Based on the side lengths alone, could the triangles be similar?

No, the sides are not proportional.
Yes, the sides are in the ratio 2:5.
Yes, the sides are in the ratio 4:5.
Yes, the sides are in the ratio 1:5.

Answer:

39

Step-by-step explanation:

Answer:

4% of 975 is 39

Step-by-step explanation:

4% of 975 = 0.04 x 975 = 39

Answer

4% of 975 is 39

Answer:

[tex](120\degree,-180\degree)[/tex]

Step-by-step explanation:

The given parametric equation is

x=2t  

y= -3t

The coordinates of any point lying on this curve can be obtained by substituting the parameter value.

Given the parameter value, t=60

We have

[tex]x=2(60\degree)=120\degree[/tex]

and

[tex]y=-3(60)=-180\degree[/tex]

Therefore the point[tex](120\degree,-180\degree)[/tex]

lie on this parametric curve.

Answer:

-9/2 , 3/2

Step-by-step explanation:

The coordinates of the midpoint of the line segment that has endpoints (-3,4) and (-6,-1) are (-4.5, 1.5).

Suppose we've two endpoints of a line segment as A(p,q), and B(m,n), then let the midpoint be M(x,y) on that line segment. Then, its coordinates are x =(p+m)/2 and y = (q+n)/2.

Given the endpoints of the line segment are A(-3,4) and B(-6,-1), then the coordinates of the midpoint will be,

x = (-3-6)/2 = -9/2 = -4.5

y = (4-1)/2 = 3/2 = 1.5

Hence, the coordinates of the midpoint of the line segment that has endpoints (-3,4) and (-6,-1) are (-4.5, 1.5).

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Answer:

Potential roots:  [tex]\frac{9}{4},\frac{9}{2},9,\frac{3}{4},\frac{3}{2},3, \frac{1}{4},\frac{1}{2},1[/tex]

Step-by-step explanation:

Simply put, the rational roots theorem tells us that if there are any rational roots of a polynomial function, they must be in the form

±  [tex]\frac{FactorsOfa_{0}}{FactorsOfa_n}[/tex]

Where

a_n is the number before the highest power of the polynomial, and

a_0 is the constant in the polynomial

From the polynomial shown, we have a_n = 9 and a_0 = 4

The factors of 9 are 9, 3, 1

and

The factors of 4 are 4,2,1

So, if there are any rational roots, they would be:

±  [tex]\frac{FactorsOfa_{0}}{FactorsOfa_n}[/tex]

±  [tex]\frac{9,3,1}{4,2,1}[/tex]

Which is  ±   9/4, 9/2, 9/1, 3/4, 3/2, 3/1, 1/4, 1/2, 1/1

or

[tex]\frac{9}{4},\frac{9}{2},9,\frac{3}{4},\frac{3}{2},3, \frac{1}{4},\frac{1}{2},1[/tex]

Using the Rational Root Theorem, the polynomial f(x) = 9x^4 - 2x^2 - 3x + 4 has potential rational roots which are ±4, ±2, ±1, and their counterparts divided by 3. In the complex number system, every nth-order polynomial can be factored into n roots, including imaginary roots for equations that lack real solutions.

Rational Root Theorem and Potential Roots

The Rational Root Theorem is a useful tool for identifying all potential rational roots of a polynomial equation. When applying this theorem to the given polynomial f(x) = 9x^4 - 2x^2 - 3x + 4, we note that the potential rational roots are the divisors of the constant term (in this case, 4) divided by the divisors of the leading coefficient (in this case, 9). Therefore, the potential roots are ±4, ±2, ±1, and their counterparts divided by 3, which are ±4/3, ±2/3, and ±1/3. To determine which of these are actual roots, each must be tested in the polynomial equation.

The concept of complex number system further elaborates on polynomials by stating that every nth-order polynomial can have up to n roots, factored into linear factors in accordance with the fundamental theorem of algebra. In the case of second-order polynomials, the real number system may not yield roots for equations like x² + 1, but in the complex number system, such polynomials do have roots and can be factored as (x - i)(x + i), for instance.

Final answer:

To find the amount Carl and Linda Munson will have accumulated in 10 years, you can use the formula for compound interest. Plugging in the given values, their 401k retirement account will have approximately $3,639.48 after 10 years.

Explanation:

To find the amount Carl and Linda Munson will have accumulated in 10 years, we can use the formula for compound interest:

A = P(1+r)^n

Where:

A = amount accumulated after n years

P = principal amount

r = interest rate (in decimal form)

n = number of years

Using the given information, P = $2,100, r = 8% (or 0.08), and n = 10. Plugging these values into the formula:

A = $2,100(1+0.08)^10

Simplifying the expression:

A = $2,100(1.08)^10

Calculating the value:

A ≈ $3,639.48

Therefore, Carl and Linda Munson will have approximately $3,639.48 accumulated in their 401k retirement account after 10 years.

Answer:

{6, 16, 24}

Step-by-step explanation:

The least common multiple is the least number that is common to the multiples of two or more numbers.

The LCM of 2,3,4 is 12

The LCM of 6,16,and 24 is 48

The LCM of 3,8, 12 is 24.

The LCM of 6,8, 12 is 24.

The numbers that have the least common multiple of 48 is {6, 16, 24}

[tex]6=2\times 3[/tex]

[tex]16=2^4[/tex]

[tex]24=2^3\times 3[/tex]

The LCM is the product of the highest powers of the common factors

[tex]2^4\times3=48[/tex]

Analyzing the given function F(x), we can predict that it is a quartic function with various possible shapes and intersection points with the x-axis. However, a comparison or correlation to function G(x) cannot be accurately made without additional information about graph G(x).

Given the function F(x)=x^4-3x^2-1 and the unspecified G(x) graph, it's difficult to make an accurate statement without observing the shape, slope, and specific points on the G(x) graph. However, by understanding the given function F(x), we can still provide some insights. The function F(x) here is a quartic function (as the largest exponent is 4). The graph of a quartic function can have various shapes - it may have zero, one or two extreme points, and it may pass through the x-axis at zero, two or four points. It is essential to look at two-dimensional graphing to properly analyze and correlate F(x) and G(x).

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Answer:

28x + 8y + 2

Step-by-step explanation:

Combine like-terms within the parentheses, then distribute -2.

Hope this helps! :)

Answer:

B

Step-by-step explanation:

Given

- 2(3x + 12y - 5 - 17x - 16y + 4)

Simplify the parenthesis by collecting like terms

= - 2 (- 14x - 4y - 1) ← distribute the terms in the parenthesis by - 2

= 28x + 8y + 2 → B

Answer:

The correct answer is last option 80 cm

Step-by-step explanation:

From the given figure we can see a parallelogram LMNO

To find the perimeter of parallelogram

Here side length of the parallelogram  is 18 cm and 22 cm

Perimeter = sum of side lengths

= 22 + 22 + 18 + 18 = 80 cm

Therefore the perimeter of parallelogram  LMNO = 80 cm

The correct answer is last option 80 cm

The perimeter of the parallelogram is P = 80 cm

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The sum of angles of a parallelogram is 360°

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented as LMNO

Now , the measure of side MN = 18 cm

The measure of side LM = 22 cm

And , the side MN is parallel and congruent to OL

And , the side LM is parallel and congruent to side ON

So , the perimeter of parallelogram = LM + OL + ON + MN

P = 22 + 18 + 22 + 18

P = 80 cm

Hence , the perimeter is 80 cm

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Answer:

As of 2021, for this question, the answer is "The range is positive real numbers (y>0)

Step-by-step explanation:

Hope this helps somebody!

The range is all real numbers is not a characteristic of the absolute value parent function.

Hence, the option which is not a characteristic of the absolute value parent function is The range is all real numbers.

Therefore, Option A is the correct answer.

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Answer:

The area of the sector is [tex]37.68\ in^{2}[/tex]

Step-by-step explanation:

step 1

Find the area of the circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=12/2=6\ in[/tex] ----> the radius is half the diameter

substitute

[tex]A=(3.14)(6)^{2}[/tex]

[tex]A=113.04\ in^{2}[/tex]

step 2

Find the area of a sector with a central angle of (2pi/3)

Remember that

The area of [tex]113.04\ in^{2}[/tex] subtends a central angle of [tex]2\pi \ radians[/tex]

so

by proportion

Let

x----> the area of the sector

[tex]\frac{2\pi}{113.04}=\frac{(2\pi/3)}{x}\\ \\x=113.04*(2\pi/3)/(2\pi)\\ \\x=37.68\ in^{2}[/tex]

Answer:

both option (A) & (B) is description of given distribution.

Step-by-step explanation:

The outlier is a point which lies differently or far away from rest points in datasets or distribution.

Here we can self-time for one apple on the 10th day is outlier present in the distribution. Thus Option (A) is correct.

We divide the heterogeneous group into many homogeneous groups, these homogeneous group is known as Cluster. It can be seen naturally.

Also, here distribution is divided into many clusters and we can see given distribution has many clusters and one of them is from 4 to 6 days. Thus Option (B) is also a correct option here.

here are my analyses of the possible answer choices based on the image you sent:  The distribution clusters around 4-6 days and has a few potential outliers above 8 days.

here are my analyses of the possible answer choices based on the image you sent:

(A) The distribution has an outlier.

There are a few data points that are higher than the rest of the distribution, so in that sense, yes, there are outliers. However, it is important to consider what an outlier is in the context of the data. If the data is normally distributed, then outliers are data points that fall more than two standard deviations away from the mean. In this case, it is difficult to say for sure whether the data is normally distributed, so it is also difficult to say for sure whether there are outliers. However, there are a few data points that are higher than the rest of the distribution.

(B) The distribution has a cluster from 4 to 6 days.

There is a cluster of data points from 4 to 6 days, so yes, this statement is accurate.

In conclusion, the accurate descriptions of the distribution are:

The width of the garden would be found by dividing the area by the length.

Width = 324 / 24 = 13.5 feet.

Now you need to find the total perimeter of the garden:

Perimeter = 2 x length + 2 x width

Perimeter = 2 x 24 + 2 x 13.5

Perimeter = 48 + 27

Perimeter = 75 feet.

He will need 75 feet of fence.

Answer:

75 feet of fence

Step-by-step explanation:

324/24=13.5

13.5+13.5+24+24=75

Answer:

1. you start with $ 3 and save $1 each month

2. your total savings is 3 times the number of month multiplied by itself

3. you save $3 the first month and then each month the amount triples

Step-by-step explanation:

1.

as y axis represents savings while x axis represents months

the statement "you start with $ 3 and save $1 each month"

is best described by the graph of straight line having slope of 1 and intercept of 3.

2. your total savings is 3 times the number of month multiplied by itself

          = 3(x)(x)

          = 3x^2

3.  as y axis represents savings while x axis represents months

the statement  "you save $3 the first month and then each month the amount triples" is best described by the exponential graph starting to rise from point (1,3) which means $3 save at 1 month.

!

2*(l+b)

So,

2*(21+15)

2*36

=72

Answer:

Perimeter of rectangle is 72 feet.

Step-by-step explanation:

We need to find the perimeter of rectangle where

Length = 21 feet

Width = 15 feet are given.

The formula used will be: Perimeter of rectangle = 2(Length + Width)

So, Perimeter of rectangle is:

Perimeter of rectangle = 2(Length + Width)

                                      = 2 ( 21+15)

                                      = 2(36)

                                      = 72 feet.

So, perimeter of rectangle is 72 feet.

The answer is 1 and 3/4 because if you divide 21 by 12 you get 1.75 convert the decimal into a fraction and get 1 and 3/4. :)

She will need 1 3/4 cups of milk

Number of batches of pancake to be made = 3 batches

Number of cups of milk needed for each batch = 7/12

Therefore, in order to get the total number of cups of milk needed for the batches will be calculated thus:

= 7/12 × 3

= 21/12

= 1 9/12

= 1 3/4

Therefore, she will need 1 3/4 cups of milk.

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Answer:

option c

x + 4 = 64

and

option e

x = 60  

Step-by-step explanation:

Given in the question an expression

3∛x+4 = 12

∛x + 4 = 12/3

∛x + 4 = 4

Take cube on both sides of the equation

∛(x + 4)³ = 4³

x + 4 = 64

x = 64 - 4

x = 60  

Answer:

The third and the fifth equations are equivalent.

Step-by-step explanation:

First of all, you must find [tex]x[/tex] from [tex]3\cdot \sqrt[3]{x+4}=12[/tex] and check during the procedure what expressions from the options are equivalent.

The process is shown below:

From step 3, it could be said that the first, the second and the fourth options ARE NOT equivalent equations because when the left side is [tex]\sqrt[3]{x+4}[/tex], the right side must be [tex]+4[/tex], and these three options don't meet the condition.

From step 5, it could be said that the third option IS an equivalent equation because it is the same expression.

From step 7, it could be said that the fifth option IS an equivalent equation because it is the same expression.

Thus, the third and the fifth equations are equivalent.

Answer:

Step-by-step explanation:

The slope-intercept form:

y = mx  + b

m - slope

b - y-intercept (0, b)

We have (0, 2) → b = 2 and m = -1/2. Substitute:

y = -1/2x + 2            multiply both sides by 2

2y = -x + 4             add x to both sides

x + 2y = 4

the answer to this question is C

y=2x+6×

Answer:

H(G(x)) = 12x - 52

Step-by-step explanation:

We are given the following two functions:

[tex] H ( x ) = - 6 x + 8 [/tex]

[tex] G ( x ) = 1 0 - 2 x [/tex]

And we are to find the value of H(G(x)).

For that, we will apply the function of H on the function of G.

[tex]H(G(x))=H(10-2x)[/tex]

[tex] H ( G ( x ) ) = - 6 ( 1 0 - 2 x ) + 8 [/tex]

[tex]H(G(x))=-60+12x+8[/tex]

H(G(x)) = 12x - 52

Answer:

Ellen invested $60 and Bob invested $140

Step-by-step explanation:

let the two amounts invested by 3x and 7x

(notice 3x : 7x = 3 : 7 )

then 3x + 7x = 200

10x = 200

x = 20

then 3x = 3(20) = 60

and 7x = 7(20) = 140

60+140=200

Ellen invested $60, and Bob invested $140 in their business.

The student's question involves determining how much each business partner invested in their business based on a given ratio and total investment amount. Ellen and Bob invested money at a ratio of 3 to 7 with a total of $200 invested. To solve this, we need to find out what each 'part' of the ratio is worth in dollars.

Let's consider the total number of parts in the ratio, which is 3 (for Ellen) + 7 (for Bob) = 10 parts in total. Since the total amount invested is $200, each part of the ratio is worth $200 divided by 10, which is $20. Therefore:

Hence, Ellen invested $60, and Bob invested $140 in their business.

Answer:

[tex]\boxed{\text{\$810.78}}[/tex]

Step-by-step explanation:

If regular pay = $14.35/h, then

Overtime pay = 1.5 × $14.35/h = $21.525/h

[tex]\begin{array}{rcr}\text{First 40 h at \$14.35/h}& = & \$574.00\\\text{Next 11 h at \$21.525/h} & = & 236.78\\\text{Gross pay}& = & \mathbf{\$810.78}\\\end{array}\\\\\text{Rob's gross pay for the week will be }\boxed{\textbf{\$810.78}}[/tex]

Answer:

ti guarantee it is 45 degree

Step-by-step explanation:

first the opposite angle of 39 will be 39

then 39 plus 42 is 81. a triangle is 180 so the third angle is 99.

so since supplementary angles also equal to 180 the other side is 81.

same with 126 the other side is 54.

now the triangle where x is we have found 2 angles 81 and 54 so the last one will be... drumroll... 45 since a triangle equals tk 180 degree.

Answer:

Step-by-step explanation:

45

Answer:

The number per hour = 5400 ÷ 8 = 675 action figures

Step-by-step explanation:

* Lets explain how to solve the problem

- A toy manufacturer uses 90 pints of plastic to make 600 action figures

- they use 810 pints of plastic in an 8 hour shift

- To find how many action figures are made per hour we must to find

  how many action figures in an 8 hour shift and then find the number

  of the action figures per hour

∵ The toy manufacture  uses 90 pints of plastic to make 600 action

   figures

∵ They use 810 pints

- Lets find how many action figures are made by this numbers of pints

∴ 90/600 = 810/x ⇒ x is the number of action figures

- Use the cross multiplication to find x

∴ 90 x = 810 × 600

∴ 90 x = 486000 ⇒ divide both sides by 90

∴ x = 5400

∴ They will use 810 pints to make 5400 action figures

∵ They use 810 pints in an 8 hour shift

∴ They make 5400 action figures in 8 hours

- To find the number of the action figures per hour divide the number

  of them in 8 hours by 8

∴ The number per hour = 5400 ÷ 8 = 675 action figures

ANSWER

Focus:

[tex](- \frac{1}{4} ,0)[/tex]

Directrix:

[tex]x=\frac{1}{4} [/tex]

EXPLANATION

The given parabola has equation:

[tex] {y}^{2} = - x[/tex]

We compare this to the general equation,

[tex] {y}^{2} = - 4px[/tex]

Comparing the coefficient of x, we have:

-4p=-1

[tex]p = \frac{1}{4} [/tex]

The focus is (-p,0)

[tex](- \frac{1}{4} ,0)[/tex]

The equation of the directrix is

x=p

[tex]x = \frac{1}{4} [/tex]

Answer:

A

Step-by-step ex

only if youre lazy like me to read it, its A

Answer: Town 1- 5.42%, Town 4- 5.86%, Town 3- 6.63%, Town 2- 7.11%

Step-by-step explanation:

Download the app PhotoStudy it’s helpful

Answer:

G=Seven

Step-by-step explanation:

-two=g-nine

two=nine-?

two=nine-seven

-two=seven-nine

Hey!

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

Writing scientific notation in numeral is solving for the equation.

Multiply 10 to 6.4 seven times.

6.4 x 10 = 64

64 x 10 = 640

640 x 10 = 6,400

6,400 x 10 = 64,000

64,000 x 10 = 640,000

640,000 x 10 = 6,400,000

6,400,000 x 10 = 64,000,000

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

Hope This Helped! Good Luck!

Answer:

64,000,000

Step-by-step explanation:

Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

P(Black) = [tex]\frac{1}{2}[/tex]

[tex]\frac{1}{2}*\frac{1}{2}*\frac{1}{2}=\frac{1}{8}[/tex]

P(Black 3/3) = [tex]\frac{1}{8}[/tex]

The probability it will land on the black all three times out of three spins is 1/8.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Given the probability of the spinner landing on black is 1/2. Therefore, the probability it will land on the black all three times out of three spins is,

Probability = (1/2) × (1/2) × (1/2) = 1/8

Hence,  the probability it will land on the black all three times out of three spins is 1/8.

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Answer:

10:8

Step-by-step explanation: