What’s the value of x

Answer:

x = 5 ± √46

Step-by-step explanation:

\(-x^2 + 10x + 21 = 0\)

Take -1 common from L.H.S.

\(=> -1(x^2 -10x - 21) = 0\)

Take -1 to R.H.S.

\(=> x^2 - 10x - 21 = 0\)

Solve x using quadratic formula.

\(=> x = \frac{-(-10) + \sqrt{10^2 - 4 \times (-21) \times 1} }{2 \times 1} \: or \:\frac{-(-10) - \sqrt{10^2 - 4 \times (-21) \times 1} }{2 \times 1}\)

\(=> x = \frac{10 + \sqrt{100 + 84} }{2} \: or \:\frac{10 - \sqrt{100 + 84} }{2}\)

\(=> x = \frac{10 + \sqrt{184} }{2} \: or \: \frac{10-\sqrt{184} }{2}\)

\(=> x = \frac{10 + 2\sqrt{46} }{2} \: or \: \frac{10 - 2\sqrt{46} }{2}\)

\(=> x = (5 + \sqrt{46} ) \: or \: (5 - \sqrt{46} )\)

Answer:

x = 1; y = 2

Step-by-step explanation:

y = 3x − 1

y = -4x + 6

In the first equation, y = 3x - 1.

Substitute 3x - 1 for y in the second equation.

3x - 1 = -4x + 6

7x = 7

x = 1

Substitute 1 for x in the first original equation.

y = 3x - 1

y = 3(1) - 1

y = 3 - 1

y = 2

Solution: x = 1; y = 2

Answer:

Step-by-step explanation:

Start with the piecewise definition of the absolute value function

y = f(x) = |x|

\(f(x) = \left \{ {f(x);\;{x\ge=0} \atop {{-f(x);\;{x < 0}} \right.\)

Substitute x + 5 for f(x)
\(|x+5| = \left \{ {x+5;\;{x+5\ge=0} \atop {{-(x+5);\;{x + 5 < 0}} \right.\)

Note that at x = 5, |x + 5| = 0 and therefore we have a unique point (-5, -2). This is where the function changes

Simplify the inequalities
x + 5 ≥ 0  ==> f(x) =  x ≥ -5

-(x+5) < 0 ==> -x -5 < 0 = -x < 5 or x >=5

Separate the two pieces
y = (x + 5); x ≥ -5
y = -x - 5; x < -5

Subtract 2 from both sides of the function
y = (x + 5) - 2 when x ≥ -5  or y = x + 3 when x ≥ -5

y = -x - 5 - 2 when x < -5   or y = - x - 7 when x < -5

Correct answer choice is the  last one
y = x + 3 for x ≥ -5 and y = -x -7 for x < -5

If you look at the attached graph of y = |x| -2  you will see this is consistent with the above piecewise function

For example at x = -3 which is greater than x = -5, y = 0 and x+3 = -3 + 3 = 0

At x = -7 which is less than -5, also y = 0 and -x -7 = -(-7) - 7 = 7-7 = 0

Answer:

9.21 cm

Step-by-step explanation:

The value of x for the chord AC intersecting another chord ED is equal to 4 which makes the option 3). 4 correct.

When two chords are intersecting each other inside a circle, then the product of the segments of one of the chord is equal to the product of the segments of the other chord.

The chords AC and ED are interesting each other, so;

9(4x) = 8(4x + 2)

36x = 32x + 16

36x - 32x = 16 {collect like terms}

4x = 16

x = 16/4 {divide through by 4}

x = 4

Therefore, the value of x for the chord AC intersecting another chord ED is equal to 4

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Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6

Answer:

t=-3.7

Step-by-step explanation:

5 (t+3)=-3.5

solving the bracket we have;

5t+15=-3.5

collect like terms

5t=-3.5-15

5t=-18.5

divide both sides by 5;

t=-3.7

The value of t in the given algebraic expression is; t = -2.3

We are given the equation;

5(t + 3) = 3.5

Using distributive property on the left hand side, we have;

5t + (5 × 3) = 3.5

5t + 15 = 3.5

Using subtractive property of equality, subtract 15 from both sides to get;

5t + 15 - 15 = 3.5 - 15

5t = -11.5

Divide both sides by 5 to get;

5t/5 = -11.5/5

t = -2.3

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Answer:

$39.33, including sales tax.

Step-by-step explanation:

9.25% of 36 = 3.33

36 + 3.33 = 39.33

$39.33

Answer:

39.30$(Remember to add the dollar sign and 0 in the decimals place, just write it as I did)

Step-by-step explanation:

36*0.0925=3.33

3.33 is tax

rounded to nearest tenth is 3.3

36+3.3=39.3

make it into money form

39.30$

The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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The volume of the solid generated by revolving the region bounded by the curves y = 3x, y = x, and y = 9 about the y-axis can be found using the washer method.

First, let's find the points of intersection between the curves. Setting y = 3x and y = x equal to each other, we get:

3x = x

2x = 0

x = 0

So, the curves intersect at the point (0, 0).

Next, we'll find the limits of integration. The region r is bounded between y = x and y = 9. The lower limit of integration is x = 0, and the upper limit of integration is x = 3.

Now, let's consider a vertical slice of the region at a given x-value. The radius of the outer circle (larger radius) is y = 9, and the radius of the inner circle (smaller radius) is given by the equation of the line y = x. The thickness of the washer is dx.

The volume of each washer can be calculated using the formula V = π(R^2 - r^2)dx, where R is the radius of the outer circle and r is the radius of the inner circle.

For the given problem, the volume can be calculated as follows:

V = ∫[0,3] π((9)^2 - (x)^2)dx

Evaluating this integral, we get:

V = π∫[0,3] (81 - x^2)dx

 = π[(81x - (x^3)/3)]|[0,3]

 = π[(81(3) - (3^3)/3) - (81(0) - (0^3)/3)]

 = π[243 - 9]

 = 234π

Therefore, the volume of the solid generated is 234π cubic units.

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we know that

Supplementary angles sum 180 degrees

so in this problem

120 and 60and 60

Using Marked recapature formula for estimation on population size we get,

the estimate for total population size is 1200.

Marked recaputure Method :

first step is to capture and mark a sample of individuals. The assumption behind mark-recapture methods is that the proportion of marked individuals recaptured in the second sample represents the proportion of marked individuals in the population as a whole. In algebraic terms,

R/S = M/N

where R --> second time marked

S---> size of sample second time

N --> estimate population size

M ---> Marked in start point

We have given that ,

Total marked turtles by researchers (M) = 800

Second time total sample size (S) = 300

second time marked turtles(R) = 200

we have to find out estimate for total population size .

For this , Mark -Recapture method is very efficient to calculate estimate for total population size.

putting all known values in above formula we get, R/S = N/M

=> 200/300 = 800/N

=> 800× 300 = N× 200

=> N × 200 = 240000

=> N = 240000/200

=> N = 1200

so, the estimate for total population size is 1200.

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Hello!

-9y > 9 <=>

<=> -9y ÷ (-9) > 9 ÷ (-9) <=>

<=> y < -1 <=>

<=> y ∈ { -∞; -1 }

Good luck! :)

One of the non-parametric tests used it as a generalized version of such Mann Whitney U test is the Kruskal-Wallis test.

One of the non-parametric tests used as an expanded version of a Mann Whitney U test is the Kruskal-Wallis test.

As a result, it has been used to investigate the null hypothesis, which claims that 'k' samples were taken from populations that were either identical or similar and had medians that were similar or slightly similar.

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The x-intercept represents that after 10 in. of rain, there are mosquitoes in that area.

The function is quadratic. The standard form of the quadratic equation is;

f(x) = ax² + bx + c

Here (a, b, c) are the real numbers and (x) is the variable. For the first point (0,0). The equation becomes,

f(0) = a(0)² + b(0) + c

c = 0

For the second point (1,9). The equation becomes,

f(1) = a(1)² + b(1) + 0

9 = a + b   ----(1)

For the third point (3, 21). The equation becomes,

f(3) = a(3)² + b(3) + 0

21 = 9a + 3b   ----(2)

Solving eq 1 and eq 2 simultaneously gives;

a = -1 and b = 10

Thus, our quadratic equation is;

f(x) = -x² + 10x

At f(x) = 0, x = 10.

Thus, x-intercept is at x = 10

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Answer:

\(d = 5\)

General Formulas and Concepts:

Order of Operations: BPEMDAS

Distance Formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Step-by-step explanation:

Step 1: Define points

(2, -3)

(5, 1)

Step 2: Solve for d

\(-14=-(-2x+2) \\ \\ 14=-2x+2 \\ \\ 12=-2x \\ \\ \boxed{x=-6}\)

Answer: x=-6

Step-by-step explanation:

a) Contribution (objective value) = $132.14

b) The firm earns $132.14 at the optimal solution.

c) An additional hour of time available for the third machine is worth $0.14 to the firm.

d) An additional 5 hours of time available for the second machine will increase the objective value by $3.69.

The best result obtained from using computer software to solve the LP problem is: X1 = 11.43, X2 = 12.86, X3 = 5.71

b) The number of unused hours at the ideal solution is:

Machine 1 still has 8.57 hours of time left.

There are no hours left on Machine 2 at the moment.

There are still 94.29 hours left on Machine 3.

c) The shadow price of the third limitation is worth an extra hour of time available for the third machine. With the exception of increasing the right-hand side of the third constraint by one unit, we can solve the LP problem using the same constraints to determine the shadow price. Using LP to solve this issue, we discover that the shadow price for the third constraint is

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Answer:

-2.8 or -14/5

Step-by-step explanation:

To divide one fraction by another, there is a really cool method called Keep Change Flip

Keep the first fraction

Change the division sign to multiplication

Flip the numbers on the last fraction

Let's try it out.

Keep the 1/5

Change the ÷ to a ×

Flip the -1/14 to a -14/1

1/5 × -14/1

Multiply the top numbers by each other first

1 × -14 = -14

Now the bottom numbers

5 × -1 = -5

The fraction we have now is -14/5

It can also be written as -2.8

The total weights of the two animals is  11. 92 × 10² Ibs

In order to determine the total weights, we take the following steps:

The weight of the animals are given as;

Now, let's add the weights:

= 5. 12 × 10² + 6. 8 × 10²

Add the values

= 11. 92

It is important to note that the powers are similar and should be written as one

We then have the sum to be;

= 11. 92 × 10² Ibs

Thus, the total weights of the two animals is  11. 92 × 10² Ibs

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Answer: the Correct answer is 1.2 x 10^3

Step-by-step explanation: You add 5.12 and 6.8 and get 11.92 x 10^2

you then need to round up to 12 and move the decimal up for scientific notation 1.2 x 10^3

The correct answer is 1.2 x 10^3

please give Branliest

No, we would not expect about 95% of the samples to have their variances within 0.008 of 0.009.

The variance of a normal distribution with mean μ and variance σ^2 is given by σ^2, which in this case is equal to (0.004)^2 = 0.000016.

The variance of the sample means, on the other hand, is given by σ^2/n, where n is the sample size. In order for about 95% of the samples to have variances within 0.008 of 0.009, we would need the sample size to be approximately equal to:

n ≈ σ^2 / (0.008 - 0.009)^2 = 62500

This means that we would need very large samples for this to be true. However, if the sample size is relatively small, then the distribution of sample means will not necessarily be normal and the Central Limit Theorem may not apply.

In that case, the distribution of sample variances will not necessarily follow the same pattern as the distribution of the population variance, and it may not be possible to make predictions about the sample variances based on the population parameters.

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Answer:

984/616 is equal to 123/77 because it is simplified, also meaning reduced by finding the GCF (greatest common factor), which in this case is 8. So therefore, when you divide the numerator of 984 by 8, you get 123, and when you divide the denominator of 616 by 8 as well, you will get 77.

Answer:

To write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 3, 6​, we can use the Linear Factorization Theorem1.

The theorem states that if a polynomial function f has zeros x = r1, x = r2, …, x = rn (where r1, r2, …, rn are distinct real numbers), then f(x) can be factored as follows:

f(x) = a(x - r1)(x - r2)…(x - rn)

where a is a nonzero constant.

So for this problem, we have:

f(x) = (x - (-2))(x - 3)(x - 6)

Multiplying this out gives:

f(x) = (x + 2)(x - 3)(x - 6)

Expanding this expression gives:

f(x) = x^3 - 7x^2 + 12x + 36

Therefore, the polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 3, 6​ is:

f(x) = x^3 - 7x^2 + 12x + 36

I hope this helps! Let me know if you have any other questions.

Step-by-step explanation:

Answer:

p= m over 2t to the 4th power -7x

Step-by-step explanation:

yb better

Answer:

1651.06 m³

Step-by-step explanation:

the volume of the whole block is base area times height :

Vb = 10 × 12 × 18

but we have to deduct the volume of the removed central cylinder.

the volume of the cylinder is again base area times height :

Vc = pi×r² × 18 = pi×3² × 18 = pi×9×18

so, the volume of the object is

V = Vb - Vc = 2160 - 508.94 = 1651.06 m³

Answer:

The mean of this test is 36.'

RATE 5 STARS NALANG PARE MARK BRAINLIEST NADEN

According to the information, the 95% confidence interval for the proportion of Americans who drink tea daily is approximately (0.2485, 0.2766). The margin of error is approximately 0.0140.

To construct a confidence interval for the proportion of Americans who drink tea daily, we can use the formula:

Where,

p = the sample proportion

Z = the critical value corresponding to the desired confidence level

n = the sample size

Given:

Now, let's calculate the confidence interval and margin of error:

According to the information, the 95% confidence interval for the proportion of Americans who drink tea daily is approximately (0.2485, 0.2766), with a margin of error of approximately 0.0140.

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The area under the curve is \(\frac{6 \sqrt{3}}{5}\).

Consider the following parametric equations:\($$x=t^2-3 t \text { and } y=\sqrt{t} \text { and the } y \text {-axis. }$$\)

The objective is to find area enclosed by the curve using the formula.

The area under the curve is given by parametric equations x=f(t), y=g(t),  and is traversed once as t increases from α to β, then the formula for calculating the area under the curve:

\($$A=\int_\alpha^\beta g(t) f^{\prime}(t) d t$$\)

The curve has intersects with y-axis. so x=0

\($$\begin{aligned}t^2-3 t & =0 \\t(t-3) & =0 \\t & =0 \text { or } t=3\end{aligned}$$\)

Now we have to draw the graph,

Let f(t)=\(t^2-3 t, g(t)=\sqrt{t}$\)

Differentiate the curve f(t) with respect to t.

\(f^{\prime}(t)=2 t-3\)

Now, find the area under the curve use the above formula.

\(\begin{aligned}A & =\int_0^3(\sqrt{t})(2 t-3) d t \\& =\int_0^3(2 t \sqrt{t}-3 \sqrt{t}) d t \\& =\int_0^3\left(2 t^{\frac{3}{2}}-3 t^{\frac{1}{2}}\right) d t \\& =\left[2 \frac{t^{\frac{5}{2}}}{\frac{5}{2}}-3 \frac{t^{\frac{3}{2}}}{\frac{3}{2}}\right]_0^3 \\& \left.\left.=\left[\frac{4 t^{\frac{5}{2}}}{5}-2 t^{\frac{3}{2}}\right]_0^3\right]^{\frac{5}{2}}\right] \\\\\end{aligned}$$\)

\(& =\left[\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}\right]-\left[\frac{4(0)^{\frac{5}{2}}}{5}-2(0)^{\frac{3}{2}}\right]\)

\($\begin{aligned}& =\left[\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}\right]-\left[\frac{4(0)^{\frac{5}{2}}}{5}-2(0)^{\frac{3}{2}}\right] \\& =\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}-0 \\& =\frac{6 \sqrt{3}}{5}\end{aligned}\)

Therefore,  the area of the curve is \(\frac{6 \sqrt{3}}{5}\).

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Answer:

3½ thats the answer your welcome