Create two groups of cards with the SAME SUM using as many cards as possible using the numbers 8 7 6 2 1 3.​

Answer:

7(x times y)

Step-by-step explanation:

Product means multiply, so it wants you to multiply two numbers and multiply THAT by 7.  So we will use two variables, in this case, I will use x and y.  X times y.  7 Times that.

Answer:

7xy

Step-by-step explanation:

Let's go by parts

The product of two numbers, since we don't know what are they we can called them x and y so the product means the multiplication

[tex]x*y=xy[/tex]

next xy has to be multiplied by 7

[tex]7*xy=7xy[/tex]

so 7xy is our answer

Answer:

-3/2.

Step-by-step explanation:

0.5 = 1/2

-1.5 = -1 1/2

= -3/2.

- 1.5 = - 15/10

- 15⁽⁵/10 = - 3/2

- ²⁾15/10 = - 30/20

- ³⁾15/10 = - 45/30

etc

Answer:

24:12 = 24/12

24/12 = 2/1 or 2

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Using the identity

cos2Θ = 1 - 2sin²Θ, then

1 - 2sin²([tex]\frac{\pi }{4}[/tex] - [tex]\frac{0}{2}[/tex] )

= cos [2([tex]\frac{\pi }{4}[/tex] - [tex]\frac{0}{2}[/tex] )]

= sos([tex]\frac{\pi }{2}[/tex] - Θ )

= cos[tex]\frac{\pi }{2}[/tex]cosΘ + sin

= 0 × cosΘ + 1 × sinΘ

= 0 + sinΘ

= sinΘ = right side

Answer:  see proof below

Step-by-step explanation:

Use the Difference Identity: sin (A + B) = sin A cos B - cos A sin B

Use the following Half-Angle Identities:  

[tex]\sin\bigg(\dfrac{A}{2}\bigg)=\sqrt{\dfrac{1-\cos A}{2}}\\\\\cos\bigg(\dfrac{A}{2}\bigg)=\sqrt{\dfrac{1+\cos A}{2}}[/tex]

Use the Pythagorean Identity: cos²A + sin²A = 1   -->   sin²A = 1 - cos²A

Use the Unit Circle to evaluate: [tex]\cos\dfrac{\pi}{4}=\sin\dfrac{\pi}{4}=\dfrac{1}{\sqrt2}[/tex]

Proof LHS → RHS

[tex]\text{Given:}\qquad \qquad \qquad 1-2\sin^2\bigg(\dfrac{\pi}{4}-\dfrac{\theta}{2}\bigg)\\\\\text{Difference Identity:}\quad 1-2\bigg(\sin\dfrac{\pi}{4}\cdot \cos \dfrac{\theta}{2}-\cos \dfrac{\pi}{4}\cdot \sin\dfrac{\theta}{2}\bigg)^2\\\\\text{Unit Circle:}\qquad \qquad 1-2\bigg(\dfrac{1}{\sqrt2}\cos \dfrac{\theta}{2}-\dfrac{1}{\sqrt2}\sin \dfrac{\theta}{2}\bigg)^2\\\\\\\text{Half-Angle Identity:}\quad 1-2\bigg(\dfrac{\sqrt{1+\cos A}}{2}-\dfrac{\sqrt{1-\cos A}}{2}\bigg)^2[/tex]

[tex]\text{Expand Binomial:}\quad 1-2\bigg(\dfrac{1+\cos A}{4}-\dfrac{2\sqrt{1-\cos^2 A}}{4}+\dfrac{1-\cos A}{4}\bigg)\\\\\text{Simplify:}\qquad \qquad \quad 1-2\bigg(\dfrac{2-2\sqrt{1-\cos^2 A}}{4}\bigg)\\\\\text{Pythagorean Identity:}\quad 1-\dfrac{1}{2}\bigg(2-2\sqrt{\sin^2 A}\bigg)\\\\\text{Simplify:}\qquad \qquad \qquad 1-\dfrac{1}{2}(2-2\sin A)\\\\\text{Distribute:}\qquad \qquad \qquad 1-(1-\sin A)\\\\.\qquad \qquad \qquad \qquad \quad =1-1+\sin A\\\\\text{Simplify:}\qquad \qquad \qquad \sin A[/tex]

RHS = LHS:   sin A = sin A  [tex]\checkmark[/tex]

Answer:

A, D, E

Step-by-step explanation:

I hope this is correct

Answer:

a d e

Step-by-step explanation:

Answer:

Rate of return = 16%

Step-by-step explanation:

The computation of the rate of the return is shown below:

Data provided in the question

Current value of the investment = $20,880 = C

Originally cost = $18,000 = O

N = Net earnings = C - O

= $20,880 - $18,000

= $2,880

Based on the above information, the rate of return is

[tex]= \frac{N}{O} \\\\ = \frac{\$2,880}{\$18,000}[/tex]

= 16%

Hence, the rate of return is 16%

Answer:

2000-1200+111

2000-1311

689 ans.

Step-by-step explanation:

by bodmas ( bracket,of,divide, multiplication, addition, substract )

so, first we'll multiply

3x400=1200

so,

2000-1200+111

second , we'll add

1200+111 = 1311

so,

2000-1311

third , at last we'll subtract

2000-1311 = 689

so,

Ans. 689

hope the ans. is correct :)

Answer:

9

Step-by-step explanation:

21 x 3/7

= 9 ( goldfish )

Answer:

9 goldfishes

Step-by-step explanation:

Total fish = 21

Number of goldfish = 3/7 of 21

                                [tex]= \frac{3}{7}*21\\\\= 3 * 3\\\\= 9[/tex]

Answer:

0.16

Step-by-step explanation:

Given;

40% males.

If two students are selected at random, probability (P) that they are both males is given as follows;

P = P(1) x P(2)

Where;

P(1) = Probability that the first one is a male

P(2) = Probability that the second one is also a male

Remember that there are 40% males.

This means that 40 out of 100 students selected is going to be a male.

Therefore, for the first selection, any of the 40 students could be selected. The probability P(1), that the first one is male is therefore;

40 / 100 = 0.4

Also,

Assuming there is replacement, for the second selection, any of the 40 students could be selected. The probability P(2), that the second one is also male is therefore;

40 / 100 = 0.4

Now, from;

P = P(1) x P(2)

P = 0.4 x 0.4

P = 0.16

The probability that they are both males is therefore 0.16

Answer:

[tex]\huge \boxed{{y=2x+5}}[/tex]

Step-by-step explanation:

y = mx + b (slope-intercept form of a line)

m is slope

b is y-intercept

The y-intercept of the line is (0, 5) or 5.

y = mx + 5

The slope of the line can be found through rise over run.

(1, 7) and (2, 9) are two points on the line.

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

m = (9 - 7)/(2 - 1)

m = 2/1 = 2

The slope of the line is 2.

y = 2x + 5

Answer: Hi! The equation for this line would be c), y = 2x + 5.

Step-by-step explanation:

Slope - intercept form: y = mx + b, where m is the slope and b is the y - intercept.

First, we should determine the y - intercept. We can observe using the graph that the line intercepts the y - axis at point (0, 5), so we take the y - coordinate (5) and insert it into our equation.

y = mx + 5

This automatically rules out options d) and b).

Next, we find the slope. The formula for finding the slope is (y2 - y1) ÷ (x2 - x1).

We need to choose two coordinates before we can calculate the slope.

Let's use (1, 7) and (0,5).

We will not insert the values into or slope formula:

(7 - 5) ÷ (1 - 0)

When we solve this, the quotient is 2.

This is our slope, and we can insert the value into our slope equation - -

y = 2x + 5

This rules out option a). So, your answer is option c), y = 2x + 5.

Hope this helps!

Answer:

To form the converse of the conditional statement, interchange the hypothesis and the conclusion. The converse of "If it rains, then they cancel school" is "If they cancel school, then it rains." To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.

Answer:

see explanation

Step-by-step explanation:

Using the double angle identity for cosine

cos2x = 2cos²x - 1

Given

cos( [tex]\frac{0}{2}[/tex] ) = [tex]\frac{1}{2}[/tex]( p + [tex]\frac{1}{p}[/tex] ) , then

cosΘ = 2[ [tex]\frac{1}{2}[/tex](p + [tex]\frac{1}{p}[/tex] ) ]² - 1

         = 2 [ [tex]\frac{1}{4}[/tex](p² + 2 + [tex]\frac{1}{p^{2} }[/tex] ) ] - 1  ← distribute by 2

         = [tex]\frac{1}{2}[/tex](p² + 2 + [tex]\frac{1}{p^{2} }[/tex] ) - 1 ← distribute by [tex]\frac{1}{2}[/tex]

         = [tex]\frac{1}{2}[/tex] p² + 1 + [tex]\frac{1}{2p^2}[/tex] - 1

        = [tex]\frac{1}{2}[/tex] p² + [tex]\frac{1}{2p^2}[/tex] ← factor out [tex]\frac{1}{2}[/tex] from each term

        = [tex]\frac{1}{2}[/tex] ( p² + [tex]\frac{1}{p^{2} }[/tex] ) ← as required

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]cos(\theta)=2cos^2(\dfrac{\theta}{2})-1\\\\=2\left(\dfrac{p+\dfrac{1}{p}}{2}\right)^2-1\\\\=\dfrac{p^2+\dfrac{1}{p^2}+2}{2}-1\\\\=\dfrac{1}{2}(p^2+\dfrac{1}{p^2})+1-1\\\\=\dfrac{1}{2}(p^2+\dfrac{1}{p^2})[/tex]

Thank you

Answer:

Step-by-step explanation:

The distance between two points can be found using the formula

[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

A(5,-8) and B(2,9)

The distance between them is

[tex] |AB| = \sqrt{ ({5 - 2})^{2} + ({ - 8 - 9})^{2} } \\ = \sqrt{ {3}^{2} + ({ - 17})^{2} } \\ = \sqrt{9 + 289} \\ = \sqrt{298} [/tex]

| AB | = 17.26267

We have the final answer as

17. 26 units to the nearest hundredth

Hope this helps you

Answer:

b.15 inches

Step-by-step explanation:

subtract 12 (2 6inch sides) from the perimeter

get 30 and divide by 2 to get 2 sides

Answer:

B. 15 inches.

Step-by-step explanation:

A rectangle shares two pairs of congruent opposite sides.

Perimeter = 42

Let:

the length of the rectangle = l

the width of the rectangle = w = 6

Perimeter = l + l + w + w

Plug in 42 for perimeter &  6 for w in the equation:

42 = l + l + 6 + 6

Combine like terms:

42 = ( l + l ) + (6 + 6)

42 = 2l + 12

Next, isolate the variable, l. Do the opposite of PEMDAS.  First, subtract 12 from both sides:

42 (-12) = 2l + 12 (-12)

42 - 12 = 2l

30 = 2l

Next, divide 2 from both sides:

(30)/2 = (2l)/2

l = 30/2

l = 15

B. 15 inches is the length of the rectangle.

Check:

l + l + w + w = 42

15 + 15 + 6 + 6 = 42

30 + 12 = 42

42 = 42 (True).

~

Answer:

x<= -4

filled in circle at -4

221 is rational since 221 = 221/1

So is 331 because 331 = 331/1

The product of any two rational numbers is also rational

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

Proof:

Let x = p/q and y = r/s be two rational numbers. The q and s values are nonzero.

Their product is

x*y = (p/q)*(r/s)

x*y = (p*q)/(r*s)

which is a ratio of two integers pq and rs, so (p*q)/(r*s) is rational

Answer:

1.) The slope of an equation expressed in the form of y= mx+b is m.

Answer:

[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]

Step-by-step explanation:

The slope of a line that is perpendicular to another will have an opposite-reciprocal slope. So, if the slope was -2, then the perpendicular slope would be [tex]\frac{1}{2}[/tex] .

[tex]y=-5x+11[/tex]

This is written in slope-intercept form:

[tex]y=mx+b[/tex]

m is the slope and b is the y-intercept. Find the opposite-reciprocal of the slope, -5:

[tex]y=\frac{1}{5} x+b[/tex]

Now we need to find the y-intercept. For this, substitute the given points for its appropriate value:

[tex](3_{x},3_{y})\\\\3=\frac{1}{5}(3)+b[/tex]

Solve for b:

Simplify multiplication:

[tex]\frac{1}{5}*\frac{3}{1}=\frac{3}{5}[/tex]

Insert:

[tex]3=\frac{3}{5}+b[/tex]

Subtract b from both sides:

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

Subtract 3 from both sides:

[tex]3-3-b=\frac{3}{5}-3\\\\-b=\frac{3}{5}-3[/tex]

Simplify subtraction:

[tex]\frac{3}{5}-3\\\\\frac{3}{5}-\frac{3}{1}\\\\\frac{3}{5}-\frac{15}{5}=-\frac{12}{5}[/tex]

Insert:

[tex]-b=-\frac{12}{5}[/tex]

Multiply both sides by - 1 to simplify b (it can be seen as -1b):

[tex]-b*(-1)=-\frac{12}{5}*(-1)\\\\b=\frac{12}{5}[/tex]

Insert:

[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]

:Done

Answer: x' = x - 2yd.

Step-by-step explanation:

When we have a function:

y = g(x)

A translation to the east (in this case the positive x-axis) of N units.

is written as:

y = h(x) = g(x - N)

then if in the beginning our variable was x, afther the translation the variable will be x - N.

Now in this case we have a translation of 2yd to the right (to the east)

Then our new variable, let's call it x', will be:

x' = x - 2yd.

Answer:

A translation of two yards east involves moving 2 units in the positive x-direction. Given any initial x-coordinate, x, the algebraic expression that represents the new x-coordinate after the translation is x + 2.

Step-by-step explanation:

Edementum answer.

Answer:

29

Step-by-step explanation:

Given the function f(x) = x/10x-3, if x = 0.30103;

substituting the value of x into the function;

f(0.30103) = 0.30103/10(0.30103) - 3

f(0.30103) = 0.30103/(3.0103 - 3)

f(0.30103) = 0.30103/0.0103

f(0.30103) = 29.226

f(0.30103) = 29 (to nearest whole number).

Answer:

The measure of [tex]x_{w}[/tex] is 4 units.

Step-by-step explanation:

According to the definition of tangent, it is equal to:

[tex]\tan f = \frac{y_{w}}{x_{w}}[/tex]

Where:

[tex]f[/tex] - Angle, measured in sexagesimal degrees.

[tex]x_{w}[/tex] - Adjacent side, measured in units.

[tex]y_{w}[/tex] - Opposite side, measured in units.

If [tex]\tan f = \frac{2}{1}[/tex] and [tex]y_{w} = 8\,units[/tex], the adjacent side is:

[tex]x_{w} = \frac{y_{w}}{\tan f}[/tex]

[tex]x_{w} = \frac{8\,units}{\frac{2}{1} }[/tex]

[tex]x_{w} = 4\,units[/tex]

The measure of [tex]x_{w}[/tex] is 4 units.

The  measure of xw is 4 units

Given the following parameters

Tan fº = 2/1

This shows that;

Opposite side YW = 2

Adjacent side XW = 1

Given that YW is  8units, using the ratio of similar sides

2/1 = 8/XW

2XW = 8

XW = 4

Hence the  measure of xw is 4 units

Learn more on similar figures here: https://brainly.com/question/2644832

Answer:

20%

Step-by-step explanation:

Step 1: Find the decrease in consumption

10kg - 8kg = 2kg

So the family decrease their consumption of sugar by 2kg

Step 2: We have to find what percent did the family reduce their sugar consumption

We can divide how much they reduced by with the original amount

2kg/10kg = 1/5 kg or 20%

Therefore the family reduced the consumption of sugar by 20$

Answer:

27%

Step-by-step explanation:

27/100

Percent means out of 100

27%

Answer:

27 percent

Step-by-step explanation:

:)

Answer:

A graph that goes through (4, 0), (8, -3), (0, 3), and (-4, 6)

Step-by-step explanation:

Hello!

To find what this looks like it is easier to put it into slope-intercept form which is y = mx + b

To get our equation to look like that we have to get y by itself

3x + 4y = 12

Subtract 3x from both sides

4y = -3x + 12

Divide both sides by 4

[tex]y =- \frac{3}{4}x + 3[/tex]

We now know the y-intercept is (0, 3)

Now we follow the slope to give us more points

More points are (4, 0), (8, -3), and (-4, 6)

The answer would be a graph that goes through those points.

Hope this helps!

Answer:

7 1/5

Step-by-step explanation:

You said that she poured 1 1/5 pouches in each cup. There are 5 cups, so multiply 1 1/5 by 5.

(e.g)

1 1/5+1 1/5= 3 because 1+1=2 & 1/2+1/2=1 so you add them and get 3

Do that twice and you get 6

then you have 1 one more cup left so add 1+6=7 then add the half 7+1 1/2=7 1/2

Your Welcome

Answer:

x² - 3x - 18 = 0

Step-by-step explanation:

x/3 - 6/x = 1

x²/3 - 6 = x

x² - 18 = 3x

x² - 3x - 18 = 0

Answer:

k = h/9.

Step-by-step explanation:

√(h/k) = 3

Squaring both sides:

h/k = 9

9k = h

k = h/9.

Answer:

k=h/9

Step-by-step explanation:

sqrt(h/k)=3

1. square both sides

h/k=3^2

2. make k the subject

k=h/9

la primera sale 1/3

la segunda 1/4

la tercera tambien 1/4

en la cuarta se puede hacer un grafico o un planteo de ecuacionas de igual manera te va a salir 1/5

y en la quinta tambien se puede hacer un grafico o un planteo de ecuacionas de igual manera te va a salir 1/8