Answer:
[tex]p(x)=-x^3-2x^2+5x+6.[/tex]
Step-by-step explanation:
If a cubic polynomial has zeros [tex]x_1,\ x_2,\ x_3,[/tex] then it has a form
[tex]p(x)=a(x-x_1)(x-x_2)(x-x_3).[/tex]
In your case, zeros are -3, -1 and 2, then the polynomial is
[tex]p(x)=a(x-(-3))(x-(-1))(x-2),\\ \\p(x)=a(x+3)(x+1)(x-2).[/tex]
If [tex]p(0)=6,[/tex] then
[tex]p(0)=a(0+3)(0+1)(0-2)=6,\\ \\-6a=6,\\ \\a=-1[/tex]
and
[tex]p(x)=-(x+3)(x+1)(x-2)=-x^3-2x^2+5x+6.[/tex]
Which expression is equivalent to pi*-80
Answer:
-80*pi
Step-by-step explanation:
pi*-80 can be written alternatively as -80*pi.
What is e-1/2f when e=15 and f=2
Answer:
14
Step-by-step explanation:
Replace with the values
15-1/2(2) = 15-1 = 14
Answer:
14
Step-by-step explanation:
e-1/2f
Let e =15 and f =2
We can substitute these values into the expression
15 - 1/2 (2)
15 - 1
14
3/4 (2a − 6) + 1/2 = 2/5 (3a + 20) what is the value of a
Answer:
A= 40
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3/4 (2a-6)+1/2=2/5(3a+20)
(3/4) (2a) + (3/4) (-6) + 1/2 = (3a) + (2/5) (20)
(distribute)
3/2a + -9/2 + 1/2 = 6/5a + 8
(3/2 a) + ( -9/2 + 1/2 ) = 6/5a + 8 (Combine like terms)
3/2a + -4 = 6/5a + 8
3/2a -4 = 6/5a+8
Step 2: Subtract 6/5a from both sides.
3/2a - 4 - 6/5 a = 6/5a + 8 - 6/5 a
3/10 a - 4= 8
Step 3: Add 4 to both sides.
3/10a -4 +4 = 8 + 4
3/10 a = 12
Step 4: Multiply both sides by 10/3
(10/3) * (3/10a) = (10/3) * (12)
a = 40
Answer:
40
Step-by-step explanation:
Jeff uses 116Rubber bands to make a rubber band ball. He estimates that he has used 448 rubber bands to make 12 rubber band bottles of the same size. Use estimation to check and explain whether his answer is reasonable or not.
Answer:
His answer is not reasonable.
Step-by-step explanation:
448 rubber bands to make 12 rubber band bottles of the same size.
450 divided by 10 is about 45 rubber band per rubber band bottle.
This is nowhere near the the 116 rubber bands to make a rubber band ball.
If the are about the same size, we should use about the same number of rubber bands.
If he used about 100 rubber bands per rubber band bottle * 12 bottles, that would be about 1200 rubber bands.
what are the steps to solve an inequality like: |n + 8| > 3 ??????
[tex]|n+8|>3\iff n+8>3\ \vee\ n+8<-3\qquad\text{subtract 8 from both sides}\\\\\boxed{n>-5\ \vee\ n<-11}[/tex]
Which expression is equivalent to 1/√121x^9y^8z^10
Answer:
1/(11 x^(9/2) y^4 z^5)
or
sqrt(x)/ 11 x^5 y^4 z^5
Step-by-step explanation:
1/ sqrt(121x^9y^8z^10)
Lets simplify the denominator
sqrt(121x^9y^8z^10)
Break it into pieces
sqrt(121) sqrt(x^9) sqrt(y^8) sqrt(z^10)
11 sqrt (x^8) sqrt(x) y^4 z^5
11 x^4 y^4 z^5 * sqrt(x)
Putting this back in
1
----------------------------
11 x^4 y^4 z^5 * sqrt(x)
But we dont want a sqrt root in the denominator
Multiply by sqrt(x)/sqrt(x)
sqrt(x)
----------------------------
11 x^4 y^4 z^5 * sqrt(x) sqrt(x)
sqrt(x)
----------------------------
11 x^4 y^4 z^5 * x
sqrt(x)
----------------------------
11 x^5 y^4 z^5
How do you do this 89.25 ×7 1/4
Answer:
647.0625
Step-by-step explanation:
Crystal is writing a coordinate proof to show that the diagonals of a parallelogram bisect each other. She starts by assigning coordinates as given. A parallelogram graphed on a coordinate plane. The parallelogram is labeled A B C D. The coordinates of vertex A are 0 comma 0. The coordinates of vertex B a comma 0. The coordinates of vertex C are not labeled. The coordinates of vertex D are b comma c. Diagonals A C and B D intersect at point E whose coordinates are not labeled. Drag and drop the correct answer into each box to complete the proof. The coordinates of point C are (a + b,). The coordinates of the midpoint of diagonal AC¯¯¯¯¯ are ( a+b2 ,). The coordinates of the midpoint of diagonal BD¯¯¯¯¯ are (a+b2, c2) . AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E with coordinates (, c2 ). By the definition of midpoint, ≅CE¯¯¯¯¯ and BE¯¯¯¯¯≅ . Therefore, diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ bisect each other.
Answer: The coordinates of the midpoint of diagonal AC are [tex](\frac{a+b}{2} , \frac{c}{2} )[/tex]. The coordinates of the midpoint of diagonal BD are [tex](\frac{a+b}{2} , \frac{c}{2} )[/tex] AC and BD intersect at point E with coordinates [tex](\frac{a+b}{2} , \frac{c}{2} )[/tex]. By the definition of midpoint, CE ≅ EA and BE ≅ ED Therefore, diagonals AC and BD bisect each other.
Step-by-step explanation:
Since, here the coordinates of A ≡ (0,0) B ≡ (a, 0) D≡ ( b,c)
And, here ABCD is the parallelogram.
Therefore AB = CD
If y is the y-coordinate of C Then C≡(a+b, y)
⇒ [tex]a^2 + 0 = (a)^2 + (y-c)^2[/tex]
⇒ y =c
Thus, C≡(a+b, c)
The coordinates of the midpoint of diagonal AC are,
[tex](\frac{a+b}{2} , \frac{c}{2} )[/tex]
And, The coordinates of the midpoint of diagonal BD are,
[tex](\frac{a+b}{2} , \frac{c}{2} )[/tex]
Since, by the below diagram AC and BD are intersecting at point E,
Where the coordinates of E are,
[tex](\frac{a+b}{2} , \frac{c}{2} )[/tex]
Thus, E is the mid point of Both the segments AC and BD
Because, BE = ED and AE = EC
Therefore, we can say that both AC and BD bisect each other.
Answer:
the coordinate point C are (a+b,c)
The coordinates of the midpoint of diagonal AC¯¯¯¯¯ are (a+b/2, c/2)
The coordinates of the midpoint of diagonal BD¯¯¯¯¯ are (a+b/2, c/2)
AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E with coordinates (a+b/2, c/2)
By the definition of midpoint, AE¯¯¯¯¯≅CE¯¯¯¯¯and BE¯¯¯¯¯≅DE¯¯¯¯¯
Step-by-step explanation:
What is the value of f(–1)?
Answer:
The answer is: 1
Step-by-step explanation: f(1) = -1, so f(-1) must be 1.
The value of the function by using a given table would be, f (- 1) = 0
Hence, option 3 is true.
Given that,
The function to find the value, f (- 1)
Used the concept of function which stated that, A relation between a set of inputs having one output each is called a function.
Now from the given table,
At x = - 5;
f (- 5) = 4
Similarly,
At x = - 1;
f (- 1) = 0
Therefore, the value of function f (- 1) would be 0.
So, Option 3 is true.
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The complete question is shown in the attached image.
what are three ways to say x>5 in words
Final answer:
The inequality x>5 can be stated as 'x is greater than five,' 'five is less than x,' or 'x exceeds five,' each conveying that the value of x is larger than 5.
Explanation:
There are several ways to express the inequality x > 5 in words. Here are three different expressions:
x is greater than five.Five is less than x.x exceeds five.All these expressions communicate the idea that the value of x is more than 5. When you're working with inequalities, it's important to be familiar with different ways to verbalize them as it can help in understanding and communicating mathematical concepts.
The figure below shows a rectangular prism and a cube: How many such cubes are required to completely pack the prism without any gap or overlap? 240 900 1,440 3,658
Answer:
Bruh no one has still answered u?!
Step-by-step explanation:
Answer:
Answer??
Step-by-step explanation:
Using the GCF, what is the factored form of 24v – 84?
Answer:
12(2V -7)
Step-by-step explanation:
Using the Greatest Common Factor, we need to find factor out the greatest common factor of the two numbers ; 24 and 84. That is; the greatest number that can divide 24 and 84
The easiest way to find the greatest common factors is;
1. To first find the factors of each number
2. Find the common factors of the two numbers
3. Find the greatest number among those factors
Factors are number that can divide a number without a remainder.
Factors of 24 are; 1, 2, 3, 6, 8, 12 and 24
Factors of 84 are; 1, 2, 3, 6, 7, 12, 14, 42 and 84
common factors are the factors that are common between the two numbers. That is; factors we can find in 24 and as well as 84
common factors are; 1, 2, 3, 6, and 12
Greatest Common Factor : This is also known as the highest common factor, it is the highest among the common factors.
Greatest Common Factor is 12.
Now after we've gotten our Greatest Common Factor(GCF), The next is to factor out this Greatest Common Factor(GCF);
24v - 84 = 12(2v - 7)
Therefore, the factored form of 24v - 84 is 12(2v -7)
The factored form of the given expression is 12(2v-7)
Equations are expressions separated by an equal sign
Greatest common factor is the highest value that can go in a particular expressions
Given the expression 24v - 84
Find that factors of both terms
24v = 12 × 2v
84 = 12 × 7
Since 12 is common to both terms, hence the GCF form of the expression will be written as;
24v - 84 = 12(2v - 7)
Hence the factored form of the given expression is 12(2v-7)
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Please help will give brainliest
The coordinates of point F are (8, 4) and the coordinates of point G are (−4, 9) .
What is the slope of the line that is perpendicular to FG¯¯¯¯¯?
Enter your answer as a simplified fraction in the box.
Answer:
[tex]\frac{12}{5}[/tex]
Step-by-step explanation:
First, we need to find the gradient (slope) of the FG line.
To do this we must use the gradient formula:
[tex]\frac{y2 - y1}{x2 - x1}[/tex]
y1 and x1 have to be in the same coordinate set,
x1 = 8, y1 = 4 the (8 , 4) set
x2 = -4, y2 = 9 the (-4 , 9) set
[tex]\frac{9 - 4}{-4 - 8}[/tex]
[tex]\frac{5}{-12}[/tex]
Which is the gradient of FG line.
To find the equation of a line perpendicular to this line, you must do [tex]\frac{-1}{gradient}[/tex]
[tex]\frac{-1}{\frac{5}{-12} }[/tex]
= [tex]\frac{12}{5}[/tex]
So that means the gradient of the line perpendicular to FG is
[tex]\frac{12}{5}[/tex]
on a scale drawing, the scale is inch = 1 foot. What are the dimensions on the scale drawing for a room that is 15 feet by 16 feet?
Answer:
15 inches by 16 inches
OR
1 foot 3 inches by 1 foot four inches
A runner increases his velocity from 0 m/s to 20 m/s in 2.0s. What was his average acceleration?
change in velocity = 20 - 0 = 20
change in time = 2 seconds
Divide the change in velocity over the change in time: 20/2 = 10
The average acceleration is 10 m/s^2
I.e, each second, the speed increases by 10 m/s
Runner's average acceleration was 10 m / s²
The average acceleration refers to how fast the runner is going in relation to time.
It is calculated by the formula:
= Change in speed / Time
Change in distance here is:
= 20 m/s - 0 m/s
= 20 m/s
The acceleration is therefore:
= 20 / 2
= 10 m/s²
In conclusion, the runner was accelerating at a rate of 10 m/s².
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an hour of vacuuming and mopping uses 280 calories this is 40% of the number of calories burned by riding bikes for 1 hour what's the total number of calories burned by riding the bicycle for 2 hours
Riding a bicycle for one hour burns 700 calories. Therefore, biking for two hours burns a total of 1400 calories.
To solve this question, we need to understand that vacuuming and mopping for an hour burns 280 calories, which is 40% of the calories burned by biking for the same time. The first step is to determine the total number of calories burned when biking for one hour.
Let x represent the total number of calories burned by biking for one hour. According to the problem, 40% of x is 280 calories, which we can write as:
0.40x = 280 calories
To find the value of x, we divide both sides of the equation by 0.40:
x = 280 / 0.40
x = 700 calories
Thus, biking for one hour burns 700 calories. Now to find out the total number of calories burned by biking for two hours, we simply multiply this number by 2:
Total calories for 2 hours of biking = 700 calories × 2
Total calories for 2 hours of biking = 1400 calories
The answer is that riding the bicycle for two hours burns a total of 1400 calories.
The rectangle shown has a perimeter of 44 cm and the given area. Its length is 7 more than twice its width. Write and solve a system of equations to find the dimensions of the rectangle.
The length of the rectangle is __ cm and the width of the rectangle is __ cm
Answer:
The length of the rectangle is 17 cm and the width of the rectangle is 5 cm.
Step-by-step explanation:
Given the measurements in the question, you can set up two different equations to find the length and width of the rectangle. First, the formula for the perimeter of a rectangle is: P = 2W + 2L, where W = width and L=length. In this problem the L is '7 more than twice its width', this means our first equation is:
L = 2W + 7
Next, we can use this expression in our formula for perimeter to get our second equation:
P = 2W + 2(2W + 7) or 44 = 2W + 2(2W + 7)
Distribute: 44 = 2W + 4W + 14
Combine like terms: 44 = 6W + 14
Subtract 14 from both sides: 44 - 14 = 6W + 14 - 14 or 30 = 6W
Divide 6 from both sides: 30/6 = 6W/6 or W = 5
Now, solve for L: L = 2(5) + 7 or L = 10 + 7 = 17
So, the width is 5cm and the length is 17 cm.
The length of the rectangle is 17 cm and the width of the rectangle is 5 cm
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that perimeter of a rectangle is 44 cm.
Its length is 7 more than twice its width.
Length=2w+7
Width=w
Perimeter=2(Length+Breadth)
44=2(2w+7)+2w
Apply distributive property on right hand side
44=4w+14+2w
44=6w+14
Subtract 14 on both sides
30=6w
Divide both sides by 5
5=w
So width of rectangle is 6cm and length is 2(5)+7=10+7=17 cm
Hence, the length of the rectangle is 17 cm and the width of the rectangle is 5 cm
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The equation below describes a circle. What are the coordinates of the center of the circle? (X-4)^2+ (y+12)^2=17^2
Answer:
(4,-12)
Step-by-step explanation:
The equation of a circle has the following form:
[tex](x-h)^2+(y-k)^2=r^2[/tex] where (h,k) is the center of a circle with radius r.
Our equation is:
[tex](x-4)^2+(y+12)^2=17^2[/tex]
The center is (4,-12).
Answer:
(4,-12)
Step-by-step explanation:
which graph represents the function f(x)=-3x-2?
heres a trick: if you go to desmos.com/calculator you can type in your equation and it will show you it on the graph.
since f(x)=y you can say y=-3x-2 and it will show you!
Answer:
Option D.
Step-by-step explanation:
The given function is
[tex]f(x)=-3^x-2[/tex]
We need to find the graph of given function.
At x=0,
[tex]f(0)=-3^(0)-2=-3[/tex]
Similarly, substitute the different values of x and find the values of y.
Table of values
x y
-1 -2.33
0 -3
1 -5
2 -11
3 -29
Plot these ordered pairs on a coordinate plane and connect them by a free hand curve. The graph of given function is is shown below.
Therefore, the correct option is D.
What is (7-4n)*6? I NEEEEEEEEED HEELPPPPPP
Answer:
n=1.75
Step-by-step explanation:
(7-4n)*6=0
We simplify the equation to the form, which is simple to understand
(7-4n)*6=0
Reorder the terms in parentheses
(+42-24n)=0
Remove unnecessary parentheses
+42-24n=0
We move all terms containing n to the left and all other terms to the right.
-24n=0-42
We simplify left and right side of the equation.
-24n=-42
We divide both sides of the equation by -24 to get n.
n=1.75
Answer:
42 - 24n
Step-by-step explanation:
This is an expression, not an equation. We can simplify
(7-4n)*6
Distribute the 6
7*6 - 4n*6
42 - 24n
f(x) = x + 5 If you know that the range is {0, 10}, then... The domain must be ??
Answer:
domain {- 5, 5 }
Step-by-step explanation:
given values in the range, that is values of y then to find the domain equate f(x) to the given values in the range, that is
x + 5 = 0 ⇒ x = - 5
x + 5 = 10 ⇒ x = 10 - 5 = 5
domain is x ∈ { - 5, 5 }
Divide r+5/r2+5r-14 by r2+4r-21/r-2
Answer:
r+5 r^2+4r-21
-------------- / --------------------
r^2+5r-14 r-2
r+5 r-2
= -------------- x --------------------
r^2+5r-14 r^2+4r-21
r+5 r-2
= -------------- x --------------------
(r+7)(r-2) (r+7)(r-3)
r+5
= -----------------
(r+7)^2 (r-3)
hope it helps
Step-by-step explanation:
how do u find the axis of symmetry for f(x) = 3(x+4)^2 + 1
Answer:
x= -4 is the axis of symmetry
Step-by-step explanation:
The parabola is written in the form y = a (x-h)^2 +k
The vertex is (h,k) and the axis of symmetry is at x=h.
Given f(x) = 3(x- -4)^2 + 1, the vertex is (-4,1) so the axis of symmetry is x= -4
Two parallel lines are crossed by a transversal . What is the value of k?
Answer:
the answer issss
Step-by-step explanation:
k=60
Answer:
The value of is equal to [tex]k=60\°[/tex]
Step-by-step explanation:
we know that
[tex](2k+11)\°=131\°[/tex] -----> by alternate exterior angles
solve for k
[tex]2k=131\°-11\°[/tex]
[tex]k=120\°/2=60\°[/tex]
jeff invested 3000 in an account that earn 6.5% interest compounded annually. the formula for compound is A(t)=p(1+i)t. how much did jeff have in the account after 3 years
Answer:
Jeff had in the account 3,623.85 after 3 years
Step-by-step explanation:
Investment: p=3,000
Interest: i=6.5%=6.5/100→i=0.065
Time (in years): t=3
A(3)=?
A(t)=p(1+i)^t
t=3→A(3)=p(1+i)^3
Replacing the given values:
A(3)=3,000 (1+0.065)^3
A(3)=3,000 (1.065)^3
A(3)=3,000 (1.207949625)
A(3)=3,623.848875
Rounding to the nearest hundredth:
A(3)=3,623.85
Find the length of x
Answer:
x=5/2
Step-by-step explanation:
We can use ratios of similar triangles to help solve the problem.
side x 5
-------- = --------------- = ---------------
hypotenuse 4 8
Using cross products
x*8 = 4 * 5
8x = 20
Divide each side by 8
8x/8 = 20/8
x = 5/2
Are these fractions proportional? 1/3 = 6/20
Answer:
They are not proportional.
Step-by-step explanation:
To check if the fractions are proportional, we can use cross products.
1 6
----- = --------------
3 20
1 * 20 = 3 * 6
20 = 18
This is not true, so they are not proportional.
Answer,
No
Explanation,
To find out if a pair of fractions are proportional you can use cross multiplication. Only fractions that are equivalent to eachother are proportional.
1/3 = 6/20
1 * 20 = 20
3 * 6 = 18
As we can see they are not equivalent, therefore it is not proportional.
Hope This Helps :-)
If I ate 5 candies from the box containing 9 candies, I ate 5/9 of all candies. So 5 is 5/9 of 9. What part of 12 is 7?
PLZ HELLLP
A cargo ship traveled 150 nautical miles in 6 hours at a constant speed. How far did the cargo ship travel in one hour
Answer:
25 nautical miles
Step-by-step explanation:
We need to find the rate. We can do so using the formula, distance = rate * time
d= rt
We know the distance and the time, so we need to solve for the rate
d/t = rate
d= 150 nautical miles
t = 6 hours
d/t = 150 nautical miles /6 hours
rate = 25 nautical miles per hour
So in 1 hour we can go 25 nautical miles
Answer:
25 nautical miles.
Step-by-step explanation:
Givens
d = 150 nautical milest = 6 hoursr = ???Equation
d = r * tSolution
150 nautical miles = r * 6 hours Divide by 6 hours150 nautical miles/6 hours = r * 6 hours / 6 hours25 nautical miles / hour = rTwo men and 7 women can together do a piece of work in 4 days. It is done by 4 men and 4 women in 3 days. How long would it take for one man or one woman to do the work
Answer:
12 days
Step-by-step explanation:
Time taken by one man = x days , and that by 1 boy = y days
work done in 1 day by one man = 1/x
work done in 1 day by one boy= 1/y
work done by 2 men in one day = 2/x
work done by 7 boys in one day = 7/y
2/x + 7/y = 1/4 -----> [ 1]
work done by 4 men in one day = 4/x
work done by 4 boys in one day = 4/y
4/x + 4/y = 1/3 ----> [2]
Multiplying equation 1 by , 2 ,
2(2/x + 7/y = 1/4 )
= 4/x + 14/y = 1/2 ---> [3]
solving equations 2 and 3
4/x + 4/y = 1/3
- 4/x + 14/y = 1/2
==============
-10/y = 2-3/6
-10/y = -1/6
-1/6y = -10
y = -10 × 6/-1
= 60
2/x + 7/y = 1/4
2/x + 7/60 = 1/4
7/60 - 1/4 = -2/x
-8/60 = -2/x
-120 = -8x
x = -120/-8
x = 15
=================================
Time taken by 1 man to do the whole job = 15 days
time taken by 1 boy to do the whole job = 60 days
time taken by one boy and one man to do one day's work = 1/60 + 1/15
= 1/60 + 4/60
= 5/60 = 1/12
Together they can do it in 12 days !