Summer school math problem

Answer:

1.75 × 10⁶

Step-by-step explanation:

7,000,000 ÷ 4 = 1750000

Which is 1.75 × 10⁶ in standard form

Answer:

-4

Step-by-step explanation:

bc it is

.......................

OPTION A is the correct answer.

Given:

The function is:

[tex]f(x)=-2x^2+7x+4[/tex]

To find:

Express the quadratic equation in the form of [tex]f(x)=a(x-h)^2+k[/tex], then state the minimum or maximum value,axis of symmetry and minimum or maximum point.

Solution:

The vertex form of a quadratic function is:

[tex]f(x)=a(x-h)^2+k[/tex]              ...(i)

Where, a is a constant, (h,k) is the vertex and x=h is the axis of symmetry.

We have,

[tex]f(x)=-2x^2+7x+4[/tex]

It can be written as:

[tex]f(x)=-2\left(x^2-3.5x\right)+4[/tex]

Adding and subtracting square of half of coefficient of x inside the parenthesis, we get

[tex]f(x)=-2\left(x^2-3.5x+(\dfrac{3.5}{2})^2-(\dfrac{3.5}{2})^2\right)+4[/tex]

[tex]f(x)=-2\left(x^2-3.5x+(1.75)^2\right)-2\left(-(1.75)^2\right)+4[/tex]

[tex]f(x)=-2\left(x-1.75\right)^2+2(3.0625)+4[/tex]

[tex]f(x)=-2\left(x-1.75\right)^2+6.125+4[/tex]

[tex]f(x)=-2\left(x-1.75\right)^2+10.125[/tex]                ...(ii)

On comparing (i) and (ii), we get

[tex]a=-2,h=1.75,k=10.125[/tex]

Here, a is negative, the given function represents a downward parabola and its vertex is the point of maxima.

Maximum value = 10.125

Axis of symmetry : [tex]x=1.75[/tex]

Maximum point = (1.75,10.125)

Therefore, the vertex form of the given function is [tex]f(x)=-2\left(x-1.75\right)^2+10.125[/tex], the maximum value is 10.125, the axis of symmetry is [tex]x=1.75[/tex] and the maximum point is (1.75,10.125).

Given:

Modeling: Slope intercept equation of a line

To find:

The slope intercept equation of a line.

Solution:

The slope intercept equation of a line is defined as:

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

Where, m is the slope and b is the y-intercept.

It means the line intersects the y-axis at (0,b).

For example: The slope of a line is 2 and its y-intercept is 1, then the slope intercept of the line is:

[tex]y=2x+1[/tex]

Therefore, the slope intercept form of a line is [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept.

Answer:

Lines  C and D

Step-by-step explanation:

For a pair of lines to be perpendicular ,

    the product of their slope must be - 1 .

Slope of A:

[tex]2x - 3y = 6\\\\-3y = -2x + 6\\\\y = \frac{-2x}{-3} + \frac{6}{-3}\\\\[/tex]

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

Slope of B:

[tex]3x - 2y = - 9\\\\-2y = - 3x - 9\\\\y = \frac{-3x}{-2} - \frac{9}{-2}\\\\y =\frac{3x}{2} + \frac{9}{2}\\\\slope_B = \frac{3}{2}[/tex]

Slope of C:

[tex]y = - \frac{3}{2}x - 5 \\\\slope_C = -\frac{3}{2}[/tex]

Slope of D:

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

Product of the slopes = - 1

[tex]slope_A \times slope_B = \frac{2}{3} \times \frac{3}{2} = 1 \neq - 1 \\\\Therefore, not\ perpendicular.\\\\Slope_B \times slope_C = \frac{3}{2} \times \frac{-3}{2} = \frac{-9}{4} \neq -1\\\\Therefore , not \ perpendiucalr.\\\\Slope_C \times slope_D = -\frac{3}{2} \times \frac{2}{3} = - 1\\\\Therefore , perpendicular\\\\\\Slope_A \times slope_D = \frac{2}{3} \times \frac{2}{3} = \frac{4}{9} \neq 1\\\\therefore , not \ perpendicular.[/tex]

Answer:

Step-by-step explanation:

[tex]\frac{5}{10}*\frac{-4}{12}-\frac{1}{3}-\frac{4}{12}*\frac{2}{10}\\\\=\frac{1}{2}*\frac{-1}{3}-\frac{1}{3}-\frac{1}{3}*\frac{1}{5}\\\\= \frac{-1}{3}[\frac{1}{2}+1+\frac{1}{5}]\\\\=\frac{-1}{3}[\frac{1*5}{2*5}]+\frac{1*10}{1*10}+\frac{1*2}{5*2}]\\\\=\frac{-1}{3}[\frac{5}{10}+\frac{10}{10}+\frac{2}{10}]\\\\=\frac{-1}{3}[\frac{5+10+2}{10}]\\\\=\frac{-1}{3}*\frac{17}{10}\\\\=\frac{-17}{30}[/tex]

Answer:

I suck at math but take a picture and put it in the app called "Math-way" or "Photo-math" I'm a senior and still use these

Answer:

24

Step-by-step explanation:

p/2 = 12.

To leave the p alone, multiply 2 from both sides.

p = 24

Answer:

X=(d - 2)/4 is the answer of your question

Answer:

[tex]2x - 35273 = 5361925 \\ 2x = 5361925 + 35273 \\ 2x = 5397198 \\ x = \frac{5397198}{2} \\ x = 2698599[/tex]

[tex]\displaystyle\ 2x-35273=5361925\\\\2x=53\underline{61925}+\underline{35273} \\\\2x=5397198\\\\\\x=\frac{5397198}{2} =2698599\\\\\underline{x=2698599\qquad }\\\\2\cdot 2698599-35273=5361925\\\\5397198-35273=5361925\\\\5361925=5361925[/tex]

Answer:

Hey Mate! Here's your answer.

Step-by-step explanation:

One packet of biscuits requires 2½ cups of flour = \frac{5}{2}25

One packet of biscuits requires 1 \times \frac{2}{3}1×32

One packet of biscuits requires 1 \times \frac{2}{3}1×32cups of sugar. = \frac{5}{3}35

Total ingradiants for one packet of biscuits =

Total ingradiants for one packet of biscuits =( \frac{5}{2} + \frac{5}{3} ) = \frac{15 + 10}{6} = \frac{25}{6}(25+35)=615+10=625

Then, total quantity of both ingredients used in 10 such packets of biscuits =

Then, total quantity of both ingredients used in 10 such packets of biscuits =10 \times ( \frac{25}{6} ) = 5 \times ( \frac{25}{3} ) = \frac{125}{3} = 41 \times \frac{2}{3}10×(625)=5×(325)=3125=41×32

Hope it helped you!

Step-by-step explanation:

let wrong answers be y

let right answer be x

3x-1y=79

find another equation

Answer:

The helicopter costs 54 dollars and 9% of 54 is 4.86.

Step-by-step explanation:

9% of what number = 4.86

... is equivalent to:

9% × ? = 4.86

---------------------------------

- Percent (%) means 'out of one hundred'-

(100 × 4.86) ÷ 9 =

486 ÷ 9 =

54

3 and 4

Step-by-step explanation:

y=5x

y=5(0)

y=0

y=5x

y=5(10)

y=50

y=5x

y=5(51)

y=255

y=5x

y=5(400)

y=2000

Answer:i don’t know

Step-by-step explanation:i don’t know

Answer:

8/7 min  = [tex]1 \frac{1}{7} minutes[/tex]

Step-by-step explanation:

A rate 2 2/3 = 8/3 min per tank

B rate 2 min per tank

thus:

A rate = 3/8 tank per min

B rate = 1/2 tank per min

A+ B =  3/8 + 4/8 = 7/8 tank per min

7/8 x = 1

x = 8/7 min

Answer:

The central angle of the arc is 288 degrees.

Step-by-step explanation:

The correct question is

A circle has a circumference of 8. It has an arc of length 32/5 . What is the central angle of the arc,in the degrees?

we know that The circumference of the circle subtend a central angle of 360 degrees

so using a proportion

Find out the central angle for an arc of length 32/5

Answer:

it must be 85 (approx.)

Step-by-step explanation:

Answer:

1.2055 × 10⁴

Step-by-step explanation:

10,000 + 2,000 + 50 + 5

= 12,055

Writing 12,055 in standard form

The first digit in standard form should be between 1 and 10

Therefore, the first digit in 12,055 is 1 then point other numbers

As in 1.2055

There are 4 digits after the decimal point.

So we have 10⁴

12,055 = 1.2055 × 10⁴

Check:

1.2055 × 10⁴

= 1.2055 × 10,000

= 12,055

[tex]\displaystyle\ \boxed{a^m\cdot a^n=a^{m+n}}\\\\4^{3c} \cdot 4^{5c}=\frac{4}{16} \\\\4^{3c+5c}=4^{-1}\\\\8c=-1\\\\c=-\frac{1}8}[/tex]

Answer:

Null set

Step-by-step explanation:

Odd(0)

Even (E)

Prime (P)

Answer:

Its A since the other person didnt say it

Step-by-step explanation:

Answer:

(3x + 7y)^2 =  9 x^2 + 42xy + 49y^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

First we'll simplify this using the Sum Identity for sin(x + y) where [tex]x=\frac{3\pi}{2}[/tex] and y = x. Notice we have 2 of those so we simplify first into

[tex]2sin(\frac{3\pi}{2}+x)=-2[/tex] and divide away the 2 on the left to get

[tex]sin(\frac{3\pi}{2}+x)=-1[/tex] and now we'll expand:

[tex]sin\frac{3\pi}{2}cosx+cos\frac{3\pi}{2}sinx=-1[/tex] and go to your unit circle to find the sin and cos of [tex]\frac{3\pi}{2}[/tex] and fill in where they go:

(-1cosx + 0sinx) = -1 which simplifies to

-1cosx = -1 so

cosx = 1 and

x = 0 or 2π, depending upon what your interval is.

Answer:

Sila put a wrong number in her calculator when multiplying the numerators.

Step-by-step explanation:

StartFraction 12 kilometers Over 1 EndFraction times StartFraction 0.62 miles Over 1 kilometer EndFraction times StartFraction 5280 feet Over 1 mile EndFraction = 392,832 feet

Correct calculation:

12 km/ 1 * 0.6miles / 1km * 5280 feet / 1 mile

= (12km * 0.62 miles * 5280 feet) / (1 * 1 km * 1 mile)

= 39,283.2 feet

Sila's calculation:

12 km/ 1 * 0.6miles / 1km * 5280 feet / 1 mile

= 392,832 feet

Answer:

Step-by-step explanation:

The easiest way to solve this is with calculus, believe it or not. The position function is

[tex]s(t)=-16t^2+64t[/tex]. The first derivative of this is the velocity function:

v(t) = -32t + 64. From physics, we know that at the max height of an object's path, the velocity is equal to 0, so setting this velocity equation equal to 0 and solving for time, will tell us the time it took to get to the max height (which we don't know yet, but we will in a bit):

0 = -32t + 64 and

-64 = -32t so

t = 2 seconds. It takes 2 seconds to reach a max height. Plugging that 2 in for t in the position function will tell you the max height that corresponds to this time:

[tex]s(2)=-16(2)^2+64(2)[/tex] and

s(2) = 64 feet.

So the max height is 64 feet and it is reached at 2 seconds after launching.

Also from physics we know that at halfway through a parabolic path, which is also the max height, we are halfway through time-wise as well. That means that if it takes 2 seconds to reach the max height from the ground, it will take another 2 seconds to fall to the ground.

So the total time the rocket is in the air is 4 seconds: 2 seconds to reach the max height and another 2 to fall back down.

Answer:

Step-by-step explanation:

Answer:

a. [tex]\frac{4\pi }{3}[/tex]

b. 240

Step-by-step explanation:

all you have to do to find a coterminal angle is to add or subtract 360 or [tex]2\pi[/tex] from the angle, so:

a. [tex]\frac{10\pi }{3} -2\pi =\frac{4\pi }{3}[/tex]

b. -120 + 360 = 240