Write The Polynomial In Standard Form. Then Identify The Leading Term And The Constant Term. Select The (2024)

Given:-

[tex]f(x)=9.2(x)+11[/tex]

To find:-

[tex]f(12)[/tex]

So to find the required value. we substitute 12 for x. so we get,

[tex]\begin{gathered} f(x)=9.2(x)+11 \\ f(12)=9.2(12)+11 \\ f(12)=110.4+11 \\ f(12)=121.4 \end{gathered}[/tex]

So the required solution is 121.4

The Solution:

The correct answer is Yes, they are congruent.

Given the two triangles in the picture on the Question section.

We are asked if triangle ABC is congruent to triangle DEF (Answer Yes or No with an explanation of your answer).

Explanation:

[tex]\begin{gathered} AB\cong DE\text{ (Reason: same marks on the length)} \\ \\ BC\cong EF\text{ (same marks)} \\ \\ \angle B\cong\angle E=90^o \\ \end{gathered}[/tex]

By congruency theorem of Side-Angle-Side, it follows that:

[tex]\Delta ABC\cong\Delta DEF[/tex]

Therefore, the correct answer is Yes, both triangles are congruent.

Given:

[tex]c_n=n(n+1)[/tex]

Required:

To find the first four terms of the sequence.

Explanation:

The first term is,

When n=1,

[tex]\begin{gathered} c_1=1(1+1) \\ =1\times2 \\ =2 \end{gathered}[/tex]

When n=2,

[tex]\begin{gathered} c_2=2(2+1) \\ =2\times3 \\ =6 \end{gathered}[/tex]

When n=3,

[tex]\begin{gathered} c_3=3(3+1) \\ =3\times4 \\ =12 \end{gathered}[/tex][tex]undefined[/tex]

Answer:

The scatterplot appears to have a positive correlation.

Here's why:

We can generally draw a direct line on the scatterplot. See below:

As we can see above, the data points are following a trend wherein as x-increases, y-increases. Although some data points may deviate a little lower or a little higher than the line, they still follow the trend of the line which is towards the northeast (positive correlation).

Step-by-step explanation:

Let the missing angle be x

The sum of the angles in a right angle triangle is 90 degrees

49.1 + x = 90

Subsr

Given

[tex]x^3−x^2−4x+4[/tex]

EXPLANATION

Part 1: Since the constant in the given equation is 4,the integer root must be a factor of 4. The possible values are

Answer:

[tex]\pm1,\pm2,\pm4[/tex]

Part 2: The remainder theorem says when a polynomial a(x) is divided by a linear polynomial b(x) whose zero is x = k, the remainder is given by r = a(k). In this case for one of the possible values to be a root, it must give a zero result when inserted in the original expression.

Therefore,

[tex]\begin{gathered} when\text{ }x=1 \\ f(1)=1^3-(1)^2-4(1)+4=1-1-4+4=0 \\ when\text{ }x=2 \\ f(2)=2^3-(2)^2-4(2)+8=8-4-8+4=0 \end{gathered}[/tex]

Answer: Therefore, 1 and 2 are roots of the polynomial

Part 3:

Let the last factor of the polynomial be ax+b

Therefore,

[tex]\begin{gathered} (x-1)(x-2)(ax+b)=x^3-x^2-4x+4 \\ By\text{ comparison of terms} \\ ax^3=x^3 \\ \therefore a=1 \\ Also \\ 2b=4 \\ b=\frac{4}{2}=2 \end{gathered}[/tex]

The factors of the equation are therefore;

Answer: (x-1)(x-2)(x+2)

The correlation coefficient is used to find how strong a relationship is between data. We have, as a general rule the following:

1) r=1 indicates a strong positive relationship

2) r= -1 indicates a strong negative relationship

3)r=0 indicates no relationship at all.

In this case we have:

Experiment 1: r=0, therefore, there is no relationship

Experiment 2: r=0.28, here we have a weak linear relationship (since it's closer to 0)

Experiment 3: r=0.82, there is a strong positive relationship

Experiment 4: r=0.73, here we have a somewhat strong positive relationship

Answer:

The radius is changing at a rate of 2 cm/s

Explanation:

Here, we want to get the rate at which the radius of the balloon is changing

Mathematically, the formula for the volume of a sphere is:

[tex]\begin{gathered} V\text{ = }\frac{4}{3}\times\pi\times r^3^{}^{} \\ \\ \frac{dv}{dr}\text{ = 4}\times\pi\times r^2 \end{gathered}[/tex]

From the question:

[tex]\frac{dv}{dt}\text{ = 1231.5 }[/tex][tex]\frac{dr}{dt}\text{ = ?}[/tex][tex]\frac{dr}{dt}\text{ = }\frac{dv}{dt}\times\frac{dr}{dv}[/tex]

dr/dv is the reciprocal of dv/dr

Thus, we have it that:

[tex]\begin{gathered} \frac{dr}{dt}\text{ = 1231.5 }\times\frac{1}{4\times3.142\times7^2} \\ \\ \frac{dr}{dt}\text{ = 2 }\frac{cm}{s} \end{gathered}[/tex]

We have the given equation that represents the distance D from home after x hours of driving:

a)

To graph the equation, we use the distance on the y-axis and the hours on the x-axis.

We need to find the points:

When x=1,

[tex]\begin{gathered} D=1600-100x \\ D=1600-100(1) \\ D=1500 \\ \text{Hence, we have the point (1,1500)} \end{gathered}[/tex]

When x=2,

[tex]\begin{gathered} D=1600-100x \\ D=1600-100(2) \\ D=1400 \\ \text{Hence, we have the point (2,1400)} \end{gathered}[/tex]

When x=3

[tex]\begin{gathered} D=1600-100x \\ D=1600-100(3) \\ D=1300 \\ \text{Hence, we have the point (3,1300)} \end{gathered}[/tex]

When x=4

[tex]\begin{gathered} D=1600-100x \\ D=1600-100(4) \\ D=1600-400 \\ D=1200 \\ \text{Hence, we have the point (4,1200)} \end{gathered}[/tex]

When x= 5

[tex]\begin{gathered} D=1600-100x \\ D=1600-100(5) \\ D=1100 \\ \text{Hence, we have the point (5,1100)} \end{gathered}[/tex]

Plot the points to get the graph.

b) The slope is given by the rate of change, in this case, the range of change is 100 because this number depends on x. where x represents the number of hours.

c) If Jim is driving after 6 hours, then, we need to replace x = 6 on the distance equation.

Hence:

[tex]\begin{gathered} D=1600-100x \\ D=1600-100(6) \\ D=1000 \end{gathered}[/tex]

Therefore, after 6 hours Jim is 1000km far away from home.

Yes, you are.

1) Let's proceed with the addition of these numbers:

[tex]\begin{gathered} 200029282+29282=200058564 \\ 200058564=200058564 \end{gathered}[/tex]

Adding it up, we can find the same result.

2) Then the answer is yes, you are correct 200029282+29282=200058564

In this problem the least temperature will be the greater negative number so it would be:

[tex]-5.8\to-4.2\to-4.1\to-1.5[/tex]

The typical number of days of rain for each city is given by the center of the measurements, that is the median.

Half the months had a number of rainy days below the median, and the other half above the median. That's why the median is a good measure for a typical number of rainy days for each city.

Therefore, the city with the largest median (center) is the one with the largest typical number of days of rain: Seattle.

Now, the better measure of spread to use in this case is the interquartile range. This range is the difference between the beginning and the end of the box in the boxplot. It shows how the 50% closest to the center measurements spread (25% below the center, and 25% above the center).

So, for Seattle, this is spread is:

17-7.5 = 9.5

Therefore:

Spread for Seattle: _9.5____ days

Then, the city with the lowest variation in the days of rain each month is the one with the lowest spread: Las Vegas.

Answer

y = -0.25x + 2

y = -¼(x) + 2

Explanation

The slope and y-intercept form of the equation of a straight line is given as

y = mx + b

where

y = y-coordinate of a point on the line.

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

b = y-intercept of the line.

So, we need to calculate the slope for this line.

y-intercept is the point where the line crosses the y-axis.

b = 2

For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as

[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]

For this question, we will pick two points on it

(x₁, y₁) and (x₂, y₂) are (0, 2) and (4, 1)

[tex]\text{Slope = }\frac{1-2}{4-0}=\frac{-1}{4}=-0.25[/tex]

Recall that

y = mx + b

m = -0.25

b = 2

y = -0.25x + 2

Hope this Helps!!!

Answer:

Explanation:

If a coordinate point (x, y) is dilated by a factor of k, the resulting coordinate will be (kx, ky)

Given

K = 7

Coordinates

A(-3, 2)

B(4, 2)

C(-1, -1)

If they are dilated by a factor of 7, the resulting coordinates will be;

A' (7(-3), 7(2)) = A'(-21, 14)

B' (7(4), 7(2)) = B' (28, 14)

C' (7(-1), 7(-1)) = C' (-7, -7)

Hence the co

The formula that the physicists told was

[tex]h(t)=-16t^2+v_0t+h_0[/tex]

We know that

v₀ = 400 ft/s

h₀ = 2400 ft

Then let's put it into the formula

[tex]\begin{gathered} h(t)=-16t^2+400t+2400 \\ \\ \end{gathered}[/tex]

We want to know then it will land on the desert, in other words, when the height is equal to zero, then

[tex]-16t^2+400t+2400=0[/tex]

Then we must solve that quadratic equation, to solve it let's first divide all by 16

[tex]\begin{gathered} -16t^2+400t+2400=0 \\ \\ -t^2+25t+150=0 \end{gathered}[/tex]

Because it's an easier equation to solve and the solution is the same. Now we can apply the quadratic formula

[tex]t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Plug the values

[tex]\begin{gathered} t=\frac{-25\pm\sqrt{25^2-4\cdot(-1)\cdot150}}{2\cdot(-1)} \\ \\ t=\frac{-25\pm\sqrt{625+4\cdot150}}{-2} \\ \\ t=\frac{25\pm\sqrt{625+600}}{2} \\ \\ t=\frac{25\pm\sqrt{1225}}{2} \\ \\ t=\frac{25\pm35}{2} \\ \\ t=\frac{25+35}{2}=\frac{60}{2}=30\text{ seconds} \end{gathered}[/tex]

We can ignore the other solution because it's negative and negative time is not a valid solution. Therefore, 30 seconds after its launch, the rocket will land in the desert

To graph, first find the x and y intercept

That is;

Put x = 0

y = 3(0) - 5 = -5

(0, -5)

Then put y = 0 and solve for x

0 = 3x - 5

3x = 5

x=3/5 = 0.6

(0.6, 0)

The points are : (0, -5) and ( 0.6 , 0)

Answer:

3843

Explanation:

To convert 2874 to base 9, we need to divide by 9 as follows:

So, the remainder is 3 and the quotient is 319. Then, divide 319 again by 9

Then, the remainder is 4 and the quotient 35. Finally, we divide 35 by 9 to get the remainder 8 and quotient 3.

Therefore, the number in base 9 will be

3843

We start by the last quotient which is 3 and then we type the remainders from last to first, so they are 8, 4, and 4.

Therefore, the answer is

3843 in base 9.

Answer: 3843 base 9 which is choice C

==================================================

Explanation:

The idea is to repeatedly divide by 9 to find the quotient & remainder pairs. Each quotient is then the numerator of the next fraction. We stop the process once we arrive to a quotient of 0.

This is what that process looks like. The remainders are highlighted in bold.

2874/9 = 319 remainder 3

319/9 = 35 remainder 4

35/9 = 3 remainder 8

3/9 = 0 remainder 3

Read the remainders in reverse to form the answer 3843 base 9

Notice in the steps above that each quotient is then treated as the numerator for the next line. Eg: the quotient 319 is the numerator for the next fraction down 319/9. Each time we divide over 9 which is the base we wish to convert to.

Be careful not to read the remainders from the top down. The answer is NOT 3483, which means choice B is a trick answer.

Given the points:

(x1, y1) ==> (1, 4)

(x2, y2) ==> (6, 9)

Let's find the slope between the points.

To find the slope between the points, apply the formula:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Substitute values into the formula:

[tex]\begin{gathered} m=\frac{9-4}{6-1} \\ \\ m=\frac{5}{5} \\ \\ m=1 \end{gathered}[/tex]

Therefore, the slope betwen the points is 1

ANSWER:

1

Given the following equation of a line:

[tex]2x-5y=-12[/tex]

Find the slope and the y-intercept of the line.

The slope-intercept form of a line is:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

Solving the given equation for y:

[tex]\begin{gathered} 2x-5y=-12 \\ \text{Subtract 2x} \\ -5y=-2x-12 \\ Divide\text{ by -5:} \\ y=\frac{-2x-12}{-5} \\ \text{Simplify:} \\ y=\frac{2}{5}x+\frac{12}{5} \end{gathered}[/tex]

Comparing with the generic equation above, we find:

slope: m = 2/5

Y-intercept: b = 12/5

[tex]g(x)=x^3-x^2-4x+4[/tex]

End behavior: You have the leading coefficient (number write in front of the variable with the largest exponent) of +1 and the polynomial degree is odd (3).

For this features the end behavior is: falls to left and rises to right.

Y-intercept: The value of g(x) when it cross the y-axis (when x is 0)

Substitute the x in the equation by 0 and evaluate the function:

[tex]\begin{gathered} g(0)=0^3-0^2-4(0)+4 \\ g(0)=4 \end{gathered}[/tex]y-intercept: 4

To find the zeros:

Equals the function to 0

[tex]x^3-x^2-4x+4=0[/tex]

Factor:

-Factor x²

[tex]x^2(x-1)-4x+4=0[/tex]

-Factor -4:

[tex]x^2(x-1)-4(x-1)=0[/tex]

-Factor (x-1):

[tex](x-1)(x^2-4)=0[/tex]

Write the second factor as a substraction of squares:

[tex]\begin{gathered} (x-1)(x^2-2^2)=0 \\ \\ a^2-b^2=(a+b)(a+b) \\ \\ (x-1)(x+2)(x-2)=0 \end{gathered}[/tex]

Equal each factor to 0 and solve x:

[tex]\begin{gathered} x-1=0 \\ x=1 \\ \\ x+2=0 \\ x=-2 \\ \\ x-2=0 \\ x=2 \end{gathered}[/tex]

Then, the zeros of g(x) are: x=1, -2, 2

we have that

the number 7 is greater than zero

therefore

7 > 0

the answer is

>

Solution

For this case we have the following equation:

[tex]y=3x^2+16x-12[/tex]

a= 3, b= 16, c= -12

Then we can use the quadratic formula given by:

[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]

Replacing we got:

[tex]x=\frac{-16\pm\sqrt[]{16^2-4(3\cdot-12)}}{2\cdot3}=\frac{-16\pm\sqrt[]{400}}{6}=\frac{-16\pm20}{6}[/tex]

Then the final answer would be:

x= 4/6= 2/3

x= -6

Ping has eaten 7.5 slices so far.

Step - by - Step Explanation

What to find?

The number of slice ping has eaten.

Given:

• Amount Ping ate yesterday = 5.8 slices.

,

• Amount Ping ate today = 1.7 slices.

To get the total number of slice she has eaten, add up the number of slice eaten yesterday and today.

That is;

Hence, she has eaten 7.5 slice so far.

Answer:

7.5

Step-by-step explanation:

5.8+1.7=7.5 (slices)

The final answer will be (we first do the multiplications, then the divisions, and then the addition)

[tex]\frac{389}{5}=77.8[/tex]

Solution

Step 1:

Convert cm to feet

1 foot = 30.48cm

Step 2

a)

[tex]\begin{gathered} Area\text{ of the flower bed = Length }\times\text{ Breadth} \\ \\ =\text{ }\frac{122}{30.48}\text{ }\times\text{ }\frac{63}{30.48} \\ \\ =\text{ 8.27 square feet} \end{gathered}[/tex]

b)

[tex]\begin{gathered} Number\text{ of mulch = }\frac{8.27}{2.2} \\ \\ =\text{ 3.76058} \\ \\ \approx\text{ 4} \end{gathered}[/tex]

Rafael needs to buy 4 bags of mulch to completely cover his flower bed.

c)

Each bag of mulch costs $3.64

[tex]\begin{gathered} Cost\text{ for 4 bags = 4 }\times\text{ 3.64} \\ \\ =\text{ \$14.56} \\ \\ =\text{ \$15} \end{gathered}[/tex]

The magnitude of the rotational symmetry in a square is 4.

The rotational symmetry of a geometric figure is the number of times you can rotate the geometric figure so that it looks exactly the same as the original figure.

So when we roll up a square and stopped when every side is at the bottom, the square is still congruent to its original figure. Since a square has 4 sides, we can roll it up 4 times, every 90 degrees rotation.

-3x + y = 4

can be rewritten as follows:

3x -3x + y = 3x + 4

y = 3x + 4

this equation of a line and the equation y = 3x - 2, are parallel (they have the same slope but different y-intercept). Then there is no intersection between. In consequence, there is no solution for the system of equations.