Write and solve an equation to find the value of x and the missing angle measures.

A rectangle is similar to another rectangle if its corresponding angles are congruent, and its sides are proportional.

To check if 11 and 14 could be the side lengths of a similar rectangle, we can set up the proportion:

10/14 = 11/x

Simplifying this proportion, we get:

5/7 = 11/x

Multiplying both sides by x, we get:

5x/7 = 11

Multiplying both sides by 7/5, we get:

x = 77/5

So, 11 is not a possible side length for a similar rectangle with side lengths 10 and 14.

Similarly,

To find the side lengths of a similar rectangle, we can set up a proportion:

10/14 = x/21

Simplifying this proportion, we get:

5/7 = x/21

Multiplying both sides by 21, we get:

x = 15

So, the side lengths of the similar rectangle are 15 and 21.

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Answer:

a = 0.9

Step-by-step explanation:

For the quadratic equation \(\boxed{ax^2 + bx + c = 0}\) to have exactly one real root, the value of its discriminant, \(\boxed{b^2 - 4ac}\), must be zero.

For the given equation:

\(y = ax^2 - 6x + 10\),

• a = a

• b = -6

• c = 10.

Substituting these values into the formula for discriminant, we get:

\((-6)^2 - 4(a)(10) = 0\)

⇒ \(36 - 40a = 0\)

⇒ \(36 = 40a\)

⇒ \(a = \frac{36}{40}\)

⇒ \(a = \bf 0.9\)

Therefore the value of a is 0.9 when the given quadratic has exactly one root.

Answer:

Step-by-step explanation:

Diameter of the Circle refer to a line passing through the centre and meets the circumference at opposite ends. And it twice as long as Radius.

1)   Radius is given  3yd

so, diameter is  double of radius  2*3=6yd

Radius= 3yd

Diameter=6yd

2)   Diameter is given  92 in

so, radius is half of diameter  92/2=  46 inch

Radius= 46 in

Diameter= 92 in

3)    Radius is given 23 ft

so, diameter is double of radius 23*2 = 46 ft

Radius = 23 ft

Diameter = 46 ft

4)   Diameter is given 36 in

so, radius is half of diameter 36/2 = 18 in

Radius = 18 in

Diameter = 36 in

5) Radius is given 19 ft

so, diameter is double of radius 19*2 = 38 ft

Radius = 19 ft

Diameter = 38 ft

6) Diameter is given 12yd

so, radius is half of diameter  12/2 = 6yd

Radius = 6yd

Diameter = 12yd

Answer:

Step-by-step explanation:

Using the pythagorean theorem, we can solve to find C.

a^2 + b^2 = c^2

So it will be 15^2 + 20^2 = c^2

Simplify:

225 + 400 = c^2

625 = c^2

Square root both sides of the equation and you will get:

25 = c

c = 25

(a) The length of the unknown side is 25 yd

For perimeter, just add 20 + 15 + 25

(b) So the perimeter is 60 yd

The formula for area of a triangle is:

Area = (Base x Height) / 2

Now, we can plug in the numbers.

Base = 15

Height = 20

(15 x 20) / 2

300 / 2

= 150

(c) The area of the triangle is 150yd^2

Answer:

C,D,E,F

Step-by-step explanation:

A amplitude is 2

B period is 4pi

Answer:

f option is write

Step-by-step explanation:

because it is true

mark me brainlist

where r = 19 feet, h = 40 feet, and θ varies from 0 to 8π (4 complete revolutions) as t varies from 0 to 4.

An equation is a mathematical statement that shows the equality of two expressions, which are separated by an equals sign (=). An equation can have variables, constants, coefficients, and operators. The variables are represented by letters, and their values can change depending on the context of the problem. The constants are fixed values, and the coefficients are the numbers that multiply the variables. The operators are mathematical symbols that indicate the operation to be performed, such as addition (+), subtraction (-), multiplication (*), division (/), and exponentiation (^). Solving an equation means finding the value(s) of the variable(s) that satisfy the equation.

Given by the question.

Let's start by defining the necessary parameters. The radius of the staircase is given as 19 feet, and the height is given as 40 feet. The staircase makes 4 complete revolutions, so the total height of the staircase is 4 times the height of one revolution, which is 40 feet.

To find a vector parametric equation for the helical path, we need to consider the circular motion around the center axis, as well as the motion along the axis. Let's define the following parameters:

r: radius of the staircase (19 feet)

h: height of one revolution (40 feet)

θ: angle of rotation around the center axis (in radians)

z: height along the center axis

The circular motion around the center axis can be described by the following parametric equation:

x = r cos(θ)

y = r sin(θ)

z =???

To find the equation for z, we need to consider the motion along the center axis. Since it takes one hour to stroll up one revolution, and there are 4 revolutions in total, the time it takes to stroll up the entire staircase is 4 hours. Therefore, we can use t as a parameter that varies from 0 to 4, and define z as:

z = (h/4) t

Note that we divide h by 4 to scale the parameter t to the interval [0,4].

Putting it all together, the vector parametric equation for the helical path is:

r(t) = <r cos(θ), r sin(θ), (h/4) t>

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The total cash due at signing is $3,700 at the local dealership..

The addition operation in mathematics adds values on each side of the operator.

For example 4 + 2 = 6

The total cash due is calculated as:

Down payment: $1,800

Security deposit: $400

Acquisition fee: $300

Total: $1,800 + $400 + $300

Apply the addition operation, and we get

= $3,700

Thus, the total cash due at signing is $3,700.

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Answer:

144

Step-by-step explanation:

\(x^2+24x +144\\\\=x^2 + 2\cdot 12x +12^2\\\\=(x+12)^2\)

Answer:

20°

Step-by-step explanation:

Step 1:

x + 40° = 3x       Vertical ∠'s

Step 2:

40° = 2x      Subtract x on both sides

Step 3:

x = 40° ÷ 2     Divide

Answer:

x = 20°

Hope This Helps :)

Answer:

y-1= -1/3(x+3)

Step-by-step explanation:

y-y1=m(x-x1)

y-1=m(x+3)

the slope is rise over run

the slope is -1/3

Answer:

y - 1 = 3/2 (x + 3)

Step-by-step explanation:

To find the equation of a line parallel to the given line and passing through the point (-3, 1), we can use the point-slope form of a linear equation. The point-slope form is given by:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is the given point and m is the slope of the line.

First, let's calculate the slope of the given line using the two points (-2, -4) and (2, 2):

slope = (y₂ - y₁) / (x₂ - x₁)

= (2 - (-4)) / (2 - (-2))

= 6 / 4

= 3/2

Since the line we want to find is parallel to the given line, it will have the same slope. Therefore, the slope (m) of the new line is also 3/2.

Now we can substitute the values into the point-slope form using the point (-3, 1):

y - 1 = (3/2)(x - (-3))

y - 1 = (3/2)(x + 3)

The equation in point-slope form of the line parallel to the given line and passing through the point (-3, 1) is:

y - 1 = 3/2 (x + 3)

Answer:

the sole proprietor is personally liable for damages the injured woman is awarded by the courts.

Step-by-step explanation:

The value of the given expression is 2

According to the rule;

P is parenthesis

E is exponent

D is division

M is the multiplication

A is addition

S is subtraction

Given the expression below;

-4.(4+2)+234 divide by 9

For the parenthesis

-4(6)+234 ÷ 9


D is for division

-4(6)+234 ÷ 9

-4(6)+26

Expand to have:

-24 + 26

Take the sum to have:

-24+26 = 2

Hence the value of the given expression is 2

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Answer:

see multiply the input by twos and subtract three from the result to get the output

Step-by-step explanation:

\(f(x) = 2x - 3\)

\(y = 2x - 3\)

Answer:-(-1,026/3

Step-by-step explanation:

The difference in volume between the two boxes would be = 156in³

To calculate the difference in volume between the boxes is the find the individual volume of the boxes using the formula ;

Volume = length×width×height.

For box 1 = length = 12in, width = 7¾in, height= 2in

Vol = 12×7¾×2 = 186in³

For box 2; length = 3⅔in, width = 3½in, height= 2⅓in

Volume = 3⅔×3½×2⅓ = 30

The difference = 186-30 = 156in³

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One can be able to  test to see if a diagram made using digital tools is a construction or just a drawing based on estimation by:

Digital Construction is known to be a term that connote  the act of using digital technologies to be able to make construction to be more better and  with higher quality.

Note that  a lot of the new technologies have been seen to have proven themselves and gives  a lot of opportunities for the construction,

In the use of the digital tools, one can Construct a line or a line segment and then uses the move tool to drag some points around, and then watch to see what happens.

Therefore,  One can be able to  test to see if a diagram made using digital tools is a construction or just a drawing based on estimation by:

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It will take the acrobat 1/4 of a second to land safely on the net.

Velocity is a physical quantity that measures the rate at which an object moves in a particular direction. It is measured in terms of distance traveled per unit of time, usually expressed in terms of meters per second (m/s). Velocity is a vector quantity, meaning it has both a magnitude and a direction. It is an important concept in physics and is used to understand the motion of objects and forces.
The quadratic equation representing the height h of the acrobat t seconds after the jump can be written as follows: \(h=-16t^2+4t+25\).
To find the time it takes for the acrobat to land safely on the net, we need to solve for t when h=5. We can do this by substituting 5 for h into the equation and solving for t:
\(h=-16t^2+4t+25\\\\5=-16t^2+4t+25\\\\=-16t^2+4t-20=0\\\\(4+\sqrt{64})/(-32)=t\\ \\t=(4+8)/(-32)\\\\t=1/4\)
Therefore, it will take the acrobat 1/4 of a second to land safely on the net.
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Answer:

x = 7, y = 2

Explanation:

equations given:

x + 7y = 21

x + 4y = 15

make "x" the subject:

x + 7y = 21

x = 21 - 7y .........equation 1

x + 4y = 15

x = 15 - 4y .......equation 2

Solving both the equations simultaneously:

15 - 4y = 21 - 7y

-4y + 7y = 21 - 15

3y = 6

y = 6 ÷ 3

y = 2

If y is 2

Then x = 21 -7y;

x = 21 - 7(2)

x = 21 - 14

x = 7

x + 7y= 21

7 goes to RHS = X+ y = 21/7-3

x + 4y = 15

4 goes to RHS= x+y = 15/4 = 3.75

Answer:

20°

Step-by-step explanation:

Formula given  C= 5(F-32)

                                  9

We know that F= 68

We can now change the F to 68

C= 5(68-32) ⇒ C= 5(36)   ⇒  C= 180 or 5X36

        9                      9                          9

Now we divide 180 by 9.

C= 20°

Best of luck!

The temperature of 68°F in degrees Celsius is 20 degrees Celsius.

Temperature is given at 68°F and we need to convert the temperature into degrees Celsius using the given formula.

We will use this formula:

\(C =( F - 32 ) \times \frac{5}{9}\)

to convert Fahrenheit into degrees Celsius and vice versa.

Applying the above formula.

We have,

F = 68

Substituting in the formula we get,

\(C =( 68 - 32 ) \times \frac{5}{9}\)

\(C = 36 \times \frac{5}{9}\\C=4\times5\\C = 20\)

Thus we have C = 20 degrees Celsius.

The temperature of 68° F in degrees Celsius is 20 degrees Celsius.

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Answer:

hxbcncncncncncn

Step-by-step explanation:

hhjncnnfnf

Answer:

D, \(\frac{7(x-4)}{6}\)

Step-by-step explanation:

Basically you have to simplify the (x² - 16). Since it is the difference of 2 squares, it's simplified as (x + 4)(x - 4). Now that everything is simplified, you can start doing the multiplication.

\(\frac{(x+4)(x-4)}{6x} *\frac{7x}{(x+4)}\), You can cancel out the (x+4)'s

\(\frac{(x-4)}{6x} *{7x}\), There is a common factor between 7x and 6x. The common factor is x. So cancel out both "x".

You end up with this, \(\frac{7(x-4)}{6}\)

a) The angle swept out  since kelsey started skiing: 1.1498 radians

b) The distance Kelsey skied:  3.334 km

In this question, we have been given Kelsey is skiing along a circular ski trail that has a radius of 2.9 km. she starts at the 3-o'clock position and travels in the ccw direction. kelsey stops skiing when she is 1.185 km to the right and 2.647 km above the center of the ski trail.

Consider the following figure for reference.

We need to find the angle θ and the distance kelsey skied (i.e., the arc length)

Here, the horizontal distance x = 1.185 km and the vertical distance y = 2.647 km

a. the tangent of angle θ would be,

tan(θ) = y/x

tan(θ) = 2.647/1.185

tan(θ) = 2.2337

θ = arctan(2.2337)

θ = 65.88°

θ = 1.1498 radians

b. The length of the arc is:

s = rθ

s = 2.9 * 1.1498

s = 3.334 km

Therefore, a) the angle swept out : 1.1498 radians

b) the distance Kelsey skied:  3.334 km

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Answer:

250

Step-by-step explanation:

because 147 rounded is 150 14 is 10 and 85 is 90 these added together are 250

Answer:

7.010 if it's wrong im sorry

Answer:

Explanation:

Here, we want to get the value of the slope of the line that is perpendicular to the given line

The first condition to understand is that the second line is perpendicular to the first

When two lines are perpendicular, the product of their slopes is equal to -1

Mathematically, let us call the slope of the second line m2

Thus:

According to the Empirical Rule, 99.7% of the measures fall within 3 standard deviations of the mean in the normal distribution.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

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The independent variable in this data is the speed of the car. This is because the congressman is trying to determine whether or not the gas mileage improves at lower speeds.

The dependent variable is the gas mileage, because it is the variable that is being measured and that is affected by the independent variable.

The other variables in this data are the weight of the car, the type of engine, and the year of the car. However, these variables are not being changed in this experiment, so they are not considered to be independent variables.

The data shows that the gas mileage of the Toyota Camry improves as the speed of the car decreases. This supports the claim of the supporters of the bill to reduce the speed limit.

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Answer:

Step-by-step explanation:

Let x represent the amount loaned at 14%. Then the total interest earned is ...

  0.14x +0.12(33,500 -x) = 4,370

  0.02x = 350 . . . . . . . . . . subtract 4020 and simplify

  x = 17500 . . . . . . . . . divide by 0.02

The amount loaned at 12% is $33,500 -17,500 = $16,000.

  $17,500 was loaned at 14%

  $16,000 was loaned at 12%