Mathematics College

A rectangular storage container with an open top is to have a volume of 10 m3. the length of this base is twice the width. material for the base costs $10 per square meter. material for the sides costs $6 per square meter. find the cost of materials for the cheapest such container. (round your answer to the nearest cent.)

Answers

Answer 1
Refer to the diagram shown below.

The volume of the container is 10 m³, therefore
x*2x*h = 10
2x²h = 10
h = 5/x²        (1)

The base area is 2x² m².
The cost is $10 per m², therefore the cost of the base is
(2x²)*($10) = 20x²

The area of the sides is
2hx + 2(2xh) = 6hx = 6x*(5/x²) = 30/x m²
The cost is $6 per m², therefore the cost of the sides is
(30/x)*($6) = 180/x

The total cost is
C = 20x² + 180/x

The minimum cost is determined by C' = 0.
That is,
40x - 180/x² = 0
x³ = 180/40 = 4.5
x = 1.651
The second derivative of C is
C'' = 40 + 360/x³
C''(1.651) = 120 >0, so x = 1.651 m yields the minimum cost.

The total cost is
C = 20(1.651)² + 180/1.651 = $163.54

Answer: $163.54

A Rectangular Storage Container With An Open Top Is To Have A Volume Of 10 M3. The Length Of This Base

Related Questions

if pictures width 4+w and the length measures 8w+2, how much longer is the picture than it is wide?

Answers

 8w + 2
-  w + 4
________
7w - 2

Hope this helps!



The picture is 7w - 2 units longer than it is wide, this is found by subtracting the width (4+w) from the length (8w+2).

To find out how much longer the picture is than it is wide, we must compare the picture's length and width. Given the picture's width is 4+w and the length is 8w+2, we subtract the width from the length to find the difference:

Length - Width = (8w+2) - (4+w) = 8w + 2 - 4 - w = 7w - 2.

Therefore, the picture is 7w - 2 units longer than it is wide.

what is the greatest common factor of 15 and 27

Answers

The greatest common factor of 15 and 27 is 3. It is the greatest factor of 27 and 15 that can be divided from both numbers without any more factors shared by both numbers in the two numbers. 

Final answer:

The greatest common factor of 15 and 27 is 3, which is the largest number that divides both numbers without a remainder.

Explanation:

The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. To find the GCF of 15 and 27, list the factors of each number:

Factors of 15: 1, 3, 5, 15

Factors of 27: 1, 3, 9, 27

The common factors of 15 and 27 are 1 and 3. The largest of these is 3, therefore the greatest common factor of 15 and 27 is 3.

The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours. the life of this bulb is normally distributed. what is the probability that a randomly selected bulb would last longer than 1150 hours?

Answers

For any normal random variable X with mean ÎĽ and standard deviation Ď , X ~ Normal( ÎĽ , Ď ), (note that in most textbooks and literature the notation is with the variance, i.e., X ~ Normal( ÎĽ , Ď² ). Most software denotes the normal with just the standard deviation.) You can translate into standard normal units by: Z = ( X - ÎĽ ) / Ď Moving from the standard normal back to the original distribuiton using: X = ÎĽ + Z * Ď Where Z ~ Normal( ÎĽ = 0, Ď = 1). You can then use the standard normal cdf tables to get probabilities. If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed. This is called the Central Limit Theorem. If a sample of size is is drawn from a population with mean ÎĽ and standard deviation Ď then the sample average xBar is normally distributed with mean ÎĽ and standard deviation Ď /âš(n) IYou can translate into standard normal units by: Z = ( X - ÎĽ ) / Ď Moving from the standard normal back to the original distribuiton using: X = ÎĽ + Z * Ď Where Z ~ Normal( ÎĽ = 0, Ď = 1). You can then use the standard normal cdf tables to get probabilities. If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed. This is called the Central Limit Theorem. If a sample of size is is drawn from a population with mean ÎĽ and standard deviation Ď then the sample average xBar is normally distributed with mean ÎĽ and standard deviation Ď /âš(n) IYou can translate into standard normal units by: Z = ( X - ÎĽ ) / Ď Moving from the standard normal back to the original distribuiton using: X = ÎĽ + Z * Ď Where Z ~ Normal( ÎĽ = 0, Ď = 1). You can then use the standard normal cdf tables to get probabilities. If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed. This is called the Central Limit Theorem. If a sample of size is is drawn from a population with mean ÎĽ and standard deviation Ď then the sample average xBar is normally distributed with mean ÎĽ and standard deviation Ď /âš(n) in You can translate into standard normal units by: Z = ( X - ÎĽ ) / Ď Moving from the standard normal back to the original distribuiton using: X = ÎĽ + Z * Ď Where Z ~ Normal( ÎĽ = 0, Ď = 1). You can then use the standard normal cdf tables to get probabilities. If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed. This is called the Central Limit Theorem. If a sample of size is is drawn from a population with mean ÎĽ and standard deviation Ď then the sample average xBar is normally distributed with mean ÎĽ and standard deviation Ď /âš(n) in this question we have X ~ Normal( ÎĽx = 1000 , Ďx² = 2500 ) X ~ Normal( ÎĽx = 1000 , Ďx = 50 ) Find P( X > 1150 ) P( ( X - ÎĽ ) / Ď > ( 1150 - 1000 ) / 50 ) = P( Z > 3 ) = P( Z < -3 ) = 0.001349898 Find P( X < 1100 ) P( ( X - ÎĽ ) / Ď < ( 1100 - 1000 ) / 50 ) = P( Z < 2 ) = 0.9772499

P(-9,1);m=1 use slope intercept form to write an equation of a line passing through the given point and having the given slope. Express answer in Standord form

Answers

Passes through (-9, 1) and has a slope of 1. Put answer into Standard Form :)

Use slope-intercept form to answer this question.

Remember, slope-intercept form is : y=mx+b, where m=slope, b=y-intercept.

Our m=1, our b=1

So, simply plug these into the equation.

y=mx+b → y = (1)x + (1)

Simplify.

y = x + 1 → Slope-intercept form.

However, we want this in standard form.

Standard form : Ax+Bx=C

In Standard Form, "x" and "y" are on the same side, so we must subtract x from both sides.

-x + y = 1 ← Standard Form

~Hope I helped!~

write a comparison sentence to resent this equation 6 times 7 equals 42

Answers

6*7=42 ......................................

A comparison sentence for the equation '6 times 7 equals 42' using multiplication.

Comparing the given equation '6 times 7 equals 42' using a sentence:

In comparison to the equation 6 times 7 equals 42, the sentence '7 multiplied by 6 results in 42' represents the relationship between the factors and the product.

Janelle has 4 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at a speed of 7mph and walks back at a speed of 3mph how long should she plan to spend walking back?

Answers

Final answer:

Janelle should plan to spend 3 hours walking back.

Explanation:

To find out how long Janelle should plan to spend walking back, we need to calculate the total time it takes her to run and walk. Since she runs at a speed of 7mph, she completes the distance of the race in 1 hour (4 miles / 7mph = 0.57 hours = 1 hour). Therefore, she spends 1 hour running and 3 hours left for walking. To find out the distance she walks back, we use the formula distance = speed x time. Since she walks at a speed of 3mph, the distance she walks back is 3mph x 3 hours = 9 miles.

What is the unit rate of 15 degrees in 2 hours.

Answers

The unit rate of 15 degrees in 2 hours.
It says here that in 2 hours, there are 15 degrees.
So we need to find the unit rate of this given situation per hours.
There are 2 hours
so you'll divide 2 by 15 to get the unit rate of the given situation
15 divided by two is 7.5
So the unit rate would be 7.5 degrees per hour.

find the measure of <ghk <hki and <hkj show your work or wite and explanation

Answers

check the picture below.

Felicity is placing a rectangle in the coordinate plane. She knows that the longer side of the rectangle is 3 times its shorter side. She places the longer side on the x-axis.

What coordinates should she assign to the top-right vertex of the rectangle?








Answers

Enter your answer in the boxes.The top-right vertex of the rectangle is:
(3a , a)

Answer:

(3a,a)

Step-by-step explanation:

As you know the component on the X vertex is the first that is represented when setting point coordenates, and the second value is in the Y vertex, as you can see the value for Y is a, and in the problem says that the longer side is three times the short side, since the Y vertex is the short side, that means the X vertex will have the longer side, making it 3a. So the coordenates will be (3a,a).

Which of the following statements are equivalent to the statement "price increased by 100%"?

Choose all correct answers.

(A) The price doubled
(B) The price is 150% of the price before
(C) The price was reduced by a quarter
(D) The price became a half of what it was before
(E) The price is now 1.5 of what it was before
(F) The price now is 66 2/3 % of what it was before
(G) The price now is 200% of what it was before
(H) The price is 75% of what it was before

Answers

The statements equivalent to a price increase of 100% are that the price doubled and the price is now 200% of the original. These statements mean the new price is twice the original amount.

When analyzing statements that describe a price increase of 100%, it is important to understand that this means the new price is twice the original price. Among the listed statements, the correct ones that are equivalent to a 100% increase in price are:

(A) The price doubled

(G) The price now is 200% of what it was before

These are equivalent because if a price doubles, it is 100% more, making the new price 200% of the original. This can be seen in practical examples, such as if a gumball costs 25 cents and the price doubles, it becomes 50 cents, or 200% of its original cost.

9.17/15.00
Is this a A+ or A or B or C

Answers

9.17/15 is very close to 9/15, or 3/5. 3/5 is the same as 60/100, which would be a D.
9.17/15.00 = 0.61, or about 61 percent.

That would likely earn a grade of D, unless the grading scale used is different from the usual 91-100, 81-90, 71-80, 61-70, 51-60.

Peter wants to borrow $3,000. He has two payment plans to choose from. Plan A is 4% interest over 6 years. Plan B is 5% interest over 4 years. Using the formula mc024-1.jpg for payment, m, which statement best compares the plans?
Plan A has a monthly payment of about $23 less and a total interest charge of $120 less than plan B.
Plan A has a monthly payment of about $23 less and a total interest charge of $120 more than plan B.
Plan A has a monthly payment of about $23 more and a total interest charge of $120 more than plan B.
Plan A has a monthly payment of about $23 more and a total interest charge of $120 less than plan B

Answers

To determine which payment plan is better for borrowing $3,000, Plan A or Plan B, one must calculate both the monthly payments and total interest charges using the given annual interest rates and compounding periods for each plan and compare the results accordingly.

Peter wants to borrow $3,000 and is considering two different payment plans. To compare these plans, we need to calculate the monthly payment and total interest charge for each.

Plan A has an annual interest rate of 4%, compounded monthly over 6 years (or 72 months). Using the formula for monthly payment (m), we can find the monthly payment for Plan A:

 m = P[r(1+r)^n] / [(1+r)^n-1]
Where:

P is the principal amount ($3,000)r is the monthly interest rate (annually 4%, monthly 0.04/12)n is the number of payments (6 years x 12 months/year = 72 months)

Similarly, Plan B has an annual interest rate of 5%, compounded monthly over 4 years (or 48 months). We use the same formula to calculate the monthly payment for Plan B.

After calculating m for both plans, we can also calculate the total interest paid by multiplying the monthly payment by the number of payments and subtracting the principal amount from the result for each plan. Then, we can compare the monthly payments and total interest charges between Plan A and Plan B.

Hannah travels 6 times as many minutes than Raoul does. Together, they travel 63 minutes. How many minutes does Hannah travel? Draw a model and wrote an equation to solve.

Answers

let h represent the # of minutes that Hannah travels and r the # of minutes that Raoul travels.  Then h + r = 63 min.     We are told that h=6r.

Then 6r + r = 63 min, so:

7r = 63 min, and    r=63 min  / 7   = 9 min.

Raoul travels for 9 minutes and Hannah travels for 6(9 minutes) = 54 minutes.

Over the last three evenings, Latoya received a total of 79 phone calls at the call center. The first evening, she received 6 fewer calls than the third evening. The second evening, she received 3 times as many calls as the third evening. How many phone calls did she receive each evening?

Answers

We need to represent the numbers of calls symbolically:

Third evening:      x calls
First eve:              x-6 calls
Second evening:  3x calls

Find x.  Add up these three numbers    x, x-6 and 3x and equate your sum to 79:

x+x-6+3x = 79.  Then 5x=79+6, or 5x = 85.  Thus, x = 17.

17 calls on the 3rd night, 
17-6 calls on the 1st night, and 
3(17) = 51 calls on the 2nd night.

Check!  Add together 17, 11 and 51.  Do these add up to 79?   Yes. 
The first evening she received 15.2 calls. The second night she received 42.6. The third evening she received 21.2

PLEASE HELP!
Yolanda will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $57 and costs an additional $0.11 per mile driven. The second plan has an initial fee of $50 and costs an additional $0.13 per mile driven.

For what amount of driving do the two plans cost the same?
What is the cost when the two plans cost the same?

Answers

For the first plan, we can write it as 57+0.11m if m represents the miles driven due to that we have a base value of 57 but add $0.11 per mile . Similarly, for the second plan we can write 50+0.13m. Since we want them to be equal, we have 57+0.11m=50+0.13m. Subtracting 0.11m as well as 50 from both sides, we get 0.02m=7. Next, we can multiply both sides by 50 to get 350=the amount of miles needed for them to be the same. For the cost, we can plug 350 into either expression to get 57+0.11*350=95.5 dollars

(algebra)
Solve for x.
Fx-gx=h

Answers

Fx-gx=h
Fx/f-gx/g=h/fg
x-x=h/fg
x=h/fg

If we solve the equation which is (F × x ) - (g × x ) = h , we will get the value of x as x = h / ( F - g ).

What is algebra ?

Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.

An equation is given which is :

(F × x ) - (g × x ) = h

We have to solve this equation to get the value of the variable x.

So, the value of x can be calculated as :

(F × x ) - (g × x ) = h

Taking common x from LHS :

x ( F - g ) = h

Dividing by ( F - g ) on both sides we get :

[ x ( F - g ) / ( F - g )] = h / ( F - g )

or

x = h / ( F - g )

Therefore , if we solve the equation which is (F × x ) - (g × x ) = h , we will get the value of x as x = h / ( F - g ).

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Which equation represents a line that passes through (–9, –3) and has a slope of –6?

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -9}}\quad ,&{{ -3}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies -6 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-3)=-6[x-(-9)] \\\\\\ y+3=-6(x+9)\implies y+3=-6x-54\implies y=-6x-57[/tex]

The function g(x) = –x2 + 16x – 44 written in vertex form is g(x) = –(x – 8)2 + 20. Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = –x2 + 16x – 44?

Answers

It was moved up 20 units

Answer:

the graph of f(x) will be reflected over x axis, moved 8 units to the right and shifted 20 units up to get g(x)

Step-by-step explanation:

The function [tex]g(x) = -x^2 + 16x - 44[/tex] written in vertex form is [tex]g(x) = -(x - 8)^2 + 20[/tex]

The parent function is f(x)=x^2

Now we compare parent function f(x) and g(x)

In g(x), negative sign at first

f(x) ----> -f(x) , the graph is reflected across x axis

f(x)-----> f(x-h), the graph will be transformed h units to right

f(x)----> f(x) +k , the graph will be transformed k units up

[tex] g(x) = -(x - 8)^2 + 20[/tex], the graph of f(x) will be reflected over x axis, moved 8 units to the right and shifted 20 units up to get g(x)

What is the factorization of g3 – 125?

(g– 5)(g2 + 5g + 10)
(g – 25)(g2 + 25g + 625)
(g – 5)(g2 + 5g + 25)
(g – 25)(g2 + 5g + 125)

Answers

[tex]\bf \textit{difference of cubes} \\ \quad \\ a^3+b^3 = (a+b)(a^2-ab+b^2)\qquad (a+b)(a^2-ab+b^2)= a^3+b^3 \\ \quad \\ a^3-b^3 = (a-b)(a^2+ab+b^2)\qquad (a-b)(a^2+ab+b^2)= a^3-b^3 \\\\ -------------------------------\\\\ g^3-125\implies g^3-5^3\implies (g-5)(g^2+5g+5^2) \\\\\\ (g-5)(g^2+5g+25)[/tex]

Answer: (C) (g – 5)(g2 + 5g + 25)

The function f(x) is graphed on the coordinate plane.

What is f(−2) ?

Enter your answer in the box.

f(−2) = ?

Answers

f(-2)=-2  it would be a straight line   f(-2) is also equal to y so basically it would be y=-2

PLEASE HELP ASAP!!/BRAINLIEST/5 STARS/HEART(THX)!

Jimmy is going to pack his backpack for a trip. His backpack is 60 cubic litres. He has a pile of equipment that takes up 43 cubic litres and then he has his sleeping bag that takes up 23 cubic litres. Let r be the amount of room left in his backpack. Which equation could you use to determine if he has enough room in his backpack.

A) r = 23 + 43
B) r = 23 + 43 + 60
C) 23 + 43 + r = 60
D) 23 + r = 60 + 43

Answers

To start, we know these facts:

His backpack is 60 cubic L
His equipment is 43 cubic L
His sleeping back is 23 cubic L
R = amount of room left.

The best formula to use is
C) 23 + 43 + R = 60

This is because we want to be able to solve for R in order to find how how much space he has left.

23 + 43 + R = 60
66+ R = 60
66-66 + R = 60-66
R = -6
He is over his amount by 6.

ANSWER:
C) 23 + 43 + R = 60

The equation for the given situation is 23 + 43 + r = 60. Therefore, option C is the correct answer.

Given that, Jimmy backpack is 60 cubic liters. He has a pile of equipment that takes up 43 cubic liters and then he has his sleeping bag that takes up 23 cubic liters.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let r be the amount of room left in his backpack.

Total space in backpack = A pile of equipment +  Sleeping bag + Room left

So, 60 = 43+23+r

The equation for the given situation is 23 + 43 + r = 60. Therefore, option C is the correct answer.

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What is a distributive property of 72 divided by 4

Answers

Answer:

[tex]\frac{72}{4}=18[/tex]

Step-by-step explanation:

To find : What is a distributive property of 72 divided by 4 ?

Solution :

The distributive property of division is given by,

[tex]\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}[/tex]

We have to divide 72 by 4,

So, Re-write 72 as 60+12.

Substitute,

[tex]\frac{72}{4}=\frac{60+12}{4}[/tex]

[tex]\frac{72}{4}=\frac{60}{4}+\frac{12}{4}[/tex]

[tex]\frac{72}{4}=15+3[/tex]

[tex]\frac{72}{4}=18[/tex]

Therefore, [tex]\frac{72}{4}=18[/tex]

Final answer:

While the distributive property is typically relevant for multiplication over addition or subtraction, you can apply it to division by first rewriting the division as multiplication by the reciprocal. For example, 72 divided by 4 can be rewritten as 72 times 1/4, and then distributed over a sum or difference.

Explanation:

The distributive property involves multiplication and addition or subtraction, not division. However, if we interpret your question in a bit different way, we can make use of the distributive property for division. To start, dividing 72 by 4 is the same as multiplying 72 by 1/4. So, we can rewrite it as follows:

72 * 1/4

The distributive property is applied when you multiply a number by a sum or a difference. For example, in case of [tex]72*1/4 = (40+32)*1/4[/tex], it would distribute as: [tex]40*1/4 + 32*1/4[/tex]. It gives us 10 + 8 = 18 which is the correct answer. This way, the distributive property can be used in division if the division is expressed as a multiplication.

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If Sam has 6 different hats and 3 different scarves, how many different combinations could he wear

Answers

18

He can wear a different hat with one scarf so if that is multiplied by 6*3 you will get 18 different combinations that Sam can wear

If Sam has 6 different hats and 3 different scarves, the number of combinations he could wear is: 18 ways.

Given the following data:

Number of hats = 6 hats.Number of scarves = 3 scarves.

How to determine combinations.

In this exercise, the number of ways 6 different hats and 3 different scarves can be worn without any form of repetition should be calculated by using a combination.

Mathematically, combination is given by this formula:

[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]

Where:

n is the number of items.r is the number of times of choosing items.

For Sam's combination:

[tex]_hC_s = 6 \times 3[/tex]

Sam = 18 ways.

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9+(6-6)x4-(-7-(-2)) solved in order of operations

Answers

the answer is 22 hope this helps 

Estimated the difference
645,908 + 335,297
_ - _ = _

Answers

My answer is in the attachment below. Please comment below any questions, comments, or concerns related to this answer.
Have a great day!

What is the solution of -8/2y-8=5/y+4 - 7y+8/y^2-16

Answers

Answer:

y = 8

Step-by-step explanation:

[tex]Domain:\\\\2y-8\neq0\ \wedge\ y+4\neq0\ \wedge\ y^2-16\neq0\\\\2y\neq8\ \wedge\ y\neq-4\ \wedge\ y^2\neq16\\\\y\neq4\ \wedge\ y\neq-4\ \wedge\ y\neq\pm\sqrt{16}\\\\y\neq4\ \wedge\ y\neq-4\ \wedge\ y\neq-4\ \wedge\ y\neq4\\\\\boxed{y\neq-4\ \wedge\ y\neq4}\\\\===========================[/tex]

[tex]\dfrac{-8}{2y-8}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-16}\\\\\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-4^2}\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}-\dfrac{7y+8}{(y-4)(y+4)}\qquad\text{multiply both sides by (-2)}\\\\\dfrac{8}{y-4}=-\dfrac{10}{y+4}+\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{add}\ \dfrac{10}{y+4}\ \text{to both sides}\\\\\dfrac{8}{y-4}+\dfrac{10}{y+4}=\dfrac{14y+16}{(y-4)(y+4)}[/tex]

[tex]\dfrac{8(y+4)}{(y-4)(y+4)}+\dfrac{10(y-4)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\\\\\dfrac{8(y+4)+10(y-4)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{use the distributive property}\\\\\dfrac{8y+32+10y-40}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{combine like terms}\\\\\dfrac{(8y+10y)+(32-40)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\\\\\dfrac{18y-8}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\iff18y-8=14y+16\\\\18y-8=14y+16\qquad\text{subtract 14y from both sides}[/tex]

[tex]4y-8=16\qquad\text{add 8 to both sides}\\\\4y=24\qquad\text{divide both sides by 4}\\\\y=8\in D[/tex]

Answer:

6

Step-by-step explanation:

The graph shows a line and two similar triangles.

Answers

Answer:

Option C. is the correct option.

Step-by-step explanation:

The given line in the graph passes through two points (0, 3) and (3, 7).

We have to find the equation of the line.

Since y = mx + c is the standard equation of a line

where m = slope of the line

c = y - intercept

Slope of a line m = [tex]\frac{(y-y')}{(x-x')}[/tex]

Now we put the values of x and y to find the slope of this line.

m = [tex]\frac{7-3}{3-0}=\frac{4}{3}[/tex]

Since (0, 3) passes through the line

3 = 0 + c

c = 3

Equation of the line will be

[tex]y=\frac{4}{3}x+3[/tex]

Option C. is the answer.

Answer:

me dony know

Step-by-step explanation:

In the circle graph above, you can see that 47% of the company's monthly income is used to pay the owner's personal salary. If the amount of the owners's personal salary was $2,176.10 this month, what was the company's total monthly income this month?

Answers

The answer to this question would be: $4630

In this question, 47% of the company income is used to pay owner's personal salary, which was $2,176.10
Then, to find the company total income the calculation would look like this:

owner's personal salary= 47% * total company income
$2,176.10= 0.47 * total company income
total company income= $2,176.10/ 0.47 = $4630

Final answer:

To find the total monthly income, set up a proportion using the percentage of the owner's salary with the given amount. Solve for the total income to find the answer.

Explanation:

In the circle graph above, the owner's personal salary represents 47% of the company's monthly income. This means that $2,176.10 is 47% of the total monthly income. To find the total income, you can set up a proportion: $2,176.10 is to 47% as X is to 100%. Solving this equation gives you the company's total monthly income as $4,635.

Which linear system has a solution of
[tex]x = 2 \: and \: y = - 3[/tex]

Answers

bear in mind that, a "solution" so-called, or a zero, or a root, is really just an x-intercept of the graph, namely, where does the graph touch the x-axis?  that's a zero/root/solution/x-intercept.

now, about those two lads above, check the picture below.

notice, that, the horizontal line, by definition will never touch the x-axis, whilst the other one does, at x = 2.

Given the equation −4 Square root of x minus 3= 12, solve for x and identify if it is an extraneous solution

Answers

i believe ur answer is 12 and is extraneous

Answer:

[tex]x=\frac{225}{16}[/tex] is an extraneous solution.      

Step-by-step explanation:

Given : Equation [tex]-4\sqrt x-3=12[/tex]

To find : Solve for x and identify if it is an extraneous solution?

Solution :

Step 1 - Write the equation,

[tex]-4\sqrt x-3=12[/tex]

Step 2 - Add 3 both sides,

[tex]-4\sqrt x-3+3=12+3[/tex]

[tex]-4\sqrt x=15[/tex]

Step 3 - Squaring both sides,

[tex](-4\sqrt x)^2=(15)^2[/tex]

[tex]16x=225[/tex]

Step 4 - Divide both side by 16,

[tex]\frac{16}{16}x=\frac{225}{16}[/tex]

[tex]x=\frac{225}{16}[/tex]

For extraneous solution, Substitute the value of x back in the equation.

[tex] -4\sqrt (\frac{225}{16})-3=12[/tex]

[tex]-4\times\frac{15}{4}-3=12[/tex]

 [tex]-15-3=12[/tex]

[tex]-18\neq12[/tex]

The value of x does not satisfy the equation which means the value of x is an extraneous solution.

So, [tex]x=\frac{225}{16}[/tex] is an extraneous solution.

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