.The diagonal of a quadrilateral shaped field is 32 m and the perpendiculars dropped on it from the remaining opposite vertices are 10m and 14m. Find the area of the field.

Answer:

16 m^2

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 (b1+b2) *h

   = 1/2 ( 6+10) * 2

   = 16 m^2

===============================================

Explanation:

If we replace x with 0, then we get...

f(x) = 3x^2-8x+2

f(0) = 3(0)^2 - 8(0) + 2

f(0) = 3(0) - 8(0) + 2

f(0) = 0 - 0 + 2

f(0) = 2

Showing that the input x = 0 leads to the output y = f(x) = 2

The answer is between choice A and choice D because of this. Something like choice B is eliminated because this table shows x = 0 leading to y = -3 which is not correct.

-----------

Let's plug in x = 1

f(x) = 3x^2-8x+2

f(1) = 3(1)^2 - 8(1) + 2

f(1) = 3(1) - 8(1) + 2

f(1) = 3 - 8 + 2

f(1) = -5 + 2

f(1) = -3

So x = 1 leads to y = -3. We can rule out choice D and confirm it is choice A.

We don't need to try other x values since we have the answer, but I recommend practicing with other x values to help confirm that the first table is the answer.

Answer:

7234.56 in³

Step-by-step explanation:

4/3πr³

4/3 (3.14)(12)³

7234.56 in³

Answer:

7,234.56 cm^2

Step-by-step explanation:

We want to find the volume of the beach ball. The beach ball is in the shape of a sphere. The formula for the volume of a sphere is :

[tex]V=\frac{4}{3} \pi r^3[/tex]

We know the width, or diameter of the sphere is 24 cm. We need to find the radius. The radius is half the diameter.

r= d/2

r= 24 cm/2

r= 12 cm

The radius is 12 cm, and we can substitute it into the formula.

[tex]V=\frac{4}{3} \pi (12 cm) ^3[/tex]

First, evaluate the exponent.

(12 cm)³= 12 cm * 12cm * 12 cm= 144 cm² * 12 cm = 1728 cm³

[tex]V=\frac{4}{3} \pi * 1728 cm^3[/tex]

Substitute 3.14 in for pi.

[tex]V=\frac{4}{3} * 3.14 * 1728 cm^3[/tex]

Multiply all three numbers together.

[tex]V= 4.18666666 * 1728 cm^3[/tex]

[tex]V= 7234.55999 cm^3[/tex]

Round to the nearest hundredth. The 9 in the thousandth place tells us to round the 5 to a 6  in the hundredth place.

[tex]V= 7234.56 cm^3[/tex]

The volume of the beach ball is 7,234.56 cubic centimeters and choice 3 is correct.

Answer:

Step-by-step explanation:

The slope of a line between two points can be found by using the formula

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(5,–10) and (-3,-10)

Their slope is

[tex]m = \frac{ - 10 + 10}{ - 3 - 5} = \frac{0}{ - 8} = 0[/tex]

We have the final answer as

Slope = 0

Hope this helps you

Answer:

0

Step-by-step explanation:

Answer: 2√313

Step-by-step explanation:

Pythagorean theorem: a²+b²=c²

c²=a²+b²

c²=24²+26²

c²=576+676

c²=1252

c=√1252

c=2√313

Hope this helps!! :)

Please let me know if you have any question or need any further explanation

Answer:

<MON = 57°

Step-by-step explanation:

they are complementary angles so they add up to 90°

3x - 15 + 5x - 23 = 90

8x - 38 = 90

8x = 128

x = 16

5(16) - 23 = 57

Answer: Yes. They are thesame

Step-by-step explanation:

Of the 30 girls who tried out for the basketball team at Prescott Junior High, 12 were selected. In this scenario the ratio will be:

= 12/30

= 2/5

= 2:5

Of the 40 boys who tried out, 16 were selected. In this scenario, the ratio will be:

= 16/40

= 2/5

= 2:5

The ratio for both are thesame as we got 2:5 for both.

Answer:

85° (C).

Step-by-step explanation:

35° should go over to the other side of the line:

180 - 35 = 145°

Find angle 1:

145 + 130 + angle 1 = 360°

360° = 275° + angle 1

angle 1 = 360 - 275

angle 1 = 85°

85° which is C is the answer.

Answer:

Your correct answer is option C. 85 degrees.

Step-by-step explanation:

35 degrees goes over to the other side of the line:

180 - 35 = 145°

All you need to do is find angle 1.

145 + 130 + angle 1 = 360 degrees

360 degrees = 275 degrees + angle 1

angle 1 = 360 - 275

angle 1 = 85 degrees.

Therefore, option C. is the correct answer.

Answer:

46 and 64

Step-by-step explanation:

4 + 6 = 10

6 + 4 = 10

64 - 46 = 18

Answer:

[tex]\boxed{A. 2,016 km^2}[/tex]

Step-by-step explanation:

Hey there!

TSA is calculated using,

TSA = 2wl + 2lh + 2hw

Plug in the given info.

w = 18

l = 18

h = 19

TSA = 2(18)(18) + 2(18)(19) + 2(19)(18)

TSA = 648 + 684 + 684

TSA = 2,016km²

Hope this helps :)

The total surface area of the cuboid is km². Therefore, option A is the correct answer.

The given dimensions are length=19 km, width=18 km and height=18 km.

We need to find the total surface area of the given cuboid.

Total surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, TSA=2lw+2lh+2hw, to find the surface area.

Now, TSA = 2(18)(18) + 2(18)(19) + 2(19)(18)

TSA = 648 + 684 + 684=2016 km²

The total surface area of the cuboid is km². Therefore, option A is the correct answer.

To learn more about the total surface area of the cuboid visit:

https://brainly.com/question/27537575.

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Answer:Real numbers must be complete in order to fill the number line.

Step-by-step explanation: No steps I got this answer from my algebra notes.

Completeness as a property of real numbers ensures that the limit of a sequence exists within the set due to the absence of gaps or missing points

Completeness of real numbers means that there are no gaps in between a sequence of real numbers or on a real number line.

The importance of completeness of real numbers is of particular importance in other to ensure that mathematical calculations and analysis hold for all sequence of real numbers in a set.

With the presence of gaps or holes in real numbers, then the limit of a sequence of real numbers may not exist within a specified set.

Learn more : https://brainly.com/question/16492781?

Answer:

13b

Step-by-step explanation:

Add 4b and 9b together because they are like terms,

so 4b + 9b = 13b

Answer:

13b

Step-by-step explanation:

4b+9b

Combine like terms

13b

Answer:

Proportional: second and third, non-proportional: first and fourth

Step-by-step explanation:

Proportional relationships are linear functions that pass through the origin. Using this definition, we can conclude that the proportional relationships are the second and third options whereas the non-proportional relationships are the first and fourth options.

Answer:

proportional relationship: the second one and the third one the first and the fourth one

Non-proportional relationship: the first and the fourth one

Step-by-step explanation:

Like the first person said, a proportional relationship is when a linear line passes thru the origin, which is known as (0,0), so the second and the third are the only ones that do that, plus they have a y-intercept of a 0 and the others don't.

Answer:

Yes and closed interval

Step-by-step explanation:

The computation is shown below:

For the sum and the reciprocal as small as the possible equation is as follows

[tex]\(\frac{d}{dx}\left(x+\frac{1}{x}\right)=0.\)[/tex]

Now take out the derivates,

So,

[tex]\(1-\frac{1}{x^2}=0,\)[/tex]

or we can say that

[tex]\(x^2-1=0\rightarrow x=\pm1.\)[/tex]

As the only positive number is to be determined i.e

x = 1

So this problem needed the optimization over a closed interval and the same is to be considered.

Answer: $7.00

Step-by-step explanation:

each foot is $1, so times 7 is 7 dollars.

Answer:

49

Step-by-step explanation:

7 x 1 is 7.

7 x 7 is 49.

49 is answer.

Answer:

Quadrant IV

Step-by-step explanation:

If x > 0 the we are in quadrants 1 or 4

If Y < 0 we are in quadrants 3 or 4

Since both are true, we are in quadrant 4

Quadrant 2

x axis is left to right

y axis is up and down

Answer:

Step-by-step explanation:

[tex] \sf{x + 3(2x - 5) = 6}[/tex]

Distribute 3 through the parentheses

⇒[tex] \sf{x + 6x - 15 = 6}[/tex]

Collect like terms

⇒[tex] \sf{7x - 15 = 6}[/tex]

Move constant to right hand side and change it's sign

⇒[tex] \sf{7x = 6 + 15}[/tex]

Add the numbers

⇒[tex] \sf{7x = 21}[/tex]

Divide both sides of the equation by 7

⇒[tex] \sf{ \frac{7x}{7} = \frac{21}{7} }[/tex]

Calculate

⇒[tex] \sf{x = 3}[/tex]

Hope I helped!

Best regards!

The value of x is 3 for the equation x + 3(2x-5) = 6.

Two or more expressions with an Equal sign is called as Equation.

The given equation is x + 3(2x-5) = 6

x plus three times of two times of x minus five equal to six.

We need to find the value of x.

x + 3(2x-5) = 6

Apply distributive property.

x+6x-15=6

7x-15=6

Add 15 on both sides

7x=6+15

7x=21

Divide both sides by 7

x=3

Hence, the value of x is 3 for the equation x + 3(2x-5) = 6.

To learn more on Equation:

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Answer:

don't ask many questions at 1time

Answer:  I will start it by squaring both sides of the equation.  

The solution is  x = 5 or x=-1

Step-by-step explanation:

[tex]\sqrt{8x+9} =x+2[/tex]     Square the left and right sides. The square root of 8x+9 squared is 8x+9  and the x+2 squared is x^2 + 4x +4. We will now have the new equation,

8x + 9 = [tex]x^{2}[/tex] + 4x + 4   now set them equal zero first sutract x^2 from both sides

-x^2       -x^2

-x^2 + 8x + 9 = 4x +4      subtract 4x from both sides      

          -4x            -4x

-x^2 +4x + 9 = 4        Finally subtract 4 from both sides

               -4    -4

-x^2 + 4x +5 = 0    Remember the largest degree has a negative coefficient so divide them all by -1.

x^2 - 4x -5 = 0        Now find two numbers that their product is -5 and their sum is -4.     the numbers  1 and -5 works out.

Now rewrite the whole equation as,

x^2+ 1x -5x -5=0      Factor by grouping on the left side

x(x+1) -5(x+1)= 0      Factor out x+1

(x+1)(x-5) = 0         Now apply the zero product

x+1 = 0     or x-5 = 0

   -1    -1          +5   +5

x = -1   or  x = 5

Answer:

7m+8

Step-by-step explanation:

distributive prop then pemdas

Answer:

No.

Step-by-step explanation:

A function must past the Vertical Line Test. We know that our equation x² + y² = 5 is a circle, and so some x-values have the same y-values, etc. Since not every x-value has its own y-value, our equation is not a function.

We can see this using a graph:

Since the vertical line test passes 2 points with the same x-value, it is not a function.

Step-by-step explanation:

It is given that,

Speed of Anna is x miles/hour

Speed of Sara is 10 mi/h

We need to find an expression that represents the average of Anna's and Sara's speeds. Average of two objects is given by :

[tex]v=\dfrac{v_1+v_2}{2}[/tex]

ATQ,

[tex]v=\dfrac{x+10}{2}[/tex]

The above expression represents the average speed of Anna and Sara.

Answer:

3.4147

Step-by-step explanation:

Answer:

the number rounded to the nearest ten thousandth is : 3.4147

Step-by-step explanation:

3.41469 Round to ten thousandths

put the number in value chart:

ones   .   tenth       hundredth    thousandth     ten thousandth   h.thousandth

   3      .    4                1                    4                                6                      9

now look at the number after the ten thousandth it is 9 which is more than five , five and more add one to the value below

add (1) to 6

the number rounded to the nearest ten thousandth is : 3.4147

==============================================

Explanation:

T(P) is the notation applying the translation rule T(x,y) = (x+5, y+4) to the point P(2,3)

The x+5 means we add 5 to the x coordinate of P. We have x = 2 become x+5 = 2+5 = 7. The point P shifts 5 units to the right to go from (2,3) to (7,3)

Then the point shifts 4 units up to arrive at (7, 7). We shift 4 units up due to the y+4 in the translation rule.

Or put another way, y = 3 is the y coordinate of P. So y+4 = 3+4 = 7 is the new y coordinate.

Answer:

15 inches

Step-by-step explanation:

Hello!

To find the perimeter of a rectangle we have to add all the sides

l + l + w + w = p

We know the length is 6 inches more than the width

l = w + 6

We can put w + 6 for l

w + 6 + w + 6 + w + w = p

We can simplify this

4w + 12 = p

The perimeter is no more than 48

4w + 12 = 48

Subtract 12 from both sides

4w = 36

Divide both sides by 4

w = 9

Now we can put 9 in for w in the equation to find the length

l = 9 + 6

l = 15

The answer is 15 inches

Hope this helps!

Answer:

some considerations before choosing which career or path you will take career wise for the future is what you enjoy doing. what is also very important is understanding how many classes of college or university is required if you are up to the challenge and how many years it'll take before starting that career.

Answer:

a. A testable prediction about the relationship between variables

Step-by-step explanation:

A hypothesis is the FIRST step in conducting research or experimenting. In other terms, a scientific guess based on limited knowledge. Contrary to our hypothesis, conclusion comes last in researching and states the summary of the information gathered.

The reason why it isn't letter D is because a hypothesis's provability can only be determined once you have your conclusion, which is after you have conducted a research or experiment.

The letters B and C are too unrelated to what an hypothesis is.

- 8th grade student :)) (also buried under her own mountain of assignments and activities)

Answer:

Extraneous solution for Equation x + 1 = √7x + 15 : x = - 2

Step-by-step explanation:

We are given the equation x + a = √bx + c. As the hint says, let's substitute 7 for x first, receiving the following equation.

7 + a = √7b + c

Now let's say a = 1 and c = 8. Through substitution we solve for b,

7 + 1 = √7b + 8

8 = √7b + 8

8² = (√7b + 8)²

64 = 7b + 8

7b = 64 - 8 = 56

b = 56 / 7 = 8

Therefore, the equation x + 1 = √8x + 8 ( substitute the value of b ) will have a solution of x = 7. Let's simplify this equation and see if we receive any extraneous solutions.

x + 1 = √8x + 8

(x + 1)² - (√8x + 8)² = 0

(x + 1)² - 8x + 8 = 0

(x + 1)² - 8(x + 1) = 0

(x + 1)(x + 1 - 8) = 0

(x + 1)(x - 7) = 0

x = - 1 and x = 7

We already know that x = 7, but x = - 1 is not an extraneous solution. Therefore let's simplify the equation x + 1 = √7x + 15 and see if we receive any extraneous solutions.

(x + 1)² - (√7x + 15)² = 0

(x + 1)² - 7x + 15 = 0

x² - 5x - 14 = 0

(x - 7)(x + 2) = 0

x = 7 and x = - 2

In this case x = - 2 is an extraneous solution. We can check by substituting it back into the equation x + 1 = √7x + 15.

- 2 + 1 = √7(- 2) + 15

- 1 = √- 14 + 15

- 1 = √1

- 1 ≠ 1 - hence proved that x = - 2 is our extraneous solution

The equation with extraneous solution is [tex]x +5 = \sqrt{6x + 4[/tex]

The equation is given as:

[tex]x + 2 = \sqrt{3x + 10[/tex]

The form of the equation is given as:

[tex]x +a = \sqrt{bx + c[/tex]

Now, we assume that x = 7.

So, the equation becomes

[tex]7 +a = \sqrt{7b + c[/tex]

Assume that the value of a is 5

[tex]7 +5 = \sqrt{7b + c[/tex]

Add 7 and 5

[tex]12 = \sqrt{7b + c[/tex]

Square both sides of the equation

[tex]144= 7b + c[/tex]

Assume that the value of b is 6.

So, the equation becomes

[tex]144= 7(6) + c[/tex]

[tex]144= 42 + c[/tex]

Assume that c is 4

[tex]144= 42 + 4[/tex]

[tex]144= 46[/tex]

The above equation is false because 144 does not equal 46.

The values of a, b and c that makes the equation false are:

[tex]a=5[/tex]

[tex]b = 6[/tex]

[tex]c = 4[/tex]

So, we have:

[tex]x +a = \sqrt{bx + c[/tex]

[tex]x +5 = \sqrt{6x + 4[/tex]

Hence, the equation with extraneous solution is [tex]x +5 = \sqrt{6x + 4[/tex]

Read more about extraneous solutions at:

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Answer:

Option (F)

Step-by-step explanation:

From the figure attached,

ΔABC is a right triangle.

m∠A + m∠B + m∠C = 180°

m∠A + 90° + x° = 180°

m∠A = 180 - (90 + x)

        = (90 - x)°

By applying cosec rule in this triangle,

csc(A) = [tex]\frac{\text{Hypotenuse}}{\text{Opposite side}}[/tex]

csc(90 - x) = [tex]\frac{\text{AC}}{\text{BC}}[/tex]

                 = [tex]\frac{5}{3}[/tex]

                 = 1.67

Therefore, Option (F) will be the correct option.