Answer:
the guy is right
Step-by-step explanation:
Find the equation of the parabola with focus (2, 3) and directrix y = -1.
es
Answer:
Below in bold.
Step-by-step explanation:
Let (x, y) be a point on the parabola. As the graph is a parabola, the distance of this point to the focus is equal to the distance of this point from the directrix. So:
√(( x - 2)^2 + (y - 3)^2) = y - (-1)
Squaring both sides:
(x - 2)^2 + (y - 3)^2 = (y + 1)^2
x^2 - 4x + 4 + y^2 - 6y + 9 = y^2 + 2y + 1
x^2 - 4x + 4 + 9 - 1 = 2y + 6y
8y = x^2 - 4x + 12
y = 1/8(x^2 - 4x + 12)
or we can write it as
y = 1/8x^2 - 1/2 x + 3/2.
Solve for x: 2(10-2x) = 4(3x + 1). Write your answer as a fraction.
Answer:
[tex]\boxed{x=1}[/tex]
Step-by-step explanation:
[tex]2(10-2x) = 4(3x + 1)[/tex]
[tex]\sf Expand \ brackets.[/tex]
[tex]20 - 4x = 12x + 4[/tex]
[tex]\sf Subtract \ 12x \ and \ 20 \ from \ both \ sides.[/tex]
[tex]20 - 4x - 12x - 20 = 12x + 4 - 12x - 20[/tex]
[tex]-16x = -16[/tex]
[tex]\sf Divide \ both \ sides \ by \ -16.[/tex]
[tex]\displaystyle \frac{-16x}{-16} =\frac{-16}{-16}[/tex]
[tex]x=1[/tex]
━━━━━━━☆☆━━━━━━━
▹ Answer
x = 1
▹ Step-by-Step Explanation
2(10 - 2x) = 4(3x + 1)
Simple terms are written last:
2(-2x + 10) = 4(3x + 1)
Distributive Property:
-2 * 2x + 2 * 10 = 4 * 3x + 4
x = 1
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
HELP ME PLEASE !! A duck paddles 4 yards downstream in 24 seconds. It takes the duck 40 seconds to paddle the same distance upstream. How fast can the duck paddle in still water ? What is rate of the current? Duck speed: _____ Current: ________ And if possible you can show me the steps?
Answer:
1. duck will travel in still water paddles 4 yards = 38,7 sec
up stream speed = 0,63 mph
down stream speed = 0,68 mph
The box plots display the same data set for the number of touchdowns a quarterback threw in 10 seasons of play. Including outlier: A number line goes from 5 to 30. The whiskers range from 5 to 29, and the box ranges from 18 to 26. A line divides the box at 21.5. Excluding outlier: A number line goes from 5 to 30. The whiskers range from 17 to 29, and the box ranges from 19 to 27. A line divides the box at 21. There is an asterisk at 5. Complete the statements describing the effect of the outlier on the measures of variability. The outlier of the data set is . The range of the data set including the outlier is more than the one excluding the outlier. The interquartile range of the data set including the outlier is more than the one excluding the outlier. The outlier had the most effect on the .
Answer:
5
12
0
range
Step-by-step explanation:
i just did it, these are the right answers.
Answer:
5,12,0, and the last answer is range
Step-by-step explanation:
Did it on Edge2021. Hope this helps!
Kaitlyn can build a shed in 6 days. Mark can build the same shed in 8 days. Which equation can be used to find d, the number of days it would take Kaitlyn and Mark to build the shed together? Rate (Sheds per Day) Time (Days) Fraction Completed Kaitlyn One-sixth d One-sixth dd Mark One-eighth d One-eighth dd One-sixth d minus one-eighth d = 48 One-sixth d + one-eighth d = 48 One-sixth d minus one-eighth d = 1 One-sixth d + one-eighth d = 1
Answer:
One-sixth d + one-eighth d = 1
Step-by-step explanation:
When they work together, their rates of completion add. They want to build one shed, so the number of sheds being built is ...
(Kaitlyn's sheds per day)×(days Kaitlyn works) +(Mark's sheds per day)×(days Mark works) = 1 shed
(1/6)d + (1/8)d = 1 . . . . matches the last choice
2x3 + 10x2 − 4x2y − 20xy
Answer:
-20xy -8y+26
Step-by-step explanation
First Multiply 2 by 3.
6 + 10 x 2 - 4 x (2y) - 20xy
Then Multiply 10 by 2.
6+20-4x(2y)-20xy
After that Multiply 2 by -4.
6+20-8y-20xy
Lastly add 6 and 20.
26 -8y -20xy
three babies A,B and C cry out at interval time. Baby A cries out at every 20 mins, while B cries out at every 30 mins and C cries out at every 40 mins. if they are observed at the same time, after what time will the three of them cry together?
A. after 20 minutes
B. after 30 minutes
C. after 40 minutes
D. after 120 minutes
1. Move the slider to choose a scale
factor greater than 1. Where is point
P"?
A company determined that for each $1 increase in the price of their product, the
number of items sold will decrease by 2. Their predicted weekly profit with a
price increase of x dollars is represented by the function
f(x)= – 2x2+20x +150.
By how many dollars
should they increase the price of their product to
maximize their weekly profits?
15
200
150
5
Answer:
To have maximum profit, the price must be increased by 5,
Step-by-step explanation:
Given that the price increase function is:
f(x) = -2x² + 20x + 150,
For maximum profit, then f(x) = 0.
Putting f(x) = 0, we have
-2x² + 20x + 150 = 0
Or
x² - 10x - 75 = 0
(x + 5)(x - 15) = 0
x = -5
Or
x = 15
Again, differentiating f(x) and equating to zero, we have
-4x + 20 = 0
4x = 20
x = 20/4
= 5
To have maximum profit, the price must be increased by 5,
You buy a new computer for $1,500. The value of the computer decreases by 6%
every year. How much is the computer worth after 4 years?
$999.80
$1,171.05
$1,008.50
$1,225.35
Answer:
$1171.05
Step-by-step explanation:
1500 × (1-(6 / 100))⁴
Answer:
Hey there!
Each year, the computer is (100-6), or 94% of it's original value.
Thus, we have:
Original: 1500
First year: 1500(0.94)
Second year: 1500(0.94)(0.94)
Third year: 1500(0.94)(0.94)(0.94)
Fourth year: 1500(0.94)(0.94)(0.94)(0.94)
Fourth year: 1171 dollars.
Hope this helps :)
The university theater uses a combination of one letter (A - Z) and two digits (0 - 9) to identify their reserved seats. How many reserved seats are
possible using a combination of one letter followed by two digits. EXPLAIN how to solve this problem in your own words.
Answer:
Hey There!! The answer to this is Correct option: 1) 2600 The letter has a total of 26 possible values (from 'a' to 'z'), and each digit has a total of 10 possible values (from 0 to 9).
So, to find the number of reserved seats possible, we just need to multiply the number of possible values of each letter and digit.
We have one letter and two digits, so we have:
26 * 10 * 10 = 2600 possible reserved seats
Thus, Correct option: 1)
Hope It Helped!~ ♡
ItsNobody~ ☆
The total number of combinations of one letter followed by two digits is 2600 option (1) 2600 is correct.
What are permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
The missing options are:
1.) 26002.) 2343.) 2604.) 2106We have:
The university theater uses a combination of one letter (A - Z) and two digits (0 - 9) to identify their reserved seats
As we know, in the alphabet(A to Z) there are the 26 letters and total number of digits (0 to 9) is 10
A total number of combinations of letters followed by two digits can be calculated as follows:
As we have one letter and two digits
= 26×10×10
= 2600
, so we have:
26 * 10 * 10 = 2600 possible reserved seats
Thus, the total number of combinations of one letter followed by two digits is 2600 option (1) 2600 is correct.
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Which function is the inverse of f(x) = -5x-4?
1
4
1
4
O 8(x)3x -
F () --3x+
O F1(x) = -4x+5
Of '(x) = 4x+4
Answer:
The inverse is -1/5x -4/5
Step-by-step explanation:
f(x) = -5x-4
y = -5x-4
Exchange x and y
x = -5y -4
Solve for y
Add 4 to each side
x+4 = -5y
Divide by -5
-1/5x -4/5 = -5y/-5
-1/5x -4/5 = y
The inverse is -1/5x -4/5
Answer:
[tex]\huge\boxed{f^{-1}(x) = -\frac{x+4}{5}}[/tex]
Step-by-step explanation:
[tex]f(x) = -5x-4[/tex]
Replace y = f(x)
[tex]y = -5x-4[/tex]
Exchange values of x and y
[tex]x = -5y -4[/tex]
Solve for y
[tex]x = -5y - 4[/tex]
Adding 4 to both sides
[tex]x + 4 = -5y[/tex]
Dividing both sides by -5
[tex]y = -\frac{x+4}{5}[/tex]
Replace y = [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x) = -\frac{x+4}{5}[/tex]
What is the relationship between Za and Zb
A- vertical angles
B- complementary angles
C-supplementary angles
D-none of the above
their sum is 90° so they're complementary
write the slope- intercept form of the equation for the line
y=-8/7x-3/2
y=7/8x-3/2
y=-7/8x-3/2
y=-3/2x+7/8
Answer: All options are in slope-intercept form
i hope this helps .
Step-by-step explanation:
1.
[tex]\mathrm{For\:a\:line\:in\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is}\:\\\mathbf{m}\:\mathrm{and}\:\mathbf{y}\:\mathrm{intercept\:is}\:\mathbf{b}\\y=-\frac{8}{7}x-\frac{3}{2}\\[/tex]
2.
[tex]\mathrm{For\:a\:line\:in\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is}\:\\\mathbf{m}\:\mathrm{and}\:\mathbf{y}\:\mathrm{intercept\:is}\:\mathbf{b}\\\\y=\frac{7}{8}x-\frac{3}{2}[/tex]
3.
[tex]\mathrm{For\:a\:line\:in\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is}\:\\\mathbf{m}\:\mathrm{and}\:\mathbf{y}\:\mathrm{intercept\:is}\:\mathbf{b}\\\\y=-\frac{7}{8}x-\frac{3}{2}[/tex]
4.
[tex]\mathrm{For\:a\:line\:in\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is}\:\\\mathbf{m}\:\mathrm{and}\:\mathbf{y}\:\mathrm{intercept\:is}\:\mathbf{b}\\\\y=-\frac{3}{2}x+\frac{7}{8}\\[/tex]
can somewon help me plz
Answer:
=1468 in ^3
Step-by-step explanation:
Find the volume of the container as if the corner was still there
V = l*w*h
V = 10 * 10 *15
= 1500
Subtract the missing corner
The volume of the missing piece is
V = l*w*h
= 2*4*4
= 32
V = 1500-32
=1468 in ^3
Answer:
It is 1468 inches cubed.
Step-by-step explanation:
You first want to the volume of the entire shape by multiplying the length, width, and height, which is 10, 10, and 15. They multiply to become 1500 inches cubed. You then want to find the volume of the smaller rectangular shape, so multiply 4, 4, and 2. And that equals 32. So subtract the volume of the big shape that we found, 1500, by the volume of the small one, which is 32. That equals 1468 inches cubed. You want to subtract the volume of the big one by the small one because the volume is just the big shape with a small shape cut out of it. So whenever you get one of these problems, just find the volume of both shapes, the big one and the small one, and subtract the small one from the big one.
Determine what type of model best fits the given situation: Farmer Joe has 1,000 bushels of corn to sell. Presently the market price for corn is $5.00 a bushel. He expects the market price to increase by $0.15 per week. For each week he waits to sell, he loses ten bushels due to spoilage. A. none of these B. exponential C. quadratic D. linear
Answer:
The correct option is;
C. Quadratic
Step-by-step explanation:
The given information are;
The quantity of corn Farmer Joe has to sell = 1,000 bushels
The present market price for corn = $5.00 a bushel
The amount by which he expects the market price to rise per week =$0.15
The number of bushels lost to spoilage per week = 10
Therefore, we have;
The value of the corn = Amount of corn left × Price of corn
The price of the corn per bushel with time = 5 + 0.15×t
The amount of corn left = 1000 - 10×t
Where;
t = Time in minutes
Therefore, the total value of corn = (1000 - 10×t)×(5 + 0.15×t) = -1.5·t²+100·t+5000 which is a quadratic model.
Therefore, the correct option is a quadratic model.
The tee for the fifth hole on a golf course is 355 yards from the tee. On that hole, Marsha hooked her ball to the left, as sketched below. Find the distance between Marsha’s ball and the hole to the nearest tenth of a yard.
Answer:
184
Step-by-step explanation:
Find the perimeter of the triangle
Answer:
26 units
Step-by-step explanation:
Answer:
657.88 i guess becuz by using pythagoras i got 320 for the hypotenous
How does it do? thank you very much
sorry this subject is physic.
Name five fractions whose values are between 1/8 and 1/5
The five fractions whose values are between 1/8 and 1/5 will be 13/100, 7/50, 3/20, 4/25, and 9/50.
What is a number line?A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.
The fraction numbers are given below.
1/8 and 1/5
Convert the fraction number into decimal numbers. Then we have
0.125 and 0.20
The five fractions whose values are between 1/8 and 1/5 will be given as,
0.13, 0.14, 0.15, 0.16, 0.18
13/100, 14/100, 15/100, 16/100, 18/100
13/100, 7/50, 3/20, 4/25, 9/50
The five fractions whose values are between 1/8 and 1/5 will be 13/100, 7/50, 3/20, 4/25, and 9/50.
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A rectangular prism has a volume of 285.6. cubic feet. The prism is 12 feet long and 3.4 feet wide. What is the height of the prism? A. 7 ft B. 15 ft C. 19 ft D. 22 ft Please include all work!!
Answer:
A. 7 ft
Step-by-step explanation:
Volume is Length * Width * Height
12 * 3.4 * Height = 285.6
285.6 / 12 = 23.8
23.8 / 3.4 = 7
Given the regular decagon, what is the measure of each numbered angle? A. m∡1 = 72°; m∡2 = 18°; m∡3 = 36° B. m∡1 = 18°; m∡2 = 36°; m∡3 = 72° C. m∡1 = 36°; m∡2 = 72°; m∡3 = 18° D. m∡1 = 36°; m∡2 = 18°; m∡3 = 72°
Answer:
D. m∡1 = 36°; m∡2 = 18°; m∡3 = 72°
Step-by-step explanation:
The 10 central angles are all the same for the regular decagon, so each is 1/10 of 360°. Angle 1 is 36°.
Angle 2 is half of angle 1, since the altitude shown is an angle bisector. Angle 2 is 18°.
Angle 3 is the complement of angle 2. It is the other acute angle in the triangle that has angle 2 marked. Angle 3 is 72°.
what is 10% of $14,580
Answer:
1458
Step-by-step explanation:
10% * 14580
Change to decimal form
.10 * 14580
1458
Answer:
1458
Step-by-step explanation:
14,580 multiply that by .1
Given: m || n and p is a transversal
Prove: mAngle2 = mAngle7
Horizontal and parallel lines m and n are cut by transversal p. On line m where it intersects line p, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 2, 4, 3. On line n where it intersects line p, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 5, 6, 8, 7.
What is the missing reason in the proof?
Statement Reason
1. m || n and p is a transversal 1. given
2. ∠2 ≅ ∠3 2. ver. ∠s theorem
3. m∠2 = m∠3 3. def. of congruent
4. ∠3 ≅ ∠7 4. corr. ∠s theorem
5. m∠3 = m∠7 5. def. of congruent
6. m∠2 = m∠7 6. ?
corresponding angles theorem
alternate interior angles theorem
transitive property
subtraction property
Answer:
∠2 ≅ ∠6
Step-by-step explanation:
An isotope of lead, 201Pb, has a half-life of 8.4 hours. How many hours ago was there 70% more of the substance? (Round your answer to one decimal place.) hr
Step-by-step explanation:
half life time-50%-8.4hr
so for 10%- 8.4/5=1.68 hr
now for 70%
1.68 × 7 = 11.76 hrs
to one decimal place - 11.8hrs
11.8 hours ago, there were 70% more of the substance if an isotope of lead has a half-life of 8.4 hours.
What is half-life?Half life is the time that it takes for half of the original value of some amount of a radioactive element to decay.
Half-life period - 50% -8.4hours
so for 10%- 8.4/5 = 1.68 hour
now for 70%
1.68 × 7 = 11.76 hours
To one decimal place - 11.8hours
Hence, 11.8hours is the answer.
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If f(x) = x2 – 2x and g(x) = 6x + 4, for which value of x does (f+g)(x) = 0?
O -4
O-2
O 2
O 4
Answer:
x = -2
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask ;)
The value of the function (f+ g)(x) = 0 then x = -2.
What is Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given:
f(x) = x² - 2x and g(x) = 6x + 4
As, (f+g)(x) = 0
x² - 2x + 6x + 4 = 0
x² + 4x + 4 =0
x² + 2x + 2x + 4 = 0
x(x+2) + 2 (x +2 )= 0
(x + 2)(x+2) = 0
(x+ 2)²= 0
x+ 2= 0
x = -2
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3. State the general version of the recursive formula.
72,54, 36, 18,0
Answer:
a(1) = 72
a(n) = a (n-1) - 18
Step-by-step explanation:
This is a simple series of multiplication of 18 . If we divide all the numbers by 18 we get
72/18, 54/18, 36/18. 18/18, 0/18
4 , 3 , 2 , 1 , 0
So we can see that the numbers are in decreasing order as the multiples of 18.
in other words the first term is a= 72
from which we subtract 18 and get 54 and so on.
So the general rule would be
a(1) = 72
a(n) = a (n-1) - 18
Where n and (n-1 ) are subscripts. We are just subtracting 18 from the number to get the answer.
72-18= 54
54-18= 36
36-18= 18
18-18=0
3(2x - 4) = 4(x + 1)
X=__?
Answer:
8!
Step-by-step explanation:
SIMPLIFY
6X-12=4X+4
PUT LIKE TERMS TOGETHER
6X-4X=4+12
SIMPLIFY
2X=16
X=16/2
X=8
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
Hey there! I'm happy to help!
First, let's use the distributive property to remove the parentheses. We multiply the number on the outside by each number on the inside.
3(2x-4)
We multiply the 3 by the 2x, giving us 6x, and we multiply the 3 by the -4, giving is -12.
4(x+1)
We do 4 times x which is 4x, and 4 by 1, which is 4.
This gives us this equation.
6x-12=4x+4
Now, we want to solve for x. We want to move all the numbers to the right side and all the x's to the left side so we can figure out what x is equal to.
6x-12=4x+4
We add 12 to both sides, canceling it out on one side and adds it to the other to keep the equation at the same value.
6x=4x+16
We subtract 4x from both sides.
2x=16
We divide both sides by 2.
x=8
Have a wonderful day! :D
What is 22% of $900?
Answer:
198
Step-by-step explanation:
Of means multiply and 22% as a decimal is 0.22, so multiply 0.22 by 900.
900*0.22=198
Answer:
198
Step-by-step explanation:
22% of 900
of means multiply
22% * 900
Change to decimal form
.22 * 900
198
Plot the function
y = (x + 1)(x - 3) by following these steps:
4
Step 1: Plot the x-intercepts of the function.
Answer:
Zoom it to see well
Step-by-step explanation:
The equation of the parabola is y = (x - 1)² - 4. Then the vertex of the parabola is at (1, -4) and the parabola passes through (0, -1) and (0, 3).
What is the parabola?It is the locus of a point that moves so that it is always the same distance from a non-movable point and a given line. The non-movable point is called focus and the non-movable line is called the directrix.
The equation is given below.
y = (x + 1)(x - 3)
We know that the equation is a parabolic equation.
And the value of y at -1 and 3 is zero.
The equation can be written as
y = x² - 2x -3
y = (x - 1)² - 4
And the vertex of the parabola is at (1, -4).
The graph is shown below.
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