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Calculate the measure of segment KL
HELP PLS
Which graph shows the solution to this system of inequalities?
y>-1/3x+1
y>2x-3
Given:
The system of inequalities is:
[tex]y>-\dfrac{1}{3}x+1[/tex]
[tex]y>2x-3[/tex]
To find:
The graph of the given system of inequalities.
Solution:
We have,
[tex]y>-\dfrac{1}{3}x+1[/tex]
[tex]y>2x-3[/tex]
The related equations are:
[tex]y=-\dfrac{1}{3}x+1[/tex]
[tex]y=2x-3[/tex]
Table of values for the given equations is:
[tex]x[/tex] [tex]y=-\dfrac{1}{3}x+1[/tex] [tex]y=2x-3[/tex]
0 1 -3
3 0 3
Plot (0,1) and (3,0) and connect them by a straight line to get the graph of [tex]y=-\dfrac{1}{3}x+1[/tex].
Similarly, plot (0,-3) and (3,3) and connect them by a straight line to get the graph of [tex]y=2x-3[/tex].
The signs of both inequalities are ">". So, the boundary line is a dotted line and the shaded region or each inequality lie above the boundary line.
Therefore, the graph of the given system of inequalities is shown below.
What is the solution set to this equation? Log2(x - 2) + log2x = 3
The required, solution set to the given equation is {4}. Option A is correct.
What are logarithmic functions?A logarithmic function is a mathematical function that represents the logarithm of a number with respect to a given base. In other words, it is a function that relates a number to its logarithm. The general form of a logarithmic function is f(x) = logₐ(x).
Using the product rule of logarithms, we can combine the two logarithms on the left-hand side of the equation:
log2(x - 2) + log2x = log2[(x - 2) * x] = log2(x² - 2x)
So the given equation becomes:
log2(x² - 2x) = 3
2³ = x² - 2x
8 = x² - 2x
x² - 2x - 8 = 0
Factor this quadratic equation as:
(x - 4)(x + 2) = 0
x - 4 = 0, which gives x = 4
x + 2 = 0, which gives x = -2
However, the logarithm function is only defined for positive values of x, so the only possible solution is:
x = 4
Therefore, the solution set to the given equation is {4}.
Learn more about logarithmic function here:
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a and b are complementary angles and a and c are supplementary angles. If a=xº, (a) express b and c in terms of x
(b) find c - b.
Step-by-step explanation:
a + b = 90
a + c = 180
a) If a = x, the. we can write
x + b = 90 and x + c = 180
or
b = 90 - x
c = 180 - x
b) c - b = (180 - x) - (90 - x)
= 180 - x - 90 + x
= 90
6. (15 points) Lucy can mow her yard in 3 hours and 15 minutes. Her brother Will
can mow the same yard in 4 hours and 45 minutes. How long will it take them to
mow the lawn together?
How to solve?
Answer:
1 hour 56 minutes
Step-by-step explanation:
Given :
Time taken by Lucy = 3 hours 15 minutes = 3.25 hours
Time taken by brother = 4 hours 45 minutes = 4.75 hours
Rate = 1 / time taken
Lucy's rate = 1 / 3.25
Brother's rate = 1 / 4.75
Combined rate = Lucy's rate + brother's rate
Combined rate = 1/3.25 + 1/4.75
Combined rate = 0.5182186
Time taken if they work together = 1/ combined rate
= 1 / 0.5182186
= 1.9296 hours
= 1 hour (0.9296 * 60) minutes
= 1 hour 56 minutes (approximately)
4 out of every 5 students made it to class on Monday. If there are 7500 students enrolled how many made it to class?
Answer:
6000
Step-by-step explanation:
7500x4/5=6000
or
7500/5=1500
1500x4=6000
Find the equation of a line parallel to y'= -8x+6.
Answer:
The equation must include -8 as the slope
Step-by-step explanation:
Hi there!
Two key points to keep in mind:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0).Parallel lines always have equal slopesGiven the equation y=-8x+6, we can identify that -8 is in the place of m in y=mx+b, making it the slope.
For a line to be parallel to y=-8x+6, it would have to have a slope of -8 as well. This is the only quality a line needs to be parallel to this given line.
I hope this helps!
Evaluate the given equation for the indicated function values. pls help
Answer:
The answer in each numeral is:
f(4) = 28f(10) = -19f(-5) = -33f(9) = -9Step-by-step explanation:
To obtain the result in each case, you must replace the variable (n) by the value that appears in the second case, I'll explain it with the first exercise:
1. f(n) = 5n + 8 f(4) = ?As you can see, in the second doesn't appear f(n), but f(4), that means you must replace the "n" in the equation by 4, if we do this, we obtain:
1. f(4) = 5*(4) + 8f(4) = 20 + 8f(4) = 28The first answer is 28, now we'll continue with the next exercises:
2. f(n) = -2n + 1f(10) = -2*(10) + 1f(10) = -20 + 1f(10) = -193. f(n) = 6n - 3f(-5) = 6*(-5) - 3f(-5) = -30 - 3f(-5) = -334. f(n) = -nf(9) = -9In this form, you can prove the answers are: 28, -19, -33, and -9 respectively.
Solve Only estimation
Answer:
3a)1680
b)2620
4a)2130
b)13300
c)460
d)7540
Step-by-step explanation:
3a)1500+180
b)2800-170
4a)1800+330
b)7300+6000
c)670-210
d)8000-460
Answer:
a) 1600
b) 2600
c) 2200
d) 13200
e) 500
Step-by-step explanation:
a) 1463 + 179
1400 + 200
1600
b) 2806 - 176
2800 - 200
2600
c) 1831 + 329
1900 + 300
2200
d) 7345 + 5893
7300 + 5900
13200
e) 665 - 213
700 - 200
500
A man takes a 375-mile trip to Miami. His large car gets 18 miles per gallon, and his small car gets 32 miles
per gallon. How many gallons of gas will he save if he takes the smaller car?
Answer: 9 gallons
Step-by-step explanation:
How many gallons needed for small car: 375/32 = 11.7 or 12
How many gallons for large car: 375/18 = 20.8 or 21
21-12 = 9
Half of a set of the parts are manufactured by machine A and half by machine B. Six percent of all the parts are defective. Three percent of the parts manufactured on machine Are defective. Find the probability that a part was manufactured on machine A, given that the part is defective. (Round your answer to 4 decimal places.) Probability
Answer:
0.25 = 25% probability that a part was manufactured on machine A, given that the part is defective.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Defective
Event B: Manufactured by machine A.
Six percent of all the parts are defective.
This means that [tex]P(A) = 0.06[/tex]
Probability that a part is defective and was manufactured on machine A
3% of the parts manufactured on machine A are defective, manufacture A is responsible for 50% of the parts. So
[tex]P(A \cap B) = 0.03*0.5 = 0.015[/tex]
Find the probability that a part was manufactured on machine A, given that the part is defective.
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.015}{0.06} = 0.25[/tex]
0.25 = 25% probability that a part was manufactured on machine A, given that the part is defective.
Graph the Image of square KLMN after a translation 3 units left .
Answer:
N' (-8,9) K' (-8,3) L' (-2,3) M' (-2,9)
Step-by-step explanation:
To translate the square 3 units to the left you would subtract 3 from the x-coordinates of the points shown.
The coordinates of the translated square KLMN is given by K' (-8,3) L' (-2,3) M' (-2,9) N' (-8,9)
What is Translation?A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
Given data ,
Let the square be represented as KLMN
Now , the coordinates of the square KLMN is
K ( -5 , 3 ) L ( 1 , 3 ) M' ( 1 , 9 ) N' ( -5 , 9 )
Now , let the translated square be represented as K'L'M'N'
When translating the square to three units to the left , the x coordinate of the square gets reduced by 3
So , the new coordinate of the square will be ( x - 3 , y )
Substituting the values in the equation , we get
K' = K ( -5 - 3 , 3 )
L' = L ( 1 - 3 , 3 )
M' = M ( 1 - 3 , 9 )
N' = N ( -5 - 3 , 9 )
So , on simplifying the equation , we get
The translated square is K' (-8,3) L' (-2,3) M' (-2,9) N' (-8,9)
Hence , the translated square is K' ( -8,3 ) L' ( -2,3 ) M' ( -2,9 ) N' ( -8,9 )
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A museum has a model of an Egyptian pyramid. It has a rectangular base that is 10 feet by 8 feet, with a height of 12 feet.
What is the volume of the pyramid?
Answer: 320ft^3
Step-by-step explanation:
Assuming the pyramid is just a normal rectangular pyramid and isn't made of stairs...
10x8x12/3 = 320 ft^3
I need help I’ll give u brainlest
Answer:
[tex]252[/tex] cubic yards
Step-by-step explanation:
[tex]V=lwh[/tex]
Volume = length * width * height
[tex]V=7*4*9[/tex]
[tex]V=252[/tex]
Answer:
252 yd³
Step-by-step explanation:
Volume of rectangular prism = length * width * height
= 9 * 7 * 4 yd³
= 252 yd³
What is the surface area of a square pyramid if the base has an area of 16 cm2 and the lateral faces have a slant
height of 12 cm?
O 112 cm
O 208 cm2
O 400 cm?
O 640 cm
Answer:
640
Step-by-step explanation:
pleas check my answer
Answer:
112
Step-by-step explanation:
If you add all the triangle faces and the square.
Solve this proportion mentally by scaling up or scaling down.
Answer: 63 miles
Step-by-step explanation: 21 miles x 3 = 63 miles
you times it by 3 because to get 3 gallons to 9 gallons, you have to multiply it by 3
i already have A but I do not have B
Answer:
-4 , -1 , -2 , 0 , +1 , +3
Step-by-step explanation:
Answer:
the integers -4,-2,-1,0, +1, +3
Step-by-step explanation:
because when you put them in order you find which pairs are located between -5 and +5
-8,-4,-2,-1,0,+3,+8,+9
which tells you that
-4,-2,-1,0, +1, +3 are between -5 and +5
find the inverse function of F(x) = 1/2x-6
Answer:
[tex]F^{-1} (x) = 2x + 12[/tex]
Step-by-step explanation:
Let's assume F(x) = y, then
[tex]y = \frac{1}{2} x - 6[/tex]
Let us solve the equation for x.
[tex]y + 6 = \frac{1}{2} x[/tex]
[tex]2y + 12 = x[/tex]
Next, replace y with x and also replace x with F⁻¹(x)
Answer: [tex]F^{-1} (x) = 2x + 12[/tex]
A university classifies its classes as either "small" (fewer than 40 students) or "large." A dean sees that 62% of Department A’s classes are small, while Department B has only 40% small classes. She wonders if she should cut Department A’s budget and insist on larger classes. Department A responds to the dean by pointing out that classes for third- and fourth-year students tend to be smaller than classes for first- and second-year students. The following three-way table gives the counts of classes by department, size, and student audience. Write a short report for the dean that summarizes these data. Start by computing the percents of small classes in the two departments and include other numerical and graphical comparisons as needed. Here are the numbers of classes to be analyzed: CSIZE
Department Year Size Count
A First Large 2
A First Small 0
A Second Large 9
A Second Small 1
A Third Large 5
A Third Small 15
A Fourth Large 4
A Fourth Small 16
B First Large 18
B First Small 2
B Second Large 40
B Second Small 10
B Third Large 4
B Third Small 16
B Fourth Large 2
B Fourth Small 14
Total 158
Answer:
trffhuuuygreertttf 5
Step-by-step explanation:
fffffffftfdeerrr10
A phone manufacturer wants to compete in the touch screen phone market. He understands that the lead product has a battery life of just 5 hours. The manufacturer claims that while the new touch screen phone is more expensive, its battery life is more than twice as long as that of the leading product. In order to test the claim, a researcher samples 45 units of the new phone and finds that the sample battery life averages 10.5 hours with a sample standard deviation of 1.8 hours.a. Select the relevant null and the alternative hypotheses. b-1. Calculate the value of the test statistic.b-2. Find the p-value.
Answer:
a)
The null hypothesis is [tex]H_0: \mu \leq 10[/tex]
The alternative hypothesis is [tex]H_1: \mu > 10[/tex]
b-1) The value of the test statistic is t = 1.86.
b-2) The p-value is of 0.0348.
Step-by-step explanation:
Question a:
Test if the battery life is more than twice of 5 hours:
Twice of 5 hours = 5*2 = 10 hours.
At the null hypothesis, we test if the battery life is of 10 hours or less, than is:
[tex]H_0: \mu \leq 10[/tex]
At the alternative hypothesis, we test if the battery life is of more than 10 hours, that is:
[tex]H_1: \mu > 10[/tex]
b-1. Calculate the value of the test statistic.
The test statistic is:
We have the standard deviation for the sample, so the t-distribution is used to solve this question
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
10 is tested at the null hypothesis:
This means that [tex]\mu = 10[/tex]
In order to test the claim, a researcher samples 45 units of the new phone and finds that the sample battery life averages 10.5 hours with a sample standard deviation of 1.8 hours.
This means that [tex]n = 45, X = 10.5, s = 1.8[/tex]
Then
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{10.5 - 10}{\frac{1.8}{\sqrt{45}}}[/tex]
[tex]t = 1.86[/tex]
The value of the test statistic is t = 1.86.
b-2. Find the p-value.
Testing if the mean is more than a value, so a right-tailed test.
Sample of 45, so 45 - 1 = 44 degrees of freedom.
Test statistic t = 1.86.
Using a t-distribution calculator, the p-value is of 0.0348.
PLS HELP! WILL GIVE BRAINLIEST IF CORRECT!
What is the value of P for the following triangular prism?
36 cm
48.5 cm
48 cm
36.5 cm
Answer:
36 cm
Step-by-step explanation:
if p is perimeter then 10+13+13=36 is the correct answer
guys plz help i’m struggling
Answer:
0.46017
Step-by-step explanation:
Given :
Mean score = 75
Standard deviation, s = 10
Areum's score = 76
Probability of scoring higher than Areum is given by :
P(x > 76)
The standardized score : (x - mean) / standard deviation
P(x > 76) = P[Z > (76 - 75) / 10]
P[(Z > 0.1)] = 0.46017 (Z probability calculator)
= 0.46017
A candy distributor needs to mix a 40% fat-content chocolate with a 60% fat-content chocolate to create 150 kilograms of a 52% fat-content chocolate. How many kilograms of each kind of chocolate must they use?
Answer:
60 kg of 40% and 90 kg of 60%
Step-by-step explanation:
Let the amount of 40% chocolate be x.
Let the amount of 60% chocolate be y.
x + y = 150
0.4x + 0.6y = 0.52 * 150
x + y = 150
4x + 6y = 780
-4x - 4y = -600
(+) 4x + 6y = 780
--------------------------
2y = 180
y = 90
x + y = 150
x + 90 = 150
x = 60
Answer: 60 kg of 40% and 90 kg of 60%
PLS HELPP MEE !!
Use a calculator to find the r-value of these data. Round the value to three decimal places.
The Answer is -0.985
I just took the test.
B
(3y + 11)
116°
4y
р с
А
Find the measure of ZA.
mZA
Answer:
an exterior angle is equal to the sum of the two opposite interior angles.
3y + 11 + 4y = 116
Step-by-step explanation:
First combine like terms 7y + 11 = 116
Then undo addition or subtraction.
Then undo multiplication and division to get the value of y.
1. EF is (a secant of, tangent to) OX.
2. DF is a (chord, locus) of OX.
3. AABC is made of (chords in, tangents to) OX.
4. ZDEF is an (intercepted arc, inscribed angle) of OX.
Answer:
1 . EF is a secant of OX
2. DF is a chord of OX.
3. AABC is made of tangents to OX
4. ∠DEF is an inscribed angle of OX.
Step-by-step explanation:
Secant is line which intersects a circle from two distant points. Locus is a set of points which is same distance from the center of a circle. Chord is a straight line whose end points lie on circular arc of a circle. Tangent is a line which touches the circle at one point only.
Please answer my question correctly.
Nonsense/Plagiarized = Report
Find the perimeter or circumference and area of each figure. Round to the nearest tenth.
Solution:-The circumference of a circle with radius r is given by C = 2πr. The radius of the circle is 4 in.
Substitute 4 for r.
[tex]\sf{C=2πr}[/tex]
[tex]\sf{ \: \: \: \: =2π(4)}[/tex]
[tex]\sf{ \: \: \: \: ≈{\color{darkviolet}{25.1}}}[/tex]
Answer:-The circumference of the circle is about 25.1 in.
======================The area of a circle with radius r is given by A = πr².
Substitute 4 for r.
[tex]\sf{A = πr²}[/tex]
[tex]\sf{ \: \: \: \: = π(4)²}[/tex]
[tex]\sf{ \: \: \: \: ≈{\color{magenta}{50.3}}}[/tex]
Answer:-The area of the circle is about 50.3 in².
======================#Hope it helps!
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32
The angles shown are supplementary. What is the value of x? 0
(2 Points)
(5x5°
95°
O 180 degree
• 17 degree
O 22 degree
45 degree
HELPP I NEED THIS ASAP ITS FOR MY FINALSS
Answer:
17degrees
Step-by-step explanation:
The sum of two supplementary angles is equation 180degrees. Hence:
5x+95 = 180
5x = 180-95
5x = 85
x = 85/5
x = 17
Hence the value of x is 17
2. Kayli swam 0.7 kilometers at the school swimming pool. How many meters did she swim?
Kayli swam
meters in the swimming pool.
Answer:
To convert kilometres to metres, divide the value by 1000.
0.7 ÷ 1000 = 700 metres
Kayli swam 700 meters in the swimming pool
Hope this helps!
Write the coordinates as an ordered pair for any point that is a solution to the of inequality graphed below.
Answer:
The inequality that represents the graph must have the following form:
[tex]y > -4\cdot x + 6[/tex]
Step-by-step explanation:
First, we need to determine the equation of the line which represents the "lower" bound of the inequality:
[tex]y = m\cdot x + b[/tex] (1)
Where:
[tex]x[/tex] - Independent variable, horizontal axis.
[tex]y[/tex] - Dependent variable, vertical axis.
[tex]m[/tex] - Slope.
[tex]b[/tex] - Intercept.
Given two distinct points of the line, we can solve for both slope and intercept: [tex](x_{1}, y_{1}) = (1, 2)[/tex], [tex](x_{2}, y_{2}) = (0, 6)[/tex]
[tex]m + b = 2[/tex] (2)
[tex]b = 6[/tex] (3)
The solution of the system is: [tex]m = -4[/tex], [tex]b = 6[/tex]
Then, the inequation must have the following form:
[tex]y > -4\cdot x + 6[/tex]