Factorisation:
[tex]\rightarrow \sf 20mn-15m[/tex]
take 5m as common term
[tex]\rightarrow \sf 5m\left(4n-3\right)[/tex]
solving/simplifying:
[tex]\rightarrow \sf \left(\dfrac{5}{6}z\:+\:5\right)+\left(-\dfrac{1}{3}z-4\right)[/tex]
[tex]\rightarrow \sf \dfrac{5}{6}z+5-\dfrac{1}{3}z-4[/tex]
[tex]\rightarrow \sf \dfrac{5}{6}z-\dfrac{1}{3}z+5-4[/tex]
[tex]\rightarrow \sf \dfrac{5}{6}z-\dfrac{1(2)}{6}z+1[/tex]
[tex]\rightarrow \sf \dfrac{5-2}{6}z+1[/tex]
[tex]\rightarrow \sf \dfrac{3}{6}z+1[/tex]
[tex]\rightarrow \sf \dfrac{1}{2}z+1[/tex]
Answer:
[tex]5m(4n - 3)[/tex]
[tex]\dfrac12z+1[/tex]
Step-by-step explanation:
Given expression:
[tex]20mn-15m[/tex]
Rewrite 20 as [tex]4\cdot 5[/tex]
Rewrite 15 at [tex]3 \cdot 5[/tex]
Therefore,
[tex]20mn-15m=4\cdot 5m\cdot n-3 \cdot 5m[/tex]
Factor out common term [tex]5m[/tex] :
[tex]\implie 5m(4n-3)[/tex]
-------------------------------------------------------------------------------------
Given expression:
[tex]\left(\dfrac56z + 5\right)+\left(-\dfrac13z-4\right)[/tex]
Simplify:
[tex]\dfrac56z+5-\dfrac13z-4[/tex]
Group like terms:
[tex]\dfrac56z-\dfrac13z+5-4[/tex]
Combine like terms:
[tex]\dfrac12z+1[/tex]
help please
find the value
Answer:
t = 9 cm
Step-by-step explanation:
Use Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs and c is the hypotenuse of a right triangle)
Given:
a = 12b = tc = 15a² + b² = c²⇒ 12² + t² = 15²
⇒ 144 + t² = 225
⇒ t² = 225 - 144
⇒ t² = 81
⇒ t = √81
⇒ t = ±9
⇒ t = 9 only as length is always positive
Solution:
Pythagoras theorem can only be used in:
Right trianglesScalene right trianglesIsosceles right triangles.Since this is a scalene right triangle, we can use Pythagoras theorem to solve the missing length of the triangle.
=> The formula for Pythagoras theorem is a² + b² = c².Finding a, b, and c:
Let "a" be 12 cm and "b" be "t" cm."c" is the largest side of the triangle. This means that "c" is 15 cm, as it is the largest side of the triangle.Setting up the equation:
a² + b² = c²=> 12² + t² = 15²Simplifying the squares:
=> (12)(12) + t² = (15)(15)Subtracting (12)(12) both sides:
=> t² = -(12)(12) + (15)(15)=> t² = -144 + 225=> t² = 81Taking a square root both sides:
=> √t² = √81=> t = ±9Since the length cannot be negative, the value of t must be positive.
The final answer is...
t = 9Solve this quadratic equation by completing the square
x^2=12x+17
Answer:
[tex]\large\boxed{\red{\sf x =6+\sqrt{53},6-\sqrt{53}} }[/tex]
Step-by-step explanation:
We would like to solve the given quadratic equation by completing the square method .The given equation is ;
[tex]\longrightarrow x^2=12x +17[/tex]
Subtract 12x to both sides ,
[tex]\longrightarrow x^2-12x = 17 [/tex]
Here the co-efficient of x² is already 1 . So , we shall rewrite it as ,
[tex]\longrightarrow x^2-2(6)(x) = 17 [/tex]
Add 6² on both sides ,
[tex]\longrightarrow x^2-2(6)(x) + 6^2=17+6^2 [/tex]
Now LHS is in the form of (a-b)² = a²-2ab+b² ; so that ;
[tex]\longrightarrow (x -6)^2 = 17+36 [/tex]
Simplify RHS ,
[tex]\longrightarrow (x-6)^2=53 [/tex]
Put square root on both sides,
[tex]\longrightarrow (x-6) = \pm\sqrt{53}[/tex]
Add 6 on both sides,
[tex]\longrightarrow x = 6\pm\sqrt{53} [/tex]
Separate the two solutions ,
[tex]\longrightarrow \underline{\underline{x =6+\sqrt{53},6-\sqrt{53}}} [/tex]
And we are done!
Solve for x.
√10x−29=x−2
Enter your answers in the boxes.
Answer:
x = 11, 3
Step-by-step explanation:
√(10x - 29) = x - 2
(√(10x - 29))² = (x - 2)²
10x - 29 = x² - 4x + 4
-10x + 29 -10x + 29
x² - 14x + 33
(x - 11) (x - 3)
x - 11 = 0; x - 3 = 0
+ 11 +11 +3 +3
x = 11 x = 3
I hope this helps!
Find the measure of the missing angels.
Answer:
'b' and 'c' = 119 degrees
Step-by-step explanation:
Given that this is a basic intersection of straight lines, we can assume 'b' and 'c' are equal as well as the given angle and it's opposite. Given 61 degrees and and two straight lines we can just take 180 degrees - 61 degrees and we get 119 degrees, I solved for 'b', but this will give the same answer for 'c', as 'b' and 'c' are equal.
Answer:
B = 119°
C = 119°
Step-by-step explanation:
The value of back to back angles are the same when the lines are straight.Therefor there are two 61° they add together to make 122°You can then subtract 122 from 360 to get 238.Then take 238 and divide it by 2, to get your answer which is 119° for both.Find the length of the third side. If necessary, round to the nearest tenth. 6 7
Answer:
Use the Pythagorean theorem
Side = sqrt(7^2 - 6^2)
Side = sqrt(49-36)
Side = sqrt(13)
Rounded to nearest tenth = 9.22
Hope it helps!!!Brainliest pls!!!Don’t mind my handwriting but can someone help me please
Answer: A: 3/5
Step-by-step explanation:
He made 9 shots
He attempted 15
The ratio will be 9/15, which can be simplified to 3/5
Have a nice day :)
Answer:
A) 3/5
Step-by-step explanation:
No.of baskets attempted = 15
No.of baskets made = 9
Given, To find the ratio of no.of baskets made to no.of baskets attempted
Then,9:15 (or) 9/15
If we simplify 9/15, we get 3/5
THANKYOUPlease mark me as brainliest
A company has been forced to reduce its number of employees. Today the company has 34% fewer employees than it did a year ago. If there are currently 297 employees, how many employees did the company have a year ago?
The area of the triangle is 3 square miles.
h
2 mi.
What is the triangle's height, h?
Answer:
3 mi
Step-by-step explanation:
Use the equation for area of a triangle, A = 1/2 * base * height. Plug in the numbers you have and solve for the height, You get that 3 = 1/2 * 2 * h, and that h = 3.
Hopefully this helps- let me know if you have any questions!
what is 15x1300-1000+14=?
Answer:
18514 if im wrong then sorry but i dont think its wrong
Step-by-step explanation:
what is 1/4 as a percentage
Answer:
The answer is 25%
Step-by-step explanation:
1/4=.25
.25=25%
Answer:
★ 1/4 written as a percent is 25%. To get this answer, divide 1 into 4. 1/4=0.25. Now, multiply 0.25 by 100 to get 25.
Step-by-step explanation:
Hope you have a great day :)
Find the slope of the line joining the points (2, 5) and (3, 1)
Slope = change in Y / change in x
slope = (1-5) /(3-2)
Slope = -4/1
Slope = -4
Answer:
slope = -4
Step-by-step explanation:
The formula for finding slope is (y2 - y1)/(x2 - x1)
x1 = 2
y1 = 5
x2 = 3
y2 = 1
Plugging in our numbers,
(1 - 5)/(3 - 2) = -4/1
= -4
(-10,2) and (-5,-1) find the midpoint
Step-by-step explanation:
solve accordingly to the picture
What is the equation in slope-intercept form of the line that passes through the points (8,-10) and (0, -12)? O y=-1/4x + 12 O y = 1/4x - 12 O y = 4x + 12 O y = 4x - 12
Answer:
y=12xO+b(i think)
Step-by-step explanation:
Joseph went to visit his grandmother with his parents .They drove 240 miles in 4 hours .What was the average speed they were traveling? Be sure to show your work on how the answer is 60 miles per hour
Answer:
Average speed was 60mph so 240 ÷ 4 = 60
The perimeter of a rectangular red sticker is 32 millimeters. The sticker is 12 millimeters wide. How tall is it?
Answer:
4 millimeters
Step-by-step explanation:
(32-24)/2
If x = -12, then solve:
-X =
(Please help me need answer by 1pm)
Answer:
-x = 12
Step-by-step explanation:
x = -12
if you multiply both sides of the equation by -1, you get
-1x = -12 * -1
-x = 12
Answer:
12
Step-by-step explanation:
So what we know is that x is equal to negative 12. To make this easier you can say that -x is the same as -1 times x like shown below,
-1 × [tex]x[/tex] is the same as -X
We can replace the x with -12 and a negative times a negative is a positive so the answer would be 12.
If you want me to explain it more let me know, but hopefully this helps and have a great day!
Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high
temperature of 83 degrees occurs at 5 PM and the average temperature for the day is 65 degrees. Assuming
t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.
Answer:The temperature at 4 AM is 41 degrees.
Step-by-step explanation:
We have an average temperature of 45 degrees and a high of 53 degrees. That makes the midline 45 and the amplitude 8.
We could spend some time trying to figure out how to get a graph in which x=0 corresponds to midnight. However; that is not necessary. We can use any sinusoidal function we want, as long as we understand which part of the graph corresponds to what hour of the day.
So with midline 45 and amplitude 8, let's choose a simple function:
f%28x%29+=+45%2B8sin%28x%29
The time at which we are to find the temperature, 8 AM, is 8 hours before 4 PM, which is the time when the temperature is maximum. 8 hours is 1/3 of a day, so we want to find the temperature 1/3 of a cycle before 4 PM.
Since we are using a sine function with no horizontal shift, the time of maximum temperature, 4 PM, corresponds to 1/4 of the way through a cycle, at pi/2.
We want to go back 1/3 of a cycle, or (2/3)pi, from pi/2; that puts us at -pi/6.
That makes it easy to find the temperature at 4 AM without a calculator:
45%2B8%2Asin%28-pi%2F6%29+=+45%2B8%28-.5%29+=+45-4+=+41
The temperature at 4 AM is 41 degrees.
Answer:
probably he temperature at 4 AM is 41 degrees.
Step-by-step explanation:
A box contains 15 identical balls - Six of the balls are redo 5 blue and the rest white. If three balls are selected one after one the other without replacement Find the probability that, are All three balls are red.
The answer is three red balls
Suppose a jar contains 9 red marbles and 15 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
Answer:
[tex] \frac{3}{23} [/tex]
Step-by-step explanation:
Since we start with 24 marbles, 9 of which are red, the probability of selecting a red marble is 9/24. The red marble is not put back, so there are now 23 marbles, 8 of which are red. It follows that the probability of selecting a second red marble is 8/23. So the probability of selecting a red marble and then another red marble is
[tex] \frac{9}{24} \times \frac{8}{23} = \frac{3}{8} \times \frac{8}{23} = \frac{3}{23} [/tex]
Graph the following function:
f(x) = x² +5x - 6
What are the x-intercepts?
What is the y-intercept?
What is the maximum or minimum value?
Answer:
x-intercept(s): (1,0),(-6,0)
y-intercept: (0,-6)
I am not sure about the maximum and minimum value sorry
A pallet of toggle bolts weighs 516 kilograms. If a warehouse has 82 pallets what is their total weight
Answer:
1 pallet = 516kg
82 pallets = 516*82 = 42,312kg
The triangle shown below has a base of 6 inches and a height of 4 inches. 6 What is the area, in square inches, of this triangle?
Answer:
Step-by-step explanation:
formula = b*h : 2
=> 4*6:2=24:2=12
simplify the radical expression.
3√0.125b3
0.5b
−0.5b
5b
−5b
Answer:
Simplify the radical expression. 3√0.125b3 0.5b −0.5b 5b −5b - did not match any documents.
Suggestions:
Make sure all words are spelled correctly.
Try different keywords.
Try more general keywords.
Try fewer keywords.
Step-by-step explanation:
Which of the following relations represent a function?
A. {(-1,-3),(3,2),(3,7)}
B.{(-1,4),(2,7),(3,7)}
C.{(-3,7),(3,-7),(3,7)}
D. {(-1,4),(-1,7),(3,5)}
100 POINTS
#A
(-1,3)(3,2)(3,7)3 has two images 2,7 hence not a function
#B
(-1,4)(2,7)(3,7)Every domain has unique range hence function
#C
(-3,7)(3,-7)(3,7)3 has two images hence not a function
#4
-1 has two images hence not a function
Can someone help me with this please
Answer:
17 is the answer for #4
A segment that connects the center of a circle to a point on the circle is
called a. ____
Answer:
The a line segment from the center of the circle to any point on the circle is a radius of the circle.
Step-by-step explanation:
Answer:
radius
Step-by-step explanation:
State if three numbers can be the measure of a triangle.
12, 12, 20
10,3,7
7,7,11
24, 9, 12
Given that r = 9.2 m and = 17", work out AB rounded to 3 SF
Answer:
2.813 m
Step-by-step explanation:
x = 9.2 θ = 17 AB=?
Looking at our angle we have an adjacent side & need to find the opposite side.
So tan θ = opp/adj
tan 17 = AB/9.2
AB = 9.2tan17
AB = 2.813 m
426429418417422435420410432435423426409437436429411426411438422428413414Consider this data as a sample of the population.(a) Calculate a point estimate of the mean oxide thickness for all wafers in the population. (Round your answer to 3 decimal places.)(b) Calculate a point estimate of the standard deviation of oxide thickness for all wafers in the population. (Round your answer to 2 decimal places.)(c) Calculate the standard error of the point estimate from part (a). (Round your answer to 2 decimal places.)(d) Calculate a point estimate of the median oxide thickness for all wafers in the population. (Express your answer to 1 decimal places.)(e) Calculate a point estimate of the proportion of wafers in the population that have oxide thickness greater than 430 angstrom. (Round your answer to 4 decimal places.)(a) The point estimate of the mean oxide thickness is Entry field with correct answer424.091 Angstroms.(b) The point estimate of the standard deviation of oxide thickness is Entry field with incorrect answer Angstroms.(c) The point estimate of the standard error of the mean is Entry field with incorrect answer Angstroms.(d) The point estimate of the median oxide thickness is Entry field with incorrect answer417.5 Angstroms.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
426 429 418 417 422 435 420 410 432 435 423 426 409 437 436 429 411 426 411 438 422 428 413 414
A) Point estimate of the mean(m) : (ΣX) /n
Sample size(n) = 24
(426+429+418+417+422+435+420+410+432+435+423+426+409+437+436+429+411+426+411+438+422+428+413+414) / 24
= 10167 / 24
= 423.625 (3 decimal places)
b) Calculate a point estimate of the standard deviation of oxide thickness for all wafers in the population
s = √[Σ(X - m)² / (n - 1)]
Using calculator :
s = 9.277
s = 9.28 ( 2 decimal places)
C.)
Standard Error of point estimate :
SE = s/√n
SE = 9.28 / √24
SE = 1.8942720
(d) Calculate a point estimate of the median oxide thickness for all wafers in the population.
Median = 0.5 (n +1)th term
0.5(25) = 12.5th term ;
(12th + 13 th term)/2
(423 + 426) / 2
= 849/2
= 424.5
(e) Calculate a point estimate of the proportion of wafers in the population that have oxide thickness greater than 430 angstrom
Number of oxide thickness greater than 430 = 6
(number greater than 430 / total number of oxides)
= 6 / 24
= 1/4
= 0.25
Which category do all of these shapes belong to?