[tex]\\ \sf\longmapsto 16-2r=3r+6r+1[/tex]
[tex]\\ \sf\longmapsto 16-2r=9r+1[/tex]
[tex]\\ \sf\longmapsto 16-1=9r+2r[/tex]
[tex]\\ \sf\longmapsto 11r=15[/tex]
[tex]\\ \sf\longmapsto r=\dfrac{15}{11}[/tex]
Answer: r = 15/11
Step-by-step explanation:
Given
16 - 2r = 3r + 6r + 1
Combine like terms
16 - 2r = 9r + 1
Add 2r on both sides
16 - 2r + 2r = 9r + 1 + 2r
16 = 11r + 1
Subtract 1 on both sides
16 - 1 = 11r + 1 - 1
15 = 11r
Divide 11 on both sides
15 / 11 = 11r / 11
[tex]\boxed{r=\frac{15}{11} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
How to solve this pythagoras theorem
Answer:
see explanation
Step-by-step explanation:
The hypotenuse is the longest side thus is (4x + 1)
The legs are 2x and (4x - 1)
Using Pythagoras' theorem, then
(4x + 1)² = (2x)² + (4x - 1)² ← expanding factors
16x² + 8x + 1 = 4x² + 16x² - 8x + 1 , that is
16x² + 8x + 1 = 20x² - 8x + 1 ( subtract 20x² - 8x + 1 from both sides )
- 4x² + 16x = 0 ( multiply through by - 1 )
4x² - 16x = 0 ← factor out 4x from each term
4x(x - 4) = 0
Equate each factor to zero and solve for x
4x = 0 ⇒ x = 0
x - 4 = 0 ⇒ x = 4
Now x > 0, thus x = 4
2x = 2(4) = 8
4x - 1 = 4(4) - 1 = 16 - 1 = 15
4x + 1 = 4(4) + 1 = 16 + 1 = 17
Thus
perimeter = 8 + 15 + 17 = 40 cm
if f(x)=x-6 and g(x)=x^1/2(x+3), find g(x) X f(x)
Answer:
[tex]\bold{f(x)\cdot g(x)=\big x^\frac52-3\big x^\frac32-18\big x^\frac12}[/tex]
Step-by-step explanation:
[tex]f(x)=x-6\ ,\qquad g(x)=\big x^\frac12(x+3)\\\\\\f(x)\cdot g(x)=(x-6)\cdot\big x^\frac12(x+3)=\big x^\frac12(x^2-3x-18)=\big x^\frac52-3\big x^\frac32-18\big x^\frac12[/tex]
How to simplify fractions (please also right down rules when doing so, ((like x+x = x or axa=)
Question is
-2a(2b-3a)
Answer:
[tex] - 2a(2b - 3a) = - 2a2b + 2a3a \\ = - 4ab + 6 {a}^{2} \\ thank \: you[/tex]
Which equation can be used to solve for x in the following diagram?
PLS ANSWER I NEED HELP BRAINLIST AND A THANK YOU WILL BE REWARDED
Answer:
D. 4x+5x=180
Step-by-step explanation:
Answer:
D. 4x + 5x = 180
Step-by-step explanation:
The two angles form a straight line and a straight line equals 180°. So, the sum of the two angles has to equal 180°.
4x + 5x = 180
9x = 180
x = 20°
Hope that helps.
In a mathematics class, half of the students scored 89 on an achievement test. With the exception of a few students who scored 48, the remaining students scored 79. Which of the following statements is true about the distribution of scores?
A. The mean is less than the median.
B. The mean and the median are the same.
C. The mean is greater than the mode.
D. The mean is greater than the median.
Answer:
A. The mean is less than the median.
Step-by-step explanation:
Half the students scored 89. The next highest score is 79. So the median is (79 + 89) / 2 = 84.
A few students scored 48, so the mean is slightly lower than the mean of 79 and 89.
Therefore, the mean is less than the median.
Answer:
A. The mean is less than the median.
Step-by-step explanation:
Say that half the students answered 79, and the rest 89.
We'd have a distribution something like this:
79 79 79 89 89 89
The median is in the smack middle. Since we have an even number of scores, the median would be the number between the 2 middle numbers. Here, that's 79 and 89. Thus, the median is 84.
The mean is the "average" of all values. Since we have an equal number of 79s to 89s, the mean would also be in the middle of those values (balancing an equal number on both sides). So, the mean would also be 84.
HOWEVER, we have an unspecified number of 48's.
The distribution looks something like
48 79 79 89 89 89
The median is still the same, smack middle between the 2 values in the middle. 84.
But the mean has changed. We have smaller values on the left. The mean is brought down by these 48 values. It doesn't matter how many, the fact that we have at least 1 will bring the mean, the average, down.
Find the circumference of this circle
using 3 for TT.
C ~ [?]
24
C = id
Answer:
72
Step-by-step explanation:
The diameter is 24
pi is approximated by 3
The circumference is given by
C = pi *d
= 3 * 24
= 72
3y-4(5x-3y+y²) expand and simplify
Answer:
23x + 12y + -4xy^2
Step-by-step explanation:
So lets first expand
3y (-4 x(5x - 3y + y^2)
let's ignore 3y for now
Since 5x - 3y + y^2 can't be simplified, we move on to multiplying each number.
note: Capital X = Multiplying symbol
___________________________________
-4 X 5x, -4 X - 3y, -4 X y^2
= -20x + 12y + -4xy^2
now we bring back the 3x
3x - -20x + 12y + -4xy^2
so now we simplify, by finding like terms
= 23x + 12y + -4xy^2
Pleaseeeeee
Within 9 hours, the number of stars seen went from 190 to 33 as the sun started to rise. Find out how many stars are getting hidden by the sunlight each hour.
Answer:
Approximately 17
Step-by-step explanation:
Number of starts getting hidden in 9 hours = 190 - 33
= 157
Therefore the nun of starts getting hidden in 9 hours is 157
9 hours = 157 stars
1 hours = x
Cross multiply
9 × x = 157 × 1
9x = 157
Divide both sides by 9
x = 157 ÷ 9
x = 17.4
Therefore 17.4 stars are getting hidden every hour.
Answer:
17 4/9 stars per hour
Step-by-step explanation:
First find the decrease in the number of stars
190-33 = 157
Divide by the hours that passed
157/9
17 4/9 stars per hour
Identify the cross section shown
circle
rectangle
triangl
trapezoid
It is a rectangle
The shaded thing
Must click thanks and mark brainliest
Number17) Find length of CD.
Answer:
2.4
Step-by-step explanation:
similar triangles
Therefore
4/CD = 5/3
CD= 12/5
Let $DEF$ be an equilateral triangle with side length $3.$ At random, a point $G$ is chosen inside the triangle. Compute the probability that the length $DG$ is less than or equal to $1.$
[tex]|\Omega|=(\text{the area of the triangle})=\dfrac{a^2\sqrt3}{4}=\dfrac{3^2\sqrt3}{4}=\dfrac{9\sqrt3}{4}\\|A|=(\text{the area of the sector})=\dfrac{\alpha\pi r^2}{360}=\dfrac{60\pi \cdot 1^2}{360}=\dfrac{\pi}{6}\\\\\\P(A)=\dfrac{\dfrac{\pi}{6}}{\dfrac{9\sqrt3}{4}}\\\\P(A)=\dfrac{\pi}{6}\cdot\dfrac{4}{9\sqrt3}\\\\P(A)=\dfrac{2\pi}{27\sqrt3}\\\\P(A)=\dfrac{2\pi\sqrt3}{27\cdot3}\\\\P(A)=\dfrac{2\pi\sqrt3}{81}\approx13.4\%[/tex]
Answer:
13.44%
Step-by-step explanation:
For DG to have length of 1 or less, point G must be contained in a sector of a circle with center at point D, radius of 1, and a central angle of 60°.
The area of that sector is
[tex]A_s = \dfrac{n}{360^\circ}\pi r^2[/tex]
[tex]A_s = \dfrac{60^\circ}{360^\circ} \times 3.14159 \times 1^2[/tex]
[tex] A_s = 0.5254 [/tex]
The area of the triangle is
[tex] A_t = \dfrac{1}{2}ef \sin D [/tex]
[tex]A_t = \dfrac{1}{2}\times 3 \times 3 \sin 60^\circ[/tex]
[tex] A_t = 3.8971 [/tex]
The probability is the area of the sector divided by the area of the triangle.
[tex]p = \dfrac{A_s}{A_t} = \dfrac{0.5254}{3.8971} = 0.1344[/tex]
Michael is using a number line to evaluate the expression –8 – 3. A number line going from negative 12 to positive 12. A point is at negative 8. After locating –8 on the number line, which step could Michael complete to evaluate the expression?
Answer:
move to the left 3 more spaces
Step-by-step explanation:
you are at -8 already. Therefore, you (-3) more spaces, so you go to the left three more spaces. Use the saying keep change change to help with this.
Keep the first number sign, change the next sign, and the next sign.
Answer:
d
Step-by-step explanation:
In this 3x3 square, you can use only numbers from 1-9, to make all the rows and columns equal to 15. Good luck to the person solving this and just know that I and lots more people thank you for solving this!
Answer:
Hello,
Step-by-step explanation:
The well-known magic square. (first apparition in China).
Here it the methode du Marquis de Liouville: (odd square:3,5,7,9,11,13,...)
We are going to put successively the number from 1 to n² (here n=3)
We imagine that the square is put on a sphere;
We begin in the middle of the last line where we put 1
ICI:
We move in direction SE of one case and put le next number
until we reach of multiple of n
After have reached a multiple of n, we move verticaly of one case
and we go to ICI until we reach n²
How to find the area of the shaded region
Answer:
61 cm^2.
See below.
Step-by-step explanation:
What are the dimensions of the matrix?
The order of a matrix is m×n where m is the number of rows and n is the number of columns.
can you count and find what are m and n here?
Answer:
Step-by-step explanation:
Number of rows X Number of columns
Rows = 3
Columns = 2
answer = 3x2
Find the distance between the two points (-4,4) and (1,0)
Answer:
The answer is
[tex] \sqrt{41} \: \: \: units[/tex]Step-by-step explanation:
The distance between two points can be found by
[tex] \sqrt{ ({x _{1} - x_{2} })^{2} + ({y_{1} } - y_{2} )^{2} } [/tex]
where
( x1 , y1) and ( x2 , y2) are the points
So the distance between (-4,4) and (1,0) is
[tex] \sqrt{( { - 4 - 1})^{2} + ( {4 - 0})^{2} } [/tex][tex] = \sqrt{ ({ - 5})^{2} + {4}^{2} } [/tex][tex] = \sqrt{25 + 16} [/tex]We have the final answer as
[tex] \sqrt{41} \: \: \: units[/tex]Hope this helps you
The length of the shadow of a pole on level ground increases by 90m when the angle of elevation of the sun changes from 58° to 36°.Calcule the height of the pole
===================================================
Work Shown:
x = starting length of the shadow
y = height of the pole
tan(angle) = opposite/adjacent
tan(58) = y/x
1.6003345 = y/x
1.6003345x = y
x = y/1.6003345
x = (1/1.6003345)y
x = 0.62486936y
-------------------------
When the angle changes, the adjacent side gets 90 meters longer
tan(angle) = opposite/adjacent
tan(36) = y/(x+90)
0.72654253 = y/(0.62486936y+90)
0.72654253(0.62486936y+90) = y
0.453994166y + 65.3888277 = y
65.3888277 = y-0.453994166y
65.3888277 = 0.546005834y
0.546005834y = 65.3888277
y = 65.3888277/0.546005834
y = 119.758478075162
y = 119.76
The height of the pole is about 119.76 meters.
1. Check the divisibility of the following numbers by 2, 3, 9 and 11 a) 76543 b) 98765436
2. Which of the following numbers are divisible by 4 or 8? a) 67894 b) 9685048
WILL MARK THEM AS BRAINLIST
Answer:
1. ( I didnt understand the question but I divided them using the calculator.)
A.) 76543
÷ 2= 38,271.5
÷ 3= 25,514.333...
÷ 9= 8,504.777...
÷ 11= 6,958.454545...
B.) 98765436
÷ 2= 49,382,718
÷ 3= 32,921,812
÷ 9= 10,973,937.333...
÷ 11= 8,978,676
2. B
A.) 67894
÷ 4= 16,973.5
÷ 8= 8,486.75
B.) 9685048
÷ 4= 2,421,262
÷ 8= 1,210,631
Explanation:
I used the calculator to divide.
I hope this helps! I'm sorry if it's wrong.
On weekdays, Kiki walks 2 miles in the morning and 1 mile in the evening On Saturdays, she walks 4 miles.
5 x 2 + 1 + 4 Where should I put the Parentheses
BTW I'm 5th Grade
Answer:
5(2+1)+4
Step-by-step explanation:
You know that the average college student eats 0.75 pounds of food at lunch. If the standard deviation is 0.2 pounds of food, then what is the total amount of food that a cafeteria should have on hand to be 90 percent confident that it will not run out of food when feeding 50 college students?
Answer: $53.95
Step-by-step explanation:
Given: [tex]\mu=0.75[/tex] pounds
[tex]\sigma= 0.2[/tex] pounds
n= 50
Two tailed critical z-value for 90% confidence level = 1.645
Let x be the total amount of food that a cafeteria should have on hand to be 90 percent confident that it will not run out of food .
z-score = [tex]\dfrac{x-\mu}{\sigma}[/tex] [tex]=\dfrac{x-0.75}{0.2}[/tex]
Then, [tex]\dfrac{x-0.75}{0.2}=1.645[/tex]
[tex]x-0.75=1.645\times0.2\\\\\Riightarrow\ x-0.75=0.329\\\\\Rightarrow\ x= 0.329+0.75\\\\\Rightarrow\ x= 1.079[/tex]
Foe 50 students, total amount of food = 1.079 x 50 = $53.95
hence, the cafeteria should have food of amount $53.95 so that it is be 90 percent confident that it will not run out of food.
When trying to determine where to shade on the inequality below, why is it unhelpful to test the point (4,0)?
vs-ſ=+2
Answer:
It will not be very helpful to use this point because it lies on the x-axis. Which doesn't show what area to shade.
Step-by-step explanation:
Lisa kicked a ball against the wall at the indicated angle. What is the measure, in degrees, of <1?
Answer:
68°
Step-by-step explanation:
since the ball is placed or comes from a straight line (which is the wall) it means that when you add all those angles the final answer has to be 180 because angles in a straight line add up to 180°
68°+44°+1=180
112°+1=180
1=180-112
=68°
I hope this helps
The measure of ∠1 is 68 degrees.
We have Lisa who kicked a ball against the wall at the indicated angle.
We have to determine the measure of the angle 1 in degrees.
What is the angle of a straight line ?A straight line has an angle of 180 degrees.
According to question, we have -
∠3 = 68 degrees
∠2 = 44 degrees
Therefore -
∠3 + ∠2 + ∠1 = 180
68 + 44 + ∠1 = 180
112 + ∠1 = 180
∠1 = 180 - 112
∠1 = 68 degrees
Hence, the measure of ∠1 is 68 degrees.
To solve more questions on Finding unknown variable visit the link below -
https://brainly.com/question/28012367
#SPJ2
What two numbers multiply to negative 12 and add up to negative 13
Answer:
−13.8654599313 and 0.8654599313
Step-by-step explanation:
The two numbers of interest will be the solutions to ...
xy = -12
x +y = -13
Substituting for y, this becomes the quadratic ...
x(-13 -x) = -12
x^2 +13x = 12 . . . . . multiply by -1
x^2 +13x +6.5^2 = 12 +6.5^2 . . . . . complete the square
(x +6.5)^2 = 54.25
x = -6.5 ± √54.25 . . . . . . take the square root, subtract 6.5
x ≈ -13.865499313 or 0.8654599313
The value of y is the other of these two numbers. So, the two numbers of interest are {-13.865499313, 0.8654599313}.
BRAINLIEST graphing question
Answer:
Step-by-step explanation:
simplify. multiply and remove all perfect squares from inside the square root. assume A is positive. 3 square root 5a times 8 square root 35a2
Answer:
I did this same answer on another app
hope this help☺️
a girl walk to her anteys house and it took 45 minats and she gose to school it took her 61 minates and how many minats was it all together
Answer:
45+61=106
the answer for this question is 106 minutes
Step-by-step explanation:
Answer:
106 minutes/1hour 46 minutes
Step-by-step explanation:
45+ 61 :106
I need help ASAP!!!Please explain how you got your answer
Answer:
See the pic below.
Step-by-step explanation:
I erased the incorrect answers and filled in the correct answers with numbers.
(x2 - 41)2 + (yz - Yı) to the find the length of the segment
62. Use the distance formula d =
from (6,0) and (-5, 4).
Answer:
√137
Step-by-step explanation:
[tex](x_1, y_1) = (6, 0)\\(x_2, y_2) = (-5, 4)\\\\d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\d = \sqrt{(-5-6)^2+(4-0)^2}\\ d = \sqrt{(-11)^2+(4)^2}\\ d = \sqrt{121+16}\\ d = \sqrt{137}\: or \:11.7[/tex]
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 24.2 σ=24.2. You would like to be 98% confident that your estimate is within 1 of the true population mean. How large of a sample size is required?
Answer:
use a z* value accurate to TWO places for this problem. (Not z = 2)
Step-by-step explanation:
Answer:
33
Step-by-step explanation:
;)
9(p−4)=−18 p= I am not great at math, please explain just a little bit
Answer:
[tex]\large \boxed{{p=2}}[/tex]
Step-by-step explanation:
9(p-4) = -18
Expand brackets.
9p -36 = -18
Add 36 on both sides.
9p -36 + 36 = -18 + 36
9p = 18
Divide both sides by 9.
(9p)/9 = 18/9
p = 2
Answer:
p = 2
Step-by-step explanation:
9(p - 4) = -18
You are solving for the variable, p. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operation, and =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
~
First, divide 9 from both sides:
(9(p - 4))/9 = (-18)/9
(p - 4) = -18/9
p - 4 = -2
Isolate the variable, p. Add 4 to both sides:
p - 4 (+4) = -2 (+4)
p = -2 + 4
p = 4 - 2
p = 2
Check. Plug in 2 for p in the equation:
9(p - 4) = -18
9(2 - 4) = -18
9(-2) = - 18
-18 = -18.
~