7. A trapezoid has an area of 77 square feet. The longer base of a trapezoid measures 13 ft and the height measures 7 ft. What is the length of the shorter base?​

The length of side KL is approximately 4.8 cm.

To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all sides of the triangle. In other words:

a/sin(A) = b/sin(B) = c/sin(C)

Where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides.

Using the Law of Sines, we can set up the following proportion:

l/sin(L) = m/sin(M)

Where l is the length of side KL, L is the measure of angle KLM (which is 72 degrees), m is the length of side LM, and M is the measure of angle KML (which we can find by subtracting L from 180 degrees).

M = 180 - L

= 180 - 72

= 108 degrees

Now we can substitute the given values into the proportion and solve for l:

l/sin(72) = 5.9/sin(108)

l = sin(72) * (5.9/sin(108))

≈ 4.8 cm (rounded to the nearest 10th of a centimeter)

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Answer:

9.75

Step-by-step explanation:

-25 = -4p + 19

-25 - 19 = -4p

-39 ÷ -4 = p

9.75 = p

Answer:

26%

Step-by-step explanation:

Answer:

192

Step-by-step explanation:

1 Pound = 16 Ounces

So 16 (ounces) x 12 (dollars) = 192 (ounces)

16 x 12 = 192

Answer:

  1 1/3 ounces

Step-by-step explanation:

The weight you can purchase is proportional to the amount you want to spend. There are 16 ounces in a pound.

Where x is the quantity you can buy with $1, the proportion is ...

  (16 oz)/($12) = x/$1

  4/3 oz = x . . . . . . . . . multiply by $1. The amount you can buy with $1.

1 1/3 ounces can be bought with $1.

Answer:

It would be 40 Orange Juice cup

Step-by-step explanation:

Cause 12 times 5 would equal 60

So if you times 5 and 8 it would be 40

Answer:

24 chickens, 4 roosters, 20 more chickens then roosters

Step-by-step explanation:

Answer:

24 chickens

28 total chickens and roosters

there are 20 more chickens than roosters

Step-by-step explanation:

4 x 6 = 24 chickens

24+4= 28 total

24-4= 20 more chickens

Answer:

Your answer is correct.

Step-by-step explanation:

Answer:

The answer should be 64.21 or 64

Step-by-step explanation:

Help this Helped

The maximum displacement is 5 centimeters.

The time required for one oscillation is π seconds.

The frequency is 1 / π Hz.

Equation to model the motion of the object is x(t) = 5 × cos(2t)

The maximum displacement from equilibrium can be determined by observing that the object is pulled down 5 centimeters from its rest position.

In simple harmonic motion, the amplitude represents the maximum displacement from equilibrium.

The period of oscillation is given as π seconds.

The period (T) is the time required for one complete oscillation.

The frequency (f) is the reciprocal of the period and represents the number of oscillations per unit time.

Thus, the frequency is the inverse of the period: f = 1 / T.

To model the motion of the object, we can use the equation for simple harmonic motion:

x(t) = A×cos(ωt + φ)

A = 5 centimeters (maximum displacement),

T = π seconds (period),

f = 1 / π Hz (frequency).

To find ω, we can use the relation ω = 2π / T:

ω = 2π / π = 2 radians/second.

The equation to model the motion of the object is:

x(t) = 5 × cos(2t)

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Answer:

True

Step-by-step explanation:

I'm pretty sure it true, sry if it's not

Answer:

884.4

Step-by-step explanation:

Answer:

The original price is 895.12$

I haven't done percent in ages, lmk if you get it right
kudos to any other answer besides this

Step-by-step explanation:

Answer:

0,2

Step-by-step explanation:

The value of the car after 3 years is $79, 000

To determine the value, we have to use the formula;

Value = Initial value × (1 - Depreciation rate)ⁿ

Substitute the values given, we get;

Remaining value after 3 years = $100,000 × (1 - 0.10)³

Expand the bracket, we get;

Value after 3 years = $100,000 × (0.90)³

Find the cube value and substitute, we have;

Value after 3 years = $100,000 × 0.729

Multiply the values, we have;

Value after 3 years = $72,900

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Answer:

the answer is d

Step-by-step explanation:

Given:

Foci: (-3, -1) and (5, -1)

Vertices: (-2, -1) and (4, -1).

Find: equation of the hyperbola in standard form

Solution:

As we can see in the coordinates of both its foci and vertices, they all lie on the same y-coordinate which is at -1. Therefore, the transverse axis of this hyperbola is parallel to the x-axis.

The pattern of the equation of the hyperbola in standard form parallel to the x-axis is:

where (h, k) is the center of the hyperbola.

Now, to determine the center of the hyperbola, we use the coordinates of the vertices. The center of the hyperbola is located at the center of the two vertices.

Between x = -2 and x = 4, the center is 1. Hence, the center of the hyperbola is located at (1, -1). Hence, h = 1 and k = -1.

In a hyperbola, "a" is the distance from the center to the vertex. The distance between 1 and 4 is 3. Therefore, the value of "a" is 3.

In a hyperbola, "c" is the distance from the center to the focus. The distance between 1 and 5 is 4. Therefore, the value of "c" is 4.

To determine the value of "b", we can use the formula below:

Let's replace "a" and "c" in the formula with the values that we have calculated.

Therefore, the value of "b" is √7.

Going back to the pattern of the equation of the hyperbola in standard form, let's plug in the value of h = 1, k = -1, a = 3, and b = √7.

Then, simplify.

The standard equation of the hyperbola with the given properties is:

Answer: To confuzing

Step-by-step explanation:

The area of the circle with the given radius is 201.088 square units.

The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr², where r is the radius of the circle.

Given that, the radius of a circle is 8 units.

Here, area of a circle

= 3.142×8²

= 3.142×64

= 201.088 square units

Therefore, the area of the circle is 201.088 square units.

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Answer:

A Linear

B Quadratic

C Quadratic

D Linear

Step-by-step explanation:

The measurement of the given angle is a 90 degree.

According to the statement

We have to find that the measurement of this angle.

So, For this purpose, we know that the

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

From the given information:

In the given figure, the measurement of the angle we have to find.

A 90-degree angle is a right angle and it is exactly half of a straight angle. It always corresponds to a quarter turn.

And from the figure it is clearly visible that the line of the angle exactly matches with the 90 degree.

Then the angle is 90 degree.

So, The measurement of the given angle is a 90 degree.

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After answering the provided question, we can state that As a result, 145.62 square feet of glass are required to cover the entire pyramid.

A pyramid is a polygon formed by connecting points known as bases and polygonal vertices. For each hace and vertex, a triangle known as a face is formed. A cone with a polygonal shape. A pyramid with a floor and n pyramids has n+1 vertices, n+1 vertices, and 2n edges. Every pyramid is dual in nature. A pyramid contains three dimensions. A pyramid is made up of a flat tri face and a polygonal base that come together at a single point known as the vertex. A pyramid is formed by connecting the base and peak. The base's edges form triangle faces known as sides that connect to the top.

To determine how much glass is required to cover the entire pyramid, we must first determine the total surface area of the pyramid, including the base.

The formula for calculating the surface area of each triangular face is:

(1/2) x width x height

27.31 square feet = (1/2) x 7 feet x 7.79 feet

24 square feet = (1/2) x 6 feet x 8 feet

Simply multiply the length and width to find the area of the rectangular base:

7 feet by 6 feet equals 42 square feet

As a result, the total surface area of the pyramid is:

145.62 square feet = 2 (27.31 square feet) + 2 (24 square feet) + 42 square feet

As a result, 145.62 square feet of glass are required to cover the entire pyramid.

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Answer: 102.53

Step-by-step explanation:  I calculated all the numbers you gave me and then added them to get 102.53

Answer:

the answer is the second choice

Step-by-step explanation:

A truth table deconstructs a logic function by outlining all possible outcomes the function might achieve.

A truth table offers a way to map out the potential truth values in an expression and predict their results. The table has a row for each conceivable combination of truth values and a column for each variable in the expression. There is also a column that displays the results of each set of values.

For propositional logic formulations, this tool builds truth tables. There are numerous formats available for entering logical operators. As an illustration, the propositional formula p q r could be represented as p / q -> r, p and q => not r, or p && q ->!r. You can enter the connectives and as T and F.

P Q (Q ∧ P)

F F F

F T F

T F F

T T T

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Answer:

Using the slope-intercept form, the slope is 2 2 .

Step-by-step explanation:

The equation of a perpendicular line to y=2x+4 y = 2 x + 4 must have a slope that is the negative reciprocal of the original slope.

The Solution for the given system of equations is (-2) and \((\frac{5}{3})\).

The given are linear equations as follow:
y = \(\frac{2}{3}x\) + 3              .. ... ...(1)
and x  = -2.          .. .... ...(2)

We already know the first part of the solution (x) which is -2.  We can find the other part (y) by putting the value of equation (2) in equation (1).

By putting the values of x in equation (1), we get

y = \((\frac{2}{3})(-2)\) + 3
y = \(\frac{-4}{3}\) + 3

Taking the L. C. M of denominators which will be '3', we get:

y = \(\frac{-4 + 9}{3}\)

y = \(\frac{5}{3}\)

So the second part (y) of the solution of the given equation is \(\frac{5}{3}\).

Hence, the overall solution to the given system of equation is \((-2, \frac{5}{3})\).

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The simultaneous equations 2x + y = 6 and x + y/2 = 3 are dependent because both equations are the same and they have an infinite number of solutions that satisfy both equations.

A system of simultaneous equations is called dependent if it has infinitely many solutions. In other words, one equation in the system can be obtained by adding or subtracting multiples of the other equation(s), or if all the equations represent the same line or plane in higher dimension.

We can write the equations as:

2x + y = 6...(1)

x + y/2 = 3...(2)

equation (2) can be rewritten as follows:

(2x + y)/2 = 3 {simplifying the left hand side to a single denominator}

2x + y = 2 × 3 {cross multiplication}

2x + y = 6

We can observe that equations (1) and (2) are the same. Any value of x and y that satisfies the equation 2x + y = 6 will also satisfy the second equation, x + y/2 = 3.

In conclusion, the simultaneous equations 2x + y = 6 and x + y/2 = 3 are dependent because both equations are the same, hence they have an infinite number of solutions that satisfy both equations.

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9514 1404 393

Answer:

  (c)  (4, 3)

Step-by-step explanation:

The next step in the solution of System B is to divide by 15 1/2. This will result in the equation ...

  x = 4

The only answer choice that has x = 4 is the ordered pair (4, 3). That ordered pair is the solution to the system.

__

  (15 1/2)x = 62   ⇒   (31/2)x = 124/2   ⇒   x = (124/2)/(31/2) = 124/31 = 4

Answer:

c

Step-by-step explanation:

got it right on the test

The coordinate of the point after transformation is: (3, -4)

The coordinate initially is given as (0, -4).

Moving one unit to the left means a deduction of 1 unit from the x coordinate to get:

(0 - 1, -4)

= (-1, -4)

Moving by 4 units to the right means an addition of 4 units to x coordinate to get:

(-1 + 4, -4)

= (3, -4)

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Answer:

\( \frac{9}{10} \times 54 = \frac{9 \times 54}{10} = \frac{486}{10} = 48 \frac{6}{10} = \frac{243}{5} \)

The answer for it is diagram B because it does not cross or have parallel lines