The sum of two numbers is 57, and their difference is 27. What are the two numbers?

The correct graph for the function f(x) = x3 - 4x2 - x + 4 should intersect the y-axis at 4, should have three x-intercepts and should fall to the left and rise to the right. From given options, the best representation would be a cubic polynomial that has x intercepts negative 1, 1, and 4, and intersects the y axis at a point between 0 and 5.

To choose the correct graph of the function f(x) = x3, we need to consider its properties: the y-intercept, x-intercepts, and overall shape. The y-intercept can be found by substituting x = 0 into the equation, which gives us f(0) = 4. Thus, we are looking for a graph that crosses the y-axis at 4.

The x-intercepts of the function are the values of x for which f(x) = 0. In this case, solving this equation might be complex, but we should look for a graph with 3 x-intercepts as it's a cubic equation.

As for the overall shape, since the function is cubic and the sign of the leading coefficient is positive, its graph falls to the left and rises to the right. Therefore, the graph that best represents the function is a graph of a cubic polynomial that falls to the left and rises to the right, has x intercepts negative 1, 1, and 4, and intersects the y axis at a point between 0 and 5.

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Answer:

We have the following equation:

i(4-7i)

Multiplying:

4i - 7(i^2)

So we know that i = sqrt(-1), then i^2 = -1.

For that reason:

4i - 7(i^2) = 4i - 7(-1) = 4i + 7

So the answer is: 4i +7

Answer for the problem is 4i-7i^2

Answer:

7

Step-by-step explanation:

If 6 is x, then it would be (6-3)2+1. 6-3 is 3, 3 times 2 is 6, 6+1=7

The answer is 7... Just Plug 6 into x and then solve

Using line of best fit and correlation coefficient, the correlation coefficient of determination represent the percentage of data that is closest to the lines of best fit.

Line of best fit refers to the "a line through a scatter plot of data points that best expresses relationship between those points". Lines of best fit is used to describe data and predict data where the new data will appear. Examples for lines of best fit is 'Least square method'.

Two variables wherein "change in the value one variable produces a change in the variable other variable then it is called variables are correlated or there is a correlation coefficient".

According to the question,

In order to determine the correlation between two variables on a graph using line of best fit and correlation coefficient.

Correlation coefficient holds only if there is a linear correlation between the variables; that is the relationship between the variables is linear in graph. Variation in 'y' is caused by variation in 'x' on graph . Variation in 'x' is caused by variation 'y' on graph. Variable 'x' and variable 'y' are jointly dependent on graph. This is how we determine the correlation coefficient between two variables on the graph.

Line of best fit suppose (x₁, y₁) (x₂, y₂) ..... (xₙ, yₙ) be 'n' pairs of values on a graph to determine the line of best for this data. Assume 'y = a + b x' as a line of best fit (trend line). Using the principle of least squares we can determine the parameter 'a' and 'b'. It can be shown that 'a' and 'b' are determined by the equation.

n a + b∑ x = ∑y  -->(1)

a ∑x +b ∑x² = ∑x y  --->(2)

These equations are called Normal equation. Therefore, the line of best fit is y=a x+ b where 'a' and 'b x' are given by the equation. This is how we determine the correlation or relationship between two variables on a graph.  

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Answer:

1.732050808

Step-by-step explanation:

https : // www. desmos. com/ scientific

EDIT square root of 3

The exact value of tan240° is the same as tan60° because of the periodicity of the tangent function and the fact that 240° lies in the third quadrant of the unit circle. The value of tan60° is √3 or about 1.732.

To find the exact value of tan240°, we should recall that the tangent function is periodic with a period of 180°, meaning tan(θ) is the same as tan(θ + 180°). Also, in the unit circle, 240° lies in the third quadrant, where tangent values are positive because both sine and cosine are negative. Therefore, tan240° is the same as tan(240° - 180°), which is tan60°. The exact value of tan60° is √3) or approximately 1.732. This calculation leverages trigonometric principles and the geometric interpretation of angles on the unit circle, demonstrating how to derive accurate values for trigonometric functions in specific angular contexts.

Answer:

[tex]\dfrac{5}{36}[/tex]

Step-by-step explanation:

When tossing two number cubes, Leon can get  such sample space

[tex]\begin{array}{cccccc}(1,1)&(1,2)&(1,3)&(1,4)&(1,5)&(1,6)\\(2,1)&(2,2)&(2,3)&(2,4)&(2,5)&(2,6)\\(3,1)&(3,2)&(3,3)&(3,4)&(3,5)&(3,6)\\(4,1)&(4,2)&(4,3)&(4,4)&(4,5)&(4,6)\\(5,1)&(5,2)&(5,3)&(5,4)&(5,5)&(5,6)\\(6,1)&(6,2)&(6,3)&(6,4)&(6,5)&(6,6)\\\end{array}[/tex]

There are 36 possible outcomes. Only (1,5), (2,4), (3,3), (4,2), (5,1) gives the sum of 6.

Hence, the probability that Leon will toss a sum of 6 is

[tex]\dfrac{5}{36}[/tex]

The probability that Leon will toss a sum of 6 is;

P(that Leon will toss a sum of 6) = 5/36

A cube here is same as a dice.

Now, a dice has 6 faces numbered from 1 to 6.

Now,we want to find the probability of tossing a sum of 6.

When we have 2 dices, the possible number of sums we can have are 36 total possible outcomes.

Now, the number of outcomes out of the 36 that can sum up to 6 are;

(1, 5), (2, 4), (3, 3), (5, 1) and (4, 2).

Thus, there are 5 possible sums that can be 6.

Therefore;

P(that Leon will toss a sum of 6) = 5/36

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Answer:

26 cm

Step-by-step explanation:

Tangents drawn to a circle from a point outside the circle are equal in length.

On the left side the tangents are 4/ 4 and 3/3

On the right side the tangents are 2/ 2 and 4/4

Calculating perimeter from the bottom left clockwise

perimeter = 4 + 4 + 3 + 3 +2 + 2 + 4 + 4 = 26 cm

Where are the answers choices

Answer:  tends to become smaller

Step-by-step explanation:

In statistics and probability , the  law of large​ numbers says that as we increase the size of the sample, then the sample mean will get closer to the true value of population mean.

Therefore, the complete statement will be :

According to the law of large​ numbers, as more observations are added to the​ sample, the difference between the sample mean and the population mean​ tends to become smaller.

Answer:

The rule of dilation centered at the origin is (x , y) → (2x , 2y) ⇒ answer A

Step-by-step explanation:

* Lets talk about dilation

- A dilation is a transformation that changes the size of a figure.  

- It can become larger or smaller, but the shape of the

 figure does not change.  

- The scale factor, measures how much larger or smaller  

 the image will be

- If the scale factor greater than 1, then the image will be larger

- If the scale factor between 0 and 1, then the image will be smaller

- The dilation rule for any point (x , y) is (kx , ky), where k is the

  factor of dilation centered at origin

* Now lets solve the problem

- The figure KLMN has for vertices:

  K (3 , -3) , L (3 , 4) , M (5 , 4) , N (5 , -3) ⇒ (1)

- The image K'L'M'N' of figure KLMN after dilation about the origin

  has four vertices:

   K' (6 , -6) , L' (6 , 8) , M' (10 , 8) , N' (10 , -6) ⇒ (2)

- From (1) and (2)

# (3 , -3) ⇒ (6 , -6)

# (3 , 4) ⇒ (6 , 8)

# (5 , 4) ⇒ (10 , 8)

# (5 , -3) ⇒ (10 , -6)

- Each point in KLMN multiplied by 2

∴ The scale of dilation is 2

∴ The rule of dilation centered at the origin is (x , y) → (2x , 2y)

Answer: A) (x, y) → (2x, 2y)

The pre-image is enlarged. The coordinates of KLMN have been multiplied by 2.

Answer:

Most likely 60-75%

Step-by-step explanation:

60-75 is where most of the data points lie, so it is most likely that the actual percentage is within that interval.

The answer is 10 as the diameter because it says to estimate pi as 3. Since we know the circumference is 30 we can reverse it to find the diameter, since Circumference is pi time diameter.

Answer:

d = 10 km

Step-by-step explanation:

Circumference is equal to pi times diameter

C = pi *d

We know the circumference is 30

30 = pi *d

Let pi = 3

30 = 3d

Divide each side by 3

30/3=3d/3

10 =d

The diameter is 30 km

Answer:

The correct answer is A) 1/2 pound

Step-by-step explanation:

Answer:

[tex]|KL|=7\sqrt{2}[/tex]

Step-by-step explanation:

The given triangle is a right triangle.

The m<K=45 degrees.

This means the measure of <L is  also 45 degrees.

This implies that;

|LM|=|KM|=7 units.

From the Pythagoras Theorem;

[tex]|KL|^2=|LM|^2+|KM|^2[/tex]

[tex]|KL|^2=7^2+7^2[/tex]

[tex]|KL|^2=2(7^2)[/tex]

[tex]|KL|=\sqrt{2(7^2)}[/tex]

[tex]|KL|=7\sqrt{2}[/tex]

Option C is correct.

The answer is:

The third option,

[tex]KL=7\sqrt{2}[/tex]

Since we are working with a right triangle, we can use the following identity:

[tex]Sin(\alpha)=\frac{y}{hypothenuse}[/tex]

We are given:

[tex]\alpha =45\°\\LM=y=7[/tex]

[tex]hypothenuse=KL[/tex]

Then, substituting and solving we have:

[tex]Sin(45\°)=\frac{7}{hypothenuse}[/tex]

[tex]Hypothenuse=KL=\frac{y}{Sin(45\°)}=\frac{7}{\frac{\sqrt{2} }{2} } \\\\Hypothenuse=KL=7\sqrt{2}[/tex]

Hence, the answer is the third option,

[tex]KL=7\sqrt{2}[/tex]

Have a nice day!

Answer:

16.47 in.

Step-by-step explanation:

Add the lengths of the sides:

3.4 in. + 5.75 in. + 7.32 in. = 16.47 in.

The perimeter of the triangle will be equal to 16.47 in. The correct option is B.

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.

The perimeter is defined as the sum of all the sides of the figure. The perimeter of the triangle is the sum of all three sides of the triangle.

Given that the three sides of a triangle measure 3.4 inches, 5 inches, and 7.32 inches.

The perimeter of the triangle is calculated as,

P = 3.4 in. + 5.75 in. + 7.32 in.

P = 16.47 in.

Therefore, the perimeter of the triangle will be equal to 16.47 in. The correct option is B.

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The sum evaluates to 144. See the linked question in the comments for details.

Answer:

[tex]\$806.14[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

Part 1)

Find the interest rate r

we have  

[tex]t=1\ years\\ P=\$575\\ r=?\\n=1\\A=\$615[/tex]  

substitute in the formula above  and solve for r

[tex]\$615=\$575(1+\frac{r}{1})^{1*1}[/tex]  

[tex]\$615=\$575(1+r)[/tex]  

[tex]r=(615/575)-1\\ \\ r=0.07[/tex]

The interest rate is 7%

Part 2)

we have  

[tex]t=4\ years\\ P=\$615\\ r=0.07\\n=1\\A=?[/tex]  

substitute in the formula

[tex]A=\$615(1+\frac{0.07}{1})^{1*4}[/tex]  

[tex]A=\$615(1.07)^{4}=\$806.14[/tex]  

Answer:

neither am i bro no worries

Step-by-step explanation:

no cap

Answer:

Step-by-step explanation:

It's parallel to the side BC, from a known theorem (the segment linking the midpoints of two sides of a triangle is parallel to the third, and its lenght is half of it.

Answer:

Okay I might not be right on this one but, I believe you divide 27 and 3. As to the part about simplifying, you might want to give me so details.

Step-by-step explanation:

There you go, you didn’t show the representation but I drew one.

Answer:

[tex]\$34[/tex]

Step-by-step explanation:

step 1

Avery

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=12\ years\\ P=\$2,100\\ r=7 7/8\%=7.875\%=0.07875[/tex]  

substitute in the formula above  

[tex]A=\$2,100(e)^{0.07875*12}=\$5,402.91[/tex]

step 2

Morgan

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=12\ years\\ P=\$2,100\\ r=8 1/4\%=8.25\%=0.0825\\n=1[/tex]  

substitute in the formula above  

[tex]A=\$2,100(1+\frac{0.0825}{1})^{1*12}=\$5,436.94[/tex]  

step 3

Find the difference

[tex]\$5,436.94-\$5,402.91=\$34.03[/tex]

To the nearest dollar

[tex]\$34.03=\$34[/tex]

Answer:A?

Step-by-step explanation:

Answer:

x = 55.6

Step-by-step explanation:

In this triangle, the hypotenuse is the unknownj.  The sine function relates the hypotenuse, the angle and the side opposite the angle:

sin Ф = opp / hyp

Here, sin 20° = 19 / x.  This can be rearranged as x = 19 / sin 20°

This works out to x = 19 / 0.342, or 55.6.

x = 55.6

Answer:

Part 1) [tex]\$250[/tex] is not enough to cover the cost of 4 tickets

Part 2) She would need to work an additional 14 hours to purchase 4 concert tickets

therefore

No, she would need to work an additional 14 hours to purchase 4 concert tickets

Step-by-step explanation:

step 1

Find the cost of 4 tickets

[tex]4*(75+12.95)=\$351.80[/tex]

so

[tex]\$351.80> \$250[/tex]

therefore

[tex]\$250[/tex] is not enough to cover the cost of 4 tickets

step 2

Find the number of hours needed to work to cover the difference

The difference is equal to

[tex]\$351.80-\$250=\$101.80[/tex]

Let

x-----> the number of hours needed to work to cover the difference

The inequality that represent the situation is

[tex]7.50x \geq 101.50[/tex]

[tex]x \geq 101.50/7.50[/tex]

[tex]x \geq 13.5\ hours[/tex]

The minimum number of hours is 14

Answer:

Median: 46

Mean: about 46.9

Range: 72

Step-by-step explanation:

Median:

Put them in order

11 27 33 46 50 78 83

Then find the middle value which is 46.

Mean:

Add them all together then divide by the number of values

(11+27+33+46+50+70+83)/7

about 46.8571

Range:

Highest value-lowest value

83-11

72

To solve for the median, mean, and range of the given data set, we will follow these steps:
**Step 1: Organize the Data Set**
First, we must organize the data set in ascending order to calculate the median. The given data set is: 83, 27, 11, 78, 50, 33, 46.
Arranging the numbers, we get:
11, 27, 33, 46, 50, 78, 83
**Step 2: Find the Median**
The median is the middle value of a data set when it's ordered from least to greatest. Since there are seven numbers, the middle one will be the fourth value (since there are three numbers on each side of it).
So, the median is: 46
**Step 3: Calculate the Mean**
To calculate the mean (average), we sum all the numbers and then divide by how many numbers there are.
Mean = (Sum of all numbers) / (Number of numbers)
Sum = 11 + 27 + 33 + 46 + 50 + 78 + 83 = 328
Number of numbers = 7
Mean = 328 / 7 = 46.857 (approximately)
**Step 4: Find the Range**
The range is the difference between the highest and lowest values in the data set.
Minimum value = 11
Maximum value = 83
Range = Maximum value - Minimum value
Range = 83 - 11 = 72
**Summary:**
Median: 46
Mean: Approximately 46.857
Range: 72

A triangle's sides are suppose to add up to 360 degrees. So create a alegbraic equation with x as the variable. So the equation should add up to 720 degrees for two triangles.

720 = 15x - 3 + 56

720 = 15x + 53

667 = 15x

x = 44.5 (rounded to tenth)

Tell me if I'm incorrect.

Answer:

x = 3

Step-by-step explanation:

The line segment is an angle bisector thus the following ratios are equal

[tex]\frac{32}{24}[/tex] = [tex]\frac{6x+6}{9x-9}[/tex], that is

[tex]\frac{4}{3}[/tex] = [tex]\frac{6x+6}{9x-9}[/tex] ( cross- multiply )

4(9x - 9) = 3(6x + 6) ← distribute parenthesis on both sides

36x - 36 = 18x + 18 ( subtract 18x from both sides )

18x - 36 = 18 ( add 36 to both sides )

18x = 54 ( divide both sides by 18 )

x = 3

Answer:

y=2x  when x>5

Step-by-step explanation:

y=|x−5|+|x+5|

If x > 5 then x-5 is greater than 0 so we can remove the absolute value bars from the first term

x>5 then x+5 >0 so we do not need the absolute value bars on the second term

y = x-5 + x+5

Combine like terms

y = x+x-5+5

y = 2x

Answer:

Place them in a line.

Step-by-step explanation:

Take the First cube and place it on the paper

Then place another cube behind that cube

Repeat with remaining cubes

Should end up with a line of cubes that create a rectangular prism.

Ramon cannot form a rectangular prism using exactly 5 cubes because a rectangular prism has 6 faces, which would each be formed by a cube. To create even the smallest possible rectangular prism, he would need at least 6 cubes.

No, Ramon cannot make a rectangular prism using exactly 5 cubes. A rectangular prism is a three-dimensional figure with six faces that are rectangles. It would not be possible to form a rectangular prism using only 5 cubes because to form a rectangular prism you need at least 6 cubes.

Each cube would represent one face of the rectangular prism.

This is because a rectangular prism has 3 dimensions: length, width, and height. Even if you make the smallest possible rectangular prism, you would need a minimum of 6 cubes (1 cube length, 1 cube width, and 6 cubes high). If he has only 5 cubes, at least one dimension (length, width, or height) would be incomplete.

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Answer:

The answer is √58 = 7.62

Step-by-step explanation:

So, if you draw this down, you will see that the direct distance is hypotenuse c of a right triangle which sides are 3 blocks (1 south and 2 north) and 7 blocks (4 west and 3 east).

Use the Pythagorean theorem:

c² = a² + b²

a = 3

b = 7

c² = 3² + 7²

c² = 9 + 49

c² = 58

c = √58

c = 7.62

Answer:

It's this graph

Step-by-step explanation:

I ran into this one on an assignment

Sounds like you have

[tex]\displaystyle\lim_{n\to\infty}\sum_{k=1}^n\left(1+\frac kn\right)^2\frac1n[/tex]

which translates to the sum of the areas of [tex]n[/tex] rectangles with dimensions [tex]\left(1+\dfrac kn\right)^2[/tex] (height) and [tex]\dfrac1n[/tex] (width). This is the right-endpoint Riemann sum for approximating the area under [tex]x^2[/tex] over the interval [1, 2].

Answer:

Option C

Step-by-step explanation:

We are given that

[tex]\lim_{n\rightarrow\infty}\sum_{k=1}^{n}(1+\frac{k}{n})^2\times \frac{1}{n}[/tex]

We have to find the definite integral for the given summation.

We know that

[tex]\lim_{n\rightarrow \infty}\sum_{k=a}^{n}f(a+k\frac{b-a}{n})(\frac{b-a}{n}=\int_{a}^{b}f(x)dx[/tex]

Using the formula

a=1

[tex]\frac{b-a}{n}=\frac{b-1}{n}[/tex]

[tex]\frac{b-1}{n}=\frac{1}{n}[/tex]

[tex]b-1=1[/tex]

[tex]b=1+1=2[/tex]

[tex]\lim_{n\rightarrow\infty}\sum_{k=1}^{n}(1+\frac{k}{n})^2\times \frac{1}{n}=\int_{1}^{2}x^2 dx[/tex]

Option C is true.

answer for this question is (d) 3

To find the x-coordinate of the point of intersection of the two given lines, set the equations equal and solve for x, revealing that the x-coordinate is 3 (D).

The question involves finding the x-coordinate of the point of intersection of two lines represented by the equations y = –6x + 20 and y = 5x – 13. To find the point of intersection, we can set the two equations equal to each other because at the point of intersection, the y-values (and x-values) for both equations will be the same.

Setting the equations equal to each other:

–6x + 20 = 5x – 13

Adding 6x to both sides and adding 13 to both sides gives:

33 = 11x

Dividing both sides by 11:

x = 3

Therefore, the x-coordinate of the point of intersection of the two lines is 3, which corresponds to answer choice D.

if we take 20 to be the 100%, what is 11 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 20&100\\ 11&x \end{array}\implies \cfrac{20}{11}=\cfrac{100}{x}\implies 20x=1100 \\\\\\ x=\cfrac{1100}{20}\implies x=55[/tex]