what is the equation for this line

Answer:

x = -2 , y = -3 , z = 3

Step-by-step explanation:

Solve the following system:

{-x - 5 y - 5 z = 2 | (equation 1)

4 x - 5 y + 4 z = 19 | (equation 2)

x + 5 y - z = -20 | (equation 3)

Swap equation 1 with equation 2:

{4 x - 5 y + 4 z = 19 | (equation 1)

-x - 5 y - 5 z = 2 | (equation 2)

x + 5 y - z = -20 | (equation 3)

Add 1/4 × (equation 1) to equation 2:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - (25 y)/4 - 4 z = 27/4 | (equation 2)

x + 5 y - z = -20 | (equation 3)

Multiply equation 2 by 4:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - 25 y - 16 z = 27 | (equation 2)

x + 5 y - z = -20 | (equation 3)

Subtract 1/4 × (equation 1) from equation 3:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - 25 y - 16 z = 27 | (equation 2)

0 x+(25 y)/4 - 2 z = -99/4 | (equation 3)

Multiply equation 3 by 4:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - 25 y - 16 z = 27 | (equation 2)

0 x+25 y - 8 z = -99 | (equation 3)

Add equation 2 to equation 3:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - 25 y - 16 z = 27 | (equation 2)

0 x+0 y - 24 z = -72 | (equation 3)

Divide equation 3 by -24:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - 25 y - 16 z = 27 | (equation 2)

0 x+0 y+z = 3 | (equation 3)

Add 16 × (equation 3) to equation 2:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - 25 y+0 z = 75 | (equation 2)

0 x+0 y+z = 3 | (equation 3)

Divide equation 2 by -25:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x+y+0 z = -3 | (equation 2)

0 x+0 y+z = 3 | (equation 3)

Add 5 × (equation 2) to equation 1:

{4 x + 0 y+4 z = 4 | (equation 1)

0 x+y+0 z = -3 | (equation 2)

0 x+0 y+z = 3 | (equation 3)

Subtract 4 × (equation 3) from equation 1:

{4 x+0 y+0 z = -8 | (equation 1)

0 x+y+0 z = -3 | (equation 2)

0 x+0 y+z = 3 | (equation 3)

Divide equation 1 by 4:

{x+0 y+0 z = -2 | (equation 1)

0 x+y+0 z = -3 | (equation 2)

0 x+0 y+z = 3 | (equation 3)

Collect results:

Answer: {x = -2 , y = -3 , z = 3

Answer:

Yes it will be greater, he is moving back 3 feet so what you are doing is taking the leg (a2) and multiplying it by 3. Once you do, you see triangle 1 has double and so did triangle 2. Triangle 1 was originally 5.6 (rounded to 6) than went up to 26.1. Triangle 2 was originally 24 and went up to 74.7 (or 75)

Step-by-step explanation:

Triangle 1 (when multiply by 3)

a2+b2=c2

7(square to 2)+b2=27(square to 2)

49+b2=729

-49       -49

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

b2=680

(square root it)

b=26.1 Rounded to nearest tenth

Triangle 2:

a2+b2=c2

7(square to 2)+b2=75(square to 2)

49+b2=5625

-49      -49

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

b2=5576

(square root it)

b=74.7 (or 75 rounded to nearest tenth)

Hope this helps anyone who needs it :)

Yes, the distance from his eyes to the top of the tree will also be greater.

A function is a relation between a dependent and independent variable.

Mathematically, we can write → y = f(x) = ax + b.

Given is that Javier moves backward so that his horizontal distance from the tree is greater.

Before moving backward, the distance from Javier's eyes to the top of the tree can be written as -

cosФ = b/h

h = b/cosФ

Now, we can see that -

h [tex]\alpha[/tex] b

As base increases, the hypotenuse length or the distance from Javier's eyes to the top of the tree will increase.

Therefore, yes, the distance from his eyes to the top of the tree will also be greater.

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Answer: 14

Step-by-step explanation:

100% of 14

= 100/100 × 14/1

14

Answer:14

Step-by-step explanation:

Percent= 100%

From= 14

Value= [tex]\frac{100}{100}[/tex] x 14= 1x 14 =14

Answer:

4p-6

Step-by-step explanation:

distribute within parenthesis:

-4+8p-4p-2

Combine like terms

4p-6

i hope this helps u

please give thx and a brainliest to level up

Answer:

2(-2-4p)+2(-2p-1)

-4-8p -4p-2

-12p-6

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

Siw's age is 10 years old

Mona's age is 8 yers old

Mother's age is 40 years old

Step-by-step explanation:

Let

x ----> Siw's age

y ---> Mona's age

z ---> Mother's age

we know that

Siw is a fourth as old as mother

so

[tex]x=\frac{1}{4}z[/tex] ----> equation A

Mona is a fifth as old as mother

so

[tex]y=\frac{1}{5}z[/tex] ----> equation B

Mother is 22 years older than the two girls together.

so

[tex]z=x+y+22[/tex] ----> equation C

substitute equation A and equation B in equation C

[tex]z=\frac{1}{4}z+\frac{1}{5}z+22[/tex]

solve for z

Multiply by 20 both sides to remove the fraction

[tex]20z=5z+4z+440[/tex]

[tex]20z-9z=440\\11z=440\\z=40\ years[/tex]

Find the value of x

[tex]x=\frac{1}{4}(40)=10\ years[/tex]

Find the value of y

[tex]y=\frac{1}{5}(40)=8\ years[/tex]

therefore

Siw's age is 10 years old

Mona's age is 8 yers old

Mother's age is 40 years old

Answer:

ion know

Step-by-step explanation:

you figure it out

Answer:

56

Step-by-step explanation:

6 X 8 = 48

7 X 8 = 56

Answer:

56/48

Step-by-step explanation:

you multiply both sides by 8.

f(x) =2x+5

=2*3+5

=6+5

=11

=b

Answer:

b) 11

Step-by-step explanation:

step 1: f(3)=2(3)+5

substitute (plug in) the value of x which in here is 3

step 2: 2(3)=6 +5= 11

follow order of operations

P - parenthesis

E- exponent

MD- multiply and divide from left to right

AS- add and subtract from left to right

22.8 gms

Step-by-step explanation:

Step 1:

Given,

Mass of the element = 590 gms

Percentage decay per minute = 19.5%

Step 2 :

Fraction of the element remaining at the end of 1 minute = 1 - 0.195 = 0.805

Hence the fraction of element remaining after 15 minutes  = [tex]0.805^{15}[/tex] = 0.03863

So the mass of the element remaining after 15 minutes = 0.03863 * 590 = 22.8 rounded off to the nearest 10th of a gram

mass of the element remaining after 15 minutes = 22.8 gms

Answer:

22.8

Step-by-step explanation:

answered on delta math and got it correct

Answer:

vertex is 4

Step-by-step explanation:

y = (x-4)^2 + 7

(x-4) (x-4)

x * x = x^2

x * -4 = -4x

-4 * x = -4x

-4 * -4 =16

x^2 - 8x + 16

y = x^2 -8x + 16 + 7

y =  x^2 -8x + 23

       a     b     c

formula to find vertex: -b / 2a

= -b / 2a

= - (-8) / 2 (1)

= 8 / 2

= 4

vertex = 4

(what i did was work out the exponent outsite the parentesis then i got the equation i wanted, and from that equation i used the formula to find the vertex and i just plugged the numbers of the equation into the formula and work it out)

Answer:

(4,7)

Step-by-step explanation:

The equation for a parabola can be written as

y = a(x-h)^2 +k  where (h,k) is the vertex

given f(x) = (x-4)^2+7

The vertex is (4,7)

Answer:

The lender reduces the amount of principal that the borrower owes, with no expectation of repayment. Debt Forgiveness is analogous to a principal reduction. This is a more effective way to reduce payments than either lowering the interest rate on the mortgage, or extending the terms.

Answer:

they avoid foreclosure cost

Step-by-step explanation:

took the bullet

Answer:

The mom is 5 feet 3 inches

Step-by-step explanation:

Step 1:  Make an equation

m = 1 3/4 * 3

Step 2:  Solve

m = (4/4+3/4) * 3

m = 7/4 * 3

m = 21/4

m = 5.25

m = 5 feet 3 inches

Answer:  The mom is 5 feet 3 inches

Answer:

5 and 1/4

Step-by-step explanation:

3 times 1.75 = 5.25

Answer:

A turkey sandwich would cost $6.50 and the salads would be $5.50

Step-by-step explanation:

The cost of a turkey sandwich is $4.5 and the cost of a salad is $3.5.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the employees at a bank ordered 4 turkey sandwiches and 2 salads at a local deli. The total cost of the order was $25.

The cost will be calculated as,

4t + 2s = 25

s = t - 1

Substitute the value of s in the first equation,

4t + 2s = 25

4t + 2(t - 1)= 25

4t + 2t - 2 = 25

6t - 2 = 25

t = $4.5

The cost of salad will be,

S = t - 1

S = 4.5 - 1

S = $3.5

Therefore, the cost of a turkey sandwich is $4.5 and the cost of a salad is $3.5.

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Answer:

-3, -2 1/2, -2 2/5, -2 3/10, -2

Step-by-step explanation:

Answer: from least to greatest =

-2 ; -2 3/10; -2 2/5; - 2 1/2, -3

Step-by-step explanation:

Step 1: Convert fraction to decimal

Step 2: arrange in the order

Step 3: be mindful of the sign (-)

Answer:

Theta=38° to the nearest degree

Step-by-step explanation:

Answer:

2 1/3 or 7/3

Step-by-step explanation:

I would simplify it to 14/3 and 7/3 then subtract which you get 7/3 then simplify it to the original state which is 2 1/3. Hope this helps :)

Step-by-step explanation:

Answer:

90 sheep?

Step-by-step explanation:

1 sheep= 1 pound

1 cow= 10 pounds

total amount made= 100 pounds

100 ÷ 1 (the cost for sheep) = 100 sheep

100 - 90 (the cost of cows) = 10

10 sheep

Answer:

21 sheep

Step-by-step explanation:

100 = x + y + 8z

10x + y + z = 100

x = 1

y + 8z = 99

y + z = 90

x = 2

y + 8z = 98

y + z = 80

x = 3

y + 8z = 97

y + z = 70

x = 4

y + 8z = 96

y + z = 60

x = 5

y + 8z = 95

y + z = 50

x = 6

y + 8z = 94

y + z = 40

x = 7

y + 8z = 93

y + z = 30

7z = 63

z = 9

y = 30 - 9 = 21

x = 7 (7 cows)

y = 21 (21 sheep)

z = 9 (9×8 = 72 chicken)

Question 1:

The given formula is

[tex]I=\frac{PTR}{100}[/tex]

To make T, the subject we multiply both sides by 100:

[tex]100I=\frac{PTR}{100} \times 100[/tex]

This becomes

[tex]100I=PTR[/tex]

Divide both sides by PR

[tex]T=\frac{100I}{PR}[/tex]

b) Amanda's principal is , P=€2565

The interest rate is 3.5% p.a. that is R=3.5

We want to find how many years, her money will gain an interest of I=€718.20

We substitute into the formula for T,

[tex]T=\frac{100 \times 718.20}{2565 \times 3.5}[/tex]

This simplifies to:

T=8

Therefore it will take 8 years

2) Percentage profit

[tex] = \frac{profit}{cost \: price} \times 100\%[/tex]

The cost price of the 80 articles €200

The selling price is 3.5×80=€280

The profit =€280-€200=€80

The percentage profit is now

[tex] = \frac{80}{200} \times 100\%[/tex]

[tex] = 0.4 \times 100\%[/tex]

[tex]40\%[/tex]

The percentage profit is 40%

Question 3)

Let the original price of the calculator be x.

Then 85% of this price will be:

[tex] \frac{85}{100} \times x[/tex]

This is the same as€32.89

We equate and solve for x.

[tex] \frac{85}{100} x= 32.89[/tex]

[tex]0.85x = 32.89[/tex]

[tex]x = \frac{32.89}{0.85} [/tex]

[tex]x = 38.69[/tex]

The original price is €38.69

y/(5 + 3) = 5/y

y/8 = 5/y

y² = 40

y = 2√10

5/x = x/3

15 = x²

√15 = x

Answer:

  3.9

Step-by-step explanation:

The right triangles are all similar, so the ratio of short side to long side is the same for all:

  3/x = x/5

  15 = x^2 . . . . . . . . multiply by 5x

  x = √15 ≈ 3.9

Final answer:

To find the limits for the middle 58% of charitable contributions in Pennsylvania, calculate the Z-scores and use them to determine the lower and upper limits.

Explanation:

Given data: Average charitable contribution = $792, Standard deviation = $108

Find middle 58% limits:

Answer:

-4 and +6

Step-by-step explanation:

The signs of 4 and 6 that will get you to a 2 are

[tex] - 4[/tex]

and

[tex] + 6[/tex]

Putting the two together gives

[tex] - 4 + 6 = 6 - 4 = 2[/tex]

This means that, starting from -4 on the number line , move 6 units to the right.

This will land you on 2

Answer:

The number is 5

Step-by-step explanation:

I like to do the equation backwards, so x*7+1/4=9 becomes:

9*4=36

36-1=35

35/7=5

And there is your answer!!!

Answer:

B) 6 tan(35°)

Step-by-step explanation:

from the right angle tan° = opposite / adjacent

therefore tan (35°) = (x) / 6

by multiplying 6 to both sides

tan (35°)  * 6 = (x) / 6 * 6

therefore (x) = 6 tan (35°)

Answer:

B

Step-by-step explanation:

I did it on usatestprep

Answer:

Step-by-step explanation:

1/2(-9+n)=20

n=40+9

n=49

Answer:

49

Step-by-step explanation:

Sum means add

-9+n

Multiply this by 1/2

1/2(-9+n)

This is equal to 20

1/2(-9+n) = 20

Solve

Multiply each side by 2 to get rid of the fraction

2*1/2(-9+n) = 20*2

-9+n = 40

Add 9 to each side

-9+9 +n = 40+9

n = 49

To simplify the expression xz^3*4x^4z^5, the exponents of the like bases are added together resulting in 4x^5z^8. This application of exponent rules shows that the exponents on the same base are summed during multiplication.

To simplify the expression xz^3*4x^4z^5, we need to apply the rules of exponents. Specifically, when multiplying two expressions with the same base, we add their exponents.

Beginning with the variable x, we have an implied exponent of 1 on the standalone x, so when combined with x^4, we get x^(1+4), which simplifies to x^5.

Next, we apply the same rule to the variable z.

The expression z^3 multiplied by z^5 becomes z^(3+5), which simplifies to z^8. Finally, we multiply these results by the constant 4 to get our simplified expression:

4x^5z^8.

As an example to clarify this process, imagine a simpler case like (5^3)^4.

This could be written out as multiple fives multiplied by each other, illustrating that the exponents are indeed added together when multiplying like bases, just as we did with x and z in our original expression.

Answer:6750

Step-by-step explanation:

Final answer:

The jumbo-sized box, created by tripling each dimension of a regular-sized box that holds 250 toothpicks, will have a volume 27 times greater. Therefore, it will hold 250 × 27 = 6,750 toothpicks.

Explanation:

The question is asking how many toothpicks a jumbo-sized box can hold if it is created by tripling the length, width, and height of a regular-sized box that holds 250 toothpicks. To find the answer, we need to consider the volume of the boxes because the toothpicks are arranged in three-dimensional space.

The volume of a box is calculated by multiplying its length by its width by its height. If we triple each of these dimensions for the jumbo box, the new volume will be 27 times the volume of the original box (since 3 × 3 × 3 = 27). Therefore, if the original box holds 250 toothpicks, the jumbo box will hold 250 × 27 toothpicks.

To find the total number of toothpicks:

Multiply the number of toothpicks in the original box (250) by 27.

Calculate 250 × 27 to get 6,750 toothpicks.

Thus, the jumbo-sized box would be able to hold 6,750 toothpicks.

Answer:

Negative 4 n + 8 + 9 n minus 2 and 5 n + 6

Step-by-step explanation:

3v + 5 - (9v + 2)

3v + 5 - 9v -2 = -6v + 3

-6v + 6

(NO)

-6n + 3 - (2n + 2)

-6n + 3 - 2n - 4 = -8n - 1

-8n + 6

(NO)

-4n + 8 + 9n - 2 = 5n + 6

5n + 6

(YES)

Answer:

The answer is c