MATHEMATICS HIGH SCHOOL

What is the slope of a line that passes through (–14,13) and (7,0)? A. 21/13
B. -13/21
C. 13/21
D. -21/13

Answers

Answer 1
Answer:

Answer:

Option B is correct.

-(13)/(21)

Step-by-step explanation:

Slope of the line that passes through the point is given by:

\text{Slope} = (y_2-y_1)/(x_2-x_1)

As per the statement:

A line that passes through (–14,13) and (7,0)

then;

\text{Slope} = (0-13)/(7-(-14))

⇒\text{Slope} = (-13)/(7+14)

⇒\text{Slope} = (-13)/(21)

Therefore, the slope of a line that passes through (–14,13) and (7,0) is,  -(13)/(21)
Answer 2
Answer: the answer is choice b.
y2-y1/x2-x1

0-13/ 7-(-14)
-13/7+14
-13/21

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How many roots does the function have?f(x)= x^6 + 2x^5 - 2x^4 + 3x^3 + 4x^2 - 5x +7


A. 21

B. 2

C. 6

D. 7

Answers

Answer:

  C.  6

Step-by-step explanation:

The degree of the polynomial function is 6. The "fundamental theorem of algebra" tells you the number of roots is equal to the degree of the polynomial.

f(x) has 6 roots.

Find the limit. lim (x-5)/((x^2)-25) x-> 5+

Answers

\lim_(x \to 5) (x-5)/( x^(2) -25) =( (0)/(0) ) = \n =\lim_(x \to 5) (x-5)/((x-5)(x+5))= \n =\lim_(x \to 5) (1)/(x+5)= \n = (1)/(5+5)= (1)/(10) = 0.1

Suppose the surface area of a sphere is 324π square units. What is the volume, in cubic units, of this sphereA) 9π
B) 81π
C) 324π
D) 972π

Answers

Answer:

Option D is correct

972 \pi is the volume, in cubic units, of this sphere

Step-by-step explanation:

Surface area of sphere(S) and volume of sphere (V) is given by:

S = 4 \pi r^2

V = (4)/(3) \pi r^3                 .....[1]

As per the statement:

Suppose the surface area of a sphere is 324π square units

⇒S = 324π square units

then;

324 \pi = 4 \pi r^2

Divide both side by 4 \pi we have;

81 = r^2

or

r^2= 81

⇒r = √(81) = 9 units

We have to find  the volume, in cubic units, of this sphere.

Substitute the given value in [1] we have;

V = (4)/(3) \pi \cdot 9^3 = (4)/(3) \pi \cdot 729

Simplify:

V = 4 \cdot \pi \cdot 243 = 972 \pi cubic units

Therefore, 972 \pi is the volume, in cubic units, of this sphere
D would be the answer

The length of a rectangle is 10 mm longer than its width. Its perimeter is more than 80 mm. Let w equal thewidth of the rectangle.
(a) Write an expression for the length in terms of the width.
(b) Use these expressions to write an inequality based on the given information.
(c) Solve the inequality, clearly indicating the width of the rectangle

Answers

P=L+L+W+W=2(L+W)
P>80
2(L+W)>80
divide 2
L+W>80

L is 10 more than W
L=10+W

A. L=10+W

B. L+W>80

C.
L+W>80
sub L=10+W
10+W+W>80
minus 10
2W>70
divid 2
W>35
W is mor than 35
We know that the length (L) of the rectangle in question is 7mm longer than its width (W). Let's represent that as the following:
L=7+W

A rectangle's perimeter (the total sum of its sides) will be made my 2 sides representing the length  (2L) and 2 sides representing the width (2W).  We also know that this rectangle's perimeter is greater than 62. Since eventually we are solving for W, let's state all expressions in terms of W:
2L=2(7+W)
2(7+W)+2W>62
14+2W+2W>62
14+4W>62
4W>62-14
4W>48
W>48/4
W>12
If the rectangle's perimeter is greater than 62, then the width  will be greater than 12. Let's confirm this:
Perimeter=2L+2W
P=2(7+12)+2(12)
P=14+24+24
P=62
So we can see that if the perimeter is to surpass 62, W needs to be greater than 12 and L ( which is also 7+W) needs to be greater than 19.

NEED ANSWER ASAP!! WILL GIVE POINTS AND MARK AS BRAINLIEST!!!

Answers

Answer:

what has become of this site????

Step-by-step explanation:

they literally told me to pay a fee for being greatful for points

Which of the following is the equation of a line parallel to the line y=3x+2, passing through the point (10,1)?A. 3x - y=29
B. 3x + y=29
C. -3x-y=29
D. 3x + y=29

Answers

Answer:

Option A

Step-by-step explanation:

We have to find the equation of a line parallel to y = 3x + 2 and passing through (10, 1)

Slope of the given line y = 3x + 2 is 3

So line parallel to this line will have same slope = 3

Now we assume this line is y = 3x + c

It is given that a point ( 10,1 ) lies on this line.

So we put x = 10 and y = 1 in this equation to get

y-intercept

1 = 30 + c

c = - 29

Equation of the line will be y = 3x - 29

or   -3x + y = -29  ⇒ 3x - Y = 29

Option A is the answer.
I think it's A. One way you can identify if they are parallel is if both of the slopes are the same (also both have to have the same signs). 
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