Which of the following statements must be true based on the diagram below?
(Diagram is not to scale.)

First, we'll set up two equations. One for the amount of each coin and another for the value of the coins.

N will represent nickels

D will represent dimes

N + D = 30

---The problem tells us that there are 30 total coins

0.05N + 0.10D = 2.95

---Nickels are worth 5 cents and dimes are worth 10 cents, and the total value of the coins is 2.95

Now that we have our equations, we need to solve for one of the variables in the first equation. I will solve for N.

N + D = 30

N = 30 - D

Then, we take that equation and substitute our new value for N into the second equation (value) and solve for D.

0.05(30 - D) + 0.10D = 2.95

1.5 - 0.05D + 0.10D = 2.95

1.5 + 0.05D = 2.95

0.05D = 1.45

D = 29

Now that we know how many dimes there are, we can plug that value into our equation for N and solve for N.

N = 30 - D

N = 30 - 29

N = 1

Therefore, there are 29 dimes and 1 nickel.

Hope this helps!

Answer:

Hello Bro How Are You....?

Answer:

23

Step-by-step explanation:

The answer is 23 by the definition of angle bisector.

Answer:

Step-by-step explanation:

-5n^2-45=7--->-5n^2=52--->n^2=52÷(-5)= there is no answer for this question...I mean Paired power never has a negative answer.

Answer:

Value of given expression x is -4

Step-by-step explanation:

Given equation in question;

4 + 2|3x + 4| = -4

Find:

Value of given expression

Computation:

4 + 2|3x + 4| = -4

Using BODMAS rule;

⇒ 4 + 2|3x + 4| = -4

⇒ 2|3x + 4| = - 4 - 4

⇒ 2|3x + 4| = - 8

⇒ |3x + 4| = - 8 / 2

⇒ |3x + 4| = - 4

⇒ 3x + 4 = - 8

⇒ 3x = -8 - 4

⇒ 3x = -12

⇒ x = -12 / 3

⇒ x = -4

Value of given expression x is -4

Answer:

(-5, 3)

Step-by-step explanation:

Answer:

V =48 cm^3

Step-by-step explanation:

The volume of a prism is given by

V = l*w*h

V = 3*4*4

V =48 cm^3

V =48 cm^3

Step-by-step explanation:

The volume of a prism is given by

V = l*w*h

V = 3*4*4

V =48 cm^3

Answer:

the answer will be 44 I think I hoped I helped if not sorry.

Step-by-step explanation:

Answer:

D. having students write a definition for each term in their own words in their native language

Step-by-step explanation:

In Mr Fischer's mathematics class, we are presented with two categories of learners. Those that are native speakers of English and those who are learners of English.

Both categories of students would show their understanding best in this lesson if they were to write in their own native language.

The native english-speakers would have no issues writing in English, but those who are English learners would have problems communicating their understanding of the lesson in English. So it is best they give their definitions in their native language.

Answer:

[tex] = { \tt{ \frac{30}{120} + \frac{40}{120} }} \\ = \frac{7}{12} [/tex]

Answer:

It is the second option down

Step-by-step explanation:

Answer:

yes because we are leraning new things

Answer:

A) (0,-3)

Step-by-step explanation:

to get the y-intercept let x = 0, then

y = 0 + 0 -3

y = -3

Answer:

(0,-3)

Step-by-step explanation:

The y intercept is where x=0

ƒ(x) = –x^2 + 4x – 3?

f(0) = -0^2 +4(0)-3

f(0) = -3

(0,-3)

Answer:

ofc its p/q

Step-by-step explanation:

Answer:

16 y squared minus x squared

Step-by-step explanation:

The other all expressions except 16y²-x² doesn't complete the square and its difference. Then we can check 16y²-x²,

Now take the expression 16y²-x² and we can try to solve it.

We can simplify the terms separately to associate them as perfect squares,

→ 16y² = (4y)² --- (1)

→ x² = (1x)² --- (2)

Now we can take the difference of eq. (1) and eq. (2),

→ 16y²-x²

→ (4y)²-(1x)² --- (3)

Now eq. (3) shows a difference of squares.

Another representation is,

→ (4y - x) (4y + x)

→ 16y²- x²

→ (4y)²- (1x)²

Therefore, the expression 16y²-x² shows a correct difference of squares.

Answer:

its b trust

Step-by-step explanation:

The function is negative for all real values of x where x < -3 or x > -1 and the domain of the function is -∝ < x < ∝

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = - ( x + 3 ) ( x - 1 )   be equation (1)

Now , the values of x which makes the function negative are

when x < -3

f ( x ) = - ( -ve ) ( -ve ) = -ve

when x > 1

f ( x ) = - ( +ve ) ( +ve ) = -ve

So , the domain of the function is all real numbers and -∝ < x < ∝

Hence , the function is solved

To learn more about domain and range click :

https://brainly.com/question/28135761

#SPJ7

Answer:

(8x + 3)²

Step-by-step explanation:

Since our polynomial is 64x² + 48x + 9, we multiply 64x² by 9 to get 64x² × 9 = 576x² since we cannot simplify the expression any further.

Next, we need to find the factors of 576x² that add up to give 48x, these are 24x and 24x.

So the expression is re-written as

64x² + 48x + 9 = 64x² + 24x + 24x + 9

Writing out all the common factors, we have,

64x² + 48x + 9 = 8x × 8x + 3 × 8x + 3 × 8x + 3 × 3

Factorizing we have

64x² + 48x + 9 = 8x(8x + 3) + 3(8x + 3)

64x² + 48x + 9 = (8x + 3)(8x + 3)

64x² + 48x + 9 = (8x + 3)²

Answer:

Cost of each football ticket=$41.56

Cost of each  basketball ticket=$43.56

Step-by-step explanation:

Let

Cost of each football ticket=x

Cost of each basket ball ticket=y

According to question

[tex]2x+y=126.77[/tex]...(1)

[tex]x+2y=128.86[/tex] ....(2)

We have to find  the cost of each ticket.

Equation (1) multiply by 2 then we get

[tex]4x+2y=253.54[/tex]  .....(3)

Now, subtract equation (2) from (3)

[tex]3x=124.68[/tex]

[tex]x=124.68/3[/tex]

[tex]x=41.56[/tex]

Now, using the value of x in equation (2)

[tex]41.56+2y=128.86[/tex]

[tex]2y=128.86-41.56[/tex]

[tex]2y=87.3[/tex]

[tex]y=87.3/2=43.65[/tex]

Hence, cost of each football ticket=$41.56

Cost of each  basketball ticket=$43.56

Answer:

RW is congruent to WX

Step-by-step explanation:

We know that PW and WV and Angle W is vertical angle so We need to include that RW congruent to WX.

Answer:

150 degrees

Step-by-step explanation:

5 + 1 = 6

180 : 6 = 30

30 x 5 = 150

Answer:

D. distance

Step-by-step explanation:

really ? given the choices you needed help with that ?

only D makes sense. the rest is completely ridiculous and has nothing to do with driving from the house to the library.

Step-by-step explanation:

D) (A³/2)³ = A⁹/8

A³ whole to the power 3 is A⁹

2³ is 8

Answer:

HT = 17 cm

<T = 58°

<H = 32°

Step-by-step explanation:

✔️Find HT:

Since it's a right triangle, we would apply the Pythagorean Theorem given as c² = a² + b²

Where,

a = HW = 15 cm

b = WT = 8 cm

c = HT

Plug in the values:

HT² = 15² + 8²

HT² = 289

HT = √289

HT = 17 cm

✔️Find <T by applying trigonometric ratio formula:

Recall: SOH CAH TOA

Reference angle (θ) = <T

HW = 15 cm = Opposite side length

WT = 8 cm = Adjacent side length

Apply CAH:

Cos θ = Adj/Hyp

Substitute

Cos T = 8/15

T = [tex] cos^{-1}(0.5333) [/tex]

T ≈ 58°

✔️Find <H:

Sun of interior angles of a triangle = 180°

Therefore,

m<H + m<T + m<W = 180°

Substitute

m<H + 58° + 90° = 180°

m<H + 148° = 180°

m<H = 180° - 148°

m<H = 32°

Answer:

y represents the amount in the bank account after 7 months.

Step-by-step explanation:

Let karma gets x money on his birthday.

He has 60 in his account initially

He deposits teh same money for the seven months

So, the money he has after the seven months is 7 x + 60  

According to the question,

y =7 x + 60

It shows that the amount after seven months is y.  

Answer: 36

Step-by-step explanation= First let's calculate the area of the the inner rectangle so 6x4=24. Now let's add the area of the rectangle,(BY CUTTING IT INTO HALF) this part is hard but first lets add 3 cm then, 2 cm then lets add, 1 cm. So (3x2 is 6) now lets multiply that by 1, so you get 6. Multiply that by 4 it = 24 now let's add 24+24 which = 48. Hope it helps!!

Answer:

Yes it can

Step-by-step explanation:

To check wether it's a right angle triangle we need to apply the Pythagoras theorem

h^2= a^2 +b^2

Hypotenuse is always the longest side so

5^2 = 3^2 + 4^2

This is correct, so the triangle is a right angle triangle

Answer from Gauthmath

Answer:

-5 <x<-1

Step-by-step explanation:

4|x+3|<8

Divide by 4

4|x+3| /4<8/4

|x+3|<2

There are two solutions one positive and one negative, remember to flip the inequality for the negative

x+3 <2    and x+3 >-2

Subtract 3 from each side

x+3-3 <2-3   and x+3-3 >-2-3

x<-1   and x>-5

-5 <x<-1

In case of Nina:

slope of graph = speed = 48-32/6-4 = 16/2 =8

y-32 =8(x-4)

y-32=8x-32

y=8x

d=8t

at x= 0 i.e at t= 0

d= 0m

In case of Ryan:

slope =speed = 47.5-35=6-4 = 12.5/2 =6.25

y-35=6.25(x-4)

y-35=6.25x-25

y=6.25x+10

d=6.25t+10

at t = 0, d= 10m

RYAN had a head start of 10 m

Answer:

y = 2·x/3 - 1

Step-by-step explanation:

The endpoints of the longer base of the trapezoid = (-2, -4), and (4, 0)

The point contained on the shorter base = (3, 1)

The slope of the line representing the longer base, m, is given as follows;

m = (0 - (-4))/(4 - (-2)) = 2/3

The slope of the shorter base = The slope of the longer base = m = 2/3

The equation of the line representing the shorter base in point and slope form is therefore;

y - 1 = (2/3)·(x - 3)

∴ y = 2·x/3 - 2 + 1 = 2·x/3 - 1

The equation of the shorter side of the trapezoid is y = 2·x/3 - 1

Answer:

3.5

Step-by-step explanation:

From the graph,

x1 = 0

x2 = 4

y1 = 0

y2 = 14

Formula : -

Slope = ( y2 - y1 ) / ( x2 - x1 )

Slope

= ( 14 - 0 ) / ( 4 - 0 )

= 14 / 4

= 7 / 2

= 3.5

Answer:

7/2

Step-by-step explanation:

the slope of a line is the ratio of y/x.

it describes how many units y changes, when x changes a defined number of units.

an increase is indicated by "+", and a decrease by "-".

the point with full integer/natural numbers as coordinates is (4, 14).

that means that when coming from point 0 (0, 0) x increases by 4 units, and y increases by 14 units.

so, the slope of line is 14/4 = 7/2