Use the information on the diagonal to find: a. the length ACb. the length ABc. the perimeter of quadrilateral ABCDd. the area of quadrilateral ABCD

the point which will fall in the line is (14, 7)

Explanation:

The coordinates o f S = (2, 1)

When we draw a line from the origin (0, 0) touching the point S, we will see the next point will be (4, 2). Followed by (6, 3).

So when we look at the trend, we see that the x axis is the double of the y axis:

(2y, y) = (x, y)

(2,1 ) , (4, 2), (6, 3)

From the above, we can say the point which will fall in the line will follow that trend:

When we check the options, the only point with that trend is (14, 7).

This because (2(7), 7) = (2y, y)

Hence, the point which will fall in the line is (14, 7)

Step-by-step explanation:

Write 98 as the product of prime factors. Write the prime factors in ascending order.​

2 × 7 × 7

2 × 7 × 7 = 98

Answer: 2×7×7

Step-by-step explanation: 98= 2×7×7

Lets first know about what is prime factor :- A factor which is a Prime number and not a composite number.

prime factor in ascending order = 2,7

hence the required product of prime factor is 2×7×7 or 2×[tex]7^{2}[/tex]

Answer:

m = 3

Step-by-step explanation:

Hello!

We can solve for m by isolating the variable.

The value of m is 3.

We can use the sine rule to find the hole angle, and then find the golfer angle:

Now we can find the golfer angle:

Answer: 25.6 degrees.

Remember that

In a unit circle, the radius of the circle is 1

see the figure below to better understand the problem

we have that

and we know that

so

and we know that

so

therefore

the coordinates (x,y) are

Answer:

2x=128⁰ x=64⁰

Step-by-step explanation:

since they are corresponding angles, the other side (2x) will also be 128⁰. This means that x=64⁰

and 2x=128⁰

Answer:

The only image with edges at the given coordinates is;

Given the figure in the attached image.

we want to identify the image after a translation;

Using one of the edges of the figure;

Applying the above translation we have;

The edge of the image would be at;

Therefore, the only image with edges at the given coordinates is;

Congruent angles simply means angles that are equal. A triangle has three angles . Since one of the angle is given as 98 degree, the other 2 angles which are congruents are therefore equal. The total angle of a triangle is equals to 180 degree. Therefore,

x = 41 degree

Given:

The series is 1/3−2/21+4/147−8/1029+··

Explanation:

For the given series, the first term is,

The common ratio is,

The formula for the sum of infinite series is,

Substitute the values in the formula to determine the sum of infinite series.

Answer: 7/27

It takes 1190 minutes for Allie to drive to the store and then to the car wash.

According to the question,

We have the following information:

Time taken by Allie to drive to the store = 456 minutes

Time taken by Allie to drive to the car wash from the store = 734 minutes

Now, we have to find the total time in minutes. So, we will add the total time taken by Allie to drive to the store and then to the car wash.

(Note that the time asked in the question is in minutes. So, we do not need to change the units of given time.)

Now,

The total time taken by Allie to drive to the store and then to the car wash = Time taken by Allie to drive to the store + Time taken by Allie to drive to the car wash from the store

The total time taken by Allie to drive to the store and then to the car wash = (456 + 734) minutes

The total time taken by Allie to drive to the store and then to the car wash = 1190 minutes

Hence, the total time taken by Allie to drive to the store and then to the car wash is 1190 minutes.

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Complex number z has a power of 5 represented by (-16√3 + 16) + 4(-√3 + 3)i

Given that,

z = 1 + StartRoot 3 EndRooti, what is z5? 16 + 16StartRoot 3 EndRoot i –16 + 16StartRoot 3 EndRoot i –16 – 16StartRoot 3 EndRoot i 16 – 16StartRoot 3 EndRoot i

What is a complex number?

It is characterized as a number that can be expressed as x+iy, where x is a real number or the real portion of the complex number, y is the imaginary portion of the complex number, and I is the iota, which is just the square root of -1.

We have:

z = 1 + √3i

We have to find: z⁵

z⁵ = (1 + √3i)(1 + √3i)(1 + √3i)(1 + √3i)(1 + √3i)

z⁵ = (-2 + 2√3)(1 + √3i)(1 + √3i)(1 + √3i)

z⁵ = (-16√3 + 16) + 4(-√3 + 3)i

Therefore, the complex number z's power of 5 is -16√3 + 16) + 4(-√3 + 3)i

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The wave length of the gamma ray with a frequency of 1.0 x 10¹⁹ is 3 x 10⁻¹¹

Wave length:

Wavelength refers the distance between two peaks (or troughs) of a wave, and is therefore measured in meters.

The formula for calculating wave length is,

λ = c/v

where,

c = 3.0 × 10⁸, i.e. the speed of light, and

λ = wavelength , and

ν = frequency .

Given,

Here we have the frequency as 1.0 x 10¹⁹.

Now we need to find the wave length of the gamma ray.

Here we know that value of c = 3 x 10⁸

And the value of v = 1.0 x 10¹⁹

Wen we apply the value on the formula then we get,

λ = ( 3 x 10⁸) / ( 1.0 x 10¹⁹)

When we simplify it, then we get,

v = 3 x 10⁻¹¹

Therefore, the wavelength of the gamma ray is 3 x 10⁻¹¹.

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No, Sarita will not be able to catch up with Berti before the end of the sales year.

Berti currently has sold 16, 250 shapes

She continues to sell 340 per month.

In eight months she will be able to sell

16250 + 8 x 340

= 16250 + 2720

= 18970

Sharita has only sold 8,830 shapes

Working overtime and on weekends so that she can sell 1, 082 per month

In eight months she will be able to sell

8830 + 8 x 1082

8830 + 8656

17486

No, Sarita will not be able to catch up with Berti before the end of the sales year.

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The correct option for the fraction with polynomials is y=6.

Expressions of more than two algebraic terms that contain different powers of the same variable is a polynomial.

The polynomial fraction is an expression of polynomial divided by another polynomial.

We can solve the fraction to get the value of y as follows;

[-8/(2y-8)]= [5/(y+4)]-[(7y+8)/(y²-16)]

[-8/(2y-8)]= [5/(y+4)]-[(7y+8)/(y+4)(y-4)]

[-8/(2y-8)]= [5(y+4)-(7y+8)]/(y+4)(y-4)] (L.C.M) of the fraction

[-8/(2y-8)]= (5y-20-7y-8)/(y+4)(y-4)

[-8/(2y-8)]= (-2y-28)/(y+4)(y-4)

[-8/2(y-4)]= (-2y-28)/(y+4)(y-4)

[-8/2(y-4)]= [-2(y-14)]/(y+4)(y-4)

[-4/(y-4)]= [-2(y-14)]/(y+4)(y-4)

Multiply both sides of the equation by -(y-4)

4= 2(y-14)/(y+4)

Cross multiply

4(y+4)=2(y+14)

Divide through by 2

2(y+4)=y+14

2y+8=y+14

collect like terms

2y-y=14-8

y=6.

Hence, we can state that the value of y for the polynomial with fraction is 6.

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The total amount of money in the savings account after 11 weeks is  $1010.

The from of the equation that can be used to determine the total amount of money in the savings account is a linear equation. A linear equation is an equation that has one variable that is raised to the power of one. When a linear equation is drawn on a coordinate graph, it is usually a straight line.

The form of the linear equation is:

Total amount = amount she starts with + (number of weeks x amount of money she adds each week)

S = $350 + ($60 x W)

S = $350 + $60W

Amount she would have in 11 weeks :  $350 + ( 11 x $60)

$350 + 660 = $1010

Here is the complete question:

Lisa is putting money into a savings account. She starts with $350 in the savings account, and each week she adds $60. Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Jenny has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 11 weeks.

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Answer:

2(x + 9)

Explanation:

Let x represent the unknown value.

Double a quantity increased 9 means;

*We'll multiply the quantity by 2

*Increased by signifies addition

*Quantity means we'll put the expression after it in brackets

Let's go ahead and write the required algebraic expression;

In this session we will focus on calculating the composition of f and f.

given the function f, the composition f composition f is obtained by taking the definiton of f and replace the varaible x with the function f itself. So we are given that

So

So we have that f composition f is the function x.

A.

The number of different ways the computers can be chosen is given by a combination of 10 choose 4.

A combination of n choose p is given by the formula below:

So we have:

B.

If the first computer chosen is the one defective, the probability of the first PC being defective is 4/10, the probability of the second one not being defective will be 6/9, for the third not being defective is 5/8 and for the fourth not being defective is 4/7.

Since the defective PC can be any of the 4 bought, we need to multiply the probability above by 4. So the final probability is:

The value of sin 2x=0.8304 ,cos 2x=0.557,tan 2x=1.498 when the value of tan x is 8/15 and using the trigonometry identities as tan x as the formula in sin 2x, cos 2x, tan 2x.

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations (csc).

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.

sin 2x=2 tan x/(1+(tan x)²)

cos 2x=(1-(tan x)²)/(1+(tan x)²)

tan 2x=sin 2x/cos 2x=2 tan x/(1-(tan x)²)

Here,

tan x=8/15

sin 2x=2 tan x/(1+(tan x)²)

= 2*8/15/(1+(8/15)²)

=(16/15)/(289/225)

=(16*15)/(289)

≈0.8304

cos 2x=(1-(tan x)²)/(1+(tan x)²)

=(1-(8/15)²)/(1+(8/15)²)

=(225-64)/(225+64)

≈0.557

tan 2x=sin 2x/cos 2x

tan 2x= 0.8304/0.557

=1.498

≈1.5

When the value of tan x is 8/15, the values of sin 2x=0.8304, cos 2x=0.557, and tan 2x=1.498 using the trigonometry identities as tan x as the formula in sin 2x, cos 2x, tan 2x.

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Answer:

A. (1/2) bucket

Step-by-step explanation:

    6           11

4 ------ - 3 ------- = ?

    14          12

14 × 4 = 56

56 + 6 = 62

12 × -3 = -36

-36 - 11 = -47

 62       47

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

  14        12

 62(12)        47(14)

-------    -     -------

  14(12)         12(14)

744     658       86

------- - ------- = --------

 168     168       168

 86 ÷ 2

-------

168 ÷ 2

43

----- = 0.511

84

0.511 ≈ (1/2)

I hope this helps!

Answer:

1/2 bucket

Step-by-step explanation:

For part A. One way to know if there is a correlation between the data is to graph the data set, like this

Then, as can you see the data presents a positive linear correlation.

For part B. You can take the coordinates of two points and find the slope of the line using the formula

If you take

Now, using the slope formula, you can find the equation of the line in its slope-intercept form

Therefore, the function that best fits the data is

For part C. The slope of the plot is 10 and indicates that for every hour students spend time studying, they get 10 more points on the science test.

The y-intercept of the plot is 57 and indicates that if students study 0 hours for the science test, they will obtain 57 points as a grade.

The multiplication expression is  L×w

The expression is written as N= r+ g + w + b

The final product = 200 boxes

It is important to note that the formula for calculating the area of a rectangle is expressed as;

Area = lw

Where;

The area can be determined by multiplying the length and the width and also by then adding the boxes.

Mathematically, we have;

10( 4 + 5 + 4 + 7)

Also

L × w =  r + g + w + b

Hence,  we have that L×w is a multiplication expression.

Total number of boxes for the length = 20

Total number of boxes for the width = 10

Total area = L×w = 20×10=200

We then have;

N= r+ g + w + b

but r = g = b

Also,

L×B =  3r + w

Hence, a multiplication expression is an expression in which variables or numbers are being multiplied.

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In accordance with the system of linear equations, the ordered pair is (x, y) = (1, 2).

Ordered pairs are constructions characterized by two components, typically real numbers. The most common form of notation is (x, y). In this problem we need to resolve a system of linear equations to obtain the needed values. We find a system of two equations and two variables:

x + y = (3 - x) + (3 - y)

x - y = (x - 2) + (y - 2)

First, simplify each expression of the system:

First equation:

x + y = 6 - x - y

2 · x + 2 · y = 6

x + y = 3

Second equation:

x - y = (x - 2) + (y - 2)

x - y = x + y - 4

- 2 · y = - 4

y = 2

Second, substitute in the first equation:

x + 2 = 3

x = 1

The ordered pair is (x, y) = (1, 2).

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You have the following vertices of a triangle:

A(1,1)

B(4,1)

C(4,5)

For the translation four untis to the right, consider this kind of translation means that it is necessary to sum 4 units to the x-coordinate:

A(1,1) => A'(1+4,1) = A'(5,1)

B(4,1) => B'(8,1)

C(4,5) => C'(8,5)

Next, a translation three units up is done by adding 3 units to the y-coordinate of points A', B' and C':

A'(5,1) => A''(5,1+3) = A''(5,4)

B'(8,1) => B''(8,4)

C'(8,5) => C''(8,8)

Next, a reflection around y=-1 consists in subtracting to the y-coordinate units equivalent to the vertical distance to the line y =-1, just as follow:

for the point A''(5,4) you can notice that the vertical distance of the y-coordinate, which is 4, to the line y=-1 is 5 units, then, it is necessary to subtract 5 units to such line:

A''(5,4) => A'''(5,-1-5)=A'''(5,-6)

for the point B''(8,4), the distance is again 5 units, then, you have:

B''(8,4) => B'''(8,-1-5) = B'''(8,-6)

for the point C''(8,8) the distance from y-coordinate y=8 to the line y=-1 is 9 units, then, yu subtract 9 units to -1:

C''(8,8) => C'''(8,-1-9) = C'''(8,-10)

Hence, the final points are:

A'''(5,6)

B'''(8,-6)

C'''(8,-10)

Answer:

I gotchu

Step-by-step explanation:

1= 155

2= 222

3= 44

4= 132

5= 163