Amanda rides her bike due east for 10 km. Angela rides her bike 20 degrees south of east 12 km. How far apart are Amanda and Angela? (Round to the nearest tenth).

Answer:

2 should be distributed as 2y + 8; y = 4

Step-by-step explanation:

2(y + 4) = 4y

Distribute

2y + 8 = 4y

Step 2 is incorrect because the added instead of multiplied

Continuing on to correct the problem

Subtract 2y from each side

2y+8-2y = 4y-2y

8 = 2y

Divide by 2

8/2 = 2y/2

4 =y

Answer:

2 should be distributed as 2y + 8; y = 4

Step-by-step explanation:

Step 2 is wrong.

2(y + 4) = 4y

The step to solve is to expand brackets or distribute 2, not divide both sides by 2.

2y + 8 = 4y

Subtract both sides by 2y.

8 = 2y

Divide both sides by 2.

4 = y

Answer: C. (5, -10)

Step-by-step explanation:

When we have a point (x, y) and we do a dilation around (0,0) with a scale factor of A.

The new point will be:

(A*x, A*y)

in this case, the point is (3, -6) and the scale factor is (5/3)

Then the new point will be:

(3*(5/3), -6*(5/3)) = (5, -10)

Answer:

288 in²

Step-by-step explanation:

The formula used to solve this question is :

Lateral Surface Area = s( P1 + P2)

Where s = slant height = 2 inches

P1 and P2 = Perimeter of the bases

Perimeter of base 1 = 4 × length of the end of the small square

4 × 17 inches = 68 inches

Perimeter of base 2 = 4 × length of the end of the large square

4 × 19 inches = 76 inches

Lateral Surface Area = 2 × (68 + 76)

= 2 × 144

= 288 in²

Answer:

Correct Option: B

Step-by-step explanation:

Linear functions are the type of functions that are applied to model occurrences that rise or fall at a constant proportion. These sorts of functions are polynomial functions with a maximum exponent of one on the variable. The graphs of these kind of functions are in the form of a line.

Exponential functions are the type of functions that have the variable in exponent form. The growth rate or decline rate is either slow than quick or quick than slow.

Quadratic functions are of the form f (x) = ax² + bx + c. The graph of this function is in the form of a parabola. The graph first increases, hit a maximum, then decreases or decreases, hit a minimum, then increases.

From the provided graphs it can be seen that, the exponential function grows at approximately the same rate over the interval 0 ≤ x ≤ 1 as the quadratic function.

Answer:

bbb

Step-by-step explanation:

Answer:

A,C,D

Step-by-step explanation:

When b=0, there is a proportional relationship.

The slope in y=mx+b is the value next to x.

Using RISE/RUN when there is a change of 3 units in x, there is a change of 2 units in y.

Answer:

Sum of two rational numbers-

-10 = -5+-5

0= -5+5

15= 10+5

Step-by-step explanation:

Answer:

t=11.6

Step-by-step explanation:

sin 43=opp/hyp

sin 43=t/17

t= sin43*17

t=11.6

Answer:

Step-by-step explanation:

Given that:

OA = 7 cm, AB = 6 cm. ∠A = 90°, OA = OC = 7 cm

Using Pythagoras theorem: OB² = OA² + AB²

OB² = 6² + 7²=85

OB = √85 = 9.22 cm

to find ∠O, we use sine rule:

[tex]\frac{AB}{sin(O)}=\frac{OB}{sin(A)}\\ \\sin(O)=\frac{AB*sin(A)}{OB}=\frac{6*sin(90)}{9.22} =0.65 \\\\O=sin^{-1}0.65=40.6^o[/tex]

AOC is a minor sector with radius 7 cm and angle 40.6

The Area of the triangle OAB = 1/2 × base × height = 1/2 × OA × AB = 1/2 × 7 × 6 = 21 cm²

Area of sector OAC = [tex]\frac{\theta}{360}*\pi r^2=\frac{40.6}{360}*\pi *7^2=17.37 \ cm^2[/tex]

Area of shaded region = The Area of the triangle OAB - Area of sector OAC = 21 - 17.37 = 3.63 cm²

Perimeter of arc AC = [tex]\frac{\theta}{360}*2\pi r=\frac{40.6}{360}*2\pi *7=4.96\ cm[/tex]

CB = OB - OC = 9.22 - 7 = 2.22

Perimeter of shaded region = AB + CB + arc AC = 6 + 2.22 + 4.96 = 13.18 cm

Step-by-step explanation:

Y varies directly as cube root of x is written as

y = k³√x

where k is the constant of proportionality

when y = 3

x = 27

We have

[tex]3 = k \sqrt[3]{27} [/tex]

But ³√27 = 3

That's

3 = 3k

Divide both sides by 3

k = 1

The value of the relationship is

When x = 8

We have

Hope this helps you

Answer:

B, C, D

Step-by-step explanation:

if tan theta = 15/8 then the hypotenuse is 17

therefore the correct answers are B, C, D

Answer:

The value of x is 35

Step-by-step explanation:

In order to calculate the value of x in the  following parallelogram:  2x - 10  

2x + 50, we would have to calculate the following formula:

m<QPS+m<PQR=180°

According to the given data we have the following:

m<QPS=2x - 10  

m<PQR=2x + 50

Therefore, 2x - 10+2x + 50=180

4x+40=180

x=140/4

x=35

Answer:

y = - 4x - 10

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 4 , thus

y = - 4x + c ← is the partial equation

To find c substitute (- 4, 6) into the partial equation

6 = 16 + c ⇒ c = 6 - 16 = - 10

y = - 4x - 10 ← equation of line

Answer:

y = -4x+10

Step-by-step explanation:

Using the slope intercept form of a line

y = mx+b where m is the slope and b is the y intercept

y = -4x +b

Substituting the point in

6 = -4(-4) + b

6 = 16+b

Subtract 16 from each side

-10 =b

The equation is

y = -4x+10

Answer:

Step-by-step explanation:

The side y is across from the angle Y which is 68 degrees. Angle Y is next to both the hypotenuse (14 units) and adjacent to the side XY (5 units). If we are finding side y, we need to use one of the trig ratios that relates the angle Y to the side across from it. That would be either the sin of Y which is the side opposite y) over the hypotenuse (14) or the tan of Y which is the side opposite over the side adjacent. Either one will get you the side lengths within a tenth or hundredth of each other. Let's do both, just because. First the sine:

[tex]sin(68)=\frac{y}{14}[/tex] and

14sin(68) = y so

y = 12.98 and rounded to the nearest tenth is 13.0

Now the tangent:

[tex]tan(68)=\frac{y}{5}[/tex] and

5tan(68) = y so

y = 12.37 and rounded to the nearest tenth is 12.4.

As an integer, your answer would be 13; as a decimal it would be the 12.4

Apparently, either is fine.

Answer:

Anna's wand can cast 70 spells

Step-by-step explanation:

Elsa's wand can cast 53 spells

her wand casts 17 fewer cells than her sister Anna's

Amount of spells cast by Anna's wand = ?

We write the question down in the form of an equation

[tex]x - 17 = 53[/tex]

where [tex]x[/tex] is the amount of spells Anna's wand can cast.

we then proceed to solve by collecting like terms to different sides of the equation. We'll have

[tex]x = 53 + 17[/tex]

which leaves us with

[tex]x = 70[/tex]

This means that Anna's wand can cast 70 spells.

Answer:

(5,-6)

Step-by-step explanation:

ONE WAY:

If [tex]f(x)=x^2-6x+3[/tex], then [tex]f(x-2)=(x-2)^2-6(x-2)+3[/tex].

Let's simplify that.

Distribute with [tex]-6(x-2)[/tex]:

[tex]f(x-2)=(x-2)^2-6x+12+3[/tex]

Combine the end like terms [tex]12+3[/tex]:

[tex]f(x-2)=(x-2)^2-6x+15[/tex]

Use [tex](x-b)^2=x^2-2bx+b^2[/tex] identity for [tex](x-2)^2[/tex]:

[tex]f(x-2)=x^2-4x+4-6x+15[/tex]

Combine like terms [tex]-4x-6x[/tex] and [tex]4+15[/tex]:

[tex]f(x-2)=x^2-10x+19[/tex]

We are given [tex]g(x)=f(x-2)[/tex].

So we have that [tex]g(x)=x^2-10x+19[/tex].

The vertex happens at [tex]x=\frac{-b}{2a}[/tex].

Compare [tex]x^2-10x+19[/tex] to [tex]ax^2+bx+c[/tex] to determine [tex]a,b,\text{ and } c[/tex].

[tex]a=1[/tex]

[tex]b=-10[/tex]

[tex]c=19[/tex]

Let's plug it in.

[tex]\frac{-b}{2a}[/tex]

[tex]\frac{-(-10)}{2(1)}[/tex]

[tex]\frac{10}{2}[/tex]

[tex]5[/tex]

So the [tex]x-[/tex] coordinate is 5.

Let's find the corresponding [tex]y-[/tex] coordinate by evaluating our expression named [tex]g[/tex] at [tex]x=5[/tex]:

[tex]5^2-10(5)+19[/tex]

[tex]25-50+19[/tex]

[tex]-25+19[/tex]

[tex]-6[/tex]

So the ordered pair of the vertex is (5,-6).

ANOTHER WAY:

The vertex form of a quadratic is [tex]a(x-h)^2+k[/tex] where the vertex is [tex](h,k)[/tex].

Let's put [tex]f[/tex] into this form.

We are given [tex]f(x)=x^2-6x+3[/tex].

We will need to complete the square.

I like to use the identity [tex]x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2[/tex].

So If you add something in, you will have to take it out (and vice versa).

[tex]x^2-6x+3[/tex]

[tex]x^2-6x+(\frac{6}{2})^2+3-(\frac{6}{2})^2[/tex]

[tex](x+\frac{-6}{2})^2+3-3^2[/tex]

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

[tex](x-3)^2+-6[/tex]

So we have in vertex form [tex]f[/tex] is:

[tex]f(x)=(x-3)^2+-6[/tex].

The vertex is (3,-6).

So if we are dealing with the function [tex]g(x)=f(x-2)[/tex].

This means we are going to move the vertex of [tex]f[/tex] right 2 units to figure out the vertex of [tex]g[/tex] which puts us at (3+2,-6)=(5,-6).

The [tex]y-[/tex] coordinate was not effected here because we were only moving horizontally not up/down.

Answer:

$191,340.80

Step-by-step explanation:

Step 1

We find the amount that is paid monthly by the Lee's

We are told in the question that:

Cost of the house =$360,000

Down payment = $50,000

We are also told, the balance left after the down payment was made = Mortgage that is amortized at an

Interest rate of 5.25%

Time = 20 years

Hence, Mortgage amount = $360,000 - $50,000 = $310,000

Formula for monthly payment =

M= P[r(1+r)^n/((1+r)^n)-1)]

M = the total monthly mortgage payment.

P = the principal loan amount.

r = your monthly interest rate.

= rate/12

=5.25%/12 = 0.0525/12

= 0.004375

n = number of payments

= number of years × number of months

= 20 × 12 = 240 payments

Formula for monthly payment =

M= P[r(1+r)^n/((1+r)^n)-1)]

M = 310,000[0.004375(1 + 0.004375)^240/((1 + 0.004375)^240 ) - 1]

M = $2,088.92

Therefore, the monthly payment by the Lee's is $2,088.92

Step 2

We calculate the Total Amount paid by the Lee's in 20years because we are told in the question that they paid off their mortgage after 20 years

Total Amount paid = Monthly payments × Number of payments

= $2,088.92 × 240

= $501,340.80

Step 3

The third and final step is to calculate the Total interest paid for 20 years

Total Interest = Total amount paid - Mortgage amount

= $501,340.80 - $310,000

Total Interest: $191,340.80

Therefore,the interest will they have paid in total is $191,340.80

Answer:

  927 cubic inches

Step-by-step explanation:

The area of the octagonal base is ...

  A = (1/2)Pa

where P is the perimeter, and 'a' is the apothem. Using the given numbers, the base area is ...

  A = (1/2)(8·4)(4.83) = 77.28 . . . square inches

The volume of the prism is given by ...

  V = Bh

where B represents the area of the base, and h is the height.

  V = (77.28 in^2)(12 in) = 927.36 in^3

The volume of the prism is about 927 cubic inches.

the answer on edg is 927

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▹ Answer

Linear

▹ Step-by-Step Explanation

As x increases by 4, y increases by 6.

13 + 4 = 17

17 + 4 = 21

21 + 4 = 25

0 + 6 = 6

6 + 6 = 12

12 + 6 = 18

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the GRAPHS AND FUNCTIONS.

This here, from the graph we can see that it's a EXPONENTIAL GROWTH.

Thus the relationship is Exponential.

Answer:

7.5 jars

Step-by-step explanation:

There are 25 students in the art class.

Mr Jones is planning that for the project, each of the 25 students will need 0.3 jar of paint.

The amount of paint Mr Jones needs for this project is therefore the product of the number of students in the class by the amount of paint each student needs.

That is:

25 * 0.3 = 7.5 jars of paint

Mr Jones needs 7.5 jars of paint for the art project.

Answer: Option C, 1 unit bellow.

Step-by-step explanation:

The residual of a data point is equal to the vertical distance between the point and the regression line

If the data point is above the line, the residual is positive

if the data point is below the line, the residual is negative.

So here we have a negative residual equal to -1

This would mean that our point is 1 unit below the regression line.

Then the correct option is C.

Answer:

The answer is 1 unit below.

Step-by-step explanation:

This is because the residual is the difference between the actual value of a dependent variable & the value predicted by a regression equation. So if the data point has a residual of -1, that means that the data point lies 1 unit below the regression line.

Answer:

C

Step-by-step explanation:

This is because it has a constant rate of change.

5 x 1.5 = 7.5

6 x 1.5 = 9

7 x 1.5 = 10.5

You can find this image by dividing y by x and testing this rate of change on the other y values. Thus C is correct.

Answer:

25 children

So , each child will get 25 pens and 7 pencils

You have to find the highest common factor of 125 and 175 which is 25 and then you have to multiply it by those two numbers to find how may pens and pencils will be given to 1 child

Hope this helps and pls mark as brianliest :)

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▹ Answer

You can use a graphing calculator. Attached is a picture of it graphed.

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

1) 4a + 8

2) 12a² - 8a

3) 2a² + 8a

4) 4 - 6a

Step-by-step explanation:

The GCF of two numbers is the greatest common number each of the original two numbers can be divided by to get a whole number.

Hope it helps <3

Answer:

4     4a+8

4a   [tex]12a^{2}[/tex]+8a

2a   [tex]2a^{2} +8a[/tex]

2     4-6a

Step-by-step explanation:

Okay basicly you wand to find the biggest number that can go into both numbers

like the greatest common fact for 4a+8 would be 4 since only one of the numbers have an a you would just leave that out

Since you can take a 4 and an a out of [tex]12a^{2} \\[/tex] and out of 8a the greatest common factor would be 4a

Since you are able to take a 2 and an a out of [tex]2a^{2} +8a[/tex] your greatest common factor would be a

Since the largest number that can go into 4 and 6 is 2 your answer would be 2

Hope this helps you understand!

Answer:

The answer is 21.25cm

Step-by-step explanation:

Hope i am marked as brainliest

Answer:

The distance between two cities is 60 miles.

Step-by-step explanation:

Time taken to travel from B to A = 2 hours

Time taken to travel from A to B = 1.5 hours

Current speed = 5 mph

Let the speed of ferry in still water = u mph

When the ferry moves with the current, it will taken lesser time (i.e. A to B) and when it moves against the current it will take more time (i.e. B to A).

Let the distance between the two cities A and B = D miles

While moving with the current, speed = [tex](u+5)\ mph[/tex]

While moving against the current, speed = [tex](u-5)\ mph[/tex]

Formula for Distance = Speed [tex]\times[/tex] Time

Distance traveled in each case is same i.e. D.

So,

[tex]D = (u+5) \times 1.5 = (u-5) \times 2\\\Rightarrow 1.5u+7.5=2u-10\\\Rightarrow 0.5u =17.5\\\Rightarrow u = \dfrac{175}{5}\\\Rightarrow u = 35 \ mph[/tex]

Now,

[tex]D = (u+5) \times 1.5\\\Rightarrow D =(35+5) \times 1.5\\\Rightarrow D =(40) \times 1.5\\\Rightarrow \bold{D =60\ miles}[/tex]

So, the distance between two cities is 60 miles.

Answer:

I believe that the answer is 60 miles

Step-by-step explanation:

Answer:

(1/2)x + (1/4)y <= 200

Step-by-step explanation:

If

x = # of lbs of House blend he makes/sells a day

y = # of lbs of Exotic blend he makes/sells a day

then constraints are

(1/2)x + (1/4)y <= 200  ....................(1)

x+y <= 530  .....................................(2)

The exact answer choices are not very clear from the question, but either (or both) (1) or (2) must be one of them.  If not, please edit question or add a comment to show the answer choices.

C). (3, 29) would be your answer.

Explanation?:

Rewrite the equation in vertex form.

y = -3(x - 3)^2 + 29

use the vertex form, y = a(x - h)^2 + k, to determine the values of a, h, and k.

a = -3

h = 3

k = 29

The vertex = (h, k)/(3, 29)

Hope this helps!

Answer:

It would be c

Step-by-step explanation:

Step-by-step explanation:

The inequality is [tex]\frac{x}{-3}[/tex] >2

x is less than -6  and -6 is excluded so it will be represented by an empty circle and a line going toward negative values

so it's D