#11 Mrs Owen ordered 500 chicken wings to be shared equally among 250 guests invited to her wedding anniversary party. However the turnout was less than expected and every guest ate one more chicken wing than originally planned. If there were 92 chicken wings left after the party, how many people attended Mrs. Owen’s party?


 
#12 The total number of cherries on a plate, in a cup and in a bowl is 780. The plate contains 145 cherries. The number of cherries in the bowl is 4 times the total number of cherries on the plate and in the cup. How many cherries are in the cup?

Answer:

x squared plus two times x minus one = zero.

Step-by-step explanation:

(This is a Quadratic equation in the variable x).

Answer:

One less than the sum of square of a number  and twice the number is 0

Step-by-step explanation:

[tex]x^2+ 2x - 1 = 0[/tex]

x represents any number. x^2 represents square of a number

2x represents twice the number

[tex]x^2+2x[/tex] can be written as sum of square of a number  and twice the number

[tex]x^2+2x-1[/tex]

One less than the sum of square of a number  and twice the number

[tex]x^2+2x-1=0[/tex]

One less than the sum of square of a number  and twice the number is 0

Answer:

see explanation

Step-by-step explanation:

These are the terms of an arithmetic sequence

The n th term ( explicit rule ) for an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

d = 9 - 2 = 16 - 9 = 23 - 16 = 30 - 23 = 7 and a₁ = 2, hence

[tex]a_{n}[/tex] = 2 + 7(n - 1) = 2 + 7n - 7 = 7n - 5

The explicit rule for the sequence 2,9,16,23,30... is 7n - 5

2,9,16,23,30

= 7

The explicit rule is defined by

nth term = a + (n - 1) d

= 2 + (n - 1)7

= 2 + 7n - 7

= 7n - 5

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Answer:

see explanation

Step-by-step explanation:

x³ + y³ ← is a sum of cubes and factors as

(x + y)(x² - xy + y²) ← in factored form

Answer:

false

Step-by-step explanation:

correct me if this is wrong, but it's actually x>1

Answer:

false.

Step-by-step explanation:

Given :  2x+8>10.

To find : the solution to 2x+8>10 is x<1   true or false.

Solution : We have given that  

2x+8>10.

On subtracting both sides by 8

2x > 10 -8.

2x > 2

On dividing both sides by 2

x > 1

So,  given statement false .

Therefore, false.

Answer:

x = -7 and x = 2

Step-by-step explanation:

Look for the points on the graph where if you draw a horizontal line at y=1, you will intersect the curve.

By observation, we can see that this happens at x = -7 and x = 2

x = -7 and x = 2

Here in the diagram, we can see that, a curve is present & 6 co-ordinates on that curve are given.

We have to find the values of x correspond with f(x) = 1

f(x) = 1 means y = 1

So, if we draw a horizontal line at y = 1, which is parallel to x-axis.

Then, we can able to observe the points which are on the line y = 1.

So, the points on line y = 1 are (-7, 1) & (2, 1).

Hence, we can say that, input values that correspond with f(x) = 1 are x= -7 & x = 2.

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Yes. You should add commas next time to make it easier to read.

Answer:

Yes this is a function..

Step-by-step explanation:

We have to see the inputs and outputs for the function.

Here x represents input and y represents output.

For a relation to be a function there should be no repition in domain or input of the function i.e. every element in domain should be unique.

The domain for given relation is:

{1,-1,3,5}

All the inputs are only once mapped to the output so this relation is a function ..

Answer:

3

Step-by-step explanation:

(0,0) satisfies y > 2x - 1 but does not satisfy y ≤ x^2 - 4. C

(0,0) satisfies both inequalities.

Answer:

2160

Step-by-step explanation:

36*20=720      720*3=2160

To find the number of square inches of paper needed, multiply the length and width of each drawer to get the area, and then multiply that area by 3.

To find the number of square inches of paper needed, we need to find the area of the bottom of each drawer and then add them together. The area of a rectangle is found by multiplying its length by its width. So, for each drawer, we multiply 36 inches by 20 inches to get an area of 720 square inches.

Since there are 3 drawers, we need to multiply the area of one drawer by 3. So, the total number of square inches of paper needed is 720 square inches times 3, which equals 2160 square inches.

Therefore, the correct answer is D) 2160.

Answer: 50 degrees.

Step-by-step explanation:

To find the measure of the angle Q, you need to follow these steps:

- Knowing that:

[tex]-980= -(1,360)cos(Q)[/tex]

You can divide both sides of the equation by -1,360:

[tex]\frac{-980}{-1,360}=\frac{-1,360cos(Q)}{-1,360}\\\\\frac{49}{68}=cos(Q)[/tex]

- Finally, using  the inverse function of the cosine, Arccosine, we get:

[tex]Q=Arcos(\frac{49}{68})\\\\Q=49.89\°[/tex]

To the nearest whole degree, this is:

[tex]Q=50\°[/tex]

To model the bird population that triples each year starting with 10 birds, an exponential growth function is used: f(x) = 10 × 3^x, where x is the number of years.

To create a function that represents the scenario of birds increasing threefold each year, we need to use an exponential growth model.

The initial population of birds is 10 and then it triples every year.

Therefore, the function that describes the number of birds after x years would be:

f(x) = 10 × 3^x

Here, f(x) represents the number of birds after x years, 10 is the initial number of birds released into the habitat, and 3^x indicates that the population is growing three times each year for x years.

Final answer:

The number of birds after x years can be calculated using the exponential function B(x) = 10 × 3^x, representing the initial population of 10 birds tripling every year.

Explanation:

The scenario describes a population of birds in a new habitat growing exponentially each year. The initial population of birds is 10 (in year 0), and the population triples every year thereafter. To represent this situation mathematically, we can use an exponential function.

To find the number of birds after x years, we can use the following function:

B(x) = 10 × 3^x

Where:

B(x) is the number of birds after x years

10 is the initial number of birds

3 is the growth factor, as the population is tripling each year

x is the number of years since the birds were first released into the habitat

This equation models exponential growth and gives us the predicted population of the birds for any given year x.

Answer:

[tex]\frac{3\pi}{2}[/tex]  units to the right

Step-by-step explanation:

If we have a parent function y = Sin(x), the function

The function given is [tex]y=Sin(x-\frac{3\pi}{2})[/tex]

So from the rules, we can clearly say that it is parent function shifted RIGHT by  [tex]\frac{3\pi}{2}[/tex] units.

2nd answer choice is correct.

Answer:

x = - 7

Step-by-step explanation:

Given

3x + 5 = - 16 ( subtract 5 from both sides )

3x = - 21 ( divide both sides by 3 )

x = - 7

Two-step equations can get more difficult the higher the numbers get, but they're not too hard! ;)

To solve 3x+5=-16:

First subtract 5 from each side

Now its 3x=-21

Next divide 3 from each side

You get x=-7!

Always check your work! To check your work plug your answer "-7" into x.

So it looks like this: 3(-7)+5=-16 then distribute and solve!

You'll get -16=-16, that means its correct/true!

Answer:

This is a false statement:

Step-by-step explanation:

According to Remainder Theorem dividing the polynomial by some linear factor x + a, where a is just some number. As a result of the long polynomial division, you end up with some polynomial answer q(x) (the "q" standing for "the quotient polynomial") and some polynomial remainder r(x).

P(x)= (x+/-a) q(x)+r(x)

P(x)=(x+a) q(x)+r(x). Note that for x=-a

P(-a)=(-a+a) q(-a)+r(-a)= 0* q(-a)+ r(-a)

P(-a)=r(-a)

It means that P(-a) is the remainder not P(a)

Thus the given statement is false....

Answer:

z = 5

Step-by-step explanation:

Given

- 0.25z = - 1.25 ( divide both sides by - 0.25

z = [tex]\frac{-1.25}{-0.25}[/tex] = 5

z = 5

Answer:

z = 5.

Step-by-step explanation:

-0.25 z = -1.25

z = -1.25 / -0.25

z = 5.

Answer:

b

Step-by-step explanation:

because perimeter of rectangle is 2(l+b)

For this case we have that by definition, the perimeter of a rectangle is given by:

[tex]P = 2a + 2b[/tex]

Where:

a: It is the length of the rectangle

b: It is the width of the rectangle

We have as data that:

[tex]P = 230 \ ft\\b = 30 \ ft[/tex]

Then, replacing we have:

[tex]230 = 2a + 2 (30)[/tex]

Answer:

Option B

Answer:

[tex]\cos (115\degree)=-0.423[/tex]

Step-by-step explanation:

The parametric equations of a circle is

[tex]x=r\cos \theta[/tex] and [tex]y=r\sin \theta[/tex]

The radius of the unit circle is 1 unit.

This implies that any point on the unit circle is represented by:

[tex]x=\cos \theta[/tex] and [tex]y=\sin \theta[/tex]

where [tex]\theta[/tex] is the angle in standard position,

From the question, the given angle in standard position is [tex]115\degree[/tex].

This angle intersects the unit circle at [tex]x=-0.423[/tex]

But [tex]x=\cos \theta[/tex]

We substitute [tex]\theta=115\degree[/tex] and [tex]x=-0.423[/tex]

This implies that: [tex]\cos (115\degree)=-0.423[/tex]

Answer:

D. 148°

Step-by-step explanation:

Theorem: The measure of the angle formed by a tangent and a chord is equal to one-half the measure of the intercepted arc.

In your diagram, XZ is the chord, WZ is the tangent, and XYZ is the intercepted arc.

Per the theorem,

mXZW = ½ mXYZ = ½ × 296° = 148°

The measure of the tangent chord angle is 148°.

Answer: D: 148 is correct

Step-by-step explanation: apx :)

Answer:

[tex]\large\boxed{D.\ (x-4)^2=55}[/tex]

Step-by-step explanation:

[tex](a-b)^2=a^2-2ab+b^2\qquad(*)\\\\\\x^2-8x=39\\\\x^2-2(x)(4)=39\qquad\text{add}\ 4^2=16\ \text{to both sides}\\\\\underbrace{x^2-2(x)(4)+4^2}_{(*)}=39+16\\\\(x-4)^2=55[/tex]

Answer: the answer is D

Step-by-step explanation:

Answer:

Yes the lines are indeed parallel. The slope of AB is 2

Step-by-step explanation:

Answer:

170 m

Step-by-step explanation:

Area of a rectangle is width times length:

A = WL

Given:

A = 1764

W = L + 13

Substitute:

1764 = (L + 13) L

1764 = L² + 13L

0 = L² + 13L − 1764

0 = (L + 49) (L − 36)

L + 49 = 0, L − 36 = 0

L = -49, L = 36

Since length can't be negative, L = 36 m.

So the width is W = L + 13 = 49 m.

Perimeter of a rectangle is twice the width plus twice the length.

P = 2W + 2L

P = 2(49) + 2(36)

P = 170 m

The perimeter is 170 meters.

Answer:

B.

Step-by-step explanation:

I think I'm going to go with the plug in method here.

If you get the same value on both sides, then the point is contained on the line.

A)

4x-y=-6

Test (-1,2):  4(-1)-2=-6

4(-1)-2=-6

-4-2=-6

-6=-6

True; the equation holds for (-1,2).

Test (3,1): 4(3)-1=-6

4(3)-1=-6

12-1=-6

11=-6

False; the equation doesn't hold for (3,1).

A isn't the right choice.

B)

x+4y=7

Test (-1,2): -1+4(2)=7

-1+4(2)=7

-1+8=7

7=7

True, the equation holds for (-1,2).

Test (3,1): 3+4(1)=7

3+4(1)=7

3+4=7

7=7

True, the equation holds for (3,1).

Since the equation held for both (-1,2) and (3,1) then B is the right answer.

-------------------Let's also go ahead and find the equation another way:

(3,1) and (1,-2) are points on your line.

I'm going to write an equation for these points in slope-intercept form first which is y=mx+b where m is slope and b is y-intercept.

I will then rearrange into standard form like your choices are in.

m=slope=rise/run.

To find this, I like to line up the points and subtract and then put 2nd difference over 1st difference.

Like so:

(-1,2)

-(3,1)

---------

-4    1

The slope is 1/-4 or -1/4.

So the equation so far is y=-1/4 x+b since m=-1/4.

Now to find b, I'm going to use y=-1/4 x +b along with one of the given points on the line like (x,y)=(-1,2).

y=-1/4 x+b

2=-1/4 (-1)+b

2=1/4+b

Subtract 1/4 on both sides:

2-1/4=b

7/4=b

So the equation of the line is y=-1/4 x +7/4.

Now the goal is to write in ax+by=c form where a,b,c are integers.

Multiply both sides of y= -1/4 x +7/4 by 4 giving you:

4y=-1x+7

Add 1x on both sides:

1x+4y=7

or

x+4y=7 since 1x=x

So x+4y=7 is the answer if you prefer this way. Well anyway you prefer, this is the correct standard form for this line.

The equation of line that passes through points (-1, 2) and (3, 1) will be

x + 4y = 7

Option B is true.

What is Equation of line?

The equation of line with slope m and y intercept at point b is given as;

y = mx + b

Given that;

The points on the line are  (-1, 2) and (3, 1).

Since, The equation of line will be;

y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁)/ (x₂ - x₁) is slope of the line.

And, (x₁, y₁) is the point on the line.

Thus, Slope = (1 - 2) / (3 - (-1))

                  = (-1)/4

                  = -1/4

So, The equation of line with slope -1/4 and point (-1, 2) will be;

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

4 (y - 2) = - 1(x + 1)

4y - 8 = -x - 1

x + 4y = 8 - 1

x + 4y = 7

So, The equation of line that passes through points (-1, 2) and (3, 1) will be

x + 4y = 7

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Answer:

True

Step-by-step explanation:

Let, [tex]P_0[/tex] be the initial population,

Given,

The population is decreasing by 3%  each year,

Thus, the population after t years would be,

[tex]P=P_0 (1-\frac{3}{100})^t[/tex]

[tex]\implies P=P_0(1+\frac{-3}{100})^t[/tex]

Since, if a population is changing by a constant rate then the population after t years is,

[tex]P=P_0(1+\frac{r}{100})^t[/tex]

Where, r is the rate of changing per period.

Hence, in the given situation the population is changing by the constant rate.

Answer:

The equation that represents the line that passes through (-6,7) and (-3,6) is: y = -1/3x + 5

Step-by-step explanation:

The equation of line for point=slope form is

y-y₁ = m(x-x₁)

Finding Slope m:

m= y₂-y₁/x₂-x₁

here y₂= 6,y₁= 7,x₂= -3,x₁= -6

m = 6-7/-3-(-6)

m = -1/-3+6

m = -1/3

The slope m = -1/3 and considering point (-6,7) the equation is:

y-y₁ = m(x-x₁)

y-7 = (-1/3)(x-(-6))

y-7 = -1/3(x+6)

y-7 = -1/3x -2

y = -1/3x-2+7

y = -1/3x + 5

So, the equation that represents the line that passes through (-6,7) and (-3,6) is: y = -1/3x + 5

Answer:

F

Step-by-step explanation:

∠C is opposite ( or across from ) side AB

In the same way

∠A is opposite side BC and

∠B is opposite side AC

Answer:

c

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

So this means to replace the r you see in 4r^2-8 with 3.

Let's do that:

4(3)^2-8

Now to simplify this just use pemdas or a calculator:

4(9)-8     since 3^2 means 3*3=9

36-8

28

Answer:

28.

Step-by-step explanation:

Put r =- 3 and work it out:

That would be 4(3)^2 - 8

=  4 * 9 - 8

= 36 - 8

= 28.

Answer:

½ = x

Step-by-step explanation:

As discussed in one of my You-Tube videos on Exponential Rules, aᵐ\ⁿ, any base to the half power is the SAME AS taking the exponential denominator of that power, and setting that to the square root of the base, leaving the exponential numerator on the outside:

25¹\² = √25

25 = a [Base]

1 = m [Exponential Numerator]

2 = n [Exponential Denominator]

As you can see, it is unnecessary to put the two because by definition, any vacant root is automatically assumed as the square root, and 1, which is the exponential numerator, is on the outside, which again is unnecessary because 5¹ is 5.

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Watch the above link and subscribe to my channel [USERNAME: MATHEMATICS WIZARD].

I am joyous to assist you anytime.

Answer:

Step-by-step explanation:

[tex]3x+1=4x+(-4)\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\3x-4x+1=4x-4x-4\\\\-x+1=-4\qquad\text{subtract 1 from both sides}\\\\-x+1-1=-4-1\\\\-x=-5\qquad\text{change the signs}\\\\x=5[/tex]

Answer:

The answer is B. In step one he should have added 3 negative x-tiles to both sides.

Step-by-step explanation: