quadratic equations. A positive real number is 4 more than another. If the sum of the squares of the two numbers is 56, find the numbers.

Answer:

Step-by-step explanation:

According to given information, the arc length of a partial circle is 14.67 units.

A partial circle is a portion of a circle, usually defined by an angle that is less than 360 degrees.

To find the arc length of a partial circle, we need to know the measure of the central angle, θ, in radians.

Let's say that the central angle of the partial circle is 2π/3 radians, which corresponds to an angle of 120 degrees.

Then, the arc length, denoted by L, can be calculated using the formula:

L = rθ

where r is the radius of the circle.

Plugging in the values we have, we get:

L = 7(2π/3)

L = (14/3)π

Using 3.14 for π, we get:

L ≈ 14.67 units (rounded to two decimal places)

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Answer: ∠BDA

Step-by-step explanation:

Complementary: Either of two angles whose sum is 90°.

Starting Angle: ∠BDC

Possible Complement: ∠BDA

Answer: ∠ACD

Step-by-step explanation:

Complementary angles are angles which have a sum of 90 degrees when added together.

Angle ∠ADB is 90°

So ∠BDC and another angle should give you ∠ADB

The angle that when added to ∠BDC give you ∠ADB is ∠ACD

Answer: 2

Step-by-step explanation:

(7+2x)(9+2x)= 143 (area= length x width)

63+14x+18x+4x^2=143

4x^2+32x−80=0

x^2+8x−20=0

(x−2)(x+10)=0

x = 2 or -10

Since the length of the walkway can't be negative, the answer is 2.

Answer:

We can use the vector addition property to find the coordinates of the points M, N, and I.

Let

[tex]\bold{ A = (x_1, y_1), B = (x_2, y_2), C = (x_3, y_3), and\: D = (\frac{x_2+x_3}{2}, \frac{y_2+y_3}{2})}[/tex]

To find M, we use the fact that MA + MB = 0. Therefore, we have:

MA = -MB

A - M = -(B - M)

A - M = -B + M

2M = A + B

M =[tex]\frac{A + B}{2}[/tex]

So, the coordinates of point M are

[tex]\bold{(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})}[/tex]

To find N, we use the fact that 3NA + NC = 0. Therefore, we have:

3NA = -NC

3A - N = -(C - N)

3A - N = -C + N

4N = 3A + C

N =[tex]\frac{ 3A + C}{4}[/tex]

So, the coordinates of point N are [tex]\bold{(\frac{3x_1+x_3}{4},\frac{ 3y_1+y_3}{4})}[/tex]

To find I, we use the fact that IM + 2IN = 0. Therefore, we have:

IM = -2IN

M - I = -2(N - I)

M - I = -2N + 2I

3I = M + 2N

I = [tex] \frac{(M + 2N)}{3} [/tex]

Substituting the values of M and N that we found earlier, we get:

I = (A + B + 2(3A + C)/4)/3

Simplifying this expression, we get:

I = [tex]\frac{(7A + 2B + 2C)}{12}[/tex]

So, the coordinates of a point I are[tex]\bold{(\frac{7x_1+2x_2+2x_3}{12}, \frac{7y_1+2y_2+2y_3}{12}).}[/tex]

The solution of equation is (2, 3).

We have,

x= 3y -7.........(1)

y= x + 1.........(2)

Solving equation (1) and (2) we get

y = 3y - 7 + 1

y - 3y = -7 + 1

-2y = -6

y = -6/(-2)

y = 3

and, x = 3(3) - 7

x = 9 - 7

x = 2

Thus, the solution of equation is (2, 3).

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Answer:

The given expression is a polynomial:

f(x) = x^2 + 7x - 9 + 2x - 1

Combining like terms, we get:

f(x) = x^2 + 9x - 10

The degree of the polynomial is 2, since the highest power of x is 2.

Answer:

[tex]\frac{11}{24}[/tex] yards

Step-by-step explanation:

[tex]\frac{1}{8}[/tex] + [tex]\frac{1}{3}[/tex]  we need a common denominator which is 24

[tex]\frac{1}{8}[/tex] x [tex]\frac{3}{3}[/tex] = [tex]\frac{3}{24}[/tex]

[tex]\frac{1}{3}[/tex] x [tex]\frac{8}{8}[/tex] = [tex]\frac{8}{24}[/tex]

[tex]\frac{3}{24}[/tex] + [tex]\frac{8}{24}[/tex] = [tex]\frac{11}{24}[/tex] yards

Helping in the name of Jesus.

Answer: D 36л

Step-by-step explanation:

s = θr

where r is the radius of the circle.  given that the arc length is 6, and the central angle is π/3 radians r:

6 = (π/3)r

r = 6/(π/3) = 18/π

the circumference of the circle is given by:

C = 2πr

Substituting r = 18/π, we get:C = 2π(18/π) = 36

Answer:

  x° = 36°

Step-by-step explanation:

You want to find the angle between a secant and a tangent to a circle, where the intercepted arcs are 126° and 54°.

The angle at D, labeled x°, is half the difference of the intercepted arcs:

  x° = (126° -54°)/2 = 72°/2

  x° = 36°

__

Additional comment

The same relationship applies for the angle between two secants.

This is easy to prove by considering triangle ADE. Angle DAE is half of arc CE. The exterior angle to the triangle at E is half of arc AE. That exterior angle is equal to the sum of the remote interior angles at D and A:

  AE/2 = x° + CE/2   ⇒   x° = (AE -CE)/2

Based on the above, about  174 people out of the sample of 600 people indicated Bluetooth capability.

To know the number of individuals who shown Bluetooth capability, we have to to begin with calculate the division of individuals who chose this choice from the circle chart.

Note that:

People who Bluetooth capability =29%

Number of people = Percentage × Total sample size

= 0.29 × 600

= 174

So,  174 individuals shows that the Bluetooth capability is their favored option for the family trip.

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Joelle gave a total of 300 yards of ribbon in all

Let's assume that the total amount of ribbon Joelle has is "x" yards.

We know that 24 yards of ribbon is 8% of her total amount of ribbon. So we can write an equation:

0.08x = 24

To solve for x, we divide both sides of the equation by 0.08:

x = 24 ÷ 0.08

x = 300

Therefore, Joelle has a total of 300 yards of ribbon.

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Answer:

Step-by-step explanation: the answer is 300 just divide and you’ll get the answer that simple

Answer: n^6-25

Step-by-step explanation:

Use the distributive property to obtain: n^6-5n^3+5n^3-25

Simplify: n^6-25

Answer: n^6-25

The product of the given expression [tex](n^{3} + 5) (n^{3} - 5)[/tex] will be the second option  [tex]n^{6} - 25[/tex].

This is a simple math problem that can be solved using algebraic identities. Algebraic identities are mathematical formulas that hold true regardless of the value assigned to each of the variables. They can be used to resolve equations and simplify expressions.

In the above question, we have used the following identity:

[tex](a^{2} - b^{2} ) = (a + b) (a - b)[/tex]

In the given question, a = [tex]n^{3}[/tex] and b = 5

So putting values in the identity, we get

[tex][(n^{3})^{2} - 5^{2}] = (n^{3} + 5) (n^{3} - 5)[/tex]

On solving the left side of the equation, we get

[tex]n^{6} - 25[/tex] which is our answer to the given question.

Note: [tex](n^3)^2 = n^6[/tex] because the powers get multiplied.

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Answer:

After half hour=30 min you have 2×2500=5000 bacteria so you can use this into your equation to write:

and:

Apply the natural logarithm ln to both sides and get:

so  in units of

so your equation is now:

1] it t= 50 min substituting you get:

bacteria

2] if t= 8 h = 480 min you get:

bacteria

Step-by-step explanation:

Answer: 92.5

Step-by-step explanation:

Answer:

w = 92.5

Step-by-step explanation:

You cannot use Law of Sine in this case.

Use Law of Cosine.

They gave you 2 side length and one angle.

plug in your values into the equation and solve for w.

Let just use u, v, & w: Let u be 25 and v be 84.

[tex]w^2 = u^2 + v^2 - 2*u*v*cos(W)[/tex]

[tex]w^2 = 25^2 + 84^2 - 2*25*84*cos(102)[/tex]°

[tex]w^2=625+7056-4200*cos(102)[/tex]

[tex]w^2=7681-4200*(-0.2079116908)[/tex]

[tex]w^2=7681+873.2291014[/tex]

[tex]w^2=8554.229101[/tex]

[tex]w=\sqrt{8554.229101}= 92.48907558[/tex]

Answer:  x = 6 and y = -5.

Step-by-step explanation: Multiply the second equation by -2 to eliminate the y term:

-2(x + y) = -2(1) -> -2x - 2y = -2

Add the resulting equation to the first equation to eliminate the y term:

2x + y = 7

-2x - 2y = -2

0x - y = 5

Solve for y:

-y = 5

y = -5

Substitute y = -5 into either of the original equations and solve for x:

x + y = 1

x + (-5) = 1

x = 6

Therefore, the solution to the system of equations is x = 6 and y = -5.

The 95.44% confidence interval for the mean score, μ, of all students taking the test is 59.6 to 86.4.

A confidence interval is a range of values that is calculated from a sample of data. It provides a level of certainty, usually expressed as a percentage, that a population parameter lies within this range. It is used to estimate a population parameter, such as a mean, a proportion, or a difference between two means.

The 95.44% confidence interval for the mean score, μ, of all students taking the test can be calculated using the formula:
Confidence Interval = overbar(x) ± (1.96 x (σ/√n))
where overbar(x) is the mean score on the aptitude test, σ is the standard deviation of the population (15 in this case), and n is the sample size (5 in this case).
Plugging in the given values, we get:
Confidence Interval = 73 ± (1.96 x (15/√5))
= 73 ± (1.96 x 3)
= 73 ± 5.88
Therefore, the 95.44% confidence interval for the mean score, μ, of all students taking the test is 59.6 to 86.4.

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1. The force they must apply is 2256.3 N

2. The amount of work done = 3835.71 J

3. The work done using the ramp = 4500 J

4.  The efficiency of the ramp = 85.24%

5. When the people use inclined ramp, they don't have worry about the gravitational force that is acting on the piano. The trade off with with less force, the ramp is able to cover more distance.

1. To find force applied, used the formula; F = mg

230 x 9.8N

=2256.3N

2. To find the amount of work done, we use the formula;

W = Fd

2256.3 x 1.7 m

= 3835.71J

3. o calculate the work done using the ramp, you use the same formula you used in step 2

300N x 15m

= 4500J

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Answer:

Step-by-step explanation:

1 -E (102/234) *100 =43.6%

2- F

3-C

4-A

question 9.

Based on a cubic modeling equation, the  prediction about this data that is  most reliable is a $70k house would have 1,354 square ft.

Option A is correct.

Question 10.

The second coordinate in a scatterplot of the linearized data and  rounding the answer to the tenth place is 0.8

Option A is correct.

Question 11.

The approximate value when x=4 and rounding the answer to the nearest whole number is 1,168

Option C is correct.

The equation is given as

Log y= 0.75821x+0.03442

We substitute x = 4 into the given equation and solve for y:

log y = 0.75821(4) + 0.03442

log y = 3.07286 + 0.03442

log y = 3.10728

We take the antilogarithm of both sides,

y = 10^(3.10728)

y = 1,168.66

Rounding off, the closest answer is option  (c) 1,168.

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The solution to the simultaneous equations is x = 2 and y = -4. To obtain these values,  18 = 7x - y  is rearranged to y = 7x - 18, and then substituted into 3x + y = 2  to obtain the value of x and y.

Rearranging equation (1) to make y the subject

18 = 7x - y

Add y to both sides

18 + y = 7x

Subtract 18 from both sides

y = 7x - 18

Using the answer to part a) to solve the simultaneous equations

Substitute the expression for y from equation (1) into equation (2)

3x + (7x - 18) = 2

Simplify

10x - 18 = 2

Add 18 to both sides

10x = 20

Divide both sides by 10

x = 2

Substitute x = 2 into equation (1) to find y

18 = 7(2) - y

18 = 14 - y

Subtract 14 from both sides

4 = -y

Multiply both sides by -1

-4 = y

Therefore, the solution to the simultaneous equations is x = 2 and y = -4.

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We can begin by focusing on c on one side of the equation to help us solve it. Craig's height is 44 as a result.

A mathematical equation is a claim that two expressions are equivalent. It is divided into two sections, the left and the right, by the equal sign (=). Equation's left and right sides each have the potential to include variables, constants, and operators.

Finding the value(s) of the variable(s) necessary to make an equation true is the aim of equation solving. Algebraic techniques like simplification, substitution, and elimination can be used to solve equations.

An equation can be used to represent the following sentence:

c + 24 = 68

Craig's height is represented by c in this equation. The equal sign (=) is used to symbolise the phrase "is 68," while the phrase "is 24 more than Craig's height" is symbolised by c + 24. The formula for the problem can be solved to find the value of c, which corresponds to Craig's height.

We can begin by concentrating c on just one side of the equation in order to solve it:

c + 24 - 24 = 68 - 24

c = 44

Therefore, Craig's height is 44.

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The image is attached of the graph of the inequality y < 4x - 5.

What is the inequality equation?

An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

To graph the inequality y < 4x - 5 using the slope-intercept form, follow these steps:

Rewrite the inequality in slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.

y = 4x - 5

Plot the y-intercept on the y-axis.

The y-intercept is -5, so plot the point (0, -5).

Use the slope to find a second point on the line.

The slope is 4, so start at the y-intercept and move up 4 units and to the right 1 unit to find the point (1, -1).

Draw a dashed line through the two points.

Since the inequality is y < 4x - 5, use a dashed line to indicate that the line itself is not part of the solution.

Shade the region that satisfies the inequality.

To do this, pick a test point that is not on the line and plug its coordinates into the inequality. If the inequality is true for that point, shade the region that contains the test point. If the inequality is false for that point, shade the region that does not contain the test point.

Let's use the test point (0, 0). Plug its coordinates into the inequality to get:

0 < 4(0) - 5

This simplifies to 5 < 0, which is false. Therefore, we need to shade the region that does not contain the test point.

Since the inequality is y < 4x - 5, we need to shade the region below the dashed line.

Label the shaded region with the inequality symbol.

The inequality is y < 4x - 5, so label the shaded region below the dashed line with the symbol "<".

hence, The image is attached of the graph of the inequality y < 4x - 5.

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The value of k include the following: B. k is equal to one third.

In Mathematics, the vertex form of a quadratic function can be modeled by this formula:

y = a(x - h)² + k

Where:

Based on the information provided about the quadratic function f(x), we can logically deduce that its vertex is at (0, 0);

f(x) = a(x - h)² + k

2 = a(1 - 0)² + 0

2 = a

f(x) = 2(x - 0)² + 0

f(x) = 2x²

For the quadratic function g(x), we have;

g(x) = f(kx)

g(x) = 2(kx)²

g(x) = 2k²x²

By using the point (3, 2) from the table, we have:

2 = 2k²3²

1 = k²9

k² = 1/9

k = √(1/9)

k = 1/3 i.e one third.

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The monthly payments will thus be $1,612.81.

The annual effective rate on this loan is 5.78%.

We can use the following loan payment formula to determine the loan payment:

Loan Payment  = [tex]\\\frac{p * \frac{r}{n} }{1 - (1 + \frac{r}{n} )^{-n *t} }[/tex]

where P = borrowed amount = $69,300

r = yearly interest rate (decimal) = 0.056

n = number of times compounded per year = 12

t = number of years = 4

When we plug in the values, we get:

Loan Payment = [69300 x (0.056/12)] / [1 - (1 + 0.056/12)^(-12*4)]

= $1,612.81 (to the nearest cent)

The monthly payments will thus be $1,612.81.

We can use the following calculation to obtain the effective annual rate:

Annual Effective Rate =[tex](1 + r/n)^{n-1}[/tex]

When we plug in the values, we get:

Annual Effective Rate =[tex](1 + 0.056/12)^{12 - 1}[/tex]= 0.0578 or 5.78%

As a result, the annual effective rate on this loan is 5.78%.

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c) Population [tex]\sigma = 48[/tex]

Z = [tex]\frac{68-60 }{\frac{48 }{\sqrt{64}}}[/tex]

Z-score= 1.3333

According to the question , sample size n=64 , mean M = 68 , population mean [tex]\mu= 60[/tex]

Z = [tex]\frac{M-\mu }{\frac{\sigma }{\sqrt{n}}}[/tex]

where M = Sample Mean

[tex]\mu[/tex] = Population Mean

[tex]\sigma[/tex] = Population Standard Deviation

n = Sample Size

a) Population [tex]\sigma[/tex] = 16

Z = [tex]\frac{68-60 }{\frac{16 }{\sqrt{64}}}[/tex]

Z-score = 4

b) Population [tex]\sigma[/tex] = 32

Z = [tex]\frac{68-60 }{\frac{32 }{\sqrt{64}}}[/tex]

Z-score = 2

c) Population [tex]\sigma[/tex]= 48

Z = [tex]\frac{68-60 }{\frac{48 }{\sqrt{64}}}[/tex]

Z-score= 1.3333

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The difference in the length of dogs jump is 24 inches.

Given that, Mackenzie's dog can jump [tex]2\frac{1}{2}[/tex] =5/2 feet off the ground. Jordyn's dog can jump 1/2 foot off the ground.

We know that, 1 feet = 12 inches

Here, 5/2 feet = 5/2 ×12

= 30 inches

1/2 foot = 1/2 ×12

= 6 inches

Now, difference = 30-6 = 24 inches

Therefore, the difference in the length of dogs jump is 24 inches.

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Answer:

the answer is none of the answer choices

Answer:

the answer is none of the answer choices

The residual plot shows that the regression equation is a good model of the data because it shows a random scatter of points around a horizontal line at zero, with no pattern or trend

A residual plot is a scatter plot of the residuals against the predictor variable(s) or the fitted values. It is used to verify whether the regression equation fits the data well.

In the event that the residual plot shows a random scatter of points around a horizontal line at zero, with no pattern or trend, it shows that the regression equation is a good model of the data.

On the other hand, supposing the residual plot shows a pattern or trend, such as a curve, a U-shape, or a funnel shape, it shows that the regression equation is a bad model of the data.

Therefore, from the graph given, the residual plot shows that the regression equation is a good model of the data.

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