Solve x^2+2x=4 for x by completing the square

Answer:

Blueberry costs 9 dollars

Pumpkin costs 7 dollars

Step-by-step explanation:

Let "b" represent the price of a blueberry pie

Let "p" represent the price of a pumpkin pie

Step 1: Set equation

5b + 12p = 143 ----- 1

10b + 8p = 142 ----- 2

Step 2:  Isolate 1 for "b"

5b = 143 - 12p

[tex]b = \frac{143}{5}-\frac{12}{5}p[/tex]  ------- 3

Step 3: Substitute 3 into 2

[tex]10(\frac{143}{5}-\frac{12}{5} p )+8p=142\\286 - 24p + 8p = 142\\-24p + 8p = 142 - 286\\-16p = -144\\p = -\frac{144}{-16}\\ p = 9[/tex]

Step 4: Subsitute p = 9 into 1 for b

[tex]5p + 12(9) = 143\\5p + 108 = 143\\5p = 143 - 108\\5p = 35\\\frac{5p}{5}=\frac{35}{5}\\p = 7[/tex]

Therefore a pumpkin pie costs 7 dollars while a blueberry pie costs 9 dollars

Answer:

a. P= 5000( 1.016)^x

b. $ 6344.18

Step-by-step explanation:

The equation for finding the compound interest annually is

P = P_1 ( 1 +r)^t

Here

P = the amount after the interest has been added or the new balance

P_1= the principal amount

r= rate at which interest is charged

t= time in years

So we have

P = the new balance

P_1= the principal amount= $ 5000

r= rate at which interest is charged= 1.6 %

t= time in years= x

Putting the values in the above equation

P = P_1 ( 1 +r)^t

P = 5000 ( 1+ 1.6/100) ^x

P= 5000( 1.016)^x

b) When t= 15

Again

Putting the values in the above equation

P = P_1 ( 1 +r)^t

P = 5000 ( 1+ 1.6/100)^15

P = 5000( 1.26883637) = 6344.18185= $ 6344.18

Answer:

Step-by-step explanation:

To calculate either the profit or loss we must first find the cost price and the selling price

For the cost price

She bought 150 oranges at ¢12

Cost price = ¢ 12.00

For the selling price

She sold 6 at 30 Gp that's ¢ 0.30

If she sold 6 at ¢ 0.30

Then 150 will be 150× 0.3/ 6

Selling price = ¢ 7.50

Since the cost price is higher than the selling price she made a loss

Loss = Cost price - Selling price

Loss = ¢ 12 - ¢ 7.50

Hope this helps you

Answer:

Please find attached the required inverse of a function chart

Step-by-step explanation:

The inverse of a function is found by reversing the operations of the  function

The inverse of the function f(x) = 2·x - 4 is found as follows;

x = 2·x - 4

x + 4 = 2·x

x = (x + 4)/2 = x/2 + 2

Therefore, the inverse of the function f(x) = 2·x - 4 is f(x) = x/2 + 2

The inverse function is plotted by generating data points as follows;

[tex]{}[/tex]x         [tex]{}[/tex]          f(x)

0                2

1                  2.5

2                 3

3                  3.5

4                   4

5                   4.5

6                   5

7                   5.5

8                   6

9                   6.5

10                  7

11 [tex]{}[/tex]                   7.5

12[tex]{}[/tex]                    8

13                 8.5

14                  9

15                  9.5

16               10

I think your teacher meant to say Reflexive property instead of reflection. The reflexive property is the idea that any segment is the same length as itself. It seems like a trivial idea, but it's useful to be able to pull triangles apart like in this problem here.

Note: when naming a segment, the order of the endpoints listed doesn't matter. So that's why EU is the same as UE.

Answer:

(64x -11)/y

Step-by-step explanation:

Multiply 4x into the parenthesis.

60x + 4xy -11y

Divide by y.

(60x + 4x -11)/y

(64x -11)/y

Steps to solve:

4x + (15x + y) - 11y​

~Remove parenthesis and combine like terms

4x + 15x + y - 11y​

19x - 10y

Best of Luck!

Answer:

First, we put a point on y-axis = 2

Next, we go 2 spaces down and 1 space right

Then draw a line attaching the two points

Answer:

we put a point on y-axis = 2

we go 2 spaces down and 1 space right

Then draw a line attaching the two points

Answer:

See answer is Explanation

Step-by-step explanation:

4 divided by 25 is 0.16

6 divided by 25 is 0.24

6 x 4 = 24

4 x 25 = 100

6 x 25 = 150

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

(5÷5+5)x(5-5)=0

Step-by-step explanation:

(5÷5+5)x(5-5)=0

Answer:

12 friends

Step-by-step explanation:

If we have 3 pizzas, each cut into slices of [tex]\frac{1}{4}[/tex], then we have a total of [tex]3 \div \frac{1}{4} = 3\cdot\frac{4}{1} = 12[/tex] slices.

This means that 12 friends can share the 3 pizzas.

Hope this helped!

Answer:

12 people

Step-by-step explanation:

If everyone is getting 1/4 of the pizza then that means there are 4 slices in each pizza

[tex]\boxed{c = -4}[/tex]

First, we will use the distributive property (order of operations) to simplify the equation:

(4)(5) + (4)(−8(4c−3)) = (12)(1) + (12)(−13c)+ (−8) =

20 + (−128c) + 96 = 12 + (−156c)+ (−8)

Now, we will combine like terms to simplify the equation:

(−128c) + (20 + 96) = (−156c) + (12+ (−8) =

−128c + 116 = −156c + 4

Now we will add 156 to both sides, using inverse operations.

−128c + 116 + 156c = −156c + 4 + 156c =

28c + 116 = 4

Now we will subtract 116 from both sides:

28c + 116 − 116 = 4 − 116 =

28c = −112

Lastly, we will divide both sides by 28:

28c/28 = c

-112/28 = -4

The equation now looks like:

c = -4

Therefore, your answer is -4.

Hi there! Hopefully this helps!

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[tex]4(5-8(4c-3))=12(1-13c)-8[/tex]

Use the distributive property to multiply −8 by 4c − 3.

[tex]4(5-32c+24)=12(1-13c)-8[/tex]

Add 5 and 24 to get 29.

[tex]4(29 - 32c)=12(1-13c)-8[/tex]

Use the distributive property to multiply 4 by 29 − 32c.

[tex]116-128c=12(1-13c)-8[/tex]

Use the distributive property to multiply 12 by 1 − 13c.

[tex]116-128c=12-156c-8[/tex]

Subtract 8 from 12 to get 4.

[tex]116-128c=4-156c[/tex]

Add 156c to both sides.

[tex]116 - 128c+156c=4[/tex]

Combine −128c and 156c to get 28c.

[tex]116+28c=4[/tex]

Subtract 116 from both sides.

[tex]28c=4-116[/tex]

Subtract 116 from 4 to get −112.

[tex]28c=-112[/tex]

Divide both sides by 28.

[tex]c=\frac{-112}{28}[/tex]

Answer:

(f o g)(x) = [tex]\frac{4x+13}{4x+12}[/tex]

Domain : (-∞, -3) ∪ (-3, ∞)

Step-by-step explanation:

Given : f(x) = [tex]\frac{x-4}{x-5}[/tex]

            g(x) = 4x + 17

We have to find the value of (f o g)(x).

Since (f o g)(x) = f[g(x)]

                        = [tex]\frac{(4x+17)-4}{(4x+17)-5}[/tex]

                        = [tex]\frac{4x+13}{4x+12}[/tex]

For the Domain of the function (f o g)(x),

Given function is defined for (4x + 12) ≠ 0

4x ≠ -12

x ≠ -3

Therefore, Domain of the function will be : (-∞, -3) ∪ (-3, ∞)                    

Answer:

(a) N{A∩B} = 0

(b) N{A∪B} = 9

Step-by-step explanation:

Union of two sets: This can be defined as the sum of all the elements of the two sets without writing one element twice. it is denoted by the symbol ∪

Intersection of two sets; This is the set of elements that appears in both sets. It is denoted by the symbol ∩

From the question above,

assuming there is no repetition element in both set,

(a) The smallest number possible for N{A∩B} = 0

(b) The largest number possible for N{A∪B} = 4+5 = 9.

Answer:

351.48cm²

Step-by-step explanation:

Heron’s Formula

Find half the perimeter (30+30+26)/2=43

It’s the square root of each side subtracted from 43, multiplied together, times 43.

√(43-30)*(43-30)*(43-26)*43=√13*13*17*43=√=123539=351.481cm²

Area of triangle is, 351. 39 cm²

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

All the sides of triangles are,

⇒ 30 cm, 30 cm, and 26 cm

We know that;

⇒ Area of triangle = √ s (s - a) (s - b) (s - c)

Where, 's' is the semi perimeter of the triangle, and a, b and c are three sides of triangle.

Here, Sides are,

⇒ a = 30

⇒ b = 30

⇒ c = 26

Hence, We get;

⇒ s = (a + b + c) / 2

⇒ s = (30 + 30 + 26) / 2

⇒ s = 86 / 2

⇒ s = 43 cm

So, The area of triangle is,

⇒ Area of triangle = √ s (s - a) (s - b) (s - c)

⇒ Area of triangle = √ 43 (43 - 30) (43 - 30) (43 - 26)

⇒ Area of triangle = √ 43 × 13 × 13 × 17

⇒ Area of triangle = 13 √ 731

⇒ Area of triangle = 13 × 27.03

⇒ Area of triangle = 351. 39 cm²

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ2

Answer:

Step-by-step explanation:

5

Answer:

Hey, you don't include any points, but I can give you the rule for an 180 degree rotation.

You just need to write the same points, but negative. So going from (x,y) to

(-x,-y).

As an example let's say you wanted to rotate (3,-4) 180 degrees about the origin. The the point after the rotation would be (-3,4).

Hope that helps!

Answer:

[tex]\Large \boxed{\mathrm{The \ sum \ of \ a \ number \ and \ three \ quarters \ is \ five.}}[/tex]

Step-by-step explanation:

x + 3/4 = 5

x is the unknown number.

3/4 is added to the number.

The result is 5.

The verbal sentence to represent the equation would be:

The sum of a number and three quarters is five.

Answer:

4a - 15

100% representate the original cost of tikets,

100% = 100/100 = 1

12% discont:

12% = 12/100 = 0.12

1 - 0.12 = 0.88

0.88

then the expressión is:

4*0,88d

=3.52 d

d = original cost of each ticket

Answer:

n = -1

Step-by-step explanation:

1 - 8n - 8 = -7n - 6n - 12

Simplify

-8n - 7 = -13n - 12

Add 7 to both sides

-8n = -13n - 5

Add 13n to both sides

5n = -5

Divide both sides by 5

n = -1

Answer:

n = 1

Step-by-step explanation:

1 - 8n - 8 = -7n - 6n - 12

-8n + 7n + 6n = -12 + 8 - 1

5n = -5

n = -5/5

n = -1

probe:

1 - 8*-1 - 8 = -7*-1 - 6*-1 - 12

1 + 8 - 8 = 7 + 6 - 12 = 1

Answer:

Associative Property of Addition

Step-by-step explanation:

The associative property of addition states that if all the operations are addition, then one can group and add them in whatever order they prefer.

Hope this helps!  Tell me if I'm wrong!

Answer:

1 + 5x

Step-by-step explanation:

Like terms are terms with the same variable parts.

Let's look at each term:

3    it has no variable

5x    it has the variable x

-2    it has no variable

The terms 3 and -2 have no variables, so their variable parts are the same. They are like terms and can be combined. The term 5x has the variable part x. There is no other term with the same variable part as 5x, so 5x cannot be combined with anything.

3 + 5x - 2 =

= 3 - 2 + 5x

= 1 + 5x

Answer:

10

Step-by-step explanation:

Answer:

10 shoes

Step-by-step explanation:

Step 1: State what is known

Giles has 10 socks for every 5 pairs of shoes

He has 20 socks

Step 2: Set up the ratio

Let 'x' represent how much shoes Giles has

10 socks : 5 shoes

20 socks : x shoes

Step 3: Convert ratio into fraction

[tex]\frac{Socks}{Shoes}[/tex]

10 socks : 5 shoes = [tex]\frac{10}{5}[/tex]

20 socks : x shoes = [tex]\frac{20}{x}[/tex]

Step 4: Set ratio equal to each other and solve

[tex]\frac{10}{5}=\frac{20}{x}\\ 10x = 100\\\frac{10x}{10}=\frac{100}{10}\\x = 10[/tex]

Therefore Giles has 10 shoes when he has 20 socks

Answer:

-9 >= x

Step-by-step explanation:

5x + 1 <= 3x - 17

add 17 to both sides- that will cancel the one on the right side. And on left side it would add to 18

5x + 18 <= 3x

then subtract 5x from both sides- that will cancel the one on left side. And on the right side ur left with negative 2x

18 <= -2x

divide both sides by negative 2... since dividing by -2 u have to slip the inequality sign.

-9 => x

hi

5x+1 ≤ 3x-17

5x-3x≤ -17 -1

2x≤ -18

x≤  -18/2

x≤ -9

solutions :  x ∈ ] -∞; -9]

Answer:

Domain: [0, 12.75]

Range: [0, 590.9]

Step-by-step explanation:

Your function is missing variables.

I think you mean

h(t) = -4.922t^2 + 17.69t + 575

as the function.

We can find the time the object hits the ground. At that time, h(t) = 0, so we set the equation equal to zero and solve for t.

-4.922t^2 + 17.69t + 575 = 0

[tex] t = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

[tex] t = \dfrac{-17.69 \pm \sqrt{(-17.69)^2 - 4(-4.922)(575)}}{2(-4.922)} [/tex]

[tex] t = \dfrac{-17.69 \pm \sqrt{11633.54}}{-9.844} [/tex]

t = -9.16 s or t = 12.75 s

According to the parabola that is the path of the falling object, the object is at zero height at t = -9.16 s and t = 12.75 s. Since the object starts moving at time t = 0, the domain has to be limited to t = 0 till t = 12.75 s.

Domain: [0, 12.75]

The range is the height of the object. Maximum height occurs at the time that is the midpoint of the two times the parabola shows h(t) = 0.

tmax = (-9.16 + 12.75)/2 = 1.797

Now we use the time of maximum height to find the maximum height.

h(t) = -4.922t^2 + 17.69t + 575

h(tmax) = -4.922(1.797)^2 + 17.69(1.797) + 575

h(tmax) = 590.9

The maximum height is 590.9 m.

Range: [0, 590.9]

Answer:

[tex]10. \text{Opposite of a Difference} \implies \text{E. } -(8 -3m) = 3m - 8[/tex]

[tex]11. \text{Opposite of a Sum} \implies \text{A. } -[(-r) + 2p] = -(-r) -2p[/tex]

[tex]12. \text{Opposite of an Opposite} \implies \text{F. }-[-(9 - 2w)] = 9 - 2w[/tex]

[tex]13. \text{Multiplication by 0} \implies \text{B. }16d -(3d + 2)(0) = 16d - 0 = 16d[/tex]

[tex]\boxed{\text{The product of two numbers is equal to 0} \implies 0 \cdot a = 0}[/tex]

[tex]14. \text{Multiplication by -1} \implies \text{D. } -(4r + 3s) + t = (-1)(4r + 3s) + t[/tex]

[tex]15. \text{Distributive Property} \implies \text{C. } 5(2-x) = 10-5x[/tex]

Answer:

540

Step-by-step explanation:

since that the first is 14+19 and they are just adding 4+9 which is 13 so, the last is just a 3, and 1+1 is 2, plus the 1 that we have from the 13, then, you just add 1 on the Middle.

With 25+13 also you add normally, just add a 2 on the middle. And With the 3rd one add a 3 on the middle. So, with the last one, you add a 4 too.

Answer:

  no solution

Step-by-step explanation:

Divide by 4:

  3d -1 = 3d

Subtract 3d:

  -1 = 0 . . . . . . FALSE

There is no value of d that will make this be true. The equation has NO SOLUTION.

Answer:

-10 - 1 = x

Step-by-step explanation:

If you take -10 and subtract one, it makes the number go down lower because it's negative (example, 12 - 2 is -14)