Four students plan to rent a minivan for the weekend and equally share the rental cost. By adding one more people, they can each save $6. How much is the total rent of the car?

There are 5 consecutive odd nos.

To find : no . of terms in a series of consecutive nos .

To proceed ,

Let the series start from 7 which is an odd numbers [we can start the series from any odd number and go up to next 8 numbers]

the odd consecutive series 7 , 9 , 11 , 13 , 15 .

There are 5 numbers in total .

The 1st number is 7 and the last number is 15 .

Therefore , difference between the 1st and the last number is 15 - 7 = 8 .

Hence , there are 5 consecutive odd nos .

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The total money Avetis had left in his wallet after he bought 3 cakes is m - 3k

An equation is an expression that shows the relationship between two or more numbers and variables.

Avetis had m dollars in his wallet. He bought 3 cakes which cost k dollars each.

Hence:

Total cost of cakes = 3 * k = 3k

Total money he had left = m - 3k

The total money Avetis had left in his wallet after he bought 3 cakes is m - 3k

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Answer:

x=20

Step-by-step explanation:

1-reoder the terms

2-Move constant to the right

3-dive both sides

just hit the image and you will get a representation on how to do it

Answer:

8.5 square feet

Step-by-step explanation:

(3.4x5)/2

=8.5

Answer:

x > 2

Step-by-step explanation:

when a line has an open circle it is greater/less than the number it is on, a closed circle means it could be than number, so greater than or equal to. This equation is an open circle (so it's not equal to) and is on the 2. So you know the equation is x < or > 2. To find if it's < or >, you look at what direction the line goes. This one is to the right. If you notice the > looks like an arrow pointing to the right, so you can know > is the right symbol to use. The full equation will be read, x is greater than 2. Hope this was helpful!

Answer:

1196

Step-by-step explanation:

4,783 / 4 = 1195.75

If you round that up, you get 1196.

The agent will get $47.2746 for his commission.

So, we have to take out 6% of $787.91 in order to obtain the commission of the agent.

Then,

Therefore, $47.2746 will the agent get for his commission.

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The two numbers are 8 and - 1.

A quadratic equation is of the form ax² + bx + c = 0.It has highest degree of 2 and has two roots.

According to the given question we have to find two numbers that when we add we get 7 and when we multiply we get - 8.

This can be solved by quadratic equation

x² + 7x - 8 = 0.

x =(7±[tex]\sqrt{49 + 32}[/tex] )/2.

x = (7±[tex]\sqrt{81}[/tex] )/2.

x = (7±9)/2.

x = 8 or x = - 1 .

This can also be solved by logic and practice for small numbers like two numbers multiples to - 8 and add to 7.

a + b = 7 and a×b = - 8.

(8×-1) = -8 and ( 8 - 1 ) = 7.

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Answer:

  3

Step-by-step explanation:

You want to know the appropriate number of significant digits in the quotient of measurements 2.09×10^9 and 4.053×10^-4.

The number of significant digits in a number written in scientific notation is the count of digits in the mantissa. Numbers with more significant digits are considered to be more precise.

  2.09×10^9 . . . . has 3 significant digits

  4.053×10^-4 . . . . has 4 significant digits

When imprecise numbers are multiplied or divided, the resulting product or quotient cannot be more precise than the least precise number used. The quotient of numbers with 3 and 4 significant digits will only have 3 significant digits.

Answer:

Yes, there were people on more than 70% of the seats.

Step-by-step explanation:

Let's start with the children. We know that 2/3 of the children had seats in the Stalls, which means that the other 1/3 of the children had seats in the Circle. We know that 114 children had seats in the Circle. Therefore, we can calculate that there were 342 children total, since 114 (1/3 of the children) times 3 is 342.

In order to find how many adults there were, we can use the ratio of adults to children, 4:3. We're basically going to undo our math from the previous part. We divide 342 by 3 to determine how much 1 is. This gives us 114, which we multiply by 4 to find how many adults there were.

There were 456 adults.

There were 342 children.

456 + 342 = 798

There were 798 people in the theatre total.

To find what 70% of 1100 is, we multiply 0.7 x 1100. This gives us 770. Because 798 is more than 770, we know that there were people on more than 70% of the seats.

Answer:

-X < -2x

3x>2x

Step-by-step explanation:

The value of the given function is given as follows f(-5) ,g(2),f(4m)  are 25,-3,-12m+10.

The slope of a linear function is calculated by rearranging the equation to its general form, f(x) = mx + c; where m is the slope. The vertex of a quadratic function is calculated by rearranging the equation to its general form, f(x) = a(x – h)2 + k; where (h, k) is the vertex.

The notation y=f(x) defines a function named f. This is read as “y is a function of x.” The letter x represents the input value or independent variable. The letter y, or f(x), represents the output value, or dependent variable

F(x) is the notation for a function which is essentially the thing that does your operation to your input. You can think of a function as a little machine. You put in your input, it changes it around and gives you output in return. F(x) means it's a function f with respect to x.

f(x) = -3x+10

f(-5) = -3*-5 +10

= 15+10=25

g(x) = x^2-7

g(2)= 2^2-7

= 4-7

=-3

f(4m) = -3x+10

= -3*4m+10

=-12m +10

= -12m +10

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The values of the above functions are 25, 3, and 12m+10 for f(-5) and g(2) and f(4m), respectively.

By rearranging the equation to take on its general form, f(x) = mx + c, where m is the slope, one can determine the slope of a linear function. By rearranging the equation to its general form, f(x) = a(x - h)2 + k, where (h, k) is the vertex, one can determine the location of a quadratic function's vertex.

A function called f is defined by the notation y=f(x). This should be understood as "y is a function of x." The input value or independent variable is denoted by the letter x. The dependent variable or output value is denoted by the letter y, or f(x).

A function is essentially the item that applies your operation to your input, and its notation is F(x). A function can be compared to a tiny machine. You provide your input, which is altered and converted into output. F(x) denotes that a function is one that has respect to x.

f(x) = -3x+10

f(-5) = -3*-5 +10

= 15+10=25

g(x) = x^2-7

g(2)= 2^2-7

= 4-7

=-3

f(4m) = -3x+10

= -3*4m+10

=-12m +10

= -12m +10

Using LCM, we calculated that the two teams will share the same field on 27 September.

The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory.

The LCM of 5 and 3 is 5×3

= 15

So the two teams will share the same field after 15 days.

So, the both teams will share the same on 27 September.

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Answer: C

Step-by-step explanation:

Answer:

[tex](\sqrt[12]{8} )^x[/tex]

Step-by-step explanation:

[tex](\sqrt[3]{8} ) \frac{1}{4} x = 8\frac{1}{3} \frac{1}{4} x = 8\frac{1}{12} x = (\sqrt[12]{8} )^x[/tex]

Answer:

62.14 miles per hour

Answer: 100 km/h is equal to 62.14 mph

So, 100 km/h is equal to 62.14 miles per hour.

Answer:

62.15 mi/hr

Step-by-step explanation:

Given:

As both speed limits are given "per hour", we only need to convert 100 km to miles.  To do this, set up and solve a ratio for "miles to kilometers", where x is the number of miles to 100 km:

[tex]\implies \sf 1 : 1.609 = x : 100[/tex]

[tex]\implies \sf \dfrac{1}{1.609} = \dfrac{x}{100}[/tex]

[tex]\implies \sf \dfrac{1}{1.609} \cdot 100= x[/tex]

[tex]\implies \sf x= \dfrac{100}{1.609}[/tex]

[tex]\implies \sf x= 62.15040398...[/tex]

Therefore, 100 km/hr = 62.15 mi/hr (2 d.p.)

The union symbol between multiple intervals​ in the graph is (-7,-3)

From the graph,

I) Value of x does h(x)=-1

 x = -5

J) interval(s) of x such that h(x) > 0

x = (-∞,-7) U (-3,4]

K) interval(s) of x such that h(x) < 0

x = (-7,-3)

An abstract depiction of several points connected by lines is called a graph. The lines are referred to as edges, and each point is typically referred to as a vertex (more than one is referred to be vertices).

Graphs are a tool for connection modeling. They are employed to solve a variety of issues. A diagram that shows how a variable varies in relation to one or more other variables, such as a collection of points, lines, line segments, curves, or regions.

A grouping of all points whose coordinates meet a certain relation (such as a function).

Graphs and charts are useful visual aids because they make information accessible and quick to understand.

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Based on the amount that Velma wants to buy the house for and the fixed-rate mortgage offered by her bank, her monthly house payments will come to $919.75

The monthly house payments are constant so they are an annuity. The loan amount of $195,000 will be the present value of the annuity.

The monthly rate is:

= 3.9% / 12

= 3.9/12%

The number of periods is:
= 30 x 12

= 360 months

The monthly house payments is:

195,000 = Amount x (1 - (1 + 3.9/12%)³⁶⁰) / 3.9/12%

Amount = 195,000 / 212.01344311265715516703523151038

= $919.75

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El limite de f(x) = (2 · x² + 3 · x - 9) / (x - 1.5) cuando x = 1.5 es 4.5.

En este problema tenemos el caso de una ecuación racional cuyo numerador y denominador son polinomios.

La discontinuidad de la ecuación racional es evitable si y solo si tanto el numerador y el denominador tienen la misma raíz. La existencia de la discontinuidad evitable se comprueba mediante procedimientos algebraicos. En consecuencia, realizamos la siguiente comprobación:

f(x) = (2 · x² + 3 · x - 9) / (x - 1.5)

f(x) = [(x - 1.5) · (x + 3)] / (x - 1.5)

f(x) = x + 3

La discontinuidad es evitable y la función existe para x = 1.5, entonces:

f(1.5) = 1.5 + 3

f(1.5) = 4.5

El limite de f(x) = (2 · x² + 3 · x - 9) / (x - 1.5) cuando x = 1.5 es 4.5.

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Answer: g(-2) = 17

Step-by-step explanation:

         When finding g(-2), we will substitute all values of x for -2 in the function. First, we will substitute values in. Then, we will simplify by squaring, multiplying, and adding.

g(x) = 3x² -2x + 1

g(-2) = 3(-2)² -2(-2) + 1

g(-2) = 3(4) + 4 + 1

g(-2) = 12 + 4 + 1

g(-2) = 17

The coefficient of the term of degree two in the polynomial [tex]x^{6} + 3 - 2x^{2} + 4x^{7} - 4x[/tex] is 2

Polynomial is defined as an expression formed by the combination of a constant value and a same variable having different degrees (also called as powers).

Coefficient of the term of degree 2 in the polynomial [tex]x^{6} + 3 - 2x^{2} + 4x^{7} - 4x[/tex] is 2 because the term [tex]2x^{2}[/tex] is having the variable as x and its degree as 2 and the attached constant value is 2.

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Answer:

261 stairs

Step-by-step explanation:

If David trips twice every 9 stairs and he has tripped 58 times. We can multiply 9 by 58.

58*9=522

Since David trips twice in 9 stairs, then to find how many stairs he has climbed we need to divide 522 by 2.

522/2=261

David has climbed 261 stairs.

The set of ordered pairs {(-2, 4), (0, 2), (-1, 3), (4, -2)} belong to a function

[y = f(x)] considering the pairs are in the order of (x, y).

As per the question statement, we are provided with a set of ordered pairs: {(-2, 4), (0, 2), (-1, 3), (4, -2)}.

We are required to determine if the pairs in the set satisfy a function or not.

To solve this question, let us consider each pair in the form of (x, y) and then, we will have to find out a relation between x and y that will satisfy all the ordered pairs. If we are able to find out one such common relation or pattern, we will determine our ordered pairs as inputs and outputs of the same function, otherwise not.

We can say that, [tex][(-2)(-1)+2]=4,[/tex]

[tex][(0)(-1)+2]=(0+2)=2,[(-1)(-1)+3]=1+2)=3,\\[/tex]

And, [tex][4*(-1)]+2=[(-4)+2]=(-2)[/tex]

That is, all our ordered pairs {(-2, 4), (0, 2), (-1, 3), (4, -2)} satisfy the function [y = f(x) = {x(-1) + 2}], being in the order of (x, y).

Therefore, the set of ordered pairs {(-2, 4), (0, 2), (-1, 3), (4, -2)} are the inputs and outputs of the function [y = f(x) = {x(-1) + 2}].

       (b = q).

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Answer:

Neither

Step-by-step explanation:

MN: slope = 4/5

PQ: slope = -4/5

Two lines are parallel when their slopes are equal but their y-intercepts are different.

Two lines are perpendicular when their slopes are negative reciprocals of each other.

The negative reciprocal of 4/5 (MN) is -5/4

PQ -4/5

-5/4 [tex]\neq[/tex] -4/5

therefore the lines are Neither

It will take 44 minutes for the car to pass the truck.

Relative speed is the net speed difference between two objects when they are on the same direction we subtract and when they are on different direction we add.

According to the given question A truck enters a highway driving 60 mph which is (60/60) miles per minute = 1 mile per minute.

The car is going at a speed of 71 miles hour or (71/60) mile per minute = 1.183 miles per minute.

∴ Their relative speed difference is ( 1.183 - 1 ) = 0.183 miles.

Given the car enters the highway 8 minutes later on that time the truck will cover the distance of (1×8) = 8 miles.

so, the time needed for the car to pass the truck is (8/0.183) minutes which is = 43.7 minutes or 44 minutes.

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Answer:

[tex]{ \tt{ \int_{b} ^{a} (u) \: dv = uv - \int_{b}^{a} (v) \: du }} \\ [/tex]

Answer:

integral (u v') = uv - intgral (u' v)