y
12
11
10
9
7
NWO0065
4
-12-11-10-9-8
-65
-3-2-1
1
2 3 4 5 6
8 9 10 11 12
-2
-9
-10
-11
-12

Answer:

x = -1.5 , y = 5.17

Step-by-step explanation:

Solve the system of equation using ELIMINATION (solve for x)

x + 3y = 14

-x + y = 10

Solution

x + 3y = 14 ------- equation 1  * 1

-x + y = 10 ------- equation 2  * 3

x + 3y = 14 ------- equation 3

-(-3x + 3y = 30)------ equation 4

Using the ELIMINATION METHOD.

x-(-3x) + 3y-3y = 14-30

4x = -6

x = [tex]\frac{-6}{4}[/tex]

x = -1.5

Substuting -1.5 into equation one

x + 3y = 14

-1.5 + 3y = 14

Adding 1.5 to both sides

-1.5 + 1.5 +3y = 14 +1.5

+3y = 15.5

Dividing by the coeffient of y

[tex]\frac{3y}{3} = \frac{15.5}{3}[/tex]

y = 5.166666666666

y =5.17

Therefore x = -1.5 , y = 5.17

I need help too  cause i have a quiz for it to take please help me

Step-by-step explanation:

an account transaction log is simply a sequence of basic additions and subtractions.

he made a mistake in line 4 : $180 - $188 = -$8 and not $8.

he missed that this was going below zero and needed a "-" sign.

from there on everything else is wrong too (although the individual calculations are correct) - the balances are off by $16 (2×8 from -8 to +8) :

+$20 gave the real balance of $12 and not $28.

-$5.95 gave the real balance of $6.05 and not $22.05.

Answer:

The answer is C, the total amount spent on drinks

Answer:

Step-by-step explanation:

Using the t-distribution, it is found that the 90% confidence interval is (48.3, 48.7), hence 48.8 is not within the interval.

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 225 - 1 = 224 df, is t = 1.6517.

The other parameters are given as follows:

[tex]\overline{x} = 48.5, s = 1.8, n = 225[/tex].

Hence the bounds of the interval are given by:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 48.5 - 1.6517\frac{1.8}{\sqrt{225}} = 48.3[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 48.5 + 1.6517\frac{1.8}{\sqrt{225}} = 48.7[/tex]

The 90% confidence interval is (48.3, 48.7), hence 48.8 is not within the interval.

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The standard form of the expanded polynomial, is expressed as: 7r² - 6r - 9.

The standard form of a polynomial is expressed by writing the term with the highest exponent or power first, while the constant is written last.

Given the polynomial:

(8r² - 7r - 9) + (-r² + r)

Distribute to open the bracket

8r² - 7r - 9 - r² + r

Combine like terms

7r² - 6r - 9 (standard form)

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Answer:

1, 2, 3, 6, 13, 26, 39, 78

Step-by-step explanation:

The factors of a number are the numbers that "go into" 78 "evenly" that is, without a remainder. You can make a factor tree or divide to find the prime factors. Any combination "goes into" 78. That's why we'll include 6 and 26 on this list.

1×78

2×39

3×26

6×13

all make 78!

Answer: 3 apples

Step-by-step explanation:

Given:

12 red apples

15 green apples

8 people

Freida

..............................................................................................................................................

12 + 15 = 27

Since she is going to give the apples equally among 8 people,

27 / 8 = 3 remainder 3

Each of the 8 people will get 3 apples each.

Freida will get the remaining 3 apples.

Answer:

x<7

Step-by-step explanation:

-3(x - 4) > -2x + 5 Distribute

-3x+12>-2x+5  Subtract 12 from both sides

-3x>-2x-7 Add 2 to both sides

-5x>-7 Simplify

x<7

Answer:

x < 7.

Step-by-step explanation:

-3(x - 4) > -2x + 5

-3x + 12 > -2x + 5

-3x + 2x > 5 - 12

-x  > -7      Note: we divide by -1 so the sign flips:

x < 7.      

The depreciated value of the car after 12 years that Kyle buys for $58,000 today, which declines 23% annually, will be $2,520.

Depreciation is the reduction or decrease in the value of an asset over time.

Depreciation occurs because an asset is put to use, and undergoes wear and tear.

The current price of the car = $58,000

The annual depreciation rate = 23%

The depreciated value after one year = 0.77 (1 - 23%)

Let the number of years of depreciation = x

The worth of the car after 12 years = 58,000 x 0.77^x

= 58,000 x 0.77^12

= 58,000 x 0.04344

= $2,519.52

= $2,520

The car's depreciated value can be modeled by the exponential function (decay) abˣ, which yields $2,520 in this situation.

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Answer:

12

Step-by-step explanation:

1.4x10 is moving the decimal point one spot to the left, so it would be 14., which is just simply 14. Finally, 14-2=12 which is the answer.

Answer:

x=11800

Step-by-step explanation:

make a proportion:

2360/.2=X/1

2360(1)=.2x

x=11800

Answer:

[tex]\huge 3w^2\sqrt[4]{2\:w^{3}}[/tex]

Step-by-step explanation:

Answer:

Circle

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

(10×11)+(10×7)=110+70

The area of the kite is expressed as 1/2 × (Product of its diagonals)

In this case, we have;

Therefore, when we substitute the diagonals in the formula, we get;

When simplified, we get;

Therefore, the area of the kite is 180 ft².

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Answer:

The second answer

Step-by-step explanation:

Answer:

-3 ± √41

Step-by-step explanation:

Numerator of Quadratic Formula

⇒ -3 ± √(-3)² + 4(2)(-4)

⇒ -3 ± √9 + 32

⇒ -3 ± √41

Answer:

The answer is option B

[tex]859[/tex] [tex]m^2[/tex] [tex],[/tex] [tex]891[/tex] [tex]m^2[/tex]

Step-by-step explanation:

Step 1

Find the lateral area

we know that

The formula to calculate the lateral area is equal to

[tex]LA=Ph[/tex]

where

P is the perimeter of the base of the prism

h is the height of the prism

In this problem we have

[tex]P=4+8+8.94=20.94[/tex] [tex]m[/tex]

[tex]h=41[/tex] [tex]m[/tex]

substitute in the formula

[tex]LA=20.94*41=858.54[/tex] [tex]m^2[/tex]

[tex]LA=859[/tex] [tex]m^2[/tex]

Step 2

Find the surface area

we know that

The formula to calculate the surface area is equal to

[tex]SA=2B+Ph[/tex]

where

B is the area of the base of the prism

P is the perimeter of the base of the prism

h is the height of the prism

In this problem we have

[tex]B=8*4/4=8[/tex] [tex]m^2[/tex]

[tex]P=4+8+8.94=20.94[/tex] [tex]m[/tex]

[tex]h=41[/tex] [tex]m[/tex]

substitute in the formula

[tex]SA=4(8)+20.94*41=890.54[/tex] [tex]m^2[/tex]

[tex]SA=891[/tex] [tex]m^2[/tex]

Answer:

  14

Step-by-step explanation:

A hexadecimal (base 16) number can have any of 16 digits. Conventionally, digits 0–9 are used, along with letters A–F. The letters are assigned the values ...

  A = 10

  B = 11

  C = 12

  D = 13

  E = 14

  F = 15

Answer:

The answer is 243

Step-by-step explanation:

Since there are 3 answers for each question and a total of 5 questions, you could do 3*3*3*3*3 or 3^5. Both will equal 243. 243 is the amount of possible different combinations that exist in this problem.

Hope this helps!

Answer:

sqrt(13)

Step-by-step explanation:

The entire base is 4, so 1/2 of the base is 2

We can use the pythagorean theorem

a^2 = b^2 = c^2

2^2 + 3^2 = x^2

4+9 = x^2

13 = x^2

Taking the square root of each side

sqrt(13) = x

Check the picture below.

Answer:

A = 8 and B = 6

Step-by-step explanation:

Since (B = A - 2), we can substitute (A - 2) in for the "B" variable in the first equation to isolate "A".

(A - 5)² + (B - 3)² = 18                                 ----->  Original equation

(A - 5)² + ((A - 2) - 3)² = 18                         ----->  Plug in B = A - 2

(A - 5)² + (A - 5)² = 18                                ----->  Subtract

(A² - 10A + 25) + (A² - 10A + 25) = 18       ----->  Expand parentheses

2A² - 20A + 50 = 18                                 ------>  Add like terms

2A² - 20A + 32 = 0                                   ----->   Subtract 18 from both sides

2(A² - 10A + 16) = 0                                   -----> Remove common factor

2(A - 2)(A - 8) = 0                                      -----> Factor within parentheses

A = 2                                                         -----> Find A - 2 = 0

A = 8                                                        -----> Find A - 8 = 0

Since "A" gave two possible values, we need to plug them into both equations to see which value gives reasonable "B" values.

When A = 2:

B = A - 2                           -----> Original equation

B = 2 - 2                           -----> Plug in A = 2

B = 0                               -----> Subtract

(A - 5)² + (B - 3)² = 18       -----> Original equation

(2 - 5)² + (B - 3)² = 18       ------>  Plug in A = 2

(-3)² + (B - 3)² = 18           -----> Subtract within first parentheses

9 + (B - 3)² = 18               -----> Square value within first parentheses

(B - 3)² = 9                      ----->  Subtract 9 from both sides

B - 3 = 3                          ----->  Take square root of both sides

B = 6                               ----->  Add 3 to both sides

When A = 8:

B = A - 2                         -----> Original equation

B = 8 - 2                         -----> Plug in A = 8

B = 6                             -----> Subtract

(A - 5)² + (B - 3)² = 18       -----> Original equation

(8 - 5)² + (B - 3)² = 18       ------>  Plug in A = 8

(3)² + (B - 3)² = 18            -----> Subtract within first parentheses

9 + (B - 3)² = 18               -----> Square value within first parentheses

(B - 3)² = 9                      ----->  Subtract 9 from both sides

B - 3 = 3                          ----->  Take square root of both sides

B = 6                               ----->  Add 3 to both sides

As you can see, when A = 2, there are two possible values of "B" depending on the equation. However, when A = 8, both equations give a "B" value of B = 6. Therefore, A = 8 and B = 6 are the answers.

There are total 15 dogs, 27 cats, and 3 ferrets were adopted if the ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We have:

An animal shelter had 45 animals adopted over one week. The ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.

Combine ratio dogs:ferrets:cats = 5:1:9

Let's suppose the number of ferrets is x then:

5x + x + 9x = 45

15x = 45

x = 3

Ferrets x = 3

Dogs = 5x = 5(3) = 15

Cats = 9x = 9(3) = 27

Thus, there are total 15 dogs, 27 cats, and 3 ferrets were adopted if the ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.

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Answer:

see explanation

Step-by-step explanation:

the sum of the 3 angles in the triangle = 180° , then

∠ BAC + 51° + 90° = 180°

∠ BAC + 141° = 180° ( subtract 141° from both sides )

∠ BAC = 39°

using the tangent ratio in the right triangle

tan51° = [tex]\frac{opposite}{adjacent }[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{AC}{12.8}[/tex] ( multiply both sides by 12.8 )

12.8 × tan51° = AC , then

AC ≈ 15.8 ( to 1 dec. place )

using the cosine ratio in the right triangle

cos51° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{12.8}{AB}[/tex] ( multiply both sides by AB )

AB × cos51° = 12.8 ( divide both sides by cos51° )

AB = [tex]\frac{12.8}{cos51}[/tex] ≈ 20.3 ( to 1 dec. place )

Area of base

Area of one triangle side

Area of 4 sides

TSA

20+25=45ft²

Answer:

C)  45 ft²

Step-by-step explanation:

Formulae

Area of a square = x²  (where x is the side length)

Area of a triangle = 1/2 × base × height

The surface area of a square pyramid comprises:

⇒ area of square base = 5² = 25 ft²

⇒ area of triangular face = 1/2 × 5 × 2 = 5 ft²

⇒ Total surface area = area of square base + 4 triangular areas

                                   = 25 + 4(5)

                                   = 25 + 20

                                   = 45 ft²

Answer:

12

Step-by-step explanation

Answer:

a

34

b

17

c

46

Step-by-step explanation:

a

Lowest age = 21

Highest age = 55

Range = 34

b

Add them all together and you get 17

c

Median is middle

17 total people

Formula for median:

(n + 1)/2 = th

n is the total

17 + 1 is 18

18 halved is the 9th number

The 9th number is 46

Hi Student!

Reading the question we can pull out specific bits of information that would help us find our answer.  One of the bits of information that is useful is that we are trying to find the perpendicular line.  However, in order to determine a line that is perpendicular to the other line we first need to determine the slope of the first line.  Looking at the equation given, we can see that it follows the y = mx + b form where m is the slope and in this case our slope is 8.

Now that we have completed the information gathering, we can move onto the next part which is determining a slope that is perpendicular to that of the original line.  In order to find that we first need to negate our slope which would turn our 8 into a -8.  The second step that we need to do is take the reciprocal of the number which means that we basically flip the number and so we convert -8 into -1/8.  Looking at the given options, there is none that match our answer so that either means that the question is wrong or the choices that are given are wrong.

Answer:

90

bc i don't care about this

The equation of plane containing the points ABC is 13x+y-18z = 1035.

A plane in 3D coordinate space is determined by a point and a vector that is perpendicular to the plane. The equation of plane is defined as the position vectors and the Cartesian product of the vector perpendicular to the plane.

For the given situation,

The plane containing the points

A(10, 5, -50), B(15, 30, -45) and C(-5, 20, -60).

The equation of the plane in the form r.n=d can be represented as

[tex](r-a).[(b-a)[/tex] × [tex](c-a)]=0[/tex] ------ (1)

Let r = xi + yj +zk

a = 10i + 5j - 50k

b = 15i + 30j - 45k

c = -5i + 20j - 60k

[tex](r-a)=(x-10)i+(y-5)j+(z+50)k[/tex] ------- (2)

[tex](b-a)=(15-10)i+(30-5)j+(-45-(50))k[/tex]

⇒ [tex](b-a)=5i+25j+5k[/tex]

[tex](c-a)=(-5-10)i+(20-5)j+(-60-(50))k[/tex]

⇒ [tex](c-a)=-15i+15j-10k[/tex]

Now, [tex](b-a)[/tex] × [tex](c-a)[/tex]

⇒ [tex](5i+25j+5k)[/tex] × [tex](-15i+15j-10k)[/tex]

⇒ [tex]\begin{vmatrix}i&j&k\\5&25&5\\-15&15&-10\end{vmatrix}[/tex]

⇒ [tex]i(-250-75)-j(-50+75)+k(75+375)[/tex]

⇒ [tex]-325i-25j+450k[/tex] -------- (3)

Substitute all values in equation 1,

⇒ [tex][(x-10)i+(y-5)j+(z+50)k].[(-325i-25j+450k)]=0[/tex]

⇒ [tex]-325(x-10)-25(y-5)+450(z+50)=0[/tex]

⇒ [tex]-325x+3250-25y+125+450z+22500=0[/tex]

⇒ [tex]-325x-25y+450z=-22500-3250-125[/tex]

⇒ [tex]-325x-25y+450z=-25875[/tex]

On dividing by 25 and multiply with negative sign on both sides,

⇒ [tex]13x+y-18z=1035[/tex]

Hence we can conclude that the equation of plane containing the points ABC is 13x+y-18z = 1035.

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