What are the solutions to the quadratic equation 2x^2 + 10x - 48 = 0?
A. x= -4 and x = 6
B. X= -8 and x = 2
c. x= -6 and x = 8
D. X = -8 and x = 3

9514 1404 393

Answer:

  yes, 5

Step-by-step explanation:

There is no factor of x in every term, so we only need look at the coefficients. Those are 5, 80, 320. All are multiplies of the smallest one, 5.

The greatest common factor is 5.

The length of AC is 12.5 and the length of AD is 3.

A triangle is a three-sided polygon because it has three edges and three vertices. The most important attribute of a triangle is the sum of its internal angles to 180 degrees

Given triangle ABC,

and D is a point on AB and E is a point on AC,

and forms a triangle ADE,

and  DE is parallel to AC,

taking ΔABC and ΔBDE

∠B = ∠B  (common angle)

because DE is parallel to AC, so corresponding angles are equal,

so ∠A = ∠D

and ∠C = ∠E

ΔABC ≈ ΔBDE (triangles are similar)

since both triangles are similar the ratio of their corresponding sides is equal,

AB/BD = AC/DE = BC/BE

given BD = 2, BE = 4, DE = 5 and EC = 6

BC = EC + BE = 4 + 6

BC = 10

AC/DE = BC/BE

AC = 5(10/4)

AC = 12.5

and AB/BD = BC/BE

AB = 2(10/4)

AB = 5

AD = AB - BD

AD = 5 - 2

AD = 3

Hence AC = 12.5 and AD = 3.

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The figure is in image.

Answer:

Step-by-step explanation:

\(\frac{dy}{dx} =20x^{19}\)

Answer:

7

Step-by-step explanation:

Let the height of pyramid be h

\(v = \frac{1}{3} lwh\)

v= 224

w= 8

l= 12

224=1/3(12)(8)(h)

224=32h

h=224/32

h=7

The ratio of the area of the smaller circle to the area of the larger circle is 1/2.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

From the information, the square is inscribed in a circle and then a smaller circle is inscribed in the square.

Let the radius of smaller circle be 2r, then length of side of larger square is ✓2r and the length of side of smaller square is  

The ratio of area of smaller square to larger square is:

= 4r² / 4(✓2r)²

= 1/2

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The important variables are the two types of test questions which can be represented as :

Variables are used to represent unknown values which could be worked out in a mathematical expression or problem.

The variables or unknown in this case are the type of test questions. which are : m for multiple choice, s for short answer

Therefore, the correct option is C. m for multiple choice, s for short answer

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Answer: the rate of the water level in the cone falling when it is 5cm from the bottom of the cone is -0.1768 cm/sec

Step-by-step explanation:

Given the data in the question;

H/h = R/r

10/5 = 6/r

r 1 = 30/10 = 3

Also

10/h = 6/r

r2 = 6h/10 = 3/5 × h

Volume = 1/3πr²h

V = 1/3 × π × (3/5 × h)² × h

V =  1/3 × π × 9/25 × h³

V = 3π/25 × h³

Now

dv/dt = 3π/25 × 3 × h² × dh/dt

-5 = 3π/25 × 3 × 25 × dh/dt

-5 = 3π × 3 × dh/dt

-5 = 9π × dh/dt

dh/dt = -5/9π

dh/dt = -0.1768 cm/sec

therefore, the rate of the water level in the cone falling when it is 5cm from the bottom of the cone is -0.1768 cm/sec

Answer: You add 9 each time

Step-by-step explanation:

19 + 9 = 28 + 9 = 37 + 9 = 46 + 9 = 55

hope this helps mark me brainliest if it did

The expression that could be used to calculate the amount Trina was charged in interest for the billing cycle is  (APR / 365) x 30 days x adjusted balance.

The adjusted balance method is one of the methods for computing the finance charge (interest and other fees) for credit cards.

The adjusted balance is the ending balance determined after adjusting the opening balance with purchases and payments.

Credit card interest method = adjusted balance method

Beginning balance = $780

Purchase = $170

Payment = $210

Adjusted balance, AB = $740 ($780 + $170 - $210)

APR = 17% = 0.17 (17/100)

The interest charged = (APR / 365) x 30 days x adjusted balance

= $10.34 [(0.17/365) x 30 x $740]

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A randomized experiment with order, replacement, and no repetition is one in which the order of the outcomes matters, the same outcome can occur multiple times, and no outcome can occur more than once.

For example, drawing a card from a deck and then flipping a coin would be a random experiment with order, replacement, and no repetition. The order of the results is important because the outcome of the coin toss will depend on the outcome of the card draw.

The same result can occur multiple times because the same card can be drawn twice, and no result can occur more than once because the coin can only land heads or tails once.

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Random experiment with order, replacement and without repetition

Answer:

She needs to invest $13,636.36 right now

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

\(E = P*I*t\)

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

\(T = E + P\)

In this question:

In 15 years, so \(t = 15\)

She wants to have $30,000, so \(T = 30000\)

8% interest, so \(I = 0.08\)

We have to find P.

\(T = E + P\)

\(30000 = E + P\)

\(E = 30000 - P\)

Replacing:

\(E = P*I*t\)

\(30000 - P = P*0.08*15\)

\(30000 - P = 1.2P\)

\(2.2P = 30000\)

\(P = \frac{30000}{2.2}\)

\(P = 13636.36\)

She needs to invest $13,636.36 right now

So on solving the provided question we can say that here, in triangle ABC and XYZ;  by SSS property they are similar.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

AB = XY

AC = XZ

BC = ZY

by SSS property, they are similar.

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Answer:

1 : 3.

Step-by-step explanation:

15 : 45

Divide both numbers by 15 , we get:

1 : 3.

Answer:

y= -x + 7

Step-by-step explanation:

to get the equation of a line is y=mx+b

the slope, m, would be calculated (y1-y2)/(x1-x2)

thus we would substitute in (3--2)/(4-9)

which simplifies to 5/-5

or -1

now we know that m= -1

to solve for b we have to put the equation into point-slope form which is

y-y1= m(x-x1)

this would be y-3 = -(x-4)

y-3 = -x+4

y= -x+7

Answer:

C. can have more than one factor, each with several treatment groups.

Step-by-step explanation:

A completely randomized design can be used in experimental research of a primary factor or multiple factors. The factors could have several treatment groups which are assigned in a random manner. For example, a researcher, could want to determine the effect of a drug against a disease on a class of people. To do this, he designs a treatment group with different concentrations of the drug and a placebo group. He then gets an equal number of subjects, randomly assigning them to each of the groups. The effect of both treatments are compared to know if the drug is indeed effective against the disease the researcher is experimenting on.

Completely randomized design has found application in agricultural and environmental researches.

All three approaches yield the same result: AED4,600,000 (Expenditure Approach), AED1,600,000 (Income Approach), and AED1,800,000 (Production Approach). This consistency demonstrates that the three approaches provide equivalent measures of GDP.

To calculate the contributions to GDP of the given transactions, we can use the three approaches: the expenditure approach, income approach, and production approach. Let's calculate the GDP using each approach and demonstrate that they give the same answer.

Expenditure Approach:

GDP is calculated as the sum of all final expenditures. In this case, the final expenditures are the sales of the supercomputers.

GDP = Sales of supercomputers

= (3 * AED1,000,000) + (1 * AED800,000)

= AED3,800,000 + AED800,000

= AED4,600,000

Income Approach:

GDP can also be calculated by summing up all the incomes earned during production. In this case, the incomes include wages, interest, and taxes.

GDP = Wages + Interest + Taxes

= (Labour costs for ABC + Labour costs for Jumbo) + (Interest on debt for ABC) + (Taxes for ABC + Taxes for Jumbo)

= (AED1,000,000 + AED200,000) + AED100,000 + (AED200,000 + AED100,000)

= AED1,200,000 + AED100,000 + AED300,000

= AED1,600,000

Production Approach:

GDP can also be calculated by summing the value added at each stage of production. In this case, the value added is the sales price minus the cost of components purchased.

GDP = Sales price of supercomputers - Cost of components

= (3 * AED1,000,000) + (1 * AED800,000) - (4 * AED500,000)

= AED3,000,000 + AED800,000 - AED2,000,000

= AED1,800,000

As we can see, all three approaches yield the same result: AED4,600,000 (Expenditure Approach), AED1,600,000 (Income Approach), and AED1,800,000 (Production Approach). This consistency demonstrates that the three approaches provide equivalent measures of GDP.

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The number of square inches of cardboard that are needed to make one

the container is 18.

We have,

The volume of the triangular prism.

= Area of the triangle x height

Now,

Height = 6 in

And,

To find the area of a triangle, we can use Heron's formula.

A = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.

Let's calculate the area using Heron's formula:

s = (3.2 + 3.2 + 2) / 2 = 4.2

A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))

A = √(4.2 x 1 x 1 x 2.2)

A = √(9.24)

A ≈ 3.04 square inches

Now,

The volume of the triangular prism.

= Area of the triangle x height

= 3.04 x 6

= 18.24 in²

Now,

Area of one cardboard.

= 1² in²

= 1 in²

Now,

The number of square inches of cardboard that are needed to make one

container.

= The volume of the triangular prism / Area of one cardboard

= 18.24 in² / 1 in²

= 18.24

= 18

Therefore,

The number of square inches of cardboard that are needed to make one

the container is 18.

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Answer:here is the right answer took the test and got it right trust and believe Jonathan’s answer is reasonable because is 16, and 16 is close to 15.77.

Step-by-step explanation:

Yes, there is a difference in the shapes of the displacement-time graphs for uniform acceleration towards the positive direction, uniform acceleration towards the negative direction, uniform deceleration towards the positive direction, and uniform deceleration towards the negative direction.

Uniform acceleration towards the positive direction:

In this case, the object's velocity increases in the positive direction over time. The displacement-time graph will have a concave-upward shape, forming a curve that starts with a small slope and gradually becomes steeper as time progresses.

Uniform acceleration towards the negative direction:

Here, the object's velocity increases in the negative direction, meaning it accelerates in the opposite direction to its positive direction.

The displacement-time graph will have a concave-downward shape, forming a curve that starts with a steep slope and gradually becomes less steep as time progresses.

Uniform deceleration towards the positive direction:

In this scenario, the object's velocity decreases in the positive direction, but it still moves towards the positive direction.

The displacement-time graph will show a curve with a decreasing slope, forming a concave-downward shape, indicating that the object is slowing down.

Uniform deceleration towards the negative direction:

Here, the object's velocity decreases in the negative direction, opposing its initial direction.

The displacement-time graph will have a curve with a decreasing slope, forming a concave-upward shape, indicating that the object is slowing down but still moving in the negative direction.

In summary, the shapes of the displacement-time graphs differ based on the direction and type of acceleration (positive or negative) and whether the object is undergoing uniform acceleration or uniform deceleration. These differences can be observed through the concavity and slope of the graphs.

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Answer:

A

Step-by-step explanation:

hope this helps

Answer:

Yes, these triangles are congruent

∠E≅∠M

Step-by-step explanation:

Yes, these triangles are similar.

Proof:

Each side in LNM is \(1\frac{2}{3}\) times longer than the sides in GFE

\(30/18 = 1\frac{2}{3}\)

\(25/15=1\frac{2}{3}\)

\(20/12 = 1\frac{2}{3}\)

According CPCTC (corresponding parts of congruent triangles are congruent), angle E is similar to angle M.

Hope this helps :)

Have a good day!

Center: (2,-6)

Radius: 8

...

(x - 2)² + (y + 6)² = 64

Answer:

I'm not sure if i'm correct but i'm guessing no

Step-by-step explanation:

Answer:

The table shows the heights of the winners and runner-ups of 8 presidential elections. Find the line of regression that predicts the runner-up's height given the winner's height. Determine if the regression line is a good predictor of heights for the winners and runner-ups of presidential elections.

Winner: 69.5; 73; 73; 74; 74.5; 74.5; 71; 71

Runner-Up: 72; 69.5; 70; 68; 74; 74; 73; 76

a. y = 95.4 - 0.321x; no, because the r-value is low.***

b. y = -0.321 + 95.4x; no, because the r-value is low.

The regression line is NOT a good predictor of heights for the winners and runner-ups of presidential elections because the r-value is low

Given that:

The data given for the winners are:

69.5; 73; 73; 74; 74.5; 74.5; 71; 71

The runners up are:

72; 69.5; 70; 68; 74; 74; 73; 76

With this, we can see that a. y = 95.4 - 0.321x; no, because the r-value is low.

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Answer:

The expression for 4 less than x is: x - 4

The expression for 17 more than x is: x + 17

The expression for the product of 18 and x is: 18x

The expression for the quotient of x and 17 is: x/17

The expression for 70 less than x is: x - 70

Step-by-step explanation:

4 less than x

4 less than a number is the number subtracted by 4. So the expression is x - 4.

17 more than x

17 more than a number is the number added to 17. So the expression is x + 17.

the product of 18 and x

The product of two numbers a and b is a*b, so the product of 18 and x is 18*x = 18x

the quotient of x and 17

The quotient of two numbers a and b is a/b, so the quotient of x and 17 is x/17.

70 less than x

70 less than a number is the number subtracted by 70. So the expression is x - 70.

Answer:

D. Bimodal

Explanation:

The given histogram has two creast, each crest represent a mode. So, we can say that this is a bimodal graph. Therefore, the answer is

D. Bimodal.