What’s the sum in the diagram, a + b + c =

Answer:

Step-by-step explanation:

There are 2 very distinct and important things that we need to know before completing the problem. First is that we are given that the cos of an angle is 1/3 (adjacent/hypotenuse) and it is in the first quadrant. We also need to know that the identity for sin2θ = 2sinθcosθ.

We already know cos θ = 1/3, so we need now find the sin θ. The sin ratio is the side opposite the angle over the hypotenuse, and the side we are missing is the side opposite the angle (we do not need to know the angle; it's irrelevant). Set up a right triangle in the first quadrant and label the base with a 1 (because the base is the side adjacent to the angle), and the hypotenuse with a 3. Find the third side using Pythagorean's Theorem:

[tex]3^2=1^2+y^2[/tex] which simplifies to

[tex]9=1+y^2[/tex] and

[tex]y^2=8[/tex] so

[tex]y=\sqrt{8}=2\sqrt{2}[/tex] so that's the missing side. Now we can easily determine that

[tex]sin\theta=\frac{2\sqrt{2} }{3}[/tex]

Now we have everything we need to fill in the identity for sin2θ:

[tex]2sin\theta cos\theta=2(\frac{2\sqrt{2} }{3})(\frac{1}{3})[/tex] and multiply all of that together to get

[tex]2sin\theta cos\theta=\frac{4\sqrt{2} }{9}[/tex]

Answer:

1ft x 36ft

2ft x 18ft

3ft x 12ft

4ft x 9ft

6ft x 6ft

Step-by-step explanation:

A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees

Area of a triangle = 1/2 x base x height

If area is 18ft², then the dimensions of base x height = 18 x 2 = 36

all the possible positive integers that could represent its base and height can be determined be known by determining the factors of 36

factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, and 36

Possible dimensions of base and heights are :

1ft x 36ft

2ft x 18ft

3ft x 12ft

4ft x 9ft

6ft x 6ft

Answer:

A' : {2, 4, 5, 6, 8, 9, 10, 11, 13, 15, 16, 18}

Answer:

197.3 feet

Step-by-step explanation:

197.295 rounded to the nearest hundredth is 197.30 or 197.3

The height of the tree if the point on the ground from the tree is 92 feet will be 197.29 feet.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.

The angle of elevation to a nearby tree from a point on the ground is measured to be 65°.

The height of the tree if the point on the ground from the tree is 92 feet. Then we have

Let h be the height of the tree. Then we have

[tex]\tan 65^o = \dfrac{h}{92}\\\\ 2.1445\ = \dfrac{h}{92}[/tex]

Then we have

[tex]\rm h = 2.1445 \times 92\\\\h = 197.29\ ft[/tex]

More about the right-angle triangle link is given below.

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Answer:

(For the image) A

Step-by-step explanation:

Answer: 6 blocks

Step-by-step explanation:

Given

Volume of the rectangular prism is [tex]V=\dfrac{3}{4}\ yd^3[/tex]

Length of the cubic block is [tex]a=\dfrac{1}{2}\ yd[/tex]

Volume of each cubic block is

[tex]\Rightarrow V_o=\left (\dfrac{1}{2}\right)^3\\\\\Rightarrow V_o=\dfrac{1}{8}\ yd^3[/tex]

Suppose, n blocks are required to measure the volume of Prism

[tex]\Rightarrow V=nV_o\\\\\Rightarrow \dfrac{3}{4}=n\cdot \dfrac{1}{8}\\\\\Rightarrow n=\dfrac{3\times 8}{4}\\\\\Rightarrow n=6\ \text{blocks}[/tex]

Thus, 6 blocks are required to measure the volume of prism.

Yes that person is correct

Answer:

3x10=30   30x178=5,430

Step-by-step explanation:

[tex]3 \times 10 \times 178 \\ 30 \times 178 \\ 5340 \: \: answer[/tex]

cosine 122.2 = -0.532876276......

Answer:

B. 1/2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Functions

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 4(2)ˣ

Step 2: Evaluate

Answer:

were are the pairs?

Answer:

As the x-values go to negative infinity, the function´s values go to positive. infinity.

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

Hope it helps...

have a great day!!

Answer:

(B) As the x-values go to negative infinity, the function's values go to positive infinity.

Step-by-step explanation:

The x-values the answer choices are talking about are the values on the x-axis.

Looking at the graph, when the x-values go to negative infinity (meaning it keeps on going left, or negative), the function goes up, meaning the function goes to positive infinity.

When the x-values go to positive infinity (meaning it keeps on going right, or positive), the function goes up, meaning the function goes to positive infinity.

Out of all the answer choices, only B agrees with the observations written above.

Hope that helps (●'◡'●)

Answer:

total balls = 18 .... 3/x = 1/6

blue = 10 ... 18-(5+3) = 10

p of green = 5/18 = .277

Step-by-step explanation:

Answer

8 More minutes

Step-by-step explanation:

15+ 17 = 32

32/.8 = 40

40 - 32 = 8

Angle 4 and Angle 2 are vertical angles, meaning that they are congruent. Therefore, the measure of angle 2 is 127 degrees.

Angle 4 and Angle 3 are a linear pair, meaning that they are supplementary and add up to 180 degrees. Therefore, the measure of angle 3 is 53 degrees.

Angle 3 and Angle 1 are vertical angles, meaning that they are congruent. Therefore, the measure of angle 1 is 53 degrees.

Hope this helps!

Answer:

<1 = 53

<2 =127

<3 = 53

Step-by-step explanation:

Angles 2 and 4 are vertical angles and vertical angles are equal

<2 = <4 = 127

<1 + <2 =180 since they form a straight line

<1 + 127 = 180

< 1 = 53

<1 and <3 are vertical angles so they are equal

<1 = <3 = 53

Answer:

19.4 cm

Step-by-step explanation:

Hi there!

This is a right triangle. We're given an angle, the side adjacent to the angle and we're solving for the hypotenuse. Given this information, we can use the cosine ratio:

[tex]cos\theta=\frac{adj}{hyp}[/tex]

Plug in the given angle and side

[tex]cos71=\frac{6.3}{BC}\\BC=\frac{6.3}{cos71} \\BC=19.4[/tex]

Therefore, the length of BC is 19.4 cm when rounded to 3 significant figures.

I hope this helps!

Answer:

see below

Step-by-step explanation:

f(x) = -x^2 +4

The vertex form is

y = a(x-h)^2 +k

Rewriting

f(x) = -(x-0)^2 +4

The vertex is (0,4) and a = -1

Since a is negative we know the parabola opens downward

f(x) = -(x^2 -4)

We can find the zeros

0 = -(x^2 -2^2)

This is the difference of squares

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

Using the zero product property

x-2 =0   x+2 =0

x=2   x=-2

(2,0)  (-2,0) are the zeros of the parabola and 2 other points on the parabola

We have the maximum ( vertex) and the zeros and know that it opens downward, we can graph the parabola

Answer:

Your vertex is (4,0)

Step-by-step explanation:

Answer:

Step-by-step explanation:

C -> Percentage of people who take cold drinks

H -> Percentage of people who take hot drinks

J - > Percentage of people who take Juice

i) At least one of drinks = 17 + 3 +15 +18 +7 + 15 + 5 = 75%

ii)  Exactly two types of drinks = Percentage of people who take cold  and hot drinks + Percentage of people who take cold and Juice + Percentage of people who take hot drinks and Juices

= 15 + 13 + 7

= 35%

iii) Exactly one type of drink =  Percentage of people who take only cold drinks + Percentage of people who take only hot drinks + Percentage of people who take only juices

= 17 + 3 + 15

= 35%

iv) None of the drinks = Total percentage - at least one of the drinks

                                    = 100 - 75

                                    = 25%

The statement that is true about the variables analyzed is that there is a negative correlation between the number of miles driven and the gallons of gasoline left in the tank.

This refers to the relation or connection between two or more variables. In this case:

This has the sign -, which shows the correlation is negative. This implies that as the number of miles increase the amount of gasoline decreases.

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Answer:

£32.50

Step-by-step explanation:

my first question to the teacher : so, no windows in the living room ?

so, it is a square living room with 5.5 m side length.

but each wall is a rectangle of 2.2 × 5.5 m.

for one wall we have to deduct a door area of 1.8×0.9 m.

so, one wall

2.2 × 5.5 = 12.1 m²

4 walls

4 × 12.1 = 48.4 m²

minus one door area

1.8 × 0.9 = 1.62 m²

48.4 - 1.62 = 46.78 m² total paint area

1 L paint covers 8 m².

so, we need 46.78/8 = 5.85 liters.

she gets the paint in 2 L tins. so, she needs 3 tins (6 L).

each tin costs £13.

and because she buys 3 tins, she gets the third one for half the price (13/2 = £6.50).

so, she has to pay

2×13 + 6.50 = 26 + 6.50 = £32.50

Answer:

she should add 2 cups of water.

Step-by-step explanation:

2 : 1 = 4 : 2

Answer:

f(n+1) = f(n) - 5

Step-by-step explanation:

Just find some relationship between 2 numbers that are next to each other.

The image of the bar chart is missing and so i have attached it.

Answer:

Bus = 75

Cycle = 20

Walk = 45

Step-by-step explanation:

We are told that 50 students said they travel to school by car.

However, in the bar chart, we see that we have a portion for boys and girls

Under car, when we count along the y-axis, we will see that, there are 6 units for boys and 4 units for girls.

Thus, to find the value of a unit since number of people that took cars is 50, we have;

(6x + 4x)/2 = 50

Where x is the value of one unit. Thus;

10x/2 = 50

5x = 50

x = 50/5

x = 10

Thus, a unit is 10

Under bus;

Boys have 7 units while girls have 8 units.

Thus;

Frequency by bus = ((7 × 10) + (8 × 10))/2 = 150/2 = 75

Under cycle;

Boys have 1 unit while girls have 3 units.

Thus;

Frequency by cycle = ((1 × 10) + (3 × 10))/2 = 20

Under walk;

Boys have 5 units while girls have 4 units.

Thus;

Frequency by cycle = ((5 × 10) + (4 × 10))/2 = 45

Answer:

18225 cm²

Step-by-step explanation:

Divide 540 by 4 to get the length of all sides

540/4 = 135

Square 135 to get the max possible size

135² = 18225

18225 cm²  is the greatest possible area for the quilt.

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given

Divide 540 by 4 to obtain the length of all sides

540/4 = 135

Square 135 to acquire the max possible size

135² = 18225

18225 cm²  is the greatest possible area for the quilt.        

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Answer:

B

Step-by-step explanation:

At - infinity, the function will tend to 0 and at +infinity, the function will tend to +infinity. Those are the two extremas of the function and extremas define the range. Range is all positive real number

Step-by-step explanation:

100Km/hours......V/T

Answer:

95 degrees

Step-by-step explanation:

First find the angles within the triangle. 180 - 43 - 52 = 85, so the missing angle within the triangle is 85. The exterior angle would be supplementary to that, so 180 - 85 = 95.

Answer:

number of students who like only iphone is 36...

Step-by-step explanation:

100 is the total number..

from that 40 like both so we subtract..

100-40=60..

60 = 2x + 3x..

60 / 5 = 12..

so numbet who like iphone is 3x which is 3 * 12=36..

Answer:

° 3/2 × 4/15

Step-by-step explanation:

for checking a division problem use the product and one of the fractions to multiply. if the answer matches the other fraction then your division is correct.