Answer:
(r o q)(-1) = 20
(q o r)(-1) = -11
Step-by-step explanation:
Given
[tex]q(x) = -2x + 1[/tex]
[tex]r(x) = 2x^2 + 2[/tex]
Solving (a): (r o q)(-1)
In function:
(r o q)(x) = r(q(x))
So, first we calculate q(-1)
[tex]q(x) = -2x + 1[/tex]
[tex]q(-1) = -2(-1) + 1[/tex]
[tex]q(-1) = 2 + 1[/tex]
[tex]q(-1) = 3[/tex]
Next, we calculate r(q(-1))
Substitute 3 for q(-1)in r(q(-1))
r(q(-1)) = r(3)
This gives:
[tex]r(x) = 2x^2 + 2[/tex]
[tex]r(3) = 2(3)^2 + 2[/tex]
[tex]r(-1) = 2*9 + 2[/tex]
[tex]r(-1) = 20[/tex]
Hence:
(r o q)(-1) = 20
Solving (b): (q o r)(-1)
So, first we calculate r(-1)
[tex]r(x) = 2x^2 + 2[/tex]
[tex]r(-1) = 2(-1)^2 + 2[/tex]
[tex]r(-1) = 2*1 + 2[/tex]
[tex]r(-1) = 6\\[/tex]
Next, we calculate r(q(-1))
Substitute 6 for r(-1)in q(r(-1))
q(r(-1)) = q(6)
[tex]q(x) = -2x + 1[/tex]
[tex]q(6) = -2(6) + 1[/tex]
[tex]q(6) =- 12 + 1[/tex]
[tex]q(6) = -11[/tex]
Hence:
(q o r)(-1) = -11
Find the distance between the points ( 2.4 , -5.4 ) and ( 9.2 , -5.4 )
The distance between the points where the points are given as (2.4, -5.4) and (9.2-5.4) is 6.8 units
How to determine the distance between the points?The points are given as
(2.4, -5.4) and (9.2, -5.4)
The distance between the points is calculated as
d = √(x2 - x1)^2 + (y2 - y1)^2
Substitute the known values in the above equation
So, we have
d = √(9.2 - 2.4)^2 + (-5.4 + 5.4)^2
Evaluate the sum in the above equation
So, we have
d = √(9.2 - 2.4)^2 + (0)^2
Evaluate the difference in the above equation
So, we have
d = √(6.8)^2 + (0)^2
Evaluate the exponents in the above equation
So, we have
d = √46.24 + 0
Evaluate the sum in the above equation
So, we have
d = √46.24
Evaluate the exponents in the above equation
So, we have
d = 6.8
Hence, the distance between the points where the points are given as (2.4, -5.4) and (9.2-5.4) is 6.8 units
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Which lines in the following proof of △ABC≅△CDA have the correct justification? Select all that apply.
Options:
A. AC≅AC, Reflexive Property of Congruence
B. ∠ACB≅∠CAD, Alternate Interior Angles Theorem
C. ∠BAC≅∠DCA, Alternate Interior Angles Theorem
D. △ABC≅△CDA, SAS Triangle Congruence Theorem
Answer:
A, B, CStep-by-step explanation:
Options:
A. AC≅AC, Reflexive Property of Congruence
Correct. This is shared side of the triangles ABC and CDAB. ∠ACB≅∠CAD, Alternate Interior Angles Theorem
Correct. BC and AD are parallel and AC is transversalC. ∠BAC≅∠DCA, Alternate Interior Angles Theorem
Correct. AB and DC are parallel and AC is transversalD. △ABC≅△CDA, SAS Triangle Congruence Theorem
Incorrect. This should be ASA as we have shown above the angles A and C and included side AC are congruent.Answer:
A and B and C
theres another answer right here that explains why
What are the roots of f(x)=x^3-x^2-5x-3?
Answer:
x=3 and x=-1
Step-by-step explanation:
Given Descartes' Rule of Signs, there is only one positive root and one negative root.
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient.
So P could be +1, -1, +3, or -3, while Q could be 1 or -1.
Therefore, P/Q could be +1, -1, +3, or -3.
Then we use synthetic division to find the correct factor(s):
1 | 1 -1 -5 -3
___ 1_0_ -5
1 0 -5 | -8
So (x-1) is not a factor
-1 | 1 -1 -5 -3
___-1_2_ 3
1 -2 -3 | 0
So (x+1) is a factor where the quotient is x^2-2x-3 or (x-3)(x+1)
3 | 1 -1 -5 -3
___ 3_6_ 3
1 2 1 | 0
So (x-3) is a factor where the quotient is x^2+2x+1 or (x+1)^2
Given (x-3) and (x+1) are factors, we now use the Zero Product Property:
(x-3)(x+1)=0
x-3=0
x=3
x+1=0
x=-1
So the roots are x=3 and x=-1
how can you tell when an equation in one variable has infinitely many soultions or no solution
What is the slope of the line that passes through the points (-9,5) and (-17,5)? Write your answer in simplest form.
Answer:
0
Step-by-step explanation:
Without solving anything, we can tell that the line that crosses these points is a horizontal line because both of the y-coordinates are the same. This tells us that the slope of the line is 0.
To prove this, we can find the slope of the line by plugging the two points,[tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex], into the equation [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].
[tex]\frac{y_2-y_1}{x_2-x_1}\\\frac{5-5}{-17-(-9)}\\= \frac{0}{-17+9)}\\= \frac{0}{-8}\\= 0[/tex]
Therefore, the slope of the line that passes through the points (-9,5) and (-17,5) is 0.
I hope this helps!
The function W(t) = 40e^–0.35t models the healing of a wound after t hours, where W(t) represents the wound area in square millimeters. What relationship do W(t) and t have?
when t = 0, W(t) > 40
when t = 0, W(t) 0, W(t) > 40
when t > 0, W(t) < 40
ASAP I'm taking test
Answer:
Pretty sure its D.
Step-by-step explanation:
Whenever I made t something higher than 0 I got something less than 40|
(Sorry if I didn't make it in time and if I did I'm taking the same test rn gl homie)
The value of function W(t) will be less then 40 if t > 0 thus option (D) is correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
As per the given function,
W(t) = 40[tex]e^{-0.35t}[/tex]
By the law of indices,
W(t) = 40/[tex]e^{.035t}[/tex]
When t > 0 the value of [tex]e^{.035t}[/tex] > 1
Thus, t > 0 the value of W(t) < 40
Hence "The value of function W(t) will be less then 40 if t > 0".
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Which pair of sneakers has the lowest sale price?
Answer:
15% off $30
Step-by-step explanation:
Approximately how many years will it take $3000 to double if it is invested in an account that pays 3%
compounded monthly? Round your answer to the nearest whole year.
Answer:
24 years
Step-by-step explanation:
Total = start*(1 + interest rate / amount of times compounded per month)^(years*amount of compounds per year)
6000 = 3000*(1+0.03/4)^(4x)
6000 = 3000* ((403/400)^4)^x
2 = ((403/400)^4)^x
x = log base-((403/400)^4) of 2 = x
x = 23.19
rounding down 23 years (but you probably want a year over that to get at least 6000, so 24)
PLEASE HELP!!!
Liam had $250. Then, he and his classmates bought a present for their teacher, evenly split the $p cost among the 24 of them. How much money does Liam have left? Write your answer as an expression.
Answer: the expression would be
6000-p over 24
Step-by-step explanation:since we have given that
amount that liam has=250
amount that he and his classmates had=p
student $p will split=24
Answer:
250-p/24
Step-by-step explanation:
Khan
How many laps would be 50 miles on a 1 1/2 mile track?
Answer:
34 laps
Step-by-step explanation:
the specific answer is 33.3 but u have to round the whole number
Determina la derivada de la siguiente función implícita y^3 + x^2 In y= 4x + 2
Answer:
[tex]\dfrac{dy}{dx}=\dfrac{4y-2xy\ln y}{3y^3+x^2}[/tex]
Step-by-step explanation:
[tex]y^3+x^2\ln y=4x+2[/tex]
Diferenciando con respecto a [tex]x[/tex]
[tex]3y^2\dfrac{dy}{dx}+2x\ln y+\dfrac{x^2}{y}\dfrac{dy}{dx}=4\\\Rightarrow (3y^2+\dfrac{x^2}{y})\dfrac{dy}{dx}=4-2x\ln y\\\Rightarrow (\dfrac{3y^3+x^2}{y})\dfrac{dy}{dx}=4-2x\ln y\\\Rightarrow \dfrac{dy}{dx}=\dfrac{4y-2xy\ln y}{3y^3+x^2}[/tex]
La derivada de la función dada es [tex]\dfrac{4y-2xy\ln y}{3y^3+x^2}[/tex].
When signing the lease for her $825.00 per month rental property, Selah will have to pay the first month's rent, last month's rent, and a
security deposit equal to 25% of one month's rent. If Selah currently earns an average weekly net pay of $650.00, determine what percent
of her weekly pay she will need to save ishe wants to sign her lease in 8 weeks.
O a
2.8%
Ob 3.6%
OC 28%
Od 35.7%
Selah needs to save 35.7% of her weekly pay she will need to save if she wants to sign her lease in 8 weeks.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Starting from the bottom in 8 weeks Selah will earn $(8×650).
= $5200.
The cost of renting the property for 2 months is $(2×825).
= $1650.
And 25% of one month's rent as a security deposit is,
= (25/100)×825.
= $206.25.
So, The total amount she needs to sign is $(1650 + 206.25).
= $1856.25.
Therefore, The percentage of her weekly pay she will need to save is,
= (1856.25/5200)×100.
= 35.69% or 35.7%
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Use differentials to estimate the amount of metal in a closed cylindrical can that is 22 cm high and 10 cm in diameter if the metal in the top and the bottom is 0.4 cm thick and the metal in the sides is 0.05 cm thick. (Round your answer to two decimal places.) cm3
Answer:
97.43cm³
Step-by-step explanation:
h = 22cm
d = 10cm
r = d/2
= 10/2
= 5
dh = 2(0.4)
= 0.8
dr = 0.05
V = πr²h
dV = d(πr²h)
Such that
πd(r²h)
= π[(r²dh + hd(r²)]
dV = π[(r²dh + 2rhdr]------(1)
When we put the values above in this equation 1 above:
dV = π[(5)²*0.8 + 2*5*22*0.05]
= π(25*0.8+11)
= π31cm³
Multiply the value of pi with 31cm³
= 97.43cm³
Answer for this picture please!
Answer: The answer is 30 or B
.
Step-by-step explanation:
Answer: B. 30 ft
Step-by-step explanation: we know that 3 is corresponding to 15 and 6 to x. 3 was multiplied by 5 to get to 15, so the same must be done to 6 to get the value for x. 6 * 5 = 30.
Use proportional reasoning to determine the value of a in the proportion shown below.
25
a=1
a=25
a=10
a=15
it’s c
Answer:
c
Step-by-step explanation:
Evaluate 4^2 - 6 ÷ 2 + 3=
Answer:The correct answer is 16
Step-by-step explanation:
4^2= 16
16-6/2+3
16-3+3
13+3=16
7-5p +3qwhen p =1 and q=7
Answer: 23
Step-by-step explanation:
When p =1 and q=7
Substitute the numbers for the alphabets accordingly and answer the equation
If Max wants to build a rectangular walkway 4 ft wide by 1.5 ft deep by 20 ft long
from the house to the storage shed, what is the area of the walkway?
Square Feet
Answer:
80 ft^2
Step-by-step explanation:
The area of a rectangular walkway = L x W = 20 ft x 4ft = 80 ft
PLEASE HELP MY GRADES ARE DUE THIS WEEK
Which shape is similar to shape x?
Answer:
the c oneStep-by-step explanation:
hope it will helpAnswer:
Step-by-step explanation:
Probably C but I sure wouldn't bet the farm on it. It looks like C is about 1.5 times the size of X
4 1/2 divided by 2 3/4 equals what and this is mixed number
Answer: 1 7/11
please mark as brainliest
Answer:
1 7/11
Step-by-step explanation:
Please help!! what's the answer
Answer:
B 244
Step-by-step explanation:
You can split up the polygon into two separate rectangles, one smaller one on top and one bigger one below.
Area of smaller rectangle = 6 × (14-8)
= 36
Area of bigger rectangle = 26 × 8
= 208
Total area of polygon = 36 + 208
= 244
Who likes my banana⤵️⤵️⤵️⤵️⤵️⤵️
Answer:
damm thats really good
Step-by-step explanation:
Answer:
ooooooo me :)
Paula knows the total cost for 100 students will be $750, and the cost total cost for 150 students is $1050. What is the caterer’s fixed cost and the rate per student served?
Step-by-step explanation:
the price charged for 100 students reflects the cost per student that applies to the order as a whole.
100 * 6 = $600, so the fixed cost is 750-600 = 150.
...
We can check this by substituting in the other equation.
Does 150*6 + 150 = 1050?
150*6=900
900+150 = 1050.
Yes, it does
...
We can express this relationship by the equation:
y = mx + b
where
y = total cost
m = $6 per student
x = number of students
b = fixed costs = 150
y = 6x + 150
The caterer’s fixed cost and the rate per student served is $6 and $150
How to choose what quantity to multiply the first equation?This method is actually called method of elimination to solve a system of linear equations.
We make one specific variable's coefficients of equal magnitude so that we can subtract or add the equations and eliminate that variable to make it easy to get the value of the other variable which will then help in getting the value of the first variable (if working in dual variable system).
If we have equations:
[tex]a_1x + b_1y = c_1\\a_2x + b_2y = c_2[/tex]
then, if we want to eliminate variable x, then we have to multiply equation 1 with
[tex]-\dfrac{a_2}{a_1}[/tex]
which will make coefficient of x in first equation as
[tex]a_1 \times - \dfrac{a_2}{a_1} = -a_1[/tex]
Then adding both equation will eliminate the variable x.
Given;
Cost of 100 students= $750
Cost of 150 students= %1050
Let the fixed cost of caterer be x
and the cost per student be y
x+100y=750...(1)
x+150y=1050...(2)
solving the above equations;
50y=300
y=6
x=750-600=150
The fixed cost is $150, while the per-student cost is $6.
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Which fraction shoes unit rate that is equal to the ratio 18:2
Answer: 9/1
Step-by-step explanation:
A penguin walks 10 feet in 6 seconds. How far does the penguin walk in 45 seconds
Answer:
70 ish
Step-by-step explanation:
i need some helpppppppppp
slope-intercept form: y = mx + c, where m is the gradient and c is the y-intercept!!!
x - 26y = 52
-26y = -x + 52
y = x/26 - 2
In the figure below, the distance from A to D is y, the distance from D to C is x and the distance from A to B is h.
Using trigonometric ratios we calculate the value of the variables as approximately x and y are 5.1 units and 3.1 units respectively .
Trigonometry is the branch of mathematics that is used for solving a right angled triangle if only one data is given.
Let us consider a triangle ABC right angled at B. BC is the base of the triangle and AC is the hypotenuse , therefore AB is the perpendicular.
The various trigonometric ratios used for solving a triangle are :
sin C = AB ÷ AC
cos C = BC ÷ AC
tan C = AB ÷ BC
Now in the given figure we can see that :
In ΔABC , using the trigonometric ratio of sin
sin ∠A = BC ÷ AB
or , sin 51° × AB = BC
or, BC = 10.102...
or, BC ≈ 10.1
Again in Δ BCD , using the trigonometric ratio of cos
cos ∠D = CD ÷ BD
or, CD ≈ 5.1
In ΔABC , using the trigonometric ratio of tan
tan ∠A = BC ÷ AC
or, tan 51° = 10.1 ÷ AC
or, AC = 8.178...
or, AC ≈ 8.2
Therefore the value of y is AC-DC = 8.2 - 5.1 = 3.1 units
The values of x and y are 5.1 units and 3.1 units respectively .
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X
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Simplify the following expression.
4(20+12)+(5-3)
Answer:
[tex] = 4(32) + (2) \\ = 128 + 2 \\ = 130[/tex]
HOPE THIS HELPS
Which of the following ratios is not equivalent to the other three 2/3 4to6 8to12 4/5
Answer:
The non-equivalent ratio is 4:5.
Step-by-step explanation:
2/3 4/6 and 8/12 are equivalent because they are all multiples of each other.