How to solve this equation

Answer:

C

Step-by-step explanation:

The area (A) of the triangle is calculated using

A = [tex]\frac{1}{2}[/tex] ab sinC

where a, b are the 2 sides and C is the angle between them

here a = 9, b = 15 and C = 70°, hence

A = 0.5 × 9 × 15 × sin70° = 63.4 cm² → C

Answer:

C.[tex]63.4cm^2[/tex]

Step-by-step explanation:

I love trigonometry

the area of a triangle is equal to [tex]\frac{1}{2}*a*b*sinC[/tex]

we have a b and Angle C so just put that in the formula :)

[tex]\frac{1}{2}*9*15*sin70\\[/tex]

[tex]63.4cm^2[/tex]

When the quadratic equation is written in standard form the value of c is 8

To find the value of c when the quadratic equation -3/4 x² + 2 = 0 is written in standard form (ax² + bx + c = 0), follow these steps:

Move the constant term to the right side:

-3/4 x² = -2

Multiply both sides by -4/3 to get the standard form:

4x² = 8

Identify the coefficient of x² (a) and the constant term (c):

In this case, a = 4 and c = 8.

Therefore, when the equation is written in standard form, c = 8.

Answer:

vertex = (2, - 16)

Step-by-step explanation:

given

f(x) = (x - 6)(x + 2) ← equate to zero to find the zeros

(x - 6)(x + 2) = 0

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 2 = 0 ⇒ x = - 2

The vertex lies on the axis of symmetry which is situated at the midpoint of the zeros, hence

[tex]x_{vertex}[/tex] = [tex]\frac{6-2}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2

Substitute x = 2 into f(x) for corresponding y- coordinate of vertex

f(2) = (2 - 6)(2 + 2) = - 4 × 4 = - 16

vertex = (2, - 16)

Answer:

7

Step-by-step explanation:

Replace both instances of x in f(x) = 2x + 9 with -1:

f(-1) = 2(-1) + 9 = 7

Thus, f(-1) = 7

The value of the function f(x) = 2x + 9 at x = - 1 Or f(-1) is 7.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A function f(x) = 2x + 9.

We know, Substitution in mathematics is when we replace some specific numerical values to variables according to our wants or given in the problem.

Therefore, f(-1) = 2(-1) + 9.

f(-1) = - 2 + 9.

f(-1) = 7.

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To conclude if a parallelogram is a rectangle, we need to check if its opposite sides are congruent and if its angles are right angles.

To determine if a parallelogram is a rectangle, we need to check if its opposite sides are congruent and if its angles are right angles.

In a rectangle, opposite sides are congruent and all angles are right angles (90 degrees).

So, if we can prove that the given parallelogram has congruent opposite sides and right angles, then we can conclude that it is a rectangle.

Alternatively, we can also look for other properties of rectangles such as diagonals being congruent or the presence of perpendicular bisectors.

A conclusion that be drawn based on the parallelogram include the following: C. No; the diagonals may not be congruent.

In Mathematics and Euclidean Geometry, a rectangle is a type of quadrilateral or polygon in which its opposite sides are equal and all the angles that are formed are right angles.

Generally speaking, the diagonals of a rectangle divide it into two equal parts and this implies that, the two diagonals of any rectangle are congruent.

In this scenario, we can logically deduce that this parallelogram is not a rectangle because its diagonals may not be congruent, as no congruence symbols were shown.

Answer:7

Step-by-step explanation:

There are 15 sleeping and only 8 snoring you subtract 8 from 15 which leave you with 7 and that's how many people

By subtracting the number of travelers snoring (8) from the total number of travelers (15), we determine that there are 7 travelers not snoring.

To find out how many travelers in the hostel are not snoring, we will subtract the number of travelers who are snoring from the total number of travelers. The problem states that 8 travelers are snoring, and there are 15 travelers in total. So, we perform the following calculation:

Total travelers - Travelers snoring = Travelers not snoring

15 - 8 = 7

Thus, there are 7 travelers who are not snoring.

Answer:

Step-by-step explanation:

The solution is attached herewith.

Answer:

x = ± 8

Step-by-step explanation:

Note that

(x - [tex]\frac{1}{x}[/tex])² = x² - 2 + [tex]\frac{1}{x^2}[/tex] = 66 - 2 = 64

Take the square root of both sides

x - [tex]\frac{1}{x}[/tex] = ± [tex]\sqrt{64}[/tex] = ± 8

1) 3rd down.

2) 2nd down.

3) 1st down.

4) 6th down.

the 4 in the tens place is 10 times the 4 in the ones place

The 4 in the tenth place is the product of 10 and the 4 to its right

The number is given as:

Number = 4,444,444

The 4 in the tenth place is:

40

The 4 to its right is:

4

Divide both numbers

40/4 = 10

Hence, the 4 in the tenth place is the product of 10 and the 4 to its right

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Answer:

it's either two or three. Sorry for the short answer.

Step-by-step explanation:

In the finding of m<FOE, I think it would be 70°.

Answer:

∠FOE = 90°

Step-by-step explanation:

In this question given is m∠AOC = 120°, m∠BOD = 150°.

We have to calculate ∠FOE.

Since ∠AOB + ∠COD + ∠BOC = 180°  [ Angle at a point on a straight line ]

∠AOB + ∠COD = 180° - ∠BOC ---(1)

It is given ∠AOC = 120° = ∠AOB + ∠BOC -----(2)

and ∠BOD = 150° = ∠BOC + ∠COD ------(3)

By adding equation (2) and (3)

150 + 120 = ∠ BOC + ∠COD + ∠AOB + BOC

270 = 2∠BOC + ∠COD + ∠ AOB

Now from equation (1)

270 = 2∠BOC + (180 - ∠BOC)

270 = 180 + ∠BOC

270 -180 = ∠BOC

∠BOC = 90°

Since ∠ BOC ≅ ∠FOE   (opposite angles)

Therefore, ∠FOE = 90° is the answer.

2nd degree trinomial

A=bh and since the garden is 2 1/2 by 2 and the trench+garden= 3 1/2 by 3 the trench would be 1 by 1. So A=1x1 = 1

Answer:11/2 m sq

Step-by-step explanation:

Area of the garden =L•W

2 1/2•2=

5/2•2= 5 m sq

Area of the garden & trench =L•W

3 1/2•3 =

7/2•3 =

7•3/2=

21/2 m sq

21/2-5 =

21/2-10/2=

21-10/2=

11/2

The area of the trench is 11/2 m sq

Answer:

The fourth graph with the long dotted line shows the system.

Step-by-step explanation:

By graphing both inequalities and shading, you'll find that the overlap shows the fourth graph. Also, there was no need to ask here, you really could have just used desmos.com, it's a great online graphing tool.

Answer:

4th graph : )

Step-by-step explanation:

Answer:

11 is -1 `0 is c

Step-by-step explanation:

11 you subtract 1 from each 10 look for points on griid

Answer: The answer is H

The likelihood is 66.67% or about 67%. Hope this helped!

Answer: B. It is likely to rain on Saturday.

Step-by-step explanation:

280

42 times 100 divided 15 equals 280.

Does it have any ANSWER CHOISES!

Answer:

c = 36.87

Step-by-step explanation:

arcsin(3/5)=36.87

Answer:

Step-by-step explanation:

Answer:

[tex]\large\boxed{y=-\dfrac{1}{2}x-2}[/tex]

Step-by-step explanation:

[tex]\text{The slope-intercept form:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\======================[/tex]

[tex]\text{If}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2\ \text{are\ parallel, then}\ m_2=-\dfrac{1}{m_1}\\===========================[/tex]

[tex]\text{We have the equation of a line:}\ 3+4x=2y-9.\\\text{Convert it to the slope-intercept form:}\\\\2y-9=3+4x\qquad\text{add 9 to both sides}\\\\2y=12+4x\qquad\text{divide both sides by 2}\\\\y=6+2x\\\\y=2x+6\to m_1=2\\\\\text{therefore}\ m_2=-\dfrac{1}{2}\\\\\text{We have the equation:}\ y=-\dfrac{1}{2}x+b\\\\\text{Put the coordinates of the given point (4, -4) to the equation:}\\\\-4=-\dfrac{1}{2}(4)+b\\\\-4=-2+b\qquad\text{add 2 to both sides}\\\\-2=b\to b=-2\\\\\text{Finally we have the equation:}\ y=-\dfrac{1}{2}x-2[/tex]

Answer:   294.4 m²

Step-by-step explanation:

Separate the shaded region into two parts:

[tex]1.\ Area(A)=\pi\ r^2\ \bigg(\dfrac{\theta}{360}\bigg)\\\\\\.\qquad \qquad =\pi(11.1)^2\bigg(\dfrac{230}{360}\bigg)\\\\\\.\qquad \qquad =247.3[/tex]

[tex]2.\ \text{Use Law of cosines to find the length of the third side.}\\\text{ Then use Heron's formula to find the Area of the triangle.}\\\\s=\dfrac{11.1+11.1+20.12}{2}=21.16\\\\\\A=\sqrt{s(s-a)(s-b)(s-c)}\\\\.\ =\sqrt{21.16(21.16-11.1)(21.16-11.1)(21.16-20.12)}\\\\.\ =\sqrt{2227}\\\\.\ =47.1[/tex]

Area of shaded region = Area of (1) + Area of (2)

                                      =    247.3     +      47.1

                                      =               294.4

Answer:

294.36

Step-by-step explanation:

Find the area of the entire circle.

Subtract out the area of a sector with 130 degrees for the central angle.

Add the area of the isosceles triangle with an apex angle of 130 degrees.

Area of The entire circle

Area = pi * r^2

Area = 3.14 * 11.1^2

Area = 386.88 m^2

Area of the sector with 130 degrees for a central angle

Area_130 = (130/360) * pi * r^2

Area_130 = (130/360) * 3.14* 11.1^2

Area_130 = 139.71

Area of the triangle

1/2 central angle = 130/2 = 65

Bisect the apex angle so that each half = 65 degrees.

Sin(65) = opposite / hypotenuse

Sin(65) = Opposite / 11.1

11.1 * sin(65) = opposite

opposite = 10.06

This is 1/2 the base so the base = 2*10.06 = 20.12

The height of the triangle is found by cos(65) = adjacent/hypotenuse

hypotenuse = 11.1

Cos(65) = adjacent / hypotenuse

adjacent = hypotenuse * cos(65)

adjacent = 4.69 This is the height of the triangle.

Area of the triangle = 1/2 * 20.12 * 4.69

Area of the triangle = 47.19 m^2

Area of the Shaded Area

Area of entire circle - area of sector + area of triangle

=386.88 - 139.71 + 47.19

=294.36

Note

The area of the triangle could be done using Area = 1/2 * 11.1^2 * (2*sin(65)*cos(65) = 1/2 * 11.1^2 * sin(130) = 47.2 but you may not know all the math to do the area this way.

Step-by-step explanation:

We start with the formulas for the volumes of a cylinder and a cone.

Cylinder:

[tex] V_{cylinder} = \pi r^2 h [/tex]

Cone:

[tex] V_{cone} = \dfrac{1}{3} \pi r^2 h [/tex]

Now we calculate the two volumes.

Cylinder:

[tex] V_{cylinder} = \pi r^2 h [/tex]

[tex] V_{cylinder} = \pi \times (10~cm)^2 \times 9~cm [/tex]

[tex] V_{cylinder} = \pi \times 100~cm^2 \times 9~cm [/tex]

[tex] V_{cylinder} = 900 \pi~cm^3 [/tex]

Cone:

[tex] V_{cone} = \dfrac{1}{3} \pi \times (10~cm)^2 \times 9~cm [/tex]

[tex] V_{cone} = \dfrac{1}{3} \pi \times 100~cm^2 \times 9~cm [/tex]

[tex] V_{cone} = 300 \pi~cm^3 [/tex]

The volume of the cylinder is 900pi cm^3, and the volume of the cone is 300pi cm^3.

Now we divide the volume of the cylinder by the volume of the cone.

[tex] \dfrac{900 \pi~cm^3}{300 \pi~cm^3} = 3 [/tex]

Dividing the volume of the cylinder by the volume of the cone gives us 3, showing that the volume of the cylinder is 3 times the volume of the cone.

The volume of a cylinder is three times the volume of a cone.

To show that the volume of a cylinder is three times the volume of a cone, we need to compare their formulas. The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius and h is the height.

Let's calculate the volume of the cylinder first. Given that the radius (r) is 10 cm and the height (h) is 9 cm, we can substitute these values into the formula: V = π(10 cm)²(9 cm) = 900π cm³.

Now let's calculate the volume of the cone. Again, substituting the values for r and h, we have V = (1/3)π(10 cm)²(9 cm) = 300π cm³.

Comparing the volumes, we have 900π cm³ for the cylinder and 300π cm³ for the cone. Dividing the volume of the cylinder by the volume of the cone, we get (900π cm³) / (300π cm³) = 3. This shows that the volume of the cylinder is three times the volume of the cone

The median {Q2} is 10

Q1 is 7+7/2 which is 7

Q3 is 15+12/2 which is 13.5

Final answer:

The quartiles for the data set (5, 7, 7, 8, 10, 11, 12, 15, 17) are found by arranging the data in order and then finding the medians of the lower and upper halves. The first quartile (Q1) is 7, the median (Q2) is 10, and the third quartile (Q3) is 13.5.

Explanation:

To find the quartiles for the data set (5, 7, 7, 8, 10, 11, 12, 15, 17), you first arrange the data in ascending order, which is already done. The median (Q2) is the middle value when the data set is in order, so since there are 9 data points, the median is the fifth value, which is 10.

The first quartile (Q1) is the median of the lower half of the data. For our data set, the lower half is (5, 7, 7, 8), so the median of this set is the average of the middle two values because we have an even number of data points in the lower half. Thus, Q1 is (7 + 7)/2 = 7.

The third quartile (Q3) is the median of the upper half of the data. For our dataset, the upper half is (11, 12, 15, 17). Similarly, since this is an even set, Q3 is the average of the middle two values, (12 + 15)/2 = 13.5.

Therefore, the quartiles for this data set are:

Answer:

the answer is 16

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

add the the numbers and divide the sum by how many numbers are given

Answer:

The equation represents an even function

Step-by-step explanation:

For the function above, the value of f(x) is fixed at 3 for positive or negative values of x.

For the absolute value function below, the value of f(x) will always be positive due to the absolute symbol.

In general, a function f(x) is said to be even if;

f(-x) = f(x) such that the function is symmetrical with respect to the y-axis.

Answer:

It’s (A) 16

Step-by-step explanation:

It just is

The length of the diagonal x= 5 units( nearest whole number) in the given parallelogram.

" Diagonal is defined as the length between the opposite vertices of the given polygon."

Formula used

Cosine law

[tex]a^{2} =b^{2} +c^{2} -2bc Cos A[/tex]

According to the question,

In the given parallelogram PQRS

In ΔPQS

PQ = 6units

PS = 4 units

QS = x units

∠QPS = 55°

Apply cosine law to get the length of the diagonal we have,

   [tex]x^{2} = 6^{2} +4^{2} -2(6)(4)Cos 55\°[/tex]

⇒ [tex]x^{2} = 36 +16 -48( 0.5736)[/tex]

⇒[tex]x^{2} = 24.4672[/tex]

⇒[tex]x= 4.946[/tex]

⇒ x≈5 ( nearest whole number)

Hence,  the length of the diagonal x= 5 units( nearest whole number) in the given parallelogram.

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Answer:

true

Step-by-step explanation:

Hopefully this helps

Answer:

15^4

Step-by-step explanation: