The graph of a parabola is represented by the equation
y = ax2 where a is a positive integer. If a is multiplied
by 2, the new parabola will become

Answer:

6b - 8 = 58

6b = 66

b = 11

Each book costs $11.

Lashonda bought 11 books.

To solve this problem, we can set up an equation based on the information given. Let [tex]\( b \)[/tex] represent the number of books Lashonda bought. Each book costs $6, so the total cost before the discount is [tex]\( 6b \)[/tex]. Lashonda received a discount of $8 off of her total purchase, and she spent $58 after the discount. Therefore, the equation representing the total cost before the discount minus the discount equals the amount she spent is:

[tex]\[ 6b - 8 = 58 \][/tex]

Now, we solve for [tex]\( b \)[/tex]:

[tex]\[ 6b = 58 + 8 \][/tex]

[tex]\[ 6b = 66 \][/tex]

[tex]\[ b = \frac{66}{6} \][/tex]

[tex]\[ b = 11 \][/tex]

So, Lashonda bought 11 books.

Answer:

   x = 2/5 = 0.400

Step-by-step explanation:

Step  1  :

           1

Simplify   —

           4

Equation at the end of step  1  :

  5         1

 (— • x) -  —  = 0  

  8         4

Step  2  :

           5

Simplify   —

           8

Equation at the end of step  2  :

  5         1

 (— • x) -  —  = 0  

  8         4

Step  3  :

Calculating the Least Common Multiple :

3.1    Find the Least Common Multiple

     The left denominator is :       8  

     The right denominator is :       4  

       Number of times each prime factor

       appears in the factorization of:

Prime  

Factor   Left  

Denominator   Right  

Denominator   L.C.M = Max  

{Left,Right}  

2 3 2 3

Product of all  

Prime Factors  8 4 8

     Least Common Multiple:

     8  

Calculating Multipliers :

3.2    Calculate multipliers for the two fractions

   Denote the Least Common Multiple by  L.C.M  

   Denote the Left Multiplier by  Left_M  

   Denote the Right Multiplier by  Right_M  

   Denote the Left Deniminator by  L_Deno  

   Denote the Right Multiplier by  R_Deno  

  Left_M = L.C.M / L_Deno = 1

  Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

  L. Mult. • L. Num.      5x

  ——————————————————  =   ——

        L.C.M             8  

  R. Mult. • R. Num.      2

  ——————————————————  =   —

        L.C.M             8

Adding fractions that have a common denominator :

3.4       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

5x - (2)     5x - 2

————————  =  ——————

   8           8    

Equation at the end of step  3  :

 5x - 2

 ——————  = 0  

   8    

Step  4  :

When a fraction equals zero :

4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 5x-2

 ———— • 8 = 0 • 8

  8  

Now, on the left hand side, the  8  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  5x-2  = 0

Solving a Single Variable Equation :

4.2      Solve  :    5x-2 = 0  

Add  2  to both sides of the equation :  

                     5x = 2

Divide both sides of the equation by 5:

                    x = 2/5 = 0.400

One solution was found :

                  x = 2/5 = 0.400

Answer:

4 x 2 x 3

Step-by-step explanation:

[tex]l = 4\\\\w = 2\\h = 3\\[/tex]

Answer:

you can solve this by finding the volume of the block

Step-by-step explanation

V= lxwxh

= 3x4x2

= 24

therefore there are 24 blocks in this figure

Have a great day

Answer:

1/2 gallon=2 quarts plus 3 quarts so 5 quarts then 11/4 would be 11 quarts so 11+2+3=16 quarts

Step-by-step explanation:

If the 11/4 part is confusing you on how many quarts it actually is it simply means that for every 4 quarts you get a gallon and you have 11 quarts so you can also look at it as 2 3/4 gallons if that somehow clarifies it.

Answer:

5/4k^2

Step-by-step explanation:

P=5\dfrac{k}{6}\times \dfrac{3}{2k^3}.

We will be using the following property of exponents:

\dfrac{a^x}{a^y}=a^{x-y}.

We have

P\\\\\\=5\dfrac{k}{6}\times\dfrac{3}{2k^3}\\\\\\=\dfrac{5}{6}\times\dfrac{3}{2}k^{1-3}\\\\\\=\dfrac{5}{4}k^{-2}=\dfrac{5}{4k^2}.

Thus, the required product is \dfrac{5}{4k^2}.

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Answer: 5/4k^2

Step-by-step explanation:

Just multiply the fractions then simplify by a common factor of 3, then cancel out the common variable of k

Answer:

I am pretty sure that the answer is  

y = 3x -2

Step-by-step explanation:

given a line with slope m then the slope of a line  perpendicular to it is

 where m is the slope and b the y-intercept

I hoped this helped!!!

Answer: y=3x-5

Step-by-step explanation:

Got ot right on my test!!

Answer:

C

Step-by-step explanation:

If you don't like math you don't like geometry because geometry is math. Just like if you like geometry you like math because geometry is math

Answer:

C

Step-by-step explanation:

Since geometry is math, then if you don’t like math, you won’t like geometry.

Answer: 187.2

Step-by-step explanation:

Answer:

187.2

Step-by-step explanation:

Answer:

- time = 1second

- maximum height = 16m

Step-by-step explanation:

Given the height of a pumpkin t seconds after it is launched from a catapult modelled by the equation

f(t)=-16t²+32t... (1)

The pumpkin reaches its maximum height when the velocity is zero.

Velocity = {d(f(x)}/dt = -32t+32

Since v = 0m/s (at maximum height)

-32t+32 = 0

-32t = -32

t = -32/-32

t = 1sec

The pumpkin reaches its maximum height after 1second.

Maximum height of the pumpkin is gotten by substituting t = 1sec into equation (1)

f(1) = -16(1)²+32(1)

f(1) = -16+32

f(1) = 16m

The maximum height of the pumpkin is 16m

The answer is 0.8. What I did was I put 4 divided by 5 in my calculator

Answer:

0.8

Step-by-step explanation:

First, we have to find out what 1/5 is, so we divide 1 by 5:

Divide:

1/5=.2

Multiply by 4:

.2 times 4= .8

I hope this helps u pls give a brainliest and a thx ;)

Answer:

[tex]\mathrm{Parabola\:focus\:given}\:x^2=-20y:\quad \left(0,\:-5\right)[/tex]

Step-by-step explanation:

Given the equation

[tex]x2 = -20y[/tex]

A parabola is the locus of points such that the distance to a point the focus equals the distance to a line the directrix.

[tex]4p\left(y-k\right)=\left(x-h\right)^2[/tex] is the standard equation for an up-down facing parabola with vertex at (h, k), and a focal length |p|.

so

[tex]x^2=-20y[/tex]

[tex]\mathrm{Switch\:sides}[/tex]

[tex]-20y=x^2[/tex]

[tex]\mathrm{Factor\:}4[/tex]

[tex]4\cdot \frac{-20}{4}y=x^2[/tex]

[tex]4\left(-5\right)y=x^2[/tex]

[tex]\mathrm{Rewrite\:as}[/tex]

[tex]4\left(-5\right)\left(y-0\right)=\left(x-0\right)^2[/tex]

[tex]\left(h,\:k\right)=\left(0,\:0\right),\:p=-5[/tex]

Parabola is symmetric around the y-axis and so the focus lies a distance\ p from the center (0, 0) along the y-axis.

[tex]\left(0,\:0+p\right)[/tex]

[tex]=\left(0,\:0+\left(-5\right)\right)[/tex]

[tex]\mathrm{Refine}[/tex]

[tex]\left(0,\:-5\right)[/tex]

Therefore,

[tex]\mathrm{Parabola\:focus\:given}\:x^2=-20y:\quad \left(0,\:-5\right)[/tex]

Please check the attached figure too.

The focus of the parabola given by the equation x2 = -20y is at the coordinates (0,-5). This is calculated by finding the value of 'p' in the standard form x2 = 4py.

The equation x2 = -20y is notably a form of the parabola equation known as standard form. This version of a parabola equation is defined in the form x2 = 4py (or it could be y2 = 4px), where p is the distance from the vertex to the focus (and also to the directrix).

In the given equation, x2 = -20y, comparing it with the standard form, we find 4p = -20 by observing the coefficient of 'y'. Solving for 'p', we get p = -20/4 = -5. This means the focus of the parabola is (0,-5), because for a parabola that opens downwards (since 'p' is negative), the focus is located at the coordinates (h, k-p), where 'h' and 'k' are the coordinates of the vertex (which is the origin (0,0) in this case).

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Hi!

Answer: 200

The 2 triangles surface area add up to 120

the rectangle on the bottom is 30

The rectangle in the back is 16

And the rectangle on top is 34

So 120+30+16+34 = 200

Hope this is correct and helps!

Answer:

20cm.

Step-by-step explanation:

so the answer is 8cm

Hope this will help u...

Answer:

530.66 cm squared

Step-by-step explanation:

c = 2(3.14)r

81.64 = 2(3.14)r

Divide both sides by 6.28

The radius is 13

a = 3.14(13 squared)

a = 530.66

Answer: 530.39 cm²

Step-by-step explanation:

C=2πr, Substitute 81.64 in for C then divide 2π t get 12.99. A=πr². Plug in 12.99 for r, solve, and get 530.39 cm

Answer:

4 1/2. Root 18 simplifies to 4.242640687, which is less than 4.50

Answer:

4and 1/2

Step-by-step explanation:the square for of 18 is 4.24264 and 4 and a half is 4.5

Answer:

C) 35

Step-by-step explanation:

[tex]^7C_3 \\ = \frac{7!}{3!(7 - 3)!} \\= \frac{7!}{3! \: 4!} \\ = \frac{7 \times 6 \times 5 \times 4!}{3 \times 2 \times 1 \times 4!} \\ = \frac{7 \times 6 \times 5 \times 4!}{3 \times 2 \times 1 \times 4!} \\ = 35 \\ \huge \red{ \boxed{ \therefore \: ^7C_3 = 35}}[/tex]

Answer:

C=35

Step-by-step explanation:

⁷C₃

These is combination

using the rule it states that

ⁿCₐ= n!/(n-a)!a!

so therefore ⁷C₃= 7!/(7-3)!3! = 7!/4!3!=7x6x5x4x3x2x1/{(4x3x2x1)x(3x2x1)}

4x3x2x1 cancels itself as it appears up and down

7x6x5/6

6 cancels each itself as it appears up and down

7x5 = 35

Answer:

Part A) The length of a straight line between the school and the Fire Station is [tex]4.6\ miles[/tex]

Part B) The length of a straight line between the school and the hospital is [tex]2.1\ miles[/tex]

Step-by-step explanation:

The complete question in the attached figure

Let

The positive x-coordinates ----> East

The positive y-coordinates ----> North

The negative x-coordinates ----> West

The negative y-coordinates ----> South

take the point A (0,0) as the Middle School (reference point)

Part A) we have

Town Hall is located 4.3 miles directly east of the Middle School

so

The coordinates of Town Hall are B(4.3,0)

The Fire Station is located 1.7 miles directly North of Town Hall

so

The coordinates of Fire Station are C(4.3,1.7)

What is the length of a straight line between the school and the Fire Station?

Remember that

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(0,0) and C(4.3,1.7)

substitute

[tex]d=\sqrt{(1.7-0)^{2}+(4.3-0)^{2}}[/tex]

[tex]d=\sqrt{(1.7)^{2}+(4.3)^{2}}[/tex]

[tex]d=4.6\ miles[/tex]

Part B) we have that

The hospital is 3.1 miles west of the fire station

so

The coordinates of the hospital are D(4.3-3.1,1.7)

D(1.2,1.7)

What is the length of a straight line between the school and the hospital?

Remember that

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(0,0) and D(1.2,1.7)

substitute

[tex]d=\sqrt{(1.7-0)^{2}+(1.2-0)^{2}}[/tex]

[tex]d=\sqrt{(1.7)^{2}+(1.2)^{2}}[/tex]

[tex]d=2.1\ miles[/tex]

Answer:

50.04 pounds

Step-by-step explanation:

If 1 gallon weighs 8.34 pounds,

all you have to do is multiply 8.34 by 6

to get what 6 gallons would weigh.

To determine the weight of 6 gallons of water, multiply the weight of one gallon (8.34 pounds) by 6. Thus, 6 gallons of water weigh 50.04 pounds.

To find out how much 6 gallons of water weigh, you simply need to multiply the weight of one gallon by the number of gallons.

Since we know that one gallon of water weighs 8.34 pounds, the calculation is as follows:

6 gallons × 8.34 pounds/gallon = 50.04 pounds.

Therefore, 6 gallons of water weigh 50.04 pounds.

Answer:

See Below

Step-by-step explanation:

The function is a piecewise function defined as:

[tex]N(t)=\left \{ {{25t+150} \ 0 \leq t \leq 6 \atop {\frac{200+80t}{2+0.05t} \ t \geq 8}} \right.[/tex]

a)

We need to find the limit of the function as t goes to infinity. This means what is the max value of fish in the pond given times goes to infinity (on an on).

We will take the 2nd part of the equation since t falls into that range, t is infinity, which is definitely greater than 8.

[tex]\lim_{t \to \infty} \frac{200+80t}{2+0.05t} \\\lim_{n \to \infty} \frac{80t}{0.05t}\\ \lim_{n \to \infty} \frac{80}{0.05} =1600[/tex]

This means the maximum number of fish at this pond is 1600, no matter how long it goes on.

b)

A function is continuous at a point if we have the limit and the functional value at that point same.

Functional value at t = 8 is (we use 2nd part of equation):

[tex]\frac{200+80t}{2+0.05t}\\\frac{200+80(8)}{2+0.05(8)}\\=350[/tex]

We do have a value and limit also goes to this as t approaches 8.

So, function is continuous at t = 8

c)

We want to find is there a "time" when the number of fishes in the pond is 250, during t from 0 to 6. We plug in 250 into N(t) and try to find t. Make sure to use the 1st part of the piece-wise function. Shown below:

[tex]N(t)=25t+150\\250=25t+150\\25t=250-150\\25t=100\\t=4[/tex]

The time is 4 years when the number of fishes in the pond is 250

The answer for question 1 is C. 18ft

for question 2 is B. 63ft

for question 3 is B. 45

and for question 4 is C. 23

Lastly for question 5 the answer is 14

Answer:

50 ft.

Step-by-step explanation:

It is given that the ratio of width-to-length is 2 : 5.

Let,

Width = 2x ft

Length = 5x ft

Perimeter of the rectangle is

[tex]Perimeter=2(lenght+width)[/tex]

[tex]Perimeter=2(5x+2x)[/tex]

[tex]Perimeter=2(7x)[/tex]

[tex]Perimeter=14x[/tex]

It is given that the perimeter of the rectangle is 140 ft.

[tex]14x=140[/tex]

Divide both sides by 14.

[tex]x=10[/tex]

The value of x is 10.

[tex]Length=5x=5\times 10=50[/tex]

Therefore, the length of the rectangle is 50 ft.

Answer:

6³

Step-by-step explanation:

Answer:

6^3

Step-by-step explanation:

6*6*6

The base is 6

There are 3 sixes multiplied together so the exponent is 3

Answer:

a is the answer

Step-by-step explanation:

In the given scenario, angle 2 is formed by line segments DG and GE. Another name for angle 2 is Angle DGE (Option a).

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
As mentioned in the question, Lines EH and DF intersect at point G. Angle 2 is formed by line segments DG and GE, and angle 1 is formed by line segments EG and GF. So angle 2 is constituted by segments jointly as DGE.

Thus, Another name for angle 2 is Angle DGE (Option a).

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Answer:

it would be can D

Step-by-step explanation:

Can C have greater volume.

The amount of space inside a cylinder is its volume. You can find it by dividing the base area by the height. V =πr²h, is the formula for the volume of a cylinder with base radius r and height h.

Given:

a) Volume of Cylinder = πr²h

                                    = 3.14 x 2 x 2 x 6

                                    = 75.36 cube inches.

b) Volume of Cylinder = πr²h

                                    = 3.14 x 2.5 x 2.5 x 5

                                    = 98.125 cube inches.

c) Volume of Cylinder = πr²h

                                    = 3.14 x 3 x 3 x 4

                                    = 113.04 cube inches.

d) Volume of Cylinder = πr²h

                                    = 3.14 x 3.2 x 3.2 x 3

                                    = 94.4608 cube inches.

Hence, can C have greater volume.

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Answer: the system is consistent

The system is independent

Step-by-step explanation:

Answer:

153.3

Step-by-step explanation:

154-0.7

Answer:

153.3

Step-by-step explanation:

154.0-0.7=153.3