Eric is 8 years 4 months old. his mother is 40 years 3 months old. how old was his mother when eric was born?

Answer:

Volume = (1/2)[tex]x^{3}[/tex]           [(1/2)x^3]

Step-by-step explanation:

The volume of a right rectangular prism is given by:

Volume = (length)*(width)*(height)

Volume = (x)*(x)*((1/2)x)

Volume = (1/2)[tex]x^{3}[/tex]

Answer:

Step-by-step explanation:

According to the first statement, "Three years ago, Dedrick's age was a third of Francisca's age":

D - 3 = (1/3) * (F - 3)

According to the second statement, "In 13 years, Francisca's age will be twice Dedrick's age":

F + 13 = 2 * (D + 13)

Now, we have a system of two equations. We can solve these equations to find their current ages.

Step 1: Solve the first equation for D in terms of F:

D - 3 = (1/3) * (F - 3)

3D - 9 = F - 3

3D = F + 6

D = (F + 6) / 3

Step 2: Substitute the expression for D into the second equation:

F + 13 = 2 * ((F + 6) / 3 + 13)

Step 3: Solve for F:

F + 13 = 2 * ((F + 6) / 3 + 13)

F + 13 = 2 * (F + 6 + 39)

F + 13 = 2 * (F + 45)

F + 13 = 2F + 90

F - 2F = 90 - 13

-F = 77

F = -77

Step 4: Find D using the expression we found earlier:

D = (F + 6) / 3

D = (-77 + 6) / 3

D = -71 / 3

Now, we have found their ages, but we encounter a problem. Both Francisca and Dedrick's ages are coming out as negative, which is not meaningful in this context. It suggests that there might be an error in the initial information provided or in the equations derived from it.

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Answer:

  b, c

Step-by-step explanation:

A function is continuous if its graph can be drawn without lifting the pencil. It is decreasing wherever its slope is negative.

__

A graph of the function is attached. It has a "jump" discontinuity at x=0, so is not a continuous function.

The value of f(0) is 2, so the y-intercept is 2.

The given function is defined for all values of x, so its domain is all real numbers.

The function is decreasing for values of x > 0, so does not approach positive infinity for large positive x.

The function has a stationary point at x=0, so is not decreasing over its entire domain.

_____

Additional comment

The function is decreasing everywhere except at x=0. The point (0, 2) is the vertex of the quadratic portion of the function, so a tangent is horizontal there. At such horizontal tangent points, a function is neither increasing nor decreasing. It is tempting to ignore this exception, because the function is decreasing everywhere else.

Answer:

y = 7+2x

Step-by-step explanation:

4x = 5 - 2y __(1)

y - 2x = 7 __(2)

From eq (2) ,

y = 7 + 2x

Hence, we can substitute (7+2x) in place of y in the first equation.

Answer:

Step by step explanation:

The problem tells us that at the end of the day, there are only 5 workers left, which we must find how many days it takes to finish said work.

We start by finding the type of proportionality we have.

In this case, we have that the more workers there are, they will finish that work in less time, and the fewer workers there are, the longer it will take to finish the work. This is the inverse proportionality, to more less, to less more.

We have only 5 workers left.

In the first case there are 10 workers, and in the second case there are 5 workers left. We find the relationship between the workers in the second case among the workers in the first case.

We see that the time is found by dividing the number of days in which the 10 workers finish the work, by 1/2.

As we know, dividing two fractions is the SAME as multiplying by the inverse fraction.

[tex]\rm 30 * 2/1 \: = 60 \: days[/tex]

By so

Answer:

Point Form:

(9,12)

Equation Form:

x = 9

y = 12

Step-by-step explanation:

Answer:

[tex]\fbox{x = 9, y = 12}[/tex]

Step-by-step explanation:

[tex]\textsf {Let's solve by substitution.}[/tex]

[tex]\rightarrow \mathsf {-5x + 4y = 3}\\\rightarrow \mathsf {x = 2y - 15}[/tex]

[tex]\textsf {Substitute for x in the first equation of the system.}[/tex]

[tex]\implies \mathsf {-5(2y-15)+4y=3}[/tex]

[tex]\implies \mathsf {-10y+75+4y=3}[/tex]

[tex]\implies \mathsf {-6y=-72}[/tex]

[tex]\implies \textbf {y = 12}[/tex]

[tex]\implies \mathsf {x = 2(12) - 15}[/tex]

[tex]\implies \mathbf {x = 9}[/tex]

[tex]\textsf {The solution is : x = 9, y = 12}[/tex]

Answer:

B is correct.

Answer:

4

Step-by-step explanation:

2L=w

32=LxW

so you put the 2L as the w

which is 32=Lx2L

32=2L^2

16=L^2

4=L

*To find the width you input 4 as L*

So 8=W

The shortest side would be 4

Answer: (x+z+y)(y+z)

Step-by-step explanation:

y(x+z)+z(x+y)+y^2+z^2

Factor out y and z from the expression

= y(x+z+y)+z(x+y+z)

Factor out x + z + y from the expression

= (x+z+y)(y+z)

Answer:

1.5

Step-by-step explanation:

The average rate of change is 1.5

when x=0 , the value of y =1

when x=2 the value of y = 4

average rate of change formula = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

a= 0 , f(a)=1

b=2, f(b)= 4

4 - 1 / 2 - 0 = 3/2 = 1.5

Step-by-step explanation:

I don't know on my mommy that Is the answer

Answer:

There were 920 children and 830 adults.

Step-by-step explanation:

Let C be the number of children and A be the number of adults. Set up equations. Using the attendance of 1750 people, we can write:

c+a=1750

Using the total money collected of 9860, we can write:

3.50c+8.00a = 9860

Solve by substitution. Using (1), we solve for a to obtain (3): a=1750—c

Substutute (3) to (2) and solve for c:

3.50c + 8.00(1750 — c) = 9860

3.50e+ 14000 — 8.00c = 9860

—4.50e= —4140

c=920

Solve for a using (3):

a=1750 — 920

a=830

So, there were 920 children and 830 adults. (They better have been 6 ft apart)

The difference quotient of the expression will be 4.

f(x) = 5 + 5x + 4x²

f(3) = 5 + 5(3) + 4(3)³

= 56

Now [f(x) - f(3)]/(x - 3) will be:

= (4x² + 5x + 5 - 56)/(x - 3)

= (4x² + 5x - 51)/(x - 3)

= (4x² + 17x - 12x - 5)/(x - 3)

= (4x + 17)(x - 3)/(x - 3)

= 4x + 17

The difference quotient will be:

g(x + h) = 4(x + h) + 17

= [g(x + h) - g(x)]/h

= (4x + 4h + 17 - 4x - 17)/h

= 4h/h

= 4

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Answer:

0.4706

Step-by-step explanation:

Using trigonometric formulas we know:

[tex]sin(x) = \frac{opposite}{hypotenuse}[/tex]

Here, our opposite is the side opposite to the angle A, which in this case is the line BC which is equal to 8.

The hypotenuse is the diagonal line, which in this case is AB, and this is equal to 17.

Therefore,

[tex]sinA = \frac{8}{17} =0.4706[/tex]

Our final answer is 0.4706.

Answer:

8/17= 0.4706 is the answers for the question

Step-by-step explanation:

please mark me as brainlest

Answer:

from the image above

Triangle ABE = Triangle ADE

AE = AE ( common).

angle AEB = angle AEO ( each 90°)

AB = AD ( given).

by side angle side criteria

so area of ABE = area of ADE

similarly,

BC = DC ( given)

BEC = DEC ( 90°)

EC = EC ( 9m each)

so area of BEC = Area of DEC

Answer:

Check all of them

Step-by-step explanation:

If you are on Edg, just check all of them.

Let's take this problem step by step:

What we know:

 [tex]x+y=4\\xy=-2[/tex]

Before we solve, let's do one thing that will help us out greatly later down the road:

 [tex]x+y=4\\(x+y)^2=4^2\\x^2+2xy+y^2=16\\x^2+2(xy)+y^2=16\\x^2+2(-2)+y^2=16\\x^2+4+y^2=16\\x^2+y^2=20[/tex]<--- useful equation

Let's rearrange the problem a little bit:

 [tex]x+\frac{x^3}{y^2}+\frac{y^3}{x^2} +y=\frac{x^3}{x^2} +\frac{x^3}{y^2}+\frac{y^3}{x^2}+\frac{y^3}{y^2}[/tex]

Combine fractions of common denominators:

[tex]\frac{x^3+y^3}{x^2} +\frac{x^3+y^3}{y^2} =(x^3+y^3)*(\frac{1}{x^2}+\frac{1}{y^2} )[/tex]

Now's let factor everything apart:

 [tex](x^3+y^3)=(x+y)(x^2-xy+y^2)\\\\\frac{1}{x^2}+\frac{1}{y^2} =\frac{x^2+y^2}{x^2y^2}[/tex]

Let's use what we know and our useful equation:

 [tex](x+y)*(x^2-xy+y^2)*(\frac{x^2+y^2}{x^2y^2} )\\=4*(x^2+y^2-xy)*(\frac{20}{(xy)^2} )\\=4*(20-(-2))*\frac{20}{(-2)^2} \\=4*22*5\\=440[/tex]

The value is 440

Answer: 440

Hope that helps!

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The expression -4 (-11 + 4n) – 3(- 2n + 9) is equivalent to the expression 17 — 10n.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

⇒ -4 (-11 + 4n) – 3(- 2n + 9)

On simplifying, we have

⇒ 44 – 16n + 6n – 27

⇒ 17 — 10n

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Answer:

s = 17units

Step-by-step explanation:

For this problem, we are trying to find a specific unknown side length.

We're actually given some extraneous information (information that is not needed to solve the problem):  It isn't necessary to know that BC is 5.

If the side AD with the unknown length is part of a right triangle (the triangle in red in the attached diagram), we can use the Pythagorean Theorem to solve for AD.

It isn't clear if the diagram you were provided gives ∠ABD as a right angle,  if it only gives ∠CBD as a right angle, or if it gives both as a right angle.  Below, we prove that it doesn't matter, because regardless, both must be right angles.

Is Triangle ABD a "right triangle"?

Since B is between A and C, then the two angles ∠ABD & ∠CBD form a linear pair, and by the linear pair postulate are supplementary.  Since they are supplementary, their measures add to 180°.  Using the fact that all right angles are 90°, substitution, the subtraction property of equality, arithmetic, the measure of ∠ABD is also 90°, and thus must be a right angle.  Thus, based on the given information, both ∠ABD & ∠CBD must be right angles.

Consequently, triangle ABD is a right triangle, by definition (it is a triangle that has a right angle).

Pythagorean Theorem

Since triangle ABD is a right triangle, the Pythagorean Theorem can be applied.

The Pythagorean Theorem states that [tex]a^{2} +b^{2} =c^{2}[/tex] where "c" is the hypotenuse (the side across from the right angle) and "a" and "b" the the lengths of the two other sides (called legs) of the right triangle.  (Aside: Because of the commutative property of addition, it doesn't matter which of the two legs' lengths is used for a, and which is used for b.  The only thing that is required is that "c" be the length of the hypotenuse)

In our triangle, side AD, with unknown length "s" is the length of our hypotenuse, and sides AB and BD are the two legs.  Substituting values into the Pythagorean Theorem equation, we can solve for the unknown "s":

[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex](8)^{2} +(15)^{2} =(s)^{2}[/tex]

[tex]64 +225 =s^{2}[/tex]

[tex]289 =s^{2}[/tex]

Applying the square root property...

[tex]\pm \sqrt{289} =\sqrt{s^{2}}[/tex]

[tex]s=17 \text{ or } s=-17[/tex]

Final Solution

We discard the negative solution we obtained, since s represents the length of the side of a triangle.

s = 17units

Answer:

17

Step-by-step explanation:

Answer:

b. 66

c.56

a 0

Step-by-step explanation:

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Answer:

Kathy and Lilly

Step-by-step explanation:

Because they both are nearest to the leader distance of 5 meters

Answer:

Y + 15 = 30

Y = 30 - 15

Y = 15

15 is not equal to 20

False

Triangle ABC is similar to triangle DEC, ∠B ≅ ∠E and 3DE = 2BC

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Dilation is the increase or decrease in the size of a figure by a scale factor.

Right triangle ABC is reflected over AC, then dilated by a scale factor of 2/3 to form triangle DEC, hence:

Triangle ABC is similar to triangle DEC, corresponding angles are congruent (∠B ≅ ∠E) and DE = (2/3)BC i.e. 3DE = 2BC

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Answer: −x2+

5

x

=

7

Move

7

to the left side of the equation by subtracting it from both sides.

−

x

2

+

5

x

−

7

=

0

Once the quadratic is in standard form, the values of

a

,

b

, and

c

can be found.

a

x

2

+

b

x

+

c

Use the standard form of the equation to find

a

,

b

, and

c

for this quadratic.

a

=

−

1

,

b

=

5

,

c

=

−

7

Step-by-step explanation:

Answer:

Simplifying -16t2 + 48t + 160 = 0

Reorder the terms: 160 + 48t + -16t2 = 0

Solving 160 + 48t + -16t2 = 0 Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'. 16(10 + 3t + -1t2) = 0

Factor a trinomial. 16((5 + -1t)(2 + t)) = 0 Ignore the factor 16.

hope it helps.

Answer:

C

Step-by-step explanation:

you need to re arrange like terms

The sum of the angle 5 and angle 6 is 180 degrees. Then the correct option is C.

When two angles are said to be supplementary angles if their sum is 180 degrees.

A triangle is shown with its exterior angles.

The interior angles of the triangle are angles 2, 3, 5.

The exterior angle at angle 2 is angle 1.

The exterior angle at angle 3 is angle 4.

The exterior angle at angle 5 is angle 6.

We know that the sum of interior and exterior angle of the triangle is 180 degrees.

∠1 + ∠2 = 180°

∠3 + ∠4 = 180°

∠5 + ∠6 = 180°

Then the correct option is C.

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Answer:

Side b is approximately 4.00064cm or since the question asked for the answer to be up to one decimal point, your answer should be 4 cm

Step-by-step explanation:

First of all, this triangle isn't a right triangle. This can be proven if we assume that the triangle is a right triangle. If it is a right triangle, since, one of its angle is 30 degrees, we can find the last unknown angle to = 60 degrees. Therefore, using the side ratios of a 30-60-90 triangle, and since side b is the smallest side (because it has the smallest angle facing it), its length is one half the length of the hypotenuse, therefore making its length 4. However, the 30-60-90 ration also states that, in this case, side b * sqrt(3) should be equal to the side tha measure 7cm, which is clearly not true. Therefore, proving that this triangle isn't a rigt tirangle.

So now, let's get to solving the question. Since we found out that this isn't a right triangle, we have to use the law of cosines which states

a^2 = b^2 + c^2 - 2bc*cos(A) where A is the angle facing side a

If we do this, it comes to the solution that a is approximately 4.00064cm.

Therefore, side b measures to 4.00064cm.

ответ: д
-1/2 * 16 = -8
или 16/(-2) = -8

Answer: by rewriting equation in the form, / 1\2 16 X 4X 4 f=~1_~) (Do-2)2=g=~

Step-by-step explanation: hope this helps

Answer:

x=9

Step-by-step explanation:

Answer:

288

Step-by-step explanation:

First position choice:   4 numbers

Second                         6 numbers

Third                             6

Fourth                           6

       TOTAL 4 digit numbers   4 * 6 * 6 * 6 = 864 combos

             2 out of 6 of these will end in 3 or 5  (thus making an odd number)

                    864 * 2/6 = 288 such numbers