1. The sum of Teresa's and Cathy's weight is
118 pounds. Teresa weighs 26 pounds more
than Cathy. If Teresa's weight is T and Cathy's
weight is C, which of these systems of
equations best represents this relationship?
A) T+C = 118
T= 26
B) T+C = 118
T +26=C
C) T+C=64
T-C= 26
D) T=C + 118
T=C+26
E) None of the above

So

[tex]\\ \rm\Rrightarrow v=r\omega[/tex]

[tex]\\ \rm\Rrightarrow r=\dfrac{v}{\omega}[/tex]

[tex]\\ \rm\Rrightarrow r=\dfrac{17\pi}{6}\div\dfrac{34\pi}{3}=\dfrac{17\pi}{6}\times \dfrac{3}{34\pi}[/tex]

[tex]\\ \rm\Rrightarrow r=\dfrac{1}{4}[/tex]

[tex]\\ \rm\Rrightarrow r=0.25ft[/tex]

Convert to ft

1 min=60s

Hence

So

[tex]\\ \rm\Rrightarrow r=\dfrac{17\pi}{6}\times \dfrac{1}{680\pi}[[/tex]

[tex]\\ \rm\Rrightarrow r=\dfrac{1}{40}[/tex]

[tex]\\ \rm\Rrightarrow r=0.025in[/tex]

Convert to ft

None of the above

The radius of the smaller gear is 15 feet, Option C is correct.

Velocity is defined as the rate of change of distance of a body with respect to time

We can use the relationship between linear velocity and angular velocity for gears to solve this problem:

v = rω

where v is the linear velocity, r is the radius of the gear, and ω is the angular velocity.

We are given the linear velocity of the larger gear, which is 17π/6 inches per second.

v = 17π/6 inches per second

ω = (34π/3) / 60 radians per second

the radius of the smaller gear is:

r = v / ω

= (17π/6) / ((34π/3) / 60)

= 17π/6×60/(34π/3)

=17π/6×60×3/34π

= 1/6 ×60× 3/2

= 180/12

=15 feet

Hence,  the radius of the smaller gear is 15 feet.

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B.

   [tex]x^2-8x+97=0[/tex]

[tex]x=\frac{-(-8)\pm\sqrt{(-8)^2-4\times1\times97}}{2\times1}\left\{x=\left.\ \frac{-b\pm\sqrt{b^2-4ac}}{2a}\right\}\right.[/tex]

  [tex]=\frac{8\pm\sqrt{-324}}{2}[/tex]

  [tex]=\frac{8\pm18i}{2}\left\{i^2\right.=-1\Longrightarrow\sqrt{-1}=\left.\ i\right\}[/tex]

[tex]\Rightarrow x_1=4-9i,x_2=4+9i[/tex]

[tex]\therefore Choose\ B.[/tex]

I hope this helps you

:)

Answer: 2,990 Is the amount of Bricks Marcus will use for the wall

Step-by-step explanation:

If the wall is 130 bricks high and 23 bricks across then all you have to do is 130 x 23 which gives you 2,990

but since the question asks for best estimate just choose the answer closest to 2,990 unles they have 2,990 as an answer

Hope this Helps!

Answer:

1 7/8 - 1 5/8 = 2/8.

Step-by-step explanation:

The amount of milk in cups that Samuel had after he made biscuits is 1/4 cups.

Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.

The process of subtraction can also be termed as finding difference.

Given that,

Amount of milk Samuel had = 1 7/8 cups

Amount of milk used to make biscuits = 1 5/8 cups

We have to find the amount of milk left after he made the biscuits.

This is found by subtracting the total amount of milk by the amount of milk used to make the biscuits.

Amount of milk left = 1 7/8 - 1 5/8

                                = 2/8

                                = 1/4 cups

Hence 1/4 cups of milk will be left.

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Answer:

12h+94=250, she will need to work 13 hours.

Step-by-step explanation:

we subtract 94 from 250, 250-94=156then we divide it by 12 which equals 13, 13=h.

[tex]a = \frac{(9.5 + 23.1) \times 5.8}{2} \\ [/tex]

[tex]a = \frac{32.6 \times 5.8}{2} \\ [/tex]

[tex]a = 16.3 \times 5.8[/tex]

[tex]a = 94.54 \: \: {m}^{2} [/tex]

Answer:

Domain: allrealnumbers

Range: f(x) <= -8

Step-by-step explanation:

This equation shows that this shape is a parabola that is opening downwards (because of the negative in the -5/6)

This means it has a highest point. The x+2 means the curve is shifted/slid/tranlated to the right 2 units and the -8 at the end shows that it is slid/shifted/translated down 8 units. So the curve only exists starting from -8 and going down. That is the range f(x) <= -8

All upward and downward opening parabolas have a domain of all real numbers.

Let's see

[tex]\\ \rm\rightarrowtail y=\dfrac{-5}{6}(x+2)^2-8[/tex]

[tex]\\ \rm\rightarrowtail x\in R[/tex]

Domain is R

Now

[tex]\\ \rm\rightarrowtail y=\dfrac{-5(x+2)^2}{6}-8[/tex]

Vertex form of parabola:-

On comparing with this

Hence

Range :-

b = 14

Step-by-step explanation:

3b/7 - 1 = 5

+1

3b/7. = 6

x7

3b. = 42

÷3

b = 14

Hope this helps!

the anwer to your question is very ieasy it's b

Answer:

<B = 70°

Step-by-step explanation:

First we need to find x, lets plugin these two equations.

2x - 30 = x + 20

Then find like terms

2x = x + 50 =

x = 50

Then we plugin 50 for x

2(50) - 30 =

100 - 30 = 70

<B = 70°

Hi!

The Triangle Angle Sum Theorem states that the sum of the interior angles in all triangles will always be 180 degrees.

We can set up an equation with the given information:

40 + (2x - 30) + (x + 20) = 180

Remove parentheses:

40 + 2x - 30 + x + 20 = 180

Combine like terms:

30 + 3x = 180

Subtract 30 from both sides:

3x = 150

Divide both sides by 3:

x = 50

Now, the problem wants us to solve for angle B.

Angle B is (2x - 30) degrees. We know the value of x, so we just have to substitute:

(2x - 30)

(2(50) - 30)

100 - 30

70

Therefore, angle B is 70 degrees.

Answer:

Hope it helps................

Answer:

The first option is the best

Step-by-step explanation:

1       (1+ 07/4)^4 = 7.186 % annual

2      ( 1+.068/12)^12 = 7.0159 %   annual

3       7.1 %

4       (1 + .069/365)^365 = 7.143

Answer:

you can get 4 pieces

Step-by-step explanation:

2.5+2.5+2.5+2.5=10. or 2.5×4=10

Answer:

If it’s 10%, 90x.90 plus 0x.10 = 81.If it’s 15%, 90x.85 plus 0x.15= 76.5If it’s 20%, 90x.80 plus 0x.20= 72.If it’s 25%, 90x.75 plus 0x.25= 67.5If it’s 30%, 90x.70 plus 0x.30= 63.If it’s 40%, 90x.60 plus 0x.40= 54.If it’s 50%, 90x.50 plus 0x.50= 45.

Step-by-step explanation:

The area of the rectangle in terms of x is 2x² - 8

A rectangle is a quadrilateral with four right angles in the Euclidean plane.

Given one side of the rectangle is 2x+4 and the perimeter is 6x+4

Let the other side be y.

We know that:

perimeter = 2 × (sum of two sides)

or, 6x + 4 =  2 (2x+4+y)

or,6x + 4 = 4x + 8 + 2y

or, 2x - 4 = 2 y

or, y = x - 2

Now area of the rectangle = product of sides =  (x - 2)(2x+4)

Area = 2x² - 4x + 4x - 8

or, Area = 2x² - 8

Hence the area of the rectangle in terms of x is  2x² - 8

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Answer:

4g² - 36gh + 81h²

Step-by-step explanation:

Apply the perfect square formula: (a - b)² = a² - 2ab + b²

(2g - 9h)²​ = (2g)² - 2(2g)(9h) + (9h)²

Simplify:

2g² = 4g²

-2 · 2g = -4g · 9h = -36gh

9h² = 81h²

= 4g² - 36gh + 81h²

hope this helps!

Answer:

B. 28

Step-by-step explanation:

boy to girls

4:3 to 16:?

4x4=16

so you would do

3x4=12

Now add them, 16+12=28

Answer:

The answer is

→ [tex]3 \frac{1}{8}x + 9\frac{11}{14}[/tex]

Step-by-step explanation:

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Answer:

Let s = his speed on the outbound trip

Then s + 20 = his speed on the return trip

Let t = his travel time on the outbound trip

Then t - 10 = his travel time for the return trip

Given: d = 750

Since distance = speed x time, for the two trips we have

750 = s*t

750 = (s+20)(t-10)

Solve for t in the 1st equation, substitute in the 2nd:

750 = (s+20)(750/s-10)

Solve for s:

750 = 750 - 10s + 15000/s - 200

Simplify:

s^2 + 20s - 1500 = 0

Factor:

(s+50)(s-30) = 0

Take the positive solution, s = 30

So the rates are 30 kph and 50 kph

Answer:

Upward

Step-by-step explanation:

Upward the graph looks like the above picture.

The computation of the factors shows that the greatest number of bags that Lucia can make will be 16.

From the information given, Lucia has 48 markers and 64 stickers that she wants to give as favors for a party.

The computation of the factors shows that the greatest number of bags that Lucia can make will be calculated through then factors. This goes thus:

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48

Factors of 64 = 1, 2, 4, 8, 16, 32, and 64.

Therefore, the highest common factor is 16.

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Answer:

16

Step-by-step explanation:

Answer:

y^2 - 28/7

Step-by-step explanation:

Answer:

the expression is equal to 40

Step-by-step explanation:

When given a= 5 and b=2, you can change your expression to read

3+11(5)-9(2)

All you have to do is simplify and you are given 40 :)

The lateral area of the prism is the area of the three rectangles in the middle of the net. (The two triangles are the bases of the prism, which don't count toward lateral area.) The total length of the three rectangular prism faces is (8 +15 +17) cm = 40 cm. The width of those rectangles is 9 cm. The lateral area will be the product of this length and width:

... lateral area = (40 cm)(9 cm) = 360 cm²

Answer:

16

Step-by-step explanation:

So if 4 numbers have an average of 14, that means to find the sum of all 4 numbers, you work backwards & multiply 4x14 to get 56.

Then 56-the sum of the 3 numbers you already have (11+12+17=40)

56-40=16

To double check, to find the average of 4 numbers that total 56, you divide 56 by 4 & get 14

Area = pi x r^2

R is radius which is 1/2 the diameter

r = 18/2 = 9

area = 3.14 x 9^2

Area = 254.34 mm^2