Solve the system of equations using substitution. Show your work.

d + e = 6
d - e = 4

Answer: Audrey is less than 17 years old (possible answers 16,15,14,13...)

Answer in inequality: x<17

Step-by-step explanation:

3x + 9 < 60

3x + 9 - 9 < 60 - 9

3x < 51

x<17

Answer: x<17

EXPLAIN

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Answer:

16

Step-by-step explanation:

Let's say x is the number of bowls.  If each bowl needs 3/5 pound of clay, then the total clay needed is 3/5 * x.  We know the total amount is 10 pounds.  Therefore:

10 = 3/5 x

Divide:

x = 10 / (3/5)

To divide by a fraction, we need to multiply by the reciprocal:

x = 10 * (5/3)

x = 50/3

x = 16 ⅔

We can't have part of a bowl, so we must round down.  The potter can make 16 bowls.

Answer:

21π m, or ≈ 65.94 m

Step-by-step explanation:

Remember that π is the ratio between a circle's circumference and its diameter, or, in equation form:

[tex]\pi=\frac{c}{d}[/tex]

where c is the circumference and d is the diameter. If we want to find the circumference, we can just multiply that equation by d on both sides to get

[tex]c=\pi d[/tex]

Here, our d = 21 m, so our circumference would be

[tex]c=21\pi[/tex] m, or approximately 21(3.14) = 65.94 m

2L + 2w = 68 & L = 3w-4

2(3w-4) = 68

6w-8= 68

6w = 60

W= 10

L = 3*10-4

L= 30-4= 26

Answer:

[tex]c = 4[/tex]

Step-by-step explanation:

For this triangle we have to

[tex]A=63\\C=49\°\\c=3\°[/tex]

Now we use the sine theorem to find the length of a:

[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]

Then:

[tex]\frac{sin(A)}{a}=\frac{sin(C)}{c}\\\\a=\frac{sin(A)}{\frac{sin(C)}{c}}\\\\a=c*\frac{sin(A)}{sin(C)}\\\\a=(3)\frac{sin(63)}{sin(49)}\\\\c=4[/tex]

Answer:

No, because they do not have the same area.

Step-by-step explanation:

For the piece of paper to cover once without overlap or gaps, it must have the same area as the the total surface area of the prism.

The total surface area of the rectangular prism is: [tex]2(3.5\times2+3.5\times1.5+2\times1.5)=30\frac{1}{2}in^2[/tex]

The area of the rectangular sheet is:[tex]5\times 8=40in^2[/tex]

Since the area of the piece of paper is more than the surface area of the rectangular prism there will be an overlap.

ANSWER

A. 10,000

EXPLANATION

The given rational function is

[tex]f(x) = \frac{1}{x - 2} [/tex]

This function is not defined at x=2.

But as we are picking x-values that are closer and closer to 2, the functional values grows bigger and bigger positively or negatively without bounds.

Therefore a possible value of f(x) as x is close to 2 is 10,000.

The correct answer is A.

Answer:

The answer is -6

Step-by-step explanation:

Hope it helped you!

Answer:

B. [tex]-6[/tex]

Step-by-step explanation:

We are asked to find the negative square root of 36.

We can write our given problem as [tex]-\sqrt{36}[/tex].

We can write 36 as 6 to second power.

[tex]-\sqrt{36}=-\sqrt{6^2}[/tex]

Using radical rule [tex]\sqrt[n]{a^n}=a[/tex], we will get:

[tex]-\sqrt{6^2}=-6[/tex]

Therefore, the negative square root of 36 is negative six and option B is the correct choice.

Answer:

Part 1) The measure of angle d is 65°

Part 2) The measure of angle c is 89°

Part 3) The measure of arc a is 131°

Part 4) The measure of arc b is 47°

Step-by-step explanation:

we know that

In an inscribed quadrilateral, opposite angles are supplementary

step 1

Find the measure of angle d

∠d+115°=180°

∠d=180°-115°=65°

step 2

Find the measure of angle c

∠c+91°=180°

∠c=180°-91°=89°

step 3

Find the measure of arc a

we know that

The inscribed angle measures half that of the arc comprising

115°=(1/2)[99°+arc a]

230°=[99°+arc a]

arc a=230°-99°=131°

step 4

Find the measure of arc b

we know that

The inscribed angle measures half that of the arc comprising

∠c=(1/2)[arc a+arc b]

substitute the values

89°=(1/2)[131°+arc b]

178°=[131°+arc b]

arc b=178°-131°=47°

A figure which is formed by two rays or lines that shares a common endpoint is called an angle.

An arc is one of the portions of a circle. It is basically a part of the circumference of a circle.

The measure of the ∠d is 65 degrees.

The measure of the ∠c is 89 degrees.

The measure of the arc a is 131 degrees.

The measure of arc b is 47 degrees.

The value of each variable. For the circle, the dot represents the center.

A figure which is formed by two rays or lines that shares a common endpoint is called an angle.

An arc is one of the portions of a circle. It is basically a part of the circumference of a circle.

1. The measure of ∠d is;

∠d+ 115°= 180°

∠d= 180°-115°= 65°

The measure of the ∠d is 65 degrees.

2. The measure of ∠c is,

∠c+ 91°= 180°

∠c =180°-91° =89°

The measure of the ∠c is 89 degrees.

3. The measure of arc a is,

The inscribed angle measures half that of the arc comprising;

[tex]\rm 115=\dfrac{1}{2}[99+arc \ a]\\\\230=[99+arc a]\\\\arc \ a = 230-99\\\\arc \ a= 131[/tex]

The measure of the arc a is 131 degrees.

4. The measure of arc b is,

The inscribed angle measures half that of the arc comprising;

[tex]\rm 89=\dfrac{1}{2}[131+arc \ b]\\\\178=[131+arc \ b]\\\\arc \ b = 178-131\\\\arc \ b = 47[/tex]

The measure of arc b is 47 degrees.

To know more about Angle and Arc click the link given below.

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Final answer:

Barry is currently 13 years old and his sister is 5 years old. This is determined by setting up a system of equations based on the given information and solving for their current ages.

Explanation:

The question involves solving a system of equations to find the current ages of Barry and his sister. Let's let B represent Barry's current age and S represent his sister's current age. According to the problem, Barry is 8 years older than his sister (B = S + 8). In 3 years, Barry will be twice as old as his sister will be then (B + 3 = 2(S + 3)).

Write down the two equations: B = S + 8 and B + 3 = 2(S + 3).

Substitute B from the first equation into the second equation: (S + 8) + 3 = 2(S + 3).

Simplify and solve for S: S + 11 = 2S + 6.

Rearrange the equation to find S: S = 5.

Substitute the value of S back into the first equation to find B: B = 5 + 8, so B = 13.

Therefore, Barry is currently 13 years old and his sister is 5 years old.

Answer:

x^2-5x-24

Step-by-step explanation:

Final answer:

The product of the binomials (x + 3)(x - 8) is simplified using the FOIL method to get x² - 5x - 24. We multiply each term in the first parenthesis by each term in the second and combine like terms.

Explanation:

To multiply and simplify the expression (x + 3)(x - 8), we will use the FOIL method (First, Outer, Inner, Last). This method involves multiplying each term in the first parenthesis by each term in the second parenthesis.

First: x times x = x²

Outer: x times -8 = -8x

Inner: 3 times x = +3x

Last: 3 times -8 = -24

Next, combine like terms (-8x and +3x):

x² - 8x + 3x - 24 = x² - 5x - 24

The simplified form of the given expression is x² - 5x - 24, which corresponds to option C).

Answer: x=e

Step-by-step explanation:

x= ln(e^e)

using ln(e^x)= x x ln (e), transform the expression

x= e x ln (e)

the natural logatithm of e equals 1

x=e x 1

any expression multiplied by 1 remains the same

x=e alternative form: x= 2.71828

ANSWER

[tex]x = e[/tex]

EXPLANATION

The given logarithmic equation

[tex]x = ln_{e}(e) [/tex]

Note that

[tex] ln(e) = 1[/tex]

Using the power rule of logarithms,

[tex]x =e \ln(e)[/tex]

This gives us:

[tex]x =e (1)[/tex]

Simplify to get:

[tex]x = e[/tex]

Answer:

A: 80

Step-by-step explanation:

As we know that the trend line is [tex]y=6.8x+60[/tex], we can plug in x=3 in order to find out the estimated score for 3 hours of studying

[tex]y=6.8x+60\\\\y=6.8(3)+60\\\\y=20.4+60\\\\y=80.4[/tex]

y=80.4 is closest to A: 80

Answer:

Option A, 80

Step-by-step explanation:

Trend line is given by y = 6.8x + 60

where x = number of hours she studied

          y = score

Now we have to calculate the score for a student for studied for 3 hours.

y = 6.8 × 3 + 60

  = 20.4 + 60

  = 80.40

  ≈ 80

Option A will be the answer.

To make 88,5□1 round down to 88,500, the digit that replaces □ must be less than 5; therefore, the replacements could be :0, :2, or :4.

potential

The given number is '88,5□1' and we want to find the digit that replaces the □ and rounds the number to '88,500' when we round to the nearest hundred. An important point to remember about rounding is that if the digit in the tens place is less than 5, we round down, while if it's 5 or above, we round up. Since we want to round down to 88,500, the digit that replaces □ in the tens place must therefore be less than 5. So, the possible digits could be :0, :2, or :4.

https://brainly.com/question/28562556

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The price per ounce of ground beef, when 9 pounds cost $40.32, is $0.28.

Calculating Price per Ounce of Ground Beef

To calculate the price per ounce for ground beef when given the price for 9 pounds, we will first need to know how many ounces are in 9 pounds. Since there are 16 ounces in 1 pound, 9 pounds is equivalent to 144 ounces (9 pounds × 16 ounces/pound).

Next, we divide the total cost of the 9 pounds of ground beef by the total number of ounces to find the price per ounce. The total cost given is $40.32.

Price per ounce = Total cost \/ Total number of ounces

Price per ounce = $40.32 \/ 144 ounces

Price per ounce = $0.28

Therefore, the price per ounce of ground beef is $0.28.

5*6=20+y

30=20+y

30-20=20-20+y

10=y

Check answer by using substitution method

5*6=20+y

30=20+10

30=30

Answer is y=10

5 x 6 = 30

y + 20 = 30

y + 20 - 20 = 30 - 20

y = 10

Answer:

(6x-5)(x+2)

Step-by-step explanation:

6x²+7x-10

= (6x-5)(x+2)

Answer:

-36 • (22u + 1)

Step-by-step explanation:

Pulling out like terms :

2.1     Pull out like factors :

  -74u - 5  =   -1 • (74u + 5)

Equation at the end of step  2  :

 (6 • (58u + 1)) -  -6 • (74u + 5)

Step  3  :

Equation at the end of step  3  :

 6 • (58u + 1) -  -6 • (74u + 5)

Step  4  :

Pulling out like terms :

4.1      Pull out     6

Note that  -6 =(-1)• 6

After pulling out, we are left with :

     6 • ( (-1)  *  (58u+1) +( (-1)  *  (74u+5) ))

Step  5  :

Pulling out like terms :

5.1     Pull out like factors :

  -132u - 6  =   -6 • (22u + 1)

Final result :

 -36 • (22u + 1)

Answer:

[tex]\large\boxed{\sin2\theta=\dfrac{\sqrt3}{2},\ \cos2\theta=\dfrac{1}{2}}[/tex]

Step-by-step explanation:

We know:

[tex]\sin2\theta=2\sin\theta\cos\theta\\\\\cos2\theta=\cos^2\theta-\sin^2\thet[/tex]

We have

[tex]\sin\theta=\dfrac{1}{2}[/tex]

Use [tex]\sin^2\theta+\cos^2\theta=1[/tex]

[tex]\left(\dfrac{1}{2}\right)^2+\cos^2\theta=1\\\\\dfrac{1}{4}+\cos^2\theta=1\qquad\text{subtract}\ \dfrac{1}{4}\ \text{from both sides}\\\\\cos^2\theta=\dfrac{4}{4}-\dfrac{1}{4}\\\\\cos^2\theta=\dfrac{3}{4}\to\cos\theta=\pm\sqrt{\dfrac{3}{4}}\to\cos\theta=\pm\dfrac{\sqrt3}{\sqrt4}\to\cos\theta=\pm\dfrac{\sqrt3}{2}\\\\\theta\in[0^o,\ 90^o],\ \text{therefore all functions have positive values or equal 0.}\\\\\cos\theta=\dfrac{\sqrt3}{2}[/tex]

[tex]\sin2\theta=2\left(\dfrac{1}{2}\right)\left(\dfrac{\sqrt3}{2}\right)=\dfrac{\sqrt3}{2}\\\\\cos2\theta=\left(\dfrac{\sqrt3}{2}\right)^2-\left(\dfrac{1}{2}\right)^2=\dfrac{3}{4}-\dfrac{1}{4}=\dfrac{3-1}{4}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]

Answer:

44

Step-by-step explanation:

the mode of a set of data is the value that occurs most often, in this case it is 44

44 would be the mode of the data.

The mode of the data is the number that occurs the most. It is always best to put the numbers in order from least to greatest so we can see what number appears more than once.

18,27,28,44,44,50,67

When we look at this set of numbers, we can see that 44 appears more than any other number. Therefore, the mode of these numbers is 44.

Answer:8m+20

Step-by-step explanation:

U have too add the perimeter than multiple area

Answer:

2 and -10

Step-by-step explanation:

let the two integers be x and y.

so, x+y=-8---‐-------(1)

and,

x=y+12-------‐-----(2)

from (1) and (2),

(y+12)+y=-8

or, 2y=-8-12

or, y=-20/2

or, y=-10

substitutting the value of y in (2),

x=-10+12=2

therefore the required integers are 2 and -10.

Answer:

-20

Step-by-step explanation:

→ The sum of two integers is -8.

⇒ One will be called "x" and the other will be called "y"

→ One integer is 12 ( "y" )

Let's set up an equation x = ? and y = 12 so,

→ x + y = -8

( Substitute y for 12 )

→ x + 12 = -8

( -12 from both sides to isolate x )

→ x = -20

Answer:

V -E +F = 2

Vertices = 2 + Edges -Faces

Vertices = 2 + 90 -32

Vertices = 60

Step-by-step explanation:

____________________________________________________

Answer:

7 dollars

____________________________________________________

Step-by-step explanation:

To make solving this equation easier, lets turn the the information we got in the question into an actual equation.

Key information:

4 tickets

$12 popcorn

Spent a TOTAL of $40.

With the information above, we can use it to make an equation.

We would use the equation: y = mx + b

Since our "y" value would represent our total value, our total value is 40, so we would plug 40 into y.

Your equation should look like this:

40 = mx + b

Our "b" value represents our start value, and our start value would be 12 because we started with one $12 popcorn.

Your equation should look like this:

40 = mx + 12

Our "m" value would represent how many tickets we bought, so we would plug in 4 in m.

Our equation would be:

40 = 4x + 12

Now we can solve the equation:

We would move the 12 over to the left side of the equal sign by subtracting, then we would divide by 4.

[tex]40=4x+12\\\\28=4x\\\\7=x[/tex]

We should get ther answer of 7, that means that each ticket cost $7 dollars.

7 dollars should be your FINAL answer.

____________________________________________________

Answer:

One ticket = $7

Step-by-step explanation:

Forming the equation,

→ 4x + 12 = 40

Now the value of x will be,

→ 4x + 12 = 40

→ 4x = 40 - 12

→ x = 28/4

→ [ x = 7 ]

Hence, the value of x is 7.

Answer:

mean = 11.66666

median = 11

Step-by-step explanation:

To find the mean, add up all the numbers, then divide by how many numbers

mean = (15+9+13+18+9+6) / 6 = 70/6 = 11 .6666666

To find the median, put the numbers from smallest to largest. then take the middle number.  Since there is an even number, take the two middle numbers and average them

6,9,9,13,15,18

The two middle numbers are 9 and 13

(9+13)/2 = 22/2 = 11

Answer:

11x² -3x

Step-by-step explanation:

We have the product of a sum, of two binomials and one of the initial binomials but we'd like to know the other one.

It's very much like A + B = C, and we have both B and C, but looking to find A.

What would you do in the ABC scenario?

You'd isolate A by transforming the equation to: A = C - B

In this case, C = 12x² - 5x and B = x² - 2x...

A = (12x² - 5x) - (x² - 2x) = 12x² - 5x - x² + 2x

A = 11x² -3x

Answer:

Principal amount= $600

Time= 3 years

Rate of Interest = 6%

SI= PRT/100

= 600x6x3/100

= $108

Interest is $108

Step-by-step explanation:

Answer:

[tex]\frac{5}{21}[/tex]

Step-by-step explanation:

[tex]\frac{5}{9}[/tex] × [tex]\frac{3}{7}[/tex] = [tex]\frac{15}{63}[/tex] = [tex]\frac{5}{21}[/tex]

Answer:

5/63

Step-by-step explanation:

that would be:

 5        3                                        5

----- * ------ = (after reduction)   ----------- = 5/63

 9        7                                      3(21)

Answer:

The wide of television is [tex]43.3\ in[/tex]

Step-by-step explanation:

Let

x----> the wide of television

we know that

Applying the Pythagoras Theorem

[tex]50^{2}=x^{2}+25^{2}[/tex]

Solve for x

[tex]x^{2}=50^{2}-25^{2}[/tex]

[tex]x^{2}=1,875[/tex]

[tex]x=43.3\ in[/tex]

Answer:

The domain of (f*g) (x) is the set of all real numbers; ( -∞, ∞)

Step-by-step explanation:

(f*g) (x) simply means we obtain the product of f(x) and g(x). We are given that;

f(x)=2x

g(x)= 1/x

(f*g) (x) = f(x) * g(x)

(f*g) (x) = 2x * 1/x = 2

This is a horizontal line defined everywhere on the real line. The domain of  (f*g) (x) is thus ( -∞, ∞)

Answer:

All real numbers

Step-by-step explanation:

Given : [tex]f(x)=2x[/tex]

           [tex]g(x)= \frac{1}{x}[/tex]

To Find : the domain of (f*g) (x)

[tex]f(x)=2x[/tex]

[tex]g(x)= \frac{1}{x}[/tex]

[tex](f\cdot g)(x)=2x \times \frac{1}{x}[/tex]

[tex](f\cdot g)(x)=2[/tex]

Since the value of [tex](f\cdot g)(x)=2[/tex]

So, the domain of the function is [tex](f\cdot g)(x)[/tex] is all real numbers .