the perimeter of a rectangle is twice the sum of its length and width. The perimeter is 34 meters and its length is 2 meters more than twice its width. What is its length? ...?

Answer:

Option B is the correct answer.

Step-by-step explanation:

Refer the the figure below of the question given.

The height of radio tower = CD

CD = AD - AC

We have

       [tex]tan46=\frac{AD}{AB}\\\\AD=ABtan46=67tan46\\\\tan36=\frac{AC}{AB}\\\\AC=ABtan36=67tan36\\\\CD=67tan46-67tan36=20.70m[/tex]

Option B is the correct answer.

''90 feet in 2.5 hours'' have fastest speed.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

There are some distances and time.

Now,

For Option A;

⇒  18 feet in 20 minutes

Since, We know that;

⇒ Speed = Distance / Time

               = 18/20

               = 0.9 feet per minutes

For Option B;

⇒  90 feet in 2.5 hours

⇒ 90 feet in 150 minutes

Since, We know that;

⇒ Speed = Distance / Time

               = 90/150

               = 0.6 feet per minutes

For Option C;

⇒  20 yards in 1.5 hours

Since, 1 yards = 3 feet

⇒ 60 feet in 90 minutes

Since, We know that;

⇒ Speed = Distance / Time

               = 60/90

               = 0.67 feet per minutes

For Option D;

⇒  3 2/3 yards in 15 minutes

Since, 1 yards = 3 feet

⇒ 11 feet in 15 minutes

Since, We know that;

⇒ Speed = Distance / Time

               = 11/15

               = 0.73 feet per minutes

Hence, Clearly ''90 feet in 2.5 hours'' have fastest speed.

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Final answer:

After converting each option to the same unit of speed, it's clear that Option A with a speed of 0.9 feet per minute is the fastest.

Explanation:

To determine which speed is the fastest, we need to convert each option into the same unit of speed, typically feet per minute or meters per second for consistency. Here, we'll choose feet per minute for simplicity.

Option A: 18 feet in 20 minutes = 0.9 feet/minute

Option B: 90 feet in 2.5 hours (150 minutes) = 0.6 feet/minute

Option C: 20 yards (60 feet) in 1.5 hours (90 minutes) = 0.67 feet/minute

Option D: 3 2/3 yards (11 feet) in 15 minutes = 0.73 feet/minute

Comparing these speeds, Option A is the fastest with 0.9 feet per minute.

Solution:

As, you can see that shape 1 and shape 2 are not congruent nor the shape 1 is dilated by any factor to get the shape 2.

Both the shapes are concave polygon.

The base length of two shapes are equal .

→2 ×  AB  =  P Q  →(approx)

→BC=QR

→2 × CD= RS→→→(approx)

If translation has taken place, all the vertices has been translated by same amount.

So, option (4) is true,which is Shape 1 is not congruent to shape 2 because a sequence of rigid transformations will not map shape 1 onto shape 2."

Answer: B. negative

Step-by-step explanation:

Given: In a linear equation, the independent variable increases at a constant rate while the dependent variable decreases at a constant rate.

We know that the slope of a line is given by :-

[tex]k=\dfrac{\text{change in y}}{\text{change in x}}[/tex]

According to the given information, if independent variable increases at a constant rate while the dependent variable decreases at a constant rate, then the slope of line will be :-

[tex]k=\dfrac{\text{Negative}}{\text{Positive}}=\text{Negative}[/tex]

Hence, the slope of line = Negative.

Answer: [tex]327[/tex] [tex]\text{ounce}[/tex]

Step-by-step explanation:

Given: On the way home from school, ross wears his [tex]20[/tex] pound backpack and carries his [tex]7[/tex] ounce lunchbox.

To Find: how many ounces does he carry in total.

Solution:

Weight of Ross's backpack [tex]=20[/tex] [tex]\text{pound}[/tex]

Weight of Ross's lunchbox [tex]=7[/tex] [tex]\text{ounce}[/tex]

Now,

As unit of weight of backpack and lunchbox is different, we need to convert it.

[tex]1[/tex] [tex]\text{pound}[/tex] [tex]=16[/tex] [tex]\text{ounce}[/tex]

Now weight of backpack is[tex]=\text{weight in pound}\times16[/tex]

                                 [tex]20\times16[/tex]

                                 [tex]320[/tex] [tex]\text{ounce}[/tex]

Total ounces carried by Ross [tex]=\text{weight of backpack}+\text{weight of lunchbox}[/tex]

                                                 [tex]320+7[/tex] [tex]\text{ounce}[/tex]

Hence Total ounce carried by Ross is [tex]320+7[/tex] [tex]\text{ounce}[/tex]

A 'space cushion' increases safety by providing more time to react and decreasing the force of impact in a collision, akin to how airbags and crumple zones function in a vehicle.

The concept of a "space cushion" around your vehicle pertains to having a safe distance between your vehicle and others on the road. This increases the time you have to react to unexpected events and minimizes the force of impact during a collision, related to the physics principle of impulse. A larger space cushion effectively reduces the net force on your vehicle and its occupants by allowing more time for the vehicle to come to a stop or slow down. Features like airbags and crumple zones in cars serve a similar purpose by increasing the time over which a collision occurs, thereby reducing the impact force. This is crucial because the severity of injuries incurred during a vehicle accident is often directly related to the force exerted on the occupants.

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Answer:

The answer is C, 6.4 inches

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

Answer:

Option D.

Step-by-step explanation:

The given vertices of quadrilateral ABCD are A(-4, -4), B(-4, -2), C(-1, -2), and D(-1, -4).

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using distance formula, we get

[tex]AB=\sqrt{\left(-4-\left(-4\right)\right)^2+\left(-2-\left(-4\right)\right)^2}=\sqrt{0^2+(2)^2}=\sqrt{4}=2[/tex]

Similarly,

[tex]BC=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-2-\left(-2\right)\right)^2}=3[/tex]

[tex]CD=\sqrt{\left(-1-\left(-1\right)\right)^2+\left(-4-\left(-2\right)\right)^2}=2[/tex]

[tex]AD=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-4-\left(-4\right)\right)^2}=3[/tex]

[tex]AB = CD[/tex]

[tex]BC = AD[/tex]

Measure of diagonals:

[tex]AC=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-2-\left(-4\right)\right)^2}=\sqrt{13}[/tex]

[tex]BD=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-4-\left(-2\right)\right)^2}=\sqrt{13}[/tex]

[tex]AC = BD[/tex]

Since measure of opposite sides are equal and measure of diagonals are equal, therefore the given quadrilateral ABCD is a rectangle.

Hence, the correct option is D.

Answer: 35.86

Step-by-step explanation:

By applying the DayTimer and NightTimer plans' rules and doing the necessary calculations, the total payment on the NightTimer plan would be $33.26747.

The total power used from 7am-7pm is 275 KWH and from 7pm-7am is 265 KWH. In this case, you have used more power during the 7am-7pm period. As such, you qualify for the DayTimer plan's rate. Therefore, you pay $0.06831/KWH for the power used between 7am-7pm, which results in 275 KWH * $0.06831/KWH = $18.78575. However, since most of your power usage is from 7am-7pm, you receive a 20% discount on your night usage. The night rate, therefore, is 20% less than the DayTimer rate, which is $0.06831 * (1 - 20/100) = $0.054648/KWH. Hence, you will pay 265 KWH * $0.054648/KWH = $14.48172 for power used between 7pm-7am. By adding these two amounts together, your total payment on the NightTimer plan would be $18.78575 + $14.48172 = $33.26747.

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Answer:

Angle of intersection is one half of the sum of measurements of intercepted arcs.

Step-by-step explanation:

An inscribed angle is the angle formed by the intersection of two chords having a common endpoint in a circle.

Also, by the angles of Intersecting Chords Theorem,

When two chords intersect inside a circle, then the measure of the angle formed is one half of sum of the measure of the arcs intercepted by the angle and its vertical angle.

Which is the relationship between the angle of intersection and the intercepted arcs.

Answer:

15

7

Just to simplify the answer above.

Step-by-step explanation:

Answer:

Option B. y = 8x - 7

Step-by-step explanation:

Parallel lines don't have the common points or the points of intersection.

In a system of equations has no solutions out of which one equation is y = 8x + 7

So a line parallel to this line will have no solutions.

For parallel lines slope will be same as 8, so the equation will be

y = 8x - 7

Option B. y = 8x - 7 will be the answer.

After performing the calculations based on the provided formula and values, Katie will have approximately $9127 in her college savings account when she turns 18. The closest option given in the question would be C) $9287.

To solve this problem, you would input the given values into the formula V = P(1 + r)t where P is the principal amount (in this case $5000), r is the annual interest rate (3.5% or 0.035 when expressed as a decimal), and t is the number of years (18).

When you substitute these values in, the equation becomes V = 5000(1 + 0.035)18.

Using a calculator, you'll find that V equates to approximately $9127. Therefore, Katie will have approximately $9127 in her account when she turns 18. The correct answer among the given options is thus closest to option C) $9287.

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Answer:

[tex]y=(x+8)^{2}[/tex]

Step-by-step explanation:

we have that

The ordered pairs [tex](1, 81), (2, 100), (3, 121), (4, 144)[/tex], and [tex](5, 169)[/tex] represent a function

The rule that that represent this function is equal to

[tex]y=(x+8)^{2}[/tex]

Verify

For [tex]x=1[/tex] -----> Find the value of y in the equation

[tex]y=(1+8)^{2}=81[/tex] -----> is correct

For [tex]x=2[/tex] -----> Find the value of y in the equation

[tex]y=(2+8)^{2}=100[/tex] -----> is correct

For [tex]x=3[/tex] -----> Find the value of y in the equation

[tex]y=(3+8)^{2}=121[/tex] -----> is correct

For [tex]x=4[/tex] -----> Find the value of y in the equation

[tex]y=(4+8)^{2}=144[/tex] -----> is correct

For [tex]x=5[/tex] -----> Find the value of y in the equation

[tex]y=(5+8)^{2}=169[/tex] -----> is correct

You need to use the midpoint formula of (x1+x2)/2,(y1+y2)/2

put in the actual points will look like this. (3x+5+x-1)/2,(3y-y)/2

now solve to get (4x+4)/2,(2y)/2

finish (2x+2,y)

Final answer:

The coordinates of the midpoint of the line segment with endpoints A(3x + 5, 3y) and B(x - 1, -y) are (2x + 2, y), using the midpoint formula.

Explanation:

To find the coordinates of the midpoint of a line segment with endpoints A and B, you can use the midpoint formula, which is ((x₁ + x₂)/2, (y₁ + y₂)/2). For the given endpoints A(3x + 5, 3y) and B(x - 1, -y), substituting the coordinates into the formula gives us the midpoint coordinates as follows:

Hence, the coordinates of the midpoint of AB are (2x + 2, y).

Answer:

7 7/8 pounds

Step-by-step explanation:

Given that a bag of oranges weighs 5 1/4 pounds and you want to know how much do 1 1/2 bags weigh, the next proportion must be satisfied:

(5 1/4 pounds)/(1 bag of oranges) = (x pounds)/(1 1/2 bag of oranges)

Isolating x:

x = (5 1/4)*(1 1/2)/1

x = 7 7/8 pounds

Applying the Pythagorean theorem, the length of diagonal DF is: C. 21 cm.

The sum of the squares of the two shorter legs of a right triangle equals the square of the length of the longest leg.

Let the point of intersection of the diagonals be O.

Diagonal FD bisects diagonal EG into equal segments EO and OG. EO = OG = 24/2 = 12 cm

Find the lengths of FO and OD using the Pythagorean theorem:

FO = √(20² - 12²) = 16 cm

OD = √(13² - 12²) = 5 cm

Length of diagonal DF = FO + OD = 16 + 5 = 21 cm.

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The given statement:

The condition ∑ Fi = 0 is sufficient to assure that a rigid body is in equilibrium is a

TRUE statement.

According to the condition for the equilibrium of a rigid body, the vector sum of all the forces acting on the body must be zero.

The first condition of equilibrium for a rigid body is as follows:

                             ∑ Fi = 0

where the expression  ∑ Fi are the sum of all the forces acting on the body.

Hence, the given statement is a TRUE statement.