solve the following equation algebraically please

Answer:

f(t) = -16t² + 36

Step-by-step explanation:

f(t) = a(t - h)² + k

This is vertex form where (h, k) is the (x, y) coordinate of the vertex

The vertex is give as (0, 36)

f(t) = a(t - 0)^2 + 36

f(t) =at² + 36

use point (1, 20) to find "a"

20 = a(1²) + 36

20 = a + 36

-16 = a

f(t) = -16t² + 36

9514 1404 393

Answer:

  x -10y = 5 . . . . . infinite number of solutions

Step-by-step explanation:

We can put each equation into standard form by dividing it by its x-coefficient.

  x -10y = 5 . . . . first equation

  x -10y = 5 . . . . second equation

Subtracting the second equation from the first eliminates the x-variable to give ...

  (x -10y) -(x -10y) = (5) -(5)

  0 = 0 . . . . . . . true for all values of x or y

The system has an infinite number of solutions. Each is a solution to ...

  x -10y = 5.

Answer:

145 cups of lemonade; 2x+1.50y=425, where y=90

Step-by-step explanation:

Let us first set up an equation, where x represents number of cups of lemonande, and y represents number of candy bars. We know that every cup of lemonade costs $2, every candy bar sold costs $1.50, and that Marcia sold a total of $425. We now have equation:

[tex]2x+1.50y=425[/tex]

However, we actually know how many candy bars Marcia sold. Therefore, our y value is 90. Let's rewrite the equation:

[tex]2x+1.50*90=425\\2x+135=425\\2x=290\\x=145[/tex]

Therefore, Marcia sold 145 cups of lemonade.

I hope this helps! Let me know if you have any questions :)

Answer:

x² -1x + 3x -3

= x² +2x -3

hope it helps

Answer:

0

Step-by-step explanation:

(5.4)^2 - 5.4^2

= 5.4^2 - 5.4^2

= 5,4^2(1 - 1)

= 5.4^2(0)

= 0

Answer:

Time taken for pump B to empty pool = 1 hour.

Step-by-step explanation:

Given:

Time taken for pump A to empty pool = 4 hour

Time taken together = 48 minutes = 48 / 60 = 4/5 hour

Find:

Time taken for pump B to empty pool

Computation:

Assume;

Time taken for pump B to empty pool = a

1/4 + 1/a = 1 / (4/5)

1/4 + 1/a = 5/4

1/a = 5/4 - 1/4

1/a = (5 - 1) / 4

1/a = 1

a = 1

Time taken for pump B to empty pool = 1 hour.

Question 1

Question 2

Question 3

Answer:

f(x) = (x+5)^2 +12

The minimum value is 12

Step-by-step explanation:

f(x)=x^2+10x+37

The vertex will be the minimum value since this is an upwards opening parabola

Completing the square by taking the coefficient of x and squaring it adding it and subtracting it

f(x) = x^2+10x  + (10/2) ^2 - (10/2) ^2+37

f(x) = ( x^2 +10x +25) -25+37

    = ( x+5) ^2+12

Th is in vertex form y = ( x-h)^2 +k  where (h,k) is the vertex

The vertex is (-5,12)

The minimum is the y value or 12

Answer:

A: -21

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, y_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

[tex]y_{v} = -\frac{\Delta}{4a}[/tex]

Where

[tex]\Delta = b^2-4ac[/tex]

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].

In this question:

Quadratic function:

[tex]g(x) = x^2 - 6x - 12[/tex]

So [tex]a = 1, b = -6, c = -12[/tex].

Minimum value:

This is the y-value of the vertex. So

[tex]\Delta = b^2-4ac = (-6)^2 - 4(1)(-12) = 36+48 = 84[/tex]

[tex]y_{v} = -\frac{\Delta}{4a} = -\frac{84}{4} = -21[/tex]

The minimum value is -21, and the correct answer is given by option A.

Answer:

Step-by-step explanation:

From the given information:

a)

Assuming the shape of the base is square,

suppose the base of each side = x

Then the perimeter of the base of the square = 4x

Suppose the length of the package from the base = y; &

the height is also = x

Now, the restriction formula can be computed as:

y + 4x ≤ 99

The objective function:

i.e maximize volume V = l × b × h

V = (y)*(x)*(x)

V = x²y

b) To write the volume as a function of x, V(x) by equating the derived formulas in (a):

y + 4x ≤ 99   --- (1)

V = x²y          --- (2)

From equation (1),

y ≤ 99 - 4x

replace the value of y into (2)

V ≤ x² (99-4x)

V ≤ 99x² - 4x³

Maximum value V = 99x² - 4x³

At maxima or minima, the differential of [tex]\dfrac{d }{dx}(V)=0[/tex]

[tex]\dfrac{d}{dx}(99x^2-4x^3) =0[/tex]

⇒ 198x - 12x² = 0

[tex]12x \Big({\dfrac{33}{2}-x}}\Big)=0[/tex]

By solving for x:

x = 0 or x = [tex]\dfrac{33}{2}[/tex]

Again:

V = 99x² - 4x³

[tex]\dfrac{dV}{dx}= 198x -12x^2 \\ \\ \dfrac{d^2V}{dx^2}=198 -24x[/tex]

At x = [tex]\dfrac{33}{2}[/tex]

[tex]\dfrac{d^2V}{dx^2}\Big|_{x= \frac{33}{2}}=198 -24(\dfrac{33}{2})[/tex]

[tex]\implies 198 - 12 \times 33[/tex]

= -198

Thus, at maximum value;

[tex]\dfrac{d^2V}{dx^2}\le 0[/tex]

Recall y = 99 - 4x

when at maximum x = [tex]\dfrac{33}{2}[/tex]

[tex]y = 99 - 4(\dfrac{33}{2})[/tex]

y = 33

Finally; the volume V = x² y is;

[tex]V = (\dfrac{33}{2})^2 \times 33[/tex]

[tex]V =272.25 \times 33[/tex]

V = 8984.25 inches³

Answer:

Yes, they do

Step-by-step explanation:

Because

6+8=14>9

6+9=15>8

8+9=17>6

Answer(s):

[tex]\displaystyle y = 3sin\: (1\frac{1}{2}x + \frac{\pi}{2}) - 2 \\ y = 3cos\: 1\frac{1}{2}x - 2[/tex]

Explanation:

[tex]\displaystyle 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 -2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{3}} \hookrightarrow \frac{-\frac{\pi}{2}}{1\frac{1}{2}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1\frac{1}{3}\pi} \hookrightarrow \frac{2}{1\frac{1}{2}}\pi \\ Amplitude \hookrightarrow 3[/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 -2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1\frac{1}{3}\pi} \hookrightarrow \frac{2}{1\frac{1}{2}}\pi \\ Amplitude \hookrightarrow 3[/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 = 3sin\: 1\frac{1}{2}x - 2,[/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}{3}\: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 BACK [tex]\displaystyle \frac{\pi}{3}\:unit,[/tex] which means the C-term will be negative, and perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{3}} = \frac{-\frac{\pi}{2}}{1\frac{1}{2}}.[/tex] So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 3sin\: (1\frac{1}{2}x + \frac{\pi}{2}) - 2.[/tex] Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [0, 1],[/tex] from there to [tex]\displaystyle [1\frac{1}{3}\pi, 1],[/tex] they are obviously [tex]\displaystyle 1\frac{1}{3}\pi\:unit[/tex] apart, telling you that the period of the graph is [tex]\displaystyle 1\frac{1}{3}\pi.[/tex] 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 = -2,[/tex] in which each crest is extended three units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts horisontally, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

The value of x in the triangle is 17.51

Option C is the correct answer.

We have,

From the figure,

We can use the tangent function.

This means,

Tan = perpendicular / Base

i.e

tan 35 = x / 25

0.700 = x / 25

x = 0.700 x 25

x = 17.5

Thus,

The value of x in the triangle is 17.51.

Learn more about trigonometric identities here:

https://brainly.com/question/14746686

#SPJ6

Answer:

Correct.

Step-by-step explanation:

It looks good to me.

Good job!

[tex] \frac{35e {}^{9} }{5 {e}^{8} } \ \\ \\ \frac{7e {}^{9} }{e {}^{8} } \\ \\ \\ = 7e[/tex]

Step By Step Explanation:

Alternate Forms:

9514 1404 393

Answer:

  180 in³

Step-by-step explanation:

  V = Bh

  V = (6 in × 3 in)(10 in) = 180 in³

The volume is the product of the cross section area (6 in × 3 in) = 18 in² and the height perpendicular to that cross section, 10 in.

Answer:

Step-by-step explanation: It could be 8,7, or 2. Because these are all positive

:)

Answer:

Given the following algebraic expression 5x² + 10 Which statement is true?

a. The coefficient is 5. ( true)

b. The constant is 2

C. The power is 10

d. The constant is 5

Answer:

Length = 12 m, Width = 8 m

Step-by-step explanation:

Let the width of the rectangle is b.

Length, l = 4+b

The perimeter of the rectangle = 40 m

We know that,

Perimeter of rectangle = 2(l+b)

2(4+b+b) = 40

4+2b = 20

Subtract 2 from boths sides,

2b = 16

b = 8

Width = 8 m

Length = 4+8 = 12 m

Hence, the length and the width of the rectangle is 12 m and 8 m respectively.

Answer:

The value of f(30) is equal to 2.

Step-by-step explanation:

The given expression is :

[tex]f(x)= 10 \sin(x) - 3[/tex]

We need to find the value of f(30)

Put x = 30 in above expression.

So,

[tex]f(x)= 10 \sin(30) - 3\\\\=10\times \dfrac{1}{2}-3\\\\=5-3\\\\=2[/tex]

Hence, the value of f(30) is equal to 2.

Answer:

The best conclusion is that we are 90% that the true population proportion of Republicans that voted for Mitt Romney is between 0.7273 and 0.8106.

Step-by-step explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

In this question:

The 90% confidence interval for the proportion of Republican voters that had voted for Mitt Romney is (0.7273, 0.8106). The best conclusion is that we are 90% that the true population proportion of Republicans that voted for Mitt Romney is between 0.7273 and 0.8106.

Answer:

260

Step-by-step explanation:

145-15=130

130 x 2 = 260

Answer:

254.47 mm

Step-by-step explanation:

Answer:

Step-by-step explanation:

7

Answer:

[tex]3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }[/tex]

Step-by-step explanation:

Just to make it easier to see, [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex] and [tex]\sqrt[5]{x} = x^{\frac{1}{5} }[/tex]  This way we could more easily use the power rule of derivatives.

So if f(x) = [tex]x^{2} +x^{\frac{1}{2} } +x^{\frac{1}{5} }[/tex] then f'(x) will be as follows.

f'(x) = [tex]x^{1} +\frac{1}{2} x^{-\frac{1}{2} } +\frac{1}{5} x^{-\frac{4}{5} } = x +\frac{1}{2x^{\frac{1}{2} }} +\frac{1}{ 5x^{\frac{4}{5} }} = x +\frac{1}{2\sqrt{x}} +\frac{1}{ 5\sqrt[5]{x^4} }[/tex]

to find f'(3) just plug 3 into f'(x) so [tex]3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }[/tex]

9514 1404 393

Answer:

  B, C, A, D

Step-by-step explanation:

The depths are easier to compare if they are all in the same form. Here, it is convenient to use decimal numbers rounded to hundredths. Your calculator can help with the fractions if you are not familiar with decimal equivalents.

  A: -1.6 m = -1.60 m

  B: -4/3 m ≈ -1.33 m

  C: -1.36m = -1.36 m

  D: -17/9 m ≈ -1.89 m

Then the least deep site is the one with the depth number closest to 0.

In order from least to greatest depth, the sites are ...

  B (-1.33) > C (-1.36) > A (-1.60) > D (-1.89)

Answer:

yeah

Step-by-step explanation:

Answer:

slope of the line is 0

Step-by-step explanation:

given points are:

(-3 , 2)=(x1 , y1)

(4 , 2)=(x2 , y2)

slope =y2 - y1/x2 - x1

=2-2/4-(-3)

=0/4+3

=0/7

=0

Answer:

Answer:Uh oh! It looks like your question is missing some crucial information.

Step-by-step explanation:

You didn't include the"given line"