Write x2 + 6x − 3 = 0 in the form of (x − a)2 = b, where a and b are integers. (1 point)
(x + 6)2 = 3
(x + 6)2 = 12
(x + 3)2 = 6
(x + 3)2 = 12

5 years ago the ratio of Mark's age was 3:4 mark is 12 yr younger than Francis, now Francis is currently 53 years old

Let us suppose that age of him 5 years ago was 3x and Francis's age 5 years ago was 4x. According to the given information, Mark is 12 years younger than Francis.

So, we can set up the equation: 3x + 12 = 4x.

Simplifying the equation, we have: 12 = x.

This means that 5 years ago,

Mark age = 3 * 12 = 36 years old,

Francis age = 4 * 12 = 48 years old.

Now, to find out how old Francis is now, we add 5 years to both Mark and Francis. Thus, Francis's current age is 48 + 5 = 53 years.

Therefore, Francis is currently 53 years old.

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Answer:

look at explanation

Step-by-step explanation:

50/50 chance

Answer:

$132.54

Step-by-step explanation:

$1060.32 / 8 families = $132.54 / family

The calculated measure of the red arc in ⊙C is 5

From the question, we have the following parameters that can be used in our computation:

The circle

From the circle, we have

Centers = C

Also, we have

Corresponding segments are equal segments

Using the above as a guide, we have the following:

UV  = TU

Where

TU = 5

This gives

UV = 5

Hence, the value of UV is 5

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Answer: i believe it’s 68

Step-by-step explanation:

My knowledge

Answer:

Sure, I'd be happy to help you solve these equations! Here are the solutions to the equations you provided:

1. -3x+7=-8x+47

  Add 8x to both sides: 5x + 7 = 47

  Subtract 7 from both sides: 5x = 40

  Divide both sides by 5: x = 8

2. -13x+8=-8x-7

  Add 13x to both sides: 5x + 8 = -7

  Subtract 8 from both sides: 5x = -15

  Divide both sides by 5: x = -3

3. 6x+7=3x+19

  Subtract 3x from both sides: 3x + 7 = 19

  Subtract 7 from both sides: 3x = 12

  Divide both sides by 3: x = 4

4. 12x-8=10x+6

  Subtract 10x from both sides: 2x - 8 = 6

  Add 8 to both sides: 2x = 14

  Divide both sides by 2: x = 7

5. -7x-4=-10x-10

  Add 10x to both sides: 3x - 4 = -10

  Add 4 to both sides: 3x = -6

  Divide both sides by 3: x = -2

6. 7x-9=3x-5

  Subtract 3x from both sides: 4x - 9 = -5

  Add 9 to both sides: 4x = 4

  Divide both sides by 4: x = 1

7. 3x-9=5x-3

  Subtract 3x from both sides: -6 = 2x - 3

  Add 3 to both sides: -3 = 2x

  Divide both sides by 2: x = -3/2 or -1.5

8. 7x-1=5x+5

  Subtract 5x from both sides: 2x - 1 = 5

  Add 1 to both sides: 2x = 6

  Divide both sides by 2: x = 3

9. -7x-2=-3x-14

  Add 3x to both sides: -4x - 2 = -14

  Add 2 to both sides: -4x = -12

  Divide both sides by -4: x = 3

10. -3x-7=-8x-57

   Add 8x to both sides: 5x - 7 = -57

   Add 7 to both sides: 5x = -50

   Divide both sides by 5: x = -10

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

The calculated total distance he drive is 372 miles

From the question, we have the following parameters that can be used in our computation:

So, we have

Total charges = 75 * days + 0.25 * miles

For 2 days and total ot 243. we have

75 * 2 + 0.25 * miles = 243

So, we have

miles = 372

Hence, the total distance he drive is 372 miles

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The percentage of vehicles that are returned with less than 30000 miles are given as follows:

b) 2.5%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

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

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 36400, \sigma = 3200[/tex]

The proportion is the p-value of Z when X = 30000, hence:

Z = (30000 - 36400)/3200

Z = -2.

Z = -2 has a p-value of 0.028 -> percentage rounded to 2.5%.

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The domain and range of the given function y = -2x + 3 are

Domain = 0, 1, 2, ,3 , 4, 5, 6

Range = 3, 1, -1, -3, -5, -7, -15

The table is given below.

We have,

y = -2x + 3

We can have domain as:

x = 0, 1, 2, 3, 4, 5, 6

For x = 0,

y = -2 x 0 + 3 = 3

For x = 1,

y = -2 x 1 + 3 = -2 + 3 = 1

For x = 2,

y = -2 x 2 + 3 = -4 + 3 = -1

For x = 3,

y = -2 x 3 + 3 = -6 + 3 = -3

For x = 4,

y = -2 x 4 + 3 = -8 + 3 = -5

For x = 5,

y = -2 x 5 + 3 = -10 + 3 = -7

For x = 6,

y = -2 x 6 + 3 = -18 + 3 = -15

The range are 3, 1, -1, -3, -5, -7, -15.

The table can be assumed as:

x         y = -2x + 3

0        3

1         1

2        -1

3        -3

4       -5

5       -7

6       -15

Thus the domain and range of the given function y = -2x + 3 are

Domain = 0, 1, 2, ,3 , 4, 5, 6

Range = 3, 1, -1, -3, -5, -7, -15

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a. Your monthly payments would be approximately $275.49.

b. When the card is paid off, you will have paid approximately $3,305.88 since January 1.

c. The percentage of your total payment that is interest is approximately 6.3%.

To calculate the monthly payments, we first need to determine the interest rate per month.

Since the APR is 17%, we divide it by 12 to get the monthly interest rate: 17% / 12 = 1.42%.

a. Monthly payments:

To pay off the credit card balance in one year (12 months), we divide the total balance by the number of months:

$3100 / 12 = $258.33 (approximately)

Therefore, your monthly payment should be approximately $258.33.

b. Total amount paid:

To calculate the total amount paid since January 1, we multiply the monthly payment by the number of months (12):

$258.33 * 12 = $3,099.96

Therefore, you will have paid approximately $3,099.96 since January 1.

c. Percentage of payment as interest:

To determine the percentage of the total payment that is interest, we subtract the initial balance from the total amount paid to find the total interest paid:

Total interest = Total amount paid - Initial balance

Total interest = $3,099.96 - $3100

Total interest = $-0.04 (approximately)

The negative value implies that the balance was paid off completely before the end of the year, resulting in a small overpayment.

As a result, there is no interest to calculate as it has been paid in full.

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3√2 and 3 are the values of x and y respectively from the figure.

The given diagram is a right triangle with an acute angle of 45 degrees

We need to determine the values of variables x and y.

Applying the trigonometry identity, we will have:

sin 45 = opposite/hypotenuse
sin45 = 3/x

x = 3/sin45

x = 3/(1/√2)
x = 3√2

Similarly:

tan 45 = opposite/adjacent
tan 45 = 3/y

1 = 3/y

y = 3

Hence the values of x and y from the figure is 3√2 and 3 respectively

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The slope of the tangent to the circle at point A is -3/2.

1. The equation of a circle with center C(2, 7) is given by (x - 2)² + (y - 7)² = r², where r is the radius of the circle.

2. Since point A(8, 17) lies on the circle, we can substitute the coordinates of point A into the equation of the circle to find the value of r.

  (8 - 2)² + (17 - 7)² = r²

  6² + 10² = r²

  36 + 100 = r²

  136 = r²

  r = √136 = 2√34

3. Now that we have the radius, we can find the equation of the tangent line at point A.

  The tangent to a circle at a given point is perpendicular to the radius at that point.

  The slope of the radius can be found using the coordinates of the center and point A.

  Slope of the radius = (17 - 7) / (8 - 2) = 10 / 6 = 5/3

  The slope of the tangent line will be the negative reciprocal of the slope of the radius.

  Slope of the tangent = -1 / (5/3) = -3/5

4. However, the question asks for the slope of the tangent to the circle at point A, so we need to consider the slope of the tangent line at point A, which is the negative inverse of the slope of the radius.

  Slope of the tangent at point A = -1 / (5/3) = -3/5

5. The slope of the tangent to the circle at point A is -3/5.

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The result of the expression 20 - 6 is 14.

To solve the given expression, 20 - 6, and isolate the variable, we need to clarify whether there is an equation involved. However, in this case, the expression does not contain any variable to isolate, and it is not an equation that needs balancing. It is a straightforward arithmetic expression.

Step 1: Start with the given expression, 20 - 6.

Step 2: Evaluate the subtraction operation: 20 - 6 = 14.

Step 3: The simplified expression is now 14. However, since there is no variable present, there is no need to isolate any variable.

This means that when you subtract 6 from 20, the answer is 14. Remember that isolating a variable and balancing an equation are relevant when dealing with equations that involve variables. In this case, the expression is a simple subtraction operation, yielding a constant value of 14 as the answer.

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The values of the missing variables are:

a = 57

b = 75

c = 96

d = 150

We have,

Angle 48 is half the intercepted arc.

So,

1/2 x c = 48

c = 48 x 2

c = 96

Now,

Similarly

Angle a = 1/2 x 114

Angle a = 57

And,

The sum of the angles in a triangle = 180

a + b + 48 = 180

57 + b + 48 = 180

b = 180 - (57 + 48)

b = 180 - 105

b = 75

Now,

Angle b = 1/2 x d

75 = 1/2 x d

d = 75 x 2

d = 150

We can also see that,

114 + c + d = 360

114 + 96 + 150 = 360

360 = 360

Thus,

The values of the missing variables are:

a = 57

b = 75

c = 96

d = 150

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Answer:

074°

Step-by-step explanation:

the bearing of Y from X is the measure of the angle from the north line (N) at X in a clockwise direction to Y , that is ∠ NXY

∠ NXY = 180° - 106° = 74°

the 3- figure bearing of Y from X is 074°

The graph showing a circle with a center (-3, 2) and a radius of 3 does not represent all possible centers for a circle passing through (3, -1) with a radius of 4.

The graph represents a specific circle with its own center and radius.

To find all possible centers for a circle passing through a given point, we need to consider the locus of points equidistant from the given point.

In this case, the locus of points equidistant from (3, -1) with a radius of 4 forms another circle with a different center and radius.

The graph showing a circle with a center (-3, 2) and a radius of 3 does not represent all possible centers for a circle passing through (3, -1) with a radius of 4.

Therefore, neither student's claim is correct based on the given information.

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The probability that the first marble drawn is blue and the second marble drawn is red is 1/4 or 0.25, which can also be expressed as 25%.

To determine the probability of drawing a blue marble on the first draw and a red marble on the second draw, we need to consider the total number of marbles and the number of blue and red marbles in the bag

In this case, we have a bag with 12 blue marbles and 12 red marbles, making a total of 24 marbles.

When drawing the first marble, there is a 12/24 probability of selecting a blue marble since there are 12 blue marbles out of the total 24 marbles in the bag.

After replacing the first marble back into the bag and mixing up the marbles, the probability of drawing a red marble on the second draw is also 12/24, as there are still 12 red marbles remaining out of the total 24 marbles.

To find the overall probability, we multiply the probabilities of each event since they are independent events:

P(first marble is blue and second marble is red) = P(first marble is blue)[tex]\times[/tex]P(second marble is red)

[tex]= (12/24) \times (12/24)[/tex]

[tex]= (1/2) \times (1/2)[/tex]

= 1/4.

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The values of x and y in the figure are 3√2 and 3, respectively.

The diagram shown is a right triangle with a 45-degree acute angle.

The values of variables x and y must be determined.

Using the trigonometry identity, we get:

opposite/hypotenuse = sin 45

sin45 = 3/x

x = 3/sin45

x = 3(1/√2)

x = 3√2

Likewise,

tan 45 = opposite/adjacent

tan 45 = 3/y

1 = 3/y

y = 3

As a result, the values of x and y in the figure are 32 and 3, respectively.

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The equation of the parabola that models the cross section of the reflector is: y = (1/32)x².

To model a cross section of the reflector as a parabola that opens upward and has its vertex at the origin,

We can use the standard equation for a parabola in vertex form:

y = a(x - h)² + k

In this equation, (h, k) represents the coordinates of the vertex.

Since we want the vertex to be at the origin (0, 0), the equation becomes:

y = ax²

To determine the value of 'a,' we can use the given information that the bulb is located 8 inches from the vertex.

Since the bulb is located at the focus, we know that the distance from the vertex to the focus (f) is also 8 inches.

In a parabola, the distance from the vertex to the focus is given by the formula f = 1/(4a).

Plugging in the value of f (8) into the formula, we can solve for 'a':

8 = 1/(4a)

32a = 1

a = 1/32

Therefore, the equation of the parabola that models the cross section of the reflector is: y = (1/32)x²

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1/4 or 0.25 is the probability of both coins landing on heads.

When two coins are tossed, there are four possible outcomes: both coins can land on heads (HH), both coins can land on tails (TT), or one coin can land on heads while the other lands on tails (HT or TH).

To find the probability of both coins landing on heads, we need to determine the number of favorable outcomes (HH) and divide it by the total number of possible outcomes. The number of favorable outcomes is 1 (HH), as there is only one way for both coins to land on heads.

The total number of possible outcomes is 2 * 2 = 4, since each coin has two possible outcomes (heads or tails), and we multiply them together to account for all possible combinations.

Therefore, the probability of both coins landing on heads is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 1 / 4

Simplifying the fraction, we get:

Probability = 1/4

So, the probability of both coins landing on heads is 1/4 or 0.25.

This means that out of all the possible outcomes when two coins are tossed, there is a 1 in 4 chance that both coins will land on heads. It's important to note that the probability assumes fair and unbiased coins, where the chance of heads and tails is equal.

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Answer:  the rock will be at a height of 1,976 feet above the ground after approximately 8 seconds

Step-by-step explanation:

We can start by setting the height function equal to 1,976 and solving for t:

-16t² + 3000 = 1976

Subtracting 1976 from both sides, we get:

-16t² + 1024 = 0

Dividing both sides by -16, we get:

t² - 64 = 0

Factoring, we get:

(t + 8)(t - 8) = 0

So t = 8 or t = -8. We can ignore the negative solution since time cannot be negative.

Therefore, the rock will be at a height of 1,976 feet above the ground after approximately 8 seconds.

Answer: (A) 8 sec

Answer:

x² - y + x = 16 is 1 real solution

3x² - y + 32 = 22x is 2 real solutions

y = -x² + 6x + 12 is 1 real solution

Step-by-step explanation:

sorry i am unsure about rest, they do not have a value. good luck :)

Answer: y = 550x

Step-by-step explanation:

As per the given equation, the value of c guaranteed by the Mean Value Theorem for the function f(x) = √(9 - [tex]x^2[/tex]) over the interval [0, 3] is c = ± √(9/5).

To find the value of c guaranteed by the Mean Value Theorem for the function f(x) = √(9 - [tex]x^2[/tex]) over the interval [0, 3], we need to determine if the conditions of the Mean Value Theorem are satisfied and then find the value of c.

The Mean Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one value c in the open interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a).

In our case, the function f(x) = √(9 - [tex]x^2[/tex]) is continuous on the closed interval [0, 3] since it is a square root function and the radicand is always non-negative within this interval.

The function is also differentiable on the open interval (0, 3) since it is the square root of a differentiable function.

To find the value of c, we first calculate f(3) and f(0):

f(3) = √(9 - [tex]3^2[/tex]) = √(9 - 9) = √0 = 0

f(0) = √(9 - [tex]0^2[/tex]) = √(9 - 0) = √9 = 3

Next, we calculate f'(c):

f'(x) = (-2x)/√(9 - x^2)

We want to find the value of c such that f'(c) = (f(3) - f(0))/(3 - 0). Let's substitute the values into the equation:

(-2c)/√(9 - [tex]c^2[/tex]) = (0 - 3)/(3 - 0)

(-2c)/√(9 - [tex]c^2[/tex]) = -1

To solve for c, we can cross-multiply:

-2c = -√(9 - [tex]c^2[/tex])

Squaring both sides:

4c^2 = 9 - [tex]c^2[/tex]

Simplifying:

5[tex]c^2[/tex] = 9

Dividing both sides by 5:

[tex]c^2[/tex] = 9/5

Taking the square root of both sides:

c = ± √(9/5)

Therefore, the value of c guaranteed by the Mean Value Theorem for the function f(x) = √(9 - [tex]x^2[/tex]) over the interval [0, 3] is c = ± √(9/5).

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Answer:

1/2

Step-by-step explanation:

Slope formula:

[tex] \boxed{ \purple{ \sf \: m = \frac{ y_{2} - y_{1}}{x_{2} -x_{1} } }}[/tex]

P.S. Slope is denoted by letter m

We have;

[tex] \red \implies \green{ \tt \: m = \frac{2 - ( - 4)}{5 - 2} }[/tex]

[tex] \red \implies \green{ \tt \: m = \frac{ \cancel6}{ \cancel3} }[/tex]

[tex] \red \implies \green{ \tt \: m = \frac{ 2}{ 1} = 2} [/tex]

hello

to answer precisely, i have to see the graphs in the question but overall, the answer should look like something like the graph in the attached file

$63 + ($63 · 0.28) = $80.64

[tex]f = p + pm[/tex] where:

[tex]f[/tex] = final price: $80.64,

[tex]p[/tex] = original price: $63,

and [tex]m[/tex] = markup percent (in decimal): 28% → 0.28.

Answer:

[tex]\huge\boxed{\sf \angle AEB=86 \textdegree}[/tex]

Step-by-step explanation:

arc AB = 106°

arc CD = 66°

[tex]\displaystyle \angle AEB=\frac{1}{2} (arc \ AB+arc \ CD)[/tex]

Put the given data in the above formula.

[tex]\displaystyle \angle AEB=\frac{1}{2} (106 + 66)\\\\\angle AEB=\frac{1}{2} (172)\\\\\angle AEB=86 \textdegree \\\\\rule[225]{225}{2}[/tex]

The graph of the function y=cos(x) is shown below:

[Image of the graph of the function y=cos(x)]

The graph of the function y=cos(2x) is shown below:

[Image of the graph of the function y=cos(2x)]

The graph of the function y=cos(4x) is shown below:

[Image of the graph of the function y=cos(4x)]

As you can see, the graph of the function y=cos(4x) is the same as the graph of the function y=cos(x), but it is compressed horizontally by a factor of 4. This is because the period of the function y=cos(4x) is 2π/4=π/2, which is half the period of the function y=cos(x).

Therefore, the correct answer is A.