What is the measure of this angle?
140°
80 70 60 50 40
310 40 310 610 710 80 90 100 110 120 130 140 150
50°
170 160 150 140 130 120
50 40 30 20 10
180°
40°
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The statements that must be true about this diagram will be ∠4 > ∠1, ∠4 > ∠2, and ∠4 = ∠1 + ∠2. Then the correct options are B, C, and E.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The exterior angle of a triangle is almost always equal to the addition of the interior and opposing interior angles. The term "external angle property" refers to this feature.

By the above theorem, the equation is given as,

∠4 = ∠1 + ∠2

The statements that must be true about this diagram will be ∠4 > ∠1, ∠4 > ∠2, and ∠4 = ∠1 + ∠2. Then the correct options are B, C, and E.

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The missing diagram is attached below.

Answer:

2

Step-by-step explanation:

4-2=2 take four cows,then sell two of them you will remain with two

Answer:

Step-by-step explanation:

A solution to the inequality x < 24 is a value of x that makes the inequality true when it is substituted into the expression. In other words, when x is a solution to the inequality x < 24, it must be less than 24.

For example, some solutions to the inequality x < 24 include -5, 0, 23.5, and any other value that is less than 24. However, the numbers like 24 and greater than 24 are not solutions to the inequality x < 24.

Answer:

(3, [tex]\frac{1}{2}[/tex] )

Step-by-step explanation:

to find the point of intersection, solve the equations simultaneously.

3x + 2y = 10 → (1)

2x - 6y = 3 → (2)

multiplying (1) by 3 and adding to (2) will eliminate y

9x + 6y = 30 → (3)

add (2) and (3) term by term to eliminate y

11x + 0 = 33

11x = 33 ( divide both sides by 11 )

x = 3

substitute x = 3 into either of the 2 equations and solve for y

substituting into (1)

3(3) + 2y = 10

9 + 2y = 10 ( subtract 9 from both sides )

2y = 1 ( divide both sides by 2 )

y = [tex]\frac{1}{2}[/tex]

solution is (3, [tex]\frac{1}{2}[/tex] )

Answer: b i think

Step-by-step explanation:

Answer:

625

5 is multiplied 4 times, that is, 5 × 5 × 5 × 5 = 625

The hypotenuse of this triangle is equal to 16√5 cm.

In Euclidean geometry, Pythagorean's theorem is given by this mathematical expression:

a² + b² = c²

Where:

Note: c = 4a

Substituting the given parameters into the Pythagorean's theorem formula, we have the following;

a² + b² = c²

a² + (4√15)² = 4a²

4a² - a² = (4√15)²

3a² = 240

a² = 80

a = 4√5 cm.

For the hypotenuse, we have:

Hypotenuse, c = 4a

Hypotenuse, c = 4(4√5)

Hypotenuse, c = 16√5 cm.

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Answer:

Hypotenuse : 16cm

Shorter leg of triangle: 4cm

Step-by-step explanation:

So, we are told [tex]4\sqrt{15}[/tex]  is the longer leg, let's say this is a.

[tex]4\sqrt{15} = \sqrt{240}[/tex], the Pythagorean is [tex]a^2+b^2=c^2[/tex], we'll say b = shortest leg, which is what we're solving for.

Since the hypotenuse (c), is 4 times b I changed it to 4b in my equation.

[tex]\sqrt{240} + b = 4b[/tex], square this to get [tex]240 + b^2 = 16b^2[/tex], -b^2 on both sides

[tex]240=15b^2[/tex], then divide by 15. [tex]16=b^2[/tex], use square root and you get [tex]4 = b[/tex]

hope this helps. btw since hypotenuse is 4 times b, just do 16cm, but your answer is 4 cm

The number with the least value is n - p and the number with the greatest value is p - n.

Based on the number line (see attachment), we would assign a numerical value to the two numbers, n and p in order to determine their output (numerical value).

Assuming the variable n represents the numerical value -0.8 and the variable p represents the numerical value 0.4, we would evaluate each of the given mathematical expressions as follows;

n - p = -0.8 - 0.4

n - p = -1.2 (least value).

For the second mathematical expressions, we have the following numerical value:

n + p = -0.8 + 0.4

n + p = -0.4

For the third mathematical expressions, we have the following numerical value:

p - n = 0.4 - (-0.8)

p - n = 0.4 + 0.8

p - n = 1.2 (greatest value).

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Answer:

33<35; 3 cans for 0.98

Step-by-step explanation:

0.98÷3=0.326... rounds to 33 cents

4.14÷12=0.345 rounds to 35 cents

The distance across the lake is as follows;

d = 45 m.

Similar triangle are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.

Therefore, let's find the side d of the similar triangles DBA and ECA.

Hence, using proportion,

d / 30 = 145 + 290 / 290

d / 30 = 435 / 290

cross multiply

290d = 435 × 30

290d = 13050

divide both sides by 290

d = 13050 / 290

d = 45

Therefore,

d = 45 meters

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Answer:

  ≈ 68.8530

Step-by-step explanation:

You want the area between the curves y = 12 -2x² and y = x² -8.

The area will be the integral of the difference between the curves, between the points where the curves intersect.

  h(x) = (12 -2x²) -(x² -8) = 20 -3x² . . . . . height of a differential of area

The point where the curves intersect has an x-value that makes h(x) = 0. We choose to call the positive value 'a'. The curves also intersect at x=-a.

  h(a) = 0

  20 -3a² = 0

  a² = 20/3

  a = √(20/3) = (2/3)√15

So, the integral is ...

  [tex]\displaystyle A=\int_{-a}^a{(20-3x^2)}\,dx=\left(20x-\dfrac{3x^3}{3}\right)_{-a}^a\\\\A=2a(20-a^2) = \dfrac{4}{3}\sqrt{15}\cdot\left(20-\dfrac{20}{3}\right)\\\\A=\boxed{\dfrac{160\sqrt{15}}{9}\approx68.8530}[/tex]

The area between the curves is about 68.8530 square units.

The value of the expression is 1 / (x² [tex]y^4[/tex]).

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

[tex]x^{-2}[/tex] / [tex]y^4[/tex]

[tex]x^{-2}[/tex] can be written as 1/x².

Now,

(1/x²)/[tex]y^4[/tex]

= 1 / (x² [tex]y^4[/tex])

Thus,

The value is 1 / (x² [tex]y^4[/tex]).

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The perimeter of the triangle is 7x + y -4 feet. The correct option is B.

A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.

Given:

The sides of the triangles are 4x+5 feet, y-7 feet and 3x-2 feet.

To find the perimeter:

The perimeter of the triangle is the sum of all the sides of the triangle.

So, the perimeter = (4x+5) + (y-7) + (3x-2)

The perimeter = 4x+5 + y-7 + 3x-2

The perimeter = 4x + 3x + y +5 -7 -2

The perimeter = 4x + 3x + y +5 -9

The perimeter = 7x + y -4 feet.

Therefore, 7x + y -4 feet is the perimeter.

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The matched statements are:

1↔a, 2↔c, 3↔b, 4↔d

Mensuration is the branch of mathematics that studies the measurement of geometric figures and their parameters like length, volume, shape, surface area, lateral surface area, etc.

Given radius (r) of the cylinder, cone and sphere = r

Height (h) of the cone and cylinder = 2r

Volume of cylinder = πr²h

⇒π(r²)(2r)

⇒2πr³

Volume of cone = 1/3 πr²h

⇒1/3π(r²)2r

⇒2/3 πr³

Volume of sphere = 4/3 πr³

⇒4/3 πr³

From the above calculation we can match the given question:

1. The volume of 3 cones = 3×2/3πr³ = 2πr³ ↔ a) The volume of 1 cylinder

2.The volume of 2 cones = 2×2/3πr³=4/3πr³ ↔ c)
The volume of 1 sphere

3. The volume of 1 sphere ↔ b) 2/3 volume of 1 cylinder = 2/3×2πr³=4/3πr³

4. The volume of 1 cone ↔ d) 1/3 volume of 1 cylinder = 1/3×2πr³=2/3πr³

Hence, by the above calculation the matched statements are as follows:

1↔a, 2↔c, 3↔b, 4↔d.

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Answer:  18

Step-by-step explanation: Here's how I got my answer:

24.75 + 54.79

I added it because both the jersey AND the shorts make up a full uniform.

=79.54

Now, we need to divide the 79.54 (total cost for 1 jersey) by 1500, to find out how many/about how many jersey's she can afford. If you divide correctly, you should get 18.85843600704048. So, we need to round DOWN, because we need to see how many jerseys we can afford WITHOUT GOING OVER the budget. So, rounding down I got 18. 18 would be your answer, though you would have some money left over.

1/3 - inch cubes across the bottom layer = 30

the number of layers is 9

Total number of 1/3-inch cubes 270 cubes

The small cube inside has a dimension of 1/3

The area of the cube is 1/3 * 1/3 = 1/9

the area of the bottom layer is 2 * 1 2/3 = 10/3

the number of small cubes across the bottom is

=  10/3 / 1/9

= 30

The number of layers is calculated by division

= total height of layers / 1/3-inch side of the cube

= 3 / 1/3

= 9 layers

Total number of 1/3-inch cube

= 30 * 9

= 270 cubes

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All measures of sides and angles are listed below:

In this problem we should use trigonometry and theorems regarding triangles to determine missing sides and angles (i.e. Law of sine, law of cosine).

Case 1

Two sides and an angle opposite to unknown side are known and missing side length is found by law of cosine:

c = √(a² + b² - 2 · a · b · cos C)

Where:

(C = 62°, a = 18, b = 17)

c = √(18² + 17² - 2 · 18 · 17 · cos 62°)

c ≈ 18.046

c ≈ 18

Case 2

The larger diagonal of a rhombus bisects the two smaller angles of quadrilateral. The length of the larger diagonal of a rhombus is found by the following formula:

D = 2 · a · cos 0.5α

Where:

(a = 20, α = 54°)

D = 2 · 20 · cos 27°

D ≈ 35.640

D ≈ 35.6

Case 3

According to the law of cosine, the greater the side length, the greater the angle opposite to it:

20² = 10² + 12² - 2 · 10 · 12 · cos α

Where α is the angle opposite to the larger side, in degrees.

400 = 244 - 240 · cos α

156 = - 240 · cos α

cos α = - 13 / 20

α ≈ 130.541°

α ≈ 131°

Case 4

By using the approach used in case 1:

(C = 34°, a = 30, b = 19)

c = √(30² + 19² - 2 · 30 · 19 · cos 34°)

c ≈ 17.773

c ≈ 18

Case 5

By using the approach used in case 2:

(a = 20, α = 38°)

D = 2 · 20 · cos 19°

D ≈ 37.820

D ≈ 37.8

Case 6

By using the approach used in case 3:

18² = 12² + 16² - 2 · 12 · 16 · cos α

324 = 400 - 384 · cos α

- 76 = - 384 · cos α

cos α = 19 / 96

α ≈ 78.585°

α ≈ 79°

Case 7

By using the approach used in case 1:

(C = 58°, a = 20, b = 18)

c = √(20² + 18² - 2 · 20 · 18 · cos 58°)

c ≈ 18.506

c ≈ 19

Case 8

By using the approach used in case 2:

(a = 18, α = 34°)

D = 2 · 18 · cos 17°

D ≈ 34.427

D ≈ 34.4

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Yes, Roman's rate, in miles per hour, increase from session to session.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

A) Given that, time =2/125 and distance =9/10

So, speed = Distance/Time

= 9/10 ÷ 2/125

= 9/10 × 125/2

= 56.25 miles per hour

B) Time =3/200 and Distance =11/12

Speed = 11/12 ÷ 3/200

= 12/11 × 200/3

= 72.73 miles per hour

C) Time =3/250 and Distance =17/20

Now, speed =17/20 ÷ 3/250

= 17/20 × 250/3

= 70.83 miles per hour

Yes, Roman's rate, in miles per hour, increase from session to session.

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The number of possible triangles for the given measurement are two.

A polygon with three sides, vertex and angles refers as a triangle.

Given that, a triangle ABC, where, A = 42° a = 8.2 b = 10.4

We know that, we can determine, how many solutions there will be by using relation between a and bsinA

a > bsinA = two solutions

a < bsinA = no solution

a = bsinA = one solution

Finding relation between a and bsinA

a = 8.2 and b = 10.4 and A = 42°

bsinA = 10.4×sin42°

= 6.96

This gives, bsinA < a

Therefore, we get the case 1st,

Hence, The number of possible triangles is 2.

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Answer: 8

Step-by-step explanation:

10/2=5

6/2=d=3

c/2=4

c=8

Answer:

C = 8

Step-by-step explanation:

If the triangles are similar, then the sides are proportional. And if the hyptenuse BA is 2 times larger than the hypotenuse PR (10:5), then the long leg "C" is 2 times larger than the long leg QP. That is, its length is 4 x 2 = 8

Answer:

if x is -6,

4(-6) + 8y = -40

-24 + 8y = -40

-24 +(-40) = 8y

-24 -40 =8y

-64 = 8y

-64 ÷ 8 =8y ÷ 8

-8 = y

Answer:

-2

Step-by-step explanation:

4x + 8y = -40

since X= -6

then 4(-6) + 8y = -40

-24 + 8y = -40

8y = -40 +24

since the -24 crossed the equal to sign it becomes +24

8y = -16

8y/8 = -16/8

y = -2

The equation of the line that passed through the points, can be found to be y = -4 x + 1

The equation of a line takes the form:

y = mx + b

m = slope

b = y - intercept

The slope is:

= ( Y2 - Y1 ) / ( X 2 - X 1 )

Given the points, (-1,5) and (2,-7), the slope is:

= ( - 7 - 5 ) / ( 2 - ( - 1 ))

= - 12 / 3

= - 4

The y - intercept can be found by plugging in the slope and the value of a point into the equation:

- 7 = -4 ( 2 ) + b

b = -7 + 8

b = 1

The equation is therefore:

y = -4 x + 1

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The taxes paid for each taxable income is given as follows:

a. $400,000: $113,775.

b. $10,954: $1,095.4.

c. $108,962: $18,904.88.

d. $209,850: $47,222.5.

The amount of taxes is obtained identifying the correct interval in the table and then applying the proportions.

For a taxable income of $400,000, the tax is of $45,210 plus 35% of the income ​over $204,100, hence:

45210 + 0.35(400000 - 204100) = $113,775.

For a taxable income of $10,954, the tax is a simple 10%, hence:

0.1 x 10954 = $1,095.4.

For a taxable income of $108,962, the tax is of 12962 plus 24% over 84,200, hence:

12962 + 0.24 x (108962 - 84200) = $18,904.88.

For a taxable income of $209,850, the tax is of $45,210 plus 35% of the income ​over $204,100, hence:

45210 + 0.35(209850 - 204100) = $47,222.5.

Recapping, we identify between which two values the taxable income is located, and then apply the tax rule defined by the table for the range in which the income is located.

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Answer:

D. [tex]10^{\circ}[/tex]

Step-by-step explanation:

Let the measure of minor arc [tex]AE[/tex] be [tex]\alpha[/tex] and the measure of minor arc [tex]BD[/tex] be [tex]\beta[/tex].

Using the secant-secant theorem, [tex]\frac{\alpha-\beta}{2}=32 \implies \alpha-\beta=64^{\circ}[/tex].

By the inscribed angle theorem, [tex]\alpha=84^{\circ}[/tex].

Thus, [tex]\beta=20^{\circ}[/tex].

By the inscribed angle theorem, [tex]x=10^{\circ}[/tex].

The coordinates of point B are (8, -6).

What is midpoint?

The midpoint of a boundary is a point that is in the middle of, close to, or equally spaced from both ends of a line. the middle of something, as in the middle of a process, an event, or a situation: the middle of the negotiations. Geometry.

Given:

The point (-6,4) is reflected over the point (1,-1) and it’s image is point B.

We have to find the coordinates of point B.

Let the point (1, -1) be Midpoint M, and point B has coordinates of (x, y)

As the point A(-6, 4) reflects over the point M, it becomes the midpoint of segment AB

Using midpoint formula, finding the coordinates of the point B

[tex]1 = \frac{-6+x}{2} , -1 = \frac{4+y}{2} \\2 = -6 + x, -2 = 4 + y[/tex]

8 = x ,  -6 = y

x = 8,  y = -6

Hence, the coordinates of point B are (8, -6).

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The graph of the equation g(x) = 2(x + 1) - 2 on the coordinate plane is added as an attachment

From the question, we have the following parameters that can be used in our computation:

g(x) = 2f(x + 1) - 2

Also, we have

f(x) = 2x

Recall that, we have

g(x) = 2f(x + 1) - 2

Using the above as a guide, we have the following:

f(x) = 2x

Add 1 to x

So, we have

f(x + 1) = 2(x + 1)

Subtract 2 from the function

So, we have

f(x + 1) - 2 = 2(x + 1) - 2

Substitute f(x + 1) - 2 = 2(x + 1) - 2 in g(x) = 2f(x + 1) - 2

g(x) = 2(x + 1) - 2

Next, we plot the graph of the function

See attachment for the graph

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The equivalent of the expression of the given expression (1/3) x (3j + 6) will be j + 2.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (1/3) x (3j + 6)

Simplify the expression, then we have

⇒ (1/3) x (3j + 6)

⇒ j + 2

The equivalent of the expression of the given expression (1/3) x (3j + 6) will be j + 2.

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