What is the perimeter for this shape?

Final answer:

To factor the trinomials x^2 - 2x - 1 and x^2 - 3x + 1, you can use the quadratic formula or factoring by grouping.

Explanation:

To factor the trinomials x^2 - 2x - 1 and x^2 - 3x + 1, we can use the quadratic formula or factoring by grouping.

a) For x^2 - 2x - 1, we can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac))/(2a)

Plugging in the values, we have:

x = (-(-2) ± sqrt((-2)^2 - 4(1)(-1)))/(2(1))

x = (2 ± sqrt(4 + 4))/(2)

x = (2 ± sqrt(8))/(2)

x = (2 ± 2sqrt(2))/(2)

x = 1 ± sqrt(2)

Therefore, the factored form is: x^2 - 2x - 1 = (x - (1 + sqrt(2)))(x - (1 - sqrt(2)))

b) For x^2 - 3x + 1, we can also use the quadratic formula:

x = (3 ± sqrt(3^2 - 4(1)(1)))/(2(1))

x = (3 ± sqrt(5))/(2)

Therefore, the factored form is: x^2 - 3x + 1 = (x - (3 + sqrt(5))/(2))(x - (3 - sqrt(5))/(2))

a) x^2 - 2x - 1 = (x - 1)(x + 1)

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

a) x^2 - 2x - 1:

This trinomial is in the form ax^2 + bx + c. To factor it, we need to find two numbers that:

Multiply to ac (in this case, 1 * -1 = -1).

Add up to b (in this case, -2).

These two numbers are -1 and 1.

So, we can rewrite the trinomial as:

(x - 1)(x + 1)

Therefore, the factored form of x^2 - 2x - 1 is (x - 1)(x + 1).

b) x^2 - 3x + 1:

This trinomial is also in the form ax^2 + bx + c. To factor it, we need to find two numbers that:

Multiply to ac (in this case, 1 * 1 = 1).

Add up to b (in this case, -3).

These two numbers are -1 and -1.

So, we can rewrite the trinomial as:

(x - 1)(x - 1)

However, it is common practice to simplify repeated factors, so the fully factored form of x^2 - 3x + 1 is (x - 1)^2.

Answer:

See image attached.

Step-by-step explanation:

Final answer:

The initial setup for the equation based on the coin values and the total amount led to an incorrect result with a negative number of nickels. This suggests there was an error in the calculations or assumptions, and the equation should be revisited and the numbers checked to find the correct number of each type of coin.

Explanation:

Let's call the number of nickels Sarah has n. According to the problem, Sarah has 10 more dimes than nickels, which means she has n+10 dimes. It is also given that she has twice as many quarters as dimes, making it 2(n+10) quarters. In terms of their values, nickels are worth 5 cents, dimes are worth 10 cents, and quarters are worth 25 cents. The total value of Sarah’s coins is $9.25, which is equivalent to 925 cents.

To find the number of each coin, we can set up the following equation:

5n + 10(n+10) + 25(2(n+10)) = 925

Simplifying the equation:

5n + 10n + 100 + 50n + 1000 = 925

65n + 1100 = 925

65n = 925 – 1100

65n = -175

n = -175 / 65

n = -2.6923

This result is not possible since we cannot have a negative number of coins. It seems there was an error in the calculations or assumptions. It is important to check the equation and numbers we're using to ensure they properly represent the coin values and the total amount.

Answer:

[tex]x_{24} = a_{2} +b_{4} \\y_{13} = a_{1} - b_{3}[/tex]

:)

Answer:

it -3 and 7

Step-by-step explanation:

Answer:

2 1/3 + 1 3/4

Step-by-step explanation:

First, find a common denominator which is 12.

2 4/12 + 1 9/12

= 4 1/12 or 37/12

Answer:

No it equals to 49

Step-by-step explanation:

490÷10=49

Answer:

The answer is option b. -4

Step-by-step explanation:

Given: [tex]\frac{x-4}{4+x}[/tex]

the rational expression will be undefined at the zeros of the denominator

To find the zeros of the denominator

the denominator = 0

∴ 4 + x = 0

∴ x = -4

So, the rational expression will be undefined at x = -4

The answer is option b. -4

Answer:

b)

Step-by-step explanation:

[tex]\frac{x-4}{4+x}\ and\ 4+x\neq 0\ (we\ can't\ divide\ by\ 0)[/tex]

[tex]4+x\neq 0\\x\neq -4[/tex]

Answer:

600

Step-by-step explanation:

you round up 19 to 20 then you round up 28 to 30 and multiply 20 and 30

Answer:

20*30

= 600

About 600

C

Answer:

x=y+4

Step-by-step explanation:

Amount spent by Lia=x

Amount spent by Kiera=y

x=y+4

Answer:  [tex]k+4[/tex]

Step-by-step explanation:

You need to analize the data given in order to solve the exercise.

First, it is important to remember that, in Word problems the word "more" indicates Addition.

In this case, let "k" represents the amount of money (in dollars) that Kiera spends on her backyard.

Accordding to the information provided in the exercise, you know that Lia spends $4 dollars more on her backyard than Kiera spends on her backyard.

Therefore, you can identify that the amount of money that Lia spends can be found by adding the amount of money Kiera spends and $4.

Based on the above, you can determine that this situation can be represented with the following expression:

[tex]k+4[/tex]

Final answer:

To solve for D in the equation z = a/b + c/d, subtract a/b from both sides, combine fractions on the left side, cross multiply, and finally solve for d by dividing both sides by (bz - a).

Explanation:

To solve for D in the equation z = a/b + c/d, you need to isolate d on one side of the equation. Here's how you can do it:

When a = 2.658653234, b = 0.179825026, c = -54.56945917, and z = 17.98260265, you would substitute these values and calculate d accordingly, leading to a numerical solution for d.

Answer:

The percent increase is 18.75%.

Step-by-step explanation:

Given:

Amber got a raise, and her hourly wage increased from $8 to $9.50.

Now, to find percent increase.

Previous wage = $8.

Wage raised = $9.50.

So, to get the increased wage we subtract the previous wage from the wage raised:

[tex]\$9.50-\$8=\$1.50.[/tex]

Now, to get the percent increase:

[tex]\frac{1.50}{8} \times 100[/tex]

[tex]=\frac{150}{8}[/tex]

[tex]=18.75\%.[/tex]

Therefore, the percent increase is 18.75%.

The percent increase in Amber's hourly wage from $8 to $9.50 is 18.75%.

To find the percent increase in Amber's hourly wage, you can follow these steps:

⇒ $9.50 - $8 = $1.50.

⇒ $1.50 ÷ $8 = 0.1875.

⇒ 0.1875 × 100 = 18.75%.

Therefore, the percent increase in Amber's hourly wage is 18.75%.

Complete question:

Amber got a raise and her hourly wage increased from $8 to $9.50. What is the percent increase?

I can save $2,128 in my academic year and my roommate can save $392 in their academic year.

Step-by-step explanation:

Total housing amount= rent + electricity= $1,025 + $60= $1,085 per month

My rent is 40% of $1,085 which equals $434 a month while my roommate’s rent would be 60% of $1,085 which equals $651 a month.

The scholarship gives me $700 a month for housing out of which I spend $434 and my roommate spends $651.

I save; $700 - $434 = $266 a month

My roommate saves; $700 - $651 = $49 a month.

An academic year lasts for 8 months so my savings= $266 x 8 = $2,128

My roommate’s savings= $49 x 8 = $392  

Answer:

$2,128

Step-by-step explanation:

Expenses is allocated based on the decided ratios. Expenses and Inflows

Expenses will be calculated for 8 Months time period.

Rent = 1,025 x 8 months = $8,200

Electricity Expense = $60 x 8 = $480

Total Expense = $8,200 + $480 = $8,680

Total Scholarship = $700 x 8 = $5,600

Out of Pocket Cost = $8,680 x 40% = $3,472

Saving is the difference between The scholarship received and the Expenses made from pocket.

Saving = $5,600 - $3,472 = $2,128

Answer:

an equation for how much your phone costs per month=

.15x+10

The best approximation for the measure of angle XYZ is 39.8° ⇒ 2nd answer

Step-by-step explanation:

Let us revise the trigonometry ratios in the right triangle ABC, where B is the right angle, AC is the hypotenuse, AB and BC are the legs of the triangle

The trigonometry ratios of the angle BAC, the opposite side to this angle is BC and the adjacent side to it is AB are

In Δ XYZ

∵ ∠ YXZ is a right angle

∴ The hypotenuse is YZ

∵ The adjacent side to ∠XYZ is XY

∵ The opposite side to ∠XYZ is XZ

∵ YX = 12 units

∵ XZ = 10 units

- Use tan ratio to find the measure of the angle because you

   have the adjacent and opposite sides of the angle XYZ

∵ m∠XYZ is x

∵ [tex]tan(x)=\frac{XZ}{XY}[/tex]

∴ [tex]tan(x)=\frac{10}{12}[/tex]

- To find x use the inverse of tan(x)

∵ [tex]x=tan^{-1}(\frac{10}{12})[/tex]

∴ x = 39.8°

∴ m∠XYZ = 39.81°

The best approximation for the measure of angle XYZ is 39.8°

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Answer:

B 39.8

Step-by-step explanation:

just took the test!

Answer:

59,778

Step-by-step explanation:

The product of 729 and 82 is calculated through standard multiplication, resulting in a final product of 59,778.

The student is asking to calculate the product of two numbers, 729 and 82. To find the product, we can use basic multiplication skills. Here is the step-by-step calculation:

First, set up the multiplication:

Next, multiply 2 by each digit of 729 and write the result below the line.

Then, multiply 8 by each digit of 729, remember to shift one place to the left.

Now, add both results to get the final

product

.

The final product of 729 multiplied by 82 is 59,778.

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Answer:

The answer is 21.

Step-by-step explanation:

6 * 2 = 12 + 9 = 21

Answer:

66

Step-by-step explanation:

The equation would go like this:

6(2+9)

Next you solve for parenthesis:

6(11)

Lastly multiply:

6(11)=66

Answer:

109>21

Answer is A.

Step-by-step explanation:

When we read this example. We can conclude :

Saving account : $109

Checking : $21

So:

Wang Xiu Ying's checking account has a lower account value than her savings account.

Answer:  109>-21

B

Step-by-step explanation:

Answer:

A. 4(2y-9)

Step-by-step explanation:

Both terms are divisable by 4 and would bring them to the smallest whole degree

Answer:

your answer will be D.

Step-by-step explanation:

2x4y= 8y

2x (-18)= -36

Answer:

No

Step-by-step explanation:

120/100 is the same as 1 20/100 or 1 2/10. 1 2/10 is not greater than 100

Answer:

Step-by-step explanation:

nop

Answer:

  a = 2; r = -1

Step-by-step explanation:

a is the first term: 2

r is the ratio of successive terms: -2/2 = 2/-2 = -1.

Answer:

 a = 2; r = -1

Step-by-step explanation:

a is the first term: 2

r is the ratio of successive terms: -2/2 = 2/-2 = -1.

The solution is 900

The product of the 6th square number and 5th square number is given by the equation A = 900

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first number be a

The value of a = 6th square number

a = 6²

The value of a = 36

Let the second number be b

The value of b = 5th square number

a = 5²

The value of b = 25

Now , the equation is

A = first number x second number

Substituting the values in the equation , we get

A = 25 x 36

A = 900

Therefore , the value of A is 900

Hence , the equation is A = 900

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Final answer:

The product of the 6th square number (36) and the 5th square number (25) is 900.

Explanation:

To find the product of the 6th square number and the 5th square number, we first need to identify what those square numbers are.

A square number is a number multiplied by itself.

The 6th square number is 6², which is 36.

The 5th square number is 5², which is 25.

Now, to find the product, we multiply these two square numbers together:

36 × 25 = 900

Therefore, the product of the 6th square number (36) and the 5th square number (25) is 900.

Answer:24 oringal width

49 original length

Step-by-step explanation:

The original dimensions of the rectangular piece of metal were 30 inches by 55 inches, based on the given conditions of making an open box and its volume.

In this problem, we have a rectangular piece of metal that is being converted into an open box. Note that the length of the rectangular piece is 25 in longer than its width.

When squares with side 5 in are cut from the corners and the sides are folded up to make the open box, the dimensions of the box formed become length = w+25-10, width = w-10, and height = 5, where w is the width of the original rectangular piece.

The volume of a box is given by the product of length, width, and height. So if the volume of this box is given as 2730 cubic inches, we can write the equation (w-10)(w+15)(5)=2730.

This can be solved to give w=30 (excluding the negative solution as unrealistic for this context). Therefore, the original dimensions of the metal piece were 30 in (width) by 55 in (length).

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Answer:

Therefore the minimum mileage for which Company A will charge more than Company B is 251 miles.

Step-by-step explanation:

i) let x be the number of miles driven

ii) If Joe rents the truck from Company A the Joe will pay Company A

  = $0.8x

iii) If Joe rents the truck from Company B then Joe will pay Company B

   = $50 + $0.6x

iv) the mileage for which the rents of both companies will be equal is given by

  $0.8x = $50 + 0.6x

Therefore 0.2x = $50

Therefore x = [tex]\frac{50}{0.2} = \frac{500}{2} = 250[/tex] miles.

Therefore the minimum mileage for which Company A will charge more than Company B is 251 miles.

Answer:

The values for the two equations are x=-3 and y=1

Therefore the solution is (-3,1)

Step-by-step explanation:

Given equations are [tex]y=2x+7\hfill (1)[/tex]

[tex]y=-2x+5\hfill (2)[/tex]

To solve the given equations by Substitution method :

We are using here to solve the given equations by Substitution method because equations (1) and (2) are equivalent ( it has same solution )

Therefore we can equate the two given equations  or substitute the y value equation (1) in (2) we get

2x+7=-2x-5

Subtracting with -(2x-5) on both sides we get

2x+7-(-2x-5)=-2x-5-(-2x-5)

2x+7+2x+5=-2x-5+2x+5

4x+12=0 ( adding the like terms )

4x=-12

[tex]x=-\frac{12}{4}[/tex]

Therefore x=-3

Now substitute the value x=-3 in equation (1) we get

y=2(-3)+7

y=-6+7

Therefore y=1

The values are x=-3 and y=1

The solution is (-3,1)

Answer: $161

Step-by-step explanation: Subtract $808 from $969

Answer: he will have $161 in his account after he buys the computer and dvd player.

Step-by-step explanation:

First, do 969-808 and you simply get 161 as your answer

So, for this problem you are simply subtracting

* brainliest answer this plz....

The total cereal mixture is 45 kilograms

Solution:

Given that, cereal mixture contains Almond, Wheat, and Corn in the ratio of 3:5:7

Therefore,

Almond : Wheat : Corn = 3 : 5 : 7

Let the almond present be 3x

Let the wheat present be 5x

Let the corn present be 7x

Therefore,

Total cereal mixture = 3x + 5x + 7x

Total cereal mixture = 15x

Given that mixture contains 9 kg of almond

Almond = 9

We know that,

Almond present = 3x

3x = 9

x = 3

Therefore,

Total cereal mixture = 15x = 15(3) = 45

Thus total cereal mixture is 45 kilograms

Answer:

[tex]A=189\ mm^2[/tex]

Step-by-step explanation:

Surface Areas

Is the sum of all the lateral areas of a given solid. We need to compute the total surface area of the given prism. It has 5 sides, two of them are equal (top and bottom areas) and the rest are rectangles.

Computing the top and bottom areas. They form a right triangle whose legs are 4.5 mm and 6 mm. The area of both triangles is

[tex]\displaystyle A_t=2*\frac{b.h}{2}=b.h=(4.5)(6)=27 mm^2[/tex]

The front area is a rectangle of dimensions 7.7 mm and 9 mm, thus

[tex]A_f=b.h=(7.5)(9)=67.5 \ mm^2[/tex]

The back left area is another rectangle of 4.5 mm by 9 mm

[tex]A_l=b.h=(4.5)(9)=40.5 \ mm^2[/tex]

Finally, the back right area is a rectangle of 6 mm by 9 mm

[tex]A_r=b.h=(6)(9)=54 \ mm^2[/tex]

Thus, the total surface area of the prism is

[tex]A=A_t+A_f+A_l+A_r=27+67.5+40.5+54=189\ mm^2[/tex]

[tex]\boxed{A=189\ mm^2}[/tex]

Answer:

7/10 - 1/2 = 7/10 - 5/10 = 2/10 = 1/5 (one fifth)

Step-by-step explanation:

Answer: No

Step-by-step explanation: In order to decide whether the given fractions are equivalent, first write each fraction in lowest terms.

A fraction is written in lowest terms if the greatest common factor of the numerator and the denominator is 1.

So for our first fraction, 4/9, since the greatest common factor of 4 and 9 is 1, we know that are fraction is already written in lowest terms.

For our second fraction however, since the greatest common factor of 20 and 36 is 4, we must divide both the numerator and the denominator by 4 to write our fraction in lowest terms. This gives us 5/9.

Since 5/9 is bigger than 4/9, te fractions are not equivalent so no, 4/9 is not equivalent to 20/36.

Answer:

10.50x = 63

You'll divide 63 by 10.50 to get 6 weeks.