A 52 year-old father has a son and a daughter. The son is twice as old as the daughter. In 4 years the sum of all their ages will be 100. How old are the two siblings now?

For this case we have the following system of equations:

[tex]4x + 5y = -4\\4x + 3y = 12[/tex]

We multiply the second equation by -1:

[tex]-4x-3y = -12[/tex]

We add the equations:

[tex]4x-4x + 5y-3y = -4-12\\5y-3y = -4-12\\2y = -16\\y = \frac {-16} {2}\\y = -8[/tex]

We find the value of "x":

[tex]4x = 12-3y\\x = \frac {12-3y} {4}\\x = \frac {12-3 (-8)} {4}\\x = \frac {12 + 24} {4}\\x = \frac {36} {4}\\x = 9[/tex]

Thus, the solution of the system is given by:

[tex](x, y) :( 9, -8)[/tex]

ANswer:

(9, -8)

Answer:

x = 9 and y = -8

Step-by-step explanation:

It is given that,

4x + 5y = -4     ----(1)

4x + 3y = 12    -----(2)

To find the value of x and y

eq (1) - eq (2) ⇒

4x + 5y = -4     ----(1)

4x + 3y = 12    -----(2)

  0 + 2y = -16

y = -16/2 = -8

Substitute the value of y in eq (1)

4x + 5y = -4     ----(1)

4x + 5*-8 = -4

4x - 40 = -4

4x = -4 + 40 = 36

x = 36/4 = 9

x = 9 and y = -8

Answer:

Logically, the answer is the sphere, as it is the figure which gives maximum volume for the same total surface area. But I'll just solve them like you want it.

I'm just writing the numerical values without the units.Please resolve

Solid 1: Square Prism with each side of the base equal to 8 in. and a height of 8 in.

Volume = 8^3 = 512

Area = 8^2 * 6 = 384

V/A Ratio = 1.33 (We need the highest ratio, that's why they hired us)

Cost = $7.68

Solid 2: Square Pyramid with each side of the base equal to 10 in. and a height of 15 in.

Volume = 1/3 * 10^2 * 15 = 500

Slant height = [(10/2)^2 + 15^2]^(1/2) = root of 250 = 15.81

Area = 2*10*15.81 + 10^2 = 416.23

V/A Ratio = 1.20

Cost = $8.34

Solid 3: Cylinder with a radius of 4 in. and a height of 10 in.

Volume = pi*4*4*10 = 502.65

Area = 2*pi*4*4 + 2*pi*4*10 = 351.86

V/A Ratio = 1.43

Cost = $7.04

Solid 4: Cone with a radius of 7 in. and a height of 10 in.

Volume = (1/3)*pi*7*7*10 = 513.13

Slant height = [(7^2)+(10^2)]^(1/2) = 12.21

Area = pi*7*12.21 + pi*7*7 = 422.37

V/A Ratio = 1.21

Cost = $8.45

Solid 5: Sphere with a radius of 5 in.

Volume = (4/3)*pi*(5^3) = 523.60

Area = 4*pi*(r^2) = 314.16

V/A Ratio = 1.67

Cost = $6.28

Hence, Solid 5 must be the packaging model opted for

Step-by-step explanation:

Logically, the answer is the sphere, as it is the figure which gives maximum volume for the same total surface area. But I'll just solve them like you want it.

I'm just writing the numerical values without the units.Please resolve

Solid 1: Square Prism with each side of the base equal to 8 in. and a height of 8 in.

Volume = 8^3 = 512

Area = 8^2 * 6 = 384

V/A Ratio = 1.33 (We need the highest ratio, that's why they hired us)

Cost = $7.68

Solid 2: Square Pyramid with each side of the base equal to 10 in. and a height of 15 in.

Volume = 1/3 * 10^2 * 15 = 500

Slant height = [(10/2)^2 + 15^2]^(1/2) = root of 250 = 15.81

Area = 2*10*15.81 + 10^2 = 416.23

V/A Ratio = 1.20

Cost = $8.34

Solid 3: Cylinder with a radius of 4 in. and a height of 10 in.

Volume = pi*4*4*10 = 502.65

Area = 2*pi*4*4 + 2*pi*4*10 = 351.86

V/A Ratio = 1.43

Cost = $7.04

Solid 4: Cone with a radius of 7 in. and a height of 10 in.

Volume = (1/3)*pi*7*7*10 = 513.13

Slant height = [(7^2)+(10^2)]^(1/2) = 12.21

Area = pi*7*12.21 + pi*7*7 = 422.37

V/A Ratio = 1.21

Cost = $8.45

Solid 5: Sphere with a radius of 5 in.

Volume = (4/3)*pi*(5^3) = 523.60

Area = 4*pi*(r^2) = 314.16

V/A Ratio = 1.67

Cost = $6.28

Hence, Solid 5 must be the packaging model opted for

The slope is 5/3.hope this helps

Answer:

slope = [tex]\frac{5}{3}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, 5)

m = [tex]\frac{5-0}{0+3}[/tex] = [tex]\frac{5}{3}[/tex]

The answer is B)13

The rest of these words are to reach the minimum 20 words of an answer lol

[tex]\bf 2sin(\theta )cos(\theta )+\sqrt{3}cos(\theta )=0\implies \stackrel{\textit{common factor}}{cos(\theta )[2sin(\theta )+\sqrt{3}]=0} \\\\[-0.35em] ~\dotfill\\\\ cos(\theta )=0\implies \theta =cos^{-1}(0)\implies \theta = \begin{cases} \frac{\pi }{2}\\\\ \frac{3\pi }{2} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf 2sin(\theta )+\sqrt{3}=\implies 2sin(\theta )=-\sqrt{3}\implies sin(\theta )=-\cfrac{\sqrt{3}}{2} \\\\\\ \theta =sin^{-1}\left( -\cfrac{\sqrt{3}}{2} \right)\implies \theta= \begin{cases} \frac{4\pi }{3}\\\\ \frac{5\pi }{3} \end{cases}[/tex]

Step-by-step answer:

Given equation:

2sin(theta)cos(theta) + sqrt(3)*cos(theta) = 0  ...........................(1)

Solve for theta for 0<=theta<=2pi.

Factor out cos(theta), we get

cos(theta) * ( 2sin(theta) + sqrt(3) ) = 0

By the zero product theorem, we can conclude

cos(theta) = 0   ...................................(2)

OR  

2sin(theta) + sqrt(3) = 0  ................. (3)

Solving (2)

cos(theta) = 0 has solutions pi/2 or 3pi/2  from the cosing curve.

Solving (3)

2sin(theta) + sqrt(3) = 0  =>

sin(theta) = -sqrt(3)/2

which has solutions  4pi/3 or 5pi/3.

So the solutions to equation (1) are

S={pi/2,  4pi/3, 3pi/2, 5pi/3}

you have to calculate the SID number and then take it upon yourself and divided X it's actual number and then there's a chance and the answer would be c.72

Answer:

  To cancel a term, it is necessary to add the opposite of the term to both sides of the equation

Step-by-step explanation:

Adding opposites creates a sum of zero. Zero added to anything else does not change the its value. So, adding the opposite of a term effectively removes it from (that side of) the equation.

Answer:

2π/3 cm

Step-by-step explanation:

The formula for arc length is s = rФ, where Ф is the central angle in radians.

Thus, we must convert 30° into radians:  that'd be π/6 rad.

Then the arc length here is s = rФ = (4 cm)(π/6 rad) = 2π/3 cm

Answer

The solution for the two system of equations is (-4,2)

Explanation

Equation for slope-intercept

The equation for slope-intercept form is y = mx + b

-mx represents the slope of the equation

-b represents the y-intercept

Determine the slope and the y-intercept

The slope of the two equations can be found based on what the number in front of the x is, this term is also called the coefficient.

The y-intercept is in the form of b and is substituted normally by a positive or negative integer.

Slope: 1/4 and 2

Y-intercept: 3 and 10

You must graph these, for this problem I have provided one for you.

Determining the solution

Since this problem requires you to find the solution based on the graph you must graph the two lines and the solution is the point in which the two lines intersect.

Based on the graph I have provided for you, we can determine that the solution is (-4,2)

Checking your work

In math it's very important to check your work: plug in the solution and if it is a perfect math then the solution is correct.

[tex]\frac{1}{4} (-4)+ 3 = 2[/tex]

The solution applies to the first equation, however we must now check for the second equation.

[tex]2(-4) + 10 = 2[/tex]

The solution also applies to the second equation, so we now know that this solution is correct.

System A --> B

Equation A1 and B1 the same, but B2 changes. The change is that the whole equation is multiplied by 4. So, the answer is B and 4 goes in the blank

System B --> C

Equation B1 and C1 are the same, but C2 changes. This change is not multiplication, so our only option now is C. In C2, the x-factor is removed, which means that elimination occurred. -12/-3 = 4, so in the blank, 4 goes in.

Answer:

The volume of the pyramid is 128 cm³

Step-by-step explanation:

* Lets revise the volume of the pyramid

- The pyramid has one base and the number of side faces depends

 on the number of sides of the base

- The volume of any pyramid is 1/3 × Area of its base × its height

* Lets solve the problem

- The pyramid has a square base

- It has four side faces all of them are triangles

- It has five vertices and eight edges

- The area of the base = s², where s is the length of the side of

  the square

- The volume of the pyramid is 1/3 × s² × h, where h is the height

 of the pyramid

- The base edge length of the base is 2 cm longer than the height

 of the pyramid

- The height of the pyramid is 6 cm

∵ The length of the edge of the base is 2 cm longer than the

   height of the pyramid

∵ The height of the pyramid (h) = 6 cm

∴ The edge length of the base = 6 + 2 = 8 cm

- The area of the base = s²

∵ s = 8 cm

∴ The area of the base (s²) = 8² = 64 cm²

- The volume of the pyramid = 1/3 × s² × h

∴ Its volume = 1/3 × 64 × 6 = 128 cm³

* The volume of the pyramid is 128 cm³

The correct answer is:

128 cm^3

Hope this helps

Answer:

If you need any further help, feel free to let me know

Step-by-step explanation:

The answers are

(8-9)-(9+3)*5=-61

5+(5+5+6)+9=30

(5/3-3)= -4 over 3 or -4/3 or -1.3 or -1 1/3 depends on what your choices are but all those are correct

2*3+(4*2)/2=10

Answer:

7√2 / 2

Step-by-step explanation:

An isosceles right triangle is also known as a 45-45-90 triangle.  For such a triangle, the hypotenuse (long side) is √2 the legs.

s√2 = 7

s = 7/√2

s = 7√2 / 2

You can also show this with Pythagorean theorem.

The travel of the barnacle would be the circumference of the circle.

Circumference formula is 2 x PI x r

Circumference  = 2 x PI x 1m

= 2 x PI

If you use 3.14 for PI the circumference is 2 x 3.14 = 6.28 m.

Round the answer as needed.

25-17=8

8÷2=4

4 apples per friend.

Answer:Substitute the given values in the Law of Sines and find that the measure is 24.72°

The measure of the missing angle is approximately 113.28°.

Assuming that the missing angle is opposite to side c, we can use the Law of Sines to find the measure of the missing angle. The Law of Sines states that for any triangle ABC:

a/sin(A) = b/sin(B) = c/sin(C)

Substituting the given values, we have:

16/sin(42°) = 10/sin(B) = c/sin(C)

Solving for sin(B), we get:

sin(B) = 10*sin(42°)/16 ≈ 0.4182

Using the inverse sine function, we can find the measure of angle B:

B ≈ sin⁻¹(0.4182) ≈ 24.72°

Now, we can use the fact that the angles of a triangle add up to 180° to find the measure of the missing angle:

A + B + C = 180°

A + 42° + 24.72° = 180°

A ≈ 113.28°

Therefore, the measure of the missing angle is approximately 113.28°.

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2x - 3 = -8

    +3     + 3

2x = -5

/2    /2

x = -2.5 (Answer)

Prove.

2(-2.5) - 3 = -8

-5 - 3 = -8

-8 = -8

True.

Answer:

Answer -2.5

Step-by-step explanation:

Simple:

2x-3=-8

   +3  +3,  Add 3  on both sides of the equal sign.

2x = -5, Bring the 2x down and add the -8 + 3

2        2,  Divide by 2

x= -2.5

Hope my answer has helped you!

Answer:

12

Step-by-step explanation:

I find it convenient to use the following relation:

JL -KL +5 = JM

(x +7) -(2x -4) +5 = 3x . . . . . substituting values shown

16 -x = 3x . . . . . . . . . . . . . . . collect terms

16 = 4x . . . . . add x

4 = x . . . . . . . divide by 4

JM = 3x = 3·4 . . . . . . find the length of JM

JM = 12

Answer:

1/3

Step-by-step explanation:

This question is an application of binomial distribution model. If we consider each question as an independent trial, then for each trial there are two possible outcomes, success or failure. Success in the sense that she guesses the question correctly, and failure if the guess is wrong. Now, for each trial or question the probability of success is;

1/3

This is because each question has 3 possible answers and only 1 of them is correct.

Now if Shelly guesses on 5 multiple choice test questions in a row, the probability that she will guess the 6th question correctly is still 1/3. This is because the questions represent independent trials and the probability of success is constant in each trial just like in tossing a coin.

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

The probability isn't affected by what she guesses on the previous questions.

So basically the question is "what is the probability that Shelly will answer correctly on any one question?"

There are 3 answer choices and 1 is correct, so the probability of getting a correct answer is 1 out of 3, or, 1/3.

The graph of f(x) = [tex]2^{x+3}[/tex] is option "B" .

An exponential function is a mathematical function of the following form:

f ( x ) = [tex]a^{x}[/tex]. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.

According to the question

Represents the graph of f(x) = [tex]2^{x+3}[/tex]

f(x) = [tex]2^{x+3}[/tex] is a  exponential function

To draw the graph of f(x) = [tex]2^{x+3}[/tex]

The values will be

x                  f(x)

0                   8

1                   16

-1                   4

-2                  2

-3                  0

Hence, the graph of f(x) = [tex]2^{x+3}[/tex] is option "B" .

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The graph of the function represented by the equation f(x) = 2ˣ + 3 is (c)

From the question, we have the following parameters that can be used in our computation:

The function

Where, we have

f(x) = 2ˣ + 3

The above function is an exponential function that has been transformed as follows

Using the above as a guide, we have the following:

The graph of the function is (c)

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Answer:

f(x) = (x - 1)(x + 2)(x - 3)

Step-by-step explanation:

We are given the following function and we are to factorize it completely:

[tex] f ( x ) = x ^ 3 - 2 x ^ 2 - 5 x + 6 [/tex]

To factorize this completely, we will use the rational roots theorem.

[tex] x ^ 3 - 2 x ^ 2 - 5 x + 6 [/tex]

P = ± multiples of constant term [tex]6 = \pm1, \pm2, \pm3, \pm6[/tex]

Q = ± multiples of the coefficient of highest degree term  [tex] = \pm1[/tex]

So the factors will be [tex]\frac{P}{Q}[/tex].

The possible rational roots are [tex] 1, \pm2, \pm3, \pm6[/tex].

1 is a confirmed root and now we will use synthetic division to find the other rational roots:

1 | 1  -2  -5   6

        1   -1   -6

___________

   1   -1   -6   0    

So the polynomial will be [tex](x^2 - x - 6)[/tex] which can we factorize now.

[tex]x^2 - x - 6 = x^2 - 3x + 2x - 6[/tex]

[tex]x(x - 3) + 2(x - 3) = (x+2)(x-3)[/tex]

Therefore, the completely factorized form of the given function is f(x) = (x - 1)(x + 2)(x - 3).

Answer:

54°

Step-by-step explanation:

y is an inscribed angle.  That means that it is half the measure of the arc it intercepts.  The arc it intercepts is 108, so the angle is 54°

Check the picture below.

Answer: Option D

D. [tex]\frac{3n^{3}}{5m^{2}}[/tex]

Step-by-step explanation:

Use the following property of the exponents to simplify the expression.

We know that:

[tex]a^{-x}=\frac{1}{a^x}[/tex]

So for the expression

[tex]\frac{3m^{-2}}{5n^{-3}}[/tex]

Using the aforementioned property we have that:

[tex]\frac{3m^{-2}}{5n^{-3}}= \frac{3*\frac{1}{m^2}}{5*\frac{1}{n^3}}\\\\\\\frac{3*\frac{1}{m^2}}{5*\frac{1}{n^3}}=\frac{3n^{3}}{5m^{2}}[/tex]

Finally the answer is the option D

Answer:

The correct answer is option D

3n³/5m²

Step-by-step explanation:

Points to remember

Identities

Xᵃ * Xᵇ = X⁽ᵃ ⁺ ᵇ⁾

X⁻ᵃ = 1/Xᵃ

Xᵃ/Xᵇ = X⁽ᵃ ⁻ ᵇ⁾

To find the correct answer  

It is given that,

3m⁻²/5n⁻³

By using identities we can write,

m⁻² = 1/m²  and 1/n⁻³ = n³

3m⁻²/5n⁻³ = 3n³/5m²

Therefore the correct answer is option D.  3n³/5m²

ANSWER

A. 15 units^2

EXPLANATION

The area of kite is half the product of the diagonals.

The first diagonal has vertices at,

T(0,0) and R(5,5).

The length of this diagonal is

[tex]TR = \sqrt{ {5}^{2} + {5}^{2} } [/tex]

[tex]TR = \sqrt{25 + 25} [/tex]

[tex]TR = \sqrt{50} =5 \sqrt{2} [/tex]

The other diagonal has vertices at;

Q(0,3) and S(3,0).

The length of this diagonal is

[tex]QS = \sqrt{ {3}^{2} + {3}^{2} } [/tex]

[tex]QS = \sqrt{ 9+ 9 } [/tex]

[tex]QS = \sqrt{18} = 3 \sqrt{2} [/tex]

The area of the kite is

[tex] = \frac{1}{2} \times 3 \sqrt{2} \times 5 \sqrt{2} [/tex]

[tex] = 15 \: {units}^{2} [/tex]

Answer:

Row B. J becomes (-2,-3), K becomes (-2,-5), and L becomes (1,-5)

The correct answer is B.

The coordinates of the triangle are ...

J = (-5, -1)

K = (-5, -3)

L = (-2, -3)

All you have to do is add 3 to all of the x's of the coords

And subtract 2 from all of the y's of the coords

The expression x + 7 will determine how many cats Staci has.

Since Staci has 7 more cats than Taylor (x), we know the expression uses addition.

Answer:

D

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 1) and (x₂, y₂ ) = (1, - 2)

m = [tex]\frac{-2-1}{1+3}[/tex] = [tex]\frac{-3}{4}[/tex] = - [tex]\frac{3}{4}[/tex]

The slope of the line containing points  (-3, 1) and (1 ,-2) is Option (D) -3/4

The slope of a straight line gives the measure of its steepness and direction. It represents how steep a line can be.

The slope (m) of a straight line from two given points can be found by the formula,

Slope = m = (y2 - y1)/(x2 - x1)

where x1,x2 are the respective x-coordinates of the given points.

and y1,y2 are the respective y-coordinates of the given points .

By the problem, x1 = -3 , x2 = 1 , y1 = 1 , y2 = -2

Slope, m = (-2 -1)/(1 - (-3)) = -3/4

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Answer:

46

Step-by-step explanation:

You need to replace i with 2,3,4,5.

i=2, 6+1

3, 9+1

4, 12+1

5, 15+1

sum=46

Answer:  B) 46

Step-by-step explanation:

The summation of 3i + 1 from i = 2 to i = 5 can be calculated by finding the value of each term and then adding them up ... or.... using the formula:

i = 2: 3(2) + 1 = 7

i = 3: 3(3) + 1 = 10

i = 4: 3(4) + 1 = 13

i = 5: 3(5) + 1 = 16

       TOTAL = 46

[tex]\text{Equation: }\dfrac{a_1+a_5}{2}\times n\\\\.\qquad =\dfrac{7+16}{2}\times 4\\\\.\qquad =23\times 2\\\\.\qquad =46[/tex]

Answer:

Step-by-step explanation:

There are various guidelines that one is supposed to follow when estimating affordable rent.  For example, "rent must not exceed 40%" of one's monthly salary.  You don't mention a percentage (do that next time, please), but I will use 40% as an example.

If Gavin's gross biweekly salary is $1,120, 40% of that is

0.40($1,120) = $448 biweekly.

In this example, Gavin can afford to spend no more than $448 biweekly on rent.

4x-3(x-2)=21

4x-3x+6=21

4x-3x=21-6

x=15

is this right? let's check

4(15)-3(15-2) = 21? yes

For this case we have the following expression, we must find the value of the variable "x":

[tex]4x-3 (x-2) = 21[/tex]

We apply distributive property to the terms of the parenthesis taking into account that:

[tex]- * + = -\\- * - = +\\4x-3x + 6 = 21[/tex]

We add similar terms:

[tex]x + 6 = 21[/tex]

We subtract 6 on both sides of the equation:

[tex]x = 21-6\\x = 15[/tex]

Now, the value of x is 15

Answer:

[tex]x = 15[/tex]