Solve for 'a' in f(x) = ax² + 7x + 2 when ∆ = 33​

To find out how long it will take for the arrow to hit the enemy on the bridge, we need to find the time when the height of the arrow is 45 feet (the height of the enemy's head above the ground).

So, we can set h(t) equal to 45 and solve for t:

h(t) = − 16t²+60t + 9.5

45 = −16t² + 60t + 9.5

Rearranging the equation, we get:

16t² - 60t - 35.5 = 0

To solve for t, we can use the quadratic formula:

t = (-b ± sqrt(b² - 4ac)) / 2a

where a = 16, b = -60, and c = -35.5

Plugging in the values, we get:

t = (-(-60) ± sqrt((-60)² - 4(16)(-35.5))) / 2(16)

Simplifying the expression inside the square root, we get:

t = (60 ± sqrt(3600 + 2272)) / 32

t = (60 ± sqrt(5872)) / 32

t ≈ 0.81 or t ≈ 3.69

Since we're looking for the time when the arrow hits the enemy, we need to choose the positive solution: t ≈ 3.69 seconds.

Therefore, it will take approximately 3.69 seconds for the arrow to hit the enemy on the bridge with a perfect headshot.

Answer:

[tex]\frac{1}{-125}[/tex]

x = -125

Step-by-step explanation:

It shows the steps in the pic you attached so I didn't add those steps.

(-5)(-5)(-5) = -125

The equation for solving the side length of a cube is s = ∛V, where s is the side length of the cube, and V is the volume.

The equation for solving the side length of a cube can be expressed as s = ∛V, where s is the side length of the cube, and V is the volume. This equation can be used to calculate the side length of a cube when the volume is known. For example, if the volume of a cube is 125 cubic units, the side length can be calculated by substituting 125 for V and solving the equation: s = ∛125 = 5. This means that the side length of the cube is 5 units.

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The possible values of ∠L are 118.9 degrees (rounded to 10th of a degree).

A polygon with three sides and three angles is a triangle. It is one of the simplest geometric shapes.

To find the measure of angle L in ΔLMN, we can use the fact that the sum of the angles in a triangle is 180 degrees:

∠L + ∠M + ∠N = 180

We know that ∠N = 61 degrees, so we can substitute that value in and simplify:

∠L + ∠M + 61 = 180

∠L + ∠M = 119

We also know that the length of LM is 150 inches and the length of LN is 890 inches. We can use the Law of Cosines to find the measure of angle M:

cos M = (150² + 890² - LM²) / (2 × 150 × 890)

cos M = 0.999989 (rounded to 6 decimal places)

M = cos⁻¹(0.999989)

M ≈ 0.00114 radians

M ≈ 0.0655 degrees (rounded to 10th of a degree)

Now we can substitute the value of M into the equation we derived earlier and solve for angle L:

∠L + 0.0655 + 61 = 180

∠L = 118.9345

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Answer:

143 degrees

Step-by-step explanation:

angles on a straight line add up to 180 degrees

[tex]x + y = 180 \\ 37 + y = 180 \\ y = 180 - 37 \\ y = 143 \: degrees[/tex]

The equation of the line in slope-intercept form is: y = -25x + 100. A negative slope indicates that the battery percentage is decreasing over time.

Part A:

To write the equation of a line in slope-intercept form, we need to know the slope (m) and y-intercept (b) of the line.

From the given information, we know that the y-intercept is 100 and the x-intercept is 4. This means that after 4 hours, the battery percentage is 0%.

To find the slope, we can use the slope formula:

m = (y2 - y1)/(x2 - x1)

Choosing two points on the line, one being the y-intercept (0,100) and the other being the x-intercept (4,0), we can plug in the values:

m = (0 - 100)/(4 - 0) = -25

Therefore, the equation of the line in slope-intercept form is:

y = mx + b

y = -25x + 100

Part B:

To determine the equation, we used the fact that the y-intercept was 100 and the x-intercept was 4. We then found the slope of the line using the slope formula with two points on the line. Plugging the slope and y-intercept into the slope-intercept form equation y = mx + b gives us the final equation.

Part C:

The slope of the line is -25, which means that for every hour that passes, the battery percentage decreases by 25%. Therefore, the slope represents the rate of change of the battery percentage with respect to time. A negative slope indicates that the battery percentage is decreasing over time.

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0.24 gallons of oil should be mixed with 12 gallons of gasoline.

Therefore, 30.72 fluid ounces of oil should be mixed with 12 gallons of gasoline.

Step-by-step explanation:

a. To calculate the amount of oil needed, we need to know the ratio of gas to oil in terms of units. Since 50 parts of gas are mixed with 1 part of oil, we have:

1 gallon of gas / 50 = x gallons of oil

To find x, we substitute the given value of gas (12 gallons) and solve for x:

1 gallon of gas / 50 = x gallons of oil

12 gallons of gas / 50 = x

0.24 gallons of oil = x

Therefore, 0.24 gallons of oil should be mixed with 12 gallons of gasoline.

b. To convert gallons to fluid ounces, we multiply by 128:

0.24 gallons of oil * 128 fluid ounces/gallon = 30.72 fluid ounces of oil

Therefore, 30.72 fluid ounces of oil should be mixed with 12 gallons of gasoline.

Answer:

x = 432.

Step-by-step explanation:

We know that 24 x 18 and x x 1 are in proportion, which can be written as:

(24 x 18) / (x x 1) = k, where k is a constant of proportionality.

Simplifying the left-hand side, we get:

24 x 18 = 432

x x 1 = x

Substituting these values, we get:

432 / x = k

To solve for x, we need to find the value of k. We can do this by using the fact that the two ratios are in proportion. That is:

24 x 18 : x x 1 = 432 : k

Simplifying the left-hand side, we get:

(24 x 18) / x = 432 / k

Multiplying both sides by x and k, we get:

24 x 18 k = 432 x

Dividing both sides by 24 x, we get:

18 k / 1 = 18

Solving for k, we get:

k = 1

Substituting k = 1 into the equation 432 / x = k, we get:

432 / x = 1

Multiplying both sides by x, we get:

432 = x

Therefore, x = 432.

The linear equation that passes through (-9, -9) and has the slope m = 0 is:

y = -9

A general linear equation can be written in slope-intercept form as.

y = m*x + b

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

Here we want to find the equation of a line that passes through (-9, -9) and that has the slope m = 0.

Repplacing the slope we will get:

y = 0*x + b

And no we want it to pass throug (-9, -9), replacing these values we will get:

-9 = 0*-9 + b

-9 = b

Then the linear equation is:

y = -9

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The given polynomial written in standard form is: 3z⁴ + 2z³ + 5z

Degree: 4

Leading Coefficient: 3

Classification: Trinomial

Writing a polynomial in standard form simply means that we put the term with the highest exponent in it first and then the one with the second highest exponents second, and so on.

The polynomial we are given is:  5z + 2z³ + 3z4

Writing it in standard form gives us:

3z⁴ + 2z³ + 5z

The degree of the polynomial is defined as the value of the exponent in the leading term (if we are assuming a single variable). Thus, this given polynomial is of degree 4.

The leading coefficient is the number that the first term is multiplied by and in this problem that would be 3.

There are three terms in the given polynomial (the first term is 3z⁴, the second term is 2z³, and the 3rd term is 5z). Thus, it is a trinomial.

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The probability that the number of games you win is (a) exactly five, (b) more than six, and (c) less than three will be 0.196, 0.0082 and 0.056 respectively.

How are probabilities defined?

A probability is indeed a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages spanning form 0% to 100% can be used to describe probabilities.

1/3 of players will succeed in a game of rock-paper-scissors. Choose nine games of rock-paper-scissors, and let X represent the number of victories. With n=9 and p=1/3, X has a random variable.

(a) The likelihood of winning all five games in a row is:

P(X=5) = (9 choose 5)(1/3)⁵(2/3)⁴ = 0.196

Depending on the situation, this likelihood might or might not be seen as uncommon because it is neither extremely high nor extremely low.

(b) The probability of winning more than six games is:

P(X > 6) = P(X = 7) + P(X = 8) + P(X = 9)

= [(9 choose 7)(1/3)⁷(2/3)²] + [(9 choose 8)(1/3)⁸(2/3)¹] + [(9 choose 9)(1/3)⁹(2/3)⁰]

= 0.0082

The fact that this likelihood is so low suggests that winning and over six games is exceptional.

(c) The likelihood of winning two or fewer games is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

= [(9 choose 0)(1/3)⁰(2/3)⁹] + [(9 choose 1)(1/3)¹(2/3)⁸] + [(9 choose 2)(1/3)²(2/3)⁷]

= 0.056

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Answer:

The probability that exactly 20 out of 25 adult smartphone users use their smartphones in meetings or classes is approximately 0.002.

Answer:

144,000

Step-by-step explanation:

you multiply 18,000 by 8 since its after one year and you get 144,000.

Answer:2 4/9

Step-by-step explanation:

The measure of length MN is 31.

The measure of length KN is 45.

The measure of m∠K is 61⁰.

The measure of m∠L is 119⁰.

A parallelogram is a four-sided plane figure in which opposite sides are parallel and congruent (having the same length) and opposite angles are congruent (having the same measure). In other words, a parallelogram is a quadrilateral with two pairs of parallel sides.

The properties of a parallelogram include:

So the length MN = Length KL = 31

Length KN = Length LM = 45

Angle K = angle M = ( 180 - 119) = 61⁰

Angle L = angle N = 119⁰

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Answer:

Step-by-step explanation:

[tex]\tt y=x+2\\3x+3y=6[/tex]

Substitute y= y=x+2 into 3x+3y=6

Solve for x :-

Cancel 6 from both sides:-

Divide both sides by 6:-

Now, Let's solve for y:-

Substitute x = 0 into y=x+2

Therefore, x = 0 and y = 2.

_________________

Check:-

To check a system of equations by substitution, we plug the values for x and y into the equations, If both simplified are true then your answer is correct.

Equation 1 :-

y = x + 2

Equation 2 :-

3x+3y=6

__________________________

Hope this helps!

Answer:

x = 2 or x = 4

Step-by-step explanation:

The equation:

Has two solutions:

The values of x can be found by graphing the two functions ([tex]y = 2^{x}[/tex] and [tex]y = x^{2}[/tex]) and finding their points of intersection, or you can use numerical methods to solve the equation.

To check our work, we can simply insert 2 and 4 in as y.

For 2:

You can see that it is the same.

For 4:

They are also the same.

Therefore, x can equal either 2 or 4.

Answer:

B. 120o

Step-by-step explanation:

A parallelogram is a flat 2d shape which has four angles. The opposite interior angles are equal. The angles on the same side of the transversal are supplementary, that means they add up to 180 degrees. Hence, the sum of the interior angles of a parallelogram is 360 degrees.

t + 2t = 180

3t = 180

t = 180/3 = 60

m∠Z  = 2t = 2(60) = 120

Answer:

1. Draw a coordinate plane with a circle on it somewhere

2. B. and C.

Step-by-step explanation:

A function is a set of points that has a specific input (x-value) and a specific output (y-value). Let's take the example of y = 2x. Let's start by plugging in 1 for x. 1 will be our input value, and 2• 1 = 2 will be our y-value because the x-value was changed to get to our output, the y-value.

In a function, it is possible to have the same y-value for different x-values; take the example of y = x^2. X can have 2 values, but because it is squared, it will give the same y-value. However, a function that has the same x-values for one y-value is not a function. For example, take a circle, with the equation x^2 + y^2 = 0. This is not a function, because, for 2 y-values, it will equal the same x-value. For your answer, you can draw a coordinate plane with a circle on it. IMPORTANT: 2 x-values cannot equal one y-values in a function.

A linear function is a function that has an x and y-value, as well as sometimes a coefficient to either variable and a constant. For example, the equation y = 5x +4 is a linear function because there is one y and one x-value, a coefficient (even though it is not necessary), and a constant (even though it is not necessary). It doesn't matter where the coefficients are, but there has to be one y-value and one x-value. Since there can be only one x and y, equations like y = x^2 does not work, because there are 2 x's (in the x^2). Using this information, we can figure out the correct solutions:

A. doesn't work, because there are 3 y-values.

B. works because there is one x and y, and a coefficient (although it isn't necessary)

C. works because like b, it has only one x and y, a coefficient (although it isn't necessary)

D. doesn't work because there is only one y-value and no x-value.

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Answer:

Let the total number of cows in the herd be represented by "x". Then, according to the problem:

The first son received half the herd, or (1/2)x cows.

The second son received one fourth of the herd, or (1/4)x cows.

The third son received one fifth of the herd, or (1/5)x cows.

The fourth son received 48 cows.

We can write an equation to represent the total number of cows in the herd:

(1/2)x + (1/4)x + (1/5)x + 48 = x

To solve for "x", we can start by simplifying the fractions:

5/10x + 2/10x + 2/10x + 48 = x

Combining like terms, we get:

9/10x + 48 = x

Subtracting 9/10x from both sides, we get:

48 = 1/10x

Multiplying both sides by 10, we get:

x = 480

Therefore, the original herd had 480 cows.

Answer:

Step-by-step explanation:

To calculate the volume of sand needed to fill the long jump pit to a depth of 0.07 meters, we need to know the length and width of the pit.

Assuming that the long jump pit is a rectangular prism, we can use the formula:

Volume = length x width x depth

Let's say the length of the pit is 8 meters and the width is 3 meters. Then the volume of sand needed to fill the pit to a depth of 0.07 meters would be:

Volume = 8m x 3m x 0.07m

Volume = 1.68 cubic meters

Therefore, we would need 1.68 cubic meters of sand to fill the long jump pit to a depth of 0.07 meters.

Answer:

19.4

Step-by-step explanation:

cosФ=adjacent ÷hypotenuse

cos72° =6/x

0.309016994=6/x

∴x=6/0.31

   =19.35

   =19.4

The equation that is used to determine the number of cords in a pile of wood h ft tallis is the number of cords = 280×h×128.

What is an equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical declaration that illustrates the equality of two mathematical expressions.

Given that

The number of cords in a pile l ft long, w ft wide, and h ft tall can be estimated using the equation number of cords=lwh128.

The length of the wood pile is 14 ft and the wide is 20 ft.

The product of length and width is lw = 14×20 = 280 ft².

Putting lw= 280 in the equation number of cords=lwh128:

number of cords = 280×h×128

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Answer:

B. linear

Step-by-step explanation:

x     y

0     9

1      9 + 8

2      9 + 2(8)

3      9 + 3(8)

4      9 + 4(8)

=> linear function

Answer:

I hope that this answers your question!

Answer:

Step-by-step explanation:

To calculate the reorder level of component X, we need to find out the average weekly consumption of X.

Average consumption of X per unit of 'RED' = 0.4 kg

Average weekly production of 'RED' = 400 units

Average weekly consumption of X for producing 400 units of 'RED' = 0.4 kg/unit x 400 units/week = 160 kg/week

Assuming lead time of 3 weeks for delivery of X, the reorder level of X would be:

Reorder level of X = Average weekly consumption of X x Lead time for delivery of X

Reorder level of X = 160 kg/week x 3 weeks = 480 kg

To calculate the maximum level of X, we need to take into account the economic order quantity and the maximum storage capacity.

Economic order quantity of X = Square root of [(2 x Annual consumption of X x Ordering cost per order) / Cost per unit of X]

Assuming 52 weeks in a year:

Annual consumption of X = Average weekly consumption of X x 52 weeks/year = 160 kg/week x 52 weeks/year = 8,320 kg/year

Ordering cost per order of X = 600

Cost per unit of X = 1

Economic order quantity of X = Square root of [(2 x 8,320 kg x 600) / 1] = 2,771.28 kg (approx.)

Maximum storage capacity of X = Economic order quantity of X + Safety stock - Average weekly consumption x Maximum lead time

Assuming a safety stock of 20% of the economic order quantity and a maximum lead time of 3 weeks:

Maximum storage capacity of X = 2,771.28 kg + (0.2 x 2,771.28 kg) - (160 kg/week x 3 weeks) = 2,815.82 kg (approx.)

To calculate the maximum level of Y, we follow the same approach as for X:

Annual consumption of Y = Average weekly consumption of Y x 52 weeks/year

Average consumption of Y per unit of 'RED' = 0.6 kg

Average weekly consumption of Y for producing 400 units of 'RED' = 0.6 kg/unit x 400 units/week = 240 kg/week

Annual consumption of Y = 240 kg/week x 52 weeks/year = 12,480 kg/year

Economic order quantity of Y = Square root of [(2 x Annual consumption of Y x Ordering cost per order) / Cost per unit of Y]

Ordering cost per order of Y = 1,000

Cost per unit of Y = 1.5

Economic order quantity of Y = Square root of [(2 x 12,480 kg x 1,000) / 1.5] = 915.65 kg (approx.)

Maximum storage capacity of Y = Economic order quantity of Y + Safety stock - Average weekly consumption x Maximum lead time

Assuming a safety stock of 20% of the economic order quantity and a maximum lead time of 3 weeks:

Maximum storage capacity of Y = 915.65 kg + (0.2 x 915.65 kg) - (240 kg/week x 3 weeks) = 732.52 kg (approx.)

0.08 rounded for the nearest hundredth

Answer:

d1 - d2 ≈ 9917.4 feet ≈ 3021 meters

Step-by-step explanation:

tan(19°) = 7425/d1

tan(37°) = 7425/d2

Solving for d1 and d2, we get:

d1 = 7425/tan(19°) ≈ 22977.6 feet

d2 = 7425/tan(37°) ≈ 13060.2 feet

Therefore, the distance the plane traveled from point A to point B is:

d1 - d2 ≈ 9917.4 feet ≈ 3021 meters

Using the compound interest formula, it is obtained that it would take approximately 9.9 years for the account balance to reach $20,000.

What is Compound Interest?

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

We can use the formula for compound interest to solve this problem -

[tex]A = P(1 + \frac{r}{n})^{(nt)}[/tex]

where A is the account balance, P is the principal (the initial investment), r is the annual interest rate (as a decimal), n is the number of times per year the interest is compounded, and t is the time (in years).

In this case, we have P = 5000, r = 0.09 (9% annual interest), n = 4 (compounded quarterly), and A = 20000. We want to find t.

Substituting these values into the equation, we get -

[tex]20000 = 5000 \big(1 + \frac{0.09}{4} \big)^{(4t)}[/tex]

Dividing both sides by 5000, we get -

[tex]4 = \big(1 + \frac{0.09}{4} \big)^{(4t)}[/tex]

Taking the natural logarithm of both sides, we get -

ln(4) = 4t ln(1 + 0.09/4)

Solving for t, we get -

t = ln(4) / (4 ln(1 + 0.09/4))

Simplifying the equation, we get -

t ≈ 9.9

Therefore, the time value is obtained as 9.9 years.

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