David is now 4 years more than twice the age of Henry. If Henry will be 18 in 3 years, how old was David 2 years ago?

Answer:

[tex]$2\left(1-\frac{1}{2}\right)+3\left(1-\frac{1}{3}\right)+4\left(1-\frac{1}{4}\right)+\ldots+10\left(1-\frac{1}{10}\right)=?$[/tex]

[tex]2(\frac{2}{2} -\frac{1}{2} )+3(\frac{3}{3} -\frac{1}{3} )+4(\frac{4}{4} -\frac{1}{4} )+5(\frac{5}{5} -\frac{1}{5} )+6(\frac{6}{6}-\frac{1}{6} )+7(\frac{7}{7}-\frac{1}{7} )+8(\frac{8}{8} -\frac{1}{8} )+9(\frac{9}{9} -\frac{1}{9} )+10(\frac{10}{10} -\frac{1}{10} )\\\\=2(\frac{1}{2}) +3(\frac{2}{3})+4(\frac{3}{4})+5(\frac{4}{5}) +6(\frac{5}{6}) +7(\frac{6}{7}) +8(\frac{7}{8}) +9(\frac{8}{9}) +10(\frac{9}{10})\\\\=1+2+3+4+5+6+7+8+9\\\\=45[/tex]

Part (a)

Consecutive odd integers are integers that odd and they follow one right after another. If x is odd, then x+2 is the next odd integer

For example, if x = 7, then x+2 = 9 is right after.

========================================================

Part (b)

The consecutive odd integers we're dealing with are x and x+2.

Their squares are x^2 and (x+2)^2, and these squares add to 394.

========================================================

Part (c)

We'll solve the equation we just set up.

x^2 + (x+2)^2 = 394

x^2 + x^2 + 4x + 4 = 394

2x^2+4x+4-394 = 0

2x^2+4x-390 = 0

2(x^2 + 2x - 195) = 0

x^2 + 2x - 195 = 0

You could factor this, but the quadratic formula avoids trial and error.

Use a = 1, b = 2, c = -195 in the quadratic formula.

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(2)\pm\sqrt{(2)^2-4(1)(-195)}}{2(1)}\\\\x = \frac{-2\pm\sqrt{784}}{2}\\\\x = \frac{-2\pm28}{2}\\\\x = \frac{-2+28}{2} \ \text{ or } \ x = \frac{-2-28}{2}\\\\x = \frac{26}{2} \ \text{ or } \ x = \frac{-30}{2}\\\\x = 13 \ \text{ or } \ x = -15\\\\[/tex]

If x = 13, then x+2 = 13+2 = 15

Then note how x^2 + (x+2)^2 = 13^2 + 15^2 = 169 + 225 = 394

Or we could have x = -15 which leads to x+2 = -15+2 = -13

So, x^2 + (x+2)^2 = (-15)^2 + (-13)^2 = 225 + 169 = 394

We get the same thing either way.

Answer:

A, E or 1, 5

Step-by-step explanation:

Its not A, D

Answer:

11.2 cm

Step-by-step explanation:

Given that;

Arc Length Formula (if θ is in radians): l = ϴ × r

ϴ = angle subtended in radians

r= radius of the circle

l = 8cm × 1.4 radians

l= 11.2 cm

Answer:

The answer for this question is C

Answer:

A. The data set has an outlier

Step-by-step explanation:

The data set has an outlier because 100 is the largest number of the set.

Answer:

option b

Step-by-step explanation:

Step-by-step explanation:

let the common ratio be r

(x-6)r=(x-2)

(x-2)r=(x+10)

r = (x-2)/(x-6)

and r = (x+10)/(x-2)

so, (x-2)/(x-6)=(x+10)/(x-2)

sloving it, you'll get x=8

so the value of x is 8

Answer:

Step-by-step explanation:

I can't believe I'm doing this for 5 points, but ok!

For the first 3, we are going to multiply to find the value of that 3 x 3 matrix by picking up the first 2 columns and plopping them down at the end and then multiplying through using the rules for multiplying matrices:

[tex]\left[\begin{array}{ccccc}7&4&6&7&4\\-4&8&9&-4&8\\1&8&7&1&8\end{array}\right][/tex]  and from there find the sum of the products of the main axes minus the sum of the products of the minor axes, as follows (I'm not going to state the process in the next 2 problems, so make sure you follow it here. This is called the determinate. The determinate is what you get when you evaluate or find the value of a matrix. Just so you know):

[tex](7*8*7)+(4*9*1)+(6*-4*8)-[(1*8*6)+(8*9*7)+(7*-4*4)][/tex] which gives us:

392 + 36 - 192 - [48 + 504 - 112] which simplifies to

236 - 440 which is -204

On to the second one:

[tex]\left[\begin{array}{ccccc}-8&-4&-1&-8&-4\\1&7&-3&1&7\\8&9&9&8&9\end{array}\right][/tex] and multiplying gives us

[tex](-8*7*9)+(-4*-3*8)+(-1*1*9)-[(8*7*-1)+(9*-3*-8)+(9*1*-4)][/tex] which gives us:

-504 + 96 - 9 - [-56 + 216 - 36] which simplifies to

-417 - 124 which is -541, choice c.

Now for the third one:

[tex]\left[\begin{array}{ccccc}-2&-2&-5&-2&-2\\2&7&-3&2&7\\8&9&9&8&9\end{array}\right][/tex] and multiplying gives us

[tex](-2*7*9)+(-2*-3*8)+(-5*2*9)-[(8*7*-5)+(9*-3*-2)+(9*2*-2)][/tex] which gives us:

[tex]-126+48-90-[-280+54-36][/tex] which simplifies to

-168 - (-262) which is 94, choice c again.

Now for the last one. I'll show you the set up for the matrix equation; I solved it using the inverse matrix. So I'll also show you the inverse and how I found it.

[tex]\left[\begin{array}{cc}-4&-5&\\-6&-8\\\end{array}\right][/tex] [tex]\left[\begin{array}{c}x\\y\\\end{array}\right][/tex] = [tex]\left[\begin{array}{c}-5\\-2\\\end{array}\right][/tex] and I found the inverse of the 2 x 2 matrix on the left.

Find the inverse by:

* finding the determinate

* putting the determinate under a 1

* multiply that by the "mixed up matrix (you'll see...)

First things first, the determinate:

|A| = (-4*-8) - (-6*-5) which simplifies to

|A| = 32 - 30 so

|A| = 2; now put that under a 1 and multiply it by the mixed up matrix. The mixed up matrix is shown in the next step:

[tex]\frac{1}{2}\left[\begin{array}{cc}-8&5\\6&-4\end{array}\right][/tex]  (to get the mixed up matrix, swap the positions of the numbers on the main axis and then change the signs of the numbers on the minor axis). Now we multiply in the 1/2 to get the inverse:

[tex]\left[\begin{array}{cc}-4&\frac{5}{2}\\3&-2\\\end{array}\right][/tex] Multiply that inverse by both sides of the equation. This inverse "undoes" the matrix that's already there (like dividing the matrix that's already there by itself) which leaves us with just the matrix of x and y. Multiply the inverse matrix by the solution matrix:

[tex]\left[\begin{array}{c}x&y\end{array}\right] =\left[\begin{array}{cc}-4&\frac{5}{2} \\3&-2\end{array}\right] *\left[\begin{array}{c}-5&-2\\\end{array}\right][/tex] and that right side multiplies out to

x = 20 - 5 which is

x = 15 and

y = -15 + 4 which is

y = -11

(It works, I checked it)

composite numbers less than 12={1,3,4,6,8,9,10}

Answer:

162

Step-by-step explanation:

because this is a parallelogram :

m<2 = m<4 so

4x - 22 = 3x - 12

4x - 3x = 22 - 12

x = 10 replace x with 10 in the equation for m<4

3x - 12 is 30 - 12 = 18

m<4 and m<1 are supplementary and their sum is equal to 180

m<4 + m<1 = 180

m<1 = 180 - 18

m<1 = 162

Answer:

Domain: [tex](-\infty,\infty)[/tex]

Range: [tex]f(x) \ge 0[/tex]

Step-by-step explanation:

Given

[tex]f(x) = |x + 6|[/tex]

Required

The domain and the range

First, we calculate the domain

[tex]f(x) = |x + 6|[/tex]

The above function does not have roots or fraction, where x is the denominator. This means that the domain is all real numbers, i.e. [tex](-\infty,\infty)[/tex]

The range

The function is an absolute function; So, the minimum value is 0.

Hence, the range is:

[tex]f(x) \ge 0[/tex]

Answer:

A

Step-by-step explanation:

on edge

Answer:

D

Step-by-step explanation:

It is the law of cos

C^2= A^2+B^2-2*A*B*cosL where L is the angle between A and B

so C = 32^2 + 35^2 - 2(32)(35)cos120°

Answer:

Hello

Step-by-step explanation:

[tex]y=2x^2-12x+19\\=2(x^2-6x)+19\\=2(x^2-2*3*x+9)+19-18\\=2(x-3)^2+1\\\\Vertex\ is\ (3,1)\\\\Axis\ of\ symmetry\ is\ x=3\\\\y-intercept\ is \\\\y=2(0-3)^2+1=19\\[/tex]

Answer:

-5x - 7y

Step-by-step explanation:

Answer:

they are in order cross x with the y across from it

Step-by-step explanation:

Answer: A. 7

Concept:

Here, we need to understand the idea of evaluation.  

When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.

Solve:

Given Information

f(x) = 5x - 3

x = 2

Substitute the value into the function

f(2) = 5 (2) - 3

f(2) = 10 - 3

f(2) = 7

Hope this helps!! :)

Please let me know if you have any questions

Answer:

B

Step-by-step explanation:

n is the number of litres.

if you substitute 1 for 'n' then you will get :

C = 8 + 1.5(1)

C = $9.5

$9.50 for every litre

Answer:

C is correct

Step-by-step explanation:

The $8 charge is only once regardless of how many liters are ordered, so only answer C works.

Answer:

3,-1

Step-by-step explanation:

The image of the point (-1,3) after a rotation of 270° counterclockwise about the origin is (3, -1).

The given coordinate point is (-1, 3).

When rotating a point 270 degrees counterclockwise about the origin our point A(x, y) becomes A'(y,-x). This means, we switch x and y and make x negative.

The point (-1, 3) is rotated 270° counterclockwise about the origin becomes (3, -1).

Therefore, the image of the point (-1,3) after a rotation of 270° counterclockwise about the origin is (3, -1).

To learn more about the rotation of 270° counterclockwise visit:

brainly.com/question/9109065.

#SPJ2

Answer:

a) 3x + ky = 8

ky = 8 - 3x

x – 2ky = 5

x - 2(8 - 3x) = 5

x - 16 + 6x = 5

7x = 21

x = 3 (shown)

b) x-2ky = 5

sub x = 3, y = 1/2

3-2k(1/2) = 5

-2k = 2

k = -1

Answer:

y = -x + 4

Step-by-step explanation:

(x₁,y₁)= (5, - 1)    & (x₂,y₂)= (2 , 2)

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

         [tex]\frac{2-[-1]}{2-5}\\\\=\frac{2+1}{-3}\\\\=\frac{3}{-3}\\\\= -1[/tex]

m = -1

Equation of the line y - y₁ = m(x - x₁)

y  - [-1] = (-1)*(x - 5)

y + 1 = -x + 5      {-1 is distributed}

y = -x + 5 - 1

y = -x + 4

Answer:

4x+3y<15

This is the inequality represented by the graph

Answer:

-3/4

Step-by-step explanation:

First, let's convert the mixed numbers into improper fractions in an effort to make this problem easier to solve.

-2 1/2 as a mixed number is -5/2 and -1 3/4 as a mixed number is -7/4.

Our problem is now -5/2 - (-7/4).

We still can't solve this because the two fractions do not share a common denominator. 4 can serve as one, so -5/2 with a denominator of 4 would be -10/4.

The problem is now -10/4 - (-7/4).

Two negatives make a positive so the problem can be rewritten as -10/4 + 7/4. The final answer is -3/4.

Step-by-step explanation:

3 x 3 x 3 = 27

2 x 2 x 2 = 8

6 x 10 x 2 = 120

27+8+120=155m³

Answer:

I don't know search it up I picked B

okay it's 5 and I'm

Step-by-step explanation:

3(6+b)+2b+1

18+3b+2b+1

5b+19