Which of the following shows the situation below in function notation?

The depth of a lake at a certain point, which is a function of the distance of that point from shore, is 30 feet.

A. Distance from shore(depth) = 30 ft
B. Distance from shore(30 ft) = depth
C. Depth(distance from shore) = 30 ft
D. Depth(30 ft) = distance from shore

Answer:

C. 97,000

Step-by-step explanation:

9.7x10^4 = 9.7 x 10000 = 97,000

Final answer:

To write 9.7x10^4 in standard form, you multiply 9.7 by 10,000, resulting in 97,000. Therefore, the correct answer is C. 97,000.

Explanation:

To write 9.7x10^4 in standard form, you multiply the coefficient (9.7) by 10 to the power of 4.

Since 10^4 means 10,000, you would perform the calculation 9.7 multiplied by 10,000. Doing this gives you 97,000. Therefore, the correct answer is:

C. 97,000

Here are steps to write numbers in scientific notation or standard form from the examples provided:

To convert the number 4,500 to scientific notation, you move the decimal three places to the left to get 4.5 x 10^3.

The number 2,220,000 would be 2.22 x 10^6 in scientific notation.

A smaller number like 0.0035 would be written as 3.5 x 10^-3.

For 0.7, the scientific notation is 7 x 10^-1.

The number 858.67 would be 8.5867 x 10^2 since the decimal is moved two places to the left.

Answer:

The correct answer is (−4, −8)

Step-by-step explanation:

You have to substitute!!! :)

−3x + 4y = −20                y = x − 4

-3(4) + 4(8) = -20             8 = 4 - 4

-12 + 32 = -20                  8 = 0

20 = 20

−3x + 4y = −20                y = x − 4

-3(0) + 4(-5) = -20           -5 = 0 - 4

0 + 20 = -20                    -5 = -4

20 = -20

−3x + 4y = −20                y = x − 4

-3(-2) + 4(-6) = -20          -6 = -2 - 4

6 - 24 = -20                    -6 = -6

-18 = -20      

−3x + 4y = −20                y = x − 4

-3(-4) + 4(-8) = -20         -8 = -4 - 4

12 - 32 = -20                  -8 = -8

-20 = -20

Answer:

(-4,-8)

Step-by-step explanation:

This a system of equation that have two variables x and y and we have two equations that we have to solve simultaneously

−3x+4y=−20 ....(1)

y=x−4 ....(2)

We can substitute equation (2) and (1)

-3x+4y = −20

-3x+4(x−4) = −20

-3x + 4x -16 = -20

x = -4

Now we need to find the value of y

y=x−4 = -4 - 4 = -8

(-4,-8)

Answer:

x - 2y = -15

Step-by-step explanation:

Given: m = 1/2 and (-3, 6)

We are given slope and a point.

The equation of the line y - y1 = m (x  - x1)

y - 6 = 1/2 (x -  (-3))

y - 6 = 1/2 (x + 3)

y - 6 = 1/2x + 3/2

1/2x - y = -6 - 3/2

1/2x - y = -15/2

Taking LCD as 2, we get

x - 2y = -15

Thank you.

Answer:

1/2

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] ÷[tex]\frac{2}{3}[/tex] equals 1/2 so 1 mius that will be 1/2

Answer:

8) Sale price : 45* (100%-22%)= 45* 78/100= 35,1 $

9) 89* ( 100%-33%)= 89*67/100=59,63 $

10) 23,99* (100%-44%)= 13,43 $

11) 279,99*25/100= 69,99 $

12) Sell price= regular price* ( 100%- Markdown)

Step-by-step explanation:

Answer:

1/365 (or 1/366 in the case of a leap year.)

Answer:

$69.60

Step-by-step explanation:

20% of $58 is $11.60. So you add $11.60 + 58 which equals $69.60, so that is the total cost.

Answer:

$69.60

Step-by-step explanation:

The desired amount (total cost) is equivalent to the sum of the bill and 20% of the bill, or, equivalently, 120% of the bill.

1.20($58) = $69.60

The total cost is $69.60, including a 20% tip.

Answer:

The ascending order is [tex]8.11\times 10^{-3},435, 34\times 10^2, 1.2\times 10^7[/tex]

Step-by-step explanation:

First of all find the exact value of each number.

[tex]34\times 10^2=34\times 100=3400[/tex]

[tex]1.2\times 10^7=1.2\times 10000000=12000000[/tex]

[tex]8.11\times 10^{-3}=\frac{8.11}{1000}=0.00811[/tex]

The fourth number is 435.

Using the above calculation we can easily arrange these numbers form least to greatest.

The ascending order is

[tex]0.00811, 435, 3400, 12000000[/tex]

It can be written as

[tex]8.11\times 10^{-3},435, 34\times 10^2, 1.2\times 10^7[/tex].

Answer:

210 miles=3.5 hours×speed

3.5 hours=210 miles/speed

speed=210 miles/3.5 hours

                              I Honestly Juat Guessed

Answer:

210 miles=3.5 hours×speed

3.5 hours=210 miles/speed

speed=210 miles/3.5 hours

Hope this helps =]

Answer:

C: 8.00

Step-by-step explanation:

1 in = 2.54 cm

l = 20.32 × 1/2.54

l = 8.00 in

The length of Nancy’s mirror is 8.00 in.

Answer:

4/3 or D

Step-by-step explanation:

Let's get this equation into y=mx+b form.

m=slope b=y-int

Subtract 5 from both sides to isolate y on a side.

4x-6=3y

Divide both sides by 3 to isolate y on one side.

(4/3)x-2=y

y=(4/3)x-2

m=4/3

b=-2

So our slope is 4/3

ΔABC and ΔACD are similar. Therefore the sides are in proportion:

[tex]\dfrac{y}{7}=\dfrac{7}{6}[/tex]            multiply both sides by 7

[tex]y=\dfrac{49}{6}\\\\\boxed{y=\dfrac{1}{6}}[/tex]

Answer: 0.43

Think of 43% as 43.0%

Move the decimal 2 spots to the left to go from 43.0 to 0.43

Alternatively, use a calculator to find that 43% = 43/100 = 0.43

"percent" means "per 100", so that's why we're dividing over 100.

Answer:

16. No

18. Yes

20. Yes

Step-by-step explanation:

Because there is a right angle at at least one corner of the triangle.

Answer:

x=12

Step-by-step explanation:

16x - (8x  + 6) =90

The first step is to distribute the - sign

16x -8x -6 =90

Now we combine the like terms

8x-6 = 90

Add 6 to each side

8x-6+6 = 90+6

8x = 96

Divide each side by 8

8x/8 = 96/8

x =12

Answer:

5x+2

Step-by-step explanation:

Ok so the expression 5(x+2) is not 5x+2 because you have to use the distributive property. So with that being said:

5(x+2)=5 times x and 5 times 2

so the realest answer is 5x+10 instead of 5x+2

EXPLANATION: The error in the rewritten expression done by your 'friend' is that he/she did not multiply the five in the parenthesis by ALL terms (meaning numbers and/or variables) as he/she should have done according to the distributive property. In the distributive property, you distribute equally to all numbers and parts in the equation or expression.

Take, For example, 7(x+4). Instead of just multiplying 7 times x in the parenthesis, you would also multiply seven times to four and add that to the end of the expression, making the rewritten expression 7x+28.

So, the correct rewritten expression for this problem is 5x+10.

Answer:

f(x) = 3(x + 1)² + 2

Step-by-step explanation:

Use the method of completing the square

3x² + 6x + 5

= 3(x² + 2x) + 5

add/ subtract (half the coefficient of the x-term)² to x² + 2x

= 3(x² + 2(1)x + 1 - 1) + 5

= 3(x + 1)² - 3 + 5

f(x) = 3(x + 1)² + 2 ← in vertex form

Answer:  (a) $6,600

                (b) $28,600

Step-by-step explanation:

Interest (I) = Principal (P) x rate (r) x time (t)

I = 22,000(0.06)(5)

 = 6,600

Accrued (A) = Principal (P) + Interest (I)

A = 22,000 + 6,600

  = 28,600

The length of Line BC is 10

A figure bounded by 3 sides and all the internal angles add up to 180 ° is called a triangle.

Triangles having the same corresponding angles measures and proportional side lengths are called similar triangles.

Considering Δ AXY    and    ΔABC

                      ∠AXY       =      ∠ACB  (corresponding angles are equal)

                       ∠AYX       =      ∠ABC   (corresponding angles are equal)

                       ∠A is common in both the triangles

∴ We can say the triangles are similar .

Now, let H be the height of ΔABC and h be the height of ΔAYX

So, we can say,  [tex]\frac{XY}{BC} = \frac{h}{H}[/tex]

So,   [tex]\frac{AYX}{ABC} = \frac{7.5}{30}[/tex]

⇒    [tex]{\frac{\frac{1}{2} (XY) h }{\frac{1}{2}(BC) H } = \frac{1}{4}[/tex]

Now, substituting XY = 5 and  [tex]\frac{XY}{BC} = \frac{h}{H}[/tex]  in the above equation, we get

[tex]\frac{25}{BC^{2} } = \frac{1}{4}[/tex]

⇒ BC² = 100

⇒ BC = ± 10

Since BC is the length , so it cannot be negative.

So, the negative value is rejected.

∴  BC = 10

Option B is correct.

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Answer:

x = -3/7

Step-by-step explanation:

We are given the following equation for which we have to solve for x:

[tex]3(3x - 1) + 2(3 - x) = 0[/tex]

So we will start by expanding the equation by multiplying the common factor with the brackets to get:

[tex]9x-3+6-2x=0[/tex]

Arranging the like terms together (variables on one side of the equation and constants on the other side) to get:

[tex]9x-2x=3-6\\\\7x=-3\\\\x=-\frac{3}{7}[/tex]

Therefore, x = -3/7.

Answer:

The answer is 0.2.

Step-by-step explanation:

10-(a+b)

A=4.1 B=5.7

10-(4.1+5.7)

10-4.1-5.7

10-9.8=

0.2

Question

Anna picked 37 apples . She divided the apples equally among 7 baskets. How many apples are in each basket? How many are leftover?

Answer:

Step-by-step explanation:

37 : 7 = 5 (2 left over)

check

(7 * 5) + 2 = 37

better solution in the picture

Answer:

5 apples in each basket with 2 left over

Step-by-step explanation:

37/7 =5 R 2

brainliest pls

Answer:

425 milliliters of compound A are needed

Step-by-step explanation:

We were told that [tex]5[/tex] milliliters of compound A and [tex]6[/tex] milliliters of compound B is needed to make the drug.

This means that each drug contains 11 milliliters of both compounds.

[tex]\frac{935}{11}=85[/tex] milliliters is the volume of each drug.

Therefore the chemist needed [tex]5\times 85=425[/tex] millilirteres of compound A.

In order to find out how much of compound A is needed, we would set up a ratio using the amounts provided of compound A and B. Then, we cross multiply and solve for the unknown amount of compound A needed for the specific quantity of the drug.

This problem is about ratios. We know that specific quantities of compound A and compound B are combined to make a certain amount of the drug. However, the quantities of compound A and B are not mentioned in the question. If they were provided, we would set up a ratio equal to the total amount of the drug and cross multiply to solve for the amount of compound A needed.

An example might look something like this: if the drug is made of 2 milliliters of compound A for every 3 milliliters of compound B and we wanted to make 5 milliliters of the drug. You would set it up like this:

2 (Compound A) / 3 (Compound B) = x (Amount of compound A needed) / 5 (Total Amount of drug needed)

Cross multiplying gives us: 2 * 5 = 3 * x

This simplifies to: 10 = 3x

Dividing each side by 3 then gives the amount needed of compound A: x = 3.33 milliliters.

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A.

6x - 5y = 15

L = 6(1.8) - 5(-0.9) = 10.8 + 4.5 = 15.3

R = 15

L ≈ R

x + 2y = 0

L = 1.8 + 2(-0.9) = 1.8 - 1.8 = 0

L = R

B.

4x + 5y = 8

L = 4(1.8) + 5(-0.9) = 7.2 - 4.5 = 2.7

R = 8

L ≠ R

C.

x - 2y = 4

L = 1.8 - 2(-0.9) = 1.8 + 1.8 = 3.6

R = 4

L ≈ R

4x + 5y = 8

L = 4(1.8) + 5(-0.9) = 7.2 - 4.5 = 2.7

R = 8

L ≠ R

D.

6x - 5y = 15

L = 6(1.8) - 5(-0.9) = 10.8 + 4.5 = 15.3

R = 15

L ≈ R

x - 2y = 4

L = 1.8 - 2(-0.9) = 1.8 + 1.8 = 3.6

R = 4

L ≈ R

Yeah so your answer is gonna be

A.

After testing the approximate values (1.8, -0.9) in the systems of equations, only option A satisfies both equations with the solution approximately equal to (1.8, -0.9).

To find which system of equations has a solution of approximately (1.8,-0.9), we need to substitute the x-value into each equation to see if the corresponding y-value is approximately -0.9. Whichever system satisfies both equations with these approximate values will be our answer.

Therefore, the correct answer is option A, as it satisfies both equations with the solution approximately equal to (1.8, -0.9).

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Answer:

The set of all points on a plane equidistant to a given point

Step-by-step explanation:

"following"?

Answer:

The collection of all points in a plane that are the same distance from a given point.

Step-by-step explanation:

Answer:

$1.25

September

$30

Step-by-step explanation:

Let's take this a step a time.

First we need to find how much the price of the flowers were in September.

We know that each flower cost $1.50 on October.

The October price was a 20% increase of the September price.

To calculate for the price of the flowers on September, we can solve it like this:

Let x = Price during September

1.2x = 1.50

We used 1.2 because the price of $1.50 is 120% of the original price.

Now we divide both sides by 1.2 to find x.

[tex]\dfrac{1.2x}{1.2}=\dfrac{1.5}{1.2}[/tex]

x = 1.25

The price of the flowers during September was $1.25 each.

Now the 7th grade class earned 40% of the selling price of each flower.

40% = 0.40

To find how much they made on each month, we simply multiply the percentage to the price and the number of flowers sold.

September = 0.40 x 1.25 x 900

September = 0.5 x 900

September = $450

Now for October.

October = 0.40 x 1.50 x 700

October = 0.6 x 700

October = $420

The 7th Graders earned more on September.

They earned $30 more on September than October.

Answer: x=12, y=30

Step-by-step explanation: 180=40+5x+2y+20, 140=5x+2y+20, 120=5x+2y, 60+60=120, so 5*12=60, and 2*30=60

The value of y is determined by solving the algebraic equation presented, which after simplifying and isolating y, gives us a value of y equal to 3200.

To find the value of y, we can use the given equations and perform the necessary algebraic manipulations. The question appears to contain a regression analysis problem where ŷ, read as 'y hat', represents the estimated value of y. This value is obtained from the regression line, which helps in making predictions about y based on corresponding values of x.

Here are the steps to solve the provided equations:

Answer:

Step-by-step explanation:

The first four terms of geometric series is:

[tex]a,ar,ar^2,ar^3[/tex]

Since, we have given information that the third number is greater than 44 that means:

[tex]ar^2=a+44[/tex]

Above equation can be rewritten as:

[tex]a(r^2-1)=44[/tex]

Now, using:

[tex]a^2-b^2=(a+b)(a-b)[/tex]

Here, a=r,b=1

[tex]a(r+1)(r-1)=44[/tex]        (1)

The sum of first four terms is:

[tex]a+ar+ar^2+ar^3=220[/tex]

[tex]a(1+r+r^2+r^3)=220[/tex]

[tex]a(1(1+r)+r^2(1+r))=220[/tex]

[tex]a((1+r)(1+r^2))=220[/tex]      (2)

Divide equation (2) by (1) we get:

[tex]\frac{r^2+1}{r-1}=\frac{220}{44}[/tex]

[tex]r^2+1=5r-5[/tex]

[tex]\Rightarrow r^2-5r+6=0[/tex]

[tex]\Rightarrow r^2-3r-2r+6=0[/tex]

[tex]\Rightarrow r(r-3)-2(r-3)=0[/tex]

[tex]\Rightarrow (r-2)(r-3)=0[/tex]

[tex]\Rightarrow r=2,3[/tex]

CASE1: When r=2 in [tex]ar^2=a+44[/tex]

[tex]a(4)=a+44[/tex]

[tex]3a=44[/tex]

[tex]a=\frac{44}{3}[/tex]

CASE2:When r=3 in [tex]ar^2=a+44[/tex]

[tex]a(3)^2=a+44[/tex]

[tex]\Rightarrow 9a=a+44[/tex]

[tex]\Rightarrow 8a=44[/tex]

[tex]\Rightarrow a=\frac{44}{8}=\frac{11}{2}[/tex]

The series becomes:

From CASE1: [tex]\frac{44}{3},\frac{44\cdot 2}{3},\frac{44\cdot 2^2}{3},\frac{44\cdot 2^3}{3}[/tex]

[tex]\Rightarrow \frac{44}{3},\frac{88}{3},\frac{176}{3},\frac{352}{3}[/tex]

From CASE2: [tex]\frac{11}{2},\frac{11\cdot 3}{2},\frac{11\cdot 3^2}{2},\frac{11\cdot 3^3}{2}[/tex]

[tex]\Rightarrow \frac{11}{2},\frac{33}{2},\frac{99}{2},\frac{297}{2}[/tex]

A geometric progression is characterized by a common ratio.

The terms of the progression are: [tex]\mathbf{T_n =5.5, 16.5, 49.5,148.5}[/tex] or [tex]\mathbf{T_n =\frac{44}{3}, \frac{88}{3}, \frac{176}{3},\frac{352}{3}}[/tex]

The given parameters are:

[tex]\mathbf{S_4 = 220}[/tex]

[tex]\mathbf{T_3 = T_1 + 44}[/tex]

The third term is represented as:

[tex]\mathbf{T_3 = ar^2}[/tex]

The first term is:

[tex]\mathbf{T_1 = a}[/tex]

So, we have:

[tex]\mathbf{ar^2 = a + 44}[/tex]

Subtract a from both sides

[tex]\mathbf{ar^2 - a = 44}[/tex]

Factor out a

[tex]\mathbf{a(r^2 - 1) = 44}[/tex]

Express as difference of two squares

[tex]\mathbf{a(r + 1)(r - 1) = 44}[/tex]

Make r + 1 the subject

[tex]\mathbf{r +1 = \frac{44}{a(r -1)}}[/tex]

Recall that:

[tex]\mathbf{S_4 = 220}[/tex]

This gives:

[tex]\mathbf{a + ar + ar^2 + ar^3 = 220}[/tex]

Factor out a

[tex]\mathbf{a(1 + r + r^2 + r^3) = 220}[/tex]

Factor out r^2

[tex]\mathbf{a(1 + r + r^2(1 + r)) = 220}[/tex]

Rewrite as:

[tex]\mathbf{a(1(1 + r) + r^2(1 + r)) = 220}[/tex]

Factor out 1 + r

[tex]\mathbf{a((1 + r^2)(1 + r)) = 220}[/tex]

Substitute [tex]\mathbf{r +1 = \frac{44}{a(r -1)}}[/tex] in [tex]\mathbf{a((1 + r^2)(1 + r)) = 220}[/tex]

[tex]\mathbf{a((1 + r^2)\times \frac{44}{a(r -1)} = 220}[/tex]

[tex]\mathbf{((1 + r^2)\times \frac{44}{(r -1)} = 220}[/tex]

Divide both sides by 44

[tex]\mathbf{(1 + r^2)\times \frac{1}{(r -1)} = 5}[/tex]

Multiply through by r - 1

[tex]\mathbf{1 + r^2 = 5r - 5}[/tex]

Collect like terms

[tex]\mathbf{r^2 - 5r + 5 +1 = 0}[/tex]

[tex]\mathbf{r^2 - 5r + 6 = 0}[/tex]

Expand

[tex]\mathbf{r^2 - 2r - 3r + 6 = 0}[/tex]

Factorize

[tex]\mathbf{r(r - 2) - 3(r - 2) = 0}[/tex]

Factor out r -2

[tex]\mathbf{(r - 3)(r - 2) = 0}[/tex]

So, we have:

[tex]\mathbf{r = 3\ or\ r = 2}[/tex]

Calculate a using: [tex]\mathbf{a(r^2 - 1) = 44}[/tex]

When r = 3

[tex]\mathbf{a(3^2 -1) = 44}[/tex]

[tex]\mathbf{a(9 -1) = 44}[/tex]

[tex]\mathbf{8a = 44}[/tex]

[tex]\mathbf{a = 5.5}[/tex]

When r = 2

[tex]\mathbf{a(2^2 -1) = 44}[/tex]

[tex]\mathbf{a(4 -1) = 44}[/tex]

[tex]\mathbf{3a = 44}[/tex]

[tex]\mathbf{a = \frac{44}{3}}[/tex]

The nth term of a GP is:

[tex]\mathbf{T_ = ar^{n-1}}[/tex]

So, the terms of the progression are:

[tex]\mathbf{T_n =5.5, 16.5, 49.5,148.5}[/tex]

or

[tex]\mathbf{T_n =\frac{44}{3}, \frac{88}{3}, \frac{176}{3},\frac{352}{3}}[/tex]

Read more about geometric progressions at:

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Answer:

Option B is correct

the degree of rotation is, [tex]-90^{\circ}[/tex]

Step-by-step explanation:

A rotation matrix is a matrix that is used to perform a rotation in Euclidean space.

To find the degree of rotation using a standard rotation matrix i.e,

[tex]R = \begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}[/tex]

Given the matrix: [tex]\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}[/tex]

Now, equate the given matrix with standard matrix we have;

[tex]\begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}[/tex] =  [tex]\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}[/tex]

On comparing we get;

[tex]\cos \theta = 0[/tex]       and [tex]-\sin \theta =1[/tex]  

As,we know:

[tex]\cos \theta = \cos(90^{\circ}) = \cos( -90^{\circ})[/tex]

we get;

[tex]\theta = -90^{\circ}[/tex]

and

[tex]\sin \theta =- \sin (90^{\circ}) = \sin ( -90^{\circ})[/tex]

we get;

[tex]\theta = -90^{\circ}[/tex]

Therefore, the degree of rotation is, [tex]-90^{\circ}[/tex]

The degree of rotation represented on a matrix is measured in angles, such as degrees or radians.

The degree of rotation represented on a matrix is typically measured in terms of angles, such as degrees or radians. In order to determine the degree of rotation on a matrix, you need to identify the angle of rotation.

If the matrix is rotated clockwise, the angle is considered negative (-). If the matrix is rotated counterclockwise, the angle is considered positive (+).

For example, if a matrix is rotated 90 degrees counterclockwise, the degree of rotation would be +90°.

Answer:

b

Step-by-step explanation: