Find the value of 2a² + 5b² when a = -6 b= 2

Answers

Answer 1

Answer: -6^2 = 36 so 2x36 = 72 and 2^2 = 4 so 5x4 = 20
= 72 + 20 = 92

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Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the size of the lawn in acres. Two of his points are (3, 1.5) and (5, 2.5). Which statement describes the slope of the line through these two points?It takes Aaron about 1 hour to mow 2 acres.Aaron’s rate for mowing lawns is 0.5 acres per hour.The ratio of acres to time is 5 acres to 3 hours. The rate to mow a lawn is 0.6 hours per acre.
Divide 7/24 by 35/48 and reduce to lowest fraction
Find The Slope(-4, 6) and (-2,1)
The width of a rectangle is 61 centimeters more than the length. The perimeter is 406 centimeters. Find the length and the width.

Suppose the altitude to the hypotenuse of a right triangle bisects the hypotenuse. How does the length of the altitude compare with the lengths of the segments of the hypotenuse?a) The length of the altitude is equal to twice the length of one of the segments of the hypotenuse.
b) The length of the altitude is equal to half the length of one of the segments of the hypotenuse.
c) The length of the altitude is equal to the length of one of the segments of the hypotenuse.
d) The length of the altitude is equal to the sum of the lengths of the segments of the hypotenuse.

Answers

Answer:

Option: C is correct.

c) The length of the altitude is equal to the length of one of the segments of the hypotenuse.

Step-by-step explanation:

By the Right Triangle Altitude Theorem:

The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse.

From the figure we could say that:

$AD=√(CD\cdot DB)$

As the hypotenuse is divided into divided into two equal parts since the altitude bisects the hypotenuse of the right triangle.

This means that:

CD=DB

Hence,

$AD=\sqrt{CD^(2)}\n\nAD=CD$

Hence, we could say that:

c) The length of the altitude is equal to the length of one of the segments of the hypotenuse.

1. On a right triangle, how does the length of the median drawn to the ... lengths. D. C. B. A. Triangle ABC is a right triangle with is the median to the ... to the hypotenuse is one-half as long as the hypotenuse, ..... This segment is an altitude to both triangles, with bases. AD and DC. These two segments are equal in length.

1. What is the slope of the line that passes through the points (-2, 5) and (1, 4)?a. -3
b. -2
c. -1/3
d. 1/3

2. A line has a slope -5/3. Through which two points could this line pass?

a. (12,13) (17, 10)
b. (16, 15) (13, 10)
c. (0, 7) (3, 10)
d. (11, 13) (8, 18)

3. The pair of points (6,y) and (10, -1) lie on a line with slope 1/4. What is the value of y?

a. -5
b. -2
c. 2
d. 5

4. What is the slope of a vertical line?

a. -1
b. 0
c. 1
d. Undefined

5. The table below gives the best cost per person to rent a fishing charter boat. Find the rate of change given that it is a constant. Also explain what the rate of change means for this situation.

People l Cost ($)
2 l 110
3 l 165
4 l 220
5 l 275

a. 1/55
b. 110/1
c. 1/275
d. 55/1

Answers

1. (-2,5)(1,4)
slope = (4 - 5) / (1 - (-2) = -1 / 3

2. (11,13)(8,18)

3. (6,y)(10,-1)
slope = (-1 - y) / (10 - 6) = (-1- (-2) / 4 = 1/4
y = -2

4. undefined

5. (2,110)(3,165)
slope = (165 - 110) / (3 - 2) = 55/1
this basically means that to rent a charter boat, it will cost 55 per person

What is the nth term in the sequence:
4, 7, 12, 19, 28
Please show working out

Answers

4, 7, 12, 19, 28
1st difference +3 +5 +7 +9
2nd difference +2 +2 +2

This is a geometric sequence

The form is:
an² + bn + c
2a is always = to the second difference
2a = 2
a = 1

3a + b = 2nd term - 1st term
3(1) + b = 3
3 + b = 3
b = 0

a + b + c = 1st term
1 + 0 + c = 4
1 +c = 4
c = 3

nth term of sequence {substitute all we have found}
1n² + 0 + 3
n² + 3

Which are equivalent expressions? Check all that are true. 12x + 24y = 12(x + 2y) 12x − 24y = 12(x − 2y) 12x − 24y = 12(x ÷ 2y) 12x ÷ 24y = 12(x ÷ 2y) 12x · 24y = 12(x · 2y)

Answers

Answer:

Step-by-step explanation:

12x + 24y = 12(x + 2y)

12x - 24y = 12(x - 2y)

12x/24y = 12(x/2y)

Use the functions f(x) = 3x – 4 and g(x) = x2 – 2 to answer the following questions. Complete the tables.

x f(x)–3–1 0 2 5

x g(x)–3–1 0 2 5

For what value of the what value of the domain {–3, –1, 0, 2, 5} does f(x) = g(x) {–3, –1, 0, 2, 5} does f(x) = g(x)? Answer:

consider the relation {(–4, 3), (–1, 0), (0, –2), (2, 1), (4, 3)}.Graph the relation.
State the domain of the relation. State the range of the relation. Is the relation a function? How do you know? Answer:

2. graph the function f(x) = |x + 2|.

Answer:

consider the following expression. Rewrite the expression so that the first denominator is in factored form. Determine the LCD. (Write it in factored form.) Rewrite the expression so that both fractions are written with the LCD. Subtract and simplify.

Answer:

Answers

$1)\nf(x)=3x-4\n|\ \ \ x\ \ \ |\ \ -3\ \ \ |\ \ -1\ \ \ |\ \ \ 0\ \ \ |\ \ \ 2\ \ \ |\ \ \ 5\ \ \ |\n=========================\n|\ f(x)\ |\ \ -13\ \ |\ \ -7\ \ |\ -4\ \ |\ \ \ 2\ \ \ |\ \ \ 11\ \ |\n\nf(-3)=3\cdot(-3)-4=-9-4=-13\nf(-1)=3\cdot(-1)-4=-3-4=-7\nf(0)=3\cdot0-4=0-4=-4\nf(2)=3\cdot2-4=6-4=2\nf(5)=3\cdot5-4=15-4=11$

$g(x)=x^2-2\n|\ \ \ x\ \ \ |\ \ -3\ \ \ |\ \ -1\ \ \ |\ \ \ 0\ \ \ |\ \ \ 2\ \ \ |\ \ \ 5\ \ \ |\n=========================\n|\ g(x)\ |\ \ \ \ \ 7\ \ \ \ |\ \ -1\ \ \ |\ -2\ \ |\ \ \ 2\ \ |\ \ \ 23\ \ |\n\ng(-3)=(-3)^2-2=9-2=7\ng(-1)=(-1)^2-2=1-2=-1\ng(0)=0^2-2=0-2=-2\ng(2)=2^2-2=4-2=2\ng(5)=5^2-2=25-2=23\n\nf(x)=g(x)\ \ \ \Leftrightarrow\ \ \ x=2,\ \ \ \ because\ \ \ \ f(2)=2\ \ \ and\ \ \ g(2)=2$

$2)\nthe\ relation:\ \{(-4, 3), (-1, 0), (0, -2), (2,1), (4, 3)\}.\n\nthe\ domain:\ D=\{-4,-1,0,2,4\}\nthe\ range:\ R=\{3,0,-2,1\}\n\nThis\ relation\ is\ the\ function,\ because\ \ each\ number\n of\ the\ domain\ D\ has\ exactly\ one\ value\ in\ the\ range\ R.$

$3)\nf(x)=|x+2|\n\n|x+2|= \left \{ {\big{x+2\ \ \ \ \ if\ \ \ x \geq -2} \atop \big{-x-2\ \ \ if\ \ \ x<-2}} \right.$

Answer:

-11 and 0 for EDGE2020

f(4)= -11

If g(x)=2, x= 0

Step-by-step explanation:

Evaluate [3(5 + 6) + 2] ÷ 7