Answer:
In a nutshell, you have to graph the parabola. Where the parabola intersects the x-axis is the solutions to the quadratic equation.
Subtracting Rational Numbers Simplify –3 – 1.
Answer:
-4
Explanation:
when subtracting a positive integer from a negative, the answer becomes smaller. If the question were to ask -3-(-1) negative 3 minus negative 1, the subtraction sign becomes a addition sign, and you add 1 to -3.
Answer: -4
Step-by-step explanation: To subtract the integers -1 - 1, I would first change the minus sign to plus a negative.
So we have -1 + -1.
Now let's use a number line to find our answer.
Starting at 0, -3 moves us 3 units to the left, then from there,
-1 moves us 1 more unit to the left and we end up at -4.
So -3 + -1 is -4.
Which of the following is the sum of the slopes of the line 3x+y=1 and a line perpendicular to this line? A 0 B 13 C −83 D −6
Answer:
-8/3
Step-by-step explanation:
First find the slope of the line
3x+y = 1
Solve for y
y = -3x+1
This is in slope intercept form
y = mx+b where m is the slope
The slope is -3
The slopes of perpendicular lines multiply to -1
m* -3 = -1
m = 1/3
The line perpendicular has a slope of 1 / (3) = 1/3
The sum is -3 + 1/3
-9/2 + 1/3 = -8/3
Help pls I will give BRAINLY
Answer: The missing length is 16/3
Step-by-step explanation:
First, you have to find the proportional value between the two lengths on the first figure and the two lengths on the second figure.
The first figure’s lengths are 8 and 9, so the shorter length is 8/9 of the longer length.
Now apply the same proportional value to the second figure.
6 * 8/9 = 48/9
48/9 = 16/3
H(x)=-5x^2+10x+15h(x)=−5x 2 +10x+15h, left parenthesis, x, right parenthesis, equals, minus, 5, x, squared, plus, 10, x, plus, 15 What is the height of the stone at the time it is thrown?
Answer:
15 units
Step-by-step explanation:
Given the equation which models the path of a stone as:
[tex]H(x)=-5x^2+10x+15[/tex]
At the time when the stone was thrown
x=0
Therefore:
[tex]H(0)=-5(0)^2+10(0)+15\\H(0)=15[/tex]
The height of the stone at the time it is thrown is 15 units.
Please answer this question now in two minutes
Answer:
c. Not enough information
Find the surface area of a cylinder with radius r = 6 and height h = 14.8 to the nearest tenth of a square cm. Use π = 3.14
Answer:
783.7 square units
Step-by-step explanation:
The formula for the surface area of a cylinder is ...
A = 2πr^2 + 2πrh = 2πr(r +h)
Using the given numbers, the area is ...
A = 2(3.14)(6)(6 +14.8) = 783.7 . . . square units
Answer:
About 783.7 square cm.
Step-by-step explanation:
The formula for the surface area of a cylinder is (2 * pi *r^2) + (2 * pi * r * h).
(2 * 3.14 * 6^2) + (2 * 3.14 * 6 * 14.8) = (2 * 3.14 * 36) + (2 * 3.14 * 6 * 14.8) = 6.28 * 36 + 6.28 * 88.8 = 226.08 + 557.664 = 783.744.
So, the surface area of the cylinder is about 783.7 square centimetres.
Hope this helps!
A piece of aluminum with a mass of 100.0 g has a temperature of 20.0°C. It absorbs 1100 J of heat energy. What is the final temperature of the metal?
Answer:
31.81°CStep-by-step explanation:
Using the formula for calculating heat energy H = mcΔT
m = mass of the aluminum (in g/kg)
c = specific heat capacity of aluminum
ΔT = change in temperature = T - Ti (in °C)
T is the final temperature
Ti is the initial temperature
Given m = 100.0g, c = 0.931096J/g °C, Ti = 20°C, H = 1100J T = ?
Substituting the given values into the formula;
1100 = 100*0.931096 (T - 20)
1100 = 93.1096T - 1862.192
93.1096 T = 1100+1862.192
93.1096 T = 2962.192
T = 2962.192/93.1096
T = 31.81°C
The final temperature of the metal is 31.81°C
Answer:
31.81c
Step-by-step explanation:
1100 = 100*0.931096 (T - 20)
1100 = 93.1096T - 1862.192
93.1096 T = 1100+1862.192
93.1096 T = 2962.192
T = 2962.192/93.1096
T = 31.81°C
To steam rice, Paul uses m cups of water for every p
cups of rice. In terms of m and p, how many cups of
water are needed to steam p + 2 cups of rice?
Answer:
[tex]\frac{(p + 2)m}{p}[/tex]
Step-by-step explanation:
Given
m cups of water = p cups of rice
Required
Cups of water required for p + 2 cups of rice
The question shows a direct proportion between cups of rice and cups of water.
So, the first step is to get the proportionality constant (k)
This is calculated using the following expression;
[tex]m = k * p[/tex]
Where k represents cups of water and p represents cups of rice
Make k the subject of formula
[tex]k = \frac{m}{p}[/tex]
Let x represents cups of water when cups of rice becomes p + 2;
k becomes:
[tex]k = \frac{x}{p + 2}[/tex]
Equate both expressions of k; to give
[tex]\frac{m}{p} = \frac{x}{p + 2}[/tex]
Multiply both sides by p + 2
[tex](p + 2) * \frac{m}{p} =(p + 2) * \frac{x}{p + 2}[/tex]
[tex](p + 2) * \frac{m}{p} =x[/tex]
[tex]x = (p + 2) * \frac{m}{p}[/tex]
[tex]x = \frac{(p + 2)m}{p}[/tex]
Hence, the expression that represents the cups of water needed is [tex]\frac{(p + 2)m}{p}[/tex]
In the diagram, what is the measure of angle 1 to the nearest degree? a) 82° b) 92° c) 94° d) 98°
Answer:
98
Step-by-step explanation:
7x+4 = 88 because they are vertical angles and vertical angles are equal
7x = 88-4
7x = 84
Divide by 7
7x/7 = 84/7
x = 12
<1 and 7x-2 are supplementary angles since they form a line
<1 + 7x-2 = 180
<1 + 7(12) -2 = 180
<1 +84-2 =180
<1 +82 = 180
<1 = 180-82
<1 = 98
Answer-
98
step by step explanation -
7x+4=88
7x=84
x=12
7x-12=7*(12)-2=82
angle 1=180-82 =
98You have a wire that is 50 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum
Answer:
88.6647727273 cm²
Step-by-step explanation :
The perimeter of the square =(50/2)
= 25 cm
∴ Side of the square = (25/4)
= 6.25 cm
∴ Area of of the square = (6.25)²
= 39.0625 cm²
The circumference of the circle =(50/2)
= 25 cm
∴ 2πr = 25
⇒ r = 25/(22/7)(2)
Area of the circle = (22/7) { 25/(22/7)2} {25/(22/7)2}
= (25×25×7) / (2×2×22)
= 4365/88
= 49.6022727273 cm²
∴ Total area of the circle and the square =(49.6022727273+39.0625000000)
= 88.6647727273 cm²
Hope it helped
If yes mark BRAINLIEST!
What are the values of the variables in the triangle below? If your answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.
Answer:
x = 12y = 4√3Step-by-step explanation:
To find x we use cosine
cos∅ = adjacent / hypotenuse
x is the adjacent
8√3 is the hypotenuse
cos 30 = x / 8√3
x = 8√3 cos 30
x = 12To find y we use sine
sin∅ = opposite / hypotenuse
y is the opposite
8√3 is the hypotenuse
sin 30 = y / 8√3
y = 8√3 sin 30
y = 4√3Hope this helps you
find 1st, 2nd, 3rd, 4th and 10th nTh term. rule is 3n+4
Answer:
When n is 1
3n+4
=3*1+4
=3+4
=7
When n is 2
3n+4
=3*2+4
=6+4
=10
When n is 3
3n+4
=3*3+4
=9+4
=13
When n is 4
3n +4
=3*4+4
=12+4
=16
When n is 10
3n+4
=3*10+4
=30+4
34
The graph of the function f(x)=-(x+3)(x-1) is shown below. What is true about the domain and range of the function?
Answer:
The 3rd one is correct.
Step-by-step explanation:
Simplify.
Rewrite the expression in the form b^n
(b^3)^2
Answer: b⁶
Step-by-step explanation:
The for bⁿ can be optained by multiplying 3 and 2. If there is an exponent on the outside of the parenthesis, you multiply it with the exponent on the inside.
(b³)²=b³ˣ²=b⁶
Pleas answer this is in two minutes
Answer:
b
Step-by-step explanation:
not a because equilateral would be all equal
scalene is all different
Answer:
scalene
Step-by-step explanation:
because all sides are different.
Mr. Hughes has contributed $4000.00 per year for the last ten years into a RRSP account earning 9.00% compounded annually. Suppose he leaves the accumulated contributions for another five years in the RRSP at the same rate of interest. A) How much will Mr. Hughes have in total in his RRSP account? B) How much did Mr. Hughes contribute? C) How much will be interest?
Answer:
A) $93,504.818
B) $40,000
C) $53,504.818
Step-by-step explanation:
Yearly contribution ( periodic payment) = $4000
Period (p) = 10years
Additional period(y) = 5years
Annual interest(r) = 9% = 0.09
Future value (FV) =
periodic payment [(1 + r)^y - 1] / r
4000 [(1 + 0.09)^10 - 1 / 0.09]
4000[1.09^10 - 1 / 0.09]
4000[1.3673636 / 0.09]
4000(15.192929)
= 60771.716
If left for five more years:
FV = 60771.716(1 + r)^n
FV = 60771.716(1 + 0.09)^5
FV = 60771.716(1.09)^5
FV = 60771.716(1.5386239549)
FV = $93,504.818
B) MR. HUGHES CONTRIBUTION :
Periodic payment × p ; $4000 was deposited annually for 10 years.
$4000 × 10 = $40,000
C) Interest = Future value - contribution
$93,504.818 - $40,000
= $53,504.818
Q3. Ishah spins a fair 5-sided spinner. She then throws a fair coin.
(i) List all the possible outcomes she could get. The first one has been done for you.
(1, H)
(ii) Ishah spins the spinner and tosses the coin.
Work out the probability that she will get a 2 and a head.
Answer:
see below
Step-by-step explanation:
1.
1, H - 2, H - 3, H - 4, H - 5, H
1, T - 2, T - 3, T - 4, T - 5, T
2.
2,H is one out of 10 possible outcomes, so the probability is 1/10
Which two consecutive whole numbers does 39 lie between? Why?
5 and 6 because 39 falls between 52 = 25 and 62 = 36.
4 and 6 because 39 falls between 42 = 16 and 62 = 36.
6 and 7 because 39 falls between 62 = 36 and 72 = 49.
5 and 7 because 39 falls between 52 = 25 and 72 = 49
Answer:
Step-by-step explanation:
6 and 7
Can I get help with this problem?
Answer:
area of sector:
[tex] \frac{theta}{360} \times \pi \: {r}^{2} [/tex]
[tex] \frac{165}{360} \times \frac{22}{7} ( {8}^{2} )[/tex]
[tex] \frac{11}{24} \times \frac{1408}{7} [/tex]
[tex] \frac{1936}{21} [/tex]
[tex]92.19 \: {in}^{2} [/tex]
Answer:
the area of the sector can be rounded to [tex]92.2\,\,in^2[/tex]
Step-by-step explanation:
Use the fraction of the area of the circle associated with the red sector. Use a proportion to find the appropriate fraction knowing that a full circle [tex](360^o)[/tex] corresponds to the area:
[tex]Area=\pi\,R^2=\pi\, (8\,in)^2= 64\, \pi\,\,in^2[/tex]
then the proportion goes like:
[tex]\frac{64\,\pi\,\,in^2}{360^o} =\frac{sector}{165^o} \\ sector=\frac{64\,\pi\,165^o}{360^o}\,\,in^2\\sector\approx 92.15\,\,in^2[/tex]
Therefore, the area of the sector can be rounded to [tex]92.2\,\,in^2[/tex]
? of 72 = 45 (answer in fraction)
Answer:
5/8
Step-by-step explanation:
72 = 16/10 of 45
45 = 10/16 = 5/8 of 72
There are eight marbles in a bag. Four marbles are blue (B), two marbles are red (R) and two marbles are green (G) Steve takes a marble at random from the bag. What is the probability that Steve will take a blue marble.
Answer:
1/2
Step-by-step explanation:
There are 8 marbles in total and 4 are blue, so 4/8 are blue. Then simplify 4/8 and you will get 1/2.
Answer:
1/2 or 50%
Step-by-step explanation:
Blue= 4, Red= 2, Green= 2
Total marbles= 8
P(B)= 4/8= 1/2 or 50%
help can you also show how you do it too
Answer:
m the slope of function=-3
Step-by-step explanation:
to find the slope take two points from the graph:
(0,4), (1,1)
m= y2-y1/x2-x1
m=1-4/1-0
m=-3/1=-3
the equation : y=mx+b find b
when x=0, y=b=4
y=-3x+4
assume the graph of a function of the form y=asin(k(x+b)) is given below. which of the following are possible values for a, k, and b?
Answer:
C
Step-by-step explanation:
Okay, here we have the equation of the sine wave as;
y = asin(k(x + b))
By definition a represents the amplitude
k represents the frequency
b represents the horizontal shift or phase shift
Now let’s take a look at the graph.
By definition, the amplitude is the distance from crest to trough. It is the maximum displacement
From this particular graph, amplitude is 4
K is the frequency and this is 1/period
The period ;
Firstly we find the distance between two nodes here and that is 1/2 from the graph (3/4 to 1/4)
F = 1/T = 1/1/2 = 1/0.5 = 2
b is pi/4 ( phase is positive as it is increasing rightwards)
So the correct option here is C
Answer: it is
a=4, k=2, and b= pi/4
Step-by-step explanation:
got it right on A P E X
Need help with #11 please
Answer: The graph is a linear graph or linear function in the form y= mx + b where m is the slope and b is the y-intercept. You could plot the points (0,5) (1,4) (2,3) (4,1) and draw a straight line through them.
Step-by-step explanation:
The equation y= 5-x can be rewrite as y = -1x + 5 and it can be identify as a linear equation in slope intercept form. Now you could plot in any value of x and solve for y.
x y (x,y)
0 5 (0,5) If you put in 0 for x y will be 5
1 4 (1,4) if you put in 1 for x, y will be 4
2 3 (2,3) if you put in 2 for x, y will be 3
4 1 (4,1) if you put in 4 for x, y will be 1
5 0 (5,0) if you put in 5 for x y will be 0.
The segments shown below could form a triangle.
Answer:
B. False
Step-by-step explanation:
In order for segments to form a triangle, the sum of the lengths of the shorter two must be at least as much as the length of the longest one.
The sum of the shorter two is 6 + 5 = 11. This is not as great as 12, the length of the longest one, so no triangle can be formed.
prove the following identity: sec x csc x(tan x + cot x) = 2+tan^2 x + cot^2 x please provide a proof in some shape form or fashion :/
Answer:
Step-by-step explanation:
Hello,
Is this equality true ?
sec x csc x(tan x + cot x) = 2+tan^2 x + cot^2 x
1. let 's estimate the left part of the equation
[tex]sec(x)csc(x)(tan(x) + cot(x)) =\dfrac{1}{cos(x)sin(x)}*(\dfrac{sin(x)}{cos(x)}+\dfrac{cos(x)}{sin(x)})\\\\=\dfrac{1}{cos(x)sin(x)}*(\dfrac{sin^2(x)+cos^2(x)}{sin(x)cos(x)})\\\\=\dfrac{1}{cos(x)sin(x)}*(\dfrac{1}{sin(x)cos(x)})\\\\\\=\dfrac{1}{cos^2(x)sin^2(x)}[/tex]
1. let 's estimate the right part of the equation
[tex]2+tan^2(x) + cot^2(x)=2+\dfrac{sin^2(x)}{cos^2(x)}+\dfrac{cos^2(x)}{sin^2(x)}\\\\=\dfrac{2cos^2(x)sin^2(x)+cos^4(x)+sin^4(x)}{cos^2(x)sin^2(x)}\\\\=\dfrac{(cos^2(x)+sin^2(x))^2}{cos^2(x)sin^2(x)}\\\\=\dfrac{1^2}{cos^2(x)sin^2(x)}\\\\=\dfrac{1}{cos^2(x)sin^2(x)}[/tex]
This is the same expression
So
sec x csc x(tan x + cot x) = 2+tan^2 x + cot^2 x
hope this helps
HELP PLZZZZZZZZZZZ!!!!!!!
Answer:
A) 21/20
Step-by-step explanation:
Tangent = Opposite/Adjacent
any number that divisible by 3 is also divisible by 6 . Find a counterexample to show that the conjecture is false
Answer:
Counterexample: 21 which is divisible by 3 but not by 6.
Step-by-step explanation:
Use for example the number 21 which is divisible by 3 rendering 7, but not divisible by 6.
You can find any number with at least a factor of "3", but no factor "2" in it, so any odd number divisible by 3 would work as counterexample.
The population, P (t), of an Ontario city is modeled by the function p(t) = 14t^2 + 650t + 32,000. If t = 0 corresponds to the year 2,000. When was the population 25,000?
Answer:
The population of the city was 25,000 in 1970 and 1983.
Step-by-step explanation:
In order to find the year at which the population was 25,000 we need to make p(t) equal to that number and solve for t as shown below.
[tex]25000 = 14*t^2 + 650*t + 32000\\14*t^2 + 650*t + 7000 = 0\\t^2 + 46.43*t + 500 = 0\\t_{1,2} = \frac{-46.43 \pm \sqrt{(46.43)^2 - 4*1*500}}{2}\\t_{1,2} = \frac{-46.43 \pm \sqrt{155.75}}{2}\\t_{1,2} = \frac{-46.43 \pm 12.48}{2}\\t_1 = \frac{-33.95}{2} = -16.98\\t_2 = \frac{-58.91}{2} =- 29.5[/tex]
Since t = 0 corresponds to the year 2000, then t1 = 1983 and t2 = 1970.
how do u find rate of change on a graph
Step-by-step explanation:
The correct answer is the vertical change divided by the horizontal change between two points on a line. We can find the slope of a line on a graph by counting off the rise and the run between two points. If a line rises 4 units for every 1 unit that it runs, the slope is 4 divided by 1, or 4.
Answer:
Calculate the rise over the run/the change in y over the change in x
Step-by-step explanation:
In order to find the rate of change on a graph from a slope, you need to look at how many units up and how many units to the right. Find a solid point on the graph for both the x and y directions. Count how many units go up and how many go right. Divide how many units go up by how many go to the right and that is the rate of change on the graph.