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Answer:

The graph of the equation has a minimum.

When y = 0, the solutions are [tex]4 \pm 2\sqrt{3}[/tex]

The extreme value of the graph is (4,-12).

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

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

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].

y = x2 – 8x + 4

Quadratic equation with [tex]a = 1, b = -8, c = 4[/tex]

a is positive, so it's graph has a minimum.

Solutions when y = 0

[tex]\Delta = b^2-4ac = 8^2 - 4(1)(4) = 64 - 16 = 48[/tex]

[tex]x_{1} = \frac{-(-8) + \sqrt{48}}{2} = \frac{8 + 4\sqrt{3}}{2} = 4 + 2\sqrt{3}[/tex]

[tex]x_{2} = \frac{-(8) - \sqrt{48}}{2} = \frac{8 - 4\sqrt{3}}{2} = 4 - 2\sqrt{3}[/tex]

When y = 0, the solutions are [tex]4 \pm 2\sqrt{3}[/tex]

Extreme value:

The vertex. So

[tex]x_{v} = -\frac{-8}{2} = 4[/tex]

[tex]y_{v} = -\frac{48}{4} = -12[/tex]

The extreme value of the graph is (4,-12).

Answer:

111.35

Step-by-step explanation:

effective rate: .085/12= .007083333333333333

payment=x

[tex]3000=x(\frac{1-(1+.007083333333333333)^{-30}}{.007083333333333333})\\x=111.35[/tex]

Step-by-step explanation:

111.35

Step-by-step explanation:

effective rate: .085/12= .007083333333333333

payment=x

\begin{gathered}3000=x(\frac{1-(1+.007083333333333333)^{-30}}{.007083333333333333})\\x=111.35\end{gathered}

3000=x(

.007083333333333333

1−(1+.007083333333333333)

−30

)

x=111.35

Answer:

[tex]5x -2y = -2[/tex]

Step-by-step explanation:

Given

[tex]-2x + y = 0[/tex]

[tex]-7x + 3y = 2[/tex]

Required

Subtract (2) from (1)

This gives:

[tex]-2x - -7x +y - 3y = 0 -2[/tex]

[tex]5x -2y = -2[/tex]

Answer:

1760 cm³

Step-by-step explanation:

Volume For top "trapezoidal" prism : (14 * 4)/2 * 20 = 28 * 20 = 560

Volume for bottom rectangular prism = 6 x 10 x 20 = 60 x 20 = 1200

1200 + 560 = 1760 cm³

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

It has the same domain and range as the function f(x) = StartRoot x EndRoot. It has the same range but not the same domain as the function f(x) = StartRoot x EndRoot. It has the same domain and range as the function f(x) = negative StartRoot negative x EndRoot.

Step-by-step explanation:

810.93

Let the pressure be given by P and the volume be V.

Since pressure is inversely proportional to volume, we can write;

P ∝ [tex]\frac{1}{V}[/tex]

=> P = [tex]\frac{c}{V}[/tex]          -------------(i)

Where;

c = constant of proportionality.

When the volume of the gas is 2 cubic feet, pressure is 1000 pounds per square foot.

V = 2 ft³

P = 1000lb/ft²

Substitute these values into equation (i) as follows;

1000 = [tex]\frac{c}{2}[/tex]

=> c = 2 x 1000

=> c = 2000 lbft

Substituting this value of c back into equation (i) gives

P = [tex]\frac{2000}{V}[/tex]

This is the general equation for the relation between the pressure and the volume of the given gas.

To calculate the work done W by the gas, we use the formula

[tex]W = \int\limits^{V_1}_{V_0} {P} \, dV[/tex]

Where;

V₁ = final volume of the gas = 3ft³

V₀ = initial volume of the gas = 2ft³

Substitute P = [tex]\frac{2000}{V}[/tex], V₁ = 3ft³ and V₀ = 2ft³

[tex]W = \int\limits^{3}_{2} {\frac{2000}{V} } \, dV[/tex]

Integrate

W = 2000ln[V]³₂

W = 2000(In[3] - ln[2])

W = 2000(0.405465108)

W = 810.93016

W = 810.93 [to 2 decimal places]

Therefore, the work done by the gas for the given pressure and volume is 810.93

Answer:

Answer:

1. B. (x^2 + 4x)(x)

2. A. (x^3+4x^2)

3. 9

4. 0

5. 1

Step-by-step explanation:

Step-by-step explanation:

hear is answer in attachment

Answer:

1.  5 x 47    show tree of 5  x  47 and then stop both are pf

2.  2^2 × 5 × 23   show tree of  10 x 46 and then 2 x 5 (under10) and 2x23 (under 46) and then stop  2,2,5,23 are all pf

3. 2 x 3 x 97   show tree 3 x 194 and 2 x 97 and circle pf 2,3,97

4.  3^3 x 11  show tree of 3 x 99  then 3  x 33 then 3 x 11 to show 3,3,3,11 as pf

5. 3 x 7 x 37 show tree as  777/7  = 111/37 = 3 to show 3,7,37 as pf

6. 2^4 x 3 x 13 show tree as 2 x 312  2 x 156  2 x 78  2 x 39  3 x 13 to show 2,2,2,2,3,13 all as pf

Step-by-step explanation:

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:

D. P(X=3)+P(X=4)+P(X=5)+ ...

Step-by-step explanation:

Given

[tex]n =60[/tex]

[tex]pr = 70\%[/tex] -- proportion of adults with pet

Required

Represent at least 3 adult with pet as a probability

At least 3 means 3 or more than.

So, the probability is represented as:

[tex]P(x \ge 3) = P(3) + P(4) + P(5) + ........[/tex]

Hence;

(d) is correct

Answer:

Step-by-step explanation:

The y-intercept is super easy. The y-intercept exists when x = 0; therefore, the point given where x = 0 is found in (0, -15). That means that the y-intercept is -15. Easy enough. Now, the slope.

Since all these points are on the same line, using any 2 of them in the slope formula will get us the slope. I picked the first 2 points (1, -19) and (-4, 1):

[tex]m=\frac{1-(-19)}{-4-1}=\frac{1+19}{-5}=\frac{20}{-5}= -4[/tex]

The y-intercept is -15 and the slope is -4

Answer:

[tex]\frac{\sqrt{3} }{3} }(cos(\frac{19\pi}{12})+isin(\frac{19\pi}{12}))[/tex]

Step-by-step explanation:

Division of complex numbers in polar form is [tex]z_1/z_2=\frac{r_1}{r_2}cis(\theta_1-\theta_2)[/tex] where [tex]z_1[/tex] and [tex]z_2[/tex] are the complex numbers being divided, [tex]r_1[/tex] and [tex]r_2[/tex] are the moduli, [tex]\theta_1[/tex] and [tex]\theta_2[/tex] are the arguments, and [tex]cis[/tex] is shorthand for [tex]cos\theta+isin\theta[/tex]. Therefore:

[tex]\frac{9(cos(\frac{11\pi}{6})+isin(\frac{11\pi}{6})) }{3\sqrt{3}((cos\frac{\pi}{4})+isin(\frac{\pi}{4})) }[/tex]

[tex]\frac{9}{3\sqrt{3} }cis(\frac{11\pi}{6}-\frac{\pi}{4})[/tex]

[tex]\frac{\sqrt{3} }{3} }cis(\frac{19\pi}{12})[/tex]

[tex]\frac{\sqrt{3} }{3} }(cos(\frac{19\pi}{12})+isin(\frac{19\pi}{12}))[/tex]

Answer:

Answer:

(9-6.6)÷2=x

Step-by-step explanation:

Do it in reverse from 9 all the way to x.

Answer:

(9-6.6)÷2=x

Step-by-step explanation: since you had 9 as the answer, start there. Then subtract 6.6. You then divide that number by 2 to get x

9514 1404 393

Answer:

  B.  (-∞, 1) ∪ (1, 2]

Step-by-step explanation:

When you are looking for answers to domain questions, you are looking for values of the variable(s) that make the function undefined. Here, there is a square root involved, and the rational function has a denominator that might be zero.

The function is only defined for square roots of non-negative numbers. That is ...

  2-x ≥ 0   ⇒   x ≤ 2

The rational function is only defined for non-zero denominators, so ...

  x-1 ≠ 0

  x ≠ 1

__

So, you're looking for a domain description that includes all numbers less than or equal to 2, and excludes x=1. The attached number line shows a graph of this.

The domain divides into two parts: all numbers less than 1, and those numbers between 1 and 2 (including 2). This will be the union ...

  (-∞, 1) ∪ (1, 2]

Answer:

C

Step-by-step explanation:

3² * pi * 4 = 113

113 / pi / 3²

gives you 4

this time the radius was squared correctly XD

Answer:

C. 4m

Step-by-step explanation:

Work backwards from the formula of volume cylinder:

Formula = πr²h

113 = 3.14 * 9 * h

113/9 = 3.14 * h

12. 6 = 3.14 / h

4 = h

h = 4

Check:

Volume = 3.14*9*4

Volume = 3.14 * 36

volume = 113.04 ≈ 113

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

150

Step-by-step explanation:

The sum of the angles of a quadrilateral are 360.  Let x be the unknown angle

30+70+110+x = 360

Combine like terms

210 +x = 360

Subtract 210 from each side

210+x-210 = 360-210

x = 150

Answer:

The measures of the fourth angle is 150 .

Step-by-step explanation:

The measures of three angles of quadrilateral are 30 , 70 and 110.

Find the measures of fourth angle.

Let, the measures of fourth angle be x.

We know that sum angles of quadrilateral are 360 .

30 + 70 + 110 + x = 360

combine like terms

210 + x = 360

subtract 210 from 360.

x = 360 - 210

x = 150

Therefore, the fourth angle of quadrilateral is 150.

Answer:

0.0016 probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made.

Step-by-step explanation:

We use the normal approximation to the binomial distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

A company's sales force makes 400 sales calls, with 0.25 probability that a sale will be made on a call.

This means that [tex]n = 400, p = 0.25[/tex]

Mean and standard deviation:

[tex]\mu = E(X) = np = 400*0.25 = 100[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{400*0.25*0.75} = \sqrt{75}[/tex]

What is the probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made?

Using continuity correction, this is [tex]P(55+0.5 \leq X \leq 75-0.5) = P(55.5 \leq X \leq 74.5)[/tex], which is the p-value of Z when X = 74.5 subtracted by the p-value of Z when X = 55.5.

X = 74.5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{74.5 - 100}{\sqrt{25}}[/tex]

[tex]Z = -2.94[/tex]

[tex]Z = -2.94[/tex] has a p-value of 0.0016

X = 55.5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{55.5 - 100}{\sqrt{25}}[/tex]

[tex]Z = -5.14[/tex]

[tex]Z = -5.14[/tex] has a p-value of 0

0.0016 - 0 = 0.0016

0.0016 probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made.

Answer:

45 + m<DBC = 180

Step-by-step explanation:

m<ABD + m<DBC = 180

45 + m<DBC = 180

Answer:

Step-by-step explanation:

5x + 150 = 180

5x = 30

x = 6

Hope this help!!!

Have a nice day!!!

Answer:

Step-by-step explanation:

All three have blue eyes.

P(1 has blue eyes) = 16/100 = 4/25

P(3 have blue eyes) = 4/25 * 4/25 * 4/25

P(3 have blue eyes ) = 64/15625

If you need the decimal answer, it is .004096

No one has blue eyes out of three

The probability for this is very large.

P(no blues) = 1 - 64/15625

P(no blues) = 15561/15625  

If you need the decimal answer, it is 0.996

One has blue eyes (the other two do not).

P(1 has blue eyes) = 16/100 * 84/100*84/100

P(1 has blue eyes) = 112896/1000000

P(1 has blue eyes) = 0.112896

Answer:

hello

Step-by-step explanation:

a²+b²=c²

16²+b²=65²

256+b²=4225

b²=4225-256

b²=3969

[tex]b = \sqrt{3969}[/tex]

b=63

b=63 mi

have a nice day

Answer:

b = 63

Step-by-step explanation:

In a right angled triangle, hypotenuse squared is equal to the sum of the square of the other sides.

c² = a² + b² (where c is the hypotenuse, and a and b are the other two sides)

c =  65       , a = 16        b = ?

65² = 16² + b²

4225 = 256 + b²

4225 - 256 = b²

b² = 3969

b = [tex]\sqrt{3969}[/tex]

b = 63

check

c² = 16 ² + 63²

   = 256 + 3969

   = 4225

c = √4225

c = 65

Answer:

See Below.

Step-by-step explanation:

We want to verify the identity:

[tex]\displaystyle \frac{\sin x}{1 - \cos x} - \cot x = \csc x[/tex]

We can multiply the fraction by 1 + cos(x):

[tex]\displaystyle \frac{\sin x(1+\cos x)}{(1 - \cos x)(1+\cos x)} - \cot x = \csc x[/tex]

Difference of Two Squares:

[tex]\displaystyle \frac{\sin x(1+\cos x)}{1-\cos^2 x} - \cot x = \csc x[/tex]

From the Pythagorean Theorem, we know that sin²(x) + cos²(x) = 1. Rearranging, we acquire that sin²(x) = 1 - cos²(x). Substitute:

[tex]\displaystyle \frac{\sin x(1+\cos x)}{\sin^2 x} - \cot x = \csc x[/tex]

Cancel:

[tex]\displaystyle \frac{ 1 + \cos x}{\sin x}-\cot x = \csc x[/tex]

Let cot(x) = cos(x) / sin(x):

[tex]\displaystyle \frac{ 1 + \cos x}{\sin x}-\frac{\cos x}{\sin x} = \csc x[/tex]

Combine Fractions:

[tex]\displaystyle \frac{ 1 + \cos x - \cos x}{\sin x}= \csc x[/tex]

Thus:

[tex]\displaystyle \frac{1}{\sin x}=\csc x = \csc x[/tex]

Hence proven.

Answer:

5 th day

Step-by-step explanation:

Given :

1st day :

Time = 30 seconds

Time increases by 20% each day :

2nd day = 20% * 30 = (1.20 * 30) = 36 seconds

3rd day = 1.20 * 36 = 43.2 seconds

4th day = 1.20 * 43.2 = 51.84 seconds

5th day = 1.20 * 51.84 = 62.208

First day Aretha hold a plank for over 1 minute is the 5th day

Answer:

prational number between root2

Answer:

<A = 41.4°

Step-by-step explanation:

Recall, SOH CAH TOA

Reference angle = <A

Hypotenuse length = 8

Adjacent length = 6

Since Hypotenuse and Adjacent are involved, we would apply CAH, which is:

Cos A = Adj/Hyp

Plug in the values

Cos A = 6/8

Cos A = 0.75

[tex] A = Cos^{-1}(0.75) [/tex]

A = 41.4096221° ≈ 41.4° (nearest tenth)

Answer:

Melissa needs to drive 325 miles for the two plans to cost the same

Step-by-step explanation:

Plan A

Initial Fee = 65

Additional cost per mile = 0.50 per mile

Plan B

Initial Fee = 0

Additional cost per mile = 0.70 per mile

Required

Mile both plans will cost the same

Let

[tex]y \to cost[/tex]

[tex]x \to miles[/tex]

So, we have:

[tex]y = Initial\ Fee + Additional * x[/tex]

For plan A

[tex]y = 65+ 0.50* x[/tex]

[tex]y = 65+ 0.50x[/tex]

For plan B

[tex]y = 0 + 0.70*x[/tex]

[tex]y = 0.70x[/tex]

So, we have:

[tex]y = 65+ 0.50x[/tex] --- plan A

[tex]y = 0.70x[/tex] --- plan B

Both plans will cost the same when

[tex]y = y[/tex]

[tex]0.70x = 65 +0.50x[/tex]

[tex]0.70x -0.50x= 65[/tex]

[tex]0.20x= 65[/tex]

Divide by 0.20

[tex]x= 325[/tex]