The base angles of all trapezoids are congruent.

True or False

The area of the rectangle is 18 square units if the vertices at ​ (−6, 3) ​, ​ (−3, 6) ​ , (1, 2) , and (−2, −1).

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is defined as the two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

It is given that:

A rectangle with vertices at a​ (−6, 3) ​, ​b (−3, 6) ​ , c(1, 2) , and d(−2, −1)"

As we know,

The distance formula can be given as:

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

ab = √(x₁-x₂)²+(y₁-y₂)²

=√(-6+3)²+(3-6)²

= √18

cd =√(1+2)²+(2+1)²

= √18

Area= lxw

A=√18x√18

a=18

Thus, the area of the rectangle is 18 square units if the vertices at ​ (−6, 3) ​, (−3, 6) ​ , (1, 2) , and (−2, −1).

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Answer:

The correct option is C. The surface area of a sphere is 256π cm².

Step-by-step explanation:

Given information: The diameter of the circle is 16 cm.

[tex]r=\frac{d}{2}=\frac{16}{2}=8[/tex]

Radius of the circle is 8 cm.

Surface area of a sphere is

[tex]A=4\pi r^2[/tex]

Where, r is radius.

[tex]A=4\pi (8)^2[/tex]

[tex]A=4\pi (64)[/tex]

[tex]A=256\pi[/tex]

The surface area of a sphere is 256π cm². Therefore the correct option is C.

Step-by-step explanation: To simplify the square root of 99, first create a factor tree that has 2 branches.

99 factors as 11 × 9 and 9 factors as 3 × 3.

Since we have a pair of 3's in our factor tree, a 3 can come out of the radical. Since we have a 11 that doesn't match up, it stays inside the radical and this gives us the answer of [tex]\sqrt[3]{11}[/tex].

I have also attached my work in the image provided.

The square root of 99, when simplified as much as possible, is approximately 9.94987437.

We have,

The square root of a number is a value that, when multiplied by itself, gives the original number.

In the case of the square root of 99, there is no whole number that can be multiplied by itself to result in 99.

Therefore, the square root of 99 is an irrational number.

To find an approximate value for the square root of 99, we can use a calculator or mathematical methods.

The square root of 99 is approximately 9.94987437.

This means that when we multiply 9.94987437 by itself, we get a value close to 99.

Since 9.94987437 cannot be simplified further as a whole number or a simplified radical, it is the most accurate representation of the square root of 99.

Thus,

The square root of 99, when simplified as much as possible, is approximately 9.94987437.

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the first graph

the solid line passes through (0,-3) and (0,9)

 dotted line passes through (0,-3) and (0,-1)

 see attached sketch

To find the measure of angle d, you can use the dot product formula and inverse cosine function.

To find the measure of angle d, we need to consider the given information about vectors A and B. The vector A is represented as (122 cm, <145°) and the vector B is represented as (110 cm, <270°). The angle between two vectors can be found using the dot product formula: cos(theta) = A · B / (|A| * |B|). So, we can calculate the dot product and magnitude of vectors A and B, and then use the inverse cosine function to find the angle between them. The measure of angle d is __ degrees.

Interchange to get:
x=5y-7
Solve for y to get:
y=(1/5)x+(7/5)

so I think it might be c

Answer:

The answer is C.

Step-by-step explanation:

Step 1: Replace f(x) with y.

     f(x)=5x >>>>> y=5x

Step 2: Switch x and y.

     y=5x >>>>> x=5y

Step 3: Solve for y

     x=5y >>>> y= x/5

Then you have to do the inverse of dividing by 5. Which is multipilying by 1/5. This leaves you with,

      y= 1/5x

Step 4: Write in standard inverse notation (Replace y with f^-1(x))

      f^-1(x)=1/5x  

Note: These steps work with ANY problem where you have to find the inverse function. I hope this helps :)

Answer:

Product [tex]5.1417 *10^{8})[/tex].

Step-by-step explanation:

Given : [tex](5.91* 10^{-3} )(8.7*10^{10})[/tex].

To find : What is the product written in scientific notation.

Solution : We have given

[tex](5.91* 10^{-3} )(8.7*10^{10})[/tex].

Combine like terms

[tex]5.91 * 8.7 * 10^{-3}*10^{10})[/tex].

[tex]51.417 * 10^{-3}*10^{10})[/tex].

[tex]51.417 *10^{7})[/tex].

In scientific notation

[tex]5.1417 *10^{8})[/tex].

Therefore, Product [tex]5.1417 *10^{8})[/tex].

Answer:

B. 4

Step-by-step explanation:

Given exponential model that shows the number of mobile cellular subscriptions per 100 people in Zimbabwe since 2000,

[tex]y=a b^x[/tex]

Where,

a=1.067905095

b=1.501755837,

[tex]\implies y=1.067905095(1.501755837)^x[/tex]

Since, the number of years from 2000 to 2003 = 3,

Thus, for finding the number of subscriptions in 2003,

x = 3,

Hence, the number of mobile cellular subscriptions per 100 people in Zimbabwe in 2003 is

[tex]y=1.067905095(1.501755837)^3=3.61685122094\approx 4[/tex]

Option 'B' is correct.

Answer:

[tex]\[-6 \leqslant x \leqslant 3\][/tex]

Step-by-step explanation:

The requirement is to represent a compound inequality with all real numbers at least –6 and at most 3.

This can be broken into two parts:

a) All real numbers at least -6

[tex]\[x\geqslant -6\][/tex]

b) All real numbers at most 3

[tex]\[x \leqslant 3\][/tex]

Combining the two inequalities to generate the compound inequality:

[tex]\[-6 \leqslant x \leqslant 3\][/tex]

Answer:

Step-by-step explanation:

Point slope form of the equation with point (a,b) and slope m is given by this equation

y-b=m(x-a)

Here we are given that the slope is -1/4 so m= -1/4

and the point is (-2,9) so a =-2 and b =9

Hence plugging the values in the equation we get

y-9 = -1/4 (x-(-2))

y -9 =-1/4 (x+2)

Answer: Using operations with fractions, the diver's final location is:

- 60 3/4 meters relative to the surface of the water (60 3/4 meters below the surface of the water).

Solution:

Initial location: -50 1/4 meters

He descends another 10 1/2 meters: -10 1/2 meters

Final location = Initial location - 10 1/2 meters

Final location = - 50 1/4 meters - 10 1/2 meters

Final location = - (50+10) (1/4+1/2) meters

Final location = - 60 [(1)(1)+2(1)]/4 meters

Final location = - 60 (1+2)/4 meters

Final location = - 60 3/4 meters

To find the plane's airspeed (in still air) and wind speed, we can use the concept of relative velocity. By setting up a system of equations using the distances and times for the outbound and return trips, we can solve for the values of the airspeed and wind speed. Solving these equations, we find that the plane's airspeed is 230 mph and the wind speed is 70 mph.

To find the plane's airspeed and wind speed, we can use the concept of relative velocity. Let's assume the plane's airspeed (in still air) is P mph and the wind speed is W mph.

On the outbound trip, with a tailwind, the plane's groundspeed (the speed relative to the ground) will be the sum of its airspeed and the wind speed: P + W mph. Since the distance traveled is 840 miles and the time taken is 3 hours, we have the equation: Distance = Speed * Time, where Speed is the groundspeed. Therefore, we can write the equation as: 840 = (P + W) * 3.

On the return trip, with the same wind as a headwind, the plane's groundspeed will be the difference between its airspeed and the wind speed: P - W mph. As it took 30 minutes longer, the time taken will be 3 hours + 0.5 hours = 3.5 hours. Using the same equation, we have: 840 = (P - W) * 3.5.

Now we have a system of equations, which we can solve to find the values of P and W. Solving these equations, we get:

Airspeed (in still air) = 230 mph

Wind speed = 70 mph

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