Arrange the systems of equations that have a single solution in increasing order of x-values in their solutions. 2x+y=10
x-3y=-2

2x + y= 10
-6x -3y=-2

x+2y= 5
2x + y = 4

5x+ y= 33
x=18-4y

Y=13 -2x
8x + 4y =52

x+ 3y =5
6x-y=11

Y=10 + x
2x + 3y =45

Final answer:

The unit rate, r, per day to keep the dog at the kennel is $14.25.

Explanation:

To find the unit rate, we need to divide the total cost by the number of days. In this case, Gene paid $171 to keep his dog at the kennel for 12 days. So the unit rate, which represents the cost per day, is calculated as:

Unit rate = Total cost / Number of days

Unit rate = $171 / 12

Unit rate = $14.25 per day which is the required answer

Therefore, unit rate to keep the dog at the kennel is $14.25 per day.

Answer:

AC is 96 units

Answer:

BC - 54 units

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

∠C = 180° - (∠A + ∠B) = 180° - (80 + 50)° = 180° - 130° = 50°

Since ∠B = ∠C = 50° then the base angles of the triangle are equal hence the triangle is isosceles with

AB = AC, that is

4x - 4 = 2x + 16 ( subtract 2x from both sides )

2x - 4 = 16 ( add 4 to both sides )

2x = 20 ( divide both sides by 2 )

x = 10

⇒ BC = 5x + 4 = (5 × 10) + 4 = 50 + 4 = 54

Answer:

you add 11 inches each day

Step-by-step explanation:

q=4,-1

you need to isolate q

The solution set of the equation is {-4, 2}

Given expression:

[tex]\frac{8}{q} +2=\frac{q+4}{q-1}[/tex]

Solve for q: simplify

[tex]\frac{8}{q} +2=\frac{q+4}{q-1}\\\frac{8+2q}{q}=\frac{q+4}{q-1}\\(8+2q)(q-1)=(q(q+4)\\8q-8+2q^{2} -2q=q^{2} +4q\\2q^{2} +6q-8 =q^{2}+4q\\q^{2} +2q-8=0[/tex]

Factorize the quadratic equation to solve q

[tex]q^{2} +4q-2q-8=0\\q(q+4)-2(q+4)=0\\(q+4)=0, (q-2)=0\\q= -4, 2[/tex]

Therefore, The solution set of the equation is {-4, 2}

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Answer:

D) 0.211

Step-by-step explanation:

The probability of getting a correct answer is 1/4, so the probability of an incorrect answer is 3/4.

The probability of 2 correct and 2 incorrect is (1/4)(1/4)(3/4)(3/4) = 9/256.

There are C(4,2) = 4·3/(2·1) = 6 ways to have some combination of 2 correct and 2 incorrect out of 4 questions. So, the probability of that result is ...

... 6 · 9/256 = 27/128 =0.2109375 ≈ 0.211

Answer:

5/36

Step-by-step explanation:

Answer:

Odd

Step-by-step explanation:

The graph intersects the x-axis three times. These three intercepts are the roots of the function and form the factors or solutions for x. They also represent the degree. This is an odd degree because there are 3 roots and 3 is odd. It is at least 3 but could be higher. All odd degree polynomials have the shape of a sideways s.

Final answer:

40 child tickets and 95 adult tickets were sold.

Explanation:

Let's assume the number of child tickets sold is x.

According to the problem, the number of adult tickets sold is 15 more than twice the number of child tickets. So the number of adult tickets sold is 2x + 15.

The total income from ticket sales is $1,340. The income from child tickets is $5 times the number of child tickets and the income from adult tickets is $12 times the number of adult tickets.

Therefore, we can express the total income as the sum of the income from child tickets and adult tickets:

$5x + $12(2x + 15) = $1,340

Simplifying the equation:

$5x + $24x + $180 = $1,340

$29x = $1,340 - $180

$29x = $1,160

Dividing both sides by 29:

x = $1,160/$29

x = 40

So, the number of child tickets sold is 40, and the number of adult tickets sold is 2x + 15 = 2(40) + 15 = 80 + 15 = 95.

Therefore, 40 child tickets and 95 adult tickets were sold.

Divide both sides by -3, and replace [tex]x^2[/tex] with [tex]y[/tex]. Then

[tex]-3x^4+27x^2+1200=0\iff y^2-9y-400=0[/tex]

Factorize the quadratic in [tex]y[/tex] to get

[tex]y^2-9y-400=(y+16)(y-25)=0\implies y=-16,y=25[/tex]

which in turn means

[tex]x^2=-16,x^2=25[/tex]

But [tex]x^2\ge0[/tex] for all real [tex]x[/tex], so we can ignore the first solution. This leaves us with

[tex]x^2=25\implies x=\pm\sqrt{25}=\pm5[/tex]

If we allow for any complex solution, then we can continue with the solution we ignored:

[tex]x^2=-16\implies x=\pm\sqrt{-16}=\pm i\sqrt{16}=\pm4i[/tex]

Answer:

b) 6

Step-by-step explanation:

Since this is an isosceles triangle, the two sides are equal and the two angles are equal.

That means  

5x-3 = 2x+15

Subtract 2x from each side.

5x-2x-3 = 2x-2x+15

3x-3 = 15

Add 3 to each side.

3x-3+3 = 15+3

3x =18

Divide each side by 3

3x/3 = 18/3

x =6

Answer: the answer to this question is A because the angle is acute angle and when you solve (5x-3) it equals up to 18 when you finish figureing it out.

Step-by-step explanation:

Answer:

x=-1

Step-by-step explanation:

x+3

------- = 3 + 1/x

x+2

Get a common denominator on the right

3*x/x + 1/x

3x/x + 1/x = (3x+1)/x

x+3       3x+1

------- = ---------

x+2         x

We can use cross products to solve

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

x^2+3x = 3x*x +x + 3x*2 +2

Simplifying

x^2 + 3x = 3x^2 +7x+2

Subtract x^2 from each side

x^2 -x^2 + 3x = 3x^2-x^2 +7x+2

3x = 2x^2 +7x+2

Subtract 3x from each side

3x-3x = 2x^2 +7x -3x+2

0 = 2x^2 +4x +2

Divide by 2

0 = x^2 +2x +1

Factor

0 = (x+1) (x+1)

Using the zero product property

x+1 =0

x=-1

Answer:

The solution set is { -1 }.

Step-by-step explanation:

If we multiply each term by the LCM of x and x+ 2 ( = x(x + 2))  we get:-

x(x + 3) = 3x(x + 2)  + x + 2

x^2 + 3x = 3x^2 + 6x + x + 2

0 = 3x^2 - x^2 - 3x + 6x + x + 2

2x^2 +4x + 2 = 0

2(x^2 + 2x + 1) = 0

2( x + 1)(x + 1) = 0

x = -1    Multiplicity 2

The solution set  only contains 1 * -1 . Elements in a set are not repeated

So   its {-1}  (answer)

Answer:

<4 and <3

Step-by-step explanation:

The remote interior angles are  the two angles that are inside the triangle and away from the angle adjacent to the exterior angle.

5 is adjacent to 1

so 3 and 4 are the remote interior angles

Answer: There are 6 sections of  [tex]8\frac{1}{4}\ inches[/tex]  of rope Mario can cut from the rope .

Step-by-step explanation:

Since we have given that

Length of the rope for the tent = 7 feet

As we know that

[tex]1\ feet=12\ inches\\\\7\ feet=12\times 7=84\ inches[/tex]

Length of rope is used to tie a tarp on top of the tent = 34.5 inches

Remaining length of rope is given by

[tex]84-34.5=49.5\ inches[/tex]

According to question, the remaining rope should be cut into

[tex]8\frac{1}{4}\ inches\\\\=\frac{33}{4}\ inches[/tex]

So, Number of  [tex]8\frac{1}{4}\ inches[/tex] sections of rope Mario can cut from the rope is given by

[tex]\frac{49.5}{8\frac{1}{4}}\\\\=\frac{49.5}{\frac{33}{4}}\\\\=\frac{49.5\times 4}{33}\\\\=6[/tex]

Hence, there are 6 sections of [tex]8\frac{1}{4}\ inches[/tex] rope Mario can cut from the rope .

Answer:

6

Step-by-step explanation:

Mario has 7 feet of rope.  Since there are 12 inches in every foot, this means he has

7(12) = 84 inches of rope.

34.5 inches of the rope must be used to tie the tarp to the top; this leaves Mario with

84-34.5 = 49.5

This remaining rope will be cut into 8 1/4 inch sections.  We can also write 8 1/4 as 8.25.  To find the number of sections this length he can cut, we divide:

49.5/8.25 = 6

He can cut 6 sections this length.

To find the markup from cost to sale price, calculate the original sale price by dividing the selling price by (1 - discount percentage) which is 230

To find the markup from cost to sale price, we first need to calculate the cost price.

The item is marked down by 20% from the selling price of $440.

So, the original sale price before the discount would be $440 / (1 - 0.20) = $550.

Since the sale price is still marked up from the cost of $320, we can calculate the markup as:

$550 - $320 = $230.

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Answer:

Hang time of the basketball player is 0.83 sec.

Step-by-step explanation:

A pro basketball player has a vertical leap of 33 in.

His hang-time can be calculated by the function given by,

[tex]V=48t^2[/tex]

Where,

V = vertical leap (vertical leap is the act of raising itself in the vertical plane)

t = the time for which the object stays in the air

Putting all the values,

[tex]\Rightarrow 33=48t^2[/tex]

[tex]\Rightarrow t^2=\dfrac{33}{48}[/tex]

[tex]\Rightarrow t=\sqrt{\dfrac{33}{48}}[/tex]

[tex]\Rightarrow t=0.83\ sec[/tex]

Therefore, hang time of the basketball player is 0.83 sec.

Answer:

option-C

Step-by-step explanation:

We are given

graphs -- I , V , VI have same starting point

it means that it has same initial values

Suppose, we are given exponential function as

[tex]f(x)=a(b)^x[/tex]

Here , 'a' is initial value

we can see that initial value of graph-I is 30

so, all other graphs must also have 30 initial value

so, graphs

[tex]e,\delta , \phi[/tex]  have same initial value =30

so, option-C.......Answer

Answer: c-5 cm, 2 cm, 2 cm.

After all the deductions and exemptions, the total taxable​ income of Homer Simpson is $46,700.

Given that, income of Homer and his wife = $60000 and interest earned = $1200.

In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.

Adding this to total income, we have total taxable amount = 60000+1200 = $61200

Now, investment in tax deferred savings plan = $2500

This amount will be subtracted from total taxable income, so amount becomes = 61200-2500 = $58700

Subtract the exemptions and deductions = $12000

That is, amount becomes = 58700-12000 = $46700

Hence, the net taxable income is $46,700.

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Homer Simpson's taxable income is determined by subtracting his tax-deferred savings and total deductions from his total income. His taxable income comes to $46,700. The percentage of tax he pays depends on the U.S income tax bracket he falls under.

To calculate Homer Simpson's taxable income, we need to consider their total income, deductions, and investments. Homer's total income is the sum of his salary, $60,000 and the interest earned, $1200. So, the total income equals $60,000 + $1200 = $61,200.

Next, we subtract the total deductions which include the tax-deferred savings plan and the total deductions and exemptions they have, from the total income. Thus, the taxable income equals $61,200 - $2,500 (savings plan) - $12,000 (deductions and exemptions) = $46,700.

The U.S income tax code is based on a progressive system, so knowing the taxable income can help determine the income tax bracket Homer falls under. Given the figures, Homer's income is in the bracket that is taxed at 22% as per the 2020 basic tax tables from the Internal Revenue Service.  However, it is important to take into consideration any changes in tax laws or additional deductions they might have.

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Answer:

As long as the numbers are in equal proportion on the spinner, the probabilty of landing on an even number for the first and second spin is 1/4, or 25%.  

Step-by-step explanation:

If there are four numbers on a spinner, all in equal proportion, than the probability of getting an even number (either 4 or 6) on any spin is 2/4, or 1/2, which is also 50%.  Since the results of the first spin do not influence the results of the second spin, then they are independent events.  So, if the likelihood of landing on even each time is 1/2, then we would mutliply 1/2 by 1/2 in order to find the probability that landing on an even number would happen in both spins.  Our result would be 1/4, or 25%.  

Not sure what that dude is even saying. The answer is C- P(A and B)=2/4*2/4

Hope this helped.

Answer:

2/3

Step-by-step explanation:

A six-sided number cube labeled from 1 to 6 is rolled.

Total outcomes = 1,2,3,4,5,6= 6 outcomes

multiple of 2  are 2,4,6 so 3 outcomes

multiple of 3 are 3,6 so 2 outcomes

multiply of 2 or 3  are 2,4,3,6 so 4 outcomes

the probability of getting a multiple of 2 or a multiple of 3

= possible outcomes / total outcomes

= 4/6

now reduce the fraction, divide by 2 on both sides

the probability of getting a multiple of 2 or a multiple of 3 = 2/3

Tthe probability of rolling a multiple of 2 or a multiple of 3 on a six-sided die is [tex]\(\frac{5}{6}\)[/tex].

To find the probability of getting a multiple of 2 or a multiple of 3 when rolling a six-sided number cube, we can list out the possible outcomes and identify which ones satisfy our conditions.

The possible outcomes when rolling six-sided die are: 1, 2, 3, 4, 5, and 6:

Multiples of 2 on the die are: 2, 4, 6.

Multiples of 3 on the die are: 3, 6.

We can see that there is an overlap with the number 6, which is both a multiple of 2 and a multiple of 3. To avoid counting this outcome twice, we use the principle of inclusion-exclusion.

First, we add the number of multiples of 2 to the number of multiples of 3

- There are 3 multiples of 2.

- There are 2 multiples of 3.

So, without considering the overlap, we would have [tex]\(3 + 2 = 5\)[/tex] favorable outcomes.

However, since the number 6 has been counted twice, we subtract one instance of it from our total:

[tex]\(5 - 1 = 4\) unique favorable outcomes (2, 3, 4, 6)[/tex]

Since there are 6 possible outcomes in total when rolling a six-sided die, the probability of rolling a multiple of 2 or a multiple of 3 is the number of favorable outcomes divided by the total number of possible outcomes [tex]\(\frac{4}{6}\)[/tex].

This fraction simplifies to [tex]\(\frac{2}{3}\)[/tex]. However, we have overlooked the fact that every number on a six-sided die is a multiple of 1, and since 1 is neither a multiple of 2 nor of 3, it does not contribute to  favorable outcomes. Therefore, the only outcome that is not a multiple of 2 or 3 is number 1.

Thus, the correct probability is [tex]\(1 - \frac{1}{6} = \frac{5}{6}\)[/tex], since there is only 1 unfavorable outcome out of 6 possible outcomes.

Answer:

<A = 67

Step-by-step explanation:

The three angles of a triangle add up to 180 degrees.  We know a right angle is 90 degrees.

<A + <B + <C = 180

3x-8 + 90 + x-2 =180

Combine like terms

4x-10+90 = 180

4x+80 =180

Subtract 80 from each side

4x+80-80=180-80

4x=100

Divide each side by 4

4x/4 = 100/4

x=25

But we want to know <A

<A = 3x-8

 Substitute x=25

    =3(25) -8

    =75-8

   = 67

Answer:

67°

Step-by-step explanation:

In a right triangle, the acute angles are complementary. That means that the sum of their measures is 90 deg.

m<A + m<C = 90

3x - 8 + x - 2 = 90

4x - 10 = 90

4x = 100

x = 25

m<A = 3x - 8

m<A = 3(25) - 8

m<A = 75 - 8

m<A = 67

Answer:

the maximum height of the ball= 256 feet

7 seconds

Step-by-step explanation:

The quadratic function h ( t ) = − 16t^2 + 96t + 112 models the ball's height about the ground, h ( t ) , in feet, t seconds after it was thrown.

a= -16 , b= 96  and c= 112

To find maximum height , we find vertex

[tex]x= \frac{-b}{2a}=\frac{-96}{2(-16)}= 3[/tex]

Now plug in 3 for 't' in h(t)

[tex]h(t) = -16t^2 + 96t + 112[/tex]

[tex]h(t) = -16(3)^2 + 96(3)+ 112=256[/tex]

Hence vertex is (3, 256)

the maximum height of the ball= 256 feet

(b) when the ball hits the ground then height becomes 0

so we plug in 0 for h(t)  and solve for t

[tex]0 = -16t^2 + 96t + 112[/tex]

Apply quadratic formula

[tex]t=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]

Plug in all the values a= -16 , b= 96  and c= 112

[tex]t=\frac{-96+-\sqrt{96^2-4(-16)(112)}}{2(-16)}[/tex]

t= -1  and t= 7

time cannot be negative. So it will take 7 second to hit the ground.

The maximum height of the ball is 160 feet and it takes 4 seconds for the ball to hit the ground.

The quadratic function h(t) = -16t^2 + 96t + 112 represents the height of the ball above the ground (h(t)) in feet after t seconds since it was thrown. To find the maximum height of the ball, we need to determine the vertex of the quadratic function. The vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by the formula x = -b/2a, where x represents the time and a and b are coefficients in the quadratic equation.

In this case, the coefficient a = -16 and b = 96. Plugging these values into the formula, we get t = -96/(2 * -16) = 3 seconds. Substituting this value into the quadratic function, we find h(t) = -16(3^2) + 96(3) + 112 = 160 feet. Therefore, the maximum height of the ball is 160 feet.

To determine how many seconds it takes until the ball hits the ground, we need to find the time when h(t) = 0. Setting the quadratic equation equal to zero and solving for t, we get -16t^2 + 96t + 112 = 0. This equation can be solved using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula.

Applying the quadratic formula, we have t = (-b ± √(b^2 - 4ac)) / 2a. Plugging in the values of a = -16, b = 96, and c = 112, we get t = (-96 ± √(96^2 - 4(-16)(112))) / (2 * -16). Evaluating this expression, we get two solutions: t = 4 and t = 7. Therefore, the ball takes 4 seconds to reach the ground after being thrown.

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Answer:

$360

Step-by-step explanation:

So for 2 cases that have 12 packs its $48 which means each case cost $24, so keep that for later now look closely, they need 180 PACKAGES not cases so if there are 12 packages in one case divide 180/12 and you will get 15, so that means you need 15 cases, so take the $24 per case and multiply that by the 15 cases you need and boom...it will cost the company $360 for next months order :)

41.848/3.4=12.308

The actual building is 12.306 times larger than the model.

Answer: 70

=====================================

Explanation:

The exterior angles (2x+12) and (2x) have corresponding interior angles 180-(2x+12) and 180-(2x)

Triangle ABC has the following interior angles

A = 112

B = 180 - 2x

C = 180 - (2x+12) = 180-2x-12 = 168-2x

Add up the interior angles for A,B,C and set the result equal to 180. Solve for x

A+B+C = 180

(112)+(180-2x)+(168-2x) = 180

112+180-2x+168-2x = 180

460-4x = 180

-4x = 180-460

-4x = -280

x = -280/(-4)

x = 70

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

Side note:

2x = 2*70 = 140 is the exterior angle for B, so 180-140 = 40 is the interior angle for angle B

2x+12 = 2*70+12 = 152 is the exterior angle for C, so 180 - 152 = 28 is the interior angle for C

Add up the interior angles to find that A+B+C = 112+40+28 = 180, so this helps confirm we have the right x value.

Answer:

1/5

Step-by-step explanation:

We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices  A(−3, 4), B(−1, 12) and C(4, −2) to the image triangle A'B'C' with vertices A' (−0.6, 0.8), B' (−0.2, 2.4) and C' (0.8, −0.4).

Center of dilation is at the origin.

To find the scale factor, we will divide the corresponding vertices of the image and pre-image.

A (−3, 4) ---> A' (−0.6, 0.8) = [tex]\frac{-0.6}{-3} , \frac{0.8}{4}=(\frac{1}{5} , \frac{1}{5})[/tex]

B(−1, 12) ---> B' (−0.2, 2.4) = [tex]\frac{-0.2}{-1} , \frac{2.4}{12} = (\frac{1}{5} , \frac{1}{5})[/tex]

C(4, −2) --->  C' (0.8, −0.4) = [tex]\frac{0.8}{4} , \frac{-0.4}{-2} = (\frac{1}{5} , \frac{1}{5})[/tex]

Therefore, the scale factor of the dilation is 1/5.

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let "Hannah" = h, and her sister = s

h = 2s

h +  s ≤ 18

Plug in 2s for h in the second equation.

(2s) + s ≤ 18

Simplify

2s + s ≤ 18

3s ≤ 18

Isolate the variable (s). Divide 3 from both sides

(3s)/3 ≤ (18)/3

s ≤ 18/3

s ≤ 6

2) The oldest Hannah's sister can be is 6 years

~

Answer:

12 years old

Step-by-step explanation:

1) 2x+x=18

2) Now solve 2x+x=18

Add alike terms

3x=18

Now divide both sides by 3 (3x/3 and 18/3)

x=6

So Hannah is 6 years old. Her sister must be 12.