what is 7 x + 7 = 2 x - 8​

Answer:

(7x+7 )(x+1 )

Step-by-step explanation:

7x²+14x+7

(7x+7 )(x+1 )

7x²+7x+7x+7

7x²+14x+7

Answer: 7(1+x)^2

Step-by-step explanation: I got it wrong because of that person at the top your welcome

There were 17 students in the group, and each student paid the same whole number of dollars for the concert tickets.

To determine the number of students in the group, we need to find a whole number that is greater than 2 and less than 20, and when multiplied by another whole number, results in a product of $391.
First, let's list some factors of 391:
1 x 391 = 391
17 x 23 = 391

Since we are looking for a number of students, we can eliminate the factorization of 1 x 391 because that would mean there is only one student in the group, which contradicts the condition in the question.
Now, let's consider the factorization of 17 x 23. In this case, the number of students in the group would be the smaller factor, which is 17. Therefore, there were 17 students in the group.
To summarize, there were 17 students in the group, and each student paid the same whole number of dollars for the concert tickets.

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Answer:

Hello,

Step-by-step explanation:

Since for all real x, f(x)=-f(x),

the function is odd.

Answer:

0.3429 is a decimal and 34.29/100 or 34.29% is the percentage for 12/35.

Answer:

24 : 70

Step-by-step explanation:

12 : 35

Multiply each side by 2

12*2  : 35*2

24 : 70

The correct option is -2. The range of function is found to be minimum is -2.

A function's global minimum is its lowest value across the entire function's range, whereas a localized minimum is its lowest value within a specific local area.

From the given graph of the function:

To get the lowest point of the range of the function, check the value where graph is turning.

This, shows the minima of the function which is -2 at x = 3.

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The complete question is attached-

Answer:

\(\frac{2}{7}\)

Step-by-step explanation:

Another name for 1 is \(\frac{7}{7}\)

\(\frac{7}{7}\) - \(\frac{5}{7}\) = \(\frac{2}{7}\)

Answer:An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.

Step-by-step explanation:basically its more than 90 degrees

Answer:

An obtuse triangle is a triangle where one of the interior angles measures more than 90°

The function f(x,y) = 6 + x ln(xy-7) is differentiable at the point (4,2).

We can find the partial derivative fx(x,y) by applying the chain rule of differentiation to the function f(x,y) = 6 + x ln(xy-7), as follows:

fx(x,y) = ln(xy-7) + x(1/(xy-7))(ydx/dx)

= ln(xy-7) + 1/(y-7)*x

where dx/dx = 1 is the derivative of x with respect to itself. Similarly, the partial derivative fy(x,y) can be obtained as:

fy(x,y) = x(1/(xy-7))(xdy/dy)

= x/(xy-7)

where dy/dy = 1 is the derivative of y with respect to itself.

To show that fx and fy are continuous at the point (4,2), we need to evaluate them at that point and show that the resulting values are finite. Substituting x = 4 and y = 2 into the equations for fx and fy, we get:

fx(4,2) = ln(1) + 1/(2-7)4 = -4/5

fy(4,2) = 4/(42-7) = -4/3

Since both fx(4,2) and fy(4,2) are finite, we can conclude that the partial derivatives of f exist and are continuous at (4,2).

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Complete Question:

Explain why the function is differentiable at the given point.

f(x, y) = 6 + x ln(xy − 7), (4, 2)

The partial derivatives are fx(x, y) =

and fy(x, y) =

The optimal strategy is to pick door 1 and stay - this will give you a 50 percentage chance of winning the car.

The optimal strategy to win the game show is to pick door 1 initially and stay. This is because door 1 has the car 50% of the time, which is the highest chance of any of the three doors. If you switch to a different door, then you would have a 40% chance of winning if you switched to door 2, and a 10% chance of winning if you switched to door 3. Since door 1 has the highest chance of having the car, it is the optimal choice to initially select door 1 and stay. By doing so, you have a 50% chance of winning the car.

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The number of ways 9 yellow marbles can be divided among 4 distinguishable cups is 126.

Dividing 9 marbles among 4 cups is a combination problem. The number of combinations is given by the formula C(n + r - 1, r - 1), where n is the number of items (marbles) and r is the number of groups (cups). In this case, n = 9 and r = 4. Plugging these values into the formula, we get:

C(9 + 4 - 1, 4 - 1) = C(12, 3) = (12 * 11 * 10) / (3 * 2 * 1) = 220

This means that there are 220 ways to divide 9 yellow marbles into 4 distinguishable cups. However, since the cups are distinguishable, each combination is counted multiple times, once for each permutation of the cups. The number of permutations of n items taken r at a time is given by the formula n! / (n - r)!. In this case, the number of permutations is 4! = 4 * 3 * 2 * 1 = 24.

So, the total number of ways to divide 9 yellow marbles into 4 distinguishable cups is 220 / 24 = 9. This means that there are 126 distinct ways to divide 9 yellow marbles among 4 distinguishable cups.

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Answer:

pic 1 goes first second pic second slot

Step-by-step explanation:

The sum of 17.25 and 1.725, to the nearest integer, is 19.

First, let's add the two numbers together: 17.25 + 1.725 = 19.975

Next, we need to round the sum to the nearest integer. To do this, we need to look at the tenths place of the number. Since the tenths place is a nine, we need to round up to the nearest integer.

In this case, the nearest integer is 19.

To check our answer, we can add the two numbers together again using a calculator and confirm that the answer is 19.

To make sure we understand how to round to the nearest integer, let's look at another example. If we add 3.45 + 2.735, the sum is 6.185.

Looking at the hundredths place, we see that it is a five. Since five is greater than or equal to five, we need to round up to the nearest integer.

In this case, the nearest integer is 7.

To check our answer, we can add the two numbers together again using a calculator and confirm that the answer is 7.

In summary, to round a number to the nearest integer, we need to look at the tenths place. If the tenths place is greater than or equal to five, we round up to the nearest integer. If it is less than five, we round down to the nearest integer.

Therefore, the sum of 17.25 and 1.725, to the nearest integer, is 19.

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The sum of 17.25 and 1.725 is 18.975. To the nearest integer, this number is rounded up to 19.

Rounding to the nearest integer involves finding the closest whole number to a decimal or fractional number. When the decimal portion of a number is greater than or equal to 0.5, the number is rounded up to the next whole number. When the decimal portion of a number is less than 0.5, the number is rounded down to the previous whole number. In this case, the decimal portion of 18.975 is greater than 0.5, so the number is rounded up to 19.

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The probability that a randomly selected registered voter who is a Republican believes that global warming is a serious issue is 0.44 or 44%.

Let A be the event that the selected voter is a Republican, and B be the event that the selected voter believes that global warming is a serious issue.

We need to find P(B|A), the conditional probability of B given A.

Using the information given in the table, we can fill in the following probabilities:

P(A) = 500/1200 = 5/12 (since there are 500 registered voters who are Republicans out of a total of 1200 registered voters)

P(B) = 790/1200 = 79/120 (since there are 790 registered voters who believe that global warming is a serious issue out of a total of 1200 registered voters)

P(A and B) = 220/1200 (since there are 220 registered voters who are Republicans and believe that global warming is a serious issue out of a total of 1200 registered voters)

Then, we can use the formula for conditional probability:

P(B|A) = P(A and B) / P(A)

P(B|A) = (220/1200) / (5/12)

P(B|A) = 0.44

Therefore, the probability is 0.44 or 44%.

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_____The given question is incomplete, the complete question is given below:

what is the probability that a randomly selected registered voter who is a republican believes that global warming is a serious issue?

Opinions on Global Warming Nonissue Serious Concern Total Democratic 50 450 500 Political Party Republican 280 220 500 Independent 80 120 200 Total 410 790 1200

Answer:

5/8 yards

Step-by-step explanation:

Amount Used: 3/8 yard

Amount Remaining : 1/4

Amount started with  = Amount Used + Amount Remaining

We need to find the common denominator for 8 and 4.

3/8 stays 3/8, and 1/4 becomes 2/8    (multiply the numerator and                      

                                                                denominator of 1/4 by 2)

3/8 + 2/8 = 5/8

-Chetan K

Answer:

b) 5/8 yard

Step-by-step explanation:

3/8 of the spool is used to make a bow.

She has 1/4 left. 1/4 = 2/8.

2/8 + 3/8 = 5/8

The ladder reaches approximately 0.314 meters up the wall.

To find the exact height that the ladder reaches up the wall, we can use trigonometry.

Given:

The ladder has a length of 6 meters.

The angle between the ground and the ladder is 3 degrees.

Let's denote the height the ladder reaches up the wall as h.

In a right triangle formed by the ladder, the height h, and the base of the triangle (the distance from the wall to the ladder's base), we have the following:

sin(theta) = opposite/hypotenuse

sin(3) = h/6

To find h, we can rearrange the equation:

h = sin(3) * 6

Using a calculator, we can evaluate sin(3) to be approximately 0.05234.

Therefore, the height that the ladder reaches up the wall is:

h = 0.05234 * 6

h ≈ 0.314 meters

So, the ladder reaches approximately 0.314 meters up the wall.

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The function y(t) = (a/k) * e^(kt) is the solution to the given differential equation dy/dt = k(a*y - 1).

The given differential equation is dy/dt = k(a*y - 1). To find which of the given functions is a solution, we need to substitute each function into the differential equation and check if the equation holds true.

Let's consider the given functions:

a) y(t) = a^2 * e^(kt) - This function is not a solution to the differential equation because when we substitute it into the equation, we don't get a valid equality. The left side becomes dy/dt = a^2 * k * e^(kt), while the right side becomes k(a * (a^2 * e^(kt)) - 1). These two expressions are not equal, so this function is not a solution.

b) y(t) = (a/k) * e^(kt) - This function is a solution to the differential equation. When we substitute it into the equation, the left side becomes dy/dt = k * (a/k) * e^(kt) = a * e^(kt), and the right side becomes
k * (a * ((a/k) * e^(kt)) - 1) = a * e^(kt). Since the left side and the right side are equal, this function satisfies the differential equation and is a solution.

Therefore, the function y(t) = (a/k) * e^(kt) is the solution to the given differential equation dy/dt = k(a*y - 1).

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Answer:

Option A.

Step-by-step explanation:

The general transformation works as follows:

T<a,b>(x, y) = (x + a, y + b)

Then for our transformation, we will have:

T<0,7>(x, y) = (x, y + 7)

So now that we know how the transformation works, we need to apply it to the vertices.

Looking at the graph we can see that the vertices are:

X = (-4, -5)

W = (-3, -3)

L = (-5, -2)

Then the new points will be:

X' = (-4, - 5 + 7) = (-4, 2)

W' = (-3, -3 + 7) = (-3, 4)

L' = (-5, -2 + 7) = (-5, 5)

Then the correct option is A.

Answer:

∠ BCA = 75°

Step-by-step explanation:

∠ ABC = 90° ( angle in a semicircle )

then the 2 remaining angles in Δ ABC = 90° , that is

∠ BAC + ∠ BCA = 90° ( ∠ BCA = 5 × ∠ BAC )

∠ BAC + 5 ∠ BAC = 90°

6 ∠ BAC = 90° ( divide both sides by 6 )

∠ BAC = 15°

Then

∠ BCA = 90° - 15° = 75°

Step-by-step explanation:

\(2x + 3y = 12 \\ 3y = - 2x + 12 \\ y = - \frac{2}{3} x + 4\)

slope is -2/3

y intercept is 4

Answer:

The slope is -2/3 and the y intercept is 4

Step-by-step explanation:

2x + 3y = 12

Slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

2x + 3y = 12

Subtract 2x from each side

2x-2x+3y = -2x+12

3y = -2x+12

Divide by 3

3y/3 = -2x/3 +12/3

y = -2/3 x +4

The slope is -2/3 and the y intercept is 4

The rate of change, in square inches per second, of the area of the region at the instant when R is 44 inches and r is 33 inches is

8363 square inches

The rate of change is the derivative, the rate of change is calculated by differentiation the area

formula for area of concentric circle is given by

Area A = π(R^2 - r^2) =

R = radius of the inner circle

r = radius of the outer circle

δA/δt = δA/δRδr * δRδr/δt

δA/δt = π * (2RδR/δt - 2rδr/δt)

δA/δt = π * 2(R * δR/δt - r * δr/δt)

where R = 44 and δR/δt = 22

r = 33 and δr/δt = -11

= 2π(44 * 22 - 33 * -11)

= 2π (968 - -363)

=  2π (1331)

= 2662π

= 8362.9196 square inches

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Answer:

1: 5/6

2: 3 1/6

3: 12/25

hope this helps!!

p.s

    comment if wrong

The radius of a circle having the equation x² + y² + 8x - 6y + 21 = 0 is 2  units .

In the question ,

it is given that ,

the circle is having the equation ⇒ x² + y² + 8x - 6y + 21 = 0 ,

we know that ,

general equation of circle is written as x² + y² + 2fx + 2gy + c = 0 ;

so , radius of circle is calculated using the below formula ,

radius = √(f² + g² - c)

On comparing,  given equation of circle with general equation of circle ,

we get , the values of f = 4 and g = -3 .

So after substituting the values of f , g and c in the radius formula ,

we get ,

radius = √(16 \(+\) 9 - 21)

= √(16 \(+\) 9 - 21)

= √(25 - 21) = √4 = 2 .

Therefore , the given circle has radius = 2 units .

The given question is incomplete , the complete question is

What is the radius of a circle whose equation is x² + y² + 8x - 6y + 21 = 0  ?

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Answer:

Quadratic formula – is the method that is used most often for solving a quadratic equation. If you are using factoring or the quadratic formula, make sure that the equation is in standard form.

There are three basic methods for solving quadratic equations: factoring, using the quadratic formula, and completing the square.

Step-by-step explanation:

The thickness of the given circle made of the sample gold is 77.4 microns.

We know, the density of a material is the ratio of the mass of the material to the volume of the material.

Density = mass/volume

Therefore, volume = mass/density

Here, the density of the gold = 19.3 gm/cm³

Mass of the gold is = 285 mg = 0.285 gm

Therefore, the volume of the given gold is

= mass/density

= 0.285/19.3 cm³

= 0.0148 cm³

The circular sheet of gold has a radius of 0.78 cm.

Therefore, the area of the circular sheet is

= πr² cm²

= π(0.78)² cm²

= 1.911 cm²

Therefore, the thickness of the circular sheet is

= volume of the sheet/ area of the sheet

= 0.0148 cm³/ 1.911 cm²

= 7.74 × 10⁻³ cm

= 7.74 × 10⁻⁵ m

= 77.4 × 10⁻⁶ m

= 77.4 microns

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Answer:

2x + y = 4

Step-by-step explanation:

2x + y = 9 => y = -2x + 9

Parallel lines have the same slope so m = -2

Given (-1,6)

y = mx + b

6 = -2(-1) + b

6 = 2 + b

b = 4

so y = -2x + 4 or 2x + y = 4

The appropriate sample size for the population is 170.

Given that,

The students are conducting a survey about which teacher the students admire the most.

The population is the 300 students in the fifth and sixth grades.

We have to find the appropriate sample size for the population.

Here, it is conducting a survey.

Let confidence level be 95% and the margin of error be 5%.

Then sample size = 169 using the theorem.

So here sample size close to 169 is 170.

Hence the sample size is 170.

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The complete question is,

The students are conducting a survey about which teacher the students admire the most. The population is the 300 students in the fifth and sixth grades. What is an appropriate sample size for the population?

A. 10 B. 45 C. 170 D. 300

The interval the value of the function (f - g)(x) is negative is (-∞, 2]

A function is a rule or definition that maps an input variable unto an output such that each input has exactly one output.

The equations on the possible graphs in the question, obtained from a similar question posted online are;

f(x) = x - 3

g(x) = -0.5·x

(f - g)(x) = x - 3 - (-0.5·x) = 1.5·x - 3

(f - g)(x) = 1.5·x - 3

Therefore; The x-intercept of the function (f - g)(x) = 1.5·x - 3 is; (f - g)(x) = 0 1.5·x - 3

1.5·x - 3 = 0

1.5·x = 3

x = 3/1.5 = 2

x = 2

The y-intercept is the point where, x = 0, therefore;

(f - g)(0) = 1.5×0 - 3 = -3

The interval the function is negative is therefore;

The equations of the possible graphs of the function, obtained from a question posted online are;

f(x) = x - 3, g(x) = -0.5·x

The interval the function (f - g)(x) is negative is required

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Answer:

function

Step-by-step explanation:

no repeated domain means its a function