%2B%5Cfrac%7By%5E%7B2%7D%20%7D%7B4%7D%3D1)
We then determine the distance c from the center to the focus;
![c^{2}=a^{2}-b^{2}](https://tex.z-dn.net/?f=c%5E%7B2%7D%3Da%5E%7B2%7D-b%5E%7B2%7D)
![c=\sqrt{25-4}=\sqrt{21}](https://tex.z-dn.net/?f=c%3D%5Csqrt%7B25-4%7D%3D%5Csqrt%7B21%7D)
The foci of the ellipse are thus; (
,0), (
,0)