13. Sofia's car can travel 228 miles on 6 gallons of gas.
a. Write an equation to represent the distance, y, in miles Sofia's
car can travel on x gallons of gas.
The most appropriate choice for unitary method will be given by-
y =38x is the equation to represent the distance, y, in miles Sofia's
car can travel on x gallons of gas.
What is unitary method?
Unitary method is the method in which the value of single unit can be calculated from the value of multiple unit and value of multiple unit can be calculated from the value of single unit.
Sometimes value of single unit is more than value of multiple unit
For example - Relationship between price of a commodity and quantity of a commodity
Sometimes value of single unit is less than value of multiple unit
For example - Relationship between number of men and number of days taken by those men to do a work
Here,
Let y be the distance travelled by Sofia's car in miles and let Sofia's
car can travel on x gallons of gas.
On 6 gallons of gas, Sofia's gas can travel 228 miles
On 1 gallon of gas, Sofia's car can travel [tex]\frac{228}{6}[/tex] miles
On 1 gallon of gas, Sofia's car can travel 38 miles
On x gallons of gas, Sofia's car can travel 38x miles
By the problem,
y = 38x
This is the equation to represent the distance, y, in miles Sofia's
car can travel on x gallons of gas.
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The picture shows a triangular island:Which expression shows the value of q?s over sin 55 degreess over cos 55 degreesr sin 55°r cos 55°q?
A right triangle is a triangle with a right angle. The opposite side to the right angle is called the hypotenuse and the other sides are the legs. Given an angle in a right triangle, the ratio between the leg adjacent to the angle and the hypotenuse is equal to the cosine of the angle.
Using this relation in our problem, we have the following:
[tex]\cos(55^o)=\frac{s}{q}[/tex]Solving this expression for q, we have:
[tex]\begin{gathered} \cos(55^o)=\frac{s}{q} \\ q\cos(55^o)=s \\ q=\frac{s}{\cos(55^o)} \end{gathered}[/tex]And this is our answer.
[tex]\frac{s}{\cos(55^o)}[/tex]A group of students is arranging squares into layers to create a project. The first layer has 4 squares. The second layer has 8 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer?
(d) f(1) = 4 f(n) = 4 + d(n-1) , n>0 is the arithmetic formula to find the number of layers in the project
In the above question it is given that
A project is being created by a group of students by arranging layers.
The first layer is having 4 layers and as we move to the next layers, it is getting 2 times of the number of layers in the first layer.
i,.e f(1) = 4
Number of layers in the second layer = 8 layers
f(2) = 4.2 = 8
Now, we need to find the general arithmetic formula to determine the subsequent n number of layers in the project
As the subsequent layers are getting n times of the first layer, so we'll also find the similar arithmetic formula where addition to the first layer with n times of it is happening
So, after checking all the given options we find, (d) as the appropriate option
f(1) = 4
f(n) = 4 + d(n-1) , n>0
We'll find the number of layers in the 3 layers
Here, n = 3
Putting in the formula, we'll find.
f(3) = 4 + d(3-1)
f(3) = 4 + d(2)
where d(2) = 8 (given)
so, f(3) = 4 + 8 = 12
Hence, f(1) = 4 f(n) = 4 + d(n-1) , n>0 is the arithmetic formula to find the number of layers in the project
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I'll send you the question
We know that
< means smaller than
≤ means smaller or equal to
> means greater than
≥ means greater or equal to
We want to find a number (let's call it x), greater than -34
Since, > means greater than, we use this symbol:
y > -34
Answer: Dcan someone help me really quick
Answer:
21
Step-by-step explanation:
63 divided by 3 is 21
210 divided by 10 is 21
PLS HELP
Lisa needs at least 870 gigabytes of storage to take pictures and videos on her upcoming vacation. She checks and finds that she has 200 gigabytes available on her phone. She plans on buying additional memory cards to get the rest of the storage she needs. Lisa is going to use memory cards that each hold 256 gigabytes.
Let C represent the number of memory cards that Lisa buys.
Which inequality describes this scenario?
The inequality that describes this scenario would be; A. 200 + 256C ≥ 870.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions. If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.
Given that lisa checks and finds that she has 200 gigabytes available on her phone. It is going to use memory cards that each hold 256 gigabytes.
Let consider that C represent the number of memory cards that Lisa buys.
Then the inequality ;
200 + 256C ≥ 870
Hence, The inequality that describes this scenario would be; A. 200 + 256C ≥ 870.
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whats the anwser to 8ab - 5ab I want to know
Answer:
3ab
Step-by-step explanation:
i hope you don't want to know how i did this :)
5.
What is the LCD of 1, 3
4x x(x-4)
A. (x-4)(x+2)
B. 4x(x²+2x-8)
and
5?
x(x+2)
C. 4x(x-4)(x+2)
D.
x(x-4)(x+2)
4
Select the algebraic definition for the piecewise function graph.
Y=2x+4
y=4
Y=-2x+8
The answers (C) and (D) are accurate:.
F(x) = 4; 0 = x 2 and F(x) = -2x + 9; 2 = x 4 respectively.
How a piecewise function is defined?A piecewise function's graph has a large number of curve elements. It means that, depending on the value of the input, it has a wide range of definitions. To put it another way, a piecewise function reacts differently to the input.
It follows that:
The image displays the piecewise function:
Observing the piecewise function's graph
Every value in the domain is associated to exactly one value in the range according to the function, which may be thought of as a unique kind of connection with a predefined domain and range.
F(x) = 4; 0< = x < 2
F(x) = -2x + 9; 2 < = x < 4
Thus, F(x) = 4; 0< = x < 2 and F(x) = -2x + 9; 2 < = x < 4 the option (C) and (D) are correct.
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The correct question is:
" 2) Select the algebraic definition for the piecewise function graph.
F(x){_____ 0< = x < 2
{_____ 2 < = x < 4
A. 2x-8
B. 2
C. -2x+8
D. 4
E. 2x-4"
The Earth is approximately 8.0 x 103 miles in diameter, from pole to pole.What number is the distance equivalent to? A- 800 thousand milesB- 80 thousand milesC- 8 thousand milesD- .8 thousand miles
Answer
Option C is correct.
8.0 × 10³ miles = 8 thousand miles.
Explanation
The number given in scientific notation is
8.0 × 10³ miles
= 8.0 × 1000 miles
= 8000 miles
= 8 thousand miles.
Hope this Helps!!!
Please tell me what −7 7/8+3.7−(−15.9) is...
A line through (-1,b) and (c,8) is parallel to a line through (-6,3) and (0,12). Find values of b and c that make the above statement true.
Answer:[tex]b=4, c=-7[/tex]
Step-by-step explanation:
Parallel lines have the same slope.
The slopes of the lines are [tex]\frac{8-b}{c+1}[/tex] and [tex]-\frac{3}{2}[/tex].
Therefore, [tex]\frac{8+b}{c+1}=-\frac{3}{2}[/tex], and one possible pair is [tex]b=4, c=-7[/tex].
Find a translation that has the same effect as the composition of translations
Translation that has the same effect as the composition of translations is
(x, y)→ ( x+2 , y+7 )
Composition of two reflections can be expressed as translation. Composition of reflections over parallel lines always has the same effect as a translation. Combination of two or more transformations is called composition of translation.
In this case :
As given in the question , 9 units are added from the x-coordinate in the first transformation and then 7 units are subtracted. So, the sum is:
+9-7 = +2
Observe that, in the first transformation, 1 units are added to the y-coordinate and then 6 units are added. The sum is:
+6+1 = +7
Then, the single Translation that has the same effect as the given Composition of translation is calculated to be:
(x, y)→ ( x+2 , y+7 )
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Express in decimal notation. 5.51×10^-4
Step-by-step explanation:
Answer:
= 5.51 × 10⁻⁴
scientific notation
= 5.51e-4
scientific e notation
= 551 × 10⁻⁶
engineering notation
millionth; prefix micro- (u)
= 5.51 × 10⁻⁴
standard form
-4
Order of Magnitude
for scientific and standard forms
= 0.000551
(real number)
= five hundred fifty-one millionths
word form
The I-70 grade west of Denver has a grade of 5%. The horizontal length of the roadway (run)
is 5.5 miles. What is the change in elevation from the top of the grade to the bottom of the
grade in feet?
The change in the elevation is 0.275 miles.
What is an elevation?An elevation simply means the her that above the sea level. It's used to describe a geographical location.
Thethe change in elevation from the top of the grade to the bottom of the grade in feet will be:
= Percentage of change × Length given
= 5% × 5.5 miles
= 0.05 × 5.5 miles
= 0.275 miles.
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Sandy Island Beach is building a new Snack Shack based on a scale drawing that is 60 centimeters by 20 centimeters and uses the scale 1 cm : 1.5 m.
A new Snack Shack is being constructed at Sandy Island Beach which dimensions are 90 centimeters by 30 centimeters.
What is a scale image?Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object
Sandy Island Beach is building a new Snack Shack based on a scale drawing that is 60 centimeters by 20 centimeters which are given in the question
Here the scale 1 cm : 1.5 m
As per the given scale, the dimensions would be as
60 centimeters :
⇒ 60 × 1.5 = 90
20 centimeters :
⇒ 20 × 1.5 = 30
Therefore, a new Snack Shack is being constructed at Sandy Island Beach which dimensions are 90 by 30 cm.
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Which answer would be a sufficient counter example to the statement below? “Two angles that are supplementary are always different measures”
The counter example to the statement “Two angles that are supplementary are always different measures” is 90° and 90°.
What are supplementary angles?Supplementary angles are those angles that sum up to 180 degrees
In other words, two Angles are Supplementary when they add up to 180 degrees.
For example 130 degrees and 50 degrees are supplementary angles.
The statement says "two angles that are supplementary are always
different measures".
Therefore, the counter example to this statement is 90 degrees and 90 degrees. This is because they are the same and it still sum to 180 degrees.
In other words, the angles are supplementary and the same which is counter example to the statement.
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F(11/10) if f(x) = 2x -7
PLUG IN
[tex] \frac{11}{10} [/tex]
in the place of x in the function and simplify.
[tex]f( \frac{11}{10} ) = 2( \frac{11}{10} ) - 7 \\ f( \frac{11}{10} ) = \frac{22}{10} - 7 \\ f( \frac{11}{10} ) = \frac{ - 48}{10} \\ f( \frac{11}{10} ) = \frac{ - 24}{5} [/tex]
ATTACHED IS THE SOLUTION
Hello!
To solve for f(11/10)
==> must simply plug '11/10' into x's position in the equation
[tex]f(\dfrac{11}{10} )=2(\dfrac{11}{10} )-7=\dfrac{11}{5} -7=\dfrac{11}{5} -\dfrac{35}{5} =-\dfrac{24}{5}[/tex]
Hope that helps!
Use the information given to enter an equation in standard form.
Slope is 2, and (3, 5) is on the line.
Standard form of equation is 3x + 5y = 2.
Define equation.Ax+ By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful. A linear equation has the conventional form Ax+ By=C. A slope-intercept form equation (y=mx+ b) must have the x and y on the same side of the equal sign and the constant on the opposite side in order to be converted to standard form. To relocate terms, use inverse operations.
Slope = 2
Points = (3, 5 )
Standard form of equation,
Ax + By = C
Equating,
3x + 5y = 2
Standard form of equation is 3x + 5y = 2.
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x+y-7
-2x - 2y = -14
What’s y and x ?
Answer:
Step by step solution of a set of 2, 3 or 4 Linear Equations using the Substitution Method x-y=7;2x-2y=14 Tiger Algebra Solver.
Step-by-step explanation:
which polynomial function f(x) has a leading coefficient of 1, roots -4, 2, and 9 with multiplicity 1, and root -5 with multiplicity 3?
The expression for f(x) is: [tex]f(x)=(x+4) , (x-2) , (x-9) ,(x+5),(x+5),(x+5)[/tex]
We know that for any polynomial equation with roots:
[tex]a_{1}, a_{2}, a_{3} ,...[/tex]
with multiplicity:
[tex]m_{1}, m_{2}...[/tex]
the equation for the polynomial is given by:
[tex]f(x)=(x-a_{1}) ^{m_{1} }, (x-a_{2}) ^{m_{2} }...[/tex]
If the leading coefficient is negative we may take '-' sign in the starting of the expression.
Here we are given that, f(x) has a leading coefficient of 1, roots -4, 2, and 9 with multiplicity 1, and root -5 with multiplicity 3
Hence, f(x) is given by:
= [tex]f(x)=(x-(-4)) ^{1 }, (x-2) ^{1}, (x-9) ^{1},(x-(-5)) ^{3}[/tex]
= [tex]f(x)=(x+4) , (x-2) , (x-9) ,(x+5),(x+5),(x+5)[/tex]
Hence, the expression for f(x) is: [tex]f(x)=(x+4) , (x-2) , (x-9) ,(x+5),(x+5),(x+5)[/tex]
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The White family purchases a new pool table on a no-interest-for-one-year plan. The cost is $2,665. There is a d dollars down payment. If they make a minimum monthly payment of m dollars until the last month, express their last month’s payment algebraically.
The last month's payment for this family can be algebraically expressed this way: 2665 - d - 11m.
How can we algebraically represent the last month's payment?We can obtain an algebraic statement for the last month's payment when we assign alphabetic values to the variables provided.
First, the price is the primary figure that is = 2665
The down payment is represented with the alphabet d dollars.
The monthly payment is denoted by m dollars.
Since we are given a duration of one year or twelve months, we will have to subtract one month from 12 to give us, 11 months.
Given these substitutions, the algebraic statement can be represented thus:
2665 - d - 11m.
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g(y)= y - 15/y
h(y) = − 3y
Evaluate.
h(g(5)) =
Help guysssssssssssssssssssssssssssssssssssssssssssss
Answer:
i think the answer is 2<x<5
Step-by-step explanation:
What is the slope of the line that passes through the points (-10, 9)
and (-10, 18)? Write your answer in simplest form.
Hello!
What is the equation for the slope:
[tex]\hookrightarrow \text{Slope}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
(x₁,y₁): a random point on the line ⇒ (-10,9) (x₂,y₂): another random point on the line ⇒ (-10,18)[tex]Slope =\dfrac{18-9}{-10-(-10)} =\dfrac{9}{0} \\[/tex]
Thus the slope is undefined:
Hope that helps!
PLEASE HELP ME SOLVE THESE TWO ANSWERS!!
Answer:
:]
Step-by-step explanation:
x, x+2
Equation: 2x+4=2x+4
All real numbers
b) it is an identity, it has infinite solutions.
Geometry Question on Foundations, Need Help.
Answer:
Plane RAT
Step-by-step explanation:
:]
Pat and Alex have a combined total of £63.
The ratio of Pat’s money to Alex’s money is 5 : 2
They each spend an equal amount on sweets.
The ratio of Pat’s money to Alex’s money is now 3 : 1
How much did Pat spend on sweets?
Answer:
£4.50
Step-by-step explanation:
ratio of Pat : Alex = 5 : 2 = 5x : 2x ( where x is a multiplier )
then
5x + 2x = 63
7x = 63 ( divide both sides by 7 )
x = £ 9
Pat has 5 × £9 = £45
Alex has 2 × £9 = £18
let the amount they spend on sweets be x , then ratio of money is 3 : 1
so 45 - x : 18 - x = 3 : 1
express the ratio in fractional form and equate proportionally
[tex]\frac{45-x}{18-x}[/tex] = [tex]\frac{3}{1}[/tex] ( cross- multiply )
45 - x = 3(18 - x)
45 - x = 54 - 3x ( add 3x to both sides )
45 + 2x = 54 ( subtract 45 from both sides )
2x = 9 ( divide both sides by 2 )
x = 4.5
Pat spent £4.50 on sweets
What is the effect on the graph of f(x) = x2 when it is transformed toh(x) = 1/4x2 - 11?A. The graph of f(x) is horizontally stretched by a factor of 4 andshifted 11 units to the right.B. The graph of f(x) is vertically compressed by a factor of 4 andshifted 11 units down.C. The graph of f(x) is horizontally compressed by a factor of 4 andshifted 11 units down.D. The graph of f(x) is vertically compressed by a factor of 4 andshifted 11 units to the right.SUBMIT
As per transformation of graph, h(x) = 1/4x² - 11 represents that the graph of f(x) is horizontally compressed by a factor of 4 and shifted down by 11 units.
To know the effect on the graph
Given, the graph is f(x) = x².
We know that, at the time of horizontally compressing a graph we need to multiply it by a factor of (1/a).
Again, at the time of shifting a graph up we need to add a positive number of (b).
Therefore, a = 4 and b = - 11.
Now, if we horizontally compress f(x) it by a factor of (1/4) then it be (1/4)x².
Again, if we shifted down f(x) by 11 units, then it be (1/4)x² - 11.
Therefore, h(x) = (1/4)x² - 11 represents that the graph of f(x) is horizontally compressed by a factor of 4 and shifted 11 units down.
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There are 100 students in Year 10.
Each student studies exactly one of French, German, and Spanish.
X girls study French and there are 3X girls in total.
2Y boys study German.
There are 35 students studying Spanish of which Y are boys.
Which of the following is an expression for the total number of students studying German?
The expression which correctly represents the number of students studying German as required is; 3y + 2x -35.
Which expression correctly represents the number of students studying German?It follows from the task content that the number of students studying German be determined from the given information.
Therefore since the total number of students is; 100.
35 students study Spanish of which y are boys, therefore, the number of girls studying Spanish is; (35 - y).
Also, since there are 3x girls in total and x of which study French, the remaining 2x study Spanish and German.
Hence, the number of girls who study German is; 2x - (35 - y).
Therefore, the total number of students (boys and girls) who study German is; 2y + 2x - (35 - y).
= 3y + 2x -35.
Ultimately, the total number of students who study German are; 3y + 2x -35.
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