Miranda and Jean are planning a trip together. They want to drive, but they're not sure whose car to take. Jean's car uses gallons of gasoline to travel miles. Miranda's car can go miles on gallons of gasoline. Whose car is more fuel efficient, and what is the car’s fuel efficiency in miles per gallon?
is more fuel efficient. Her car gets miles per gallon.

Carla skateboarded 28/15 miles farther than Alex.

To find out how much farther Carla skateboarded than Alex, we first calculate the total distance each student skateboarded:

Next, we find the difference:

Carla - Alex = 21/5 - 7/3 = 63/15 - 35/15 = 28/15 miles.

Therefore, Carla skateboarded 28/15 miles farther than Alex.

Answer:

hope it help!

Step-by-step explanation:

have a nice day

Graph with its function by translating the graph of y= √x is marked below.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Given,

y = √x

However, y= √x only displays the positive y values on a graph since you can never square a negative integer because no two identical numbers multiplied together are negative, among other reasons.

Making a function is standard. Since a function may only have one value for each input, we define x as the positive real integer such that (√x)2=x for every positive real √x.

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Answer:

r = ±1/√7

a₁ = 7 − √7

Step-by-step explanation:

The first term is a₁ and the second term is a₁ r.

a₁ + a₁ r = 48/7

The sum of an infinite geometric series is S = a₁ / (1 − r)

a₁ / (1 − r) = 7

Start by solving for a₁ in either equation.

a₁ = 7 (1 − r)

Substitute into the other equation:

7 (1 − r) + 7 (1 − r) r = 48/7

1 − r + (1 − r) r = 48/49

1 − r + r − r² = 48/49

1 − r² = 48/49

r² = 1/49

r = ±1/√7

When r is positive, the first term is:

a₁ = 7 (1 − r)

a₁ = 7 (1 − 1/√7)

a₁ = 7 − 7/√7

a₁ = 7 − √7

The value of the common ratio r is 1/√7 and the first term is 7 − √7 in the geometry progression.

The geometric series defined as a series represents the sum of the terms in a finite or infinite geometric sequence. The successive terms in this series share a common ratio.

The nth term of a geometric progression is expressed as

Tₙ = arⁿ⁻¹

The first term is a

So the second term is a r.

a + ar = 48/7

The sum of an infinite geometric series is :

S = a / (1 − r)

a / (1 − r) = 7

Solve for a,

a = 7 (1 − r)

Substitute value into the equation:

7 (1 − r) + 7 (1 − r) r = 48/7

1 − r + (1 − r) r = 48/49

1 − r + r − r² = 48/49

1 − r² = 48/49

r² = 1/49

r = ±1/√7

When r is positive, the first term will be:

a = 7 (1 − r)

a = 7 (1 − 1/√7)

a = 7 − 7/√7

a = 7 − √7

Thus, the value of the common ratio r is 1/√7 and the first term is 7 − √7 in the geometry progression.

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Step-by-step explanation:

An exponential function has the form:

y = a · b^x

Are you sure you copied the problem correctly?  Perhaps instead of minus, you meant multiplication:

f(x) = 620 · 7.8^x

If so, then a = 620 and b = 7.8.

Answer:

The correct option is 1.

Step-by-step explanation:

It is given that a system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped.

Let y be the depth of a toy and x is time, in seconds.

In the given graph a solid horizontal line passes through the point (0,-1) and shaded region is above the line. So, the inequality of red line is

[tex]y\geq -1[/tex]

The depth of a toy can be less than -1. It means the pool is 1 meter deep.

The blue line is a dashed line which passes through (0,0) and (2,-1).

So the slope of line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-0}{2-0}=-\frac{1}{2}[/tex]

The equation of blue line is

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

where, m is slope and b is y-intercept.

[tex]y=-\frac{1}{2}x+0[/tex]

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

The shaded region is below the line so the required inequality is

[tex]y< -\frac{1}{2}x[/tex]

it means the toy sinks at a rate of less than 1/2 meter per second.

Therefore the correct option is 1.

Answer:The Answer is A

Step-by-step explanation: I took the test on edge

Answer:

c=-5

d=1

Step-by-step explanation:

[tex](cy^2)(4y^d)=-20y^3[/tex]

I'm going to reorder the left-hand side.  Multiplication is commutative.

[tex](4c)(y^2y^d)=-20y^3[/tex]

Since the bases are the same in [tex]y^2y^d[/tex] and the operation is multiplication, I'm going to add the exponents giving me:

[tex]4cy^{2+d}=-20y^3[/tex]

So this implies we have two equations to solve:

[tex]4c=-20[/tex] and [tex]2+d=3[/tex]

So the first equation can be solved by dividing both sides by 4 giving you [tex]c=-5[/tex].

The second equation can be solved by subtracting 2 on both sides giving you [tex]d=1[/tex].

Answer:

(4,5)

Step-by-step explanation:

The vertex is written in vertex form.

y = a(x - b)^2 + c

Vertex: (b,c)  Notice the sign change on b.

So for your equation, you get (4,5) No sign change on the 5.

Answer: (4, 5)

Proof of validity is shown below.

No Solution

Brainliest Please :)

Answer:

5/8

Step-by-step explanation:

3/8 + 1/4

We need to get a common denominator of 8

3/8 remains 3/8

We change 1/4 by multiplying by 2/2

1/4 *2/2 = 2/8

3/8 + 1/4

3/8+2/8

5/8

Answer:

720

Step-by-step explanation:

The mean of a set of credit scores is u=690 and o=14.

mean = 690  and standard deviation SD = 14

We use z- score formula

z= 3.3 given

Plug in the values and find out x

Multiply 14 on both sides

46.2 = x- 690

Now add 690 on both sides

x= 736.2

Credit score is 720 that comes under 736.2

Answer:

sqrt(545)

Step-by-step explanation:

The distance between 2 points can be found by

d = sqrt( (x2-x1)^2 + (y2-y1)^2)

  = sqrt( (6--10)^2 + (8--9)^2)

      sqrt( (6+10)^2 + (8+9)^2)

        sqrt( (16)^2 + (17)^2)

      sqrt( 256+289)

    sqrt(545)

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-10}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[6-(-10)]^2+[8-(-9)]^2}\implies d=\sqrt{(6+10)^2+(8+9)^2} \\\\\\ d=\sqrt{256+289}\implies d=\sqrt{545}\implies d\approx 23.35[/tex]

Let d = discriminant

d = b^2 - 4ac

Let a = 2, b = 4 and c = -9

We now plug and chug.

d = (4)^2 - 4(2)(-9)

d = 16 - 8(-9)

d = 16 + 72

d = 88

Answer:

А. 88

Step-by-step explanation:

2х^2 + 4x - 9

This is in the form

ax^2 +bx +c

where a=2 b=4 and c=-9

The discriminant is

b^2 -4ac

Substituting into the equation

4^2 -4(2) (-9)

16 - (-72)

16+72

88

Answer:

25/36

Step-by-step explanation:

(2/3)/(24/25)

Solve. Change the division to multiplication, and flip the second fraction:

(2/3) * (25/24)

Multiply across:

(2 * 25)/(3 * 24) = 50/72

Simplify if necessary. Divide common factors:

(50/72)/(2/2) = 25/36

25/36 is your answer.

~

Answer:

-4

Step-by-step explanation:

We are given the following expression which we are to solve:

[tex] ( - 4 ) 5 - ( - 6 ) ( - 4 ) + 4 0 [/tex]

Since this expression includes brackets as well has plus and minus signs, so we will follow the standard order of operations to solve this expression.

Solving the brackets first to get:

[tex] ( - 2 0 ) - ( 2 4 ) + 4 0 [/tex]

Now adding all the terms up to get:

-4

Answer: -2x+10

Step-by-step explanation:

you just multiply x and -5 by -2

Answer:

a. Arithmetic

b. [tex]a_{n} = a_{n-1} + 15[/tex]

c. [tex]a_{n} = 15n + 125[/tex]

Step-by-step explanation:

A sequence is arithmetic when the difference between one term and the next is a constant. On the other hand, a sequence is geometric when the next term is found by multiplying the previous by a constant.

In this case, the next term of the sequence can be found by adding $15. Therefore, the sequence is ARITHMETIC ✔️

The recursive formula will be the following: [tex]a_{n} = a_{n-1} + 15[/tex]

The explicit formula is the following: [tex]a_{n} = 15n + 125[/tex]

Answer:

Option D, 34.5 cm

Step-by-step explanation:

Length of arc is represented by (rθ)

Where r = radius and θ = angle at the center formed by arc in radians.

length of arc = [tex]33\times (\frac{\Theta}{180})\pi[/tex]

                     = [tex]33\times (\frac{60\pi}{180})[/tex]

                      = (33 × π/3)

                      = (11π)

                      = 11 × 3.14

                      = 34.5 cm

Option D, 34.5 cm is the answer.

Answer:

Step-by-step explanation:

[tex]x+6y=18\\\\x-intercept\ for\ y=0:\\\\x+6(0)=18\\x+0=18\\x=18\\\\y-intercept\ for\ x=0:\\\\0+6y=18\\6y=18\qquad\text{divide both sides by 6}\\y=3[/tex]

[tex]-a^2b\left(8+a^4b^3\right)[/tex]

When we factor out a expression, we seek the terms that are common and then take it away. This is the opposite of applying distributive. In this exercise, we need to factor the following expression:

[tex]-8a^2b-a^6b^4[/tex], so:

STEP 1: Applying exponent rules:

We know that:

[tex]a^{m+n}=a^mb^n[/tex]

So:

[tex]a^6b^4=a^2a^4bb^3[/tex]

Then, our expression remains:

[tex]-8a^2b-a^2a^4bb^3[/tex]

STEP 2: Taking common factor [tex]-a^2b[/tex], we finally get:

[tex]\boxed{-a^2b\left(8+a^4b^3\right)}[/tex]

Answer:

first choice

Step-by-step explanation:

The volume of a rectangular prism is L*H*B.

So the volume of the rectangular prism pictured here is 24*10*8

The volume of a triangle prism is 1/2 *H*L*B.

So the volume of the triangle prism pictured here is 1/2 *6*24*8

The volume of the whole figure is the sum of the volume of the rectangular prism and volume of the triangular prism which is in this case:

24*10*8 + 1/2 *6*24*8.

Answer is the first choice.

(It wouldn't be third because 10 has nothing to with the triangular prism part)

Answer:

[tex]4,320\pi\ ft^{3}[/tex]  or  [tex]13,564.8\ ft^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the cylinder (well) is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]h=30\ ft[/tex]

[tex]r=24/2=12\ ft[/tex]

substitute

[tex]V=\pi (12)^{2}(30)[/tex]

[tex]V=4,320\pi\ ft^{3}[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]V=4,320(3.14)=13,564.8\ ft^{3}[/tex]

Answer:

√x+3=13

Step-by-step explanation:

The equation is √x+3=13 is radical because the unknown, x appears under a radical sign √.

To solve the equation, the unknown is left on one side of the equal sign and then both sides of the equal sign are raised to an equal power which would remove the radical sign.

For example,

√x+3=13

√x=13-3

√x=10

Removing radical.

(√x)²=10²

x=100

Answer: what equations did they provide

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that Jacob surveyed members of three different gyms and recorded the number of hours they exercised last week.

Table is as follows:

Gym     Mean       Std dev

  A            7            2.9

  B            8            4.2

  C            6            3.2

We know that std deviation is a measure of variation of the data set from the mean.  

Hence if std deviation is the least the data would be more consistent.

Here A has the least sd

Hence The members of gym show the most consistency in the number of hours they exercised last week, because the

of this data set is the one which has lowest std deviation

Final answer:

Gym A's members show the most consistency in their exercise habits because it has the lowest standard deviation (2.9) compared to Gyms B and C.

Explanation:

The members of Gym A show the most consistency in the number of hours they exercised last week, because standard deviation of this data set is the lowest. To assess consistency among data sets, we look at the standard deviation, which measures the spread of data around the mean. A lower standard deviation indicates that the data points tend to be closer to the mean. Looking at the given data for the three gyms:

Gym A has the lowest standard deviation of 2.9, which suggests the members' weekly exercise hours vary less from the mean compared to Gyms B and C, indicating more consistency.

Answer:

parallelogram

Step-by-step explanation:

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

The best name for a trapezoid with congruent legs and congruent bases is Option (B) parallelogram .

A quadrilateral with at least one pair of parallel sides is called, a trapezoid. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles trapezoid).

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Therefore, a trapezoid having parallel sides with congruent legs and bases have the opposite adjacent sides of equal lengths. The shape thus will form a parallelogram satisfying each and every property.

Thus, the best name for a trapezoid with congruent legs and congruent bases is Option (B) parallelogram .

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Answer:

A = 72 ft^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh where b is the base and h is the height

A = 1/2 (9)*16

A = 72 ft^2

A = 72ft².

We have to use the area of a triangle equation A = (b*h)/2.

A triangle with a base b = 9ft and a height h = 16ft:

A = (9ft*16ft)/2 = 144ft²/2

A = 72ft²

Answer:

[tex]\frac{25}{2}[/tex] or 12.5

Step-by-step explanation:

So if 25 - x items are sold, and they each cost x, we can write an equation for the revenue to be

y = (25 - x)x

The vertex of this equation will represent the maximum revenue.  So we need to write this equation in vertex form so we can find the vertex.

Vertex from is

y = a(x - h)^2+ k,

where (h,k) represent the vertex.

the vertex form of this equation would be

[tex]y= -(x-\frac{25}{2} )^{2} +\frac{625}{4}[/tex]

And the vertex would be

[tex](\frac{25}{2} ,\frac{625}{4})[/tex]

This means the maximum revenue will occur when x = 25/2

The maximum revenue is at a price of $11.5 each for a certain lamp

The revenue is the total amount of money that can be made from selling a number of goods.

Revenue = price * total number of items

Since the price per item is x dollars and the total number of items is 25 - x, hence:

Revenue (R) = x * (25 - x) = 25x - x²

R = 25x - x²

The maximum revenue is at dR/dx = 0, hence:

dR/dx = 25 - 2x

25 - 2x = 0

2x = 25

x = $11.5

Hence, The maximum revenue is at a price of $11.5 each for a certain lamp.

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Answer:

(- 5, 3 )

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y )

Hence

C(5, 3 ) → C'(- 5, 3 )

If ABC is reflected across the y-axis then the coordinates of c is (-5,3).

The coordinates refers to a point on the graph which are used to draw a line, a shape on the graph by plotting these points.

The coordinates of ABC presently are (1,3),(3,6),(5,3). If we just reflect ABC cross y-axis then on the second quadrant only the value of x changes, the value of y remains same. So we have to just put a negative sign in front of the value of x and it becomes -5 with the value of y=3.

Hence the coordinates of C is (-5,3).

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Answer:

(-9,9) is the correct answer

Answer:

A

Step-by-step explanation:

Since the dilatation is centred at the origin, then each of the coordinates of B are multiplied by the scale factor of 3

B(- 3, 3 ) → B'( 3 × - 3, 3 × 3 ) → B'(- 9, 9 ) → A