What is the general form for a quadratic equation? What does the equation have to be equal to, so that it can be referred to as a Quadratic equation ?

Answer:

Answer:A

Step-by-step explanation:took it

Answer:

A

Step-by-step explanation:

whole circle pointing right

Answer:

Step-by-step explanation:

Jalen lost 12 pounds in the first 3 weeks

12/3=4 per week

than the weight loss slowed by half, meaning he lost 6 pounds in 3 weeks

6/3=2 per week

84-12=72 to loose after 3 weeks

72/2=36 weeks

to loose 84 pounds you need 3+36=39 weeks

for 100 lbs

100-12=88

88/2=44

44+12=56 weeks

Answer:

268.8

Step-by-step explanation:

Let the sides of the base triangle be:

a = 8.8 cm

b = 5.7 cm

c = 6.8 cm

Let h be the length

h = 10.8 cm

The surface area is given by:

\(SA = (a + b + c)*l + 2\sqrt{ s(s - a)(s - b)(s - c)}\)

Where

\(s = \frac{a + b + c}{2} \\\\= \frac{8.8 + 5.7 + 6.8}{2} \\\\=\frac{21.3}{2} \\\\= 10.65\)

\(SA = (a + b + c)*l + 2\sqrt{ s(s - a)(s - b)(s - c)}\\\\= (8.8 + 5.7 + 6.8)*10.8 + 2\sqrt{ 10.65(10.65 - 8.8)(10.65 - 5.7)(10.65 - 6.8)}\\\\= 21.3*10.8 +2\sqrt{ 10.65(10.65 - 8.8)(10.65 - 5.7)(10.65 - 6.8)}\\\\=230.04 + 2\sqrt{ 10.65(1.85)(4.95)(3.85)}\\\\=230.04 + 2\sqrt{ 375.48}\\\\= 230.04 + 2*19.38\\\\=230.04 +38.76\\\\=268.8\)

The exponential function can be rewritten as:

f(x) = 48*e^(0.0198*x)

Here we start with the exponential function:

f(x) = 48*(1.02)^x

And we want to write this in the general form:

f(x) =a*e^(kx)

Notice that we can write the second form as:

f(x) = a*[e^k]^x

So, comparing this with the given exponential, we will get:

a = 48

e^k = 1.02

Apply the natural logarithm in both sides:

ln(e^k) = ln(1.02)

k*ln(e) = ln(1.02)

k = ln(1.02) = 0.0198

Then the exponential function is:

f(x) = 48*e^(0.0198*x)

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Answer:

Step-by-step ef(x)=-2x+5……i

and f(-3x)=?

let x=-3x so that

-2x+5=-3x

x=5

substitutinx x into… i

f(x)=-10+5=-5

f(5)=-5………ii

now f(–3x)=f(-15)

scrutinizing… ii ,we can propose that

f(-15)=15.

Thus f(-3x)=15xplanation:

f times x would equal to fx=2x+5 and i think we move the x move to the other side which makes it f=3x+5 and then we plug this equal into f(3x) (i think)  which makes it f(3x+f=3x+5)

The number of cannonballs in illustration is 506.

Math Illustrations enables you to produce more useful geometry figures for your students in less time by fusing the constraint-based design of Geometry Expressions with simple-to-use sketching and graphing features.

The number of cannonballs in the first layer = 1² = 1

Number of cannonballs in the second layer = 2² = 4

Number of cannonballs in the third layer = 3² = 9

So, the generalized formula to count the balls is given as

= n(n + 1) (2n + 1)/ 6

Here, n= the total number of layers

Put n =11

11(11 + 1)(2(11) + 1) / 6

= 11(12)(23)/6

= 3036/6
= 506

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Answer:

his journey was 22.5 kilometers long.

Step-by-step explanation:

Answer:

Step-by-step explanation:

distance = speed x time

? = 30 x 45

distance = 1350

The surface areas are 110 in², 87.6 mm² and 49 m².

Given that are solid figure, we need to find the surface area of them,

1) Triangular prism = perimeter × length + 2 × base area

= (5 + 5 + 6) × 5 + 2(3×5) = 110 in²

2) Triangular pyramid = base area + perimeter × slant height / 2

= 1/2 × 5.2 × 6 + 3 × 6 × 8/2

= 87.6 mm²

3) Cube = 4side²

= 4 × (3 1/2)²

= 4 × 3.5²

= 49 m²

Hence the surface areas are 110 in², 87.6 mm² and 49 m².

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the amοunt οf paint needed tο apply a cοat οf paint 0.1 cm tο a hemispherical dοme with a diameter οf 30 meters is apprοximately 2,002,750 cubic centimetres.

A linear equatiοn is an equatiοn οf the fοrm:y = mx + b

where y and x are variables, m is the slοpe οf the line, and b is the y-intercept.

The vοlume οf a hemisphere is given by the fοrmula:

\(V = (2/3) * \pi * r^3\)

where r is the radius οf the hemisphere.

The diameter οf the hemisphere is 30 meters, sο the radius is 15 meters.

Tο find the amοunt οf paint needed tο apply a cοat οf 0.1 cm tο the surface οf the hemisphere, we need tο find the surface area οf the hemisphere.

The surface area οf a hemisphere is given by the fοrmula:

\(A = 2 * \pi * r^2\)

Substituting the radius οf 15 meters, we get:

\(A = 2 * \pi * (15)^2\)

= 1,767.15 square meters

Nοw, we need tο cοnvert the thickness οf the paint frοm centimeters tο meters, since the radius is given in meters. 0.1 cm is equal tο 0.001 meters.

Sο, the vοlume οf paint needed is:

V = A * h

= 1,767.15 square meters * 0.001 meters

= 1.76715 cubic meters

Tο estimate this value using linear apprοximatiοn, we can use the fact that fοr small changes in the radius, the change in the vοlume οf the hemisphere is apprοximately prοpοrtiοnal tο the change in the radius. Specifically, we have:

\(dV = (2/3) * \pi * r^2 * dr\)

where dV is the change in vοlume, dr is the change in radius, and r is the initial radius.

Apprοximating the change in vοlume as the vοlume οf a cοne with base area \(\pi * r^2\) and height dr, we have:

\(dV ≈ (1/3) * \pi * r^2 * dr\)

Taking r = 15 meters and dr = 0.1 cm = 0.001 meters, we get:

\(dV ≈ (1/3) * \pi * (15)^2 * 0.001\)

≈ 0.2356 cubic meters

Therefοre, we can estimate the vοlume οf paint needed as:

V ≈ V0 + dV

≈ 1.76715 + 0.2356

≈ 2.00275 cubic meters

Finally, we need tο cοnvert this value tο cubic centimeters by multiplying by 1,000,000:

V ≈ 2,002,750 cubic centimeters

Therefοre, the amοunt οf paint needed tο apply a cοat οf paint 0.1 cm tο a hemispherical dοme with a diameter οf 30 meters is apprοximately 2,002,750 cubic centimetres.

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Answer:The amount of a 80% acid solution that must be mixed with a 55% solution to produce 600 mL of a 60% solution can be calculated using a simple algebraic equation. Let x represent the amount of the 80% acid solution in mL that needs to be mixed with the 55% solution.

The equation can be set up as follows:

0.80x + 0.55(600 - x) = 0.60(600)

Step-by-step explanation: The left-hand side of the equation represents the total amount of acid in the mixture. The first term, 0.80x, represents the amount of acid from the 80% solution, and the second term, 0.55(600 - x), represents the amount of acid from the 55% solution. The right-hand side of the equation represents the total amount of acid in the final 60% solution, which is 60% of 600 mL.

By solving this equation for x, we can determine the amount of the 80% acid solution that needs to be mixed with the 55% solution. Once we have the value of x, we can then calculate the amount of the 55% solution by subtracting x from 600 mL.

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Let x=amount of 80% solution needed

Then 600-x=amount of 30% solution needed

Now we know that the pure acid in the 80% solution (0.80x) plus the amount of pure acid in the 30% solution ((0.30)(600-x)) has to equal the amount of pure acid in the final mixture(0.40*600), so our equation to solve is:

0.80x+0.30(600-x)=0.40*600 get rid of parens

0.80x+180-0.30x=240 subtract 180 from each side

0.80x+180-180-0.30x=240-180 collect like terms

0.50x=60 divide each side by 0.50

x=120 ml---------------------amount of 80% solution needed

600-x=600-120=480 ml---------------amount of 30% solution needed

CK

120*0.80+480*0.30=0.40*600

96+144=240

240=240

Answer:

Step-by-step explanation:

Year 1: $850 * 0.91 = $773.50

Year 2: $773.50 * 0.91 = $704.69

Year 3: $704.69 * 0.91 = $641.95

...

Year 34: (continue the pattern)

We can continue this calculation for each year, but to save time, we can use an exponential decay formula:

Remaining Amount = Initial Amount * (1 - rate)^years

Substituting the values:

Remaining Amount = $850 * (1 - 0.09)^34

Calculating this expression:

Remaining Amount ≈ $850 * (0.91)^34 ≈ $255.88

After 34 years, approximately $255.88 will be left with Sally.

The average change as a simplified mixed number would be,

⇒ 1 3/4

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

The running back for the Bulldogs football team carried the ball 7 times for a total loss of 12 1/4 yards.

Now, The average change as a simplified mixed number would be,

⇒ (12 1/4) / 7

⇒ (49/4) / 7

⇒ (49 / 4×7)

⇒ 7/4

⇒ 1 3/4

Therefore, The average change is,

⇒ 1 3/4

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Answer: y + 3x + 2 = 0

Step-by-step explanation:

The formula for that is

y - y₁

-------     = -3 where x₁ = -3, y₁ = 7

x - x₁

Therefore cross multiply and solve

y - 7 = -3[( x - (-3)]

y - 7 = -3( x + 3 )

y - 7 = -3x - 9

y + 3x -7 + 9 = 0

y + 3x + 2 = 0

Answer:

y=-3x-2

Step-by-step explanation:

Hey there!

The formula is: y₂ - y₁ / x₂ - x₁

y₂ = 22

y₁ = 21

x₂ = 6

x₁ = 5

Your equation: 22 - 21 / 6 - 5

22 - 21 = 1 ← numerator (TOP number)

6 - 5 = 1 ← denominator (BOTTOM number)

We can say that the line that passes through lines (5 , 21) (6 , 22): 1/1

(or you can simply 1 because 1 ÷ 1 gives you 1)

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

In order to create 728 millilitres of the medication, 273 millilitres of component A are required.

A compound in chemistry is a material comprised of two or more separate chemical elements mixed together in a certain proportion. Chemical connections that are challenging to break are created when the elements interact with one another.

Compound A:Compound B ratio in the medication is 3:5. In other words, there are 3 millilitres of compound A and 5 millilitres of compound B for every 3+5=8 millilitres of the medicine.

We may set up a percentage using the ratio of compound A to the total volume of the medicine to determine how much compound A is required to make 728 millilitres of the drug:

3 ml x 3 ml x 3 ml

-------- = ----------

728 ml total, 8 ml overall

If we cross-multiply, we obtain:

8(x) = 3(728)

To find x, we use the formula x = 3(728)/8 = 273

In order to create 728 millilitres of the medication, 273 millilitres of component A are required.

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273 milliliters of compound A are needed to make 728 milliliters of the drug.

What are proportions?

In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:

a/b = c/d

To determine the amount of compound A needed to make 728 milliliters of the drug, we need to use the given ratio of 3 milliliters of compound A to 5 milliliters of compound B.

Let's start by finding the ratio of compound A to the total amount of ingredients (A+B) in the drug:

3 : (3+5) or 3:8

This means that for every 8 milliliters of the drug, 3 milliliters of compound A are used.

To find out how many milliliters of compound A are needed for 728 milliliters of the drug, we can set up a proportion:

3/8 = x/728

where x represents the amount of compound A needed.

To solve for x, we can cross-multiply:

8x = 3*728

8x = 2184

x = 273

Therefore, 273 milliliters of compound A are needed to make 728 milliliters of the drug.

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Answer: They are not perpendicular because their slopes are  not negative reciprocals.

Step-by-step explanation:

For these two lines to be perpendicular, their slopes have to be negative reciprocals.

Slope of FG.

F = (-4, 1)

G = (0, -2)

= (Y₂ - Y₁) / (X₂ - X₁)

= (-2 - 1) / (0 + 4)

= -3/4

Slope of HJ

J = (0 , 4)

H = (-4, -2)

Slope =  (Y₂ - Y₁) / (X₂ - X₁)

= (-2 - 4) / (-4 -0)

= 6/4

= 3/2

The slopes of these lines are not negative reciprocals so these lines are not perpendicular.

Answer:kbef;eohrjkvoubwe

cv bojbDetectives are unsure whether Kendall Postwell will be able to testify at her trial. They say it is a question of competence. What does this MOST likely mean?

A.

Kendall might be determined to be insane and not qualified to testify.

B.

The evidence in Kendall’s case is inconclusive and doesn’t prove anything.

C.

Kendall is an expert witness who has testified many times before.

D.

The police think it will hurt their case if Kendall chooses to testify.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Arc length= \(\frac{interior angle}{360} 2\pi r\)

Answer:

B. The line will fall faster as you move from left to right.

Step-by-step explanation:

As slope is decreased by 1, its shall fall much more quickly. The green line labels the line  \(y = (-\frac{2}{5} x)+2\)  and red labels the line  \(y = (-\frac{2}{5} x-x)+2\)

As the slope is decreased, the line will fall much more steeply.

Answer:

B. The line will fall faster as you move from left to right.

Step-by-step explanation:

As slope is decreased by 1, its shall fall much more quickly. The green line labels the line  \(y = (-\frac{2}{5} x)+2\)  and red labels the line  \(y = (-\frac{2}{5} x-x)+2\)

As the slope is decreased, the line will fall much more steeply.

a) The confidence level of 99% means that we are 99% sure that the interval contains the true population proportion.

b) The 99% confidence interval for the population proportion is given as follows: (0.3145, 0.4055). It means that we are 99% sure that the true population proportion is between 0.3145 and 0.4055.

c) The 95% confidence interval would be narrower, as it would have a lower critical value, thus the margin of error would also be lower.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.

The parameters for this problem are given as follows:

\(\pi = 0.36, n = 739\)

The lower bound of the interval is given as follows:

0.36 - 2.575 x sqrt(0.36 x 0.64/739) = 0.3145.

The upper bound of the interval is given as follows:

0.36 + 2.575 x sqrt(0.36 x 0.64/739) = 0.4055.

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Answer:

(a) 3, (b) 96, (c) No

Step-by-step explanation:

(a) Since we have \(p = 150 - 6q^2\) and \(p = 10q^2 + 2q\), we can set up a quadratic equation by \(150 - 6q^2 = 10q^2 + 2q\), moving all values to one side.

The equation is: \(16q^2 + 2q - 150 = 0\).

Let's use the quadratic formula to find q,

we obtain that \(q = 3\) or \(q = -3.125\)

We can ignore \(-3.125\) because supplying a negative quantity is impossible.

Hence, the answer of (a) is 3

(b) Simply substitute \(q = 3\) into either equations given in the question to find p, and the answer of (b) is 96.

(c) We want to find if there is an exact quantity that makes the TR exactly 1500.

We substitute TR = 1500,

\(1500 = 85q - 2q^2\)

Use the quadratic formula again, and we will find that the answer is "undefined".

As a result, there is not output level in which the total revenue is exactly 1500.

Answer:

5

Step-by-step explanation:

when c = 7,

substitute 7, into 35÷c

35 ÷ 7 = 5

Answer:

Step-by-step explanation:

(6y-5)+(10y-41)+(12x+22)=180

16y+12x-24=180

16y+12x=204

y=12.75

x=17

Answer:

2x^3-5x^2-28x+15 -------------------------expanded

2x^3-5x^2-28x+15--------------------simplified

Step-by-step explanation:

\left(2x-1\right)\left(x+3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

simplyfied

\left(2x^2+5x-3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

=2x^3-5x^2-28x+15

Answer:

18

Step-by-step explanation:

Answer:

Step-by-step explanation:

4/mx

The probability of earning a total of exactly 10 points in 2 turns is 1/8.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The possibilities to earn exactly ten points occur when the scores in first and second turn are as follows:

(4, 6) or (6, 4)

The probability of getting a 4 in first try and 6 in second try is:

(4, 6) = 1/4 * 1/4 = 1/16

The probability of getting a 6 in first try and 4 in second try is:

(6, 4) = 1.4 * 1/4 = 1/16

The possibilities to earn exactly ten points occur when the scores in first and second turn are as follows:

(4, 6) or (6, 4) = 1/16 + 1/ 16 = 2/16 = 1/8

Hence, the probability of earning a total of exactly 10 points in 2 turns is 1/8.

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Answer:

D. 72°

Step-by-step explanation:

Given

Adjacent = 5feet

Hypotenuse = 16feet

Using SOH CAH TOA

cos theta = adj/hyp

cos theta = 5/16

cos theta = 0.3125

theta = arccos 0.3125

theta = 71.7

theta = 72 degrees

Huda's error in evaluating (3) squared incorrectly led to the incorrect final result.

The correct answer should be -20, not 34.

Huda's error was that she evaluated (3) squared incorrectly.

Instead of calculating 3 squared as 9, she mistakenly considered it as 3. This error led to incorrect subsequent calculations and the final result of 34, which is not the correct answer.

To evaluate the expression correctly, let's go through the steps:

Negative 3 (8 minus 5) squared minus (negative 7) \(= -3(3)^2 - (-7)\)

First, we simplify the expression within the parentheses:

\(-3(3)^2 - (-7) = -3(9) - (-7)\)

Next, we evaluate the exponent:

-3(9) - (-7) = -3(9) + 7

Now, we perform the multiplication and addition/subtraction:

-3(9) + 7 = -27 + 7 = -20

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