Simplify each expression (prerequisite

skill)

A. 3x - 5 - x

B. 4x - 5y + x + 7y

C. 6-7y - 1 - 10y

D. 4(3x - y) - 2(5x + 6y)

E. 5x – (3x – 9y) + y

F. 2(4x - 6 - 7 - 8) + 3(x - 2y)

(9x – 6y) – (9x – 6y)

Answer:

x^2-12x+36

Step-by-step explanation:

The first step in solving this equation is to expand the square which makes the equation (x-6)(x-6). Then you distribute the x to both parentheses which leaves you with x^2-6x, and then you distribute the 6 to both parentheses which gives you 6x+36. Then add both binomials which leaves you with x^2-12x+36. The reason it is +36 and not -36 is because you are multiplying a negative 6 by another negative 6.

The value that the linear equation predicts for the year 2001 is 4652.15

The discrepancy between the actual and anticipated value is 2173.85

Given data;

Here, we present the dataset from the United Nations, which contains information on the number of kilowatt-hours of wind energy generated globally. The data set provides statistics on the US for 25 years, from 1990 to 2014, in millions of kilowatt-hours.

The linear equation for the first 11 years of data, from 1990 to 2000, must be determined.

To determine how much the actual value and anticipated value for the year 2001 differ in Quantity, we must first forecast the value for the year 2001 using our fitted equation with y-intercept.

It will be written as y = m(x) + c.

where,

The dependent variable is y. (in our example is quantity)

The independent variable is x. (in our example is the year)

'm' is equal to the slope of the variable X.

'C' is a constant.

The fitted equation is provided as follows:

Quantity = 186.87 (year) - 369274.72

Now that the value for the year 2001 has been provided,

Quantity = -1868.87 -369274.72 

Quantity = 4652.15

The value that the linear equation predicts for the year 2001 is 4652.15.

The precise figure for 2001 is 6806.

For the year 2001, the discrepancy between the actual and anticipated values is

6806 - 4652.15 = 2173.85

The distinction is 2173.85.

(2173.85/6806)*100 is the percentage difference.

As a result, the difference between the actual value and the forecasted value for the year 2001 is 31.94%.

Hence,

The value that the linear equation predicts for the year 2001 is 4652.15

The discrepancy between the actual and anticipated value is 2173.85

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All the batter would fit into the pan as it has more volume than half a gallon.

A cuboid is a three-dimensional closed figure which has volume along with surface area.

The volume of a cuboid is the product of its length, width, and height.

The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.

We know, One gallon is equal to 231 cubic inches.

Therefore, Half a gallon is equal to 231/2 cubic inches.

The volume of the pan is (9×4×4) cubic inches.

= 144 cubic inches.

Now, 144 > 231/2, so it would fit.

Q. Anita is baking pumpkin bread and has a half gallon of batter. She plans to pour the batter into a glass pan with a length of 9 inches, a width of 4 inches, and a depth of four. Determine if all the batter will fit in the pan.

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The missing statement are:

4.  ∠B ≅ ∠B; Reflexive Property of Equality.

5.   ΔBDE ~ ΔBAC; Side-Angle-Side (SAS) Similarity Postulate.

The missing statement are number 4 and 5.

If we say that  4. ∠B ≅ ∠B; Reflexive Property of Equality then:

∠B ≅ ∠B,

Note that  there are two triangles, which are ΔABC and ΔDBE and we also have ∠BDE ≅∠BAC and ∠B ≅ ∠B,

∠BDE + ∠B + ∠BED = 180°

∠BAC + ∠B +  ∠BCA = 180°

Hence, ∠BED = ∠BCA Substitution property of equality

That  birth ΔABC ~ ΔDBE,which is Angle Angle Similarity Postulate

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Answer: 4.∠B ≅ ∠B; Reflexive Property of Equality

5. ΔBDE ∼ ΔBAC; Angle-Angle (AA) Similarity Postulate

Step-by-step explanation:

I just took the test; this exact order should be correct. :D

Answer:

what

Step-by-step explanation:

The probability that hour 10 is the first sample at which x exceeds 1 is 0.0086.

Let X denotes the number of parts in the sample of 20 that require rework. We can model the number X of parts in a random sample of 20 that require rework with a binomial distribution \($X\sim B(20,0.01)$\). We want to find the probability that the first sample at which X exceeds 1 occurs at hour 10. To do this, we need to compute two probabilities:

- The probability that in the first 9 samples, no sample has more than 1 part needing rework.

- The probability that in the 10th sample, there are at least 2 parts needing rework.

To compute the first probability, we use the binomial distribution with n=20 and p=0.01, and note that each of the first 9 samples is independent. Thus, the probability that no sample in the first 9 has more than 1 part needing rework is

\($$P(X\le 1)^9 = \left(\binom{20}{0}(0.01)^0(0.99)^{20} + \binom{20}{1}(0.01)^1(0.99)^{19}\right)^9 \approx 0.435$$\)

To compute the second probability, we just use the binomial probability mass function with n=20 and p=0.01:

\($$P(X\ge 2) = 1 - P(X=0) - P(X=1) \approx 0.0198$$\)

Finally, we can multiply these probabilities to get the desired probability:

\($P(\text{first sample with } X > 1 \text{ is at hour } 10) = 0.435\times 0.0198 \approx \boxed{0.0086}.$\)

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Answer:

1. 1, 2, 3, 4, or 5

2. as long as it is -4, -5, -6, -7, and so on

Step-by-step explanation:

Answer:  Radeon R9 390 graphics card with a Core i5-2300 2.8GHz or FX-6350 processor

Step-by-step explanation:

Answer:

Equiangular and Equilateral

Step-by-step explanation:

I tried

Answer:

C 14

Step-by-step explanation:

here is the proportion I used to get the answer. hopefully this helps

Answer:

6m field will hold most vegetables

Answer: 3 Hours

Step-by-step explanation:

Daniel first paid for her bike, which was 20 dollars. Then she used it for 3 hours, because 20 dollars+5 dollars+5 dollars+5 dollars equals 35 dollars.

Hope this helps!

To find the slope of the line, we must find two points on the line:

          (0,1)  and  (2,4)

Slope = \(\frac{y2-y1}{x2-x1} = \frac{4-1}{2-0} =\frac{3}{2}\)

The slope is 3/2

Hope that helps!

Answer:

\(\frac{3}{2}\)

Step-by-step explanation:

Slope (m): \(\frac{y_2-y_1}{x_2-x_1}\)

Find the slope using (0,1) and (2,4)

\(m=\frac{4-1}{2-0}=\frac{3}{2}\)

\(y = mx + b\)

\(y=\frac{3}{2}x+1\)

*View the attached graph*

Hope this helps!

The probability that exactly 8 customers will arrive in a one-hour period is 0.1563, or approximately 15.63%. The probability of exactly 8 customers arriving in a one-hour period can be calculated using the Poisson distribution formula.

The formula is P(X=x) = (e^-λ * λ^x) / x!, where λ is the mean number of customers arriving in a one-hour period and x is the number of customers we want to calculate the probability for.
So in this case, λ = 8.60 and x = 8. Plugging these values into the formula, we get:
P(X=8) = (e^-8.60 * 8.60^8) / 8!
P(X=8) = 0.1563
Therefore, the probability that exactly 8 customers will arrive in a one-hour period is 0.1563, or approximately 15.63%.

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Answer:

18

Step-by-step explanation:

x + x + 7 = 43

2x + 7 = 43

     -7     -7

2x = 36

x = 18

Answer:

the answer is 2

Step-by-step explanation:

just subtract 2 -

Answer:

:Both Tim and Jasmine calculated the volume properly. Tim gave the exact answer with pi in it, whereas Jasmine multiplied by pi and then rounded

Step-by-step explanation:

Answer:  Both Tim and Jasmine calculated the volume properly. Tim gave the exact answer with pi in it, whereas Jasmine multiplied by pi and then rounded to the nearest hundreth.

Step-by-step explanation:

Answer:

(4,-2)

Step-by-step explanation:

Start off by doing everything in the parenthesis which is everyone of them so 2x-1=-2 , your problem then should look like this:

-2(3x2-5x+2) carry the 2 over so multiply the 2 to everything so

(-6x-4+10x+2) add like numbers

10x+-6=4

-4+2=-2

(4,-2)

Answer:

The slope of a line is change in Y / change in X. The slope of a horizontal line = 0, not undefined. The slope of a vertical line = undefined.

the slope of a virtual lin.e is change in Y / change in X

Answer:

You just answered my question so you can ask yours, what a sped. Now i'm doing the same thing.

Step-by-step explanation:

For a function, f(x) = 1 + 3x , the computed value of lim h→0 [f(5 + h) − f(5)]/h is equals to the three.

In Mathematics, the limit of a function is a value of the function as the input of the function tries approaches some number. Function limits are used to define continuity, integrals, and derivatives. Mathematically, let f(x) be a function and L be limit of function, f(x) at x a exist if and only if lim f(x) = lim f(x) = L

x→a⁻ x→a⁺

We have, f(x) = 1+3x and will compute lim h→0 [f(5 + h) − f(5)]/h . Firstly, determine the value of function at x = 5 , x = 5+h.

So, f(5) = 1+ 3×5 = 16 and f(5+ h) = 1+3(5+h)

= 16+ 3h

Now, lim [ f(5 + h) − f(5)]/ h

h→0

= lim [(16 + 3h) − (16) ]/ h

h→0

= lim [ 16 + 3h - 16 ]/ h

h→0

= lim [ 3h/ h ] = lim [ 3h¹h⁻¹ ]

h→0 h→0

= lim [ 3h¹⁻¹ ] = lim [ 3h⁰ ]

h→0 h→0

= lim 3 (1) = 3 ( since, x⁰ = 1 )

h→0

Hence, the required limit value is 3.

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keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(y+\cfrac{1}{4}= ~~ \stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{4}} ~~ (x-1)\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\)

so we're really looking for the equation of a line whose slope is 1/4 and that it passes through (-10 , -3)

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

\((\stackrel{x_1}{-10}~,~\stackrel{y_1}{-3})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{ \cfrac{1}{4}}(x-\stackrel{x_1}{(-10)}) \implies \stackrel{\textit{\LARGE point-slope}}{y +3= \cfrac{1}{4} (x +10)}\)

\(y+3=\cfrac{1}{4}x+\cfrac{5}{2}\implies y=\cfrac{1}{4}x+\cfrac{5}{2}-3\implies \stackrel{\textit{\LARGE slope-intercept}}{y=\cfrac{1}{4}x-\cfrac{1}{2}} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4(y)=4\left( \cfrac{1}{4}x-\cfrac{1}{2} \right)}\implies 4y=x-2 \\\\\\ -x+4y=-2\implies \stackrel{\textit{\LARGE standard}}{x-4y=2}\)

For different types of triangle, The circumcenter has different properties. The properties varies for acute, obtuse and right angle triangles.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

The spot where the three perpendicular bisectors of a triangle's sides meet and which is equally spaced from the triangle's three vertices.

Properties of circumcenter of triangle are:

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Step-by-step explanation:

the graph is like a rough movie of what the water balloon does :

first it goes up a little bit, then it stays a little bit more of less at the same height, and then it drops.

to answer the questions we really only follow the explicit meaning of the graph line :

A

during the interval of 0 and 2 seconds.

B

during the interval of 2 and 4 seconds.

C

the height of the water balloon decreases the fastest during the interval of 4 and 6 seconds (it decreases by almost 40 ft in 2 seconds).

in the intervals between 6 and 8 seconds and 8 and 10 seconds it only decreases by 20 ft in 2 seconds.

D

after 10 seconds the water balloon hits the ground (height 0 ft). from there on it will stay on the ground (0 ft). therefore, at 16 seconds it will be on the ground (0 ft).

FYI - at least on Earth this will not happen in real life : there will never be a period of time > 0 seconds where the balloon will stay flat in the air (unless something is holding it up). and any falling object (except an object with a large air resistance like a feather) will speed up during the fall and not slow down.

Answer:

6,72

Step-by-step explanation:

Answer:

1. 6 hours

2. 72 minutes

Step-by-step explanation:

For the first one, you want to find the unit rate. to do this, you find 15%*8 which is 1.2. Then, since it's 5 days a week, you multiply that by 5. 1.2*5 is 6 and that's how you get 6 hours.

For number 2, you go back to 1.2 hours. then you multiply 1.2 by 60 because there are 60 minutes in an hour. that makes 72 so 72 minutes each day

I hope that this helped!

Answer:

The mother is 56 years old while her son is 8 years old

Step-by-step explanation:

Let x be the age of the mother

Let y be the age of her son

A mother is currently 7 times older than her son

x = 7y  -------equation 1

In 4 years time, she will be 5 times older than her son

In 4 years, their ages will be

x + 4 ------mother

y + 4 ------son

x + 4 = 5(y+4)

x + 4 = 5y + 20    ----equation 2

Substitute equation 1 to equation 2

7y + 4 = 5y + 20

Transpose

7y - 5y = 20 - 4

2y = 16

y = 16/2

y = 8

Substitute y = 8 to equation 1

x = 7y

x= 7(8)

x = 56

On a coordinate graph, Jan’s house is located at (–1, 5), and Karen’s house is located at (2, –3). The approximate distance between their houses is 8.5 units.

Given, Jan's house is located at (–1, 5), and Karen's house is located at (2, –3).

We have to find the approximate distance between their houses.

Step 1: Use the distance formula to find the distance between the points.(the formula is given below) distance = sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Step 2: Assign the values from the given data and simplify the equation distance = sqrt{(2-(-1))^2+(-3-5)^2} distance = sqrt{(2+1)^2+(-8)^2} distance =  sqrt{(3)^2+(64)} distance =  sqrt{9+64} distance = sqrt{73}

Step 3: Approximate the radical value of the distance.

We know that √73 lies between √64 and √81   .i.e. √64 < √73 < √81 or 8 < √73 < 9.

Approximating to the nearest tenth, we get a distance ≈  8.5 units.

Therefore, the approximate distance between their houses is 8.5 units.

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The probability of drawing a red 7 and black face card is P ( A ) = 1/221

Given data ,

Let the probability of drawing a red 7 and black face card be P ( A )

Now , the compound probability is given by\

The number of red 7 cards = ( red of diamonds 7 + red of hearts 7 )

Probability of drawing a red 7 = 2/52

Now , the card is not replaced , so the total number of remaining cards = 51

And , number of black face cards = 6

Probability of drawing a black face card = 6/51

So , P ( A ) = 2/52 ( 6/51 )

P ( A ) = 12 / 2652

On simplifying , we get

P ( A ) = 1/221

Hence , the probability is P ( A ) = 1/221

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Answer:

13

Step-by-step explanation:

Prime numbers are only divisible by 1 or themselves.

No other factors

Answer: 25cm²

Step-by-step explanation:

Ok, so I haven't actually learnt this in school so I'm going to give it my best shot. (Don't be surprised if I get this wrong though.)

So, Quadrilaterals A and B are similar. They have the same angles. Therefore, (I'm thinking that) Quadrilateral B is just a scaled-up version of Quadrilateral A.

Here comes my theoretical part:

If one side of Quadrilateral B is 5 times longer than the same side of Quadrilateral A...

(Quadrilateral A is 3cm, and Quadrilateral B is 15cm).

... then the area of the entire Quadrilateral B should just be 5 times bigger than Quadrilateral A.

Therefore, (I'm guessing), Quadrilateral B has an area of 25cm²

Answer:

th

e last oneStep-by-step explanation:

Answer:

I think its E because it's in between E and F and E and G

Step-by-step explanation: