Answer:
B. The range is all real numbers. D. It is a quadratic function.Step-by-step explanation:
Given the functions f(x) = 3x² + 4 and g(x) = 2x − 3, to know that statements that is true about f+g, we will need to add the functions together first.
f(x)+g(x) = 3x² + 4 + 2x - 3
f(x)+g(x) = 3x²+2x +4 - 3
f(x)+g(x) = 3x²+2x + 1
The highest degree of a quadratic function is 2 and since the highest degree of the resulting function is 2, hence the resulting sum of the equations is quadratic.
Also the range of the values is all real numbers because the presence of x² in the function will always return a positive value greater than x.
Hence the correct statements are 'the range is all real numbers and it is a quadratic function'
Answer:
B AND D
Step-by-step explanation:
Machine A and Machine B are each used to make 660 widgets. It takes Machine A x hours longer to produce 660 widgets than Machine B. Machine B produces y % more widgets per hour than Machine A. How long does it take Machine A to make 660 widgets?
Answer:
A. x + 100x/y
Step-by-step explanation:
Machine A= x hours longer to produce 660 widget than machine B
Machine B produces y% more widget per hour than machine A
let
b = Number of hours it takes Machine B to make 660 widgets.
Time taken for Machine A to make the 660 widgets = x + b.
Rate of Machine B = 660/b
Rate of Machine A = 660 / (x + b).
Machine B produces y% more widgets per hour than Machine A:
660 / (x + b)(1 + y/100) = 660/b
1 / (x + b)(1 + y/100) = 1 / b
Multiply both sides by (x+b)
1 + y/100 = (x + b)/b
1 + y/100 = x/b + 1
Subtract 1 from both sides
y/100 = x/b
Take the inverse of both sides
100/y = b/x
Make b the subject
100x/y = b
b=100x/y
The time taken for Machine A to make the 660 widgets is x + b = x + 100x/y.
Answer is A. x + 100x/y
According to the number line, which statement MUST be true? A) A > 1 B) B > 4 C) C < 4 D) D < 0
Answer:
The anwser is C) C < 4
......... .
Let's make some smores! Chocolate bars come in packs of 8 and graham crackers come in packs of 12. What is the smallest number of chocolate bars and graham crackers we would need to buy so we don't have any left over?
Answer:
3 chocolate bars and 2 graham crackers
Step-by-step explanation:
8 times 3 equals 24
12 times 2 equals 24
Can some one help me on this math question its confusing ill give brainly when right!!!
Answer:
s - t = 10 - -7 = 17
Step-by-step explanation:
I only see
s - t
nothing else is there to evaluate (or calculate).
s - t = 10 - -7 = 17 (as a double "-" always turns into a "+").
you really needed help with that ?
Answer:
= s-t
= 10 - (-7)
= 10 + 7
= 17
✌✌✌✌
help me plsssssssssssssssss
Answer:
Step-by-step explanation:
I'm assuming you are trying to solve for x. I'm not sure, but that's what I figured out for the answer, so I'm gonna go with that. : )
We are looking for the value of x to make that statement true. It's going to take some trig manipulations, but if you are at this level of precalc, these identities should definitely NOT be new to you. We will begin by squaring both sides of that equation to get:
[tex]9sin^2(x)+3cos^2(x)=3[/tex]
From here we will factor out a 3 to get:
[tex]3(3sin^2x+cos^2x)=3[/tex] and then divide both sides by 3 to get:
[tex]3sin^2x+cos^2x=1[/tex]
Knowing the Pythagorean identity for the trig ratios, we will replace the sin-squared with what it is equal to in terms of cos-squared. If:
[tex]sin^2x+cos^2x=1[/tex], then
[tex]sin^2x=1-cos^2x[/tex]. Making that replacement gives us an equation with only one trig ratio in it, namely, cos:
[tex]3(1-cos^2x)+cos^2x=1[/tex] and distributing:
[tex]3-3cos^2x+cos^2x=1[/tex] which simplifies down to:
[tex]-2cos^2x=-2[/tex]. Divide both sides by -2 to get:
[tex]cos^2x=1[/tex]. When you take the square root of both sides you get:
[tex]cos(x)=1[/tex] and [tex]cos(x)=-1[/tex]. Here is where we will use the unit circle to see where the cos is 1 and where the cos is -1. You didn't give me an interval in which to work, so I am going to use from 0 degrees to 180. Within that interval, the cos is 1 at 0 degrees; within that interval, the cos is -1 at 180.
Now we need to plug those values into the original equation to see if they work. One of them may be extraneous. Plugging in 0 first:
3sin(0) + √3cos(0) = -√3. We need to see if this is true.
The sin of 0 is 0; the cos of 0 is 1, so
0 + (√3)(1) = -√3?
The left side is √3, not -√3, so 0 doesn't work. Let's try 180 now, shall we?
3sin(180) + √3cos(180) = -√3. We need to see if this is true.
The sin of 180 is 0; the cos of 180 is -1, so
0 + (√3)(-1) = -√3?
The left side is -√3 and so is the right side, so
x = 180°
Stewart is hiring a plumber to fit his shower. He charges a callout fee of £18.50 and then £x per hour after that. The plumber charges him £167.00 and it takes him 9 hours. How much does the plumber charge per hour?
Answer:
Step-by-step explanation:
Amount charges by plumber = £ 167.00
Call out fee = £ 18.50
Charge excluding the call out fee = 167 - 18.50 = £ 148.50
Total hours worked = 9 hours
Charge per hour = charge excluding the call out fee ÷ total hours
= 148.50 ÷ 9
= £ 16.50
PLEASE HELP
WILL THANK YOU AND GIVE BRAINLIEST
Answer:
15. 6444.44445
14. 484
Step-by-step explanation:
Variance 0.7775
Find the standard deviation (hint: the standard deviation is the square root of the variance)
Answer:
0.88175960442
Step-by-step explanation:
The square root of 0.7775 is 0.88175960442
The value of standard deviation will be;
⇒ 0.8803
What is mean by square root of a number?
A square root of a number is a value that multiplied by itself gives the same number.
Given that;
The value of Variance = 0.7775
Now,
Since, The standard deviation is the square root of the variance.
Hence, We can formulate;
The value of standard deviation = √0.7775
= 0.8803
Thus, The value of standard deviation will be;
⇒ 0.8803
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Geometry, please answer question ASAP
Answer: I think it would be C
Step-by-step explanation:
Answer:
the correct answer is C because its the only polygon with a caved in feature
Can you help me find all the seventh roots of unity? what do they look like graphed?
Answer:
There are seven seventh roots of unity, e2πki7 , all on the unit circle, r=1 above.
The first one is at θ=2π7=360∘7=5137 ∘ , and there are others at 4π7,6π7,8π7,10π7,12π7 and of course at 0 radians, i.e. unity itself.
How to find?
There are 4 fourth roots of unity and they are 1, i,−1 and−i
Each of the roots of unity can be found by changing the value of k k k in the expression e 2 k π i / n e^{2k\pi i/n} e2kπi/n. By Euler's formula, e 2 π i = cos ( 2 π ) + i sin ( 2 π ) = 1.
plzzzz HELP ME ASAP WILL MARK AS BRAINLEIEST
Answer:
Hey there!
Part A. This is a proportional relationship because the amount of dollars she earns per hour is constant. We can divide her total income by the number of hours she works to find that she earns 12.50 dollars per hour.
Part B. Joslyn will always earn more money than Kate because she earns more money per hour, and the slope of Joslyn's line is greater.
Let me know if this helps :)
tan α=2.4, Find: sin α and cot α
Answer:
cot α = 1/tan α = 1/2.4 = 0.42
Step-by-step explanation:
cot α=0.42
sin α = 0.92
we know that cot α = 1/tan α
thus,
cot α = 1/tan α = 1/2.4 = 0.42
we know that
sin(x)=tan(x)1+tan2(x)√
[tex]\ sin(\alpha )=tan(\alpha )/\sqrt{ 1+tan^2(\alpha )} \\sin(\alpha )= 2.4/\sqrt{1+2.4^2} = 2.4/\sqrt{1+5.76}\\sin(\alpha )= 2.4/\sqrt{6.76} = 2.4/2.6 = 12/13 = 0.92[/tex]
sin α = 0.92
Simplify 7(A - 6).
A - 6
7A - 6
7A - 42
Answer:
7A-42
Step-by-step explanation:
Select all of the numbers that are correctly written in scientific notation. 10.8\times10^{-3}10.8×10 −3 0.54\times10^60.54×10 6 1\times10^{-4}1×10 −4 7.6\times10^{2.5}7.6×10 2.5 9.8\times10^59.8×10 5
Answer:
1×10⁻⁴ and 9.8×10⁵Step-by-step explanation:
The standard form of writing a scientific notation is expressed as [tex]a.b*10^n[/tex] where a, b and n are integers. Note that a, b and n cannot be a fraction. When writing in scientific notation, the value of 'a' must not be equal to zero and it must not be a 'two digits values' but just 'a digit value'.
Based on the above conclusion, the following numbers are correctly written in scientific notation.
1×10⁻⁴ and 9.8×10⁵
- The expression 10.8×10 −3 is not correctly written because the value of a on comparison is a two digits number i.e 10.
- Also, 0.54×10^6 is not correctly written because a is zero on comparison
- 7.6×10 2.5 is not correctly written because the power is a decimal number i.e 2.5. We must only have an integer as the degree.
In a local kickball league, the ratio of college graduates with a graduate degree to non-college graduates is 1:8, and the ratio of college graduates without a graduate degree to non-college graduates is 2:3. If one random college graduate is picked, what is the probability that they hold a graduate degree
Answer:
3 / 19
Step-by-step explanation:
Given the following :
ratio of college graduates with a graduate degree to non-college graduates = 1:8
ratio of college graduates without a graduate degree to non-college graduates is 2:3
If college graduate with a degree = A
College graduate without a degree = B
Non-college graduate = C
College graduate to non college graduate = A:C
College graduate without degree to non college graduate = B:C
A:C = 1:8 - - - (1) ; B:C = 2:3 - - - (2)
Combining the two ratios :
To do so : the proportion of non college graduate should be the same in both ratios
To do this, multiply (1) by 3 and (2) by 8
A:C = 3 : 24
B:C = 16 : 24
combining both, we have :
A:B:C = 3:16:24
If one random college graduate is picked, what is the probability that they hold a graduate degree?
Total proportion of college graduate : (college graduates with degree + college graduates without degree)
A + B = (3 + 16) = 19
Proportion who hold a graduate degree = A = 3
Probability = require outcome / Total possible outcomes
Thus :
P = A / (A +B)
= 3/19
I NEED HELP ASAP PLEASE!!!
Q2 If 2w + 7 = ─9, what is the value of 15 – 4w? (4 is negative)
Q3 Solve the following equations: a) 3/4(16m − 24) = –48 (24 is negative) b) –20 = 1/6(36 + 12g)
Answer:
Q2: -17
Q3: a) -5/2 b) g = -13
Step-by-step explanation:
2w+7 = -9
2w = -9 - 7
w = -16/2
w = -8
---
15 - 4w
= 15 - 4(-8)
= 15 - 32
= -17
----------------------
Q3:
a) 3/4(16m-24) = -48
16m -24 = -48 ÷ 3/4
16m = -64 + 24
16m = -40
m = -5/2
b) -20 = 1/6(36+12g)
-20 = 1/6 × 6(6+2g)
(cross out the 6 from 1/6 and 6)
-20 = 6 + 2g
-20-2g= 6
-2g = 6+20
-2g = 26
g = 26/-2
g = -13
*HELP*
calculate the pay for the following day of a weekly time card given a wage of $12 an hour
Answer:
96 dollars and 50 cents
Step-by-step explanation:
Dtermine the answer to (−5) + 4 and explain the steps using a number line
Answer:
Step-by-step explanation:
=-5 +4
= -1
put a dot on -1 and go from -5 to -1 and then from -1 to -5
If 4SINB=3SIN(2A+B) :
Prove that:7COT(A+B)=COTA
Answer:
Step-by-step explanation:
Given the expression 4sinB = 3sin(2A+B), we are to show that the expression 7cot(A+B) = cotA
Starting with the expression
4sinB= 3sin(2A+B)
Let us re write angle B = (A + B) - A
and 2A + B = (A + B) + A
Substituting the derived expression back into the original expression ww will have;
4Sin{(A + B) - A } = 3Sin{(A + B)+ A}
From trigonometry identity;
Sin(D+E) = SinDcosE + CosDSinE
Sin(D-E) = SinDcosE - CosDSinE
Applying this in the expression above;
4{Sin(A+B)CosA - Cos(A+B)SinA} = 3{Sin(A+B)CosA + Cos(A+B)sinA}
Open the bracket
4Sin(A+B)CosA - 4Cos(A+B)SinA = 3Sin(A+B)CosA + 3Cos(A+B)sinA
Collecting like terms
4Sin(A+B)CosA - 3Sin(A+B)cosA = 3Cos(A+B)sinA + 4Cos(A+B)sinA
Sin(A+B)CosA = 7Cos(A+B)sinA
Divide both sides by sinA
Sin(A+B)CosA/sinA= 7Cos(A+B)sinA/sinA
Since cosA/sinA = cotA, the expression becomes;
Sin(A+B)cotA = 7Cos(A+B)
Finally, divide both sides of the resulting equation by sin(A+B)
Sin(A+B)cotA/sin(A+B) = 7Cos(A+B)/sin(A+B)
CotA = 7cot(A+B) Proved!
Ashish is 175 cm tall his sister Annu is 8% shorter than him what is Annu's height
pls help
Answer:
8% out of 175 = ( 8 ÷ 100 ) × 175 = 14
175 cm - 14 = 161 cm
...............
HELP ASAP ITS SO HARD! Kelsey did the following division problem. Her teacher says that the quotient she found is wrong. −2 5/6 ÷ 1 1/3 −17/6 ÷ 4/3 −6/17• 3/4 −6×3 divided by 17×4 −18/68 −9/34 A. Identify what Kelsey did wrong in her calculations. B. Find the correct quotient, showing all of your calculations.
Part A
Her steps were
[tex]-2 \frac{5}{6} \div 1 \frac{1}{3}\\\\-\frac{17}{6} \div \frac{4}{3}\\\\-\frac{6}{17} \times \frac{3}{4}\\\\-\frac{6\times 3}{17\times4}\\\\-\frac{18}{68}\\\\-\frac{9}{34}\\\\[/tex]
Kelsey made a mistake on line 3. Note how the 17/6 flips to 6/17. This is not correct. You keep the first fraction the same, but you do flip the second fraction. This only applies when you divide two fractions.
The third step should look like [tex]-\frac{17}{6}\times \frac{3}{4}[/tex]
=======================================================
Part B
Here's what she should have written
[tex]-2 \frac{5}{6} \div 1 \frac{1}{3}\\\\-\frac{17}{6} \div \frac{4}{3}\\\\-\frac{17}{6} \times \frac{3}{4}\\\\-\frac{17\times 3}{6\times 4}\\\\-\frac{51}{24}\\\\-\frac{17}{8}\\\\[/tex]
If you want to convert that improper fraction to a mixed number, then you could do something like this
[tex]-\frac{17}{8} = -\frac{16+1}{8}\\\\-\frac{17}{8} = -\frac{16}{8}-\frac{1}{8}\\\\-\frac{17}{8} = -2 \frac{1}{8}\\\\[/tex]
Or you could divide 17 over 8 using long division to get 2 remainder 1. The 2 is the quotient that goes to the left of the 1/8. The remainder of 1 is the numerator of 1/8.
Please does anyone know how to factorize x(x - 1) + 3x
Answer:
=x(x-1) +3x
= x^2-x+3x
=x^2 +2x
=x(x+2)
Step-by-step explanation:
Point B lies between points A and C, and all three points lie on point AC, which of the following is not true? A. Point B lies on segment AC B. Point C lies on ray AB C. Point A lies on ray BC D. Point C lies on line AB
Answer:
C. Point A lies on ray BC
Step-by-step explanation:
Points A and C can be connected by a segment which would be a measure of the distance between the points. Locating point B between AC, makes the three points lying on segment AC.
A ray extends from a point to infinity, a line extend to infinity on both sides, while a segment is known to have two endpoints. Therefore, points AC are the end points of the segment AC, and point B between this segment confirms that point B lies on the segment AC. Therefore, Point A lies on ray BC is not correct.
Determine the derivative of f(x) = -5x+3x from first principles first Calculate
Answer:
The derivative of the function f(x) = -5x+3x is ----> -2
Step-by-step explanation:
Please answer answer question
Answer:
The correct answer is
Step-by-step explanation:
11 square centimeters.
Hope this helps....
Have a nice day!!!!
At the end of the first year, a zoo has 10 monkeys. If the number of monkeys doubles each year, how many will there be at the end of the fifth year?
A. 120
B. 160
C. 60
D. 50
Which of the following equations has exactly one solution?
A. 4x – 4 + 2x = 6x - 4
B. 2(4x + 5) = 8x + 10
C. 4x - 8 = 4(x - 4)
D. 3x + 5 = 2x - 6
The equation with exactly one solution is 3x + 5 = 2x - 6. Option D is correct.
To determine which equation has exactly one solution, we need to solve each equation and see if we end up with a unique value for 'x'.
4x – 4 + 2x = 6x - 4
Combine the x terms on the left side: 6x - 4 = 6x - 4
This equation is an identity and holds true for all values of x. It doesn't have a unique solution.
B. 2(4x + 5) = 8x + 10
Distribute the 2 on the left side: 8x + 10 = 8x + 10
Similar to the previous equation, this equation is also an identity and holds true for all values of x.
It doesn't have a unique solution.
4x - 8 = 4(x - 4)
Distribute the 4 on the right side: 4x - 8 = 4x - 16
Subtract 4x from both sides: -8 = -16
This equation is contradictory and has no solution.
3x + 5 = 2x - 6
Subtract 2x from both sides: x + 5 = -6
Subtract 5 from both sides: x = -11
This equation has a unique solution, x = -11.
So, the equation with exactly one solution is 3x + 5 = 2x - 6. Option D is correct.
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A mother who is 35 years old has two sons, one of whom is twice as old as the other. In 3 years the sum of all their ages will be 59 years. How old are the boys at present ?
Answer:
son2: 5
son1: 10
Step-by-step explanation:
2x (son1) + x (son2) + 35 (mother) + 3 (years)*3 (people) = 59
3x = 15
x = 5
The age of each boy at present will be 2 years and 3 years.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Let the age of the sons will be x and y.
A mother who is 35 years old has two sons, one of whom is twice as old as the other. Then the equation will be
x = 2y
In 3 years, the sum of all their ages will be 59 years. Then the equation will be
x + y + x + 1 + y + 1 + x + 2 + y + 2 + 35 = 59
Simplify the equation, we have
3x + 3y + 41 = 59
6y + 3y = 59 – 41
9y = 18
y = 2
Then the value of x will be
x = 2y
x = 2(2)
x = 4
Thus, the age of each boy at present will be 2 years and 3 years.
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The price for 2 mangoes and 3 guavas is RM 8.00. The price for 3 mangoes and a guava is RM 5.00
i) Form simultaneous linear equations in two variables based on the above situation.
ii) Represent the simultaneous linear equations graphically and explain the type of solutions obtained
here is the answer for question ii
solve for x 3(x+2) = 12
Answer:
x=2
Step-by-step explanation:
3(x+2) = 12
Divide by 3
3/3(x+2) = 12/3
x+2 = 4
Subtract 2 from each side
x+2-2 = 4-2
x =2
Answer:
The value of x is equal to 2.
Step-by-step explanation:
3(x + 2) = 12
Distribute 3 to (x + 2)
3x + 6 = 12
Subtract 6 from both sides of the equation.
3x = 6
Divide 3 on both sides of the equation.
x = 2
The value of x is 2