Rewrite the equation in Ax+By=C form
y+2=-4(x-1)
Answer:
4x + y = 2
Step-by-step explanation:
y + 2 = - 4(x - 1) ← distribute parenthesis by - 4
y + 2 = - 4x + 4 ( add 4x to both sides )
4x + y + 2 = 4 ( subtract 2 from both sides )
4x + y = 2 ← in standard form
Solve -4(r-2/3)+4<-8. Show your work
Please help quickly I will give brainly and do step by step explanation thanks!
Answer:
11/3
Step-by-step explanation:
-4(r-2/3)+4<-8
-4r+8/3+4<-8
8/3+4<-8+4r
8/3+4+8<4r
44/3<4r
44/12=r
11/3=r
Please help!!
In the triangle below, b =______. If necessary, round your answer to two
decimal places.
A
38°
Answer here
8
31.6°
25
SUBMIT
Answer:
Step-by-step explanation:
38.06
What is 1/5 (3+2+5)^2
PLEASE GIVE BRAINLIEST!
thank you and have a good day :)
Answer:
20
Step-by-step explanation:
1/5(3+2+5)^2
3+2+5 = 10
10^2 = 100
100/5 = 20
Suppose we have a bag of jelly beans 82% of the jelly beans orange, 14% are black, and 4% are green. Moreover, 15% of orange are sugar free, 70% of black beans are sugar free, and 90% of green beans are sugar free Suppose we select a jelly bean at random.
1. Construct a tree diagram to represent this situation
2. Find the probability of green bean and sugar free
3. Given the bean is sugar free, what is the probability that it is an orange bean?
Please I need help
Answer:
3/50
Step-by-step explanation:
3 g, 5 r, 2 o
3 + 5 + 2 = 10
Orange = 2 jelly beans
Probability of selecting an orange jelly bean: 2/10 or 1/5
If you put the jelly bean back in, there is still 10 jelly beans.
Green = 3 jelly beans
Probability of selecting a green jelly bean: 3/10\
Multiply the probabilities:
1/5 x 3/10
= 3/50
Classify the following triangles as obtuse, acute, or right triangle, using the sidelength relationship. A. 15,16,17. B 20,18,7. C 17,144,145. D 24,32,40
A. Obtuse Triangle
B. Acute Triangle
C. Right Triangle
D. Right Triangle
What is meant by an obtuse triangle?
Obtuse-angled triangles or obtuse triangles are triangles with any one of its angles being an obtuse angle or greater than 90°. Only 180° is equal to the internal angles of an acute triangle.
Given triangles are A. 15,16,17. B 20,18,7. C 17,144,145. D 24,32,40.
If the sum of squares of least two sides is greater than the square of the largest side then it is an obtuse triangle.
If the sum of squares of least two sides is less than the square of the largest side then it is an acute triangle.
If the sum of squares of least two sides is equal to the square of the largest side then it is a right triangle.
A. side lengths are 15,16,17
[tex]15^{2}+16^{2} =481\\17^{2} =289\\481 > 289[/tex]
Therefore this triangle is an obtuse triangle.
B. side lengths are 7,18,20
[tex]7^{2} +18^{2} =373\\20^{2}=400 \\373 < 400[/tex]
Therefore this triangle is an acute triangle.
C. side lengths are 17,144,145
[tex]17^{2} +144^{2} =21025\\145^{2}=21025 \\21025=21025[/tex]
Therefore this triangle is a right triangle.
D. side lengths are 24,32,40
[tex]24^{2} +32^{2} =1600\\40^{2}=1600 \\1600=1600[/tex]
Therefore this triangle is a right triangle.
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Please help me
If a rock is thrown upward on an exoplanet of a nearby star with initial velocity
Velocity of rock when it hits the ground is -22.9955152 ft/s
What is velocity?Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time
Its position function is s(t) = –25t² + 1.86t
When it reaches back ground s(t) = 25 m/s
Substituting
s(t) = –25t² + 1.86t = 25
Using the quadratic formula (-b±√b²-4ac)/2a
(-1.86 ±√1.86-4*25*-25)2*25
(-1.86 ±√1.7298+625)50
(-1.86 ±√626.7298)/50
(-1.86÷25)50
(-1.86+25)50 or( -1.86 -25)50
48.14/50 = 0.9628
This figure is taken because its positive
Time = 0.9628 seconds
Now we need to find velocity when it reaches ground, that is velocity after 0.9628 seconds.
Differentiating s(t) equation
Substituting t = 0.9628 seconds
v(t) = –25(0.9628)² + 1.86(0.9628)
v(t) = -23.174596 + 0.1790808
Velocity of rock when it hits the ground is -22.9955152 ft/s
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guysss solve this
there are "6" eggs layed on the table
I break "2" of them
I cooked "2" of them
I ate "2" of them
how many eggs did they left?
Answer:
Step-by-step explanation:
4.
first, you broke the 2 eggs, and then cooked the eggs. after cooking them, you ate the two eggs that you cracked and cooked.
f(x)=
[tex]2 {x}^{2} [/tex] write down the equation of inverse of f
The equation of inverse of f is f-1(x) = √(x/2)
How to determiine the equation of inverse of fFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2x^2
Express as an equation
so, we have the following representation
y = 2x^2
Swap x and y
so, we have the following representation
x = 2y^2
Divide by 2
y^2 = x/2
Take the square roots
y = √(x/2)
Hence, the inverse is f-1(x) = √(x/2)
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solve for x -
[tex] {x}^{2} - 5x + 6 = 0[/tex]
tysm! "-"
Answer:
Step-by-step explanation:
This is a standard quadratic equation in the form ax^2 + bx + c = 0, where a = 1, b = -5 and c = 6. To solve for x, you can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Where ± represents the positive and negative square root, and the expression under the square root is called the discriminant (b^2 - 4ac).
So, substituting the values for a, b, and c, we have:
x = (-(-5) ± √((-5)^2 - 4 * 1 * 6)) / 2 * 1
x = (5 ± √(25 - 24)) / 2
x = (5 ± √1) / 2
Since the square root of 1 is 1, the two solutions are:
x = (5 + 1) / 2 = 3
x = (5 - 1) / 2 = 2
So, the solutions to the equation x^2 - 5x + 6 = 0 are x = 2 and x = 3.
Examine the figure below, solve for a, round to the nearest whole number.
26 is the value of a from the given figure.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
We need to find the value of a from the figure.
∠D is 46 degrees.
AD is 28, AT is 37
CosD=Adjacent side/ Hypotenuse
Cos46=a/37
0.695=a/37
a=0.697×37
a=26
Hence, the value of a is 26
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Select the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 2, centered at the origin where the endpoints are A(3,7) and B(4,9)
Answer:
To perform a dilation with a scale factor of 2 centered at the origin, we need to multiply each coordinate of the original points A and B by the scale factor of 2.
The coordinates of point A after dilation are:
A′(2 * 3, 2 * 7) = A′(6, 14)
Similarly, the coordinates of point B after dilation are:
B′(2 * 4, 2 * 9) = B′(8, 18)
So, the endpoints of the dilated line segment are A′(6, 14) and B′(8, 18).
the sum of two fractions is 5 3/8 one of the numbers is 7/9 what is the other number
Answer:
[tex]\boxed{\mathrm\bold {4\dfrac{43}{72}}}[/tex]
Step-by-step explanation:
Let the unknown fraction be x
We are given sum of the fractions = 5 3/8 and one of the fractions is 7/9
First convert 5 3/8 to an improper fraction for easier calculation
[tex]5 \dfrac{3}{8} = \dfrac{5\times 8 + 3}{8} = \dfrac{43}{8}[/tex]
Therefore we get:
[tex]\dfrac{7}{9} + x = 5\dfrac{3}{8}\\\\\dfrac{7}{9} + x = \dfrac{43}{8}\\\\[/tex]
Subtract [tex]\dfrac{7}{9}[/tex] on both sides to isolate x:
[tex]\dfrac{7}{9} - \dfrac{7}{9} + x = \dfrac{43}{8} - \dfrac{7}{9}[/tex]
[tex]x = \dfrac{43}{8} - \dfrac{7}{9}[/tex]
To compute the right side
Find the LCM of 8 and 9: 8 x 9 = 72Adjust the fractions based on LCM so we get 72 as a common denominator:[tex]\dfrac{43}{8}=\dfrac{43\cdot \:9}{8\cdot \:9}=\dfrac{387}{72}\\\\\\\dfrac{7}{9}=\dfrac{7\cdot \:8}{9\cdot \:8}=\dfrac{56}{72}\\\\[/tex]16% of the cows have already had calves. 32 have not had calves yet. How many are in the herd?
Answer:
There are approximately 38 cows in the herd.
Step-by-step explanation:
In this problem, we are asked to find the number of cows in a herd, given that 16% of the cows have already given birth to calves and 32 have not yet done so.
Assuming there are no other types of cows in the herd, we can determine that the 32 cows that have not had calves make up 84% of the herd, since they are what is left over when 16% is subtracted from 100% (the whole herd).
[tex]100\%-16\% = 84\%[/tex]
We can now create a equation that shows that 84% of the herd is 32 cows, representing the total number of cows in the herd as x.
[tex]32 \text{ cows} = 84\% \cdot x[/tex]
Finally, to solve for the number of cows in the herd, we can multiply both sides by 100/84.
[tex]\dfrac{100}{84}(32 \text{ cows}) = (84\% \cdot x)\dfrac{100}{84}[/tex]
[tex]x \approx 38 \text{ cows}[/tex]
So, there are approximately 38 cows in the herd.
You launch an object off a 55-foot cliff. If the object was launched at 85 feet/second,
determine how long it will take for the object to hit the ground below. NEAREST TENTH
Solving a quadratic equation, we will see that the object will hit the ground after 5.9 seconds.
How long it will take for the object to hit the ground below?The equation for the vertical movement of an object will be:
H(t) = -16*t^2 + v0*t + h0
Where v0 is the initial velicity, in this case 85ft/s, and h0 is the initial height, 55ft.
Then the height equation is:
H(t) = -16*t^2 + 85*t + 55
The object will hit the ground when the height is equal to zero, then we need to solve:
-16*t^2 + 85*t + 55 = 0
Using the quadratic formula we will get:
[tex]t = \frac{-85 \pm \sqrt{(85)^2 - 4*(-16)*55} }{2*-16} \\\\t = \frac{-85 \pm 103.7 }{-32}[/tex]
We only care for the positive solution, which is:
t = (-85 - 103.7)/-32 = 5.9
So it will take 5.9 seconds for the object to hit the ground.
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Consider the function f(x) = 4 − 2 sec x. Find the exact coordinates of three points on
the function where f has a horizontal tangent
The exact coordinates of points where the horizontal tangent exists are:
(0,2)
([tex]\pi[/tex],6)
([tex]-\pi[/tex],6)
What is meant by tangent?
A plane or straight line that meets a curve or curved surface at a particular place but does not cross it when extended.
Given function is f(x)=4-2secx
We can write it as
y=4-2secx
The slope of the tangent to this curve is:
[tex]\frac{dy}{dx} =-2secx*tanx[/tex]
Given that the tangent is horizontal, which means that the slope is zero.
-2secx*tanx =0 when x is multiples of [tex]\pi[/tex].
So we can take x=0, [tex]\pi[/tex], -[tex]\pi[/tex].
When x=0 ⇒ y=4-2sec0
⇒y=2
When x=π ⇒ y=4-2secπ
y=6
When x=-π⇒ y=4-2sec(-π)
y=6
Therefore the exact coordinates of points where the horizontal tangent exists are:
(0,2)
([tex]\pi[/tex],6)
([tex]-\pi[/tex],6)
The graph is attached below.
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In the state of Pennsylvania 12% of students submit box tops for education to their school. A large school district in western Pennsylvania runs a contest to see if they can increase participation. The superintendent takes a random sample of 210 students from the district and finds that 35 have submitted box tops this year. Do these data provide convincing evidence that the contest has increased participation in the box tops for education programs
Answer:
Step-by-step explanation:
All it's saying is that the 12% of the people are 35 and the 82% of people who did not submitted data is 175 people
The calculated test statistic (2.08) is greater than the critical value (1.96), we reject the null hypothesis and conclude that there is evidence to suggest that the contest has increased participation in the box tops for education program.
How to calculate the null hypothesis?To determine if the contest has increased participation in the box tops for the education program, we need to conduct a hypothesis test.
We will use a significance level of 0.05, which means we are willing to accept a 5% chance of making a Type I error (rejecting the null hypothesis when it is actually true).
Null Hypothesis: The proportion of students submitting box tops for education is still 12% (or has decreased) after the contest.
Alternative Hypothesis: The proportion of students submitting box tops for education has increased after the contest.
To test this hypothesis, we will use a one-sample proportion test. We will use the sample proportion, p' = 35/210 = 0.1667, as an estimate of the population proportion, p. The test statistic is calculated as:
z = (p' - p) / √(p x (1-p)/n)
where n is the sample size.
Under the null hypothesis, the expected value of the test statistic is 0, and the standard deviation of the test statistic is sqrt(p*(1-p)/n).
Using p = 0.12 and n = 210, we have:
z = (0.1667 - 0.12) / √(0.12 x 0.88/210) ≈ 2.08
The critical value for a significance level of 0.05 and a two-tailed test is ±1.96.
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Select the correct answer from each drop-down menu. Given: , , , and are the vertices of quadrilateral. Prove: is a square. Using the distance formula, i found that.
WXYZ must be a square, all the sides must have a length of 5.
The vertices of the quadrilateral are:
W(-1, 1), X(3, 4), Y(6,0), and Z(2, -3)
Distance can be calculated using the formula derived from Pythagoras theorem. In coordinate geometry, the distance formula is:
[tex]\sqrt{[(x_2 -x_1)^2 + (y_2 - y_1)^2]}[/tex]
We have to prove that WXYZ is a square.
Using the distance formula :
[tex]WX = \sqrt{(-1-3)^2+(1-4)^2}\\ \\WX = \sqrt{16 + 9}\\ \\WX = \sqrt{25}\\ \\WX = 5[/tex]
Since WXYZ must be a square, all the sides must have a length of 5.
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The given question is incomplete, complete question is:
Select the correct answer from each drop-down menu.
Given: W(-1, 1), X(3, 4), Y(6,0), and Z(2, -3) are the vertices of quadrilateral WXYZ.
Prove: WXYZ is a square.
Using the distance formula, I found that
…
A. all four sides have a length of 5
B. all four sides have different lengths
C. only 2 sides have the same length
D. all four sides have a length of 10
Need help with this. Keep getting answer wrong
Answer:
see image
Step-by-step explanation:
First of all, the problem might be that we need to set this up differently than how it is written.
"Subtract THIS from THAT" means that you have to put the second thing first and minus the first thing:
THAT - THIS
Next, the minus in the middle has to go to all three of the terms in the second part. This is going to change the sign of all three parts. See image.
Last, hopefully fraction addition with positive and negative signs isn't too terribly confusing.
1/5 - 2/5 is -1/5.
And -1/4 - 1/4 is -2/4, which is -1/2.
see image.
Make sure the y^2 and the y look like they are next to the whole fraction and are not on the bottom of the fraction.
f(x) = (x-7)³, find f¯¹(x).
The inverse function f-¹(x) as required to be determined from the given function; f(x) = (x-7)³ is; f¯¹(x) = ³√x + 7.
What is the inverse function f-¹(x)?It follows from the task content that the inverse function of the given function; f(x) = (x-7)³ is to be determined.
Therefore, let f(x) = y; so that we have;
y = (x - 7)³
make x the subject so that we have;
³√y = x - 7
x = ³√y + 7
By switching the variables; we have;
y = ³√x + 7
Therefore, the required inverse function; f-¹ as required is; f¯¹(x) = ³√x + 7.
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Calvin will plant lily bulbs and iris bulbs in his front garden. He will plant a total of flower bulbs and as many iris bulbs as lily bulbs. The graph below shows the number of lily bulbs (x) and the number of iris bulbs (y) Calvin will plant. Bulbs to Be Planted Which statement describes the point of intersection on the graph?
A. Calvin will plant lily bulbs.
B. Calvin will plant iris bulbs.
C. Calvin will plant lily bulbs and iris bulbs.
D. Calvin will plant lily bulbs and iris bulbs. Lily Bulbs
The statement that describes the point of intersection on the graph is Calvin will plant lily bulbs and iris bulbs. Option C
What is point of intersection of a graph?The point of intersection on the graph represents the values of x and y where both conditions are satisfied.
In this case, the point of intersection represents the number of lily bulbs (x) and the number of iris bulbs (y) that Calvin will plant such that the number of iris bulbs is equal to the number of lily bulbs.
So, the correct statement that describes the point of intersection on the graph is "Calvin will plant lily bulbs and iris bulbs".
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4 players are competing in a tennis tournament. Rosh has 50% chance of winning the the tournament. The other players craig, Phil, terry are equally likely to win. what is the probability that craig wins the tournament?
The probability of Rosh winning the tournament is 50%, which means the probability of one of the other three players winning is 50% divided by 3, or approximately 16.67% each. Therefore, the probability that Craig wins the tournament is 16.67%.
Find an equation of the circle that satisfies the given conditions. (Use the variables x and y.)
Center (−3, 2); passes through (−6, −6)
An equation of the circle that satisfies the given condition is (x+3))^2 + (y - 2)^2 = 73
Finding an equation of a circleThe formula for finding the equation of a circle is expressed as:
(x-a)^2 + (y - b)^2 = r^2
Determine the value of r^2 using the distance between two points
r^2 = (-6-2)^2 + (-6+3)^2
r^2 = 64 + 9
r^2 = 73
Given the centre (a, b) as (-3, 2), the equatio of the circle will be;
(x-(-3))^2 + (y - 2)^2 = 73
(x+3))^2 + (y - 2)^2 = 73
Hence the equation of the circle is (x+3))^2 + (y - 2)^2 = 73
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4. The running track in this diagram consists of two parallel sections with semicircular sections at each end.
Determine the area of the running track.
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How to find the area ?To find the area of the running track, you first need to find the area of the whole shape and then the area of just the inner section.
Area of whole shape :
= Area of both semicircles + Area of the rectangle
= ( π x 46. 41 ²) + ( 85 x ( 46. 41 x 2 ))
= 14, 659.06 m ²
Then, find the area of the inner section :
= ( π x 36. 41 ²) + ( 85 x ( 36. 41 x 2 ))
= 10, 356. 45 m ²
The area of the running track is :
= 14, 659.06 - 10, 356. 45
= 4, 302. 61 m ²
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Solve the triangle using law of cosines. Round answer to the nearest tenth.
Using sine law and cosine law, s is 13.6 units and T is 37.7 degrees while U is 59.3 degrees
What is law of cosineThe Law of Cosines, also known as the Cosine Formula, is a fundamental mathematical relationship between the sides and angles of a triangle. It states that the dot product of two sides of a triangle is equal to the product of the third side and the cosine of the angle between the two sides.
The general form of the Law of Cosines is:
C^2 = A^2 + B^2 - 2ABcos(C)
where C is the angle between sides A and B, and A, B, and C are the lengths of the sides of the triangle. The formula can be rearranged to solve for any one of the sides or angles given the other two.
In this problem, we can easily solve for s.
s² = 8² + 12² - 2(8)(12)cos83
s² = 184.601
s = √184.601
s = 13.6 units
The value of angle T is calculated using sine law;
13.6 / sin 83 = 8 / sin T
sin T = 8(sin 83) / 13.6
sin T = 0.58385
T = sin⁻¹(0.58385)
T = 37.7°
Using sum of angle in a triangle;
T + S + U = 180°
83 + 37.7 + U = 180
U = 180 - 120.7
U = 59.3°
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In the last several weeks, 66 days saw rain and 98 days saw high winds. In that same time period, 31 days saw both rain and high winds. How many days saw either rain or high winds?
133 days saw either rain or high winds.
What is Probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Example: If an experiment has 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event will be as follows:
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
P(r) = 66 days
P(w) = 98 days
P(both) = 31 days
P(r or w) = P(r) + P(w) - P(both)
P(r or w) = 66 + 98 - 31
P(r or w) = 133 days
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Simplify the following as much as possible
A. csc x
B. sec x
C. sin x
D. cos x
Answer:
[tex]\textsf{C.} \quad \sin x[/tex]
Step-by-step explanation:
Given rational expression:
[tex]\dfrac{\sec^2x \csc x}{\sec^2x + \csc^2 x}[/tex]
Rewrite the numerator and denominator of the given rational expression using the following trigonometric identities:
[tex]\boxed{\boxed{\begin{array}{c}\underline{\sf Trigonometric\;Identities}\\\\\boxed{\sec^2 x=\dfrac{1}{\cos^2x}} \qquad \boxed{\csc^2 x=\dfrac{1}{\sin^2 x}}\qquad \boxed{\csc x=\dfrac{1}{\sin x}}\\\\\end{array}}}[/tex]
Therefore:
[tex]=\dfrac{\dfrac{1}{\cos^2x} \cdot \dfrac{1}{\sin x}}{\dfrac{1}{\cos^2x}+\dfrac{1}{\sin^2x}}[/tex]
Multiply the fractions in the numerator, and make the denominators of the fractions in the denominator the same:
[tex]=\dfrac{\dfrac{1}{\sin x\cos^2x}}{\dfrac{\sin^2x}{\sin^2x\cos^2x}+\dfrac{\cos^2x}{\sin^2x\cos^2x}}[/tex]
[tex]=\dfrac{\left(\dfrac{1}{\sin x\cos^2x}\right)}{\left(\dfrac{\sin^2x+\cos^2x}{\sin^2x\cos^2x}\right)}[/tex]
[tex]\textsf{Apply the trigonometric identity}\;\;\boxed{\sin^2x + \cos^2 x = 1}:[/tex]
[tex]=\dfrac{\left(\dfrac{1}{\sin x\cos^2x}\right)}{\left(\dfrac{1}{\sin^2x\cos^2x}\right)}[/tex]
[tex]\textsf{Apply\:the\:fraction\:rule}\;\;\boxed{\dfrac{\frac{a}{b}}{\frac{c}{d}}=\dfrac{ad}{bc}}:[/tex]
[tex]=\dfrac{\sin^2x\cos^2x}{\sin x\cos^2x}[/tex]
Cancel the common factor cos²x:
[tex]=\dfrac{\sin^2x}{\sin x}[/tex]
Simplify:
[tex]= \sin x[/tex]
Therefore:
[tex]\large\textsf{$\dfrac{\sec^2x \csc x}{\sec^2x + \csc^2 x}=$}\;\boxed{\boxed{\sin x}}[/tex]
Solve for x with the given measures
Answer: X= -66
Step-by-step explanation:
If m angle UYV=56
Then WYX= -x-10=56
then X=-66
please help me i’ll give you brainlist
Answer:
its c
Step-by-step explanation:
1. An arithmetic sequence is given using the recursive definition: b₁ = 8 and b₁ =b₁-₁-3. Which of the
n-1
following is the value of b,? Show the work that leads to your answer.
(1) 14
(2) 2
(3) 6
(4) 4
Answer:
To find the value of b_n in an arithmetic sequence given by the recursive definition b_1 = 8 and b_n = b_{n-1} - 3, we can use the formula for the nth term in an arithmetic sequence:
b_n = b_1 + (n-1)d
where d is the common difference. In this case, d = -3.
So, we can plug in the values for b_1 and d to find b_n:
b_n = 8 + (n-1)(-3)
b_n = 8 - 3(n-1)
Now, to find the value of b_n for a specific n, we just need to substitute the value of n into the equation for b_n. For example, if we want to find b_14, we would substitute n = 14:
b_14 = 8 - 3(14-1)
b_14 = 8 - 3(13)
b_14 = 8 - 39
b_14 = -31
So, the value of b_14 is -31, and the answer is (1) 14.
