7.
NOT TO
SCALE
8.
Р
С
B
In the diagram. PQ is parallel to BC.
APB and AQC are straight lines.
PQ = 8 cm, BC = 10 cm and AB = 9 cm.
Calculate PB​

Answer:

r = -12

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

6 + 18r = 20r - 18 - 4r

Step 2: Solve for r

Given:

The relations in the options.

To find:

The relation which is a function.

Solution:

Consider the options are :

(a) {(2, 7), (6, 5), (4, 4), (3, 3), (2, 1)}

(b) {(9, −3), (9, 3), (4, −2), (4, 2), (0, 0)}

(c) {(1, 0), (3, 0), (1, 1), (3, 1) (1, 3)}

(d) {(1, 1), (2, 2), (3, 3), (4, 4), (5, 8)}

A relation is a function if there exist a unique y-value for each x-value.

In option (a), y=7 and y=1 at x=2. So, it is not a function.

In option (b), y=-3 and y=3 at x=9. So, it is not a function.

In option (c), y=0 and y=1 at x=3. So, it is not a function.

In option (d), there are unique y-value for each x-value. So, it is a function.

Therefore, the correct option is (d).

Answer:

a) The height of the small object 3 seconds after being launched is 2304 feet.

b) The small object ascends 128 feet between 5 seconds and 7 seconds.

c) The object will take 6 and 10 seconds after launch to reach a height of 2640 feet.

d) The object will take 21 seconds to hit the ground.

Step-by-step explanation:

The correct formula for the height of the small object is:

[tex]h(t) = -16\cdot t^{2}+256\cdot t+1680[/tex] (1)

Where:

[tex]h[/tex] - Height above the ground, measured in feet.

[tex]t[/tex] - Time, measured in seconds.

a) The height of the small object at given time is found by evaluating the function:

[tex]h(3\,s)= -16\cdot (3\,s)^{2}+256\cdot (3\,s)+1680[/tex]

[tex]h(3\,s) = 2304\,ft[/tex]

The height of the small object 3 seconds after being launched is 2304 feet.

b) First, we evaluate the function at [tex]t = 5\,s[/tex] and [tex]t = 7\,s[/tex]:

[tex]h(5\,s)= -16\cdot (5\,s)^{2}+256\cdot (5\,s)+1680[/tex]

[tex]h(5\,s) = 2560\,s[/tex]

[tex]h(7\,s)= -16\cdot (7\,s)^{2}+256\cdot (7\,s)+1680[/tex]

[tex]h(7\,s) = 2688\,s[/tex]

We notice that the small object ascends in the given interval.

[tex]\Delta h = h(7\,s)-h(5\,s)[/tex]

[tex]\Delta h = 128\,ft[/tex]

The small object ascends 128 feet between 5 seconds and 7 seconds.

c) If we know that [tex]h = 2640\,ft[/tex], then (1) is reduced into this second-order polynomial:

[tex]-16\cdot t^{2}+256\cdot t-960=0[/tex] (2)

All roots of the resulting equation come from the Quadratic Formula:

[tex]t_{1} = 10\,s[/tex] and [tex]t_{2}= 6\,s[/tex]

The object will take 6 and 10 seconds after launch to reach a height of 2640 feet.

d) If we know that [tex]h = 0\,ft[/tex], then (1) is reduced into this second-order polynomial:

[tex]-16\cdot t^{2}+256\cdot t +1680 = 0[/tex] (3)

All roots of the resulting equation come from the Quadratic Formula:

[tex]t_{1} = 21\,s[/tex] and [tex]t_{2} = -5\,s[/tex]

Just the first root offers a solution that is physically reasonable.

The object will take 21 seconds to hit the ground.

Answer:

I am thinking it is distributive property

Step-by-step explanation:

3x -1 +2x + 4 x +1 = 180

9x = 180

X= 20

<ABC = 59

< CB D = 40

< DBE = 81

Answer:

c

Step-by-step explanation:

jesus do be gettin buff doe

Answer:

HL

Step-by-step explanation:

The hypotenuse and the "leg" are congruent...along with the 90 degree angle.

"The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent." - Calcworkshop

Answer:

The equation which correctly relates x and y is y = 4x

Step-by-step explanation:

The equation of the direct variation is y = k x, where

∵ The variables x and y vary directly

→ Use the form of the equation above

∴ y = k x

∵ When x = 13, y = 52

→ That means the initial values of x and y are 13 and 52

∴ x = 13 and y = 52

→ Substitute them in the equation above to find k

∵ 52 = k (13)

∴ 52 = 13k

→ Divide both sides by 13

∴ 4 = k

∴ The value of k is 4

→ Substitute it in the equation

∴ y = 4x

∴ The equation which correctly relates x and y is y = 4x

This question is incomplete

Complete Question

A contestant in a game show has​ 9,000 points. The contestant answers the next question incorrectly and loses 750 points. Does the word​ "lose" suggest a positive integer or a negative​ integer? What integer represents a loss of 750​ points?

a) Positive, + 750

b) Positive , - 750

c) Negative , +750

d) Negative , - 750

Answer:

d) Negative , - 750

Step-by-step explanation:

We are told in the question that the contestant has 9000 points

Then he loses 750 points.

This means that the 750 points would be deducted from the 9000 points he the contestant has already.

The word lose is a negative and it carries the Subtraction (-) sign,

hence, lose suggests a negative integer which is given as:

-750

Option d is the correct option

A

Step-by-step explanation:

two of the triangles' corresponding angles are the same even if the side lebgths are not, making these two similar

By AA similarity triangle ABC and triangle LMN are similar. Therefore, option A is the correct answer.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

In the given triangle ABC, ∠A=50° and ∠B=75°.

In the given triangle LMN, ∠L=50° and ∠M=75°

From the given triangles,

∠A=∠L=50°

∠B=∠M=75°

By AA similarity triangle ABC and triangle LMN are similar.

Therefore, option A is the correct answer.

To learn more about the similar triangles visit:

https://brainly.com/question/25882965.

#SPJ5

Answer:

45

Step-by-step explanation:

Given that :

Voucher awarded (x) :

Repair = $50

Lose or destroy = $200

P(x):

Replacement voucher = 5%

Repair voucher = 10%

X ______ 50 ______ 200

P(x) ____ 0.1 _______ 0.05

Expected variance Var(X) :

ΣX²p(x) - E(x) ;

E(x) = Σx*p(x) = (50*0.1) + (200*0.05) = 15

ΣX²p(x) = Σ[(50^2 * 0. 1) + (200^2 * 0.05)] = 250 + 2000 = 2250

Var(X) = 2250 - 15^2 = 2025

Standard deviation = √Var(x)

Standard deviation = √2025

Standard deviation = $45

Answer:

20/20

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

Given 2w + 8 = 6, find w

found w = -1, sub it into 3w - 1

Answer:

2/3

Step-by-step explanation:

24students - 8 boys = 16 girls

16/24

2/3

Answer:

[tex]\frac{16}{24}=\frac{2}{3}[/tex]

also

[tex]\frac{8}{24} =\frac{1}{3}[/tex]

Step-by-step explanation:

Answer:

There would be 35 ducklings

Step-by-step explanation:

If the ratio to baby ducklings to mama ducks is 7 to 1 then the constant of proportionality is 7. So you take the amount of mama ducks and multiply that by 7 you get your answer.

7 x 5 = 35

Answer:

nc

Step-by-step explanation:

nc

Answer:

52

Step-by-step explanation:

Answer:

Start by using your first factor, 1. Substitute "1" for each "x" in the equation: (1)3 - 4(1)2 - 7(1) + 10 = 0.

This gives you: 1 - 4 - 7 + 10 = 0.

Because 0 = 0 is a true statement, you know that x = 1 is a solution.

Step-by-step explanation:

Start by using your first factor, 1. Substitute "1" for each "x" in the equation: (1)3 - 4(1)2 - 7(1) + 10 = 0.

This gives you: 1 - 4 - 7 + 10 = 0.

Because 0 = 0 is a true statement, you know that x = 1 is a solution.

Answer:

1 is one of them

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

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Answer:

25 34 59 62

Step-by-step explanation:

easy shi thanks

Answer:

B.

Step-by-step explanation:

All of it needs to add up to 180

So you have

2x + 4x+10 + 6x-10 = 180

Combine like terms

12x=180

Answer:

Step-by-step explanation:r=12cm,h=18cm,v=?

Vol. Of a cylinder=Πr²h

V= Π×12²×18

V= Π×144×18

V=2592Πcm³

Answer:

A=73

B=107

Step-by-step explanation:

since the angles are across from eachother they would be the same, the total angle of all 4 added together would be 360, and 73+107 would be 180, so 180+180 is equal to 360

Answer: 3 x 11 = 33

Step-by-step explanation: Hope it helped!