If f(x)=2x−2 and g(x)=x2−8x+19, then f(x)=g(x) for what values of x?




x=−1 and x=−4


x=−3 and x=−7


x=1 and x=4


x=3 and x=7

The distance from the line x=4 to the given point (-2,5) is 6 units .

Distance formula from line to point :

The distance from the line ax+by+c=0 to the point (u,v) is given by the formula

\(distance=\frac{|au+bv+c|}{\sqrt{a^{2} +b^{2} } }\)

In the given question

the equation of the line is \(x=4\)

taking all the terms to Left side we get

\(x-4=0\)

\(1.x+0.y-4=0\)

given the points (-2,5)

From above values we the values as a=1 , b=0 , c=-4 , u=-2 , v=5 .

Substituting the values in the distance formula we get

\(d=\frac{|1*(-2)+0*(5)-4|}{\sqrt{1^{2} +0^{2} } }\)

\(=\frac{|-2+0-4|}{1} \\ \\ =|-6|\\ \\ =6\)

Therefore , the distance from the line x=4 to the given point (-2,5) is 6 units.

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The standard deviation of the team members' heights is 2.35.

In statistics, the standard deviation of a data set is a measure of the amount of variation or dispersion of the data set. The standard deviation shows how much the data deviates from the mean value.

In the given problem, Brent's height translates to a z-score of -0.85 in the team's height distribution. The z-score formula is as follows: z = (x - μ) / σwhere, z = z-score, x = raw score, μ = mean, σ = standard deviation. Using the above formula,-0.85 = (74 - 76) / σ. Solving for σ,σ = (2) / 0.85σ = 2.35. Therefore, the standard deviation of the team members' heights is 2.35.

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The school will purchase 80 chairs and 10 tables.

A system having more than two equations is known as a system of equations.

Given that, the school can spend $5200 and the cost of one table is $200 and the cost of one chair is $40.

Let x represents the number of chairs purchased and y represents the number of tables purchased.

The total cost of purchasing x chairs and y tables is:

Total cost = 40x + 200y

Since the budget of the school is $5200 only, substitute "Total cost =5200" into the above equation,

5200 = 40x + 200y

Since each table requires 8 chairs, it follows:

x = 8y

Hence, the system of equations is:

5200 = 40x + 200y      (1)

x = 8y                            (2)

To solve the system of equations, substitute x = 8y into equation (1):

5200 = 40(8y) + 200y

5200 = 320y + 200y

5200 = 520y

y = 10

Substitute y = 10 into equation (2):

x = 8(10)

x = 80

Hence, the school will purchase 80 chairs and 10 tables.

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The area of the given trapezoidal site is 250,000 sq. ft.

The area of the trapezoidal with the dimensions of both bases and the height is given by the formula,

Area = 1/2 × height × (base1 + base2)

Units: square units

The given trapezoidal site has a base of 150 feet, i.e., base1 = 150 ft; a height of 2000 ft, i.e., height = 2000 ft and a parallel base of 100 feet, i.e., base2 = 100 ft.

Then, the area of the trapezoidal is

= 1/2 × 2000 × (150 + 100)

= 1/2 × 2000 × 250

= 250,000 sq. ft

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the height of the wall is approximately 84.5 feet, rounded to the nearest tenth of a foot.

We should use the tangent function for this problem.

Let h be the height of the wall. Then we have:

tan(52 degrees) = h / 62

Solving for h, we get:

h = 62 * tan(52 degrees) ≈ 84.5 feet

what is tangent?

In trigonometry, tangent (often abbreviated as tan) is a trigonometric function that relates the ratio of the length of the opposite side to the length of the adjacent side of a right triangle. It is defined as the ratio of the sine of an angle to the cosine of the same angle:

tan(θ) = sin(θ) / cos(θ)

where θ is the measure of an angle in radians or degrees.

Tangent is commonly used to find the measure of an unknown side or angle of a right triangle when given the measure of one side and one acute angle. It is also used in many real-world applications, such as in navigation, surveying, and engineering, to determine the angle of elevation or depression, as well as in calculus to find the slope of a curve at a given point.

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Answer:  the awnser is 43

Step-by-step explanation:

Answer:

25. 64

27. 10,000

Step-by-step explanation:

This is the answer because:

1) Standard form means to write the full number

2) So for 25, all you have to do is multiply 2 x 2 x 2 x 2 x 2 x 2 which is 64

3) For 27, all you have to do is multiply 10 x 10 x 10 x 10 which is 10,000

Hope this helps!

Answer:

Triangle PTS is an equilateral triangle because all sides are equal lengths.

Angle TPS and angle TSP are equal because it is an equilateral triangle.

Triangle PQS and triangle SRP are congruent because of the side-angle-side theorem.

Segment PQ is congruent to segment SR because congruent sides of congruent triangles are congruent.

Segment PR is congruent to segment SQ because congruent sides of congruent triangles are congruent.

Triangle PQR and triangle SRQ are congruent because of the side-side-side theorem.

Δ PQR and  Δ SRQ are congruent By SSS rule .

If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.

Two triangles are said to be congruent if they are of the same size and same shape. There are 5 conditions for two triangles to be congruent. They are SSS, SAS, ASA, AAS, and RHS congruence properties.

According to the question

P, Q, R and S are four points on a circle.

PTR and QTS are straight lines.

Triangle PTS is an equilateral triangle.

In ΔPTS ,

∠PTS = ∠TPS = ∠TSP = 60°

PT = PS = ST

In ΔPQS and ΔSRP

PS = SP (common side of triangle )

∠QSP = ∠RPS = 60°

∠PQS = ∠SRP  ( Angles between same base and parallels are equal)

Therefore,

ΔPQS ≅ ΔSRP    (ASA rule)

PTR = QTS (by CPCT)

PQ = SR (by CPCT)

∠QPS = ∠RSP (by CPCT)

Now , in  Δ PQR and Δ SRQ

PQ = SR (proved above )

QR = QR (common side )

PR = QS (proved above )

Therefore,  Δ PQR ≅ Δ SRQ (By SSS rule)

Hence,  Δ PQR and  Δ SRQ are congruent By SSS rule .

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Given:

Recipe 1: 4 tablespoons lemonade mix and 12 cups of sparkling water

Recipe 2: 4 tablespoons lemonade mix and 6 cups of sparkling water

Recipe 3: 3 tablespoons lemonade mix and 5 cups of sparkling water

Recipe 4: 1/2 tablespoons lemonade mix and 3/4 cups of sparkling water

Asked:

1) For Recipe 1, how many tablespoons lemonade mix per cup of sparkling water?

2) For Recipe 2, how many tablespoons lemonade mix per cup of sparkling water?

3) For Recipe 3, how many tablespoons lemonade mix per cup of sparkling water?

4) For Recipe 4, how many tablespoons lemonade mix per cup of sparkling water?

Solution:

1) Recipe 1

We will divide the cups by 12 to make 1 cup. Then divide 4 by 12 as well.

12 cups = 4 tablespoons

12 cups/12 cups = 4 tablespoons/12 cups

1 cup = 1/3 tablespoon per cup

2) Recipe 2

We will divide the cups by 6 to make 1 cup. Then divide 4 by 6 as well.

6 cups = 4 tablespoons

6 cups/6 cups = 4 tablespoons/6 cups

1 cup = 2/3 tablespoon per cup

3) Recipe 3

We will divide the cups by 5 to make 1 cup. Then divide 3 by 5 as well.

5 cups = 3 tablespoons

5 cups/5 cups = 3 tablespoons/5 cups

1 cup = 3/5 tablespoon per cup

4) Recipe 4

We will divide the cups by 3/4 to make 1 cup. Then divide 1/2 by 3/4 as well.

3/4 cups = 1/2 tablespoons

3/4 cups/3/4 cups = 1/2 tablespoons/3/4 cups

1 cup = 2/3 tablespoon per cup

ANSWERS:

Recipe 1: 1/3 tablespoon per cup

Recipe 2: 2/3 tablespoon per cup

Recipe 3: 3/5 tablespoon per cup

Recipe 4: 2/3 tablespoon per cup

If your height is 5 feet 3 inches and your weight is 120 pounds, then the BMI is 21.23

To calculate your Body Mass Index (BMI), use the following formula:

BMI = weight in kilograms / (height in meters)²

First, convert your height to meters :

5 feet 3 inches = 63 inches

63 inches = 160.02 cm

160.02 cm = 1.6002 meters

Next, convert your weight to kilograms :

120 pounds = 54.43 kg

Now, plug in these values to calculate your BMI:

BMI = 54.43 kg / (1.6002 meters)²

Divide the terms

BMI = 21.23

Therefore, your BMI is approximately 21.23

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Answer:

Point (6, -1) = (x, y)

Slope = -3

The proper linear equation is written in following form: y = mx + b (where m is slope, and b is y-intercept). Since we already have the slope, we need to find the y-intercept, b

So we plug in what we have:

y = mx + b

-1 = (-3)(6) + b, where we solve for b  

-1 = -18 + b  

b = 17

Finally, the equation of the line that passes through point (6, -1) and has a slope of -3 is y = -3x + 17

CP=SP*100÷100+P

so,

CP=10350*100÷100+15

CP=9000

Answer:

solution

Step-by-step explanation:

Let.the cp of TV be RS X

now,CP=SP-profit

or, CP=SP-profit% of Cp (as profit amount =profit % of Cp)

or, x=Rs 10350-15÷100× X

or, x= Rs 10350 _ 3X ÷20

or, x+3x ÷20 =Rs 10350

or, 23x ÷20 = Rs 10350

or, x = 10350×20 divided by 23

Therefore X =Rs 9000

Answer:

value of

a = 1

b = 2

c =1

and equation is

y = x² + 2x + 1

Step-by-step explanation:

Given quadratic equation  y = ax² + bx + c

It has  y-intercept of (0, 1)

thus, point (0,1) will satisfy equation  y = ax² + bx + c.

putting 1 in place of y and 0 in place of x in equation  y = ax² + bx + c we have

1 = a*0² + b*0 + c

c = 1

Thus, equation until now is y = ax² + bx + 1

____________________________________________________

The parabola also goes through the points (2, 9) and (-5, 16)

point (2, 9) will satisfy equation  y = ax² + bx + 1.

putting 9 in place of y and 0 in place of 2 in equation  y = ax² + bx + 1 we have

9 = a*2² + b*2 + 1

9 = 4a+2b+1

=>4a+2b = 9-1 = 8

dividing both side by 2 we have

4a/2+2b/2  = 8/2

=> 2a + b = 4

b = 4-2a

____________________________________________________

The parabola also goes through the points (2, 9) and (-5, 16)

point (-5, 16) will satisfy equation  y = ax² + bx + 1.

putting 9 in place of y and 0 in place of 2 in equation  y = ax² + bx + 1 we have

16 = a*(-5)² + b*(-5) + 1

16 = 25a-5b+1

=>25a-5b = 16-1 = 15

dividing both side by 5 we have

25a/5-5b/5 = 15/5

=> 5a - b = 3

second equation is 5a - b = 3

substituting value of b as 4-2a from first equation we have

5a - (4-2a) = 3

=> 5a - 4+2a = 3

=> 7a = 3+4 = 7

=> a = 7/7 = 1

value of b is 4-2a

substituting value of a as 1 in 4 - 2a we have

b = 4 - 2*1 = 4-2 = 2

Thus,

value of

a = 1

b = 2

c =1

and equation is

y = x² + 2x + 1

The slopes and the y-intercept of a linear function that is represented by the table is: D. the slope is 2/5 and the y-intercept is -1/3.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-2/15 + 1/30)/(-1/2 + 3/4)

Slope (m) = -0.1/0.25

Slope (m) = -0.4 or 2/5.

At data point (-3/4, -1/30) and a slope of 2/5, a linear function in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-1/30) = 2/5(x + 3/4)

y = 2x/5 - 1/3

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The personal banker given lending arrangement, the APR for your cousin's buddies who borrowed $20 and repaid $40 at the end of the month would be 120%

The annual percentage rate (APR) for your cousin's lending arrangement,  to make a few assumptions. That each lending transaction occurs on the first day of the month and is repaid on the last day of the same month. Based on these assumptions, calculate the effective APR as follows:

Calculate the interest charged for a $20 loan over one month:

Interest = $40 (repaid amount) - $20 (loaned amount) = $20

Divide the interest by the loan amount and multiply by 100 to get the monthly interest rate:

Monthly Interest Rate = (Interest / Loan Amount) ×100 = ($20 / $20) ×100 = 100%

Multiply the monthly interest rate by 12 to obtain the annual interest rate:

APR = Monthly Interest Rate ×12 = 100% ×12 = 120%

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Answer:

510

Step-by-step explanation:

please give me a brainlist

Answer:

The remainder is 40.

Step-by-step explanation:

We're applying synthetic division here.

The coefficients of this function are {1, 6, -3, 0}.  The divisor (x + 5) is represented by the monomial divisor -5.

Setting up synthetic division, we get:

-5    1    6    -3    0

            -5   -5   40

      ---------------------

       1     1    -8    40

The remainder is 40.

Answer:

many

a = 0.2

b = 0.7

Step-by-step explanation:

if a÷b is less than 1, then a must be smaller than b, so you can use any two decimals as long as a is the smaller of the two.

Answer:

Step-by-step explanation: y= x -2 i hope this helps

A) f(x) is concave down on the interval (1, 3) and (5, 7).

B) The inflection points are x = 2 and x = 6.

A) To decide the stretches where f(x) is sunken down, we search for the spans on the chart of f'(x) where the subsidiary is diminishing. From the chart of f'(x), we can see that f(x) is curved down in the stretches (1, 3) and (5, 7).

Reply: (1, 3) U (5, 7)

B) To find the intonation points of f(x), we really want to recognize the x-values where the concavity changes on the diagram of f'(x). From the chart, we can see that the concavity changes at x = 2 and x = 6.

Intonation Focuses: 2, 6

For the capability f(x) = - \(x^_4\) -\(5x^_3\)+ 4x - 2:

f is curved up on the stretches (- ∞, 2) and (6, +∞).

f is sunken down on the stretch (2, 6).

The expression focuses happen at x = 2 and x = 6.

Note: The open spans are communicated with regards to x-values, and the articulation focuses are recorded as x-arranges.

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The solution is: 1/7 is the probability of picking an even number and then picking an even number.

Here, we have,

we know that,

Probability = required outcome /all possible outcome

given that,

You pick a card at random. Without putting the first card back, you pick a second card at random. 1 2 3 4 5 6 7.

number of  possible outcome = 7

Let:

A = 1st time pick an even number

B =2nd time pick an even number

so, we get,

There are 3 even numbers in total,

for the 2nd time it will be 2 even numbers in total,

we have,

P(A) = 3/7

and,

P(B) =2/6

we know that,

The intersection between both events is equal to the product of both probabilities since the events are independent.

so, we get,

P (A∩B) = P(A). P(B)

             = 3/7 * 2/6

             = 1/7

Hence, 1/7 is the probability of picking an even number and then picking an even number.

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The correct answer is d. 10 years.

To find out how many years it will take for Jiefei to double her initial investment, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = initial investment
r = interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, Jiefei's initial investment will double, so the final amount (A) will be 2 times her initial investment (P). The interest rate (r) is given as 7.125%, which is equivalent to 0.07125. Since the interest is compounded annually, n = 1.
So the equation becomes:
2P = P(1 + 0.07125/1)^(1*t)
Simplifying the equation:
2 = (1 + 0.07125)^t
Taking the natural logarithm of both sides:
ln(2) = ln(1 + 0.07125)^t
Using the logarithmic property:
ln(2) = t * ln(1 + 0.07125)
Solving for t:
t = ln(2) / ln(1 + 0.07125)
Using a calculator:
t ≈ 9.95 years
Rounding up to the nearest whole number, it will take approximately 10 years for Jiefei to double her initial investment.

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Answer:

y=x+2

Step-by-step explanation:

Brainliest?!?!?!

The equation for the given graph is y=0.8x+2.

The coordinate points from the given graph are (0, 2) and (2.5, 0).

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

The slope from the given graph is, slope = Rise/Run

= 2/2.5

= 0.8

Put, m=0.8 and (0, 2) in y=mx+c

⇒ 2 = 0.8(0) + c

⇒ c = 2

So, the equation is y=0.8x+2

Therefore, the equation for the given graph is y=0.8x+2.

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lim n -> infinity an = 1.

To find the smallest value of M such that |an - 1| < t for all n > M, we can start by manipulating the inequality:

|an - 1| = |(n+1)/(n+2) - 1| = |n - 1| / |n + 2|

Since we want this expression to be less than t, we can write:

|n - 1| / |n + 2| < t

Multiplying both sides by |n + 2|, we get:

|n - 1| < t|n + 2|

We can split this inequality into two cases: n > 2 and n <= 2. For n > 2, we can drop the absolute values to get:

n - 1 < t(n + 2)

Expanding the right-hand side, we get:

n - 1 < tn + 2t

Solving for n, we get:

n > (1 - 2t) / (1 - t)

For n <= 2, we can drop the absolute values and reverse the inequality to get:

1 - n < t(n + 2)

Expanding the right-hand side, we get:

1 - n < tn + 2t

Solving for n, we get:

n > (1 - 2t) / (1 + t)

Therefore, the smallest value of M is the maximum of the values obtained from these two cases:

M = ceil(max((1 - 2t) / (1 - t), (1 - 2t) / (1 + t)))

Now, let's use the limit definition to prove that lim n -> infinity an = 1. We need to show that for any t > 0, there exists an integer N such that |an - 1| < t for all n > N.

Using the expression for an, we can write:

|an - 1| = |(n+1)/(n+2) - 1| = 1/(n+2)

Therefore, we need to find an integer N such that 1/(n+2) < t for all n > N. Solving for n, we get:

n > 1/t - 2

Therefore, we can choose N = ceil(1/t - 2) + 1. Then for any n > N, we have:

n > 1/t - 2

n + 2 > 1/t

1/(n+2) < t

Therefore, lim n -> infinity an = 1.

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Answer:

Step-by-step explanation:

r =  3 km

Ф = 90°

Area of a sector = \(\frac{theta}{360}*\pi *r^{2}\)

                           \(= \frac{90}{360}* 3.14 * 3 * 3\\\\= \frac{3.14*3*3}{4}\\\)

                           = 7.065 sq.km

Answer:

Solution given:

r=3km

area of sector bounded by a 90° arc=90°/360°*πr²

=¼*π*3²

=9/4 π or 7.068km²

is a required answer

\( - 15 + n= - 9 \\ - 15 + 9 = - n \\ - 6 = - n \\ 6 = n\)

Answer:

n = 6

Step-by-step explanation:

Rearrange terms

-15 + n = -9

n - 15 = -9

Add 15 to both sides of the equation

n - 15+15=-9+15

Simplify

n = 6

[RevyBreeze]

Answer:12°C

Step-by-step explanation:

Because the temperature rises +3°C in a hour, and rised for four hours. So it's 3°C*4=12°C.

By conducting this study, you will be able to identify any areas for improvement in the measurement system or operator training. This will help to ensure that the measurements are consistent and accurate, ultimately leading to a better quality product.

To assess measurement system variation among operators using handheld calipers to measure wooden floorboards, you conducted a crossed-gage R&R study using MINITAB software. You had 3 operators use the same calipers to randomly measure 10 wooden floorboards twice, resulting in a total of 60 measurements. The data was stored in a MINITAB worksheet called Floor Board.mwx.

The graphical output of the crossed-gage R&R study will show the amount of variation that is due to the measurement system, as well as the amount of variation that is due to the operators themselves. This will allow you to identify any issues with the measurement system or operator training that may be contributing to the measurement variation.

In MINITAB, you can analyze the data using the crossed gage R&R tool. This will calculate the measurement system variation, operator variation, and the total variation. The results can be presented in a graph or table format, allowing you to easily compare the different sources of variation.

By conducting this study, you will be able to identify any areas for improvement in the measurement system or operator training. This will help to ensure that the measurements are consistent and accurate, ultimately leading to a better quality product.

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The statement sqrt((x-3)^2) = 3 - x is true only when x is not equal to 3. Therefore, option 1) "x is not equal to 3" is the correct answer.

When we simplify sqrt((x-3)^2), we get |x-3|, which represents the absolute value of (x-3). On the other hand, the expression 3 - x represents the negation of x subtracted from 3.

For x ≠ 3, both |x-3| and 3 - x can be positive or negative depending on the value of x. They are not always equal to each other.

However, if we consider x = 3, the expression sqrt((x-3)^2) becomes sqrt(0^2) = 0, and 3 - x becomes 3 - 3 = 0. In this case, both sides of the equation are equal.

Therefore, the equation sqrt((x-3)^2) = 3 - x is not true for all values of x. It is true when x is not equal to 3, but false when x = 3.

Regarding option 2) "-x|x| > 0", it is unrelated to the given equation and does not provide any information about the validity of the equation sqrt((x-3)^2) = 3 - x.

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The equation of the tangent line at x=0 is y = x.

To find the equation of the tangent line at the given value of x, we need to find the derivative of the function y with respect to x and evaluate it at x=0.

Taking the derivative of y=∫[0 to x] sin(2t^2+π/2) dt using the Fundamental Theorem of Calculus, we get:

dy/dx = sin(2x^2+π/2)

Now we can evaluate this derivative at x=0:

dy/dx |x=0 = sin(2(0)^2+π/2)

        = sin(π/2)

        = 1

So, the slope of the tangent line at x=0 is 1.

To find the equation of the tangent line, we also need a point on the line. In this case, the point is (0, y(x=0)).

Substituting x=0 into the original function y=∫[0 to x] sin(2t^2+π/2) dt, we get:

y(x=0) = ∫[0 to 0] sin(2t^2+π/2) dt

      = 0

Therefore, the point on the tangent line is (0, 0).

Using the point-slope form of a linear equation, we can write the equation of the tangent line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Plugging in the values, we have:

y - 0 = 1(x - 0)

Simplifying, we get:

y = x

So, the equation of the tangent line at x=0 is y = x.

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