A ride on the roller coaster costs 4 tickets while the boat ride only costs 3 tickets. Michael went on the two rides a total of 10 times and spent a total of 37 tickets. Which equation is true?
A. r(10 – r) = 10
B. r + (10 – r) = 4 + 3
C. 4r[3(10 – r)] = 37
D. 4r + 3(10 – r) = 37

Answer:

In a linear equation  of one variable there are two terms terms containing variable and constant.

Variable means term containing x,y,z which act as variables. and constant means any rational number . In higher classes you can include real number also.

The given equation is 3x + 5x = 10

So, the solution out of four options is A) 5x = 20.

Here variable is on one side of equation and constant on other side.

But Option (D) looks absolutely correct if we replace ? by either + sign or Negative (-) sign.

Answer:

D. [tex]4x-2x=10[/tex]

Step-by-step explanation:

We have been give an equation [tex]3x+5x=10[/tex]. The equation is solved by combining like terms. We are asked to choose the equation that an be solved by combining the like terms.

Let us check our given choices one by one.

A. [tex]5x=20[/tex]

We can see that equation A will be solved by dividing 20 by 5, therefore, option A is not correct choice.

B. [tex]2(x+5)=20[/tex]

We can see that equation B will be solved by dividing 20 by 5 and then subtracting 5, therefore, option B is not correct choice.

C. [tex]\frac{x}{4}=20[/tex]

We can see that equation C will be solved by multiplying 20 by 4, therefore, option C is not correct choice.

D. [tex]4x-2x=10[/tex]

We can see that equation D will be solved by combining like terms, therefore, option D is correct choice.

Answer:

If you are asking about the difference between the two, the difference is $5,805.80

Step-by-step explanation:

To find dy/dx by implicit differentiation, differentiate both sides of the equation with respect to x. The derivative of sin(xy^2) with respect to x is cos(xy^2) * (y^2 * dx/dx + x * d(y^2)/dx). Simplify the expression to find dy/dx.

To find dy/dx by implicit differentiation, we will differentiate both sides of the equation with respect to x.

We have the equation 5+4x=sin(xy^2). Taking the derivative of both sides, the left side will be 0 since it is a constant. On the right side, we use the chain rule.

The derivative of sin(xy^2) with respect to x can be written as cos(xy^2) * (y^2 * dx/dx + x * d(y^2)/dx).

Simplifying further, dy/dx = (cos(xy^2) * (2xy^2 + x * 2y * dy/dx)) / (1 - x * 2y^2 * cos(xy^2)).

ANSWER

The correct answer is [tex]m=45,n=12[/tex].

EXPLANATION

We were given the matrix equation;

[tex]\left[\begin{array}{cc}n-1&6\\-19&m+3\end{array}\right] +\left[\begin{array}{cc}-1&0\\16&-8\end{array}\right] =\left[\begin{array}{cc}10&6\\-3&40\end{array}\right][/tex].

We must first simplify the Left Hand Side of the equation by adding corresponding entries.

[tex]\left[\begin{array}{cc}n-1+-1&6+0\\-19+16&m+3-8\end{array}\right]=\left[\begin{array}{cc}10&6\\-3&40\end{array}\right][/tex].

That is;

[tex]\left[\begin{array}{cc}n-2&6\\-3&m-5\end{array}\right]=\left[\begin{array}{cc}10&6\\-3&40\end{array}\right][/tex].

Since the two matrices are equal, their corresponding entries are also equal. we equate corresponding entries and solve for m and n.

This implies that;

[tex]n-2=10[/tex]

We got this equation from row one-column one entry of both matrices.

[tex]n=12[/tex]

Also, the row three-column three entries of both matrices will give us the equation;

[tex]m-5=40[/tex]

[tex]m=45[/tex]

Hence the correct answer is [tex]m=45,n=12[/tex].

The correct option is option 2

Every year, Sam will have 103% of the amount from the previous year.

[tex]p\%=\dfrac{p}{100}\\\\103\%=\dfrac{103}{100}=1.03[/tex]

After the first year:

[tex]1.03\cdot\$4,500[/tex]

After the second year:

[tex]1.03\cdot1.03\cdot\$4,500=\$4,500(1.03)^2[/tex]

After the t-th year:

[tex]\$4,500(1.03)^t[/tex]

Therefore we have the inequality:

[tex]\$4,500(1.03)^t\leq\$7,020\ \ \ \ |\text{divide both sides by \$4,500}\\\\(1.03)^t\leq1.56\\\\(1.03)^{15}\approx15.56\\\\\text{therefore}\ t\leq15[/tex]

Answer: 11 party bags with 1 sticker leftover

Each bag contains 4 bubbles, 8 stickers, and 5 pencils.

Step-by-step explanation:

Find the GCF of 44 (bubbles), 89 (stickers), and 55 (pencils)

44: 2 x 2 x 11

89: prime so choose 88 with 1 leftover

88: 2 x 2 x 2 x 11

55: 5 x 11

GCF = 11

Disregard the GCF to see how many of that item should go in each bag.

Bubbles: 2 x 2

Stickers: 2 x 2 x 2

Pencils: 5

A real-valued univariate function f=f(x) has a jump discontinuity at a point [tex]x_0[/tex] in its domain provided that

[tex]\lim \limits_{x\to x_0^-}f(x)=A_1[/tex]

and

[tex]\lim \limits_{x\to x_0^+}f(x)=A_2[/tex]

both exist and that [tex]A_1\neq A_2.[/tex]

As you can see at x=-3,

[tex]\lim \limits_{x\to -3^-}f(x)=6,[/tex] [tex]\lim \limits_{x\to -3^+}f(x)=9[/tex] and [tex]6\neq 9.[/tex]

Therefore, there is a jump discontinuity at x=-3.

Answer: correct choice is A.

x = 0

distribute parenthesis on both sides of the equation and simplify

3x - 7 - 4x = 10x - 8 + 1

- x - 7 = 10x - 7 ( subtract 10x from both sides )

- 11x - 7 = - 7 ( add 7 to both sides )

- 11x = 0 ( divide both sides by - 11 )

x = 0

Answer:  Five cats ate 1 and a quarter of cat food.

Step-by-step explanation

Given:-

Cat food ate by one cat = 1/4 cup

Cat food ate by five cats =[tex]5\times \frac{1}{4} \text{ [Multiplying both sides with 5 ]}\\\\=\frac{5}{4}=\frac{4+1}{4}=\frac{4}{4}+\frac{1}{4}=1+\frac{1}{4}[/tex]=1 and 1/4 cup.

Therefore cat food ate by five cats = 1 and a quarter of cup.[ here a quarter =1/4]

For this case we have the following equation:

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

If we multiply both sides of the equation by 3 we get:

[tex]2x-1 = 6 (x + 2)[/tex] ---> Multiplication Property of Equality

Applying the distributive property we have:

[tex]2x-1 = 6x + 12[/tex] ---> Distributive Property

Adding 1 on both sides of equality we have:

[tex]2x-1 + 1 = 6x + 12 + 1\\[/tex]

[tex]2x = 6x + 13[/tex] ---> Addition Property of Equality

Subtracting [tex]6x[/tex] on both sides we have:

[tex]-6x + 2x = 6x-6x + 13\\[/tex]

[tex]-4x = 13[/tex] ---> Subtraction Property of Equality

Finally, dividing by -4 on both sides we have:

[tex]\frac{-4x}{-4}= \frac{13}{-4}\\[/tex]

[tex]x = -\frac{13}{4}[/tex]---> Division Property of Equality

1. Qualitative

2. Quantitative

3. Quantitative, continuous data

4. Quantitative, discrete data

5. Quantitative, continuous data

The answer is 3 hours  40 minutes

When a line is perpendicular to another line, the slope is the negative reciprocal of the other line's slope. So in this case, the slope would be 1, since the negative reciprocal of -1 is 1/1 which is 1.

To find the y-intercept, you have to substitute the point (8,2) into y = mx + b

2 = 1(8) + b

b = -6

The equation is y = x - 6

The equation of the line which is perpendicular and goes through the point (8,2) is y = x - 6

The equation of the required line in slope-intercept form is expressed as:

y-y0 = m(x-x0) where:

Given the equation of the line as y = -x

Get the slope of the line

mx = -x

m = -1

Since the required line is perpendicular to this line, the required slope will be 1 (M = -(-1/1))

Get the required equation

Recall that;

y-y0 = m(x-x0)

y - 2 = 1(x-8)

y - 2 = x - 8

y = x - 8 + 2

y = x - 6

Hence the equation of the line which is perpendicular and goes through the point (8,2) is y = x - 6.

Learn more here: https://brainly.com/question/17003809

Hi!

Answer - Line R

Well refraction is the bending of something. I choose r because it may have refraction because of the 2 rectangles at the end of both sides.

Hope This Helps!

Answer:

B. △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.

Step-by-step explanation:

I just took the test, good luck! Have a wonderful day! :)

Transformation involves changing the position of a shape.

The correct statement is: (b) △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.

The transformation rule is given as:

[tex]\mathbf{(x,y) \to (-x,-y)}[/tex], then:

[tex]\mathbf{(x,y) \to (x,-y)}[/tex]

Rotation and reflection are both rigid transformation.

Hence, the correct option is (b):

Read more about rotation and reflection at:

https://brainly.com/question/15577335

For this case we have:

The equation in vertex form of the parabola is given by:

[tex]y = a (x-h) ^ 2 + k\\[/tex]

The vertex is (h, k) and is given by the highest or lowest point of the parabola, in this case it is observed that it is [tex](h, k) = (- 3, -1)\\[/tex]

Thus, the equation is given by:

[tex]y = a (x - (- 3)) ^ 2 + (- 1)\\\\y = a (x + 3) ^ 2-1\\[/tex]

We look for the value of a, substituting a point of the parabola in the equation in the form of vertex, we will take the point [tex](x, y) = (0,8)\\[/tex]

Substituting we have:

[tex]8 = a (0 - (- 3)) ^ 2 + (- 1)\\\\8 = a (0 + 3) ^ 2-1\\\\8 = a (3) ^ 2-1\\[/tex]

[tex]8 = 9a-1\\\\8 + 1 = 9a\\\\9 = 9a\\[/tex]

[tex]a = \frac{9}{9}\\\\a = 1\\[/tex]

Thus, the equation of the parabola is given by:

[tex]y = (x + 3) ^ 2-1\\[/tex]

Answer:

[tex]y = (x + 3) ^ 2-1[/tex]

Answer:

y = (x + 3)2 - 1

Step-by-step explanation:

[tex]\left[\begin{array}{ccc}2&4\\3&-9\end{array}\right]\\\\\det\left[\begin{array}{ccc}2&4\\3&-9\end{array}\right]=(2)(-9)-(4)(3)=-18-12=-30[/tex]

Answer:

-30 will be the determinant.

Step-by-step explanation:

We have to find the system determinant of the given matrix

[tex]\begin{bmatrix}2 & 4\\ 3 & -9\end{bmatrix}[/tex]

Determinant will be = 2(-9) - (4 × 3)

                                 = -18 -12

                                = -30

Therefore, as per given options by you in the comments.

option A is the answer.

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

the equation of a line in ' slope - intercept form ' is

y = mx + c ( m is the slope and c the y- intercept ) calculate m using the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0 , - 2 ) and (x₂ , y₂ ) = A( 6 , - 6 )

m = [tex]\frac{- 6+ 2}{6 - 0}[/tex] = [tex]\frac{-4}{6}[/tex] = - [tex]\frac{2}{3}[/tex]

y -intercept c = - 2 ( from graph )

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

Answer:

y= 126

Step-by-step explanation:

The given equation is: y= 3x-2x^2+5x^3

Substituting the value x=3 in the above equation,we get

   y= 3(3)-2(3)^2+5(3)^3

⇒y= 9-2(9)+5(27)

⇒y= 9-18+135

⇒y= 126

[tex]y\geq2-2x\\\\\text{Let's the line}\ y=2-2x\\\\for\ x=0\to y=2-2(0)=2\to(0,\ 2)\\for\ x=1\to y=2-2(1)=0\to(1,\ 0)[/tex]

[tex]\text{draw a line and shade above the line}\\\\\text{Look at the picture}[/tex]

Answer:

Graph is attached below

Step-by-step explanation:

To graph the given inequality , replace the inequality sign by = sign

y≥2−2x

y=2−2x

Now make a table , assume some random number for x and find out y

x         y=2-2x

0          2

1           0

2          -2

Now graph all the points (0,2) (1,0) (2,-2)

Now we do shading. For shading use test point (0,0)

plug in 0 for x and 0 for y

[tex]y\geq 2-2x[/tex]

[tex]0\geq 2-2(0)[/tex]

[tex]0\geq 2[/tex] is false

So shade the region that does not contain (0,0)

The graph is attached below

The answer is B. If you look at a graph of -tan (which is cot), the places the graph crosses -1 are at pi/4 plus kpi. If you add pi to pi/4, you get 5pi/4, and these two answers are in B only.

Im adding an answer so the other guy that gave an answer gets his points.

The length of toy jeep = [tex]12 \frac{1}{2}[/tex]

= [tex]\frac{25}{2}[/tex] inches

The length of actual Jeep = [tex]18 \frac{3}{4}[/tex] feet

We have to find the ratio length of a toy jeep to the length of actual jeep.

Firstly, we will make the dimensions of the both the given lengths same.

As 1 foot = 12 inches

[tex]18 \frac{3}{4}[/tex] feet = [tex]18 \frac{3}{4} \times 12[/tex] inches

=[tex]\frac{75 \times 12}{4}[/tex]

= 225 inches

So, the ratio length of toy jeep to actual jeep

= [tex]\frac{25}{2} \div 225[/tex]

= [tex]\frac{25}{2} \times \frac{1}{225}[/tex]

= [tex]\frac{1}{18}[/tex]

= 1:18

So, the ratio length of a toy Jeep to the length of a actual Jeep is 1:18.

Length of toy jeep = [tex]12\frac{1}{2}=\frac{25}{2}[/tex] inches

Length of actual jeep = [tex]18\frac{3}{4}=\frac{75}{4}[/tex] feet

Now to find the ratio between the two, we must convert both of them in same units. So, lets convert the actual jeep length in feet to inches.

1 feet = 12 inches.

So, [tex]\frac{75}{4}[/tex] feet = [tex]\frac{75}{4}\times12=225[/tex] inches

Ratio of length of toy jeep to actual jeep will be =

[tex]\frac{\frac{25}{2}}{225}[/tex]

[tex]\frac{25}{2\times225}[/tex]

[tex]\frac{25}{450}[/tex] = [tex]\frac{5}{90}[/tex]

ratio is : [tex]\frac{1}{18}[/tex] or 1:18

The number that is divisible by 3 and 9 is 40,653.

The division is the process of sharing a collection of items into equal parts and is one of the basic arithmetic operations in maths.

We may face different situations every day where we use the division technique.

Given are numbers, we need to find which of them numbers are divisible by 3 and 9,

LCM of 3 and 9 is 9,

So numbers completely divisible by 9 will also be divisible by 3.

The only number from the option which is completely divisible by 9 is 40,653.

Hence, the number that is divisible by 3 and 9 is 40,653.

Learn more about division, click;

https://brainly.com/question/21416852

#SPJ2

The answer is B I hope I helped

Answer:

the answer is B.28.7 hope i helped you learn something new

Step-by-step explanatio

I believe its asking you the formula to find the rows numbers moving forward

Examle row 5 will be 16, I believe that is B. 4n - 1

[tex]14n+6p-8n=18p\ \ \ \ |\text{subtract 6p from both sides}\\\\14n-8n=12p\\\\6n=12p\ \ \ \ |\text{divide both sides by 6}\\\\\boxed{n=2p}[/tex]

The correct solution for this equation is n = 2p.

I hope this helped! :)

f(x) = 8000 - (8000)(0.11)x

     = 8000 - 880x

f(5) = 8000 - 880(5)

     = 8000 - 4400

     = 3600

Answer: $3,600

Answer:

$4467.25

Step-by-step explanation:

We have been given that a jet ski depreciates at 11% of its original value each year. The jet ski was $8,000 as it’s time of purchase.

We will exponential decay function to solve our given problem.

[tex]y=a\cdot(1-r)^x[/tex], where,

a = Initial value,

r = Decay rate in decimal form.

[tex]r=\frac{11}{100}=0.11[/tex]

[tex]y=\$8,000\cdot(1-0.11)^5[/tex]

[tex]y=\$8,000\cdot(0.89)^5[/tex]

[tex]y=\$8,000\cdot 0.5584059449[/tex]

[tex]y=\$4467.2475592[/tex]

[tex]y\approx \$4467.25[/tex]

Therefore, the value of ski jet after 5 years would be $4467.25.

Answer:

Remainder is 36.

Step-by-step explanation:

We are given that f(x) is divided by x+3 using synthetic division, and  we are given with table attached in the image.

In synthetic division, first row represents the coefficients of dividend. From the given table, dividend is f(x)=[tex]2x^{2}-5x+3[/tex] and  since f(x) is divided by x+3, divisor is -3.

First two numbers of last row represents coefficients of quotient and last most number of third row is remainder.

And we can write f(x) as (x+3)(2x-11)+36.

Hence remainder is 36 , when f(x) is divided by x+3.

Answer:

36

Step-by-step explanation:

this i believe is the settup u were describing

Answer:

The answer is option (C), One cement bridge post weighs 9,135 pounds

Step-by-step explanation:

Step 1: Get the total volume of a cement bridge post

The cement bridge post is in the shape of a cuboid, therefor the volume of the cement bridge post can be expressed as;

Volume of cement bridge post=Base area×Length

where;

Base area=(24^2) inches square

1 foot=12 inches

Convert 24 inches to foot=24/12=2^2=4 feet²

Length=15 feet and 9 inches

1 foot=12 inches

Convert 9 inches to foot=9/12=0.75 feet

Total length=(15+0.75)=15.75 feet

replacing;

Volume of cement bridge post=(4×15.75)=63 cubic feet

Volume of cement bridge post=63 cubic feet

Step 2: Get the total weight of the cement bridge post

Total weight of the cement bridge post=Weight per cubic foot×total volume of the cement bridge post

where;

Weight per cubic foot=145 pounds per cubic foot

Total volume of the cement bridge post=63 cubic feet

replacing;

Total weight of the cement bridge post=(145×63)=9,135 pounds

One cement bridge post weighs 9,135 pounds