Simplify to create an equivalent expression, Explain why?
5(2p+1)+3(3p-1)

Answer:

C is correct

Step-by-step explanation:

If you plug in the ordered pairs from C, they always work.

Final answer:

The two lines have different slopes, with the first line having a slope of -2 and the second line having a slope of 2. Since the slopes are different, the two lines intersect at exactly one point, indicating that there is one solution.

Explanation:

To determine if two lines have no solution, one solution, or an infinite number of solutions, we need to find the slopes of each line. If the slopes are different, the lines intersect at one point, indicating one solution. If the slopes are the same, but they have different y-intercepts, the lines are parallel and there is no solution. If the slopes and y-intercepts are the same, the lines coincide and there are an infinite number of solutions.

For the first line through (-1,3) and (0,1), the slope can be calculated using the formula slope (m) = (y2 - y1) / (x2 - x1). Plugging in the values, we get:

m = (1 - 3) / (0 + 1) = -2

The second line passes through (1,4) and (0,2). Using the same formula:

m = (2 - 4) / (0 - 1) = 2

Since the slopes of the two lines are different, they will intersect at exactly one point, indicating one solution.

The system of equations has one solution since the lines intersect at a single point, confirming a unique solution.

To determine if the system of equations has no solution, one solution, or an infinite number of solutions, we need to analyze the slopes and y-intercepts of the two lines.

Step 1:

Calculate the slope of each line using the formula [tex]\(m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\).[/tex]

For the first line passing through (-1,3) and (0,1):

[tex]\[ m_1 = \frac{{1 - 3}}{{0 - (-1)}} = \frac{{-2}}{{1}} = -2 \][/tex]

For the second line passing through (1,4) and (0,2):

[tex]\[ m_2 = \frac{{2 - 4}}{{0 - 1}} = \frac{{-2}}{{-1}} = 2 \][/tex]

Step 2:

Calculate the y-intercept for each line using the slope-intercept form [tex]\(y = mx + b\)[/tex], where (b) is the y-intercept.

For the first line:

[tex]\[ 1 = -2 \cdot 0 + b_1 \][/tex]

[tex]\[ b_1 = 1 \][/tex]

For the second line:

[tex]\[ 2 = 2 \cdot 0 + b_2 \][/tex]

[tex]\[ b_2 = 2 \][/tex]

Step 3: Compare the slopes and y-intercepts.

Since the slopes are different (-2 for the first line and 2 for the second line), the lines are not parallel. Therefore, they will intersect at exactly one point, resulting in one solution for the system of equations.

Conclusion:

The system of equations has one solution.

Answer:

36.66 bushels per acre

Step-by-step explanation:

First divide 22,000 by 10 to get pounds per acre

2200 lbs/acre

But the question asks how many pounds per bushel. So now we will divide 2200 by 60

36.66 bushels per acre

Answer:

36.67bu per acre

Step-by-step explanation:

Find Pound per acre

22,000/10 = 2200 lb per acre

Find bushels per acre

60lb = 1 bu

2200/60 = 36.67bu per acre

Final answer:

The solution set of the polynomial equation can be found by testing the given sets of roots and verifying which set satisfies the polynomial equation.

Explanation:

To find the solution set of the polynomial equation x4 - 6x3 + 10x2 + 2x - 15 = 0, we need to factor the polynomial or use numerical methods to find roots. Polynomial equations of higher degrees such as quartics can often be simplified into quadratic equations or factored based on known roots or rational root theorem. Once a root is found, it can be used for polynomial division to reduce the degree of the polynomial and find other roots. One simple numerical method to guess and check roots would be to use synthetic division with possible rational roots.

However, since the question provides the sets of the roots, we only need to verify which set of roots satisfy the equation. We can use these sets as potential solutions and substitute the roots back into the equation to see if it satisfies the equation. Since complex roots always come in conjugate pairs for polynomials with real coefficients the only possible sets of roots that can be correct are {2 + i, 2 - i, -3, -1} or {2 + i, 2 - i, 3, -1}. Now we can substitute these roots into the original polynomial to determine which set is the actual solution

Answer:

[tex]CE=5.5\ units[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

we know that

According to the Perpendicular Tangent Theorem, tangent lines are always perpendicular to a circle's radius at the point of intersection

That means ----> Triangles ODC and OEC are right triangles

In the right triangle OEC

we have

[tex]OE=OD=4.8\ units[/tex] ----> radius of the circle

[tex]OC=7.3\ units[/tex]

Applying the Pythagorean Theorem

[tex]OC^2=OE^2+CE^2[/tex]

substitute the given values

[tex]7.3^2=4.8^2+CE^2[/tex]

[tex]CE^2=7.3^2-4.8^2\\CE^2=30.25\\CE=5.5\ units[/tex]

Final answer:

The length of the segment CE, which is a tangent to a circle, can be found using the properties of tangents and the Pythagorean theorem. Given OD = 4.8 and OC = 7.3, the length of CE is calculated to be approximately 5.5 units.

Explanation:

The question involves finding the length of segment CE in a configuration where segments CD and CE are tangents to a circle centered at O. Given that OD = 4.8 and OC = 7.3, to find CE, one can use the properties of tangents to a circle. Tangents drawn from the same external point to a circle are congruent. Therefore, the lengths of CD and CE are equal. Since OD and OC form a right triangle with CD (considering triangle OCD), applying the Pythagorean theorem gives us the length of CE directly.

To calculate, let CD = CE = x, hence:

After calculation:

Therefore, the length of CE is approximately 5.5 units.

Answer:

(- 4, 27 )

Step-by-step explanation:

Equate the right sides of both equations, that is

x² - 2x + 3 = - 2x + 19 ← subtract - 2x + 19 from both sides

x² - 16 = 0 ← in standard form

(x - 4)(x + 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 4 = 0 ⇒ x = - 4

Substitute these values into f(x) = - 2x + 19

f(4) = - 2(4) + 19 = - 8 + 19 = 11 ⇒ (4, 11 )

f(- 4) = - 2(- 4) + 19 = 8 + 19 = 27 ⇒ (- 4, 27 )

Answer:

Solutions are x =4 and y = 1

Step-by-step explanation:

[tex]3x-3y =9[/tex]

In this equation substitute [tex]x=7-3y[/tex], we get

[tex]3(7-3y) -3y=9\\21-9y-3y=9\\-12y= 9-21\\-12y= -12\\y=1[/tex]

now substitute y =1 in x equation,

[tex]x=7-3(1)\\x=7-3\\x=4[/tex]

Solutions are x =4 and y = 1

answer will be 6400tftfftfttfft

[tex]\text{Hey there!}[/tex]

[tex]\text{Expanded formed would be the number expanded into an addition equation}[/tex]

[tex]\text{Here is a(n) example: 699 would be expanded as 600 + 90 + 09 = 699}[/tex]

[tex]\text{Now we know what expanded is and what it should look like similar, to}\\\text{we can answer your question}[/tex]

[tex]\boxed{\bf{\underline{60 + 04}}}\leftarrow\bf which\ would\ be\ converted\ to\ 64}[/tex]

[tex]\boxed{\boxed{\mathsf{Answer: 60 +04}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

Hey "Dixie" heres why: That's why you're being told to flip the second fraction. You're recognizing that dividing by a number is the same as multiplying by the reciprocal. ... Now to multiply fractions, we simply multiply the numerators to get the new numerator and multiply the denominators to get the new denominator.

Hope it helped!

Dividing by a fraction and multiplying by its reciprocal, b/a, yield the same result as division and multiplication interact in such a way. The reciprocal (or flip) of a fraction makes it easier to perform mathematical operations like multiplication and division.

In mathematics, dividing by a fraction a/b is indeed equivalent to multiplying by its reciprocal, which is b/a. This is because of the way division and multiplication operations work.

Here's an example: If you have 4 ÷ (1/2), this can also be seen as 4 multiplied by the reciprocal of 1/2, which is 2/1, or 2. In both cases, the answer would be 8. This shows that dividing by a fraction is the same as multiplying by its reciprocal.

Therefore, when you have any number divided by a fraction, you can simplify the operation by turning it into multiplication by performing the flip (reciprocal) on the fraction you're dividing by.

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Answer:

C.

Dn = $1,750 - $75·(n - 1) ; D7 = $1,300

Step-by-step explanation:

"n" represents each year of membership. The first year that you are a member (n = 1), the fee is $1,750.

In year 2, (n = 2), the fee is $1,750 - $75, which is 75·1. If n=1, and 75 is multiplied by 1, then the formula will use (n - 1).

At this point, the answer will be either B. or C.

Substitute n = 7 into the formula to find the cost in the 7th year.

Dn = $1,750 - $75·(n - 1)

D7 = $1,750 - $75·(7 - 1)      Solve inside the brackets first.

D7 = $1,750 - $75·6     Multiply first, then subtract the product from 1750.

D7 = $1,300          Answer

Therefore the answer is C.

Answer:

  rhombus

Step-by-step explanation:

A quadrilateral with equal-length sides is a rhombus.

_____

A square is a special case of a rhombus.

Area of the heart is 178.5 cm² and Perimeter is 51.4 cm

Step-by-step explanation:

Total area of heart = Area of the square + 2 × area of the semi circle

Calculate the area of the square where side = 10 cm

⇒ Area of the square = side² = 10² = 100 cm²

Calculate the area of the 2 semicircles where radius = 10/2 = 5 cm

⇒ Area of the semicircle = 1/2 × π × r²

⇒ Area of the 2 semicircles = 2 × 1/2 × π × r² = 3.14 × 5² = 78.5 cm²

⇒ Total area of the heart = 100 + 78.5 = 178.5 cm²

Calculate the perimeter of the heart = length of 2 sides of the square + 2 × perimeter of the semicircle (since there are 2 semicircles)

⇒ Perimeter = 10 + 10 + 2 × π × r (since perimeter of semicircle = πr)

⇒ Perimeter = 20 + 2 × 3.14 × 5 = 20 + 31.4 = 51.4 cm

The area and Perimeter values of the figure are 178.5 cm² and 51.4 cm

The area of the square portion

We have;

Area of the Semicircle:

Area of Semicircle = 0.5×πr²

Area of Semicircle = 39.25

Since, we have 2 similar Semicircles :

Total Area = 100 + 78.5 = 178.5 cm²

2.)

The Perimeter of the figure ;

For the 2 Semicircles ;

Perimeter = 31.4 cm

Perimeter of the square ;

Total Perimeter = 20 + 31.4 = 51.4 cm

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500 : 1 expresses the ratio of sheets of paper to reams in simplest form ⇒ D

Step-by-step explanation:

The given is:

We need to find the ratio between the sheets of paper to the reams in simplest form

∵ The number of the sheets is 4000

∵ The number of the reams is 8

→ sheet  :  ream

→ 4000  :  8

to simplify the ratio divide the two terms by the same number

∵ 4000 ÷ 2 = 2000 and 8 ÷ 2 = 4

∵ 2000 ÷ 2 = 1000 and 4 ÷ 2 = 2

∵ 1000 ÷ 2 = 500 and 2 ÷ 2 = 1

∴ 4000 and 8 can be divided by 8 to get the simplest form

   of the ratio

→ sheet        :  ream

→ 4000 ÷ 8  :  8 ÷ 8

→ 500           :  1

∴ The ratio of sheets to reams is 500 : 1

500 : 1 expresses the ratio of sheets of paper to reams in simplest form

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Answer:

(I did both because I'm not sure which problem you are referring to.)

Left: 3.5 miles per hour

Right: *equation- 12.5+2.5x=27.5*

6 pairs of socks

Step-by-step explanation:

Left:

First, make a ratio of 0.875 miles/15 minutes. (I converted to decimal form) Next, I made another ratio of x miles/60 minutes. This tells me how many miles she ran in an hour.

Then, to get from 15 minutes to 60 minutes(1 hour), I divided 60 by 15, and got 4. Since to get from 15 to 60 is to multiply by 4 in the denominator, you will also have to multiply 0.875 by 4 in the numerator. By doing that, you will find that x is equal to 3.5 miles.

Right:

First, I made an equation 12.5+2.5x=27.5.

12.5 represents the cost of one shirt.

2.5 represents the cost of a pair of socks

x represents the unknown amount of socks.

27.5 represents the total amount of money she spent.

Next, my goal is to figure out what x is, so I substracted 12.5 from both sides in order to get x to be alone. *Result: 2.50x=15

Then, I divided 2.50 from both sides, and got x=6

I hope this helped!

Answer:

So the answer is NO, the probability of an event cannot be -0.25.

Step-by-step explanation:

i) The probability or likelihood of an event cannot be negative or less than zero.

ii) The probability of an event cannot be greater than 1.

iii) If the probability of an event is 0 then the event did not or does not happen

iv) If the probability of an event is one then the event did or does happen with 100% certainty.

v) If the probability is between 0 and 1 then the event occurs wit a certainty that is less than 100%.

vi) So the answer is NO, the probability of an event cannot be -0.25.

Final answer:

The number -0.25 cannot represent the probability of an event because probability values must be between 0 and 1, and negative values are not within this range.

Explanation:

The number -0.25 cannot be the probability of an event. In probability theory, the value assigned to the likelihood of an event occurring must be within a certain range, specifically between 0 and 1, inclusive.

A probability of 0 denotes an impossible event, whereas a probability of 1 represents an event that is certain to occur. Since -0.25 is a negative number, it falls outside of this acceptable range, therefore it cannot represent the probability of an event occurring in any valid probability distribution.

The total amount of yarn Mary has is [tex]\frac{8}{9}[/tex].

Step-by-step explanation:

Mary has;

Red yarn = [tex]\frac{1}{3}[/tex]

White yarn = [tex]\frac{2}{9}[/tex]

Blue yarn = [tex]\frac{2}{6}[/tex]

Total yarn = Red + White + Blue

Total yarn = [tex]\frac{1}{3}+\frac{2}{9}+\frac{2}{6}\\[/tex]

Taking LCM = 18

Total yarn = [tex]\frac{6+4+6}{18}[/tex]

Total yarn = [tex]\frac{16}{18}=\frac{8}{9}[/tex]

The total amount of yarn Mary has is [tex]\frac{8}{9}[/tex].

Keywords: fraction, addition

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The total amount of yarn that Mary has is the sum of the fractions representing each color of yarn. After converting all fractions to like terms with denominator 9, we find that Mary has 8/9 in total.

To calculate the total amount of yarn Mary has, you should add all the given fractions together. We have:

1/3 red yarn,

2/9 white yarn, and

2/6 (which can be simplified to 1/3) blue yarn.

To add these fractions, they need to have a common denominator. The lowest common denominator of 3 and 9 is 9. So, we get:

3/9 red yarn + 2/9 white yarn + 3/9 blue yarn = 8/9.

Therefore, the total amount of yarn Mary has is 8/9.

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Keisha drinks 1.25 quarts of water per day

Solution:

Given that,

Keisha drinks 15 quarts of water in 12 days

To find: Average amount of water that she drinks per day

Average amount of water that she drinks per day is found by dividing 15 quarts by 12 days

The formula used is:

[tex]Amount\ of\ water\ drank\ per\ day = \frac{\text{15 quarts of water}}{12\ days}[/tex]

Therefore,

[tex]Amount\ of\ water\ drank\ per\ day = \frac{15}{12}\\\\Amount\ of\ water\ drank\ per\ day = 1.25[/tex]

Thus she drinks 1.25 quarts of water per day

Answer:

its B

Step-by-step explanation:

i took the test the answer is B

please give me brainly

(6x² - 4x - 5)(2x² + 3x)

= 12x⁴ + 18x³ - 8x³ - 12x² - 10x² - 15x

= 12x⁴ + 10x³ - 22x² - 15x

so the answer is B

The values are [tex]m\angle \mathrm{ABC}=62^{\circ}[/tex], [tex]m\angle \mathrm{DBE}=62^{\circ}[/tex], [tex]m\angle \mathrm{CBE}=118^{\circ}[/tex] and [tex]m\angle \mathrm{ABD}=118^{\circ}[/tex]

Explanation:

It is given that [tex]\angle \mathrm{ABC}=4x+2[/tex] and [tex]\angle \mathrm{DBE}=5x-13[/tex]

The image having these measurements is attached below:

The angles ABC and DBE are vertically opposite.

Since, vertically opposite angles are equal, [tex]\angle \mathrm{ABC}=\angle \mathrm{DBE}[/tex]

Equating the values, we have,

[tex]\begin{aligned}4 x+2 &=5 x-13 \\2+13 &=5 x-4 x \\15 &=x\end{aligned}[/tex]

Thus, the value of x is 15. Let us substitute x in the equation to find [tex]\angle \mathrm{ABC}[/tex] and [tex]\angle \mathrm{DBE}[/tex]

Thus,

[tex]\begin{aligned}\angle A B C &=4(15)+2 \\&=60+2 \\&=62\end{aligned}[/tex]

Thus, [tex]m\angle \mathrm{ABC}=62^{\circ}[/tex]

Also, substituting x = 15 in [tex]\angle \mathrm{DBE}[/tex]

We have,

[tex]\begin{aligned}\angle DBE &=5(15)-13 \\&=75-13 \\&=62\end{aligned}[/tex]

Thus, [tex]m\angle \mathrm{DBE}=62^{\circ}[/tex]

Hence, the measure of [tex]\angle \mathrm{ABC}=62^{\circ}[/tex] and [tex]\angle \mathrm{DBE}=62^{\circ}[/tex]

To find the measure of [tex]\angle \mathrm{CBE}[/tex] and [tex]\angle \mathrm{ABD}[/tex]:

Since, the angles in a straight line add up to 180°

To find [tex]\angle \mathrm{CBE}[/tex], let us add the angles and equals to 180°

[tex]\angle \mathrm{CBE}+\angle \mathrm{DBE}=180[/tex]

Substituting the value of DBE, we have,

[tex]\angle \mathrm{CBE}+62=180[/tex]

Subtracting both sides by 62,

[tex]\angle \mathrm{CBE}=118[/tex]

Thus, the measure of [tex]\angle \mathrm{CBE}[/tex] is 118°

Since,  [tex]\angle \mathrm{CBE}[/tex] and [tex]\angle \mathrm{ABD}[/tex] are vertically opposite, they are equal.

Thus, [tex]\angle \mathrm{ABD}=118[/tex]

Thus, the measure of [tex]\angle \mathrm{ABD}[/tex] is 118°

Hence, the values of the angles are  [tex]m\angle \mathrm{ABC}=62^{\circ}[/tex], [tex]m\angle \mathrm{DBE}=62^{\circ}[/tex], [tex]m\angle \mathrm{CBE}=118^{\circ}[/tex] and [tex]m\angle \mathrm{ABD}=118^{\circ}[/tex]

Answer:

x is either 2 or 3

Step-by-step explanation:

[tex] {x}^{2} - 5x + 6 = 0 [/tex]

(x-3)×(x-2) = 0

x- 3 = 0 ➡x = 3

x -2 = 0➡ x = 2

It will take them 3 hours to meet

Step-by-step explanation:

The given is:

We need to find how long it will take them to meet

Distance = Speed × Time

∵ They will drive toward each other at the same time and meet

   each other somewhere

- That means they will drive for the same time

∵ Jack's average rates 60 mph for t hours

∴ Jack will drive a distance = 60 × t = 60 t  miles

∵ Jill's average rate is 55 mph for t hours

∴ Jill will drive a distance = 55 × t = 55 t  miles

∵ The distance between Jack and Jill is 345 miles apart

- Add their distance above and equate the sum by 345

∴ 60 t + 55 t = 345

∴ 115 t = 345

- Divide both sides by 115

∴ t = 3 hours

It will take them 3 hours to meet

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Answer:

0.2% of 50  = [tex]0.1[/tex]

Step-by-step explanation:

0.2% of 50

We have to find 0.2% of 50

     [tex]50*0.2*\frac{1}{100}[/tex]

       [tex]50*\frac{2}{10}* \frac{1}{100}[/tex]

          =[tex]\frac{5*2}{100}[/tex]

           =[tex]\frac{10}{100}\\\\ \frac{1}{10}\\\\0.1[/tex]

The 0.2% of 50 is 0.1

Answer:

0.1

Step-by-step explanation:

Step-by-step explanation:

In given figure,

AD = x, DB = 12, BE = 8 and EC = 10

To find, the value of x = ?

Use the Side-Splitting Theorem,

We know that,

[tex]\dfrac{AD}{DB} =\dfrac{BE}{EC}[/tex]

⇒ [tex]\dfrac{x}{12} =\dfrac{8}{10}[/tex]

⇒ x =[tex]\dfrac{8 \times 12}{10}[/tex]

⇒ x = [tex]\dfrac{96}{10}[/tex]

⇒ x = 9.6

∴ The value of x = 9.6

Thus, the required "option D. 9.6" is correct.

Answer:

IT GOES 8 TIMES

Answer: 8 times

Step-by-step explanation:

Answer:

7.5 quarts

Step-by-step explanation:

2 baskets ------> make 3 quarts

1 basket ---------> makes 3/2 quarts

5 baskets -------> makes 3/2   x 5 = 15/2 = 7.5 quarts

The problem involves calculating ratios or proportional relationships. We find from a known ratio that 2 baskets yield 3 quarts of tomato sauce, and using cross-multiplication, we determine that 5 baskets would produce 7.5 quarts of tomato sauce.

This is a ratio problem. Here, we see that 2 baskets of tomatoes yield 3 quarts of tomato sauce. Hence, the ratio of baskets to quarts is 2:3. Likewise, if we increase the number of baskets to 5, the amount of tomato sauce will also increase according to the ratio. To determine how much sauce that would be, use the principle of equivalent ratios, also known as cross-multiplication.

So, (2 baskets / 3 quarts) = (5 baskets / x quarts), where x is the quantity of sauce from 5 baskets. By cross-multiplying and simplifying, you get x = (5 baskets * 3 quarts) / 2 baskets, which simplifies to x = 7.5 quarts.

So, you can make 7.5 quarts of tomato sauce from 5 baskets of tomatoes.

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Step-by-step explanation:

I think that you are interested in finding the ratio between given quantities. If yes then let us find.

[tex]50 \: pound : 35 \: pound \\ = \frac{50}{35} \\ = \frac{5 \times 10}{5 \times 7} \\ = \frac{10}{7} \\ = 10 : 7[/tex]

Answer:7

Step-by-step explanation:

Gotta get rid of the shirts so 24x3 shirts is 72 and 79-72=7 which is the socks price

Answer:$7

Step-by-step explanation:3 Shirts at $24 each 24×3=$72 then subtract $72- from total cost for shirts and socks $72-$79=$7✔

Answer:

2/3

Step-by-step explanation:

photomath bud

i believe the answer is 2/3

Answer:

length = 12

width = 4

Step-by-step explanation:

Width = w

Length = l

w = l-8

l-8 + l-8 + l + l = 32

4l - 16 = 32

4l = 48

length = 12

width = 4