Using linear functions, the costs are given as follows:
A(x) = 16x + 1.B(x) = 18x.C(x) = 14.25x.For 4 hours, the difference is costs between the company that charges the most and the one that charges the least is of $15.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For Company A, we have two points on the column: (2, 33), (3, 49). Hence for one additional hour, the cost increased by $16, hence the slope is of 16 and:
A(x) = 16x + b.
When x = 2, A(x) = 33, hence we use it to find b as follows:
33 = 16(2) + b
b = 1.
Hence:
A(x) = 16x + 1.
Companies B and C have intercepts of 0, while the slopes are hourly costs, hence:
B(x) = 18x -> 9 for each half hour = 18 for an hour.C(x) = 14.25x.For 4 hours, the costs are given as follows:
A(4) = 16(4) + 1 = 65.B(4) = 18(4) = 72.C(4) = 14.25(4) = 57.The difference is:
72 - 57 = 15.
For 4 hours, the difference is costs between the company that charges the most and the one that charges the least is of $15.
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Identify the vertex, the axis of symmetry, the maximum or minimum value, and the domain and the range of each function.
y=(x-125)²+125 .
Each function's vertex, axis of symmetry, maximum or lowest value, domain, and range are all described as follows: Vertex: (125,125); range: (125,125); minimum: at y=125; x=125; maximum: no., axis of symmetry is x=125.
Describe Domain and Range.The domain of a function is the set of values that we are allowed to enter into our function.
The set of values that a function can accept as input is known as its range.
According to given data;y=(x-125)²-125
we know that;
y=(x-h)²+k
Vertex: In this form, the vertex (or, in other words, the "pointy bit") is given to us in the (h ,k);here we have (125,125).
Axis of symmetry : Two equal segments of the parabola. It moves straight up and down via the vertex.
Thus, we may formulate an equation for the vertical line that passes through the vertex. It is x=125 in this query..
Maximum and lowest values: Here, we're concerned in examining the vertex to determine whether it is at the maximum or lowest of the parabola's range (i.e., when a negative sign is placed in front of the (x-h) = 0 term, respectively).
Range: The value of range is (125,∞ )
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Lincoln High School has 75 less than 4 times as many students as Washington High School. a. Write an expression to find the number of students at Lincoln High School if Washington High School has w students. w + b. How many students are at Lincoln High School if Washington High School has 250 students? students
Answer: A. 4w+(-75)
B. 925
Step-by-step explanation:
a babysitter earns $8 an hour
Answer:
8xh h=hours
Step-by-step explanation:
8 times how ever much hour than that's all if there's tips well just add it to your answer
Consider the sequence:
5,4,3,2, . . .
The 7th term of the above sequence is
______.
The explicit rule for the nth term of the sequence is
______.
PLS HELP!
Answer:
7th term = (-1)
rule for the nth term = an = a+(n-1)d
Step-by-step explanation:
a = 5, d = a2-a1 = 4-5 = -1, n = 7
an = a+(n-1)d
a7 = 5+(7-1)(-1)
a7 = 5-6
a7 = (-1)
Help me please, thank you very much
Answer:710.4
Step-by-step explanation:
The sum of two consecutive integers is - 207. Find the two integers.
===========================================
Work Shown:
x = first integer
x+1 = second integer right after x
The two consecutive integers add to -207
(first) + (second) = -207
(x)+(x+1) = -207
2x+1 = -207
2x = -207-1
2x = -208
x = -208/2
x = -104 is the first integer
x+1 = -104+1 = -103 is the second integer
Check:
-104 + (-103) = -207
The answers are confirmed.
answer this by substitution
Answer: X=3, Y=6 z=-1
Step-by-step explanation:
A cylindrical container if radius 4 cm and height 15 cm is half filled with water. Find the volume of water in the container
Answer:
= 0.377 liters
= 377 mililiters
Step-by-step explanation:
Volume of a regular cylindrical container = л r ² h
л = 3.1416 (aprox,)
r = radius
h = height = 15cm (half filled) = 15/2 = 7.5cm
then:
Volume = 3.1416 * (4cm)² * 7.5cm
volume = 3.1416 * 16cm² * 7.5cm
volume = 377 cm³ (aproximadly)
1 cm³ = 0.001 liters
377 cm³ = 0.001*377 = 0.377 liters = 377 mililiters
100 POINS 1 QUESTION!
Answer:
Step-by-step explanation:
we cant see the question :)
Answer: If you have to fill in the chart I think you just add them together so aluminum would be +3, phosphide -3, iodide -1, and tin 0
Step-by-step explanation:
Given: <5=<16;<2=<4
Prove: <11 and <14 aré supplementary
Given the question, <11 and <14 are supplementary because they sum up to give 180 degrees. Detail below
What are supplementary angles?These are angles that sum up to give 180 degrees. On the other hand, angles on a straight line sum up to give 180 degrees.
Considering the question given above, we can prove that <11 and <14 are supplementary as follow:
<11 + <12 = 180 (angle on straight line)
But
<12 = <14 (corresponding angles)
Thus,
<11 + <14 = 180
Recall
Angle that sum up to give 180 are called supplementary angles
Therefore,
<11 + <14 = 180 => supplementary
From the illustrations given above, we can see clearly that <11 and <14 are supplementary angles
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. If there are 4.90 Cal in 10.0 g of parsley, how many joules are in 12.1 g of parsley?
The joules are in 12.1 g of parsley is 24.806936 Joules of energy
10g has 4.9 cal
1g has 4.9/10 cal
Energy in 12.1 g = 4.9 x 12.1 / 10 = 5.929 Cal = 5.929 x 4.18400 = 24.806936 Joules of energy [1 calorie = 4.18400]
In the International System of Units (SI), a joule is a unit of work or energy equal to the work done by a force of one newton acting through one meter. It is named after the English scientist James Prescott Joule and equals 107 ergs, or about 0.7377 foot-pounds. The joule is equivalent to one watt-second in electrical terms, which is the amount of energy released in one second by a current of one ampere through a resistance of one ohm.
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Write and solve an inequality for m
Answer choices:
m + 6 > 8; m > 2
m + 6 < 8; m < 14
m + 6 > 8; m > 14
m + 6 < 8; m < 2
Based on the information, it should be noted that the inequality to solve for m will be D. m + 6 < 8; m < 2.
How to illustrate the information?It should be noted that in Mathematics, an inequality is used to show the expressions that are hot the same or equal.
Based on the information given about the triangle, it should be noted that the hypothenuse which is given as 8 is the longest side of the triangle.
Therefore, the inequality to solve for m will be:
m + 6 < 8.
Collect like term
m < 8 - 6
m < 2
Therefore, based on the information, it should be noted that the inequality to solve for m will be m + 6 < 8; m < 2.
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Record: 2/7 Score: 2 Penalty: None
Nakaylah Lindsay
The Midpoint Formula
Sep 11, 7:10:42 PM
Find the midpoint of the segment with the following endpoints.
Answer:
(2, 2) and (10,8)
Submit Answer
Answer: the midpoint of the segment is (6,5)
Step-by-step explanation:
(2,2) (10,8)
[tex]\displaystyle\\ A_x=\frac{2+10}{2} \\\\A_x=\frac{12}{2} \\\\A_x=6[/tex]
[tex]\displaystyle\\A_y}=\frac{2+8}{2}\\ \\A_y=\frac{10}{2} \\\\A_y=5\\[/tex]
Thus, A(6,5)
In triangle PQR , the measure of angle Q is three times the measure of angle . The measure of angle R is 20⁰ more than the measure of angleP . Find the measure of each angle.
a. What are the unknowns in this problem?
A triangle is a shape whose all three angles have a sum of 180 degrees. So from the above definition we know that:
P + Q + R = 180
Q=3P
T=P + 20
Therefore:
P + 3P + P + 20 = 180
5P + 20 = 180
5P = 160
P = 32
Q = 3(32) = 96
R = 32 + 20 = 52
To Additional Control P + Q + R = 32 + 96 + 52 = 180 °Degree
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Divide. State any restrictions on the variable. 3x²-9 x / x-2 ÷ x² - 9 / 4 x-8
The division of given rational expression 3x²-9 x / x-2 ÷ x² - 9 / 4 x-8 is 12x / x + 3 provided x ≠ -3
In this question,
we have been given a complex rational expression [tex]\frac{3x^{2} -9x}{x-2}\div \frac{x^2-9}{4x-8}[/tex]
We need to find the division of given rational expression.
We rewrite given rational expression as,
3x²-9 x / x-2 ÷ x² - 9 / 4 x-8
= 3x²-9 x / x-2 / x² - 9 / 4 x-8
= (3x²-9 x / x-2) × (4 x-8 / x² - 9 )
= [tex]\frac{3x(x-3)}{x-2}\times \frac{4(x-2)} {(x+3)(x-3)}[/tex]
= 12x / x + 3 .........(provided x ≠ -3)
Therefore, the division of given rational expression 3x²-9 x / x-2 ÷ x² - 9 / 4 x-8 is 12x / x + 3 provided x ≠ -3
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Hong will rent a car for the weekend. He can choose one of two plans. The first plan has no initial fee but costs $0.90 per mile driven. The second plan has an initial fee of $55 and costs an additional $0.70 per mile driven. How many miles would Hong need to drive for the two plans to cost the same?
Answer:
61 miles
Step-by-step explanation:
0.90 x 61 = 54.9
What are the solutions of the rational equation?
a. x-1 / x+2 = x² + 2 x-3/x+2
The solutions of the rational equation x-1 / x+2 = x² + 2 x-3/x+2 are x = -2 and x = 1
In this question,
We have been given a rational equation.
x-1 / x+2 = x² + 2 x-3/x+2
We need to find the solution of given rational equation.
Here, the denominator is same on the both sides.
x-1 / x+2 = x² + 2 x-3/x+2
⇒ x - 1 = x² + 2 x-3
⇒ x² + 2x - 3 - x + 1 = 0
⇒ x² + x -2 = 0
We solve above quadratic equation.
⇒ x² + 2x - x - 2 = 0
⇒ x(x + 2) - (x + 2) = 0
⇒ (x + 2)(x - 1) = 0
⇒ x + 2 = 0 or x - 1 = 0
⇒ x = -2 or x = 1
Therefore, the solutions of the rational equation x-1 / x+2 = x² + 2 x-3/x+2 are x = -2 and x = 1
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There are 8 roses and 6 daisies in a vase What is the ratio of all flowers in the vase to roses
Answer:
14 to 8
Step-by-step explanation:
8 roses+6 daisies=14 is all the flowers in the vase
Please help asap will give brainliest. Find X and bac
By using the fact that the two angles whose measures are expressed in terms of x are vertical angles, we will see that x = 8.
Then using that we will see that the measure of angle BAC is 63 degrees.
How to find the value of x?On the given diagram, we can see that the two angles whose measures are expressed in terms of x are vertical angles, thus, these two angles have the same measure, then we can write a linear equation that helps us to find the value of x, which is:
(2x + 3) = (4x - 5)
Solving the linear equation for x we get:
2x + 3 = 4x - 5
3 + 5 = 4x - 2x
8 = 2x
8/2 = x = 4
So we can see that the value of x is 4.
Now we want to find the measure of angle BAC.
We can see that the measure of angle BAC plus the measure of the angle to its right will be a right angle, then we can write:
m∠BAC + (4x - 5)° = 90°
Replacing the value of x we get:
m∠BAC + (4*8 - 5)° = 90°
m∠BAC + 27° = 90°
m∠BAC = 90° - 27° = 63°
We conclude that the measure of angle BAC is 63 degrees.
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Solve each equation. Check your solutions. x /2 = x + 1/4
⊂ Hey, ausemkattom2559 ⊃
Answer:
x = 1
Step-by-step explanation:
Given:Solve each equation.
Check your solutions.
x /2 = x + 1/4
Solving:
From the given: [tex]\frac{x}{2}=\frac{x+1}{4}[/tex]
Applying fraction cross multiply: [tex]\mathrm{if\;\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c}[/tex]
[tex]x\cdot \:4=2\left(x+1\right)[/tex]
Distribute:
[tex]x\cdot \:4=2x+2[/tex]
Subtract 2x from both sides:
[tex]x\cdot \:4-2x=2x+2-2x[/tex]
[tex]2x=2[/tex]
Divide both sides by 2:
[tex]\frac{2x}{2}=\frac{2}{2}[/tex]
x = 1
As a result, x = 1
Check Answer:
We can substitute to check our solution:
1/2 = 1 + 1/4
1/2 = 1/2
Hence, x = 1
xcookiex12
9/12/2022
PLEASE HELP?
Pedro went to the store and spent $36.85. He paid with a $50 bill. How much money will he get back as
change? Show All Your Work for full credit.
Answer:
Step-by-step explanation:
change = dollar_amount - spent_amount
change = 50 - 36.85
change = 13.15
Find the slope of the line through each pair of points. (0,-1/2) and (7/5, 10)
The slope of the line with points (0,-1/2) and (7/5, 10) is 7.5
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x
We also refer to this tan as the line's slope
We know that slope, slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
For the pairs of points (0,-1/2) and (7/5, 10)
⇒ m = [tex]\frac{10 - (-1/2)}{(7/5) - 0}[/tex]
⇒ m = [tex]\frac{21/2}{(7/5) }[/tex]
⇒ m = 15/2
⇒ m = 7.5
Hence, the slope of the line with points (0,-1/2) and (7/5, 10) is 7.5
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Find the missing term(s) of each arithmetic sequence. -1, □, 11,. . . .
The missing term is 6.
Here the sequence is -1,__, 11...
An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
Here the sequence is in an arithmetic sequence, as there is a common difference between the two numbers.
To find the nth term of the sequence we have a formula:
[tex]a_{n}[/tex] = a + (n-1)d
From this we can find a common difference, as we know the 3rd term of the sequence.
[tex]a_{3}[/tex] = -1 + (3-1) d
11 = -1 + 2d
2d = 12
d = 6
Now we have to the 2nd term of the series we have
[tex]a_{2}[/tex] = -1 + (2-1) 6
= -1 + 6
= 5
Therefore the 2nd i.e., the missing term of the sequence is 5
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an elevation more than 18000 feet above sea level is considered extremely high altitude. supplementary oxygen is recommended when climbing extremely high altitudes. a mountaineer plane to climb a mountain with an elevation of 6282 meters. is supplementary oxygen recommended for the climb? why?
Based on the elevation that the mountaineer has to climb of 6,282 meters, supplementary oxygen is needed because this distance is above 18,000 feet.
How many feet is the mountaineer climbing?The limit for what is considered extremely high altitude is given in feet so the mountaineer's elevation of 6,282 meters needs to be converted to feet.
1 meter in feet is 3.28084 feet.
6,282 meters in feet is therefore:
= 6,282 x 3.28084
= 20,610.24 feet
This distance is more than the 18,000 feet above sea level which makes it extremely high altitude and so supplementary oxygen is needed.
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What is the least common denominator for the rational expressions 1 / x² -5 x-6} and 1/x²-12 x+36 ? Show your work.
The least common denominator for the rational expressions 1/x²-5x-6 and 1/x²-12 x+36 is (x-6)(x+1)(x-6).
In the given question
[tex]=\frac{1}{x^{2} -5x-6} , \frac{1}{x^{2} -12x+36}[/tex] ...(i)
First we will factor each denominator
So,
x²-5x-6
On splitting the factors of the above expression , we get
(x+1)(x-6) ....(ii)
x²-12x+36
On splitting the factors of the above expression , we get
(x-6)(x-6) ...(iii)
Substituting the value of (ii) and (iii) in (i) ,we get ;
[tex]=\frac{1}{(x+1)(x-6)} , \frac{1}{(x-6)(x-6)}[/tex]
As the LCM of denominator is the Least common denominator , we have
LCM of (x+1)(x-6) and (x-6)(x-6)
LCM=(x-6)(x+1)(x-6)
Hence the LCD is (x-6)(x+1)(x-6).
Therefore , the least common denominator for the rational expressions 1/x²-5x-6 and 1/x²-12 x+36 is (x-6)(x+1)(x-6).
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There are 80 animals on a farm. 52 of the animals are chickens.
a) What fraction of the animals are chickens?
Give your answer in its simplest form.
b) Write your answer to part a) as a decimal.
The fraction of the animals in chickens is 52/80 which is 0.65 in decimal form.
What are fractions?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters. In mathematics, there are six types of fractions: proper/improper fractions, mixed fractions, equivalent fractions, and like/, unlike fractions. A fraction has two parts: the numerator and the denominator.So, (A) The fraction of the animals is chickens: 52/80
Simplest form: 13/20
(B) In decimal form: 0.65
Therefore, the fraction of the animals in chickens is 52/80 which is 0.65 in decimal form.
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Under her cell phone plan, Jocelyn pays a flat cost of $35 per month and $5 per
gigabyte. She wants to keep her bill under $55 per month. Use the drop-down menu
below to write an inequality representing g, the number of gigabytes she can use
while staying within her budget.
g
Submit Answer
Answer:
< 5 gigabytes
Step-by-step explanation:
Let the number of gigabytes be represented as: g
Under her cell phone plan, Nicole pays a flat cost of $35 per month and $5 per gigabyte. She wants to keep her bill under $60 per month.
Under $60 = less than (<) $60
Hence, our inequality equation is given as:
$35 + $5 × g < 60
35 + 5g < 60
Collect like terms
5g < 60 - 35
5g < 25
g < 25/5
g < 5 gigabytes
Therefore, the number of gigabytes she can use while staying within her budget less than 5 gigabytes
1=t +√2t-3. please show your working
Answer: t=2
Step-by-step explanation:
[tex]1=t+\sqrt{2t} -3\\1-1=t+\sqrt{2t}-3-1\\0= t+\sqrt{2t} -4\\Thus,\\t+\sqrt{2t} -4=0\\Let`s\ \sqrt{t} =x\geq 0\\\Rightarrow\ x^2+\sqrt{2} x-4=0\\x^2-\sqrt{2} x+2\sqrt{2}x-4=0\\ x(x-\sqrt{2})+2\sqrt{2} ( x-\sqrt{2})=0\\ (x-\sqrt{2})(x+2\sqrt{2})=0\\\\x-\sqrt{2} =0\\ x-\sqrt{2}+\sqrt{2}=0+\sqrt{2} \\ x=\sqrt{2}\\ \Rightarrow\ t=(\sqrt{2})^2\\ t=2\\\\x+2\sqrt{2} =0\\x+2\sqrt{2} -2\sqrt{2} =0-2\sqrt{2} \\x=-2\sqrt{2} \notin(x\geq 0)[/tex]
Simplify by combining like terms. -a² + 2b² + (1/4) a²
The Simplified value is [tex]\frac{-3}{4} a^{2} +2b^{2}[/tex].
Like terms are defined as terms that have same variable and and same power.
For Example ; 2a² , 6a² are like terms.
In the given question ,
[tex]=-a^{2} +2b^{2} +\frac{1}{4} a^{2} \\ \\ =-a^{2} +\frac{1}{4} a^{2} +2b^{2}[/tex]
[tex]=a^{2}(-1+\frac{1}{4} )+2b^{2}[/tex] ( taking a² common )
taking LCM and solving further we get
[tex]=a^{2} (\frac{-4+1}{4} )+2b^{2}[/tex]
[tex]=\frac{-3}{4} a^{2} +2b^{2}[/tex]
Therefore , The value by combining Like terms in -a² + 2b² + (1/4) a² is [tex]\frac{-3}{4} a^{2} +2b^{2}[/tex].
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Point Q is the midpoint of GH. GQ = 2x + 3, and GH = 5x - 5. What is the length of GQ?
Enter your answer in the box.
Answer:
[tex]\displaystyle 25 = GQ[/tex]
Step-by-step explanation:
If point Q is the centre of GH, then QH and GQ are equivalent segments. So, double the length of GQ, set it equal to the length of GH, then solve for x:
[tex]\displaystyle \boxed{4x + 6} = 2[2x + 3] \\ \\ 5x - 5 = 4x + 6 \hookrightarrow -11 = -x \hookrightarrow \boxed{\boxed{11 = x}}[/tex]
Plug the result into the expression for the length of GQ to get twenty-five units.
I am joyous to assist you at any time.
