In the figure, mAB = 39° and mCD = 17°. The diagram is not drawn to scale.


What is the value of x?
A. 56°
B. 47.5°
C. 28°
D. 19.5°

Answer:

You're correct

The slope is -2/5; and the y-intercept is  -1/3

Step-by-step explanation:

Slope = (-13/30 + 1/30) / (1/4 + 3/4)

= (-12/30) / ( 4/4)

= - 2/5

Slope intercept form: y = mx + b, where b = y-intercept

b = y - mx

b = (-3/5) - (-2/5)(2/3)

b = -3/5 + 4/15

b = -9/15 + 4/15

b = -5/15

b = -1/3

Answer

Slope = -2/5; y-intercept = -1/3

The slope and the y-intercept of the linear function is;

Option A; slope is -2/5 and y-intercept is -1/3

      m = (y2 - y1)/(x2 - x1)

Let's make use of the first 2 coordinates to get the slope;

x1 = -3/4

x2 = -1/2

y1 = -1/30

y2 = -2/15

m = (-2/15 + 1/30)/(-1/2 + 3/4)

m = (-1/10)/(1/4)

m = -2/5

We know equation of a line in slope intercept form is;

y = mx + c

where m is slope and c is y-intercept

-1/30 = (-2/5)(-3/4) + c

-1/30 - 3/10 = c

c = -1/3

Thus, y-intercept is -1/3 and slope is -2/5

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Answer:

-2

Step-by-step explanation:

The team skipped 8 times, causing them to lose 8 points. They also guessed correctly 6 times, causing them to gain 6 points. 6 points won - 8 points lost = -2 points total.

For this case we have that the figure shown is composed of three triangles and a square. By definition, the area of a triangle is given by:

[tex]A = \frac {1} {2} b * h[/tex]

Where:

b: It's the base

h: It's the height

We have 3 triangles, then the sum of their areas will be:

[tex]A = \frac {1} {2} (9 * 3.5) + \frac {1} {2} (2 * 2) + \frac {1} {2} (5 * 2)\\A = 15.75 + 2 + 5\\A = 22.75 \ units ^ 2[/tex]

On the other hand, the area of a square is given by:

[tex]A = l ^ 2[/tex]

Where:

l: It's the side of the square

According to the figure we have:

[tex]A = 2 ^ 2\\A = 4 \ units ^ 2[/tex]

So, the total area is:

[tex]A_ {t} = 22.75 + 4\\A_ {t} = 26.75 \ units ^ 2[/tex]

Answer:

[tex]A_ {t} = 26.75 \ units ^ 2[/tex]

Answer: 25 heads 25 tails

Step-by-step explanation: you would have a 50/50 chance to get heads or tails so sence there are 2 sides you would get 25 heads and 25 tails

Answer: 25 Times Head And 25 Time Tails

Step-by-step explanation: If you flip a dime in the air and if you flip it 50 times, there is an equally likely chance of flipping heads or tails. Equally likely chance means 50%. Ofcourse, it's not very likely that it would be exactly 25 times for heads and tails. Therefore, if I flipped a dime 50 times I would expect it to land  near 25 times on heads and 25 times around tails.

Have A Great Day!

Answer and explanation:

a) the equation would be:

          w=55m

*w= words

*m=minutes

b) w=55(20)

   w=1,100

There are 1,100 typed in 20 minutes.

hope this helps :)

The variable expression representing the number of words an office assistant types in 'm' minutes can be depicted as '55m'. When evaluated for 20 minutes, the assistant types 1100 words.

The subject of the question is Mathematics, which covers the aspect of forming expressions and evaluating them. This is a practical application of Algebra.

Here, the office assistant types 55 words per minute. We can represent the number of words typed in 'm' minutes as a variable expression, using multiplication. The expression is '55m', implying the assistant types '55m' words in 'm' minutes.

To evaluate the expression for 20 minutes, substitute 'm' with '20'. So, 55*20 = 1100. Therefore, the assistant types 1100 words in 20 minutes.

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Answer:

1)m=9ft and n=10ft

2) p=10cm and r=18cm

3) s=4mi and t=8mi

Step-by-step explanation:

1)

Finding 3rd angle:

F= 180-(90+60)

 = 180-150

 =30

Now using law of sines to find sides m and n

m/sinD = 5/sinF

m= sin60(5/sin30)

  = 8.66

   = 9

n/sinE= 5/sin30

n= sin90(5/sin30)

  = 10

hence m=9ft and n=10ft

2)

Finding 3rd angle:

F= 180-(90+60)

 = 180-150

 =30

Now using law of sines to find sides p and r

p/sinF = 21/sinE

p= sin30(21/sin90)

  = 10.5

   = 10

r/sinD= 21/sin90

r= sin60(21/sin90)

  = 18.18

  =18

hence p=10cm and r=18cm

3)

Finding 3rd angle:

F= 180-(90+60)

 = 180-150

 =30

Now using law of sines to find sides s and t

s/sinF = 3√6/sinD

s= sin30(3√6/sin60)

  = 4.24

   = 4

t/sinE= 3√6/sinD

t= sin90(3√6/sin60)

  = 8.48

  = 8

hence s=4mi and t=8mi !

Answer:

Answer:

{x ∈ R ∣ x ≠ 4/5}

Step-by-step explanation:

Answer:

domain is set of all real number except 4/5

Step-by-step explanation:

[tex]f(x)= \frac{x-3}{x}[/tex]

[tex]g(x)=5x-4[/tex]

Now we find (fºg)(x)

(fºg)(x)=f(g(x))

We plug in g(x) inside in f(x)

[tex]f(g(x))=f(5x-4)= \frac{(5x-4)-3}{5x-4}[/tex]

Now simplify the numerator

[tex]f(g(x))=\frac{(5x-4)-3}{5x-4}=\frac{5x-7}{5x-4}[/tex]

To find out domain we set the denominator =0 and solve for x

[tex]5x-4=0[/tex]

Add 4 on both sides

[tex]5x=4[/tex]

Divide both sides by 5

[tex]x=\frac{4}{5}[/tex]

So domain is set of all real number except 4/5

the answer is Chelsea spent more than $12.75

Option 4, 'Chelsea spent more than $12.75,' matches the given inequality d > 12.75, as it directly corresponds with the 'greater than' symbol in the inequality. So, option 4 is correct.

The inequality d > 12.75 translates to "d is greater than 12.75." Looking at the options provided, we can find a situation that matches the inequality by understanding the meaning of the inequality symbol. Option 4, which says "Chelsea spent more than $12.75," directly corresponds to the inequality given. In this scenario, the amount Chelsea spent (d) is greater than $12.75, which is exactly what the inequality d > 12.75 signifies.

Answer:

x = -3 , y = -6

Step-by-step explanation:

Solve the following system:

{4 x - 3 y = 6 | (equation 1)

{x + 2 y = -15 | (equation 2)

Subtract 1/4 × (equation 1) from equation 2:

{4 x - 3 y = 6 | (equation 1)

{0 x+(11 y)/4 = (-33)/2 | (equation 2)

Multiply equation 2 by 4/11:

{4 x - 3 y = 6 | (equation 1)

{0 x+y = -6 | (equation 2)

Add 3 × (equation 2) to equation 1:

{4 x+0 y = -12 | (equation 1)

{0 x+y = -6 | (equation 2)

Divide equation 1 by 4:

{x+0 y = -3 | (equation 1)

{0 x+y = -6 | (equation 2)

Collect results:

Answer:  {x = -3 , y = -6

Answer: Multiplying and Dividing are inverse operations

Multiplying by a number is the same as dividing by its reciprocal

Step-by-step explanation:

Answer:

Multiply and divide are inverse operations.

Multiply by a number is the same as divide by its reciprocal.

Step-by-step explanation:

To divide by a fraction, you can multiply by its inverse.

If a number is defined as a/b, then the reciprocal of the number is b/a.

The given equation is

[tex]\frac{5}{8}\div \frac{2}{3}=\frac{5}{8}\times \frac{3}{2}[/tex]

Here, [tex]\frac{3}{2}[/tex] and [tex]\frac{2}{3}[/tex] are inverse of each other.

Reason 1:

Multiply and divide are inverse operations.

Reason 2:

Multiply by a number is the same as divide by its reciprocal.

$275*.15(15%)=41.25 (this is the amount of the discount)

$275-$41.25=$233.75 (cost of jacket after discount)

$233.75* .0725=$16.946(round to $16.95, this is the amount of the sales tax).

If you want to know the total cost after tax just add $16.95 to the discounted price of $233.75. The price you pay for the jacket is $250.70.

Answer:

$16.95

Step-by-step explanation:

A department store is having a 15% off sale on all winter coats.

The cost of the winter coat that you purchased = $275

The price after discount of 15% = 275 -(15% × 275)

                                                    = 275 - (0.15 × 275)

                                                    = 275 - 41.25

                                                    = $233.75

Sales tax rate on that location = 7.25%

Sales tax which you would pay = 7.25% × 233.75

                                                    = 0.0725 × 233.75

                                                    = $16.9468 ≈ $16.95

You have to pay $16.95 sales tax.

ANSWER

y=x+5

EXPLANATION

We can observe the following pattern among the x and y-values.

9=4+5

12=7+5

18=13+5

22=17+5

24=19+5

Hence, in general, the function rule is

y=x +5

Answer: Third option.

Step-by-step explanation:

You need to substitute a value of "x" (input value) provided in the table into each function and observe in the value of "y" obtained (output value) matches with the coorresponding output value shown in the table.

For [tex]x=4[/tex]

First option:

[tex]y = 5x\\y = 5(4)\\y=20[/tex]

Second option:

 [tex]y = x + 3\\y = 4 + 3\\y=7[/tex]

Third option:

 [tex]y = x + 5\\y = 4 + 5\\y=9[/tex]

(This one matches with the function table)

Fourth option:

 [tex]y = 3x\\y = (3)(4)\\y=12[/tex]

Then the answer is: [tex]y = x + 5[/tex]

Answer:

1. 5/6 cakes  2.3/10 pizzas  3.  4/8=1/2 bars  4. 12/20= 3/5 chips 5. 10/17 carrots

Step-by-step explanation:

ANSWER

9cm

EXPLANATION

The volume of a square pyramid is calculated using the formula;

[tex]V = \frac{1}{3} {l}^{2}h[/tex]

where h=12cm is the height of the pyramid and l is the length of each side of the square base.

The volume is V=324.

We substitute the values in to the formula and solve for l.

[tex]324 = \frac{1}{3} {l}^{2} \times 12[/tex]

[tex]324 = 1 {l}^{2} [/tex]

[tex] {l}^{2} = \frac{324}{4} [/tex]

[tex] {l}^{2} = 81[/tex]

[tex]l = \sqrt{81} = 9[/tex]

The length of each side of the square base is 9 cm.

Answer:

1050 ft²

Step-by-step explanation:

Enlarging the polygon by a factor of 5 has the effect of increasing the area by a factor of 5², that is 25

new area = 25 × 42 = 1050 ft²

Answer:

If the function is [tex]y=\sqrt{x+6} -7[/tex] , the domain are all values of x  greater than or equal to -6

If the function is [tex]y=\sqrt{x+6-7}[/tex] , the domain are all values of x  greater than or equal to 1

Step-by-step explanation:

First case

we have

[tex]y=\sqrt{x+6} -7[/tex]

we know that

The radicand  of the function must be greater than or equal to zero

so

[tex]x+6 \geq 0[/tex]

[tex]x\geq-6[/tex]

the solution is the interval---------> [-6,∞)

therefore

The domain are all values of x  greater than or equal to -6

Second case

we have

[tex]y=\sqrt{x+6-7}[/tex]

so

[tex]y=\sqrt{x-1}[/tex]

we know that

The radicand  of the function must be greater than or equal to zero

so

[tex]x-1 \geq 0[/tex]

[tex]x\geq 1[/tex]

the solution is the interval---------> [1,∞)

therefore

The domain are all values of x  greater than or equal 1

For this case we have the following system of two equations with two unknowns:

[tex]-2x + y + 6 = 0\\2x + y-8 = 0[/tex]

Adding both equations we have to eliminate the variable "x":

[tex]y + y + 6-8 = 0[/tex]

Adding common terms, keeping in mind that different signs are subtracted and the sign of the major is placed:

[tex]2y-2 = 0\\2y = 2[/tex]

Answer:

[tex]2y = 2[/tex]

Option A

Answer:

Step-by-step explanation:

-7/3, -2 5/8, -2.9

-2 1/3, -2 5/8, -2 9/10

-2 9/10, -2 5/8, -2 1/3

this is the order from least to greatest

-2.9, -2 5/8, -7/3

Answer:

The answer is -2.9, -2[tex]\frac{5}{8}[/tex], -[tex]\frac{7}{3}[/tex]

Step-by-step explanation:

Since the numbers get higher, the negative numbers that are like -2.9 and -2.3 are considered to be less than -1.9 because they are on the left side further from -1.9 and since -1.9 is closer to 0, it is greater than -2.9 and -2.3. The way I explained is just an example.

Answer:

[tex]Area=176cm^2[/tex]

Step-by-step explanation:

The area of a trapezoid is calculated using the formula:

[tex]Area=\frac{1}{2}(Sum\:of\:bases)\times height[/tex]

We substitute the values into the formula to obtain:

[tex]Area=\frac{1}{2}(12+10)\times16[/tex]

We simplify the parenthesis to get:

[tex]Area=\frac{1}{2}(22)\times16[/tex]

We simplify further to obtain;

[tex]Area=176cm^2[/tex]

Answer:

Option 1: 176 cm^2

Step-by-step explanation:

In order to find the area of trapezoid, we need to know the length of two sides(bases) and the vertical height to trapezoid

Here in the given trapezoid

base1 = a = 10cm

base2 = b= 12cm

and

h = 16 cm

The formula for area of trapezoid is:

[tex]Area = \frac{1}{2} (a+b)*h[/tex]

Putting the values

[tex]= \frac{1}{2} (10+12) * 16[/tex]

[tex]= \frac{1}{2} (22)(16)[/tex]

[tex]= \frac{1}{2} * 352[/tex]

[tex]Area = 176 cm^{2}[/tex]

Option 1 is the correct answer..

ANSWER

12 ft

EXPLANATION

The volume of a cylinder is calculated using the formula

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

From the question, the volume was given as 540π ft³ .

The height is given as 15 ft.

We substitute the values to obtain:

[tex]540\pi=\pi {r}^{2} \times 15[/tex]

This implies that;

[tex] {r}^{2} = \frac{540\pi}{15\pi} [/tex]

We simplify to get;

[tex] {r}^{2}=36[/tex]

Take positive square root to obtain:

[tex]r = \sqrt{36} [/tex]

[tex]r = 6ft[/tex]

The diameter is twice the radius.

Hence the diameter is 12ft

The answer is:

The diameter of the cylinder is equal to 12 feet.

Why?

To find the diameter of the cylinder we need to use the formula to calculate its volume.

So,  we have:

[tex]Volume=\pi *r^{2}*h[/tex]

We are given the following dimensions of the cylinder:

[tex]Volume=540\pift^{3}\\\\Height=15ft^{3}[/tex]

Now, using substituting and isolating the radius in order to find the diameter, we have:

[tex]Volume=\pi *r^{2}*h\\\\r^{2}=\frac{Volume}{\pi *h} \\\\r=\sqrt{\frac{Volume}{\pi *h} }[/tex]

Therefore, we have:

[tex]r=\sqrt{\frac{Volume}{\pi *h}}\\\\r=\sqrt{\frac{540\pi ft^{3}}{\pi *15ft}}\\\\r=\sqrt{36ft^{2} }=6ft[/tex]

We know the radius, then, calculating the diameter we have:

[tex]diameter=2*radius=2*6ft=12ft[/tex]

Hence, we have that the diameter of the cylinder is equal to 12 feet.

Have a nice day!

Answer:

144ft^2

Step-by-step explanation:

since it's a kite, there are two pairs of congruent (exactly the same shape) triangles

bc of this you can find one triangle from each pair and double it

e.g.

[tex] \frac{6 \times 8}{2}=24[/tex]

[tex] \frac{12 \times 8}{2}= 48[/tex]

so you would do 2(24+48)=144

The question involves calculating the volume of a right rectangular prism and dividing it by the volume of a unit cube to find out how many such cubes can fit inside the prism.

The question is about finding how many unit cubes, each with edge lengths of 1/2 meter, can fit inside a right rectangular prism whose edge lengths are 4/5 meter, 3/4 meter, and 5/8 meter. To solve this, we first calculate the volume of the prism and then divide it by the volume of a unit cube to determine how many such cubes can fit inside the prism.

Step-by-step Solution:

By applying the above steps, we'll know the exact number of unit cubes that can fit inside the given right rectangular prism.

Standard deviation is a number used to tell how measurements for a group are spread out from the average (mean), or expected value. A low standard deviation means that most of the numbers are close to the average. A high standard deviation means that the numbers are more spread out.

It is a measure of the average distance between the values of the data in the set and the mean. A low standard deviation indicates that the data points tend to be very close to the mean; a high standard deviation indicates that the data points are spread out over a large range of values.

So, good standard deviation is 5 = Very Good, 4 = Good, 3 = Average, 2 = Poor, 1 = Very Poor, The mean score is 2.8 and the standard deviation is 0.54.

Hope this helps :)

6x^2 - 37x + 22

Use the FOIL method to multiply the binomials.

First monomial in each binomial: 3x * 2x = 6x^2

Outside monomials: 3x * -11 = -33x

Inside monomials: -2 * 2x = -4x

Last monomial in each binomial: -2 * -11 = 22

Now, just add: 6x^2 - 33x - 4x + 22 = 6x^2 - 37x + 22

Answer:

6x^2 - 37x + 22

Step-by-step explanation:

Answer:

25x^2-40x+16

Step-by-step explanation:

(5x-4)(5x-4)

= 25x^2-20x-20x+16

=25x^2-40x+16

356,000 would be the answer I believe

Answers:

4668.

Step-by-step explanation:

355790

3 +1 5 +1 5 +1 7+1 00

466800

=4668

Answer:

The mean will stay the same.

The standard deviation will decrease.

Step-by-step explanation:

For the 5 cards, she has received, the mean will be:

μ=(∑x)/n

=125/5

=25

The mean is 25 and the standard deviation is 10.  

σ=10

If a new card is received with $25, then the sum will be $150  

So the new mean will be:

μ'=(∑x)/n

=150/6

=25

And the new standard deviation will be:  

σ'= 9.12

We can clearly see that  

μ= μ'

and

σ> σ'

So the mean will remain the same and standard deviation will decrease. .

Answer:

1/4(x+y)(x-y)

Step-by-step explanation:

We can first factor out the shared 1/4 and it now looks like,

1/4(x^2-y^2)

Since x^2-y^2 is a difference of squares, which is a^2-b^2 = (a+b)(a-b), we can change x^2-y^2 to (x+y)(x-y). So our answer is:

1/4(x+y)(x-y)

The probability that a student doesn't have lice, given that the student tested negative is 99.40%.

Correct option is (D).

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

As per the given diagram:

The probabilities of different events is given in the diagram.

Probability that a student doesn't have lice, given that the student tested negative P(B):

[tex]\frac{P(Test \: shows \: negative) \times P(Student \:has\: no\: lice)}{P(Test\: shows \:negative) \times P(Student\: has\: no\: lice) + P(Test\: shows\: positive) \times P(Student\: has\: no\: lice)}[/tex]

= [tex]\frac{0.94 \times 0.72}{0.94 \times 0.72 + 0.06 \times 0.72}[/tex]

= 0.994

Which is equal to 99.40%

Hence, the probability that a student doesn't have lice, given that the student tested negative is 99.40%.

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Answer:

I think D would be the answer.

Step-by-step explanation:

The most people would see it on the website, making it, if you ask me, the most likely answer.

The sampling method "He asks three random households from each street in his neighborhood" option (a) is correct.

It is defined as the group of data having the same entity which is related to some problems. The sample is a subset of the population, it is a part of the population.

We have a sampling method:

From the provided statement, the best sampling method would be he asks three random households from each street in his neighborhood.

Thus, the sampling method "He asks three random households from each street in his neighborhood" option (a) is correct.

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