Answer: 1/2
Step-by-step explanation:
solving bracket first we get
2 - 9/6
multiplying and dividing 2 by 6 we get
12/6 - 9/6
=3/6 = 1/2
Answer:
1/2
Step-by-step explanation:
(6-4)-9/6
= (2)-9/6
= 12/6-9/6
= 3/6
= 1/2
What is the value of discontinuity of x^2+8x+4/x^2-x-6? Choices:
Answer:
-2
Step-by-step explanation:
Hello,
First of all, let's check the denominator.
[tex]x^2-x-6 \ \ \text{ *** How to factorise it ...? ***}\\\\\text{*** The product of the roots is -6=-2*3 and their sum is 1 ***}\\\\x^2-x-6=x^2-3x+2x-6=x(x-3)+2(x-3)=(x+2)(x-3)[/tex]
Now, let's see the numerator.
[tex]x^2+8x+4 \ \text{ *** -2 is not a zero as ***}\\\\(-2)^2+8*(-2)+4=4-16+8=-4\\\\\text{*** 3 is not a zero as ***}\\\\3^2+8*3+4=9+24+4=37\\[/tex]
So we cannot factorise the numerator with (x+2) or (x-3)
Then, -2 and 3 are the the discontinuities of the expression.
There is only -2 in the list, this is the correct answer.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
How much water is wasted by the leaky faucet in 1 day? 15 drips per 30 seconds
Answer:
a. 43,200 drips
b. 4 gallons (approximately, actual value is 3.8)
c. 61 cups(approximately, actual value is 60.8, using 3.8 gallons and not 4 gallons)
Step-by-step explanation:
Here, we have a faucet wasting water at a rate of 15 drips per 30 seconds, now we want to calculate the number of drips wasted in a day
To find this, what we need to do is fund the number of seconds in a day first
There are 24 hours with 60 minutes, with each minute having 60 seconds
So the number of seconds in a day = 24 * 60 * 60 = 86,400 seconds
Now 15 drips is wasted in 30 seconds
x will be wasted in 86,400 seconds
x = (15 * 86400)/30 = 43,200 drips are wasted in a day
b. Mathematically , there are about 3,000 drips in a liter of water
So;
3,000 drips = 1 liter
43,200 drips = x liter
x = 43200/3000 = 14.4 liters of water
Mathematically,
1 liter = 0.264 gallons
So 14.4 liters = 14.4 * 0.264 = 3.8 gallon
which is equal to 4 gallons of water approximately
c. Mathematically;
1 gallon = 16 cups of water
So 3.8 gallons of water will measure 3.8 * 16 = 60.8 which is approximately 61 gallons of water
7 3/8 + (-4 1/2) ÷ (-5 2/3) Please Explain
Answer:
7 3/8 + (-4 1/2) ÷ (-5 2/3) = 8 23/136
Step-by-step explanation:
1) First I turned all the mix numbers into improper fractions:
7 3/8 ----> ( 7(8)+3/8) = 59/8, 4 1/2 ----> (4(2)+1/2) = 9/2, 5 2/3 ----> (5(3)+2/3) = 17/3
So now it should look like this: 59/8 + (-9/2)÷(-17/3)
2) Now our goal is to divide both of the improper fractions (-9/2)÷(-17/3),
- We first apply our fraction rule: -a/-b = a/b (when we have two negatives they cancel out each other and make a positive)
Our Case, From this:-9/2 ÷ -17/3 = To This: 9/2 ÷ 17/3
3) Now we can divide the fractions using this rule: a/b ÷ c/d = a times d / b times
Our Case, From This: 9/2 ÷ 17/3 To This: 9(3)/2(17) Which Gives Us: 27/34
(9 x 3 = 27, 2 x 17= 34)
So now it looks like this: 59/8 +27/34
4) Our look goal is to have the same denominator (which is the bottom part of the fraction) which are 8 and 34
To find it we find the LCM or Least Common Multiple of 8 and 34
(The LCM of a, b is the smallest positive number that is divisible by both a and b) which in this case a and b are 8 and 34
LCM is 136
5) We adjust our two fractions based on the LCM,
(Multiply each numerator ( top part of the fraction) by the same amount of needed to multiply its corresponding denominator to turn it to the LCM 136.
From This: 59/8 and 27/34 To This: 1003/136 and 108/36 ( 59(17)/8 (17) = 1003/136, 27(4)/34(4) = 108/306
6) Finally we can add the numerator (1003 and 108) together: 1003+108= 1111 and now we are left with 1111/136
Then we turn our improper fraction back into a mix number: 1111/138= 8 23/136
Answer:
[tex]\frac{1111}{136} = 8 \frac{23}{136}[/tex]
Step-by-step explanation:
We want to simplify:
[tex]7 \frac{3}{8} + \frac{ -4 \frac{1}{2} }{ -5 \frac{2}{3} }[/tex]
First, convert all the fractions to improper fractions:
[tex]\frac{59}{8} + \frac{ - \frac{9}{2} }{ - \frac{17}{3} } \\\\= \frac{59}{8} + \frac{27}{34}[/tex]
Find the LCM of the denominators:
[tex]\frac{(17 * 59) + (4 * 27)}{136} \\\\ = \frac{1003 + 108}{136}\\ \\= \frac{1111}{136} \\\\= 8 \frac{23}{136}[/tex]
a
simplified form of -3 + 2(x - 1)?
8. Which expression
a. -X + 1
b. 2x-5
c. 2x - 4
d. -X-1
Answer:
2x -5
Step-by-step explanation:
-3 + 2(x - 1)
Distribute
-3 +2x -2
Combine like terms
2x -5
Answer:
5x -2
Step-by-step explanation:
PLs help ASAP will make you brainist
Answer:
c.18
Step-by-step explanation:
32/24=1.33333333333
40/30=1.33333333333
24/1.33333333333=18
Side ST correlates to side BC. Let's use these two sides to find the scale factor between the two triangles
[tex]\text{Scale Factor}=\dfrac{30}{40}=\dfrac{3}{4}[/tex]
Triangle ABC has side lengths are the 3/4 smaller than that of RTS. The value of x is the length of side AC, which correlates with side RS
Multiply 24 by 3/4 to find the value of x
[tex]x=\dfrac{3}{4}\times24=18[/tex]
This is answer choice C. Let me know if you need any clarifications, thanks!
Find the mean and standard deviation. Show all work. 1. X 0 1 2 3 4 P(x) .07 .38 .22 .13
Answer:
Mean = 2.14
Standard deviation = 2.40
Step-by-step explanation:
The calculation of mean and standard deviation is shown below:-
[tex]X = .07\times0 + 0.20\times 1 + 0.38\times 2 + 0.22\times 3 + 0.13\times 4\\\\ = 0 + 0.2 + 0.76 + 0.66 + 0.52[/tex]
= 2.14
So, the mean is 2.14
Now, For computing the standard deviation first we need to find out the variance which is shown below:-
Variance is
[tex]Var(X) = P(X^2) - [P(X)]^2\\\\ P(X^2) = .07\times (0^2) + .20\times (0^1) + .38\times (0^2) + .22\times (0^3) +0.13\times (0^4)[/tex]
After solving the above equation we will get
= 5.78
Now, the standard deviation is [tex]= \sqrt{Variance}[/tex]
[tex]= \sqrt{5.78}[/tex]
= 2.404163056
or
= 2.40
If f(x)= x/2 -2 and g(x) = 2x² + x - 3, find (f + g)(x).
O A. x²-6
O B. 2x²+ 3/2x +1
O C. 2x² - x/2 +1
O D. 2x² + 3/2 x-5
Answer:
Step-by-step explanation:
Its d
ese
i). nx n2 =343 (2mks)
I
Answer:
Are you asking what the value of x is if [tex]n^{x} * n^2 = 343[/tex] ?
Step-by-step explanation:
I promise I will mark as brainiest
There are 18 rectangles inside the playing field. And if you include the fence around the field, that makes 19.
2.) Evaluate 6a² if a = 4
Answer:
96
Step-by-step explanation:
We simply need to plug in a = 4 so 6a² = 6 * 4² = 6 * 16 = 96.
Find the center and radius of x^2 – 18x + y^2 -10y = -6. part two write x2 – 18x + y2 -10y = -6 in standard form
Answer:
see explanation
Step-by-step explanation:
I will begin with part two, first.
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius.
Given
x² - 18x + y² - 10y = - 6
Using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(- 9)x + 81 + y² + 2(- 5)y + 25 = - 6 + 81 + 25, that is
(x - 9)² + (y - 5)² = 100 ← in standard form
with centre = (9, 5 ) and r = [tex]\sqrt{100}[/tex] = 10
In the figure, ABC is mapped onto XYZ by a 180° rotation. Angle B corresponds to which angle in XYZ?
Answer:
x
Step-by-step explanation:
How many solutions does this system have? y = 3 x minus 5. y = negative x + 4. one two an infinite number no solution
Answer:
One
Step-by-step explanation:
It is given that,
y = 3x-5 ....(1)
y = -x+4 .....(2)
We can solve the above equations using substitution method. Put the value of y from equation (1) to equation (2) such that,
[tex]3x-5 = -x+4\\\\3x+x = 5+4\\\\4x = 9\\\\x=\dfrac{9}{4}[/tex]
Put the value of x in equation (1) we get :
[tex]y = 3x-5\\\\y = 3\times \dfrac{9}{4}-5\\\\y=\dfrac{7}{4}[/tex]
It means that the value of x is [tex]\dfrac{9}{4}[/tex] and the value of y is [tex]\dfrac{7}{4}[/tex]. Hence, the given equations has only one solution.
Answer:
1
Step-by-step explanation:
Find the volume in cubic meters, of the 3-Dimensional composite
figure.
8m
5m
Answer:
890 m^3 to the nearest whole number.
Step-by-step explanation:
Volume = volume of the cylinder + volume of the hemisphere:
= π r^2 h + 1/2 * 4/3 π r^3
= π*5^2 * 8 + 1/2 * 4/3 π 5^3
= 890.12
n the diagram below, points $A,$ $E,$ and $F$ lie on the same line. If $ABCDE$ is a regular pentagon, and $\angle EFD=90^\circ$, then how many degrees are in the measure of $\angle FDE$?
[asy]
size(5.5cm);
pair cis(real magni, real argu) { return (magni*cos(argu*pi/180),magni*sin(argu*pi/180)); }
pair a=cis(1,144); pair b=cis(1,72); pair c=cis(1,0); pair d=cis(1,288); pair e=cis(1,216);
pair f=e-(0,2*sin(pi/5)*sin(pi/10));
dot(a); dot(b); dot(c); dot(d); dot(e); dot(f);
label("$A$",a,WNW);
label("$B$",b,ENE);
label("$C$",c,E);
label("$D$",d,ESE);
label("$E$",e,W);
label("$F$",f,WSW);
draw(d--f--a--b--c--d--e);
draw(f+(0,0.1)--f+(0.1,0.1)--f+(0.1,0));
[/asy]
Answer:
18
Step-by-step explanation:
Each interior angle of a regular pentagon is 108 degrees. So Angle AED is 108 degrees. Since Angle AEF is a straight line (180 degrees), Angle FED is 72. This is because 180-108 = 72. Now, since a triangle has a total of 180 degrees, we add 72 and 90, because those are the 2 degrees we have calculated. This gives us a total of 162. Now, we subtract 162 from 180 to find out the degree of Angle FDE. This is 18. So our final answer is 18.
Sidenote: I hope this answer helps!
The properties of a pentagon and the given right triangle formed by
segments EF and FD give the measure of ∠FDE.
Response:
∠FDE = 18°Which properties of a pentagon can be used to find ∠FDE?The given parameters are;
A, E, F are points on the same line.
ABCDE is a regular pentagon
∠EFD = 90°
Required:
The measure of ∠FDE
Solution:
The points A and E are adjacent points in the pentagon, ABCDE
Therefore;
line AEF is an extension of line side AE to F
Which gives;
∠DEF is an exterior angle of the regular pentagon = [tex]\frac{360 ^{\circ}}{5}[/tex] = 72°∠EFD = 90°, therefore, ΔEFD is a right triangle, from which we have;
The sum of the acute angles of a right triangle = 90°
Therefore;
∠DEF + ∠FDE = 90°
Which gives;
72° + ∠FDE = 90°
∠FDE = 90° - 72° = 18°
∠FDE = 18°
Learn more about the properties of a pentagon here:
https://brainly.com/question/15392368
What is the slope of the line shown below? (-2,3) (-4,-9)
Answer:
6Step-by-step explanation:
Let the points be A and B
A ( - 2 , 3 ) -------> ( x1 , x2 )
B ( -4 , -9 ) -------> ( x2 , y2 )
Now, finding the slope:
[tex]slope \: (m) = \frac{y2 - y1}{x2 - x1} [/tex]
Plug the values
[tex] = \frac{ - 9 - 3}{ - 4 - ( - 2)} [/tex]
Calculate
[tex] = \frac{ - 12}{ - 4 - ( - 2)} [/tex]
When there is a (-) in front of an expression in parentheses , change the sign of each term in expression
[tex] = \frac{ - 12}{ - 4 + 2} [/tex]
Calculate
[tex] = \frac{ - 12}{ - 2} [/tex]
Reduce the fraction with -2
[tex] = 6[/tex]
Hope this helps..
Best regards!!
A circle with center A and radius three inches is tangent at C to a circle with center B, as shown. If point B is on the small circle, what is the area of the shaded region? Express your answer in terms of \pi.
Answer:
27π Sq in.
Step-by-step explanation:
Circle A is equal to 9π sq inches. (Radius squared times Pi), Segment BC is a radii of Circle B and the diameter of Circle A. Meaning Circle B's radius is 6 inches. The area of circle B would be 36π sq inches. Now we subtract Circle A's area from Circle B's area(36π sq in. - 9π sq in.), the area of the shaded region is 27π sq in.
f(x)=x^2. What is g(x)?
Answer:
A
Step-by-step explanation:
With this one, you can just plug in 3 into each of the equations until the answer is 1.
When u plug 3 into x for solution A.
(1/3)×3=1
1^2=1
Answer:
[tex]\boxed{ \mathrm{A} }[/tex]
Step-by-step explanation:
The point is given (3, 1)
x = 3
y = 1
y = (1/3x)²
Plug x as 3 and y as 1.
The equation should be equal.
1 = (1/3(3))²
1 = 1²
1 = 1 True
Natasha and her two dogs were walking on a perfectly straight road when her two dogs ran away from her in opposite directions. Her beagle is now \dfrac{25}{4} 4 25 start fraction, 25, divided by, 4, end fraction meters directly to her right, and her labrador is \dfrac{51}{20} 20 51 start fraction, 51, divided by, 20, end fraction meters directly to her left. Which of the following expressions represents how far apart the two dogs are?
Answer:
[tex]\dfrac{74}{20}=3.7 meters[/tex]
Step-by-step explanation:
Hello!
1) Since no other data has been given. Suppose Natasha is in the center and the beagle is to the right.
[tex]\dfrac{25}{4} \:meters[/tex]
2) The labrador is [tex]\dfrac{51}{20}\: to\: the\: left.[/tex]
[tex]\dfrac{25}{4} -\dfrac{51}{20} =\dfrac{(5*25)-51}{20} \\\dfrac{(125-51}{20} =\dfrac{74}{20}[/tex]
Answer:
The answer is B :D hope this helps
Step-by-step explanation:
In a local ice sculpture contest, one group sculpted a block into a rectangular based pyramid. The dimensions of the base were 3 m by 5 m, and the pyramid was 3.6 m high. Calculate the amount of ice needed for this sculpture.
Answer:
18m square
Step-by-step explanation:
Formula for rectangular- based pyramid is L x W x H divided by 3
= 3 x 5 x 3.6 divided by 3 = 18
So you would need 18 m square for the sculpture
In a local town, 54,000 families have incomes less than $25,000 per year. This number of families is 60% of the families that had this income level 12 years ago. What was the number of families who had incomes less than 25,000 per year 12 years ago
Answer: 90,000
Step-by-step explanation:
From the question, we are informed that in a local town, 54,000 families have incomes less than $25,000 per year. We are further told that this number of families is 60% of the families that had this income level 12 years ago.
To calculate the number of families who had incomes less than 25,000 per year 12 years ago goes thus:
Let the the number of families who had incomes less than 25,000 per year 12 years ago be represented by x.
Since we are told that this number of families is 60% of the families that had this income level 12 years ago. This means that:
60% of x = 54,000
60/100 × x = 54,000
0.6 × x = 54,000
0.6x = 54,000
Divide by 0.6
0.6x/0.6 = 54000/0.6
x = 90,000
The number of families who had incomes less than 25,000 per year 12 years ago was 90,000.
S and T are two-digit positive integers that have the same digits but in reverse order. If the positive difference between S and T is less than 40, what is the greatest possible value of S minus T
Answer :Answer: Did you get helped on this one?
Step-by-step explanation: okay yup yup have a good day OKAY
Step-by-step explanation: HAVE A GOOD ONE OKAY
please tell me the method and answer of 2nd question
Answer:
see explanation
Step-by-step explanation:
In a trapezium the lower base angle is supplementary to the upper bas angle on the same side, thus
4x + 91 - 9x + 59 = 180, that is
- 5x + 150 = 180 ( subtract 150 from both sides )
- 5x = 30 ( divide both sides by - 5 )
x = - 6
Thus
∠ N = - 9x + 59 = - 9(- 6) + 59 = 54 + 59 = 113°
∠ K = 4x + 91 = 4(- 6) + 91 = - 24 + 91 = 67°
Drag a statement or reason to each box to complete this proof.
If -5(x + 8) = -25, then x =
-3
A lake has a small patch of lily pads and every day the patch grows to double its size. It takes 32 days for the patch to cover the lake – how long would it take the patch to cover half the lake?
Answer:
It took 31 days for the patch to cover half the lake
Step-by-step explanation:
The patch grows to double its size everyday
the patch completely covers the lake in 32 days
Since the patch doubles itself everyday, this means that the previous day before the 32nd day, the lake was just half covered.
Therefore, the the patch covered half the lake on the 31st day, i.e it took 31 days for the patch to cover half the lake
In a survey men in a certain country (ages 20-29), the mean height was 62.8 inches with a standard deviation of 2.8 inches, what height represents the 99th percentile?
Answer:
the height that represents the 99th percentile is 69.324 inches
Step-by-step explanation:
Given that :
the mean height = 62.8 inches
standard deviation = 2.8 inches
For 99th percentile;
Let X be the random variable;
SO, P(Z≤ z) = 0.99
From the standard normal z tables
P(Z )= 2.33
The standard z score formula is :
[tex]z = \dfrac{X- \mu}{\sigma}[/tex]
[tex]2.33 = \dfrac{X- 62.8}{2.8}[/tex]
2.33 × 2.8 = X - 62.8
6.524 = X - 62.8
6.524 +62.8 = X
69.324 = X
X = 69.324
Therefore; the height that represents the 99th percentile is 69.324 inches
EXPLANATION NEEDED:
In right triangle ABC, ∠ B is a right angle and sin ∠ C = x. cos ∠ A =
a. √x² - 1
b. √1 - x²
c. x
d. √x² + 1
e. x²
Answer:
C. xStep-by-step explanation:
AC denotes the length of the hypotenuse and AB and BC denote the lengths of the other two sides, so:
[tex]\cos(\angle A)=\dfrac{AB}{AC}=\sin(\angle C)=x[/tex]
Please answer it now in two minutes
Answer:
y = 4
Step-by-step explanation:
Using the tangent ratio in the right triangle and the exact value
tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{4\sqrt{3} }[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )
y × [tex]\sqrt{3}[/tex] = 4[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
y = 4
Answer:
y=4
Step-by-step explanation:
If we have a triangle with angles A, B, and C. The law of sines says that the proportion between the sin of angle A and its opposite side is equal to the proportion between the sin of angle B and its opposite side and it is equal to the proportion between the sin of angle C and its opposite side.
So, by the law of sines we can say that:
[tex]\frac{sen(60)}{4\sqrt{3} } =\frac{sen(30)}{y}[/tex]
Solving for y, we get:
[tex]sin(60)*y=4\sqrt{3}*sin(30)\\\frac{\sqrt{3} }{2}y=4\sqrt{3}*0.5\\ \frac{1}{2} y=4*0.5\\y = 4[/tex]
Find the least number which must be subtracted from the following numbers to make it a perfect square i) 2361 ii) 26535 iii)16160 iv) 4401624
What interval includes all possible values of x, where –3(6 – 2x) ≥ 4x + 12? (–∞, –3] [–3, ∞) (–∞, 15] [15, ∞) SORRY THIS IS THE FULL QUESTION
Answer:
[15, ∞).
Step-by-step explanation:
–3(6 – 2x) ≥ 4x + 12
-18 + 6x ≥ 4x + 12
6x - 4x ≥ 12 + 18
2x ≥ 30
x ≥ 15
This means that the minimum of x is 15, and the most is infinity, which is the same thing as [15, ∞).
Hope this helps!