What kind of triangle is this?

Answer:

27\(ft^{2}\)

Step-by-step explanation:

\(\frac{20}{6}\) = \(\frac{21 + x}{x}\)  Cross multiple and solve for x

20x = 6(21 + x)  Distribute the 6

20x = 126 + 6x  Subtract 6x from both sides

14x = 126  Divide both sides by 14

x = 9  

Now that we know EC is 9 we can calculator the area of the triangle

a = \(\frac{lw}{2}\)

a = \(\frac{(9)(6)}{2}\)

a = \(\frac{54}{2}\)

a = 27

Proved that at least one zero lies in the interval x  = 1 and x = 2 for the given polynomial

The polynomial is given by

f(x) = \(x^3\) - 6x + 1

We have to show that at least one zero lies in the given interval for the given polynomial using the intermediate value theorem

When the value of x = 2

Substitute the value of x in the polynomial

f(2) = (2)^3 - 6(2) + 1

= 8 - 12 + 1

= -3

When the value of x = 3

Substitute the value of x in the polynomial

f(3) = (3)^3 - 6(3) + 1

= 27 - 18 + 1

= 10

Here the value of f(2) is negative and the value of f(3)  is positive therefore there is at least one real zero between x = 1and x = 2

Hence, proved that at least one zero lies in the interval x  = 1 and x = 2 for the given polynomial

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Answer:

BRAINLIEST PLZZZZ

Step-by-step explanation:

Also given that (x+1) is factor of given polynomial p(x).

Need to determine value of constant c.

We will be solving above problem using factor theorem.

Factor theorem says that if ( x – a) is a factor of any polynomial f(x) , then f(a) = 0.

As in our case f(x) = p(x) and factor of p(x) is (x + 1) , which can be rewritten as (x – ( -1)) , so "a" in our case is -1 .

According to factor theorem p(-1) = 0

On substituting x = -1 , in given expression of p(x) we get

Hence value of c in the given polynomial is 1

Answer:

c = - 3

Step-by-step explanation:

\( \because \) (x+1) is a factor of the polymonial \( p(x)=5x^4+7x^3-2x^2-3x+c\)

Let (x + 1) =0\( \implies \) x = - 1

\( \therefore \) at x = - 1, p(x) =0.

\(p(x)=5x^4+7x^3-2x^2-3x+c \\ \\ 0 = 5( { - 1})^{4} + 7( { - 1})^{3} - 2( { - 1})^{2} - 3( - 1) + c \\ \\ 0 = 5 \times 1 + 7( - 1) - 2 \times 1 + 3 + c \\ \\ 0 = 5 - 7 - 2 + 3 + c \\ \\ 0 = 7 - 7 + 3 + c \\ \\ 0 = 3 + c \\ \\ c = - 3\)

So, the simpler form of the radical expression 4 sqrt 1296 x^16y^12 is 144x^14y^14 sqrt (x) sqrt (y).

To simplify the radical expression 4 sqrt 1296 x^16y^12, we need to first factor the number inside the radical. 1296 can be factored into 36 x 36, which simplifies to 6^4. So, the expression becomes 4 sqrt (6^4 x^16y^12).
Next, we can simplify the expression further by using the property of exponents that says a^m x a^n = a^(m+n). This means that we can combine the exponents of x and y, which gives us 4 sqrt (6^4 x^(16+12) y^(12+16)). Simplifying this, we get 4 sqrt (6^4 x^28 y^28).
Now, we can simplify the radical expression even further by using the property that says sqrt (a x b) = sqrt (a) x sqrt (b). Applying this to our expression, we get 4 x 6^2 x sqrt (x^28) x sqrt (y^28). Simplifying this further, we get 144x^14y^14 sqrt (x) sqrt (y).
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Answer:

Number 2: -3/10 (I think)

Number 4: 10a-5b-4

Number 6: x=5/2

Number 8: x=6

Step-by-step explanation:

Number 2:

3ysquared/2y-4x2

3(-1)squared/2(-1)-4x2

3x1/2(-1)-4x2

3x1/-10

-3/10

(I might be wrong with this one though)

Number 4:

10a-3b-4-2b

10a-5b-4

Number 6:

2(-3x+8)=4x-9

-6x+16=4x-9

-6x+16-16=4x-9-16

-6x=4x-25

-6x-4x=4x-25-4x

-10x=-25

-10x/-10=-25/-10

x=5/2

Number 8:

1(4x-8)/4=-x+10

4x-8/4=-x+10

4x-8/4+x=-x+10+x

8x-8/4=10

4x8x-8/4=4x10

8x-8=4x10

8x-8=40

8x-8+8=40+8

8x=48

8x/8=48/8

x=6

Answer: b

Step-by-step explanation:

The correct statment is the amount spent to manufacture each radio.

An equation is an expression that shows the relationship between two or more numbers and variables.

We have given that the cost of manufacturing the radios is;

c(r) = 5.25r + 125

where, r is the number of radios

This is a linear function and the general form of a linear function as;

f(x) = mx + b

Here m represents the slope of the function or the rate of change of the function while b represents the intercept of the initial value of the function.

From the given function we have;

m = 5.25

b = 125

Which means that 5.25 represents the rate of change of the function. It mean the value by which the value of r changes the function.

In other words,the correct statment is the amount spent to manufacture each radio.

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well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)

\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)

The most appropriate chart to see the correlation between car mileage and year the car was built for various car models would be a scatterplot chart.

In a scatterplot chart, each point represents a pair of values: one value on the x-axis (in this case, year the car was built) and another value on the y-axis (in this case, mileage). By plotting these pairs of values for each car model in the sample, we can visually examine the relationship between mileage and year built for each car model and determine if there is a correlation between the two variables.

A line chart is used to display data that changes over time, typically for a single variable. A heatmap chart is used to show the magnitude of values for different categories using different colors. Therefore, neither of these chart types would be appropriate to show the correlation between mileage and year built for various car models.

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In point estimation, data from the sample is used to estimate the population parameter. This is done by taking a sample from the population and then using the data from the sample to estimate the population parameter. The sample statistic is used as an estimate of the population parameter.

The mean of the sample is also used as an estimate of the population mean. Point estimation is a statistical technique for estimating population parameters from a sample of data. It is based on the idea that the sample statistics such as the mean or proportion can be used to estimate the population parameters such as the population mean or proportion. The accuracy of the estimate depends on the size of the sample and the variability of the data.

In summary, in point estimation, the data from the sample is used to estimate the population parameter. The sample statistic, such as the mean of the sample, is used as an estimate of the population parameter.

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Answer:

A C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Leah wants to earn at least 120 dollars a month and she has two job options. This is written as

5x + 8y > 120

She also can't work more than 20 hours, leading us to the second equation

x + y = 20

First we solve for one variable

y = 20 - x

then substitute it into the first equation

5x + 8(20 - x) = 120

Solve for x

5x + 160 - 8x = 120

3x = 40

     x = 40/3

Then we solve for y

y = 20 - x

     y = 20/3

x < 40/3

y > 20/3

B and D will not work because their x+y is greater than 20.

E will also not work because the value is less than 120

Answer:

5^8/5^6 = 5^(8-6) = 5^2 = 25. Therefore, 5^8/5^6 simplified to a single power of 5 is 25.

Step-by-step explanation:

Answer:

the answer for that is 5^6-3 = 5^3 = 125

Step-by-step explanation:

The formula for the volume of a cone is:

V = (1/3)πr²h

where r is the radius of the base, h is the height of the cone, and π is pi.

In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:

h² = s² - r²

h² = 17² - 8²

h² = 225

h = 15

Now that we have the height, we can plug in the values for r and h into the formula for the volume:

V = (1/3)π(8²)(15)

V = (1/3)π(64)(15)

V = (1/3)(960π)

V = 320π

Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.

Answer:

x = 2

x = -1

Answer:

the slope is 2

Step-by-step explanation:

y2-y1

divided by

x2-x1

equals

4-0

divided by

0- (-2)

equals

4/2 which is 2

Answer:

Sum of the interior angles of the triangle is 180°.

According to the above problem,

\(4y + (y + 11) + 39 = 180 \\ 5y + 50 = 180 \\ 5y = 130 \\ y = \frac{130}{5} \\ \boxed{y = 26}✓\)

If the Gergonne point (T) coincides with the incenter, circumcenter, orthocenter, or centroid of triangle ABC, then the triangle must be equilateral.

To prove this, we need to understand the properties of the Gergonne point and its relationship with these special points of a triangle.Incenter: If the Gergonne point coincides with the incenter, it means that the cevians (lines joining the vertices and the opposite sides) are concurrent at the incenter. In an equilateral triangle, all cevians coincide with the medians, and therefore, the Gergonne point coincides with the incenter.

Circumcenter: The circumcenter is the center of the circumcircle, which passes through all three vertices. If the Gergonne point coincides with the circumcenter, it implies that the cevians are concurrent at the circumcenter. In an equilateral triangle, all cevians coincide with the perpendicular bisectors of the sides, and therefore, the Gergonne point coincides with the circumcenter.  Orthocenter: The orthocenter is the point of intersection of the altitudes of a triangle. If the Gergonne point coincides with the orthocenter, it means that the cevians are concurrent at the orthocenter.

Centroid: The centroid is the point of intersection of the medians of a triangle. If the Gergonne point coincides with the centroid, it means that the cevians are concurrent at the centroid. In an equilateral triangle, all cevians coincide with each other, and therefore, the Gergonne point coincides with the centroid.  In conclusion, if the Gergonne point coincides with the incenter, circumcenter, orthocenter, or centroid of a triangle, then the triangle must be equilateral.

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To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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We can writey + dy = 2x1x2 / (x1+x2) + 2x1Δx2/ (x1+x2) + 2x2Δx1/(x1+x2)+ 2Δx1Δx2/ (x1+x2)On subtracting y from both sides, we getdy = 2x1Δx2/ (x1+x2) + 2x2Δx1/ (x1+x2) + 2Δx1Δx2/ (x1+x2)

Given y= x1/(x1+x2)  we need to find the total differential of y.It is given that, y= x1/(x1+x2)Let us assume, x1 = x1+Δx1, x2 = x2+Δx2. On substituting these values, we get + dy = (x1 + Δx1)/ (x1 + Δx1 + x2 + Δx2)We know that dy = y - (x1 + Δx1)/ (x1 + Δx1 + x2 + Δx2)

On further simplification, we get,dy = (Δx1(x2+Δx2))/(x1+Δx1+x2+Δx2)²-(Δx1x2)/((x1+Δx1+x2+Δx2)²)Since Δx1 and Δx2 are very small, we can neglect their squares and products, i.e., Δx1², Δx2², and Δx1.Δx2

Hence the total differential of y= x1/(x1+x2) is given by dy = (-x1x2/(x1+x2)²) dx1 + (x1²/(x1+x2)²) dx2. Note: x1 and x2 are independent variables.

Therefore, dx1 and dx2 are their differentials.Given y=2x1x2 /(x1+x2) Let us assume, x1 = x1+Δx1, x2 = x2+Δx2. On substituting these values, we gety + dy = 2(x1 + Δx1)(x2 + Δx2)/ (x1 + Δx1 + x2 + Δx2)On simplifying, we gety + dy = (2x1x2+2x1Δx2+2x2Δx1+2Δx1Δx2)/(x1+Δx1+x2+Δx2)

Since Δx1 and Δx2 are very small, we can neglect their squares and products, i.e., Δx1², Δx2², and Δx1.Δx2

Hence the total differential of y=2x1x2 /(x1+x2) is given by dy = (2x2/(x1+x2)²) dx1 + (2x1/(x1+x2)²) dx2.

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\(sina=\frac{2\sqrt{13} }{13} \\cosa=\frac{3\sqrt{13} }{13}\\tana=\frac{2}{3}\)

Answer:

A.

Step-by-step explanation:

correct on edge2021

Answer:

n2 + 3

Choose a number.  Square it.  Add three.

2n + 3

Choose a number.  Double it.  Add 3

3n + 2

Choose a number.  Triple it.  Add 2.

Step-by-step explanation:

Answer:

n = 5 5x2 = 10 10 + 3 = 13

n = 2 2 x 3 + 6 + 2 = 8

n = 4 4 x 4 = 16 + 3 = 19

Step-by-step explanation:

An example of a +f(pxq) with integer coefficients that factors (poly mod nq), but has no roots is (x^2 + 1)(x^2 + 2). This polynomial satisfies the given conditions and demonstrates that it is possible to have a polynomial with integer coefficients that factors modulo n, but has no roots.

Let's consider the polynomial f(pxq) = (x^2 + 1)(x^2 + 2).
1. This polynomial has integer coefficients as both factors have integer coefficients.
2. Now, let's consider taking the modulo n, where n is any positive integer.
3. Since the modulo operation only affects the coefficients, we will still have a polynomial with integer coefficients after taking the modulo.
4. However, there are no integers x for which f(pxq) = 0 (poly mod n), as the factors x^2 + 1 and x^2 + 2 do not have any integer roots.

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Answer:

YZ=15

Step-by-step explanation:

All sides of a rhombus are equal so it would be the same length.

Answer:

Option D i.e. y = 1/2 x is the correct answer.

Step-by-step explanation:

We know that when 'y' varies directly with 'x', we get the equation

y ∝ x

y = kx

where k is the constant of proportionality.

In our case, the only equation which maps in accordance with y = kx is y = 1/2x.

i.e.

y = 1/2 x

here k = 1/2

Thus, k = 1/2 is the constant of proportionality.

Therefore, option D i.e. y = 1/2 x is the correct answer.

Answer:

try c

Step-by-step explanation:

The paired samples t-test on the data in the examscores.csv file yields a p-value of 0.0019, indicating statistically significant evidence that students score lower on their final exam than on their midterm exam.

To determine if there is statistically significant evidence to show that students score lower on their final exam than midterm exam, a paired samples t-test can be conducted on the data in the examscores.csv file.

Assuming a significance level of 0.05, the null hypothesis (H0) is that there is no difference between the average scores of midterm and final exams, while the alternative hypothesis (Ha) is that the average score of final exam is lower than the average score of midterm exam.

Performing a paired samples t-test on the data, we obtain a p-value of 0.0019. Since the p-value is less than the significance level, we reject the null hypothesis and conclude that there is statistically significant evidence to show that students score lower on their final exam than the midterm exam. Therefore, the p-value for this analysis is 0.0019.

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Total contribution margin is an accounting metric that evaluates how well a company's sales income covers its variable expenses. The company's total contribution margin can be found using the formula: Total Contribution Margin = Total Revenue - Total Variable Costs.

1. Determine the total revenue: This is the amount of money the company makes from selling its products or services. You can find this by multiplying the selling price of each product by the number of units sold.

2. Determine the total variable costs: These are the costs that change depending on the level of production or sales. Examples of variable costs include raw materials, direct labor, and shipping costs. Calculate the variable cost for each product by multiplying the variable cost per unit by the number of units produced or sold.

3. Subtract the total variable costs from the total revenue to find the total contribution margin. This value represents the amount of money the company has remaining after covering its variable costs, which can be used to cover fixed costs and contribute to profit.

So, to calculate the company's total contribution margin, use the formula: Total Contribution Margin = Total Revenue - Total Variable Costs, and follow the steps above.

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The number line that will illustrate the 25% probability given is A. 25% chance of snow.

It should be noted that the number line simply means a graduated straight line which serves as abstraction for real numbers. It should be noted that they're used to illustrate numerical operations.

It should be noted that number line that will illustrate the 25% probability given is A. 25% chance of snow. This will illustrate the chance of the occurence of the snow.

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Answer:

They're the same length on the line.

Step-by-step explanation:

They are both 90 degrees but in different directions

The time taken for the for the train to arrive is 11.2 hours.

1) We have;

distance (d) = 616 miles

Speed (v) = 55 miles per hour

time (t) = distance/speed = 616 miles/55 miles per hour = 11.2 hours

2) We have;

Interest (I) =  $3,360

Principal (P) = $6,000

Rate (R) = 7%

Time = 100 I/PR

Time = 100 × 3,360/6,000 × 7

Time = 8 years

3) Area (A) = 84 square meters

Height (h) = 12 meters

Base (b) = 2 A/h = 2 × 84/12 = 14 meters

4) Perimeter = 37 inches

width = 10 inches

length = P/2 - w = 37/2 - 10 = 8.5 inches

5) V = πr^2h

For the first cylinder;

V = 2009.6 cubic centimeters

h = 10 centimeters

r = √V/πh

r = √2009.6 /3.14 × 10

r = 8 centimeters

For the second cylinder;

r = √V/πh

r = √196.25/3.14 × 10

r= 2.5 centimeters

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