Answer:
1,29
Step-by-step explanation:
74*2pi/360
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Determine the equation of a cubic polynomial function with roots at (3,0), (2,0) and (-4,0) that also passes through the point (1,30).
Step-by-step explanation:
Step 1: Setting Up the Factors
Our roots are 3, 2, and -4 so
our factors are
[tex](x - 3)(x - 2)(x + 4)[/tex]
Step 2: Initial Test to see if the result equal 30
Let a be a constant, such we have
[tex]a(x - 3)(x - 2)(x + 4) = 30[/tex]
Plug in. 1 for x.
[tex]a(1 - 3)(1 - 2)(1 + 4) = 30[/tex]
[tex]a( - 2)( - 1)(5) = 30[/tex]
[tex]a(10) = 30[/tex]
[tex]a = 3[/tex]
So our equation is
[tex]3(x - 3)(x - 2)(x + 4)[/tex]
Or if you want it simplifed
[tex]3( {x}^{2} - 5x + 6)(x + 4) = 3( {x}^{3} + - {x}^{2} - 14x + 24) = 3 {x}^{3} - 3 {x}^{2} - 42x + 72[/tex]
Answer:
[tex]f(x)=3(x-3)(x-2)(x+4)[/tex]
Step-by-step explanation:
General form of a cubic polynomial function with 3 roots:
[tex]f(x)=a(x-b)(x-c)(x-d)[/tex]
where:
a is some constant to be foundb, c and d are the roots of the functionGiven roots:
(3, 0)(2, 0)(-4, 0)Substitute the given roots into the general form of the function:
[tex]\implies f(x)=a(x-3)(x-2)(x-(-4))[/tex]
[tex]\implies f(x)=a(x-3)(x-2)(x+4)[/tex]
To find the value of a, substitute the given point (1, 30) into the equation:
[tex]\begin{aligned} f(1) & = 30\\\implies a(1-3)(1-2)(1+4) & =30\\a(-2)(-1)(5) & = 30 \\10a & = 30\\\implies a & = 3 \end{aligned}[/tex]
Therefore, the equation of the cubic polynomial function is:
[tex]f(x)=3(x-3)(x-2)(x+4)[/tex]
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When water flow in two Hoses. The first is four times the second's speed, what is the ratio of the radius of the first to the second?
Answer:
4:1
Step-by-step explanation
this should be the answer from how u gave the question, also can i get brainliest ;)
Select the correct answer. If the factors of quadratic function g are (x − 7) and (x + 3), what are the zeros of function g? A. -7 and 3 B. -7 and -3 C. -3 and 7 D. 3 and 7
Answer:
C
Step-by-step explanation:
given the factors are (x - 7) and (x + 3)
equate each factor to zero and solve for x
x - 7 = 0 ⇒ x = 7
x + 3 = 0 ⇒ x = - 3
Henry recorded the number of miles he biked each day for a week. His milles were 25,40,35, 25, 40, 60, and 75.
Enter the data into the statistics calculator
What is the standard deviation of the milles Henry bilked to the nearest tent?
Several paint mixtures are made by mixing blue paint and white paint. Paint Colors Blue Paint White Paint Mixture A 5 cups 12 cups Mixture B 6 cups 6 cups Mixture C 4 cups 12 cups Mixture D 5 cups 6 cups Which mixture has the highest ratio of blue paint to white paint? mixture A mixture B mixture C mixture D
The correct answer is option B which is mixture B will have the highest ratio of blue paint.
What is a ratio?In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.
The given ratios are:-
Mixture A = [tex]\dfrac{5}{12} = 0.41[/tex]
Mixture B = [tex]\dfrac{6}{6}= 1[/tex]
Mixture C = [tex]\dfrac{4}{12}= 0.33[/tex]
Mixture B = [tex]\dfrac{5}{6}=0.83[/tex]
Here the ratio of mixture B is the highest among all the options available.
Therefore the correct answer is option B which is mixture B will have the highest ratio of blue paint.
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NEED HELP ASAP!!!!!
Triangle ABC and DEF are similar. Answer the following questions:
a. What relationship can you write for the angles of these two triangles?
b. What is the length of the missing side?
Answer:
a)<BAC = EDC,<DEC =ABC,ACB=DFE
b)7
Step-by-step explanation:
According to the definition, two triangles are similar if their corresponding angles are congruent and corresponding sides are proportional. Hence, we can find the dimensions of one triangle with the help of another triangle. If ABC and DEF are two similar triangles, then by the help of below-given formulas, we can find the relevant angles and side lengths.
∠A = ∠D, ∠B = ∠E and ∠C = ∠F
AB/DE = BC/EF= AC/DF
It takes 6 hours for 2 people to build a swing set. Can you use the proportion 2 - 6 = 5 - h to determine the number of hours h it will take 5 people to build the swing set? Explain.
The number of hours, h it will take 5 people to build the swing set is; 2.4 hours
What is the number of hours it will take 5 people to build the swing set?From the task content, it follows that it took 6 hours for 2 people to build the swing set, hence, it follows that it'd take 12 hours for 1 person to build the swing.
However, when the work is divided between 5 People, the time taken is therefore; 12/5 = 2.4hours.
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DF=
Help me please:))
Answer:
[tex]\fbox {DF = 20}[/tex]
Step-by-step explanation:
Given :
ΔSDF ~ ΔRTY = 4 : 9 (Ratio of similitude)SF = RT - 2TY = RY + 9SD = 8Step 1 : Find RT
SD : RT = 4 : 98 : RT = 4 : 9RT = 18Step 2 : Find SF
SF = RT - 2SF = 18 - 2SF = 16Step 3 : Find RY
SF : RY = 4 : 916 : RY = 4 : 9RY = 36Step 4 : Find TY
TY = RY + 9TY = 36 + 9TY = 45Step 5 : Find DF
DF : TY = 4 : 9DF : 45 = 4 : 9DF = 20Answer:
DF = 20
Step-by-step explanation:
Triangle SDF has side lengths SD, DF, SF.
Triangle RTY has side lengths
RT = (9/4)SD
RY = (9/4)SF
TY = (9/4)DF
"SF is 2 less than RT" Given
SF = RT - 2
SF = (9/4)SD - 2
"SD = 8" Given
SF = (9/4)(8) - 2
SF = 16
"TY is 9 more than RY" Given
TY = RY + 9
(9/4)DF = (9/4)SF + 9
(9/4)DF = (9/4)(16) + 9
(9/4)DF = 45
DF = 45 × 4/9
DF = 20
What is the measure of angle CED?
There are two triangles labeled ABC and DCE with a common vertex C. In triangle ABC, angle BAC is labeled as y, and angle ABC is labeled as 65 degrees. In triangle DCE, angle CDE is labeled as 65 degrees
y over 2, because Triangle ABC is congruent to triangle DCE
y, because Triangle ABC is similar to triangle EDC
y + 65 degrees, because Triangle ABC is similar to triangle DCE
115 degrees − y, because Triangle ABC is congruent to triangle DCE
The measure of angle CED is y. The correct option is the second option- y, because Triangle ABC is similar to triangle EDC
Similar trianglesFrom the question, we are to determine the measure of angle CED
In the diagram, we can observe that ΔABC is similar to ΔEDC
This is by the Angle-Angle similarity theorem
The theorem states that
If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other
Thus,
Angle CAB = Angle CED
In the diagram,
Angle CAB = y
∴ Angle CED = y
Hence, the measure of angle CED is y. The correct option is the second option- y, because Triangle ABC is similar to triangle EDC
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ها ( در محمود) و
Which expression is equivalent to
O
x²7 (3√7)
Step-by-step explanation:
please mark me as brainlest
URGENT PLEASE HELP
If a+b= -5, find |a+b|+5 / |-a-b|
Answer:
2
Step-by-step explanation:
[tex]a+b=-5[/tex]
[tex]-(a+b)=-a-b=5[/tex]
[tex]\frac{|-5| + 5}{|5|}[/tex]
[tex]\frac{5+5}{5}[/tex]
[tex]2[/tex]
Answer:
2
Step-by-step explanation:
Given:
a + b = -5To find -a - b
Factor out the common term -1:
⇒ -a - b = -(a + b)
Substitute a + b = -5:
⇒ -a - b = -(-5)
Apply rule -(-x) = x:
⇒ -a - b = 5
Therefore:
[tex]\begin{aligned}\implies \sf \dfrac{|a+b|+5}{|-a-b|} & = \sf \dfrac{|-5|+5}{|5|}\\\\& = \sf \dfrac{5+5}{5}\\\\& = \sf \dfrac{10}{5}\\\\& = \sf 2\end{aligned}[/tex]
Note: |-x| = x
Find the value of x. Round to the
nearest tenth.
12
x=[?]
Answer:
17.1
Step-by-step explanation:
Given we have one side and one degree, we can use the trigonometric function "tangent" to solve this right triangle.
Remember that tangent is opposite side over adjacent side, so lets set up the equation:
[tex]tan(35)=\frac{12}{x}[/tex]
Now solve:
[tex]x(tan(35))=12\\x=\frac{12}{tan(35)}[/tex]
As a result, x is equal to approximately 17.1
Any questions feel free to ask :)
Juan is making a fruit salad. He has grapes, watermelon, apples, pineapple, bananas, mangoes, honeydew, and cantaloupe. He wants his fruit salad to contain five different fruits. How many ways can he make the fruit salad if it must contain watermelon?
The number of ways that he can make the fruit salad if it must contain watermelon is 35.
What is Permutation and combination?Selection of the one object from the given samples with replacement or without replacement is called as the permutation. The selection of the items from the sample as they are different with each other.
The salad contains water melon, now we have to select 4 more fruits out of 7.
Using combination
[tex]^{n{C}_r[/tex] = n! / r! (n-r)!
[tex]^{7}C_4[/tex] = 7!/ 4! (7-4)!
= 7*6*5*4! / 4! * 3*2
= 35
Hence, number of ways that he can make the fruit salad if it must contain watermelon is 35.
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Answer: 35 on edge got it right
Step-by-step explanation:
what is the area of stuvwx in the parallelogram below?
Answer:
fuz what hhde you ha thewebsite and it
There are 7 pieces of pie left over in the cafeteria l. If 5 pieces are apples and 2 are cherry, what fraction of the remaining pieces are cherry?
Answer:
2/7
Step-by-step explanation:
To find the fraction that are cherry, take the number that are cherry and put that over the total number of pieces
2 cherry
----------------
7 total
The fraction that are cherry are 2/7
if cospheta =3/5 and pheta is located in the fourth quadrant, then sin2pheta=_____
-8/25
24/5
-24/25
8/25
Step-by-step explanation:
if cospheta =3/5 and pheta is located in the fourth quadrant, then sin2pheta=_____
-8/25
24/5
-24/25
8/25
The correct answer for this question is 8/25
What is 2b - a? If b=12 and a=5
Answer:
24-5=19
Step-by-step explanation:
1. (2b)= 2(12)
2. a=5
3. 24-5
4.9
Please help me with my math
If a(x) = 3x 1 and b (x) = startroot x minus 4 endroot, what is the domain of (b circle a) (x)?
The composite function (boa)(x) is equivalent to √3x-3
Composite functionGiven the following functions
a(x) = 3x +1
b(x) = √x - 4
To determine the composite function (boa)(x)
b(a(x) = b(3x +1)
Substitute 3x + 1 into b(x) to have:
(boa)(x)= √(3x + 1) - 4
(boa)(x) = √3x-3
Hence the composite function (boa)(x) is equivalent to √3x-3
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8. (08.03 LC)
A set of equations is given below:
Equation C: y = 3x+7
Equation D: y = 3x + 2
How many solutions are there to the given set of equations? (1 point)
One solution
OTwo solutions
O Infinitely many solutions
No solution
Answer: No solution
Step-by-step explanation:
The red line is y=3x+7 and the blue line is y=3x+2
The lines do not intersect at any time. Therefore, this set of equations has no solution. I hope this helps! Pls mark brainliest!! :)
PLEASE I NEED HELP!!!!!
How does a person answer pythogoras rule with out a calculator.
Answer:
well by using the formulae a²+b²=c² with "a" being the opposite "b" being the adjacent and "c" being hypotenuse
Answer:
BY LEARNING Pythagorean Theorem Formula Proof using Similar Triangles
Step-by-step explanation:
In a right-angled triangle, the Pythagoras Theorem Formula is expressed as:
c2 = a2 + b2
Where,
'c' = hypotenuse of the right triangle
'a' and 'b' are the other two legs.
How many eight-digit numbers can be formed if the leading digit cannot be a zero
and the last number cannot be 1 or 0?
Answer:
81 x 10^6
Step-by-step explanation:
x0000000
11111111x
22222222
33333333
....................
88888888
99999999
---------------------
The first digit and 8th digit column has only 9 numbers and the rest 6 column have 10 possible numbers
9 x 9 x 10^6 = 81 x 10^6
Which equation represents the line that is parallel to y= 3 and passes through (-2,-8) ?
Answer:
y = - 8
Step-by-step explanation:
y = 3 is a horizontal line that includes all of the x coordinates
just need to find parallel
y = - 8
how can i soolve it?
Answer:
x = 4 y = 1
Step-by-step explanation:
Opposite sides are equal , so
2x-3y = 5
x+5y =9 <====== multiply this by -2 and add to first equation
-13y = -13
then y = 1 and x + 5y = 9 so x = 4
Find the inequality represented by the graph
Which is true of dependent events?
a.) the probability of all dependent events can be calculated using the or formula
b.) you can use a two-way frequency table to calculate the conditional probability of events that are dependent.
c.) the outcome of one event has no effect on the outcome of a second event.
d.) you can find the and probability of dependent events using the formula
branliest to correct answer please no guessing
As per the attached picture Option fourth "the probability of all dependent events can be calculated using the OR formula P(A or B) = P(A) + P(B) - P(A and B)" is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
As we know the dependent events are dependent on what happened before.
Let A and B be dependent events:
Event B will be dependent on the Event A
P(A or B) = P(A) + P(B) - P(A and B)
Thus, option fourth "the probability of all dependent events can be calculated using the OR formula P(A or B) = P(A) + P(B) - P(A and B)" is correct.
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The mass of a box of bolts is 3/4 kg and the mass of a box of screws is 3/5 kg.
a Which box has the greater mass?
b Calculate the difference in mass between the 2 boxes.
Answer:
a) The mass of a box of bolts is greater.
b) 3/20 kg
Step-by-step explanation:
a) Firstly, you have to make the denominators of the two fractions the same (by finding the LCM of the denominators).
The LCM of 4 and 5 is 20.
Converting 3/4 into denominator 20:
[tex]\frac{3 * 5}{4 * 5}[/tex]
= 15/20
Converting 3/5 into denominator 20:
[tex]\frac{3 * 4}{5 * 4}[/tex]
= 12/20
Now comparing the numerators:
15 > 12
Hence,
3/4 > 3/5
b) Difference of the boxes can be done by subtracting the numbers with the same denominator:
15/20 - 12/20
= 3/20 kg
Hope this helps and feel free to give me brainliest! :)
The radius of a circle is 7 kilometres. What is the length of a 90° arc?
Answer:
Step-by-step explanation:
Problem
Solve for xxx.
5x^2 + 60x + 180 = 05x
2
+60x+180=0
Answer:
x = -6
Step-by-step explanation:
5x² + 60x + 180 = 0
5 x 180 = 900
you need 2 numbers that multiplies into 900 and adds into 60. these numbers are 30 and 30. now we can rewrite it
5x² + 30x + 30x + 180 = 0.
split it in half and factorise
5x(x + 6) + 30(x + 6) = 0
this means the brackets are:
(5x + 30)(x + 6) = 0
5x + 30 = 0
5x = -30
x = -6
x + 6 = 0
x = -6
therefore, x = -6.
if f(x)=-x+8 and f(-4), then the result is 12
True or False?
[tex] \sf \blue{True✅}[/tex]
Step-by-step explanation:Given,
[tex]f(x) = - x + 8 \: and \: f( - 4)[/tex]
Solution:
[tex] f( x) = - ( - 4) + 8 \\ \\ = 4 + 8 \\ \\ = 12[/tex]
Hope it help you