Answer:
The solution set is therefore {-10, 2}
Step-by-step explanation:
The absolute value equation |3x + 12| = 18 has two distinct solutions.
|3x + 12| = 18 may be rewritten as
3x + 12 = 18 and
-(3x + 12) = 18
The first equation immediately above becomes 3x = 6 after we subtract 12 from both sides. Therefore, x = 6/3, or x = 2.
Simplifying the second equation yields -3x - 12 = 18. To solve this for x, we add 12 to both sides, obtaining -3x = 30.
Dividing both sides by -3 yields x = -10.
The solution set is therefore {-10, 2}
Find the reference angle of the following angles:405°, 750°, ‒ 210°, 495° ‒660°, 480°
Answer:
Step-by-step explanation:
405÷180=2×180+45,45°
750=180×4+30,30°
-210+180=-30,30°
495÷180=2×180+135,180-135=45°
-660°+360=-300°+360=60,60°
480-360=120,180-120=60,60°
what is the domain of the function shown in the graph below?
answer type: Interval, all real numbers, all values except one, all values except two
interval:
Answer:
all values except one (-2)
Step-by-step explanation:
The function heads off toward infinity at x=-2, so it is not defined there. The function is defined for all values except one.
Given that F( x ) = x 2 + 2, evaluate F(1) + F(5).
Hi there! :)
Answer:
[tex]\huge\boxed{f(1) + f(5) = 30}[/tex]
Given:
[tex]f(x) = x^{2} + 2[/tex]
Evaluate [tex]f(1) + f(5)[/tex]
Solve for each:
[tex]f(1) = (1)^{2} + 2 = 3[/tex]
[tex]f(5) = (5)^{2} + 2 = 27[/tex]
[tex]27 + 3 = 30[/tex]
Answer:
30
Step-by-step explanation:
In a certain freshman class, the number of girls is 83 less than twice the number of boys(b). The total number of students in that freshman class is 259. How many boys and girls are in that class.
Answer:
Boys = 114
Girls = 145
Step-by-step explanation:
Boys = b
Girls = 2b-83
b+2b-83=259
3b=259+83
3b=342
b=114
Boys = b = 114
Girls = 2b-83=228-83=145
The number of boys is 114 and the number of girls is 145
The given expression in algebraic form is written as:
let the number of boys = b
then, the number of girls, g = 2b - 83
given total number of students, t = 259
To find:
the number of boys and girls in the class.Set the following equations to find the number of boys and girls:
number of boys + number of girls = total number of students
[tex]b + g = 259\\\\b + 2b -83 = 259\\\\3b = 259+83\\\\3b = 342\\\\b = \frac{342}{3} \\\\b = 114\\\\The \ number \ of \ girls = 2(114) - 83 = 145[/tex]
Thus, the number of boys is 114 and the number of girls is 145
Learn more here: https://brainly.com/question/17765207
What is the result of subtracting the second equation from the first?
Answer: 11x - 8y = -9
Step-by-step explanation:
Subtract it by terms.
8x - (-3x) = 11x
-4y - (4y) = -8y
-4-5= -9
order it
11x - 8y =-9
Use a number line to approximate the value of :
Answer:
9 < [tex]\sqrt{88}[/tex] < 10
Step-by-step explanation:
[tex]\sqrt{88}[/tex] = 9.38083152
Answer:
Third option
Step-by-step explanation:
Notice that √88 is close to √81 wich is 9.
● √88 is greater than √81 so it is greater than 9.
● √88 is less than √100 wich is 10
● so √88 is between 9 and 10
help me plz can somewon help me
Answer:
4*10^6
Step-by-step explanation:
Answer:
4 × 10^6Step-by-step explanation:
[tex]\frac{8\times 10^2^4}{2\times 10^1^8}=\\\\\mathrm{Divide\:the\:numbers:}\:\frac{8}{2}=4\\\\=\frac{10^{24}\times \:4}{10^{18}}\\\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\\\\frac{10^{24}}{10^{18}}=10^{24-18}\\\\=4\times \:10^{24-18}\\\\\mathrm{Subtract\:the\:numbers:}\:24-18=6\\\\=10^6\times \:4\\\\10^6=1000000\\\\=1000000\times \:4\\\\=4000000\\\\= 4\times10^6[/tex]
find the mean, median, mode, and midrange. Then decide which you think is the most meaningful measure of average for that data set. For larger data sets, you should consider using technology. The number of beds at all licensed hospital in Hillsborough County, Florida, in 2015: 98 120 493 206 73 102 183 870 76 60 60 112 147 1,018 201
Answer:
mean = 254.6
median = 120
mode = 60
midrange = 958
For average data sets i prefer by finding the mean
Step-by-step explanation:
mean :
(98+120+493+206+73+102+183+870+76+60+60+112+147+1018+201) ÷ 15 = 254.6
median : 60 60 73 76 98 102 112 120 147 183 201 206 493 870 1018
find the middle number
= 120
mode :
number that is more than one
= 60
midrange :
highest number - smallest number
= 1018 - 60
= 958
What will come in the circle
I will even rate who ever answer
And give brainliest
Answer:
1st circle: 1.25
Second circle: 2
Step-by-step explanation:
We can use the cross product property here to find the value of what's in the circles.
Let's first look at the first two fractions.
[tex]\frac{x}{5} = \frac{1}{4}[/tex]
We can multiply the cross values and divide by the number that is diagonal to the variable.
[tex]5\cdot1 = 5\\5\div4 = 1.25[/tex]
So 1.25 goes in the first circle.
Now let's look at the last two circles and use the same property to find the missing value.
[tex]\frac{1}{4} = \frac{0.5}{x}\\ 4\cdot0.5 = 2\\2\div1 = 2[/tex]
So 2 goes in the second circle.
Hope this helped!
Answer:
x = 5/4
Step-by-step explanation:
Use the variable 'x' instead of 'the circle.' Then:
x 1
----- = ------
5 4
Cross-multiplying, we get
4x = 5, and so x = 5/4
4. Multiple-Choice
1. Two complementary angles measure (12r - 18)° and (5x + 23)°. What
is the measure of the smaller angle?
(1) 5°
(2) 42°
(3) 48°
(4) 90°
I already know that the answer is 42 but I don’t know how to get that! Please help.
Sry i couldn't find the answer
Answer:
(2) 42°
Step-by-step explanation:
Copy of the given problem:
4. Multiple-Choice
1. Two complementary angles measure (12r - 18)° and (5x + 23)°. What
is the measure of the smaller angle?
(1) 5°
(2) 42°
(3) 48°
(4) 90°
Solution:
The sum of the measures of complementary angles is 90 deg.
12r - 18 + 5x + 23 = 90
We have 1 equation with two different variables, so we cannot solve the equation to find unique values of the variables.
I assume the above is an error, and both variables should be the same.
12r - 18 + 5r + 23 = 90
Combine like terms on the left side. Terms with r are combined. Terms with no variable are combined.
12r + 5r - 18 + 23 = 90
17r + 5 = 90
Subtract 5 from both sides.
17r = 85
Divide both sides by 5.
r = 5
The measures of the angles are:
12r - 18 = 12(5) - 18 = 60 - 18 = 42
5r + 23 = 5(5) + 23 = 25 + 23 = 48
The measures of the two angles are 42° and 48°.
The smaller angle measures 42°
Answer: (2) 42°
I know how to do it but right now I'm cooking and have no time please say if the first part is right and the second part will be much appreciated!
Part A is correct. We have x+15 as the length and x+3 as the width. Convention usually has the width be the smaller of the two.
------------------
Part B will have you replace x with 8 and simplify
length = x+15 = 8+15 = 23
width = x+3 = 8+3 = 11
the rectangle is 23 yards by 11 yards, so the area is 23*11 = 253 square yards
Answer:
Below
Step-by-step explanation:
As we see the area is expressed as second degree polynomial
We have already a side wich is (x+15)
● x^2 +18x + 45 = w × (x+15)
● w = (x^2 +18x+45)/(x+15)
Using the eucledian division we get:
● w = x+3
Since x^2 +18x +45 = (x+15) × (x+3)
So your answer was right
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's calculate the dimensions if x= 8 yards
● the length
x+15 = 8+15 = 23 yards
● the width
x+3 = 8 + 3 = 11 yards
● the area
(x+15)×(x+3) = 23 × 11 = 253 yards^2
Perform the indicated operations. (2x+5y+z-6)+(6x-4y-z+7)+(-4x+y-3z-4)
Answer:
your anwser is 4 x + 2 y − 3 z − 3
Step-by-step explanation:
Simplify:4 x + 2 y − 3 z − 3
Answer:
4x + 2y - 3z -3.
Step-by-step explanation:
2x+5y+z-6)+(6x-4y-z+7)+(-4x+y-3z-4)
Removing the parentheses:
= 2x + 5y + z - 6 + 6x - 4y - z + 7 - 4x + y - 3z - 4
Bringing like terms together:
= 2x + 6x - 4x + 5y - 4y + y + z - z - 3z - 6 + 7 - 4
Simplifying like terms we have:
4x + 2y - 3z -3.
Abby and Katy are selling cheesecakes. There are apple and pecan cheesecakes. Abby sold 14 pecan and 3 apple cheesecakes for a total of $113. Katy sold 7 pecan and 8 apple cheesecakes for a total of $180. What's the cost of one pecan cheesecake and one apple cheesecake?
How would I set this up?
If you want to set up the equations:
let the cost of one apple cheesecake be [tex] a[/tex] and the cost of one pecan cheesecake be $p$
from Abby, $14p+3a=113$
and from Katy....?
then solve for both variables
can you take it from here?
What is the mode of the data represented in the dot plot shown in the image? A. 0 B. 1 C. 2 D. 3 Show all work!
Answer:
2
Step-by-step explanation:
The mode is the number that appear most often
The number with the most dots is 2
The mode is 2
The mode in any data set is the number that gets represented the most.
As you can see on the plot, the number that gets represented the most is 2.
Best of Luck!
HELP!!! SHOW WORK PLEASE.
[tex]\dfrac{x}{4}=\dfrac{x+9}{4+12}\\\\16x=4(x+9)\\16x=4x+36\\12x=36\\x=3[/tex]
can somebody help me with this math problem
Answer:
D). 137
Step-by-step explanation:
1). 40 % of 50 = 20
50 + 20 = 70
2). 40 % 70 = 28
70 + 28 = 98
3). 40 % of 98 = 39.2, basically 39
98 + 39 = 137
137 is the right answer
Pls make my answer brainiest))))
Jack is building a square garden. Each side length measures 777 meters. Jack multiplies 7\times77×77, times, 7 to find the amount of space in his garden is equal to 494949 square meters. Which measurement does 494949 square meters represent?
in the figure above, pqrs is a parallelogram. What is the value of x?
Answer:
x = 162 degrees.
Step-by-step explanation:
m < RSP = 180 - 72
= 106 degrees (adjacent angles)
m < Q = m < RSP ( Opposite angles in a parallelogram are equal).
So m < Q = 180 degrees.
m < x = 360 - 90 - 108
= 360 - 198
= 162 degrees.
Using the appropriate angle theorems, the value of the angle, x in the parallelogram would be 162°
At angle S :
S + 72 = 180 (sum of straight line angles)
S = 180° - 72°
S = 108°
S = Q (opposite angles of a parallelogram)
Q = 108°
Hence,
Q + x + right angle = 360° (sum of angles at a point)108° + x + 90 = 360
x = 360 - (108 + 90)
x = 162°
Hence, the value of x is 162°
Learn more : https://brainly.com/question/16144029
please solve this fast
Answer:
69
Step-by-step explanation:
What is the coefficient of x5y5 in the expansion of (x + y)10?
Answer:
C=252
Step-by-step explanation:
Given:
x^5y^5
(x+y)^10
Find the coefficient of x^5y^5
To get the coefficient of x^5y^5,
we will put r = 5, in the below given general term.
The general term is : nCr =x^ry^n-r
We get:
Coefficient is = 10C5
= 10!/5!*5!
= 252
The coefficient of x^5y^5 is 252
C. 252
Lisa read 46 pages on Sunday, 15 pages on Monday, and 19 pages on Tuesday. Which of the following is closest to the mean number of pages she read over the three-day period? A. 19 pages B. 21 pages C. 27 pages D. 35 pages Show all work!!
Answer:
C. 27 pages
Step-by-step explanation:
First, add all of the numbers together
15+19+46
That would be 80.
Then, once you have the numbers added, divide the number you by how many numbers there are.
80 divided by 3 = 26.7 (rounded)
Now that you have the answer 26.7, that tells you that the answer is 27 pages.
Answer:
c.27
Step-by-step explanation:
You have to add 46,15, and 19 together which gets you 80. Then you divide it by 3 and you get 26.(something) since its a decimal, you need a whole number. You round to 27 because its the closest. (When finding the mean, you must add the numbers and divide by how many numbers there are (3))
Calculate the average speed in miles per hour of a journey of 36 miles which took 45 minutes. with explanation pls thx
Answer:
= 48 miles/hour
Step-by-step explanation:
Speed=distance/time
Speed = 36/0.75
Type the correct answer in each box. If necessary, use / for the fraction bar.
Complete the statements about series A and B.
Series A: 10 + 4 +8/5 + 16/25 + 13/125 + ...
Series B: 1/5 + 3/5 + 9/5 + 27/5 + 81/5 +...
Series (a or b) has an r value of (blank) where 0<|r|<1. So, we can find the sum of the series. The sum of the series is (blank)
Answer:
Step-by-step explanation:
Given two series A and B;
Series A: 10 + 4 +8/5 + 16/25 + 13/125 + ...
Series B: 1/5 + 3/5 + 9/5 + 27/5 + 81/5 +...
Both series are geometric series since they have the same common ratio. Given the geometric series T₁, T₂, T₃, T₄..., the common ratio r is expressed as [tex]\frac{T_2}{T_1} =\frac{T_3}{T_2} =\frac{T_4}{T_3} = r[/tex].
a) For series A, Given T₁ = 10, T₂ = 4, T₃ = 8/5 and T₄ = 13/125
Its common ratio is expressed as [tex]\frac{4}{10} =\frac{8/5}{4} =\frac{13/125}{8/5} = 2/5[/tex]
Hence the common ratio of series A is 2/5
The sum to infinity of the geometric series will be expressed as [tex]s_\infty = \dfrac{a}{1-r}[/tex]
Note that the sum to infifnity is used since the series is tending to infinity.
a is the first term if the series = 10
r - 2/5
On substituting this values into the formula;
[tex]s_\infty = \dfrac{10}{1-2/5} \\\\s_\infty = \dfrac{10}{3/5} \\\\s_\infty = 10* 5/3\\s_\infty = 50/3[/tex]
Hence the sum of the series is 50/3
b) For the series B;
Series B: 1/5 + 3/5 + 9/5 + 27/5 + 81/5 +...
The common ratio of the series is expressed as shown;
[tex]\frac{3/5}{1/5} =\frac{9/5}{3/5}= \frac{27/5}{9/5 } = r\\ r = (3/5 * 5/1) = 9/5*5/3 = 27/5*5/9 = 3[/tex]
Hence its common ratio is 3.
Sun of the series is expressed similarly as:
[tex]s_\infty = \frac{a}{1-r}\\ s_\infty = \frac{1/5}{1-3}\\\\s_\infty = \frac{1/5}{-2}\\\\[/tex]
[tex]s_\infty = 1/5 * -1/2\\s_\infty = -1/10[/tex]
Hence the sum of series B is -1/10
The graph below shows the relationship between the number of months different students practiced baseball and the number of games they won:
The title of the graph is Baseball Games. On x axis, the label is Number of Months of Practice. On y axis, the label is Number of Games Won. The scale on the y axis is from 0 to 22 at increments of 2, and the scale on the x axis is from 0 to 12 at increments of 2. The points plotted on the graph are the ordered pairs 0, 1 and 1, 3 and 2, 5 and 3, 9 and 4, 10 and 5, 12 and 6, 13 and 7, 14 and 8,17 and 9, 18 and 10,20. A straight line is drawn joining the ordered pairs 0, 1.8 and 2, 5.6 and 4, 9.2 and 6, 13 and 8, 16.5 and 10, 20.5.
Part A: What is the approximate y-intercept of the line of best fit and what does it represent? (5 points)
Part B: Write the equation for the line of best fit in slope-intercept form and use it to predict the number of games that could be won after 13 months of practice. Show your work and include the points used to calculate the slope. (5 points)
Answer:
(A) The y-intercept of the line is 1.82.
(B) The number of games that could be won after 13 months of practice is 26.
Step-by-step explanation:
The data from the provided graph is:
X Y
0 1
1 3
2 5
3 9
4 10
5 12
6 13
7 14
8 17
9 18
10 20
Here,
X : Number of Months of Practice
Y : Number of Games Won
(A)
Compute the y-intercept of the line as follows:
[tex]a=\frac{\sum Y\cdot \sum X^{2}-\sum X\cdot \sum XY}{n\cdot \sum X^{2}-(\sum X)^{2}}[/tex]
[tex]=\frac{122\cdot 385-55\cdot 814}{11\cdot 385-(55)^{2}}\\\\=1.818\\\\\approx 1.82[/tex]
The y-intercept of the line is 1.82.
The y-intercept is the average value of the dependent variable, here the number of games won, when the value of the independent variable, here number of months of practice, is 0.
So, a y-intercept of 1.82 indicates that on average 1.82 can be won if the number of months of practice is 0.
(B)
Compute the slope as follows:
[tex]b=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{n\cdot \sum X^{2}-(\sum X)^{2}}[/tex]
[tex]=\frac{11\cdot 814-55\cdot 122}{11\cdot 385-(55)^{2}}\\\\=1.855\\\\\approx 1.86[/tex]
The equation for the line of best fit in slope-intercept form is:
[tex]y=1.82+1.85x[/tex]
Predict the number of games that could be won after 13 months of practice as follows:
[tex]y=1.82+1.85x[/tex]
[tex]=1.82+(1.85\timex 13)\\=25.87\\\approx 26[/tex]
Thus, the number of games that could be won after 13 months of practice is 26.
Mary bought 10 quarts of juice at the grocery. How many gallons of juice did she buy? A. 1.4 gal B. 2.5 gal C. 3.5 gal D. 4.5 gal
Answer:
2.5 gallons (B)
Step-by-step explanation:
1 gallon is equal to 4 quarts. So, if Mary bought 10 quarts, that is 10/4 gallons. Simplified, 10/4=5/2=2.5 gallons.
Hi. Please i need help with this question.
Find the operation used in determining each of the values in the diagram.
Workings Please.
Answer:
3*3+1=10
4*4+5=21
Step-by-step explanation:
You square the number in the first box
3*3=9
4*4=16
And add the number in the second box with the result.
3*3=9+1=10
4*4=16+5=21
Hope this helps ;) ❤❤❤
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
We must square the number on the left box, then add with the number in the right box to get the result in the boxes below.
3² + 1 = 9 + 1 = 10
4² + 5 = 16 + 5 = 21
When purchased, a beach ball is deflated and packaged flat. The package states that when inflated to its maximum capacity, the radius of the inflated ball is 7.6 inches. To the nearest hundredth of a cubic inch, how much air will occupy the space contained by the inflated beach ball? Use 3.14 for [tex]\pi[/tex]. In your final answer, include all of your calculations.
Step-by-step explanation:
V=(4/3) * πr^3
V=(4/3) * π * 7.6 ^3
V=(4/3) * π * 438.976
V= π * 585.301333
V = 1837.85 inch^3
3.14 for pi btw
Phillip deposited $5,670 into a savings account 19 years ago. The account has an interest rate of 4.1% and the balance is currently $12,356.04. How often does the
interest compound?
Answer:
$12165.97
Step-by-step explanation:
100 + 4.1 = 104.1%
104.1% = 1.041
$5670 x 1.041^19 = $12165.97
Answer:
daily
Step-by-step explanation:
To answer this try plugging in each type of compund: daily, monthly, quarterly, and annually.
5670(1+0.041/365)^(365*19)
= 12356.04
365= daily
so your answer would be that the interest compounds daily.
The number of oranges that Joe has is a multiple of 6. When he sells one orange, the number of oranges is a multiple of n. If n is a positive integer less than 10, how many possible values are there for n?
Answer:
2
Step-by-step explanation:
The number of oranges he has is a multiple of 6, so the number can be
6, 12, 18, 24, 30, 36, 42, 48, 54, etc.
He sells one orange, so now he an have:
5, 11, 17, 23, 29, 35, 41, 47, 53, etc.
All numbers above up to 53 are multiples of 1, so n can be 1.
Also 5 and 35 are multiples of 5, so n can be 5.
All numbers other than 5 and 35 are prime.
Answer: 2
PLEASE HELP ME WITH MY HOMEWORK!! ASAP! WILL PICK BRAINLIEST! DUE IN 15 MINUTES!!!
Answer:
watch 11:39 . clock is 11:24 . 210m . 1mm . 12 degrees . 3/4hrs .
Step-by-step explanation:
Step-by-step explanation:
10. It says the watch is 9 minutes fast and the time announced is 11:30 that will be 9 minutes added to the 11:30 which will give 11:39
Now, for the clock , it says the clock is 6 minutes slow, that will be 11:30 - 6 minutes the six minutes will be minused from the 30 minutes which will give 11:24
11. since it is 10 m above the ground and the full length is 220 m which part of is under the ground since we are given the length above the ground in order to find the length of the ground we say 220-10 which will give 210
so the distance of the bottom of the drill from there ground level is 210
12. x + 5
x - 3
to give their difference that will be 5+3 which will be 8
cross check
using 5 to represent x
5+5 =10
5-3 =2
the difference between them is 8 you can use another number to represent x but the difference will still be 8
13. To find the temperature if the frozen meat that will be 34 + 22 degree that gives 56
14. it says she was at the airport 1hr 30 minutes before the appointed time so if the plane was to take off by 9:00 that means she reached there 7:30 then it was 9:00 the plane was late again for 3/4 of hour late so 60 minutes makes up an hour that gives 60×3/4 that gives 45 meaning the plane was late for another 45 minutes how long does she wait that gives 1hr 30 minutes plus 45 minutes convert all to minutes =60 minutes + 30 minutes + 45 minutes which is 135 minutes convert to hour 2 minutes gives 120 seconds so 135-120 =15
so she waited at the airport for 2 hrs 15 minutes
15. since out of the 6400 Dani he paid his debt of 600 and gave it sola who has only 1900
that will be 6400-600 and 1900+600
so sola has 2500 while Dani has 5800
16. she can only pay back 40
B. (not sure)
17. meaning the sister owes 800 naira
b. by 1700+800 =2500
18. that gives 950000-97000 =853000