Find the area of this triangle.

Answer:

  f(x) = 3x³ -6x² -21x -12

Step-by-step explanation:

You want a polynomial function that touches the x-axis at x = -1, crosses it at x = 4, and goes through the point (-2, -18).

Each zero (p) of a polynomial corresponds to a linear factor (x -p). If the zero has even multiplicity, the function will not change sign there, but will touch the x-axis and "bounce".

The requirements indicate a factor (x +1) with even multiplicity, and a factor (x -4). The least-degree such polynomial will have the factored form ...

  f(x) = a(x +1)²(x -4)

The value of this polynomial at x = -2 is ...

  f(-2) = a(-2 +1)²(-2 -4) = -6a

We want this to be -18, so ...

  -6a = -18   ⇒   a = 3

Then the factored polynomial is ...

  f(x) = 3(x +1)²(x -4)

When we multiply this out, we get ...

  f(x) = 3x³ -6x² -21x -12

__

Additional comment

The attached graph verifies the desired characteristics.

Answer:

The first graph is (-8,1). The second graph has no solution. The third graph is (1,3). The last graph has infinite solutions. Taking the graphs from left to right.

Step-by-step explanation:

The solution of a graph is determined at where the two lines of the graph intersect. When there is no intersection, but there are two graphs, then there is no solution but when there is only one line in the graph, the graph has infinite solutions.

Answer:

Answer in image

Step-by-step explanation:

Graph 1: Graph 1 is matched with (-8,1) because it intersects the other line only once, and they intersect at (-8,1).

Graph 2: Graph 2 has no solution because the lines never intersect. They're Parallel, and parallel lines never intersect. (We can't conclude they are parallel, but since they do not intersect in the picture, they have no solution.)

Graph 3: Graph 3 is matched with 1 sol. (1,3) because the lines intersect once, and they intersect at (1,3).

Graph 4: Graph 4 is matched with infinitely many solutions because the two lines are the same line. They are on top of each other meaning that at any point on the graph they will always be intersecting.

-Hope this helped

Answer:

x > 6

Step-by-step explanation:

Given

3(x + 4) - 5(x - 1) < 5 ← distribute and simplify left side

3x + 12 - 5x + 5 < 5

- 2x + 17 < 5 ( subtract 17 from both sides )

- 2x < - 12

Divide both sides by - 2, reversing the symbol as a result of dividing by a negative value.

x > 6

To answer this question, we are required to find the first and third quartile for the given data set. The given data set is as follows:3 6 4 18 3 6 4 26 47 5 13 4 7 6 4 49 66.

To find the first and third quartiles, we need to organize the data set in ascending order, which gives:3 3 4 4 4 5 6 6 7 13 18 26 47 49 66. Here, the number of data values is 15. So, we can find the quartiles using the following formula:\(Q1 = (n + 1)/4th termQ3 = 3(n + 1)/4th term\). Let's calculate the first and third quartiles now.

First quartile, Q1 Using the formula, we have\(Q1 = (15 + 1)/4th termQ1 = 4th term\)Now, the fourth term in the ordered data set is 4. Hence,Q1 = 4

Third quartile, Q3 Using the formula, we have\(Q3 = 3(15 + 1)/4th termQ3 = 12th term\) Now, the twelfth term in the ordered data set is 49. Hence,Q3 = 49Therefore, the first and third quartiles for the given data set are 4 and 49 respectively.

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No function f(r,θ) is given, we cannot evaluate the integral further.

To write ∬rfda as an iterated integral in polar coordinates for the given region rr, we need to determine the limits of integration for r and θ.

Let's first look at the region rr. From the given graph, we can see that the region is bounded by the circle with radius 3 centered at the origin. Therefore, we can express the region as:

r ≤ 3

To determine the limits for θ, we need to examine the region rr more closely. We can see that the region is symmetric about the x-axis, which means that the limits for θ are:

0 ≤ θ ≤ π

Now, we can write the iterated integral as:

∬rfda = ∫₀³ ∫₀ᴨ f(r,θ) r dθ dr

where f(r,θ) is the integrand function and r and θ are the limits of integration. Note that r is integrated first, followed by θ.

In this case, since no function f(r,θ) is given, we cannot evaluate the integral further.

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At least 75% of healthy adults have body temperatures within 2 standard deviations: 98.26 °F. Minimum possible body temperature within this range:97.14 °F,maximum possible body temperature:99.38 °F.

Using Chebyshev's theorem, we can determine a lower bound on the percentage of healthy adults with body temperatures within 2 standard deviations of the mean. We can also calculate the minimum and maximum possible body temperatures within this range based on the given mean and standard deviation.

Step 1: Apply Chebyshev's theorem, which states that for any data set, regardless of its shape, at least (1 - 1/k^2) of the data falls within k standard deviations of the mean. In this case, k = 2.

The percentage of healthy adults with body temperatures within 2 standard deviations of the mean is at least (1 - 1/2^2) = (1 - 1/4) = 75%.

Step 2: Calculate the minimum and maximum possible body temperatures within 2 standard deviations of the mean.

Minimum temperature = mean - (2 * standard deviation)

Maximum temperature = mean + (2 * standard deviation)

Substitute the given values: minimum temperature = 98.26 - (2 * 0.56) = 97.14 °F and maximum temperature = 98.26 + (2 * 0.56) = 99.38 °F.

Therefore, at least 75% of healthy adults have body temperatures within 2 standard deviations of 98.26 °F. The minimum possible body temperature within this range is 97.14 °F, and the maximum possible body temperature is 99.38 °F.

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The solutions to the equation (x + 2)(x - 4) = 0 are x = -2 and x = 4.

To solve the equation (x + 2)(x - 4) = 0 using the zero product property, we set each factor equal to zero and solve for x.

Setting (x + 2) = 0:

x + 2 = 0

x = -2

Setting (x - 4) = 0:

x - 4 = 0

x = 4

So the solutions to the equation (x + 2)(x - 4) = 0 are x = -2 and x = 4.

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To achieve the maximum output from his electrical system, Steve should set the input to 6, the x-coordinate of the vertex of the parabola described by the equation \(y = -x^2 + 12x - 20\).

To find the input that will result in the maximum output of the electrical system, we need to find the vertex of the parabola described by the equation \(y = -x^2 + 12x - 20\). The vertex of a parabola is the point where the curve reaches its highest or lowest point, depending on whether the parabola opens upward or downward. In this case, the coefficient of \(x^2\) is negative, which means the parabola opens downward, and the vertex represents the maximum point.

We need to find the vertex of the parabola given by the equation \(y = -x^2 + 12x - 20\). The vertex of a parabola with equation \(y = ax^2 + bx + c\) is given by the formula x = -b/2a.

In this case, a = -1, b = 12, and c = -20, so the x-coordinate of the vertex is:

x = -b/2a = -12/(2*(-1)) = 6

Therefore, the input at which Steve will reach his maximum output is x = 6.

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Answer:

The answer is x = 4

Step-by-step explanation:

1. First you need to distribute the 3/4 * (x + 8). This looks like (3/4) * (x) + (3/4) * (8) = 9

2. Next you simplify the distributed equation, 3/4x + 6 = 9

3. Now subtract 6 from both sides, 3/4x = 3

4. Multiply both sides by 4/3, 4/x * 3/4x = 3 * 4/3

5. Simplify, x = 4

Answer:

D

Step-by-step explanation:

Aaaaaaaaaaaaaaaaaaaa

Answer:

Full drum 80 dollars

one lid missing

earn 10 dollars less

Step-by-step explanation:

We need to find the surface area

SA = 2 pi r^2  + 2 pi rh

The diameter is 2 so the radius = 2/2 =1

SA = 2 * pi * 1^2  + 2 * pi * 1 * 3

      = 2 pi + 6pi

      = 8pi

Using pi = 3.14

SA = 8 *3.14 = 25.12 ft^2

We get 3.18 per ft^2

25.12 * 3.18 =79.88

To the nearest dollar

80 dollars

If one of the lids is missing

SA =  pi r^2  + 2 pi rh

        pi + 6pi

        7 pi

Using pi = 3.14

SA = 7 *3.14 = 21.98 ft^2

We get 3.18 per ft^2

21.98 * 3.18 =69.90

To the nearest dollar

70

The difference is 10 dollars

Answer:

\(\Huge \boxed{\mathrm{a) \ \$ \ 80}} \\\\\\\\ \Huge \boxed{\mathrm{b) \ \$ \ 10}}\)

\(\rule[225]{225}{2}\)

Step-by-step explanation:

Surface area of the cylinder :

2πr² + 2πrh

The diameter is 2 ft, so the radius is 1 ft.

⇒ 2π(1)² + 2π(1)(3)

⇒ 8π ≈ 25.13

$3.18 is getting payed per square foot.

⇒ 25.13 × 3.18

⇒ 79.9221171073 ≈ 80

If the lid was missing:

πr² + 2πrh

π(1)² + 2π(1)(3)

7π ≈ 21.99

$3.18 is getting payed per square foot.

⇒ 21.99 × 3.18

⇒ 69.9318524689 ≈ 70

The difference :

80 - 70 = 10

$10 less if the lid is missing.

\(\rule[225]{225}{2}\)

To find the area between two vectors U and V, we can use the formula:    || U x V || = || U || || V || sin(θ)

where U x V is the cross product of U and V, || U || and || V || are the magnitudes of U and V respectively, and θ is the angle between U and V.

Given U = <2, 1, -3> and V = <1, 5, 0>, we can first find the cross product U x V:

U x V = <(1*(-3) - 51), (-31 - 02), (25 - 1*1)> = <-8, -3, 9>

Next, we calculate the magnitudes of U and V:

|| U || = \(\sqrt{(2^2 + 1^2 + (-3)^2)}\) = \(\sqrt{14}\)

|| V || = \(\sqrt{(1^2 + 5^2+ 0^2) } = \sqrt{26}\)

Now, we can find the angle θ between U and V using the dot product:

cos(θ) = (U · V) / (|| U || || V ||)

= (<2, 1, -3> · <1, 5, 0>) / \((\sqrt{(14)} * \sqrt{(26)})\)

= (-5) / \(\sqrt{14} * \sqrt{(26)}\)

θ = arccos(-5 /\(\sqrt{14} * \sqrt{(26)}\))

Finally, we can calculate the area using the formula:

|| U x V || = || U || || V || sin(θ)

=\(\sqrt{14} * \sqrt{(26)}\) * sin(θ)

Evaluating the expression, we get:

|| U x V || = \(\sqrt{14} * \sqrt{(26)}\) * sin(arccos(-5 /\(\sqrt{14} * \sqrt{(26)}\)))

The exact value of the area depends on the precise value of sin(arccos(-5 / \(\sqrt{14} * \sqrt{(26)}\))), which can be calculated using a calculator.

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The frequency of 1 is option (d) 973

Reselecting cases means selecting a subset of data that meets specific criteria. In this case, you will need to identify which cases to keep based on certain conditions. After reselecting cases, the next step is to define the variable TX + Y. This means that you will perform an operation on two existing variables, T and Y, and create a new variable that is the sum of T and Y. The result will be a numerical variable.

To summarize, you will need to follow these steps:

Reselect cases based on specific criteria.

Define the variable TX + Y as the sum of T and Y.

Recode the numerical variable into a categorical variable with two categories: G-1 İFT <= 10 and G=0 if T>10.

Calculate the frequency of category 1 in the new variable G.

Finally, to answer the question, you will need to calculate the frequency of category 1 in the variable G. This means that there are 973 cases where the value of TX + Y is less than or equal to 10.

The correct answer is option d. 973.

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Answer:

30%

Step-by-step explanation:

Original price (100%) = $130

Discounted price = $91

Discount = 130-91 = $39

$130 = 100%

$1 = 100/130

$39 = 100/130 × 39 = 30 %

% discount = 30%

The simple interest she will have to pay equals R 1275, and the total she will pay equals R 9775 for her TV over the past 3 years.

Thuli wants to buy TV, and a bank offers to loan her the money at an interest rate.

Principal, P = R 8,500

Interest Rate, R = 5%

Time, t = 3 year

Simple interest is defined as an interest charge that borrowers pay their lenders for a loan. It is calculated using the principal only. Formula for SI is written as SI = (P×T×R)/100

Here, SI = Simple interest

P = Principal (sum of money borrowed)

R = Rate of interest p.a

T = Time (in years)

We have to calculate simpled interest she will have to pay also calculate the total she will pay.

So, Simple interest = (8500×3×5)/100

= 85× 15 = R 1275

Now, total she will have to pay = Principle + SI

= 8500 + 1275

= R 9775

Hence, required total she will pay is R9775.

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Answer:

First answer lol

Step-by-step explanation:

is the domain by any chance x ≥-2?

Answer:

Review the images

Step-by-step explanation:

Remember, the "x" is the hypotenuse.

Despite being aware of his impending death, John Steinbeck was engaged in a project to build a house.

During the final stages of his life, John Steinbeck, the renowned American author, was involved in a project to build a house. Despite the knowledge of his terminal condition, he focused his efforts on this endeavor. The act of building a house can be seen as a significant undertaking that requires planning, coordination, and dedication.

While specific details about the house project are not provided, it can be inferred that Steinbeck's involvement in this venture reflected his enduring spirit and determination, even in the face of his impending mortality. Building a house is a symbol of creation, stability, and leaving a lasting legacy. It is a testament to Steinbeck's unwavering passion for life and his commitment to pursue meaningful endeavors until the very end.

Although Steinbeck's literary contributions are widely celebrated, his engagement in the house-building project during his final days showcases his multidimensional nature and his desire to leave a tangible mark on the world. It serves as a reminder of the resilience of the human spirit and the power of pursuing personal projects and dreams, even in challenging circumstances.

In conclusion, despite being aware of his impending death, John Steinbeck dedicated his time and energy to a project of building a house, showcasing his determination and commitment to leaving a lasting legacy.

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Answer:

x = 10

Step-by-step explanation:

The secant- secant angle 3x is half the difference of the intercepted arcs, that is

3x = \(\frac{1}{2}\) (4x + 50 - 30 )

3x = \(\frac{1}{2}\) (4x + 20) = 2x + 10 ( subtract 2x from both sides )

x = 10

The area of the polygon is 80 units².

What is a Polygon?

A polygon is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides.

Dividing the polygon into parts marked in the attached figure so as to calculate the area easily.

For triangle, DEF

Area = \(\frac{1}{2} bh\)

        = \(\frac{1}{2}\) × 3 × 4

       = 6 units²

For triangle BCD

Area = \(\frac{1}{2}bh\)

        = \(\frac{1}{2}\) × 2 × 4

        = 4 units²

For trapezoid ABFG,

Area = \(\frac{1}{2} (a + b) h\)

        = \(\frac{1}{2}\) × (5.5 + 12) × 8

        = 70 units²

Hence, total area = 6 + 4 + 70

                             = 80 units².

Therefore, the total area of the polygon is 80 units².

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The correct rule to describe the function g as a function of f and gives the correct rule is that g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

The correct rule to describe the function

g(x) = 3f(x)

in terms of the function f(x) = x³-2x²+7x-11 is that

g(x) = 3(x³-2x²+7x-11) and thus

g(x) = 3x³-6x²+21x-33.

In order to obtain the function g(x) from the given function f(x), it is necessary to multiply it by a constant, in this case 3.

Therefore, g(x) = 3f(x) means that g(x) is three times f(x).

Thus, we can obtain g(x) as follows:

g(x) = 3f(x) = 3(x³-2x²+7x-11) = 3x³-6x²+21x-33

Therefore, the correct rule to describe the function g as a function of f and gives the correct rule is that

g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

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The perimeter of a pentagon is equal to the sum of the lengths of all its sides. If the perimeter of the pentagon is 58 units, we can set up an equation to solve for z:

11 + 2z + 32 - 2 + 10 + 2 + 3 = 58

Simplifying the equation:

60 + 2z = 58

Subtracting 60 from both sides:

2z = -2

Dividing both sides by 2:

z = -1

So, the value of z is -1.

Answer:

D

Step-by-step explanation:

Answer:

y=2x+4

Step-by-step explanation:

From(0,4)

Equation in slope intercept form

Answer:

-3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

4x + 2y = 12

x − y = 3

Make it able to cancel the variable y.

x*2 − y*2 = 3*2

2x − 2y = 6

Add the equations together now that y can be canceled out. Add each like term of the separate equations together.

   4x + 2y = 12

+  2x − 2y = 6

   6x + 0 =  18

6x = 18

6      6

x = 3

I hope this helps!

Answer:

π 36 m^2

Step-by-step explanation:

C = 2π R = 12π m --> R = 6m

A = π R^2 = π 36 m^2

Answer:

Step-by-step explanation:

In the question we are given that circumference of circle is 12π m . And we are asked to find the area of circle in term of π .

Solution : -

For finding area of circle we need to find the radius of circle . In the question circumference of circle is given . So we can find radius of circle using it . We know that ,

\( \qquad \quad \pink{\underline{\pink{\boxed{\frak{Circumference_ {(Circle) }= 2\pi r}}}}}\)

Where ,

But as in the question , it is given that we have to find the area in term of π. So we aren't using π as 3.14 or 22/7 .

Now, Radius :

\( \longrightarrow \qquad \: 12 \cancel{\pi }= 2 \cancel{\pi} r\)

Step 1 : Cancelling π and we get :

\( \longrightarrow \qquad \:12 = 2r\)

Step 2 : Dividing both sides by 2 :

\( \longrightarrow \qquad \: \cancel{\dfrac{12}{2} } = \dfrac{ \cancel{2}r}{ \cancel2} \)

On further calculations we get :

\( \longrightarrow \qquad \: \boxed{ \bf{r = 6 \: m}}\)

Finding Area :

As we have find the radius of circle above so we can find its area easily . We know that ,

\( \qquad \: \qquad \pink{\underline{\pink{ \boxed{{\frak{ Area_{(Circle)} = \: \pi r {}^{2} }}}}}}\)

Now substituting value of radius :

\( \longmapsto \: \qquad \quad\pi (6) {}^{2} \)

\( \longmapsto \: \qquad \quad \pi \times \: 6 \times 6\)

\( \longmapsto \: \qquad \quad \pi \times 36\)

We get :

\( \longmapsto \: \qquad \quad \blue{\underline{\blue{\boxed{\frak{ \bf{36 \pi \: m {}^{2} }}}}}}\)

Answer:

13/b I think

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

If ( x + 5) is a factor of p(x) then p(- 5) = 0

p(- 5)

= (- 5)³ + 4(- 5)² + 2(- 5) + 35

= - 125 + 100 - 10 + 135

= 0

Since p(- 5) = 0 then (x + 5) is a factor of p(x)

Answer:

(x +5 ) is a factor

Step-by-step explanation:

x + 5 = 0

x = -5

P(x) = x³ + 4x² + 2x + 35

P(-5) = (-5)³ + 4*(-5)² + 2*(-5) + 35

      = -125 + 4*25 - 10 + 35

     = -125 + 100 - 10 + 35

     = -25 -10 +35

     = -35 + 35

    = 0

P(-5) = o. So, (x +5 ) is a factor