Which of the following are solutions to the equation below?

Check all that apply.

(3x + 4)2 = 14

Answer:

  3 mph

Step-by-step explanation:

Let c represent the current of the river in miles per hour. Then the ratio of speed downstream to speed upstream is ...

  (21 +c)/(21 -c) = 2.4/1.8

  1.8(21 +c) = 2.4(21 -c) . . . . . . multiply by 1.8(21-c)

  37.8 + 1.8c = 50.4 -2.4c . . . . eliminate parentheses

  4.2c = 12.6 . . . . . . . . . . . . . . . add 2.4c-37.8

  c = 3 . . . . . . . . . . . . . . . . . . . .divide by 4.2

The current of the river is 3 miles per hour.

Answer:  ordinal

Step-by-step explanation:

There are 4 levels of measurements scales :-

1. Nominal scale : It is used when we categorize the data on the basis of the characteristic such as Religion, Gender , etc.

2. Ordinal scale : It is used when we can order attributes according to their ranks. For example : First > Second > Third and so on.

3. Interval scale : It provides the characteristic of the difference between any two categories. For example : Fahrenheit scale to measure temperature.

4. Ratio scale : It has all the qualities of nominal, ordinal, and interval measures and in addition a "true zero" point. For example : Age.

From the above definitions , A level of measurement describing a variable whose attributes are rank-ordered and have equal distances between adjacent attributes are ordinal measures.

Answer:

a

Step-by-step explanation:

Given

x² + 20x + 100 = 36 ( subtract 36 from both sides )

x² + 20x + 64 = 0 ← in standard form

Consider the factors of the constant term ( + 64) which sum to give the coefficient of the x- term ( + 20)

The factors are + 16 and + 4, since

16 × 4 = + 64 and 16 + 4 = + 20, hence

(x + 16)(x + 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 16 = 0 ⇒ x = - 16

x + 4 = 0 ⇒ x = - 4

Answer:

5/7

Step-by-step explanation:

We need the Pythagorean Theorem here.

If you have a right triangle, you can use the equation a^2+b^2=c^2 where a and b are legs and c is the hypotenuse.

Plug in your information.

(3/7)^2+(4/7)^2=c^2

Simplify what you can.

9/49+16/49=c^2

25/49=c^2

Square root both sides.

5/7=c

Answer:

5/7.

Step-by-step explanation:

Let the hypotenuse = h , then:

h^2 = (3/7)^2 +(4/7)^2    ( By the Pythagoras Theorem).

h^2 = 9/49 + 16/49

h^2 = 25/49

h =  5/7.

Answer:

C

Step-by-step explanation:

The answer is C

Answer:

Your answer would be C

Step-by-step explanation:

I got it right on edge <3

Answer:

-7 is real and complex

Step-by-step explanation:

Every number is complex.

Complex numbers are in the form of a+bi where a and b are real numbers.

Pure imaginary are complex numbers with a being 0.

Real numbers are complex number with b being 0.

-7 is a real number and a complex number.

(It doesn't have an imaginary part)

-7 is a real and complex number.

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Answer:

  A.  $14,500

Step-by-step explanation:

The van depreciates ($16000 -1000 = $15000 in 5 years, so $3000 per year. It will be assumed to depreciate half that amount in half a year, so will be worth $1500 less than $16000 at the end of the first calendar year. The book value will be $14,500.

Final answer:

The book value of the minivan at the end of Year 1 is $14,500 after accounting for 6 months of straight-line depreciation of $1,500 from the original cost of $16,000.

Therefore, the correct answer is A. $14,500.

Explanation:

The student's question is related to calculating the book value of a minivan at the end of year 1 using the straight-line depreciation method. To find the book value, we need to first calculate the annual depreciation expense and then subtract it from the original cost of the minivan.

First, we calculate the annual depreciation expense:

Purchase price of minivan: $16,000

Residual value: $1,000

Useful life: 5 years

So, the annual depreciation expense is
(

$16,000

-

$1,000

) /

5 years

= $3,000 per year.

Since the minivan was bought on July 3, we need to account for a partial year of depreciation for year 1. Assuming the end of the year is December 31, that's 6 months (July through December) of depreciation in the first year. Therefore, it would be
$3,000 / 2 = $1,500 for 6 months.

To find the book value at the end of Year 1, we subtract the depreciation for the first 6 months from the purchase price:
$16,000 - $1,500 = $14,500.

Answer:

  D.  -1.8

Step-by-step explanation:

A graphing calculator can show you this easily, as can any calculator or spreadsheet that helps you evaluate the functions at different values of x.

The graphs cross at approximately x = -1.8.

Answer:

Step-by-step explanation:

d

Answer:

Nelson burned the most calories per hour

Explanation:

To solve this question, we will get the amount calories burned by each in one hour and then compare the two values

To do this, we will divide the total amount of calories burned by the total time

1- For Sabra:

We are given that she burnt 845 calories in [tex]3\frac{1}{25}[/tex] (which is equivalent to 3.25) hours

Therefore:

Calories burnt in an hour = [tex]\frac{845}{3.25}=260[/tex] calories/hour

2- For Nelson:

We are given that he burnt 1435 calories in [tex]4\frac{7}{8}[/tex] (which is equivalent to 4.875) hours

Therefore:

Calories burnt in an hour = [tex]\frac{1435}{4.875}=294.36[/tex] calories/hour

3- Comparing the two values:

From the above calculations, we can deduce that Nelson burned the most calories per hour

Hope this helps :)

Answer:

Nelson burned more cal/hr than Sabra at a rate of 294.36 cal/hr.

Step-by-step explanation:

To find out how many calories per hour each person burned, divide the amount of calories they burned by the amount of hours they spent exercising.

Sabra: 845 cal / 3.25 hr = 260 cal/hr

Nelson: 1435 cal / 4.875 hr = 294.36 cal/hr

260 < 294.36, so Nelson burned more calories/hour than Sabra.

Answer:

Step-by-step explanation:

The vertex order ABC is clockwise in the original figure and also in the first image: A'B'C'. The altitude from AC to B is up in the original and left in the first image, indicating a rotation 90° CCW.

  The first transformation is a rotation 90° CCW.

The vertex order of A''B''C'' is CCW, indicating a reflection. The direction of the altitude from A''C'' to B'' is still to the left, so the reflection must be over a horizontal line. We find the x-axis bisects the segments A'A'', B'B'', and C'C'', confirming that it is the line of reflection.

  The second transformation is reflection across the x-axis.

_____

Algebraically, the transformations are ...

  1st: (x, y) ⇒ (-y, x)

  2nd: (x, y) ⇒ (x, -y)

Both together: (x, y) ⇒ (-y, -x).

Answer:

a = sqrt( 3x+1)

Step-by-step explanation:

f(x) = sqrt(x-1)

g(x) = 3x+2

(f°g)(x) means replace g(x) in f(x) every place you see an x

(f°g)(x) = sqrt( g(x) -1)

          = sqrt( 3x+2 -1)

     Simplifying

          =sqrt( 3x+1)

The change in the X values is in multiples of 2.

The change in the h(x) values need to be: -0.3 x 2 = -0.6

Now find the h(x) values that have a difference of -0.6

A negative value is a decrease.

2 to 4 is an increase.

4 to 6 is an increase.

6 to 8 is an increase.

8 to 10 is an increase.

10 to 12 = 20-19.8 = 0.2

12 to 14 = 19.8 - 19.2 = 0.6

The two columns are 12 and 14

Answer:

Exterior

Step-by-step explanation:

In any triangle an exterior angle is equal to the sum of the two opposite interior angles.

Answer: She will have $700 left over.

Step-by-step explanation: Since we know that a rectangle has two sides with the measurement, we can add the sides. 37+37+25+25=124. The fencing in 124 feet in total. Multiply the 124 feet by the price per foot. 124 x 75 =9,300. Subtract the price from your total amount of money. 10,000 - 9,300 = $700. She will have $700 left over.

Answer:

there would be $700 left over

Step-by-step explanation:

There are 216 different meals available when you select an appetizer, an entrée, and a dessert from the restaurant's menu.

Given that there are 6 choices for the appetizer, 12 choices for the entrée, and 3 choices for the dessert.

Total number of choices:

6 (choices for appetizer) × 12 (choices for entrée) × 3 (choices for dessert) = 216 different meals

Therefore, there are 216 different meals available when you select an appetizer, an entrée, and a dessert from the restaurant's menu.

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There are 216 possible meals. This answer is obtained by applying the counting principle in mathematics, which multiplies together the choices for each part of the meal (appetizer, entrée, dessert).

This problem regards the counting principle in mathematics, which is a way of finding the total number of possible outcomes for a series of events. In this case, the events are choosing an appetizer, entrée, and dessert. The counting principle tells us that we can find the total number of possible meals by multiplying together the number of choices for each part of the meal.

Thus, we can solve this problem as follows:

By the counting principle, we multiply these together to get the total number of possible meals: 6 * 12 * 3 = 216 meals.

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Answer:

[tex]5-10i[/tex]

Step-by-step explanation:

we know that

To subtract two complex number, subtract the real parts and subtract the imaginary parts

so

[tex](a+bi)-(c+di)=(a-c)+(b-d)i[/tex]

we have

[tex](7-4i)-(2+6i)[/tex]

so

[tex](7-4i)-(2+6i)=(7-2)+(-4-6)i=5-10i[/tex]

Answer: About 8.5 cubic yards

Step-by-step explanation:

Given : The length of the garden = 16 ft.

The width of the garden = 34 ft.

The depth of the thick layer of topsoil on the garden = 5 inch

=[tex]\dfrac{5}{12}\text{ ft.}[/tex]               [Since 1 foot = 12 inches]

The volume of a rectangular prism :-

[tex]V=l*w*h[/tex], where l is length , w is width and h is height.

The number of cubic feet of topsoil required will be

[tex]V=16\times34\times\dfrac{5}{12}=\dfrac{680}{3}\text{cubic feet}[/tex]

Since 1 yard = 3 feet

[tex]1\text{ foot}=\dfrac{1}{3}\text{ yard}[/tex]

[tex]V=\dfrac{680}{3}\times\dfrac{1}{3}\times\dfrac{1}{3}\times\dfrac{1}{3}=8.3950617284\approx8.50\text{cubic yards}[/tex]

Answer:

The correct option is 1.

Step-by-step explanation:

Given information: AD = 25, CD = 5, DB = 1 and CD⊥AB.

According to the Pythagoras theorem,

[tex]hypotenuse^2=base^2+perpendicular^2[/tex]

In triangle BCD,

[tex]CB^2=DB^2+CD^2[/tex]

[tex]CB^2=1^2+5^2[/tex]

[tex]CB^2=26[/tex]

Taking square root both sides.

[tex]CB=\sqrt{26}[/tex]

In a right angled triangle,

[tex]\sin\theta=\frac{opposite}{hypotenuse}[/tex]

[tex]\sin B=\frac{CD}{CB}[/tex]

[tex]\sin B=\frac{5}{\sqrt{26}}[/tex]

[tex]\sin B=0.980580675691[/tex]

[tex]\sin B\approx 0.9806[/tex]

Therefore the correct option is 1.

Answer:

0.9806 is the correct answer.

Step-by-step explanation:

Answer:

A = 196 pi m^2

Step-by-step explanation:

The area of a circle is given by

A = pi * r^2

The radius is 14

A = pi *14^2

A = 196 pi m^2

Answer:

196π m2

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

C is your answer. Since this is a parallelogram, is means that there are two sets of sides with the same length. Because the measurement of angle K is 82 the angle directly opposite would have the same measurement. That's why angle M is also 82. When you add all the angles of a quadrilateral it adds up to 360 degrees. multiply 82 by 2 to get 164 and subtract that from 360 to get 196. you then have to divide that by 2 and you will get 98 which is the measurement for both angles L and N

Answer:

The correct answer is option C.

m<L = 98°, m<M = 82° and m<N = 98°

Step-by-step explanation:

From the figure we can see a parallelogram KLMN

Properties of parallelogram

1)Opposite sides are equal and parallel.

2) Opposite angles are equal.

3) Adjacent angles are supplementary.

To find the correct option

It is given that, m<K = 82°

By using properties of parallelogram we get

m<L = 98°, m<M = 82° and m<N = 98°

Therefore the correct answer is option C

Answer:

  B.  x ≈ 13/8

Step-by-step explanation:

We assume that one iteration consists of determining the midpoint of the interval known to contain the root.

The graph shows the functions intersect between x=1 and x=2, hence our first guess is x = 3/2.

Evaluation of the difference between the left side expression and the right side expression for x = 3/2 shows that difference to be negative, so we can narrow the interval to (3/2, 2). Our 2nd guess is the midpoint of this interval, so is x = 7/4.

Evaluation of the difference between the left side expression and the right side expression for x = 3/4 shows that difference to be positive, so we can narrow the interval to (3/2, 7/4). Our 3rd guess is the midpoint of this interval, so is x = 13/8.

_____

The sign of the difference at this value of x is still negative, so the next guess would be 27/16. It is a little hard to tell what the question means by "3 iterations." Evaluating the function for x=13/8 will be the third evaluation, so the determination that x=27/16 will be the next guess might be considered to be the result of the 3rd iteration.

Answer:

B. x=13/8

Step-by-step explanation:

#platofam

Answer:

[tex]4x^{3}+8x^{2} +4x+3[/tex]

Step-by-step explanation:

Hello

To simplify the polynomial we must eliminate the parentheses

by definition

[tex]ax^{n}*bx^{m} =abx^{n+m}[/tex]

[tex](2x-1)(2x^{2} +5x+3)+(3x+6)\\(4x^{3} +10x^{2} +6x-2x^{2} -5x-3)+(3x+6)\\\\We\ add\ the\ similar\ terms\\\\(4x^{3}+8x^{2} +x-3)+(3x+6)\\\\4x^{3}+8x^{2} +4x+3[/tex]

I hope it helps

Have a great day

Answer:

Its A

Step-by-step explanation:

Just took it.

Answer:

Step-by-step explanation:

It is convenient to let a spreadsheet or graphing calculator do the repetitive evaluation of a function like this. That simplifies the work and reduces errors.

The function is shown in the attachment written in Horner form, which is convenient for evaluation by hand or using a calculator.

Let the width = X, then the length would be 5x ( 5 times as long as the width).

The perimeter is adding the 4 sides.

x + x + 5x + 5x = 70

Combine the like terms:

12x = 70

Divide both sides by 12:

x = 70/12

x = 5.83

The width = 5.83 cm.

The length = 5 x 5.83 = 29.15

Now round each length to the nearest tenth:

5.8 and 29.2 cm.

The answer is d.

Answer:

0.68

Step-by-step explanation:

Given

Mean = μ = 6 cm

SD = σ = 1.5 cm

We have to find the z-scores for 4.5 and 7.5

z-score for 4.5 = z_1 = (x-μ)/σ = (4.5-6)/1.5 = -1.5/1.5 = -1

z-score for 4.5 = z_2 = (x-μ)/σ = (7.5-6)/1.5 = 1.5/1.5 = 1

We have to find area to the left of z-scores

Using the rule of thumb for SD from mean, 68% of data lies between one standard deviation from mean. So the probability of choosing a band with length between 4.5 and 7.5 cm is 0.68 ..

Answer:

Step-by-step explanation:

Put the numbers in the formula and do the arithmetic. For repetitive calculations, it is convenient to define a function in a graphing calculator or spreadsheet.

Answer:

11 years old

Step-by-step explanation:

Let Jimmy's age be represented as x. His big brother's age is x+5 and his sister's age is 2x. Adding these gives us 4x+5=29. Solving for x gives us 6. His brother's age is 6+5=11.

11 years old is Jimmy's brother.

Let Jimmy's age be represented as x. His big brother's age is x+5 and his sister's age is 2x. Adding these gives us 4x+5=29. Solving for x gives us 6. His brother's age is 6+5=11.

J=Jimmy's age; S=sister's age=2J; B=brother's age=J+5

.

J+S+B=29

J+(2J)+(J+5)=29

4J+5=20

4J=24

J=6

Jimmy is 6 years old.

B=J+5=6+5=11

ANSWER: Jimmy's brother is 11 years old.

.

CHECK:

S=2J=2(6)=12

Jimmy's sister is 12 years old.

.

J+S+B=29

6+12+11=29

29=29.

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Answer:

= 1/2[sin2Acos7A + cos2Asin7A + sin2Acos7A - cos2Asin7A]

we cut out

cos2Asin7A - cos2Asin7A

then we have

=1/2[sin2Acos7A + sin2Acos7A ]

= 1/2*2[ sin2Acos7A ]

cut out 2 we get

#sin2Acos7A

Answer:

95%

Step-by-step explanation:

For a given sample data, the width of the confidence interval would vary directly with the confidence level i.e. more the confidence level,  wider will be the confidence interval.

This is because the critical value associated with the confidence level(e.g z value) becomes larger as the confidence level is increased which results in an increased interval.

The confidence interval for a population proportion is given by the formula:

[tex]p \pm z\sqrt{\frac{pq}{n} }[/tex]

So, for a fixed value of p,q and n, the larger the value of z the wider will be the confidence interval.

Hence 95% confidence interval will be wider than 80% confidence interval.

The 95% confidence interval is wider than the 80% confidence interval because it includes a larger area under the curve of a normal distribution, offering a higher level of confidence the true population parameter falls within this range.

In statistical analysis, especially for polls like the one mentioned about favorite pies, the confidence interval plays a significant role in interpreting the reliability of the results. The 95% confidence interval is wider than the 80% confidence interval. This is because a higher confidence level, in this case 95%, means we are more sure that the actual population parameter lies within the interval, but in order to gain this certainty, the interval necessarily needs to be wider.

This can also be understood in the context of a normal distribution. For a 95% confidence interval, we are including a larger area under the curve of the distribution, thus the interval has to be wider than the one for the 80% confidence interval, which covers a smaller area.

It's important to note, however, that a wider confidence interval doesn't necessarily imply better predictability. It simply means there's a higher level of confidence that the true population parameter falls within the specified range.

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