1. Triangle ABC has an angle of ABC = 60°, AB = 3 √3 cm and BC = 4 √3 cm. Determine the length of AC.
Answer:
see below
Step-by-step explanation:
you can use cosine law
(3 sqrt3)^2 + (4 sqrt3)^2 - 2(3 sqrt3)(4sqrt3)cos60 = AC^2
AC = sqrt39
Please help!!! Having some trouble with this! Tom, Jim, and Matt want to build a castle next to their swing set. The castle is as wide as the swing set, and 6 feet long. The additional play area is enlarged to yield the following layout:|
Length = 7 + 2x [L]
Breadth = 6 + x [B]
So, Area = L × B
=> Area = (7 + 2x) (6 + x)
=> Area = 7 × 6 + 7x + 2x × 6 + 2x²
=> Area = 42 + 7x + 12x + 2x²
=> Area = 2x² + 19x + 42
Option B is correct.
Any questions, you may ask.
Answer: b.) 2x² + 19x + 42
Area of rectangle:
⇒ Length × Width
⇒ (6 + x) × (7 + 2x)
apply distributive method: (a + b)(c + d) = ac + ad + bc + bd⇒ 6(7) + 6(2x) + x(7) + x(2x)
simplify
⇒ 42 + 12x + 7x + 2x²
arrange
⇒ 2x² + 19x + 42
If you could answer this thank you!
Answer: 55°
Step-by-step explanation:
Hi!
since an angle bisector splits it in half,
110°, being the entire angle divided by 2 = 110/2 = 55°
Can someone help me out in these geometry fill in the blanks? It’s urgent, gotta have answers fast
Answer:
Vertical angles are equal
Step-by-step explanation:
-
[tex]vertical \: angles \: are \: equal[/tex]
[tex]3y = 150[/tex]
The sum of two supplementary angles equals 180 degrees
Therefore 6x +150=180
The data show the heights in feet of 14 roller coasters. find the mean, median, midrange, and mode for the data.
The mean of the heights of roller coaster is 27.92 feet, median is 21, mode is 16 and mid range is 35.5.
Given heights in feet of 14 roller coaster 11,12,13,14,16,21,25,26,31,40,51,55,60.
We have to calculate the mean, median, mid range and mode for the data.
Mean is the sum of numbers divided by the numbers.
Mean=∑X/n
∑X=11+12+13+14+16+21+25+26+31+40+51+55+60
=391
n=14
Mean=391/14
=27.92 feet.
Median is the central value of the data given.
Median=(n/2)th term ,when n is even, ( n/2)th term, (n+1)/2th term when n is odd.
Median=14/2th term=7th term which is 21.
Mode is the number which has higher frequency.
Mode is 16 because it comes 2 times.
Mid range is the sum of upper value and lower value of data divided by 2.
Mid range=(11+60)/2==35.5.
Hence the mean is 27.92 feet, median is 21 feet, mid range is 35.5 feet, mode is 16 feet.
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Question is incomplete as the values of height should be included as under:
11,12,13,14,16,16,21,25,26,31,40,51,55,60.
PLS HELP ITS URGENT I HAVE LIKE A COUPLE QUESTIONS LEFT IM STUCK ON THIS
Answer: 3[tex]i[/tex]
Step-by-step explanation: The reason for this is because [tex]i[/tex] =
[tex]\sqrt{-1}[/tex], and when [tex]\sqrt{-1}[/tex] is multiplied to [tex]\sqrt{9}[/tex], it becomes [tex]\sqrt{-9}[/tex]. Since [tex]\sqrt{9}[/tex] can be simplified to 3, we can just multiply [tex]i[/tex] to 3. This becomes 3[tex]i[/tex].
Hope this helped!
Answer:
3i
Step-by-step explanation:
Enter the first 4 terms of the sequence defined by the given rule. assume that the domain of each function is the set of whole numbers greater than 0. f(n) = (2n + 2)2 the first 4 terms of the sequence are , , , and .
The first four terms of the sequence are 8,12,16 and 20.
What is a Sequence?A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. Similar to a set, it has members (also called elements, or terms). The length of the series is the number of elements (potentially infinite). In contrast to a set, the same items might appear more than once in a sequence at various points, and unlike a set, the order is important. A sequence can be described formally as a function from natural numbers (the positions of the sequence's elements) to the items at each of those positions. An indexed family, which is a function from an index set that may not be a set of numbers to another set of elements, can be thought of as a generalization of the idea of a sequence.Given the function is f(n) = (2n+2)2
Now, we want first four terms, therefore, putting 1, 2, 3, 4 in the sequence we get:
f(1) = (2*1+2)2 = 8
f(2) = (2*2+2)2 = 12
f(3) = (2*3+2)2 = 16
f(4) = (2*4+2)2 = 20
Hence, The first four terms of the sequence are 8,12,16 and 20.
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Evaluate the expression 9 - z when z = 4.
Answer:
its 5 5+4=9
Step-by-step explanation:
f(x)=x(4x+9)(x-2)(2x-9)(x+5) has zeros at x = -5, x = -9/4, x=0, x=2, and x =9/2. what is the sign of f on the interval 0
Answer:
Just look at the other answer
Step-by-step explanation:
Answer:
f is always positive on the interval.
Step-by-step explanation:
What is the equation of a circle whose radius is 16 units and center is at (2,-5)?
Answer:
The general equation of the circle is [tex]( {x - a})^{2} + ({y - b})^{2} = {r}^{2} \\ therefore \: we \: \: have \: \\ ( {x - 2})^{2} + (y - ( - 5)) {}^{2} = ({16})^{2} \\ ({x - 2})^{2} + ( {y + 5})^{2} = 256[/tex]HOPE THIS HELPS!HELP MATES, HELP!
Mustafa was asked whether the following equation is an identity:
Answer: Mustafa is incorrect. He made a mistake in step 2.
Step-by-step explanation: Mustafa was certainly correct in step 1 that x(9x+3) + 3(x+3) is 9x^2 + 6x + 9. However when he was factoring, he made a mistake.
(3x + 3)^2 is NOT equal to 9x^2 + 6x + 9. Rather, (3x + 3)^2 is equal to 9x^2 + 18x + 9. If you want to double check this, use FOIL.
The correct factoring of 9x^2 + 6x + 9 is actually 3(3x^2 + 2x + 3). So, Mustafa made a mistake in step 2.
Area=
Help me please!! Thanks :)
Answer:
80π
Step-by-step explanation:
Circle O with radius IO:
large radius = IO = 12 = R
Circle O with diameter JK
IJ = JK = KL = 2 × IO = 24
IJ = JK = KL = 24/3 = 8
small radius = 8/2 = 4 = r
The shaded area is a semicircle of radius 12 minus a semicircle of radius 4 plus two semicircles of radius 4.
That is the same as
1 semicircle of radius 12 plus 1 semicircle of radius 4
A = πR²/2 + πr²/2
A = π(12² + 4²)/2
A = 160π/2
A = 80π
(score for question 3: ... of 10 points) 3. the table shows the test scores and the sleep averages of several students. test score (%) 88 75 76 92 96 94 83 90 99 65 7788 82 83 94 97 7 6.5 average sleep (h) 6 7.5 8 7 6.5 8 8.5 5 7 8 9 9 9 8.5 8.5 (a) write the least squares regression equation that models the data. let x = the test score and y = average sleep. (b) use the equation to determine the approximate test score of a student who sleeps an average of 8 hours a night. show your work. answer: 1
The linear regression model obtained by fitting the data points is Y = 0.0914X1 - 0.3741.
How to illustrate the regression?x = test score
y = average sleep
Slope = 0.0914
intercept = - 0.3741
The test score of a student that sleeps 8 hours
y = 8
8 = 0.0914X1 - 0.3741
8 + 0.3741 = 0.0914X1
X = 8.3741 / 0.0914
X = 91.62
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a doctor at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 99% confident that her estimate is within 3 ounces of the true mean
The sample size that gives 99% confidence level and estimate will be within 3 ounces is 0.7386[tex](standard deviation)^{2}[/tex].
Given confidence level 99% and margin of error is 3 ounces of true mean.
Margin of error is the difference between the actual values and the calculated value of mean.
Sample size is the number of items taken from the population as a sample for research.
We have to find the sample size.
First we have to find the z value for the corresponding p value of 0.99.
z value=2.58
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
3=2.58σ/[tex]\sqrt{n}[/tex]
[tex]\sqrt{n}[/tex]=2.58/3 σ
Squaring both sides
n=[tex]2.58^{2}[/tex]σσ
Hence the sample size needed is 2.58 ([tex](standard deviation)^{2}[/tex].
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A commitee is consist of 6 men and 4 woman ,a sub commitee is made by randomly choosen three commitee members .what is the probability that(a)they are all woman (b) two of them are men
Answer:
a) 1/30
b) 1/6
Step-by-step explanation:
a) There are 10 people total and a group of 3 is being chosen. However, they all need to be women:
For the first person, the probability of it being a woman is 4/10
For the second person, the probability of it being a woman (with the prerequisite that the first was a woman) is 3/9
For the third (with the same requirements) is 2/8
If we multiply all of the fractions together, we get: [tex]\frac{1}{30}[/tex]
b) There are 10 people total and a group of 3 is being chosen. However, two of them need to be men, and 1 needs to be a woman:
For the first person, the probability of it being a man is 6/10
For the second person, the probability of it being a man (with the prerequisite that the first was a man as well) is 5/9
For the third person, the probability of it being a woman (because it can only be two men) is 4/8
If we multiply all the fractions together, we get: [tex]\frac{1}{6}[/tex]
Line K has a slope of -5. Line J is perpendicular to line K. What is the slope of line K?
If line J is perpendicular of line K, they should cross to make an X. If the slope of line K is -5, Line J would be 5.
which factor tree for the graph the function below? Check all that apply.
f(x)= 4•5^x
The statements that are true are B, C, and F.
Which facts are true about the exponential function?
Here we have the exponential function:
[tex]f(x) = 4*5^x[/tex]
We can see that the initial value is 4, and the base is 5. Because the base is larger than 1, this is an exponential growth function.
The statements that are true are:
B: The domain of an exponential function is always the set of all real numbers.
C: Is an exponential growth, so yes, it is increasing.
F: The y-intercept is given by evaluating the function in x = 0, when you do that, you get the initial value, which is 4. So the y-intercept is (0, 4).
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If LM = 3x + 5, MN = 4x, and LN
=
11x7, select all that are true
a. x=3
b. x=7
c. lm = 14
d. lm = 28
e. ln = 26
f. ln =54
We have that x = 3, LM = 14 and LN = 2. options A, C and E
How to determine the value
We known that the three sides are on a straight line
LM + MN = LN
Let's substitute the values, we have
3x + 5 + 4x = 11x - 7
Collect like terms
3x + 4x - 11x = -7 -5
-4x = -12
x = -12/ -4
x = 3
LM = 3x + 5 = 3(3) + 5 = 14
LN = 11x - 7 = 11(3) -7 = 33 -7 = 26
Thus, we have that x = 3, LM = 14 and LN = 2. options A, C and E
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Select the two expressions equal to the area of this figure in square centimeters.
Answer:
1.(6*4) + (18*6) + (6*4)
1.(6*10) + (6*6) + (6*10)
Step-by-step explanation:
there are two ways to break this shape into three rectangles:
1.Top right rectangle, Top left rectangle, Bottom long rectangle
2. Left rectangle, Middle square, Right rectangle.
Help me with answer to these questions and sorry that it is in spanish.
The computation of the decimals are illustrated below.
How to calculate the values?1. 7/4 + √5
= 1.75 + 2.24
= 3.99
2. -✓2 + 9
= -1.41 + 9
= 7.59
3. 2 - 5/4
= 2 - 1.25
= 0.75
4. 7.93 + 1/7
= 7.93 + 0.14
= 8.07
5. π + ✓5
= 3.14 + 2.24
= 5.38
6. ✓2 + 13/4 - 3
= 1.41 + 3.25 - 3
= 1.66
7. 8.5 - 12.65
= -4.15
8. 4 + ✓3 - 11/3
= 4 + 1.73 - 3.67
= 2.06
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Which of the Following illustrates how to find the difference of
12a ^2b and —5a^2b?
Answer:
17a^2b
Step-by-step explanation:
Difference = subtracting
12a ^2b - (-5a^2b)
12a ^2b + 5a^2b
17a^2b
Evaluate if t=2 and x=3: 3(2x² - £)
a.) 102
b.) 30
c.) 48
d.) 12
A cylindrical container 30cm in diameter holds approximately 30 litres of oil. how far does the oil level fall after 1 litre of oil has been used
The fall in the level of oil is 1.4147 cm when the total volume of oil consumed is 1 liter.
We assume the drop in the level of water to be d cm.
Since the container is cylindrical in shape, its volume is given as:
V = πr²h, where V is the volume, r is the radius, and h is the height.
In the question, we are given that the diameter of the can is 30 cm.
Hence its radius = 30/2 = 15 cm.
The capacity of the container is given to be 30 liters or 30*1000 = 30000 cm³.
The volume of the oil used = 1 liter or 1*1000 = 1000 cm³.
Thus, substituting V = 1000, r = 15, and h = d, in the formula of the volume, V = πr²h, we get:
1000 = π(15)²(d),
or, d = 1000/(225π) = 1.4147.
Thus, the fall in the water level is 1.4147 cm.
Therefore, the fall in the level of oil is 1.4147 cm when the total volume of oil consumed is 1 liter.
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What is the slope of the line that passes through (0,5) and (10,0)?
Answer:
-1/2
Step-by-step explanation:
slope is change in y / change in x
change in y is -5 bc y decreases by 5
change in x is 10 bc x increases by 10
-5/10 simplifies to -1/2
Evaluate the following
a) 5 ÷ 2 (mod 6)
b) 9 ÷ 7 (mod 7)
c) 3 × 2 ÷ 5 (mod 7)
Neither 2 nor 7 have inverses mod 6 or 7, respectively, so the expressions in (a) and (b) cannot really evaluated... At least we can evaluate (c) :
[tex]5\times3 \equiv 15 \equiv 1 \pmod 7 \\\\ \implies 3\times2\div5 \equiv 3\times2\times3 \equiv18 \equiv \boxed{4 \pmod{7}}[/tex]
Solve x ^ 2 - 3x = - 8 using the quadratic formula.
Answer: [tex]\frac{3 +- \sqrt{23}i}{2}[/tex] If using complex numbers, or undefined if using all real numbers
Step-by-step explanation:
Moving -8 to the left side of the eq by adding both sides by 8=
x^2-3x+8=0
The quad formula:[tex]\frac{-b +- \sqrt{b^2-4ac}}{2a}[/tex]
a=1 b=-3 c=8
Inserting a b c values into formula: [tex]\frac{-(-3) +- \sqrt{(-3)^2-4(1)(8)}}{2(1)}[/tex]
Simplifying: [tex]\frac{3 +- \sqrt{9-32}}{2}[/tex]
[tex]\frac{3 +- \sqrt{-23}}{2}[/tex] Since the square root of a negative number doesn't exist in the set of real numbers, the equation is undefined.
OR
[tex]\frac{3 +- \sqrt{23}i}{2}[/tex] Using complex numbers i, to replace the negative number created by subtracting 9-32.
What is the y-value of the solution to the system of equations {3x+4y=42x−4y=6?
The value of y for the system of equation is -1/2 .
What is a System of Equation ?A system of equation is a set of equation that have common solution
The set of equation given is
3x+4y=4
2x−4y=6
To solve the system , Elimination method will be used
Add equation 1 and 2 to eliminate y
5x = 10
x = 2
Substitute the value of x in equation 1 to determine y
3x +4y = 4
6 + 4y = 4
4y = -2
y = -1/2
Therefore the value of y for the system of equation is -1/2 .
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Damien and Anna are counting fish. They have 4 tanks with 4 fish and 5 tanks with 2 fish. They are planning to fill an order for 3 fish today. Which expression shows how many fish they will have in stock after the 3 are sold. 4×4+5×2−3 3−4×4+5×2 4+4×5+2−3 4×4×5×2−3
GIVEING BRAINLYEST!
Answer:
The answer is 4×4+5×2−3.
Step-by-step explanation:
This is because, in the original amount, they had 4 tanks with 4 fish and 5 tanks with 2 fish. 4x4 is 16 and 5x2 is 10. Then you add them together to get 26. But, you have to subtract 3 because of the order of 3 fish, which equals 23. The equation 4×4+5×2−3 shows that.
Arc CD is 1/4 of the circumference of a circle. What is the radian measure of the central angle?
T
Step-by-step explanation:
The radians is just the length of the arc, so if you had a unit circle where the radius was 1, the length of that entire circle would be [tex]2\pi[/tex] since the circumference of any circle is [tex]2\pi r[/tex] except r is 1 so the length is just [tex]2\pi[/tex]. So if you take 1/4 of this you get [tex]\frac{2\pi}{4}[/tex] which can be simplified to [tex]\frac{\pi}{2}[/tex]
Answer:
Step-by-step explanation:
Comments
You need to get the radian measure of the circle.
The radian measure of the entire circle is 2 * pi
To get the radian measure of 1/4 of the circle, just divide by 4.
2 pi / 4 = pi/2
The central angle is = to 1/4 of the circumference of the circle.
So the central angle is also pi/2
Answer: pi/2
Figure AAA is a scale image of figure BBB.
Figure AAA maps to figure BBB with a scale factor of \dfrac{2}{7}
7
2
start fraction, 2, divided by, 7, end fraction.
What is the value of xxx?
Figure A maps to figure B with a scale factor of 4/9, hence the value of x is x = 54
What is a transformation?Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.
Dilation is the increase or decrease in the size of a figure.
Figure A maps to figure B with a scale factor of 4/9, hence:
4/9 * x = 16
x = 54
Figure A maps to figure B with a scale factor of 4/9, hence the value of x is x = 54
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