Answers
hello
the question is a quadratic equation and we are asked to use completing the squares method.
to solve this, let's use some basic steps
step 1
divide through the equation by the coefficient of x^2
\(\begin{gathered} x^2+4x-60=0 \\ \frac{x^2}{1}+\frac{4x}{1}-\frac{60}{1}=\frac{0}{1} \\ x^2+4x-60=0 \end{gathered}\)step 2
now we have to know that
\(\begin{gathered} ax^2+bx+c=0 \\ where\text{ we can relate this to out own equation} \\ x^2+4x-60 \\ a=1,b=4,c=-60 \end{gathered}\)\(x^2+4x=60\)step 3
complete the square on the left hand side of the equation and balance this by adding the same value on the right hand side of the equation
\(\begin{gathered} x^2+4x+4=60+4 \\ (x+2)^2=64 \end{gathered}\)step 4
take the square roots on both sides of the equation
\(\begin{gathered} (x+2)^2=64 \\ \sqrt[]{(x+2)^2_{}}=\sqrt[]{64} \\ x+2=\pm8 \\ x=2+8=10 \\ or \\ x=2-8=-6 \end{gathered}\)from the calculations above, the value of x is either 10 or -8
Related Questions
A......... divides a two-dimensional shape into two congruent shapes
Answers
Answer:
A diagonal
Step-by-step explanation:
Pls help!!!
Find the solution set of the inequality with the given replacement set:
20x - 4 > 24, x = {0, 1, 2, 3}
Answers
Answer:
{2,3}
Step-by-step explanation:
as when we solve we will get 7/5
that is 1.5
and x > 1.5
so answer is 2 and 3
plz mark as brainliest if it helps
Need help with this math. 40 Points
Answers
The equivalent equations are;
A = 1/2h(b1 + b2)b1 = 2A/h - b2b1 = 2(A -1/2hb2)/hWhich of these are equivalent?For equations to be equivalent they must be reduced to obtain the same terms. Thus if the terms that are found on an equation are not similar it is not possible to think that the equations are by any means equivalent.
Given the four equations as we have them in the question, the following equations are equivalent;
A = 1/2h(b1 + b2)b1 = 2A/h - b2b1 = 2(A -1/2hb2)/hLearn more about equivalent equations;https://brainly.com/question/28263804?
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Question
From a point P on a level ground and directly west of a pole, the angle of elevation of the top of the pole is 45° and from point Q east of the pole, the angle of elevation of the top of the pole is 58°. If |PQ|= 10m, calculate, correct to 2 significant figures, the:
a) distance from P to the pole;
b) height of the pole.
Answers
a) The distance from point P to the pole is: 6.2 m
b) The height of the Pole is: 6.2 m
How to find the distance and height from angle of elevation?The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.
Now, we are given that:
The angle of elevation of the top of the pole = 45°
Angle of elevation of the top of the pole = 58°.
|PQ|= 10m
a) PR is distance from point P to the pole and using trigonometric ratios, gives us:
PR/sin 58 = 10/sin(180 - 58 - 45)
PR/sin 58 = 10/sin 77
PR = (10 * sin 58)/sin 77
PR = 8.7 m
b) P O can be calculated with trigonometric ratios as:
P O = PR * cos 45
P O = 8.7 * 0.7071
P O = 6.2 m
Now, the two sides of the isosceles triangle formed are equal and as such:
R O = P O
Thus, height of pole R O = 6.2 m
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Which decimal number is equal to
2/4?
Answers
Answer:
.5
Step-by-step explanation:
2/4 2 goes into 2 1 time and 2 goes into 4 2 times so therefore 2/4 is = 1/2
1/2= .5
A scuba diver descends from the surface at a rate of 34 feet per minute.
What is the position of the scuba diver relative to the surface after diving for 4 minutes?
Answers
Answer:
The answer is -136
Step-by-step explanation:
you multiply -34 by 4 which gives you -136
(Hope this help)
Plz, help. In the picture below.
Answers
Answer:
I don't know sorry
Step-by-step explanation:
PLEASE HELP ME, THIS MEANS EVERYTHING TO ME ITS APART OF MY FINALS.❗
The ages of students who play racquetball at a school are shown in the histogram below.
How many students play racquetball at the school?
A.
60
B.
51
C.
54
D.
57
Answers
Answer:
Uhhhh... 54?
Step-by-step explanation:
Just add them together.
82 decrease by 10 percent
Answers
Answer:
Percentage decrease = 10% × 0.82
New value = 0.82 - Percentage decrease
Let me know if this helps! :)
i need help!!!! does anyone know this..!!???
Answers
The period of oscillation is 3 seconds
What is period of oscillation?A Oscillation is the periodic change of a measure around a central value or between two or more states, usually in time.
The time taken for an oscillating particle to complete one cycle of oscillation is known as the Period of oscillating particle. It is measured in seconds
Oscillation can also be vibration or revolution or cycle.
Therefore, using the graph to determine the period. Then the wave particle made a complete oscillation at 3 second.
This means that the period of the particle is 3 seconds.
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I need the answer plsss
Answers
Answer: 12.5
Step-by-step explanation: Well 50 diviedby 4 = 12.5
Xavier is buying fencing to surround his garden if his garden has a perimeter of 30 yards and fencing cost six dollars a yard how much money will he need for the fencing
Answers
Answer:
$180
Step-by-step explanation:
If the perimeter is 30 yards and each yard costs $6 you times 30 and 6 and you get $180
What is the volume of a cylinder, in cubic cm, with a height of 19cm and a base
diameter of 10cm? Round to the nearest tenths place.
Answers
Answer:
549.8 cm (cubed)
Step-by-step explanation:
D3lt4 m4th 4n$wer
The question is in the picture.
Answers
Easy way to do this, divide 24 with 3, you will get 8. That means 8 is 1/3 of 24. To get 2/3 you just add 8+8 which equals to 16
The lengths of two sides of a triangle are shown.
Side 1: 8x2 - 5x - 2
Side 2: 7x - x2 , 3
The perimeter of the triangle is 4xJ - 3x?
Part A: What is the total length of the two sides, 1 and 2, of the triangle? Show your work. (4 points)
Part B: What is the length of the third side of the triangle? Show your work. (4 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? justify your answer. (2
points)
Answers
The Total length of two sides based on the information will be 7x²+2x+1
The Length of the third side will be 4 x³-10x²-7.
How to calculate the lengthTotal length of two sides= Side 1 + Side 2
= 8x² − 5x − 2+ 7x − x²+ 3
= 8x²-x²-5x+7x-2+3
= 7x²+2x+1
Length of the third side = Perimeter - Total length of two sides
Length of the third side=4x³ − 3x² + 2x − 6-(7x²+2x+1)
= 4x³ − 3x² + 2x − 6-7x²-2x-1
= 4 x³-10x²-7
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Write 0.000064 in scientific notation.
Question 5 options:
A)
6.4 × 10–5
B)
6.4 × 105
C)
6.4 × 10–6
D)
0.64 × 10–4
Answers
Answer:
The answer is A
Step-by-step explanation:
The slope of the tangent line to the curve y= 3/x
at the point 5, 3/5 is-
The equation of this tangent line can be written in the form y = mx + b
where:
m is:
b is:
Answers
The tangent line at that point is:
y = (-3/25)*x + 6/5
so m = -3/25, and b = 6/5
How to find the slope of the tangent line?To find the slope at that point, we need to evaluate the derivative at that point.
y = 3/x
The derivative is:
y' = -3/x²
When x = 5, we have:
y' = -3/5² = -3/25
So that is the slope, m.
Now let's find the line.
The line must pass trhough the point (5, 3/5), then:
3/5 = (-3/25)*5 + b
3/5 = -3/5 + b
3/5 + 3/5 = b
6/5 = b
The equation of the line is:
y = (-3/25)*x + 6/5
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Please help it’s due
Answers
Answer:
c,
Step-by-step explanation:
have a good day, glad I could help :)
Mackenzie has some red, yellow and blue marbles. She has 3200 more red marbles than yellow marbles. She has 3840 more blue than yellow. She gives 1490 blue marbles away. How many more red marbles than blue marbles does she have left?
Answers
Answer:
850
Step-by-step explanation:
Mackenzie has 3200 more red marbles than yellow,
(y + 3200 = r)
And she also has 3840 more blue marbles than the yellow marbles,
(y + 3840 = b)
Then let's assume that Mackenzie has 1 yellow marble.
1 + 3200 = 3201 red marbles
1 +3840 = 3841 blue marbles
If she gives away 1490 blue marbles away, then she is left with 2351 blue marbles.
(3841 - 1490 = 2351)
Now she's left with 2351 blue marbles, and 3201 red marbles.
r - b =?
3201 - 2351 = 850
Mackenzie has 850 more red marbles than blue marbles.
(If you want, you can change the number of yellow marbles, but it will be the same answer.)
Look at the screenshot
Answers
Answer:
37.5 is the answer to the problem
13.6.4 Quiz: The Quadratic Formula
Which two values of x are roots of the polynomial below?
x²-3x+5
O A. X=3--11
x3
O B. X=-3-17
I c. x= -3+
-3+ VTT
I D. X=
3-√23
Ex=
3+ -11
DEX=
3+29
Answers
The mean temperature for the first 4 days in January was 7°C. The mean temperature for the first 5 days in January was 9°C. What was the temperature on the 5th day?
Answers
Answer:
If the mean was 7 for the first 4 days that means the sum of temperatures of the first 4 days was 7 * 4 = 28. Similarly, the sum of temperatures of the first 5 days was 9 * 5 = 45 so that means that the temp. on the 5th day was 45 - 28 = 17°C.
Answer:
11 C
Step-by-step explanation:
To find the mean (average), you have to add all and divide by 2, so if you reverse this, you get (7 + X)/2 = 9 , 9 * 2 - 7 = 11
The Ozzie Chocolate Company is preparing to offer a new product in its candy offerings, the Minty Dark Chocolate Bite bar. Material costs per new candy bar are
$0.25 for chocolate, $0.02 for sugar, and $0.03 for mint flavoring. Labor costs of the new product are approximately $0.15 per bar. Adding a production line devoted to the new candy will cost $250,000 per year.
(a) If the sales price is $1.40 per candy bar, how many must the company make per year in order to break even? Assume that each bar made is sold at full price.
(b) What is the company's profit or loss if they make and sell 270,000 candy bars at the $1.40 price in the first year?
(c) About 20% of the food consumed in the U.S. is imported. Production in many industries has been offshored. What ethical issues do companies face when presented with the decision to move operations?
Answers
Answer:
a) 263,158
b) $164,500
c) Ethical issues companies face when deciding to move operations: job loss for employees, poor working conditions and exploitation of workers, negative environmental impact,...
Step-by-step explanation:
a)
Total cost = (0.25 + 0.02 + 0.03 + 0.15) x + 250,000
Total revenue = 1.40x
Setting the two equations equal to each other and solving for x, we get:
(0.45)x + 250,000 = 1.40x
0.95x = 250,000
x ≈ 263,158
b)
If the company sells 270,000 candy bars at $1.40 each, the total revenue generated is:
270,000 * $1.40 = $378,000
The total cost of producing 270,000 candy bars is:
(0.25 + 0.02 + 0.03 + 0.15) * 270,000 + $250,000 = $213,500
Therefore, the company's profit is:
$378,000 - $213,500 = $164,500
c)
Ethical issues companies face when presented with the decision to move operations: job loss for employees, poor working conditions and exploitation of workers, negative environmental impact,...
Drag the values from the problem and fill in the blanks to create and solve a system of equations.
Overview
KM
First
<
Previous
>
Skup
Huck has a handful of coins. There are 13 total
coins and he only has nickles and dimes. He knows
that he has $1.05 in total money. How many dimes
and nickles does he have?
x + y = |(13
Let x = # of nickels
Let y = # of dimes
y = ||1.05
Equation for the
number of coins
Remember
X
Give up
X +
Equation for the
value of the coins
Submit
X =
y =
Answers
Answer: uhhh
Step-by-step explanation:
well give u brainliest What is the value of the function when x=−2?
Enter the answer in the box.
Answers
The value of the given function when x = -2 is; y = 1
How to interpret Linear Graphs?
We are given a linear graph as seen in the given image. Now, in graphs like these, there are input values which are x-values while there are also output values which are values on the y-axis.
Now, looking at the graph, we can see that;
At x = 5, y = -6
At x = 4, y = -5
At x = 3, y = -4
At x = 2, y = -3
At x = 1, y = -2
At x = 0, y = -1
At x = -1, y = 0
At x = -2, y = 1
Thus, we can conclude that the value of the given function when x = -2 is, y = 1
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How do you write the unit rate for 1/5÷1/15
Answers
Answer:
3
Step-by-step explanation:
1/5 / 1/15 = 3
I need help with these
Answers
Answer:
1) C (9)
2) A (8)
3) A (12)
4) C (0)
5) C (9)
6) B (10)
7) D (12) | x = 11
8) B (11) | x = 12
Phineas puts $600 into a certificate of deposit that earns 3.09%. If the money is
compounded monthly, how much will it be worth in 4 years?
Answers
Answer:
$678.83
Step-by-step explanation:
Given :
Principal, P = $600
Rate = 3.09% = 0.0309
Period, t = 4 years
Compounding times per period, n = 12 (monthly)
The compound interest formula :
A = P(1 + r/n)^nt
A = 600(1 + 0.0309/12)^(12*4)
A = 600(1 + 0.002575)^48
A = 600(1.002575)^48
A = 600 * 1.1313834
A = 678.83004
Worth in 4 years = $678.83
ax=b(c+x) make x the subject of the formula
Answers
ax=bc+bx
(a-b)x=bc
x =bc/(a-b)
no guess please explain
