Number 1 statement is false
Not all 4 sided shapes are parallelograms
Number 2 statement is true
All rhombuses are paralleogram
Number 3
some rectangles are square though not all rectangles are square
Number 4
All squares are paralleloprams, this is also true
2. Determine the equation of the asymptote for the following exponential functions: *y=2x-3 b. y = (3)* + 2 c. ** y = 2(3)* d. 2 + 3x I *** a.
a) y = -3
b) y = 2
c) y = 0
d) y = 2
Explanation:The asymptote is the constant added to the expression of the variable
a) y = 2^x - 3
Theexpression of the variable = 2^x
The number after it is is - 3
So the asymptote is y = -3
b) y = (1/3)^x + 2
The number added to the expression of the variable is 2
Asymptote is y = 2
c) y = 2(3)^x
y = 2(3)^x + 0
The expression of the variable = 2(3)^x
There is no number added to the expression of the variable
Hence, Asymptote is y = 0
d) 2 + 3^x
[tex]\begin{gathered} The\text{ function is not equated to y} \\ Since\text{ we are told they are all exponntial function,} \\ \text{let 2 + 3}^x\text{ = y} \end{gathered}[/tex]The expression of the variable = 3^x
The number added to this expression is 2
Asymptote is y = 2
The shore, a rope, and a dock that is 8 meters long enclose a rectangular swimming area along thelakeshore. The length of swimming area is 6 meters more than its width and the swimming area must bemore than 180 square meters. If the rope is 34 meters long, then what are the dimensions of theswimming area?
So we have two conditions, the first one is that the length (L) of the swimming area is 6 meters more than the width (W) so:
[tex]L=6W[/tex]and the other condition is that the area is 180 square meters so we can writte it like:
[tex]180=L\cdot W[/tex]Now we have 2 equations and 2 ingognitas so we can replace the first equation into the second equation like this:
[tex]180=(6W)\cdot W[/tex]and we solve for W so
[tex]\begin{gathered} 180=6W^2^{} \\ W^2=\frac{180}{6}=30 \\ W=\sqrt[]{30}=5.5 \end{gathered}[/tex]Now with the value of W we can replace it in the first equation so:
[tex]L=6(5.5)[/tex]so:
[tex]L=33[/tex]The dimensions are:
[tex]\begin{gathered} \text{length}=33m \\ \text{width}=5.5m \end{gathered}[/tex]Divide 180 into two parts such that the first part is 12 less thantwice the second part.a 100, 80b 90,90c 116, 64d 99. 81
You can find a math expression dividing the statment as follow:
Divide 180 into two parts such that: x and y
the first part: X
is 12 less than: X= -12
twice the 2(
second part: Y
the first (X) part is 12 less than twice the second part (Y):
X=2Y-12
Prior to making deposits of $75 and $50 Marian had a balance of $102in her checking account. How much must she deposit so that her balance winbe at least $300 and she can avoid a service fee
Marian had a balance of $102
Then she made two deposits, one of $75 and the other for $50
We can calculate the balance of her checking account after the deposits were done
New balance = $102 + $75 + $50 = $227
The account needs to have at least $300 to avoid a service fee, so we calculate how much is needed to complete that amount
New deposit = $300 - $227 = $73
So, if Marian deposits at least $73, the account balance will be $300 or more
Answer: She must deposit at least $73
Examples: Find the area of the following figures.1.6cm10cm7cm4cm
The figure below is a Trapezium.
Let's write out the formula for the area of a trapezium,
[tex]\text{Area of a trapezium=}\frac{1}{2}(a+b)h[/tex]1) Let us write out the data given in the first figure,
[tex]\begin{gathered} a=7\operatorname{cm} \\ b=10\operatorname{cm} \\ h=4\operatorname{cm} \end{gathered}[/tex]Let us solve for the area of the figure,
[tex]\begin{gathered} \text{Area of the trapezium=}\frac{\text{1}}{2}(7+10)\times4 \\ =\frac{1}{2}(17)\times4 \\ =34cm^2 \end{gathered}[/tex]The area of the trapezium is 34cm².
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:1.7 * 10^5 m
Step-by-step explanation:
find the excluded value(s) of x in the rational expression f(x)= x^2+7x/ x^+14x+49so how am I supposed to combine like terms and get to the answer
Given
[tex]f(x)=\frac{x^2+7x}{x^2+14x+49}[/tex]
Procedure
Factoring
[tex]\begin{gathered} f(x)=\frac{x(x+7)}{(x+7)(x+7)} \\ f(x)=\frac{x}{x+7} \end{gathered}[/tex]Answer:
x ≠ – 7
I need help with my math
Step 1: write out the formula for slope
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]Step2: Identify the point in the diagram
[tex]\begin{gathered} (-2,-4)\text{ and (2,2)} \\ x_1=-1,x_2=2,y_1=-4,y_2=2 \end{gathered}[/tex]Step3: Substitute the value into the given formula above
[tex]\begin{gathered} \text{Slope}=\frac{y_2-y_1}{x_2-x_1} \\ =\text{ }\frac{2-(-4)}{2-(-2)} \\ =\frac{2+4}{2+2} \\ =\frac{6}{4} \end{gathered}[/tex][tex]\text{slope}=\frac{3}{2}[/tex]Hence the slope of the line is 3/2
is 1/8 greater than 18%
Consider than 18% in decimal is 0.18.
Next, take into that 1/8 = 0.125
0.18 is great
Our family has a small pool for relaxing in the summer that holds 1500 gallons of water. I decided to fill the pool for the summer. When I had 5 gallons of water in the pool, I decided that I didn't want to stand outside and watch the poik fill, so I had to figure out how long it would take so that I could leave, but come back to turn off the water at the right time. I checked the flow on the hose and found that it was filling the pool at a rate of 2 gallons every minute. Use a table, a graph, and a equation to create a mathematical model for the number of gallons of water in the pool ar minutes?
Let the volume, as a function of time t, be v:
v(t) = 5 + 2t
v(t) = 5 + 2t
The mathematical model is v(t) = 5 + 2t
Part EWhat is a possible explanation for why the y-intercept is negative for all three functions?
In this problem
x -----> number of meals sold
y ----> profit
Remember that
the y-intercept is the value of y, when the value of x is zero
In this context
the y-intercept is the value of the profit when the restaurant begin or start to sell meals
In this case, the y-intercept is negative, which means when the restaurant started, there have a negative profit (loss) {the cost is greater than the revenue) because the number of meals sold is zero.
Answer:
The restaurants incur costs to prepare meals, such as labor and supplies, before any meals are sold. So, the restaurants will lose money until they sell a number of meals equal to the first x-intercept.
Step-by-step explanation:
Edmentum
I need help with this math problem I have a picture that I can show you of what it is
The 18 % off of the listed price x can be denoted as,
[tex]\frac{100-18}{100}x=0.82x[/tex]18% more than the amount x can be denoted as,
[tex]\frac{100+18}{100}x=1.18x[/tex]3/10 of the origianl voulme x drained out is denoted as,
[tex]x-\frac{3}{10}x=\frac{10x-3x}{10}=\frac{7x}{10}[/tex]3/10 stock is added,
[tex]x+\frac{3}{10}x=\frac{10x+3x}{10}=\frac{13x}{10}[/tex]4x+3y=14-yx-5y=23. IF (x, y) is a solution to the system of equationsabove, what is x - y?A) 1B)C) 3D) 18
C. 3
Based on her recipe, Elena knows that 5 servings of granola have 1,750 calories. which equation can be used to represent the relationship between the number of calories, c, and the number of servings of granola, g?
Answer:
c = 350g
Explanation:
To find the relationship, we will use proportions. So, we know that 5 servings of granola have 1,750 calories and it will be equivalent to g servings of granola with c calories. Therefore, the proportion is:
[tex]\frac{\text{Granola}}{\text{Calories}}=\frac{5}{1,750}=\frac{g}{c}[/tex]So, using cross multiplication, we get:
[tex]5\cdot c=1,750\cdot g[/tex]Then, solving for c, we get:
[tex]\begin{gathered} 5c=1750g \\ \frac{5c}{5}=\frac{1750g}{5} \\ c=350g \end{gathered}[/tex]So, the answer is: c = 350g
can you please give me some more information about this
We can see that the segment is defined by the points (-5, 5) & (-3, -4).
Now, we calculate the mid-point by using the following expression:
[tex]mp=(\frac{x_2-x_1}{2},\frac{y_2-y_2}{2})[/tex]So, now we replace:
[tex]mp=(\frac{-5-(-3)}{2},\frac{-4-5}{2})\Rightarrow mp=(-1,\frac{1}{2})[/tex]So, the mid point is (-1, 1/2).
can u help me with the boxplot of Area 1?
In order to create a boxplot of the Area 1 dataset, first let's put the dataset in crescent order:
[tex]12,24,30,32,35,44,45,56,57,59,61,65,68,92,100.[/tex]Since the set has 15 elements, the median is the 8th element, so the median is 56.
The median will divide the set into two smaller sets with 7 elements each. The first interquartile (IQ1) is the median of the first subset (so it will be the 4th element), and the third interquartile (IQ3) is the median of the second subset (so it will be the 12th element).
So the first interquartile is 32 and the third interquartile is 65.
Now we need the lower and upper limit of the set.
The lower limit is 12 and the upper limit is 100.
Now, creating the boxplot, we have:
Two sides of a triangle have the followingmeasures. Find the range of possiblemeasures for the third side.
The sum of the lengths of any two sides of a triangle must be greater than the third side.
So:
A+B>C
B+C > A
C+A > B
Given the 2 sides: 31 and 44, suppose they are sides A and B:
44-31 < c < 44+31
Range
13 < C < 75
what is the equation of the line that passes through the point[tex]( - 3 - 11)[/tex]y=2x-4
Answer
To check if a line passes through a point replace x in the equation
For example:
y= 2x-4
replacing
y = 2*( -3) -4
y= -6-4
y = -10
So then y= 2x-4 passes through the point (-3, -10)
You have 3 6 sided dice. One is red one is blue one is green What is the probability that you roll a one on the red die a 2 on the blue die and a 3 on the green
Solution
Step 1
[tex]Probability\text{ of any event = }\frac{number\text{ of required outcomes}}{number\text{ of sample space}}[/tex]Step 2:
For each die, the number of sample space is (1 ,2,3,4,,6)
Note: AND represent multiplication
Step 3:
The probability that you roll a 1 on the red die a 2 on the blue die and a 3 on the green
[tex]\begin{gathered} =\text{ }\frac{1}{6}\text{ }\times\text{ }\frac{1}{6}\text{ }\times\text{ }\frac{1}{6} \\ \text{= }\frac{1}{216} \end{gathered}[/tex]Final answer
[tex]\frac{1}{216}[/tex]Rachel practiced 1/2 of an hour on Monday, 1/3 of an hour on Tuesday, 1/4 of an hour on both Wednesday and Thursday, and 1/2 of an hour on Friday. Find how many minutes she practiced each day and then find how many minutes she practiced in all during the week.
ANSWER and EXPLANATION
We want to find the number of minutes she practiced each day and in total.
An hour is equal to 60 minutes.
On Monday, she practiced 1/2 of an hour. To convert this to minutes, multiply 1/2 by 60 minutes. That is:
[tex]\begin{gathered} \frac{1}{2}\cdot60 \\ \Rightarrow30\min \end{gathered}[/tex]On Tuesday, she practiced for 1/3 of an hour. That is:
[tex]\begin{gathered} \frac{1}{3}\cdot60 \\ \Rightarrow20\min \end{gathered}[/tex]On Wednesday, she practiced for 1/4 of an hour. That is:
[tex]\begin{gathered} \frac{1}{4}\cdot60 \\ \Rightarrow15\min \end{gathered}[/tex]On Thursday, she practiced for 1/4 of an hour. That is also equal to:
[tex]\Rightarrow15\min [/tex]On Friday, she practiced for 1/2 of an hour. That is equal to:
[tex]=>30\min [/tex]To find the total number of minutes that she practiced in all during the week, find the sum of the number of hours for all the days given.
[tex]\begin{gathered} 30+20+15+15+30 \\ \Rightarrow110\min \end{gathered}[/tex]She practiced for 110 minutes during the week.
If f(x) = (x + 3)4, find the inverse of f.f -1(x) = x1/4 - 3f -1(x) = x1/4 + 3f -1(x) = 3x1/4f -1(x) = x1/4 /3
Given:
The function
[tex]f(x)=(x+3)^4[/tex]Required:
FInd inverse of f.
Explanation:
Function inverse definition
[tex]\text{ A function }g\text{ is the inverse of function f if for }y=f(x),x=g(y).[/tex]Now,
[tex]\begin{gathered} y=(x+3)^4 \\ \text{ Replace x with y} \\ x=(y+3)^4 \\ \text{ Solve for y,} \\ x=(y+3)^4 \\ y=x^{\frac{1}{4}}-3 \end{gathered}[/tex]Answer:
Option A is correct.
Suppose you roll a pair of six-sided dice and add their totals.(a) What is the probability that the sum of the numbers on your dice is 9 or 11? (b) What is the probability that the sum of the numbers on your dice is an even number or a number less than 6? (c) What is the probability that the sum of the numbers on your dice is a prime number or a number greater than 5?
Rolling a pair of six-sided dice, we have the following sample space:
(a) The probability that the sum of the numbers on your dice is 9 or 11 is
P(X = 9) + P(X = 11)
= 4/36 + 2/36
= 6/36
= 1/6
(b) The probability that the sum of the numbers on your dice is an even number or a number less than 6 is:
P(X = even) + P(X < 6)
= 21/36 + 10/36
= 31/36
(c) The probability that the sum of the numbers on your dice is a prime number or a number greater than 5?
P(X = prime) + P(X > 5)
= 14/36 +
How do I write an equation of a line passing through
The equation is:
[tex]y=\frac{1}{2}x+2[/tex]Explanation:Given the point (2, 3), and the equation:
y - 4 = -2(x + 3) .............................................(1)
[tex]\begin{gathered} y=-2x-6+4 \\ =-2x-2 \end{gathered}[/tex]Comparing with the equation of a line:
[tex]y_{}=mx+b[/tex]where m is the slope, and b is the y-intercept
The slope in (1) is -2
Note that perpendicular lines have their slopes as negative reciprocals of each other.
The negative reciprocal of -2 is 1/2
The equation of a line perpendicular to (1) is:
[tex]y=\frac{1}{2}x+b[/tex]Applying the given point (2, 3), we have x = 2, y = 3
[tex]\begin{gathered} 3=\frac{1}{2}(2)+b \\ \\ b=3-1=2 \end{gathered}[/tex]The equation is therefore;
[tex]y=\frac{1}{2}x+2[/tex]The sales tax for an item was $6.80 and it cost $340 before tax. Find the sales tax rate. Write the answer as a percentage.
Answer: 1.788%
Explanation
Given
• Sales tax for an item: $6.80
,• Total cost before tax: $340
Procedure
To find the sales tax rate we have to divide the sales tax against the total cost as follows:
[tex]\frac{6.08}{340}=0.01788[/tex]To convert it to percent we have to multiply times 100%:
[tex]0.01788\times100\%=1.788\%[/tex]1. Identify the population and the sample of the following scenarios,Part A: A survey of 1353 American Households found that 18% of the households own acomputer,Part B: A recent survey of 2625 elementary school children found that 28% of thechildren could be classified obese,Part C: The average weight of every dh person entering the mall within three hourperiod was 146 lb.
Let's begin by listing out the information given to us:
The population refers to the entire group from which you want to make a conclusion
The sample refers to the specific subject from whom data is obtained
Part A
Population = 1353
Sample = 18% of the population = 18% * 1353 = 243.54 ≈ 244
Part B
Population = 2625
Sample = 28% of the population = 28% * 2625 = 735
Part C
Population = every person that came into the mall
Sample = every person that came into the mall within the 3 hour period
At a gas station each leader of gas cost $3 but there's a promotion that for every beverage you purchase you save 20 cents on gas is your total savings on gas proportional to the number of beverages you purchase?
Input data
$3 per gas
0.20 cents savings per beverages
Procedure
Yes, your total savings on gas proportional to the number of beverages you purchases.
For every beverage purchased, there is a saving of $0.20
s = savings
Ernesto already has 6 flowers in his garden and his garden he will grow 4 more flowers per seed packet he plants.let s represent the number of seed packets he plants and f represent the total number of flowers he will have. Complete the equation that represent the relationship between s and f
What is the product?6 2/5, 5/6, 1 1/4
Given
[tex]6\frac{2}{5},\frac{5}{6},1\frac{1}{4}[/tex]Product means multplication
[tex]6\frac{2}{5}\times\frac{5}{6}\times1\frac{1}{4}[/tex]Change the mixed fraction to improper fraction
[tex]\begin{gathered} \frac{32}{5}\times\frac{5}{6}\times\frac{5}{4}=\frac{4}{1}\times\frac{1}{3}\times\frac{5}{1} \\ \frac{4}{1}\times\frac{1}{3}\times\frac{5}{1}=\frac{20}{3}=6\text{ }\frac{2}{3} \end{gathered}[/tex]The final answer
[tex]6\text{ }\frac{2}{3}\text{ or }6.6667[/tex]3 5 6 Graphs and Tables: To determine matching graphs and tables you would use your answer choices to plug in x values and solve to see if you get the correct y value for each pair. 10. 9. Which linear equation matches the table shown? The equation y = 3x - 4 represents the relationship in which of the following tables? 3 10 5 7 6 9 2 11 2 10 y у 6 18 11 17 23 29 35 3 y - 2 3 A. y = x + 8 X - - O B. y = 4x - 1 y-10 -> - C. y = 3x + 2 14 17 20 D. y = 5x - 4
Determine the linear equation for the table.
[tex]\begin{gathered} y-17=\frac{23-17}{7-5}(x-5) \\ y-17=\frac{6}{2}(x-5) \\ y=3x-15+17 \\ y=3x+2 \end{gathered}[/tex]So equation for the table is y = 3x + 2.
move the numbers to the blanket to order them from least to greatest value.
The given numbers from least to greatest are
• 1 - 21 = -20
,• -0.89
,• 0.4
,• 0.5
,• 9/8 = 1.125
To order the number from least to greatest, we just have to know the value of each one. For example, 1 - 21 equals -20, this will be the least number because it has the greatest absolute value as a negative number. Then, we have -0.89, which is greater than -20. And so on.