Answer:
5x3+9x2+15x+27
Step-by-step explanation:
The expression that is equivalent to (mn)(x) is 5x³ + 9x² + 15x + 27.
Option A is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example: so
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To find the product of m(x) and n(x), we need to multiply the two polynomials term by term:
m(x) = x² + 3
n(x) = 5x + 9
mn(x) = (x² + 3) (5x + 9)
Multiplying the two polynomials using the distributive property.
mn(x) = 5x³ + 9x² + 15x + 27
Thus,
The expression that is equivalent to (mn)(x) is 5x³ + 9x² + 15x + 27.
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Need help with this khan academy question. Plus minus square root of negative nine equals plus or minus
Answer:
3i
Step-by-step explanation:
3i x 3i = -9
-3i x -3i = -9
Therefore the square root of -9 is 3i or -3i
The simplified radical expression ±√(-9) is ±3i
The expression ±√(-9) involves finding the square root of a negative number. In the real number system, this is not possible, as no real number multiplied by itself will result in a negative value. To overcome this limitation, mathematicians introduced the concept of imaginary numbers. The imaginary unit, denoted by 'i,' is defined as √(-1).
Now, let's simplify the expression ±√(-9) step by step:
Step 1: Begin by recognizing that √(-9) is the square root of -9.
Step 2: Since √(-1) is 'i,' we can rewrite √(-9) as √(9) * √(-1).
Step 3: The square root of 9 (√9) is 3.
Step 4: Replace √(-1) with 'i.'
Step 5: The final result is 3i.
Therefore, the simplified form of ±√(-9) is ±3i.
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Write the equation of the line that passes through the point (7,-1) that has a slope of 0.
Answer:
y=0x-1
Step-by-step explanation:
y=0(x)+c
-1=0(7)+c
-1=0+c
C=-1
heloo hello HELPP FAST OR ILL DIE
Answer:
f(-7)= 21
Step-by-step explanation:
-(-7)^2-10(-7)
-7^2-10×-7
-49-10×-7
-49-(-70)
-49+70
21
What number is represented by point B?
4/5
1 4/5
1 5/4
2 1/5
Answer:
1 5/4
Step-by-step explanation:
Which function has the graph with the greatest y-intercept?
Answer:
The greatest y-intercept c = 6
Step-by-step explanation:
we know that
slope-intercept form y = mx +c
a) Given that f(x) = [tex]6x + \frac{1}{6}[/tex]
[tex]y = 6x + \frac{1}{6}[/tex]
comparing y = mx +c
slope of the line m = 6 and Y - intercept c= 1/6
b) Given that f(x) = [tex]6x -6[/tex]
y = 6x -6
comparing y = mx +c
slope of the line m = 6 and Y - intercept c= -6
c)
Given that f(x) = [tex]\frac{1}{6} x +6[/tex]
y = [tex]\frac{1}{6} x +6[/tex]
comparing y = mx +c
slope of the line m = [tex]\frac{1}{6}[/tex] and Y - intercept c= 6 ( greatest intercept)
d)
Given that 6 k(x) = x
k(x) = [tex]\frac{1}{6} x[/tex]
y = [tex]\frac{1}{6} x[/tex]
comparing y = m x +c
The slope of the line m =[tex]\frac{1}{6}[/tex] and Y-intercept c=0
Final answer:-
The greatest y-intercept c = 6
Answer:
C. h(x)=1/6x+6
Step-by-step explanation:
What is 35% divided by 200
Answer:
0.00175
Step-by-step explanation:
4-(3-5)=?
-4
-2
6
12
Answer:
6
Step-by-step explanation:
3 - 5 = -2
4 - (-2) = 6
When subtracting a negative from a positive number you add them together to get you sum or difference.
The circumference of a coin is 167 cm. What is the radius? What is the diameter?
Answer:
Radius, r = 26.57 cm and diameter = 53.14 cm
Step-by-step explanation:
Given that,
The circumference of a coin, C = 167 cm
We need to find the radius and the diameter of the coin.
The formula for the circumference of a circle is given by :
[tex]C=2\pi r[/tex]
Where
r is radius of coin
[tex]r=\dfrac{C}{2\pi}\\\\r=\dfrac{167}{2\pi}\\\\r=26.57\ cm[/tex]
Diameter, d = 2r
d = 2(26.57) cm
= 53.14 cm
Hence, this is the required solution.
onyango wishes to fence a rectangular research plot using 100 m of wire .one end of the plot has a wall already erected .calculate the maximum area that he can fence
Answer:
1250 m²
Step-by-step explanation:
Let x and y denote the sides of the rectangular research plot.
Thus, area is;
A = xy
Now, we are told that end of the plot already has an erected wall. This means we are left with 3 sides to work with.
Thus, if y is the erected wall, and we are using 100m wire for the remaining sides, it means;
2x + y = 100
Thus, y = 100 - 2x
Since A = xy
We have; A = x(100 - 2x)
A = 100x - 2x²
At maximum area, dA/dx = 0.thus;
dA/dx = 100 - 4x
-4x + 100 = 0
4x = 100
x = 100/4
x = 25
Let's confirm if it is maximum from d²A/dx²
d²A/dx² = -4. This is less than 0 and thus it's maximum.
Let's plug in 25 for x in the area equation;
A_max = 25(100 - 2(25))
A_max = 1250 m²
Please help me please! It would be amazing if you can!
Answer:
A- Brady multiplied the first equation by 5 and the second equation by 3.
B- He can use elimination for his next step. 15y and -15y will cancel each other out, 20x-18x is 2x...50-48 is 2 so 2x=2 divide and x is 1
C- x=1 y=2
Step-by-step explanation:
Compare -5 and -3.
Answer:
Simplifying then comparing both terms
−5 and −3, −5 is less than −3, which means that the first term is less than the second term. −5 < −3
Step-by-step explanation:
Hope this helps have a good day^^
Solve for the missing side of the triangle.
Round off answer to the nearest thousandths
(3 decimal places)
SOH CAH TOA
x =
239
14
Х
Answer:
x = 5.943
Step-by-step explanation:
Reference angle = 23°
Side opposite to reference angle = x
Adjacent side = 14
Therefore, we would apply TOA to find x.
Thus:
tan (23) = x/14
Multiply both sides by 14
14 × tan(23) = x
5.94264742 = x
x = 5.943 (to 3 decimal places)
Which sentence correctly compares the rates Bill and Kevin drove on their trips? (A) Bill drove at a rate that was 10 miles per hour slower than the rate Kevin drove. (B) Bill drove at a rate that was 10 miles per hour faster than the rate Kevin drove. (C) Bill drove at a rate that was 20 miles per hour slower than the rate Kevin drove. (D) Bill drove at a rate that was 20 miles per hour faster than the rate Kevin drove.
Answer:
Not sure
Step-by-step explanation:
For the function
g(x) = 1/3x-2, find g(3a – 6)
Answer:
g(3a – 6) = a - 4
Step-by-step explanation:
g(x) = 1/3x - 2
g(3a – 6) = 1/3(3a – 6) - 2
= a - 2 - 2
= a - 4
Answer:
g(3a - 6) = a - 4
Step-by-step explanation:
If you start with g(x) = 1/3 x - 2
Then whatever x = on the left, must take on the value on the right.
g(3a - 6) = 1/3 (3a - 6) - 2 Notice the x is gone and 3a - 6 has taken it's place.
Now you must distribute the 1/3 for both 2a and 6
g(3a - 6) = 1/3 * 3a - 1/3 * 6 - 2
g(3a - 6) = a - 2 - 2
g(3a - 6) = a - 4
Pls help I need a good grade on this I’ll brainlest
Answer:
the second is better deal
the unit rate for the better deal is $4.07
Is 70.24 greater or less then 70.240
Answer:
They're both the same
Answer:
70.24 is less then 70.240
Step-by-step explanation:
please follow me
describe what is being done in each step while solving the equation -2x + 6 +6x = 6 ( 2x -3 )
-2x + 6 + 6x = 12x - 18
4x + 6 = 12x - 18
6 = 8 × - 18
24 = 8x
3=x
please solve!
-2x + 6 + 6x = 6 (2x - 3) this is the equation
-2x + 6 + 6x = 12x - 18 distributive property has been applied
4x + 6 = 12x - 18 like terms have been added
6 = 8x -18 4x has been subtracted from both sides
24 = 8x -18 has been added to both sides
3 = x 8 has been divided from both sides
I hope this helps! Let me know if I need to explain more or if I got something wrong. Have a nice day!
18 is the product of 6 and x.
how would i show my work
Answer:
3
Step-by-step explanation:
x x6=18
x=3
Answer:
(18=6 times x) you would divide both sides by 6 since inverse operations and to leave the x by itself. 18/6 is 3 so 3=x
Given g(x)= 3x−4, solve for x when g(x) =5.
Answer:
x = 3
Step-by-step explanation:
5 = 3x - 4
9 = 3x
x = 3
A sculptor uses a constant volume of modeling clay to form a cylinder with a large height and a relatively small radius. The clay is molded in such a way that the height of the clay increases as the radius decreases, but it retains its cylindrical shape. At time t=c, the height of the clay is 8 inches, the radius of the clay is 3 inches, and the radius of the clay is decreasing at a rate of 1/2 inch per minute.
Write an expression for the rate of change of the radius of the clay with respect to the height of the clay in terms of height h and radius r.
Answer:
[tex]\frac{dr}{dh} =-\frac{r}{2h}[/tex]
Step-by-step explanation:
The volume of a cylinder is given by the formula:
V = πr²h,
Where V is the volume, r is the radius of the cylinder and h is the height of the cylinder.
We are to express the rate of change of the radius of the clay with respect to the height of the clay in terms of height h and radius r.
That means we express dr / dh in terms of height h and radius r. To do this, we have to first differentiate the volume with respect to the height, i.e. find dV / dh:
V = πr²h
[tex]\frac{dV}{dh}= \frac{d}{dh} (\pi r^2h)\\\\\frac{dV}{dh}= \pi r^2 + 2\pi rh \frac{dr}{dh} \\\\The\ volume\ is\ constant\ hence\ \frac{dV}{dh}=0.\ We\ get\ that:\\\\0= \pi r^2 + 2\pi rh \frac{dr}{dh}\\\\- \pi r^2 =2\pi rh \frac{dr}{dh}\\\\ \frac{dr}{dh}=-\frac{\pi r^2}{2\pi rh}\\\\ \frac{dr}{dh}=-\frac{r}{2h}[/tex]:
Write the mixed number as an improper fraction.
3 3/5
Answer:
3 3/5 as an improper fraction = 18/5
Answer:
18/5
Step-by-step explanation:
To find the improper fraction change the whole number into a fraction:
3 *5/5 = 15/5 which is the same as 3
then add the remaining 3/5 to the fraction
15/5 + 3/5
= 18/5
Which diagram best shows that 14x2 + 21x in factored form is 7x(2x + 3)?
Answer: B
Step-by-step explanation:
Fourth diagram represent the 14x²+21x in factored form is 7x(2x + 3)
What is Number system?A number system is defined as a system of writing to express numbers.
The given expression is 14x²+21x
Fourteen x square plus twenty one times of x.
x is the variable and plus is the operator.
14x²+21x
We need to take 7x as common from two terms.
When the quadratic expression is a product of two factors where each one is a linear expression, this is called the factored form.
Seven x is product of two times of x plus three.
7x(2x+3)
The fourth diagram represent the 14x²+21x in factored form is 7x(2x + 3)
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5^(11x+23)=125^(7x)
how to solve for x
What is the interval of convergence
Answer:
The interval of converges of a power series is the interval of input values for which the series converges.
Step-by-step explanation:
A pail contains a certain amount of water. After Peter used it to fill a 1.5 liter can, a 750 milliliter bottle, and a 2 liter 250 milliliter tin, he realized that he had a liter of water left in the pail. How much water was in the pail at first? Write your answer in liters and milliliters. Show your work.
Answer:
Let the amount of water at beginning be x
x-1.5-0.750-2.250=1
x=5.5 litre
Step-by-step explanation:
Therefore there was 5 litre 5 mililters of water in the pail.
Answer:5500 ml or 5.5 liters
Step-by-step explanation:
First, we should note that there are 1000 milliliters in 1 liter of liquid.
So, in milliliters, Peter filled three containers with 1500 ml, 750ml, and 2250 ml with 1000ml left over.
To find the total amount, we find the sum of all the milliliters:
1500 + 750 + 2250 + 1000 = 5500 ml
Again, we know that there are 1000 milliliters in 1 liter of liquid, so:
= 5.5 liters
Select the correct answer from each drop-down menu. Prism M and pyramid N have the same base area and the same height. Cylinder P and prism Q have the same height and the same base perimeter. Cone Z has the same base area as cylinder y, but its height is three times the height of cylinder Y. The figures and have the same volume.
Answer:
sm[tex]prism M and Cylinder P\\[/tex][tex]Plato[/tex]
Step-by-step explanation:
can you write a equation with a slope of 3 and a y-intersept of (0,4)
Answer:
y=3x+4
Step-by-step explanation:
y=mx+b
m=3
b=4
just plug it in
on a scale drawing of a park, the sand box is 2 inches wide. The actual sand box is 8 feet wide. What is the scale of the drawing.
2 inches : 8 feet
simplified scale:
1 inch : 4 feet
Can somebody please help me with this question?
Answer:
a. 76 cm
b. 16 in.
c. 225 cm
Step-by-step explanation:
a. Converting 30 inches to centimetres:
When y(inches) = 30, x (centimetres) = 76
So, 30 in. = 76 cm
b. When x (cm) = 40, y (in.) = 16
So, 40 cm = 16 in.
c. Given that a fence is 7 ft 6 in. high, and 1 ft = 12 in., to find the height of the fence in cm, first convert the height to in.
Convert 7ft to inches:
If 1 ft = 12 in., then,
7 ft = 7*12 = 84 inches
The height of the fence in inches = 84 + 6 = 90 inches
Using the graph, find the unit rate using any point on the line, say (100, 40):
Unit rate = y/x = inches/centimeters =
Unit rate (m) = 40/100 = ⅖
Write an equation for the line:
To do this, substitute m = ⅖ into y = mx
Equation: y = ⅖x
Let's convert the height of the fence, 90 inches, to centimetres:
To convert to cm, substitute y = 90 into y = ⅖x
Thus:
90 = ⅖*x
5*90 = 2x
450 = 2x
Divide both sides by 2
450/2 = x
225 = x
Height of the fence in cm = 225 cm
The ratio of the number of Claire's stamps to the number of John's
stamps is 2:3. If John has 24 stamps, how many stamps does Claire have?
Answer:
Claire has 16 stamps
Step-by-step explanation:
Proportions
If two variables are proportional, their ratio is constant. For example, the distance traveled by car is proportional to the time it travels at a constant speed. We write it as d:t=constant.
It's known the number of Claire's stamps to the number of John's stamps is 2:3 and John has 24 stamps.
This means the following relation must stand:
[tex]\displaystyle \frac{C}{J}=\frac{2}{3}[/tex]
Where C is the number of stamps of Claire and J is the number of stamps of John. We know J=24, thus:
[tex]\displaystyle \frac{C}{24}=\frac{2}{3}[/tex]
Solving for C:
[tex]\displaystyle C=24\cdot\frac{2}{3}[/tex]
C = 16
Claire has 16 stamps
