If you add 10 grams of sugar into 30 grams of 20 % sugar syrup, you will make ____ grams of ____% sugar syrup.

Answer:

f is a function because each student, or each element of the domain, corresponds to one element of range.

Step-by-step explanation:

function is each input has one output. input is domain, output is range

Step-by-step explanation:

[tex]\displaystyle \boxed {y = sin\:(x + \frac{\pi}{2})} \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{2}} \hookrightarrow \frac{-\frac{\pi}{2}}{1} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 1[/tex]

OR

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 1[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = sin\:x,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{2}\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{2}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{2}} = \frac{-\frac{\pi}{2}}{1}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = sin\:(x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a wourd problem to wourk with, you MUST use the above formula for calculating the period. Onse you do that, the rest should be easy. Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended one unit beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

Properties of y = cos(x)

The cosine wave is a sinusoidal function (sine and cosine waves are the same except for a horizontal shift).

It is a continuous function and so its domain is (-∞, ∞)

The center line is y = 0

The Amplitude (the height from the center line to the peak) is 1, and so its range is -1 ≤ x ≤ 1

The y-intercept is at (0, 1)

Its period (length of one wave) is 2π (360°)

Answer:

a=110 b=35 c= 10 d=55 e=14 f=10

Step-by-step explanation:

a = 11c , 180-70=110

b=2*35 =70

c= 11*10=110

2d=110 , d=55

e=5*14=70

7f=70 , f=10

Answer:

1/4

Step-by-step explanation:

quartered pie

Answer:

1/4

Step-by-step explanation:

there's four total triangles and only one is shaded purple. that is one of the four triangles.

Answer:

a cross section

Step-by-step explanation:

duhh who did not know that

Answer:

[tex]( - 0.5 , - 4.5 )[/tex]

Step-by-step explanation:

Rewrite the equation in vertex form.

Complete the square for

[tex]2 {x}^{2} + 2x - 4[/tex]

Use the form

[tex]a {x}^{2} + bx + c[/tex]

to find the values of a, b, and c.

a = 2

b = 2

c = −4

Consider the vertex form of a parabola.

[tex]a(x + d) ^{2} + e[/tex]

Find the value of d using the formula

[tex]d = \frac{b}{2a} [/tex]

[tex]d = \frac{1}{2} [/tex]

Find the value of e using the formula

[tex]e = c - \frac{ {b}^{2} }{4a} [/tex]

[tex]e = - \frac{9}{2} [/tex]

Substitute the values of a, d, and e into the vertex form

[tex]2(x + \frac{1}{2} ) ^{2} - \frac{9}{2} [/tex]

Set y equal to the new right side.

[tex]y = {2(x + \frac{1}{2}) }^{2} - \frac{9}{2} [/tex]

Use the vertex form, 

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

to determine the values of a, h, and k.

a = 2

h = -1/2

k = -9/2

Find the vertex (h,k).

[tex]( - \frac{1}{2} , - \frac{9}{2} )[/tex]

Answer:

The answer is 80, give me brainliest answer:)

Answer:56

Step-by-step explanation: Since there are 1344 baseballs and 24 baseballs in each carton. You divide 1344 by 24 and get 56.

Hope I helped! :)

Answer:

y=4

Step-by-step explanation:

I'm a little rusty at this but y=4 should be the correct answer.

Hope this helps!

Answer:

i think people do that so the products don't get destroyed. like, you wouldn't put bread and canned foods in the same bag. or maybe it's to organize them by category, etc. so when you get home to put up the groceries, they're all in the same place. like all the fridge items are in this bag. i don't know honestly. just my opinion.

Step-by-step explanation:

hope it helps?

Answer:

The Gold team has 8 swimmers and the silver team also has 8 swimmers.

Step-by-step explanation:

Let T be the total number of swimmers on the Gold team. Since, the Gold team has a 2:3 ratio of 11 year olds to 12 year olds, the number of 11 year old is T' = 2/(2 + 3) × T = 2T/5 and the number of 12 year olds is T" = 3/(2 + 3) × T = 3T/5.

The silver team has a 3:8 ratio of 11 year olds to the total swimmers. Let T₁ be the number of 11 year old swimmers in the silver team. So, from the ratio 3:8, the number of 11 year old swimmers in the silver team is 3 and the total number of swimmers in the silver team is 8.

Since the number of 11 year old swimmers in both teams are the same, then

2T/5 = 3

T = 3 × 5 ÷ 2

T = 15/2

T = 7.5

T≅ 8

So, the Gold team also has 8 swimmers.

So, the Gold team has 8 swimmers and the silver team also has 8 swimmers.

The surface area of the cylinder after dilation is: 36 units².

Surface area of a cylinder = 2πrh + 2πr²

Find the surface area of the cylinder before dilation:

Surface area = 2πrh + 2πr² = 2(π)(9)(9) + 2(π)(9²)

Surface area = 324π units²

Surface area of the cylinder after dilation = 324π × (1/3)²

= 324π × 1/9

= 36 units²

Thus, the surface area of the cylinder after dilation is: 36 units².

Learn more about surface area of cylinder on:

https://brainly.com/question/14657844

B. Correct

Hi there !

27 : 6 = 4 r3

27 = 6×4 + r3

27 = 24 + 3

27 = 27

(correct)

Good luck !

Answer:

81

Step-by-step explanation:

2. substitute values

(2+3+4)²

2. solve brackets first

(9)²

3. evaluate

9² = 81

Answer:

40

Step-by-step explanation:

Any regular polygon has exterior angles  = to 360 / number of sides.

so a 9-gon has 9 sides. The exterior angle = 360 / 9 = 40

Each exterior angle will be 40 degrees.

Try it with simpler n-gons. A triangle has 3 sides. The exterior angle is 360 / 3 = 120

A square has 4 sides. Each exterior angle is 360 / 4 = 90

Answer:

1. put an open circle going left on 4

2.put a closed circle going right on 1

3.put a closed circle going left from -5

4.put an open circle going right at 10

Step-by-step explanation:

I am learning this right now in  math class

Answer:

A. Yes

Step-by-step explanation:

Hi there!

We are given the equation of the line [tex]y=\frac{1}{7}x-4[/tex], and we want to see if the point (7, -3) is on that line.

If the point is on the line, then it means that the point is a solution to the equation, meaning that if we plug its values into the equation, it will make a true statement.

This is because a line is made up of an infinite number of points, and they go on forever (there are no endpoints on a line), and so many, many points will belong to that line. The equation of the line simply shows how we can manipulate x and y to find points that belong to that line.

Anyway, in order to figure out if the point is a solution to the equation, we can substitute its values into the equation and see if the statement it makes is true or not

So substitute 7 as x and y as -3

[tex]-3=\frac{1}{7} (7)-4[/tex]

Multiply

-3=1-4

Simplify

-3=-3

This is an identity, which is true.

Therefore, the answer is A, which would be yes.

Hope this helps!

See more on this topic here: https://brainly.com/question/25855355

Answer:

$185,000

Step-by-step explanation:

29600 / 16 = 1850 (which is 1%)....1850 X 100% = $185,000.

Answer:

f=21

Step-by-step explanation:

The equation you could write is -4f=-84. Solving this (dividing by -4 on both sides), your answer is that f=21.

Answer:

f = 21

Step-by-step explanation:

Hope this helps!

I tried to write an explanation but it wouldn't let me for some reason

Answer:

495

Step-by-step explanation:

9 + 2 = 11

11 x 45 = 495

you'd get 495 if you did 2+9 45 times.

Step-by-step explanation:

1) y=1

Obviously this is a line with a constant ordinate and parallel to the x-axis, it admits no x-intercepts since it cannot intersect the x-axis

The y-intercept is the point of coordinates (0,1)

Find the derivative of the function and solve it equal to zero to find the coordinates of the vertex

y=1

y'=1 =>0=1 Impossible

So it admits no vertex.

2)

x=3

Similarly this is a line with a constant abscissa and parallel to the y-axis.It does not have a y-intercept since it cannot intersect the y-axis.

The x intercept is the point of coordinates (1,0)

This function admits no derivative since it is a function independent of the x value (constant x)

Therefore it has no intercepts.

3)

f(x)=3x+2

Solve for f(0) to find the y-intercept

f(0)=3(0)+2=2

X-intercept (2,0)

Solve f(x)=0 to find the x-intercept(s)

3x+2=0

3x=-2

x=-2/3

Y-intercept (-2/3,0)

Find the derivative and solve it equal zero to find the coordinates of the vertex:

f(x)=3x+2

f'(x)=3

3=0 impossible, so this function admits no vertex.

4)

f(x)=x²+3x+4

to find the y-intercept solve x=0 or in other words, find f(0)

f(0)=0²+3(0)+4=4

y-intercept is (0,4)

to find the x-intercept(s) solve f(x)=0

x²+3x+4=0

find the roots to this equation

∆=b²-4ac

∆=3²-4(1)(4)

∆=9-16

∆=-7<0

which implies this function admits no x-intercepts

5)

f(x)=-x²+4x+16

f(0)=-(0)²+4(0)+16

f(0)=16

Y-intercept (0,16)

f(x)=0

-x²+4x+16=0

""Solve using the quadratic formula'"'

You get the roots:

x¹=-2.47 x²=6.47

x-intercepts (-2.47,0) (6.47,0)

f'(x)=-2x+4

f'(x)=0

-2x+4=0

-2x=-4

x=2

Find f(2)=-(2)²+4(2)+16=-4+8+16=20

Vertex (2,20)

6)

f(x)=-2x²+x+2

f(0)=-2(0)²+0+2=2

Y-intercept (0,2)

f(x)=0

-2x²+x+2=0 'use the quadratic formula'

x¹=-0.78 x²=1.78

x-intercepts (-0.78,0) (1.78,0)

f'(x)=-4x+1

f'(x)=0

-4x+1=0

-4x=-1

x=1/4=0.25

f(0.25)=-2(0.25)²+0.25+2=2.125

Vertex (0.25,2.125)

Answer:

r = 2/3p

A trail mix recipe asks for 4 cups of raisins for every 6 cups of peanuts.

There is proportional relationship between the amount of raisins, r (cups), and the amount of peanuts, p (cups), in this recipe.

The ratio of raisins and peanuts = 4:6  or 2:3

It would be same for every mixture.

If r cups of raisins and p cups of peanuts then their mixture ratio is r:p

Step-by-step explanation:

pls heart and give brainliest

The equation where the constant of proportionality is greater than 1 is [tex]\mathbf{p = 1.5r}[/tex], and the equation where the constant of proportionality is less than 1 is [tex]\mathbf{r = 0.67p}[/tex]

(a) Constant of proportionality greater than 1

Represent peanuts with p, and raisins with r.

So, the ratio is given as:

[tex]\mathbf{p : r = 6 : 4}[/tex]

Express as fraction

[tex]\mathbf{\frac pr = \frac 64}[/tex]

Multiply both sides by r

[tex]\mathbf{p = \frac 64r}[/tex]

[tex]\mathbf{p = 1.5r}[/tex]

(b) Constant of proportionality less than 1

In (a), we have:

[tex]\mathbf{p = 1.5r}[/tex]

Divide both sides by 1.5

[tex]\mathbf{r = \frac{1}{1.5}p}[/tex]

[tex]\mathbf{r = 0.67p}[/tex]

The graphs of [tex]\mathbf{p = 1.5r}[/tex] and [tex]\mathbf{r = 0.67p}[/tex] are the same.

See attachment for the required graph

Read more about proportionality constants at:

https://brainly.com/question/18707816

Answer:

Three consecutive means 3 numbers right next to each other.

So how we’re gonna do that.
Multiple ways.

Way #1, guess and check method

So the final result has to be -6.

Using common knowledge we know if we add a negative with a negative you’d get a smaller negative.

And also if you add negative that in which the number is greater then the positive number, then it’ll also be negative.

Positive + positive is impossible here so that already crossed out a ton of options.
Let’s explore the negative view perspectives.
Since -6 is a pretty easy integer, you can easily guess with small numbers.

First attempt: -1 + -2 + -3 = -6
There -1, -2, and -3.

Way #2, algebraically

So what is a consecutive integer.
It’s a number that comes after another so for example.

1, 2, 3

The pattern is + 1.
There has to be a base so we can do for example “x”.
x, x+1, x+2

There’s 3 consecutive integers.

If you replace x with any number, the numbers given should be consecutive.

So using that knowledge youc an solve for the interger needed here which is -6.
x + x+1 + x+2 = -6
Simplify and solve.

3x+3= -6
3x= -9

x= -3

So using that -3, we can subside into the expressions from before.
x, x+1, x+2

-3, -3 + 1, -3 +2
-3, -2, -1

They are consecutive.

Answer:

-6, -5, -4

Step-by-step explanation:

Answer:

[tex]Bag \: A, \: 6 \: kg \: for \: \$4.14 \: : is \: the \: better - value.[/tex]

Step-by-step explanation:

[tex]at \: the \: rate \: of \: 6 kg \: for \: \$4.14 \\ 2.5kg \: will \: cost \to \\ \frac{2.5 \times 4.14}{6} = 1.725 \\ hence \: \$1.725 \: is \: less \: than \: \$1.80 \\ therefore \: the \: first \: bag \: has \: \\ the \: better \: value.[/tex]

♨Rage♨

Answer:

7

Step-by-step explanation:

Find (h°g)(0) can also be expressed as h(g(0)).  Begin by calculating g(0).  To evaluate the function g at 0, replace each x with 0.  g(0) = (0)²-7(0).  (0)²-7(0) is equal to 0 so now 0 becomes the input for h.  Evaluate h(0) by replacing each x with 0 in the h function.  h(0) = 7 - 4 (0)² = 7 - 0 = 7.