Answer:
The cost is $43.2
Step-by-step explanation:
The first thing to do here is to calculate the amount of energy consumed.
From the question, we are told that this is;
Power * Time
From the question, power = 1600 watts
Time = 9 hours
So amount of energy consumed = 1600 watts * 9 hours = 14,400 watts hour
It should be known that energy is measured in Kilowatts hour ; So therefore 14,440 watts hour is 14,440/1000 kwh = 14.4 kwh
Now, the cost per unit of energy is $3.00 per kwh
So the cost of using 14,400 watts hour would be 14.4 * 3 = $43.2
Write an equation of the line that is perpendicular to y = 1/2x +3 and passes through the point
(10,-5)
Answer:
y = -2x+15Step-by-step explanation:
[tex]y = 1/2x +3\\m =1/2\\m_1m_2 = -1\\1/2m_2 =-1\\m_2= -2\\(10 ,-5)\\x = 10\\y = -5\\y = mx+b \\-5 = -2(10) + b\\-5=-20+b\\-5+20 =b\\b = 15\\m = -2\\Substitute -given -values- into- slope -intercept-form\\y = mx+b\\y = -2x+15[/tex]
Mike put 304 baseballs into 8 trash bins. He put the same number of baseballs in each bin. He took 5 trash bins of baseballs to the baseball field. How many baseballs did he take?
Answer:
190 Baseballs
Step-by-step explanation:
Since he put 304 baseballs into 8 trash cans with an equal amt. in each,
--> we do 304/8 to find how much baseballs we put in each
=> 304/8 = 38
Now, we takes 5 of these 38 trash cans filled with balls to the field
--> we would do 5 x 38 => 5 x 38 = 190
and Thus, we have our answer of 190 baseballs
Hope this helps!
consider a polynomial f(x)=ax^3 + bx^2 + x + 2/3.if x + 3 is a factor of f(x) and f(x) is divided by x + 2, then we get remainder as 5. find the values of a and b.
Answer:
a = 2/27
b = 13/27
Step-by-step explanation:
The given polynomial is presented as follows;
f(x) = a·x³ + b·x² + x + 2/3
Given that x + 3 is a factor, we have;
f(-3) = 0 = a·(-3)³ + b·(-3)² - 3 +2/3 = 0
-27·a + 9·b - 3 + 2/3 = 0
-27·a + 9·b = 7/3........(1)
Also we have
(a·x³ + b·x² + x + 2/3) ÷ (x + 2) the remainder = 5
Therefore;
a·(-2)³ + b·(-2)² + (-2) + 2/3 = 5
-8·a + 4·b - 2 + 2/3 = 5
-8·a + 4·b = 2 - 2/3 = 4/3........(2)
Multiplying equation (1) by 4/9 and subtracting it from equation (2), we have;
-8·a + 4·b - 4/9×(-27·a + 9·b) = 4/3 - 4/9 × 7/3
-8·a + 12·a = 8/27
4·a = 8/27
a = 2/27 ≈ 0.0741
imputing the a value in equation (1) gives;
-27×2/27 + 9·b = 7/3
-2 + 9·b = 7/3
9·b = 7/3 + 2 = 13/3
b = 13/27 ≈ 0.481.
If ∠R is given and the values of r and q are given, then explain whether the Law of Sines or the Law of Cosines should be used to solve for ∠Q.
Answer:
To solve a triangle is to find the lengths of each of its sides and all its angles. The sine rule is used when we are given either a) two angles and one side, or b) two sides and a non-included angle. The cosine rule is used when we are given either a) three sides or b) two sides and the included angle.
Step-by-step explanation:
We just saw how to find an angle when we know three sides. It took quite a few steps, so it is easier to use the "direct" formula (which is just a rearrangement of the c2 = a2 + b2 − 2ab cos(C) formula). It can be in either of these forms:
cos(C) = a2 + b2 − c22ab
cos(A) = b2 + c2 − a22bc
cos(B) = c2 + a2 − b22ca
Answer:
Law of cosines, two sides and the included angle known
Step-by-step explanation:
double check that the question is exactly the same to make sure you get the question correct
"If ∠P is given and the values of r and q are given, then explain whether the Law of Sines or the Law of Cosines should be used to solve for p."
what is the value of the discriminators of f f(x)=x^2-3x+18
Answer:
-63
Step-by-step explanation:
Compare ...
f(x) = x^2 -3x +18
to the standard form ...
f(x) = ax^2 +bx +c
and you will see that ...
a = 1, b = -3, c = 18.
__
The value of the discriminant is ...
d = b^2 -4ac
d = (-3)^2 -4(1)(18) = 9 -72 = -63
The discriminant is -63.
The ratio of cement : sand : aggregate in a mix of concrete is 1 : 3 : 3. Sang wants to make 112 kg of concrete. How much sand does he need?
Answer: 48
Step-by-step explanation:
The share of sand in the mixture is 3/7
To make 112 kgs. of concrete, he will need
3/7 x 112 = 48 units of sand
Answer:
48 kgsolution,
Ratio of cement:sand:aggregate
=1:3:3
Total of ratios=1+3+3
=7
Total concrete=112 kg
Amount of sand required:
[tex] \frac{ratio \: of \: sand}{total \: ratio} \times amount \: of \: concrete \\ = \frac{3}{7} \times 112 \\ = 48 \: kg[/tex]
Hope this helps...
Good luck on your assignment...
Find x
a) 21 √2
b)7
c)21 √2/2
d)21 √3/2
Answer:
C
Step-by-step explanation:
Use the sine ratio in the left, right triangle to find the common side to both triangles and the exact values
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , thus
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{opp}{7\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2 × opp = 21 ( divide both sides by 2 )
opp = [tex]\frac{21}{2}[/tex]
Now consider the right triangle on the right, using the cosine ratio
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{\frac{21}{2} }{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
x = [tex]\frac{21}{2}[/tex] × [tex]\sqrt{2}[/tex] = [tex]\frac{21\sqrt{2} }{2}[/tex] → C
Multiply the polynomials. (2x^2 + 6x + 6)(3x – 2)
Hey there! :)
Answer:
6x³ + 14x² + 6x - 12.
Step-by-step explanation:
Given:
(2x² + 6x + 6)(3x - 2)
Multiply each term in the first polynomial by both terms in the second:
3x( 2x² + 6x + 6) - 2(2x² + 6x + 6) =
6x³ + 18x² + 18x - 4x² - 12x -12 =
Combine like-terms:
6x³ + 14x² + 6x - 12.
Find the inequality represented by the graph
Answer:
y ≥ -2/3x +3
Step-by-step explanation:
incline is -2/3
and intercept with y-axis is 3
so the equation of the line is
y = -2/3x +3
Since the intended area in the graph I above the line, we now know enough to find the right one question:
y ≥ -2/3x +3
Answer: y>-2/3x+3 because the line is dotted its >
Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 495495 and standard deviation 118118 . You choose an SRS of 100 students and average their SAT Critical Reading scores. If you do this many times, the standard deviation of the average scores you get will be close to 118100=1.18118100=1.18 . 118100√=11.8118100=11.8 . 118100⎯⎯⎯⎯⎯⎯√=1.09118100=1.09 . 118118 .
The question is not typed properly! Complete question along with answer and step by step explanation is provided below.
Question:
Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 495 and standard deviation 118 .
You choose an SRS of 100 students and average their SAT Critical Reading scores. If you do this many times, the standard deviation of the average scores you get will be close to
a. 118
b. 118/100=1.18
c. 118/√100= 11.8
d. cannot be determined
Answer:
The standard deviation of the sample would be
[tex]s = \frac{\sigma}{\sqrt{n}} \\\\s = \frac{118}{\sqrt{100}} \\\\s = 11.8[/tex]
The correct option is (c)
Therefore, the standard deviation of the average scores you get will be close to 11.8
Step-by-step explanation:
From the given information,
The population mean SAT critical reading score is
[tex]\mu = 495[/tex]
The population standard deviation is
[tex]\sigma = 118[/tex]
You choose an SRS of 100 students and average their SAT Critical Reading score.
[tex]n = 100[/tex]
Since the sample size is quite large then according to the central limit theorem,
The mean sample will be the same as the population mean SAT critical reading score.
[tex]\bar{x} = \mu = 495[/tex]
The standard deviation of the sample would be
[tex]s = \frac{\sigma}{\sqrt{n}} \\\\s = \frac{118}{\sqrt{100}} \\\\s = 11.8[/tex]
The correct option is (c)
Therefore, the standard deviation of the average scores you get will be close to 11.8
Which of the following are roots of the polynomial function?
Check all that apply.
F(x) = x^3-6x^+7x-2
Answer:
C, D, and F
Step-by-step explanation:
The roots of the cubic polynomial are 1, (5+√17)/2, and (5-√17)/2 options (C), (D), and (F) are correct.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have a cubic or third-degree polynomial:
F(x) = x³ - 6x² + 7x - 2
To find the all possible roots of the cubic polynomial
By using the trial and error method:
Plug x = 1
F(1) = 1 - 6 + 7 - 2
F(1) = 8 - 8
F(1) =0
x = 1 is one of the roots of the polynomial.
We can write the cubic polynomial in the factored form:
F(x) = (x - 1)(x² -5x + 2)
We have a quadratic polynomial:
= x² -5x + 2
To find the roots of the quadratic polynomial use the quadratic formula:
a= 1, b = -5, and c =2
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\rm x = \dfrac{-(-5) \pm\sqrt{(-5)^2-4(1)(2)}}{2(1)}[/tex]
After solving:
x = (5+√17)/2
x = (5-√17)/2
Thus, the roots of the cubic polynomial are 1, (5+√17)/2, and (5-√17)/2 options (C), (D), and (F) are correct.
Learn more about Polynomial here:
brainly.com/question/17822016
#SPJ5
In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JK=24 and JM=18, find JL.
Answer:
JL ≈ 32
Step-by-step explanation:
The triangle JKL has a side of JK = 24 and we are asked to find side JL. The triangle JKL is a right angle triangle.
Let us find side the angle J first from the triangle JKM. Angle JMN is 90°(angle on a straight line).
using the cosine ratio
cos J = adjacent/hypotenuse
cos J = 18/24
cos J = 0.75
J = cos⁻¹ 0.75
J = 41.4096221093
J ≈ 41.41°
Let us find the third angle L of the triangle JKL .Sum of angle in a triangle = 180°. Therefore, 180 - 41.41 - 90 = 48.59
Angle L = 48.59 °.
Using sine ratio
sin 48.59 ° = opposite/hypotenuse
sin 48.59 ° = 24/JL
cross multiply
JL sin 48.59 ° = 24
divide both sides by sin 48.59 °
JL = 24/sin 48.59 °
JL = 24/0.74999563751
JL = 32.0001861339
JL ≈ 32
ANSWER ASAP PLEASE!!!!!!!!!!!! THANKS!!!!!!!!! :)
Answer: the answer is A
Step-by-step explanation:
Liam wants to treat some friends to lunch. He has $50 and knows that lunch will cost about $8 per person, p. How many people can Liam buy lunch for?Part A- Write and solve an inequality to represent the Situation
Answer:
T ≥ 8x
50 ≥ 8x .......1
x ≤ 6
Liam can buy lunch for 6 people.
Step-by-step explanation:
Let x represent the number of people Liam can buy lunch for.
Given;
Lunch cost per person r = $8 per person
The total amount he has T = $50
The cost of buying lunch for c people is;
C = $8 × x
C = 8x
Therefore, to be able to buy lunch for them, the total cost C must be less than the total amount he has.
T ≥ C
Substituting C, we have;
T ≥ 8x
50 ≥ 8x ,.......1
Solving the inequalities;
8x ≤ 50
x ≤ 50/8
x ≤ 6.25
To the nearest whole number;
x ≤ 6
Liam can buy lunch for 6 people.
Please help me Thank u
Answer:
Step-by-step explanation:
Fist let's have a look :
(AB) is parallel with (CD) and there is a line crossing them both.Now the first question : What is the size x ?
We notice that x and 53° are vertically opposite so they are corresponding angles so the size of x is 53°The second question : what is the size of y ?
We notice that y and 53° are alternate angles so they are corresponding angles with same size y=53°The trick is to khow the situation where we have corresponding angles
What is Pascal's triangle.
Answer:
Pascal's triangle is a triangular array of the binomial coefficients. It is used to find combinations.
Answer:
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.
Step-by-step explanation:
Which is the value of g(-5) it g(x) = 3,4x - 8?
Answer:
g(-5)=-25
Step-by-step explanation:
Module 6 What is the line of best fit? Why do we want the sum of the residuals to be as close to zero as possible?
Answer:
zero residual equals zero mean
A line of best fit is a straight line that shows the appropriate correlation among scatter plots of a given data. It is majorly used when the plotted points are not linear, it can be used to express the relationship between dependent and independent variables.
The sum of the residuals should be close to zero because it shows that the line of best fit is accurately drawn. Thus, it implies that there is a linear relationship between the two variables. Since he residual is close to zero, the graph could be said to be a linear graph.
In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JK=24 and JM=18, find JL.
Answer:
JL = 32
Step-by-step explanation:
We are told in the above question that:
In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JK=24 and JM=18, find JL.
From the attached diagram, we can see that
JL : JK = JK: JM
Therefore,
JL/ JK = JK /JM
Where JL = Unknown
JK = 24
JM = 18
JL/ 24 = 24/18
Cross Multiply
24 × 24 = JL × 18
Divide both sides by 18
JL = (24 × 24) /18
JL = 576/18
JL = 32
f(x)=-3√(x-3)-1 which of the following graphs corresponds to the function above
Answer:
Step-by-step explanation:
graph attached
Answer:
graph y
Step-by-step explanation:
Tim has 39 pairs of headphones and 13 music players. Tim wants to sell all the headphones and music players in identical packages what is the greatest number of packages time can make
Answer:
He will have 13 packages containing 3 pairs of headphones and 1 music player each.
Step-by-step explanation:
He has 39 pairs of headphones and 13 music players.
He wants to sell both set of items in identical packages.
To do this he has to divide them in such a way that the same number of both set of objects are in every box.
Let us find the ratio of the pairs of headphones to music players:
39 : 13 = 3 : 1
Therefore, dividing the pairs of headphones into 3 parts and the music players into 1 part, he can have identical packages.
So, he will have 13 packages containing 3 pairs of headphones and 1 music player each.
Please please please urgent help❤️❤️❤️
Answer:
its G(2)
Step-by-step explanation:
Gg
Can somebody plz help me
Answer: A
Step-by-step explanation:
2x²-2x-9=0
this is a quadratic equation so we will use the quadratic formula .
Δ= b²-4*a*c
b= -2a= 2c= -9let's calculate Δ to khow how many solutions this equations have .
Δ= (-2)²-4*2*(-9)
= 76
we notice that 76>0
so this equation has two solutions : (-b-√76)/4 and (-b+√76)/4
let's calculte the values : (-b-√76)/4= [tex]\frac{-2-\sqrt{76} }{4}[/tex] (-b+√76)/4=[tex]\frac{-2+\sqrt{76} }{4}[/tex]the trick here is to notice that :
[tex]\sqrt{76}[/tex] = [tex]\sqrt{19*4}[/tex]
= [tex]\sqrt{19} *\sqrt{4}[/tex]
= 2[tex]\sqrt{19}[/tex]
Now we will simplify Δ by factoring by 2
[tex]\frac{2*(-1(+/-)\sqrt{19} }{2*2}[/tex] = [tex]\frac{-1(+/-)\sqrt{19} }{2}[/tex]so the answer is a .
the sum of the ages of an uncle and nephew 2 years ago was 40.In 2 years time from now the age of the uncle will be 3 times that of his nephew by then.Find their ages now
Answer:
Uncle is 34. Nephew is 10.
Step-by-step explanation:
Let u equal the age of the uncle, and n equal the age of the nephew.
First, two years ago, the sum of their ages was 40. We can represent this by subtracting 2 from each variable. Thus:
[tex](u-2)+(n-2)=40[/tex]
[tex]u+n-4=40[/tex]
[tex]u+n=44[/tex]
Next, in two years time, the uncle will be three times as old as his nephew. We can represent this by adding 2. Thus:
[tex]u+2=3(n+2)[/tex]
We now have a system of equations and can solve accordingly.
First, from the first equation, we can determine that:
[tex]u=44-n[/tex]
We can substitute this into the second equation.
[tex](44-n)+2=3(n+2)[/tex]
[tex]46-n=3n+6[/tex]
[tex]40=4n[/tex]
[tex]n=10[/tex]
Thus, the nephew's age is 10.
And the uncle's age is 44-10 or 34.
Triangles X Y Z and E G F are shown. Side X Y is 3.0 inches and angle Y Z X is 107 degrees. Side F G is 2.4 inches and side E F is 1.3 inches. Angle G E F is 48 degrees. Given ΔXYZ ≅ ΔEGF, find the measurements of the unknown sides and angles. ZX = in. EG = in. M∠X = ° m∠G = °
Answer:
ZX = 1.3 in
EG = 3.0 in
M∠X = 48°
M∠G = 25°
Step-by-step explanation:
As we can see in the attached figure that these two triangles are identical i.e their corresponding sides and angles are equal
Therefore if we say that
ZX = EF
So ZX = 1.3 in.
Now the same is applied for other sides and angles
EG = XY
So, EG = 3.0 in
M∠X = M∠E
hence, M∠X = 48°
For the M∠ G,
The angle is
= 180° - 107° - 48°
= 25°
Hence, the M∠ G is 25°
Franklin's grandmother opened a savings account with $275 to help him save money for college. Franklin will deposit $55 each month. His grandmother will deposit $40 each month. If Franklin makes no additional deposits or withdrawals, which equation can be used to find A, the amount of money in Franklin's savings account after p months?
Answer:
X = 275 + 95p
Step-by-step explanation:
Hello,
This question requires us to write an expression to find how much he would've saved over a certain period of time.
Initial deposit = $275
Franklin's monthly deposit = $55
Franklin grandmother's deposit = $40
Let the amount he would've saved over a certain period of time p = x
X = 275 + (55 + 40)p
X = 275 + 95p
Eg, how much would he have saved in 5 months
X = 275 + 95(5)
X = 275 + 475
X = $750
I.e in 5 months, he would've saved $750
HELP 25 PTS ASAP!!!!!! BRAINLIEST
We can solve for the y-intercepts of both f(x) and h(x) by plugging in 0 as x. f(0) = -6(0)-3 = -3
h(0) = -2cos(pi)-1 = -2(-1)-1 = 1
So the y-intercept of f(x) is -3 and of h(x) is 1. We can then conclude that h(x) has a greater y-intercept than f(x) because 1>-3.
..........help lol xD
Answer:
equilateral
acute
Step-by-step explanation:
equilateral = all equal angles
acute = all angles less than 90
Answer:
D. Equilateral
Step-by-step explanation:
An equilateral triangle is a three sided shape with sides of the same size. Since all the sides in the image are 9cm, it is considered as an equilateral triangle.
Hope this helps
what is the slope of these lines that contain these points (-1,10) (1,2) (3,-6) (5,-14)
Answer:
-4
Step-by-step explanation:
y = -4x + 6 is the equation and -4 is the slope
Please help me.I want an accurate answer and true answer.
Answer:
m∠x = 65°
m∠y = 81°
m∠z = 34°
Step-by-step explanation:
Since we have 2 transversals and a pair of parallel lines, we can see that at ∠A it equals 65°. If we use the Corresponding Angles Theorem, the m∠A = m∠x. Therefore, x = 65°
To find y, we know that a line is 180°. So, 180 - (65 + 34) = 81°
To find z, we know that all angles in a triangle add up to 180°. So, 180 - (81 + 65) = 34°. Alternatively to find z, we could use Alternate Interior Angles Theorem.