x represents the amount of gas in the tank, has a domain described by which inequality
[tex]0 \leq x \leq 3[/tex]
This is further explained below.
What is inequality?Generally, A typical 3-gallon lawnmower requires 0.6 gallons of petrol per hour.
This circumstance is modeled by a function, where x is the volume of gas in the tank.
The lawnmower's gas tank has a maximum capacity of gallons and may be completely empty (having 0 gallons of gas).
In conclusion, a function's domain is
[tex]0 \leq x \leq 3[/tex]
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What is the answer to 5x+10=-15?
Answer:
-5
Step-by-step explanation:
5x + 10 = -15
a) Subtract 10 from both sides.
5x + 10 - 10 = -15 - 10
5x = -25
b) Divide both sides by 5.
5x/5 = -25/5
-25/5 = -5
Your answer would be -5
The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 30 pints of a mixture that is 70% pure fruit juice?
20 of the 65 percent pure fruit juice, 10 of the 90 percent pure fruit juice.
What is percentage ?A fraction that is parts out of 100 is referred to as a percentage.100% is the totality. The percentages that make up a whole add up to 100%.When representing a percentage as a number, the % symbol is used. A decimal, fraction, mixed number, integer, or other type of number can be used.In a grid of 100 squares, shading can be used to represent a percentage.
First, we define our variables: let x be the number of pints of the first fruit drink (65% pure fruit juice), and y be the number of pints of the second fruit drink (90%pure fruit juice).
We know that there are 30 total pints of the mixture. Thus:
x+y=30
We also know that 90%of those 30 pints will be pure fruit juice, and all of the pure fruit juice will come from xor y.
For x pints of the first juice, there is .65x pure fruit juice. Similarly, for ypints of the first juice, there is .90y pure fruit juice. Thus, we get:
.65x+.90y=30 ×0.7
Now we solve. First I'll get rid of the decimals in the second equation by multiplying by 100:
65x+90y=2100
Multiply the first equation by 65 on both sides to be able to cancel out one of the terms:
65x+65y=1950
Subtract the second equation from the first equation:
25y=250
y=10
Thus, we need 10 pints of the second fruit juice (90%pure fruit juice). This means that we need 30−10=20 pints of the first fruit juice (65% pure fruit juice).
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Write a system that would produce the graph below
Answer:
2x -y ≥ -53x +y < 10x +2y > 0Step-by-step explanation:
You want a system of inequalities that will define the area within the triangle with vertices (-2, 1), (1, 7), and (4, -2), including only the left side.
Linear equationsAn equation through points (x1, y1) and (x2, y2) can be written as ...
(y2 -y1)x -(x2 -x1)y = x1·y2 -x2·y1
Removing any common factor from the coefficients, and making sure the leading coefficient is positive will put this in standard form.
For points (-2, 1) and (1, 7), the equation of the line can be ...
(7 -1)x -(1 -(-2))y = (-2)(7) -(1)(1)
6x -3y = -15 . . . simplify
2x -y = -5 . . . . . divide by 3 (shading is right of the solid line)
For points (1, 7) and (4, -2), the equation of the line can be ...
(-2 -7)x -(4 -1)y = (1)(-2) -(7)(4)
-9x -3y = -30 . . . simplify
3x +y = 10 . . . . . . divide by -3 (shading is left of the dashed line)
For points (4, -2) and (-2, 1), the equation of the line can be ...
(1 -(-2))x -(-2 -4)y = (4)(1) -(-2)(-2)
3x +6y = 0 . . . simplify
x +2y = 0 . . . . divide by 3 (shading is right of the dashed line)
InequalitiesIn each of the above equations, the x-coefficient is positive. This means the equal sign can be replaced with > when shading is right of the line, and with < when shading is left of the line.
There will be an "or equal to" symbol when the line is solid.
This means our inequalities are ...
2x -y ≥ -53x +y < 10x +2y > 0Please help me solve this problem 20 points
Answer:
56
Step-by-step explanation:
[tex]\binom{8}{3}=\frac{8!}{5!3!}=56[/tex]
Evaluate the expression: No 4m2 when m = 3
We solve as follows:
[tex]f(3)=4(3)^2\Rightarrow f(3)=36[/tex]The solution is 36.
Wat 8x3 to get a answer
Answer:
24
Step-by-step explanation:
PLEASE HELPP ME
Solve the absolute value equation, making sure to show all steps of your work.
-1/3|2x - 4|=-6
The required solution of the given absolute value equation is 11 and -7.
Given that,
An absolute value equation is given, -1/3|2x - 4|=-6.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given expression.
-1/3|2x - 4| = -6
|2x - 4| = -6 (-3)
|2x -4| = 18
(2x - 4) = ±18
Now.
Taking (+)
2x - 4 = 18
x = 11
Similarly,
Taking (-)
2x - 4 = -18
x = -7
Thus, the required solution of the given absolute value equation is 11 and -7.
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What is the slope of a line that passes through the points: (3, 1) and (-2, 2)? Please no links, and get to the point quickly.
Answer:
-1/5 is the slope
Step-by-step explanation:
the equation
y2-y1 over x2-x1
In the diagram below ∠1≅∠2 and m∠CFB=124°. Find each of the following.m∠1=___m∠2=___ m∠3=___m∠4=___m∠CFB= 124°
Angles and lines
We are given the following information
Angle 1 is congruent with angle 2. They have equal measures
Angle CFB measures 124°
Note that angles 4 and F are linear because they are formed by the intersection of two lines.
Linear angles add up to 180°
This means that the measure of angle 4 is:
m angle 4 = 180° - m CFB
m angle 4 = 180° - 124°
m angle 4 = 56°
now note angle 4, 1, and 2 form a straight angle of 180°. This means that
m angle 4 + m angle 1 + m angle 2 = 180°
Since angles 1 and 2 are congruent:
m angle 4 + 2* m angle 1 = 180°
Knowing that m angle 4 = 56°:
56° + 2* m angle 1 = 180°
Subtracting 56°:
2* m angle 1 = 124°
Solving:
m angle 1 = 124° / 2 = 62°
Thus, both angles 1 and 2 measure 62°
Finally, being angles 3 and 4 vertical angles (opposed by a vertex), they are congruent, thus
m angle 3 = m angle 4 = 56°
The solution is given below:
The graph of f(x) is shown. Sketch the graphs of the following functions.1/2f (x)
1/2f(x) where f = 1 is plotted and sketched on the graph.
(Refer the graph attached below)
What are graphs of functions?The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph.We could also say that the graph of f is the graph of y = f. (x). As a result, the graph of an equation is a particular instance of the graph of a function. To determine if a graph represents a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and only ever touches it at one point. The graph is not a function if the vertical line touches it at more than one location.So, let locate function 1/2f(x) on the graph:
Where f = 1(Refer to the graph attached below)Sketch the region as follows.Therefore, 1/2f(x) is plotted and sketched on the graph.
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Evaluate the following expression
28-(-2/3)x 9.6
Answer:
34.4
Step-by-step explanation:
check whether x=1 is a solution of 3x-8
Answer: its 3
Step-by-step explanation: i looked it up and i found a quiz with the same question it was correct
Can someone help me with the answer
The area of triangle ABC is 17.5 or 35/2
To solve this, we need to know the base and height of the triangle.
In this case, the base is the side AB, and the height is the side BC
Now we can count the units to get the lenght of the sides:
AB is 7 units long
BC is 5 units long.
Now we can use the formula for the area of a triangle:
[tex]A=\frac{bh}{2}[/tex]Where A is the area, b is the base and h is the height.
Putting the values of b and h:
[tex]A=\frac{7\cdot5}{2}=\frac{35}{2}=17.5[/tex]Then the area is 35/2 or 17.5 square units
Pleasee helpp
Identify where T goes if X is the midpoint of BT
The location of T is 3 units from the midpoint X or 6 units from the endpoint B
Midpoint of a Line
In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
Since one of the endpoints is BX and the endpoint is XT and the midpoint is X.
The distance between B and X is 3 units.
Since X is the midpoint, the distance between X and T is equal to 3 units.
Therefore, the distance between B and T is 6 units and the location of T is 3 units from X or 6 units from T.
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The image shows a quadrilateral inscribed in a circle. 12 11 10 9 8 7 6 5 4 3 2 1 0 2 3 4 -7 -10 -11 -12 -12-11-10 9 8 7 012 3 4 5 6 7 8 9 10 11 12 hat is the value of x ? A 23.1 B 21.1 C 25.1 D 22.6 E 19.1
We have a quadrilateral inscribed in a circle.
The quadrilateral is a trapezoid.
When we have a quadrilateral inscribed in a circle, opposite angles are supplementary.
Then, we can write:
[tex]\begin{gathered} m\angle C+m\angle B=180\degree \\ 4x+(4x+11)=180 \\ 8x=180-11 \\ 8x=169 \\ x=\frac{169}{8} \\ x=21.125 \\ x\approx21.1 \end{gathered}[/tex]Answer: x = 21.1
Use numerals instead of words.
Explain how to compare the products of two expressions without multiplying the numbers.
Since 40 x (951-686) can be rewritten as * 5x (951-686), the value of 40 x (951-686) is
of 5 x (951-685).
Since 40 x (951-686) can be rewritten as 5x (951-686), the value of 40 x (951-686) is 8 times as value of 5 x (951-685).
In what ways does multiplication compare?A multiplicative comparison compares two expressions so that they are produced when one is multiplied by a certain number.
You must be able to distinguish between the given expressions in order to do that.
So the expression 40 x (951-686) can be rewritten as 5 x (951-686), the value of 40 x (951-686) is 8 times of the expression 5 x (951-685) as we can notice here.
Without engaging in a complicated multiplication process we have to comprehend the two expressions to find the difference between the respective products.
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Find the coefficient of the x^2 term in the expansion of (5x-2)^6 //Series and sequences precalculus
We need to expand the term:
[tex](5x-2)^6[/tex]This seems like a colossal task, we would need to multiply (5x-2) 6 times. However, we can use a useful tool that is called the 'Pascal's triangle'
I'll paste an image of it above
We will use it in this way:
Each one of the rows, represent the n in the term:
[tex](x+y)^n[/tex]So, if we have the expression (x+y) we will pay attention to the upper row, if we have (x+y)^2 we will need the second row, and so on.
In our case, we need the 6th row.
Now, usually a term of the form
[tex](x+y)^6=ax^6+bx^5y+cx^4y^2+dx^3y^3+ex^2y^4+fxy^5+gy^6[/tex]As we say, look at the 6th row of the triangle, the numbers a, b, c,..., and g are given there!
[tex]\begin{gathered} a=1 \\ b=5 \\ c=10 \\ d=10 \\ e=5 \\ f=1 \end{gathered}[/tex]And we need the term that corresponds to x^2, we need the number e=5!
So, after the expansion, the coefficient of the term x^2 will be equal to 5
Tyler was making a meal for his family. For every 3/4 pound of beef, the recipe calls for 9/8 cups of broccoli. How many cups of broccoli would be needed for a pound of beef?
Group of answer choices
1/2 cup of broccoli per beef
1 and ½ cup of broccoli per beef
2/3 pound of broccoli per beef
5/4 cup of broccoli per beef
Proportionately, the number of cups of broccoli needed for a pound of beef is B. 1 and ½ cups of broccoli per beef.
What is proportion?Proportion refers to the numerical quantity or relationship of one variable to another, which are set equal to each other.
Proportions, like ratios, use fractional values because they show the quantity of one variable in another.
We state proportions in fractions, decimals, or percentages.
The proportion of 3/4 pound of beef to broccoli = 9/8 cups of broccoli
3/4 pound = 0.75 pound
9/8 cups = 1.125 cups
The number of cups of broccoli for a pound of beef = 1.5 cups (1.125/0.75)
1.5 cups = 1½ cups
Thus, given the proportional relationship presented, for a pound of beef, Tyler would need 1½ cups of broccoli.
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dean is going to deliver some goods. he charges £7.00 an hour and 40p per mile for delivery.
he writes down his mileage before and after he has made his journey. this journey takes 2h and 45minutes.
how much does he charge to deliver these goods?
Answer:
See below
Step-by-step explanation:
Time charge = 2.75 hr * £7.00/hr = £ 1`9.25
Mileage charge = ( 25423 - 25263) mi * 40p / mile = 6400 p
(edited: forgot to multiply by 40p)
Now add the two charges together : 19 + (.25 * 240) + 6400/240 =
£ 45.92
( I think <===if I correctly did the monetary conversion between pence and pounds! <=== I used 240 p = 1£ )
Step-by-step explanation:
what we were not told is, if he charges a full hour for a fraction of an hour, or only a corresponding fraction of his hourly rate.
I assume the first : charging a full hour for any fraction of an hour spent.
it took him 2h and 45 minutes, so that is 3 hours charged.
and he was driving
25423 - 25263 miles = 160 miles
so, he charges
3×7 + 160×0.40 = 21 + 64 = £85
if he charges also fractions of his hourly rate, then his hourly charge would be
2 3/4 × 7 = (2×4 + 3)/4 × 7 = 11×7/4 = 77/4 = £19.25
in total that would be
19.25 + 64 = £83.25
Let -3 -5 be a point on the terminal
We have a terminal point (-3,-5).
We have to find cos(θ), csc (θ and tan)(θ.)
We can locate the terminal point and the angle as:
The cosine of this angle will be negative, as ( is located in the third quadrant)
The hypotenuse of this right triangle will be called R and we can calculate it using the Pythagorean theorem:
[tex]\begin{gathered} R^2=x^2+y^2 \\ R=\sqrt[]{x^2+y^2} \end{gathered}[/tex]We can estimate the cosine as:
[tex]\begin{gathered} \cos (\theta)=\frac{x}{R} \\ \cos (\theta)=\frac{-3}{\sqrt[]{(-3)^2+(-5)^2}} \\ \cos (\theta)=\frac{-3}{\sqrt[]{9+25}} \\ \cos (\theta)=\frac{-3}{\sqrt[]{34}} \\ \cos (\theta)=\frac{-3\sqrt[]{34}}{34} \end{gathered}[/tex]We can now relate this to the csc(θ) as:
[tex]\begin{gathered} \csc (\theta)=\frac{1}{\sin (\theta)} \\ \csc (\theta)=\frac{1}{\frac{y}{R}} \\ \csc (\theta)=\frac{R}{y} \\ \csc (\theta)=\frac{\sqrt[]{34}}{-5} \\ \csc (\theta)=-\frac{\sqrt[]{34}}{5} \end{gathered}[/tex]Finally, we can calculate the tangent as:
[tex]\begin{gathered} \tan (\theta)=\frac{y}{x} \\ \tan (\theta)=\frac{-5}{-3} \\ \tan (\theta)=\frac{5}{3} \end{gathered}[/tex]Answer:
cos(θ) = -3√34/34
csc(θ) = -√34/5
tan(θ) = 5/3
Write the equation of a line that is parallel to the line 2x - 3y = 5 and passes through the point (3, -1)
Answer:
The equation of the line is 2x - 3y = 9
Step-by-step explanation:
Given:
Write the equation of a line that is parallel to the line 2x - 3y = 5 and passes through the point (3, -1)
Solve:
- The line is parallel to the line 2x - 3y = 5
⇒ the slope of the line = the slope of the line 2x - 3y = 5
- Rearrange the terms of the equation to be in the form
⇒ y = mx + c to find the slope of it
2x - 3y = 5 → subtract 2x from both sides
-3y = 5 - 2x ⇒ divide two sides by -3
y = 5/-3 - 2x/-3 ⇒ y = 2/3 x - 5/3
The slope of the line is 2/3
Given that: The line passes through point (3, -1)
Lets use the rule to find the equation of the line:
y - (-1)/x - 3 = 2/3
y + 1/x - 3 = 2/3 ⇒ by using cross multiplication
3(y + 1) = 2(x - 3) ⇒ open the brackets
3y + 3 = 2x -6 ⇒ put x and y on one side
2x - 3y = 3 + 6
2x - 3y = 9
The equation of the line is 2x - 3y = 9
~Kavinsky
What is the volume??
what is volume answer the volume is your topic for to day
What percent of 240 is 132? pls I need it now
Answer:
55%
Step-by-step explanation:
Answer:
55%
132 is 55% of 240
Step-by-step explanation:
Can you explain the steps for the y intercept and slope. x-10 = 4y
I came up with (10, 0)
A can of cola has 41 grams of sugar in each
12-ounce can. If you drink nine cans over the span
of a week, how many pounds of sugar have you
consumed during that week from the soda?
The amount in pounds of sugar consumed during that week from the soda is 0. 0677 pounds
What is proportion?A proportion can be defined as an equation in which two elements, or numbers are being set equal to each other.
It is known as a mathematical comparison between two elements or things.
It is also defined as a comparative relation on the basis of size or magnitude of elements, quantity and numbers.
From the information given, we have that;
41 grams of sugar is in each 12-ounce can
To determine the ounces in 9 cans, we have;
If 41 grams = 12 cans
Then, x = 9 cans
cross multiply
x = 41(9)/12
expand the bracket
x = 30. 75 grams
Let's convert grams to pounds
1 gram = 0. 0022 pounds
30. 75 grams = x
x = 30. 75(0. 0022)/1
x = 0. 0677 pounds
Hence, the value is 0. 0677 pounds
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Tickets for the monster truck rally cost $12 for children and $20 for adults. Last
night 400 total tickets were sold for a total of $6000. Use c for the child tickets and
a for adult tickets. If one of the equations for this system is a + c = 400, write
the second equation for this system below.
Answer:
500
Step-by-step explanition
12-children
20-adults
400 sold for 6000
c-children were
500
group 1 bought 9 tickets and received a 120 discount, group 2 bougt 3 tickets and recived a 30 dollar discount both groups spentthe total amount of money on tickets
the price of each ticket was the same
what was the cost of each ticket?
The cost of each ticket bought by each of the group is $15.
What is the cost of each ticket?The linear equation that represents the total cost spent by group 1 on the tickets is:
Amount spent = total amount spent on the tickets - discount
9x - 120
The linear equation that represents the total cost spent by group 2 on the tickets is:
3x - 30
Where:
x = is the cost of the tickets
If both groups spend the same amount, the above two linear equations would be equal to each other
3x - 30 = 9x - 120
In order to determine the value of x, take the following steps:
Combine similar terms together: 120 - 30 = 9x - 3x
Add similar terms: 90 = 6x
Divide both sides by 6
x = 90 / 6
x = 15
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2yd - 1ft = _____yd ______ft?
Answer: 1yd 2ft
Explanation
s we have a subtraction, we have to have the same units. Thus, in order to do so we have to consider that 1 yd = 3ft:
[tex]\frac{3ft}{1yd}[/tex]Then, converting 2yf to ft:
[tex]2yd\cdot\frac{3ft}{1yd}=6ft[/tex]Now, we can make the subtraction:
[tex]6ft-1ft=5ft[/tex]Finally, we can convert 3 ft to one yd:
[tex]3ft\frac{1yd}{3ft}=1yd[/tex]and we have 2 ft left.
Suppose
f
(
x
)
f
(
x
)
is an nth order polynomial, with a leading coefficient of 1. Find the compact expression
f
(
n
)
(
x
)
f
(
n
)
(
x
)
. That is, what is the solution (in terms of n) if you take the derivative to respect of
x
x
some n times?
Answer:
Hi
Step-by-step explanation: how are you doing
Find the equation of the exponential function that goes through the points (0,3) and (3,375).
The equation of the exponential function that goes through the points (0,3) and (3,375) is y = 5(3)^x
Exponential equationThe standard form of an exponential equation is given as y = ab^x
Using the coordinate points on the graph (0,3) and (3,375).
The equivalent equations are;
375 = ab^3
3 = ab^0
From equation2;
a= 3
Substitute into equation 1;
375 = 3b^3
b^3 = 375/3
b^3 = 125
b = 5
Determine the equation
y = 3ab^x
y = 3(5)^x
This gives the required exponential equation
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