Find the solution of this system of equations -4x-y=-18 , -7x+y=-4

Answer:

Yellow Paint: 0.44736842105%

Red Paint: 0.19736842105%

Water: 0.35526315789%

Step-by-step explanation:

Yelow:

30 x 0.3 = 9

8 + 9 = 17

30 + 8 = 38

17/38 = 0.44736842105%

Red:

30 x 0.25 = 7.5

7.5/38 = 0.19736842105%

Water:

30 x 0.45 = 13.5

13.5/38 = 0.35526315789%

Answer:

There is a 1 and 6 chance (16.666...%)

Step-by-step explanation:

59 mi/hr × (5280 ft/mi) × (1 hr / 3600 s) = 86.53 ft/s

Rounded to the nearest whole number, the speed is approximately 87 ft/s.

Answer:

Step-by-step explanation:

the translation (x,y) --> (x+6,y-4):

(1, 5)--> (1+6,5-4)=(7,1)

(2, 2)--> (2+6,2-4)=(8,- 2)

(6, 3)--> (6+6,3-4)=(12,- 1)

the image of A triangle has vertices of (1, 5), (2, 2), and (6, 3) is :

the triangle has vertices of (7, 1), (8,- 2), and (12, -1)

ANSWER

(0,2)

EXPLANATION

The mapping point A has coordinate (0,2).

We want to find the coordinates of this point after a rotation of -90° about the origin.

In other words, we want to find the image of this point after a rotation of 90° anticlockwise.

The rule is

[tex](x,y) \to( - y,x)[/tex]

This implies that

[tex](2,0) \to(0,2)[/tex]

Answer: Option D

phase

Step-by-step explanation:

By definition, the cosine function has the following form

[tex]y = cos (x - \phi)[/tex]

Where [tex]\phi[/tex] is known as the phase angle

By definition the sinx function is equal to the cosx function with a phase shift of [tex]\frac{\pi}{2}[/tex]

So if we have the function

[tex]y = cos (x - \phi)[/tex] and we want to transform it into the function [tex]y=sin(x)[/tex] then [tex]\phi = \frac{\pi}{2}[/tex]

Finally

[tex]y = cos(x - \frac{\pi}{2})=sin(x)[/tex]

the answer is the option D

Final answer:

The cosine function aligns with the sine function by introducing a phase shift, typically represented by phi (φ), indicating that D. phase is the correct answer.

Explanation:

The cosine function can be made to have the same values as the sine function for each angle by including a shifted phase in the calculation. This shift is referred to as a phase shift and is typically represented by the Greek letter phi (φ).

In the context of trigonometric functions, a phase shift will slide one function over to match that of another.

Specifically, when the sine function is shifted left by 90 degrees (π/2 radians), it aligns perfectly with the cosine function, indicating that the sine and cosine are out of phase by 90 degrees.

Thus, the correct answer is D. phase.

Hello There!

-The Numbers Ordered From Least To Greatest-

-59   -41   -23   -11

The closer the number is to zero, it is going to be a bigger number than a number far away from zero.

Answer:

  A.  4

Step-by-step explanation:

The common ratio will be the ratio of any adjacent pair of y-values:

  32/8 = 128/32 = 512/128 = 2048/512 = 4

Answer:

The exact volume of an oblique cylinder is [tex]V=2,000\pi\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The Cavalieri's principle states that if two or more figures have the same cross-sectional area at every level and the same height, then the figures have the same volume

so

The volume of the oblique cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]h=20\ cm[/tex]

[tex]r=10\ cm[/tex]

substitute

[tex]V=\pi (10)^{2} (20)[/tex]

[tex]V=2,000\pi\ cm^{3}[/tex]

Answer:

the volume of an oblique cylinder is V=2,000\pi\ cm^{3}

Answer:

  100 lbs

Step-by-step explanation:

Let x represent the number pounds of $60 coffee that should be used to create the mix. The total cost of the mix will be ...

  60x + 90·50 = 70(x+50)

  60x +4500 = 70x +3500 . . . . simplify

  1000 = 10x . . . . . . . . . . . . . . . . subtract 3500+60x

  100 = x . . . . . . . . . . . . . . . . . . . divide by 10

The merchant should use 100 pounds of the $60 coffee.

_____

The cost of the mix parts and the total mix is figured from ...

  (dollars/lb)×(lbs) = dollars

Answer:

8x^2+3x

Step-by-step explanation:

What I read is 2x+8x^2-4x+5x

combining like terms means putting the terms that have the same variable part together

8x^2 is the only one that doesn't have any terms like it as far as the variable part

so 8x^2+2x-4x+5x

We just need to figure out 2-4+5 which is -2+5=3

So the answer is 8x^2+3x

Answer:

10x

Step-by-step explanation:

Note the place values of the value 3 in both of the decimals.

The value of the 3 in 46.132 is in the hundredths place.

The value of the 3 in 8.553 is in the thousandths place.

Divide thousands with hundreds: 1000/100 = 10

The value of the 3 in 46.132 is 10x larger than the value of 3 in 8.553

~

Answer:

B. 10.

Step-by-step explanation:

This is the number of combinations of 3 from 5.

5C3  = 5! / 3! (5-3)!

= 5*4*3*2*1 / 3*2*1 * 2*1

= 5*4/2*1

= 10.

Answer: 10 i think

Step-by-step explanation:

Answer:

h = 2 and k = 6

Step-by-step explanation:

Since the lines intersect at (- 3, 1) then this is the solution to the system of equations.

That is x = - 3 and y = 1

Substitute these values into the equations and solve for h and k

hx - 4y = - 10

- 3h - 4 = - 10 ( add 4 to both sides )

- 3h = - 6 ( divide both sides by - 3 )

h = 2

Similarly

kx + 3y = - 15

- 3k + 3 = - 15 ( subtract 3 from both sides )

- 3k = - 18 ( divide both sides by - 3 )

k = 6

Answer:

Option A.Exponential decay, 55% decrease

Step-by-step explanation:

we have

[tex]f(x)=54(0.45)^{x}[/tex]

This is a exponential function of the form

[tex]f(x)=a(b)^{x}[/tex]

where

a is the initial value

b is the base

b=(1+r)

r is the rate of change

In this problem

a=54

b=0.45

so

0.45=1+r

r=0.45-1

r=-0.55

Convert to percentage

r=-55% ------> is negative because is a exponential decay

Answer:

Exponential decay, 55% decrease

Step-by-step explanation:

[tex]f(x) = 54(0.45)^x[/tex]

General exponential growth function is [tex]y=a(1+r)^x[/tex]

exponential growth function is [tex]y=a(1-r)^x[/tex]

The value of 1-r is less than 1 then it is exponential decay

In the given f(x) , the 1-r is 0.45 that is less than 1

So it is exponential decay.

[tex]1-r= 0.45[/tex]

Subtract 1 on both sides

[tex]r=0.55[/tex]

Multiply by 100 to get %

r= 55%

Exponential decay, 55% decrease

Answer:

5.5% per year

Step-by-step explanation:

Using Formula A = P (1 + rt)

Where

A = Final amount = $10,000 + $6,600  = $16,600

P = Principal = Beginning Amount = $10,000

t = time = 12 years

r = rate in $/year (which we need to find)

Assembling the formula

A = P (1 + rt)

16,600 = 10,000 (1 + 12r)

[tex]\frac{16,600}{10,000}[/tex] = 1 + 12r

1.66 = 1 + 12r

1.66 - 1 = 12r

0.66 = 12 r

r = 0.055 = 5.5%

Answer:

C. [tex]490 \textrm{ units}^{2}[/tex]

Step-by-step explanation:

The formula for surface area is

LA + 2B

LA indicated Lateral Area and can be found multiplying perimeter of base by the height.

7 + 7 + 14 + 14 = 42 * 7 = 294

Multiply the LA from above with the area of base times 2.

98 * 2 = 196

294 + 196 = 490, so the surface area of the rectangular prism is 490 units.

To find the surface area of a rectangular prism, add up the areas of all six faces by multiplying length by width.

To find the surface area of a rectangular prism, you need to add up the areas of all six faces. Each face is a rectangle, so to find the area, you multiply the length by the width. Then, you add up the areas of all the faces to get the total surface area.

For example, if the length of one side is 4 units, the width is 2 units, and the height is 3 units, the surface area would be:
Face 1: 4 units x 2 units = 8 square units
Face 2: 4 units x 2 units = 8 square units
Face 3: 4 units x 3 units = 12 square units
Face 4: 4 units x 3 units = 12 square units
Face 5: 2 units x 3 units = 6 square units
Face 6: 2 units x 3 units = 6 square units
Total surface area: 8 + 8 + 12 + 12 + 6 + 6 = 52 square units.

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Answer:

11.15 packs of paper are used in 5 days; therefore, 133.85 are left

Step-by-step explanation:

Set this up as ratio with days on top and packs of paper on the bottom.  Filling in the ratio with the info we have, keeping in mind we are looking for packs of paper left after 5 days:

[tex]\frac{days}{packs}:\frac{65}{145}=\frac{5}{x}[/tex]

Cross multiply to get 65x = 725 and x = 11.15.  This represents the number of packs used.  To get the number of packs remaining, subtract 11.15 from 145 to get 133.85 remaining after 5 days.

Answer:

x=7 satisfy the equation, so it is the solution.

x=4 doesn't satisfy the equation so it is extraneous solution.

Step-by-step explanation:

The equation given is:

[tex]\sqrt{x-3}+5=x[/tex]

Adding -5 on both sides

[tex]\sqrt{x-3}=x-5[/tex]

Taking square on both sides

[tex](\sqrt{x-3})^2=(x-5)^2[/tex]

Now solving

[tex]x-3 = x^2 -10x+25\\Arranging\\x^2-10x-x+3+25=0\\x^2-11x+28=0\\Factorizingx^2-7x-4x+28=0\\\\x(x-7)-4(x-7)=0\\(x-4)(x-7)=0\\x-4=0 \,\,and\,\, x-7=0\\x=4 \,\,and\,\, x=7[/tex]

Verifying solutions:

Putting x=4 in the equation

[tex]\sqrt{x-3}+5=x[/tex]

[tex]\sqrt{4-3}+5=4[/tex]

[tex]\sqrt{1}+5=4[/tex]

[tex]1+5=4[/tex]

[tex]6\neq 4[/tex]

So, x=4 doesn't satisfy the equation so it is extraneous solution.

Now Putting x=7 and verifying

[tex]\sqrt{x-3}+5=x[/tex]

[tex]\sqrt{7-3}+5=7[/tex]

[tex]\sqrt{4}+5=7[/tex]

[tex]2+5=7[/tex]

[tex]7=7[/tex]

x=7 satisfy the equation, so it is the solution.

Answer:

= 7

Step-by-step explanation:

Answer:

Mean = 47.52 degrees

Step-by-step explanation:

We will use the following method to find the mean

Class interval     Frequency(f)     Class Mark(X)     fx

40-44                      3                              42               126

45-49                      4                              47               188

50-54                     10                             52               520

55-59                      6                              57               342

60-64                      2                              62               124

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

                               25                                                1188

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

The formula for mean is:

Mean = ∑fx / ∑f

= 1188/25

= 47.52 degrees

The computed mean is less than the actual mean of 51.8 degrees ..

Answer:

p = q

Step-by-step explanation:

There are 180 degrees in a triangle. If you subtract 50 and 60 from 180, you get 70. If you subtract 30 an 80 from 180, you get 70. therefore p = q.

Answer:

The equation of the nth term is an = -621 + 42n

Step-by-step explanation:

* Lets revise the arithmetic sequence

- There is a constant difference between each two consecutive numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic sequence:

- U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

- Un = a + (n – 1)d, where a is the first term , d is the difference

  between each two consecutive terms

, n is the position of the term

* Lets solve the problem

∵ an = a + (n - 1)d

∴ a14 = a + (14 - 1)d

∴ a14 = a + 13d

∵ a14 = -33

∴ a + 13d = -33 ⇒ (1)

- Similar we can find another equation from a15

∵ a15 = a + (15 - 1)d

∴ a15 = a + 14d

∵ a15 = 9

∴ a + 14d = 9 ⇒ (2)

- We will solve equations (1) and (2) to find a and d

* Lets subtract equation (2) from equation (1)

∴ (a - a) + (13 - 14)d = (-33 - 9)

∴ -d = -42 ⇒ × both sides by -1

∴ d = 42

- Substitute this value of d in equation (1) or (2)

∵ a + 13d = -33

∵ d = 42

∴ a + 13(42) = -33

∴ a + 546 = -33 ⇒ subtract 546 from both sides

∴ a = -579

* Now lets write the equation of the nth term

∵ an = a + (n - 1)d

∵ a = -579 and d = 42

∴ an = -579 + (n - 1) 42 ⇒ open the bracket

∴ an = -579 + 42n - 42

∴ an = -621 + 42n

* The equation of the nth term is an = -621 + 42n

Answer:

a 16

Step-by-step explanation:

16 x 12 = 192 plates

496 total plates - 192 = 304

304 packages of 8 plates

304 / 8 = 38 sets of 8 plates

38 + 16 = 54 packs of plates

Answer:

The correct answer is option B.  -18

Step-by-step explanation:

It is given an expression : 3 × (50 – 62) ÷ 2

To find the answer we have to use BODMAS principle

BODMAS means that the order of operations

B- Bracket, O - of , D - Division, M - Multiplication, A - Addition and  

S - Subtraction

To find the correct option

Step 1: Do the bracket first

3 × (50 – 62) ÷ 2 =  3 × (-12) ÷ 2

(Multiplication and division are in the order of appearance)

Step 2: Multiplication  

3 × (-12) ÷ 2 = -36  ÷ 2  

Step 3 : Division

-36 ÷ 2 = -18

The correct option is option B.  -18

Answer:

=-18

Step-by-step explanation:

3×(50-62)÷2

Using PEMDAS,  we first evaluate the parentheses. 50-62=-12

The new expression becomes

3×⁻12÷2

We now perform the multiplication in the order in which they occur.

3×-12=-36 and -36÷2= -18

=-18

Answer:

The vertex of the parabola is (2 , 2) ⇒ answer B

Step-by-step explanation:

* Lets revise the equation of a parabola

- The equation is in the form (x − h)² = 4p (y − k), where h and k are the

 vertex of the parabola

- If  p > 0, the parabola opens up  

- If p < 0, the parabola opens down

* Lets solve the problem

∵ The equation of the parabola is (x - h)² = 4p (y - k)

∵ The equation of the parabola is (x - 2)² = -12 (y - 2)

- By comparing the two equations

∴ 4p = -12 ⇒ divide both sides by 4

∴ p = -3 ⇒ -3 < 0

∵ p < 0

∴ The parabola opens down

- From the two equations

∴ h = 2 ⇒ the x-coordinate of the vertex

∴ k = 2 ⇒ the y-coordinate of the vertex

∴ The vertex of the parabola is (2 , 2)

The vertex of the given parabola (x - 2)^2 = -12(y - 2) is at the point (2, 2), which corresponds to Option B.

The vertex of the parabola defined by the equation (x - 2)^2 = -12(y - 2) can be found by identifying the point (h, k), where the equation fits the general form (x \\- h)^2 = 4p(y \\- k). Here, h and k represent the coordinates of the vertex, and p indicates the distance from the vertex to the focus or directrix. The given equation can be rearranged to match the general form with h = 2 and k = 2, making the vertex (2, 2). Hence, the correct answer is Option B.

Answer:

x=5

Knowing that the length of the rectangle is 9, we can simply multiply this by 2 since there are two sides that will equal the same. This gets us 18. If we subtract that from 28, we get 10. There are four sides in a rectangle, meaning we have two sides left. This leaves us to divide 10 by two to get a final answer of the width of the retangle being 5 centimeters.

The value of x, which represents the width of the rectangle, can be found by inserting the given length and perimeter into the perimeter formula of a rectangle, P = 2L + 2W. Then, solve for W to get the value of x.

The first step to solve this problem is to understand the formula for the perimeter of a rectangle. This formula is P = 2L + 2W, where P is the perimeter, L is the length and W is the width. We know that the length (L) is 9 cm and the perimeter (P) is 28 cm based on the problem given. We are looking to find the value for x which represents the width (W).

Let's substitute the given values into the formula:
28 = 2(9) + 2W.

This simplifies to:
28 = 18 + 2W.

Now, let's solve for W by subtracting 18 from both sides of the equation:
10 = 2W.

To isolate W, divide both sides of the equation by 2:
W = 5
So, the value of x, which represents the width of the rectangle, is 5 cm.

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Answer:

  -8

Step-by-step explanation:

For roots r and s, the quadratic can be factored ...

  f(x) = (x -r)(x -s) = x^2 -(r+s)x +rs

Then the value of r^2+s^2 can be determined from the coefficient of x (-(r+s)) and the constant (rs) by ...

  r^2 +s^2 = (-(r+s))^2 -2(rs) = (r^2 +2rs +s^2) -2rs = r^2 +s^2

Comparing this to your given equation, we have the coefficient of x as (-2m) and the constant term as (m^2+2m+3). Forming the expression ...

  (x-coefficient)^2 -2(constant term)

we get ...

  r^2 +s^2 = (-2m)^2 -2(m^2 +2m +3) = 2m^2 -4m -6

  r^2 +s^2 = 2(m -1)^2 -8

The minimum value of this quadratic expression is where m=1 and the squared term is zero. That minimum value is -8.

Answer:

  84.8 in³

Step-by-step explanation:

The formula for the volume of a cylinder is ...

  V = πr²h

The volume Mary will be filling will be 3/4 of the 9-inch height of the vase, so is ...

  V = π(2 in)²(3/4·9 in) = 27π in³ ≈ 84.8 in³

_____

Comment on the answer

In more conventional units of measure, that is very nearly 3 pints of water.

Answer:

  A.  8, 10, 14

Step-by-step explanation:

As a rough cut, a triangle will be obtuse if the longest side is about 1.4 or more times the length of the second-longest side. This derives from the relationship in an isosceles right triangle, where the hypotenuse is √2 ≈ 1.414 times the length of the two equal-length sides. If one side is shorter than the other, and the hypotenuse is still 1.414 times the length of the second-longest side, then the triangle is no longer a right triangle, but is an obtuse triangle.

Here, the first selection has a middle-length side of 10 and a longest side of 14, about 1.4 times 10. It is an obtuse triangle.

_____

More rigorously, you can see if the sum of the squares of the short sides is less than the square of the longest side. If so, the triangle is obtuse. (The Law of Cosines will tell you the angle opposite the longest side must have a negative cosine, so must be greater than 90°.)

Our answer choices are ...

  A. 8^2 + 10^2 = 164 < 14^2 = 196 . . . . . obtuse

  B. 9^2 + 12^2 = 225 = 15^2 . . . . . . . . . . right

  C. 10^2 +14^2 = 296 > 17^2 = 289 . . . . . acute

  D. 12^2 +15^2 = 369 > 19^2 = 361 . . . . . acute

Answer:

A) 8, 10 and 14

correct on edg2020 :)

Answer:

see explanation

Step-by-step explanation:

Find equivalent routes for the directed lines, that is

(a)

FE = FA + AB + BE = b + a - 3b = a - 2b

(b)

BC = BE + ED + DC = - 3b + a + 2b = a - b

(c)

FC = FA + AB + BE + ED + DC

     = b + a - 3b + a + 2b = 2a