Tonya wrote the equation below which solves for x.

x=150-6y

Which equation is equivalent to Tonya’s equation?

Answer:

I think it may be B, but double check

Answer:

B and D

Step-by-step explanation:

Considering the multiple choices and let us assume that x = 2,

Option A would be equal to [tex]\frac{3}{4}x[/tex],

so if x = 2, then;

        [tex]\frac{3}{4}x[/tex] = 1.5 (which is less than x)

Option B would give [tex]\frac{5}{4} x[/tex],

so if x = 2, then;

       [tex]\frac{5}{4} x[/tex] = 2.5 ( which is greater than x)

From option C,

      [tex]\frac{7}{8} x[/tex] = 1.75 (which is less than x)

From option D,

     [tex]\frac{9}{8} x[/tex] = 2.25 ( which is greater than x)

So, options B and D are expressions whose values are greater than x.

Check the picture below.

Answer:

Step-by-step explanation:

The cost function is

[tex]C=10n+150[/tex]

Where [tex]n[/tex] is the number of buckets of apples sold.

The revenue is defined as

[tex]r=15n[/tex]

The image attached shows both functions graphed in the same coordinate system. According with the graph, the break-even point is at (30,450), that is, 30 of buckets sold and $450 of revenue and cost.

In other words, we need to sell 30 buckets to have the cost and revenue equals.

Therefore, the answer is A.

Answer:

x =  -12.42    or  x = 2.42

Step-by-step explanation:

x^2 + 10x - 13 = 17

To solve this using the completing the square method, we will follow the  steps below;

First, we will add 13 to both side of the equation, we want only the x variable to be on the left-hand side of the equation

x^2 + 10x - 13 + 13 = 17 + 13

x^2 + 10x  = 30

The next step is to add both-side of the equation  by square of half of the coefficient of x (that is ; half of 10 is 5, then we will add 5²  to both-side of the equation)

x^2 + 10x + 5²  = 30 + 5²

Then we can now factorize the left-hand side of the equation and at the same time simplify the right-hand side of the equation

(x + 5)²   =   30 + 25

(x + 5)²   = 55

We will then take the square root of both-side of the equation

√(x + 5)²   = ±√55

x + 5  =  ±√55

To get the value of x, we will subtract 5 from both-side of the equation

 x + 5 - 5   =  ±√55 - 5

x =  ±√55  -  5

Either x = + √55 -5  = 7.42 -5 = 2.42

OR

x = -√55 - 5   = -7.42 - 5 = -12.42

Therefore either x =  -12.42    or  x = 2.42

 x =  -12.42    or   2.42

B. 25 Km. The measure of BC is 25 km.

The easiest way to solve this problem is using the cosine theorem c = √a²+b²-2ab*cos A.

BC = √AC²+AB²-2(AC)(AB)*cos A

BC = √(21km)²+(14km)²-2(21km)(14km)*cos 89°

BC = √441km²+196km²-588km²*(0.017)

BC =√637km²-10.26km²

BC = √636.74km²

BC = 25.03km ≅ 25

Answer:

[tex]\large\boxed{f^{-1}(x)=\dfrac{x+4}{3}=\dfrac{1}{3}x+\dfrac{4}{3}}[/tex]

Step-by-step explanation:

[tex]f(x)=3x-4\to y=3x-4\\\\\text{exchange x to y and vice versa}\\\\x=3y-4\\\\\text{solve for y}\\\\3y-4=x\qquad\text{add 4 to both sides}\\\\3y=x+4\qquad\text{divide both sides by 3}\\\\y=\dfrac{x+4}{3}[/tex]

Answer:

5/6 (if including 3)       4/6 (not including 3)

Step-by-step explanation:

1 and 2 are less than 3

4 and 6 are even

that leaves 5 and 3.

so 4 of the numbers are even or less than 3

Probability of rolling even number or number less than 3 is 2/3.

Probability is defined by the possibility of the event to happen which is ratio of no. of favorable outcomes and the total no. of outcomes.

Probability of event = P(E) = No. of favorable outcomes/Total No. of outcomes

Here given that the dice is fair and six-sided is rolled.

Total no. of outcomes by rolling the dice=6 i.e. {1,2,3,4,5,6}

No. of favorable outcomes of getting even no. =3 i.e. {2,4,6)

Probability of rolling an even no.=P(even)= No. of favorable outcomes/Total No. of outcomes = 3/6

No. of favorable outcomes of getting no. less than 3 =2 i.e. {1,2}

Probability of rolling no. less than 3=P(<3) =No. of favorable outcomes/Total No. of outcomes = 2/6

No. of favorable outcomes of getting even no and number less than 3 =1 i.e. {2}

Probability of rolling an even no. and no. less than 3 =P(even and <3) = P(even ∩ <3)= No. of favorable outcomes/Total No. of outcomes = 1/6

As we know P(A∪B)=P(A)+P(B)-P(A∩B)

Probability of rolling an even no.or no. less than 3 = P(even or <3) = P(even ∪ <3)= P(even)+P(<3)-P(even ∩ <3)

=(3/6)+(2/6)-(1/6)

=4/6

=2/3

Therefore probability of rolling even number or number less than 3 is 2/3.

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Answer:

Osvoldo does not meet his goal

He had to have eaten at least 66 grams of whole grains to meet his goal.

Step-by-step explanation:

step 1

Find out the 30% of the grams of carbohydrates that Osvoldo ate today

Remember that

30%=30/100=0.30

so

0.30(220)=66 grams

step 2

Compare the 30% of the grams of carbohydrates that Osvoldo ate today with the 55 grams of whole grains

we know that

To Osvoldo meet his goal the 55 grams of whole grain must be greater than or equal to the 30% of the grams of carbohydrates that Osvoldo ate today

55 < 66

therefore

Osvoldo does not meet his goal

He had to have eaten at least 66 grams of whole grains to meet his goal.

Answer:

Option C [tex]1,102\ in^{2}[/tex]

Step-by-step explanation:

we know that

The lateral surface area of a cylinder is equal to

[tex]LA=2\pi rh[/tex]

we have

[tex]r=13.6\ in[/tex]

[tex]h=12.9\ in[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]LA=2(3.14)(13.6)(12.9)[/tex]

[tex]LA=1,101.76\ in^{2}[/tex]

Round to the nearest square inch

[tex]LA=1,102\ in^{2}[/tex]

Answer:

b

becasue to find his current weight you would use what you know and the amount of lbs he added (represented as x)

96 + x

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

m = 3

n = 1

Equation

m(m - n)     Substitute the givens

Solution

3(3 -1 )        Evaluate what is inside the brackets.

3(2)      multiply

6

Answer:

m=3 and n-1 ,find m2- mn

Step-by-step explanation:

Answer:

The area is 5.5 cm squared.

Step-by-step explanation:

To find the area, you have to find the areas of the rectangle and the triangle separately and then add your two values together.

The formula for the area of a rectangle is as follows:

[tex]A=lw[/tex]

In this formula, "l" refers to length and "w" refers to width.

As shown in the diagram, your length is 1.5 cm and your width is 2 cm.

Simply plug these numbers into the formula and simplify.

[tex]A=1.5*2\\A=3[/tex]

The area of the rectangle is 3 cm squared.

Next, find the area of the triangle. The formula for the area of a triangle is as follows:

[tex]A=\frac{1}{2} bh[/tex]

In this formula, "b" refers to the measure of the base and "h" refers to the measure of the height.

Your base (b) is 2 cm.

To find your height, subtract the length of the rectangle (1.5 cm) from the total length of the shape (4 cm). This will give you a height of 2.5 cm.

Next, plug your values into the formula and simplify.

[tex]A=\frac{1}{2} *2*2.5\\A=1*2.5\\A=2.5[/tex]

The area of the triangle is 2.5 cm squared.

Add the area of the rectangle (3 cm squared) to the area of the triangle (2.5 cm squared), and you have the area of the entire figure (5.5 cm squared).

Note: Carlos' mistake in the problem is that he forgot to subtract the length of the rectangle from the length of the entire shape, and incorrectly used 4 cm as his height for the triangle rather than 2.5 cm.

Answer:

80

Step-by-step explanation:

Let's say M is the number of men, W is the number of women, and C is the number of children.

M + W + C = 270

M/W = 4/5

W/C = 10/9

We have three equations and three variables, so we can solve this.  Let's use substitution.

W = 5/4 M

C = 9/10 W

Substitute into the first equation:

M + 5/4 M + 9/10 W = 270

Substitute again:

M + 5/4 M + 9/10 (5/4 M) = 270

Solve:

M + 5/4 M + 9/8 M = 270

8/8 M + 10/8 M + 9/8 M = 270

27/8 M = 270

M = 80

There are 80 men on the train.

Answer:

The measure of arc a is 86°

Step-by-step explanation:

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

so

86°=(1/2)[arc c+arc a]

see the attached figure with letters to better understand the problem

In this problem

Triangles ABO and CDO are congruent by SSS postulate theorem

∠AOB=∠COD

∠AOB=arc a -----> by central angle

∠COD=arc c -----> by central angle

therefore

The measure of arc a is congruent with the measure of arc c

arc a=arc c

so

86°=(1/2)[2arc a]

86°=[arc a]

arc a=86°

Answer: 3p+5=11

Step-by-step explanation:

3p+5=11

-5 -5

3p=6

3p/3=6/3

P=2

$2

The cost of each pencil is $2.

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Number of pencils = 3

Number of notebook = 1

Cost of a notebook = $5

Total cost = $11

Let number of pencil be p.

Lela purchased three mechanical pencils and a notebook is

⇒ [tex]3p+5=11[/tex]

⇒ [tex]3p=11-5[/tex]

⇒ [tex]3p=6[/tex]

⇒ [tex]p=\frac{6}{3}[/tex]

⇒ [tex]p=2[/tex]

Hence we can conclude that the cost of each pencil is $2.

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Answer:

Option D is correct.

Step-by-step explanation:

Original Price of car = $38,000

Current Price of car = $28,500

The residual value of Sally's leased car = x = ?

Residual value * Original Price = Current Price

x * 38,000 = 28,500

x = 28,500/38,000

x = 0.75

Since we need to find percentage

Multiply the residual value with 100 i.e,

0.75 * 100 = 75%

Option D is correct.

Answer:

1705/64

Step-by-step explanation:

A geometric series contains terms that are in the form [tex]a_1\cdot(r)^{n-1}[/tex] where [tex]a_1[/tex] is the first term and [tex]r[/tex] is common ratio.

A common ratio is the number that is used to find the next term by multiplying previous term by [tex]r[/tex].

Now we can use a formula and we would be using [tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex] where n is the number of terms you are adding and [tex]a_1[/tex] is the first term and r is the common ratio.

Before we do that, I'm going to do this without that formula. Sum means we are just going to add these terms after finding them.

The first term is 20.

The second term is (1/4)(20)=5.

Third term is (1/4)(5)=5/4.

Fourth term is (1/4)(5/4)=5/16.

The fifth term is (1/4)(5/16)=5/64.

Now we add them (20)+(5)+(5/4)+(5/16)+(5/64)

Putting this into the calculator gives me: 1705/64.

Now let's do the formula way as well.

Again we have:

r=1/4

[tex]a_1=20[/tex]

n=5 since we adding the first 5 terms:

[tex]S_5=\frac{20(1-(\frac{1}{4})^5}{1-\frac{1}{4}}[/tex]

[tex]S_5=\frac{20(1-\frac{1}{1024}){\frac{3}{4}}[/tex]

[tex]S_5=\frac{20-\frac{20}{1024}}{\frac{3}{4}}[/tex]

Dividing by 3/4 is the same as multiply by 4/3.

[tex]S_5=(20-\frac{20}{1024})\frac{4}{3}[/tex]

[tex]S_5=20 \cdot \frac{4}{3}-\frac{20}{1024}\cdot\frac{4}{3}[/tex]

[tex]S_5=\frac{80}{3}-\frac{5}{256} \cdot \frac{4}{3}[/tex]

[tex]S_5=\frac{80}{3}-\frac{20}{256 \cdot 3}[/tex]

[tex]S_5=\frac{80}{3}-\frac{5}{64 \cdot 3}[/tex]

[tex]S_5=\frac{80}{3}-\frac{5}{192}[/tex]

Multiplying first fraction by 64/64:

[tex]S_5=\frac{80(64)}{3(64)}-\frac{5}{192}[/tex]

[tex]S_5=\frac{5120}{192}-\frac{5}{192}[/tex]

{tex]S_5=\frac{5115}{192}[/tex]

Dividing to and bottom by 3:

[tex]S_5=\frac{1705}{64}[/tex].

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}[/tex]

[tex]\bf A=5000\left(1+\frac{0.08}{12}\right)^{12\cdot 15}\implies A=5000(1.00\overline{66})^{180}\implies A\approx 16534.61[/tex]

Answer:

B

Step-by-step explanation:

Given

6x³ + 6 ← factor out 6 from each term

= 6(x³ + 1)

x³ + 1 is a sum of cubes and factors as

x³ + 1 = (x + 1)(x² - x + 1)

Hence

6x³ + 6 = 6(x + 1)(x² - x + 1)

With factor (x + 1) → B

Answer:

b) x + 1

Step-by-step explanation:

you can either

1) take (6x³ + 6) and divide by all the choices to see which one gives you a factor. You will realize that if you divide this by option b, you will be able to factorize the equation as follows:

(6x³ + 6) = 6(x+1)(x²−x+1)

Hence option b is a factor

or

2) (my preferred method), utilize the properties of functions and roots.

Let function f(x) = 6x³ + 6

any value of a which gives f(a) = 0 is a root , i.e (x-a) is a factor.

In this case, lets consider option b

let x + 1 = 0 -------> or x = -1

substitute this into the function f(x)

f(-1) = 6 (-1)³ + 6

f(-1) = -6 + 6 = 0

hence x = -1 is a root , or (x+1) is a factor.

as a sanity check, lets try choice a) x -1

let x - 1 = 0 -------> or x = +1

substitute this into the function f(x)

f(1) = 6 (1)³ + 6

f(1) = 6 + 6 = 12 ≠0

hence x = 1 is NOT a root , or (x-1) is NOT a factor.

You can do the same for c and d and find that they too are NOT factors.

5x^4

Step-by-step explanation:

simply we take 5x^4 bec. it can be divided by 40 and 135

Answer: 245 [tex]in^{2}[/tex]

Step-by-step explanation:

You can find the Surface Area of a figure by adding up the areas of each shape.

First you have to find the area of the base.

7×7 = 49

Then you can find the area of the 4 triangles that complete the pyramid.

Formula for area of a triangle: [tex]\frac{1}{2} bh[/tex] (one half of base times height)

[tex]\frac{1}{2} (14*7) = x\\\frac{1}{2} 98 = x\\x = 49[/tex]

Since all the triangles are the same, you only have to calculate that once.

Now you just add everything together, and that's your surface area.

[tex]49+49+49+49+49= 245[/tex]

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Answer:  245

Step-by-step explanation:

first you have to 7 for the square which = 14

then after that you do 1/2 b x h = 1/2  7 x 14= 3.5 x 14= 49 but then you have 4 triangles so 49 x 4=196.     Then  49 + 196= 245  

Answer:

(f-g)(x) = x-3

Step-by-step explanation:

Given

f(x) = 3x-2

and

g(x) = 2x+1

We have to find (f-g)(x)

So,

(f-g)(x) = f(x)-g(x)

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

= 3x-2-2x-1

=x-3

Hence,

(f-g)(x) = x-3

Answer:

( f - g ) ( x ) = x - 3

Step-by-step explanation:

We are to find [tex] ( f - g ) ( x ) [/tex] given that [tex] f ( x ) = 3 x - 2 [/tex] and [tex] g ( x ) = 2 x + 1 [/tex].

So basically we have to subtract the function g from function f.

[tex] ( f - g ) ( x ) = f(x) - g(x) [/tex]

Substituting the given functions in the above equation to get:

[tex] ( f - g ) ( x ) = (3x - 2) - (2 x + 1 ) [/tex]

[tex] ( f - g ) ( x ) = 3x - 2 - 2 x - 1  [/tex]

[tex] ( f - g ) ( x ) = 3x - 2 x - 2 - 1  [/tex]

[tex] ( f - g ) ( x ) = x - 3 [/tex]

Answer:

C (2, -5/2)

Step-by-step explanation:

To find the midpoint of two points

mid = (x1+x2)/2, (y1+y2)/2

       = (2+2)/2, (4+-9)/2

       = 4/2, -5/2

       =2,-5/2

Answer:

[tex]a_n=-3a_{n-1}[/tex] where [tex]a_1=2[/tex]

Step-by-step explanation:

Recursive means you want to define a sequence in terms of other terms of your sequence.

The common ratio is what term divided by previous term equals.

The common ratio here is -6/2=18/-6=-54/18=-3.

Or in terms of the nth and previous term we could say:

[tex]\frac{a_n}{a_{n-1}}=r[/tex]

where r is -3

[tex]\frac{a_n}{a_{n-1}}=-3[/tex]

Multiply both sides by the a_(n-1).

[tex]a_n=-3a_{n-1}[/tex] where [tex]a_1=2[/tex]

Answer:

see explanation

Step-by-step explanation:

A recursive rule allows us to obtain any term in the sequence from the previous term.

These are the terms of a geometric sequence with common ratio r

r = - 6 ÷ 2 = 18 ÷ - 6 = - 54 ÷ 18 = - 3

Thus to obtain a term in the sequence multiply the previous term by - 3

[tex]a_{n+1}[/tex] = - 3 [tex]a_{n}[/tex] with a₁ = 2

Answer:

4

Step-by-step explanation:

-36-9+14-31+66

=4

Since + - = - and - - = +

Answer:

y  ≥ 14.

Step-by-step explanation:

y - 27 ≥ -13 Add 27 to both sides:

y  ≥ 14 (answer).

For this case we must find the solution of the following inequality:

[tex]y-27 \geq-13[/tex]

We must add 27 to both sides of the inequality:

[tex]y \geq-13 + 27[/tex]

We know that different signs are subtracted and the sign of the major is placed.[tex]y \geq14[/tex]

So, the solution is [tex]y \geq14[/tex]

Answer:

Option C

Check the picture below.

Step-by-step explanation:

Given : The sales of a certain product after an initial release can be found by the equation [tex]s=12\sqrt{4t}+ 10[/tex], where s represents the total sales (in thousands) and t represents the time in weeks after release.

To find : Make a table of values, graph the function and use the graph to estimate the sales 12 weeks after release ?

Solution :

The equation [tex]s=12\sqrt{4t}+ 10[/tex]

where, s represents the total sales (in thousands) and t represents the time in weeks after release.

We put t=1,2,3,.....,12 and create a table

 t            [tex]s=12\sqrt{4t}+ 10[/tex]

 1                    34

 2                   43.94  

 3                   51.56

 4                   58

 5                   63.66

 6                   68.78

 7                   73.49  

 8                   77.88

 9                   82

 10                  85.89

 11                   89.59

 12                  93.13

Answer:

[tex]\large\boxed{B.\ x=\pm1\ and\ x=\pm2\sqrt2}[/tex]

Step-by-step explanation:

[tex]x^4-9x^2+8=0\\\\x^{2\cdot2}-9x^2+8=0\qquad\text{use}\ (a^n)^m=a^{nm}\\\\(x^2)^2-9x^2+8=0\\\\\text{substitute}\ x^2=t\geq0\\\\t^2-9t+8=0\\\\t^2-t-8t+8=0\\\\t(t-1)-8(t-1)=0\\\\(t-1)(t-8)+0\iff t-1=0\ \vee\ t-8=0\\\\t-1=0\qquad\text{add 1 to both sides}\\t=1\geq0\\\\t-8=0\qquad\text{add 8 to both sides}\\t=8\geq0[/tex]

[tex]t=x^2\to x^2=1\ \vee\ x^2=8\\\\x^2=1\Rightarrow x=\pm\sqrt1\to x=\pm1\\\\x^2=8\Rightarrow x=\pm\sqrt8\to x=\pm\sqrt{4\cdot2}\to x=\pm\sqrt4\cdot\sqrt2\to x=\pm2\sqrt2[/tex]

Answer:

Step-by-step explanation:

Given is the equation of 4th degree in x,

[tex]x^4 - 9x^2 + 8 = 0[/tex]

Substitute [tex]x^2=u[/tex]

[tex]u^2-9u+8=0\\(u-1)(u-8)=0[/tex]

u=1 and u =8

i.e. [tex]x^2=1\\x^2 =8[/tex]

Solving we get

[tex]x=1,-1,2\sqrt{2}, -2\sqrt{2}[/tex]

Option B is right.

For this case we have that a percentage equivalent to[tex]\frac {1} {8}[/tex]is given by:

[tex]x = \frac {1} {8} * 100 =[/tex] 12.5%

Then, according to the steps, it is observed that Harriet made an incorrect division, deboa multiply. So, the second step is the wrong one.

Answer:

Option B