Simplify by factoring or distributing:
1.) 2(x + 3) =
2.) 2(x + 3 + y) =
3.) −5 (2x − 3) =
4.) –5(–8w + p) =
5.) 20 + 32w =
6.) 84 + 36z =
7.) (2x - 6)(5x + 7) =
8.) (y - 10)(4y + 2) =

Answer:

x = 2 ± [tex]\sqrt{15}[/tex]

Step-by-step explanation:

x² - 4x - 11 = 0 ( add 11 to both sides )

x² - 4x = 11

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 2)x + 4 = 11 + 4

(x - 2)² = 15 ( take square root of both sides )

x - 2 = ± [tex]\sqrt{15}[/tex] ( add 2 to both sides )

x = 2 ± [tex]\sqrt{15}[/tex]

Answer:

28 square meters.

Step-by-step explanation:

The total area - the grass area = the cement area.

36 - 8 = 28.

28 square meters.

The next step to derive the quadratic formula is x² + (b/a)x + (b²/2a²)= -c/a + (b²/2a²)

An equation is an expression that shows the relationship between two or more variables and numbers.

Step 1:

ax² + bx + c = 0

Step 2:

ax² + bx = -c

Step 3:

x² + (b/a)x = -c/a

Step 4:

x² + (b/a)x + (b²/2a²)= -c/a + (b²/2a²)

The next step to derive the quadratic formula is x² + (b/a)x + (b²/2a²)= -c/a + (b²/2a²)

Find out more on equation at: https://brainly.com/question/13763238

#SPJ1

Answer:

19 units

Step-by-step explanation:

JM is 40 units, and it is composed of JH and HM. HM is 21 units, and so JH must be the remaining units.

40 - 21 = 19

Brainliest, please :)

Answer:

D

Step-by-step explanation:

    [tex]\sf Sin \ \theta =\dfrac{opposite \ side }{hypotenuse} =\dfrac{12}{37}[/tex]

To find the adjacent side use  Pythagorean theorem.

      Opposite side² + adjacent side² = hypotenuse²    

                                  adjacent side² = hypotenuse² - opposite side²

                                                           = 37² - 12²

                                                           = 1369 - 144  

                                                           = 1225

                                  adjacent side = √1225

                                                          = 35

[tex]\sf tan \ \theta =\dfrac{Opposite \ side }{adjacent \ side}\\\\tan \ \theta = \dfrac{12}{35}[/tex]                                                                                                                                                              

Answer:

The answer is 7.199 x 10^4 hectares

Step-by-step explanation:

Let's set x as the total land area in 2017.

x * (1 + 6.4%) = 76,600

x * (1 + 0.064) = 76,600

x * 1.064 = 76,600

x = 76,600 / 1.064

x = 71,992.48

x = 7.199 * 10^4 hectares

Answer:

[tex](x + 5) {}^{2} = - 12(y - 1)[/tex]

Amanda needs to pay 1440 cedis for purchasing 8 cakes on discounted price.

Cost price is the amount we pay to buy an item at which it is available.

Here,

Selling price of a cake = 200 cedis

Discount because of sale = 10% on each unit.

                                              (Only if 4 cakes purchased at a time)

Amanda purchased 8 cakes

So, Amanda need to pay only 90 percent of the total amount.

Total cost price of 8 cakes for Amanda = (200 X 90%) X 8

                                                                  = 180 X 8

                                                                  = 1440

Thus, Amanda needs to pay 1440 cedis for purchasing 8 cakes on discounted price.

Learn more about Cost Price from:

https://brainly.com/question/11027396

#SPJ1

Answer: C. Y = 5x + 5

Step-by-step explanation:

    We need to write, or decide on, the equation for the blue line as this line represents the trend line for this scatter plot. We will write this in slope-intercept form. See attached for a visual.

    First, we will find our slope. We will use [tex]\frac{rise}{run}[/tex] for this since we have a graph with clear points. See attached, we count up [5] and then count to the right [1] for a slope of 5.

     -> Slope = 5

   Now, we will find our y-intercept. This is where the line intersects the y-axis. The line hits the y-axis at point (0, 5) giving us a y-intercept of 5.

     -> Y-intercept = 5

   Lastly, we will write our equation and decide on an answer.

y = mx + b

y = (5)x + (5)

Y = 5x + 5

             C. Y = 5x + 5

The digit on the right side of each equation so that each equation has an integer solution are 2.74, 3.78 and 1986.5 respectively.

35x - 11 = 107

35x = 107 - 11

35x = 96

x = 96/35

x = 2.74

9m + 34 = 68

9m = 68 - 34

9m = 34

m = 34/9

m = 3.78

7965 - 4m = 19

-4m = 19 - 7965

-4m = -7946

m = -7946/-4

m = 1986.5

Learn more about equation:

https://brainly.com/question/3069172

#SPJ1

The expression square root of 25/49 can be given as 5/7

An equation is an expression that shows the relationship between two or more variables and numbers.

Inequality is the non equal comparison of two or more numbers and variables.

The solution to the system of inequalities x – 4y < 4 and y < x + 1 is shown in the graph.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

its c

Step-by-step explanation:

The a gallon of orange juice will cost $ 3.0 more than a gallon of milk.

The size of the orange juice in gallon is calculated as follows;

1 ounce = 0.0078125 gal

5.5 ounce = ?

= 0.043 gallon

Total volume of 6 pack = 6 x 0.043 gal = 0.258 gal

0.258 gal = $1.79

1 gal = ?

= $ 6.94

= $ 6.94 - $ 3.99

= $2.95

≈ $ 3.0

Thus, the a gallon of orange juice will cost $ 3.0 more than a gallon of milk.

Learn more about cost here: https://brainly.com/question/1153322

#SPJ1

Answer:

(f + g)(x) = x² + 4x - 4  

Step-by-step explanation:

The statement (f + g)(x) is the same as f(x) + g(x). In other words, the question simply wants you to add the two functions together.

f(x) = 4x + 1

g(x) = x² - 5

(f + g)(x)                                  <----- Original statement

f(x) + g(x)                                <----- Rewrite

(4x + 1) + (x² - 5)                     <----- Substitute the equations in f(x) and g(x)

4x + x² - 4                              <----- Add 1 and -5

x² + 4x - 4                              <----- Rearrange the terms

Option d) is correct, i.e. a rotation, then a dilation. Transformation will create a pair of similar but not congruent triangles.

Which composition of transformations will create a pair of similar, not congruent triangles?

In congruent geometry, the shapes that are so identical. can be superimposed to themselves.

When triangle is rotated, than position of angles will change. Aftermath the dilation of the triangle would increase the proportion of the sides, but angles remains equal, by which the triangle remain similar but not congruent.

Thus, a rotation, then a dilation transformation will create a pair of siilar but not congruent triangles.

Learn more about congruent geometry here.
https://brainly.com/question/12413243

#SPJ1

Answer:

D. a rotation, then a dilation

Step-by-step explanation:

got it right on edge 23

Answer:

40.1

Step-by-step explanation:

Because the order of operations (Bodmas or Pedmas) tells you to add from left to right. So you would do 18.79 + 2.11 = 20.9, then you would do 20.90 + 1.92 (Add 0 at the end of 20.9) = 22.81. Then you will add 22.81 + 17.28 = 40.1. So your answer is 40.1. Hope this helps!

Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.

We know that the sum of angles of a triangle is always. In ΔXYZ,

[tex]\angle A + \angle B + \angle C=180^0[/tex]

[tex]35^0+\angle Y+47^0=180^0[/tex]

[tex]\angle y=98^0[/tex]

In both triangles, it is noticed that the sides AC and XZ are equal. In given triangles [tex]\angle A=\angle X=35^0[/tex]and.[tex]\angle B = \angle Y =98^0[/tex]

By the AAS rule of congruence, ΔABC and ΔXYZ are congruent triangles, therefore we can transform ΔABC to ΔXYZ. For the transformation of ΔABC to ΔXYZ translate the vertex having the same angle and rotate the triangle to align the sides and angles.

Since vertex X and vertex A have the same angle, therefore we translate vertex X to vertex A and rotate ΔXYZ to align the sides and angles.

Hence the correct option is d.

To learn more about vertex visit:

https://brainly.com/question/525947

#SPJ1

Answer:

D: Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.

Step-by-step explanation:

edge 2022

The Sample mean,Sample Variance, Standard deviation is mathematically given as

Generally, the equation for Sample mean is  mathematically given as

[tex]x = \frac{1}{N}(\sum xifi )[/tex]

Where

[tex]\sum xifi=80+135+220+145+72+258[/tex]

[tex]\sum xifi=910[/tex]

Therefore

x=1/42 (910)

x=21.66

Sample Variance

[tex]\sigma = \frac{1}{N-1}(\sum xi^2fi-(\frac{1}{N}(\sum xifi^2 )) )[/tex]

Where

[tex]\sum xi^2fi=640+2025+4840+4205+2592+11094[/tex]

[tex]\sum xi^2fi=25396[/tex]

Therefore

[tex]\sigma = \frac{1}{41}(25396-(\frac{1}{42}(910^2 )) )[/tex]

[tex]\sigma=138.52[/tex]

Standard deviation.

[tex]\mu=\sqrt{\sigma^2}\\\\\mu=\sqrt{138.52}[/tex]

[tex]\mu=11.769[/tex]

In conclusion,

x=21.66

[tex]\sigma=138.52[/tex]

[tex]\mu=11.769[/tex]

Read more about Probabllity

https://brainly.com/question/11234923

#SPJ1

Answer:

x=−9 and y=8

Step-by-step explanation:

Let's solve your system by elimination.

2x+3y=6;4x−y=−44

Multiply the first equation by -2,and multiply the second equation by 1.

−2(2x+3y=6)

1(4x−y=−44)

Becomes:

−4x−6y=−12

4x−y=−44

Add these equations to eliminate x:

−7y=−56

Then solve−7y=−56for y:

−7y=−56

-7y/-7 = = -56/-7

(Divide both sides by -7)

y=8

Now that we've found y let's plug it back in to solve for x.

Write down an original equation:

2x+3y=6

Substitute8 for y in 2x+3y=6:

2x+(3)(8)=6

2x+24=6(Simplify both sides of the equation)

2x+24+−24=6+−24(Add -24 to both sides)

2x=−18

2x/2 = -18/2 (Divide both sides by 2)

x=−9

Answer:

x=−9 and y=8

Answer:

x = -9

y = 8

Step-by-step explanation:

(using substitution)

4x-y = -44

4x + 44 = y

substitute (4x+44) as y in the other equation

2x + 3(4x+44) = 6

2x+12x+132 = 6

14x = -126

x = -9

then plug -9 as x into one of the equations to find y

4(-9) - y = -44

-36-y=-44

-y=-8

y=8

then check the answer by plugging in the values of x and y (-9 and 8) for x and y in one of the equations

4(-9) - (8) = -44

you get: -44 = -44, which is true, so the x and y values are correct

Answer: 20

Step-by-step explanation:

     We will set up a proportion to solve.

[tex]\displaystyle \frac{?}{16}=\frac{15}{12}[/tex]

   Now, we will cross-multiply.

12 * ? = 16 * 15

12? = 240

? = 20

By using properties for trigonometric functions and trigonometric expressions, we find that the exact value of the sine of the angle 5π/12 radians is [tex]\frac{\sqrt{2+\sqrt{3}}}{2}[/tex].

Trigonometric functions are trascendent functions, these are, that cannot be described algebraically. Herein we must utilize trigonometric formulae to calculate the exact value of a trigonometric function:

[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{1 - \cos \frac{5\pi}{6} }{2} }[/tex]

[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{1 + \cos \frac{\pi}{6} }{2} }[/tex]

[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{1 + \frac{\sqrt{3}}{2} }{2} }[/tex]

[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{2+\sqrt{3}}{4} }[/tex]

[tex]\sin \frac{5\pi}{12} = \frac{\sqrt{2+\sqrt{3}}}{2}[/tex]

By using properties for trigonometric functions and trigonometric expressions, we find that the exact value of the sine of the angle 5π/12 radians is [tex]\frac{\sqrt{2+\sqrt{3}}}{2}[/tex].

To learn more on trigonometric functions: https://brainly.com/question/15706158

#SPJ1

Answer:

[tex]2 * 10^3 * 1,02^t[/tex]

Step-by-step explanation:

Let [tex]S = 2000 = 2 * 10^3[/tex] dollars be our investment, [tex]r = 2\%[/tex] - our interest rate. In order to simplify things, I suggest bringing the variable [tex]p[/tex] into play: [tex]p = 1 + \frac{r}{100}[/tex]. So, after year [tex]1[/tex] we will have [tex]S_{1} = S + \frac{r}{100}S = S(1 + \frac{r}{100} ) = Sp[/tex]. After year [tex]2[/tex]: [tex]S_{2} = S_{1}p = Sp * p = Sp^2[/tex]. After year [tex]t[/tex]: [tex]S_{t} = S_{t - 1}p = Sp^t[/tex]. Besides, we can count [tex]p[/tex]. Indeed, [tex]p = 1 + \frac{r}{100} = 1 + \frac{2}{100} = \frac{100}{100} + \frac{2}{100} = \frac{102}{100} = 1,02[/tex]. Therefore, [tex]V(t) = Sp^t = 2 * 10^3 * 1,02^t[/tex].

Step-by-step explanation:

Answer:

11 mushrooms

Step-by-step explanation:

Let's take two sets of numbers that fulfill the requirements (2 and 24 | 5 and  27)

In the first case, there are 26 mushrooms, and to have an equal amount they each need 13. Collin had to give 11 mushrooms to Sophie.

In the second case, there are 32 mushrooms, and they both need 16 each. So in this case, Collin also had to give 11 to Sophie.

The answer is 11 mushrooms.

Answer:

1

Step-by-step explanation:

[tex]i^4=1\\\\i^{36}=(i^{4})^9=(1)^9=1[/tex]

The statement which the diagram shows is that the length of GH is half of the length of KL . Option B

The midsegment theorem holds that any segment that forms the joining midpoints of two sides of a triangle is parallel to half the length of the third side.

It can be seen that the length of GH is half of the length of KL as deduced from the diagram

Therefore, the statement which the diagram shows is that the length of GH is half of the length of KL . Option B

Learn more about the midsegment theorem here:

https://brainly.com/question/7423948

#SPJ1

Answer:

4p-3

Explaination

when we subtract

4p-3 -3p-6

it will give us p _9

The gradient of line A is -2. 67

Gradient = slope = Δy/ Δx

We have,

y2 = 3

y1 = -5

x2 = -3

x1 = 0

Substitute the values

Gradient = [tex]\frac{3 - (-5)}{-3 -0}[/tex]

Gradient = [tex]\frac{3 + 5}{-3}[/tex]

Gradient = [tex]\frac{8}{-3}[/tex]

Gradient = -2. 67

Thus, the gradient of line A is -2. 67

Learn more about gradient here:

https://brainly.com/question/21727173

#SPJ1

cos θ = [tex]\frac{-4\sqrt{65} }{65}[/tex], sin θ = [tex]\frac{-7\sqrt{65} }{65}[/tex], cot  θ  = 4/7, sec  θ = [tex]\frac{-\sqrt{65} }{4}[/tex], cosec  θ  = [tex]\frac{-\sqrt{65} }{7}[/tex]

Trigonometric Ratios are values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Sin θ: Opposite Side to θ/Hypotenuse

Tan θ: Opposite Side/Adjacent Side & Sin θ/Cos

Cos θ: Adjacent Side to θ/Hypotenuse

Sec θ: Hypotenuse/Adjacent Side & 1/cos θ

Analysis:

tan θ = opposite/adjacent = 7/4

opposite = 7, adjacent = 4.

we now look for the hypotenuse of the right angled triangle

hypotenuse = [tex]\sqrt{7^{2} + 4^{2} }[/tex] = [tex]\sqrt{49+16}[/tex] = [tex]\sqrt{65}[/tex]

sin θ = opposite/ hyp = [tex]\frac{7}{\sqrt{65} }[/tex]

Rationalize, [tex]\frac{7}{\sqrt{65} }[/tex] x [tex]\frac{\sqrt{65} }{\sqrt{65} }[/tex] = [tex]\frac{7\sqrt{65} }{65}[/tex]

But θ is in the third quadrant(180 - 270) and in the third quadrant only tan and cot are positive others are negative.

Therefore, sin θ = - [tex]\frac{7\sqrt{65} }{65}[/tex]

cos   θ  = adj/hyp = [tex]\frac{4}{\sqrt{65} }[/tex]

By rationalizing and knowing that cos  θ  is negative, cos θ  = -[tex]\frac{-4\sqrt{65} }{65}[/tex]

cot θ  = 1/tan θ  = 1/7/4 = 4/7

sec θ  = 1/cos θ  = 1/[tex]\frac{4}{\sqrt{65} }[/tex] = -[tex]\frac{-\sqrt{65} }{4}[/tex]

cosec θ  = 1/sin θ  = 1/[tex]\frac{\sqrt{65} }{7}[/tex] = [tex]\frac{-\sqrt{65} }{7}[/tex]

Learn more about trigonometric ratios: brainly.com/question/24349828

#SPJ1

The question is incomplete. Please read below to find the missing content.

D) cumulative is an argument that should be set to FALSE.

If we use cumulative =fake then we are able to get a precise probability

If we use cumulative= genuine, we will get less than or equal to possibility.

A sequence of actions wherein the effects are always unsure. I was tossing a coin, deciding on a card from a deck of playing cards, and throwing a cube. occasion. It is a single final result of a test. Getting a Head at the same time as tossing a coin is an occasion.

When using BINOM.DIST to calculate a probability mass function, which argument should be set to FALSE? Select an answer

A) number_s

B) probability_s

C) trials

D) cumulative

Learn more about the probability mass function here https://brainly.com/question/14705158

#SPJ4