Answer:
d. The cost of natural gas (y) = $0.83 per unit
Step-by-step explanation:
The explanation is shown below:-
the equation of system is:
750x + 17y = 141.61 (i)
300x + 30y =75.90 (ii)
as x indicates the cost of electricity and y indicates the costs of natural gas.
we will solve the both equation with the help of multiplication for (i) by 30 and for (ii) 75
[tex]30\times (750x + 17y) 30\times 141.61\\\\[/tex]
after solve the above equation we will get
22,500x + 510y = 4248.3 (iii)
[tex]75\times (330x + 30y) = 75\times 75.90[/tex]
after solve the above equation we will get
22500x + 2250y = 5692.5 (iv)
After deducting the equation (iii) and (iv) we will get
1740 y = 1444.2
After Dividing by 15 both sides,
116y = 96.28
So, Katrina simplify the above system using linear equation and reach at the equation that is
116 y = 96.28
By Division property of equality defines that divide the equal no. of both sides of an equation:
by Division of 116 to both sides of an equation, to get y:
[tex]\frac{116y}{116} = \frac{96.28}{116}[/tex]
y = 0.83
So, the natural gas is $0.83 per unit
Answer:
d
Step-by-step explanation:
Which of these triangle pairs can be mapped to each other using both a translation and a reflection across the line containing AB? Triangles X Y Z and A B C are congruent. Triangle X Y Z is reflected across a line to form triangle A B C. It is also slightly higher than triangle A B C. Triangles A B C and A Y C are congruent and share common side A C. Triangle A B C is reflected across line A C to form triangle A Y C. Triangles A B C and X Y Z are congruent. Triangle X Y Z is slightly higher and to the right of triangle A B C. Triangles A B C and X Y Z are congruent. Triangle A B C is rotated to the right to form triangles X Y Z. Triangle X Y Z is also higher and to the right of triangle A B C.
Answer:
B. Triangles A B C and A Y C are congruent and share common side A C. Triangle A B C is reflected across line A C to form triangle A Y C.
Step-by-step explanation:
Translation and reflection are examples of methods of rigid transformation. Translation ensure that each point on a given figure is moved the same distance with respect to the reference plane. Reflection involves the flipping of a given figure across a given line.
From the question, both reflection and transformation would map the triangles into one another. Since the reference line contains AB, then the two triangles are congruent and would share a common side.
Thus, the triangle pairs that can be mapped into each other is that of option B.
Based on the information given, the triangle pairs that can be mapped to each other using both a translation and a reflection across the line containing AB will be A. Triangles X Y Z and A B C are congruent. Triangle X Y Z is reflected across a line to form triangle A.
Triangles.The triangle pair that can be mapped to each other using both translation and reflection across line containing AB is the first triangle pair.
The first figure consists of ΔXYZ and ΔABC that are a reflection of each other across the line AB and a translation.
Learn more about triangles on:
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Taylor had \$147$147dollar sign, 147. Then she spent \$42$42dollar sign, 42 on sneakers. Then, Taylor earned \$53$53dollar sign, 53 by winning a race in her new sneakers! Estimate how much money Taylor has left
Answer:
She has 158 dollars.
Step-by-step explanation:
This problem tells us that originally Taylor had 147 dollars, but she spent 42 dollars on sneakers, thus she now has [tex]147-42 = 105[/tex] dollars. However, she later won a race wearing those sneakers and earned 53 dollars, therefore she now has [tex]105 + 53 = 158[/tex] dollars.
Thus, Taylor has 158 dollars left now.
squirrel, 37 feet up in a tree, sees a dog 29 feet from the base of the tree. Find the measure of the angle of
depression to the nearest degree.
Answer:
angle of depression = 38.1°
Step-by-step explanation:
tan x = 29/37
tan x= 0.784
x = tan-¹ 0.784
x = 38.1°
Hey I need to write a note to my grandma for her birthday can someone help plz
Answer:
Happybday have a graet day miss uad
Step-by-step explanation:
Answer:
Step-by-step explanation:
Dear grandma,
Thank you for your infinite life and wisdom. I hope you have a wonderful birthday this year. You are the best! Although right now isn't the best time of the year, I still wish you a happy birthday and a healthy life.
I think that would work...
Denise bought 116 ounces of beans for a bean dip. She bought both 15-ounce cans and 28-ounce cans, and the total number of cans she bought was 6. Which of these systems of equations can be used to determine the number of 15-ounce cans and the number of 28-ounce cans that she bought? Assume x represents the number of 15-ounce cans and y represents the number of 28-ounce cans. x + y = 6. 15 x + 28 y = 116. x + y = 6. 28 x + 15 y = 116. x + y = 116. 15 x + 28 y = 6. x + y = 116. 28 x + 15 y = 6.
Answer:
2 28ounce cans and 4 15ounce cans
Step-by-step explanation:
28+28=56 and 15+15+15+15=60
56+60=116
Answer:
your answer is the second option
Step-by-step explanation:
What is the answer to... 5m+8n-2(3m-n)? Show step by step
Answer:
The answer is
10n - mStep-by-step explanation:
5m+8n-2(3m-n)
Expand the terms in the bracket
That's
5m + 8n - 6m + 2n
Group like terms
We have
8n + 2n + 5m - 6m
Simplify
The final answer is
10n - m
Hope this helps you
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
Domain: 0 [tex]\leq[/tex] t [tex]\leq[/tex] 40 Range: 0 [tex]\leq[/tex] V(t) [tex]\leq[/tex] 200
Step-by-step explanation:
The domain is greater than or equal to 0 and less than or equal to 40 because in 40 months, she will lose all her money ($5 x 40months = $200) since she loses 5 dollars per month. Not to mention, time can't be negative in any situation. For the range, the value has to be greater than or equal to zero and less than or equal to 200 because she only has $200, the more time she spends using the phone, the more money she will lose over the course of the month( limiting her time). I hope this helps!
Answer:
Domain: [tex]0\leq t\leq 40[/tex]; Range: [tex]0\leq V(t)\leq 200[/tex]
Step-by-step explanation:
The price of the cellphone was initially of $200. Each month, its price decreases by $5. Then, you have that for 200/5 = 40 month the price of the cellphone will be of $0.
The price of any object always will have a positive value. If V(t) is a function that describes the price of the cellphone in time t, with t in months, you have that the domain of the function is given by the total amount of months on which the cellphone has some price, that is, for:
[tex]0\leq t\leq 40[/tex]
The range of the function is the price of the cellphone. Its initial price was $200 (maximum price) and its final price after 40 months is $0 (minimum price). Hence, the range of the function is:
[tex]0\leq V(t)\leq 200[/tex]
The ratio of the same side interior angles of two parallel lines is 1:14. Find the measures of all eight angles formed by the parallel lines and transversal.
Answer:
At the intersection of the first parallel line with the transversal, a = 12°, c = 168°, d = 12°, e = 168°. Counting counterclockwise from a.
At the first intersection of the second parallel line with the transversal, b = 168°, f = 12°, g = 168°, h = 12°. Counting clockwise from b.
Step-by-step explanation:
At the intersection of the first parallel line with the transversal, a = 12°, c = 168°, d = 12°, e = 168°. Counting counterclockwise from a.
At the first intersection of the second parallel line with the transversal, b = 168°, f = 12°, g = 168°, h = 12°. Counting clockwise from b.
Step-by-step explanation:
Let a be the first interior angle. Since they are in 1:14, the second same side interior angle is b = 14a.
We know that the sum of interior angles equals 180°.
So, a + b = 180°
a + 14a = 180°
15a = 180°
a = 180/15
a = 12°
At alternate angle to the other interior angle, b adjacent to a is c = b = 14a = 14 × 12 = 168°
The angle vertically opposite to a is d = a = 12°
The angle vertically opposite to a is b = e = 168°
At the intersection of the second parallel line and the transversal, the angle alternate to a is f = a = 12°
the angle vertically opposite to angle b is g = b = 168°
the angle vertically opposite to f is h = 12°
Answer:
168 degrees and 12 degrees
Step-by-step explanation:
i cant explain on here but i hope this helps :)
HELP
for his long distance phone service, tony pays a $5 monthly fee plus 9 cents per minute. last month, Tony's long distance bill was $17.96. for how many minutes was Tony billed?
Answer:
144 min.
Step-by-step explanation:
y=0.09x+5 ( x is the number of minutes, y is the bill amount)
17.96=0.09x+5
17.96-5=0.09x
x=12.96/0.09=144 minutes
a girl spent 2/3 of her pocket money and was left with $1800.00 . How much was her pocket money
Answer: She had $5400
Step-by-step explanation:
We will let x represent the total amount of money in her pocket .
So we know that 1/3 of x has to equal 1800 because 2/3 of the money is already been spent so 1/3 will of the money will be left.
1/3 * x = 1800 solve for x by divide both sides by 2/3
x=5400
Check.
1/3 * 5400 =1800
find the truth set of 2x-6≤5(3-x)
Answer:
x∈(-∞,3]
Step-by-step explanation:
2x-6<=5*3-5x
2x-6<=15-5x
+5x +5x
7x-6<=15
+6 +6
7x<=21
:7 :7
x<=3
x∈(-∞,3]
A pair of parallel lines is cut by a transversal: A pair of parallel lines is cut by a transversal. The interior angle made on the left by the intersection of the upper parallel line and the transversal is divided into 2 parts by a slanting line. One part of this angle is labeled as x, and the other part is labeled as 20 degrees. The interior angle made on the right by the intersection of the lower parallel line and the transversal is labeled as 80 degrees. What is the measure of angle x? 60 degrees 70 degrees 80 degrees 100 degrees
A regular octagon is inscribed inside a circle. The perimeter of the octagon is units. A: What is the measure of a side of the octagon? B: What is the measure of a central angle of the octagon? C: What is the approximate measure of the apothem of the octagon (to the nearest hundredth of a unit)? D: Using your answer to part C, what is the approximate area of the octagon (to the nearest whole )?
Answer:
Explained below.
Step-by-step explanation:
Consider the diagram of a regular octagon is inscribed inside a circle.
Suppose the perimeter if the octagon is 8a.
(a)
Compute the measure of a side of the octagon as follows:
[tex]\text{Perimeter}=8\times side\\\\8\times side=8a\\\\side=a[/tex]
Thus, the side of the octagon is a units.
(b)
The sum of all angles of around a point is 360°.
Consider the point P on the octagon.
The sum of all the angle surrounding P will be 360°.
There are a total of 8 angle surrounding the point P.
Then the measure of central angle is:
[tex]\text{Central Angle}=\frac{360^{o}}{8}=45^{o}[/tex]
Thus, the measure of central angle is 45°.
(c)
The line segment from the center of an octagon to the midpoint of a side, perpendicular to said side, is known as the apothem.
Consider the diagram.
In the diagram the line segment PC is an apothem, that is perpendicular to the AB.
The measure of segment AC = a/2 and the measure of segment PA is r (radius of the circle).
Compute he measure of PC as follows:
[tex]PA^{2}=PC^{2}+AC^{2}\\\\PC^{2}=PA^{2}-AC^{2}\\\\PC=\sqrt{PA^{2}-AC^{2}}[/tex]
[tex]=\sqrt{r^{2}-\frac{a^{2}}{4}}[/tex]
Thus, the measure of the apothem of the octagon is[tex]\sqrt{r^{2}-\frac{a^{2}}{4}}[/tex].
(d)
The area of an octagon is:
[tex]\text{Area}=2(1+\sqrt{2})a^{2}[/tex]
Scarlett Squirrel teaches a hula dancing class to young squirrels. 141414 squirrels showed up to class on Monday, 101010 squirrels on Tuesday, 888 squirrels on Wednesday, 101010 squirrels on Thursday, and 121212 squirrels on Friday. Find the mean number of the squirrels
Answer:
93107
Step-by-step explanation:
add all of the numbers together
divide by 5 since there are 5 numbers
you would get 92106.8
so round that up since you cannot have 1/8 of a squirrel
Hope this helps!!
pls help me with this (ill give brainliest)
Answer:
72.96
Step-by-step explanation:
Let the first circle's radius be r and quarter circle's radius be R
Area of circle = π[tex]r^{2}[/tex]
= 3.14 × 8 × 8
= 200.96 [tex]cm^{2}[/tex]
Area of quarter circle = π[tex]R^{2}[/tex]/4
= 3.14 × 16 × 16
= 803. 84/4
=200.96
Area of shaded portion = (Area of Quarter circle - Area of semi-circle ACD - Area of triangle ABC) + (Area of the circle - Area of semi-circle ACD - Area of triangle ABC)
Area of Semi-circle = Area of the circle divided by 2
= 100.48
Area of triangle = [tex]\frac{bh}{2}[/tex]
= [tex]\frac{16 * 8}{2}[/tex]
= 64
Therefore, The area of shaded portion= (200.96-100.48-64) + (200.96 - 100.48 - 64)
= 36.48 +36.48
=72.96
Please answer this in two minutes
Answer:
[tex] s = 14.1 [/tex]
Step-by-step explanation:
Given:
<S = 31°
SQ = r = 9
SR = q = 21
s = ?
To find s, use the Law of Cosines:
s² = r² + q² - 2rs*cos(S)
[tex] s^2 = 9^2 + 21^2 - 2*9*21*cos(31) [/tex]
[tex] s^2 = 81 + 441 - 378*0.8572 [/tex]
[tex] s^2 = 522 - 324.02 [/tex]
[tex] s^2 = 197.98 [/tex]
[tex] s = 14.1 [/tex] (nearest tenth)
A company is designing boxes to ship their product to stores. The design team decides that the width of the box should be five feet shorter than the length, and the height of the box should be three feet longer than the width. Due to shipping constraints, the length of the box can be no greater than six feet. The volume of the box, V(x), can be modeled by a polynomial function, where x is the length of the box. Which of the following correctly models the situation above and gives the correct domain?
Answer:
see below
Step-by-step explanation:
You can work this based only on the domain. You don't need to figure the volume, though you can if you want to check the answer further.
x represents the length of the box, which has a restriction that it can be no greater than 6 ft. This tells you x ≤ 6. However, the width is 5 ft shorter than the width, so its value is x-5. But we know the width must be greater than zero:
0 < x -5
5 < x
So, the constraints on the domain of x are ...
5 < x ≤ 6 . . . . . . only matches the last choice, (5, 6]
___
Checking the volume
The height is 3 more than the width, so the volume is ...
V = LWH = (x)(x -5)(x -5 +3) = x(x -5)(x -2) = x(x^2 -7x +10)
V = x^3 -7x^2 +10x
I am stuck pls I need help
Answer:
HF is 20 m away from the tower which makes it the base of a triangle
tan 30= opp/adj=PF/HF
PF=tan 30°(20)=11.547
tan 50=T F/20 ⇒ T F=20*tan 50= 23.835
PT= T F-PF= 23.835-11.547=12.288 m
b ) the distance from point H to the power is the hypotenuse
cos 50=adj/hyp
hypo(HT)= 20/cos 50=31.114
(HF at a new angle=40)
tan 40=opp/adj = T F/HF
HF=T F/tan40=23.835/tan 40=28.405
What is the slope of a line perpendicular to one with a slope of {-2}{3}.
Answer:
3/2
Step-by-step explanation:
Perpendicular lines have slopes that multiply to -1
m * -2/3 =-1
Multiply by -3/2 to isolate m
m * -2/3 * -3/2 = -1 * -3/2
m = 3/2
The perpendicular line has a slope of 3/2
The area of the trapezoid is 40 square units.
What is the height of the trapezoid?
6
3 units
5 units
10 units
10
12 units
Answer:
5 units
Step-by-step explanation:
Image of the trapezoid is attached.
To find the height of the trapezoid (image attached), let's take the formula for area of a trapezoid.
The formula for area of a trapezoid is:
[tex] A = (\frac{a + b}{2}) h [/tex]
Here, a and b represents the bases of the trapezoid.
a = 6
b = 10
h which represents height is unknown.
A = 40
Substitute figures:
[tex] 40 = (\frac{6 + 10}{2}) h [/tex]
[tex] 40 = (\frac{16}{2}) h [/tex]
[tex] 40 = 8 * h [/tex]
Solve for h:
[tex] h = \frac{40}{8} [/tex]
[tex] h = 5 [/tex]
The height of the trapezoid is 5 units
Answer:
5 units
Step-by-step explanation:
Which statement is true about the end behavior of the graphed function?
Answer:
The correct answer is "As the x-values go to positive infinity the function's value go to positive infinity".
Step-by-step explanation:
If we start analyzing this function at a value of x that is really small, which would be close to negative infinity and we increase the value of x, we will notice that the y-value will also increase. Therefore if we go far into the left, that is, we apply minus infinity to the function we will receive an output that is equal to minus infinity. When the value of x approach 0, the value of the function also approaches 0. Finally when we go far into the right, to positive infinity the function will also go to infinity. Therefore the correct answer is "As the x-values go to positive infinity the function's value go to positive infinity".
the diagrams shows a right-angled triangle. find the size of angle x. give your answer correct to 1 decimal place.
Answer:
1. 40.8 degrees
2. 65.6 degrees
Step-by-step explanation:
1.
sin(x) = opposite / hypotenuse = 17/26
x = arcsin(17/26) = 40.83 degrees
2. tan(x) = opposite / adjacent = 11/5 = 2.2
x = arctan(11/5) = 65.56 degrees
The cost of renting a car is $39 plus $0.75 per mile. Which type of
function can represent this situation?
A) linear
B) exponential
Answer:
linear
Step-by-step explanation:
We can write this in the form
y = mx+b
where m is the .75 per mile and b is the 39 dollars
y = .75x + 39
Two trains 150 miles apart are traveling toward each other along the same track. The first train goes 60 miles per hour; the second train rushes along at 90 miles per hour. A fly is hovering just above the nose of the first train. It buzzes from the first train to the second train, turns around immediately, flies back to the first train, and turns around again. It goes on flying back and forth between the two trains until they collide. If the fly's speed is 120 miles per hour, how far will it travel?
Answer:
120 miles
Step-by-step explanation:
Distance = 150 miles
train 1 = 60 mph
train 2 = 90 mph
directions of trains = towards each other
Time to meet = 150/(60+90) = 150 miles / 150 mph = 1 hour
Speed of fly = 120 mph
Since fly has been flying for one hour, it travelled 120 miles.
write 4.83×10⁵ as an ordinary number
Answer:
483,000
Step-by-step explanation:
hope this helps :)
Answer:
The answer is 483,000 as an ordinary number
Step-by-step explanation:
Add the polynomial
(6s3+9s+10)and(3s3+4s-10)
PLEASE HELP!!! ASAP!!!
Answer:
9s³ ⁺ 13sStep-by-step explanation:
6s³ + 9s + 10 + 3s³ + 4s - 10
Collect like terms
6s³ + 3s³ + 9s + 4s + 10 - 10
Since, two opposites add up to zero, remove them from the expression
6s³ + 3s³ + 9s + 4s
add the like terms
9s³ + 13s
hope this helps..
best regards!!
Answer:
9s^3+13s
Step-by-step explanation:
Add each term:
9s^3+13s
I hope this helps...
And plz mark me brainliest!!
2. The length of a rectangle is 5 cm more than its width. If the perimeter of the rectangle
is 40 cm, find the area of the rectangle.
Answer:
93.75 cm^2
Step-by-step explanation:
The breadth = x cm
length=x+5 cm
perimeter =2 (l+b) which becomes
2 (x+5+x)=4x+10 cm:
4x+10=40
4x=30
x=30/4=7.5
so, breadth = 7.5 cm
length = 12.5 cm,
area = 12.5*7.5 = 93.75
Step-by-step explanation:
perimeter of the rectangle= 2(length+width)
let the known width be 'x'
length be 5+x
40 = 2(5+x+x)
40 = 10+2x+2x
40-10 = 4x
30/4 = 4x/4
x = 7.5
width=7.5cm
length= 7.5+5 = 12.5cm
area = length×width
area = 12.5×7.5 = 93.75cm²
A village P is 10km from a lorry station,Q on a bearing 065°.another village R is 8km from Q on a bearing 155°.calculate;1.the distance of R from P to the nearest kilometer and 2.the bearing of R from P to the nearest degree.
Answer:
Step-by-step explanation:
find the difference between the two angles first:
155-65=90 degrees
d is the distance d:
d^2=a^2+b^2-2ab cos(90)
d^2=10^2+8^2-2(10)(8)cos(90)
d^2=164
d=√164=12.81
the bearing of R from P to the nearest degree:
180-155=35 degrees
Max must take 10 steps to go the same distance as three of his dad's steps. His dad takes 30 steps to walk down the hall. How many steps must Max take to walk down the same hall?
Max : 10 steps : Dad: 3 steps.
So it you multiply those each by ten, you get
100 steps : 30 steps.
30 Dad steps is 100 Max steps, so you get the answer, which is 100!
The steps taken by Max is 100.
what is arithmetic operators?A mathematical function that performs a calculation on two operands is known as an arithmetic operator. Common arithmetic makes use of them, and the majority of computer languages include a set of such operators that can be used in equations to carry out a variety of sequential calculations.
Given
steps taken by Max = 10
Steps taken by his Dad = 3
both steps of Dad and steps of Max should be in ratio
3/10 …(1)
steps taken by his Dad = 30
let steps taken by Max = x
ratio = 30/x …..(2)
equation 1 equals equation 2
3/10 = 30/x
x = (30 x 10)/3
x = 100
Hence Max must take 100 steps.
Learn more about arithmetic operators;
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Simplify (5 + 1)^2 - (12 + 3^2) = %3.
A. 29
B. -39
C. 5
D. -63
Answer:
29
Step-by-step explanation:
(5+1)^2-(12+3^2)/3 Add 5 and 1 = 6.
6^2-12+3^2/3 Calculate 6 to the power of 2 = 36.
36-12+3^2/3 Calculate 3 to the power of 2 = 9.
36-12+9/3 Add 12 and 9 = 21.
36-21/3 Divide 21 by 3 = 7.
36−7 Subtract 7 from 36 to get 29.