To know the expression that is less than 1 when x=4
we will need to check each expression
As for the first one;
[tex](\frac{3}{x^2})^0[/tex]anything raise to the power of zero will give 1, since the o affects all that is in the bracket, then the expression is 1
Hence it is not less than 1
For the second expression;
[tex]\frac{x^0}{3^2}=\frac{4^0}{9}=\frac{1}{9}[/tex]The value is less than 1
For the third expression;
[tex]\frac{1}{6^{-x}}[/tex]substituting x=4 in the above expression
[tex]\frac{1}{6^{-4}}[/tex]The above is the same as;
[tex]undefined[/tex]Match each expression on the left with its sum on the right. Some answer options on the right will not be used.
To match the expression with the sum, what you have to do is solve each sum.
Remember that to sum/subtract two fractions, both of them should be expressed using the same denominator,
1)
[tex]-\frac{2}{3}+\frac{5}{6}[/tex]The denominators of these fractions are "3" and "6", the least common denominator between both values is 6. To express the first fraction as its equivalent with denominator 6, you have to multiply it by 2:
[tex]-\frac{2\cdot2}{3\cdot2}+\frac{5}{6}=-\frac{4}{6}+\frac{5}{6}[/tex]Now you can proceed to add both fractions:
[tex]-\frac{4}{6}+\frac{5}{6}=\frac{-4+5}{6}=\frac{1}{6}[/tex]The result for this sum is 1/6
2)
[tex]\frac{7}{12}+(-\frac{3}{4})[/tex]First, simplify both symbols, when a plus symbol and a minus symbol and next to each other, the plus sign gets canceled:
[tex]\frac{7}{12}+(-\frac{3}{4})=\frac{7}{12}-\frac{3}{4}[/tex]To subtract both fractions the first step is to express them using the same denominator. The least common denominator between 12 and 4 is 12, to express -3/4 as its equivalent with denominator 12, you have to multiply the fraction by 3:
[tex]\frac{7}{12}-\frac{3\cdot3}{4\cdot3}=\frac{7}{12}-\frac{9}{12}[/tex]Next, subtract both fractions:
[tex]\frac{7}{12}-\frac{9}{12}=\frac{7-9}{12}=-\frac{2}{12}[/tex]The result is no in its simplest form, 2 and 12 are divisible by 2, so to simplify the fraction you have to divide the numerator and denominator by 2:
[tex]-\frac{2\div2}{12\div2}=-\frac{1}{6}[/tex]The result for this expression is -1/6
3)
[tex]-\frac{1}{4}+\frac{3}{8}[/tex]Same as before, the first step is to express both fractions with the same denominator. the least common denominator for both fractions is 8. To express -1/4 as its equivalent with denominator 8, you have to multiply the fraction by 2
[tex]-\frac{1\cdot2}{4\cdot2}+\frac{3}{8}=-\frac{2}{8}+\frac{3}{8}[/tex]Next, add both fractions:
[tex]-\frac{2}{8}+\frac{3}{8}=\frac{-2+3}{8}=\frac{1}{8}[/tex]The result for this sum is 1/8
So the corresponding matches are:
[tex]\begin{gathered} 1)-\frac{2}{3}+\frac{5}{6}=\frac{1}{6} \\ 2)\frac{7}{12}+(-\frac{3}{4})=-\frac{1}{6} \\ 3)-\frac{1}{4}+\frac{3}{8}=\frac{1}{8} \end{gathered}[/tex]help ! it may or may not have multiple answers
From the given problem, there are 3 computer labs and each lab has "s" computer stations.
So the total number of computers is :
[tex]3\times s=3s[/tex]Mr. Baxter is ordering a new keyboard and a mouse for each computer, since the cost of a keyboard is $13.50 and the cost of a mouse is $6.50.
Each computer has 1 keyboard and 1 mouse, so the total cost needed for 1 computer is :
[tex]\$13.50+\$6.50[/tex]Since you now have the cost for 1 computer, multiply this to the total number of computers which is 3s to get the total cost needed by Mr. Brax :
[tex]3s\times(13.50+6.50)[/tex]Using distributive property :
[tex]a(b+c)=(ab+ac)[/tex]Distribute s inside the parenthesis :
[tex]3(13.50s+6.50s)[/tex]One answer is 1st Option 3(13.50s + 6.50s)
Simplifying the expression further :
[tex]\begin{gathered} 3(13.50s+6.50s) \\ =3(20.00s) \end{gathered}[/tex]Another answer is 4th Option 3(20.00s)
Create a quadratic function in one of the forms and show how to convert it to the other two forms.
Create a quadratic function in one of the forms and show how to convert it to the other two forms.
Step-by-step explanation:
1) Standard form: y = ax2 + bx + c where the a,b, and c are just numbers.
[tex]y=ax^2+bx+c[/tex]2) Factored form: y = (ax + c)(bx + d) again the a,b,c, and d are just numbers.
[tex]y=(ax+c)(bx+d)[/tex]3) Vertex form: y = a(x + b)2 + c again the a, b, and c are just numbers.
[tex]y=a(x+b)^2+c[/tex]The vertex of the parabola is written as (h, k) where b is the x - coordinate and c - is the y - coordinate
A group of 23 students want to see the show at the planetarium. Tickets cost $11 for each student who is a member of the planetarium’s frequent visitor program and $13 for each student who is not a member. The total cost of the students’ tickets is $261.
Out of 23 students 19 students are the member of planetarium's frequent visitor program and 4 students are not the members.
Given,
The total number of students in a group = 23
Cost of ticket for member of planetarium's frequent visitor program = $11
Cost of ticket for the student who is not a member = $13
The total cost of the students ticket = $261
Lets take,
The number of students with membership = x
The number of students without membership = y
Total number of students, x + y = 23 -----------(1)
Now,
Total cost for the tickets, 11x + 13y = 261
Now, Multiply 13 with (1)
We get,
13x + 13y = 299
Solve for x
13x + 13y = 299 -
11x + 13y = 261
2x + 0 = 38
2x = 38
x = 38/2
x = 19
Now, put x in (1)
19 + y = 23
y = 23 - 19
y = 4
That is,
The number of students with membership is 19 and the number of students without membership is 4.
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Joy took off from a stop light and increased her speed until she reaches the speed limit. She kept her speed steady until she saw a sign saying the speed limit has been increased. Select the graph that represents this situation.
We are presented with a group of graphs in which the x-axis represents time and the y-axis represents speed.
We are told that Joy started by accelerating when she took off, which means the graph should start with a line with positive slope.
She then maintained her speed, which means the slope of the line is 0, orin other words, the line is parallel to the time axis.
Finally, we are told that she saw a sign saying the speed limit had been increased, so she probably accelerated again, meaning the line should have a positive slope again.
Thus, the graph representing the situation is the third option.
How to solve this problem? (the answer is 262 Hz). i want to know the step by step on how to solve the equation given. if it helps, i am a grade 10 student. (YES, this is a MATH problem)
The frequency of middle C = 262 Hz
Explanation:The formula for calculating the frequency, F hertz, of a note n seminotes above the concert pitch is:
[tex]F\text{ = 440(}\sqrt[12]{2})^n[/tex]This can be re-written as:
[tex]F=440(2^{\frac{n}{12}})[/tex]Middle C is 9 semitones below the concert pitch
That is, n = -9
To find the frequency of middle C, substitute n = -9 into the equation for F
[tex]\begin{gathered} F=440(2^{\frac{-9}{12}}) \\ F\text{ = 440(}0.5946) \\ F\text{ = }261.62\text{ Hz} \\ F\text{ = 262 Hz (to the nearest hertz)} \end{gathered}[/tex]The frequency of middle C = 262 Hz
The cost, c(x) in dollars per hour of running a trolley at an amusement park is modelled by the function [tex]c(x) = 2.1x {}^{2} - 12.7x + 167.4[/tex]Where x is the speed in kilometres per hour. At what approximate speed should the trolley travel to achieve minimum cost? A. About 2km/h B about 3km/h C about 4km/D about 5km/hr
The equation is modelled by the function,
c(x) = 2.1x^2 - 12.7x + 167.4
The general form of a quadratic equation is expressed as
ax^2 + bx + c
The given function is quadratic and the graph would be a parabola which opens upwards because the value of a is positive
Since x represents the speed, the speed at which the he
A governor has been working to decrease the unemployment rate but it has gone up by 3%. In an effort to undermine the governor, a media outlet releases a bar graph comparing the unemployment rate before and after the governor took office.Which of the following tactics did the media outlet use to create this graph?A. Comparison chartsB. SizingC. Missing informationD. Axis and scaling manipulation
From the given graph, let's determine the tactics which the media outlet used to create the graph.
From the graph, we can see that the scaling of the y-axis was manipulated.
The numbers in the y-axis starts from 8%, while a normal graph is suposed to start from 0%.
Although the graph is correct, but the scaling of the y-axis is misleading. This is because when you look at the graph, you will think there is a major difference between unnemployment before and unemployment after.
Therefore, the tactics the media outlet used to create this graph can be said to be Axis and Scaling manipulation.
Axis and scaling manipulation is a method used in producing misleading graphs to make the data look worse or better than it actually is. This method leads to incorrect conclusions,
ANSWER:
D. Axis and Scaling manipulation.
Question 1
Is the sequence arithmetic: 78, 785, 7855, 78555, ...
O No
5 pts
Yes
Next >
The sequence is not arithmetic
What is a sequence?
A sequence in mathematics is an enumerated collection of items in which repetitions are permitted and order is important. It, like a set, has members (also called elements, or terms). The length of the series is defined as the number of items (which might be infinite). Unlike a set, the same components can occur numerous times in a sequence at various points, and the order does important. Formally, a sequence may be defined as a function from natural numbers (the sequence's places) to the items at each point. The concept of a sequence may be extended to include an indexed family, which is defined as a function from an arbitrary index set.
The given sequence 78, 785, 7855, 78555, ... is not arithmetic.
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162-317-3113-510Is this relation a function?
can you see my messages?
Araceli filled a cone-shaped container with a variety of colored sand to give as a gift to a friend. The volume of a cone is represented by the expression below, where r is the radius of the base of the cone and h is the height of the cone.radius = 3 1/23 5/3 is the height
The volume of the cone is 45.28 cubic inches.
The amount of sand inside the cone is measured by its volume.
Based on the numbers for the radius and height, the cone's volume is 45.28 cubic inches.
The volume of a cone is the measure of how much space a cone takes up. Cone height and base radius both affect how much space the cone takes up.
The volume of the cone is given by V = [tex]\frac{1}{3}\pi r^{2} h[/tex]
The value of the radius is r = [tex]3\frac{1}{23} = \frac{70}{23}[/tex]
The value of Height is h = [tex]3\frac{5}{3} = \frac{14}{3}[/tex]
So, the Volume of the cone =[tex]V =\frac{1}{3}\pi r^{2} h[/tex]
[tex]V =\frac{1}{3}\pi r^{2} h\\\\V = \frac{1}{3}\pi (\frac{70}{23}) ^{2} \frac{14}{3} \\\\V = 45.28[/tex]
The volume of the cone is 45.28 cubic. inches
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Given f(x) = 2x - 1 h(x) = x^2 + 1Find f[h(7)]
Answer:
[tex]f\lbrack h(7)\rbrack\text{ = 99}[/tex]Explanation:
Given the functions:
[tex]\begin{gathered} f(x)=2x-1 \\ h(x)=x^2+1 \end{gathered}[/tex]We want to find:
[tex]f\lbrack h(7)\rbrack[/tex]First of all, we need to find:
[tex]f\lbrack h(x)\rbrack[/tex]This is done by inserting the value of h(x) into f(x)
So, we have:
[tex]\begin{gathered} f\lbrack h(x)\rbrack=2(x^2+1)-1 \\ =2x^2+2-1 \\ =2x^2+1 \end{gathered}[/tex]Substituting 7 for x in f[h(x)], we have f[h(7)]
[tex]\begin{gathered} f\lbrack h(7)\rbrack=2(7^2)+1 \\ =2(49)+1 \\ =98+1 \\ =99 \end{gathered}[/tex]Which is what we are looking for.
A student council president wants to learn about the preferred theme for the upcoming spring dance. Select all the samples that are representative of the population.
The idea of being representative of the population is actually reflecting the characteristics (features) we want to study of the whole population.
In this case, the samples that better represent the whole population are B and D. Why? Because they give us the possibility of taking a student of every grade. The other options, excluding the "bus option" and the first option, fail doing that. Finally, these options (bus option and lunch option) are related to the council president.
The graph shows the distance a car traveled, y, in x hours: What is the rise-over-run value for the relationship represented in the graph?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
point 1 (2 , 60) x1 = 2 y1 = 60
point 2 (4 , 120) x2 = 4 y2 = 120
Step 02:
slope formula
[tex]m\text{ = }\frac{y2-y1}{x2-x1}[/tex][tex]m\text{ = }\frac{120-60}{4-2}=\text{ }\frac{60}{2}=30[/tex]The answer is:
30
I got the picture and will send it to you show the coordinates of the points that create the shape of the image
We have the following:
[tex]\begin{gathered} P(1-1,-3+3)\rightarrow P^{\prime}(0,0) \\ Q(3-1,-1+3)\rightarrow Q^{\prime}(2,2) \\ R(4-1,-3+3)\rightarrow R^{\prime}(3,0) \end{gathered}[/tex]now,
The answer is:
given A(2, 3), B(8, 7), C(6 1), which will make line AB perpendicular to line CD?D(9, 3)D(4, 4)D(3, 3)D(8, 4)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
A(2, 3), B(8, 7), C(6 1)
Step 02:
Line AB
Slope formula
m = (y2 - y1) / (x2 - x1)
A (2 , 3) x1 = 2 y1 = 3
B (8 , 7) x2 = 8 y2 = 7
[tex]m\text{ = }\frac{7-3}{8-2}=\frac{4}{6}=\frac{2}{3}[/tex]Step 03:
Slope of the perpendicular line, m’
m' = -1 / m
[tex]m\text{'}=\text{ }\frac{-1}{m\text{ }}=\text{ }\frac{-1\text{ }}{\frac{2}{3}}\text{ = -}\frac{3}{2}[/tex]Step 04:
Line CD
m' = (y2 - y1) / (x2 - x1)
C (6 , 1) x1 = 6 y1 = 1
D ( x2, y2) x2 = x2 y2 = y2
[tex]-\frac{3}{2}=\text{ }\frac{y2-1}{x2-6}[/tex][tex]\frac{3}{2}=\frac{1-y2}{6-x2}[/tex]We must test the numerical values to verify equality,
x2 = 9
y2 = 3
[tex]\frac{3}{2}=\frac{1-9}{6-3}\text{ = }\frac{-8}{3}\text{ }[/tex]x2 = 4
y2 = 4
[tex]undefined[/tex]How far is the girl from the monument that is 30 ft high? Round your answer to a nearest foot. Show your work.
Given:
The diagram is shown alongside.
The height of the monument is 30 ft high.
The angle of elevation is 63 degrees
The objective is to find the distance between the monument and where the girl is standing.
Since it forms a right angled triangle so we can apply trigonometric ratios:
Now,
[tex]\tan 63^{\circ}=\frac{perpendicular}{\text{base}}[/tex]Perpendicular = 30 ft
Base = ?
Substituting the values,
[tex]\begin{gathered} \tan 63^{\circ}=\frac{30}{\text{base}} \\ \text{Base}=\frac{30}{\tan63^{\circ}} \\ \text{base}=\frac{30}{1.962610} \\ \text{base}=15.285767422\text{ ft} \end{gathered}[/tex]Therefore, the girl is at a distance of 15 ft from the monument.
Solve the Equation , I tried multiplying that 6 to the numbers in the parentheses but i couldnt get it
To start we will do what you said, multiply the 6, so:
6*(n-4)=3n
6n-6*4=3n
6n-24=3n
6n=3n+24
6n-3n=24
3n=24
n=24/3
n=8
So the answer is: 8
. Calculate: (81)3/2
Calculate:
[tex]81^{\frac{3}{2}}[/tex]The fractional exponent can be written as:
[tex]\sqrt[2]{81^3}=(\sqrt[]{81})^3[/tex]The square root of 81 is 9, thus:
[tex](\sqrt[]{81})^3=9^3=729[/tex]3 166.40 266.24 3. Consider the following functions which all have an or decay? By what percent? Rewrite as (1+r) or (1-r) f(t) = 30(1.04) p(x) = 30(0.65)Solve f(t)
ANSWER
Function f(t) represents a growth by 4%
EXPLANATION
If the function represents a decay it is written as:
[tex]f(t)=a(1-r)^t[/tex]and if it represents a growth it's:
[tex]f(t)=a(1+r)^t[/tex]We can see if it's a growth or decay by looking at the number we have between parenthesis: if it's greater than 1, then it's a growth and if it's less than 1 then it's a decay.
For function f(t) we have
[tex]1+r=1.04[/tex]Therefore, r = 0.04 which, expressed as a percent is 4%
Express 2x-3y=-6 into y=mx+b
For this problem, we are given a certain expression and we need to write it in the "y=mx+b" form.
We need to isolate the "y" variable on the left side to solve this problem. We have:
[tex]\begin{gathered} 2x-3y=-6\\ \\ 2x-3y-2x=-6-2x\\ \\ \frac{-3y}{-3}=\frac{-6}{-3}-\frac{2x}{-3}\\ \\ y=2+\frac{2}{3}x\\ \\ y=\frac{2}{3}x+2 \\ \\ \end{gathered}[/tex]The expression is y = (2/3)x+2.
Lines AD and BC are parallel. What is the angle measurement of Angle DAE(Point A)?D150°45°BсFYour answer
Solution
For this case we can find the angle:
m < ECB = 30º
And we can find the angle CEB and we got:
m < CEB = 180 -30 - 45 = 105
And then the angle DAE would be:
m < DAE = 30º
What is the the measure and length of arc MC
As given by the question
There are given that the measuring circle.
Now,
From the given circle, the length of the MN is 28 units, because the half of the length of the MN is 14. So just multiply by 2 into half of the given value.
Hence, the length of MN is 28 units.
Now,
For the measure of MN:
The measurement of the angle MN is 74 degrees.
Hence, a measure of arc MN is 74 degrees. and the length of segment MN is 28 units.
How do I tell if a parabola has a minimum or a maximum?
We can write the equation of a parabola in two different ways:
The standard form:
[tex]\begin{gathered} y=ax^2+bx+c \\ a\ne0 \end{gathered}[/tex]And the vertex form:
[tex]y=a(x-h)^2+k[/tex]If the parabola has a minimum or a maximum depends on the leading coefficient (the coefficient of x²) or in both cases the coefficient a.
Let's see the cases:
[tex]a>0_{\text{ }}(a_{\text{ }}is_{\text{ }}positive)[/tex]If a is positive, the parabola opens upwards, so the parabola has a minimum.
[tex]a<0_{\text{ }}(a_{\text{ }}is_{\text{ }}negative)[/tex]If a is negative, the parabola opens downwards, so the parabola has a maximum
Using the area formula A=LW (where A is the area L is the length and W is the width ) which of the following formulas would you use to solve for width ?
Answer:
W = A/L
Step-by-step explanation:
We are given the following formula:
A = LW
We want to solve for the width W. So
LW = A
L multiplies W, so it can go to the other side of the equality dividing. Then:
W = A/L
using the given quadratic function f(x)=x^2+2x-15, find the following information"Coordinates of x- intercept(zero) as ordered pairs"
the given expression is
f(x) = x^2 + 2x - 15
we will find x intercept by putting f(x) = 0
x^2 + 2x - 15 = 0
x^2 + 5x - 3x - 15 = 0
x(x +5) -3(x + 5) = 0
(x +5) (x -3) = 0
x = -5 & x = 3
so the ordered pairs are
(-5, 0) and (3, 0)
Cleo can paint a room in 8 hours, while Phil can paint the same room in 6 hours. If they paint theroom together, how long will it take them to paint the room?How many hours and how many minutes?
According to the given data we have the following:
Cleo can paint a room in 8 hours, so this is=1/8x
Phil can paint the same room in 6 hours=1/6x
In order to calculate how long it take them to paint the room we would solve the following equation:
(1/6)(x)+(1/8)(x)=1
To solve this equation we would first multiply both sides by 24
Hence:
24*(1/6)(x)+24*(1/8)(x)=24
4x+3x=24
7x=24
x=24/7
x= 3 3/7 hours
Therefore It will take them 3 and 3/7 hours to pain the room.
In minutes it will take to them 205 minutes.
11) a- 15 > 40-6 +3a) 12) 366b-1) > 18 - 3b a-151-46-67+1-useBay 9-15 124-12a atiza324+15 13a339 ay/9 13) 26 + m 2 5(-6 +3m) 14) 20-2p>-2lp
Answer
11) a > 3
12) b > (2/3)
Explanation
11) a - 15 > -4 (-6 + 3a)
a - 15 > 24 - 12a
a + 12a > 24 + 15
13a > 39
Divide both sides by 13
(13a/13) > (39/13)
a > 3
In graphing inequality equations, the first thing to note is that whenever the equation to be graphed has (< or >), the circle at the beginning of the arrow is usually unshaded.
But whenever the inequality has either (≤ or ≥), the circle at the beginning of the arrow will be shaded.
Then, the direction of the graph depends on the direction of the inequality sign, for example, the answer here says a is greater than 3. So, the graph will start with an unshaded circle and cover the numbers greater than 3.
12) 3 (6b - 2) > (8 - 3b)
18b - 6 > 8 - 3b
18b + 3b > 8 + 6
21b > 14
Divide both sides by 21
(21b/21) > (14/21)
b > (2/3)
This answer is similar to that of number 11. For the graph, it will start with an unshaded circle and move towards the numbers greater than (2/3)
Hope this Helps!!!
Becky borrowed $580.00 from the bank. The loan had a 13.5% simple
annual interest rate, and she paid off the bill over 18 months. What was
the total amount, including interest, Becky paid for the loan?
Work Shown:
P = 580
r = 0.135
t = 18 months = 18/12 = 1.5 years
A = P*(1+r*t)
A = 580*(1+0.135*1.5)
A = 697.45
The oil tank in your car is leaking at a rate of 1.2 oz per mile driven you drove 15 miles how many cups of oil did your car leak
we know that
The unit rate is equal to
1.2 oz per mile
so
To obtain the number of ounces
multiply the unit rate by the number of miles driven
1.2*(15)=18 oz
step 2
Convert ounces to cups
Remember that
1 oz=0.125 cups
so
18 oz=18*0.125=2.25 cups
therefo
