H(x)=-2x-5, find h(-2)

(sinB+1)(cosBtanB-1)

Karo-lina-s [1.5K]

Here you go!!! I hope this helps

6 0

2 years ago

Find the point, M, that divides segment AB into a ratio of 5:2 if A is at (1, 2) and B is at (8, 16).

d1i1m1o1n [39]

Since M divides segment AB into a ratio of 5:2, we can say that M is 5/(5+2) of the length of AB. Therefore 5/7 × AB.
distance of AB = d
5/7×(x2 - x1) for the x and 5/7×(y2 - y1) for the y
5/7×(8 - 1) = 5/7 (7) = 5 for the x
and 5/7×(16 - 2) = 5/7 (14) = 10 for the y
But remember the line AB starts at A (1, 2),
so add 1 to the x: 5+1 = 6
and add 2 to the y: 10+2 = 12
Therefore the point M lies exactly at...
A) (6, 12)

4 0

3 years ago

Maths functions question!!

Marina86 [1]

Answer:

5) DE = 7 units and DF = 4 units

6) ST = 8 units

$\textsf{7)} \quad \sf OM=\dfrac{3}{2}\:units$

8) x ≤ -3 and x ≥ 3

Step-by-step explanation:

<u>Information from Parts 1-4:</u>

brainly.com/question/28193969

$f(x)=-x+3$

$g(x)=x^2-9$

A = (3, 0) and C = (-3, 0)

Points A and D are the <u>points of intersection</u> of the two functions.

To find the x-values of the points of intersection, equate the two functions and solve for x:

$\implies g(x)=f(x)$

$\implies x^2-9=-x+3$

$\implies x^2+x-12=0$

$\implies x^2+4x-3x-12=0$

$\implies x(x+4)-3(x+4)=0$

$\implies (x-3)(x+4)=0$

Apply the zero-product property:

$\implies (x-3)= \implies x=3$

$\implies (x+4)=0 \implies x=-4$

From inspection of the graph, we can see that the x-value of point D is <u>negative</u>, therefore the x-value of point D is x = -4.

To find the y-value of point D, substitute the found value of x into one of the functions:

$\implies f(-4)=-(-4)=7$

Therefore, D = (-4, 7).

The length of DE is the difference between the y-value of D and the x-axis:

⇒ DE = 7 units

The length of DF is the difference between the x-value of D and the x-axis:

⇒ DF = 4 units

To find point S, substitute the x-value of point T into function g(x):

$\implies g(4)=(4)^2-9=7$

Therefore, S = (4, 7).

The length ST is the difference between the y-values of points S and T:

$\implies ST=y_S-y_T=7-(-1)=8$

Therefore, ST = 8 units.

The given length of QR (⁴⁵/₄) is the difference between the functions at the same value of x. To find the x-value of points Q and R (and therefore the x-value of point M), subtract g(x) from f(x) and equate to QR, then solve for x:

$\implies f(x)-g(x)=QR$

$\implies -x+3-(x^2-9)=\dfrac{45}{4}$

$\implies -x+3-x^2+9=\dfrac{45}{4}$

$\implies -x^2-x+\dfrac{3}{4}=0$

$\implies -4\left(-x^2-x+\dfrac{3}{4}\right)=-4(0)$

$\implies 4x^2+4x-3=0$

$\implies 4x^2+6x-2x-3=0$

$\implies 2x(2x+3)-1(2x+3)=0$

$\implies (2x-1)(2x+3)=0$

Apply the zero-product property:

$\implies (2x-1)=0 \implies x=\dfrac{1}{2}$

$\implies (2x+3)=0 \implies x=-\dfrac{3}{2}$

As the x-value of points M, Q and P is negative, x = -³/₂.

Length OM is the difference between the x-values of points M and the origin O:

$\implies x_O-x_m=o-(-\frac{3}{2})=\dfrac{3}{2}$

Therefore, OM = ³/₂ units.

The values of x for which g(x) ≥ 0 are the values of x when the parabola is above the x-axis.

Therefore, g(x) ≥ 0 when x ≤ -3 and x ≥ 3.

8 0

1 year ago

Read 2 more answers

John could not decide, but he had 9 dollars he could spend on fruit kabobs that cast 1.75 dollars and smoothies that cost 2.50 d

IrinaK [193]

Answer:

One fruit kabob and one smoothie

Two fruits kabobs and two smoothies

Three fruit kabobs and one smoothie

One fruit kabob and two smoothies

Explanation:

In this situation, the basic combination John can afford is simply to buy one fruit kabob and one smoothie ( $1.75 + $ 2.50 = $4.25) because he wants at least one unit of each item. Additionally, it is possible to add more units of each item to create new combinations or possibles, just make sure they do not total more than 9 dollars, which is the money John has. Here are some of the possible combinations:

Two fruit kabobs and two smoothies

Fruit kabobs: $1.75 x 2 = $3.5

Smoothies: $ 2.50 x 2 = $5

Total: $8.5

Three fruit kabobs and one smoothie

Fruit kabobs: $1.75 x 3 = $5.25

Smoothie: $2.50

Total: $7.75

One fruit kabob and two smoothies

Fruit kabob: $1.75

Smoothies: $2.50 x 2 = $5

Total: $6.75

5 0

3 years ago

For the first 3% of Hanna's salary, her employer matches 100% of her 401(k) contributions, and from 3% to 12%, Hanna's employer

AleksAgata [21]

Answer:

My apex said 3000..idk if you need it anymore. I have no idea how to solve it either.

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers