Give your answer in its simplest form.

Answer:

a₂ = 13

a₃ = 11

Step-by-step explanation:

Given a₁ = 15

The recursive formula is given as:  [tex]$ a_n = a_{n - 1} - 2 $[/tex]

This means that [tex]$ n^{th }[/tex] term is determined by subtracting 2 from the [tex]n -1^{th }[/tex] term.

Here, [tex]$ a_1 = 15 $[/tex]

Therefore, [tex]$ a_2 = a_1 - 2$[/tex]

= 15 - 2 = 13

Now, [tex]$ a_3 = a_2 - 2 $[/tex]

= 13 - 2 = 11

Therefore, a₂ = 13

a₃ = 11

Let the number be x. "Three times a number increased by 10" is mathematically translated as

3x + 10

"is equal" is mathematically translated as twenty less than six times the number" is mathematically translated as

6x - 20

The whole sentence "Three times a number increased by ten is equal to twenty less than six times the number" is translated as

3x + 10 = 6x - 20

We now solve the above linear equation to find the number x

3x - 6x = - 20 - 10

- 3x = - 30

x = 10

Check answer

Three times a number increased by ten : 3 × 10 + 10 = 40

Twenty less than six times the number : 6 × 10 - 20 = 40

Final answer:

The simple linear equation given can be solved by defining the unknown number as 'x', setting up the equation, and solving for 'x'. After isolating x on one side, the result is that x equals 10.

Explanation:

The question is a classic example of a simple linear equation in one variable. We can define a variable, let's call it x, to represent the number in question. The problem statement translates to the equation:

3x + 10 = 6x - 20

Now, let's solve for x by isolating it on one side of the equation:

Subtract 3x from both sides:

10 = 3x - 20

Add 20 to both sides to get:

30 = 3x

Finally, divide both sides by 3 to find x:

x = 10

Therefore, the number we are looking for is 10.

Answer:

(5,1)

Step-by-step explanation:

Equation of a straight ine in slope intercept form is [tex]y-y_{1} =m\times(x-x_{1} )[/tex]. from that calculate the both equations of straight lines sidewalks1 and sidewalks2 they are x+y=6 and 2x+y=11 on solving both of the equations we get the value of x to be 5 and the value of y to be 1.hence the system of linesr equations intersect at the point (5,1).

Answer:

Option C.

Option E.

Step-by-step explanation:

Let be "f" the price of a loaf of French bread, "w" the price of the grain bread and "c" the price of the cinnamon raisin bread.

We know that Melissa paid twice as much for the whole grain bread as for the French bread. This can be represented with this equation:

[tex]w=2f[/tex]       [Equation 1]

Since she paid $2.50 more for the cinnamon raisin bread than for the whole grain bread, we can write this equation:

[tex]c=w+2.50[/tex]       [Equation 2]

The total amount of money she spent was $11.25, then:

[tex]f+w+c=11.25[/tex]     [Equation 3]

Now you must substitute the Equation 1 into the Equation 2:

[tex]c=2f+2.50[/tex]      [Equation 4]

Substituting the [Equation 1] and the [Equation 4] into the [Equation 3], you get:

[tex]f+2f+(2f+2.50)=11.25[/tex]

If you simplify the equation, you get:

[tex]5f=8.75[/tex]

The correct equations that describe this situation are: A. f + f + (f + 2.50) = 11.25 and D. 2f + 2.50 = 11.25.

The correct equations that describe this situation are:

To solve this problem, let's assign variables to represent the prices. Let f be the price of a loaf of French bread. According to the information given, the whole grain bread costs twice as much as the French bread, so its price is 2f. The cinnamon raisin bread costs $2.50 more than the whole grain bread, so its price is (2f + 2.50). The total cost of the 3 loaves is $11.25, so we can set up the equations:

Simplifying these equations gives us the correct choices A and D.

Answer:

[tex]f(x)=20(2.5^x)[/tex]

Step-by-step explanation:

we know that

The function of the graph is a exponential function of the form

[tex]f(x)=a(b^x)[/tex]

Looking at the graph

we have the points

(0,20) and (1,50)

Remember that if a point lie on the graph, then the point must satisfy the function

Verify each case

For x=1, f(x)=50

case 1) we have

[tex]f(x)=20(1.5^x)[/tex]

For x=1

[tex]f(1)=20(1.5^1)=30[/tex]

so

[tex]30\neq 50[/tex]

therefore

This function is not represented by the graph

case 2) we have

[tex]f(x)=20(1.4^x)[/tex]

For x=1

[tex]f(1)=20(1.4^1)=28[/tex]

so

[tex]28\neq 50[/tex]

therefore

This function is not represented by the graph

case 3) we have

[tex]f(x)=20(2.5^x)[/tex]

For x=1

[tex]f(1)=20(2.5^1)=50[/tex]

[tex]50=50[/tex]

For x=0

[tex]f(0)=20(2.5^0)=20[/tex]

[tex]20=20[/tex]

therefore

This function is represented by the graph

case 4) we have

[tex]f(x)=20(2.25^x)[/tex]

For x=1

[tex]f(1)=20(2.25^1)=45[/tex]

so

[tex]45\neq 50[/tex]

therefore

This function is not represented by the graph

Answer:

f(x)=20(2.5)x

Step-by-step explanation:

did the test and was correct

Answer:

Total number of people in the line for the dunking machine is 8.

Step-by-step explanation:

Here, let us assume the number of people in the line for hoop shoot = 12

So, the number of people in the line for cakewalk

=  One- Third of the number of people in line for Hoop Shoot

= [tex]\frac{1}{3}  \times 12 = 4[/tex]

Also, the number of people in the line for dunking machine

=  2 x ( The number of people in line for Cakewalk)

=  2  x  4  = 8

Hence, the total number of people in line for the dunking machine is 8.

Final answer:

To find the number of people in line for the dunking machine when given the number in line for the hoop shoot, we calculate the cake walk line as one-third of the hoop shoot line, then double that for the dunking machine line, resulting in 8 people.

Explanation:

Given that the line for the dunking machine was twice as long as the cake walk line and that the cake walk line was one-third the length of the hoop shoot line, we can derive the relationship between the numbers of people in line for each activity.

First, since there were 12 people in line for the hoop shoot, and given that the cake walk line was one-third of this, the cake walk had 12 / 3 = 4 people in line.

Next, since the dunking machine line was twice as long as the cake walk line, it had 4 × 2 = 8 people in line.

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:

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

Where:

m: It's the slope

b: It is the cut-off point with the y axis

According to the statement we have two points through which the line passes:

[tex](x_ {1}, y_ {1}): (2,2)\\(x_ {2}, y_ {2}): (12, -3)[/tex]

We found the slope:

[tex]m = \frac {y_ {2} -y- {1}} {x_ {2} -x_ {1}} = \frac {-3-2} {12-2} = \frac {-5} {10 } = - \frac {1} {2}[/tex]

Thus, the equation is of the form:

[tex]y = - \frac {1} {2} x + b[/tex]

We substitute one of the points and find "b":

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

Finally, the equation is of the form:

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

We write the equation of the standard form[tex]ax + by = c[/tex]

[tex]y-3 = -\frac {1} {2} x\\2y-6 = -x\\x + 2y = 6[/tex]

ANswer:

[tex]x + 2y = 6[/tex]

Answer:

C

Step-by-step explanation:

THe markup is the difference between the Selling Price and Cost.

As a percentage, we would get the markup in terms of cost.

First,

Selling Price = 4.50

Cost = 3.00

So,

Markup = SP - Cost = 4.50 - 3.00 = 1.50

As a percentage, we would divide the markup by cost and then multiply the answer by 100. That's:

1.50/3 = 0.5 * 100 = 50%

THe markup is 50%

C is the correct answer.

Answer:

C

Step-by-step explanation:

The markup is the difference between the Selling Price and Cost.

As a percentage, we would get the markup in terms of cost.

First,

Selling Price = 4.50

Cost = 3.00

So,

Markup = SP - Cost = 4.50 - 3.00 = 1.50

As a percentage, we would divide the markup by cost and then multiply the answer by 100. That's:

1.50/3 = 0.5 * 100 = 50%

The markup is 50%

C is the correct answer.

Answer:

5.4

Explanation:

a²+b²=c²

2²+5²= 4+25

4+25=29

Now we have to square root the 29 which would make the answer 5.4

5.4 is the slant height of the triangular prism.

The given figure is a triangular based pyramid and in order to determine the slant height, we will apply the pythagoras theorem as shown:

Hypotenuse = s

Opposite = 5

Adjacent = 4/2 = 2

According to the theorem:

hyp² = opp² + adj²

Substitute

s² = 5² + 2²

s² = 25 + 4

s² = 29

s = 5.4

Hence the slant height, s, of the triangular prism is 5.4

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The perimeter of given rectangle can be given by: [tex]14x-6[/tex]

Step-by-step explanation:

Let

L be the width of the rectangle and

W be the width of the rectangle

Here,

L = 6x-2

W=x-1

The perimeter of rectangle is given by:

[tex]P=2(L+W)[/tex]

Putting the values of L and W

[tex]P=2[(6x-2)+(x-1)]\\=2(6x-2+x-1)\\=2(7x-3)\\=14x-6[/tex]

The perimeter of given rectangle can be given by: [tex]14x-6[/tex]

Keywords: Rectangle, Perimeter

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Answer:

No

Step-by-step explanation:

-3/0 is actually undefined because dividing by zero is undefined but 0/-3=0 because 0 divided by anything is 0.

Answer:

Well, a parallelogram is a four-sided figure with opposite sides parallel. A rectangle is a figure with four straight sides and four right angles, and two of those sides are adjacent and unequal So, in short, all rectangles are parrolegrams but not all parrolelograms are rectangles. The answer would be: Yes, it is possible.

Yes, it is possible for Brooke to draw a parallelogram that is not a rectangle.

Yes, it is possible for Brooke to draw a parallelogram that is not a rectangle. A parallelogram is a quadrilateral with opposite sides that are parallel. While a rectangle is a specific type of parallelogram with four right angles, other parallelograms can have angles that are not right angles. For example, a rhombus is a parallelogram with all sides congruent, but its angles are not right angles.

Answer:

x=0 and x=8

Step-by-step explanation:

The x-intercept is on the x-axis, so we must find x when y=0. f(x) is basically y and y=0, so 0=x^2-8x= x(x-8). For x(x-8) to equal  0, either x is equal to 0 (x=0) or x-8 is equal to 0 (so x is equal to 8). So the two intercepts are x = 0 and x = 8.

I hope this helped! :)

Answer:

You are 48 inches

Step-by-step explanation:

You would just do the opposite of multiplication which is division so do 60/1.25 is 48 inches

Answer:

The width is 5 inches and the height is 18 inches.

Step-by-step explanation:

The area of a triangle can be calculated as:

A = w*h/2

where w is the width of the base, and h is the height.

then we have that:

w*h/2 = 45 in^2

and the height is 2 less than 4 times the width.

h = 4*w - 2in

then we have a system with 2 equations:

w*h/2 = 45 in^2

h = 4*w - 2in

We can replace the second one in the first one and solve it for w.

w*(4*2 - 2in)/2 = 45 in^2

2w^2 - w = 45in^2

2w^2 - w - 45in = 0

then we have to solve the quadratic equation:

the solutions are:

w = (1 +- √(1^2 - 4*2*(-45))/(2*2) = (1 + - √361)/4

where we have two solutions for w, one for each sign of the square root.

we obviously need to take the positive solution (because we can not have a negative length)

w = (1 + √361)/4 = 5in

now, we can replace it in the equation "h = 4*w - 2in" to get the height.

h = 4*5in - 2in = 18in

The width and height of the triangle can be calculated using the given information and the equations for the area of a triangle and the relationship between the width and height.

The subject of this question is algebraic problem solving, specifically involving the concept of an area of a triangle. First, we need to remember that the area of a triangle is calculated using the formula A = 1/2 * base * height. We know that the area equals 45 square inches, so we can write an equation: 45 = 1/2 * width * height. Additionally, the question states that height is two less than four times the width, which is another equation: height = 4 * width - 2.

Now, we can substitute the height (which is 4 * width - 2) into our formula for the area. This gives us the equation: 45 = 1/2 * width * (4 * width - 2), which will allow us to solve for the width of the triangle. After solving for the width, we can use the equation height = 4 * width - 2 to find the height of the triangle.

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Answer:

68+28k

Step-by-step explanation:

Answer:

Let the two nos. Be x and y

xy = -32

x - y = -12

(x-y)^2 = (x+y)^2 - 4xy

144 = (x+y)^2 + 128

16 = (x+y)^2

Therefore x+y = +4, -4

When x+y = +4, x-y = -12

x = -4, y = 8

When x+y = -4, x-y = -12

x= -8, y = 4

Hope this helps!

Answer:

Step-by-step explanation:

Numbers : 8 or -8       4, or -4

-8*4=-32             -4+8=  -32

-8-4= -12             -4-8 = -12

Answer:

[tex]64=2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2=2^6[/tex]

Step-by-step explanation:

Gabrielle and John each

wrote the prime factorization of 64.

64 can be break into 32 times 2

32 can be break into 16 times 2

16 can be break into 8 and 2

8 can be break into 4 times 2

4 can be break into 2 times 2

So 64 is equal to 2 times 2 times 2 times 2 times 2 times 2

[tex]64=2^6[/tex]

The question involves analyzing the prime factorization of the number 64, which should be 2¶. The correctness of Gabrielle and John's factorizations can be checked by ensuring the base is 2 and the power is 6. Any deviation from this would indicate a mistake in their factorization.

The question concerns the prime factorization of the number 64. A prime factorization is the expression of a number as a product of prime numbers. For the number 64, which is a power of 2, the prime factorization should be 2¶ since 64 is 2 multiplied by itself 6 times (2 x 2 x 2 x 2 x 2 x 2).

If Gabrielle and John wrote their prime factorizations of 64 differently, at least one of them has made an error. To verify if their prime factorizations are correct, they should end up with the same base number, which is 2 in this case, raised to the same power, which should be 6 for the number 64. Any other combination of numbers in the factorization would be incorrect, since 64 is not divisible by any other prime numbers.

When analyzing their work, one should check if they thoroughly factored the number down to only prime numbers and did not mistakenly include a composite number or an incorrect exponent in the factorization. To correct errors, divide the number progressively by the prime number 2 until the quotient is 1. Each division step represents an exponent in the prime factorization of 64.

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Without further information or context like a diagram, it's not possible to accurately determine the measure of angle 1 based on the given measure of angle 7.

Without a diagram or additional information, it's impossible to definitively determine the measure of angle 1 (m∠1) based only on the measure of angle 7 (m∠7 = 50°). In geometry, the relationship between two angles can vary largely depending on their position relative to each other. For instance, if angle 1 and angle 7 are complementary angles, m∠1 would be 40°. However, if they're supplementary, m∠1 would be 130°. If they're vertical or corresponding angles, m∠1 would be equal to m∠7, which is 50°.

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Answer:

0.0008235

Step-by-step explanation:

8.235 x 10⁻⁴

10 to the exponent of a negative number means the decimal place is moved to the left to make the number smaller.

Move the decimal place 4 over the left.

0.0008235

Answer:

All possible values for the number of tables that the store must sell in order to meet the requirements are 9, 10, 11, 12, 13.

Step-by-step explanation:

Let x be the number of chairs sold and y be the number of tables sold.

Chairs are sold for $50 each, then x chairs cost $50x.

Tables are sold for $250 each, then y tables cost $250y.

In total, x chairs and y tables cost $(50x+250y).

Every day, the store can ship no more than 36 pieces, then

[tex]x+y\le 36[/tex]

Every day, the store must sell at least $3,400 worth of chairs and tables, then

[tex]50x+250y\ge 3,400[/tex]

If 23 chairs were sold, then x = 23. Substitute it into the inequalities:

[tex]23+y\le 36\Rightarrow y\le 13\\ \\50\cdot 23+250y\ge 3,400\Rightarrow 250y \ge 2,250,\ \ \ y\ge 9[/tex]

Thus [tex]9\le y\le 13[/tex]

This means all possible values for the number of tables that the store must sell in order to meet the requirements are 9, 10, 11, 12, 13.

Answer:

9,10,11,12,13

Step-by-step explanation:

cuz

Answer with Step-by-step explanation:

We are given that

M is the mid point of AB

[tex]\angle A=\angle B[/tex]

We have to match the reasons with statements given in proof.

Proof:

1.Statement:[tex]\angel A=\angle B[/tex], M is the midpoint of AB

Reason: Given

2.Statement:[tex]AM=MB[/tex]

Reason: Definition of midpoint

3.Statement:[tex]AC=BC[/tex]

Reason:Opposite sides of equal angle are equal.

4.Statement:[tex]\triangle AMC\cong \triangle BMC[/tex]

Reason:SAS Postulate

Answer:

Proof is below.

Step-by-step explanation:

Given: < A = < B , M is the midpoint of AB

Definition of midpoint: AM = MB

Sides opposite = <'s are equal: AC = BC

Triangle AMC congruent to triangle BMC: SAS

Hence, proved.

Answer:

Answer is (-5,1)

Step-by-step explanation:

Plug in the values and find the only one in the shaded region.

Answer:

I think it would be D, (1,2)

Answer:

$8 each

Step-by-step explanation:

Cost of the gift= $90- $42= $48

Each friend pays: $48 divided by 6= $8

The total cost of the gift is $48, which is calculated by subtracting the change received ($42) from the amount paid ($90). Divided by six friends, each friend pays $8 for the gift.

Calculating Individual Payments for a Gift

To determine how much each friend pays for the gift, we first need to calculate the total cost of the gift. The friends together paid $90, and they received $42 in change. This means that the actual cost of the gift is the amount paid minus the change received:

Total cost of the gift = $90 - $42 = $48

Since six friends are sharing the cost equally, we divide the total cost by the number of friends to find out how much each person pays. To find the amount each friend pays:

Cost per friend = Total cost of the gift / Number of friends

Cost per friend = $48 / 6 = $8 per friend.

Therefore, each friend pays $8 for the gift.

Answer:

12.252, 12.26, 12.387, 12.4

Step-by-step explanation:

These are the only numbers in a series that are always increasing.

The first series (0.13, 0.31, 0.04, 0.5) and fourth series (6.009, 6.015, 6.241, 6.2) all have an area where they decrease (0.04 and 6.2 respectively).

The second series of numbers is in decreasing order, rather than increasing order. This can not be the answer.

Step-by-step explanation:

C. will be your answer.

Answer:

n > 3

Step-by-step explanation:

n - 5 > -2

Add 5 to both sides

n > 3

-5 is neither greater or equal to -2.

-2 is greater than -5.

Or, if you meant if 5 is greater than or equal to -2, then 5 is greater than -2.

Edit: Oh, wait nevermind I didn't see the N there

How do I delete my answer?

Answer:

x^7

Step-by-step explanation:

(x^5)(x^2)=x^(5+2)=x^7

Answer:

[tex]\large\boxed{x=13\dfrac{79}{107}\approx13.74}[/tex]

Step-by-step explanation:

[tex]x(0.07)+x=14.70\qquad\text{combine like terms}\\\\(0.07+1)x=14.70\\\\1.07x=14.70\qquad\text{divide both sides by 1.07}\\\\x=\dfrac{14.70}{1.07}\\\\x=\dfrac{14.70\cdot100}{1.07\cdot100}\\\\x=\dfrac{1470}{107}\\\\x=13\dfrac{79}{107}\approx13.74[/tex]

Answer: 13/30 remaining

Step-by-step explanation:

well... 1 - 2/5 - 1/6 = 13/30 remaining

we use "1" to denote the money she began with