A set of weights includes an 8 lb. barbell and 6 pairs of weight plates. Each pair of plates weighs 15 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in pounds can be represented by f(x) = 15x + 8. What is the range of the function for this situation?

Answer:

[tex]m = 3b+6[/tex]

Step-by-step explanation:

Given

[tex]f(x)=3x^2 - 9[/tex]

Required

The average rate over [tex][2,b][/tex]

Average rate (m) is calculated using:

[tex]m = \frac{f(b) - f(a)}{b - a}[/tex]

Where

[tex][a,b] = [2,b][/tex]

So, we have:

[tex]m = \frac{f(b) - f(2)}{b - 2}[/tex]

Calculate f(b) and f(2)

[tex]f(x)=3x^2 - 9[/tex]

[tex]f(b)=3b^2 - 9[/tex]

[tex]f(2)=3*2^2 - 9 = 12 - 9 = 3[/tex]

So, we have:

[tex]m = \frac{f(b) - f(2)}{b - 2}[/tex]

[tex]m = \frac{3b^2 - 9 - 3}{b - 2}[/tex]

[tex]m = \frac{3b^2 - 12}{b - 2}[/tex]

Expand the numerator

[tex]m = \frac{3b^2 + 6b-6b-12}{b - 2}[/tex]

Factorize

[tex]m = \frac{b(3b + 6)-2(3b+6)}{b - 2}[/tex]

Factor out 3b + 6

[tex]m = \frac{(b -2)(3b+6)}{b - 2}[/tex]

Cancel out b - 2

[tex]m = 3b+6[/tex]

Answer:

Step-by-step explanation:

Two triangles are said to be congruent if all their corresponding sides and corresponding angles are equal to each other.

Given that L is the midpoint of KN an MP, hence:

KL = LN; and ML = LN

Also, ∠KLM = ∠PLN (vertical opposite angles are congruent to each other)

Since ∠KLM = ∠PLN, KL = LN; and ML = LN, we can hence say that triangle KLM and triangle LNP are congruent triangles using Side-angle-side (SAS) triangle congruency theorem.

The SAS theorem states that if two sides and one included angle of one triangle is equal to two sides and an included angle of another triangle, then both triangle are congruent

Answer:

6x: 312

x: 52

Step-by-step explanation:

Let the deck be denoted by x then

6x:  312

There are 312 cards in 6x decks

In 1 deck x there are 312/6= 52 cards

6x: 312

6x/6: 312/6        Cancelling both sides by 6

x: 52

In ratio both the sides are divided by the same number to get equivalent fractions.

In 1 deck there are 52 cards

m<H + m< D = 180°

Since m<H and m<D are supplementary angles.

128°+m<D =180°

m<D = 180-128

m<D = 52°

Answer: m<D = 52°

Answer:

angle D=52 degree

Step-by-step explanation:

In supplementrary angles sum of two angles is always 180 degree

angle H +angle D=180 degree (since they are supplementary angles)

sbstitute the value of H

128 + angle D=180

angle D=180-128

angle D=52 degree

therefore angle D is 52 degree.

Answer:Hope This Helps ☺️

Step-by-step explanation:

She is not correct because she did not substitute the same number in both expressions in Step 1

Step-by-step explanation:

CASE 1: substitute 1 for x to both sides of the equations

L.H.S

-(4x-5)+2(x-3)

-(4 (1) - 5)+ 2(1-3) = - (-1) + 2(-2) = 1 - 4 = -3

R.H.S

-2x - 5

-2(1) - 5 = -2-5 = -7

Hence for x= 1

-(4x-5)+2(x-3) ≠ -2x -5

Because -3 ≠ -7

CASE 2: substitute -1 for x to both sides of the equations

L.H.S

-(4x-5)+2(x-3)

-(4 (-1) - 5)+ 2(-1-3) = - (-9) + 2(-4) = 9 - 8 = 1

R.H.S

-2x - 5

-2(-1) - 5 = 2-5 = -3

Hence for x= -1

-(4x-5)+2(x-3) ≠ -2x -5

Because 1 ≠ -3

Answer:

She is not correct because she did not substitute the same number in both expressions in Step 1

Answer:

45ml

Step-by-step explanation:

10 kg needs 18mL

So, 1kg = 1.8ml

25kg needs = 1.8kg/ml x 25 kg

25 kg dog would need 45ml.

Answer:

45 ml

Step-by-step explanation:

Weight of the dog and quantity of medicine is in Direct proportion.

Let the quantity required for 25 Kg dog =x

10 : 18 :: 25 : x

Product of extremes = product of means

10 * x = 18 * 25

[tex]x = \frac{18 * 25}{10}\\\\x = 9 * 5 \\\\x = 45[/tex]

Answer:

Option d

Step-by-step explanation:

→ Perimeter of rectangle = 2(l + w)

→ 14 = 2(4 + w)

→ 14 ÷ 2 = 4 + w

→ 7 = 4 + w

→ 7 - 4 = w

→ 3 ft = w

Therefore, width is 3 ft. (Option D)

Answer:

Isang Kilong Pako

Step-by-step explanation:

Ang pako po ay metal at ang bigas po ay grain lang kung ikukumpara mo sa isang butil ng bigas at pako, diba pako po ang mas mabigat, kung isang kilo pa po ehh mas mabigat na po iyon kaysa sa bigas.

Thank you Please mark as Brainliest :>

Answer:

Step-by-step explanation:

what do you know about the angles of a triangle? They make 180° right?

since you know that, now you can find  angle  Y  , by using the triangle on the left,   and you can find X by using the triangle on the right,  then,  when you know  X & Y , use both of those to find  Z  :)   got it?

Answer:

we know that a triangle's angles MUST add up to 180 degrees.

We can look at the triangle with the angles of 55, 80, and y. As the angles must add to 180, 55+80+y must be 180. Therefore, we find that y is equal to 45.

We can look at the triangle with the angles of 100, 60, and x. As the angles must add to 180, 100+60+x must be 180. Therefore, we find that x is equal to 20.

We then look at the triangle formed from x, y, and z. As the angles must add to 180, x+y+z must be 180. x is 20, y is 45, so 20+45+z = 180. Thus, z is 115.

So:

y = 45

x = 20

z = 115.

Answer:140 cm

Step-by-step explanation: If they ran twice: 70*2=140cm

Answer:

a. £25142.86

b. £16833.33

Step-by-step explanation:

According to the Question,

Given, The Salary Of 7 People in An Office are,

Andy ⇒ £9500

Bevan ⇒ £25000

Cheryl ⇒ £13250

Deva ⇒ £75000

Elliott ⇒ £12750  

Frankie ⇒ £29500

Grace ⇒ £11000

a. The mean income = Total Sum of Salaries ÷ Number of Workers

Mean = (9500+25000+13250+75000+12750+29500+11000) ÷ 7

Mean = 176000 / 7 ⇒ £25142.86

b. Now, The Mean income After Excluding Deva's Salary is,

Mean = (9500+25000+13250+12750+29500+11000) ÷ 6

Mean = 101000 / 6 ⇒ £16833.33

Step-by-step explanation:

hey :) I can't help you BUT there is a very good app I recommend it's called "algebrator". I really hope it helps you :)

Answer:

The answer is below

Step-by-step explanation:

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse side is equal to the sum of the square of the remaining sides. The hypotenuse is the longest side (that is side opposite to the 90° angle).

In right angle triangle ABD:

AB² = AD² + BD²     (1)

In right angle triangle ACD:

AC² = AD² + CD²      (2)

Also:

AC² + AB² = BC²       (3)

But BC = BD + CD

AC² + AB² = (BD + CD)²     (4)

Adding equation 1 and 2 gives:

AB² + AC² = (AD² + BD²) + (AD² + CD²)  

AB² + AC² = 2AD² + BD² + CD²

substituting AC² + AB² = (BD + CD)²:

(BD + CD)² = 2AD² + BD² + CD²

BD² + 2(BD)(CD)+ CD² = 2AD² + BD² + CD²

2AD² = 2(BD)(CD)

AD² = BD * CD

Answer:

y = -1/7

Step-by-step explanation:

Mathematically, the distance between two points on a coordinate plane can be calculated using the formula;

d = √(x2-x1)^2 + (y2-y1)^2

for the first two points;

(5,y) and (1,4) ; we have

d = √(5-1)^2 + (y-4)^2

d = √(y-4)^2 + 16

For the other two;

(5,y) and (10,-3)

We have ;

d = √(5-10)^2 + (y + 3)^2

d = √(y+ 3)^2 + 25

from the question, these two distances are equal

all we have to do here is to equate the two distances

So we have it that;

(y-4)^2 + 16 = (y + 3)^2 + 25

y^2 -8y + 16 + 16 = y^2 + 6y + 9 + 25

-8y + 32 = 6y + 34

-8y -6y = 34-32

-14y = 2

y = -2/14

y = -1/7

Answer:

about 22 square units

Step-by-step explanation:

sana makatulong

Answer:

C: About 22 square units

Step-by-step explanation:

YW

Answer:

22.68

Step-by-step explanation:

SOH (opp/hyp)

sin34 = 12/x

(x)sin34 = 12 - divide sin34 on both sides

x = 12/sin34

x = 22.68

Answer:

12?

Step-by-step explanation:

4x4= 16(area)

2x2=4(area menor)

16-4= 12

Answer: 3x^2-2x+1

Step-by-step explanation:

Answer:

3x² - 2x + 1

Step-by-step explanation:

To get 3x²

6x³ ÷ 2x

To get -2x

-4x² ÷ 2x

To get +1

2x ÷ 2x

Answer:

Used another answer on Brainly

Step-by-step explanation:

If 3 notebooks are 1.29 each, that’s 3.87 on notebooks. two dozen pencils at 3.45 a dozen is 6.90. add 3.87, 6.90, and 14.85 for a total of $25.62.

If 3 notebooks are 1.29 each, that’s 3.87 on notebooks. two dozen pencils at 3.45 a dozen is 6.90. add 3.87, 6.90, and 14.85 for a total of $25.62.

Answer:

Will cost 123 dollars.

Step-by-step explanation:

Find perimeter (50 m)

50 meters = 164 ft

164/10 ft = 16.4 ft

16.4 ft x 7.50 = 123 Dollars

Hope this helps. Consider giving brainliest :)

Answer:

cos 62=adjacent/hypotenuse

cos62=x/6

x=cos 62*6

x=2.8units

Answer:

x ≈ 2.8 units

Step-by-step explanation:

find measure of ∠B:  180-(90+62) = 28°

law of sines:

sin90°/6 = sin28°/x

1/6 = sin28°/ x

cross-multiply to get:

x = 6·sin28°

x ≈ 2.8 units

Answer:

Find the degree, leading term, and leading coefficient.

Polynomial Degree:  

3

Leading Term:  

8x^3

Leading Coefficient:  

8

Step-by-step explanation:

Answer:

Option (3)

Step-by-step explanation:

Properties for the vertical stretch or shrink of a function,

If a function is f(x) = k|x|

1). Function will be vertically stretched if k > 1

2). Function will have a vertical shrink if 0 < k < 1

To fit the given data graph of f(x) = |x| will vertically shrink without any translation along x or y-axis.

And the value of k will be, 0 < k < 1.

Therefore, g(x) = [tex]\frac{1}{3}f(x)[/tex] will be the transformed graph.

Therefore, Option (3) will be the correct option.

Answer:

3rd option

Step-by-step explanation:

The zeros ( where the graph crosses the x- axis ) are x = 3 and x = 7

The corresponding factors are then (x - 3) and (x - 7)

The equation is then

f(x) = a(x - 3)(x - 7) ← a is a multiplier

To find a substitute any point on the graph into the equation.

Using (8, 15 ) , then

15 = a(8 - 3)(8 - 7) = a(5)(1) = 5a ( divide both sides by 5 )

3 = a

Thus

f(x) = 3(x - 3)(x - 7)

Answer:

option a is right cz both have same value itz 1/root 2 hope it may help u

Answer:

0.60 & 60%

Step-by-step explanation:

Answer:

2%

Step-by-step explanation:

Answer:

m<S = 38°

Step-by-step explanation:

Given:

m<R = (x + 17)°

m<S = (2x - 2)°

m<T = (5x + 5)°

Required:

m<S

Solution:

First, we will need to determine the value of x by creating an equation. Thus:

m<R + m<S + m<T = 180° (sum of triangle)

Plug in the values

(x + 17)° + (2x - 2)° + (5x + 5)° = 180°

x + 17 + 2x - 2 + 5x + 5 = 180

Add like terms

8x + 20 = 180

8x + 20 - 20 = 180 - 20

8x = 160

8x/8 = 160/8

x = 20

Find m<S:

m<S = 2x - 2

Plug in the value of x

m<S = 2(20) - 2 = 40 - 2

m<S = 38°