Question 2 Multiple Choice Worth 5 points)
(03.01 LC)
The leg of a right triangle is 2 units and the hypotenuse is 4 units. What is the length, in units, of the other leg of the triangle?
O2 units
0 6 units
O V12 units
O V20 units

Answer:

Because to get a straight line you need a scale. Otherwise you will not be able to graph a straight line.

Hope this helps:)

Answer: (2, -4) and (7, -1)

Step-by-step explanation:

Ok, the solutions of the system of inequalities are all the points that lie on the blue shaded part of the graph or in the solid line.

So, in order to see if the points are solutions of the system, then you need to locate the point in the graph and see if it is inside the shaded region or in the solid line (only in the segment that "touches" the shaded region).

Now, we want to find the equation of the solid line, we can see that it passes through the points (0, 6) and (6, 0)

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

Then, in this case, the slope is:

a = (0 - 6)/(6 - 0) = -1.

And to find the value of b, we have that when x = 0, y = 6.

y = 6 = -1*0 + b

6 = b

The equation is:

y = -1*x + 6

(-1, 5) is not in the blue region nor in the solid line, so this is not a solution.

(7, - 1) this point is near the solid line, let's test it:

y(7) = -1*7 + 6 = -1

So the point (7, -1) is on the solid line, and is the other solution of the system.

Answer:

32

Step-by-step explanation:

We can call the number x. 75% can be expressed as 0.75 so we can write the following equation: 0.75x = 24. Dividing both sides by 0.75 to get rid of the coefficient of x, we get that x = 32.

Answer:

32.

Step-by-step explanation:

Let's say the number we are trying to find is x.

24 = 0.75x

0.75x = 24

x = 24 / 0.75

x = 32

Hope this helps!

Answer:

-1/3y +8 = x

Step-by-step explanation:

y=26−(3x+2)

Distribute

y = 26 -3x-2

Combine like terms

y = 24 -3x

Subtract 24 from each side

y -24 = -3x

Divide each side by -3

y / -3 -24/-3 = -3x/-3

-1/3y +8 = x

Answer:

Yes it is valid

Step-by-step explanation:

A square is a geometric shape which is also known as a Quadrilateral. This means that it has 4 sides.

For a square, it's 4 sides are equal to one another or we can put it in other words as the length of the 4 sides of a square are congruent to one another.

From the above question, we are asked that:

"If a square has a side length of 3, it's area is 9. Is it valid or invalid?"

The above statement is valid. This is because, the formula for the Area of a Square is given as

L × L = L²

Where L = Side length = 3

Area = 3 × 3 = 3²

Area = 9

Therefore, the statement is valid.

Answer:

B) x < 9

Step-by-step explanation:

√x < 3

(√x)² > 3²

x < 9

Answer:

194.25meters

Step-by-step explanation:

The distance around the running track is calculated as:

Perimeter of the first semi circle + Perimeter of the second circle +50m + 50m

Semi circle has a length or diameter of = 30m

r = 30/2 = 15m

Perimeter of a circle = 2πr

Hence for a semi circle = 2πr/2 = πr

Perimeter of the first semi circle = π × 15

= 47.123889804m

Perimeter of the second semi circle is the same hence,

π × 15 = 47.123889804m

The distance around the running track

= 47.123889804m + 47.123889804m + 50m + 50m

= 194.24777961m

Approximately= 194.25meters.

Answer:

D. 1 real; 4 complex  

Step-by-step explanation:

1. Calculate the total number of roots

The fundamental theorem of algebra states that any polynomial of degree n has n roots.

Your polynomial is fifth degree, so it has five roots.

2. Calculate the number of real roots

We can use Descartes' rule of signs to determine the number of real roots:

The number of positive real roots is the same as the number of changes in the sign of the coefficients of ƒ(x) or less than by an even number.

The number of negative real roots is the same as the number of changes in sign of the coefficients of the terms of f(-x) or less than this by an even number.

(a) Number of positive real roots

The coefficients of ƒ(x) are

+1 +3 +8 +14 +16 + 8  

There are no changes of sign, so there are no positive real roots.

(b) Number of negative real roots

(i) Find f(-x)

f(-x) = -x⁵+ 3x⁴ - 8x³ + 14x² - 16x + 8

(ii) Count the changes of sign

The coefficients of f(-x) are

-1 ∥ +3 ∥ -8 ∥+14 ∥ -16 ∥ +8

There are five changes of sign.

Thus, the number of negative roots is five, three, or one.

So far, we know that we have five roots. None is positive, and there could be one, three, or five negative real roots.

3. Confirm by sketching the graph

The real roots are the points at which the graph crosses or touches the x-axis.

The graph (see below) crosses the x-axis at only one point.

Thus. we have

Answer:

i think the answer is either $68.25 or $110

i hope this helped

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Answer:

M = 45°

Step-by-step explanation:

a²=b²+c²-2bc Cos A

m² = n² + p² - 2np cos M

(5.1)² = (7.2)² + (5.3)² - 2(7.2)(5.3) cos M

26.01 = 51.84 + 28.09 - 76.32 cos M

-53.92 = -76.32 cos M

0.7065 = cos M

M = [tex]cos^{-1 }[/tex](0.7065)

M = 45°

Because 9 × 10 equals 90

Then 7×90=7×9×10

Answer:

2/3

Step-by-step explanation:

1) Move the 7a to the other side

2) Move the 3

3) Combine like terms

4) Divide by 9

5) Answer is 2/3

Answer:

a=2/3

Step-by-step explanation:

All this problem needs is some knowledge of how an = sign and basic equations work

7a-3=3-2a

7a+2a=3+3  (Sign becomes opposite on the other side of the equation)

9a=6

a=2/3

Thank you for your time!

Answer:

y+1/12.5=2/5

or,5y+5=25

ory=20/5

so, y=4

Step-by-step explanation:

hope it helps you

Answer:

(L ⋅ W)(x) = 28x3 − 16x2 + 8x

Step-by-step explanation:

I took the test hope it helps :3

The area of the rectangle is (L · W) (x) = 28x³ - 16x² + 8x. Thus, the correct option is C.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Given the length of the rectangle is L(x)=4x, and the width is W(x)=7x²-4x+2. Therefore, the area of the rectangle in terms of x is,

L(x)×W(x) = 4x × (7x²-4x+2)

(L · W) (x) = 28x³ - 16x² + 8x

Hence, the area of the rectangle is (L · W) (x) = 28x³ - 16x² + 8x. Thus, the correct option is C.

Learn more about the Area:

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Answer:

C

Step-by-step explanation:

Here, we want to state the interval that has the highest frequency.

What we are asked here is the range of values where we have the the most common salary.

For 0-10, we have 1 ( Estonia)

For 11-20, we have 1 (Israel)

For 21-30 , we have 0

For 31-40, we have 1 ( Greece)

For 41-50, we have 5

For 51-60, we have 3

For 61-70, we have 1 (Luxembourg)

So 41-50 is the class with the highest frequency

Answer:

-5/24

Step-by-step explanation:

make the denominators the same!

Answer:

Second option is the correct answer

[tex] {3}^{ - 4} [/tex]

Step-by-step explanation:

[tex] {3}^{ - 8} . {3}^{4} = {3}^{ - 8 + 4} = {3}^{ - 4} [/tex]

Answer:

The answer is D because you multiply the exponents so -8 times 4 is -32

Hope this helps and plz mark branliest!

Step-by-step explanation:

Answer:

76 degrees.

Step-by-step explanation:

Let as consider O is the center of the circle . So from the figure it is clear that

[tex]\angle AOB=44^{\circ}[/tex]

[tex]\angle COD=118^{\circ}[/tex]

By central angle theorem, central angle subtended by an arc is twice of inscribed angle of the same arc.

We know that, [tex]\angle BAD=97^{\circ}[/tex] and angle BOD is the central angle subtended by arc BD.

[tex]\angle BOD=2\times \angle BAD[/tex]

[tex]\angle BOD=2\times 97^{\circ}[/tex]

[tex]\angle BOD=194^{\circ}[/tex]

Now,

[tex]\angle BOD=\angle BOC+\angle COD[/tex]

[tex]194^{\circ}=\angle BOC+118^{\circ}[/tex]

[tex]194^{\circ}-118^{\circ}=\angle BOC[/tex]

[tex]76^{\circ}=\angle BOC[/tex]

[tex]m(arc(BC))=76^{\circ}[/tex]

Therefore, the measure of arc BC is 76 degrees.

Answer:

y = -x +2

Step-by-step explanation:

y =x  has a slope of 1

Perpendicular lines have slopes that multiply to -1

m* 1 = -1

The slope of the perpendicular line is -1

We have a slope and a point

y = mx+b

y= -1x+b

Substitute the point into the equation

-3 = -1(5) +b

-3 =-5 +b

Add 5 to each side

-3+5 = b

2 =b

y = -x +2

Answer:

d= 6

r= 6/2

r=3

V= π. r². h

V= π . 3². 14

V= π. 9 . 14

V= π 126 cm³

V= 126 π cm³ (π not in number)

hope it helps^°^

Answer:if you use the formula it is 126 pi cm cubed

The answer is c

Step-by-step explanation:

Answer:

[tex]\huge\boxed{a = b-5}[/tex]

Step-by-step explanation:

Let the number be a

So, the given condition is:

a = b-5

Answer:

[tex]\Huge \boxed{a=b-5}[/tex]

Step-by-step explanation:

Let the number be [tex]a[/tex].

[tex]a[/tex] is equal to 5 less than [tex]b[/tex].

5 is subtracted from [tex]b[/tex].

Answer:

The triangle is not equilateral.

Step-by-step explanation:

Distance formula:

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

Distance from (a, a) to (-a, -a):

[tex] d_1 = \sqrt{(-a - a)^2 + (-a - a)^2} [/tex]

[tex] d_1 = \sqrt{(-2a)^2 + (-2a)^2} [/tex]

[tex] d_1 = \sqrt{8a^2} [/tex]

Distance from (-a, -a) to (-3a, 3a):

[tex] d_2 = \sqrt{(-3a - (-a))^2 + (3a - (-a))^2} [/tex]

[tex] d_2 = \sqrt{(-2a)^2 + (4a)^2} [/tex]

[tex] d_2 = \sqrt{20a^2} [/tex]

Distance from (-3a, 3a) to (a, a):

[tex]d_3 = \sqrt{(-3a - a)^2 + (3a - a)^2}[/tex]

[tex]d_3 = \sqrt{(-4a)^2 + (2a)^2}[/tex]

[tex]d_3 = \sqrt{20a^2}[/tex]

The three sides do not have the same length, so the triangle is not equilateral.

Answer:

x=6

Step-by-step explanation:

The crocodile river is y = 4

The road will intersect at ( 6,4)

We have two points on the line

(6,7) and (6,4)

The slope is

m = (y2-y1)/(x2-x1)

   = (4-7)/ (6-6)

  = -3/0

The slope is undefined

That means the equation is in the form

x=

Since the x coordinate is 6

x=6

Answer:

The distance between two points on a number line can be found by taking the absolute value of the difference of the coordinates.

Step-by-step explanation:

Answer:

(6/7)/(12/21) = 4/x

the first part of the expression :

when divide fraction: turn the sign from ÷ to × and flip the second fraction

(6/7)×(21/12)=4/x

126/84=4/x ( simplify the fraction 126/84)

GCF of 126 and 84 is 42 ( 126/48=3 and 84/42=2)

3/2=4/x ( cross multiplication ( butterfly)

1.5=4/x

1.5x=4

x=4/1.5=2.6666.......

Answer:

$635

Step-by-step explanation:

$5x7 birdhouses=$35want

So, $35+$600=$635 total!

I hope this helps you!

Multiplication is the process of multiplying. The cost of building 7 birdhouses will be $635.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

The cost of the birdhouse is the sum of the fixed cost, which is the setup cost of the business of $600, and the variable cost is the cost that is needed to make a single house, therefore, $5.

Now, the total cost of making n number of houses will be,

Cost of making n house = Fixed cost + variable cost

                                        = $600 + $5(n)

Further, the table can be filled using the above formula by substituting the value of n for the number of houses. Therefore,

Number of bird houses     Total cost to build

       1                                     $600+$5(1) = $605

       2                                    $600+$5(2) = $610

       3                                    $600+$5(3) = $615

       4                                    $600+$5(4) = $620

       5                                    $600+$5(5) = $625

       6                                    $600+$5(6) = $630

       7                                    $600+$5(7) = $635

Hence, the cost of building 7 birdhouses will be $635.

Learn more about Multiplication here:

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Answer:

NL  = 440 /13  or 33.85 (to two decimals)

Step-by-step explanation:

Consider triangles JKL and NML

angle JLK = angle NLM           vertical angles

angle KJL = angle MNL           given

Therefore triangles JKL and NML are similar

By proportion of corresponding sides of similar triangles,

NL / JL = LM / LK

Substitute given values

NL / 20 = 22 / 13

solve for NL

NL = 20*22 / 13 = 440 /13  or 33.85 (to two decimals)

Answer:

[tex]\huge \boxed{33.85}[/tex]

Step-by-step explanation:

JL is similar to NL. KL is similar to ML.

We can use ratios to solve.

JL/KL = NL/ML

Let the length of NL be x.

20/13 = x/22

Cross multiply.

13 × x = 22 × 20

13x = 440

Divide both sides by 13.

(13x)/13 =440/13

x = 440/13 = 33.846154...

Answer:

Area=1,288.88m²

Step-by-step explanation:

A circular hall(big room) has a hemispherical roof.The greatest height is equal to the inner diameter.Find the area of the floor,given that the capacity of the hall is 43510 cubic meter

Solution

let

diameter = D

radius,r = D/2

Greatest height = D

height of cylindrical part (h)= D-r = r

radius of cylindrical part = r

area of floor = πr²

volume = volume of cylindrical part + volume of hemispherical part

= πr²h + 2/3 πr³

Recall h=r

volume = πr³ + 2/3 πr³

43510=5/3πr³

Make r the subject

r=3√(43510*3)/5π

=3√(130,530/15.7

=3√8,314.01

=20.26

Area of floor = πr²

=3.14*(20.26)²

=3.14*410.47

=1,288.88m²

Answer:

see below

Step-by-step explanation:

6 - (3x+10) + 4(2 - x) =15

Distribute

6 - 3x -10 +8 -4x = 15

Combine like terms

4 -7x = 15

Subtract 4 from each side

4 -7x-4 =15-4

-7x =11

Divide each side by -7

-7x/-7 = 11/-7

x = -11/7