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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Please help me with my math
What is the probability that a random chosen male voter is a registered Democrat? Round your answer to the nearest tenth of a percent.
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 :)
]Which statements are true? Check all that apply.
The equation |–x – 4| = 8 will have two solutions.
The equation 3.4|0.5x – 42.1| = –20.6 will have one solution.
The equation StartAbsoluteValue StartFraction one-half EndFraction x minus StartFraction 3 Over 4 EndFraction EndAbsoluteValue equals 0. = 0 will have no solutions.
The equation |2x – 10| = –20 will have two solutions.
The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions.
The equation StartAbsoluteValue StartFraction 1 Over 8 EndFraction x minus 1. EndAbsoluteValue equals 5. = 5 will have infinitely many solutions.
The correct answers are:
1. The equation |-x -4| = 8 will have two solutions. (True)
5. The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions. (True)
What is Equation?
An equation is a mathematical statement with an 'equal to =' symbol between two expressions that have equal values.
1. The equation |-x -4| = 8 will have two solutions. (True)
|-x - 4| = 8
-x -4 = ±8
-x -4 = 8 and -x -4 = -8
-x = 8 + 4 and -x = -8 + 4
-x = 12 and -x = -4
x = -12 and x = 4
Therefore, it has two solutions x ∈ {-12, 4}
2. The equation 3.4|0.5x - 42.1| = -20.6 will have one solution. (False)
Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.
3. The equation |1/2x - 3/4| = 0 will have no solutions. (False)
|(1/2)x - 3/4| = 0
(1/2)x - 3/4 = ±0
Since ±0 is the same
(1/2)x = 3/4
x = 2X3/4
x = 3/2
Therefore, it has one solution x = 3/2
4. The equation |2x – 10| = –20 will have two solutions. (False)
Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.
5. The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions. (True)
|0.5x – 0.75| + 4.6 = 0.25
|0.5x – 0.75| = 0.25 - 4.6
|0.5x – 0.75| = -4.35
Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.
6. The equation |(1/8)x - 1| = 5 will have infinitely many solutions. (False)
|(1/8)x - 1| = 5
(1/8)x - 1 = ±5
(1/8)x - 1 = 5 and (1/8)x - 1 = -5
(1/8)x = 5 + 1 and (1/8)x = -5 + 1
(1/8)x = 6 and (1/8)x = -4
x = 6X8 and x = -4X8
x = 48 and x = -32
Thus, it has two solutions x ∈ {48, -32}
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Part b how do these functions differ from functions you have used in algebra in the past?
The functions differ from functions that I have used in algebra in the past as the functions can be combined and are more about rotation rather than where they move.
What is a function?It should be noted that a function simply means an equation where the x that is plugged into the equation will yield exactly on e y from the equation.
In this case, the functions differ from functions that I have used in algebra in the past as the functions can be combined and are more about rotation rather than where they move.
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A culture started with 2,000 bacteria. After 2
hours, it grew to 2,400 bacteria. Predict how
many bacteria will be present after 10 hours.
Round your answer to the nearest whole
number.
P
Aekt
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
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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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 you8. (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!! :)
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
Can somebody help me and tell me if i’m right or not because I don’t know how to do this
Find the value of y.
Answer:
y = 5
Step-by-step explanation:
Since the lines are parallel, same side interior angles are supplementary.
That allows us to solve for x.
7x + 17 + 5x - 5 = 180
12x = 168
x = 14
The angles 23yand 5x - 5 are supplementary, so the sum of the measures equals 180°.
23y + 5x - 5 = 180
We already know that x = 14.
23y + 5(14) - 5 = 180
23y = 115
y = 5
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
Oliver wants to buy apples and blueberries to make a fruit tart. Apples cost $3.50 per pound and blueberries cost $3.25 per pound. How many pounds of fruit does he buy if he buys 2 pounds of apples and 3 pounds of blueberries? How many pounds of fruit does he buy if he buys xx pounds of apples and y pounds of blueberries?
Total pounds, 2 pounds of apples and 3 pounds of blueberries:
Total pounds, xx pounds of apples and y pounds of blueberries:
Need answer quickly as possible!
The total pounds of fruits bought if he buys 2 pounds of apples and 3 pounds of blueberries is $16.75.
The total pounds of fruits bought if he buys x pounds of apples and y pounds of blueberries is $3.50x + $3.25y.
What is the total pounds of fruits bought?The total pounds of fruits bought = (pounds of apples x cost per pound) + (pounds of blueberries x cost per pound)
($3.50 x 2) + (3.25 x 3)
$ 7 + 9.75 = $16.75
($3.50 x x) + (3.25 x y)
$3.50x + $3.25y
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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.
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?
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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The radius of a circle is 7 kilometres. What is the length of a 90° arc?
Answer:
Step-by-step explanation:
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
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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
Find the inequality represented by the graph
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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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
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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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.
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
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
ها ( در محمود) و
Which expression is equivalent to
O
x²7 (3√7)
Step-by-step explanation:
please mark me as brainlest
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
