Answers
By the concept of set builder notification
(b) 4
(c) 6
(d) -6
What is the set builder notification?In mathematics, the set-builder notation is used to express a set's elements or specify the conditions that each member of the set must meet. for instance The notation for the set builder is A = x Z | x 4 for the supplied set A =..., -3, -2, -1, 0, 1, 2, 3, 4. Sets can also be expressed using an interval or an equation by using the set-builder notation. In many cases, sets with an infinite number of elements have their elements written and represented in this way. These include integers, real numbers, and natural numbers, among other popular forms of numbers. One (or more) variables from these categories are utilized in this.
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Related Questions
The longest side of a triangle is 5in longer than the shortest side. The medium side is 4 inches longer than the shortest side. If the perimeter of the triangle is 21 inches, what are the lengths of the three sides?
Answers
The perimeter of a triangle is given by the sum of all it is sides.
Now, we have the next measures:
- The longest side of a triangle is 5in longer than the shortest side.
- The medium side is 4 inches longer than the shortest side
Then, the perimeter is given by:
P = (s+5)+(s+4)+s
If the perimeter is P=21 inches:
21 = (s+5)+(s+4)+s
Solve for s:
21 = s+5+s+4+s
21 = 3s + 9
21-9 = 3s
12 = 3s
s = 12/3
s= 4
Therefore,
The shortest side of the triangle is 4 inches.
The medium side is s+ 4 = 4+ 4 = 8 inches
The longest side is s+5 = 4+5 = 9 inches
What is the volume air enclosed in a pyramid-shape tent whose square base measures 8 dm by 8 dm and whose height is 6dm?
Answers
We have to calculate the volume of the pyramid with the following dimensions:
We can express and calculate the volume as:
[tex]\begin{gathered} V=\frac{1}{3}A_bh \\ V=\frac{1}{3}(8\cdot8)\cdot6 \\ V=\frac{64*6}{3} \\ V=128\text{ }dm^3 \end{gathered}[/tex]Answer: the volume is 128 dm³
HELPPPPPP PLEASEEEEEEEEEEEEEE
Answers
Answer:
Option C, [tex]f(x)=-3x^2-6xh-3h^2+2x+2h+1[/tex]
Step-by-step explanation:
Oooo the ol canvas quiz yeesh.
Anyway, for this sort of problem, anywhere in your second equation that you see an x, sub for (x+h).
[tex]f(x)=-3x^{2} +2x+1[/tex]
[tex]f(x)=-3(x+h)^{2} +2(x+h)+1\\[/tex]
You must foil the first part
[tex]f(x)=-3(x^2+h^2+2xh)+2(x+h)+1\\[/tex]
Now distribute to eliminate the parentheses
[tex]f(x)=-3x^2-3h^2-6xh+2x+2h+1[/tex]
As your answer choice has it:
[tex]f(x)=-3x^2-6xh-3h^2+2x+2h+1[/tex]
89, 81,96, 85, 93, 70, 66, 64, 68, 70MeanMedianMode(s)Range
Answers
Okay, here we have this:
Considering the provided data set, we are going to calculate the requested data, so we obtain the following:
Mean:
It corresponds to the result of adding all the data and dividing it by the amount of data, then we have:
Mean=(89+81+96+85+93+70+66+64+68+70)/10
Mean=782/10
Mean=78.2
Median:
First we will order the data from smallest to largest and the value that is in the center will be the median:
Sorted Data Set: 64, 66, 68, 70, 70, 81, 85, 89, 93, 96
Since 70 and 81 are in the middle, the median will be their average.
Median=(70+81)/2=151/2=75.5
Mode:
It is the data that is repeated the most, in this case it is 70 because it is twice
Range:
It is the difference between the smallest and largest value, then:
Range=96-64=32
What is the sign of when x > 0 and y < 0 ?
Answers
The number line always goes from negative to positive :
It increases from left to right
SInce negative is always on the left side of the zero
Snumber greater than zero are always positive
i.e. x > o
Ashgn in a bakery yves these options,• Option : 12 cupcakes for $29Option B. 24 cupcakes for $561. Find each unit price, Just type the number in your answer. (Don't forget to divide tothe thousandths place to help you round to the hundredths place.)Option :Option :2. Which option is the best deal per cupcake and gives the lowest unit price. Type A or
Answers
1) To find each unit price, let's find out the unit rate. Setting a proportion.
Option A
cupcakes price
12 ------------------- 29
1 --------------------x
Cross multiplying it:
12x = 29 Divide both sides by 12
x =2.42
Each cupcake costs $ 2.42
Option B
24 ------------ 56
1 ------------ y
24y = 56
y =$2.33 per cupcake.
2) The best deal for buying cupcakes is found in Option B. Since the price is lower per cupcake
3) Hence, the answers are:
Option A = $2.42 per cupcake
Option B =$2.33 per cupcake
Best Deal: Option B
Which of the following is a solution to the inequality below?
Answers
Answer:
q = -1
Step-by-step explanation:
We are given the inequality [tex]11-\frac{64}{q} > 60[/tex]
We want to find out which value of q is a solution to the inequality. In other words, which value of q makes the statement true?
We can substitute the values given for q into the inequality to see this.
Let's start with q=2.
Replace q with 2.
[tex]11-\frac{64}{2} > 60[/tex]
Divide 64 by 2.
64/2= 32
11 - 32 > 60
Subtract 32 from 60
11-32 = -21
-21 > 60
The inequality reads "-21 is greater than 60", which is false (negative numbers are less than positive ones).
This means q=2 is NOT an answer.
Next, let's try q=-2
[tex]11 - \frac{64}{-2 } > 60[/tex]
64/-2 = -32
11 - - 32 > 60
- - 32 means subtracting a negative, which is the same as adding 32 to 11.
11 + 32 > 60
43 > 60
This is also NOT true (it reads "43 is greater than 60").
So q=-2 is also NOT an answer.
Now, let's try q = -1
[tex]11-\frac{64}{q} > 60[/tex]
[tex]11-\frac{64}{-1} > 60[/tex]
64/-1=-64
11 - -64 > 60
11 + 64 > 60
75 > 60
This reads "75 is greater than 60".
This is a true statement, meaning q = -1 IS an answer.
We are technically done, but just to be sure, we can check q=1 as well.
[tex]11 - \frac{64}{q} > 60[/tex]
[tex]11 - \frac{64}{1} > 60[/tex]
11 - 64 > 60
-53 > 60
This reads "-53 is greater than 60", which is false.
So this confirms that q = -1 is the only option that is an answer.
Are the two triangles similar? If so, state the reason and the similarity statement
Answers
Two sides are in same proportion and the included angle is common as per SAS. Therefore, both the triangles are similar.
Triangle:
A triangle is the three-sided polygon, which has three vertices. The three sides are interconnected with each other end to end at a point, which forms the angles of the triangle.
Here there are two triangles KLP and KMN. And the sum of all three angles of the two triangle is equal to 180 degrees.
Given,
Here we have the two triangle and we need to find that they are similar or not.
For that we have to calculate the total length of the sides of the triangle,
That,
KM = KL + LM
KM = 8 + 2 = 10
Similarly,
KN = KP + PN
KN = 12 + 3 = 15
In triangles KLP & KMN,
KL/KP = 8/12 = 2/3
Similarly, for the triangle KMN,
KM/KN = 2/3
Here the angles have the same values so they are parallel. Which states that, Angle O is common in both the triangles.
Therefore, the two sides are in same proportion and the included angle is common (SAS) . Hence both the triangles are similar.
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Converting between metric units of volume and capacityA water tower has a volume of 874 m³.Find how many liters of water it would take to completely fill thewater tower. Use the table of conversion facts, as needed.LXS?Conversion facts for volume and capacity1 cubic centimeter (cm³) = 1 milliliter (mL)1 cubic decimeter (dm³) = 1 liter (L)1 cubic meter (m³) = 1 kiloliter (KL) I need help with this math problem
Answers
Given: A water tower has a volume of 874 m³
To Determine: How many liters of water it would take to completely fill the
water tower
Solution
Please note that 1 cubic meter (m³) = 1 kiloliter (KL)
Therefore
[tex]\begin{gathered} 1m^3=1KL \\ 874m^3=xKL \\ Cross-multiply \\ x=874KL \end{gathered}[/tex]Also note that Kilo means 1000
Therefore
[tex]\begin{gathered} 874KL=874\times1000L \\ =874000L \end{gathered}[/tex]Hence, the water tower will be completely fill with 874000 liters(L)
lmk quick please i need to turn this in
Answers
Answer:
2x^2 + 12x
Step-by-step explanation:
The perimeter is the sum of all the sides of a geometric figure.
So x^2 + 6x - 3 + 5x + 3 + x^2 - x
Add like terms:
2x^2 + 12x
The reason I said 2x^2 + 12x here is that this is likely a misprint, and you'll have to ask your teacher about this. Since the 3s (3 and -3) cancel each other out, but there are only 10 x's, your true answer is 2x^2 + 10x.
However, it is more likely that the misprint concerns the x^2 - x, meaning it was meant to be x^2 + x, which would give you answer A. The idea that the problem is just missing a random 9 somewhere is much more farfetched.
I would select answer A.
This is a complicated and incorrectly formatted question. Hope this helps!
Answer:
D
Step-by-step explanation:
Question 8 Let h(t) = –1612 +64 + 80 represent the height of an object
Answers
To find the time it takes the object to reach the maximum height we need to remember that this happens in the axis of symmetry of the parabola described by the function:
[tex]h(t)=at^2+bt+c[/tex]The axis of symmetry is given as:
[tex]t=-\frac{b}{2a}[/tex]in this case we have that a=-16 and b=64, then we have:
[tex]t=-\frac{64}{2(-16)}=\frac{-64}{-32}=2[/tex]Therefore it takes 2 seconds to the object to reach its maximum height.
Now, to find the maximum height we plug this value of t in the equation, then we have:
[tex]\begin{gathered} h(2)=-16(2)^2+64(2)+80 \\ =-16(4)+128+80 \\ =-64+128+80 \\ =144 \end{gathered}[/tex]therefore the maximum height is 144 ft.
In the national park, the ratio of black bear bears to grizzly bears is 3:1. If the park had 12 grizzly bears, how many black bears would it have?
Answers
The number of black bears in the national park is 36
Here, given the ratio of black bears to grizzly bears, and the number of grizzly bears, we want to find the number of blackbears the national park has
Let the number of black bears be x
what this mean is that the total number of bears in the park is (x + 12)
The total ratio of the two is 3 + 1 = 4
Matematically;
[tex]\begin{gathered} \frac{3}{4}\text{ }\times\text{ (x + 12) = x} \\ \\ 3(x\text{ + 12) = 4 }\times\text{ x} \\ \\ 3x\text{ + 36 = 4x} \\ 4x-3x\text{ = 36} \\ \\ x\text{ = 36} \end{gathered}[/tex]Graph a line that contains the point 2 (-5, -6) and has a slope of 3 Y 6 4 2 2 -6 -4 2 4 6 -4- -6-
Answers
the graph of a line passing through point
[tex](x_1,y_1)[/tex]with gradient m
is given by
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y+6=3(x+5) \\ \Rightarrow y+6=3x+15 \\ \Rightarrow y=3x+9 \end{gathered}[/tex]Which of these steps will eliminate a variable in this system?3x-3y=66x+9y=3OA. Multiply the first equation by 3. Then subtract the second equationfrom the first.B. Multiply the first equation by 2. Then add the equations.C. Multiply the first equation by 2. Then subtract the second equationfrom the first.OD. Multiply the second equation by 2. Then subtract the secondequation from the first.
Answers
The given system of equation is:
[tex]\begin{gathered} 3x-3y=6 \\ 6x+9y=3 \end{gathered}[/tex]Multiply through the first equation by 2:
[tex]\begin{gathered} 6x-6y=12 \\ 6x+9y=3 \end{gathered}[/tex]Subtract the second equation from the first equation to get:
[tex]-15y=9[/tex]Therefore, the steps that will eliminate the variable x are:
Multiply the first equation by 2. Then subtract the second equation from the first.
Choice C
Which equation has a solution of 34 for y?Select all the correct answers.A.8y=9B.y−1=−14C.4y=6D.7−y=614E.12y=9F.214+y=4
Answers
SOLUTION
We want to know which of the options would give us
y = 34,
Let's try A. 8y = 9
This becomes
[tex]\begin{gathered} 8y=9 \\ to\text{ get y, we divide both sides by 8} \\ \frac{8y}{8}=\frac{9}{8} \\ y=1\frac{1}{8} \end{gathered}[/tex]We didn't get y = 34, hence A is incorrect.
Let's try B. y − 1= − 14
This becomes
[tex]\begin{gathered} y-1=-14 \\ \text{collecting like terms } \\ y=-14+1 \\ y=-13 \end{gathered}[/tex]B too is incorrect.
Let's try C. 4y = 6
[tex]\begin{gathered} 4y=6 \\ \text{divide both sides by 4 we have } \\ \frac{4y}{4}=\frac{6}{4} \\ y=\frac{3}{2} \\ y=1\frac{1}{2} \end{gathered}[/tex]C too is incorrect
Let's check D. 7 − y = 614
[tex]\begin{gathered} 7-y=614 \\ \text{collecting like terms we have } \\ y=7-614 \\ y=-607 \end{gathered}[/tex]D too is incorrect
A company has been forced to reduce its number of employees. Today the company has 29% fewer employees than it did a year ago. If there are currently355 employees, how many employees did the company have a year agoemployees?
Answers
to solve this, question, we would have to convert the percentage to fractions or decimals.
Let x represent the numbers of employees the had a year ago
[tex]\begin{gathered} \frac{29}{100}\times x=355 \\ 0.29x=355 \\ \text{divide both sides by the coefficient of x} \\ \frac{0.29x}{0.29}=\frac{355}{0.29} \\ x=1224.127 \\ x\approx1224 \end{gathered}[/tex]a year ago, the company had 1224 empolyees
27. Ava surveys teachers for how long it takes them to drive to school eachmorning. She records each response in the dot plot shown.5 10 15 20 25 30 35 40 45 50 55 60Length of Drive (minutes)Ava considers drives of 55 minutes or more as not typical. Given this,which measure of the entire data set represents the most typicaldriving time?meanrangemedianmean absolute deviation
Answers
EXPLANATION
The measure that represent the most typical driving time is the mean.
10 Zara writes a sequence of five numbers. The first number is 2. The last number is 18. Her rule is to add the same amount each time. Write the missing numbers. 2,____ ,_____,______, 18
Answers
If the first number is 2. The last number is 18. The sequence of five numbers will be 2,6,10,14,18.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.
It is given that, the first number is 2 and the last number is 18,
a = 2
L=18
n=5
a₅=5
a₅=a+(5-1)d
18=2+4d
4d = 18-2
4d = 16
d= 16 / 4
d=4
The terms of the sequence are,
a₁=2
a₂=2+4=6
a₃=6+4=10
a₄=10+4=14
a₅=14+4=18
Thus, if the first number is 2. The last number is 18. The sequence of five numbers will be 2,6,10,14,18.
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I need help with 7 3/4 + 1 5/6
Answers
we have
7 3/4 + 1 5/6
step 1
Convert mixed number to an improper fraction
7 3/4=7+3/4=31/4
Remember taht
If you multiply 31/4 by (1.5/1.5) you obtain an equivalent fraction
so
(31/4)(1.5/1.5)=46.5/6
multiply by 10/10
465/60
1 5/6=1+5/6=11/6
multiply by 10/10
(11/6)(10/10)=110/60
step 2
Adds the fractions
465/60+110/60=575/60
simplify
Convert to mixed number
575/60=540/60+35/60=9+35/60
simplify the fraction 35/60
35/60=7/12
so
we have
9+7/12=9 7/12
the answer is 9 7/12Without needing to graph determined the number of solutions for this system
Answers
Given the system of equations:
[tex]\text{ x + y = 6}[/tex][tex]\text{ y = -x + 6}[/tex]The two equations appear to be just the same, thus, we are only given one system of equations.
Therefore, the answer is letter B. It has infinite solutions because the two equations are just the same line.
Question 19 of 25What are the more appropriate measures of center and spread for this dataset?000:oooo000000000Select two choices: one for the center and one for the spread.I A: Better measure of spread: interquartile range (IQR)O B. Better measure of center: medianI c. Better measure of spread: standard deviationD. Better measure of center: mean
Answers
Measures of center:
The mean is usually the better measure of center, however, this measure is greatly affected by extreme values (very low or very high values). If the data set is strongly skewed or has extreme values, the mean will be affected and won't reflect the true center of the said data set.
The median separates the data set in halves and is not affected by extreme values.
Given that this data set is strongly skewed to the left, the best measure of center will be the median.
Measures of dispersion:
The standard deviation is usually the most preferable measure of dispersion. But, one of
1. It is h before closing time at the grocery store. It takes about h for Jane to find 1 item on her shopping list. How many items can she find before the store closes? (a) Create a model or write an equation for the situation. (b) Find the solution. Explain what you did. (c) State the solution as a full sentence.
Answers
GIVEN
The time left before the store closes is 3/4 h while the time taken to find one item is 1/8 h.
QUESTION A
Let the number of items that can be gotten before the store closes be N.
The number of items can be calculated using the formula:
[tex]N=\text{ number of hours left}\div\text{ number of hours used to find one item}[/tex]Therefore, the equation to get the number of items will be:
[tex]N=\frac{3}{4}\div\frac{1}{8}[/tex]QUESTION B
The solution can be obtained by division.
Apply the fraction rule:
[tex]\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]Hence, the solution will be:
[tex]\begin{gathered} \frac{3}{4}\div\frac{1}{8}=\frac{3}{4}\times\frac{8}{1} \\ \Rightarrow\frac{3\times\:2}{1\times\:1}=6 \end{gathered}[/tex]The answer is 6.
QUESTION C
Jane can find 6 items before the store closes.
It takes chuck 24 minutes to type and spell check 14 pages. Find how many pages he can type and spell check in 1.5 hours. Remember to convert 1.5 hours to minutes
Answers
In order to find how many pages can be typed, first let's convert 1.5 hours to minutes:
[tex]\begin{gathered} 1\text{ hour}\to60\text{ minutes} \\ 1.5\text{ hour}\to x\text{ minutes} \\ \\ \frac{1}{1.5}=\frac{60}{x} \\ x=60\cdot1.5 \\ x=90 \end{gathered}[/tex]Then, to find the number of pages, let's do the following rule of three:
[tex]\begin{gathered} 14\text{ pages}\to24\text{ minutes} \\ x\text{ pages}\to90\text{ minutes} \\ \\ \frac{14}{x}=\frac{24}{90} \\ 24x=14\cdot90 \\ x=\frac{14\cdot90}{24}=52.5 \end{gathered}[/tex]Therefore Chuck can type and spell check 52.5 pages in 1.5 hours.
A diver starts out at 342 feet below the surface (or – 342 feet). She then swims upward 237 feet.Use a signed number to represent the diver's current depth.
Answers
Given:
A diver starts at 342 feet below the surface, which means -342 feet.
Now, she swims 237 feet upward.
It shows that she is moving in a positive direction.
So, the current depth of diver is,
[tex]-342+237=-105[/tex]The depth is -105 feet, which shows that the diver is still 105 feet below the surface.
Help!!!! (Show ur work)
There are two questions
Answers
Answer:
Question 1: 3
Question 2: $120
Step-by-step explanation:
Set up a proportion
[tex]\frac{inches}{miles}[/tex] = [tex]\frac{inches}{miles}[/tex] fill in the numbers that you know and solve for the unknow.
[tex]\frac{5}{2}[/tex] =[tex]\frac{7.5}{m}[/tex] Cross multiply
5x =7.5(2)
5x = 15 Divide both sides by 5
x = 3
If we take 40% off that means that we leave 60% on
Percent means per hundred
[tex]\frac{60}{100}[/tex] When you divide by hundred, you move the decimal two places to the left.
200(.6)
$120.00
The height of a triangle is 4x more than the base, and the area of the triangle is 6 square units. Find the length of the base. Let x =the length of the base.
Write a quadratic equation in factored form. Write entire equation
Answers
Answer:
The length of the base is:
3 unitsThe resulting quadratic is
x² - 3= 0Step-by-step explanation:
Base = x
Height = 4x
Area, A = 1/2* base * Height
A = (1/2) * (x) * (4x)
A = 2x² (1)
But, A = 6 (2)
Since (1) = (2);
2x²= 6
x²= 3
Resulting quadratic:
x² - 3= 0
For the difference between 2 squares:
a² - b² = (a-b)(a+b)
Using that identity, we can factorize our quadratic:
(x-3)(x+3) = 0
So, we have 2 roots:
x = 3 and x = -3
Now, noting that length must take a positive value, we go for the first:
x = 3
CONCLUSION:The length of the base is:
3 unitsThe resulting quadratic is
x² - 3= 0Quadrilateral OPQR is dilated by a scale factor of 2/3 to form quadrilateral O'P'Q'R'. What is the measure of side RO?
Answers
Divide side R'O' (8) by th scale factor (2/3)
8 : 2/3= 12
A bee produce 0,05 ml of honey per day, how many litres of honey can the bee produce in its lifetime if they live for 28 days?
Answers
Given:
A bee produce 0.05 ml of honey per day
We will find how many liters of honey can the bee produce in its lifetime if they live for 28 days
Let it produces x ml
So, using the ratio and proportions
[tex]\frac{0.05}{1}=\frac{x}{28}[/tex]Solve for x:
[tex]x=0.05\times28=1.4ml[/tex]Convert ml to liters
1 liter = 1000 ml
So, 1.4 ml = 0.0014 liters
So, the answer will be
The bee can produce honey in its lifetime = 0.0014 liters
Just do all 25 points If can show how it works it will be better thanks
Answers
a) Given:
The length of the side of a square is,
[tex]\frac{1}{5}cm[/tex]To find:
The area of the square.
Explanation:
Using the formula of the area of the square,
[tex]\begin{gathered} A=a^2 \\ A=(\frac{1}{5})^2 \\ A=\frac{1}{25}cm^2 \\ A=0.04cm^2 \end{gathered}[/tex]Final answer:
The area of the square is,
[tex]0.04cm^2[/tex]True or False? A circle could be circumscribed about the quadrilateral below.B82"O A. TrueA 105°98° cO B. False75%
Answers
Solution
For this case since we want to verify if a circle can be circumscribed in the quadrilateral we can use the following Theorem:
Theorem: If a quadrilateral is incribed in a circle then the opposite sides are supplementary
And we cna verify:
105+ 98= 203
82 +75= 157
Then we can conclude that the answer is:
False