Determine the measure of angle BFE 1 ) 69 degrees 2 ) 112 degrees 3 ) 11 degrees 4 ) 224 degrees

Two angles whose sum is 180° are called supplementary angles. The correct option is C.

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

In the given Image, ∠a and ∠b are supplementary angles to each other. Therefore, the correct option is C.

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Answer:

orange: 0.2$, apple: 0.4$

Step-by-step explanation:

we mark the price of an orange x and the price of an apple y. then we write down Maggie's and Tanya's purchases as a set of equations:

10 oranges and 5 apples for 4$ means:

[tex]10x + 5y = 4[/tex]

9 oranges and 3 apples for 3$ means:

[tex]9x + 3y = 3[/tex]

we use the second equation to isolate y:

[tex]3y = 3 - 9x \\ y = 1 - 3x[/tex]

and plug it in the first equation:

[tex]10x + 5(1 - 3x) = 4 \\ 10x + 5 - 15x = 4 \\ 1 = 5x \\ x = 0.2[/tex]

and then we find y:

[tex]y = 1 - 3 \times 0.2 \\ y = 0.4[/tex]

Answer:

21/4

Step-by-step explanation:

Answer:

[tex]\frac{42}{8}[/tex]

Step-by-step explanation:

• First multiply the numerators:

6 x 7 = 42

• Then multiply the denominators:

(6 doesn't have a denominator, which is the same as having a denominator of 1)

1 x 8 = 8

∴ The answer is [tex]\frac{42}{8}[/tex] .

[tex]\tan 61^{\circ}=\frac{59}{x}\\\\x=\frac{59}{\tan 61^{\circ}} \approx \boxed{32.7}[/tex]

Answer:

Ans : 3578.83 feet from the ground

Step-by-step explanation:

You can use sine theory so

sine 32 = height/6400

6400 x sine 32 = height

Easy

The simplification form of the provided expression 6543549 ² × 4³ ÷8 is 3.4254×10¹⁴

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have a mathematical expression:

= 6543549² × 4³ ÷ 8

Using BODMAS

= 6543549² × 8

= 3.4254×10¹⁴

Thus, the simplification form of the provided expression 6543549 ² × 4³ ÷8 is 3.4254×10¹⁴

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See the graph in the image.

They are congruent because the word congruent means the same shape and size and if you look at the picture angle RAM and angle ZMA have the same shape and the same size.

Answer:

6 : 1

Step-by-step explanation:

The length is the longer side compared to the width.

Hence, the length is 42 inches and width is 7 inches.

Taking the ratio :

Answer:

1 : 6

Step-by-step explanation:

42 /7 = 6

We will have to simply the ratios in order to get the answer.

Answer

D

Step-by-step explanation:

The probability of 5 successes given n = 12, x = 5, and p = 0.25 is approximately 0.082 by solving binomial probability.

The correct answer is A) 0.082.

The probability of x successes given the probability p of success on a single trial, with n trials, can be calculated using the binomial probability formula:

[tex]P(x) = (n_C_x) * p^x * (1-p)^{(n-x)[/tex]

In this case, n = 12, x = 5, and p = 0.25. Let's substitute these values into the formula:

[tex]P(5) = (12C5) * (0.25)^5 * (1-0.25)^{(12-5)[/tex]

Using the combination formula ([tex]n_C_r[/tex]) to calculate ([tex]{12}_C_5[/tex]):

[tex]P(5) = (12!)/(5!(12-5)!) * (0.25)^5 * (0.75)^7[/tex]

Simplifying the combination:

[tex]P(5) = (12!)/(5!7!) * (0.25)^5 * (0.75)^7[/tex]

Calculating the factorial terms:

[tex]P(5) = (12111098)/(54321) * (0.25)^5 * (0.75)^7[/tex]

[tex]P(5) = 792 * 0.0009765625 * 0.1334838867[/tex]

P(5) ≈ 0.082

Therefore, the probability of 5 successes given n = 12, x = 5, and p = 0.25 is approximately 0.082 by solving binomial probability.

The correct answer is A) 0.082.

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When the bird is 2 feet away from the first fence post, it reaches its minimum height of 4 feet  , Minimum at (2,4)

Therefore Option C and D is the correct answer.

The equation for a quadratic function is given by

y = a(x-h)² +k²

where (h,k) is the extreme value(vertex).

Here the equation given is

y = x²-4x +8

y = x²-4x+4+4

y = (x-2)² +4

Here the value of a = 1 , h = 2 and k = 4

The extreme value is at (2,4)

Therefore When the bird is 2 feet away from the first fence post, it reaches its minimum height of 4 feet  , Minimum at (2,4)

Therefore Option C and D is the correct answer.

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Using it's concept, it is found that there is a 0.6 = 60% probability that the flower is NOT A ROSE.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 6 + 5 + 4 = 15 flowers, out of which 5 + 4 = 9 are not roses, hence the probability is given by:

p = 9/15 = 0.6 = 60%.

0.6 = 60% probability that the flower is NOT A ROSE.

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The correct Option is Option C: The radius of the cardboard tube of 85th loop of paper is 4.92cm

The arithmetic sequence is the sequence where every term is increased or decreased by a fixed number from the previous number.

Here the outer radius of the tube is 2.4 cm

the thickness of the paper is 0.3mm= 0.03cm

i.e. in every loop the increase in the radius of the loop is 0.03cm

then the radius in every sequence will be  2.40, 2.43, 2.46, 2.49, 2.52, .....

so here it is clear that it is an arithmetic sequence with a common difference of 0.03.

nth term of the sequence, aₙ = a₁ + (n - 1)d where a₁ is the first term, n is the index of the loop, and d is a common difference.

here a₁ =2.40

d=0.03

n=85

the radius of tube of the 85th loop will be= r= 2.40+(85-1)0.03= 2.40+ 2.52= 4.92

Therefore The radius of the cardboard tube of the 85th loop of paper is 4.92cm

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Answer:

a)(0,k)

b)(0,-k)

Step-by-step explanation:

Given:

[tex] \begin{cases} y = a {x}^{2} + k \\ y = a {x}^{2} - k \end{cases}[/tex]

Taking the derivative of y's yields

[tex] \begin{cases} y '= \dfrac{d}{dx} a {x}^{2} + k \\ \\ y '= \dfrac{d}{dx} a {x}^{2} - k \end{cases} \\ \implies\begin{cases} y '= 2a x\\ \\ y '=2ax\end{cases} [/tex]

Now set y' to 0 and solve for x:

[tex] \implies\begin{cases} 2a x = 0\\ \\ 2ax = 0\end{cases} \\ \implies\begin{cases} x= 0\\ \\ x= 0\end{cases} [/tex]

plug in the value of x into the original equation thus

[tex] \begin{cases} y = a ({0}^{2}) + k \\ y = a ({0}^{2} )- k \end{cases}\\ \implies \begin{cases} y = k \\ y= - k \end{cases} [/tex]

Hence,

In the ΔIJH, the value of the cosec (I) is [tex]1\frac{9}{56}[/tex].

Given ΔIJH the length of the hypotenuse is 65,  the length of the base is 33, and the length of the opposite side is 56.

We have to find the value of the cosec (I).

A function of an arc or angle that is most easily represented in terms of the ratios of pairs of sides of a right-angled triangle, such as the sine, cosine, tangent, cotangent, secant, or cosecant.

We know cosec (I) = hypotenuse / opposite side

Substitute the values

cosec (I) = 65/56

              = [tex]1\frac{9}{56}[/tex]

Hence the value of cosec (I) is [tex]1\frac{9}{56}[/tex].

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Answer:

£196 and 400cm

Step-by-step explanation:

3.5^2 = 12.25 will give the whole floor

12.25 × 16 = 196

20^2= 400cm is the front cover of the book

Solution 1 :-

>> -3 (3 - x) = 2x + 5

>> -3 × (3 - x) = 2x + 5

>> -9 + 3x = 2x + 5

>> 3x - 2x = 9 + 5

>> x = 14

Solution 2 :-

>> -6 - 9p = 3p

>> -9p - 3p = 6

>> -12p = 6

>> p = -1/2

Solution 3 :-

>> -5 (-4 - a) = 3a + 8

>> -5 × (-4 - a) = 3a + 8

>> 20 + 5a = 3a + 8

>> 5a - 3a = 8 - 20

>> 2a = -12

>> a = -12 / 2

>> a = -6

Solution 4 :-

>> s - 6 = -5s

>> s + 5s = 6

>> 6s = 6

>> s = 6 / 6

>> s = 1

Answer:

1) x = 14

2) p = - [tex]\frac{1}{2}[/tex]  (- 1/2)

3) a = -6

4) s = 1

work shown in image :)

hope this helps!!

Answer: 484/5

Step-by-step explanation:

For this word problem, it seems confusing with the wording but the equation would just be:

968÷10=x

solving for x, we get 484/5.

Answer:

The answer will be equation

Answer:

2.15%

Step-by-step explanation:

If you were to get the z-score for both 500 and 550 and then get the probability of both those z-scores. After getting the probability you would subtract both probability and get your answer.

Z-score:

550-400/2=3

500-400/2=2

Probability:

3 (from the Z-table) is .9987

2 (from the Z-table) is .9772

.9987-.9772= .0215

.0215 as a percentage is 2.15%

Mean: 400

Standard deviation: 50

Check to see if 500 and 550 fall within the standard deviations:

400+2(50) =500

400+3(50) =550

These values lie between the 2nd and 3rd deviations, so

the value is 0.0235

Percentage: 2.35%

Hope it helps!

Answer:

It will take 55.08 seconds.

Step-by-step explanation:

6 seconds = 210m

1 second = (210÷6)

= 35m

1928m ÷ 35m

=55.08 seconds

Answer = it will take 55.08 seconds to travel 1928m

cylindrical-shaped aquarium is to be filled with water for the newly bought salt water fishes. How much salt water is needed if the aquarium has a 2 ft radius of its base and a height of 3 ft?

Volume = πr²h

V = (3.14) (2)² (3)

V = (3.14) (4) (3)

V = 37.68 ft³

37.68 ft³ of salt water is needed to fill the cylindrical aquarium.

Mr. Lee is buying a spherical water tank for his tomato plantation. How much water could be stored if the water tank has a radius of 2 meters?

Volume = (4/3) πr³

V = (4/3) (3.14) (2)³

V = (4/3) (3.14) (8)

V = (4/3) (25.12)

V = 33.493 m³

Mr. Lee can store 33.493 m³ of water in the spherical tank.

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The equation of the function is g(x)=(x+7)² -2 , Option D is the correct answer.

A function is a mathematical statement that defines relation between two variables.

The f(x) = (x+7)²

The equation for g(x) is ?

graph of function f of x open upward and has its vertex at (-7,0).

Graph of function g of x opens upward and has its vertex at (-7,2).

g(x) is formed by the translation of the function f(x) such that it's vertex is (-7,-2)

Therefore the equation of the function is

g(x)=(x+7)² -2

Therefore , the translation is a shift of the function f(x) 2 units down

Option  D is the correct answer.

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33333333333333333333333333333333333

Answer:

check image below

Step-by-step explanation:

1) [tex]\overline{EJ} \parallel \overline{KF}, \overline{JG} \parallel \overline{KH}, \overline{EF} \cong \overline{GH}[/tex] (given)

2) [tex]\overline{FG} \cong \overline{FG}[/tex] (reflexive property)

3) [tex]\overline{EG} \cong \overline{FH}[/tex] (segment addition postulate)

4) [tex]\angle JEF \cong \angle KFG, \angle JGE \cong \angle KHF[/tex] (if two parallel lines are cut by a transversal, the corresponding angles are congruent)

5) [tex]\triangle EJG \cong \triangle F\text{ }KH[/tex] (SAS)

Answer:

Given:

Let, the slope of the line passing through the point ( m) = -2

The line passing through the point M(-1,-3)= (x1 , y1)

The equation of the line passing through the point M(-1,-3) is

y-y1 = m (x-x1)

or, y-(-3) = -2 (x-(-1))

or, y+3 = -2 (x+1)

or, y+3 = -2x-2

or, 2x+y = -2-3

Hence, 2x+y =-5 is the required equation.

(a) is the correct answer .

Answer:

About 3.5

Step-by-step explanation:

To get slope, you essentially need to find the rise (the y values) over run (the x values). You'll most likely see the formula for slope written like this:

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

Thankfully, you have the values you need to solve the problem!

x1 = 2

x2 = 6

y1 = 7

y2 = 21

So plugging these numbers in, we get:

[tex] \frac{(21) - (7)}{(6) - (2)} \\ \\ \frac{14}{4} \\ \\ 3.5 [/tex]

[EDIT: I misread 6 as 5. Answer has been updated!]