how do i anser this question

Given:

The quadratic equation is:

[tex]10m^2-7m+3=0[/tex]

To find:

The solutions for the given equation by using the quadratic formula.

Solution:

If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then the quadratic formula is:

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

We have,

[tex]10m^2-7m+3=0[/tex]

Here, [tex]a=10,b=-7,c=3[/tex]. Using the quadratic formula, we get

[tex]m=\dfrac{-(-7)\pm \sqrt{(-7)^2-4(10)(3)}}{2(10)}[/tex]

[tex]m=\dfrac{7\pm \sqrt{49-120}}{20}[/tex]

[tex]m=\dfrac{7\pm \sqrt{-71}}{20}[/tex]

[tex]m=\dfrac{7\pm i\sqrt{71}}{20}[/tex]             [tex][\because \sqrt{-a}=i\sqrt{a},a>0][/tex]

Therefore, the solution set of the given equation is [tex]\left\{\dfrac{7- i\sqrt{71}}{20},\dfrac{7+ i\sqrt{71}}{20}\right\}[/tex]. Hence, the correct option is D.

Answer:

MATH is not a parallelogram

Step-by-step explanation:

(sqrt means squareroot)

To prove that quadrilateral MATH is a parallelogram, we can use the following formula:

A quadrilateral is a parallelogram if and only if both pairs of opposite sides are congruent.

In other words, if the lengths of the sides opposite each other in a quadrilateral are the same, then the quadrilateral is a parallelogram.

To prove that MATH is a parallelogram, we need to show that both pairs of opposite sides are congruent.

The first pair of opposite sides consists of segment MA and segment TH. To show that these sides are congruent, we can use the Distance Formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Where (x1, y1) and (x2, y2) are the coordinates of the two points that define the line segment.

Substituting the coordinates of points M and A, we get:

d = sqrt((-3 - (-5))^2 + (2 - (-2))^2)

= sqrt((-3 + 5)^2 + (2 + 2)^2)

= sqrt(8^2 + 4^2)

= sqrt(64 + 16)

= sqrt(80)

= 8.944

Substituting the coordinates of points T and H, we get:

d = sqrt((1 - 3)^2 + (-2 - 2)^2)

= sqrt((-2)^2 + (-4)^2)

= sqrt(4 + 16)

= sqrt(20)

= 4.472

Since 8.944 is not equal to 4.472, we cannot conclude that MA and TH are congruent. Therefore, MATH is not a parallelogram.

4π

As shown in the diagram, triangle XYZ is a right triangle. Therefore, its area (A) is given by:

A = [tex]\frac{1}{2}[/tex] x b x h      -------------(i)

Where;

A = 18[tex]\sqrt{3}[/tex]

b = XZ = base of the triangle

h = YZ = height of the triangle = 6

Substitute these values into equation(i) and solve as follows:

18[tex]\sqrt{3}[/tex] =  [tex]\frac{1}{2}[/tex] x b x 6

18[tex]\sqrt{3}[/tex] =  3b

Divide through by 3

6[tex]\sqrt{3}[/tex] =  b

Therefore, b = XZ = 6[tex]\sqrt{3}[/tex]

Now, assume that the circle is centered at O;

Triangle XOZ is isosceles, therefore the following are true;

(i) |OZ| = |OX|

(ii) XZO = ZXO = 30°

(iii) XOZ + XZO + ZXO = 180°   [sum of angles in a triangle]

=>  XOZ + 30° + 30° = 180°

=>  XOZ + 60° = 180°

=>  XOZ = 180° - 60°

=>  XOZ = 120°

Therefore we can calculate the radius |OZ| of the circle using sine rule as follows;

[tex]\frac{sin|XOZ|}{XZ} = \frac{sin|ZXO|}{OZ}[/tex]

[tex]\frac{sin120}{6\sqrt{3} } = \frac{sin 30}{OZ}[/tex]

[tex]\frac{\sqrt{3} /2}{6\sqrt{3} } = \frac{1/2}{|OZ|}[/tex]

[tex]\frac{1}{12} = \frac{1}{2|OZ|}[/tex]

[tex]\frac{1}{6} = \frac{1}{|OZ|}[/tex]

|OZ| = 6

The radius of the circle is therefore 6.

Now, let's calculate the length of the arc XZ

The length(L) of an arc is given by;

L = θ / 360 x 2 π r          ------------------(ii)

Where;

θ = angle subtended by the arc at the center.

r = radius of the circle.

In our case,

θ = ZOX = 120°

r = |OZ| = 6

Substitute these values into equation (ii) as follows;

L = 120/360 x 2π x 6

L = 4π

Therefore the length of the arc XZ is 4π

The experimental probability of spinning a number less than 3.

7/25.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The total number of spuns.

= 8 + 6 + 9 + 11 + 9 + 7

= 50

Total number of spuns of the spinner less than 3.

= 8 + 6

= 14

The probability of spinning a number less than 3.

= 14/50

= 7/25

Thus,

The probability is 7/25.

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Answer:

67

Step-by-step explanation:

The interior angles of triangles always equal 180 degrees. That means that angle R is equal to 67.

Therefore, angle U is equal to 67, as corresponding angles are the same.

Hope that this helps!

Answer:

10

Step-by-step explanation:

Step-by-step explanation:

2 q and 7 dimes kkkkkkkkk

Answer:

q = 2

d = 7

Step-by-step explanation:

System of Equations:

d + q = 9

10d + 25q = 120

Use Substitution:

let d = 9 - q

10(9 - q) + 25q = 120

90 - 10q + 25q = 120

15q = 30

q = 2

d = 7

Answer:

The answer is B.

Step-by-step explanation:

Its B because the lower the altitude the higher the pressure, and in this case the air towards the ground is being moved up, which is letting cold air sink back down.

Answer:

A) 5t + 10s = 132.50

B) 3t + 5s = 69.50

We multiply B) by -2

B) -6t -10s = -139.00 then we add A)

A) 5t + 10s = 132.50

-t = -6.50

t-shirt price = 6.50

Source: http://www.1728.org/unknwn2.htm

Step-by-step explanation:

Answer:

[tex](a)\ Area = 24in^2[/tex]

[tex](b)\ Area = 60in^2[/tex]

Step-by-step explanation:

Given

See attachment for the dimension of the block

Solving (a): Area of the front face

From the attachment, the front face has the following dimension.

[tex]Length = 4in[/tex]

[tex]Width = 6in[/tex]

The area is calculated as:

[tex]Area = Length *Width[/tex]

[tex]Area = 4in * 6in[/tex]

[tex]Area = 24in^2[/tex]

Solving (b): Area of the top and bottom faces

The top and bottom faces have the same dimension

From the attachment, the top face has the following dimension.

[tex]Length = 5in[/tex]

[tex]Width = 6in[/tex]

The area of the top is calculated as:

[tex]Area = Length *Width[/tex]

[tex]A_1 = 5in * 6in[/tex]

[tex]A_1 = 30in^2[/tex]

The area of the top and the bottom faces is:

[tex]Area = 2 *A_1[/tex] ---- because the top and bottom faces have the same dimension

[tex]Area = 2 *30in^2[/tex]

[tex]Area = 60in^2[/tex]

201.06 square units (rounded to 2 decimal places) is the area of the given circle.

The formula for the area A of a circle is A = πr², where r is the radius of the circle and π is the famous, well-known irrational number pi equal to 3.14159 (rounded to 5 decimal places).

Given that the circle's diameter is 16, and that a circle's radius is equal to half its diameter, the following conclusions can be drawn:

r = d/2

= 16/2

= 8

A=πr2

AND HALF THE DIAMETER IS THE RADIUS (r)

r=8

A= πr2 = π (8) squared = 64 * π = 200.96

or,

Now, substituting the values of r and π into the formula for the area of a circle, we get

A = πr²

= (3.14159)(8²)

= (3.14159)(64)

= 201.06 square units (rounded to 2 decimal places) is the area of the given circle.

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The score of Larry is 32 points.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

Ervin scores half as many points in a game as Larry.

If Larry scored x points,

then the points of Ervin are x/2 points.

Here, x = 16,

So,

Ervin's points = Larry's points

The equation is,

16 = x/2

x = 16(2)

x = 32 points

Therefore, 32 points are the score of Larry.

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Answer:

Y=2000(1.05)^x

Step-by-step explanation:

This is because 2000 is the fixed beginning value and should stay by itself.

While the interest rate of 5% is 1.05 because the amount of money George will have will be going up based on the fixed beginning value.

The area of the rectangle is 69.12 square inches.

We know that for a rectangle of length L and width W, the area is given by the formula:

A = L*W

Here we know that the length is 14.4 inches, then:

L = 14.4 in

And the width is one-third of that length, then we can write:

W = (1/3)*L

Replacing the value of L, we will get:

W = (1/3)*14.4 inches

W = 4.8 inches.

Then the area of the rectangle is:

A=  (4.8 in)*(14.4 in) = 69.12 in²

That is the area of the rectangle.

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Answer:

n = 7

n = -3

Step-by-step explanation:

4n+6 = n²-15

4n = n² - 21

n² - 4n - 21 = 0

(n-7)(n+3) = 0

n = 7

n = -3

Answer: [tex]219.94\ cm^2[/tex]

Step-by-step explanation:

Given

The central angle of a sector measures [tex]175^{\circ}[/tex]

The radius of the circle is [tex]r=12\ cm[/tex]

The area of the sector is given by

[tex]\Rightarrow A=\dfrac{\theta }{360^{\circ}}\pi r^2[/tex]

Insert the values

[tex]\Rightarrow A=\dfrac{175^{\circ}}{360^{\circ}}\cdot \pi \times 12^2\\\\\Rightarrow A=219.94\ cm^2[/tex]

On solving the provided question, we can say that the required probability is = 13/204.

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

probability of 1st card =  1/4

since the card is not replaced

total number remaining cards = 51

second card 13/51

the required probability is = 13/204

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8x-12+3x+5=180(sum of straight angles)

8x+3x-12+5=180

11x-19=180

11x=180-19

11x=161

x=161÷11

Step-by-step explanation:

sum of straight angles are 180

Answer:

c

Step-by-step explanation:

use that the sum of angles in a triangle is 180°

you know 2 angles so you can find the third

x= 180 -90-48 =42°

Answer:

c. x = 42 degrees

Step-by-step explanation:

A right triangle is 90 degrees

90 - 48 = 42

So, the measure of x is 42 degrees

Answer:

1157.09

Step-by-step explanation:

Answer:

19a - 6

Step-by-step explanation:

Answer:

4a + 3 ( 5a - 2 )

= 4a + [ 3 ( 5a - 2 ) ]

= 4a + [ 15a - 6 ]

= 4a + 15a - 6

= 19a -6

Answer: Hypotenuse

Step-by-step explanation:

The Hypotenuse is known as the longest side of a triangle.

Answer:

1. 2 runners

2. 25 runners

3. 24%

4. 15 runners

5. 60%

6. uh I think it's asking the same thing as 3, so 24%?

Using the fact that the triangles are similar, we will see that:

x = 5.626

On the image we can see two triangles, such that one is inscribed on the other.

Just because of that, it is obvious that the two triangles are similar.

And because the triangles are similar, the quotients between correspondent sides must be equal, that allows us to write the equation:

3/x = 8/15

The quotient is "left side over the bottom side"

We can solve that equation for x:

3/x = 8/15

3 = (8/15)*x

(15/8)*3 = x

45/8 = x

5.625 = x

That is the value of x.

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Answer:

The difference is 2:1.5

Step-by-step explanation:

Answer:

[tex]\boxed{22}.[/tex]

Step-by-step explanation:

Since Elliott drove for a total of 10 hours, and he drove for 120 miles while it was raining and 300 miles after the rain stopped, we know that he drove for a total of 120 + 300 = <<120+300=420>>420 miles.

If he drove for a total of 10 hours and covered a distance of 420 miles, then his average speed was 420 miles / 10 hours = <<420/10=42>>42 mph.

Since Elliott drove 20 mph faster after the rain stopped than he did while it was raining, then we know that his speed while it was raining was 20 mph slower than his average speed of 42 mph. That means his speed while it was raining was 42 mph - 20 mph = <<42-20=22>>22 mph.