4x5 – 16x2 + 13x8 in standard form

Answer:

Step-by-step explanation: so u are going to put it like this x- -6 =5

Next u subtract -6 from both sides

x=11

Answer:

x=10

Step-by-step explanation:

Final answer:

The area of the trapezoid can be found by decomposing it into a rectangle and two triangles. Using the given dimensions, x = 4 units, y = 5 units, and h = 7 units, the calculated area of the trapezoid is 35 square units.

Explanation:

To find the area of the trapezoid using decomposition, we can break it down into simpler shapes whose area we can calculate more easily. Here, we will break the trapezoid into a rectangle and two triangles.

Let's identify the dimensions of the trapezoid: the top base (x), the bottom base (y), and the height (h). The student has provided that x = 4 units, y = 5 units, and h = 7 units.

The area of the rectangle that forms part of the trapezoid is the product of its base (x) and height (h):

Area of Rectangle = x * h = 4 units * 7 units = 28 square units

Next, we have two right triangles with one of the legs being the difference in the length of the bases (y - x) and the other leg equal to the height (h). The area of one triangle will be:

Area of Triangle = 0.5 * (y - x) * h = 0.5 * (5 units - 4 units) * 7 units = 3.5 square units

Since there are two identical triangles, we double this value:

Total Area of Triangles = 2 * 3.5 square units = 7 square units

Now we can sum the area of the rectangle and the total area of the triangles:

Total Area of Trapezoid = Area of Rectangle + Total Area of Triangles = 28 square units + 7 square units = 35 square units

Therefore, the area of the trapezoid is 35 square units.

Final answer:

The area of the trapezoid can be calculated by decomposing it into simpler shapes and using the formula A = ½(h)(b1 + b2), resulting in 31.5 units² for the given measurements.

Explanation:

To find the area of the trapezoid using decomposition, given that x = 4 units, y = 5 units, and h = 7 units, we need to decompose the trapezoid into simpler shapes like rectangles and triangles.

The area of a trapezoid can be found using the formula A = ½(h)(b1 + b2), where h is the height and b1 and b2 are the lengths of the two parallel bases. As there is no visual provided, and we are given three measurements, we must assume these represent the height and the bases of the trapezoid. The area is then calculated as follows:

Area of Trapezoid = ½(7)(4 + 5) = ½(7)(9) = ½(63) = 31.5 units².

Answer: 19/20

Step-by-step explanation:

7/10 turns into 14/20

1/4 turns into 5/20

14/20 + 5/20

14 + 5 over 20

= 19/20

19/20 is in simplest form.

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

[tex]\mathsf{What\ is\ \dfrac{7}{10}+\dfrac{1}{4}\ in\ simplest\ form?}[/tex]

[tex]\text{First, look for the lowest common denominator (LCD) of the fractions.}\\\text{If you did the calculations correctly, you should've came up with 20 as}\\\text{your LCD}[/tex]

[tex]\mathsf{Here\ is\ how so: \dfrac{7\times2}{10\times2}+\dfrac{1\times5}{4\times5} = \ ?}[/tex]

[tex]\mathsf{7\times2=14\leftarrow first\ numerator}\\\mathsf{10\times2=20\leftarrow first\ denominator}[/tex]

[tex]\mathsf{1\times5=5\leftarrow second\ numerator}\\\mathsf{4\times5=20\leftarrow second\ denominator}[/tex]

[tex]\mathsf{Your\ new\ equation\ SHOULD\ look\ like\ this: \dfrac{14}{20}+\dfrac{5}{20}}[/tex]

[tex]\text{Since, your DENOMINATORS are ALIKE we can KEEP IT}[/tex]

[tex]\mathsf{Which\ leaves\ us\ with\ the\ last\ step\ of\ the\ problem}[/tex]

[tex]\mathsf{ \dfrac{14+5}{20}}}[/tex]

[tex]\mathsf{14+5=19\leftarrow your\ new\ numerator}\\\\\mathsf{20 = 20\leftarrow your\ new\ denominator}[/tex]

[tex]\boxed{\boxed{\bf{Answer: \mathsf{\dfrac{19}{20}}}}}\checkmark[/tex]

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

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

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:

  rhombus

Step-by-step explanation:

A quadrilateral with equal-length sides is a rhombus.

_____

A square is a special case of a rhombus.

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

Learn more about fractions at:

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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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The compound inequality 5 \u2264 4x - 1 < 7 results in the solution set [1.5, 2) when solved and graphed. In interval notation, it is expressed as [1.5, 2).

To solve the compound inequality 5 \<= 4x - 1 < 7, we split it into two separate inequalities and solve them individually:

The solution set is the interval [1.5, 2). To graph this solution, plot a closed circle at 1.5 and an open circle at 2, and shade the region in between. In interval notation, the solution set is represented as [1.5, 2).

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!

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.

To determine which line the point lies on, you can just plug in one of the numbers into the equations to see if it equals out.

(2, -1)  I will use the 2 and plug it in for x in the equation.

y = 2x + 1

y = 2(2) + 1

y = 5            The point does not lie on this line because when x = 2, y = 5  (2, 5)

y = x + 5

y = 2 + 5

y = 7          The point does not lie on this line because when x = 2, y = 7  (2, 7)

y = 2x - 5

y = 2(2) - 5

y = 4 - 5

y = -1           The point does lie on this line because when x = 2, y = -1  (2, -1)

y = x - 2

y = 2 - 2

y = 0      The point does not lie on this line because when x = 2, y = 0  (2, 0)

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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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:

IT GOES 8 TIMES

Answer: 8 times

Step-by-step explanation:

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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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:

5 flowers

Step-by-step explanation:

To get the answer you do 7-2

so she has 5 flowers left.

7-2=5

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:

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.

Answer:

C is correct

Step-by-step explanation:

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

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

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:

(- 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

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: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:

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

Answer:

The final balance is $10,792.14.

The total compound interest is $2,792.14.

Step-by-step explanation:

Final answer:

Explanation on calculating the amount of $8000 principal at 5% compounded annually after 6 years using compound interest formula.

Explanation:

The question: $8000 principal earning 5% compounded annually after 6 years.

Step-by-step explanation:

Use the compound interest formula: A = P(1 + r/n)^(nt) where A is the amount, P is the principal, r is the rate, n is the number of times interest is compounded per year, and t is the time in years.

Plug in the values: P = $8000, r = 0.05, n = 1 (compounded annually), t = 6.

Calculate: A = $8000(1 + 0.05/1)^(1*6)

A = $10,720.77.

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]

Juan paid 70.16 % of the original price of the jacket.

Step-by-step explanation:

Step 1:

Given details, Original Selling Price of the jacket = 85.50

New Selling Price of the jacket = 59.99

Step 2:

To determine what percentage of the old price is the new price, we have to use percentage calculation.

[tex]x/100\times 85.50 = 59.99[/tex]

Step 3:

Substitute in the formula, the given values

x = [tex](59.99/85.50) \times 100[/tex]

  = [tex](0.7016) \times 100[/tex]

  = [tex]70.16[/tex]

Therefore, percentage paid is 70.16%