Justin opens a savings account with $4. He saves $2 each week. Does a linear function or a nonlinear function represent this situation? Explain.

Answer:

see the explanation

Step-by-step explanation:

we know that

An isosceles triangle has two equal sides

step 1

Find the coordinates of point X (midpoint of segment AC)

we have

A(0,2a), C(2a,0)

The formula to calculate the midpoint between two points is equal to

[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

substitute the values

[tex]X(\frac{0+2a}{2},\frac{2a+0}{2})[/tex]

[tex]X(a,a)[/tex]

step 2

Find the length side AX

the formula to calculate the distance between two points is equal to

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

we have

A(0,2a), X(a,a)

substitute

[tex]AX=\sqrt{(a-2a)^{2}+(a-0)^{2}}[/tex]

[tex]AX=\sqrt{(-a)^{2}+(a)^{2}}[/tex]

[tex]AX=a\sqrt{2}\ units[/tex]

step 3

Find the length side BX

the formula to calculate the distance between two points is equal to

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

we have

B(0,0), X(a,a)

substitute

[tex]BX=\sqrt{(a-0)^{2}+(a-0)^{2}}[/tex]

[tex]BX=\sqrt{(a)^{2}+(a)^{2}}[/tex]

[tex]BX=a\sqrt{2}\ units[/tex]

step 4

Compare the length side AX and BX

[tex]AX=a\sqrt{2}\ units[/tex]

[tex]BX=a\sqrt{2}\ units[/tex]

[tex]AX=BX[/tex]

so

The triangle AXB has two equal sides

therefore

Triangle AXB is an isosceles triangle

Answer:

Soooooooooooooo

Step-by-step explanation:

Okay.... Let me look up how to do this

Answer:

The total number of lower reserved tickets is 304  and

The total number of upper reserved tickets is 42  

Step-by-step explanation:

Given as :

The total tickets purchased = 346

The price for lower tickets = $ 9.50

The price for upper tickets = $ 8.00

The total amount spent on tickets = $ 3224

Let the number of lower tickets = L

The number of upper tickets = U

Now, According to question

L + U = 346     ........1

And 9.50 L + 8 U = 3224    ....2

so , 8 ( L + U ) = 346 × 8

or, 8 L + 8 U = 2768

And 9.50 L + 8 U = 3224

Now, solving equation

( 9.50 L + 8 U ) - ( 8 L + 8 U ) = 3224 - 2768

Or, 1.50 L + 0 = 456

Or, L = [tex]\frac{456}{1.50}[/tex]

∴   L = 304

Put the value of L in eq 1

So, L + U = 346  

I.e U = 346 - L

Or, U = 346 - 304

∴   U = 42

Hence The total number of lower reserved tickets is 304  and

The total number of upper reserved tickets is 42   .  Answer

2 brown, 8 yellow, 8 green, thus our sample space is 2+8+8 = 18.

What is the probability that the card is NOT yellow?  How many non-yellow are there?  well 2 + 8 = 10, favorable outcomes.

[tex]\bf \cfrac{\stackrel{\textit{favorable outcomes}}{10}}{\underset{\textit{sample space}}{18}}\implies \cfrac{5}{9}\implies 0.\overline{555}\qquad \approx \qquad 55.6\%[/tex]

Answer:

16 ounces of clay he need.

Step-by-step explanation:

Given:

Reggie had 2-pound bricks of clay and his job is to give 4 ounces of clay to each student.

There are total 28 students.

Now, to get how much ounces of clay does the each student  have first we multiply the number of students to the number of ounces of clay.

Number of students × Number of ounces of clay:

[tex]28\times 4[/tex]

[tex]112[/tex]

Now, total amount of clay ounces Reggie had= 3×32=96 ounces. (1 pound = 16 ounces, 2 pound = 32 ounces.)

So, the total amount of clay he need is = [tex]112-96[/tex]

                                                                 = [tex]16[/tex]

Therefore, 16 ounces of clay he need.

Answer:

Reggie requires 16 Ounces more clay.

Step-by-step explanation:

Given:

Reggie took from shelf 3 of 2 pounds bricks of clay from shelf.

1 pound = 16 ounces

2 pounds = 32 ounces

Total Clay Reggie has in ounces = [tex]3\times 32\ ounces = 96 \ ounces[/tex]

Total Students in his class = 28 students

his job is to distribute 4 ounces of clay to each child

Total number of clay required for whole class in ounces = [tex]28\times4 = 112[/tex]

Remaining Amount of clay requires in ounces = Total number of clay required for whole class in ounces - Total Clay Reggie has in ounces = [tex]112 \ ounces - 96 \ ounces = 16 \ ounces[/tex]

Hence, Reggie requires 16 Ounces more clay to distribute among the whole class

Step-by-step explanation:

cotx=t

t^2-6t-5=0

t=cotx=1or5

The standard form of a parabola with points through (2, 0) (3, 2) (4, 6)

is y = x² - 3x + 2 ⇒ 3rd answer

Step-by-step explanation:

The standard form of a parabola is y = ax² + bx + c, where a, b , c are constant

To find a , b , c

∵ The standard form of a parabola is y = ax² + bx + c

∵ The parabola passes through points (2 , 0) , (3 , 2) , (4 , 6)

- Substitute the coordinates of each point in the equation

Point (2 , 0)

∵ x = 2 and y = 0

∴ 0 = a(2)² + b(2) + c

∴ 0 = 4a + 2b + c

- Switch the two sides

∴ 4a + 2b + c = 0 ⇒ (1)

Point (3 , 2)

∵ x = 3 and 2 = 0

∴ 2 = a(3)² + b(3) + c

∴ 2 = 9a + 3b + c

- Switch the two sides

∴ 9a + 3b + c = 2 ⇒ (2)

Point (4 , 6)

∵ x = 4 and y = 6

∴ 6 = a(4)² + b(4) + c

∴ 6 = 16a + 4b + c

- Switch the two sides

∴ 16a + 4b + c = 6 ⇒ (3)

Subtract equation (1) from equations (2) and (3)

∴ 5a + b = 2 ⇒ (4)

∴ 12a + 2b = 6 ⇒ (5)

- Multiply equation (4) by -2 to eliminate b

∴ -10a - 2b = -4 ⇒ (6)

- Add equations (5) and (6)

∴ 2a = 2

- Divide both sides by 2

∴ a = 1

Substitute the value of a in equation (4) to find b

∵ 5(1) + b = 2

∴ 5 + b = 2

- Subtract 5 from both sides

∴ b = -3

Substitute the value of a and b in equation (1) to find c

∵ 4(1) + 2(-3) + c = 0

∴ 4 - 6 + c = 0

- Add like terms

∴ -2 + c = 0

- Add 2 to both sides

∴ c = 2

Substitute the values of a , b , c in the standard form above

∵ y = ax² + bx + c

∵ a = 1 , b = -3 , c = 2

∴ y = (1)x² + (-3)x + (2)

∴ y = x² - 3x + 2

The standard form of a parabola with points through (2, 0) (3, 2)

(4, 6) is y = x² - 3x + 2

There is another solution you can substitute the x-coordinate of each point in each answer to find the corresponding value of y, if the value of y gives the same value of the y-coordinate of the point for the three points then this answer is the standard form of the parabola

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Answer:

C. y = x^2 - 3x + 2

Step-by-step explanation:

(4,6)

6 = 4² - 3(4) + 2

6 = 16 - 12 + 2

6 = 6

2 = 2

(3,2)

2 = 3² - 3(3) + 2

2 = 9 - 9 + 2

2 = 2

(2,0)

0 = 2² - 3(2) + 2

0 = 4 - 6 + 2

0 = 0

Answer:2 hrs

Step-by-step explanation:

x+2x+3x=12

6x=12

x=2

Answer:

(cosx + 2)(cosx - 1)

Step-by-step explanation:

Using the trigonometric identity

cos²x + sin²x = 1 ⇒ sin²x = 1 - cos²x

Given

cosx - sin²x - 1

= cosx - (1 - cos²x) - 1

= cosx - 1 + cos²x - 1

= cos²x + cosx - 2

= (cosx + 2)(cosx - 1) ← in factored form

Answer:

The other half of the coordinate is 9  

Step-by-step explanation:

Given as :

The points is ( a , 5 )

The line equation is 4 x - 7 y = 1

Now if the given points lies on the given line , then it must satisfy the line equation

So , We have to  put the points on the given line

I. e 4 x - 7 y = 1

And the points as ( x , y ) = ( a , 5 )

So , 4 × a - 7 × 5 = 1

Or, 4 a - 35 = 1

or, 4 a = 1 + 35

Or , 4 a = 36

∴  a = [tex]\frac{36}{4}[/tex]

I.e  a = 9

So, The value of coordinates as ( a , 5 ) is ( 9 , 5 )

Hence The other half of the coordinate is 9  . Answer

Bar graphs are effective for illustrating and comparing quantitative categories like size, quantity, rates, and distances. The bars can represent different entities and their height indicates a numerical or percentage value. This visual comparison aids in identifying data patterns, trends and relationships.

Bar graphs are a useful form of data representation in mathematics, especially when needing to illustrate and compare quantitative categories such as size, quantity, rates, and distances. In these graphs, just as it shows in Figure A7 and Figure A8, the bars can denote different categories like countries or years, and the height of the bars on the vertical axis signifies a numerical or a percentage value. The strength of bar graphs lies in their ability to provide a visual comparison, making it easier to spot patterns, trends, and the relationships between data.

Other types of graphs, such as line graphs and pie charts, have their unique uses, too. A line graph is best for showing the relationship over time between two variables, like the unemployment rate. Pie charts demonstrate how something is divided into parts, such as how a group of people or a sum of money is distributed.

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Answer:

Step-by-step explanation:

[tex]x^2-3x=28\qquad\text{subtract 28 from both sides}\\\\x^2-3x-28=0\\\\x^2+4x-7x-28=0\qquad\text{distribute}\\\\x(x+4)-7(x+4)=0\\\\(x+4)(x-7)=0\iff x+4=0\ \vee\ x-7=0\\\\x+4=0\qquad\text{subtract 4 from both sides}\\\boxed{x=-4}\\\\x-7=0\qquad\text{add 7 to both sides}\\\boxed{x=7}[/tex]

Answer:

x = -4 or x = 7

Answer:

C) The probability that Jacob gets a mule deer is 1/7.

Step-by-step explanation:

Let us assume the number of mule deer in the woods  = m

So, the number of whitetail deer  = 6 x ( Number of mule deer) = 6 (m) = 6 m

Also, the total number of deer = Mule deer + whitetail deer

                                                    =  m + 6 m = 7 m

Let E: Event of Picking a mule deer in the woods.

[tex]\textrm{P(E)}  = \frac{\textrm{Number of favorable observations}}{\textrm{ Total number of observations }}[/tex]

So, here [tex]\textrm{P(Picking a mule deer )}  = \frac{\textrm{Number of Mule deers in the woods}}{\textrm{ Total number of deer }}  = \frac{m}{7m}  = \frac{1}{7}[/tex]

or, P(E) = 1/7

Hence, the  probability that Jacob gets a mule deer is 1/7.

Answer:

C) The probability that Jacob gets a mule deer is 1/7.

Step-by-step explanation:

Let us assume the number of mule deer in the woods  = m

So, the number of whitetail deer  = 6 x ( Number of mule deer) = 6 (m) = 6 m

Also, the total number of deer = Mule deer + whitetail deer

                                                   =  m + 6 m = 7 m

Let E: Event of Picking a mule deer in the woods.

So, here

or, P(E) = 1/7

Hence, the  probability that Jacob gets a mule deer is 1/7.

Answer:

Step-by-step explanation:

[tex](h+k)(x)=h(x)+k(x)\\\\\bold{METHOD\ 1:}\\\\k(x)=x-2,\ h(x)=x^2+1\\\\(k+h)(2)=h(2)+k(2)\\\\\text{Calculate}\ h(2)\ \text{and}\ k(2).\\\text{Put}\ x=2\ \text{to the equations of the functions}\\\\h(2)=2^2+1=4+1=5\\k(2)=2-2=0\\\\\text\\\\\text{Substitute:}\\\\(h+k)(2)=5+0=5[/tex]

[tex]\bold{METHOD\ 2:}\\\\k(x)=x-2,\ h(x)=x^2+1\\\\(h+k)(x)=h(x)+k(x)=(x^2+1)+(x-2)=x^2+x-1\\\\(h+k)(2)-\text{put}\ x=2\\\\(h+k)(2)=2^2+2-1=4+2-1=6-1=5[/tex]

The transformations are needed to transform the graph of f(x) to the graph of g(x) are:

vertical translation 1 unit up ⇒ 2nd answer

horizontal translation 5 units left ⇒ 4th answer

Step-by-step explanation:

Let us revise the translation:

∵ f(x) = 8x

∵ g(x) = (8x + 5) + 1

- From the notes above translation to the left h units added x by h

∵ 8x is added by 5

∴ f(x) translated 5 units to the left

- From the notes above translation up k units added f(x) by k

∵ f(x) is added by 1

∴ f(x) translated 1 unit up

The transformations are needed to transform the graph of f(x) to the graph of g(x) are:

vertical translation 1 unit up

horizontal translation 5 units left

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the answers are

horizontal translation 5 units left

vertical translation 1 unit up

I failed lol :((

15 students will not be able to ride on bus for the field trip.

Step-by-step explanation:

No. of seats in one bus = 22 seats

1 seat is for 2 students, therefore, one bus can sit students;

No. of students in one bus = 22*2 = 44 seats

Total buses = 5

One bus can have 44 students, 5 buses can have;

5 buses = 44*5 = 220 students

Total students = 235

As the buses can have 220 students;

Students left = Total students - No. of students in 5 buses

[tex]Students\ left=235-220=15\ students[/tex]

15 students will not be able to ride on bus for the field trip.

Keywords: multiplication, subtraction

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Final answer:

There are 15 seventh-grade students who will not be able to ride on a bus for the field trip, as the total bus seating capacity is for 220 students and there are 235 students going on the trip.

Explanation:

The subject of this question is Mathematics, specifically a problem involving division and subtraction to determine the number of students who will not have a seat on the buses. To solve this, we need to calculate the total seating capacity of all buses and then find the difference between the number of students and the total seating capacity.

Each bus has 22 seats and each seat can accommodate 2 students, so each bus can carry 22 x 2 = 44 students. There are 5 buses, so the total seating capacity is 5 x 44 = 220 students.

There are 235 seventh-grade students going on the field trip. To find out how many will not be able to ride the bus, we subtract the total seating capacity from the number of students: 235 - 220 = 15 students will not be able to ride on a bus for the field trip.

She should plant 14 plants in each row

Step-by-step explanation:

Given

Total pepper plants = 196

As the plants have to be in square shape, the number of rows and the plants in each row will be equal

Let x be the number of rows

Then

[tex]x^2 = 196\\[/tex]

Taking square root on both sides

[tex]\sqrt{x^2} = \sqrt{196}\\x = 14[/tex]

Hence,

She should plant 14 plants in each row

Keywords: Square root, Radicals

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Final answer:

After rounding to the nearest cent, the total payable sum is $419.78.

Explanation:

To calculate the total amount paid for an item with a sales tax, you first need to find the amount of sales tax by converting the tax rate from a percentage into a decimal. In this case, the sale amount is $399.79 and the sales tax is 5%.

Convert the percent to a decimal by dividing by 100:

5% ÷ 100 = 0.05

Next, multiply the sale amount by the decimal tax rate to find the amount of sales tax:

$399.79 × 0.05 = $19.9895

Since we usually round money to the nearest cent, round $19.9895 to $19.99.

Finally, add the amount of sales tax to the original sale amount to find the total amount paid:

$399.79 + $19.99 = $419.78

Therefore, the total amount paid including sales tax is $419.78.

The distance between those two points is 41 and in decimal form to the nearest tenth, that's 6.4

Explanation:

Use the distance formula: √(x2 - x1)² + (y2 - y1)²

Then we plug in our x's and y's:

√(4 - (-1))² + ((-1) - 3)²

Then you simplify:

√(5)² + (-4)²   = √25 + 16

√41 (And if you need to, you can put this into decimal form.)

Answer:

6.4

Step-by-step explanation:

Use the distance formula and then fill in points for the variables.

Answer:

width is 12 feet. Length is 32 feet.

Step-by-step explanation:

Answer:

Length= 52 Width= 44

Step-by-step explanation:

It cost $5 for his brother's ticket.

Step-by-step explanation:

Let,

Micheal's ticket price= x

His brother ticket price = y

According to given statement;

x+y=12    Eqn 1

y = x-2    Eqn 2

Putting value of y from Eqn 2 in Eqn 1

[tex]x+(x-2)=12\\x+x-2=12\\2x=12+2\\2x=14\\[/tex]

Dividing both sides by 2;

[tex]\frac{2x}{2}=\frac{14}{2}\\x=7[/tex]

Putting x=7 in Eqn 2

[tex]y=7-2\\y=5[/tex]

It cost $5 for his brother's ticket.

Keywords: linear equation, substitution method

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Answer: y=4, x=-2

Step-by-step explanation:

line r must have the equation y=4 to go through point (-2,4)

line s must have the equation x=-2 to go through point (-2,4)

To find the correct dimensions of a scaled drawing or the actual dimensions based on a scale factor, multiply the scaled dimensions by the denominator of the scale factor. For a scale factor of 1/200, if a scaled drawing has dimensions of 1 meter by 1 meter, the actual dimensions would be 200 meters by 200 meters, yielding an area of 40,000 square meters.

To determine the correct dimensions of a scaled drawing or the actual dimensions based on a scale factor, it is essential to understand the ratio that the scale factor represents. If the scale factor for a drawing is given as 1/200, it signifies that every unit of measurement on the drawing represents 200 of the same units in the actual size.

For example, let's assume you have a scaled drawing with dimensions of 1 meter by 1 meter, and the scale factor is 1/200. To find the actual dimensions, you would multiply the scaled dimensions by the scale factor's denominator:

Once you know the actual dimensions, finding the area involves multiplying the length by the width. Using our example:

When creating or analyzing scale drawings, remember to apply the scale factor consistently to each dimension to obtain accurate results.

Answer:

the creature 268 inches tall

Step-by-step explanation:

set it up and cross multiply!

10 = 40

67    X

67*40=10*X

2680=10X

then divide 10 from both sides:

so X=268

Answer:

6,9!

Step-by-step explanation:

Goodluck on your I-Ready!

To find the ordered pair with an x-value of 6, we need to look at the pattern for x and find the corresponding value for y. Using the pattern provided, the ordered pair would be (6, 18).

The problem states that Sonya is making a pattern of values for x and a pattern of values for y. We are asked to find the ordered pair that continues the patterns and has an x-value of 6.

To solve this, we need to look at the pattern for the x-values and find the corresponding value for y. Once we have the y-value, we can form the ordered pair (x, y) with x = 6.

For example, let's say the pattern for x is: 1, 2, 3, 4, 5

And the pattern for y is: 3, 6, 9, 12, 15

In this case, we can see that for x = 6, the corresponding y-value would be 18. So the ordered pair would be (6, 18).

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Answer:

Explanation:

The figure contains a table with the monthly payment on a a $100 loan in function of the number of months (term in months) and the annual percent rates (8.00%, 10.00%, 12.00%, 14.00%).

You find the monthly payment on an $100 loan for the terms of the installment loan obtained by Corey Griffin, in the cell resulting from the intersection of the row for 18 months and the column for the rate of 8.00%. That is 5.91.

The meaning of that value is that it must repaid $5.91 monthly, per each $100 of loan.

Hence, for the $1,000, you compute the monthly payment in this way:

Now, to find the finance charge, compute the total payments and subtract the amount of the loan:

Thus, the finance charge is $63.80 (option A).

Answer:

y = 8

Step-by-step explanation:

8 + 24 = 32

32/4 = 8

Answer:

Step-by-step explanation:

y+24/4=8

y+24=8*4

y+24=32

y=32-24

y=8

Answer:

The fractions like [tex](\frac{8}{2}), (\frac{16}{4}), (\frac{44}{11} )[/tex] could  represent the part of the beads that are red.

Step-by-step explanation:

The given question is incomplete. Here is the complete question:

Miranda is braiding her hair. Then she will attach beads to the braid, she wants 1/3 of the beads to be red. If the greatest number of beads that will fit on the braid is 12, what other fractions could represent the part of the beads that are red?

Now, total number of beads to be fit on the braid   = 12

The desirable amount of red beads = 1/3

So, now as the number of red beads Miranda can use

= 1/3 ( Total beads used)  

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

or, out of total 12 beads, 4 beads are red.

⇒The total number of red beads = 4

Hence,  the fractions like [tex](\frac{8}{2}), (\frac{16}{4}), (\frac{44}{11} )[/tex] could represent the part of the beads that are red.

Miranda can use fractions with 12 in the denominator to represent the portion of red beads on her braid. Possible fractions include 1/12, 2/12, 3/12, 4/12, 5/12, 6/12, and so on up to 11/12.

Miranda wants 1/12 of the beads to be red on her braid. Since the greatest number of beads that will fit on the braid is 12, the other fractions that could represent the part of the beads that are red must also be fractions with 12 in the denominator to be comparable.

Possible fractions representing red beads out of a total of 12 beads are:

These represent all the simple fraction options for the number of red beads based on the constraint of having a maximum of 12 beads.

29000 x 0.04 = 1,160

29000 - 1,160 = answer

27,840 = answer  

Hope this helps!

Answer:

29,000, percentage decreased by 4% (percent) of its value = 27,840

Answer:

-427

Step-by-step explanation:

5-8 x 54

It is a very simple numerical simplification. We have to use the BODMAS rule to determine the value of this simplification. At first, we see that there is no bracket, so we will go to "or." Since there is no "or," we will go to the "divide" rule. Again, there is no "Divide," so we will go to the "Multiplication" rule.

= 5 - (8 x 54)

= 5 - 432

Now, we will deduct 432 from 5. Since 432 is a negative number, the answer will be a negative value.

= -427

The simplification answer = -427

Answer:   53   -10      -50

Step-by-step explanation:

50 + 3 = 53     50 - 60 = -10     50 - 100 = -50

[tex]3[/tex] increased by [tex]50[/tex] is equal to [tex]53[/tex].

[tex]3[/tex] decreased by [tex]60[/tex] is equal to [tex]-57[/tex].

[tex]3[/tex] decreased by [tex]100[/tex] is equal to [tex]-97[/tex].

To increase a number [tex]a[/tex] by [tex]b[/tex] means to add [tex]a[/tex] to [tex]b[/tex]. Increase is denotes by sign [tex]+[/tex]

To decrease a number [tex]a[/tex] by [tex]b[/tex] means to subtract [tex]b[/tex] from [tex]a[/tex]. Decrease is denoted by sign [tex]-[/tex]

[tex]3[/tex] increased by [tex]50[/tex] is equal to [tex]\boldsymbol{3+50}[/tex] which is equal to [tex]53[/tex].

[tex]3[/tex] decreased by [tex]60[/tex] is equal to [tex]\boldsymbol{3-60}[/tex] which is equal to [tex]-57[/tex].

[tex]3[/tex] decreased by [tex]100[/tex] is equal to [tex]\boldsymbol{3-100}[/tex] which is equal to [tex]-97[/tex].

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