Five years ago, Victor was twice as old as his daughter Anika. In 10 years, the sum of their ages will equal 90. Find their ages now.

Answer:

(r - c)(4), is the profit made in George's new store after 4 months which is $4,500

Step-by-step explanation:

The given parameters for George's store are;

The amount of revenue George makes each month, r(x) = x² + 6·x + 10

The expenses each month, c(x) = x² - 4·x + 5

Where;

x = The number of months the store has opened the doors

r(x) and c(x) are measured in hundreds of dollars

The amount of profit from the store, P = Revenue - Expenses

Therefore, the profit made on a given month, x, is P(x), which is found as follows;

P(x) = r(x) - c(x) = (r - c)(x)

Therefore, (r - c)(4) = P(4), is the profit realized from George's new store, after 4 months

(r - c)(4) = 4² + 6·4 + 10 - (4² - 4·4 + 5) = 45

Answer:

The new store will have a profit of $4500 after its fourth month in business.

Step-by-step explanation:

I took the quiz

Answer:

180m cubed

Step-by-step explanation:

Multiply the length, width, and height together: 6×6×5=180

Answer:

Formula of a rectangular prism:

L x W x H

Now we place in the numbers and solve:

5 x 6 x 6 = 180 m3

Answer: -3x+y=-4

Step-by-step explanation:

Standard form is Ax+By=C. In y=Mx+b form, it would be y=3x-4. To put it into standard form you subtract 3x from both sides. So then you have -3x+y=-4.

Answer:

Step-by-step explanation:

Use this formula:

[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex] where A(t) is the amount after the compounding is done, P is the initial investment (our unknown), r is the interest rate in decimal form, n is the number of compoundings per year, and t is the time in years. Filling in:

[tex]520=P(1+\frac{.03}{12})^{(12)(3)}[/tex] and simplifying that a bit:

[tex]520=P(1+.0025)^{36[/tex] and a bit more:

[tex]520=P(1.0025)^{36[/tex] and even  bit more:

520 = P(1.094551401) and divide to get

P = $475.30

Answer:

⊥

Step-by-step explanation:

d and b meet at a 90 degree angle ( as shown by the box)

The lines are perpendicular (⊥)

Answer:

14

Step-by-step explanation: B is the midpoint of AC, in other words it is the halfway point.

So A to B should be equal to B to C

Our expression is:

2x + 9 = 37

Subtract 9

2x = 28

Divide by 2

x = 14

Answer:

because they are both in the circle

Step-by-step explanation:

Answer:

common difference = 4

Step-by-step explanation:

common difference is the difference between the successive term and its preceding term.

let's take the successive term of -20 that is - 16

common difference (d) = successive term - preceeding term

= -16 -(-20)

= -16 + 20

= 4

if we take the successive term of -16 that is -12

we'll get the same common difference.

d = -12 -(-16)

d = -12 + 16

d = 4

this means that the common difference for an AP remains constant.

Answer:

just add a small amount to the 2.8 and square the result

Step-by-step explanation:

x x^2

2.8 7.84

2.81 7.8961

2.82 7.9524

2.83 8.0089

2.84 8.0656

2.85 8.1225

2.86 8.1796

2.87 8.2369

Answer:

D. Closed circle on 8, shading to the right.

Answer:

20

Step-by-step explanation:

Multiply 4/7 with 35, this will get you 140/7, which simplifies to 20 employees

Answer:

D

Step-by-step explanation:

[tex]f(x)=\frac{1}{x+5} -1\\let~f(x)=y\\y=\frac{1}{x+5} -1\\flip~x~and~y\\x=\frac{1}{y+5} -1\\x+1=\frac{1}{y+5} \\y+5=\frac{1}{x+1} \\y=\frac{1}{x+1} -5\\f^{-1}(x)=\frac{1}{x+1} -5\\x+1\neq 0\\x\neq -1[/tex]

Answer:

700 parts

Step-by-step explanation:

To find the total amount of parts in the shipment, all we need to do is divide.

6% = 0.06

42 / 0.06 = 700

Best of Luck!

Answer:

The speed is 20.8  m/s

Step-by-step explanation:

If a projectile ascends vertically, and after 3 seconds it reaches its maximum height, calculate the velocity that it carries to the middle of its downward trajectory

Let the maximum height is h and initial velocity is u.

From first equation of motion

v = u + at

0 = u - g x 3

u = 3 g.....(1)

Use third equation of motion

[tex]v^2 = u^2 - 2 gh \\\\0 = 9 g^2 - 2 gh \\\\h = 4.5 g[/tex]

Let the speed at half the height is v'.

[tex]v^2 = u^2 + 2 gh \\\\v'^2 = 0 + 2 g\times 2.25 g\\\\v'^2 = 4.5\times 9.8\times9.8\\\\v' = 20.8 m/s[/tex]

Answer:  2 distinct complex solutions (ie non real solutions).

Work Shown:

The given equation is in the form ax^2+bx+c = 0, so

a = 1, b = 3, c = 8

Plug those into the formula below to find the discriminant

D = b^2 - 4ac

D = 3^2 - 4(1)(8)

D = -23

The discriminant is negative, so we get two nonreal solutions. The two solutions are complex numbers in the form a+bi, where a & b are real numbers and [tex]i = \sqrt{-1}[/tex]. The two solutions are different from one another.

Answer:

Discriminant: -23

Number of real roots: 0

Step-by-step explanation:

For a quadratic in standard form [tex]ax^2+bx+c[/tex], the discriminant is given by [tex]b^2-4ac[/tex].

In [tex]x^2+3x+8[/tex], assign:

The discriminant is therefore:

[tex]3^2-4(1)(8)=9-32=\boxed{-23}[/tex]

For any quadratic:

Since the quadratic in the question has a discriminant less than 0, there are no real solutions to this quadratic.

Answer:

8/10

Step-by-step explanation:

Answer:

6 + 12/13, or 90/13 people will be served

Step-by-step explanation:

Ratios stay the same, no matter the quantity.

Given this, we can say that (13 grapes / 3 people) = (30 grapes / x amount of people)

13/3 = 30 / x

multiply both sides by 3 to remove a denominator

13 = 30 * 3 /x

multiply both sides by x to remove the other denonimator

13 * x = 30 * 3

13 * x = 90

divide both sides by 13 to isolate the x

x = 90/13 = 6 + 12/13 ≈6.92 people

Answer:

Option B

<F = 26°

<D = 64.01°

FD = 89

Answered by GAUTHMATH

For right triangle EFD,  m ∠F ≈ 26°, m ∠D ≈ 64.01° and FD = 89

The correct answer is an option (B)

It is the longest side of the right triangle.

For a right triangle,

[tex]a^{2}+ b^{2} = c^{2}[/tex], where c is hypotenuse and a, b area other two sides of the right triangle

For given example,

We have been given a right triangle EFD with hypotenuse FD.

Also, EF = 80, ED = 39

Using the Pythagoras theorem,

[tex]\Rightarrow FD^{2}= EF^{2} + ED^{2}\\\\ \Rightarrow FD^{2}= 80^{2} + 39^{2}\\\\ \Rightarrow FD^2 = 6400 + 1521\\\\ \Rightarrow FD^2 = 7921\\\\\Rightarrow FD = 89[/tex]

Consider, sin(F)

[tex]\Rightarrow sin(F)=\frac{ED}{FD} \\\\\Rightarrow sin(F)=\frac{39}{89}\\\\ \Rightarrow sin(F)=0.4382\\\\\Rightarrow \angle F=sin^{-1}(0.4382)\\\\\Rightarrow \angle F=25.98^{\circ}\\\\\Rightarrow \angle F\approx 26^{\circ}[/tex]

Now, consider sin(D)

[tex]\Rightarrow sin(D)=\frac{FE}{FD}\\\\ \Rightarrow sin(D)=\frac{80}{89}\\\\ \Rightarrow \angle D = sin^{-1}(0.8988)\\\\\Rightarrow \angle D = 64.009^{\circ}\\\\\Rightarrow \angle D \approx 64.01^{\circ}[/tex]

Therefore, for right triangle EFD,  m ∠F ≈ 26°, m ∠D ≈ 64.01° and FD = 89

The correct answer is an option (B)

Learn more about Pythagoras theorem here:

https://brainly.com/question/343682

#SPJ2

Answer:

x = 4

Step-by-step explanation:

The line DE is parallel to AC and divides the sides proportionally, that is

[tex]\frac{BD}{AD}[/tex] = [tex]\frac{BE}{CE}[/tex] , substitute values

[tex]\frac{x+2}{x}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )

3x = 2(x + 2) = 2x + 4 ( subtract 2x from both sides )

x = 4

Answer:

the sin of 28 degree is 28

Step-by-step explanation:

it's the same degree in radians I hope this help

Complete question is;

A soccer ball was kicked through the air and it followed the path. Let h(s) = −3s² +75 represent the height of the soccer ball after s seconds.

Find the time at which the soccer ball hits the ground.

Answer:

s = 5 seconds.

Step-by-step explanation:

We are given the function;

h(s) = −3s² +75

Where;

h(s) is height at time s

s is the time taken

Now, the time at which the time at which the soccer ball hits the ground would be at h(s) = 0 since height is at 0 point.

Thus;

−3s² +75 = 0

−3s² = -75

s² = 75/3

s² = 25

s = √25

s = 5 seconds.

Answer:

only the first one...

a "FUNCTION" has a UNIQUE relation between each input and output...

notice the middle one the -2 goes to BOTH th2 10 & -7 that makes it NOT a FUNCTION

Step-by-step explanation:

Answer:

seats in each bus

Step-by-step explanation:

total no.of seats = 64

so, the no.of seats in each bus = 64/2 =32

therefore ,  b denotes the no.of seats in each bus

PLEASE MARK ME AS BRAINLIEST .

Answer:

hypotenuse ≈ 44 inches

Step-by-step explanation:

Using Pythagoras' identity

The square on the hypotenuse is equal to the sum of the squares on the other two sides.

let the hypotenuse be h , then

h² = 23² + 38² = 529 + 1444 = 1973 ( take square root of both sides )

h = [tex]\sqrt{1973}[/tex] ≈ 44 inches ( to the nearest inch )

Answer:

j=|x|

Step-by-step explanation:

Answer:

hope this helps you

have a great day