2. Use a graph to find the solution.

You want to set up an aquarium and need to determine what size tank to buy...

The equation of line in the slope intercept form is c = 1.5 ( t ) + 12 where t is the number of toppings and c is the total cost

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the total cost of pizza with toppings be = c

Let the number of toppings be = t

Let the initial cost of the pizza be = $ 12

Let the cost of each toppings be = $ 1.50

So , the total cost of the pizza with toppings c =  ( cost of each toppings x number of toppings ) + initial cost of the pizza

Substituting the values in the equation , we get

Total cost of the pizza with toppings c = 1.50 ( t ) + 12

Therefore , the value of A is c = 1.50 ( t ) + 12

Hence , the equation is c = 1.50 ( t ) + 12  with slope m = 1.50 and y intercept as 12

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Final answer:

The equation in slope-intercept form for the total cost C of a pizza with t toppings when a pizza costs $12 and each additional topping costs $1.50 is C = 1.50t + 12.

Explanation:

To find the equation in slope-intercept form for the total cost C of a pizza with t toppings at a pizza parlor that charges $12 for a large cheese pizza and $1.50 for each additional topping, we can establish a relationship between the number of toppings and the total cost. Let's use the slope-intercept form of the linear equation, y = mx + b where y is the total cost, m is the cost per topping, x is the number of toppings, and b represents the base price of the pizza without toppings.

The base price of the pizza is $12, which is the y-intercept, and the additional cost per topping is $1.50, which is the slope. Therefore, the equation that represents the total cost C of the pizza with t toppings is:

C = 1.50t + 12

To find the number of answers that are not choice B, subtract the number of answers that are choice B from the total number of questions.

To find the number of answers that are not choice B, we first need to calculate the number of answers that are choice B. Since 25% of the answers are choice B, we can multiply the total number of questions (20) by 0.25 to find that there are 5 answers that are choice B. To find the number of answers that are not choice B, we subtract the number of answers that are choice B from the total number of questions. So, the number of answers that are not choice B is 20 - 5 = 15.

[tex]a_n=n^2-n\\\\\text{Put}\ n=1,\ n=2,\ n=3,\ n=4,\ n=5\ \text{to the equation}.\\\\n=1\to a_1=1^2-1=1-1=0\\\\n=2\to a_2=2^2-2=4-2=2\\\\n=3\to a_3=3^2-3=9-3=6\\\\n=4\to a_4=4^2-4=16-4=12\\\\n=5\to a_5=5^2-5=25-5=20\\\\Answer:\ \boxed{0,\ 2,\ 6,\ 12,\ 20}[/tex]

Answer: -1, 2, 7, 14, 23

Step-by-step explanation:

aₙ = n² - 2

for n=1

a₁ = 1² - 2 = 1-2= -1

for n=2

a₂ = 2² - 2 = 4-2 =2

for n= 3

a₃ =3² - 2 = 9-2=7

for n=4

a₄= 4² - 2 = 16-2=14

for n=5

a₅= 5² - 2=25-2=23

Therefore, the first five terms of the sequence are; -1, 2, 7, 14 and 23

Answer:

1) Translation

2) Rotation

3) Reflection  

Step-by-step explanation:

To make ΔDEF ≅ ΔD'E'F' , we will carry on the following steps:

Step 1: Translate ΔD'E'F' in upward direction, the figure will remain same but it will shift a little in upwards direction.

Step 2 : Rotate ΔD'E'F' about 180°. The figure obtained will be reflection of the original image ΔDEF.

Step 3 : Reflect ΔD'E'F'.

This implies that ΔDEF≅ΔD'E'F'.  

Answer: 27 grams

Step-by-step explanation:

m(x) = 64(0.75)ˣ

m(3) = 64(0.75)³

      = 64(.421875)

      = 27

Answer:

∠NET = 63°

Step-by-step explanation:

We are given a figure with a circle A and a line ET which is tangent to the circle at the point T. Also, the measure of the angle TNG is given to be 27° and we are to find the measure of angle NET.

If we recall the point of tangency, we will remember that the point where a tangent touches the radius of a circle is always a right angle.

That makes the angle NTE to be 90°.

Putting the sum of these angles equal to 180 to get:

90 + 27 + ∠NET = 180

∠NET = 180 - 90 - 27

∠NET = 63°

Answer:

50

Step-by-step explanation:

if x years past  she is twice her daughter's age,

so  we get:

28+x=2(3+x)

x=22,    22+28=50

Answer:

Step-by-step explanation:

Thank you that helped me with mine

eg:

L is 26, C is 4, how many years until L is 2 times as old as C?

26+x=2(4+x)

26+x=8+2X

-8 -8

18+x=2x

-x -x

18=1x

in 18 years L will be 2 times as old as C

Final answer:

The blanks are filled with 'straight line' as angles on a straight line sum to 180°, which is a key concept in geometry related to the properties of angles and triangles.

Explanation:

The sum of the measures of angle 5 and angle 6 is equal to 180° and the sum of the measures of angle 2 and angle 3 is equal to 180° because angles on a straight line measure 180°. This concept is related to the geometric property that when two angles lie on the same line and add up to form a straight angle, their measures sum up to 180°.

In geometry, specifically the study of polygons and angles, we learn that a triangle is a three-sided figure lying on a plane with three angles adding up to 180°. This is called the Triangle Sum Theorem, which is fundamental to understanding the properties of triangles and other polygons.

Answer:

Perimeter = 32.44 unit

Area of triangle = 30 unit²

Step-by-step explanation:

By distance formula distance between (a,b) and (c,d) is [tex]\sqrt{(c-a)^2+(d-b)^2}[/tex]

So, we have

      [tex]AB=\sqrt{(16-2)^2+(2-8)^2}=15.23\\\\BC=\sqrt{(16-6)^2+(2-2)^2}=10\\\\AC=\sqrt{(2-6)^2+(8-2)^2}=7.21[/tex]

Perimeter = 15.23 + 10 + 7.21 = 32.44 unit

We have [tex]s=\frac{15.23+10+7.21}{2}=16.22[/tex]

Area of triangle[tex]=\sqrt{s(s-AB)(s-BC)(s-AC)}=\sqrt{16.22(16.22-15.23)(16.22-10)(16.22-7.21)}=30[/tex]

Area of triangle = 30 unit²

[tex]f(x)=4\cdot2^x\\\\y-intercept\ for\ x=0:\\\\f(0)=4\cdot2^0=4\cdot1=4[/tex]

Answer: Third option (bottom left)

Step-by-step explanation: We want to find which one of the graphs is the graph of the function f(x) = 4*2^x

Let's analyze some interesting points.

f(0) = 4*2^0 = 4*1 = 4

So we need to find the graph that passes through the point (0,4) (this means that intercepts the y-axis in the 4)

The graph that passes through the point (0,4) is the third option (bottom left one)

Answer:

$12.60

Step-by-step explanation:

To find this, you need to remember this equation:

Starting amount x [tex]\frac{100 - percent}{100}[/tex]

Plug these values in:

18 x [tex]\frac{70}{100}[/tex] = 12.6

So the clearance price was $12.60!

Final answer:

By converting the total amount of pizza into an improper fraction and dividing it by the portion each student ate, it's determined that 13 students were fed.

Explanation:

To find out how many students were fed, we first need to convert the total amount of pizza available into a form that can be easily divided by the portion each student eats. The total pizza available is 3 1/4 small pizzas. Since each student ate 1/4 of a pizza, we can see how many times 1/4 fits into 3 1/4 to determine the number of students.

We convert 3 1/4 into an improper fraction to make the calculation easier. 3 1/4 is equivalent to 13/4. Now, we divide 13/4 by 1/4 to find out how many students were fed. This is equivalent to multiplying 13/4 by the reciprocal of 1/4, which is 4/1.

13/4 × 4/1 = 13, meaning that 13 students were fed.

Answer:

1. 29/4

2. 5

3. 6

4. 14/3

5. 29/27

Step-by-step explanation:

Answer: You the answer

Step-by-step explanation: cause your fine

[tex]\frac{y-307,650}{x-9} = 850\\\\y-307,650 =850(x-9)\\\\multiply\\\\y =307,650 +850(x -9)\\\\y =307,650+850(16-9)\\\\y= 313,600[/tex]

The linear equation can be formed as P = P0 + rt. Replacing each variable with the values from the problem, we find that the population of Beth's town on her 16th birthday will be approximately 319,600.

The question refers to a situation of linear growth. It states that the population of Beth's town grows at a constant rate of 850 people per year. If on Beth's 9th birthday the population was 307,650, we can create a linear equation to find the population when she turns 16. This linear equation can be represented as follows: P = P0 + rt, where P is the future population, P0 is the initial population, r is the rate of growth, and t is the time elapsed.

In Beth's situation, we will let her 9th birthday be the starting point (time zero). So, P0 is 307,650, r is 850, and t is 7 (the years from her 9th birthday to her 16th birthday). Plugging these values into our equation gives us P = 307,650 + 850 * 7. Solving the equation gives us P = 313,650 + 5,950 = 319,600. Therefore, the estimated population of Beth's town on her 16th birthday is 319,600.

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Answer:

[tex]P(x)=12.50x-150.[/tex]

Step-by-step explanation:

Let x be the number of tickets sold. If a theater group charges $12.50 per ticket for its opening play of the season, then x tickets cost $12.50x. Production costs for the play are $150. Then the profit the theater group earns from selling x tickets is

[tex]P(x)=12.50x-150.[/tex]

Answer:

$8779.52

Step-by-step explanation:

24% = 0.24.

Each year the value of the car = 1 - 0.24 = 0.76 of the previous year.

Value after 3 years = 20,000 * (0.76)^3

=  $8779.52

Answer:

F(-4) = -3313

Step-by-step explanation:

To solve this, let x=-4

f(x) = 3x^5 + 4x^3-x+11

f(-4) = 3(-4)^5 + 4(-4)^3 -(-4) +11

     = 3(-1024) +4 (-64) +4+11

    = -3072 - 256+15

     = -3313

Answer:

This means the function touches the x-axis at -1 but does not cross.

Step-by-step explanation:

A polynomial graph has several features we look for to determine the equations.

This means the function touches the x-axis at -1 but does not cross.

SX is equal to UX

US and Rt are the lines which make the center of the parallelogram. Hence the center of both lines is X so both the lines must be present at the same distance from the mid point. US is divided in two equal parts on point X and we know that center point is always equidistant from the end points. X must be equidistant from both UX and SX so we can say that SX = UX.

f(x) = 4x - 18

f(-3) - put x = -3 to the equation of the function

f(-3) = 4(-3) - 18 = -12 - 18 = -30

f(x) = -46

We have the equation:

4x - 18 = -46       add 18 to both sides

4x = -28    divide both sides by 4

x = -7

Answer:

see below

Step-by-step explanation:

The "fundamental theorem of algebra" tells you the number of roots of a polynomial is equal to its degree. This includes real and complex roots and counts repeated roots the number of times they are repeated. (Real numbers are a subset of Complex numbers, so the choice of "complex" for this problem is appropriate.)

_____

The given quadratic can be solved using the quadratic formula:

for ax²+bx+c=0, the solutions are

... x = (-b±√(b²-4ac))/(2a)

Here, a=2, b=-4, c=-1, so ...

... x = (4 ±√(16 -4·2·(-1)))/(2·2)

... x = (2±√6)/2

Answer:

1. complex    2. 2+6      3. 2-6

Step-by-step explanation:

i took the test :)

Answer:

I would say...

C.)x - 5 = 3 (x + 2)

Really really sorry if I'm wrong...

One thing I can say is that when it says 5 less than a #, that means the # is being subtracted from another #...

The correct equation for the situation 'Five less than a number is equal to three times the sum of the number and two' is x - 5 = 3(x + 2).

The correct equation for this situation is C.) x - 5 = 3(x + 2).

Here's how you can decipher the sentence: 'Five less than a number' translates to 'x - 5' in mathematical terms where 'x' stands for the number. 'Is equal to' signifies the equality sign '='. Finally, 'three times the sum of the number and two' corresponds to '3(x + 2)', where 'x' is the number, '2' is the two and '3' the three times mentioned in the equation. So, putting it all together gives you

x - 5 = 3(x + 2).

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Joe has 8 green pepper plants and 28 red pepper plants in his garden.

Let's denote the number of green pepper plants as G and the number of red pepper plants as R.

According to the given information, the ratio of green pepper plants to red pepper plants is 2 to 7.

This can be written as G:R = 2:7.

It is also mentioned that there are 20 more red pepper plants than green pepper plants. This can be written as R = G + 20.

Now, we can substitute the value of R from the second equation into the first equation:

G:G+20 = 2:7

By cross-multiplying, we have 7G = 2(G+20).

Simplifying the equation, we get 7G = 2G + 40.

Subtracting 2G from both sides, we have 5G = 40.

Dividing both sides by 5, we get G = 8.

Therefore, there are 8 green pepper plants and 8 + 20 = 28 red pepper plants in Joe's garden.

Answer:

[tex]\$164.5[/tex]

Step-by-step explanation:

Bonnie deposits $70.00 into a new savings account.

The account earns 45% simple interest per year.

She neither added or removed from the savings account for 3 years.

We know that,

[tex]i=\dfrac{P\cdot r\cdot r}{100}[/tex]

here,

i = interest,

P = principal = $70,

r = rate of interest = 45%,

t = time = 3 years,

Putting the values,

[tex]i=\dfrac{70\cdot 45\cdot 3}{100}=\$94.5[/tex]

So the total amount will be,

[tex]=\text{Principal}+\text{Interest}[/tex]

[tex]=70+94.5[/tex]

[tex]=\$164.5[/tex]

Answer:

its 4.5 not 45

Step-by-step explanation:

Answer:

None of the Above

Step-by-step explanation:

As it is given that

cosФ= 3/2

and Ф lies in quadrant 4

Now in quadrant 4 we know that by the rules of trigonometry that

cos Ф is positive in 4th quadrant also in 4th quadrant

and sinФ is negative in 4th quadrant

also we know that by simple rules of trigonometry in a right angled triangle

cos Ф=[tex]\frac{Base}{Hypotenuse}[/tex] =[tex]\frac{3}{2}[/tex]

now from the law of trigonometry

cos²Ф+sin²Ф=1

From this we derive the value of sinФ

solving the equation

sin²Ф=1-cos²Ф

Putting in the values of cos Ф

sin²Ф=1-[tex](\frac{3}{2})^{2}[/tex]

sin²Ф=1-[tex](\frac{9}{4})[/tex]

solving the fraction

sin²Ф=[tex](\frac{4-9}{4})[/tex]

sin²Ф=[tex](\frac{-5}{4})[/tex]

so taking square root of both sides

[tex]\sqrt{sin^{2}\alpha}=\sqrt{\frac{-5}{4} }[/tex]

here

[tex]\alpha[/tex]=Ф

so it becomes

sin Ф=[tex]\frac{\sqrt{-5} }{2}[/tex]

as we know that in imaginary numbers

[tex]\sqrt{-1}[/tex] = ι

so the given becomes

sin Ф=[tex]\frac{{-5ι} }{2}[/tex]

Which is the value of sin Ф

And in the given values we can see that it is none of the values

Also seeing the question we can see that the question is absurd because

cos Ф= base / hypotenuse

in our question we can see that base =3 and hypotenuse = 2

but in real geometry this is the rule that hypotenuse can never be smaller then base either it is equal to base or greater then base

the formula for finding value of finding hypotenuse is

hypotenuse ² = base ² + perp ²

so this formula shows that if perp is 0 then hypotenuse will be equal to base

in other cases it would be greater then base

Answer:

- 1/ 2

Step-by-step explanation

-1\ 2

Use the Pythagorean identity, sin2Θ + cos2Θ = 1 to get sinΘ = ±1 - cos2Θ, then solve for sinΘ.

Answer:

angle(ADB)=angle(CBD)

ADC+DCB=180

AE=CE

Step-by-step explanation:

we will verify each options

option-A:

we know that

ABCD is a parallelogram

so, AD and BC are parallel

and alternate interior angles are always equal

so,

angle(ADB)=angle(CBD)

so, this is TRUE

option-B:

we know that

ABCD is a parallelogram

so, AD and BC are parallel

so, we get

ADC+DCB=180

so, this is TRUE

option-C:

Since, AC is a diagonal of parallelogram

so, E is the mid-point between AC

AE=CE

[tex]angle(DEC)\neq angle(DEA)[/tex]

so, this is FALSE

option-D:

Since, AC is a diagonal of parallelogram

so, E is the mid-point between AC

AE=CE

so, this is TRUE

option-E:

Since, AC and DB are diagonals of parallelogram

so, they can not be equal

so, this is FALSE

So the first thing we need to do is set up an equation (using x to represent the number). Then, we'll solve it to get the answer.

Step 1: Translate the word problem into an equation

Word problem: The sum of nine and six-tenths and a number is thirteen and two-tenths.

Equation: [tex]9 \frac{6}{10}[/tex] + x = [tex]13 \frac{2}{10}[/tex]

Step 2: Isolate x by subtracting [tex]9 \frac{6}{10}[/tex] from each side

[tex]9 \frac{6}{10}[/tex] + x -  [tex]9 \frac{6}{10}[/tex] = [tex]13 \frac{2}{10}[/tex] -  [tex]9 \frac{6}{10}[/tex]

Step 3: The numbers on the left cancel out, leaving x alone

x =  [tex]3 \frac{6}{10}[/tex]

Step 4: Convert the answer to decimals

x = 3.6

Answer:

its B

Step-by-step explanation:

Answer:

60 percent

Step-by-.step explanation:

You need to convert 3/5 to a percentage.

This is 3*100 / 5

= 300 / 5

= 60 per cent

Final answer:

Roasted beans retain 3/5 of their initial weight, which is equivalent to 60% when converted to a percent.

Explanation:

To convert this fraction to a percentage, we follow the steps outlined in the explanation: dividing the numerator by the denominator to get a decimal value, and then multiplying by 100 to express it as a percentage. In this case, 3 divided by 5 equals 0.60, which when multiplied by 100 gives 60%.

The roasted beans retain approximately 3/5 of their initial weight after roasting. To determine what percentage of their initial weight they retain, we convert the fraction 3/5 to a percent. To do this:

Therefore, roasted beans retain 60% of their initial weight.