Becky is planning a 2 100-mile trip to St. Louis to visit a college. Her car averages 30 miles per gallon
About
how many gallons will her car use on the trip?
O 12
O 70
067
034
The number of gallons of fuel required for 200 miles will be 6.7 gallons. The correct option is C.
What is an expression?In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.
Given that Becky is planning a two 100-mile trip to St. Louis to visit a college. Her car averages 30 miles per gallon.
The total miles covered in two trips will be,
100 + 100 = 200 miles
The amount of fuel will be calculated as:-
Fuel = 200 / 30
Fuel = 6.7 gallons
Therefore, the fuel quantity will be 6.7 gallons.
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How do I solve this
Answer:
Step-by-step explanation:
well, I'd just multiply each option out using FOIL
First, Outside, Inside, Last
A) (x + 2√3i)(x - 2√3i)
First x(x) = x²
Outside x(- 2√3i) = - 2x√3i
Inside x(2√3i) = 2x√3i
last (- 2√3i)(2√3i) = -(2²)(√3²)(i²) = -4(3)(-1) = 12
add them all up x² + 12 looks like it works for me
B) = x² + 36
C) = x² + 4√3 + 12
D) = x² - 12
a plane flies 5.0km due north from a point O and then 6.0km on a bearing of 060° the pilot then changes course on a bearing of 120° for 4.0km. find how far and in what direction the plane is from the starting point?
The plane flies a distance of approximately 10.536 kilometers in straight line and with a bearing of approximately 035°.
A plane that travels a distance [tex]r[/tex], in kilometers, with a bearing of [tex]\theta[/tex] sexagesimal degrees can be represented in standard position by means of the following expression:
[tex]\vec r = r\cdot (\sin\theta, \cos \theta)[/tex] (1)
We can obtain the resulting vector ([tex]\vec R[/tex]) by the principle of superposition:
[tex]\vec R = \Sigma_{i=1}^{n} [r_{i}\cdot (\sin \theta_{i}, \cos \theta_{i})][/tex] (2)
If we know that [tex]r_{1} = 5\,km[/tex], [tex]\theta_{1} = 0^{\circ}[/tex], [tex]r_{2} = 6\,km[/tex], [tex]\theta_{2} = 60^{\circ}[/tex], [tex]r_{3} = 4\,km[/tex] and [tex]\theta_{3} = 120^{\circ}[/tex], then the resulting vector is:
[tex]\vec R = 5\cdot (\sin 0^{\circ}, \cos 0^{\circ}) + 6\cdot (\sin 60^{\circ}, \cos 60^{\circ}) + 4\cdot (\sin 120^{\circ}, \cos 120^{\circ})[/tex]
[tex]\vec R = (5\sqrt{3}, 6) \,[km][/tex]
The magnitude of the resultant is found by Pythagorean theorem:
[tex]\|\vec R\| = \sqrt{R_{x}^{2}+R_{y}^{2}}[/tex]
And the bearing is determined by the following inverse trigonometric relationship:
[tex]\theta_{R} = \tan^{-1} \left(\frac{R_{y}}{R_{x}}\right)[/tex] (3)
If we know that [tex]R_{x} = 5\sqrt{3}\,km[/tex] and [tex]R_{y} = 6\,km[/tex], then the magnitude and the bearing of the resultant is:
[tex]\|\vec R\| = \sqrt{(5\sqrt{3})^{2}+6^{2}}[/tex]
[tex]\|\vec R\| \approx 10.536\,km[/tex]
[tex]\theta_{R} = \tan^{-1} \left(\frac{6}{5\sqrt{3}} \right)[/tex]
[tex]\theta_{R} \approx 34.715^{\circ}[/tex]
The plane flies a distance of approximately 10.536 kilometers in straight line and with a bearing of approximately 035°.
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solve each system of linear equations 3x+y=9, 7x+y=32
Answer:
x=23/4, y=-33/4
Step-by-step explanation:
3x+y=9
7x+y=32
3x+y=9
y=9-3x
7x+y=32
7x+(9-3x)=32
7x+9-3x=32
4x+9=32
4x=23
x=23/4
3x+y=9
3(23/4)+y=9
69/4+y=9
y=-33/4
The solution set to the given system of linear equations is -
{x} = 5.75 and {y} = - 8.25.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a system of linear equations as -
3x + y = 9
7x + y = 32
We can write -
3x + y = 9
y = 9 - 3x
Now, we can write the equation as -
7x + y = 32
7x + 9 - 3x = 32
4x + 9 = 32
4x = 23
x = 5.75 .... (1)
The, we can write {x} as -
y = 9 - 3 x 5.75
y = 9 - 17.25
y = - 8.25 ... (2)
Therefore, the solution set to the given system of linear equations is -
{x} = 5.75 and {y} = - 8.25.
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Pls help I’ll brainlest I’m failing
Step-by-step explanation:
why ? you have started it correctly already, as I can see by the margins you made on the graph.
you analyzed the problem correctly, approached the solution correctly and gathered all necessary data.
so, I am not sure, what your problem is.
if you don't know what a slope is, then I don't understand why you did what you did so far.
the slope is expressed as the ratio
y coordinate change / x coordinate change
when going from one point to the other.
for these 2 points you marked, you also showed that
x changes by +2 (from 2 to 4).
y changes by +6 (from -4 to 2).
so, the slope is +6/+2 = 3.
that's it. that is all to it.
Evaluate the difference quotient for the given function.
f(t) = g(t) h(t) , where g(t) = cos(t) and h(t) =sin(t)
Assuming you mean f(t) = g(t) × h(t), notice that
f(t) = g(t) × h(t) = cos(t) sin(t) = 1/2 sin(2t)
Then the difference quotient of f is
[tex]\dfrac{\frac12 \sin(2(t+h)) - \frac12 \sin(2t)}h = \dfrac{\sin(2t+2h) - \sin(2t)}{2h}[/tex]
Recall the angle sum identity for sine:
sin(x + y) = sin(x) cos(y) + cos(x) sin(y)
Then we can write the difference quotient as
[tex]\dfrac{\sin(2t)\cos(2h) + \cos(2t)\sin(2h) - \sin(2t)}{2h}[/tex]
or
[tex]\boxed{\sin(2t)\dfrac{\cos(2h)-1}{2h} + \cos(2t)\dfrac{\sin(2h)}{2h}}[/tex]
(As a bonus, notice that as h approaches 0, we have (cos(2h) - 1)/(2h) → 0 and sin(2h)/(2h) → 1, so we recover the derivative of f(t) as cos(2t).)
i need help with this question pls
Answer:
etra cheese
Step-by-step explanation:
mark me brainleist
log, a Consider the graph of the function f 2- X O -2 2 4 6 8 10 -2 - What are the features of function gif g(t) = -|(r) - 1; oyintercept at (0,-1) X-intercept at (1,0) range of (-1,00) domain of (0, 0) vertical asymptote of g = 0
Answer:
X-intercept at (1/2 ,0)
domain of (0, infinity)
Vertical asymptote of x = 0
Step-by-step explanation:
Plato I got it right on the test
(−3, −1), (−1, 5) Find the slope of the line that passes through the pair of points.
[tex]slope = \frac{ 5 - ( - 1)}{ - 1 - ( - 3)} \\ [/tex]
[tex]slope = \frac{5 + 1}{ - 1 + 3} \\ [/tex]
[tex]slope = \frac{6}{2} \\ [/tex]
[tex]slope = 3[/tex]
Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. Together they charged a total of $2750.
What was the rate charged per hour by each mechanic if the sum of the two rates was $205 per hour?
-Whats the First mechanic: $ -----per hour
-Whats the Second mechanic: $ ---- per hour
The square below represents one whole.
What percent is represented by the shaded area?
Izzo's Pizza sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what she found.
Type of Crust Number Sold
Thin crust
344
Thick crust
391
Stuffed crust 155
Pan style
185
Based on this information, or the next 3500 pizzas she sells, how many should she expect to be thin crust? Round your answer to the nearest whole number. Do
not round any intermediate calculations.
Answer all of them plzz
Answer:
a) (2x+3) (x+4)
b) (5x-3) (x-1)
c) (-2x-3) (x-3)
d) 3(x-1) (3x-8)
e) -2(3x+5) (x-2)
f) h(4x-3) (3x-4)
g) -(x-3) (x+7)
h) (3x-2) (x+3)
i) 2(2x+1) (x-2)
j) (3h+2) (h-7)
Step-by-step explanation:
your welcome :)
Answer:
a)
(x+4)(2x+3)
b)
(x-2)(5x-3)
c)
(-x+3)(2x-3)
d)
3(x-1)(3x-8)
e)
2(-x+2)(3x+5)
f)
h(3x-4)(4x-3)
g)
(x+7)(-x+3)
h)
(x+3)(3x-2)
i)
2(x-2)(2x+1)
j)
(h-7)(3h+2)
Hope this helps!
6/7 divided by 12/14 please show the work
Answer:
1
Step-by-step explanation:
When dividing one fraction by another, the best way to solve it is to multiply by the reciprocal. The reciprocal just flipping the fraction over. So you would leave the 6/7 and the multiply by 14/12( because you are multiplying by the reciprocal). When you do that, you then can just multiply the top and the bottom to form one fraction. The numerator is 6*14 = 84, and the denominator is 7*14 = 84. So you are left with 84/84 which anything over itself is equal to one.
Hope this helps!
Professor Lee Xiao teaches an online class. She is paid $2,409 for up to 25 students,
plus an extra of $136 for every student beyond 25.
Professor Xiao is paid $3,262 for the class. How many students did she have? (Round
to the nearest integer).
acha
Answer:
25 + 6 = 31
Step-by-step explanation:
Her actual pay is 3262
Her base rate is 2409 Subtract to get the amount over the base
Amount of + 25 853
So how many student more does that amount to?
853 / 136 = 6.27
If you have to round to the nearest integer, the answer is 6.
#3
Determine whether the ratios are equivalent.
5:2 and 30: 12
o equivalent
not equivalent
Answer:
yes
Step-by-step explanation:
Ratios are equivalent if they are multiples or divisors of each other.
5 : 2 ( multiply both sides by 6 )
= 30 : 12
or
30 : 12 ( divide both sides by 6 )
= 5 : 2
Thus 5 : 2 and 30 : 12 are equivalent ratios
Answer:
equivalent
Step-by-step explanation: 5 x 6 = 30 2 x 6 = 12
(07.03 LC)
Identify the factors of x2 - 8x - 20. (1 point)
O (x + 4Nx - 5)
O (x + 5)(x - 4)
O (x - 10)(x + 2)
O (x-2)(x + 10)
Answer:
(x - 10)(x + 2)
Step-by-step explanation:
We are looking for two things that multiply together to give us
x^2 - 10x - 20
These things are binomials, such as (x+2) or (x-7) or (x+8) or (x-5)
We know the first term in the binomial has to be x, because x times x is x^2.
And then we are looking for two numbers that multiply to -20 but also add up to -8.
-10 and 2 multiply to make -20 and add up to -8 so we pick the answer (x-10)(x+2)
Answer:
Option C
Step-by-step explanation:
x² - 8x - 20
x² - (10x - 2x) - 20
x² - 10x + 2x - 20
x(x - 10) + 2(x - 10)
(x - 10)(x + 2)
Hence
Option C is correct
1. It is a way of comparing two or more quantities having the same units. * 1 point O a. decimal O b. addends . O c. ratio O d. numerals 2. Which of the following fractions is appropriate equivalent fraction of 3/4. 1 point O a. 4/8 O b. 9/12 O c. 10/15 Oc O d. 12/17
Answer:
Step-by-step explanation:
Equivalent fractions for 1/4
From this chart, we can observe that the equivalent fractions of 1/4 are: 2/8, 3/12, 4/16,... Two fractions are said to be equivalent if their values (decimal/graphical) are the same. We usually multiply the numerator and denominator of a fraction by the same number to get its equivalent fraction.
20% of a number is 184. What is the number
Answer:
20% is 184
100% is x
x= 184 • 100/20
x= 920
1. How can you tell by looking at each graph that a proportional relationship exists between the quantities? 2. Find the constant of proportionality for each graph. Write your answer as y = kx.
Answer:1. How can you tell by looking at each graph that a proportional relationship exists between the quantities?
relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate. For each point (x, y) on the graph, ž is equal to k, where k is the unit rate. The point (1, k) is a point on the graph.
2. Find the constant of proportionality for each graph. Write your answer as y = kx.
y = kx or y = k/x, where k determines how the two variables are related to one another. This k is known as the constant of proportionality.
Step-by-step explanation:
88, 89, 86, 90, 83, 81, 89
What is the median number
A 88
B. 89
C 90
D. 86
Please answer this I really need help
Answer:
The answer is 90.
Step-by-step explanation:
90 is in the middle
Answer:
d
Step-by-step explanation:
cause i said so
6. Expand the brackets: a) 3(x - y) )
Answer:
3x-3y
Step-by-step explanation:
3(x-y)
open the brackets:
(3×x)-(3×y)
= 3x-3y
Find x round. your answer to the nearest tenth of a degree
Answer:
x = 55.6
Step-by-step explanation:
Recall the 3 main trig functions
Sin = opposite / hypotenuse
Cos = adjacent / hypotenuse
Tan = opposite / adjacent
Note that hypotenuse = longest side length
We want to find angle "x".
We are given its opposite side length ( 19 ) as well as the adjacent side length
When dealing with the opposite and adjacent we use tan
Tan = Opp / Adj
Opp = 19 and Adj = 13
Tan(x) = 19/13
* take the inverse tan of both sides *
x = 55.6
Solve -2/3x > 8 or -2/3x < 4.
{x | x > -12 or x < -6}
{x | -12 < x < -6}
{x | x < -12 or x > -6}
{x | x < -12 or x > -6}
=========================================================
Explanation:
Let's solve the first inequality for x.
(-2/3)x > 8
-2x > 8*3
-2x > 24
x < 24/(-2)
x < -12
The inequality sign flips when we divide both sides by a negative value.
Let's do the same for the second inequality.
(-2/3)x < 4
-2x < 4*3
-2x < 12
x > 12/(-2)
x > -6
The conclusion of each section is that x < -12 or x > -6 which points us to choice C as the final answer.
Side note: The intervals x < -12 and x > -6 do not overlap in any way. There's a gap between the two pieces. We consider these intervals to be disjoint. The number line graph is below.
I NEED HELP PLSSS GEOMETRY
Answer:
Its the first one (top left option)
Step-by-step explanation:
ur in a rush so i wont explain, pls give me brainliest
Which of the following rules represents the function shown in the table?
f(x)=n+3
f(x)=3n
f(x)=1/3n
Answer:
f(x)=3n
Step-by-step explanation:
We can see it goes x=2 to y=6 this has been times by 3, x=-1 to y=-3 also times by 3 and x=0 y=0 0x3=0
In a chess club there are 10 males and 15 females. What percentage of the club is females?
Answer:
Step-by-step explanation:
A pencil at a stationery store costs $1, and a pen costs $1.50. Shawn spent $12 at the store. He bought a total of 9 items. Which system of equations can be used to find the number of pencils (x) and pens (y) he bought? (5 points)
1.5x + y = 12
x = 9y
x + 1.5y = 12
x + y = 9
x + 9y = 12
x = 1.5y
9x + y = 12
x = 1.5y
Answer:
9 = x + y
1x + 1.5y = 12
Step-by-step explanation:
9 (number of items) = x (number of pencils) + y (number of pens)
1x (cost of x number of pencils) + 1.5y (cost of y number of pen s)= 12 (total cost)
Sean has three dollars more than twice as much money as Peter if Sean has $10 how much money does Peter have
Answer:
peter has $3.50
Step-by-step explanation:
3.50 times 2 is 7 plus 3 is 10
The cost of a bag of fruits is proportional to the number of pounds. The cost for 1 ⅕ pound of fruit is $6.54. How much does a pound of fruits cost? Write an equation based on your answer.
From the computation done, the cost of the pound of fruits based on the information will be $5.45.
From the information given, it's stated that the cost of a bag of fruits is proportional to the number of pounds and that cost for 1 ⅕ pound of fruit is $6.54.
Therefore, to calculate the cost of a pound of fruit, this will be:
= 6.54 / 1 ⅕
= 6.54 / 1.2
= $5.45
Therefore, the pound of fruits cost $5.45.
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