Answer:
rational: -3.786, 8/17, 8.23, 10.86731234, 0.75, √.49 = 0.7
irrational: 3π, √11
Step-by-step explanation:
Any number that can only be represented completely using symbols, such as π or √, is an irrational number.
If the number can be expressed as the ratio of two integers, it is a rational number. Such numbers include proper and improper fractions, integers, any number you can write with a finite number of digits, and any repeating decimal, regardless of the length of the repeat.
In the triangle below, the sec X is x/z
Answer:
false
Step-by-step explanation:
It's false. Entirely. No hesitation.
The sec(X) = 1 / Cos(X)
Cos(x) = y / z
1/cos(x) = 1//y/z
1/cos(X) = 1/1 * z/y
1/cos(X) = z/y
sec(X) = z/y
Yea it's false
I know I'm late but I hope it helped a little haha
A biology class conducts a bird count every week during the semester. Using the number of species counted each week, a student finds a 95% confidence interval of (16.34,18.69) for the mean number of species counted. Knowing that species have to be whole numbers, the student reports that 95% of the bird counts saw 16, 17, or 18 species. Comment on the student's report.
Answer:
A student finds a 95% confidence interval of (16.34,18.69) for the mean number of species counted. This is a valid interval because the mean number of species or any population mean does not necessarily have to be a whole number, as stated by the student.
This given confidence interval of (16.34,18.69) helps us to simply estimate the mean species counted.
Type the correct answer in the box. Use numerals instead of words. For this problem, a non-integer answer should be entered as a fraction in simplest form using / as the fraction bar. Malik randomly picked two numbers from 1 to 9 (including 1 and 9). The same number could be picked more than once. The first of the two numbers he picks is odd and less than 5. What is the probability that the sum of the two numbers Malik picks is less than 5, given that the first number is odd and less than 5?
Answer:
P (sum of two numbers is < 5) =2/9
Step-by-step explanation:
There are two numbers that can be picked such that the first number odd and less than 5: 1 and 3.
Then, the numbers that can be drawn with these numbers should be from: 1, 2, 3, 4, 5, 6, 7, 8 or 9.
The number of total possibilities = 18
Out of these, the following are the four possible options to have a sum which is less than 5 and 1:
1 and 1
1 and 2
1 and 3
3 and 1
So P (sum of two numbers is < 5) = [tex]\frac{4}{18}[/tex] = 2/9
Answer:
Step-by-step explanation:
2/9 is right because i just took it and got a 5/5
9. Nick has desigied a diamond-shaped kite as shown below. The measures of so me sides of the kite, are marked in the
figure. Find the value of x (JUSTIFY)
Answer:
[tex]x=\frac{10\sqrt{6}}{7}\ in[/tex]
Step-by-step explanation:
step 1
In the right triangle DOC
Find the measure of side DO
Applying the Pythagoras Theorem
[tex]DC^{2}=DO^{2}+OC^{2}[/tex]
substitute the given values
[tex]7^{2}=DO^{2}+5^{2}[/tex]
[tex]DO^{2}=7^{2}-5^{2}[/tex]
[tex]DO^{2}=49-25[/tex]
[tex]DO^{2}=24[/tex]
[tex]DO=2\sqrt{6}\ in[/tex]
step 2
In the right triangle DOC
Find the sine of angle ∠ODC
sin(∠ODC)=OC/DC
substitute
[tex]sin(ODC)=5/7[/tex] -----> equation A
step 3
In the right triangle DOP
Find the sine of angle ∠ODP
sin(∠ODP)=OP/DO
substitute
[tex]sin(ODP)=x/2\sqrt{6}[/tex] -----> equation B
step 4
Find the value of x
In this problem
∠ODC=∠ODP
so
equate equation A and equation B
[tex]5/7=x/2\sqrt{6}[/tex]
[tex]x=\frac{10\sqrt{6}}{7}\ in[/tex]
Select the correct answer.
What is the product of
Answer:
29
Step-by-step explanation:
I'm going to write both of this as improper fractions.
That is the mixed fraction [tex]a\frac{b}{c}[/tex] can be written as the improper equivalent fraction of [tex]\frac{ca+b}{c}[/tex] assuming [tex]a[/tex] is positive.
So we are going to write [tex]-3\frac{1}{3}[/tex] as [tex]-\frac{3(3)+1}{3}[/tex].
Simplifying that gives us [tex]-\frac{10}{3}[/tex].
Now for [tex]-8\frac{7}{10}=-\frac{10(8)+7}{10}=-\fraC{87}{10}[/tex].
Now we are ready to find the product which just means multiply:
[tex]\frac{-10}{3} \cdot \frac{-87}{10}[/tex]
To multiply fractions you just multiply straight across on top and straight across on bottom unless you see a common factor on and bottom to cancel (and I do; I see 10)
[tex]\frac{-1}{3} \cdot \frac{-87}{1}[/tex]
[tex]\frac{87}{3}[/tex]
Negative times negative is positive.
Anyways time to write 87/3 as a mixed fraction.
How many 3's are in 87? 29 with no remainder
Answer:
29
Step-by-step explanation:
its close... ish
Use an appropriate technology to simulate 2 cards being drawn from a 52-card deck of playing cards. Do not return the first card to the deck before drawing the second card. Perform 50 trials of this experiment.
Answer:
see below
Step-by-step explanation:
Attached is the output of a computer program that picked two different numbers at random from the set 1-52, then converted those numbers to a suit and value.
Such a program could be written in a spreadsheet or any of a variety of computer languages.
Maggie had a bag of peanuts that weighed 2.84 pounds. She took some of the peanuts out of the bag. The bag then weighed 1.24 pounds. What was the weight of the peanuts that Maggie took out of the bag?
Answer:
Step-by-step explanation:
1.6 pounds
Complete the synthetic division problem below.
Answer:
B
Step-by-step explanation:
This was originally a third degree polynomial:
[tex]2x^3+4x^2-4x+6[/tex], to be exact.
When you divide by -3, you are basically trying to determine if x + 3 is a zero of that third degree polynomial. The quotient is always one degree lesser than the polynomial you started with, and if there is no remainder, then x + 3 is a zero of the polynomial and you could go on to factor the second degree polynoial completely to get all 3 solutions. To perform the synthetic division, you always first bring down the number in the first position, in our case a 2. Then multiply that 2 by -3 to get -6.
-3| 2 4 -4 6
-6
2 -2
So far this is what we have done. Now we multiply the -3 by the -2 and put that up under the -4 and add:
-3| 2 4 -4 6
-6 6
2 -2 2
Now we multiply the -3 by the 2 to get -6 and put that up under the 6 and add:
-3| 2 4 -4 6
-6 6 -6
2 -2 2 0
That last row gives us the depressed polynomial, which as stated earlier here, is one degree less than what you started with:
[tex]2x^2-2x+2[/tex]
Answer: OPTION B
Step-by-step explanation:
You need to follow these steps:
- Carry the number 2 down and multiply it by the the number -3.
- Place the product obtained above the horizontal line, below the number 4 and add them.
- Put the sum below the horizontal line.
- Multiply this sum by the number -3.
- Place the product obtained above the horizontal line, below the number -4 and add them.
- Put the sum below the horizontal line.
- Multiply this sum by the number -3.
- Place the product obtained above the horizontal line, below the number 6 and add them.
Then:
[tex]-3\ |\ 2\ \ \ \ \ 4\ \ -4\ \ \ \ \ \ 6\\\.\ \ \ \ \ |\ \ \ \ -6\ \ \ \ \ 6\ \ \ -6[/tex]
[tex]-----------------[/tex]
[tex].\ \ \ \ \ \ 2\ \ \ -2\ \ \ \ 2\ \ \ \ \ 0[/tex]
Therefore, the quotient in polynomial form is:
[tex]2x^2-2x+2[/tex]
What are mutually exclusive events?
Events in which event#1 must happen before event #2
Events in which event#1 and event#2 must happen at the same time
Events in which event#1 must happen after event#2
Events in which neither event is dependent upon the other
Answer:
The correct answer would be option D, Events in which neither event is dependent upon the other.
Step-by-step explanation:
Mutually exclusive events are the events which cannot occur at the same time. If there are two events, then in mutually exclusive situation, both events can not happen at the same time. One event will happen at a time. Mutually exclusive events are also called disjoint. Both events are not dependent upon one another. The occurrence of one event would not change the occurrence of the other event. The most appropriate and suitable example of mutually exclusive events is the tossing of a coin. Either tails will come or heads. Both events can't happen at the same time, and also not both events are dependent upon each other.
Answer:
Events in which neither event is dependent upon the other
Step-by-step explanation:
Events that are independent and cannot happen at the same time.
Use the drawing tool(s) to form the correct answer on the provided number line.
Consider the functions below.
f(x)= |3x| + 3
g(x)= –x^2 + 8x – 5
Represent the interval where both functions are increasing on the number line provided. (Picture provided)
Answer:
see the attachment
Step-by-step explanation:
f(x) is increasing for x > 0.
g(x) is increasing for x < 4.
Both functions are increasing on the open interval (0, 4). It will be graphed with a solid line between 0 and 4, and with open circles at 0 and 4. See the black line on the x-axis of the attachment for an example of such a graph.
The school band is scheduled to march in the annual parade, but the band's starting point is changed the day before the parade. The band director calls three band members. Each band member calls three other band members. Then these band members each call three members. How many band members, including the band director, are notified of the new starting point?
Question 8 options:
20 members
12 members
13 members
40 members
Answer:
There are 40 band members including the band director that were notified of the new starting point
Step-by-step explanation:
The diagram below shows the band director at the top, then the three band members he called, then the next band members, and so forth.
Answer: i got 19
Step-by-step explanation:
Find the terminal point on the unit circle determined by 3 pi/4 radians
Answer:
[tex](\frac{-\sqrt{2}}{2},\frac{\sqrt{2}}{2})[/tex]
Step-by-step explanation:
Unit circle has a radius of 1.
So x=cos(3pi/4)=-sqrt(2)/2 and y=sin(3pi/4)=sqrt(2)/2
So the ordered pair is (-sqrt(2)/2 , sqrt(2)/2)
The terminal point for the unit circle that is determine by the [tex]$\frac{3 \pi}{4} $[/tex] radians is
[tex]$\left( -\frac{1}{\sqrt 2}, \frac{1}{\sqrt 2} \right) . $[/tex]
We know the coordinates of the terminal point will be :
[tex]$x= \cos \left( \frac{3 \pi}{4} \right)$[/tex] and [tex]$y= \sin \left( \frac{3 \pi}{4} \right)$[/tex]
Therefore,
[tex]$x= \cos \left( \pi - \frac{ \pi}{4} \right)$[/tex]
[tex]$x= - \cos \frac{\pi}{4}$[/tex]
[tex]$=-\frac{1}{\sqrt 2}$[/tex]
And
[tex]$y= \sin \left( \frac{3 \pi}{4} \right)$[/tex]
[tex]$y = \sin \left( \frac{\pi}{2} + \frac{\pi}{4} \right)$[/tex]
[tex]$=\cos \frac{\pi}{4}$[/tex]
[tex]$=\frac{1}{\sqrt 2}$[/tex]
Therefore the terminal points are : (x, y) = [tex]$\left( -\frac{1}{\sqrt 2}, \frac{1}{\sqrt 2} \right) . $[/tex]
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Write an equation of the line below.
Answer:
[tex]\large\boxed{y=4x+3}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of aline:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfraxc{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have the points:
(-2, -5)
y-intercept (0, 3) → b = 3
Calculate the slope:
[tex]m=\dfrac{3-(-5)}{0-(-2)}=\dfrac{8}{2}=4[/tex]
Put the value of the slope and the y-intercept to the equation of a line:
[tex]y=4x+3[/tex]
The equation of the line through (-2, -5) and (0, 3) is y = 4x + 3, obtained using the point-slope form with the calculated slope and one of the given points.
To find the equation of the line passing through the given coordinates (-2, -5) and (0, 3), we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) are the coordinates of a point on the line, and m is the slope.
First, calculate the slope (m) using the given coordinates:
m = (y2 - y1) / (x2 - x1)
m = (3 - (-5)) / (0 - (-2)) = 8 / 2 = 4
Now, choose one of the points, let's use (-2, -5), and substitute the values into the point-slope form:
y - (-5) = 4(x - (-2))
y + 5 = 4(x + 2)
Simplify the equation:
y + 5 = 4x + 8
Isolate y:
y = 4x + 3
Therefore, the equation of the line passing through the points (-2, -5) and (0, 3) is y = 4x + 3.
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What is the next term in the sequence? 7, 18, 29, 40, . . .
Answer:
first Let's find the common difference
an=a1+(n-1)d
let's take A2 that is 18
so 18=7+(2-1)d
18=7+d
d=11
so the next term is going to be 40+11 that is 51
WILL GIVE 20 points PLEASE ANSWER ITS URGENT
Brainliest answer guaranteed
URGENT
Answer:
[tex]y=-6.6[/tex] and [tex]y=10.6[/tex]
Step-by-step explanation:
The given ellipse has equation:
[tex]\frac{(y-2)^2}{64}+\frac{x^2}{9}=1[/tex].
The center of this ellipse is (h,k)=(0,2)
We use the equation: [tex]a^2-b^2=c^2[/tex] to determine the foci.
[tex]\implies 64-9=c^2[/tex]
[tex]\implies 55=c^2[/tex]
[tex]\implies c=\pm \sqrt{55}[/tex]
The directrices are given by [tex]y=k\pm\frac{a^2}{c}[/tex]
[tex]y=2\pm\frac{64}{\sqrt{55}}[/tex]
[tex]y=2\pm8.6[/tex]
[tex]y=2-8.6[/tex] and [tex]y=2+8.6[/tex]
The equation of the directrices are:
[tex]y=-6.6[/tex] and [tex]y=10.6[/tex]
The correct answer is D
Tyrese's sister is 41 inches tall. A ride at the amusement park states that riders must be at least 52 inches tall to ride. Which statements describe how much taller Tyrese's sister must be to ride? Check all that apply. At least 11 inches no more than 11 inches a maximum of 11 inches a minimum of 11 inches fewer than 11 inches at most 11 inches
Answer:
See below.
Step-by-step explanation:
52 inches - 41 inches = 11 inches
She needs to be at least 11 inches taller to be at least 52 inches tall.
Statements that describe how much taller she must be:
(The correct answers are in bold and checked with the square root symbol, √.)
at least 11 inches √
no more than 11 inches
a maximum of 11 inches
a minimum of 11 inches √
fewer than 11 inches
at most 11 inches
Answer:
Step-by-step explanation:
at least 11 inches
a minimum of 11 inches
Find the equation in slope-intercept form that describes a line through (4, 2) with slope 1/2
Answer:
y = 1/2 x
Step-by-step explanation:
We have the slope of 1/2 and a point of (4,2)
We can use point slope form
y-y1 = m(x-x1)
y-2 = 1/2(x-4)
Distribute
y-2 = 1/2x -2
Add 2 to each side
y-2+2 = 1/2 x -2+2
y = 1/2 x
This is in slope intercept form
When a warehouse opened, it had an inventory of 6,000 items. Every month, the inventory increases by 3,000 items.
Which graph has the most appropriate scales and units for this situation?
Answer:
The first two graphs are the exact same but it is the first two.
Step-by-step explanation:
Answer:
In the beginning ,number of inventory in the warehouse =6,000
Increment in each month in inventory in the warehouse=3000
So, writing the above situation in terms of linear equation
if,y is the number of inventory after x months
y=6000 +3000x
Correct graph is attached below
⇒Items in Inventory(Thousands) ----X axis
⇒Number of Months since Opening----Y axis
What is the area of the sector bound by the center of the circle and arc CD in the circle below?
Circle A is shown with a radius labeled 8 feet and a central angle marked 35 degrees.
a
9.42 ft2
b
19.54 ft2
c
34.89 ft2
d
88.31 ft2
Answer:
b. 19.54 ft²
Step-by-step explanation:
Measure of the central angle made by the arc CD = 35 degrees
Measure of radius of circle = r = 8 feet
Area of the sector is calculated as:
[tex]A=\frac{1}{2}r^{2} \theta[/tex]
Where the angle [tex]\theta[/tex] is in radians.
35 degrees in radian would be = [tex]35 \times \frac{\pi}{180} = \frac{7 \pi}{36}[/tex]
Using the values in the formula, we get:
[tex]Area = \frac{1}{2} \times (8)^{2} \times (\frac{7 \pi}{36} )\\\\ Area = 19.54[/tex]
Thus, the area of the sector bounded by arc CD would be 19.54 ft²
S=4T-7 T= what is the answer please
Answer:
(S+7)/4 = T
Step-by-step explanation:
S=4T-7
We want to solve to T
Add 7 to each side
S+7=4T-7+7
S+7 = 4T
Divide each side by 4
(S+7)/4 = 4T/4
(S+7)/4 = T
Which linear inequality is represented by the graph?
y > 2/3x – 2
y < 2/3x + 2
y > 2/3x + 1
y < 2/3x – 1
Answer:
y < 2/3 x - 1 is the linear inequality which represented by the graph ⇒ 4th answer
Step-by-step explanation:
* Lets explain how to solve the problem
- At first lets find the equation of the line
∵ The line passes through points (3 , 1) and (-3 , -3)
∵ The form of the equation is y = mx + c, where m is the slope of the
line and c is the y-intercept
- The rule of the slope of any line passes through points (x1 , y1) and
(x2 , y2) is m = (y2 - y1)/(x2 - x1)
- The y-intercept means the intersection between the line and the
y-axis at point (0 , c)
∵ (3 , 1) and (-3 , -3) are two points on the line
- Let (x1 , y1) is (3 , 1) and (x2 , y2) is (-3 , -3)
∴ The slope of the line m = (-3 - 1)/(-3 - 3) = -4/-6 = 2/3
∵ The line intersects the y-axis at point (0 , -1)
∴ c = -1
∵ The equation of the line is y = mx + c
∴ The equation of the line is y = 2/3 x + -1
∴ The equation of the line is y = 2/3 x - 1
- If the shaded part is over the line then the sign of inequality is ≥ or >
- If the shaded part is under the line then the sign of inequality is ≤ or <
- If the line represented by solid line (not dashed), then the sign of
inequality is ≥ or ≤
- If the line represented by dashed line (not solid), then the sign of
inequality is > or <
∵ The shading part is under the line
∵ The line is dashed
∴ The sign of the inequality is <
∴ y < 2/3 x - 1
* y < 2/3 x - 1 is the linear inequality which represented by the graph
The linear inequality represented by the graph is y < (2/3) * x - 1
To solve the problem, we can follow these steps:
Find the equation of the line that passes through the points (3, 1) and (-3, -3). The equation of a line is in the form y = mx + c, where "m" is the slope and "c" is the y-intercept.
Use the slope formula to calculate the slope (m) of the line. The slope formula is given by m = (y2 - y1) / (x2 - x1), where (x1, y1) is (3, 1) and (x2, y2) is (-3, -3).
Calculate the slope (m):
m = (-3 - 1) / (-3 - 3) = -4 / -6 = 2/3
Determine the y-intercept (c), which is the point where the line intersects the y-axis. In this case, it's at point (0, c).
Since the line passes through (3, 1), we can use this point to find the y-intercept:
1 = (2/3) * 3 + c
1 = 2 + c
c = -1
Now that we have the slope (m) and the y-intercept (c), we can write the equation of the line:
y = (2/3) * x - 1
Determine the direction of the shading in the inequality. If the shaded region is under the line, the sign of the inequality is "<."
Determine the style of the line on the graph. If the line is dashed, the sign of the inequality is also "<."
Combine the information to form the linear inequality:
y < (2/3) * x - 1
So, the linear inequality represented by the graph is:
y < (2/3) * x - 1
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Simplify the product using FOIL (2x-7)(5x+5)
Answer:
10x^2-25x-35
Step-by-step explanation:
FOIL means first, outer, inner, and last.
The first term of each pair is 2x and 5x.
The outer term of each pair is 2x and 5.
The inner term of each pairs are -7 and 5x.
The last term of each is -7 and 5.
Now we just have to multiply the terms I pairs above:
First: (2x)(5x)=10x^2
Outer: (2x)(5)=10x
Inner: (-7)(5x)=-35x
Last: (-7)(5)=-35
------------------------------Add the terms:
10x^2-25x-35
Which expression represents the number
Answer:
8 + i
Step-by-step explanation:
What you need to simplify this is the following "definitions" of i to different powers.
[tex]i^1=i[/tex]
[tex]i^2=-1[/tex]
[tex]i^3=i^2*i=-1*i=-i[/tex]
[tex]i^4=1[/tex]
Now we can sub these in for the various powers of i in our expression:
[tex]6(1)+6(-i)-2(-1)+\sqrt{-1*49}[/tex]
Simplifying a bit:
[tex]6-6i+2+\sqrt{i^2*49}[/tex]
Since we know that the square root of i-squared is i, and that the square root of 49 is 7, we can get rid of the radial sign as follows:
6 - 6i + 2 + 7i
And the final answer, in a + bi form, is
8 + i
which of the following circles lie completely in the fourth quadrant
Answer:
C.(x-5)²+(x+5)=9
D (x-9)²+(y+9)²=16
Step-by-step explanation:
Use a graph tool to visualize the circle.See attached
You can also see that in the options
C. circle has center (5,-5) and radius 3 which will form in 4th quadrant
D. Circle has center (9,-9) and radius 4 which will still form in 4th quadrant
My clock chimes two times 15 minutes after the hour, four times 30 minutes after the hour and six times 45 minutes after the hour. The clock also chimes eight times on each hour in addition to chiming the number of times equal to the hour. (So at 2:00 p.m., the clock chimes $8 + 2 = 10$ times.) Starting at 12:05 a.m., how many times does the clock chime in a 24-hour period?
Answer:
612 times does the clock chime
Step-by-step explanation:
Given data
two times 15 minutes after the hour
four times 30 minutes after the hour
six times 45 minutes after the hour
clock chimes 8 + 2 = 10 times
to find out
how many times does the clock chime in a 24-hour period
solution
we can say clock chimes from 12:05 - 1:05 is for this 1 hour
2 +4+6+8 = 20 + 1
and clock chimes from 1:05 - 2:05 is for this 1 hour is 20 +2
and we know for 24 hours clock chimes is 20 × 24 i.e
= 480 + 2 × ( 1 +2 + ... +11 ) .....................1
we know
2 × ( 1 +2 + ... +11 ) will be = 2 × (n) × (n+1) / 2
here n is 11 so
= 2 × (n) × (n+1) / 2
= 2 × (11) × (11+1) / 2
= 132
so now put this in equation 1
we get
clock chime in a 24-hour period = 480 + 132
clock chime in a 24-hour period = 612
so 612 times does the clock chime in a 24-hour period
Answer:
636
Step-by-step explanation:
Look at the picture for explanation:)
What are the zeroes of f(x) = x2 - x-2?
Ox=-2, 1
Ox=2, -1
Ox=-2, -1
O x = 2,1
Answer:
Simplifying
0x =-2, 1
0 * x =-2.1
Apply rule () *a = 0
0=-2.1
Step-by-step explanation:
Therefore, the zeroes of the function [tex]\( f(x) = x^2 - x - 2 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = -1 \).[/tex]
To find the zeroes of the quadratic function [tex]\( f(x) = x^2 - x - 2 \),[/tex] we need to solve for [tex]\( x \)[/tex] when [tex]\( f(x) = 0 \)[/tex]. This means we need to find the values of [tex]\( x \)[/tex]that make the function equal to zero.
We can solve this quadratic equation by factoring or using the quadratic formula. Let's use the quadratic formula:
For a quadratic equation in the form [tex]\( ax^2 + bx + c = 0 \)[/tex], the solutions [tex]\( x \)[/tex] are given by:
[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]
For our equation [tex]\( f(x) = x^2 - x - 2 \)[/tex], we have [tex]\( a = 1 \), \( b = -1 \)[/tex], and [tex]\( c = -2 \)[/tex]. Substituting these values into the quadratic formula:
[tex]\[ x = \frac{{-(-1) \pm \sqrt{{(-1)^2 - 4(1)(-2)}}}}{{2(1)}} \][/tex]
[tex]\[ x = \frac{{1 \pm \sqrt{{1 + 8}}}}{2} \][/tex]
[tex]\[ x = \frac{{1 \pm \sqrt{9}}}{2} \][/tex]
[tex]\[ x = \frac{{1 \pm 3}}{2} \][/tex]
So, the solutions are:
[tex]\[ x_1 = \frac{{1 + 3}}{2} = 2 \][/tex]
[tex]\[ x_2 = \frac{{1 - 3}}{2} = -1 \][/tex]
Q14: Rent for a 3-bedroom apartment is regularly $936 per month. Apartment management is now offering one month free for a 12-month lease. If you sign a one year lease and apply the free month equally across months, how much is your monthly lease amount?
Answer:
$858
Step-by-step explanation:
You pay for 11 of the 12 months, so the average monthly payment is ...
(11/12)×$936 = $858
Jan and Wayne went to the store to buy some groceries. Jan bought 2 cans of corn beef hash and 3 cans of creamed chipped beef for $4.95. Wayne bought 3 cans of corn beef hash and 2 cans of creamed chipped beef for $5.45.
Which assignment of variables can be used in finding the cost of each item in the word problem on the left?
a. J = the number of cans Jan bought
W = the number of cans Wayne bought
b. H = the unit price of corn beef hash
C = the unit price of creamed chipped beef
c. J = the total cost of Jan’s bill
W = the total cost of Wayne’s bill
Answer:
B
Step-by-step explanation:
If the angle that the sun makes with the side of a building is 75°, and the distance from the top of the building to the tip of its shadow is 25 feet, what is the length of its shadow? 144.89 feet 12.84 feet 48.3 feet 24.15 feet
Answer:
24.15 feet
Step-by-step explanation:
The shadow is opposite the specified angle, and the distance from its tip to the building edge is the hypotenuse of the relevant right triangle. Then the applicable relation is ...
Sin = Opposite/Hypotenuse
(25 ft)sin(75°) = Opposite = shadow length
24.15 ft = shadow length