Answer:
Step-by-step explanation:
4x^5 + 7x^3
x^3(4x^2 + 7)
The GCF is x^3
simplify 6(x - 4) +9
To simplify use the distributive property first. Multiply 6 by each value inside the parentheses:
6(x-4) + 9
6x -24 + 9
Now combine like terms to get the final answer:
6x - 15
I need help with five math questions please help
Answer:
-5X+2Y-2
Step-by-step explanation:
-5X-7-2+2Y+7
-5X-2+2Y
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
PLEASE HELP Polynomial Graph Studies Polynomials are great functions to use for modeling real-world scenarios where different intervals of increase and decrease happen. But polynomial equations and graphs can be trickier to work with than other function types. In mathematical modeling, we often create an equation to summarize data and make predictions for information not shown on the original display. In this activity, you’ll create an equation to fit this graph of a polynomial function. Part A Describe the type of function shown in the graph. Part B What are the standard form and the factored form of the function? Part C What are the zeros of the function? Part D Use the zeros to find all of the linear factors of the polynomial function. Part E Write the equation of the graphed function f(x), where a is the leading coefficient. Use the factors found in part D. Express the function as the product of its leading coefficient and the expanded form of the equation in standard form. Part F Use the y-intercept of the graph and your equation from part E to calculate the value of a. Part G Given what you found in all of the previous parts, write the equation for the function shown in the graph.
Answer:
Here's what I get
Step-by-step explanation:
Part A
The graph shows a polynomial of odd degree. It is probably a third-degree polynomial — a cubic equation.
Part B
The standard form of a cubic equation is
y = ax³ + bx² + cx + d
The factored form of a cubic equation is
y = a(x - b₁)(x² + b₂x + b₃)
If you can factor the quadratic, the factored form becomes
y = a(x - c₁)(x - c₂)(x - c₃)
Part C
The zeros of the function are at x = -25, x = - 15, and x = 15.
Part D
The linear factors of the function are x + 25, x + 15, and x - 15.
Part E
y = a(x + 25)(x + 15)(x - 15) = a(x + 25)(x² - 225)
y = a(x³ + 25x² - 225x - 5625)
Part F
When x = 0, y = 1.
1 = a[0³ +25(0)² - 225(0) - 5625] = a(0 + 0 - 0 -5625) = -5625a
a = -1/5625
Part G
[tex]y = -\dfrac{1}{5625}( x^{3} + 25x^{2} - 225x - 5625)\\\\y = \mathbf{ -\dfrac{1}{5625} x^{3} - \dfrac{1}{225}x^{2} + \dfrac{1}{25} x + 1}[/tex]
Answer
Actually, the answer should be -0.0007(x+20)(x+5)(x-15)
Step-by-step explanation:
This is continuing off of the previous answer
PART C
The zeros should be (15,0), (-5,0), and (-20,0)
PART D
x - 15, x + 5, and x + 20
PART E
a(x - 15)(x + 5)(x + 20)
Standard: [tex]a(x^{3} + 10x^{2} -275x-1500)[/tex]
PART F
The y-intercept is at (0,1), so we replace the x's with 0:
1 =[tex][(0)x^{3} +10(0)x^{2} -275(0)-1500][/tex] and this gives us (0+0-0-1500) which also equals -1500
Then we do [tex]\frac{1}{-1500}[/tex] which gives us -0.0006 repeating which rounds to -0.0007
a= -0.0007
PART G
Just place the numbers where they should go and your answer is
y =-0.0007(x + 20)(x + 5)(x - 15)
the placement for (x + 20) (x + 5) and (x - 15) doesn't matter as long as they are behind -0.0007
Please Help me with this math question
Find the derivative of f(x) = -2x2 + 11x at x = 9.
Answer:
The value of the derivative at x = 9 is -25
Step-by-step explanation:
Here in this question, we are told to find the derivative of the given equation at the point where x = 9
What we need to do here is simply, differentiate f(x), then substitute that value x = 9 into the differentiated equation
In notation form, what we are to find is f’(9)
So;
f(x) = -2x^2 + 11x
f’(x) = -4x + 11
So therefore;
f’(9) = -4(9) + 11
f’(9) = -36 + 11
f’(9) = 11-36
f’(9) = -25
Kapil deposited Rs. 1600 in a bank on 1st January 2005. Find the amount in his bank account on 1st January 2006, if the bank pays interest at 8% per annum and the interest is calculated every year on 30th June and 31st December.
Answer:
SI=PRT/100
=10000*5*42/12*100
=1750
SI=1750
TOTAL AMOUNT=PRINCIPLE+SI
=10000+1750
=101750
A students wants to report on the number of movies her friends watch each week. The collected date are below:
0, 0, 1, 1, 2, 2, 2, 14
which measure of center is most appropriate for this situation and what's its value?
A.) Median; 1.5
B.) Median; 3
C.) Mean; 1.5
D.) Mean; 3
Answer:
A.) median; 1.5
Step-by-step explanation:
Hello!
The median is the number that is in the middle when the numbers are listed from least to greatest
0, 0, 1, 1, 2, 2, 2, 14
We can take one from both sides till there are one or two numbers left
0, 1, 1, 2, 2, 2
1, 1, 2, 2
1, 2
If there are two numbers left we add them then divide by 2 to get the median
1 + 2 = 3
3 / 2 = 1.5
The answer is A.) median; 1.5
Hope this helps!
Please answer this question now
Answer:
156.6 square yards
Step-by-step explanation:
To find the surface area of the pyramid, find the area of each surface and add them together.
formula for area of a triangle = 1/2(b·h)
1. There are three triangles with a base of 9 and a height of 9
1/2(9·9) = 40.5
Multiply by the three triangles
40.5 · 3 = 121.5
2. There is one triangle with a base of 9 and a height of 7.8
1/2(9·7.8) = 35.1
3. Add the areas of all surfaces
121.5 + 35.1 = 156.6
Tatenda takes ttt seconds to mow a square meter of lawn and Ciara takes ccc seconds to mow a square meter of lawn. Tatenda mows 700700700 square meters of lawn per week and Ciara mows 750750750 square meters of lawn per week. Which expressions can we use to describe how many more seconds Tatenda spends than Ciara spends mowing lawns during 444 weeks? Choose 2 answers: Choose 2 answers: (Choice A) A 4(750c-700t)4(750c−700t)4, left parenthesis, 750, c, minus, 700, t, right parenthesis (Choice B) B 3000c+2800t3000c+2800t3000, c, plus, 2800, t (Choice C) C 2800t-3000c2800t−3000c2800, t, minus, 3000, c (Choice D) D 4(700t-750c)4(700t−750c)4, left parenthesis, 700, t, minus, 750, c, right parenthesis (Choice E) E 4(700t+750c)4(700t+750c)
Answer:
C.) 4(750c-700t) ; D.) 2800t - 3000c
Step-by-step explanation:
Time taken :
Tatenda = t sec/m^2
Ciara = c sec/m^2
Tatenda = 700m^2 per week
Ciara = 750m^2 per week
Which expressions can we use to describe how many more seconds Tatenda spends than Ciara spends mowing lawns during 4
Total Time taken over four weeks :
Tatenda = 4(t * 700) = 4(700c)
Ciara = 4(c * 750) = 4(750c )
Number of seconds Tatenda spends more than Ciara : meaning Tatenda spends more seconds than
Tatenda - Ciara
4(700t) - 4(750c) = 4(700t - 750c)
4(700t - 750c)
Or
4(700t - 750c) = 2800t - 3000c
2800t - 3000c
Which point represents the opposite of 0 on the number line? A B C D E
Answer:
C: 0
Step-by-step explanation:
Let's use 1 for an example first. The opposite of 1 is -1. 2 = -2, 3 = -3, and so on. Since there is no such thing as -0, our answer would be C, 0. It is not -5, -2, 2, or 7 because those are not the negatives of 0.
Hint: is the picture
Alonso estimated the distance across
a river as 1232 meters. What is the
approximate distance across the river to
the nearest thousandth of a meter?
Answer:
1232.000
Step-by-step explanation:
Estimated distance across the river=1,232 meters
Find the approximate distance across the river to
the nearest thousandth of a meter
Note: Thousandth is having 3 values after the decimal point
This means we will round 1,232 meters to the nearest thousandth
1,232 is an whole number and decimal point can only be added at the end like this 1,232.
So we need 3 values after the decimal point.
We must add only values that wouldn't change the original 1,232 meters.
Therefore, zero (0) will be added
1232.000
Is to the nearest thousandth
how do you find the length of the hypotenuse when you have only the length of the altitude of the hypotensuse and a length of a leg?
Answer:
By using The Pythagorean Theorem:
[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \[/tex]
/Hypotenuse/ = [tex]\sqrt\ /Length of altitude/^{2} + /Length of leg/^{2} \}[/tex]
Step-by-step explanation:
The Pythagorean theorem states that: Given a Right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides ( Here, being the length of the altitude and length of leg). That is,
[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \[/tex] and hence,
/Hypotenuse/ = [tex]\sqrt\ /Length of altitude/^{2} + /Length of leg/^{2} \}[/tex]
For example, If the length of the altitude is 4m and the length of leg is 3m. Using The Pythagorean theorem, the length of the hypotenuse will be
[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \\\/Hypotenuse/ = \sqrt{/Length of altitude/^{2} + /Length of leg/^{2}} \\/Hypotenuse/ = \sqrt{4^{2} + 3^{2} }[/tex]
[tex]/Hypotenuse/ = \sqrt{16+9} \\/Hypotenuse/ = \sqrt{25} \\/Hypotenuse/ = 5m[/tex]
The length of the hypotenuse for the given example will be 5m.
This is how to find the length of an hypotenuse.
Could someone clarrify this for me Factor completely 3x^2 + 2x − 1. (3x + 1)(x − 1) (3x + 1)(x + 1) (3x − 1)(x + 1) (3x − 1)(x − 1)
Answer:
(3x-1) (x+1)
Step-by-step explanation:
3x^2 + 2x − 1
3x^2 factors into 3x and x
-1 factors into -1 and 1
We want a postive 2x
(3x-1) (x+1)
Answer:
(3x-1)(x+1)
Step-by-step explanation:
3x² + 2x − 1
when factorizing , first look at the constant number( in this case it is 1 prime number), then find the GCF if found.
(3x )(x ) first step : 3x*x=3x^2
(3x- ) (x+ ) the sign for the constant is minus so the factoring has to be minus and plus on each side
(3x-1)(x+1) look at the 2x it has positive sign, means the sign is plus:
3x-1
x+1
regular standard multiplication
3x(x)-1(x)+1(3x)-1
3x²+2x-1
A random number generator chooses 2 numbers between 1 and 5. This table demonstrates all possible outcomes. 1 2 3 4 5 1, 1 1, 2 1, 3 1, 4 1, 5 2 2, 1 2, 2 2, 3 2, 4 2, 5 3 3, 1 3, 2 3, 3 3, 4 3, 5 4 4, 1 4, 2 4, 3 4, 4 4, 5 5 5, 1 5, 2 5, 3 5, 4 5, 5 What is the probability that the computer will pick two 5s?
Answer as a fraction = 1/25
Answer in decimal form = 0.04
Answer in percent form = 4%
Explanation:
There are 5*5 = 25 different outcomes, of which only one outcome has 5,5. The probability of picking two 5s is 1/25 = 0.04 = 4%
Answer:
4%
Step-by-step explanation:
Which type(s) of symmetry does the following object have?
Select all that apply.
Answer: You are correct. There is only one answer and that is choice B) vertical line of symmetry.
We can draw a vertical line through the center to have one half mirror over this line to get the other half. We can't do the same with a horizontal line or any other kind of line.
We do not have rotational symmetry. Rotating the figure will produce an image different from the original. The angle of rotation is some angle x such that 0 < x < 360.
Answer:
Theres more than one answer so b and a
Step-by-step explanation:
(a²b²-c²)(a²b²+c²)
simplify
Answer:
a⁴b⁴ - c⁴
Step-by-step explanation:
The difference of squares formula states that (a - b)(a + b) = a² - b². In this case, a = a²b² and b = c² so a² - b² = (a²b²)² - (c²)² = a⁴b⁴ - c⁴.
Answer:
a^4b^4 - c^4.
Step-by-step explanation:
(a²b²-c²)(a²b²+c²)
Difference of 2 squares:
= (a²b²)^2 - (c²)^2
= a^4b^4 - c^4.
The ratio of the units digit to the tens digit of a two-digit number is one-half.The tens digit is 2 more than the units digit. Find the number.
Answer:
Number : 42
Step-by-step explanation:
This number will be a two - digit number, and hence we can say that it is yz. The ratio of the units digit to the tens digit is given by 1 / 2, so z / y = 1 / 2.
In addition the tens digit is 2 more than the units digit, so y = z + 2. We therefore have the following system of equations,
y = z + 2,
z / y = 1 / 2
Substituting the first equation into the second we receive z / z + 2 = 1 / 2. Using this we can solve for z.
z / z + 2 = 1 / 2 ( Cross - Multiply )
z + 2 = 2z, z = 2
And knowing z we can solve for y. y = z + 2 = 2 + 2 = 4. Therefore our number is 42.
If the sphere shown above has a radius of 17 units, then what is the approximate volume of the sphere?
A.
385.33 cubic units
B.
4,913 cubic units
C.
6,550.67 cubic units
D.
3,275.34 cubic units
Answer:
20582.195 unitsStep-by-step explanation:
This problem is on the mensuration of solids.
A sphere is a solid shape.
Given data
radius of sphere = 17 units
The volume of a sphere can be expressed as below
[tex]volume = \frac{4}{3}\pi r^3[/tex]
Substituting our data into the expression we have
[tex]volume = \frac{4}{3}*3.142*17^3[/tex]
[tex]volume = \frac{4}{3}*3.142*4913\\\\volume = \frac{61746.584}{3}= 20582.195[/tex]
The volume of the sphere is given as
20582.195 units
The Fairy Tale Spectacular is coming to town. Admission to the fair costs $32.50 and each ride costs $0.80. You have $50 to spend at the Fairy Tale Spectacular including admission. Write and solve an inequality to determine the maximum number of rides you can enjoy at the Fairy Tale Spectacular?
Answer:21
Step-by-step explanation:
50-32.5=17.5
17.5/0.8=21.875
20 POINTS! ***CORRECT*** ANSWER GETS BRAINLIEST!!!!
The fraction model below shows the steps that a student performed to find a quotient.
Which statement best interprets the quotient?
A. There are 5 1/6 three-fourths in 4 1/8
B. There are 5 1/6 three and one-eights in 3/4
C. There are 5 1/2 three and one-eights in 3/4
D. There are 5 1/2 three-fourths in 4 1/8
Answer:
(D) There are [tex]5 \frac{1}{2}[/tex] three-fourths in [tex]4 \frac{1}{8}[/tex]
Step-by-step explanation:
We can see that in this model, the student tried to put [tex]\frac{3}{4}[/tex] into [tex]4 \frac{1}{8}[/tex]. We know this because the top of Step 2 is [tex]4 \frac{1}{8}[/tex] and he is counting how many fourths in the bottom.
So this becomes the division statement:
[tex]4 \frac{1}{8} \div \frac{3}{4}[/tex].
We can convert [tex]4 \frac{1}{8}[/tex] into a mixed number by multiplying 8 and 4, then adding 1.
[tex]\frac{33}{8} \div \frac{3}{4}[/tex].
Multiply by the reciprocal:
[tex]\frac{33}{8} \cdot \frac{4}{3} = \frac{132}{24}[/tex]
Which simplifies down to
[tex]\frac{11}{2}[/tex], which is just [tex]5 \frac{1}{2}[/tex] in improper form.
Hope this helped!
Answer:
D
Step-by-step explanation:
What is the 8th term for this sequence -3, -12, -48, -192,...
Answer:
-49152
Step-by-step explanation:
The pattern is:
multiply for 4
then:
-3, -12, -48, -192, -768, -3072, -12288, -49152
Need help on the third question. how do i generalise the number of ways to win.(check the attatchment)
Answer:
2n+2 ways to win
Step-by-step explanation:
You generalize by observing patterns in the way you solve the smaller problems.
The number of winning moves is 2n+2: the total of the number of diagonals, columns, and rows.
For an n×n board, there are 2 full-length diagonals, n columns, and n rows, hence 2+n+n = 2n+2 ways to win.
Use distributive property to evaluate the expression 5(4/1/5)
Answer:
21
Step-by-step explanation:
4[tex]\frac{1}{5}[/tex] = [tex]\frac{21}{5}[/tex]
5 × [tex]\frac{21}{5}[/tex] = (5×21)/5
[tex]\frac{105}{5}[/tex] = 21
A building meets the ground at a right angle. The top of a 10-foot ladder is placed against the bottom edge of a window in the building, and the base of the ladder is placed 6 feet from where the building meets the ground. Could you use lines and text to draw and label a diagram that represents this situation?
Greetings from Brasil...
Its attached the diagram of the situation.....
The ground is 8 feet from the bottom edge of the window
How far up from the ground is the bottom edge of the window?We start by representing the building, the ladder and the ground in a sketch.
See attachment for diagram
From the diagram, the distance (d) from ground to the bottom edge of the window is calculated using Pythagoras theorem:
10^2 = d^2 + 6^2
Evaluate the squares
100 = d^2 + 36
Evaluate the like terms
d^2 = 64
Take the square root of both sides
d = 8
Hence, the ground is 8 feet from the bottom edge of the window
Read more about Pythagoras theorem at:
https://brainly.com/question/343682
#SPJ6
How many solutions does the nonlinear system of equations graphed below
have?
y
10+
-10
10
-10
A. One
B. Two
0
O
C. Four
O
D. Zero
Answer:
D. zero
Step-by-step explanation:
Since the graphs do not intersect, there are zero solutions.
The number of solutions on the graph is zero
How to determine the number of solutions?The graph shows a linear equation (the straight line) and a non linear equation (the curve)
From the graph, we can see that the straight line and the curve do not intersect
This means that the graph do not have any solution
Hence, the number of solutions on the graph is zero
Read more about non-linear graphs at:
https://brainly.com/question/16274644
#SPJ5
Which fractions are equal to 0.375?
Answer:
375/ 1000
Step-by-step explanation:
it is technically correct
Step-by-step explanation:
Convert 0.375 to a simplified fraction by setting up our equation like this:
[tex]\frac{375}{1000} =\frac{x}{y}[/tex]
Then, we find the GCF for both numbers, which is 125. So, we divide both numbers by 125.
[tex]\frac{375}{125}=3\\\\\frac{1000}{125}=8[/tex]
Our simplified fraction: 3/8.
To find more equivalent fractions, multiply the numerator and denominator by the same number (example: 2, 3).
Some fractions equal to 0.375:
[tex]\frac{3}{8}, \frac{6}{16}(*2), \frac{9}{24} (*3)[/tex]
I hope I've helped you out!
On Wednesday at camp, Samuel went for a hike at 6:30 A.M. The hike took 2 hours and 15 minutes. As soon as he got back from the hike, Samuel played volleyball for 1 hour. What time did Samuel finish playing volleyball?
Answer:
9:45 A.M.
Step-by-step explanation:
First, add the time that took him to hike:
6:30 + 2 hours and 15 minutes = 8:45 A.M.
Next, add the 1 hour that he played volleyball for:
8:45 + 1 hour = 9:45 A.M.
So, he finished playing volleyball at 9:45 A.M.
Answer:
9:45 am
Step-by-step explanation:
He went at 6:30 am to a hike.
It took him 2 hours 15 minutes
=> 6 : 30
+ 2 15
=> 8 : 45
He came back from the Hike at 8:45 am
He played volleyball for 1 hour.
=> 8 : 45
+ 1
=> 9 : 45
He finished playing volleyball at 9:45 am
a standard number cube has six labeled sides labeled 1-6. think about rolling a number cube one time. why is it just as likely that the cube will show and even number as an odd number
Answer:
This is because there are equal counts of both even and odd numbers
Step-by-step explanation:
Here in this question, we are concerned with stating the reason why it is likely that a standard number cube have the same probability for showing an even number as well as an odd number.
In the number cube, the odd numbers are 1,3 and 5. While the even numbers are 2,4 and 6.
From here, we can see that there are three set of each number types. What this automatically means is that the probability of selecting an even number will be equal to the probability of selecting an odd number. Thus, we can say that it is just as likely that the cube will show an even number as an odd number because each of the type of numbers have 3 values each.
help will mark brainlist if it correct If each edge of a cube is increased by 2 inches, the
A. volume is increased by 8 cubic inches
B. area of each face is increased by 4 square
C. diagonals of each face is increased by 2 inches
D. sum of these edges is increased by 24 inches
Answer:
D. sum of these edges is increased by 24 inches -- True
Step-by-step explanation:
Given a cube and its edge is increased by 2 inches.
To study the effect of this increase in the Volume, area of each face, diagonal and sum of edges.
Solution:
Let the side of original cube = a inches.
Formula for volume of cube:
[tex]V =side^3 = a^3[/tex]
If the side is increased by 2 inches, the side becomes (a+2) inches.
So, new volume, [tex]V' = (a+2)^3[/tex]
Using the formula:
[tex](x+y)^3 =x^3+y^3+3xy(x+y)[/tex]
[tex]V' = (a+2)^3 = a^3+8+3\times 2 \times a(a+2)=a^3+8+6a(a+2)[/tex]
So, [tex]V' = V + 8+6a(a+2)[/tex]
Volume increased by 8+6a(a+2) [which is not equal to 8]
So, statement is false:
A. volume is increased by 8 cubic inches -- False
Each face in a cube is a square.
Area of each face, A = [tex]side^2 = a^2[/tex]
New area, A' = [tex](a+2)^2[/tex]
Using the formula: [tex](x+y)^2 =x^2+y^2+2xy[/tex]
[tex]A' = a^2+4+4a[/tex]
Area increased by 4+4a [which is not equal to 4 sq inches]
B. area of each face is increased by 4 square inches -- False
Diagonal of each face = [tex]a\sqrt2[/tex]
Increase of 2 in the edge:
New diagonal = [tex](a+2)\sqrt2 = a\sqrt2+2\sqrt2[/tex]
So, increase of [tex]2\sqrt2[/tex] not 2.
C. diagonals of each face is increased by 2 inches -- False
There are 12 number of edges in a square.
So sum of all 12 edges = 12a
When edge is increased by 2, sum of all edges = 12(a+2) = 12a + 24
An increase of 24.
D. sum of these edges is increased by 24 inches -- True
If f(x) = 4x + 15, then f(-3) = ?
Answer:
[tex]\Huge \boxed{3}[/tex]
Step-by-step explanation:
The function is given :
f(x) = 4x + 15
For f(-3), the input for the function f(x) is -3.
Replace the x variable with -3.
f(-3) = 4(-3) + 15
Evaluate.
f(-3) = -12 + 15
f(-3) = 3
The output for f(-3) is 3.
Answer: f(-3) = 3
Step-by-step explanation: Notice that f is a function of x.
So we want to find f(-3).
We find f(-3) by plugging -3 in for x,
everywhere that x appears in the function.
So we have 4(-3) + 15.
4(-3) is -12 so we have -12 + 15 which is 3.
So f(-3) is 3.
