5c+4 = 2 (c – 5)
What is the solution?

C. Triangles A and B are similar.

To find out the similar triangles, we should check if their corresponding angles are congruent and their corresponding sides are proportional.

Triangle A angles = 67° and 23°, and the third angle must be 90° (since the angles in a triangle add up to 180°). So, we shall use the Pythagorean theorem to find the length of the third side:

\(\sqrt(13^2 - 5^2)\) = \(\sqrt144\)) = 12

So, the side lengths of Triangle A are 5, 12, and 13.

Triangle B angles = 67° and 37°, 3rd angle = 76°. We will use the Law of Sines to find the length of 3rd side:

10/sin(67°) = 20/sin(76°)

sin(76°) = (20sin(67°))/10 = 2sin(67°)

sin(76°)/sin(23°) = 2sin(67°)/sin(23°) = 2(5/13) = 10/13

So, the side lengths of Triangle B are 10, 20, and 13*(10/13) = 10.

Triangle C's side lengths 26, 23, and 24. We can use the Law of Cosines to find its angles:

cos(A) = (23² + 24² - 26²)/(22324) = 25/46

A = cos⁻¹(25/46) ≈ 56.8°

In the same way, let's find the other angles of Triangle C:

cos(B) = (24² + 26² - 23²)/(22426) ≈ 63.2°

cos(C) = (23² + 26² - 24²)/(22326) ≈ 60.0°

Triangle C's angles are ≈ 56.8°, 63.2°, and 60.0°.

Now we check the triangles that are similar:

A. Triangles A and C are not similar because they have no congruent angles or proportional sides.

Same goes to B. Triangles A, B, and C.

But C. Triangles A and B are similar because they have congruent angles of 67°.

We can check if their sides are proportional:

5/10 = 1/2

12/20 = 3/5

13/10 = 1.3

So, the sides of Triangle A are proportional to the sides of Triangle B with a ratio of 1:2:1.3.

D. Triangles B and C are not similar, have no congruent angles or proportional sides.

Therefore, triangles A and B are similar.

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The required surface area of the rectangular box with square base is equals to 768 square inches

Let us consider the side length of the square base of the box be x inches.

And the height of the box be h inches.

Volume of the box is 2,048 cubic inches, we have,

V = x^2 × h

⇒x^2 × h = 2,048

Minimum surface area of the box,

A = x^2 + 4xh

To minimize A, we can use the volume equation to eliminate h in terms of x.

Solving for h, we get,

⇒ h = 2,048/x^2

Substituting this value of h into the equation for A, we get,

A = x^2 + 4x(2,048/x^2)

Simplifying the above equation, we get,

A = x^2 + 8,192/x

Minimum value of A,

Take the derivative of A with respect to x, set it equal to zero, and solve for x,

⇒ dA/dx = 2x - 8,192/x^2 = 0

⇒ 2x = 8,192/x^2

⇒x^3 = 4,096

⇒x = 16

Minimum surface area of the box is,

A = 16^2 + 4(16)(2,048/16^2)

   = 768 square inches

Therefore, the minimum surface area of the box is 768 square inches.

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The particular solution is y(t) = -2 * e^(-4t) * cos(3t) - (8/3) * e^(-4t) * sin(3t).

The given differential equation is y′′ + 8y′ + 25y = 0, with initial conditions y(0) = -2 and y′(0) = 20.

To determine the behavior of the solutions, we can consider the characteristic equation associated with the differential equation: r^2 + 8r + 25 = 0.

By solving this quadratic equation, we find two complex conjugate roots: r = -4 + 3i and r = -4 - 3i.

The general solution of the differential equation is then given by y(t) = c1 * e^(-4t) * cos(3t) + c2 * e^(-4t) * sin(3t), where c1 and c2 are constants determined by the initial conditions.

Using the given initial conditions, we can find the particular solution. Substituting t = 0, y(0) = -2 gives c1 = -2. Substituting t = 0, y′(0) = 20 gives c2 = -8/3.


The behavior of the solutions is oscillating with decreasing amplitude. The exponential term e^(-4t) causes the amplitude to decrease over time, while the trigonometric terms cos(3t) and sin(3t) cause the oscillation.

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The number of cups of vinegar that Mike used lies between the whole numbers 2 and 4

If Mike used one cup of vinegar for each salad dressing recipe, then he used a total of 3 cups of vinegar (1 cup x 3 recipes = 3 cups).

However, the question states that he used "a cup of vinegar" in each recipe, which could mean that he used slightly less than one cup, exactly one cup, or slightly more than one cup.

Assuming that Mike used at least 3/4 cup of vinegar in each recipe (which is still close to "a cup"), then he used a minimum of 2 and 1/4 cups of vinegar in total (3/4 cup x 3 recipes = 2 and 1/4 cups).

Assuming that Mike used at most 1 and 1/4 cups of vinegar in each recipe (which is still close to "a cup"), then he used a maximum of 3 and 3/4 cups of vinegar in total (1 and 1/4 cups x 3 recipes = 3 and 3/4 cups).

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Since KI = KE and IT = IE, KITE is a kite, Kites are two sets of quadrilaterals with identical adjacent edges.

KE = √17

IT = 3√5

TE = 3√5

A kite is a quadrilateral having reflection symmetry across a diagonal in Euclidean geometry.

A kite has two equal angles and two pairs of adjacent equal-length sides as a result of its symmetry.

The name "deltoids" can also refer to a deltoid curve, an unrelated geometric object that is occasionally studied in relation to quadrilaterals.

Kites are also known as deltoids. If a kite is not convex, it may alternatively be referred to as a dart.

So, the quadrilateral KITE's vertices are K(0, -2), I(1, 2), T(7,5), and E. (4,-1).

Using the formula for distance:

KE = √(-1 - (-2))² + (4 - 0)² = √17

IT = √(5 - 2)² + (7 - 1)² = 3√5

TE = √(-1 -5)² + (4 - 7)² = 3√5

Therefore, since KI = KE and IT = IE, KITE is a kite, Kites are two sets of quadrilaterals with identical adjacent edges.

KE = √17

IT = 3√5

TE = 3√5

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Answer:

the statement is not true 0 is not equal to 125

Step-by-step explanation:

The flowerpot goes approximately 0.056448 meters (or 5.6448 cm) above the top of the window.

To determine the height above the window top that the flowerpot reaches, we can use the concept of projectile motion. Since the flowerpot goes up and then down, we can assume it follows a parabolic trajectory.

Let's break down the problem and calculate the height:

Given:

Total time in view (t): 0.48 s

Height of the window (H): 2.12 m

Since the flowerpot goes up and then down, the total time can be divided into two equal halves: the time going up and the time going down. Thus, each half of the time will be t/2 = 0.48 s / 2 = 0.24 s.

We can use the formula for vertical displacement in projectile motion:

Vertical displacement (Δy) = (1/2) × acceleration (a) × time (t)²

Since the acceleration due to gravity (g) acts downwards, we have:

Acceleration (a) = -g, where g ≈ 9.8 m/s²

Now let's calculate the height above the window top:

Calculate the displacement while going up:

Δ\(y_{up}\) = (1/2) × (-g) × (t/2)²

Δ\(y_{up}\) = (1/2) × (-9.8 m/s²) × (0.24 s)²

Calculate the displacement while going down:

Δ\(y_{down}\) = (1/2) × (-g) × (t/2)²

Δ\(y_{down}\) = (1/2) × (-9.8 m/s²) × (0.24 s)²

Calculate the total height above the window top:

Height above window top = Δ\(y_{up}\) + Δ\(y_{down}\)

Now let's substitute the values into the equations and calculate the height:

Δ\(y_{up}\)  = (1/2) × (-9.8 m/s²) × (0.24 s)²

Δ\(y_{up}\)  = -0.028224 m

Δ\(y_{down}\) = (1/2) × (-9.8 m/s²) × (0.24 s)²

Δ\(y_{down}\) = -0.028224 m

Height above window top = Δ\(y_{up}\)  + Δ\(y_{down}\)

Height above window top = -0.028224 m + (-0.028224 m)

Height above window top = -0.056448 m

Therefore, the flowerpot goes approximately 0.056448 meters (or 5.6448 cm) above the top of the window.

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You would need to represent the table's legs and support structure as beams, compute the plywood's load-bearing capacity, and figure out the maximum weight the table can hold before breaking in order to solve this problem.

Determining the ideal tabletop dimensions for a given surface area is another potential quadratic equations challenge.

Let's assume that the width of the table is x feet, then its length would be 2x feet. The perimeter of the table would be:

P = 2(width + length)

P = 2(x + 2x)

P = 6x

The legs would be placed 6 inches from the corners, so the length of the tabletop would be reduced by 1 foot (12 inches) on each side. Thus, the length and width of the table would be:

Length = 2x - 2(1 ft)

= 2x - 2

Width = x - 2(1 ft) = x - 2

The area of the table would be:

A = Length x Width

A = (2x - 2)(x - 2)

A = \(2x^2 - 6x + 4\)

dA/dx = 4x - 6

4x - 6 = 0

x = 1.5

Substituting x = 1.5 into the area function, we get:

A = 2\((1.5)^2\) - 6(1.5) + 4

A = 1

Therefore, the maximum area of the table is 1 square foot, and the dimensions of the tabletop should be 3 feet by 6 feet to achieve this maximum area.

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Correct Question:

Design or make a sketch plan of a table made out of a 3/4 inch by 4 feet by 8 feet plywood, and 2 inches by 3 inches by 8 feet plywood. Using your design or sketch plan, show the solutions in your formulated problems involving quadratic equations.

it will cost #150 to have a party with 9 people, and it will cost #260 to have a party with 20 people

Graph is attached:

What is Piecewise function?

A piecewise function is used to relate multiple functions at different intervals

The cost for 9 people

This means that:

n=9

When n = 9, the cost function is:

C(9)=150

Hence, it will cost #150 to have a party with 9 people

The cost for 20 people

This means that:

n=20

When n = 20, the cost function is:

C(20)=260

Hence, it will cost #260 to have a party with 20 people

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Answer: 8575/2

Step-by-step explanation:

Answer:

Her mean quiz score is 92.25%.

Answer:

92.25

Step-by-step explanation:

Mean is the same as average. Add all the scores together and then decide by the number of scores.

(92+94+100+83)÷4

369÷4=92.25

Answer: Rotation

Step-by-step explanation:

From the figure , we can observe that both figure A and b are absolutely congruent.

To translate a figure to make congruent images , we use rigid motions (Translation, Reflection, Rotation)

It is Rotation because of we move Figure A 180 degrees clockwise about the fixed point O, we will get Figure B .

It cannot be reflection because both figures are not mirror images.

It cannot be translation because all points on Figure A is not moving , as point O remained at same position throughout this which is not possible in translation.

The BMW 7 series car loses 72.6% of its value in 5 years, so after 8 years, the car will have depreciated further. Using exponential decay, the car's value can be estimated to be $19,444.15 after 8 years.

To solve for the value of the BMW 7 series after 8 years, we can use the formula for exponential decay:

A = P * e^(-rt)

where A is the final amount, P is the initial amount, r is the rate of decay, and t is the time. In this case, the initial amount P is $86,000 and the rate of decay r is 72.6% over 5 years, or 0.726/5 = 0.1452 per year. We want to find the value after 8 years, so t is 8.

Plugging these values into the formula, we get:

A = $86,000 * e^(-0.1452*8)

A = $19,444.15

Therefore, the BMW 7 series car will be worth approximately $19,444.15 after 8 years, assuming the rate of depreciation remains constant. However, it's important to note that this is just an estimate and the actual value could vary based on factors such as the condition of the car and market demand.

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The value of x in quadrilateral cdef inscribed in circle is (b) 44.

To find the value of x, we can use the property that opposite angles in an inscribed quadrilateral are supplementary (their measures add up to 180°).

Given that quadrilateral CDEF is inscribed in circle A, we have:

m∠CFE + m∠CDE = 180°

Substituting the given angle measures:

(2x + 6)° + (2x - 2)° = 180°

Combining like terms:

4x + 4 = 180

Subtracting 4 from both sides:

4x = 176

Dividing both sides by 4:

x = 44

Therefore, the value of x is 44.

The correct answer is:

b. 44

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The radius of the spherical part is 3 inches and the length of the tube is 21 cm.

The capacity of a cylinder, which determines how much material it can hold, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, can be immersed in it uniformly.

Given that the volume when the water is fully dipped is 4554 / 7 cm³. The volume when the length is 9 cm empty is 396 cm³.

The two equations can be formed as below:-

4554 / 7 = πr²l + (2/3)πr³

396 = πr²( l - 9 ) + (2/3)πr³

Subtract the second equation from the first,

( 4554 / 7 ) - 396 = 9πr²

9πr² = 254.5

r² = 9

r = 3 cm

The length will be calculated as:-

4554 / 7 = πr²l + (2/3)πr³

4554 / 7 = π( 3 )²l + (2/3)π(3)³

l = 21 cm

Therefore, the tube's length is 21 cm, and the spherical part's radius is 3 inches.

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(a) The amount of time she has walked (in hours) when she is x kilometers from Newbury Heights.

(b)  \(D^{-1}(x) = \frac{(10.4 - x)} {4}\). (c) \(D^{-1}(5.2) = 1.3\).

(a) The statement that best describes \(D^{-1}(x)\) is:

The amount of time she has walked (in hours) when she is x kilometers from Newbury Heights.

(b) To find \(D^{-1}(x)\), we need to solve the equation for t in terms of x. We can rewrite the original equation as:

x = 10.4 - 4t

Now, let's isolate t:

4t = 10.4 - x

t = (10.4 - x) / 4

Therefore, \(D^{-1}(x) = \frac{(10.4 - x)} {4}\).

(c) To find \(D^{-1}(5.2)\), we substitute x = 5.2 into the equation we found in part (b):

\(D^{-1}(5.2) = \frac{ (10.4 - 5.2)}{4}\\D^{-1}(5.2) = \frac{ 5.2}{4} \\D^{-1}(5.2) = 1.3\)

Therefore, \(D^{-1}(5.2) = 1.3\).

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The complete question:

Kira is walking. D(t), given below, is her distance in kilometers from Glenn City after t hours of walking.

D(t) = 10.4 - 4t

a) Which statement best describes \(D^{-1}(x)\)?

a.  Her distance from Newbury Heights (in kilometers) after she has walked x hours.

b. The ratio of the amount of time she has waked (in hours) to her distance from Newbury Heights (in kilometers),

c. The reciprocal of her distance from Newbury Heights (in -kilometers) after walking x hours.

d. The amount of time she has walked (in hours) when she is x kilometers from Newbury Heights.

b) \(D^{-1}(x)\) =

c) \(D^{-1}(5.2) =\)

For triangle BCD, the measure of segment:

1) CD = 64 units

2) CE = 26 units

3) HD = 33 units

4) GD = 29 units

5) HG = 15.75 units

6) HF = 8.1 units

Here, H is the circumcenter of ΔBCD

We know that the circumcenter of a triangle is nothing but the point where the perpendicular bisectors of three sides of that triangle intersect.

This means that EH, FH and GH are perpendicular bisectors of three sides of ΔBCD

We know that a perpendicular bisector always divides a line segment through its midpoint.

So, for side CB, CE = EB

Here, EB = 26 units

⇒ CE = 26 units

and, CB = CE + EB

CB = 26 + 26

CB = 52 units

Similarly, for side CD of triangle BCD:

CF = FD

here, FD = 32 units

⇒ CF = 32 units

And CD = CF + FD

⇒ CD = 64 units

Similarly, for side BD of triangle BCD:

BG = GD

Here, BD = 58 units

So, GD = 1/2 (BD)

GD  = 29 units

Now, we can observe that ΔCHD is an isosceles triangle.

So, CH = HD

⇒ HD = 33 units

In triangle GHD using Pythagoras theorem,

HG = \(\sqrt{HD^2-GD^2}\)

HG = \(\sqrt{33^2-29^2}\)

HG = 15.75 units

Similarly, in triangle CFH using Pythagoras theorem,

HF = \(\sqrt{HC^2-FC^2}\)

HF = \(\sqrt{33^2-32^2}\)

HF = 8.1 units

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Find the complete question below.

Answer:

Yes and no.  It depends on how you set up the problem.  You can set it up as an addition or a subtraction problem.  As a subtraction problem you would use zero pairs, but it you rewrote the expression as an addition problem then you would not need zero pairs.

Step-by-step explanation:

You can:

You can add 7 zero pairs.

_ _ _ _ _ _ _ _ _ _ _  The 4 negative and 7 zero pairs.  

            + + + + + + +

I added 7 zero pairs because I am told to take away 7 positives, but I do not have any positives so I added 7 zero pairs with still gives the expression a value to -4, but I now can take away 7 positives.  When I take the positives away, I am left with 11 negatives.

_ _ _ _ _ _ _ _ _ _ _.

I can rewrite the problem as an addition problem and then I would not need zero pairs.

- 4 - 7 is the same as -4 + -7  Now we would model this as

_ _ _ _

_ _ _ _ _ _ _

The total would be 7 negatives.

Answer:

\(x=6.25\)

Step-by-step explanation:

FM=3.2x

JG=40

Generally the diagonal of a rectangle are equal to each other and diagonal bisects each other

Therefore

\(2FM=JG\)

\(2*(3.2x)=40\)

\(x=40/6.4\)

\(x=6.25\)

Answer:

x=6.25

Step-by-step explanation:

Using area of the rectangle, we can find that the new flower garden will be 13m in length (greater dimension).

The formula for calculating a rectangle's area can be used to determine how much space the rectangle takes up within its perimeter. Multiplying the length by the width yields the area of a rectangle (breadth).

As a result, the following formula can be used to determine the area of a rectangle whose length and breadth are "l" and "w," respectively. The rectangle's area is L × W. A rectangle's area is therefore equal to length * width.

Now here the dimensions of the rectangle are, l = 13m and b, = 9m.

Area of the rectangle is 13 × 9 = 117m².

Now the area of the rectangle is increased to 221m².

So, when we increase the length from 13 m to 17m and the breadth from 9m to 13m, we get area = 17 × 13 = 221m².

Therefore, length of the new garden will be 17m long.

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Answer:x = 12,5

using thales's theorem, we have:

\(\frac{15}{15+36}=\frac{20}{6x-7}\\\\<=> 6x-7=\frac{20.(15+36)}{15}=68\\\\<=>x = \frac{68+7}{6}=12.5\)

Step-by-step explanation:

Given :-

To find :-

Solution :-

As we know that ,

Substitute ,

Answer:16/20 equals 4/5

Step-by-step explanation:they are asking what is the probability that it is green so we know that 16 counters is green and total counters is 20 so it’s 16/20 and then you simplify it the answer is 4/5

The statistical technique that provides a numerical estimate of the maximum/worst loss that could be expected in a given time period with a given level of confidence or probability is value at risk (VaR).

VaR is commonly used in risk management to measure potential losses in financial portfolios or investments. It quantifies the amount of potential loss, typically expressed in monetary terms, that a portfolio may experience over a specified time horizon and at a certain level of confidence.

It helps investors and risk managers assess and control the potential downside risk associated with their investments. VaR takes into account the distribution of returns and the desired level of confidence to estimate the potential downside risk. Standard deviation and coefficient of variation are not direct measures of maximum loss but are related to risk assessment.

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Answer:

yes

Step-by-step explanation:

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hope it helps

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Answer:

Step-by-step explanation:

using the pemdas method

121-1= 120

57*120= 6840-120= 6720

Answer:

It's B

Step-by-step explanation:

Functions can be represented by tables and equations

The function represented by the table is f(x) = x + 1

From the table, we have the following ordered pairs

(x,y) = (-1,0) (0,1) (1,2) and (2,3)

Notice that the difference between the x and y values is 1.

So, we have:

y - x = 1

Add 1 to both sides

y = x + 1

Express as a function

f(x) = x + 1

Hence, the function represented by the table is f(x) = x + 1

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