Answer:
Option C: y=-1/2x + 8
Step-by-step explanation:
So we have the options:
A) y=2x+5
B) y=-1/2x+4
C)y=-1/2x+8
D)y=-2x+5
But first let's define what parallel even is. When two lines are parallel it means that there slope is the same value and the same sign, while there y-intercepts are different, because if they were the same, then they wouldn't be parallel, they would just be the same exact line.
So we're given the equation in standard form. To find the slope we can change it so it's in the form of y=mx+b. This can be done by simply isolating y. The reason we want it in the slope-intercept form is because m represents the slope and b represents the y-intercept. m is the slope because as x increases by 1 the y-value will increase by m. So the "rise" will be m and the "run" will be 1, thus the slope will be m/1 or in other words m because the slope is defined as rise/run. So let's start the steps to isolating y
Original equation
2x+4y=16
Subtract 2x from both sides
4y=-2x+16
Divide both sides by 4
y = -1/2x + 4
Here we have it in slope-intercept form. In this case the slope, or m, is -1/2 and the y-intercept or b is 4. So now let's look at the other equations.
Option A: This equation has a slope of 2, which is not the same as -1/2 so it is not parallel
Option B: This equation has a slope of -1/2 which is the same as -1/2 so it might be parallel. But look at the y-intercept it's 4, that's the same y-intercept as the original equation. This means the two equations are equal and not parallel
Option C: This equation has a slope of -1/2 which is the same as -1/2 so it might be parallel. It has a y-intercept of 8 which is not the same as 4, so the two lines are parallel and not equal! This is the answer
Complete the point-slope equation of the line through (6,4)(6,4)left parenthesis, 6, comma, 4, right parenthesis and (7,2)(7,2)left parenthesis, 7, comma, 2, right parenthesis. use exact numbers.
The point-slope equation of the line is y-2=-2(x-7)
How will we find the equation of line?
First, we will find the slope of line using the given points then put slope and point in the formula to get equation of line.
We can find the equation as shown below:
Given points (6,4) and (7,2)
slope(m)= (2-4)/ (7-6)
m=-2/1
m=-2
The point slope form:
(y-y1) = m(x-x1)
y1=2, x1=7
putting in formula
(y-2) = -2(x-7)
y-2=-2(x-7)
Hence, the point-slope equation of the line is y-2=-2(x-7)
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Answer:
Step-by-step explanation:
Rashaad leans a 22-foot ladder against a wall so that it forms an angle of 65° with the ground. How high up the wall does the ladder reach? Round vour answer to the nearest hundredth of a foot if necessary.
The ladder reaches 19.938 foot high from the ground on the wall.
What is a Right Angled Triangle ?A right angled triangle is a triangle that has one of its angle measure as 90 degree.
It is given that
Ladder Length = 22 foot
The angle between the ladder and the ground is 65 degree.
When the ladder leans on a wall , the wall makes 90 degree with the ground and the ladder is the hypotenuse of the right angled triangle formed.
The figure is attached with the answer.
sin 65 = Height of the wall / Hypotenuse
0.9063 = Height of the wall / 22
Height of the wall = 19.938 foot
Therefore the ladder reaches 19.938 foot high from the ground on the wall.
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Answer:
19.94
Step-by-step explanation:
PLS HELP! Which statement is true about the given function?
The statement which is true about the given graph is that f(x)<0 in the interval (-∞,3) which is option 3.
Given Graph of a function
We have to choose a statement which is correct about the function whose graph is given.
The graph of a function tells us about the domain and range of the function. The values on y axis are the codomain of the function and the values on x axis are the values of domain.
When we see the graph we can find that x=-∞ to x=3 the values are negative means when we put the values of x less than 0 we will get negative number. For example if we put the value of x=-1, we will get -20 which is a negative number.
Hence the third statement is true for the given graph which is that it has values less than zero in the interval (-∞,3).
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When simplifying the fraction 2x/4, madison wrote 2x/4 = 2x. EXPLAIN WHY her answer is wrong and write the correct answer.
Answer:
x/2
Step-by-step explanation:
Madison didn't cancel the common factor of 2 and that 4 that is why she is wrong.
Hope this helps pls brainliest have a nice day :>
what is
x. 10-x 3 D N C X = [?]
Equations are written by equating the expressions to each other. The value of x is 7
Equations and expressionsEquations are written by Equating the expressions to each other.
Given the equation below:
10 - x = 3
Subtract 10 from both sides
10 - x - 10 = 3 - 10
-x = -7
Multiply both sides by -1
-(-x) = -(-7)
x = 7
Hence the value of x is 7
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Calculate the force acting on a body of mass 0.8kg (g=9.8*-2; F=mg)
The force acting on a body of mass 0.8 kg is F = 7.84 kg-m-s⁻² or F = 7.84 N
What is mass?A tangible body's mass is the amount of matter it possesses. It's also a metric of inertial or the resistance to velocity when a net force is exerted.
We have:
The mass of the body m = 0.8 kg
As we know,
F = mg
F is the force acting on the body and g is the acceleration due to gravity.
g = 9.8 m-s⁻²
F = (0.8)(9.8)
F = 7.84 kg-m-s⁻²
or
F = 7.84 N
Thus, the force acting on a body of mass 0.8 kg is F = 7.84 kg-m-s⁻² or F = 7.84 N
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Joaquin deposits $1,000 into an account that accrues 4% annual interest continuously compounded. What is the value of his investment after 3 years to the nearest cent?
Deposit: $1,000
Annual interest: 4% = 0.04
Years: 3
For this type of question, when the question asks you to "continuously compound", you use this formula: [tex]Pe^{rt}[/tex]
Solving:
[tex]1000e^{(0.04)(3)} \\1000e^{0.12} \\=1127.50[/tex]
The value of Joaquin's investment after 3 years = 1,127.50$
Which of the following sets represents the range of the diagram below? 2 3. 00 4 4 5 5 f(x) O A. {2, 4, 5) OB. (1, 3, 4, 5} OC. (2, 3, 4, 5, 6, 7} D. {1, 2, 3, 4, 5)
Answer:
D
Step-by-step explanation:
the answer is D because the range is the lowest possible value up to the highest possible value and when listed it doesn't repeat
Each of the performers at a circus convention is either a unicyclist, a mime or an aerial artist. The ratio of unicyclists to mimes is 3: 14 The ratio of unicyclists to aerial artists is 9 : 11 There are 88 aerial artists. What percentage of the performers are unicyclists? Give your answer to 2 d.p.
Answer:
14.52% are unicyclists
Step-by-step explanation:
First, we can use proportions to find the number of unicyclists at the convention. Since we know that the ratio of unicyclists to aerial artists is 9:11, and there are 88 aerial artists, we can set up the following equation:
[tex]\frac{9}{11}=\frac{x}{88}[/tex]
If we cross multiply, we get that 11x = (88)(9). After we divide through by 11 to isolate x, we get that x = (8)(9) = 72
Second, we have to figure out the number of mimes at the convention to figure out the total number of people there. We know that the ratio of unicyclists to mimes is 3:14, and the number of unicyclists is 72. So, we can set up the following proportion:
[tex]\frac{3}{14}=\frac{72}{y}[/tex]
If we cross multiply, we get that 3y = 1008, or y = 336 mimes
The total number of people at the convention is 336 mimes + 72 unicyclists + 88 unicyclists = 496. Now we have to figure out what percent of 496 is 72 (the number of unicyclists). If we let z = the percentage, we can simply set up an equation that says that 72 is z% of 496:
[tex]72=0.01z*496\\0.01z=0.14516\\z=14.52[/tex]
This means that approximately 14.52% of the performers are unicyclists.
Answer:
14.52%
Step-by-step explanation:
U/A = 9/11 and A = 88 multiply by 8/8 ( to get A=88 as given)
9/11 * 8/8 = 72/88 = U / A so U = 72
Then U/M = 3/14 multiply by 24/24 ( to get U = 72 as found above)
then U/M= 72 / 336 M = 336
U / ( A + U + M ) x 100% = 14.52 %
Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges.
help :((
25x^-4-99x^-2-4=0
How do I solve for this?
Given
[tex]25x^{-4} - 99x^{-2} - 4 = 0[/tex]
consider substituting [tex]y=x^{-2}[/tex] to get a proper quadratic equation,
[tex]25y^2 - 99y - 4 = 0[/tex]
Solve for [tex]y[/tex] ; we can factorize to get
[tex](25y + 1) (y - 4) = 0[/tex]
[tex]25y+1 = 0 \text{ or } y - 4 = 0[/tex]
[tex]y = -\dfrac1{25} \text{ or }y = 4[/tex]
Solve for [tex]x[/tex] :
[tex]x^{-2} = -\dfrac1{25} \text{ or }x^{-2} = 4[/tex]
The first equation has no real solution, since [tex]x^{-2} = \frac1{x^2} > 0[/tex] for all non-zero [tex]x[/tex]. Proceeding with the second equation, we get
[tex]x^{-2} = 4 \implies x^2 = \dfrac14 \implies x = \pm\sqrt{\dfrac14} = \boxed{\pm \dfrac12}[/tex]
If we want to find all complex solutions, we take [tex]i=\sqrt{-1}[/tex] so that the first equation above would have led us to
[tex]x^{-2} = -\dfrac1{25} \implies x^2 = -25 \implies x = \pm\sqrt{-25} = \pm5i[/tex]
HEELLLPPMEEEEEEEE PLS 30 pointss
Suppose that x≠0 and y≠0. We know from our work in this section that 1/x∙1/y is equivalent to 1/xy. Is it also true that 1/x+1/y is equivalent to 1/(x+y)? Provide evidence to support your answer.
Answer:
No
Step-by-step explanation:
Let's assume that x=2 and y=3.
1/2+1/3≠1/5
Also, when adding fractions, you cannot simply add the denominator. You have to make the denominators of all fractions the same and then add.
So, if you are given 1/x +1/y, you should get (y+x)/xy, not 1/(x+y)
There are 8 apples and 14 oranges in the bowl. What is the ratio of apples to total fruit in the bowl?
O a 7/11
Ob 4/7
Oc 4/11
Od 7/4
Answer:
C
Step-by-step explanation:
Solution
There are 8 apples in the bowl
There are 8 + 14 = 22 total fruits in the bowl.
Ratio apples / total = 8 / 22. But that is not the answer. You can divide top and bottom of the ratio by 2.
When you do that, you get 4/11 which is C
Answer: 4/11 or C
I'm renting to own a house for $80,000 I paid down $6000 leaving a balance of $74,000 For the past eight years I’ve paid 768.57 a month. How much have I paid from May 2014 to July 2022?
The total amount you have paid from May 2014 to July 2022 is $75,319.86
Balance of rentTotal cost of the house = $80,000Amount paid down = $6000Amount to balance = $74,000Amount paid per month = $768.57May 2014 to July 2022 = (12 × 8) + 2= 96 + 2
= 98 months
Total amount paid from May 2014 to July 2022 = $768.57 × 98 months
= $75,319.86
The total amount paid so far from May 2014 to July 2022 is $75,319.86
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A scientist claims that 9% of viruses are airborne. If the scientist is accurate, what is the probability that the proportion of airborne viruses in a sample of 533 viruses would differ from the population proportion by less than 3%
The probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% is 0.006.
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
μρ=ρ
The standard deviation of this sampling distribution of sample proportion is:
σρ=[tex]\sqrt \frac{p(1-p)}{n}[/tex]
The information provided is:
n = 533
p = 0.09
As the sample size is quite large, i.e. n = 533 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by a Normal distribution.
The mean and standard deviation are:
μρ=ρ=0.09
σρ=[tex]\sqrt \frac{p(1-p)}{n}[/tex]=[tex]\sqrt\frac{0.09(1-0.09)}{533}=0.01239[/tex]
Compute the probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% as follows:
[tex]p(p^-p > 0.03)=P(p^ > 0.12) \\=P(z > \frac{0.12-0.9}{0.012}) \\= P(Z > 2.5) \\= 1-P(Z > 2.5) \\ = 1- 0.993 \\ = 0.00621[/tex]
Thus, the probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% is 0.006.
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1. Vanessa and Renita are having a friendly competition at work. Their job is to unpack boxes. Vanessa has unpacked 3 fewer than twice the amount of boxes than Renita. Together they have unpacked 15 boxes. How many boxes did each uNpack
The number of boxes renita and Vanessa has unpacked each is 6 and 9 boxes respectively.
EquationNumber of boxes renita has unpacked = xNumber of boxes Vanessa has unpacked = 2x - 3Total boxes both unpacked = 15x + (2x - 3) = 15
x + 2x - 3 = 15
3x = 15 + 3
3x = 18
x = 18/3
x = 6
Therefore,
Number of boxes renita has unpacked = x
= 6 boxes
Number of boxes Vanessa has unpacked = 2x - 3
= 2(6) - 3
= 12 - 3
= 9 boxes
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Answer:
Step-by-step explanation:
The number of boxes renita and Vanessa has unpacked each is 6 and 9 boxes respectively.
Equation
Number of boxes renita has unpacked = x
Number of boxes Vanessa has unpacked = 2x - 3
Total boxes both unpacked = 15
x + (2x - 3) = 15
x + 2x - 3 = 15
3x = 15 + 3
3x = 18
x = 18/3
x = 6
Therefore,
Number of boxes renita has unpacked = x
= 6 boxes
Number of boxes Vanessa has unpacked = 2x - 3
= 2(6) - 3
= 12 - 3
= 9 boxes
Select the correct answer.
Convert sqrt3 + i to polar form.
The polar form of any complex number can be written as
[tex]z = |z| e^{i\arg(z)}[/tex]
where [tex]\arg(z)[/tex] is the argument of [tex]z[/tex], i.e. the angle it makes with the positive real axis in the complex plane.
If [tex]z=\sqrt3+i[/tex], then [tex]z[/tex] has modulus
[tex]|z| = \sqrt{\left(\sqrt3\right)^2 + 1^2} = \sqrt4 = 2[/tex]
and argument
[tex]\arg(z) = \tan^{-1}\left(\dfrac1{\sqrt3}\right) = \dfrac\pi6[/tex]
Then
[tex]\sqrt3 + i = 2e^{i\frac\pi6} = 2 \left(\cos\left(\dfrac\pi6\right) + i \sin\left(\dfrac\pi6\right)\right)[/tex]
pls help lol !!! i am unsure about this
The component form of the vectors shown is (-6, -5)
Difference of vectorsIn order to determine the component of the vectors shown, we will subtract the coordinate points from both each other.
Given the vector coordinates on the line. as (-5, -3) and (1, 2). Take the difference;
Difference = [(-5-1), (-3-2])
Difference = (-6, -5)
Hence the component form of the vectors shown is (-6, -5)
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Work out quickly will give brainiest
Sara has rs. 836 with her. she gives 9/11 of this to her sister. out of the remaining money, she gives rs. 38 to her brother. she now has a fraction of the original amount is left with her?
The original amount Sara has left is 172/209
The calculation can be done as follows
Let y represent the amount left
9/11 × 836
= 7524/11
= 110
Y can be calculated as follows
Y + 38 +110= 836
148 + Y= 836
Y= 836 - 148
Y= 688
Therefore the fraction is
688/836
= 172/209
Hence the fraction of the original amount left is 172/209
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You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available to be sold in this lottery. In this lottery there are one $475 prize, two $95 prizes, and four $30 prizes. Find your expected gain or loss. (Round your answer to two decimal places.)
There is a profit of $39.7.
It is given that there 100 tickets costing $10 per ticket.
You must look first for the probability of the 4 prizes which are $475, $195, $30, and no prize.
P ($475 prize) = 1/100 or 0.01
P ($95 prize) = 2/100 or 0.02
P ($30 prize) = 4/100 or 0.04
P (No prize) = 100/100 – 1+2+4/100 =93/100 .93
Expected gain or loss is computed by: (P(x)* n)
E= (475-10)*.01 + (95-10)*0.02 + (30-10)* 0.04 + (-10)*.93
= 46.5 + 1.70 + 0.8 – 9.3
E = 39.7
There is a profit of $39.7.
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Please help me on this geometry question
Question: 7 After seven years, the age of father will be 4 times the age of his daughter. If x stands for the present age of the daughter and y stands for the present age of the father, which of th following linear equations represents the above statement?
x+y-17=0
2xy-187=0
x+y+17=0
2xy+187=0
Answer:
Here is your answer
Step-by-step explanation:
Step -1: Forming equations.
Let, present age of son = x
And, present age of father = 3x+3
3 years later, age of son = x+3
age of father = 3x+3+3=3x+6 ...(i)
According to the given condition, age of father = 10+2(x+3) ...(ii)
Step -2: Solving for x
From (i) and (ii)
∴3x+6=10+2(x+3)
⇒3x+6=10+2x+6
⇒3x−2x=10+6−6
⇒x=10
∴Present age of son = 10
and present age of father = 3x+3=3×10+3=33
Hence, son’s present age is 10 years and father’s
Please explain this.
Angles EBA and DBC are congruent. The three angles EBA, EBD, and DBC are together supplementary, so their measures sum to 180°. This means
x + (4x + 11°) + x = 180°
6x + 11° = 180°
6x = 169°
x = (169/6)°
Then the measure of angle D is
2x + 8° = 2 (169/6)° + 8° = (193/3)°
The interior angles of any triangle sum to 180°, so if y is the measure of angle C, we have
(169/6)° + (193/3)° + y = 180°
y = (175/2)° = 87.5°
Suppose a large shipment of laser printers contained 12% defectives. If a sample of size 406 is selected, what is the probability that the sample proportion will be greater than 13%
The probability that the sample proportion will differ from the population proportion by less than 6% is 0.992.
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
цр = р
The standard deviation of this sampling distribution of sample proportion is:
бр = √ρ(1-ρ)÷n
The information provided is:
ρ = 0.22
ⁿ = 276
As the sample size is large, i.e. n = 276 > 30, the Central limit theorem can be used to approximate the sampling distribution of sample proportion.
Compute the value of P(р-p<0.06) as follows:
P(р-p<0.06) = P(р-p ÷ бp<0.06 ÷√0.22(1 - 0.22) ÷ 276
= P ( Z < 2.41 )
= 0.99202
≈ 0.992
Thus, the probability that the sample proportion will differ from the population proportion by less than 6% is 0.992.
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At times, latitudes with values higher than ________ degrees can have ~ 24 hours of continuous sunshine.
At times, latitudes with values higher than 66.5 degrees can have ~ 24 hours of continuous sunshine.
Locations above the Arctic Circle (north of latitude 66.5 degrees, 90 degrees minus the tilt of the Earth's axis) are exposed to 24-hour sunlight. Below the Arctic Circle (latitude 66.5 degrees south), there is 24-hour darkness.
When at the equator, the sun is directly above – at the poles, the sun is on the horizon. However, regardless of the current location (from the pole to the equator), all parallels are bisected, so we have 12 hours a day and 12 hours a night in all locations.
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Can someone help me please.
Answer: A
Step-by-step explanation:
The angle opposite the shortest side in a triangle has the smallest measure.
In right triangle ABC, ZB is the right angle and mZC = 30°. If AC= 10, what Is AB?
OA 5
OB. 5√3
OC 20
OD. 5√3
Answer:
i think its c wouldve helped if i saw a pic of the triangle tho
Step-by-step explanation:
The length of side AB is 5√3.
Option B is the correct answer.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
We can use trigonometry to solve this problem.
Let's start by finding the length of BC.
sin(30°) = BC/AC
sin(30°) = BC/10
BC = 5
Now, we can use the Pythagorean theorem to find the length of AB.
AB² = AC² - BC²
AB² = 10² - 5²
AB² = 75
AB = 5√3
Therefore,
The length of side AB is 5√3.
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Find the measure of angle ABD.
Answer:
x=58
Step-by-step explanation:
Exterior angle of one interior angle in a triangle is equal to the sum of the other two remote interior angles. (Ext. Angle Th.) So, 3x-32=84+x
2x=116
x=58
HEEEEEEEEEELP i dont get it
The ordered pair is (-9, -25) and the word statement is if x is equal to -9, then the value of h(x) is -25
Functions and tablesFrom the given table, f(x) = y means that the corresponding value of y given a value x.
For the function h(-9), we need to find the equivalent value of h(x) when x is -9. Hence h(-9) is -25
The ordered pair is (-9, -25) and the word statement is if x is equal to -9, then the value of h(x) is -25
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