What equation could be used to find the missing leg length a in a right triangle with a hypotenuse of 60 and leg length of 51?

Answer:

\frac{2\cot \left(-240^{\circ \:}\right)\cos \left(-1050^{\circ \:}\right)-\cot ^2\left(50^{\circ \:}\right)}{\sec ^2\left(40^{\circ \:}\right)}

Step-by-step explanation:

ok

Answer:

Simplifying

41 = 12d + -7

Reorder the terms:

41 = -7 + 12d

Solving

41 = -7 + 12d

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '-12d' to each side of the equation.

41 + -12d = -7 + 12d + -12d

Combine like terms: 12d + -12d = 0

41 + -12d = -7 + 0

41 + -12d = -7

Add '-41' to each side of the equation.

41 + -41 + -12d = -7 + -41

Combine like terms: 41 + -41 = 0

0 + -12d = -7 + -41

-12d = -7 + -41

Combine like terms: -7 + -41 = -48

-12d = -48

Divide each side by '-12'.

d = 4

Simplifying

d = 4

Answer:

(5a^2-4)*(25a^4+20a^2+16)

Step-by-step explanation:

Answer:

Its B, (5a^2-4)(25a^4+20a^2+16)

Step-by-step explanation:

Edge 2020

Answer:

15

Step-by-step explanation:

Try 1, 2, 3, or 4 blue pencils. Then green is 6 times as many. Red must be the rest to make up 20 total.

No. of blue        No. of green      No. of red

1                          6                           13

2                        12                           6

3                        18                           -1

You can't have 3 blue pencils because 3 blue + 18 green = 21 pencils, and there are only 20.

If you have 1 blue and 6 green, then there must be 13 red, but red must be less than green, and 13 is not less than 6.

The only possibility is

2 blue, 12 green, 6 red

If you start taking out pencils, when you take out the first 14 they may be all blues or green, so only when you take out the 15th pencil do you know for sure there must be 1 green pencil.

Answer:

Step-by-step explanation:

let width=x

length=3x

area=3x×x=3x²

3x²=192

x²=192/3=64

x=√64=8

width=8 m

length=3×8=24 m

Answer:

Solution,

Let the length be 3x meter.

Let the width be X meter

Area of rectangle= 192 square metres

Now,

Area of rectangles= length * breath

[tex]192 = 3x \times x \\ 192 = 3 {x}^{2} \\ {x}^{2} = \frac{192}{3} \\ x^{2} = 64 \\ x = \sqrt{64} \\ x = 8 \: meter[/tex]

Replacing value,

[tex] \: \: \: 3 \times x \\ \: \: = 3 \times 8 \\ \: \: \: \: = 24[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

Step-by-step explanation:

x=✓64*36=✓8^2*6^2

x=8*6

x=48

Answer:

a) x = 128 degrees

b) Angle APD is the arc angle, which is equal to the central angle x subtended by the arc.  Therefore angle APD = 128 degrees (and not 116 degrees)

Step-by-step explanation:

Given:

attached diagram

ABC is a straight line

Solution:

a) Find x

ABC is a straight line

angle ABD = supplement of CBD = 180-CBD = 180-116 = 64 degrees.

x is the central angle of the arc APD

so angle ABD is the inscribed angle which equals half of the arc angle =>

angle ABD = x/2 = 64 degrees

Solve for x

x/2 = 64

x = 2*64

x = 128 degrees

b.

Angle APD is the arc angle, which is equal to the central angle x subtended by the arc.  Therefore angle APD = 128 degrees (and not 116 degrees)

Answer:

x = 3

Inverse matrix:

[tex]A^{-1} = \begin{pmatrix} \frac{1}{9} & \frac{2}{9} \\ \frac{1}{3} & -\frac{1}{3} \end{pmatrix} \quad[/tex]

Step-by-step explanation:

Determinant: ad - bc

a = 3, b = 2, c = 3, d = -1

3 * (-1) - (2 * x) = -9

-3 - 2x = -9

-2x = -6

x = 3

For matrix

[tex]A = \begin{pmatrix}a & b\\c & d\end{pmatrix} \quad[/tex]

the inverse is

[tex]A^{-1} = \dfrac{1}{ad - bc}\begin{pmatrix}d & -b \\-c & a\end{pmatrix}\quad[/tex]

Here we have: det = -9

a = 3, b = 2, c = 3, d = -1

Inverse matrix:

[tex]A^{-1} = \dfrac{1}{-9}\begin{pmatrix} -1 & -2 \\ -3 & 3 \end{pmatrix}\quad[/tex]

[tex]A^{-1} = \begin{pmatrix} \frac{-1}{-9} & \frac{-2}{-9} \\\frac{-3}{-9} & \frac{3}{-9}\end{pmatrix} \quad[/tex]

[tex]A^{-1} = \begin{pmatrix} \frac{1}{9} & \frac{2}{9} \\\frac{1}{3} & -\frac{1}{3}\end{pmatrix}\quad[/tex]

Answer:

To answer the question above,

If you entered your test scores correctly, then your choices are off the wall.  

The median is 87  

The mode is 89  

The mean is 85.833...  

There is not a mode of 91 !  

I hope this helps

Step-by-step explanation:

Answer.

Step-by-step explanation:

Answer:

5/3

Step-by-step explanation:

it should be y/x

you can count 5 up and 3 over

Answer:

8/5

Step-by-step explanation:

You can use the formula [tex]\frac{y_{1}-y_{2}}{x_{1}-x_{2}}[/tex] with a pair of points [tex](x_{1},y_{1})[/tex][tex](x_{2},y_{2})[/tex]. We can use points (1,4) and (-4,-4). Plugging in the equation we get (4-(-4))/(1-(-4)), which simplifies to 8/5, which is the slope.

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Quadrilaterals.

Basically we know that, the sum of opposite angles of a quadrilateral inscribed in a circle is always 180°.

so applying this law here, we get as,

2X + (3X-10) = 180°

=> 5X - 10° = 180°

=> 5X = 190°

=> X = 190°/5

=> X = 38°

thus the angle X= 38°.

Answer:

The volume of the cone is 1006.9in³

Step-by-step explanation:

Given

[tex]Height = 18.8\ in[/tex]

[tex]Diameter = 14.3\ in[/tex]

Required

Calculate the volume;

The volume of a cone is calculated as thus;

[tex]V = \frac{1}{3} \pi r^2h[/tex]

Where V represents volume; r represents radius; and h represents height

The radius is calculated as thus;

[tex]r = \frac{1}{2}Diameter[/tex]

[tex]r = \frac{1}{2} * 14.3[/tex]

[tex]r = 7.15[/tex]

Substitute [tex]r = 7.15[/tex]; [tex]h = 18.8[/tex] and [tex]\pi = \frac{22}{7}[/tex]

[tex]V = \frac{1}{3} \pi r^2h[/tex] becomes

[tex]V = \frac{1}{3} * \frac{22}{7} * 7.15^2 * 18.8[/tex]

[tex]V = \frac{1}{3} * \frac{22}{7} * 51.1225 * 18.8[/tex]

[tex]V = \frac{22* 51.1225 * 18.8}{3 * 7}[/tex]

[tex]V = \frac{21144.266}{21}[/tex]

[tex]V = 1006.86980952[/tex]

[tex]V = 1006.9\ in^3[/tex] (Approximated)

Hence, the approximated volume of the cone is 1006.9in³

Answer:1006.5

Step-by-step explanation:

Answer:

The expressions are not equivalent.

Step-by-step explanation:

The answers would be 196 and 193 for t = 8

The answers would be 76  and 73 for t = 3

Answer:

Greater than the original = 2, 4

Less than the original = 5

Same as the original = 1, 3

Step-by-step explanation:

Let the original value be x.

1. A $30 increase followed by a $30 decrease.

New value [tex]=x+30-30=x[/tex], it is same as original value.

2. A 20% decrease followed by a 40% increase.

Afer 20% decrease.

New value [tex]=x-\dfrac{20}{100}x=x-0.2x=0.8x[/tex]

Afer 40% increase.

New value [tex]=0.8x+\dfrac{40}{100}(0.8x)=0.8x+0.32x=1.12x[/tex], it is greater than original value.

Similarly check the other values.

3. A 100% increase followed by a 50% decrease.

New value [tex]=x+\dfrac{100}{100}x-\dfrac{50}{100}(x+x)=x[/tex], it is same as original value.

4. A 75% increase followed by a 33% decrease

New value [tex]=x+\dfrac{75}{100}x-\dfrac{33}{100}(x+0.75x)=1.1725x[/tex], it is greater than the original value.

5. 55% decrease followed by a 25% increase

New value [tex]=x-\dfrac{55}{100}x+\dfrac{25}{100}(x-0.55x)=0.5625x[/tex], it is less than the original value.

Therefore, Greater than the original = 2, 4, Less than the original = 5, Same as the original = 1, 3 .

A 100% increase followed by a 50% decrease

A $30 increase followed by a $30 decrease

55% decrease followed by a 25% increase

A 20% decrease followed by a 40% increase

A 75% increase followed by a 33 1/3% decrease

Answer:

The correct statements are:

1: mEFD = mEGD

3: mED = mFD

5: mFD = 120°

Step-by-step explanation:

Let's analyse each statement:

1: mEFD = mEGD

Let's find the value of the angle ECD, using the sum of the internal angles of a quadrilateral:

[tex]60 + 90 + 90 + mECD = 360[/tex]

[tex]mECD = 120\°[/tex]

The angle ECD is a central angle, related to the arc ED, so the arc ED also has 120°.

The angle EFD inscribes the arc ED, so we have:

[tex]mEFD = mED/2[/tex]

[tex]mEFD = 120/2 = 60\°[/tex]

So the angles mEFD and mEGD are equal. The statement is TRUE.

2. mEGD = mECD

This statement is FALSE, because mEGD = 60° and mECD = 120°

3. mED = mFD

If mED is 120° and mEF = mFD, we have:

[tex]mED + mEF + mFD = 360[/tex]

[tex]2*mFD = 360 - 120[/tex]

[tex]mFD = 120\°[/tex]

So the statement is TRUE, both arcs have 120°.

4. mEF = 60°

This statement is FALSE, because we calculated before that mEF = mFD = 120°

5. mFD = 120°

This statemente is TRUE, because we calculated before that mFD = 120°.

So the correct statements are 1, 3 and 5

The true statements are: [tex]\angle EFD =\angle EGD[/tex], [tex]\overset{\huge\frown}{FD} = \overset{\huge\frown}{ED}[/tex] and [tex]\overset{\huge\frown}{FD} =120[/tex]

Start by calculating the measure of angle ECD.

We have:

[tex]\angle ECD = 2 * \angle EGD[/tex]

So, we have:

[tex]\angle ECD = 2 * 60[/tex]

[tex]\angle ECD = 120[/tex]

The above means that:

[tex]\overset{\huge\frown}{ED} = 120[/tex]

So, the measure of angle EFD is:

[tex]\angle EFD = 0.5 * \overset{\huge\frown}{ED}[/tex]

[tex]\angle EFD = 0.5 * 120[/tex]

[tex]\angle EFD = 60[/tex]

From the question, we have:

[tex]\angle EGD = 60[/tex]

So, it is true that:

[tex]\angle EFD =\angle EGD[/tex]

To calculate the measure of arc FD, we have:

[tex]\overset{\huge\frown}{FD} + \overset{\huge\frown}{DE} + \overset{\huge\frown}{EF} =360[/tex]

Lengths EF and DE are congruent.

So, we have:

[tex]2\overset{\huge\frown}{FD} + \overset{\huge\frown}{DE} =360[/tex]

[tex]\overset{\huge\frown}{DE} = \overset{\huge\frown}{ED} = 120[/tex]

So, we have:

[tex]2\overset{\huge\frown}{FD} + 120 =360[/tex]

Divide through by 2

[tex]\overset{\huge\frown}{FD} + 60 =180[/tex]

Subtract 60 from both sides

[tex]\overset{\huge\frown}{FD} =120[/tex]

This means that:

[tex]\overset{\huge\frown}{FD} = \overset{\huge\frown}{ED}[/tex] and [tex]\overset{\huge\frown}{FD} =120[/tex] are true

Hence, the true statements are: [tex]\angle EFD =\angle EGD[/tex], [tex]\overset{\huge\frown}{FD} = \overset{\huge\frown}{ED}[/tex] and [tex]\overset{\huge\frown}{FD} =120[/tex]

Read more about cyclic theorems at:

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Answer:

C

Step-by-step explanation:

It is an iscoceles triangle because there are 180 degrees in a triangle and the right angle plus the 45 degree equals 135 and 180 minus 135 is 45.

Since it is an iscoceles triangle that means that n = 3 and the pythagorean theorom says that a^2 + b^2 = c^2 which means that m = 3^2 plus 3^2 with a root.

3^2 is 9 so you get 18

the root of 18 is infinite, however can be simplified to 3 root to 2 because 3 times 3 equals 9 times 2 equals a root of 18

Hope this helps!

Answer:

Step-by-step explanation:

x + 2x + 4x = 49

7x = 49

x = 7

2(7)= 14 hours he worked on Wednesday

Answer:

the amount of fuel consumed every 100 kilometers is 62.5 litres.

Step-by-step explanation:

To determine the amount of fuel consumed every 100 kilometers.

Note: since the graph is a straight line graph (linear graph) the amount of fuel consumed every 100 kilometers is constant (i.e the same for every 100 kilometers). So, we only need to derive the amount of fuel consumed any 100 kilometers on the graph.

From the graph, the amount of fuel consumed for the first 100 kilometers is;

[tex]F = F_0 - F_{100} .........................1[/tex]

[tex]F_0 = 500\\F_{100} \simeq 437.5\\[/tex]

substituting into equation 1.

[tex]F = F_0 - F_{100} \\F = 500 - 437.5\\ F = 62.5 litres\\[/tex]

Therefore, the amount of fuel consumed every 100 kilometers is 62.5 litres.

Answer:500

Step-by-step explanation:got it on Kahn

Answer:

B) 128.3 square yards

Step-by-step explanation:

A = (n/360 deg)(pi)r^2

where n = central angle of sector.

A = (75/360)(3.14159)(14 yd)^2

A = 128.3 yd^2

Answer:

B. 128.3 yards

Step-by-step explanation:

Area of a Sector Formula: A = ∅/360πr²

Simply plug in our variables:

A = 75/360(π)(14)²

A = 5π/24(196

A = 128.3

Answer:

[tex]\boxed{OptionA}[/tex]

Step-by-step explanation:

More than always indicates "ADDITION". So the mathematical operation is "+".

Answer:

A. +

Step-by-step explanation:

The key word in the phrase is "more than"

That signifies an increase of value which is addition's main function

If the number that was represented in the phrase is x, then we could write out an equation

x=q+15

Answer:

A

Step-by-step explanation:

The zeroes of the function are the x values when f(x) = 0 so we can write:

0 = x² + x - 30

0 = (x + 6)(x - 5) (To factor this we need to find 2 numbers that have a sum of 1 and a product of -30; these numbers are 6 and -5)

x + 6 = 0 or x - 5 = 0 (Use Zero Product Property)

x = -6, 5

Hey there! :)

Answer:

A. x = -6 and x = 5.

Step-by-step explanation:

Given:

f(x) = x² + x - 30

Factor the equation by finding two numbers that sum up to 1 and multiply into -30. We get:

-5, 6

Use these to express this quadratic function in factored form:

f(x) = (x - 5) (x + 6)

Set each factor equal to 0 to solve for the zeros of the equation:

0 = x - 5

x = 5

-------------

0 = x + 6

x = -6

Therefore, the correct answer is A. x = -6 and x = 5.

Answer: draw a straight line trough point B, same thing with the second one,for the third you must draw a straight line from the angle across to the segment. (make sure all of the intersections are 90 degrees

The number of possible outcomes there could be at the end of their game is 6 outcomes

This is a permutation problem since it required arrangement

If Alex, Toby, and Samuel are playing a game together and at the end, they will make a classification with one of them in first  place, one of them in Second place and one of them in Third place, this can be done in 3! ways

Since n! = n(n-1)(n-2)!

Hence 3! = 3(3-1)(3-2)

3! = 3 * 2 * 1

3! = 6 ways

Hence the number of possible outcomes there could be at the end of their game is 6 outcomes

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Answer:

The length of the missing segment is 36

Step-by-step explanation:

Given

The figure above

Required

Determine the missing segment

Let the missing segment be represented with x

Given that, there exist parallel lines between the two triangles;

The relationship between the sides of the triangles is as follows;

[tex]\frac{20}{24} = \frac{30+20}{24+x}[/tex]

[tex]\frac{20}{24} = \frac{50}{24+x}[/tex]

Cross Multiply

[tex]20 * (24 + x) = 24 * 50[/tex]

[tex]20 * (24 + x) = 1200[/tex]

Divide both sides by 20

[tex]\frac{20 * (24 + x)}{20} = \frac{1200}{20}[/tex]

[tex](24 + x)= \frac{1200}{20}[/tex]

[tex]24 + x= 60[/tex]

Subtract 24 from both sides

[tex]24 - 24 + x = 60 - 24[/tex]

[tex]x = 60 - 24[/tex]

[tex]x = 36[/tex]

Hence, the length of the missing segment is 36

Answer:

WHAT

Step-by-step explanation:

Answer:

radius

Step-by-step explanation:

That "fixed distance" is the 'radius' of the circle.

Answer:

4).  (x + 2)^2 + (y - 1)^2 = 25.

Step-by-step explanation:

x^2 + y^2 + 4x - 2y - 20 = 0

x^2 + 4x + y^2 - 2y = 20

Completing the square on the x and y terms:

(x + 2)^2  - 4 + (y - 1)^2 - 1 = 20

(x + 2)^2 + (y - 1)^2 = 20 + 4 + 1

(x + 2)^2 + (y - 1)^2 = 25.

The standard equation of the circle with the given equation is (x+2)²+(y-1)²=25. Therefore, option 4 is the correct answer.

The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle. The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.

The standard equation of a circle with center at (x₁, y₁) and radius r is (x-x₁)²+(y-y₁)²=r²

The given circle equation is x²+ y²+4x-2y-20=0.

Here, x²+ y²+4x-2y=20

By completing the square on the x and y terms:

Now, add 4 on both the sides of an equation, we get

x²+ y²+4x-2y+4=20+4

x²+4x+4+y²-2y=24

Add 1 on both the sides of an equation, we get

(x+2)²+y²-2y+1=24+1

(x+2)²+(y-1)²=25

The standard equation of the circle with the given equation is (x+2)²+(y-1)²=25. Therefore, option 4 is the correct answer.

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