The ratio of a to b is 3 to 1, and the ratio of b to c is 1 to 5. What is the value of 2a+3b/ 4b+3c?
A. 3/16
B. 9/19
C. 1/2
D. 5/7
E. 18/19

Answer:

a)2x=4

x=days

b)

c) x means how much money he has and y is how many days

Step-by-step explanation:

Answer:

decimal form: 7.46410161 or the exact form: x = 4 + 2 √ 3

Step-by-step explanation:

Answer:

4 + 2√3

Step-by-step explanation:

x - 2 = √4x

Domain: √4x ≥ 0 ⇒ x - 2 ≥ 0 ⇒ x ≥ 2

(x - 2)² = (√4x)²

x² - 4x + 4 = 4x

x² - 8x + 4 = 0

D = (- 8)² - 4(1)(4) = 48 = (4√3)²

\(x_{1}\) = \(\frac{8+4\sqrt{3} }{2}\) = 4 + 2√3 ≈ 7.4641

\(x_{2}\) = \(\frac{8-4\sqrt{3} }{2}\) = 4 - 2√3 ≈ 0.5359 < 2 ⇒ \(x_{2}\) is extraneous root

Answer:

x=5

Step-by-step explanation:

you need to get the variable on one side and the constant on the other

So first, you need to simplify: 9x-8x would be x

so now you have x-3=7-x you need to add the x to both sides to get 2x-3=7 then you need to add the 3 to both sides.

now you have 2x=10

divide by 2 on both sides and you will get x=5

The true statements about g(x) = x2 - 4x + 3 and f(x) = x2 - 4x are

The functions are given as:

\(g(x) = x^2 - 4x + 3\)

\(f(x) =x^2 - 4x\)

Start by differentiating the function g(x)

g'(x) = 2x - 4

Set to 0

2x - 4 = 0

Add 4 to both sides

2x = 4

Divide by 2

x = 2 ----- this represents the axis of symmetry of function g(x)

Substitute x = 2 in \(g(x) = x^2 - 4x + 3\)

\(g(2) = 2^2 -4*2 + 3\)

g(2) = -1

This means that the vertex of the function g(x) is (2,-1)

Next, differentiate the function f(x)

f'(x) = 2x - 4

Set to 0

2x - 4 = 0

Add 4 to both sides

2x = 4

Divide by 2

x = 2 ----- this represents the axis of symmetry of function f(x) (same as g(x))

Substitute x = 2 in \(f(x) =x^2 - 4x\)

\(f(2) = 2^2 -4 * 2\)

f(2) = -4

This means that the vertex of the function f(x) is (2,-4)

By comparing the vertices (2,-4) and (2,-1).

We can see that (2,-4) is below (2,-1).

Hence, the true statements are (a) and (b)

Which statements about functions g(x) = x2 - 4x + 3 and f(x) = x2 - 4x are true? Select all that apply.

A. The vertex of the graph of function g is above the vertex of the graph of function f.

B. The graphs have the same axis of symmetry.

c. Function f has a maximum value and function g has a minimum value.​

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Answer:

17

Step-by-step explanation:

5x2=10

8 1/2x2=17

The constant of variation is 2/3, and when x = -0.5, the value of y is -1/3.

In a direct variation equation of the form y = kx, the constant of variation, k, represents the relationship between the variables y and x. To find the constant of variation, we can use the given data points. Let's use the point (3, 2). By substituting x = 3 and y = 2 into the equation, we have 2 = k * 3. Solving for k, we get k = 2/3.

Now, with the constant of variation, k = 2/3, we can find the value of y when x = -0.5. Substituting x = -0.5 into the equation y = kx, we have y = (2/3) * (-0.5). Simplifying this expression, we find y = -1/3. Therefore, when x = -0.5, the value of y is -1/3.

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Answer:

D.Mica spent $45.50 on 7 wiffle ball sets. How much does it cost for one set?

Step-by-step explanation:

A.Cost of 1 gallon=3.79

Cost of 10.3 gallon=\(3.79\times 10.3=39.037\)

It can not be solved b y division of decimals.

B.Let x be grade got by Maria in her next test.

Grades obtained by Marian in her 4 previous test are  given by

75.3,92.1,78.6 and 81.0

According to question

\(75.3+92.1+78.6+81.0\geq 400\)

\(327+x\geq 400\)

\(x\geq 400-327\)

\(x\geq 73\)

It can not be solved b y division of decimals.

C.Helena saved money=$45

Cost of dress=$78.00

78-45=33

She needs to save $33 more.

It can not be solved b y division of decimals.

D.Cost of 7 wiffle ball sets=$45.50

Cost of 1  ball set=\(\fra{45.50}{7}=\)$6.5

It can be solved b y division of decimals.

Option D is true.

D.Mica spent $45.50 on 7 wiffle ball sets. How much does it cost for one set?

Answer:

the answer is d

Step-by-step explanation:

We have that, finding the horizontal component of the reaction at A in pounds, it is 866.03 pounds, with zero horizontal component in the negative direction.

To determine the horizontal component of the reaction at A, we first need to draw a free-body diagram of the given structure. So, we can use the equation of equilibrium for the horizontal direction to find the horizontal component of the reaction at A. The equation of equilibrium for the horizontal direction is as follows:

∑Fx=0∑Fx=0

Equilibrium equation for the horizontal direction, where ∑Fx is the sum of all forces acting horizontally in the positive direction and in the negative direction. Let's draw the free body diagram of the given structure: Here, RAY is the horizontal component of the reaction at A. We can see that there is no force acting horizontally in the negative direction.

Therefore,∑Fx=RAx∑Fx=RAx

Now, we need to find the force that acts horizontally in the positive direction. In the free body diagram, we can see that:

∑Fx=1000cos30°=866.03∑Fx=1000cos30°=866.03

Therefore

∑Fx=RAx=866.03RAx=866.03

So the horizontal component of the reaction at A is 866.03 pounds. Therefore, the answer is 866.03 (positive).

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Value of x = 42.5 ° and measure of angle 4 = 37.5 ° .

measure of angle 3 = measure of angle 8

( 3 x + 15 ) ° = ( x + 100 ) °

2 x = 85

x = 42.5 °

measure of angle 3 + measure of angle 4 = 180 °

measure of angle 3 = ( 3 x + 15 ) °

                                 = ( 3 * 42.5 ) + 15  

                                  = 142.5 °

Hence , measure of angle 4 = 180 - 142.5 ° = 37.5 ° .

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if the family gives up two nights in the hotel, they could afford d) 5 meals

The family has a budget of $800 for meals and hotel accommodations. If they could afford eight nights in a hotel without buying any meals, we can determine the cost of one night at the hotel. To do this, we can divide the total budget by the number of nights:

$800 / 8 nights = $100 per night

Now, let's consider the scenario where the family gives up two nights in the hotel. This would free up $200 from their budget ($100 per night x 2 nights). We can then use this amount to determine how many meals the family can afford by dividing the available funds by the cost of one meal:

$200 / $40 per meal = 5 meals

Therefore, if the family gives up two nights in the hotel, they could afford 5 meals. The correct answer is d. 5.

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See

Compare to slope intercept form of line y=mx+b

Rate of change is slope

So

it's

Answer:

$2.50 per mile

Step-by-step explanation:

Given that,

→ y = mx + b

→ y = 2.5x + 7

The rate of change in cost per mile is,

→ slope

→ m

→ [ $2.5 ]

Hence, rate of change in cost is $2.5.

Answer:

(2 - 3i)(4+2i)

(2 x 4)(2 x 2i) (-3i x 4) (-3i x 2i)

8 x 4i x -12i -6i^2

6i^2 - 12i x 32

Step-by-step explanation:

Answer:

6i² - 8i + 8

Step-by-step explanation:

1. Expand Brackets: 8 + 4i - 12i - 6i²

2. Simplify equation: 8 - 8i - 6i²

3. Rearrange: 6i² - 8i + 8

Answer:

The system is consistent.

Step-by-step explanation:

Answer:

  (b)  There is not enough information to know whether the system is consistent or inconsistent.

Step-by-step explanation:

Given a system of equations consists of two lines with the same slope, you want to know whether the system is consistent or inconsistent, whether the lines are perpendicular, or if there is enough information to tell.

Lines with the same slope are either parallel or coincident. If they are parallel, the system of equations is inconsistent. If they are coincident, the system of equations is consistent.

Parallel or coincident lines are not perpendicular. Perpendicular lines have opposite reciprocal slopes.

Since we cannot tell whether the lines are parallel or coincident from the given description, we have to say, "there is not enough information to know."

Answer:

b=22/15 or 1.46 repeating

Step-by-step explanation:

If In a class of 29 students, 19 are female and 14 have an A in the class then 2 male students have an A in the class.

We can calculate the number of students who are male and have an A in the class by subtracting the given values from the total number of students.

Total students = 29

Female students = 19

Male students = Total students - Female students = 29 - 19 = 10

Students with an A = 14

Male students without an A = 8

To calculate the number of male students with an A, we subtract the number of male students without an A from the total number of male students.

Male students with an A = Male students - Male students without an A = 10 - 8 = 2

Therefore, there are 2 male students who have an A in the class.

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Answer:

-x + 5y = 4

5y = x + 4

y = x/5 + 4/5

Slope: 1/5

Y-intercept: 4/5

5y - x = 15

5y = x + 15

y = x/5 + 3

Slope: 1/5

Y-intercept: 3

2y - 3x = 7

2y = 3x + 7

y = 3/2x + 7/2

Slope: 3/2

Y-intercept: 7/2

2y = 5x + 7

y = 5/2x + 7/2

Slope: 5/2

Y-intercept: 7/2

To decide whether it is sensible for Stacy to utilize the ordinary show for the inspecting conveyance of the test extent, we got to check whether the conditions for utilizing the typical conveyance estimation are met. The conditions are:

The test estimate is expansive sufficient

The test information is autonomous

The populace is at slightest 10 times bigger than the test

The test estimate, in this case, is 50. To check whether it is expansive sufficient, ready to utilize the run the show of thumb that the test measure ought to be at the slightest 10% of the populace estimate.

Hence, based on these conditions, it is sensible for Stacy to utilize the ordinary demonstration for the inspecting conveyance of the test extent. She can accept that the testing dispersion is roughly typical with a cruel of p = 0.11 and a standard deviation of sqrt[(p(1-p))/n] = sqrt[(0.11(0.89))/50] = 0.05.

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Answer:

(-1/6, -7/12)

Step-by-step explanation:

From the second equation, we get:

2y = x - 1

y = (1/2)x - 1/2

Substituting for y in the first equation, we get:

7x - 2(1/2)x + 1 = 0

7x - x + 1 = 0

6x + 1 = 0

6x = -1

x = -1/6

Substituting back into the second equation to find y:

2y = (-1/6) - 1

2y = -7/6

y = -7/12

Therefore, the solution is (-1/6, -7/12).

To check, we substitute these values into both equations:

7(-1/6) - 2(-7/12) = 1

-7/6 + 7/6 = 1

1 = 1

This is true, so our solution is correct.

To find the inverse, interchange the variables and solve for

y.

f^-1(x)=√2x,−√2x

The volume of the figure formed when triangle ABC is rotated continuously about segment AC is approximately 78.5 cubic units.

To find the volume of the figure formed when triangle ABC is rotated continuously about segment AC, we can use the method of cylindrical shells.

First, let's visualize the triangle ABC and the line segment AC on the coordinate plane:

To calculate the volume, we integrate the areas of the infinitesimally thin cylindrical shells formed during rotation.

The height of each cylindrical shell is the length of segment BC, which is the distance between points B and C. In this case, BC has a length of 3 units.

Now, let's consider an arbitrary point (x, y) on segment BC. The x-coordinate of this point varies from 0 to 3, and the y-coordinate remains constant at 5. The distance of this point from segment AC is given by x.

The circumference of the cylindrical shell at this point is given by 2πx (since the radius is x), and the infinitesimal height of the shell is dy (since the shell has no thickness).

Thus, the differential volume of the cylindrical shell can be expressed as dV = 2πx dy.

To find the total volume, we integrate this expression over the range of x from 0 to 3:

V = ∫[0,3] 2πx dy

Integrating with respect to y, we obtain:

V = 2π ∫[0,5] x dy

The limits of integration for y are from 0 to 5, the y-coordinates of points C and B.

Evaluating this integral, we get:

V = 2π [x²/2] [0,5]

V = π [x²] [0,5]

V = π (5² - 0²)

V = 25π

Rounding the volume to the nearest tenth, we have:

V ≈ 78.5 cubic units.

Therefore, the volume of the figure formed when triangle ABC is rotated continuously about segment AC is approximately 78.5 cubic units.

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Answer:

y=2x+6

y=2x+6

Explanation:

Given the equation:

The equation written as a system of equations is:

Opening the bracket in the first equation gives:

Answer:

32% goes to 30%. 22% goes to 20%. 74% goes to 70%. 51% goes to 1/2.

Step-by-step explanation:

Just treat is as rounding. When you round, 32 goes to 30 because the 2 is 4 or less. 22 and 74 each respectively round to 20 and 70. 1/2 is equal to 50%. And 51% rounds to 50%, or 1/2.

The correct value of the percent on the left with the appropriate estimate on the right is,

32% - 30%

22% - 20%

74% - 70%

51% - 1/2

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

To match the percent on the left with the appropriate estimate on the right.

Now, We can simplify as;

32% = 0.32

22% = 0.22

74% = 0.74

51% = 0.51

20% = 0.20

70% = 0.70

1/2 = 0.5

30% = 0.3

Thus, The correct value of the percent on the left with the appropriate estimate on the right is,

32% - 30%

22% - 20%

74% - 70%

51% - 1/2

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Answer:

That's too many questions in one.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

1/10 = 10/100

So 10/100 + 88/100 = 98/100

Answer:

B

Step-by-step explanation:

they are similar and 7 / 5 = 21 / 15

Answer:

2nd option

Step-by-step explanation:

15 is a multiple of 5 (5x3=15) and 21 is a multiple of 7 (7x3=21).

Answer:

the answer is going to be 42 \(in^{2}\)

Step-by-step explanation:

12 x 13 divided by 2 = 78

6 x 6 = 36

78 - 36 = 42

Thus, the correct answer is: C. The Stafford loan will have a lower balance of $431.17 at the time of repayment.

In order to evaluate the Unsubsidized Stafford Loan against the PLUS Loan, a comparison of their balances upon repayment after 6 months of graduation is necessary.

Having taken out a loan of $9,529 with an annual interest rate of 5.95% compounded monthly, and after an interest accumulation period of 18 months, the Stafford Loan balance at this point in time stands roughly around $10,365.86.

On the other hand, the PLUS Loan's equilibrium at graduation is recorded at $10,172.23, but including a 6-month interest accumulation period along with an annual incrementation percentage of 6.55% that is compounded monthly equals to approximately $10,797.03 when due for repayment.

To summarize, based on the balance comparisons, it is concluded that the Stafford loan owes a lower amount at repayment which is different by $431.17 compared to the PLUS Loan.

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