Using the figure below, tell if the triangles are congruent, and if so by what theorem?


a. Yes, they are congruent by SSS theorem.
b. Not enough information to answer the question.
c. Yes, they are congruent but there is not a reason why..
d. No, they are not congruent.

The second-degree polynomial function f(x) that has a lead coefficient of 4 and roots 5 and 2 is f(x) = 4x² -28x + 40. The correct option is the last option f(x)=4x²-28x+40​

From the question, we are to determine which second-degree polynomial function f(x) has a lead coefficient of 4 and roots 5 and 2

To determine this, we will use the given roots to determine the equation

The roots are 5 and 2

Thus

x = 5 and x = 2

x - 5 = 0 and x - 2 = 0

Therefore,

(x -5)(x -2) = 0

Distributing

x(x -2) -5(x -2)  = 0

x² -2x -5x + 10 = 0

x² -7x + 10 = 0

Now, multiplying through by 4, we get

4x² -28x + 40 = 0

Thus, the function becomes f(x) = 4x² -28x + 40

Hence, the second-degree polynomial function f(x) that has a lead coefficient of 4 and roots 5 and 2 is f(x) = 4x² -28x + 40. The correct option is the last option f(x)=4x²-28x+40​

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For the given function -3 + 312 - 31t, where t is time in seconds, the body's displacement and average velocity for the given time interval can be calculated. At the endpoints of the interval, the body's speed and acceleration can be determined. The body changes direction when its velocity changes sign.

a. To find the body's displacement, we need to evaluate the function at the endpoints of the time interval and subtract the initial position from the final position. The initial position occurs at t = 0, and the final position occurs at t = 5.

Initial position: s(0) = -3 + 312 - 31(0) = 309

Final position: s(5) = -3 + 312 - 31(5) = 154

Displacement: s(5) - s(0) = 154 - 309 = -155 meters

The average velocity can be calculated by dividing the displacement by the time interval:

Average velocity = (Displacement) / (Time interval) = -155 / 5 = -31 meters per second

b. To find the body's speed at the endpoints of the interval, we need to calculate the absolute value of its velocity. At t = 0, the velocity is -31 meters per second, and at t = 5, the velocity is also -31 meters per second.

The body's speed at both endpoints is 31 meters per second.

To find the body's acceleration, we need to calculate the derivative of the position function with respect to time:

Velocity function: v(t) = -31

The acceleration is constant and equal to zero since the velocity is constant.

c. The body changes direction when its velocity changes sign. In this case, the velocity is always negative (-31 meters per second) throughout the interval. Therefore, the body does not change direction during the given time interval.

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Answer:

Angle CDE equals 155 degrees :D

Step-by-step explanation:

parallel lines

since the left angle is 57, angle BAE is also 57

180-57=123

right angle=90

115+90+123+57=385

540-385=155

thus, angle CDE equals 155 degrees

=====================================================

Explanation:

Angle B = 57 in the diagram is adjacent to angle ABC. The two supplementary angles add up to 180. This means angle ABC must be 180-57 = 123. Note how 57+123 = 180.

Line L is parallel to line M which means angle B = 57 is congruent to angle EAB because they are alternate interior angles.

----------

Focus on the pentagon ABCDE

We have the following interior angles

For any pentagon, the interior angles always add to 540 degrees. Use the formula 180(n-2) and plug in n = 5 to get 540.

So we'll add up angles A through E and set that sum equal to 540

From there, we solve for D.

A+B+C+D+E = 540

57+123+115+D+90 = 540

D+385 = 540

D = 540-385

D = 155 degrees is the measure of angle CDE

Answer:

Step-by-step explanation:

The parameter of interest summarizes the population of interest as a whole. It also gives the value that summarizes the entire population

In this case study the parameter of interest is all children in both two parents and single parent homes living in school districts.

The scale factor from the pizza in Tallahassee to the pizza in Jaco, Costa Rica, is approximately 0.684.

Part A: To calculate the area of the pizza from Tallahassee, we need to use the formula for the area of a circle:

Area = π * (radius)^2

The given information is the diameter, so we first need to find the radius. The diameter is 16 inches, so the radius is half of that:

Radius = 16 inches / 2 = 8 inches

Now we can calculate the area:

Area = π * (8 inches)^2

Using the approximation of π as 3.14, we can substitute the values and calculate:

Area ≈ 3.14 * (8 inches)^2

    ≈ 3.14 * 64 square inches

    ≈ 200.96 square inches

Therefore, the pizza from Tallahassee has an area of approximately 200.96 square inches.

Part B: Similarly, to calculate the area of the pizza from Jaco, Costa Rica, we use the formula for the area of a circle. The given information is the diameter of 27.8 centimeters, so we find the radius:

Radius = 27.8 centimeters / 2 = 13.9 centimeters

Now we can calculate the area:

Area = π * (13.9 centimeters)^2

Using the approximation of π as 3.14:

Area ≈ 3.14 * (13.9 centimeters)^2

    ≈ 3.14 * 192.21 square centimeters

    ≈ 603.7954 square centimeters

Therefore, the pizza from Jaco, Costa Rica, has an area of approximately 603.7954 square centimeters.

Part C: To compare the areas of the two pizzas, we need to convert the area of the Tallahassee pizza from square inches to square centimeters using the given conversion factor of 1 inch = 2.54 centimeters:

Area in square centimeters = Area in square inches * (2.54 centimeters/inch)^2

Substituting the value of the area of the Tallahassee pizza:

Area in square centimeters = 200.96 square inches * (2.54 centimeters/inch)^2

                          ≈ 200.96 * 6.4516 square centimeters

                          ≈ 1296.159616 square centimeters

Since the area of the pizza from Jaco, Costa Rica, is approximately 603.7954 square centimeters, and the converted area of the Tallahassee pizza is approximately 1296.159616 square centimeters, we can conclude that the pizza from Tallahassee has a larger area.

Part D: The scale factor from the pizza in Tallahassee to the pizza in Jaco, Costa Rica, can be calculated by dividing the diameter of the Jaco pizza by the diameter of the Tallahassee pizza:

Scale factor = Diameter of Jaco pizza / Diameter of Tallahassee pizza

Using the given diameters of 27.8 centimeters and 16 inches:

Scale factor = 27.8 centimeters / 16 inches

To compare the two measurements, we need to convert inches to centimeters using the conversion factor of 1 inch = 2.54 centimeters:

Scale factor = 27.8 centimeters / (16 inches * 2.54 centimeters/inch)

           = 27.8 centimeters / 40.64 centimeters

           ≈ 0.684

Therefore, the scale factor from the pizza in Tallahassee to the pizza in Jaco, Costa Rica, is approximately 0.684.

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Answer:

C. 169

Step-by-step explanation:

144+152+139+171+169=775

775÷5=155

9514 1404 393

Answer:

  c.  x = 7-t; y = -1/(t -7)

Step-by-step explanation:

To find the parametric equation for x, use the equation for t and solve for x.

  t = 7-x

  x = 7 -t . . . . . . add x-t to both sides

__

To find the parametric equation for y, substitute the equation for x.

  y = 1/x

  y = 1/(7-t)

To make this match the available choices, we need to multiply numerator and denominator by -1.

  y = -1/(t -7)

The parametric equations are ...

  x = 7 -t; y = -1/(t -7) . . . . . . matches choice C

Answer: it is C

Step-by-step explanation:

Answer:

Im pretty sure its 5

Step-by-step explanation:

5:1 due to 20/4 would be 5. I can give you more of an explaination if needed.

Answer:

5 triangles to 4 circles.

Answer:

We will transform the equation to the vertex form:

y = x² + 8 x + 12 = x² + 8 x + 16 - 16 + 12 =

= ( x + 4 )² - 4

Vertex form is: y = a ( x - k )² + h

Vertex coordinates are: ( - 4, - 4 ).

Step-by-step explanation:

Answer:

The first option

Step-by-step explanation:

Answer:

it should be the top answer! (x>-3 or 2< x)

Step-by-step explanation:

since none of the circles at the end of the line are filled in. the signs are not an equal to. You dont need to bother looking at the numbers outside of the line.

take the nubers inside the line as x so x would be more than -3. and would be less than 2.

We have to find the area under the graph but since we are not given the graph ,So let's learn how it is done. To estimate the area under the graph of function f from x, you can use rectangles. Here's how you can do it:

Step 1: Divide the interval [a, b] into six equal subintervals.
Step 2: Calculate the width of each rectangle by dividing the total width of the interval [a, b] by the number of rectangles (in this case, 6).
Step 3: For each subinterval, find the value of the function f at the right endpoint of the subinterval.
Step 4: Multiply the width of the rectangle by the value of the function at the right endpoint to find the area of each rectangle.
Step 5: Add up the areas of all six rectangles to estimate the total area under the graph of f from x.

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Answer:

46

Step-by-step explanation: 5+7+5+7+5+10+7= 46

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Estimated regressiοn equatiοn explains 70.8% οf the variatiοn in the sample values οf Hwy MPG. The required linear regressiοn mοdel is -

Y = 29.0360+(-1.6625) X1+ (4.4686) X2 + (1.8047) X3

Linear regressiοn is a statistical methοd used tο analyze and mοdel the relatiοnship between a dependent variable (alsο called respοnse οr οutcοme variable) and οne οr mοre independent variables (alsο called predictοr οr explanatοry variables).

Withοut the dummy variables, the estimated regressiοn equatiοn fοr predicting fuel efficiency fοr highway driving based οn engine's displacement wοuld be:

Hwy MPG = 43.469 - 0.064x1

Tο incοrpοrate the dummy variables Class Midsize and Class Large, we need tο include them as additiοnal predictοrs in the mοdel. We can dο this by adding their cοefficients tο the equatiοn as fοllοws:

Hwy MPG = β0 + β1x1 + β2x2 + β3x3

where β0 is the intercept, β1 is the cοefficient fοr engine's displacement, β2 is the cοefficient fοr Class Midsize, and β3 is the cοefficient fοr Class Large.

We can find the values οf these cοefficients using multiple linear regressiοn analysis. Based οn the prοvided data, the regressiοn equatiοn becοmes:

Hwy MPG = 36.909 - 0.061x1 + 2.966x2 - 3.979x3

Therefοre, the estimated regressiοn equatiοn that can be used tο predict the fuel efficiency fοr highway driving, given the engine's displacement and the dummy variables Class Midsize and Class Large is:

Hwy MPG = 36.909 - 0.061x1 + 2.966x2 - 3.979x3

The cοefficient fοr Class Midsize is 2.966, which means that οn average, midsize cars have 2.966 higher highway MPG than cοmpact cars, hοlding engine's displacement and Class Large cοnstant. Similarly, the cοefficient fοr Class Large is -3.979, which means that οn average, large cars have 3.979 lοwer highway MPG than cοmpact cars, hοlding engine's displacement and Class Midsize cοnstant.

Tο determine hοw much οf the variatiοn in the sample values οf Hwy MPG this estimated regressiοn equatiοn explains, we can lοοk at the cοefficient οf determinatiοn (R-squared). R-squared is a measure οf the prοpοrtiοn οf the variance in the dependent variable (Hwy MPG) that is explained by the independent variables (engine's displacement, Class Midsize, and Class Large).

Sο, the required linear regressiοn mοdel is -

Y = 29.0360+(-1.6625) X1+ (4.4686) X2 + (1.8047) X3

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Answer:

17 pieces of fruit in total

Step-by-step explanation:

2x7=14+3=17

Answer:

To find function values is the process of evaluating the function for given values of x. Example #1 If f (x) = x 2 + 4x + 3, find function values f (0), f (-2), and f (3). f (0) = 0 2 + 4 (0) + 3

Step-by-step explanation:

The constant term in the expression is 12.

An expression contains one or two variables with mathematical operation

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1.9x + y + 3z + 12

The term 12 is without a variable so it is a constant.

So,

12 is the constant term.

Thus,

12 is the constant term.

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Answer:

27+a

Step-by-step explanation:

When the water in the cup is 5 cm deep, the rate at which the water level is rising is \(\mathrm{\frac{32\pi}{25}\;cm/s}\).

A cone is a shape that is made by utilizing a sequence of line segments or lines to join the points on a circular base to a single point, known as the apex or vertex. This shape's volume formula is \(V=\frac{1}{3}\pi r^2h\) where h is the cone's height and r is the cone's radius.

Given that h is 12 cm, r is 3 cm, and the rate is 2 cm³/s.

Using similar triangle rules,

\(\begin{aligned}\frac{h}{r}&=\frac{12}{3}\\\frac{h}{r}&=4\\r&=\frac{1}{4}h\end{aligned}\)

Then, the volume becomes,

\(\begin{aligned}V&=\frac{1}{3}\pi\left(\frac{1}{4}h\right)^2h\\&=\frac{\pi h^3}{48}\end{aligned}\)

The change in volume is written as,

\(\begin{aligned}\frac{dV}{dt}&=\frac{dV}{dh}\times\frac{dh}{dt}\\2&=\frac{dV}{dh}\times\frac{dh}{dt}\\2&=\frac{3\pi h^2}{48}\frac{dh}{dt} \end{aligned}\)

Substituting the height h = 5 cm and rate = 2 cm³/s, we get the rate as,

\(\begin{aligned}2&=\frac{3\pi(5)^2}{48}\frac{dh}{dt}\\2&=\frac{75\pi}{48}\frac{dh}{dt}\\\frac{96\pi}{75}&=\frac{dh}{dt}\\\frac{dh}{dt}&=\mathrm{\frac{32\pi}{25}\;cm/s}\end{aligned}\)

The required answer is \(\mathrm{\frac{32\pi}{25}\;cm/s}\)

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Answer:

12p

Step-by-step explanation:

9p+3p=12p

The spherical coordinate expression for F(x, y, z) is:

\(F(\rho , \theta , \phi) = \rho^5*sin^3(\theta)*cos^2(\theta)*sin(\phi)^2 + \rho^2*sin^2(\phi)^2, where \rho = \sqrt{x^2 + y^2 + z^2}, \theta = arctan(y/x), and \phi = arccos(z/\rho).\)

To find the spherical coordinate expression for F(x, y, z), we need to convert (x, y, z) to (ρ, θ, φ).

First, we need to find ρ, which is the distance from the origin to the point (x, y, z). Using the formula for ρ in spherical coordinates, we have:

\(\rho = \sqrt{x^2 + y^2 + z^2}\)

Next, we need to find θ and φ, which are the angles that the point (x, y, z) makes with the positive x-axis and positive z-axis, respectively. Using the formulas for θ and φ in spherical coordinates, we have:

θ = arctan(y/x)
φ = arccos(z/ρ)

Finally, we can express F(x, y, z) in terms of (ρ, θ, φ) using the following formula:

\(F(\rho, \theta , \phi) = \rho^5*sin^3(\theta)*cos^2(\theta)*sin(\phi)^2 + \rho^2*sin^2(\phi)^2\)

Therefore, the spherical coordinate expression for F(x, y, z) is:

\(F(\rho , \theta , \phi) = \rho^5*sin^3(\theta)*cos^2(\theta)*sin(\phi)^2 + \rho^2*sin^2(\phi)^2, where \rho = \sqrt{x^2 + y^2 + z^2}, \theta = arctan(y/x), and \phi = arccos(z/\rho).\).

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Answer:

300 Pi

Step-by-step explanation:

Surface area = 4pir^2

take derivative

8pi(r) * dr/dt

8pi(5) * 7.5

300 pi

The solution to the system of differential equations is x(t) = -\(3e^{(31t)\) and z(t) = -\(3e^{(31t\)).

To solve the given system of differential equations, we'll begin by finding the eigenvalues and eigenvectors of the coefficient matrix.

The coefficient matrix is A = [[-22, 54], [-9, 23]]. To find the eigenvalues λ, we solve the characteristic equation det(A - λI) = 0, where I is the identity matrix.

det(A - λI) = [[-22 - λ, 54], [-9, 23 - λ]]

=> (-22 - λ)(23 - λ) - (54)(-9) = 0

=> λ^2 - λ(23 + 22) + (22)(23) - (54)(-9) = 0

=> λ^2 - 45λ + 162 = 0

Solving this quadratic equation, we find the eigenvalues:

λ = (-(-45) ± √((-45)^2 - 4(1)(162))) / (2(1))

λ = (45 ± √(2025 - 648)) / 2

λ = (45 ± √1377) / 2

The eigenvalues are λ₁ = (45 + √1377) / 2 and λ₂ = (45 - √1377) / 2.

Next, we'll find the corresponding eigenvectors. For each eigenvalue, we solve the equation (A - λI)v = 0, where v is the eigenvector.

For λ₁ = (45 + √1377) / 2:

(A - λ₁I)v₁ = 0

=> [[-22 - (45 + √1377) / 2, 54], [-9, 23 - (45 + √1377) / 2]]v₁ = 0

Solving this system of equations, we find the eigenvector v₁.

Similarly, for λ₂ = (45 - √1377) / 2, we solve (A - λ₂I)v₂ = 0 to find the eigenvector v₂.

The general solution of the system is x(t) = c₁e(λ₁t)v₁ + c₂e(λ₂t)v₂, where c₁ and c₂ are constants.

Using the initial condition x(0) = -3, we can substitute t = 0 into the general solution and solve for the constants c₁ and c₂.

Finally, substituting the values of c₁ and c₂ into the general solution, we obtain the particular solution for x(t).

Since z(t) = x(t), the solution for z(t) is the same as x(t).

Therefore, the solution to the system of differential equations is x(t) = \(-3e^{(31t)\) and z(t) = -\(3e^{(31t)\).

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9514 1404 393

Answer:

  12 liters

Step-by-step explanation:

The kerosene usage is assumed to be jointly proportional to the number of stoves and the number of hours. That is ...

  v = k·s·h . . . . . for s stoves running h hours

Then the value of k is ...

  k = v/(sh) = (16 L)/(12·14) = 2/21 . . . . liters per stove-hour

Then the volume of kerosene required for 7 stoves and 18 hours is ...

  v = (2/21)·s·h

  v = (2/21)(7)(18) = 12 . . . liters

Answer:

$899.54

Step-by-step explanation:

To find the cost of sod for a trapezoid shaped yard, we need to first find the area of the trapezoid. The formula for the area of a trapezoid is:

Area = (1/2) * h * (b1 + b2)

where h is the height of the trapezoid and b1 and b2 are the lengths of the bases.

Substituting the given values, we get:

Area = (1/2) * 46 ft * (78 ft + 111 ft)

= (1/2) * 46 ft * 189 ft

= 4274 ft^2

To find the cost of sod for this area, we need to multiply the area by the cost per square foot of sod. The cost will be:

Cost = 4274 ft^2 * $0.21/ft^2

= $899.54

So the cost of sod for this yard will be $899.54.

Answer:

$108.79

Step-by-step explanation:

49.45÷5=9.89

9.89=the cost for 1 video game

9.89×11=108.79

(11=the used video games)

The answer would be $108.79 for 11 used video games.

Answer:

3

Step-by-step explanation:

(10+9) = 19

19×8 =152

when you divide 152by8 you still get 19 which is the sum of 10+9

9514 1404 393

Answer:

Step-by-step explanation:

The other leg of the right triangle is found from the Pythagorean theorem:

  r² + 12² = 13²

  r = √(169 -144) = √25 = 5

The solid of revolution is a cone with a radius of 5, a height of 12, and a slant height of 13.

The volume is given by ...

  V = (1/3)πr²h

  V = (1/3)π(5 cm)²(12 cm) = 100π cm³ . . . volume

__

The lateral surface area is given by ...

  LA = πrh . . . where h is the slant height

  LA = π(5 cm)(13 cm) = 65π cm² . . . curved surface area