Write a quadratic equation in standard form with the given roots. a. Write a quadratic equation with a double root of -5.

Answer:

A.

Step-by-step explanation:

Let's think of this as a clock.  We can see that the 2 lines start in the same place, around 3 o'clock.  Next, one of the line segments shifts down to around 6 o'clock.  Next, it shifts to about 9 o'clock.  Logically, the next step (in a clock) would be 12 o'clock, making A the correct choice.

We can also just use a regular circle, with one of the line segments moving 90 degrees each time.

Hope this helps! :)

Arcs get their angle measure from the central angle they're in, in this case the central angle of 86°, central to arcED, has a counterpart of a twin vertical angle across the center, since both vertical angles are identical twins that means the central angle for arcAB is 86° also, and that's the arcAB's measure too.

x=7

Pretty Simple..                                                                          h                                                        h                h                                                                                      

The value of the variable 'x' will be 20. Then the third vertice of the triangle is (20, 4).

The vertices of the triangle are (x₁, y₁), (x₂, y₂), and (x₃, y₃).

Then the area of the triangle will be

Area = 1/2 |[(x₁y₂ + x₂y₃ + x₃y₁) - (y₁x₂ + y₂x₃ + y₃x₁)]|

The vertices of the triangle are given as,

(x₁, y₁) ⇒ (5, 2)

(x₂, y₂) ⇒ (x, 4)

(x₃, y₃) ⇒ (0, 3)

Then the area will be

Area = 1/2[{5 × 4 + x × 3 + 0 × 2} – {2 × x + 4 × 0 + 3 × 5}]

25/2 = 1/2 [20 + 3x – 2x – 15]

25 = [x + 5]

x = 25 – 5

x = 20

The value of the variable 'x' will be 20. Then the third vertice of the triangle is (20, 4).

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We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot.

A statistical test is required to determine whether the length of the left foot is greater than the length of the right foot. The null hypothesis states that there is no difference in average length between the left and right feet. The alternative hypothesis is that the left foot's average length is greater than the right foot's average length.

This hypothesis is one-tailed, as we are only interested in whether the left foot is longer than the right foot. We are not considering the possibility that the right foot could be longer than the left foot.

A t-test can be used to determine whether the difference in average length between the left and right feet is statistically significant. We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot if the p-value of the t-test is less than the chosen significance level (e.g., 0.05).

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To find the unit rate, we need to determine how much distance Margo covers in one unit of time. We can do this by dividing the distance by the time.

Distance = 1/4 mile

Time = 1/12 hour

Unit rate = Distance ÷ Time

Unit rate = (1/4 mile) ÷ (1/12 hour)

We can simplify this division by multiplying both the numerator and denominator by the least common multiple of 4 and 12, which is 12.

Unit rate = (1/4 mile) ÷ (1/12 hour) x (12/12)

Unit rate = (3/4 mile) ÷ 1 hour

Unit rate = 3/4 mile per hour

Therefore, Margo's unit rate is 3/4 mile per hour. This means that she can cover a distance of 3/4 mile in one hour of walking.

Answer:

3mph

Step-by-step explanation:

1/12 of an hour will be 5 min. In 5 min she can walk 1/4 mile then in one hour she can walk 1/4 x 12. This means her rate will be 3 miles per hour.

60/12 = 5

12 x 1/4 = 12/4 = 3

Answer:

\(48\pi = \frac{1}{3} \pi {4}^{2} \times h \\ we \: omit \: \pi \: each \: sides \\ \\ 48 = \frac{16}{3} \times h \\ h = \frac{3 \times 48}{16} = 3 \times 3 = 9\)

A piecewise function formed by two equations with domains a≤x

In this case the two equations are:

They are both polynomials so we know they are continuous in their respective domains. Then we just need to compare the values of f and h at x=-1 which is the value where their domains meet. Then the first step would be evaluating the first equation at x=-1:

Then we evaluate the second equation at x=-1:

Then we have to look for the value of n that makes h(-1)=f(-1). Then we equalize these two results:

And we solve this equation for n. We can start by adding 2 to both sides:

And we divide both sides by 3:

The first step to find n is evaluating the first equation for x=-1. Then the answer is the fourth option.

Mean: 34.125, Median: 31.5, Mode: 38

Mean: 19.222, Median: 18, No mode

Mean: 8.611, Median: 8, Mode: 8

Let's find the mean, median, and mode for each set of numbers:

Set: 40, 38, 29, 34, 37, 22, 15, 38

Mean: To find the mean, we sum up all the numbers and divide by the total count:

Mean = (40 + 38 + 29 + 34 + 37 + 22 + 15 + 38) / 8 = 273 / 8 = 34.125

Median: To find the median, we arrange the numbers in ascending order and find the middle value:

Arranged set: 15, 22, 29, 34, 37, 38, 38, 40

Median = (29 + 34) / 2 = 63 / 2 = 31.5

Mode: The mode is the number(s) that appear(s) most frequently in the set:

Mode = 38 (appears twice)

Set: 26, 32, 12, 18, 11, 14, 21, 12, 27

Mean: Mean = (26 + 32 + 12 + 18 + 11 + 14 + 21 + 12 + 27) / 9 = 173 / 9 ≈ 19.222

Median: Arranged set: 11, 12, 12, 14, 18, 21, 26, 27, 32

Median = 18

Mode: No mode (all numbers appear only once)

Set: 3, 3, 4, 7, 5, 7, 6, 7, 8, 8, 8, 9, 8, 10, 12, 9, 15, 15

Mean: Mean = (3 + 3 + 4 + 7 + 5 + 7 + 6 + 7 + 8 + 8 + 8 + 9 + 8 + 10 + 12 + 9 + 15 + 15) / 18 ≈ 8.611

Median: Arranged set: 3, 3, 4, 5, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 12, 15, 15

Median = 8

Mode: Mode = 8 (appears 4 times)

Mean: 34.125, Median: 31.5, Mode: 38

Mean: 19.222, Median: 18, No mode

Mean: 8.611, Median: 8, Mode: 8

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Multiplication of the given matrix is not possible by definition of matrix multiplication.

Since, To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Expression for multiply,

⇒ [4, 0, -1, 2, -3, -1] x [0, 1, -3, 1]

Since, We can see that;

First matrix have order 1 x 6

And, Second matrix have order 1 x 4

We know that;

Matrix multiplication is possible when number of column in first matrix is same as number of rows in second matrix.

Hence, By given matrices we get;

Number of column in first matrix (6) ≠ number of rows in second matrix (1)

So, Multiplication of the given matrix is not possible by definition of matrix multiplication.

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Answer:

d, 6 units

Step-by-step explanation:

its 6 units im pretty sure. hope this helped

Answer:

-1

Step-by-step explanation:

-b+10b+2b+17=6

9b+2b+17=6

11b+17=6

11b=6-17

11b=-11

b=-1

Answer: y

Step-by-step explanation:

Slope intercept form is written as

Y=mx+b, so you’d solve for the variable y

Problem 1

-------------------------------------

Explanation:

1/4 = 0.25

She eats 25% of a pizza in 12 minutes

We can form the ratio 0.25/12

This ratio is then set equal to x/18. The value of x represents what proportion of the pizza is eaten after 18 minutes.

Solve for x

0.25/12 = x/18

0.25*18 = 12x ..... cross multiply

4.5 = 12x

12x = 4.5

x = 4.5/12

x = 0.375

x = 375/1000

x = (125*3)/(125*8)

x = 3/8

She ate 3/8 of the whole pizza in 18 minutes.

There are 8 slices in a full pizza, so (3/8)*8 = 3 means that she ate 3 slices.

Or you could say "eating 3 slices out of 8 total means she ate 3/8 of the full pizza".

===================================================

Problem 2

-------------------------------------

Explanation:

We'll use the same idea as before. Though now we're setting 0.25/12 equal to x/30

Solving for x leads to...

0.25/12 = x/30

0.25*30 = 12x

7.5 = 12x

12x = 7.5

x = 7.5/12

x = 0.625

x = 625/1000

x = (125*5)/(125*8)

x = 5/8

She will eat 5/8 of the pizza in 30 minutes.

Answer:

40,000 x 0.83 = 33.2 */*15000 =0.0021

Step-by-step explanation:

Multiply  than divide

Answer:

x= a

Step-by-step explanation:

The solution is in the attached file.To get the solution,you have to equate to zero

Answer:

1122

If you do 18 (the first number in the sequence) plus 69 because you have to do 70 minus 1 equals 69. So 18 plus 69 then you times 16 (how many you have to get to the next number).

18+69×16=1122

Step-by-step explanation:

Answer:

If you make 3/6 into a fraction form it is 1/3 if you simplify it.

Hope that helps.

Therefore, the sample size was approximately 1360 Americans.

In statistics, a sample is a subset of a larger population. It is a representative selection of individuals or objects taken from the population of interest to be studied. Samples are often used in statistical analysis because it is usually impractical or impossible to collect data from the entire population.

Here,

The survey states that 20% of American households own 2 pets, and the survey was conducted on 1000 Americans. Since we are trying to identify the sample size, we can use the formula:

sample proportion = x / n

where x is the number of households that own 2 pets, and n is the sample size.

We are given that 20% of the sample own 2 pets, so we can write:

0.20 = x / n

Multiplying both sides by n, we get:

n * 0.20 = x

Simplifying, we get:

n = x / 0.20

We don't know the value of x, but we can estimate it using the proportion of households that own 2 pets in the entire population. According to a study by the American Pet Products Association, about 68% of American households own at least one pet, and about 40% of pet-owning households own two or more pets. Assuming that these percentages hold true for the survey sample as well, we can estimate that:

x = 0.40 * 0.68 * 1000

= 272

Substituting this value into the equation above, we get:

n = 272 / 0.20

= 1360

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Hubble's constant in units of km/s/million LY is approximately 21.47.

what is  approximately ?

Approximately means close to or nearly, but not exactly. It is used to indicate that a value or number is an estimation or approximation, rather than an exact value. It is often used when a precise value is not necessary or when the exact value is unknown or difficult to determine.

In the given question,

To convert Hubble's constant from km/s/Mpc to km/s/million LY, we need to multiply it by a conversion factor that accounts for the difference in distance units. We can use the fact that 1 Mpc is equal to 3.26 million LY:

1 Mpc = 3.26 million LY

Therefore, to convert Hubble's constant from km/s/Mpc to km/s/million LY, we can use the following conversion factor:

1 Mpc / 3.26 million LY

Multiplying Hubble's constant by this conversion factor gives:

H = 70 km/s/Mpc x (1 Mpc / 3.26 million LY) = 21.47 km/s/million LY

Therefore, Hubble's constant in units of km/s/million LY is approximately 21.47.

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Answer:

Yes

Step-by-step explanation:

R-2 < 9; when R=8

8-2 < 9

because

6 < 9 (reads as "6 is less than 9")

By answering the presented question, we may conclude that Therefore, equation there is no solution to the system of equations. The answer is: There is no solution.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

To graph the system of equations, we can first rewrite them in slope-intercept form:

3x + y = 6 => y = -3x + 6

3x + 3y = 12 => y = -x + 4

Now, we can plot the two lines on the same coordinate plane:

   |          

 4 +--------*      

   |       /      

   |      /        

 3 +-----/-----*  

   |    /          

   |   /          

 2 +--/---------*  

   | /            

   |/            

 1 +*---------*---

   |              

   0--+--+--+--+--  

      0  1  2  3  

The first line, y = -3x + 6, has a y-intercept of 6 and a slope of -3, which means that for every increase of 1 in x, y decreases by 3. The second line, y = -x + 4, has a y-intercept of 4 and a slope of -1, which means that for every increase of 1 in x, y decreases by 1.

We can see that the two lines are parallel, which means they never intersect. Therefore, there is no solution to the system of equations.

The answer is: There is no solution.

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The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.

To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.

Actual quotient:

Dividing 54,114 by 29, we get:

54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)

Estimated quotient:

Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:

54,000 ÷ 30 = 1,800

Difference between actual and estimated quotient:

Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379

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Let:

x = population in 1790 = 4000000

y = population in 2003

so:

The required, given polynomial has exactly 4 roots, which may be real or imaginary or a combination of both.

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial, and trinomial, etc. ax+b is a polynomial.

Here,
The fundamental theorem of algebra states that every non-constant polynomial with complex coefficients has exactly as many roots (zeros) as its degree. In this case, the degree of the polynomial is 4, so it has exactly 4 complex roots.

However, it is not clear whether any of the roots are real or imaginary, or whether they are all complex. To determine this, we would need to use methods such as the rational root theorem, synthetic division, or the quadratic formula to find the roots of the polynomial.

Without actually finding the roots, we can say that the polynomial has exactly 4 roots, which may be real or imaginary or a combination of both.

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Answer:

Let's denote the two legs of the right triangle as a and b, and the hypotenuse as c. We know that c = √41, so we can use the Pythagorean theorem to relate a and b to c:

c^2 = a^2 + b^2

Substituting c = √41, we get:

(√41)^2 = a^2 + b^2

41 = a^2 + b^2

We also know that the perimeter of the triangle is:

perimeter = a + b + c = 9 + √41

Substituting c = √41, we get:

a + b + √41 = 9 + √41

a + b = 9

Now we have two equations with two unknowns (a and b):

a^2 + b^2 = 41

a + b = 9

We can solve this system of equations by substitution. Solving the second equation for a, we get:

a = 9 - b

Substituting this into the first equation, we get:

(9 - b)^2 + b^2 = 41

81 - 18b + 2b^2 = 41

2b^2 - 18b + 40 = 0

b^2 - 9b + 20 = 0

(b - 4)(b - 5) = 0

So we have two possible solutions: b = 4 and b = 5. We can find the corresponding value of a using a = 9 - b:

a = 5 and b = 4 or a = 4 and b = 5

Therefore, the two legs of the right triangle are 4 and 5.

Answer:

Dimensions 30 in x 30 in x 15 in

Surface Area = 2,700 in²

Step-by-step explanation:

Let 'r' be the length of the side of the square base, and 'h' be the height of the bin. The volume is given by:

\(V=13,500=h*r^2\\h=\frac{13,500}{r^2}\)

The total surface area is given by:

\(A=4*hr+r^2\)

Rewriting the surface area function as a function of 'r':

\(A=4*\frac{13,500}{r^2} *r+r^2\\A=\frac{54,000}{r}+r^2\)

The value of 'r' for which the derivate of the surface area function is zero, is the length for which the area is minimized:

\(A=54,000*r^{-1}+r^2\\\frac{dA}{dr}=0= -54,000*r^{-2}+2r\\\frac{54,000}{r^2}=2r\\ r=\sqrt[3]{27,000}\\r=30\ in\)

The value of 'h' is:

\(h=\frac{13,500}{30^2}\\ h=15\ in\)

The dimensions that will ensure the minimum surface area are 30 in x 30 in x 15 in.

The surface area is:

\(A=4*15*30+30^2\\A=2,700\ in^2\)

Answer:

Step-by-step explanation:

x + y = 40

x>y

(11/2)y - (13/4)*x = - 25

x = 40 - y

(11/2)y - (13/4)(40-y) = - 25      multiply by 4

22y - 13( 40 - y) = - 100

22y - 520 + 13y = -400         Add 520

35y = 120

y = 120 / 35

y = 3 3/7

x = 40 - y

x = 36 4/7

The reflection of point (-6, -5) across the x-axis will give (-6, 5)

A reflection point occurs when a figure is constructed around a single point, known as the point of reflection or center of the figure.

Given is a point (-6, -5), we need to find the coordinates of the point when it is reflected across the x-axis,

The rule for a reflection across the x-axis -:

The rule for reflecting over the x-axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.

i.e, (x, y) → (x, -y)

Therefore,

(-6, -5) → (-6, 5)

Hence, the reflection of point (-6, -5) across the x-axis will give (-6, 5)

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The question is incomplete, the question is solved for:

Reflect point (-6, -5) across x-axis