The ages of 3 brothers are consecutive even integers. Three times the age of the youngest brother exceeds the oldest brother's age by 48 years. What is the age of the younger brother?
A. 14
B. 18
C. 22
D. 26

Answer: C.

[tex]Mx+Ny=P\\(2M-R)x+(2N-S)y=P-2[/tex]

Step-by-step explanation:

Given: The system [tex]Mx+Ny=P\\ Rx+Sy=T[/tex] has the solution (1,3), where M,N,P,R,S and T are non zero real numbers.

A.

[tex]Mx+Ny=P\\ 7Rx+7Sy=7T[/tex]

Divide 7 on both sides on the second equation , we will get

[tex]Mx+Ny=P\\ Rx+Sy=T[/tex]

Thus, this system has solution (1,3)

B.

[tex](M+R)x+(N+S)y=P+T.......(1)\\\\ 7Rx+7Sy=7T................(2)[/tex]

Subtract equation (2) from equation (1), we get

[tex]Mx+Ny=P\\ Rx+Sy=T[/tex]

Thus, this system has solution (1,3)

C.

[tex]Mx+Ny=P...........(1)\\\\(2M-R)x+(2N-S)y=P-2T............(2)[/tex]

We can rewrite the equation (2) as

[tex]2Mx-Rx+2Ny-Sy=P-2T............(3)[/tex]

Multiply 2 on both sides of equation (1), we get

[tex]2Mx+2Ny=2P.........(4)[/tex]

Subtract equation (3) from (4), we get

[tex]Rx+Sy=P+2T[/tex]

But [tex]Rx+Sy=T[/tex]

Thus, this system does not have solution as (1,3).

D.

[tex]\frac{M}{2}+\frac{N}{2}=\frac{P}{2}\\\\Rx+Sy=T[/tex]

Multiply 2 on both sides on the first equation , we will get

[tex]Mx+Ny=P\\ Rx+Sy=T[/tex]

Thus, this system has solution (1,3)

Answer: The answer is [tex]1\dfrac{28}{99}.[/tex] .

Step-by-step explanation: The given rational number is

[tex]R=1.\bar{28}.[/tex]

We are to select the correct expression from the options  that is equivalent to the given rational number.

Let us consider that

[tex]x=1.\bar{28}\\\\\Rightarrow x=1.28\bar{28}\\\\\Rightarrow 100\times x=100\times 1.28\bar{28}\\\\\Rightarrow 100x=128.\bar{28}\\\\\Rightarrow 100x=128+.\bar{28}\\\\\Rightarrow 100x=127+x\\\\\Rightarrow 100x-x=127\\\\\Rightarrow 99x=127\\\\\Rightarrow x=\dfrac{127}{99}\\\\\Rightarrow x=1\dfrac{28}{99}.[/tex]

Thus, the correct option is [tex]1\dfrac{28}{99}.[/tex]

Variable 1: X= number of craft activities

Variable 2: Y= number of sports activities

Equation: X + Y=15

Answer:

B. Square

D. Rhombus

Step-by-step explanation:

If you take a rhombus ABCD, its all sides are congruent. Lets take E as the point where the diagonals of a rhombus meet. Now it is known fact that the point where diagonals meet, they bisect each other.

Since, for sides, AB , CD,AD and CB are congruent

For diagonals, AC = BD

As E is the bisecting point for diagonals,

AE = EC and ED = EB

Now by SSS postulate, we can prove that all four triangles formed by rhombus are congruent

ΔAED , ΔBEC , ΔEDC and ΔAEB are congruent

Now the angles

∠AED, ∠AEB, ∠CED and ∠CEB are congruent as well,

So, we know that sum of interior angles of any quadrilateral is 360°

So each angle is 360/4 = 90°

This calculation is valid for square as well.

Answer:

B and D

Step-by-step explanation:

cya

Answer:

The required form of the given expression is : (a + 4)(b + 1)

Step-by-step explanation:

The given expression is : ab + 4 + a + 4b

We need to factor he given expression and arrange the factors in the alphabetic order.

To find the factors of the given expression, we need to use the concept of algebra :

ab + 4 + a+ 4b

First rearranging the terms in order to form the factors :

= ab + 4b + 4 + a

= b(a + 4) + 1(4 + a)

= b(a + 4) + 1(a + 4)

= (b + 1)(a + 4)

Now, the factors in the alphabetic order :

= (a + 4)(b + 1)

Hence, the required form of the given expression is : (a + 4)(b + 1)

Final answer:

Square trinomials and difference of squares binomials can be rewritten into separate factors using methods such as completing the square, the difference of squares method, and factoring by grouping.

Explanation:

Completing the square method: Rewrite square trinomials by completing the square to factor them into separate factors. For example, [tex]x^2 + 6x + 9[/tex] can be written as (x + 3)(x + 3).

Difference of squares method: Rewrite binomials with a difference of squares by factoring them into separate factors. For instance, [tex]x^2 - 4[/tex] can be expressed as (x + 2)(x - 2).

Factoring by grouping: For more complex trinomials, you can use the method of factoring by grouping to rewrite them as separate factors.

A. The figure given in A is a square pyramid and the formula for the surface area of this figure is:

A = l w + l sqrt [(w/2)^2 + h^2] + w sqrt [(l/2)^2 + h^2]

where l and w are the lengths of the base and h is the height of the pyramid. Since the base is square, so:

l = w = 16 in

h = 15 in

Substituting:

A = 16 * 16 + 16 sqrt [(16/2)^2 +15^2] + 16 sqrt [(16/2)^2 + 15^2]

A = 256 + 272 + 272

A = 800 in^2

B. We are given a cone, the formula for surface area is:

A = πr (r + h^2 + r^2)

where h is the height = 8 in and r is the radius = 3 in

Substituting:

A = π * 3 (3 + sqrt (8^2 + 3^2))

A = 34.63π in^2 = 108.80 in^2 

Answer:

C: Put a point 5 units to the left of zero.

Step-by-step explanation:

To complete the square for the expression x^2 - 18x, add 81 to become a perfect square trinomial in the form (x - 9)^2.

To complete the square for the expression x^2 - 18x, we need to add a constant term to the expression in such a way that it can be factored as a perfect square trinomial. First, we take half of the coefficient of the linear term and square it:

Half of -18 is -9, and when we square it we get 81. Therefore, adding 81 to the expression gives us x^2 - 18x + 81. This can be factored as (x - 9)^2. So the value that completes the square is 81.

https://brainly.com/question/36246034

#SPJ11

Answer with explanation:

The exponential function is

 [tex]3^y=7\\\\ \text{taking log on both sides}\\\\y\log3=\log7\\\\y=\frac{\log7}{\log3}\\\\y=\log_{3}7\\\\y=\frac{0.8450}{0.477}\\\\y=1.77[/tex]

It is equation of a line, parallel to X  axis.

Drawn the graph of the function , which cuts the y axis at ,(1.77,0).

None of the curve matches with the given Options.

Answer:

Option 4th is correct

the domain of the following relation R is:

[tex]\{-3, 1, 6\}[/tex]

Step-by-step explanation:

Domain is the set of all values of x-coordinates where function is defined.

Given the Relation:

[tex]R = \{(6, -2), (1, 2), (-3, -4), (-3, 2)\}[/tex]

The ordered pairs are in the form of (x, y)

Domain = Set of all values of x.

In the given relation:

x-values = { 6, 1, -3}

⇒[tex]\text{Domain} = \{-3, 1, 6\}[/tex]

therefore, the domain of the following relation R is:

[tex]\{-3, 1, 6\}[/tex]

so use a basic formula here:

area of a circle = πr²

and the circumference of a circle = πd

a)

therefore the area of the pool cover is π multiplied by the radius² (which is the diameter of the pool cover plus the extra 12 inches divided by two, so the radius is 21/2 or 10.5) is 346.36(to two decimal places.)

b)

Using the same diameter, we can work out the length of the rope by multiplying the diameter (10.5) by π, which is 32.99 (to two decimal places).

Answer:

option C is correct

[tex]8x^5+24x^3+48x^2[/tex]

Step-by-step explanation:

As per the statement:

The length(l), width(w) and height(h) of the rectangular prism are:

l = 4x

w = 2x

[tex]h = x^3+3x+6[/tex]

We have to find volume.

Use the formula:

[tex]V = lwh[/tex]

Substitute the given values we have;

[tex]V = 4x \cdot 2x \cdot (x^2+3x+6)[/tex]

⇒[tex]V = 8x^2 \cdot (x^3+3x+6)[/tex]

Using distributive property, [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]

then;

[tex]V = 8x^5+24x^3+48x^2[/tex]

Therefore, the volume of the rectangular prism is, [tex]8x^5+24x^3+48x^2[/tex]

Answer:

[tex]x^2-4[/tex]

Step-by-step explanation:

Sally found that a solution of x = 2 was extraneous for her function.

Extraneous solution is a solution that makes the denominator 0

Possible denominator are given . LEts plug in 2 for x and check which option gives us 0

[tex]4x+8=4(2)+8= 16[/tex]  

[tex]2x+12=2(2)+12=4+12= 16[/tex]

[tex]x^2-4= (2)^2-4= 4-4=0[/tex]

[tex]x^2-16= (2)^2-16= 4-16= 12[/tex]

[tex]x^2-4[/tex] gives us 0 when we plug in 2 for x.

So x=2 was extraneous solution for [tex]x^2-4[/tex]

Linear pair Postulate. Two angles are a linear pair if the angles are adjacent and the two unshared rays form a line. Below is an example of a linear pair: The linear pair postulate states that two angles that form a linear pair are supplementary.

We will see that the exact value is √2/2 = 0.707, and the reference angle is 45°.

We know that for any angle θ we have that:

sin(θ) = sin(θ + n*360°)

Where n is an integer value.

To find the reference angle of a given angle θ, we just need to find a value of n such that:

0 ≤  θ + n*360° ≤ 360°

So we can write our angle in the normal range.

in this case, our angle is -135°

Then we can write:

0 ≤  -135° + n*360° ≤ 360°

Is immediate to notice that we must take n = 1

0 ≤  -135° + 1*360° ≤ 360°

0 ≤  -135° + 1*360° ≤ 360°

0 ≤  225° ≤ 360°

Now we know that θ = 225°.

Ok, this lies on the third quadrant, when an angle lies on the third quadrant, to get the reference angle you just need to subtract 180°.

We will get:

225° - 180° = 45°

So the reference angle is 45°.

Finally, to get the exact value we use:

sin (-135°) = sin(225°) = cos(45°) = √2/2 = 0.707

If you want to learn more about trigonometry, you can read:

https://brainly.com/question/8120556

Answer: 10, 15, 24 is your answer

Step-by-step explanation:

You are given the graph of four straight lines, P, Q, R, and S. You are asked to find which line corresponds to the function of f(x) = 4x - 3. The easiest way to answer this is to plug in the values of the coordiante points used for each graph.

f(x) = 4x - 3 = y

y = 4x - 3

for graph of line S we have the coordinates (0, -3) and (2, 5)

(0, -3)

-3 = 4(0) - 3

-3 = -3

(2,5)

5 = 4(2) - 3

5 = 8 - 3

5 = 5

So the answer is the graph of line S.