Ayanna bought three dozen donuts from Dunkin Donuts. She wants to share these between herself and three friends. How many donuts will each person get? Show work and explain how you got the answer.

Answer:

[tex]3x^2 + 2x - 1 = 3(x-\frac{1}{3})(x+1)[/tex]

Step-by-step explanation:

Answer:

(3x-1)(x+1)

Step-by-step explanation:

I like to factor by grouping.

a=3

b=2

c=-1

To get those values I compared 3x^2+2x-1 to ax^2+bx+c.

Now our objective to help us factor this is:  Find two integers that multiply to be a*c and add up to be b.

a*c=3(-1)

b=2

Guess what? Our numbers are already visible to us; that doesn't always happen. However, a*c=3(-1) and b=2=3+(-1).

So we are going to replace our 2x with 3x+-1x or -1x+3x. Either one is fine; they are the same thing.

3x^2+2x-1

Replacing 2x with -1x+3x.

3x^2-1x+3x-1

Grouping first 2 terms together and grouping 2nd 2 terms together.

(3x^2-1x)+(3x-1)

Now we are going to factor each grouping.

x(3x-1)+1(3x-1)

Now notice we have two terms here x(3x-1) and 1(3x-1).  Both of these terms have a common factor of (3x-1).  We are going to now factor out (3x-1).

(3x-1)(x+1)

Answer:

The required absolute inequality is |x - 78| ≤ 20.

Step-by-step explanation:

Consider the provided information.

Let $x is monthly charge.

The monthly charges for a basic cable plan = $78

it is given that it could differ by as much as $20

So, the maximum charges can be $78 + $20,

And, the minimum charges can be $78 - $20,

The value of x is lies from $78 - $20 to $78 + $20

Which can be written as:

78 - 20 ≤ x and x ≤ 78 + 20

-20 ≤ x - 78 and x - 78 ≤ 20

Change the sign of inequality if multiplying both side by minus.

20 ≥ -(x - 78) and x - 78 ≤ 20

⇒ |x - 78| ≤ 20

Thus, the required absolute inequality is |x - 78| ≤ 20.

Answer:

220 glasses.

Step-by-step explanation:

Quantity of fruit juice = 13 liters 200 ml

Number of glasses of each capacilty 60ml can be filled = ?

The quantity of fruit juice has 2 units. one is liter and the other is milliliter.

So we will convert liter into milliliter.

We have the quantity 13 liters 200 ml:

We know that:

1 liter = 1000 ml

Hence we have 13 liters so 13 will be multiplied by 1000 to convert it into milliliter.

13 * 1000 = 13000 ml

Now we have 13000 ml 200ml

Notice that we have two milliliters, so we will add both the quantities to make it one.

(13000+200)ml = 13200ml

Total quantity of fruit juice = 13200ml

Now divide the total quantity by the capacity of 60ml

=13200ml/60ml

= 220 glasses

It means that 220 glasses can be filled....

Answer:

7, 3 and 0

Step-by-step explanation:

10, 3, 5, 7

Because the numbers are differ by prime numbers less than 10, i.e, the difference between the numbers are 7,5 and next will be 3.

8, 5, 4, 3.

The difference between the numbers are 3, 4 and similarly it will be differ by 5 which means next will be no. 3.

12, 6, 3, 0.

The numbers are differ by 6, 9 and next will be differ by 12 resulting the next no. 0.

Answer:

95 degrees

Step-by-step explanation:

The sum of the two angles 10 and 7 must be 180 degrees, so 180-85 = 95 degrees.

Answer:

m∠7 = 95°

Step-by-step explanation:

From the figure attached,

Rails N and P are parallel and vertical post L works as transverse.

Therefore, by the property of parallel lines, sum of interior angles formed by the transverse are supplementary.

In other words, ∠7 and ∠10 are interior angles and both are supplementary angles.

m∠7 + m∠10 = 180°

Since m∠10 = 85°

m∠7 + 85 = 180

m∠7 = 180 - 85

m∠7 = 95°

Answer:

16x³ + 9x² + 9x + 13

Step-by-step explanation:

Given

6x³ + 8x² - 2x + 4 and 10x³ + x² + 11x + 9

Sum the 2 expressions by adding like terms, that is

= (6x³ + 10x³) + (8x² + x²) + (- 2x + 11x) + (4 + 9)

= 16x³ + 9x² + 9x + 13

Answer:

=64 ft

Step-by-step explanation:

The wire, the pole and the flat surface form a right triangle with a base angle of 40°. The pole is the height of the triangle and is opposite the angle 40°.

Therefore we can use the trigonometric ratio -sine of the angle 40° -to find the height.

Sin∅ =opposite/hypotenuse

opposite=hypotenuse × sin∅

=100ft × Sin 40°

=64.28ft

≅64 ft

Answer:

[tex]\frac{x^2}{25}+\frac{y^2}{9}=1[/tex]

Step-by-step explanation:

[tex]\frac{(x-h)^2}{a^2}+\frac[(y-k)^2}{b^2}=1[/tex]

her center [tex](h,k)[/tex], and [tex]a[/tex] is the horizontal radius, and [tex]b[/tex] is the vertical radius.

So the center is [tex](h,k)=(0,0)[/tex].

[tex]a=5[/tex] because (5,0) has a distance of 5 from (0,0).

[tex]b=3[/tex] because (0,-3) has a distance of 3 from (0,0).

So the equation is:

[tex]\frac{(x-0)^2}{5^2}+\frac{(y-0)^2}{3^2}=1[/tex]

Simplifying a bit:

[tex]\frac{x^2}{25}+\frac{y^2}{9}=1[/tex]

Final answer:

The equation of the ellipse with a vertex at (5,0) and a co-vertex at (0, -3) with the center at the origin is [tex]\(\frac{x^2}{25} + \frac{y^2}{9} = 1\).[/tex]

Explanation:

The equation of an ellipse in standard form with a center at the origin can be derived from its vertices and co-vertices. For an ellipse centered at the origin, the standard form of the equation is [tex]\(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\)[/tex], where a is the semi-major axis and b is the semi-minor axis. Given that one vertex is at (5,0), we can deduce that the semi-major axis a is 5. Since a co-vertex is at (0, -3), the semi-minor axis b is 3. Thus, the equation of the ellipse in standard form is [tex]\(\frac{x^2}{5^2} + \frac{y^2}{3^2} = 1\), or \(\frac{x^2}{25} + \frac{y^2}{9} = 1\).[/tex]

[tex]\tan x=0[/tex] for [tex]x=n\pi[/tex], where [tex]n[/tex] is any integer. The inverse tangent function returns numbers between [tex]-\dfrac\pi2[/tex] and [tex]\dfrac\pi2[/tex]. The only multiple of [tex]\pi[/tex] in this range is 0, so [tex]\tan^{-1}0=0[/tex].

Then

[tex]\sin\left(\tan^{-1}0\right)=\sin0=\boxed0[/tex]

To evaluate sin(Tan^-10), we find that the angle whose tangent is 0 also has a sine of 0, thus the answer is 0.

The question asks to evaluate sin(Tan-10), which is essentially asking for the sine of the angle whose tangent is 0. We know that tangent is the ratio of sine to cosine, and when the tangent is 0, it means that the sine must be 0 as long as the cosine is not 0. Given that the cosine of 0 degrees (or 0 radians) is 1, and the sine of 0 degrees is 0, we can conclude that sin(Tan-10) is 0.

Answer:

50

Step-by-step explanation:

This is an isosceles triangle which means opposite sides are congruent implies the base opposite angles at the base congruent.

So both of bottom angles are 65 each.

We know the sum of the interior angles of a triangle are 180 degrees.

So we have 65+65+x=180.

Combine like terms:

130+x=180

Subtract 130 on both sides:

x=180-130

x=50

Answer:

[tex]1.17*10^{10}[/tex]

Step-by-step explanation:

wee know that

To multiply two numbers in scientific notation, multiply their coefficients and add their exponents

In this problem we have

[tex](2.6*10^{1})*(4.5*10^{8})=(2.6*4.5)*10^{1+8}=11.7*10^{9}=1.17*10^{10}[/tex]

Answer:

X || Z

Step-by-step explanation:

We are not told about any lines being perpendicular, so we cannot conclude any lines to be perpendicular.

Theorem:

If two lines are parallel to the same line, then the two lines are parallel to each other.

X is paralle to Y; Z is parallel to Y.

Line X and Z are parallel to the same line, Y, so lines X and Z are parallel.

Answer: X || Z

In mathematics, if lines X and Y are parallel, and lines Y and Z are parallel, then lines X and Z are also parallel. This is known as the transitive property.

In mathematics, when we say one line is parallel to another, we mean they are moving in the same direction and they will never intersect. In the case of X being parallel to Y and Y being parallel to Z, according to the transitive property in mathematics, it follows that X would be parallel to Z. To visualize this, imagine three straight lines on a piece of paper. If Line X and Line Y never meet and continue in the same direction, and Line Y and Line Z also follow the same rule, then logically, Line X and Line Z must also be continuing in the same direction and never intersecting, hence they are essentially parallel to each other.

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Answer:

3i[tex]\sqrt{5}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

and [tex]\sqrt{-1}[/tex] = i

Given

[tex]\sqrt{-45}[/tex]

= [tex]\sqrt{9(5)(-1)}[/tex]

= [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex] × [tex]\sqrt{-1}[/tex]

= 3 × [tex]\sqrt{5}[/tex] × i

= 3i[tex]\sqrt{5}[/tex]

Answer:

M=T = angle A

try it

then. find angle a the sum of palleogram is .... then 12+A=....

angle A=........

Answer:

57 children

54 adults

Step-by-step explanation:

Let's call x the number of children admitted and call z the number of adults admitted.

Then we know that:

[tex]x + z = 111[/tex]

We also know that:

[tex]3.25x + 4z = 401.25[/tex]

We want to find the value of x and z. Then we solve the system of equations:

-Multiplay the first equation by -4 and add it to the second equation:

[tex]-4x - 4z = -444[/tex]

[tex]3.25x + 4z = 401.25[/tex]

----------------------------------

[tex]-0.75x = -42.75[/tex]

[tex]x =\frac{-42.75}{-0.75}\\\\x=57[/tex]

Now we substitute the value of x in the first equation and solve for the variable z

[tex]57 + z = 111[/tex]

[tex]z = 111-57[/tex]

[tex]z = 54[/tex]

Answer:

Number of children=57

Number of adults=54

Step-by-step explanation:

We can start by forming simultaneous equations from the information provided.

Let the number of children be x and adults be y, then the the sum of the amount collected from both children and adults=3.25x+4y=401.25

The total number of people in attendance x+y=111

Let us solve these equations simultaneously.

3.25x+4y=401.25

x+y=111

Using substitution method.

y=111-x

3.25x+4(111-x)=401.25

3.25x+444-4x=401.25

-0.75cx=-42.75

x=57

Number of children=57

Adults=111-57

=54

Answer:

[tex]35+50x\le 1325[/tex]

Step-by-step explanation:

So y=mx+b tells us the initial amount is b (also known as the y-intercept).

Anyways you have to pay a one time fee of 35 dollars and then it is 50 dollars per month.

Let x represent the number of months she goes to yoga.

If she goes 1 month it costs her 35+50.

If she goes 2 months it costs her 35+50+50 or just 35+50(2).

If she goes 3 months it costs her 35+50+50+50 or just 35+50(3).

If she goes x months it costs her 35+50x.

Now she only has 1325.

So we want the cost of her x months to be less than or equal to 1325 because she doesn't have more than that.

So we want [tex]35+50x\le 1325[/tex]

Answer:

C

Step-by-step explanation:

Since she want to use her savings of $1325 it means that that is all the money Abbey is going to use so it means that the $1325 is greater or equal to the money she can or is going to spend. There is a one time fee of $35 which is going to be added to it and a monthly fee of $50. Since you don't know how many months, it'll be replaced with an x. so the equation will be 35+50x≤$1325

Answer:

[tex]\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]

Step-by-step explanation:

I'm going to write 105 as a sum of numbers on the unit circle.

If I do that, I must use the sum identity for sine.

[tex]\sin(105)=\sin(60+45)[/tex]

[tex]\sin(60)\cos(45)+\sin(45)\cos(60)[/tex]

Plug in the values for sin(60),cos(45), sin(45),cos(60)

[tex]\frac{\sqrt{3}}{2}\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\frac{1}{2}[/tex]

[tex]\frac{\sqrt{3}\sqrt{2}+\sqrt{2}}{4}[/tex]

[tex]\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]

Sin 105 degrees is equivalent to (√6 - √2) / 4.

The exact value of sin 105 degrees can be determined using trigonometric identities. Knowing that sin (90 + θ) = cos θ, we can rewrite sin 105 degrees as sin (90 + 15) degrees.

Applying the identity, sin (90 + 15) degrees equals cos 15 degrees.

Utilizing the trigonometric values of common angles, cos 15 degrees can be expressed as (√6 - √2) / 4.

This value is derived from trigonometric relationships, providing an exact representation of sin 105 degrees without resorting to decimal approximations.

The probability of guessing a 3-digit pin correctly on the first attempt, when repetition of digits is allowed, is 1 out of 1000, or 0.001.

The subject under scrutiny is related to the concept of probability in mathematics. To solve this, we need to consider that there are 10 possible digits (0 to 9) on the keypad for each of the 3 input spots in the pin. Since a digit can be repeated, each spot has 10 possibilities. The total number of possible pin combinations is thus 10*10*10 = 1000.

The probability of guessing the pin correctly on the first attempt would be 1 (since there's only one correct pin) divided by the total number of possibilities, which is 1000. Therefore, the probability of this happening is 1/1000 or 0.001.

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The probability of a correct guess on the first try is 1/729.

In this scenario, the thief must randomly guess the correct three-digit pin code from a 9-key keypad where repetition of digits is allowed. To determine the probability of a correct guess on the first try, we need to calculate the ratio of favorable outcomes to total outcomes.

There are 9 possible digits to choose from, and repetition is allowed. Therefore, the number of outcomes is 9 raised to the power of 3 (since the thief needs to guess a three-digit pin code). This gives us 729 total outcomes. There is only one favorable outcome in this case, which is the correct pin code. Therefore, the probability of a correct guess on the first try is 1/729.

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Answer:

C

Step-by-step explanation:

Given the roots of the polynomial are x = - 6, x = 1 and x = 4 the the factors are

(x + 6), (x - 1) and (x - 4)

The polynomial is the product of the factors, that is

f(x) = a(x - 1)(x - 4)(x + 6) ← a is a multiplier

let a = 1 and expand the first pair of factors

f(x) = (x² - 5x + 4)(x + 6)

     = x(x² - 5x + 4) + 6(x² - 5x + 4) ← distribute both parenthesis

     = x³ - 5x² + 4x + 6x² - 30x + 24 ← collect like terms

f(x) = x³ + x² - 26x + 24 → C

Answer:

x^3 + x^2 - 26x + 24.

Step-by-step explanation:

Knowing the roots we can immediately write it in factor form as follows:

f(x) = (x + 6)(x - 1)(x - 4).

Note that when  f(x) = 0 each of the factors can be zero and , for example, when  x + 6 = 0 then x = -6.

We now expand the  expression:

(x + 6)(x - 1)(x - 4)

= (x + 6)(x^2 - 4x - 1x + 4)

= (x + 6)(x^2 - 5x + 4)

= x(x^2 - 5x + 4) + 6(x^2 - 5x + 4)

= x^3 - 5x^2 + 4x + 6x^2 - 30x + 24    Adding like terms:

= x^3 + x^2 - 26x + 24.  (Answer).

Answer:

Answer:

Option B is correct.

Step-by-step explanation:

We will compare the interest earned by both.

Tasha: p = $5000

r = 6% or 0.06

n = 1

So, Amount after a year will be = = $5300

And amount the next year with p = 5300: 5300*1.06= $5618

Additional $5000 at 8%

Here the amount will be = =5400

Next year amount with p = 5400 : 5400*1.08 = $ 5832

Amount in total Tasha will have in 2 years = 5618+5832 = 11450

Thomas:

p = 10000

r = 7% or 0.07

n = 1

After a year the amount will be = =$10700

Amount Next year with p = 10700 : 10700*1.07 = $11449

*****Just after 1 year we can see that Tasha's total amount is high than Thomas. This means at the same consistent rate, each year Tasha's amount will always be higher than Thomas.

So, option B is correct. Tasha’s investment will yield more over many years because the amount invested at 8% causes the overall total to increase faster.

Answer:

B) Tasha’s investment will yield more over many years because the amount invested at 8% causes the overall total to increase faster.

Step-by-step explanation:

I just took the test on edge

Answer:

254 and 180

Step-by-step explanation:

First of all we will define mode

"A mode is the most frequent value in the data"

In order to find mode the data is observed and the data value with most number of occurrence is called mode.

A data set can have more than one modes.

So in the given data,

The repeated data values are:

254 = two times

180 = two times

So the modes are 254 and 180 ..

Answer:

Mode of staff wages =   £180

, and  £254

Step-by-step explanation:

Points to remember

Mode of a data set is the most repeating item in the given data set.

To find the mode of staff wages

The given data set is,

£254, £254, £310, £276, £116, £90, £312, £180, £180, £536, £350, £243, £221, £165, £239, £700

Ascending order of data set

£90,  £116,  £165, £180, £180,  £221, £239, £243, £254, ,£254, £276,  £310,  £312, £350,  £536,  £700

Most repeating data = £180 , and  £254

Mode of staff wages =   £180 , and  £254

Answer:

C) 1287 cubic feet

Step-by-step explanation:

To find the volume of a rectangular prism the formula is length time width times height. That means area=9*11*13 which is 1287 or C.

Answer:

P(factor of 56)=5/8

P(multiple of 3)=1/4

Step-by-step explanation:

The positive factors of 56 are 1,2,4,7,8,14,28,56.

The factors of 56 on the spinner are 1,2,4,7, and 8.  There are 5 numbers there that are factors of 56.

There are 8 numbers to land on in all.

So the P(factor of 56)=5/8.

Multiples of 3 are 3,6,9,...

The multiples of 3 on the spinner on the board are 3 and 6.  There are 2 numbers there that are multiples of 3.

There are 8 numbers to land on in all.

So the P(multiple of 3)=2/8 which reduced to 1/4.  I divided top and bottom by 2.

Answer:

the answer is D. all real numbers greater than or equal to 2.

Step-by-step explanation:

looking at the graph, half of a parabola is curved upwards, and will never stop going up. looking at (1, 2), the dot (instead of circle) indicates the range is greater than or equal to itself, which is 2.

Option: d is the correct answer.

  d.   all real numbers greater than or equal to 2

Domain of a function--

The domain of the function is the set or collection of all the x-values for which the function is well defined.

Range of a function--

The range of  a function is the set of all the values which are attained by a function in it's defined domain.

By looking at the graph we observe that the function is continuously increasing and the function takes all the real values greater than as well as equal to 2( since there is a closed circle at (1,2) )

            Hence, the range is: [2,∞)

Use the substitution method

f(x)= 6x-4

f(8)= 6(8)-4

f(8)= 48-4

f(8)= 44

Answer is f(8)= 44

Answer:

Step-by-step explanation:

[tex]f(x)=6x-4\\\\\text{Put x = 8 to the equation:}\\\\f(8)=6(8)-4=48-4=44[/tex]

Answer:

x = 6, y = 9

Step-by-step explanation:

One of the properties of a parallelogram is

The diagonals bisect each other, hence

2x = y + 3 → (1)

2y = 3x → (2)

Rearrange (1) in terms of y by subtracting 3 from both sides

y = 2x - 3 → (3)

Substitute y = 2x - 3 into (2)

2(2x - 3) = 3x ← distribute left side

4x - 6 = 3x ( add 6 to both sides )

4x = 3x + 6 ( subtract 3x from both sides )

x = 6

Substitute x = 6 into (3) for value of y

y = (2 × 6) - 3 = 12 - 3 = 9

Hence x = 6 and y = 9

Answer: 1

Step-by-step explanation:

A formula for the slope of a line is rise/run.

First let’s find the ‘rise’

To find the rise, we must look at the difference between the elevation of the points. We can find the rise by subtracting y1 from y2. 7-3=4, so the rise is 4

Run is the same concept. We must subtract x2 - x1.

2-(-2)=2+2=4

So the rise is 4 and the run is 4. There for rise/run = 4/4 =1

The slope of the line is 1

Answer:

Option C and E are correct.

Step-by-step explanation:

We need to solve the following equation

(2x+3)^2=10

taking square root on both sides

[tex]\sqrt{(2x+3)^2}=\sqrt{10}\\2x+3=\pm\sqrt{10}[/tex]

Now solving:

[tex]2x+3=\sqrt{10} \,\,and\,\,2x+3=-\sqrt{10}\\2x=\sqrt{10}-3 \,\,and\,\,2x=-\sqrt{10}-3\\x=\frac{ \sqrt{10}-3}{2} \,\,and\,\,x=\frac{-\sqrt{10}-3}{2}[/tex]

So, Option C and E are correct.

Answer: E .√10 - 3 / 2 or

c. -√10 - 3 / 2

Step-by-step explanation:

(2x + 3)^2 = 10

take the square root of bothside

√(2x + 3)^2 = ±√10

2x + 3 = ±√10

subtract 3 from bothside

2x = ±√10 - 3

Divide bothside by 2

x = ±√10 - 3 / 2

Either x = √10 - 3 / 2 or

x = -√10 - 3 / 2

Answer:

Step-by-step explanation:

Use FOIL: (a + b)(c + d) = ac + ad + bc + bd

(x - 4)(x + 3) = (x)(x) + (x)(3) + (-4)(x) + (-4)(3)

= x² + 3x - 4x - 12          combine like terms

= x² + (3x - 4x) - 12

= x² - x - 12

Answer:

Step-by-step explanation:

You have a dangling bracket. I'm not sure what to make of it. I will solve it as

(x - 4)(x + 3) if this is not correct, could you leave me a note.

x^2 + 3x - 4x - 12

x^2 - x - 12

If you meant

(x - 4(x + 3)) then it would be solved as

x - 4x - 12     combine the xs

-3x - 12

dangling brackets are to math what dangling modifiers are to English.

Running up a tree, I saw a squirrel.

If you mean anything but that you were running up a tree, the sentence is incorrect.