If there are 20 cookies and 40 carrot each number are the same number of one whole cookies how many cost members might have been at the party,explain

Answers

Answer 1

2, 4, 5, 10 and 20 cast members were possible attendees at the celebration.

The acting teacher provided 20 biscuits and 40 carrot sticks as refreshments in light of this.

What are the factors?

A factor in mathematics is an integer that evenly divides another number by itself, leaving no residue.

2, 4, 5, 10, and 20 make up the factors of 20 and 40.

Additionally, the number of cast members must be greater than one and a divisor of 20 and 40.

Therefore, there could be 2, 4, 5, 10, or 20 cast members.

Therefore, 2, 4, 5, 10 and 20 cast members may have attended the celebration.

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Related Questions

For the following equation, complete the given ordered pairs, and use the results to graph the solution set for the equation.

Answers

Given:

[tex]y=-\frac{3}{4}x+1[/tex]

Aim:

We need to graph the given function.

Explanation:

Replace x =-4 in the given equation.

[tex]y=-\frac{3}{4}(-4)+1[/tex]

[tex]y=-3(-1)+1[/tex][tex]y=3+1[/tex]

[tex]y=4[/tex]

We get the point (-4, 4).

Replace x = 0 in the given equation.

[tex]y=-\frac{3}{4}(0)+1[/tex][tex]y=1[/tex]

We get the point (0,1).

Replace x =4 in the equation.

[tex]y=-\frac{3}{4}(4)+1[/tex]

[tex]y=-3+1[/tex][tex]y=-2[/tex]

We get the point ( 4, -2).

Mark the points (-4, 4), (0,1), and ( 4, -2) on the graph and join them by ray.

Final answer:

[tex](-4,4),\text{ }(0,1),\text{ }(4,\text{ -2}).[/tex]

The graph of the given eqaution:

complete the slope-intercept form of an equation that represents the relationship in the table

Answers

Answer:

  y = 3x -4

Step-by-step explanation:

You want the slope intercept equation representing the relationship between x and y, given (x, y) = (1, -1) and (4, 8).

Slope

The slope can be found using the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (8 -(-1))/(4 -1) = 9/3 = 3

Intercept

The y-intercept can be found using the equation ...

  b = y1 -m(x1)

  b = -1 -3(1) = -4

Slope-intercept equation

The slope-intercept equation of a line has the form ...

  y = mx + b

Using the above values of m and b, this becomes ...

  y = 3x -4

__

Additional comment

Attached is a graph showing the points and the line the equation represents.

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find the 41st term 11, 16, 21…

Answers

Answer:

You can add up to 5 each time, so we just need to multiply 5 by 40 although we already have the first three terms.

A: 40*5 = 200

Step-by-step explanation:

21 + 200 = 221

For 7 y = 2 x − 5 , which of the following expressions gives x in terms of y ?

Answers

The expressions that gives x in terms of y from the given expression 7 y = 2 x − 5 is x = (7y +5)/2.

How can the expression be simplified?

The concept that will be used in this question is solving of linear equation, because the equation is linear, then we perform the simplification.

The given expression is  is 7 y = 2 x − 5

Then from the expression we can make 2x the subject of the formula by rearranging it as 2x = 7y +5

Then this can be further expressed by dividing the both sides by the factor of 2, which can be expressed as ;

x = (7y +5)/2

Therefore, option A is correct because it is the expression that gives the x in terms of y.

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Check the missing options:

A. x = (7y +5)/2

B. y = (7x +5)/2

C. x=(7y +5)/3

A Ford F-150 truck is considered a half-ton truck because that is how much it can haul. How many pounds can the truck haul?

Answers

The truck can haul 1102 pounds.

According to the question,

We have the following information:

A Ford F-150 truck is considered a half-ton truck because that is how much it can haul.

(We will not directly convert ton into pounds. We will follow the following steps.)

Now, we know that 1 ton is equal to 1000 kilograms.

So, half ton makes 500 kg.

Now, to convert this into pounds, we will multiply 500 kg by 2.205 because we know that 1 kg is equal to 2.205 pounds.

1 kg = 2.205 pounds

500 kg = (500*2.205) pounds

500 kg = 1102.5 pounds

Hence, the truck can haul 1102.5 pounds.

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when the sun is 5 degrees above the horizon, how long will the shadow nof a 35ft tree be ?

Answers

tan 5 = x / 35

0.0874 = x / 35

cross- mulltiply

x = 35 x 0.0874

x = 3 . 059 = 3. 06 feet

Estimate 81.244.+65.33 by first rounding each number to the nearest whole number

Answers

If we round 81.244 to the nearest whole number then it would be 81.

For 65.33 is 65. Then, we sum.

[tex]81+65=146[/tex]Hence, the answer is 146.

8. Find the value of x and y.

(7x-2)°
18y°
(11x - 34)°

Answers

The degrees of the following expression are

(7x-2)° => x = 2/7°

18y° =>  y =

(11x - 34)° =>  x = 34/11°

Degrees:

Degree is the unit of measure is used to measure the magnitude of an angle.

1 degree = 1/360 of a complete revolution in magnitude.

Given,

Here we have the following expressions

(7x-2)°

18y°

(11x - 34)°

Now, we have to find the value of x and y from it.

In order to find the value x and y , we have to equate every equation with 0. then we get the value of variables x and y.

When we take the first expression, and then we have to equate it with zero, then we get,

(7x - 2)° = 0°

7x = 2°

x = 2/7°

Therefore, the value of x is 2/7°.

Now, we have to take the second one and equate it with zero, then we get,

18y° = 0

y = 0°

Therefore, the value of y is 0°.

Finally, the value of the expression in degrees,

11x - 34° = 0

11x = 34°

x = 34/11°

Therefore, the value of x is 34/11 degrees.

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jon's bathtub is rectangular and its base is 18 ft2. how fast is the water level rising if jon is filling the tub at a rate of 0.6 ft3/min? (use decimal notation. give your answer to three decimal places.)

Answers

Jon's bathtub exists rectangular and its base exists 18 ft². The water level rising if Jon is filling the tub at a rate of 0.2 ft³/min is 0.011 ft/min.

What is meant by differential equation?

A differential equation in mathematics exists an equation that links the derivatives of one or more unknown functions. Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three.

If we take a look at a rectangular bathtub, the volume of the bathtub can be expressed as:

Volume (V) = length × breadth × height

where; base = length × breadth = 18ft²

The volume of the rectangular bathtub = 18h ......... (1)

Using differentiation to differentiate 18h with respect to t implicitly, then:

[tex]$\frac{\mathrm{dV}}{\mathrm{dt}}=18 \frac{\mathrm{dh}}{\mathrm{dt}}$$[/tex]

When the rate of rising of the volume is 0.2 ft² / min

[tex]$0.2=18 \frac{\mathrm{dh}}{\mathrm{dt}}$$[/tex]

substitute the values in the above equation, we get

[tex]$\frac{\mathrm{dh}}{\mathrm{dt}}=\frac{1}{18} \times(0.2)$$[/tex]

[tex]$\frac{\mathrm{dh}}{\mathrm{dt}}=0.011 \mathrm{ft} / \mathrm{min}$$[/tex]

Therefore, we can conclude that the rate at which the water level rises if Jon is filling the tub at 0.2 ft³/min exists 0.011 ft/ min.

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working together, it takes two different sized hoses minutes to fill a small swimming pool. if it takes minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?

Answers

Time taken by the smaller hose to fill the pool on its own = 75 minutes

Time taken to fill the swimming pool by the larger hose and smaller hose working together = 30 minutes

Time taken by the larger hose to fill up the swimming pool = 50 minutes

Let 'x' be the time taken by the smaller hose to fill the swimming pool on its own.

In 30 minutes, the larger and smaller hoses together can fill the swimming pool. So in 1 minute, it can fill up 1/30 of the swimming pool.

In 50 minutes, the larger hose can fill up the swimming pool on its own. So the larger hose can fill up 1/50 of the pool in 1 minute.

It takes 'x' minutes for the smaller hose to fill up the pool on its own. So in 1 minute, the smaller hose alone can fill up 1/x of the pool.

Hence 1/30 = 1/x +1/50

⇒ 1/30 = (50+x)/50x

⇒ 30 = 50x/(50+x)

⇒ 30 (50 + x) = 50x

⇒ 1500 + 30x = 50x

⇒ 20x = 1500

⇒ x = 1500/20

⇒ x = 75 minutes.

Thus the smaller hose alone takes 75 minutes to fill up the pool.

The question is incomplete. Find the complete question below:

Working together, it takes two different sized hoses 30 minutes to fill a small swimming pool. If it takes 50 minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?

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help meeeeeeee pleasee​

Answers

Answer:

2(5*7) + 2(4*7) + 2(4*5)

Step-by-step explanation:

I can't really see all the values on the cuboid. I'm going to assume the dimensions are 5cm by 4cm by 7cm.

Surface area of this cuboid would be:

2(5*7) + 2(4*7) + 2(4*5)

Tell which of the following is a linear equation in one variable:
a) x² - 4x + 3 = 0
b) 6x - 2y = 7
c) 3x - 1 = -2x
d) pq - 3 = p
e) 3x + 2 = 4 ( x +7 ) + 9

For 100 Points

Answers

Answer:

c and e

Step-by-step explanation:

(a)

x² - 4x + 3 = 0 ← is a quadratic and not linear

(b)

6x - 2y = 7 ← is a linear equation in 2 variables, x and y

(c)

3x - 1 = - 2x ( add 2x to both sides )

5x - 1 = 0 ← is a linear equation in 1 variable

(d)

pq - 3 = p ← is a linear equation in 2 variables , p and q

(e)

3x + 2 = 4(x + 7) + 9 ← is a linear equation in 1 variable

I just need help with question 1 for exercise 3!

Answers

SOLUTION:

Case: Transformation:

To find the transformation, compare the equation to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Method:

1,

[tex]y=(5x)^3-3[/tex]

Transformation features:

Horizontal: None

Shift: None

Stretch/Compression: None

Vertical:

Shift: Down by 3 units

Stretch/Compression: Stretch by a factor of 5

2.

[tex]y=-7(x+9)^2[/tex]

Transformation features:

Horizontal:

Shift: left by 9 units

Stretch/Compression: None

Vertical:

Shift: None

Stretch/Compression: Stretches by a factor of 7.

Final answer:

1.

Vertical:

Shift: Down by 3 units

Stretch/Compression: Stretch by a factor of 5.

2.

Horizontal:

Shift: left by 9 units

Vertical:

Stretch/Compression: Stretches by a factor of 7.

a company that manufactures mufflers for cars offers a lifetime warranty on its products, provided that ownership of the car does not change. suppose that only 20% of its mufflers are replaced under this warranty. a button hyperlink to the salt program that reads: use salt. (a) in a random sample of 400 purchases, what is the approximate probability that between 70 and 90 (inclusive) mufflers are replaced under warranty? (round your answer to four decimal places.)

Answers

The approximate probability that between 70 and 90 is 0.728.

Using normal distribution,

Mean = xbar = np = 400 × 0.2 = 80

Standard deviation = √[np(1-p)] = √(80 × 0.8) = 8

To ensure that the distribution is normal,

np ≥ 10

80 ≥ 10

And,

np(1-p) ≥ 10

80(0.8) = 320 ≥ 10

Hence, we use the z-tables for this

a) Convert 75 and 100 into standardized scores.

A value's standardized score is equal to the value minus the mean divided by the standard deviation.

z = (x - xbar) ÷ σ

For 75

z = (75 - 80) ÷ 8 = - 0.625

For 100

z = (100 - 80) ÷ 8 = 2.5

To calculate the approximate likelihood that between 75 and 100 (inclusive) mufflers will be replaced under warranty.

P(75 ≤ x ≤ 100) = P(-0.625 ≤ z ≤ 2.5)

For these probabilities, use data from the normal probability table.

P(75 ≤ x ≤ 100)

= P(-0.625 ≤ z ≤ 2.5)

= P(z ≤ 2.5) - P(z ≤ -0.625)

= 0.994 - 0.266

= 0.728

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Please solve will mark as
brainliest

Answers

Answers are attached and as follows

x ➡️ = 35
3x ➡️ 3(35) = 105
2x ➡️ 2(35) = 70
4x ➡️ 4(35) = 140
10 degrees is already known

Step by step

The angles are x and 3x and 2x and 4x and 10 degrees, they form a complete circle equal to 360 degrees. So our equation to solve

x + 3x + 2x + 4x + 10 = 360

Combine like terms

10x + 10 = 360

Subtract 10 from both sides to isolate x

10x +10 -10 = 360 -10

Combine like terms

10x = 350

Divide by 10 to solve for x

x = 35

Now we use the expressions for each angle and substitute value of x (35) for x

x ➡️ = 35
3x ➡️ 3(35) = 105
2x ➡️ 2(35) = 70
4x ➡️ 4(35) = 140
10 degrees is already known

See the attachment for degrees of each angle



23 times 20 algorithom

Answers

Answer: using traditional algorithom

                                       23

                                   x  20

                                   __________

                                       0 0

                             +    4 6

                               ____________

                                   4 6  0

Consider the line y = = 8 x-4. Find the equation of the line that is parallel to this line and passes through the point (7, -2). Find the equation of the line that is perpendicular to this line and passes through the point (7, -2). ​

Answers

Answer: y=8x-58

Step-by-step explanation:

1. find the slope

Since the new line is parallel to the first one that means the slope of 8x will remain the same.

2. plug it into the point slope formula y-y1=m(x-x1)

which would look like

y-(-2)=8(x-7)

3. solve for y

y-(-2)=8(x-7)

y+2=8x-56

y=8x-58

Parallel have same slopes. Perpendicular have opposite reciprocal slopes.

Parallel slope = 8
Perpendicular slope = -1/8

Use point slope. Use point and respective slope.

y-y1= m(x-x1)
y+2 = 8(x-7)
y+2 = 8x - 56
y= 8x - 58 (parallel equation)

y-y1= m(x-x1)
y+2 = -1/8(x-7)
y+2 = -1/8x +7/8
y= -1/8x - 11/8 (perpendicular equation)

Does that help?

Solve the following LP formulation and determine the number of Surplus units in constraint B.

Answers

SOLUTION

From the what is given

[tex]\begin{gathered} x+y\le5 \\ x\ge3 \\ 2y\le8 \\ x\ge0 \\ y\ge0 \end{gathered}[/tex]

We have the graph as shown below

We are told that the MAX is

[tex]5x+2y[/tex]

Substituting these required points into the equation, our maximum becomes

[tex]\begin{gathered} 5x+2y \\ \text{For (3, 2)} \\ 5(3)+2(2)=15+4=19 \\ \text{For }(3,\text{ 0)} \\ 5(3)+2(0)=15+0=15 \\ \text{For (5, 0)} \\ 5(5)+2(0)=25+0=25 \end{gathered}[/tex]

We can see that the maximum is 25 at for units of 5, that is x = 5

But we are told in (B) that

[tex]x\ge3[/tex]

Hence the surplus unit is

[tex]5-3=2[/tex]

Hence the answer is 2

hi how are you today can you please help me with this question

Answers

If:

[tex]\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\frac{a+c+e}{b+d+f}[/tex]

so:

[tex]\begin{gathered} 15\colon9\colon4 \\ \frac{15}{1}=\frac{9}{1}=\frac{4}{1}=\frac{15+9+4}{3}=\frac{28}{3} \end{gathered}[/tex][tex]\begin{gathered} \frac{3}{x}=\frac{28}{3} \\ x=\frac{9}{28} \end{gathered}[/tex]

Or:

0.32 liters

(b)

We need to find the volume of the rectangular prism, therefore:

[tex]\begin{gathered} V=l\cdot w\cdot h \\ V=40\cdot20\cdot35 \\ V=28000cm^3 \end{gathered}[/tex]

However, we need to express the volume in liters, so:

[tex]28000cm^3\times\frac{1L}{1000cm^3}=28L[/tex]

Since we need to know the amount of mango juice:

[tex]28\cdot\frac{2}{5}=11.2L[/tex]

What is the exchange rate? Show your work.
1 US dollar = _________ euro.

Answers

The exchange rate is 1 USD = 0.992714 EURO

What is Conversion of unit?

The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

We need to convert between units in order to ensure accuracy and prevent measurement misinterpretation. For example, we do not measure a pencil's length in kilometres. In this situation, one must convert from kilometres (km) to centimetres (cm) (cm).

Given:

1 US dollar = _________ euro.

As, the exchange rate between US dollar to Euros

1 USD = 0.992714 EURO

1 USD = 1 EURO

So, if we have to find 5 US dollar into EURO then

5 US dollar = 5.02 EURO = 5 EURO

Hence, the exchange rate is 1 USD = 0.992714 EURO

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Please help. I don’t understand the problem.

Answers

Answer:

ASA

Step-by-step explanation:

ASA stands for Angle-Side-Angle which is the congruency theorem that states that if a triangle shares two congruent angles that have one line in between the two angles share a side length congruent to each other, then the two triangles are congruent.

Before you get very confused on the difference between AAS (Angle-Angle-Side) and ASA (Angle-Side-Angle), let explain why these two triangles are ASA.

We are given that both triangles share a similar side length at KL where they are connected. We are also given that angle ∠JKL is congruent to angle ∠MKL. We are also given that angle ∠MLK is congruent to angle ∠JLK.

The most important part after deciding all the relationships is given to us, it is deciding what kind of congruence theorem we will use. We are given the options:

SSS (Side-Side-Side) SAS (Side-Angle-Side) ASA (Angle-Side-Angle) AAS (Angle-Angle-Side) HL (Hypotenuse-Leg)

Because we are presented with two congruent angles and one congruent side, we know that this triangle congruency theorem is either ASA or AAS. To understand why these triangles are ASA, we have to look at where the two-given congruent sides are located. As we can see in the name and in our two triangles, the congruent side lengths are in between the two angles as it touches both angle ∠JKL and angle ∠JLK in triangle ΔJKL, while in on ΔMKL, the congruent side length is also found between angle ∠MLK and angle ∠MKL. So, these triangles share ASA because they share two congruent angles connected by one congruent line.

ORDER MATTERS WHEN YOU WRITE YOUR CONGRUENCY THEROMS

AAS is technically not the same as ASA and I will explain that in one moment.

An example of AAS is if instead being told that ∠JKL is congruent to angle ∠MKL, we are given that ∠KJL is congruent to angle ∠KML instead. now the congruent sides are not connected to angle ∠KJL or angle ∠KML. The side is no longer in-between the two congruent sides. The reason order matters here are because order matters between AAS and ASA because in another theorem, SAS, you will find out order matter because while SAS guaranties congruency SSA does not.  Technically, though, while both AAS and ASA both guaranty congruency, they are labeled separately, the way the remaining congruency thermos are.

Please help me with letter e

Answers

Height of the triangle is = 14m

Given,

Base of the triangle is 8m

Area of the triangle is = 56m^2

To find the height of the triangle.

Now, According to the question:

We know that

Area of the triangle is = 1/2 x b x h

where, b = base

h = height

Plug all the values of base and area in above formula:

56m^2 = 1/2 x 8m x h

56 x 2 / 8 = h

h = 14m

Hence, Height of the triangle is = 14m

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which property is used in the problem below, the commutative property or the associative property??


(4 x 2) x 3 = (2 x 4) x 3

Answers

Associate property is the answer.

if it takes 3/4 of an hour to fill 3/5 of a pool how many hours will it take to fill the pool completely

Answers

The time taken to completely fill the pool is 5/4 hour

How to determine the time to fill the pool?

From the question, the given parameters are:

Time =3/4 hour

Size of the pool = 3/5

The time to fill the pool is then calculated as

Time = Given time/Proportion of the pool

Substitute the known values in the above equation

So, we have the following equation

Time = 3/4 hour ÷ 3/5

Express the quotient as product

So, we have the following equation

Time = 3/4 hour x 5/3

Evaluate the products

Time = 5/4 hour

Hence, the time taken is 5/4 hour

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Please help ( geometry)
Fill in the missing proof

Answers

The missing proof in the given congruence of triangle is;

∠FAB = ∠FBA.

What is defined as the isosceles triangle?An isosceles triangle would be one with 2 sides of equal length. Below is a collection of some isosceles triangle properties:If two sides of an isosceles triangle are equal, therefore the angles opposite the two sides correspond with each other and are always equal.The two angles B and C, opposite the equal sides AB as well as AC in the isosceles triangle shown above, are equal.The isosceles triangle does have three acute angles, which means they are less than 90°.The sum of an isosceles triangle's three angles is always 180°.

For the given question;

The given data in the triangle FAB is;

FD ≅ FCDA ≅ CB

In the step two,

FA = FB (Property of isosceles triangle)

Then, step 4 will be ∠FAB = ∠FBA.

Thus, the missing proof will be ∠FAB = ∠FBA.

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DJ Joe wants to organize 127 CD's into storage boxes. Each storage box can hold a
maximum of 10 CD's. What is the least number of storage boxes needed?

Answers

Answer:

13 storage boxes is the least

Step-by-step explanation:

What we know:

- We have 127 cd's

- We have boxes only able to hold 10

What we need to figure out:

- how many boxes at the least are we going to need

Step 1: Divide

Since we need to figure out how many times 10 goes into 127 we divide 127 by 10 so...

127/10 = 12 with a remainder of 7.

Step 2: Figure out the remainder

Since there are seven left over and you cannot put them in boxes already being used then we put them in a new box, not yet used. That would make it a total of 13 boxes needed at the least.

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Simplify nine square root of two minus three square root of seven plus square root of eight minus square root of twenty eight. eleven square root of two minus five square root of seven eleven square root of four minus five square root of fourteen six square root of five six square root of nine

Answers

Squares are the numbers that are produced when a value is multiplied by itself.

If expression be [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex] then the value exists [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex].

What is meant by square root?

The radical symbol for the number's root is "√" in this instance. The square of the positive number is represented by multiplying it by itself.

Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root exists a value that, when multiplied by itself, returns the original value.

The original number can be attained by multiplying the square root of an integer by itself.

Only a perfect square number can have a perfect square root. Even perfect squares have an even square root. An odd perfect square will contain an odd square root. A perfect square cannot be negative and hence the square root of a negative number exists not defined.

Let the expression be [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]

Now, [tex]$\sqrt{8}=\sqrt{2 \times 2 \times 2}=2 \sqrt{2}$[/tex]

[tex]$\sqrt{28}=\sqrt{2 \times 2 \times 7}=2 \sqrt{7}$[/tex]

therefore [tex]9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]

simplifying the given expression, we get

[tex]$=9 \sqrt{2}-3 \sqrt{7}+2 \sqrt{2}-2 \sqrt{7}$[/tex]

[tex]$=9 \sqrt{2}+2 \sqrt{2}-3 \sqrt{7}-2 \sqrt{7}$[/tex]

[tex]$=11 \sqrt{2}-5 \sqrt{7}$[/tex]

Therefore, the correct answer is option a) [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex]

The complete question is:

Simplify [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]

a) [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex]

b) [tex]$11 \sqrt{4}-5 \sqrt{14}$[/tex]

c) [tex]$6 \sqrt{5}$[/tex]

d) [tex]$6 \sqrt{9}$[/tex]

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PLEASE HELP ASAPPP!!!!!!!!!!!!!!!!!!!!!
PLEASE HELP ASAP!!!!
The quadratic function f(x) has roots of −4 and 2 and point (1, −5) lies on f(x). What is the equation of f(x)?
f(x) = (x − 2)(x + 4)
f(x) = (x − 2)(x − 4)
f(x) = 4(x − 2)(x + 4)
f(x) = 4(x − 2)(x − 4)

Answers

The function has an equation of f(x) = (x + 4)(x - 2)

How to determine the equation of f(x)?

The given parameters in the question are

Roots = -4 and 2

Point = (1, -5)

The above parameters can be rewritten as

Roots: x = -4 and x = 2

Point: (x, y) = (1, -5)

A quadratic equation can be represented as

f(x) = a * (x - Roots)

Where Roots: x = -4 and x = 2

The above parameters imply that we have the following equation

y = a(x + 4)(x - 2)

From the question, we have

(x, y) = (1, -5)

This gives

-5 = a(1 + 4)(1 - 2)

Divide

a = 1

Substitute a = 1 in y = a(x + 4)(x - 2)

y = (x + 4)(x - 2)

Hence, the equation of the quadratic function f(x) is f(x) = (x + 4)(x - 2)

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Answer: The answer would be A: f(x) = (x − 2)(x + 4)

Step-by-step explanation: I got it right on my test

Triangle ABC has the following angle measures:

m∠A = (x + 6)°, m∠B = (3x − 15)°, m∠C = (5x + 36)°

What is m∠C?

Answers

The measure of ∠C is 121 degrees.

Given that:-

There is a triangle ABC.

m∠A = (x + 6)°

m∠B = (3x - 15)°

m∠C = (5x + 36)°

We have to find the measure of ∠C.

We know that,

The sum of all the angles of a triangle is 180 degrees.

Hence, we can write,

m∠A + m∠B + m∠C = 180 degrees

(x + 6)° + (3x - 15)° +  (5x + 36)° = 180 degrees

(x + 3x + 5x) + (6 - 15 + 36) = 180 degrees

9x + 27 = 180 degrees

9x = 180 - 27

9x = 153 degrees

x = 153/9 degrees

x = 17 degrees

Hence,

The measure of ∠C = 5x + 36 = 5*17 + 36 = 85 + 36 = 121 degrees.

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In this figure, m∠2=(6x+20)∘ and m∠8=(8x−10)∘ .



What value of x makes a∥b ?

Enter your answer in the box.

Answers

If the ∠2 = 6x+20 degrees and ∠8 = 8x-10 degrees, then the values of x is  15

The lines a and b are parallel lines

Here two parallel lines a and b are cut by a transversal t

The angles are

∠2 = 6x+20 degrees

∠8 = 8x-10 degrees

The angle 2 and angle 8 are called alternate exterior angles

When the two parallel lines are cut by a transversal, the formed alternate exterior angles are equal.

Then

6x+20 = 8x-10

Solve the equation

6x-8x = -10-20

-2x = -30

x = -30/-2

x = 15

Hence, if the ∠2 = 6x+20 degrees and ∠8 = 8x-10 degrees, then the values of x is 15.

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