Answer:
see below
Step-by-step explanation:
f(x) = 5x^3 +1, g(x) = – 2x^2, and h(x) = - 4x^2 – 2x +5
f(-8) = 5(-8)^3 +1 = 5 *(-512) +1 =-2560+1 =-2559
g( -6) = -2 ( -6) ^2 = -2 ( 36) = -72
h(9) = -4( 9)^2 -2(9) +5 = -4 ( 81) -18+5 = -324-18+5=-337
Factored completely, the expression 2y^2 + 12y-54 is equivalent to
a. 2(y + 9)(y - 3)
b. 2(y - 3)(y-9)
c. (y+ 6)(2y - 9)
d. (2y + 6)(y-9)
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]
Triangle DEF is an isosceles, so AngleDEF Is-congruent-toAngleDFE. A horizontal line has points C, F, E, G. 2 lines extend from the line at points F and E to form an isosceles triangle with point D. Angle DEF measures 75°. What is the measure of angle CFD? 105° 125° 150° 165°
Answer:
105 degrees
Step-by-step explanation:
Angle DEF measures 75°.Triangle DEF is an isosceles, so AngleDEF Is-congruent-toAngleDFE.
the angles all together is 180 degrees
so 180 - 75 = 105 degrees
The measure of angle CFD is 105 degrees.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
Angle DEF = 75°.
Triangle DEF is isosceles, so Angle DEF Is-congruent-to Angle DFE.
Angle DFE + Angle CFD = 180 (angle on a straight line)
so 180 - 75 = 105 degrees
Thus, Angle CFD = 105 degree
Learn more about the triangles;
https://brainly.com/question/2773823
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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
In 1860, gingham cloth sold for
$0.25 per yard. Mrs. Olsen bought
16.4 yards to make clothes for her
whole family. How much did she
spend on cloth?
Answer:65.6
Step-by-step explanation:
So $0.25 per yard
16.4/$0.25=65.6
A machine lifts up containers of coal from the mine and lowers empty containers down. The machine uses an electric motor connected to a 600 V d.c. supply.The maximum current in the motor is 4000 A. *Calculate the maximum power available from the motor. Give your answer in MW* power = voltage x current i believe
Answer:
The maximum power available to the motor is 2.4 MW
Step-by-step explanation:
The power of a circuit that has a current, I, and a voltage, V, is given by the relation
Electrical power, P = I²R = I× I×R = I × V
Therefore given that the parameters are;
Voltage in the d.c. power supply = 600 V d.c.
Maximum current in the motor = 4000 A
Therefore, we can find the power as follows;
Maximum motor power = Voltage × Current
The maximum motor power, P available = 600 V × 4000 A = 2400000 W which on converting to MW becomes;
The maximum power available to the motor , P = 2.4 MW.
if a truck starts from rest and its has acceleration of 4m/s 2. for second ,calculate its final velocity .what will be the distance travelled by the truck during the time interval?
Answer:
The answer is given below
Step-by-step explanation:
Let us assume the truck accelerates for 4 seconds.
Given that:
Initial velocity (u) = 0 (starts from rest),
acceleration (a) = 4 m/s²
time (t) = 4 s
Final velocity (v) = ?,
Distance (s) = ?
To calculate the final velocity, we use the formula:
v = u + at
Substituting values gives:
v = 0 + 4(4)
v = 0 + 16
v = 16 m/s
The final velocity is 16 m/s²
To calculate the distance traveled by the truck, we use the equation:
[tex]s=ut+\frac{1}{2}at^2\\ Substituting\ values\ into\ the\ equation:\\s=0(4)+\frac{1}{2}(4)(4)^2\\s=0+2(16)\\s=0+32\\s = 32\ meters[/tex]
The distance traveled by the truck during the time interval is 32 meters
It takes 6 hours to reach London from Minneapolis. Amanda took a flight to London from Minneapolis and reached at 7:15 pm London time. At what time did she depart Minneapolis at London time?
i will mark as brainliest
please explain I will mark as brainliest
Answer:
1:15 pm
Step-by-step explanation:
It takes 6 hours to reach London from Minneapolis and she reached Minneapolis at 7:15pm so
7:15 - 6 = 1:15
A hemisphere is exactly one-half of a sphere. Find the volume of a hemisphere where the radius is 6 m. (Round to the nearest tenth)
Answer:
144π or 452.4
Step-by-step explanation:
Volume of a Sphere Formula: V = 4/3πr³
Step 1: Plug in 6 for r
V = 4/3π(6)³
V = 288π
Step 2: Divide by 2
V = 288π/2
V = 144π
Keith is the leading goal scorer for a team in an ice hockey league . Last season , he scored 42 goals in 82 games . Assuming he scores goals at at a constant rate , what is the slope of the line that represents this relashonships if the number of games is is along the x-axis and the number of goals is along the y-axis
Answer: The slope is 21/41.
Step-by-step explanation:
IF the goals he scores is at a constant rate the we know if you would have to graph it, it will go through the origin.
To find the slope of a constant relationship,you will divide the y value by the x value.Now it indicates to us that x is the number of games while y is the number of goals.
so 42/82 which reduces to 21/41 has to be the slope .
Answer:
it’s 21/41 or A (I got a 100% on the test)
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
ANSWER A
Step-by-step explanation:
Answer:
it has a horizontal asymptote at y=O
Step-by-step explanation:
answer is A.
because A linear parent function is the equation y = x or f(x) = x.
If the polynomial in the numerator is a lower degree than the denominator, the x-axis (y = 0) is the horizontal asymptote.
Geometry -true or false- After we prove that a theorem is true it becomes a definition
Answer:
False
Step-by-step explanation:
A definition produces out of nothing a new mathematical entity. But a theorem utilizes some relation between previously defined mathematical entities.
Usually a theorem must be verified by a proof of its correctness on the basis of generally accepted statements or on the basis of previously established statements which might include other theorems.
x+x/7 + 1/11 (x + x/7) = 60
Answer:
X= 48.125
Step-by-step explanation:
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
solve for x. 5x+9=24
Answer: x=3
Step-by-step explanation:
5x+9 =24 subtract 9 from both sides
-9 -9
5x = 15 Divide both sides by 5
x = 3
Answer:
[tex]5x = 24 - 9 \\ 5x = 15 \\ x = \frac{15}{5} \\ x = 3[/tex]
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
What is the equivalent radian measure of 540°?
1
radians
3
radians
radians
3
3x radians
DONE
Answer: 3π
I don't see 3π in your answer choices, but I'm assuming the "3x" is supposed to be 3π.
Step-by-step explanation:
To convert from degrees to radians, you multiply by π/180.
[tex]540*\frac{\pi }{180} =3\pi[/tex]
NEED MATH HELP NOW. Please solve for the x-intercept. Please show work.
Answer:
x = 1 and x = 3.
Step-by-step explanation:
y = 2[tex]x^{2}[/tex] - 8x + 6
y = 2([tex]x^{2}[/tex] - 4x + 3)
y = 2(x - 3)(x - 1)
So, the x-intercepts would be at...
x-3 = 0
x = 3
and
x - 1 = 0
x = 1
Hope this helps!
Please answer this question fast in two minutes
Answer:
lines NP and OP are intersecting
Step-by-step explanation:
they touch at point P
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.
Wyatt solved the following equation:
x + 1/2 (6x − 4) = 6
it due today!!! I will give the first answer brainliest.
Answer:
x = 2
Step-by-step explanation:
x + 1/2 (6x - 4) = 6
Expand the brackets.
x + 3x - 2 = 6
Add like terms.
4x - 2 = 6
Add 2 on both sides.
4x = 6 + 2
4x = 8
Divide 4 into both sides.
x = 8/4
x = 2
Answer:
x=5/4
Step-by-step explanation:
In the diagram, ∠ADE ≅ ∠ABC. The ratios and are equal.
Answer:
[tex]\frac{AD}{AB} = \frac{AE}{AC} = \frac{DE}{BC}[/tex]
Step-by-step explanation:
According to the given situation, as we know that the triangle which is ADE and triangle which is ABC are the same
. (as in the diagram)
So, the ratio of their corresponding sides are the same or an equal so that it can be reached at the truth which is here below:
[tex]\frac{AD}{AB} = \frac{AE}{AC} = \frac{DE}{BC}[/tex]
With the help of a diagram, we can better understand which has been attached.
The ratios AD : DB and AE : EC are equal.
What is 45% as a fraction in simplest form
⇒Answer:
[tex]\frac{9}{20}[/tex]
⇒Step-by-step explanation:
Well 45% is saying it is 45% out of 100,
So we can make the following fraction
45/100
Then we simplify by dividing 45 and 100 by 5
Hence, the answer is [tex]\frac{9}{20}[/tex]
Help im stuck on this question
Work out the area of the rectangle using a calculator and
giving your answer as a mixed number.
22 cm
5 cm
1
Note: To enter a mixed number in the answer boxes, please use the following method:
Type the fractional part of the mixed number first (e.g. for 6 first enter 5)
Then use the keyboard arrows to return to the front of the box and type the whole number (e.g. for 6
5 enter 6).
Answer:
11 17/21 cm²
Step-by-step explanation:
5 1/6 = (5*6 + 1)/6 = 31/6
2 2/7 = (2*7 + 2)/7 = 16/7
A = 31/6*16/7 = 496⁽²/42 = 248/21 = 11 17/21 cm²
Which number is a perfect cube?
O9
O 18
0 27
O 36
Answer:
27
Step-by-step explanation:
9 is not a perfect cube.
18 is not a perfect cube.
27 is a perfect cube.
∛27 = 3
36 is not a perfect cube.
Answer:
27
Step-by-step explanation:
We want a number time itself times itself
27 = 3*3*3
27 = 3^3
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
What is the height, x, in the triangle below? A. 2√5 B. 5 C. 5√2 D. 10
Answer:
D:10
Step-by-step explanation:
find hyp. first
sin 45=opp/hyp.
√2/2=10/hyp.
hyp.=20/√2 0r 10√2
Pythagorean theorem: a²+b²=c²
now find x²=(10√2)²-10²
x²=200-100
x²=100
x=√100=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
Why does the second part of the problem cos x turns into cos x^2 explain the problem.
Step-by-step explanation:
It's not cos x^2
[tex]\cos^2x\neq\cos x^2[/tex]
----------------------------------------------
[tex]\cos x-\dfrac{\sin x\sin x}{\cos x}=\dfrac{\cos x\cos x}{\cos x}-\dfrac{\sin x\sin x}{\cos x}=\dfrac{\cos^2-\sin^2x}{\cos x}[/tex]
It's the same as
[tex]3-\dfrac{2}{3}=\dfrac{3\cdot3}{3}-\dfrac{2}{3}=\dfrac{3^2-2}{3}[/tex]