Answer:
[tex] f(x) = (x-4)(x-\frac{1}{2})^2 = x^3-5x^2+4.25x -1 [/tex]
Step-by-step explanation:
Recall, if we have a polynomial of the form [tex](x-a)^k \cdot (x-b)^m[/tex], then we say that a is a zero of multiplicity k and b is a zero of multiplicty m. For example, in the polynomial of the form [tex](x+5)^10(x-2)^3[/tex] -5 is a zero of multiplicity 10 and 2 is a zero of multiplicity 3. If we want to know the degree of the polynomial, just add the multiplicity of both zeros (13 in our example).
In this case, we know that the degree of our polynomial should be at least 3(multiplicity 2 and multiplicity 1). So, lets take the polynomial of the form
[tex]f(x)=(x-a)(x-b)^2)[/tex].
In here, a is a zero with multiplicity 1 and b is a zero with multiplicity 2. We are also given that
[tex] f(0) = -1 = (0-a)(0-b)^2 = -a\codt b^2[/tex].
Which implies that [tex] 1 = a\cdot b^2[/tex]. Since the square of any number is a positive number, it must happen that a>0. So, we have that
[tex]b= \pm \sqrt[]{\frac{1}{a}}[/tex].
We can choose any value of a and solve for b. Let us choose a=4. So we can have b=1/2 or b=-1/2. Let's use b=1/2. So our polynomial would be
[tex] f(x) = (x-4)(x-\frac{1}{2})^2 = x^3-5x^2+4.25x -1 [/tex]
which we can easily check that f(0)=-1.
a beetle is 1.8cm long. a drawing of the beetle is made using a scale of 5:1. what is the length of the beetle in the drawing?
Answer: The length of the beetle in the drawing is 9 cm.
Step-by-step explanation:
Hi, since is a scaling up scale, we have to multiply the original length of the beetle (1.8 cm) by 5 to obtain the length of the beetle in the drawing.
Mathematically speaking
5 x 1.8 = 9 cm
The length of the beetle in the drawing is 9 cm.
This type of scale is used to increase in size.
Feel free to ask for more if needed or if you did not understand something.
During the sale, the price of the video camera was marked down 14%. The sale price of the video camera was $744.57. What was the original price of the video camera?
Answer:
848.81
Step-by-step explanation:
find 14 percent of 744.57 then add that to 744.57
The original price of the video camera was $866.50.
Explanation:To find the original price of the video camera, we can use the following equation:
Original price - (14% of original price) = Sale price
Let's assign the variable x to represent the original price. We can set up the equation:
x - 0.14x = $744.57
Simplifying the equation, we get:
0.86x = $744.57
Dividing both sides of the equation by 0.86, we find that:
x = $866.50
So, the original price of the video camera was $866.50.
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Which expression is modeled by this set of arrows on the number line
-6 divided by (- 3) -6 divided by 3
6 divided by (- 3)
6 divided by 3
Answer:
A
Step-by-step explanation:
they are both -
Answer: I think It is B) because it's definitely not C). But it could also be A like the answer above said. (I'm very very sorry if it's not correct!)
B) -6÷3 ?
Jeff has $ 8 and he needs to pay his sister $ 3 . How much will he jeff have after paying his sister ?
Answer:
5
Step-by-step explanation:
if he has 8 and gives 3 to his sister he will be left with 5 later
19. Thomas has a recipe for punch that calls for 2 quarts of juice and 3 quarts of soda.
He wants to
modify this recipe to make more punch but wants the same ratio of juice to soda. He has 5
quarts of juice. How much soda should he use in his punch?
NO
in icbaring
tor marked 100% off The original nrica of the cioater is on
Answer:
7.5 quarts of soda
Step-by-step explanation:
Kindly refer to the attached image for explanations
the diameter of a sphere is 4 centimeters which represents the volume of the sphere 32/3 cm
Answer: 32 cm
Step-by-step explanation:
Hi, the options of the questions are •
32 cm
87 cm
54 cm
167 cm
The formula for the volume of a sphere is
V = 4/3 πr³
Where r is the radius.
Since the radius is equal to the diameter divided by 2:
r = d/2= 4 /2 = 2 cm
Replacing in the formula
V = 4/3 π 2³
Solving
V = 4/3 π 8= 33.51 cm
So, the correct option is 32 cm, which closest to the value.
Feel free to ask for more if needed or if you did not understand something.
What does 2/6 +1/4 equal?
Answer:
7/12
Step-by-step explanation:
4/12 + 3/12
Multiply the 2/6 by 2 and the 1/4 by 3
Answer:
Step-by-step explanation:
LCM of 6, 4 = 12
[tex]\frac{2}{6}+\frac{1}{4}=\frac{2*2}{6*2}+\frac{1*3}{4*3}\\\\=\frac{4}{12}+\frac{3}{12}\\\\=\frac{7}{12}[/tex]
A fossil is found that contains 10% of the amount of carbon- 14 found in a living being. About how old is the fossil?
A) 19,200 years
B) 15,300 years
C) 17,600 years
D) 20,700 years
Answer: 19,200 years
Step-by-step explanation:
What is the slope of (2,6) (-3,-7)
Answer:
[tex]\frac{13}{5}[/tex]
Step-by-step explanation:
Remember this??- [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Now substitue the points on that! It should look like this!- [tex]\frac{6-(-7)}{2-(-3)}[/tex]
Now SOLVE!! You should get- [tex]\frac{13}{5}[/tex]
There ya go!! Stay Safe, Stay at Home!! =)
The cube root shown has been written as a product where one of the factors is a perfect cube. RootIndex 3 StartRoot 162 EndRoot = RootIndex 3 StartRoot 27 EndRoot times RootIndex 3 StartRoot 6 EndRoot The simplest form of RootIndex 3 StartRoot 162 EndRoot is a RootIndex 3 StartRoot b EndRoot, where a = b = .
Answer:
a=3 b=6
Step-by-step explanation:
The cube root of 162 has been factored into the cube root of 27 and the cube root of 6. The simplest form is thus 3 times the cube root of 6, so a = 3 and b = 6.
Explanation:The student is working on finding the cube root of 162 and has already correctly factored this into the cube root of 27 times the cube root of 6. To simplify this, we recognize that 27 is a perfect cube (3³), so the cube root of 27 is 3. Therefore, the simplest form of ∛162 can be written as:
∛162 = ∛27 × ∛6
This simplifies to:
3 × ∛6
Where the ∛ symbol represents the cube root. As such, in the form ∛a∛b, where 'a' is the cube root of a perfect cube and 'b' is the remaining factor, we have a = 3 and b = 6 for this equation.
162 was factored into a product of 27 (a perfect cube) and 6, which cannot be further simplified in terms of cube roots.
a cylindrical bucket has a radius of 6 inches and a height of 18 inches. What is the minimum number of buckets of water needed to completely fill a spherical storage tank that has a radius of 15 inches?
Answer:
Minimum 7 buckets of water is needed to completely fill spherical storage tank.
Step-by-step explanation:
We are given the following in the question:
Cylindrical bucket:
Radius, r = 6 inches
Height = 18 inches
Volume of bucket = Volume of cylinder
[tex]V = \pir^2 h \\V = 3.14\times (6)^2\times 18\\V =2034.72\text{ cubic inches}[/tex]
Spherical storage tank:
Radius, r = 15 inches
Volume of tank = Volume of sphere =
[tex]V =\dfrac{4}{3}\pi r^3\\\\\V = \dfrac{4}{3}\times 3.14\times (15)^3\\\\V = 14130\text{ cubic inches}[/tex]
Number of baskets required =
[tex]n = \dfrac{\text{Volume of tank}}{\text{Volume of bucket}}\\\\n =\dfrac{14130}{2034.72} = 6.94 \approx 7[/tex]
Thus, minimum 7 buckets of water is needed to completely fill spherical storage tank.
Write the coordinates of point A after dilation with a scale factor of 3, centered at the origin.
Given:
Given that the graph of the triangle ABC.
The coordinates of the triangle are A(2,-1), B(-1,1) and C(1,-2)
We need to determine the coordinates of the point A after the dilation with a scale factor of 3 centered at the origin.
Coordinates of the point A after dilation:
The general rule for a coordinate to dilate a factor of c from the origin is given by
[tex](x, y) \rightarrow (cx, cy)[/tex]
Thus, applying the above rule, the coordinate A(2,-1) is dilated by a scale factor of 3 about the origin, we get;
[tex](2,-1)\rightarrow (3(2), 3(-1))[/tex]
Simplifying, we get;
[tex](2,-1)\rightarrow (6,-3)[/tex]
Thus, the coordinates of point A after dilation with a scale factor of 3 centered at the origin is (6,-3)
The area of a square is 9 sq. cm. One side length is 3 cm. What is the other side length?
Answer: 3
Step-by-step explanation: 3x3 is 9, and one side is 3 and we have square centimeters so 3 squared or 3x3 is 9 which makes my answer correct, sorry if it was bad explanation this was the easiest question ive answered, plz follow me at twitch, at InfernoEliteGamingYT21
About what percent of the village women
took between 48 and 56 minutes to collect
one container of water?
0%
25%
100%
50%
Water Collection Times in Minutes
HHHHHHH++++++++++++++++++++
40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Answer:
Exact percentage = 87.5%
Explanation:
We need to find out the percent of the women in the village.
So the percent of one unit is represented by 56/64.
we want 56 out of 64 as a percentage
we multiply by the 100 .
=0.875*100
=87.5 %
So, final answer is 87.5%
If h = 18 units and r = 8 units, then what is the volume of the cone shown above? A. B. C. D.
1,205.76 units^3 or 384 π
Here is why:
The formula for the volume of a cone is:
[tex]V=\frac{1}{3}\pi r^2 h[/tex]
We can plug in.
[tex]V=\frac{1}{3}*3.14*8*8*18[/tex]
= 1,205.76 units^3
~
If you are looking for the exact answer, we will leave π.
[tex]V=\frac{1}{3}*\pi*8*8*18[/tex]
= 384 π
Write the formula for absolute value function if its graph has the vertex at point ( 1/3 ,−3) and passes through the point (1,1).
Answer:
y=|6x-2|-3
Step-by-step explanation:
I can see y=|x-1/3|-3 is a tempting answer, it does have its vertex at (1/3,-3) but it doesn't go through (1,1). This graph needs to be steeper, so we need to multiply x and the -1/3 coefficient next to it.
We multiply x and -1/3 each by 6, and boom! The graph goes through (1,1) and the vertex is still maintained at (1/3,-3) The -3 outside of the function doesn't change because the vertex's y-coordinate is -3, so it must stay the same.
The formula for the absolute value function with the vertex at ([tex]\frac{1}{3}[/tex], -3) and passing through (1, 1) is f(x) = 6|x - [tex]\frac{1}{3}[/tex]| - 3.
To write the formula for an absolute value function with a given vertex and point, we can use the standard form of an absolute value function, which is f(x) = a|x - h| + k, where (h, k) is the vertex of the function. In your question, the vertex is at the point ([tex]\frac{1}{3}[/tex], -3) and the function passes through the point (1, 1).
We can start by substituting the vertex into the formula, which gives us f(x) = a|x - [tex]\frac{1}{3}[/tex]| - 3. To find the value of 'a', we use the fact that the function also passes through the point (1, 1). Substituting x = 1 into the formula gives us 1 = a|1 - [tex]\frac{1}{3}[/tex]| - 3 → 1 = a([tex]\frac{2}{3}[/tex]) - 3 → a = 6. So, the function formula is f(x) = 6|x - [tex]\frac{1}{3}[/tex]| - 3.
solve using comparison method.
a. 2x + 3y = 17 and 3y = 15 - x
Answer:
(2, [tex]\frac{13}{3}[/tex] )
Step-by-step explanation:
Given the 2 equations
2x + 3y = 17 → (1)
3y = 15 - x → (2)
Substitute 3y = 15 - x into (1)
2x + 15 - x = 17, that is
x + 15 = 17 ( subtract 15 from both sides )
x = 2
Substitute x = 2 into either of the 2 equations for corresponding value of y
Substituting in (1)
2(2) + 3y = 17
4 + 3y = 17 ( subtract 4 from both sides )
3y = 13 ( divide both sides by 3 )
y = [tex]\frac{13}{3}[/tex]
Solution is (2, [tex]\frac{13}{3}[/tex] )
Rearranging...
3y + x = 15
3y + 2x = 17
Using elimination method
2x - x = -15 + 17
X = 2
From equation.... 2
3y + 2 = 15
3y = 15 - 2
3y = 13
Y = 13/3
::x = 2 while y = 13/3
I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least $600$ pounds more than each of her trucks, but no more than $\frac{1}{3}$ of the total load her four trucks combined can carry. Based on these facts, what is the greatest load I can be sure that my large truck can carry, in pounds?
Answer:
there is no greatest load
Step-by-step explanation:
Let x and y represent the load capacities of my truck and my neighbor's truck, respectively. We are given two relations:
x ≥ y +600 . . . . . my truck can carry at least 600 pounds more
x ≤ (1/3)(4y) . . . . . my truck carries no more than all 4 of hers
Combining these two inequalities, we have ...
4/3y ≥ x ≥ y +600
1/3y ≥ 600 . . . . . . . subtract y
y ≥ 1800 . . . . . . . . multiply by 3
My truck's capacity is greater than 1800 +600 = 2400 pounds. This is a lower limit. The question asks for an upper limit. The given conditions do not place any upper limit on truck capacity.
Answer:
[tex]\large \boxed{\text{2400 lb}}[/tex]
Step-by-step explanation:
We have two condition:
Let x = the load of your truck
and y = load of their trucks Then
(1) x ≥ y + 600
4y = the total load of their four trucks
⅓ × 4y = the load of load of your truck
(2) ⁴/₃x ≤ y
Calculations:
[tex]\begin{array}{lrcll}(1) & x & = & y+ 600\\(2)& x & =&\dfrac{4}{3}y\\\\(3)& x - 600 & =&y&\text{Subtracted 600 from each side of (1)}\\& x & = & \dfrac{4}{3}(x - 600)&\text{Substituted (3) into (2)}\\\\&3x & = & 4(x - 600)&\text{Multiplied each side by 3}\\\end{array}[/tex]
[tex]\begin{array}{lrcll}&3x & = & 4x - 2400&\text{Distributed the 4}\\&3x + 2400 & = & 4x&\text{Added 2400 to each side}\\ & x & = & \mathbf{2400}&\text{Subtracted 3x from each side}\\\end{array}\\\text{The greatest load my truck can carry is $\large \boxed{\textbf{2400 lb}}$}}[/tex]
Mary more likely to draw a red ball followed by a green ball or a blue ball among the first two balls to be drawn?
A. Mary is more likely to draw a blue ball among the first two balls to be drawn, because
OB. Mary is more likely to draw a red ball followed by a green ball, because
C. Mary is more likely to draw a red ball followed by a green ball, because
OD. Mary is more likely to draw a blue ball among the first two balls to be drawn, because
Reset
Next Question
Answer:
c
Step-by-step explanation:
beacuse in the question it says mary is more likley to draw a green ball after a red ball
A computer randomly selects a number from the given set.
11.2.5. 10. 25, 30, 36}
What is the probability that an even number is sele
Enter your answer as a fraction, in simplest form, in the box.
P(even)=
Step-by-step explanation:
Given
{ 11 , 2 , 5 , 10 , 25 , 30 , 36}
No of sample space, n(s) = 7
Even numbers = 2 , 10 , 30 ,36
No of favourable cases, n(e) = 4
Now
Probability that an even number will be selected is, P(even) = n (e) / n(s)
= 4/ 7
Hope it will help you :)
Graph the system of linear equations.
{x=0
{y=1/2
Which of the following points is the one true solution?
A)( 1/2,0)
B)(1/2,1/2)
C)(0, 0)
D)(0,1/2)
Answer:its d i hope i helped
Step-by-step explanation:
Answer:
The answer is (0,1/2)
Step-by-step explanation:
Think of how you would put x y if you had a chart x on the left and y on the right, hope this helps :^)
Todd has 35 pieces of candy. He decides to give 5 pieces of candy to each of his friends. How many friends will he be able to give candy to?
Answer:
6 or 7
Step-by-step explanation:
if he does not take any himself, the answer is 7 as
35/5=7
if he takes 5 himself, the answer is 6 because
35-5=30
30/5=6
Todd will be able to give candy to 7 friends.
Explanation:To find out how many friends Todd will be able to give candy to, we need to divide the total number of candy pieces he has (35) by the number of candy pieces he wants to give to each friend (5).
35 ÷ 5 = 7
Todd will be able to give candy to 7 friends.
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There are 6 houses on a small street. Each house has
a family with 4 children, 2 cats and a dog.
1. How many children are there living on this street?
2. How many pets are there living on this street?
Answer:
There are 24 children living on the street. There are 18 pets living on the street.
Step-by-step explanation:
The answer is 24 chilren because you have to multiply the amount of children and the amount of houses in the street. When you do that you get 24.
There are 18 pets living on the street because in total 3 pets are living in EACH house. 6×3=18.
Use the diagram to find the measures of all the angles, given that m∠2=159∘.
Answer:
m∠1=21°, m∠2=159°, m∠3=21°, m∠4=159°
Step-by-step explanation:
All of the angles added up = 360°
We know that angles 2 and 4 are the same, due to angle rules.
If all of the angles, added up, equal 360, and angles 2 and 4 are equal, we have an equation. Note: m∠2=159°
159+159+x+x=360 *x represents the measure of both angles 1 AND 3, since they are identical*318+x+x=360318+2x=360subtract 318 from BOTH sides2x=42divide BOTH sides by 2x=21m∠x represents the measure for angle 1, along with the measure of angle 3.HOPE THIS HELPED! Brainliest??
Given that m∠2=159∘, any vertical angle to it will also measure 159∘. Use the angle sum property of triangles to calculate any other angle in a triangle.
Explanation:To find the measure of all the angles in the diagram, you'll have to use your understanding of angle relationships. Since you've been provided that m∠2=159∘, you can use this to calculate the measures of the rest. When dealing with a pair of vertical angles, remember that they are equal. Therefore, if m∠2=159∘, then its vertical angle will also measure 159∘. Also, using the angle sum property of triangles, which states that the sum of all interior angles of a triangle sum to 180∘, you can calculate the missing angles if the diagram indicates a triangle.
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Tysm for all the help i will reply!
Hi there! Hopefully this helps!
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The Answer: a decline in prices.
Make x the subject of:
2x + a = b (x - 2)
Answer:
no solution
Step-by-step explanation:
e. These are loans that accrue interest from the day you get them and they have a fixed
interest rate of 6.8%.
Answer:
Step-by-step explanation:
Sounds like "continuous compounding."
Here, A = Pe(0.068t), where t is the number of years.
Final answer:
Subsidized Stafford Loans are for undergraduates with financial need and the government pays the interest while in school. Unsubsidized Stafford Loans are for all students and accrue interest immediately. Private loans often have variable interest rates and are less advantageous than federal loans.
Explanation:
Subsidized Stafford Loans are offered to undergraduate students with financial need, and the interest is paid by the government while the student is in school, during deferment periods, and for six months after graduation, commonly referred to as the grace period. The interest rate is fixed and typically lower than that of unsubsidized loans. The maximum loan amount varies, but it can go up to $12,500 per year of schooling.
Unsubsidized Stafford Loans do not require demonstrating financial need and are available to both undergraduate and graduate students. Interest accrues from the time the loan is disbursed, and the student is responsible for all of it, including while they are in school. Like subsidized loans, they also have a fixed interest rate and a maximum loan amount of up to $12,500 per year for undergraduates and $20,500 per year for graduate students.
Private loans are provided by banks, credit unions, or other financial institutions and can have variable interest rates, which means the rate may increase or decrease over time. Private loans are less favorable compared to federal loans due to higher interest rates and less flexible repayment options.
Other options like Direct PLUS Loans and Direct Consolidation Loans are also available for specific student populations and situations. PLUS Loans are for graduate or professional students and parents, whereas Consolidation Loans allow combining federal loans into one.
Since federal loans offer lower interest rates and more flexible repayment terms than private loans, they are generally the preferred choice for students. Aid offices often guide students to preferred lenders, but it's essential to understand all options and choose loans wisely.
In ∆ABC, ∠A is a right angle and m∠B = 45°. Find BC.
3 sides of the triangle ABC and the side A is a right angle 11ft
11 ft
11/2 ft
/22 ft
2/11ft
Answer:
22ft
Step-by-step explanation:
How do I solve a special right triangle
Answer:
Step-by-step explanation:
In an isosceles right triangle, the angle measures are 45°-45°-90°, and the side lengths create a ratio where the measure of the hypotenuse is sqrt(2) times the measure of each leg as seen in the diagram below.And with a 30°-60°-90°, the measure of the hypotenuse is two times that of the leg opposite the 30° angle, and the measure of the other leg is sqrt(3) times that of the leg opposite the 30° also seen in the diagram below.look at the examples below~
Final answer:
To solve special right triangles, utilize the mnemonic SOHCAHTOA and apply the Pythagorean theorem along with trigonometric functions to find side lengths and angles.
Explanation:
To solve a special right triangle, you'll need to use various relationships between the sides and the angles. A popular mnemonic for remembering these relationships is "SOHCAHTOA", which stands for Sine equals Opposite over Hypotenuse, Cosine equals Adjacent over Hypotenuse, and Tangent equals Opposite over Adjacent. It's useful for finding the values of the sides and angles of a right triangle.
For problems involving right triangles, if you have the length of one side (x) and the hypotenuse (r), you can use the Pythagorean theorem to find the length of the other side. The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
Moreover, you can find the angles aside from the right angle by applying trigonometric functions such as sine, cosine, or tangent, which relate the angles to the lengths of the sides. For example, the sine of an acute angle would be the length of the opposite side divided by the length of the hypotenuse. The cosine would be the adjacent side divided by the hypotenuse, and the tangent would be the opposite side divided by the adjacent side.
A ball rolls 4.34 feet each second. how far will it roll in 2.8 seconds
Answer:
12.152
Step-by-step explanation: