Answer:
(b) (x + 1 ≤ 1) ∩ (x + 1 ≥ 1) = {x | x = 0}
Step-by-step explanation:
Here, the given expression is : {x | x = 0}
So, the ONLY element in the given set = {0}
Now, take each option and solve the given expression:
(a) x + 1 < -1
Adding -1 BOTH sides, we get:
x + 1 -1 < -1 -1
or, x < - 2 ⇒ x = { -∞ , .... , -4,-3}
Also, x + 1 < 1
Adding -1 BOTH sides, we get:
x + 1 -1 < 1 -1
or, x <0 ⇒ x = { -∞ , .... , -4,-3,-2,-1}
So, (x + 1 < -1) ∩ (x + 1 < 1) = { -∞ , .... , -4,-3}∩ { -∞ , .... , -4,-3,-2,-1}
= { -∞ , .... , -4,-3}
⇒ (x + 1 < -1) ∩ (x + 1 < 1) ≠ {0}
Similarly, solving
(b) (x + 1 ≤ 1) ∩ (x + 1 ≥ 1)
(x + 1 ≤ 1) = x≤ 0 = { -∞ , .... , -4,-3,-2,-1, 0}
(x + 1 ≥ 1) = x ≥ 0 = {0,1,2,3,... ∞}
⇒ (x + 1 ≤ 1) ∩ (x + 1 ≥ 1) = {0}
(b)(x + 1 < 1) ∩ (x + 1 > 1)
(x + 1 < 1) = x < 0 = { -∞ , .... , -4,-3,-2,-1}
(x + 1 > 1) = x > 0 = { 1,2,3,... ∞}
⇒ (x + 1 ≤ 1) ∩ (x + 1 ≥ 1) = Ф
Hence, (x + 1 ≤ 1) ∩ (x + 1 ≥ 1) = {x | x = 0}
(x + 1 ≤ 1) ∩ (x + 1 ≥ 1) = {x | x = 0}
There are 142 laptops and desktop computers in a lab. There are 6 more laptops than desktops. What is the total number of laptops in the lab
Answer:
77 laptops and 65 desktops
Step-by-step explanation:
142/2=71
71+6=77
71-6+65
Answer:
74 Labtops
Step-by-step explanation:
you first have to subtract 6 from 142
142-6= 136
divide 136 by two.... for the labtops and the computers.
136 ÷ 2 = 68
68 is the number of desktops...to find the number of labtops you just need to add 6 again.
68 + 6 = 74 Labtops
To check your answer you can just add
74+68 and if it equals to what you started with then that's your answer
74 + 68 = 142
What is 2432 divided by 102344
Answer:
42.0
Step-by-step explanation:
You spend $288 on clothes. Shirts cost $24 and pants cost $32. you buy a total of 10 items
Answer:
I have bought 4 shirts and 6 pants.
Step-by-step explanation:
Let I have bought x number of shirts and y number of pants.
So, the two equation that we can write from the given conditions are
x + y = 10 ............. (1) and
24x + 32y = 288 ...... (2)
Now, solving equations (1) and (2) we get
24x + 32(10 - x) = 288
⇒ 8x = 320 - 288 = 32
⇒ x = 4
And y = (10 - 4) = 6
Therefore, I have bought 4 shirts and 6 pants. (Answer)
f(x) = -2x2 – 7x + 4
What’s the vertex?
Answer:
( - 7/4, 81/8 )
Step-by-step explanation:
4[z + 3(Z - 1)] = 36
How do you solve this problem?
Answer:
3
Step-by-step explanation:
4[z+3(z-1)]=36
z+3(z-1)=36/4
z+3z-3=9
4z-3=9
4z=9+3
4z=12
z=12/4
z=3
Answer:
4z+2(square)2z=2(square)6
Step-by-step explanation:
4((z+3(z-1)))=36
4(z^2-z+3((z-3)))=36
4(z^2-z+3z-3)=36
4((z^2+(-z+3z)-3))=36
4(z^2+2z-3)=36
4z^2+8z-12=36
4z^2+8z=24
((4(square)z^2))+(square)8z=(square)24
4z+2(square)2z=2(square)6
. COUPONS Kendra used 35 cents more
in coupons at the store than Leanne.
Leanne used 75 cents less than Becca,
who used 50 cents more than Jaclyn.
Jaclyn used 40 cents in coupons. What
was the value of the coupons Kendra
used?
Answer:
Kendra used 50 cents
Step-by-step explanation:
Jaclyn used 40 cents. Becca used 50 more than Jaclyn (90). Leanna used 75 cents less than Becca (15). Kendra used 35 cents more than Becca (50).
J=40
B=90
L=15
K=50
Hope this helps! c:
Using the given information, the value of the coupons Kendra used IS 50 cents.
Substitution method: Multiple equations can be solved using the substitution method, where we substitute the value of one variable in different equations to calculate the value of other variables.
Let,
Cents used by Kendra in coupons= K
Cents used by Leanne in coupons= L
Cents used by Becca in coupons= B
Cents used by Jaclyn in coupons= J
Using the given information,
Kendra used 35 cents more in coupons at the store than Leanne,
K=L+35......................................................................................(1)
Leanne used 75 cents less than Becca,
L+75=B......................................................................................(2)
Becca used 50 cents more than Jaclyn,
B=J+50......................................................................................(3)
Jaclyn used 40 cents in coupons,
J=40
Substituting J=40 in (3),
B=90
Substituting B=90 in (2),
L=15
Substituting L=15 in (1),
K=50
Thus, Kendra used 50 cents in coupons.
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Which is an equation in point-slope form of the line that passes through the points
(-4, - 1) and (57) ?
Answer:
look at the picture shown
4/6 + 1/3 solve this plez
Yo sup??
[tex]4/6=2*2/2*3\\=2/3\\\\4/6+1/3\\=2/3+1/3\\=2+1/3\\=3/3\\=1\\[/tex]
Hope this helps
HURRY !!!! Find the slope of the line represented in the table.
Answer:
The slope is up 5 over 1
Step-by-step explanation:
Rise over run Which is 5/1
To get the answer you need to follow the x axis and then the y axis or find a point and subtract with an another point on a graph
Or rise over run if u don’t want a graph
What is 2x-3y=5
x+2y=-1
Answer:
a system of linear equations with solution (x, y) = (1, -1)
Step-by-step explanation:
The two given linear equations in x and y are consistent and independent, so will have one solution. That solution is easily found using a graphing calculator. It is (x, y) = (1, -1).
_____
"What is ..." is a pretty open question with lots of different answers that won't be helpful. If you're seeking a specific answer, it would be nice to see the question say what answer you seek.
the area of a rectangle is 45 x^8 x^9 square yards. And the length is of the rectangle is 5 x^3 x^4 yards. Which expression represent the width of the rectangle in yards
Answer:
[tex]width \: of \: the \: rectangle \\ = \frac{area \: of \: rectangle}{length \: of \: rectangle} \\ \\ = \frac{45 {x}^{8} \times {x}^{9} }{5 {x}^{3} \times {x}^{4} } \\ \\ = \frac{45 {x}^{8 + 9} }{5 {x}^{3 + 4} } \\ \\ = \frac{45 {x}^{17} }{5 {x}^{7} } \\ \\ = 9 {x}^{17 - 7} \\ \\ = 9 {x}^{10} \: yards \\ \\ \therefore \: width \: of \: the \: rectangle \\ \: \: \: \: \: \: = 9 {x}^{10} \: yards \\ [/tex]
9 ten thousands scientific notation
Answer:
0.0009) is 9x10^-4
Step-by-step explanation:
Solve for c.
3abc + b = 5
c =
c = 2 - ab
c = -
Answer:
c = [tex]\frac{5-b}{3ab}[/tex]
Step-by-step explanation:
Given
3abc + b = 5 ( isolate the term in c by subtracting b from both sides )
3abc = 5 - b ( divide both sides by 3ab )
c = [tex]\frac{5-b}{3ab}[/tex]
Answer: -b-5/3ab
Step-by-step explanation:
3abc + b = 5
3abc + b - b = 5 - b
3abc = 5 - b
3abc / 3ab = (5 - b) / 3ab
c = (5 - b) / 3ab
what is 1 third of 25 percent
Answer:
0.08333333333
Step-by-step explanation:
The mapping diagram shows a functional relationship. Complete the statements.
Answer:
f(4) =[tex]\frac{1}{2}[/tex]
x = 8
Step-by-step explanation:
f(4) =[tex]\frac{1}{2}[/tex] [ image of 4 is [tex]\frac{1}{2}[/tex]]
f(x) = 4
then x = 8 [ the preimage of 4 is 8]
Jackson buys a grape snow cone on a hot day. By the time he eats all the "snow" off the top, the paper cone is filled with 27\pi27π27, pi cm^3
3
cubed of melted purple liquid. The radius of the cone is 333 cm.
Question:
Jackson buys a grape snow cone on a hot day. By the time he eats all the "snow" off the top, the paper cone is filled with 27\pi27π27, pi cm^3 3 start superscript, 3, end superscript of melted purple liquid. The radius of the cone is 333 cm. What is the height of the cone?
Answer:
The height of the cone is [tex]9 \ cm[/tex]
Explanation:
It is given that the radius of the cone is [tex]3 \ cm[/tex]
The volume of the cone is [tex]27\pi[/tex]
The height of the cone can be determine using the formula,
[tex]$V=\frac{1}{3} \pi r^{2} h$[/tex]
Substituting the values [tex]V=27 \pi[/tex] and [tex]r=3[/tex], we get,
[tex]$27 \pi=\frac{1}{3} \pi(3)^{2} h$[/tex]
Multiplying both sides by 3, we have,
[tex]$81 \pi= 9\pi h$[/tex]
Dividing both sides by [tex]$9 \pi$[/tex], we have,
[tex]9=h[/tex]
Thus, the height of the cone is [tex]9 \ cm[/tex]
Chords NP and MQ intersect at point S in circle R.
If MS = 3, NS = 2, and SQ = 8, what is the length of SP?
Option C:
The length of SP is 12.
Solution:
In the given circle, NP and MQ are chords of the circle.
MS = 3, NS = 2, SQ = 8
To find the length of SP:
Segments of chords theorem:
If two chords intersects in the interior of a circle, then the product of the lengths of the segment of one chord is equal to the product of lengths of the segments of the other chord.
By this theorem,
NS × SP = MS × SQ
⇒ 2 × SP = 3 × 8
⇒ 2 SP = 24
Divide by 2 on both sides of the equation, we get
⇒ SP = 12
Option C is the correct answer.
The length of SP is 12.
Final answer:
Using the Intersecting Chord Theorem, we find that the length of SP is 3/4 by setting up the equation 3 * 2 = SP * 8 and solving for SP.
Explanation:
The student is asking about finding the length of a chord segment in a circle where two chords intersect. Since chords NP and MQ intersect at point S inside circle R, we can apply the Intersecting Chord Theorem.
This theorem states that the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. In formula terms, MS × NS = PS × SQ.
We are given MS = 3, NS = 2, and SQ = 8. To find the length of SP, we just substitute into the theorem's formula: (3) × (2) = SP × (8). From this, we calculate that SP = 3/4, which is the length of the segment SP.
A number increased by 3/4 of the number is 14 find the number
Answer:
8
Step-by-step explanation:
Set up an equation:
x+ (3/4)x = 14
Solve for x:
Combine like terms:
(7/4)x = 14
Divide both sides by 7/4
x = 8
if the area of a square is 64 square centimeters, what's the length of you side?
PLEASE HELP!!!
Answer:
16
Step-by-step explanation:
64÷4=16
Answer:
the answer would be 8
Step-by-step explanation:
64 is the area squared so you need to find the square root of 64 because that would be the opposite.
what is the perimeter of a football field 31 ft. by 20ft.?
Answer:102
Step-by-step explanation:you do 31+31=62 then 20+20=40 then 62+40=102
when f(x) = 5, x= ?????
Answer:
when [tex]f(x) = 5[/tex], then [tex]x=0[/tex]
Step-by-step explanation:
Considering the expression
[tex]f(x) = 5[/tex]
Rewrite the function as an equation
[tex]y = 5[/tex]
Comparing with slop-intercept form
[tex]y=mx+b[/tex]
So,
[tex]m=0[/tex]
[tex]\mathrm{Axis\:interception\:points\:of}\:5:\quad \mathrm{Y\:Intercepts}:\:\left(0,\:5\right)[/tex]
Therefore, when [tex]f(x) = 5[/tex], then [tex]x=0[/tex]
The graph for [tex]f(x) = 5[/tex] is also attached below.
Keywords: graph, function
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At a basketball game, a team made 56 successful shots. They were a combination of 1- and 2-point shots. The team scored 95 points in all. Write and solve a system of equations to find the number of each type of shot.
To find the number of each type of shot, we can create a system of equations based on the given information and solve it. The equations are x + y = 56 and x + 2y = 95.
Explanation:To solve this problem, we can create a system of equations based on the given information. Let's assume that the team made x 1-point shots and y 2-point shots. We know that the team made 56 successful shots in total, so the first equation is x + y = 56. We also know that the team scored 95 points in total, and since each 1-point shot contributes 1 point and each 2-point shot contributes 2 points, the second equation is x + 2y = 95.
Now we can solve this system of equations:
x + y = 56
x + 2y = 95
By solving these equations, we can find the values of x and y, which represent the number of 1-point and 2-point shots respectively.
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Team made 17 1-point shots and 39 2-point shots.
Let's define variables to set up the system of equations:
x: the number of 1-point shots
y: the number of 2-point shots
We know from the problem statement that:
The total number of shots is 56.
The total points scored is 95.
We can represent these conditions with the following system of equations:
Equation 1: x + y = 56
Equation 2: x + 2y = 95
Now, let's solve this system step-by-step:
Step 1: Solve Equation 1 for x:
x = 56 - y
Step 2: Substitute this expression into Equation 2:
56 - y + 2y = 95
Step 3: Simplify and solve for y:
56 + y = 95
y = 39
Step 4: Substitute y back into Equation 1 to find x:
x + 39 = 56
x = 17
Thus, the team made 17 1-point shots and 39 2-point shots.
When the value of t is 60, the value of c is 90 . Explain what this means using the problem context.
Little help!!!!!
Answer:
Step-by-step explanation:
as the temp t increases the number of cricket chirps also increases.
1: The complete table is according to the given function :
t : 40 50 60 70 80 90 100
c : 10 50 90 130 170 210 250
2: It means when the temperature is 60 Fahrenheit then the number of cricket chirps is 90 per minute.
The given function is,
c = 4t - 180
Here t represents the temperature
c represents the cricket chirps per minutes
Now plug in each temperature value and solve for c:
When t = 40:
c = 4(40) - 150
c = 160 - 150
c = 10
When t = 50:
c = 4(50) - 150
c = 200 - 150
c = 50
When t = 60:
c = 4(60) - 150
c = 240 - 150
c = 90
When t = 70:
c = 4(70) - 150
c = 280 - 150
c = 130
When t = 80:
c = 4(80) - 150
c = 320 - 150
c = 170
When t = 90:
c = 4(90) - 150
c = 360 - 150
c = 210
When t = 100:
c = 4(100) - 150
c = 400 - 150
c = 250
Therefore, the complete table is:
t : 40 50 60 70 80 90 100
c : 10 50 90 130 170 210 250
When the value of t is 60, the value of c is 90.
It means when the temperature is 60 Fahrenheit then the number of cricket chirps is 90 per minute.
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Find the value of Y so that r||s.
Answer:
y = 56
Step-by-step explanation:
the two angles are equal to 180
y - 24 +3y - 20 = 180
4y - 44 = 180
4y = 224
y = 56
Which functions have the same transformations? WILL MARK BRAINLIEST
Answer:
B) [tex]f(x)=3e^x^+^6-4[/tex]
D) [tex]f(x)=3(x+6)^2-4[/tex]
Step-by-step explanation:
I did what the other person said and I got 1/2.
The correct functions have the same transformations are,
⇒ f (x) = 3eˣ⁺⁶ - 4
And, f(x) = 3(x+6)² - 4
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
⇒ f (x) = 3 csc (x + 6) - 4
Now, In the given function;
⇒ f (x) is a translation of g(x) = 3csc x of 6 units to the left and 4 units down.
By options;
⇒ f (x) = 3eˣ⁺⁶ - 4
And, f(x) = 3(x+6)² - 4
Both function is a translation of 6 units to the left and 4 units down.
Thus, The correct functions have the same transformations are,
⇒ f (x) = 3eˣ⁺⁶ - 4
And, f(x) = 3(x+6)² - 4
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m x 12 = 12 x m
What property is this?
Answer:
[tex]It \: is \: called \: commutative \: property[/tex]
Express the following in scientific notation 77.31 × 10^4
The number 77.31 x 10^4 in scientific notation is 7.731 x 10 ^ 5. To achieve this, the decimal place was moved to the left and the power of 10 increased accordingly.
Explanation:To express the number 77.31 x 10^4 in scientific notation, we need to adjust it to fit the format 'a x 10^n', where 1 ≤ |a| < 10 and n is an integer. So, the main step is to transfer the decimal place in '77.31' to after the first digit, followed by multiplying by an appropriate power of 10.
Firstly, rewrite 77.31 as 7.731 by moving the decimal place one place to the left. Now, since our original number was multiplied by 10^4, this needs to be amended by 1 place for the movement of the decimal point. This results in 10^5, since you are now multiplying by 10 one more time than before.
Combining these, the given number is represented in scientific notation as 7.731 x 10 ^ 5.
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Part B
Solve for w, b, and r using the proportions from part A. Show your work.
Answer:
w: 100w = 80 x 35 = 2800/100 = 28 strands in one pom pom
b: 100b = 80 x 25= 2000/100 = 20 strands in one pom pom
r: 100r = 40 x 80 = 3200/100 = 32 strands in one pom pom
Step-by-step explanation:
Answer:
Step-by-step explanation:
Raman buys two packages of chicken wings. One package weighs 1.28 pounds, and the other weighs 2.63 pounds. The price of chicken wings is $3.25 per pound. What is the total cost of the chicken wings?
Total cost of the chicken wings is $12.71
Step-by-step explanation:
Step 1: Given weight of package 1 = 1.28 pounds, package 2 = 2.63 pounds and price of chicken wings per pound = $3.25Step 2: Calculate total weight of both packages = 1.28 + 2.63 = 3.91 poundsStep 3: Calculate total cost of chicken wings⇒ Total Cost = 3.91 × 3.25
⇒ Total cost = $12.71
Final answer:
To find the total cost of chicken wings, add the weights of both packages (1.28 pounds + 2.63 pounds = 3.91 pounds) and multiply by the price per pound ($3.25), yielding a total cost of $12.71.
Explanation:
The problem provided describes a scenario where Raman buys two packages of chicken wings weighing 1.28 pounds and 2.63 pounds. To calculate the total cost of the chicken wings at a price of $3.25 per pound, first, we need to determine the total weight of the chicken wings by adding the weight of both packages together. Next, we multiply the combined weight by the price per pound.
Here is the step-by-step calculation:
Add the weights of the two packages: 1.28 pounds + 2.63 pounds = 3.91 pounds.
Multiply the total weight by the price per pound: 3.91 pounds *$3.25 per pound.
Calculate the overall cost: 3.91 * $3.25 = $12.71.
Therefore, the total cost of the chicken wings is $12.71.
it’s solve system by elimination!!! plz help asap
Answer:
look at the picture shown