A punter kicks a football upward with an initial velocity of 48 feet per second. After how many seconds does the ball hit the ground? Use the formula h=rt−16t2, where h represents height in feet and r represents the initial velocity (rate) in feet per second.

A. 3
B. 6
C. 8
D. 12

a. x ∈ {-1.2, 0.2}

b. x ∈ {-4 2/3, -1 2/3}

c. x ∈ {2 2/3, 4}

For this sort of exercise, I find a graphing calculator to be very handy. While the one shown in the attachment (Desmos) can solve the equation as written, I find it convenient to recast the equation to the form f(x) = 0. The calculator finds the values of zero crossings very nicely. Some, like my TI-84, will show the value to 8 or 10 significant digits. Here, 4 digits is sufficient to determine the exact solution.

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If you want to work these by hand, you rewrite them to standard form, then use factoring, completing the square, or the quadratic formula to solve them.

a. 25x² +30x +9 -5x -15 = 0 . . . . subtract the right side

... 25x² +25x -6 = 0 . . . . . . . . . . . collect terms

... (5x+6)(5x-1) = 0 . . . . . . . . . . . . . factor (the graphing calc helps here)

... x = -6/5, 1/5

b. 9x² +60x +100 -3x -30 = 0 . . . . subtract the right side

... 9x² +57x +70 = 0 . . . . . . . . . . . . collect terms

... (3x +14)(3x +5) = 0 . . . . . . . . . . . factor

... x = -14/3, -5/3

c. 9x² -48x +64 -3x² +8x = 0 . . . . . subtract the right side

... 6x² -40x +64 = 0 . . . . . . . . . . . . collect terms

... 3x² -20x +32 = 0 . . . . . . . . . . . . factor out 2

... (3x -8)(x -4) = 0 . . . . . . . . . . . . . . factor

... x = 8/3, 4

DAY 15: The measures of the angles in a certain triangle are in the ratio 1: 5: 6. Find the measure of the smallest angle.  

x +5x +6x=180  

12x =180  

x=15º  

DAY 16: In triangle ABC, the measure of angle A = 7x - 32, the measure of angle B = 3x + 4, and the exterior angle at C has measure 12 (x - 5). Find the value of x.  

exterior angle = sum of two remote (other) interiors  

7x -32 +3x+4 =12(x-5)  

10x -28 =12x -60  

32-2x  

x=16  

DAY 17: Find the slope of the line perpendicular to the line through the points (21, 11) and (-4, -12).  

11 - -12 / 21 - -4 =23/25  

slope of perpendicular line is negative reciprocal =  

-25/23 ( no 17!)  

DAY 18: In a certain triangle, the largest angle is 6 times the smallest. The third angle is 18 less than 4 times the smallest. What is the measure of the smallest angle?  

x= smallest  

6x =largest  

third angle =4x-18  

x+6x +4x-18 =180  

11x =198  

x=18º

Answer:

y = 1 + 1/((x -1)(x -4))

Step-by-step explanation:

To get vertical asymptotes at 1 and 4, you need factors (x -1) and (x -4) in the denominator. As x approaches 1 or 4, one of these will approach zero, and the function value will approach infinity.

To get a horizontal asymptote of 1, the function must approach the value 1 when the value of x gets large (positive or negative). This can generally be accomplished by simply adding 1 to a fraction that approaches zero when x is large.

Here, we make the fraction be the one that gives the vertical asymptotes, and we simply add 1 to it.

... y = 1 + 1/((x -1)(x -4))

If you like, this can be "simplified" to ...

... y = (x² -5x +5)/(x² -5x +4)

_____

In this rational expression form, please note that the numerator and denominator have the same degree. That will be the case when there is a horizontal asymptote. (When a slant asymptote, the numerator degree is 1 higher than the denominator.) The ratio of the coefficients of the highest degree terms is the horizontal asymptote value (or the slope of a slant asymptote).

Multiply the total number of questions by the percent:

50 questions x 90% =

50 x 0.90 = 45

She answered 45 questions correctly.

Answer:

Step-by-step explanation:

1. First differences in the y-values are ...

... -5-0 = -5; -8-(-5) = -3; -9-(-8) = -1; -8-(-9) = 1; -5-(-8) = 3; 0-(-5) = 5

Second differences are ...

... -3-(-5) = 2; -1-(-3) = 2; 1-(-1) = 2; 3-1 = 2; 5-3 = 2

These 2nd differences are constant, so the points can be described by a 2nd-degree polynomial.

2. Values on the graph range from 0 to a low of -9 and back up to 0. There is a minimum at (1, -9).

3. The value at x=-1 is -5; at x=1, it is -9, which is less than -5. The function is decreasing on the interval -1 to 1.

Answer:

B. 5/12 feet

Step-by-step explanation:

We know that Eric is [tex]6\frac{1}{6}[/tex] feet tall while his brother is [tex]5\frac{3}{4}[/tex] feet tall. We are supposed to find out how many feet is Eric taller than his brother.

So basically we have to find the difference between the height of the two brothers.

First, let's just change the mixed numbers to improper fractions:

[tex]6\frac{1}{6}[/tex] = [tex]\frac{37}{6}[/tex]

[tex]5\frac{3}{4}[/tex]=  [tex]\frac{23}{4}[/tex]

Now taking their difference:

[tex]=\frac{37}{6} -\frac{23}{4}\\\\=\frac{148-138}{24}\\\\=\frac{10}{24}\\\\=\frac{5}{12}[/tex]

Therefore, Eric is 5/12 feet taller than his brother.

5.51 seconds

y = 0 when the stone hits the ground. At that point, t can be found from ...

... 0 = -16t^2 +486

... 0 = t^2 -30.375 . . . . divide by -16

... 30.375 = t^2 . . . . . . add the opposite of the constant

Take the square root to get ...

... √30.375 = t ≈ 5.51 . . . . seconds

Answer:

6 2/3 hours

Step-by-step explanation:

We assume the time of interest is the total time spent on the main road and side road.

In each case, ...

... time = distance/speed

On the main road, ...

... tmain = s/v

On the side road, ...

... tside = (2s)/(v -2)

Then the total time spent is ...

... ttotal = tmain + tside

... = s/v + (2s)/(v -2)

For s=10 and v=6, this is ...

... ttotal = 10/6 + 2·10/(6 -2) = 5/3 + 20/4 = 5/3 + 5 . . . . hours

... ttotal = 6 2/3 hours

Answer:

6 hr 40 min

Step-by-step explanation:

Answer:

See picture

Step-by-step explanation:

The rule is ...

[tex]x^{m/n}=\sqrt[n]{x^m}[/tex]

The index of the surd becomes the denominator of the exponents inside.

Answer:

x^(5/3)*y^(1/3)

Step-by-step explanation:

note (a*b)^c = a^c*b^c

the given expression can be rewritten as (x^5*y)^1/3

=x^(5/3)*y^(1/3)

ans is the 2nd choice

Answer:

Second Option is the correct answer 3/2

Step-by-step explanation:

Tangent of an angle in a triangle is given by Perpendicular of that triangle / Base of that triangle , with resoect to angle in consideration.

Tangent Ratio for angle B = Perpendicular / Base

Tangent Ratio for angle B = AC / BC

Tangent Ratio for angle B = 3/2

Hope it helps.

Thank you.

Answer:

I do believe the answer is C

Step-by-step explanation:

.004 / .0004 =

Answer:

c 10

Step-by-step explanation:

If we want to know how much bigger object A is than object B is we take object A and divide it by object B

object A        4 * 10^-3

-----------   = -------------

Object B        4 * 10 ^-4

When dividing exponents with the same base

We can subtract them.  The numbers out front get divided

4/4 * 10 ^ (-3- -4)

1 * 10 ^(-3+4)

1 * 10 ^1

10

The correct classification for each function is as follows:

1. [tex]\( y = 5x + 1 \)[/tex] - Linear

2. [tex]\( y = 23 \)[/tex] - Linear

3. [tex]\( y = 1 - 2x^2 \)[/tex]- Nonlinear

A linear function is one that can be written in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] and [tex]\( b \)[/tex] are constants, and [tex]\( x \)[/tex] is the independent variable. The graph of a linear function is a straight line.

1. For the function [tex]\( y = 5x + 1 \)[/tex], we can see that it is already in the form of a linear equation with [tex]\( m = 5 \)[/tex] and [tex]\( b = 1 \)[/tex]. Therefore, this function is linear.

2. The function [tex]\( y = 23 \)[/tex] is a constant function. Although it does not have an [tex]\( x \)[/tex] term, it can still be considered linear because it can be written as [tex]\( y = 0x + 23 \)[/tex], where the slope [tex]\( m = 0 \)[/tex] and the y-intercept [tex]\( b = 23 \)[/tex]. The graph of this function is a horizontal line, which is a special case of a linear function.

3. The function [tex]\( y = 1 - 2x^2 \)[/tex] contains an [tex]\( x^2 \)[/tex] term, which makes it a quadratic function. Quadratic functions are nonlinear because their graphs are parabolas, not straight lines. The presence of the [tex]\( x^2 \)[/tex] term means that the rate of change of [tex]\( y \)[/tex] with respect to [tex]\( x \)[/tex] is not constant, which is a key characteristic of nonlinear functions. Therefore, this function is nonlinear.

The given formula is f(x) = 20(1.2)^x

The formula is the starting amount multiplied by 1 + the percentage raised to the number of weeks.

A) the percent increase is 20% ( 1.2 in the formula is 1 +20% as a decimal)

B) the original amount is $20

C) for 2 weeks, replace x with 2 and solve:

20(1.2)^2

20(1.44) = $28.80

After 2 weeks the coupon is $28.80

D)  To solve for the number of weeks (x) set the equation equal to $100:

100 = 20(1.2)^x

Divide both sides by 20:

5 = 1.2^x

Take the natural logarithm of both sides:

ln(5) = ln(1.2^x)

Use the logarithm rule to remove the exponent:

ln(5) = x ln(1.2)

Divide both sides by ln(1.2)

x = ln(5) / ln(1.2)

Divide:

X = 8.83

At 8.83 weeks the coupon would be $100, so after 9 weeks the coupon would be greater than $100

The answer is 9 weeks.

Numerical Reasoning

Consider a set of prints that consists of 2 small prints and one large print (that is, twice as many small prints as large). The value of that set will be ...

... 2×$20 +45 = $85

To have revenue of at least $510, the studio must sell ...

... $510/$85 = 6

sets of prints. That is, the studio needs to sell at least 6 large prints and 12 small ones.

_____

With an equation

Let x represent the number of large prints the studio needs to sell. Then 2x will represent the number of small prints. Total sales will be ...

... 20·2x +45·x ≥ 510

... 85x ≥ 510

... x ≥ 510/85

... x ≥ 6

The studio needs to sell at least 6 large prints and 12 small prints.

Another equation that shares the same solutions as x²-16x+12=0 is 2x² - 32x + 24 = 0. This equation is the initial equation multiplied by 2 and thus would produce the same solutions when the quadratic formula is applied.

The equation given is a quadratic equation, which is in the form ax²+bx+c = 0. The solutions of a quadratic equation are given by the formula: -b ± √b² - 4ac / 2a. This formula can be used to find the solutions of any other quadratic equation. For the given equation, x²-16x+12=0, the values of a, b, and c are 1, -16, and 12 respectively. So, another equation with the same solutions could be 2x² - 32x + 24 = 0. This equation has the same solutions because it's simply the initial equation multiplied by 2, so this doesn't change the results of the quadratic formula.

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Answer:

2968.30 cm cube.

Step-by-step explanation:

Given is a cone and top of it is a hemisphere of radius 9 cm.

Cone has height as 17 and radius same 9 cm.

We have to find the volume of the compound shape

We find that the volume would be the sum of that of hemisphere of radius 9 cm and cone of height 17, and radius 9 cm.

Volume of compound shape = volume of cone+Volume of hemisphere

= [tex]\frac{1}{3} \pi r^{2} h+\frac{2}{3} \pi r^{3}[/tex]

substitute for h and r in the equation

Required volume =

[tex][tex]\frac{1}{3}\pi  r^{2} (h+2r) = \frac{1}{3}\pi  9^{2} (17+2(9))\\= 1441.99+1526.31\\=2968.30[/tex][/tex]

So answer is 2968.30 cm cube.

=

The solution of the expression 3a+2b/2 is -13 when a = -3 and b = -4

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

Operators which let do a basic mathematical calculation

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

Given the expression as :

⇒ 3a + 2b/2

when a = -3 and b = -4

Substitute the values of a and b

⇒ 3 × (-3) + 2 × (-4/2)

⇒ -9 - 4

⇒ -13

Hence, the solution of the expression 3a+2b/2 is -13 when a = -3 and b = -4

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Answer:

8 gallons have to be evaporated to have a 20% salt solution.

hope this helped :)

Step-by-step explanation:

.10*20=2 gallons of salt.

That leaves 18 gallons of water.

.2x=2

x=2/.2

x=10 gallons after evaporation.

18-10=8

To obtain a 20% salt solution from a 10% salt solution, 20 gallons of water must be evaporated.

To obtain a 20% salt solution from a 10% salt solution, the amount of water that needs to be evaporated can be calculated using a proportion. First, convert the percentages to decimals by dividing them by 100. Let x be the amount of water to be evaporated. The amount of salt in the initial solution is 10% of 20 gallons, or 0.10 * 20 = 2 gallons. The resulting solution will have 20% salt in a total volume of 20 - x gallons. Set up a proportion:

(2 gallons)/(20 gallons) = (0.20 * (20 - x) gallons)/(20 - x gallons)

Cross multiply and solve for x:

2(20 - x) = 0.20(20 - x)

Now solve the equation:

40 - 2x = 4 - 0.20x

2x - 0.20x = 40 - 4

1.8x = 36

x = 36/1.8

x = 20

Therefore, 20 gallons of water must be evaporated from the initial 20-gallon solution to obtain a 20% salt solution.

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The mean age decreased.

I find it convenient to look at the additions with respect to the current mean age.

The current total age is 14×34. We have added members with ages (34 -10) and (34 +2), so the new total age is ...

... (34×14) + (34 -10) + (34 +2) = (16×34) - 8

Dividing this total by 16 will give the new mean age. (We already know it is less than 34.)

... ((16×34) -8)/16 = 34 - 1/2 = 33 1/2 . . . new mean age; a decrease

Answer:

1.4 × 10^-8

Step-by-step explanation:

The chip is 14  nanometers

14 * .000000001

.000000014

Move the decimal 8 places to the right, because we need 1 number in front of the decimal for scientific notation.  The exponent will be -8 because  we moved it 8 places to the right

1.4 × 10^-8

The thickness of the silicon chip in scientific notation is 1.4 x 10^-8 m.

To express the thickness of the silicon chip in scientific notation, we need to convert the given thickness of 14 nanometers to meters.

Since 1 nanometer (nm) is equal to 0.000000001 meters, we can convert 14 nanometers to meters by multiplying it by the conversion factor:

14 nm x 0.000000001 m/nm = 0.000000014 m

Now, we can express the thickness of the chip in scientific notation:

0.000000014 m = 1.4 x 10-8 m

[tex]2a+b=\dfrac{2ab}{b}+\dfrac{bb}{b}=\dfrac{2ab}{b}+\dfrac{b^2}{b}=\boxed{\dfrac{2ab+b^2}{b}}[/tex]

half-turn

There is a point of rotational symmetry at the center of the pattern. Thus, turning it 180° (a half-turn) will map it to itself.

_____

Comment on other choices

Any sort of reflection will change it to bqbqbqbqbq. Translation puts its somewhere else, not on top of itself.

Answer:

A half turn reversal of direction (as in a staircase) either by one 180-degree turn or two right-angle turns

Step-by-step explanation:

Hope this helps :) -Mark Brainiest Please :)

A. {(5,  5), (6,  −6), (8,  7), (−9,  9)}

Compare the table contents to the ordered pairs in each relation. The first pair of table values, (5, 5) matches relations A and B, but not C or D.

The second pair of table values (8, 7), matches relation A, but not B. Since all pairs of table values show up in relation A, and we have rejected relations B, C, and D as inappropriate choices, the answer is A.

For this case, we have that by definition:

Let "x" be an angle of any vertex of a right triangle.

[tex]tangent (x) = \frac {Cathet \ opposite} {Cathet \ adjacent}[/tex]

So, if we want to find the tangent of angle A:

[tex]tangent (A) = \frac {6} {8}[/tex]

Thus, the tangent of angle "A" is [tex]\frac {6} {8}[/tex]

Answer:

[tex]\frac {6} {8}[/tex]

Option b

Answer:

4 years

Step-by-step explanation:

The exponent of 0.5 is 1 when t=4. So, half the original amount will be remaining when t=4.

Answer:

Parker is 6 years old

Step-by-step explanation:

Parker is 6 years old

Let q, p, k represent the ages of Quinn, Parker, and Karl, respectively.

... q = 2k . . . . . . Quinn is twice as old as Karl

... q = p+4 . . . . . Quinn is 4 years older than parker

... q + p + k = 21 . . . . the sum of their ages is 21

_____

We can use the first two equations to find Karl's age in terms of Parker's.

... p+4 = q = 2k

... (p+4)/2 = k

Now, we can substitute for q and k in the last equation.

... (p+4) +p +(p+4)/2 = 21

... 5/2p +6 = 21 . . . . . . collect terms

... p = (2/5)(21 -6) . . . . subtract 6, multiply by 2/5

... p = 6 . . . . . . Parker is 6 years old

Answer:

B. side-angle-side

Step-by-step explanation:

You are given that side SR matches its counterpart; angle SRT matches its counterpart; and you know side ST matches its counterpart, because they are the same segment.

Hence, you have two matching sides and the angle between them. This set of side-angle-side lets you invoke the theorem that matches that name.