Fill in the blank to complete the following sentence.

The two roots a+√b and a-√b are called _______ radicals.

Answer:

Hello cheaters lol jk, Answer is B.  

Step-by-step explanation:

more interest equals more money, if you divide the amount of the house by 6% and do the same for the other by 5, the amount for B is greater.  

The House A is more worth than House B .

Compound interest is an interest accumulated on the principal and interest together over a given time period. The interest accumulated on a principal over a period of time is also accounted under the principal.

Formula of Compound interest :

[tex]A = P (1+\frac{r}{100} )^{n}[/tex]

Where,

A = Final amount

P = initial principal

r = rate per annum

n = Time in years

According to the question

House A:

Principal = 125260

Rate = 5%

Time in years = 2

Applying Formula of Compound interest for final amount

[tex]A = P (1+\frac{r}{100} )^{n}[/tex]

[tex]A = 125260 (1+\frac{5}{100} )^{2}[/tex]

[tex]A = 125260 (1.05)^{2}[/tex]

A = 138,099.15

House B:

Principal = 120160

Rate = 6%

Time in years = 2

Applying Formula of Compound interest for final amount

[tex]A = P (1+\frac{r}{100} )^{n}[/tex]

[tex]A = 120160 (1+\frac{6}{100} )^{2}[/tex]

[tex]A = 120160(1.06)^{2}[/tex]

A = 135,011.776

Hence , House A is more worth than House B .

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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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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:

3. f(x) = 5^x

4. f(x) = 3 (8)^x

Step-by-step explanation:

3. Which function represents the data 2=>25, 3=>125, 4 =>625

You just have to plug the values of x in the equations provided and see which one fit, you stop testing for a given equation when it doesn't match the data table.

f(x) = x^4 + 9 - NO

for x = 2, 2^4 + 9 = 16 + 9 = 25 YES

for x = 3, 3^4 + 9 = 81 + 9 = 90 NO, should be 125

f(x) = 4^x + 9 - NO

for x = 2, 4^2 + 9 = 16 + 9 = 25 YES

for x = 3, 4^3 + 9 = 64 + 9 = 73  NO, should be 125

f(x) = x^5 - NO

for x = 2, 2^5 = 32 NO, should be 25

f(x) = 5^x YES

for x = 2, 5^2 = 25  YES

for x = 3, 5^3 = 125  YES

for x = 4, 5^4 = 625  YES

4. Which of the options is equivalent to f(x) = 3(2)^(3x)

By property of the powers you can easily break down the 3x exponent into a much simpler way.

[tex](2)^{3x} = (2^{3} )^{x} = 8^{x}[/tex]

From (2)^(3x) we got to 8^x, so the equation can now be written:

f(x) = 3 (8)^x, which is the first choice.

You could easily verify it with x = 2 in each equation.

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

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]

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 for this question is (d)3x2-x+6

This is the answer:)

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

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:

option B

Step-by-step explanation:

Step 1

A + B = C

[tex]A=\left[\begin{array}{ccc}8&-3\\3&y+2\end{array}\right][/tex][tex]+B=\left[\begin{array}{ccc}3x&z+4\\w&1/2y\end{array}\right][/tex]

=

[tex]C=\left[\begin{array}{ccc}x&2z\\4&y\end{array}\right][/tex]

Step 2

[tex]\left[\begin{array}{ccc}8+3x&-3+z+4\\3+w&y+2+y/2\end{array}\right][/tex][tex]=\left[\begin{array}{ccc}x&2z\\4&y\end{array}\right][/tex]

Step 3

4 equations are form

Equation 1

8 + 3x = x

8 = -2x

x = -4

Equation 2

-3 + z + 4 = 2z

1 + z = 2z

1 = z

z = 1

Equation 3

3 + w = 4

w = 1

Equation 4

y + 2 + y/2 = y

2 + y/2 = 0

4 + y = 0

y = -4

Step 4

[tex]\left[\begin{array}{ccc}3(-4)&1+4\\1&1(-4)/2\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}-12&5\\1&-2\end{array}\right][/tex]

Answer:

B

Step-by-step explanation:

I got 100% on EDGE 2020 Unit test

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:

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.

Translations, rotations, and reflections are all rigid transformations.

Answer:

im pretty sure its the first one

Answer with explanation:

When the size of Preimage is greater than size of Image than dilation factor will be less than 1 and greater than zero.

And, when Size of preimage is greater than Size of Image than dilation factor will be greater than 1.

In the given diagram

Size of Preimage > Size of Image

Dilation Factor=0 <Dilation factor <1

Option A: It has a scale factor between zero and one and is a reduction.

C. If a<0, then the parabola opens down

Answer:

[tex]\$17,500[/tex]

Step-by-step explanation:

Let

x----> that month's sales

y----> October earnings

we know that

[tex]8\%=8/100=0.08[/tex]

[tex]y=0.08x+1,400[/tex] -----> equation A

[tex]y=2,800[/tex] -----> equation B

Equate equation A and equation B and solve for x

[tex]2,800=0.08x+1,400[/tex]

[tex]0.08x=2,800-1,400[/tex]

[tex]x=1,400/0.08[/tex]

[tex]x=\$17,500[/tex]

Final answer:

The salesperson needs to earn an additional $1,400 on top of the base salary to meet the goal, which means they need to sell $17,500 worth of merchandise with an 8% commission rate.

Explanation:

To calculate the amount of merchandise the salesperson must sell to meet the goal of $2,800, we need first to understand how much more money is needed beyond the base salary. The salesperson receives a base salary of $1,400. Since the goal is $2,800, the additional amount needed from commission is $2,800 - $1,400 = $1,400.

With an 8% commission rate, we can set up an equation where the amount of merchandise sold (let's call it x) times the commission rate (0.08) equals the additional amount needed ($1,400). The equation is: 0.08x = $1,400. To find x, divide both sides by 0.08, therefore x = $1,400 / 0.08, which equals $17,500.

So, the salesperson will need to sell $17,500 worth of merchandise to meet the goal of earning $2,800 in October.

Answer:

slope=-1/4

Step-by-step explanation:

point 1: -4,-1

point 2: 0,-2

y1-y2/x1-x2

1/-4

-1/4

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.

Answer:

[tex]3,726\ m^{2}[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor

Let

z----> the scale factor

x----> corresponding side of the larger trapezoid

y----> corresponding side of the smaller trapezoid

[tex]z=\frac{x}{y}[/tex]

we have

[tex]x=64\ m[/tex]

[tex]y=12\ m[/tex]

substitute

[tex]z=\frac{64}{12}[/tex]

step 2

Find the area of the larger trapezoid

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z----> the scale factor

x----> area of the larger trapezoid

y----> area of the smaller trapezoid

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=\frac{64}{12}[/tex]

[tex]y=131\ m^{2}[/tex]

substitute

[tex](\frac{64}{12})^{2}=\frac{x}{131}[/tex]

[tex]x=(\frac{4,096}{144})(131)[/tex]

[tex]x=3,726\ m^{2}[/tex]

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:

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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Answer:

c. amplitude: 1; period: [tex]2\pi[/tex]

Step-by-step explanation:

The given function is [tex]f(t)=- \cos t[/tex]

This function is of the form;

[tex]y=A \cos Bt[/tex]

where [tex]|A|[/tex] is the amplitude.

When we compare [tex]f(t)=- \cos t[/tex] to [tex]y=A \cos Bt[/tex], we have

[tex]A=-1[/tex], therefore the amplitude of the given cosine function is [tex]|-1|=1[/tex]

The period is given by;

[tex]T=\frac{2\pi}{|B|}[/tex]

Since B=1, the period is [tex]T=\frac{2\pi}{|1|}=2\pi[/tex]

Answer:

c. amplitude: [tex]\displaystyle 1;[/tex]period: [tex]\displaystyle 2\pi[/tex]

Explanation:

[tex]\displaystyle f(t) = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 1[/tex]

With the above information, you now should have an idea of how to interpret graphs like this.

I am joyous to assist you at any time.

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:

Answer:

The correct answer is A) 1/2 pound

Step-by-step explanation:

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

The value of ∑n=14[100(−4)n−1] is -5368709100

The sequence is given as:

∑n=14[100(−4)n−1]

The above sequence is a geometric sequence, with the following properties

The sum of n terms of a geometric series is:

[tex]S_n = \frac{a* (r^n - 1)}{r - 1}[/tex]

So, we have:

[tex]S_n = \frac{100* ((-4)^{14} - 1)}{-4 - 1}[/tex]

Evaluate

[tex]S_{14} = -5368709100[/tex]

Hence, the value of ∑n=14[100(−4)n−1] is -5368709100

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The sum [tex]\(\sum_{n=1}^4 [100(-4)^{n-1}]\)[/tex] is [tex]\[\boxed{-5100}\][/tex]

To find the sum [tex]\(\sum_{n=1}^4 [100(-4)^{n-1}]\),[/tex] we will calculate the individual terms of the sequence and then sum them up.

The general term of the sequence is [tex]\(100(-4)^{n-1}\)[/tex]. Let's compute the terms from [tex]\(n = 1\) to \(n = 4\):[/tex]

1. For [tex]\(n = 1\):[/tex]

[tex]\[ 100(-4)^{1-1} = 100(-4)^0 = 100 \cdot 1 = 100 \][/tex]

2. For [tex]\(n = 2\):[/tex]

[tex]\[ 100(-4)^{2-1} = 100(-4)^1 = 100 \cdot (-4) = -400 \][/tex]

3. For [tex]\(n = 3\):[/tex]

[tex]\[ 100(-4)^{3-1} = 100(-4)^2 = 100 \cdot 16 = 1600 \][/tex]

4. For [tex]\(n = 4\):[/tex]

[tex]\[ 100(-4)^{4-1} = 100(-4)^3 = 100 \cdot (-64) = -6400 \][/tex]

Now, let's sum these terms:

[tex]\[100 + (-400) + 1600 + (-6400)\][/tex]

Perform the calculations step-by-step:

1. [tex]\(100 - 400 = -300\)[/tex]

2. [tex]\(-300 + 1600 = 1300\)[/tex]

3. [tex]\(1300 - 6400 = -5100\)[/tex]

Answer:

[tex]4w^4-7z^4+6w^2z^2[/tex]

Step-by-step explanation:

We can reformat this equation so we can vertically add.

Then, we can just add down.

Since all the degrees and the variables are the same, we only have to worry about the coefficients.

5 - 1 = 4 --> [tex]4w^4[/tex]

-7 + 13 = 6 --> [tex]6w^2z^2[/tex]

-3 - 4 = -7 --> [tex]-7z^4[/tex]

Now let's rewrite this.

[tex]4w^4-7z^4+6w^2z^2[/tex]

Answer:

Explanation:

To solve log (−5.6x + 1.3) = −1 − x graphycally, you must graph this system of equations on the same coordinate plane:

1) To graph the equation 1 you can use these features of logarithmfunctions:

        log ( -5.6x + 1.3) = 0 ⇒ -5.6x + 1.3 = 1 ⇒x = 0.3/5.6 ≈ 0.054

       x = 0 ⇒ log (0 + 1.3) = log (1.3) ≈ 0.11

        x            log (-5.6x + 1.3)

        -1           0.8

        -2           1.1

        -3           1.3

2) Graphing the equation 2 is easier because it is a line: y = - 1 - x

3) The solution or solutions of the equations are the intersection points of the two graphs. So, now the graph method just requires that you read the x coordinates of the intersection points. From the least to the greatest, rounded to the nearest tenth, they are:

Answer:

x = -2.1

& .2

Step-by-step explanation: