What is the measure of Zr?
Angles are not necessarily drawn to scale.
B
156°
4
C
0
Answers
Answer:
24°
Step-by-step explanation:
Two angles that form a linear pair are supplementary. That is, their total is 180°.
x° +156° = 180°
x° = 180° -156° = 24°
Related Questions
Exercise 3.5. For each of the following functions determine the inverse image of T = {x ∈ R : 0 ≤ [x^2 − 25}.
1. f : R → R defined by f(x) = 3x^3
2. g : R+ → R defined by g(x) = ln(x).
3. h : R → R defined by h(x) = x − 9
Answers
a. The inverse image of f(x) is f⁻¹(x) = ∛(x/3)
b. The inverse image of g(x) is [tex]g^{-1}(x) = e^{x}[/tex]
c. The inverse image of h(x) is h⁻¹(x) = x + 9
The domain of TSince T = {x ∈ R : 0 ≤ [x^2 − 25} ⇒ x² - 25 ≥ 0
⇒ x² ≥ 25
⇒ x ≥ ±5
⇒ -5 ≤ x ≤ 5.
Inverse image of f(x)
The inverse image of f(x) is f⁻¹(x) = ∛(x/3)
f : R → R defined by f(x) = 3x³
Let f(x) = y.
So, y = 3x³
Dividing through by 3, we have
y/3 = x³
Taking cube root of both sides, we have
x = ∛(y/3)
Replacing y with x we have
y = ∛(x/3)
Replacing y with f⁻¹(x), we have
So, the inverse image of f(x) is f⁻¹(x) = ∛(x/3)
Inverse image of g(x)
The inverse image of g(x) is [tex]g^{-1}(x) = e^{x}[/tex]
g : R+ → R defined by g(x) = ln(x).
Let g(x) = y
y = ln(x)
Taking exponents of both sides, we have
[tex]e^{y} = e^{lnx} \\e^{y} = x[/tex]
Replacing x with y, we have
[tex]y = e^{x}[/tex]
Replacing y with g⁻¹(x), we have
So, the inverse image of g(x) is [tex]g^{-1}(x) = e^{x}[/tex]
Inverse image of h(x)The inverse image of h(x) is h⁻¹(x) = x + 9
h : R → R defined by h(x) = x − 9
Let y = h(x)
y = x - 9
Adding 9 to both sides, we have
y + 9 = x
Replacing x with y, we have
x + 9 = y
Replacing y with h⁻¹(x), we have
So, the inverse image of h(x) is h⁻¹(x) = x + 9
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Describe a real world problem that you could solve using the volume of spheres
Answers
A toy company produces rubber balls that have a radius of 1.7 cm.
What is the volume of one rubber ball? Round to the
nearest hundredth of a centimeter.
20.58 cm3
If the price of the rubber needed to produce a ball is
$0.0045/cm3, what is the cost of producing one ball?
Round to the nearest cent.
If the company sells a ball for $0.50, how much profit
will it make on each ball?
$1.7 cm
20.58 cm^3, $0.09, $0.41
Hope this helps
You spent $24 on baking ingredients, and you sell your cupcakes at a bake sale for $4 each. You sold 25 cupcakes. Did you make enough money to buy a $60 video game?
Answers
But, you spent $24 on the ingredients, so you have to subtract that from the total amount you made
$100-$24= $76
After subtracting the cost of your baking ingredients, you can see that you made $76 dollars in profit
Therefore, you did make enough money to buy a $60 video game, as $76 is more than $60
There are 20 members of taekwondo club, 40 math club members, 60 drama
theatre members, and 30 members of science club. The researchers want to get 20
respondents out of these organizations. Identify the samples to be taken in each
organization.
Answers
⚘Refer to the attachment for solution!!~
The sample to be taken in each organization such as 2.6 in the taekwondo club, 5.3 in the math club, 8 in the drama club, and 4 in the science club.
Total members of taekwondo club = 20
Total members of math club = 40
Total members of drama club = 60
Total members of science club = 30
The researchers want to get 20 respondents out of these organizations.
What is the stratified sampling method?The stratified sampling method is the process of dividing members of data into homogenous subgroups before sampling.
The total number of members = 150
For taekwondo club
= Total members of taekwondo club /total number of members × 20
= 20/150 × 20
= 2.6
For math club
= Total members of math club/total number of members×20
= 40/150 × 20
= 5.3
For drama club
= Total members of drama club/total number of members × 20
= 60/150 × 20
= 8
For science club
= Total members of the science club/total number of members × 20
= 30/150 × 20
= 4
Therefore, The sample to be taken in each organization such as 2.6 in the taekwondo club, 5.3 in the math club, 8 in the drama club, and 4 in the science club.
Learn more about the stratified sampling method;
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34
Which expression represents the phrase below?
3 fewer than a number, P
3-p
В
p=3
C
3 +p
D
P-3
Answers
Answer:
D) P - 3
Step-by-step explanation:
"fewer than" a number means "less than" a number. So "3 fewer than" means "subtract 3" from the number.
⇒ P - 3
Answer Pls I need this question
Answers
Answer:
T = 1.5
Step-by-step explanation:
If you count all the boxes with T in them there is 6 and if you divide 6 by 9 you get 1.5, 9 divided by 6 = 1.5
Hope this helps!
To solve the equation 3 sin(2x) = 5cosx, you should rewrite it as
O A. cosx(3sinx - 5) = 0
0 B. cosx(6sinx - 5) = 0
O C. 3sinx + 5cosx = 0
Help me out
Answers
Answer:
OPTION B
Step-by-step explanation:
3sin(2x)=5cos(x)
3×(2sinxcosx)=5cos(x)
6sin(x)cos(x)=5cos(x)
6sin(x)cos(x)-5cos(x)=0 Factor out a cos(x)
cosx(6sinx-5)=0
What is the slope of the line passing through the points (-1, – 7) and (-9, - 2)?
Answers
» What is the slope of the line passing through the points (-1, – 7) and (-9, - 2)?
[tex]\color{brown} \mathbb{ANSWER:}[/tex][tex] \color{hotpink} \bold{(Slope) \: m = - \frac{5}{8} }[/tex][tex] \sf \:As \: a \: decimal: \color{hotpink} \bold{ \: m = - 0.625 }[/tex]— — — — — — — — — —
[tex] \color{darkblue} \mathbb{FORMULA:}[/tex][tex] \tt \: \underline{ \boxed{ \tt m = \frac{ y_{2} - y_{1}}{x_{2} - x_{1}}}} \\ [/tex][tex] \color{darkblue}\mathbb{GIVEN:}[/tex][tex] x_{ 1} = - 1\: \: \: \: \: \: \: y_{1} = - 7 \\ x_{2} = - 9 \: \: \: \: \: \: \: y_{2} = - 2[/tex][tex] \color{darkblue} \mathbb{SOLUTION:}[/tex][tex] \tt m = \frac{ y_{2} - y_{1}}{x_{2} - x_{1}} \\ [/tex][tex] \tt m = \frac{ ( - 2) - ( - 7)}{( - 9) - ( - 1)} \\ [/tex][tex] \tt m = \frac{ \: 5}{ - 8 \: } \\ [/tex][tex] \tt m = \underline{ \boxed{ \bold{ - \frac{ 5}{ 8 } }}} \\ [/tex][tex] \tt m = \underline{ \boxed{\bold{ - 0.625}}}[/tex]_______________❦︎_______________
if 5 is 1/4,what is the whole?
Answers
Answer:
20
Step-by-step explanation:
If 5 is 1/4, then multiply 5 by 4 to get 20
Hope this helps! :)
Have a blessed day and remember to keep smiling! :)
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Aliya has 125 stickers. Amari has twice
as many stickers as Aliya. How many
stickers does Amari have?
Answers
Answer:
250 stickers
Step-by-step explanation:
125 plus 125 is 250
Answer:
250 stickers because 125x2=250
Find the LCM and the GCF of 100 and 120.
Answers
Answer:
Step-by-step explanation:
LCM is least common multiple. It means the least multiple that both 100 and 120 have in common. 600 is the LCM. 20 is the GCF.
In ΔUVW, the measure of ∠W=90°, VU = 41, UW = 9, and WV = 40. What is the value of the cosine of ∠V to the nearest hundredth?
Answers
Answer:
∠V = 12.68°
Step-by-step explanation:
In this question, we are tasked with calculating the value of the sine of ∠V to the nearest hundredth
Kindly note that since one of the angles in the triangle equals 90°, then we are dealing with a right-angled triangle.
PLEASE VIEW ATTACHMENT TO SEE THE DIAGRAM OF THE SHAPE
Mathematically, to calculate the sine of an angle in a triangle, the ratio to use is
Sine of an angle = length of side facing angle/length of hypotenuse = opposite/Hypotenuse
From the diagram, we can see that the length of the opposite is 9 while the length of the hypotenuse is 41
Sine V = 9/41
V = arcsin (9/41)
V = arcsin (0.2195)
V = 12.68° to the nearest hundredth
The value of the cosine of ∠V is 0.98
How to determine the value of the cosine of ∠V?The given parameters are:
∠W=90°, VU = 41, UW = 9,WV = 40The cosine of V is calculated using:
cos(V) = WV/VU
So, the equation becomes
cos(V) = 40/41
Evaluate
cos(V) = 0.98
Hence, the value of the cosine of ∠V is 0.98
Read more about right triangles at:
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using the spinner below, what is the probability that you will land on red or blue?
Answers
Answer:
red is 50% blue is 25%
Step-by-step explanation:
red is half the circle so it would be 50% and blue is half of a half so 25%
which two number does the square root of 61 lie between on a number line?
Answers
The square root of 61 is about 7.81, so it lies in between the numbers 7 and 8.
Hope that helps!
Which fractions are equivalent to 812?
Answers
Answer:
812/1 = 1624/2 = 2436/3
= 3248/4 = 4060/5 = 4872/6
= 5684/7 = 6496/8 = 7308/9
= 8120/10 = 8932/11 = 9744/12
= 10556/13 = 11368/14 = 12180/15
= 12992/16 = 13804/17 = 14616/18
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
The list tends to be much bigger.
Hope this helps!
Answer:
See below.Step-by-step explanation:
Fractions equivalent to 8/12:
2/316/2424/3636/4840/60And on and on.There is an infinite amount, but this is how far I can get.
Jane has already run 6 miles this month. She plans to run an additional 2.5 miles per day.
At this rate, how long will it take Jane to run 41 miles?
Answers
Explanation: The problem asks how long it will take Jane to run 41 miles, we know Jane has ran 6 miles already so:
41-6= 35
Jane is running 2.5 miles a day therefore:
35 ÷ 2.5 = 14
Help with number 17 please
Answers
Answer:
B is the answer
Step-by-step explanation:
it goes downward if viewed left-right
12.Identify the type of triangle
Answers
Answer:
a) acute triangle
b) obtuse triangle
c) right-angled triangle
d) equilateral
e) isosceles, right-angled triangle
Step-by-step explanation:
If all the angles in the triangle are less than 90°, it is an acute triangleIf one angle in the triangle is a right angle, then it is a right-angled triangleIf at least one angle is above 90°, it is an obtuse triangleIf all the sides of the triangle are equal, it is an equilateral triangleIf two sides of the triangle are equal, it is an isosceles triangleIf no sides of the triangle are the same length, it is a scalene triangleHope this helps!
Please answer. Thanks! 7-5(2x-9)=-(-6x+10)+4
Answers
Answer:
x = 29/8
Step-by-step explanation:
7 - 5(2x - 9) = -(-6x + 10) + 4
7 - 10x + 45 = (6x - 10) + 4
-10x + 52 = 6x - 10 + 4
-10x + 52 = 6x - 6
52 + 6 = 6x + 10x
58 = 16x
x = 58/16 = 29/8
evaluate 16 + 20/t for t =4
steps please
Answers
Answer:
21
Step-by-step explanation:16+20/t, T=4 so its 16 + 20/4, 20/4 is 5, 16+5 = 21.
What is the area of the triangle?
(-5,6)
(1,3)
(-5,-3)
Answers
Answer:
27
Step-by-step explanation:
Base is 6 - (-3) = 9
height is 1 - (-5) = 6
so Area = 9 * 6/2 = 27
3 Which ordered pair is in the solution
set of the following inequality?
2x – 4y > 15
A (-8, -2)
B (3,4)
C (-4,0)
D (0,-4)
Answers
Answer:
D. (0,-4)
Step-by-step explanation:
When you plug in 0 into the x and -4 into the y variable you get 2(0)-4(-4)>15.
Then you solve and get 0+16>15.
then you at and get 16>15.
16 is greater than 15 which makes D correct
Help me this I don't understand this one show work pls
Answers
Answer:
x = 1/2
Step-by-step explanation:
10^-3x * 10^x = 10^-2x = 10^-1
Order the fractions from least to greatest 3/5 1/3 and 1/8 and 7/8
Answers
1/8, 1/3, 3/5, 7/8
Use the information given to answer the question.
The measures of angle QRS and angle SRT have a sum of 90∘.
Part A
Which statement about the relationship between angle QRS and angle SRT is true?The two angles are adjacent.
The two angles are adjacent.
The two angles are congruent.
The two angles are congruent.
The two angles are supplementary.
The two angles are supplementary.
The two angles are vertical angles.
hurry
Answers
Angles are the measures between two intersecting lines or rays
The relationship between angle QRS and angle SRT is the two angles are adjacent.
How to determine the relationshipThe given parameter is:
The sum of angle QRS and angle SRT = 90 degrees.
Complementary angles have a sum of 90 degrees.
This means that, angles QRS and SRT are complementary angles, and that can be adjacent angles
Read more about angles at:
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Answer:
Step-by-step explanation:
it's a
Which interval notation represents the set of all numbers less than or equal to -6 or greater than or equal to -2
Answers
Answer: 1≤x<12
Step-by-step explanation:
The values that are greater than or equal 1 but less than 12 are values ranging from 1 to 11 i.e {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}. Note that 1 is included because the number is greater than or equal to 1 (1 included) and less than 12(12 not included).
x≥1 and x< 12
if x≥1, it means 1≤x
combining both inequality
1≤x and x<12
1≤x<12
The interval notation that represent the set S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} will be given as S = {x: 1≤x<12}
3x ^3- 12x^2- 15x = 0
factor and solve to find all the zeros
show all work
Answers
Answer:
x = 0 ; x = -1 ; x = 5
Step-by-step explanation:
3x^3-12x^2-15x=0
-> 3x(x+1)(x-5)=0
-> 3x = 0 or x+1=0 or x-5=0
-> x = 0; x = -1 ; x = 5
.The world's tallest mammal is a giraffe at a height of 19 feet. What is the height of the giraffe in inches?????
Answers
Answer:
228 inches
Step-by-step explanation:
There are 12 inches in a foot.
19 × 12 = 228
Piper invested $4,700 in an account paying an interest rate of 4.8% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 19 years?
Answers
Answer:
The answer to the nearest CENT is A= 11699.69
Step-by-step explanation: round to the nearest cent
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4700\\ r=rate\to 4.8\%\to \frac{4.8}{100}\dotfill &0.048\\ t=years\dotfill &19 \end{cases} \\\\\\ A=4700e^{0.048\cdot 19}\implies A=4700e^{0.912}\implies A\approx 11699.69[/tex]
The value of a share of stock decreases in value at a rate of $2.70 per hour during the first 6.5 hours of
trading. Enter and solve an equation to find the decrease in the value of the share of stock during that
time. Let x represent the decrease in value of the share of stock during 6.5 hours.
Answers
Answer: the awnser will be 17.55$
Step-by-step explanation: cause you multiply 6.5 x 2.70