A girl age is 28 years younger than her father the sum of their ages is 50 years find the ages of the girl and the father

Answer:

R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}

Select all numbers that are in the domain.

-3

-1

1

Select all numbers that are in the range.

-2

0

2

Have great day :)

Step-by-step explanation:

The -3, -1, and 1 are in the domain if the domain of the function as follows R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have domain of a function:

R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}

From the above relation, we can see:

-3 is in the domain.

-1 is in the domain.

1 is in the domain.

Thus, the -3, -1, and 1 are in the domain if the domain of the function as follows R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}

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Answer:

The reflection image of P(0, 0) after two reflections is (8,-6)

Step-by-step explanation:

step 1

Find the coordinates of point P after reflection across x=4

we know that

The distance from point P to the line x=4 is equal to 4 units

so

(0,0) -----> (4+4,0) ----> (8,0)

The reflection image of P is (8,0)

step 2

Find the coordinates of point (8,0) after reflection across y=-3

The distance from point (8,0) to the line y=-3 is equal to 3 units

so

(8,0) -----> (8,-3-3) ----> (8,-6)

Answer:

  C)  ​7×10^8/(5×10^3)

Step-by-step explanation:

In cubic inches, the volume of a bucket of sand is ...

  (π/4)(20 in)²(15 in) = 1500π in³ ≈ 5×10^3 in³

__

The volume of the warehouse is

  (250 ft)(80 ft)(20 ft) = 400,000 ft³ = 4×10^5 ft³

The conversion to cubic inches is ...

  (4×10^5 ft³)(1728 in³/ft³) = 4×1.727×10^8 in³ ≈ 7×10^8 in³

Dividing the warehouse volume by the bucket volume gives the approximate number of buckets that will fit in the warehouse:

  (7×10^8)/(5×10^3) . . . . . matches choice C

Answer:

 C)

Step-by-step explanation:

Set each side of the equation equal to y, then rearrange to standard form.

  (1/2)x -5 = y . . . left side of the equal sign

  x -10 = 2y . . . . multiply by 2

  -10 = 2y -x . . . . subtract x

__

  (1/3)x +6 = y . . . right side of the equal sign

  x +18 = 3y . . . . . multiply by 3

  18 = 3y -x . . . . . subtract x

The corresponding system of equations is ...

Evaluate the function

g(x) = 2x2 + 3x – 5 for the input values -2, 0, and 3.

This is tedious math work but necessary to sharpen your skills.

Let x = -2

g(-2) = 2(-2)^2 + 3(-2) – 5

g(-2) = 2(4) - 6 - 5

g(-2) = 8 - 11

g(-2) = -3

Now let x = 0 and repeat the process.

g(0) = 2(0)^2 + 3(0) - 5

g(0) = 0 + 0 - 5

g(0) = -5

Lastly, let x = 3.

g(3) = 2(3)^2 + 3(3) - 5

g(3) = 2(9) + 9 - 5

g(3) = 18 + 9 - 5

g(3) = 27 - 5

g(3) = 22

Did you follow through each step?

Answer:

-19

-5

-14

Step-by-step explanation:

We want to write the given function in the form ax^2 + bx + c = 0.

We foil the left side.

(2x - 1)(x + 5) =0

2x^2 + 10x - x - 5 = 0

2x^2 + 9x - 5 = 0

Can you see the value of "b"?

The b-value is the coefficient of x.

So, b = 9.

Done!

Answer:

Monomial

Step-by-step explanation:

Let's look at the edfinitions of all three options.

Monomial: A polynomial with only one term is called a monomial.

Binomial: A polynomial with two terms is called a binomial.

Trinomial: A polynomial with three terms is called a trinomial.

So, according to the definition, the given polynomial is a monomial as it has only one term -2gh ..

Answer:

D

Step-by-step explanation:

Since the shape won't change, it won't deform, nothing will happen to the interior angle.

This figure is symmetric and not deformed, so the measure of the interior angle won't change no matter how many times you rotate it.

So the interior angle would still be 135º.

Correct answer D

Answer:

the answer is D on e2020

Step-by-step explanation:

Answer:

  55 mph

Step-by-step explanation:

Let x represent Bob's speed. Then John's speed is x+10, and their respective times are found by ...

  time = distance/speed

  330/x = 390/(x+10) . . . . . . . the times are the same

  330(x +10) = 390x . . . . . . .  multiply by x(x+10)

  3300 = 60x . . . . . . . . . . . . . subtract 330x

  55 = x . . . . . . . . . . . . . . . . . . divide by the coefficient of x

Bob is driving at 55 miles per hour.

Bob is driving at a speed of 55 miles per hour.

Let's denote Bob's speed as v miles per hour. Since John is driving 10 miles per hour faster than Bob, John's speed is ( v + 10 ) miles per hour.

 The time it takes to travel a certain distance is given by the formula [tex]\( time = \frac{distance}{speed} \)[/tex]

Bob and John travel for the same amount of time, so we can set their times equal to each other:

[tex]\[ \frac{330}{v} = \frac{390}{v + 10} \][/tex]

Cross-multiplying to solve for (v), we get:

[tex]\[ 330(v + 10) = 390v \][/tex]

Expanding the left side:

[tex]\[ 330v + 3300 = 390v \][/tex]

Now, let's move all terms involving (v) to one side:

[tex]\[ 390v - 330v = 3300 \][/tex]

Simplifying, we find:

[tex]\[ 60v = 3300 \][/tex]

Dividing both sides by 60 to solve for  v :

[tex]\[ v = \frac{3300}{60} \] \[ v = 55 \][/tex]

Answer

x^3-15x^2+75x-125

Answer:

Step-by-step explanation:

You need to use synthetic division to do all of these.  The thing to remember with these is that when you start off with a certain degree polyomial, what you get on the bottom line after the division is called the depressed polynomial (NOT because it has to math all summer!) because it is a degree lesser than what you started.

a.  3I   1   3   -34   48

I'm going to do this one in its entirety so you get the idea of how to do it, then you'll be able to do it on your own.

First step is to bring down the first number after the bold line, 1.

3I   1    3    -34    48

   _____________

      1

then multiply it by the 3 and put it up under the 3.  Add those together:

3I    1    3    -34    48

           3

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

      1     6

Now I'm going to multiply the 6 by the 3 after the bold line and add:

3I    1     3     -34     48                                                                                                    

             3      18

_________________

      1      6     -16

Same process, I'm going to multiply the -16 by the 3 after the bold line and add:

3I      1      3      -34      48

                3       18     -48

___________________

        1       6      -16       0

That last zero tells me that x-3 is a factor of that polynomial, AND that the depressed polynomial is one degree lesser and those numbers there under that line represent the leading coefficients of the depressed polynomial:

[tex]x^2+6x-16=0[/tex]

Factoring that depressed polynomial will give you the remaining zeros.  Because this was originally a third degree polynomial, there are 3 zeros as solutions.  Factoring that depressed polynomial gives you the remaining zeros of x = -8 and x = 2

I am assuming that since you are doing synthetic division that you have already learned the quadratic formula.  You could use that or just "regular" factoring would do the trick on all of them.

Do the remaining problems like that one; all of them come out to a 0 as the last "number" under the line.

You got this!        

Check the picture below.

The elm is 21 m tall.

Both the triangles are the same.

To find the height, by similarity we get

17 / h = 51 / 63

h = 63 * 17 / 51 = 21

The answer is 21 m.

If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar. Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.

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Answer:

Neither

Step-by-step explanation:

step 1

Verify if the lines are parallel

we know that

If two lines are parallel, then their slopes are the same

In this problem the slope of f(x) =2/7 and the slope of g(x)=7/2

Compare

2/7≠7/2

therefore

The lines are not parallel lines

step 2

Verify if the lines are perpendicular

we know that

If two lines are perpendicular, then the product of their slopes is equal to -1

In this problem the slope of f(x) =2/7 and the slope of g(x)=7/2

Multiply

2/7*7/2=1

1≠-1

therefore

The lines are not perpendicular

Answer:

d. -4.4​

Step-by-step explanation:

We know that log (a/b) = log a - log b

Since log a = 1.2 and log b = 5.6 , we can substitute these values into the equation.

                        log (a/b)  =   1.2 - 5.6

                                       = -4.4

Answer:

The answer is d. q=10 d=28 n=14

Step-by-step explanation:

x = 30°.

The triangle drawn inside the circle is an equilateral and equiangular triangle which means that its three sides and its internal angles (that measure 60°) are equal.

To find x°:

First, we can see from the image that the tangent line to circle with arrows is formed a right angle, the angle of one side of the equilateral triangle, and the angle formed with the other side of the equilateral triangle, this three angles has to form 180° respect to the tangent line:

90° + 60° + y° = 180°

y° = 180° + 150°

y° = 30°

Second, the line in the right side of the equilateral triangle form an angle of 180°, so:

60° + z° = 180°

z° = 180° - 60°

z° = 120°

Finally, the triangle formed by this lines its internal angles are x°, y°, and z° and its sum is 180°, then:

x° + y° + z° = 180°

x° + 30° + 120° = 180°

x° + 150° = 180°

x° = 180° - 150°

x° = 30°  

14,776

/////////////////////////////////////////////////////////////

equation: 14494 + 282 = 14,776

(you convert the negative 282 to positive)

Add the highest elevation with the lowest elevation, to find the total difference. 14494 + 282 = 14,776. You convert the negative 282 to positive. The total difference in elevation between these two places is 14,776.

Answer:

B) 67

Step-by-step explanation:

Answer:

785

Step-by-step explanation:

(25 - 10)² + 10(14)(4)

= 225 + 560

= 785

[tex]|\Omega|=5\cdot9=45\\|A|=3\cdot6=18\\\\P(A)=\dfrac{18}{45}=\dfrac{2}{5}[/tex]

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$20000\\ r=rate\to 7.25\%\to \frac{7.25}{100}\dotfill &0.0725\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, fifty two times} \end{array}\dotfill &52\\ t=years\dotfill &24 \end{cases}[/tex]

[tex]\bf A=20000\left(1+\frac{0.0725}{52}\right)^{52\cdot 24}\implies A\approx 20000(1.001394)^{1248} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill A\approx 113776.1384~\hfill[/tex]

Answer:

2. 10/3.

Step-by-step explanation:

The numerator x/2 + x/ 3

= 3x/6 + 2x / 6

= 5x / 6

Now divide this by x/4

5x / 6 / x/4

= 5x/6 * 4/x .    The x's cancel so this

=  20/6

=  10/3.

1. The four subintervals are [0, 2], [2, 5], [5, 6], and [6, 7]. Their respective right endpoints are 2, 5, 6, and 7. If [tex]C(t)[/tex] denotes the change in sea level [tex]t[/tex] years after 2010, then the total sea level rise over the course of 2010 to 2017 is

[tex]\displaystyle\int_0^7C(t)\,\mathrm dt[/tex]

approximated by the Riemann sum,

[tex]C(2)(2-0)+C(5)(5-2)+C(6)(6-5)+C(7)(7-6)\approx\boxed{20\,\mathrm{mm}}[/tex]

2. The sum represents the definite integral

[tex]\boxed{\displaystyle\int_1^4\sqrt x\,\mathrm dx}[/tex]

That is, we partition the interval [1, 4] into [tex]n[/tex] subintervals, each of width [tex]\dfrac{4-1}n=\dfrac3n[/tex]. Then we sample [tex]n[/tex] points in each subinterval, where [tex]1+\dfrac{3k}n[/tex] is the point used in the [tex]k[/tex]th subinterval, then take its square root.

3. The integral is trivial:

[tex]\displaystyle\int_1^4\sqrt x\,\mathrm dx=\frac23x^{3/2}\bigg|_{x=1}^{x=4}=\boxed{\frac{14}3}[/tex]

4. Using the fundamental properties of the definite integral, we have

[tex]\displaystyle\int_1^4f(x)\,\mathrm dx=e^4-e\implies2\int_1^4f(x)\,\mathrm dx=2e^4-2e[/tex]

[tex]\displaystyle\int_1^4(2f(x)-1)\,\mathrm dx=2e^4-2e-\int_1^4\mathrm dx=\boxed{2e^4-2e-3}[/tex]

5. First note that [tex]\sec x[/tex] is undefined at [tex]x=\dfrac\pi2[/tex], so the integral is improper. Recall that [tex](\tan x)'=\sec^2x[/tex]. Then

[tex]\displaystyle\int_0^{\pi/2}\sec^2\frac xk\,\mathrm dx=\lim_{t\to\pi/2^-}\int_0^t\sec^2\frac xk\,\mathrm dx[/tex]

[tex]=\displaystyle\lim_{t\to\pi/2^-}k\tan\frac xk\bigg|_{x=0}^{x=t}[/tex]

[tex]=\displaystyle k\lim_{t\to\pi/2^-}\tan\frac tk[/tex]

[tex]=k\tan\dfrac\pi{2k}[/tex]

Now,

[tex]k\tan\dfrac\pi{2k}=k\implies\tan\dfrac\pi{2k}=1[/tex]

[tex]\implies\dfrac\pi{2k}=\dfrac\pi4+n\pi[/tex]

[tex]\implies k=\dfrac2{1+4n}[/tex]

where [tex]n[/tex] is any integer.

Answer:

72* 62* & 60* 30* triangles

Step-by-step explanation:

I just remember rhombuses being made with 60 degree triangles from all the examples I did. This may be wrong though. But 90 percent confident lol.

Answer: the triangles marked 75 degrees and 45 degrees

Step-by-step explanation:

A rhombus has equal opposite obtuse angles with equal acute angles.

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=60\pi \end{cases}\implies 60\pi =2\pi r\implies \cfrac{\stackrel{30}{~~\begin{matrix} 60\pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} }{~~\begin{matrix} 2\pi\\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }=r\implies 30=r \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} r=30\\ \theta =140 \end{cases}\implies s=\cfrac{\pi (140)(30)}{180}\implies s=\cfrac{70\pi }{3} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill s\approx 73.30~\hfill[/tex]

Hello! :D

Answer:

[tex]\boxed{m=18}\checkmark[/tex]

*The answer should have a positive sign.*

Step-by-step explanation:

First, you do is switch sides.

[tex]\frac{m}{2}-7=2[/tex]

Then, you add by 7 from both sides.

[tex]\frac{m}{2}-7+7=2+7[/tex]

Add numbers from left to right.

[tex]2+7=9[/tex]

[tex]\frac{m}{2}=9[/tex]

Multiply by 2 from both sides.

[tex]\frac{2m}{2}=9*2[/tex]

Finally, multiply numbers from left to right.

[tex]9*2=18[/tex]

m=18 is the correct answer.

I hope this helps you!

Have a wonderful day! :)

:D

-Charlie

Thanks!

Answer:

m= 18

Step-by-step explanation:

Move all terms not containing "m" to the right side of the equation.

m/2 - 7= 2

Add +7 to each side.

m/2 - 7 = 2

       +7   +7

Add 2 and 7.

m/2= 9

Multiply both sides of the equation by 2

m= 9 (2)

Simplify.

m= 18

Answer:

(5,3)

Step-by-step explanation:

Look for the coordinates of the point of intersection where the 2 graphs cross. This gives the solution.

In this case, they cross at (5,3) and they intersect at only one location (i.e there is only 1 solution)

From the graph, the intersecting point will be (5, 3). Then the correct option is D.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

In a diagram, the two lines are shown.

The lines are intersecting at a point.

From the graph, the intersecting point will be (5, 3).

Then the correct option is D.

The graph is given below.

More about the linear system link is given below.

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Answer:

D. -5

Step-by-step explanation:

The denominator of the quotient is x+5. When the denominator is zero, the quotient is undefined. The denominator will be zero when x=-5.

Answer:

r = 6.40 feet

Step-by-step explanation:

Given line AB is tangent to circle O at point A, this means ∡OAB = 90°

Hence this is a right angle triangle and we can use the Pythagorean theorem.

r² + 20² = 21²

r²  = 21² - 20²

r²  = 441 - 400

r²  = 41

r  = √41 = 6.40 feet

The radius of the tank is = 6.4ft

The radius of the circle can be calculated using the Pythagorean theorem since a distance in of AB and OB where given.

The formula c²= b²+a²

Where b²= AB = 20ft

a²= AO= r

c² = OB = 21ft

Make a² the subject of formula

a² = c²-b²

= 21² - 20²

= 441-400

= 41

a= √41

a= 6.4ft

Therefore, the radius of the tank is = 6.4ft

Learn more about radius of circle here:

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