Answer:
k = r/m
Step-by-step explanation:
Simply divide both sides of the equation by m to isolate k and get your answer:
r = mk
r/m = k/m
r/m = k
Identify the Minimum value of the function y=x^2+6x+ 9
====================================================
Explanation:
You can factor x^2+6x+9 into (x+3)^2, which turns into 1(x - (-3) )^2 + 0
So y = x^2+6x+9 becomes y = 1(x - (-3) )^2 + 0
That matches with vertex form y = a(x-h)^2 + k
The vertex is (-3,0). The y coordinate of the vertex directly tells us the minimum value. We know we have a minimum because a = 1 is positive. If a < 0, then we'd have a max y value instead.
-------------------
Alternatively, compare y = x^2+6x+9 to the form y = ax^2+bx+c
We see that a = 1, b = 6, c = 9
The x coordinate of the vertex is
h = -b/(2a)
h = -6/(2*1)
h = -3
The x coordinate of the vertex is x = -3. Plug this into the original equation to find the y coordinate of the vertex
y = x^2 + 6x + 9
y = (-3)^2 + 6(-3) + 9
y = 9 - 18 + 9
y = -9 + 9
y = 0
The y coordinate of the vertex is y = 0. This is the smallest y output possible.
MIXED APPLICATIONS
21. In 1960, the average speed of passenger
aircraft within the U.S. was 235 miles per
hour. By 1978 the average speed was 1.74
times that amount. To the nearest whole
number, what was the average speed in 1978?
Help mepleaee
Answer:
Average speed of passenger aircraft in 1978 is 408.9 mph
Step-by-step explanation:
Here, in the question, we are tasked with giving the value of the average speed of the passenger aircraft in the US for the year 1978, given that it is a certain multiple of the value in 1960.
So what we will be doing here is to get the value of the average speed and it can be gotten by multiplying the average speed in 1960 by the multiple to which the speed is, now in 1978.
From the question, we can write a formula for this;
Average speed of passenger aircraft in 1978 = 1.74 * average speed of passenger aircraft in 1960
From the question, we have that the average speed of passenger aircraft in 1960 = 235 mph
Thus,
Average speed of passenger aircraft in 1978 = 1.74 * 235 = 408.9 mph
Find the missing side or angle.
Round to the nearest tenth.
B=110°
C= 30°
a=12
c=[ ? ]
Hope you understand :)
The value of angel A = 40 and side= 9.3 cm
What is sine law?The ratio of the side and the corresponding angle of a triangle is equal to the diameter of the circumcircle of the triangle. The sine law is can therefore be given as,
a/ sin A= b/ sin B= c/ sin C
The law of sines formula is used for relating the lengths of the sides of a triangle to the sines of consecutive angles. It is the ratio of the length of the side of the triangle to the sine of the angle thus formed between the other two remaining sides. The law of sines formula is used for any triangle apart from SAS triangle and SSS triangle. It says,
a/sin A = b/sin B = c/sin C
where,
a, b, and c are the lengths of the triangle
A, B, and C are the angles of the triangle.
Using angle sum property,
<A + <B + <C= 180
<A + 110 + 30 = 180
<A = 180- 140
<A= 40
Now, Using law
a/ sin A= b/ sin B= c/ sin C
12/sin 40 = c/ sin 30
c= 9.3
Learn more about sine law here:
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Matt is a quarterback on the local football team. In the first quarter, Matt threw eight passes. Three passes were completions for gains of 12, 17, and 6 yards, while two passes were completions for losses of 2 yards and 5 yards. The other three passes were incompletions. What was the total accumulated yardage for Matt in the first quarter? Pleeease help I'll award brainliest!!!
Answer:
I think it's 28 yards gained.
Step-by-step explanation:
12 + 17 + 6 = 35
2 + 5 = 7
35 - 7 = 28
Please tell me if I'm wrong
Solve the equation 3/2(y-1) =y+5 and represent the solution on number line and on the cartesian plane...... pls solve it and spam answers will be reported and if it is truly the correct answer i will 100% sure mark it as brainleist
Answer:
y = 13
Step-by-step explanation:
Step 1: Distribute
3/2y - 3/2 = y + 5
Step 2: Subtract y on both sides
1/2y - 3/2 = 5
Step 3: add 3/2 on both sides
1/2y = 13/2
Step 4: Divide both sides by 1/2
y = 13
Answer:
y = 13.
Step-by-step explanation:
3/2(y-1) = y+5
3/2y - 3/2 = y + 5
3/2y - y = 5 + 3/2
1/2y = 6 and 1/2; 6.5; 13/2
y = 13.
To check out work...
3/2(13 - 1) = 13 + 5
3/2(12) = 18
3 * 6 = 18
18 = 18
On a number line, all you need to do is plot a point where it says 13. On a cartesian plane, you would have a horizontal line that expands infinitely in each direction, where y = 13.
Hope this helps!
PLEASE HELP!!! PICKING BRAINLIEST ANSWER!
Equation: [tex]2x^2 -2x = 1[/tex]
Answer:
I hope it will help you...
Using a sheet of graph paper, solve the following system of equations graphically. Be sure to show any work, use a straight edge, and be neat. When you are finished, enter the solution set in the box below and turn in your graph paper to your teacher.
Answer:
(-1, 1)
Step-by-step explanation:
The solution is where the 2 graphs intersect.
Please please help me! Here is a graph of y=7-x for values x from 0 to 7.
Answer:
Step-by-step explanation:
hello,
pls find below the graph
we need to find the point of intersection between both lines
which is (4,3)
hope this helps
The solution for the given system of linear equations is (4, 3).
Given that, here is a graph of y=7-x for values x from 0 to 7.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
The given system of linear equations
y=7-x -------(I) and y=x-1 -------(II)
From equation (I) and (II),
7-x=x-1
⇒ 2x=8
⇒ x=4
So, y=7-x=3
Thus, (x, y)=(4, 3)
Therefore, the solution for the given system of linear equations is (4, 3).
To learn more about the graph visit:
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Please Help me I am struggling a lot and I would be very grateful!!!
If 180°<α<270°, cos α= −8/17, 270°<β<360°, and sin β= −4/5, what is sin(α+β)?
Answer:
[tex]\sin(\alpha+\beta) = -0.153[/tex]
Step-by-step explanation:
Let determine the angles behind each trigonometric expression:
[tex]\cos \alpha = -\frac{8}{17}[/tex]
[tex]\alpha = \cos^{-1}\left(-\frac{8}{17} \right)[/tex]
Given that [tex]180^{\circ}< \alpha < 270^{\circ}[/tex], the value of [tex]\alpha[/tex] is:
[tex]\alpha \approx 241.928^{\circ}[/tex]
[tex]\sin \beta = -\frac{4}{5}[/tex]
[tex]\beta = \sin^{-1}\left(-\frac{4}{5} \right)[/tex]
Given that [tex]270^{\circ}< \beta <360^{\circ}[/tex], the value of [tex]\beta[/tex] is:
[tex]\beta \approx 306.870^{\circ}[/tex]
The sine function of the sum of angles can be determined by the following identity:
[tex]\sin(\alpha + \beta)=\sin \alpha \cdot \cos \beta + \sin \beta \cdot \cos \alpha[/tex]
If [tex]\alpha \approx 241.928^{\circ}[/tex] and [tex]\beta \approx 306.870^{\circ}[/tex], then:
[tex]\sin (241.928^{\circ}+306.870^{\circ}) = (\sin 241.928^{\circ}) \cdot (\cos 306.870^{\circ}) + (\sin 306.870^{\circ})\cdot (\cos 241.928^{\circ})[/tex][tex]\sin(241.928^{\circ}+306.870^{\circ}) = -0.153[/tex]
please help to solve this question
Find H.C.F
i) x^3-y^3, x^6-y^6, x^4+ x^2y^2+y^4
Answer:
No Like terms
Step-by-step explanation:
x^3-y^3= No like terms (its simplified)
x^6-y^6= No like terms (its simplified)
x^4+ x^2y^2+y^4 = No like terms (its simplified)
Hope this helps! Have a nice day :)
Answer:
x^2+xy+y^2
Step-by-step explanation:
x^3-y^3= (x-y)((x^2+xy+y^2)x^6-y^6=(x^3+y^3)(x^3-y^3)= (x^3+y^3)(x-y)(x^2+xy+y^2)x^4+ x^2y^2+y^4= x^4+2x^2y^2+y^4 - x^2y^2= (x^2+y^2)^2 -x^2y^2=(x^2+xy+y^2)(x^2-xy+y^2)HCF is x^2+xy+y^2 as it is the factor of all three polynomials
Can someone help with this trig ? pls
Answer:
45°
Step-by-step explanation:
To find you answer, we take the inverse sin(√2/2). When you plug that into your calc, you get 45°.
Alternatively, if you learned and remembered your unit circle, inverse sin(√2/2) would be π/4.
There are d black and brown horses in a field. There are 16 more black horses than brown horses. Of the horses in the field, only 25% of them are brown. How many are black?
Answer: 24 black horses
Step-by-step explanation:
Let the number of black horses = bl and
The number of Brown horses = br
Total number of horses = d
Of the horses in the field, only 25% of them are brown. That is,
25% of d = br
0.25d = br ........ (1)
The remaining horses are black. Which will be 100% - 25% = 75%. That is,
75% of d = bl
0.75d = bl ........(2)
But according to the question, there are 16 more black horses than brown horses. That is,
bl = br + 16 ..... (3)
The total number of horses d will be
d = br + bl ...... (4)
Substitute bl in equation 3 into equation 4
d = br + br + 16
d = 2br + 16 ..... (5)
Substitutes equation (1) into the equation (5)
d = 2( 0.25d ) + 16
d = 0.5d + 16
Collect the like terms
d - 0.5d = 16
0.5d = 16
d = 16/0.5
d = 32
Substitute 32 for d in equation (2).
bl = 0.75 × 32
bl = 24 horses.
Therefore, 24 horses are black.
The height of a model rocket is 4% of the height of the actual rocket. The model is 2m high. How high is the actual rocket?
Answer:
50m
Step-by-step explanation:
The model rocket is 4% of the actual rocket and it is 2m high
That means that 4%=2m
4 fits into 100, 25 times so multiply both by 25:
100%=25*2m
100%=50m
100% being the actual rocket
hope this helped!
What is the measure of angle x?
Linear pair of angles
30
Answer:
150°
Step-by-step explanation:
every line is equal to 180°. To find an angle, like this one, you have to subtract 30° from 180°. Therefor the answer is 150°.
If you need a further explanation just let me know
If function ghas the factors (x-7) and (x + 6), what are the zeros of function g?
Answer:
x = 7, -6
Step-by-step explanation:
Since they already give you the binomial factors, all you need to do is set them equal to 0 to find your roots:
x - 7 = 0
x = 7
x + 6 = 0
x = -6
Answer:
The zeros are 7 and -6Step-by-step explanation:
(x-7)(x+6)=0
x-7=0/(x+6)
x cannot be -6
x-7=0
x=7
x+6=0/(x-7)
x+6=0
x=-6
The zeros are 7 and -6
I'm really confused, can you please help me
Answer: y=8
Step-by-step explanation:
Since DF is bisected, it means but in half. This means DU and UF are equal in length. We can set them equal to each other to find y.
2y=16 [divide both sides by 2]
y=8
Answer:
y=8
Step-by-step explanation:
when a triangle is bisected opposite sides become equal
Both sides are the same
2y=16 divide both sides by 2
y=8
A bag contains 2 red beads, 1 yellow bead and 3 green beads. A bead is chosen at random. What is the probability that it is red? a) What is the probability that it is not yellow?
Answer:
Step-by-step explanation:
Total no of beads = 2 + 1 + 3 = 6
No of red beads = 2
p ( red ) = 2/6 = 1/3
No of non - yellow beads = 5
p ( yellow ) = 5/6
Hope this helps
plz mark as brainliest!!!!!!!!
Answer:
Step-by-step explanation:
There are total 6 beads in all.
2) Since there are 5 non-yellow beads, the probability that the bead is not yellow will be 5/6
Since there are 2 red beads, the probability that the bead is red will be 2/6 = 1/3
3.5 + 1.2(6.3 – 7x) = 9.38
Answer: 0.2
Step-by-step explanation:
subtract 9.38 - 3.5 = 5.88
distribute the 1.2.
7.56 - 8.4x = 5.88
subtract 5.88 - 7.56 = -1.68
-8.4x = -1.68
divide both sides by -8.4
answer = 0.2
Giovanna used the calculations below to determine the height of a stack of 7 books that are each 2 and StartFraction 5 over 8 EndFraction inches thick. What was her error? 7 (2 and StartFraction 5 over 8 EndFraction). 7 (2 + StartFraction 5 over 8 EndFraction). 14 + StartFraction 5 over 8 EndFraction. 14 and StartFraction 5 over 8 EndFraction The fraction was not simplified in the last step. Seven was not multiplied by StartFraction 5 over 8 EndFraction. There should be a subtraction step, not an addition step. Two should have been multiplied by StartFraction 5 over 8 EndFraction.
Answer:
She didn't do the multiplication of 7 times the fraction 5/8 by using distributive property.
so the correct answer is the one that looks like:
Seven was not multiplied by StartFraction 5 over 8 EndFraction.
in your list of options.
Step-by-step explanation:
If one has a stack of seven books each [tex]2\frac{5}{8} \,\,in[/tex] thick, one should first convert the mixed number to an addition of an integer plus a fraction
[tex]2\frac{5}{8} =(2+\frac{5}{8})[/tex]
as she did, and then multiply 7 by the addition, making sure to use distributive property and multiply both terms:
[tex]7\,\,(2+\frac{5}{8})=7\,*\,12+7\,*\,\frac{5}{8}=14+\frac{35}{8}[/tex]
and she didn't do the multiplication of 7 times the fraction 5/8
What is the vertex of the equation y = -x 2 + 10x - 28?
Answer:
(5,-3)
Step-by-step explanation:
Rewrite the equation in vertex form
y =-(x-5)^2 - 3
You take the value of -5 (that would be your x value) and change it to the opposite sign -> +5
Then you take -3 (that would be your y value) and take it as it is
therefore the answer is (5, -3)
In 1000 sq. meter of land a farmer cultivated 765 kg of rice with the wastage of 23.5%.I) Find the weight of the wastage. II) Find the weight and percentage of rice cultivated.
Answer:
i. weight of wastage(kg) = 179.775 kg
ii. weight of rice cultivated = 765 kg - 179. 775 kg = 585.225 kg
percentage of rice cultivated = 100 - 23.5 = 76.5%
Step-by-step explanation:
A land of 1000 sq. meter is used to cultivate 765 kg of rice with wastage of 23.5%.
i. The wastage in percentage is 23.5% but the weight of the wastage in weight is 23.5% of 765 kg
weight of wastage = 23.5/100 × 765
weight of wastage = 17977.5/100
weight of wastage(kg) = 179.775 kg
ii. weight and percentage of rice cultivated.
weight of rice cultivated = 765 kg - 179. 775 kg = 585.225 kg
percentage of rice cultivated = 100 - 23.5 = 76.5%
The triangles shown below must be congruent.
Answer:
False
Step-by-step explanation:
The triangles are similar because the angles are the same
We know nothing about the side lengths, so we can say nothing about concurrency. They may or may not be congruent.
What is the length of AC?
Answer:
≈ 5.9
Step-by-step explanation:
AC/3= 5.5/2.8
AC= 5.5*3/2.8
AC ≈ 5.9
Please help if you think you can
Answer:
-32x-22y
Step-by-step explanation:
4x + 2y - 6(6x - 4y)
Use distributive property
4x + 2y - 6(6x - 4y)
4x + 2y - 36x -24y
-32x-22y
Step-by-step explanation:
4x + 2y - 6(6x - 4y)
To remove the parenthesis multiply 6 by the terms in the parenthesis
That is
4x + 2y - 36x + 24y
Group like terms
4x - 36x + 2y + 24y
Simplify the terms
- 32x + 26y
Divide all terms by 2
we get
- 16x + 13y
I hope this helps you
if U is the midpoint of CB, CU=18, and CB= 2x-10, then find x
Answer:
x = 23
Step-by-step explanation:
CU + UB = CB
Since U is the midpoint that means CU = UB = 18
18+ 18 = 2x-10
36 = 2x-10
Add 10 to each side
36+10 = 2x
46 =2x
Divide by 2
23 = x
Answer:
x = 23Step-by-step explanation:
CB/2 = CU
CB = (2)CU
2x - 10 = (2)18
2x - 10 = 36
Add 10 on both sides.
2x = 46
Divide both sides by 2.
x = 23
Analyzing Graphs of Parallel Lines
Which line is parallel to the line 8x + 2y = 12?
Aty
Answer:
4x+y=6
Step-by-step explanation:
8x/2+ 2y/2=12/2
What is the value of m in the figure below? In this diagram, ΔABD ~ ΔBCD.
Answer:
√126Option D is the right option.
solution,
[tex] \frac{ac}{bc} = \frac{bc}{dc} \\ or \: \frac{18}{ m} = \frac{m}{7} \\ or \: m \times \: m = 18 \times 7(cross \: multiplication) \\ or \: {m}^{2} = 126 \\ m = \sqrt{126} [/tex]
Hope this helps..
Good luck on your assignment.
Hope
An empty container has a capacity of 60000 litres to 1 significant figure Tony pours in 5400 litres of water to 1 significant figure He says “I have filled more than 10% of the container” Is he correct
Answer:
The container's capacity could be anything from 55,000 to 65,000. Exactly 10% of that is anything from 5500 to 6500.
The amount of water poured in could be anything from 5350 or 5450. That is NOT in the range above, so the answer is NO.
No, Tony is not correct.
The following information should be considered:
The container capacity could be varied from 55,000 to 65,000. Now if do exactly 10% so it should be 5,500 to 6,000.But the amount of water poured could be 5,350 or 5,450.Based on the above information we can conclude that tony is not correct.
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Expanding and Adding Expressions Use the expansion shown to simplify the expression. One-half (3 x minus two-thirds y) + 3 (StartFraction x over 2 EndFraction + one-half y) Equals (one-half) (StartFraction 3 over 1 EndFraction x) + (one-half) (Negative two-thirds y) + (StartFraction 3 over 1 EndFraction) (one-half x) + (StartFraction 3 over 1 EndFraction) (one-half y) Equals (three-halves x) + (negative one-third y) + (three-halves x) + (three-halves y) = 3x + y
Answer:
[tex]3x+\frac{7}{6}y[/tex]
Step-by-step explanation:
To simplify the expression, we first open the parenthesis, then we collect all the like terms. Lastly we simplify the like terms to its simplest form. Given that:
[tex]\frac{1}{2}(3x-\frac{2}{3} y)+3(\frac{x}{2}+\frac{1}{2}y )\\\\Firstly, we\ expand\ the\ parenthesis:\\\\=\frac{1}{2}(3x)-\frac{1}{2}(\frac{2}{3} y)+3\frac{x}{2}+3(\frac{1}{2} y)\\[/tex]
[tex]=\frac{3}{2}x-\frac{1}{3}y +\frac{3}{2}x+\frac{3}{2} y\\\\ Collecting\ like\ terms:\\\\=\frac{3}{2}x+\frac{3}{2}x-\frac{1}{3}y+\frac{3}{2}y\\\\Adding \ terms:\\\\=3x +\frac{7}{6}y[/tex]