Moussa is younger than Sophia. Their ages are consecutive even integers. Find Moussa's age if the product of their ages is 24.

The expanded equation of the function f(x) = (3x + 2)⁴ is f(x) = 81x + 216x³ + 216x² + 96x + 16

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

f(x) = (3x + 2)⁴

Using the pascal triangle at n = 4, we have the coefficients to be

Coefficient = 1     4     6     4     1

So, when the function f(x) = (3x + 2)⁴ is expanded, we have

f(x) = 1 * (3x)⁴ + 4 * (3x)³ * 2 + 6 * (3x)² * 2² + 4 * (3x) * 2³ + 1 * 2⁴

Evaluate

f(x) = 81x + 216x³ + 216x² + 96x + 16

Hence, the solution is f(x) = 81x + 216x³ + 216x² + 96x + 16

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Answer:

[tex](x-3)^2+(y+7)^2=\dfrac{361}{13}[/tex]

Step-by-step explanation:

The tangent of a circle is always perpendicular to the radius.

Therefore, the center is on a line that is perpendicular to the tangent.

Rearrange the equation of the tangent to make y the subject:

[tex]\begin{aligned}2x+3y-4&=0\\3y&=-2x+4\\y&=-\dfrac{2}{3}x+\dfrac{4}{3}\end{aligned}[/tex]

Therefore, the slope of the tangent line is -²/₃.

If two lines are perpendicular to each other, their slopes are negative reciprocals.  Therefore, the slope of the perpendicular line is ³/₂.

To write the equation of the line perpendicular to the tangent, substitute the found slope and the center point into the point-slope formula:

[tex]\begin{aligned}y-y_1&=m(x-x_1)\\\implies y-(-7)&=\dfrac{3}{2}(x-3)\\y+7&=\dfrac{3}{2}x-\dfrac{9}{2}\\y&=\dfrac{3}{2}x-\dfrac{23}{2}\end{aligned}[/tex]

The point on the circle is the point of intersection of the tangent line and the perpendicular line.  

To find the point of intersection, substitute the equation for the perpendicular line into the equation for the tangent line:

[tex]\implies \dfrac{3}{2}x-\dfrac{23}{2}=-\dfrac{2}{3}x+\dfrac{4}{3}[/tex]

[tex]\implies \dfrac{13}{6}x=\dfrac{77}{6}[/tex]

[tex]\implies x=\dfrac{77}{13}[/tex]

Substitute the found value of x into one of the linear equations and solve for y:

[tex]\implies y=-\dfrac{2}{3}\left( \dfrac{77}{13} \right)+\dfrac{4}{3}[/tex]

[tex]\implies y=-\dfrac{34}{13}[/tex]

Therefore, the point of intersection and hence the point on the circle is:

[tex]\left( \dfrac{77}{13}, -\dfrac{34}{13}\right)[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

To find r², substitute the given center of the circle (3, -7) and the found point into the equation of the circle:

[tex]\implies \left(\dfrac{77}{13} -3 \right)^2+ \left(-\dfrac{34}{13}+7\right)^2=r^2[/tex]

[tex]\implies \left(\dfrac{38}{13} \right)^2+ \left(\dfrac{57}{13}\right)^2=r^2[/tex]

[tex]\implies \dfrac{1444}{169} + \dfrac{3249}{169}=r^2[/tex]

[tex]\implies \dfrac{4693}{169}=r^2[/tex]

[tex]\implies \dfrac{361}{13}=r^2[/tex]

Therefore, the equation of the circle whose center is P(3, -7) and tangent to 2x+3y-4=0 is:

[tex]\boxed{(x-3)^2+(y+7)^2=\dfrac{361}{13}}[/tex]

Answer:

just write the value of y in the y table and replace x with the given value above : for example if x is -4

then,

y = 20*(-4)-5

Answer:

the ture was

0.6 • 25 = x

6/10=x/25

x/25=60/100

the fault

6.0 • 25 = x

x • 1.6 = 25

60/100=25/x

Therefore, the correct answer is 3,375 miles, or option (d) is the correct option.

To find out how far Paul will drive in 15 days, we need to determine his average distance per day and then multiply that number by 15. To find Paul's average distance per day, we can divide the total distance he drove in 3 days by the number of days:

675 miles / 3 days = 225 miles/day.

So Paul drives an average of 225 miles per day. If he continues to drive this same distance every day, he will drive 225 miles/day * 15 days = <<225*15=3375>>3,375 miles in 15 days.

The total distance something has traveled is divided by the total amount of time it took to traverse that distance to arrive at its average speed. Speed is the current rate of movement of something. Average speed is the speed that a vehicle travels at on average over the course of a trip.

A moving object's average speed is calculated by dividing its total distance traveled by its entire travel time. Distance traveled divided by average speed Overall Time. Meter per second is the S.I. unit of speed. KPH, or kilometers per hour, is another unit of speed.

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Answer:

Step-by-step explanation:

big oily men like u

Answer:

M:48
A:12

Step-by-step explanation:

M=4A
M-8=(A+8)2
M=2A+24
4A=2A+24
2A=24
A=12
M=48

The measure of the angle D and F can be calculated form the total measure of the Angle of the triangle that is 180.

In the triangle DEF, F is 120 degree and F is 4/3rd of E. A straight angle is just a straight line which is where it gets its name. the sum of a triangles angles 180. It is proved by angular defect and triangles area. The angle sum of a triangle will always be equal to 180°. The angle sum of a quadrilateral is equal to 360°, and a triangle can be created by slicing a quadrilateral in half from corner to corner. Since a triangle is essentially half of a quadrilateral, its angle measures should be half as well.

Angle F = 120 degree

F= 4/3 E

E= 90 degree

The sum of the angle is 180. so,

D + E + F = 180

Putting all the values we can find the measure of angle D and Angle E.

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Step-by-step explanation:

to be a triangle the sum of any 2 sides must be larger than the third side.

so,

x + 10 > 18

x + 18 > 10

18 + 10 > x

the first inequality gives us

x > 8

the third inequality gives us

28 > x

the second inequality would give us

x > -8

but with the first inequality x > 8 we have already a stronger criteria than x > -8 (if x > 8 is true, then so is automatically x > -8, but not the other way around).

therefore x > 8 is the narrower criteria and answer.

so, we have in combination

8 < x < 28

The appropriate alternative hypothesis is the opposite of null hypothesis that there is a difference in mean SSHA scores between men and women.

The alternative hypothesis is the opposite of the null hypothesis, which is typically stated as there being no difference between the two groups. In this example, the null hypothesis is that there is no difference in mean SSHA scores between men and women. The alternative hypothesis is then that there is a difference in mean SSHA scores between men and women. This can be stated as "There is a difference in mean SSHA scores between men and women". This is the appropriate alternative hypothesis for this test of significance.

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Answer:

The answer is that there are 2 green pins and 5 yellow pins remaining in the bag.

Step-by-step explanation:

There are 3 green pins in the bag at the start and Yaqub gives one to his sister, so there are 3 - 1 = <<3-1=2>>2 green pins remaining in the bag. The rest of the pins in the bag must be yellow, so there are 2 green and 7 - 2 = <<7-2=5>>5 yellow pins remaining in the bag.

Answer:2 green 5 yellow

Step-by-step explanation:

Answer:

Step-by-step explanation:

To plot the positive rational numbers on the number line, you can use the following steps:Start by drawing a number line, with 0 at the left end and positive numbers increasing as you move to the right.Place the first number, 12, on the number line. You can place it to the right of 0, since it is a positive number.Place the next number, 134.16, to the right of 12. You can place it farther to the right, since it is a larger number.Place the next number, 310/8, to the right of 134.16. Since 310/8 is equal to 38.75, you can place it slightly to the right of 134.16, but still to the left of 39.Place the next number, 0, at the left end of the number line, since it is equal to 0.Place the next number, 1, to the right of 0, since it is a positive number.Place the next number, -2.05, to the left of 0, since it is a negative number.Place the final two numbers, 2 and 3, to the right of 1, since they are both positive numbers.The resulting number line should look something like this:-2.05 0 1 2 3 12 134.16 38.75 (310/8)

The correct equation is p - 53 = 118.

⇒ p - 53 = 118

Therefore, the correct equation is p - 53 = 118.

Answer:

C. detail-oriented

Step-by-step explanation:

Haute cuisine is typically characterized by careful preparation and detail-oriented presentation.

Answer:

0

Step-by-step explanation:

Answer: y = 35/4

Step-by-step explanation:

combine like terms: -

12y = -3y - 35 - 5y

-12y = -8y - 35

Add 8y to both sides

-12y = -8y - 35

Simplify

-4y = -35

Divide both sides by the same factor

-4y = -35

-4y/-4 = -35/-4

Simplify

y = 35/4

Hope that helps :)

-Amria

The number which would be the next in the sequence of number is sixty-four i.e., 64.

In mathematics, a geometric progression is a sequence of non-zero numbers where each term after the first multiplies the previous term by a fixed non-zero number called the common ratio. In other words, a geometric progression has consecutive terms with a common ratio. Example: a , a², a³, ..., where aₙ₊₁/aₙ= a

We have , Jamie noted the following sequence: 4, 8, 16, 32, . .. on a sheet of paper. After careful study of the sequence we have provided, is a geometric sequence and the ratio between consecutive terms in the geometric sequence is : (8/4), (16/8), ....

= 2, 2, .....

We have to locate the next number in sequence. To find the next term in a geometric sequence, simply multiply the last term given by the common ratio of the sequence. So, the next number in the sequence is 32 × 2 = 64. Hence, required number is 64.

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Complete question:

Jamie wrote out the following sequence of numbers: 2, 6, 14, 30,...on a sheet of paper. What number would be the next in the equence of number?

Two triangles are similar when the corresponding angles are congruent, and the corresponding sides are proportional. Hence, option D is the most appropriate answer to the given question.

When we are given triangles, we can prove that two triangles are congruent with the given conditions by applying various tests of congruency. whereas to prove them to be similar we can use various tests of similarity.  

Similar triangles are triangles that have the same shape, but they may have different sizes.

Hence, to prove the two triangles to be similar, we have to prove the corresponding angles to be congruent and the corresponding sides to be proportional and not proportional. Hence, option D is the only right choice for the given question.

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Answer:

[tex]x=60[/tex]

Step-by-step explanation:

[tex]3x=180\\x=\frac{180}{3} \\x=60[/tex]

Answer: x^2 - 2x + y^2 - 6y + 10 = 0.

Step-by-step explanation: The power station is located 1 mi west and 3 mi north of the center of town, which means that it is located at the point (1, 3) on the coordinate plane. The power outage affected all homes and businesses within a 5 mi radius of the power station, which means that the furthest points from the station affected by the power outage are located on a circle with a radius of 5 mi.

The equation of a circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

Substituting the values for the center of the circle (h, k) = (1, 3) and the radius r = 5, the equation of the circle consisting of the furthest points from the power station affected by the power outage is:

(x - 1)^2 + (y - 3)^2 = 5^2

This simplifies to:

x^2 - 2x + 1 + y^2 - 6y + 9 = 25

Combining like terms, the equation becomes:

x^2 - 2x + y^2 - 6y + 10 = 0

This can be written in standard form as:

x^2 - 2x + y^2 - 6y + 10 = 0

Therefore, the equation of the circle consisting of the furthest points from the power station affected by the power outage is x^2 - 2x + y^2 - 6y + 10 = 0.

Answer:
He can waste 4,575 a month

Step-by-step explanation:

A dot plot is a graph of each data value plotted as a point.

In the given question, we have to fill in the blanks.

A _______ is a graph of each data value plotted as a point.

As we know that;

Data points are represented as dots on a graph with an x- and y-axis in a dot plot, sometimes referred to as a strip plot or dot chart, which is a straightforward type of data visualisation.

These kinds of graphs are employed to visually represent particular data trends or groupings. The distribution of a collection of data is shown by a dot plot, which is comparable to a histogram in that it shows the proportion of data points that fall into each category or value on the axis.

Hence, a dot plot is a graph of each data value plotted as a point.

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Answer: B. 73 degree

Step-by-step explanation:

We know that a triangle has 180 degree

62 + 84 = 146 degree

180 - 146 = 34 degree

34 degrees is the angle inside the triangle. The inside angle must add with the outside angle = 180 degree

So the outside angle is

2x = 146

x = 73

2; <3 is congruent to <6. Option B is correct.

Angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Given that Corey is making a wall-mounted bookshelf.

It has 2 shelves, with a third piece of wood intersecting them. to support the shelves, corey orders some l-brackets to put between the shelves and the crosspiece.

To find a congruent angle you must find what can fit inside the giving number the best. If we compare all of the answer is wouldn't make sense, since 7 is greater than 6 it would be wrong. So, A is Incorrect.

C is about 3 and 7. C would fit but 7 wouldn't. So, C is incorrect.

D has both 2 and 3 but also have 4 and 7 which wouldn't match. So, D is incorrect.

Hence, option B is correct,  2; <3 is congruent to <6.

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Leah currently has 14.55 out of the total of 48.50, which is approximately 30% of the total amount.

To calculate the exact percentage, you would divide 14.55 by 48.50 and then multiply the result by 100. If you do this, you find that Leah has exactly 29.941%, which rounds up to 30%.

The remaining amount of money that Leah needs to buy the necklace is 33.95, which is approximately 70% of the total. To calculate the exact percentage, you would divide 33.95 by 48.50 and then multiply the result by 100. If you do this, you find that Leah needs exactly 69.907%, which rounds down to 69%.

Therefore, Leah currently has 30% of the total amount of money needed for the necklace, and she needs 69% of the total amount of money to buy the necklace for her mother's birthday.

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The formula which would be best to find the length of line segment CD as required in the task content is; Distance Formula or Pythagorean Theorem.

It follows from the task content that the formula which is best for determining the length measure of a given line segment is to be determined.

On this note, recall that given two endpoints of a line, the distance between the two points, otherwise termed the length of the line is given by the formula;

Distance, D = √ { ( y₂ - y₁ )² + ( x₂ - x₁ )² }

Also, the distance formula is a modification of the Pythagorean theorem.

Ultimately, the formula required to determine the length of CD is; Distance Formula or Pythagorean theorem.

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Answer:

Check the image for step-by-step answer

Answer:

here is the answer:

Step-by-step explanation:

the answer is 45

Answer:

45

Step-by-step explanation:

3x3x3+18

=45