In order to determine which vehicle gets better gas mileage, we need to determine which of the two vehicles consumes less gas for each mile travelled. The car consumes 1 gallon of gas for every 32 miles. We shall now determine how many miles the truck covers to consume 1 gallon of gas.
[tex]\begin{gathered} \text{Truck} \\ 9.75gl=260\text{miles} \\ 1gl=\frac{260}{9.75}\text{miles} \\ 1gl=26.67miles \end{gathered}[/tex][tex]\begin{gathered} \text{Car} \\ 1gl=32\text{miles} \end{gathered}[/tex]Therefore, the results shows that the truck gets better gas mileage
Are the triangles congruent using AAS?
True
False
Use the drawing tool(s) to form the correct answer on the provided graph.The graph of function f is shown on the coordinate plane. Graph the line representing function g, if g is defined as shown below.g(x) = -1/2f(x + 2)
Given:
The graph of the function f is given and the function g is as:
[tex]g(x)=-\frac{1}{2}f(x+2)[/tex]Required:
To graph the function g.
Explanation:
The graph of the function f(x+2), shift the graph f(x) left 2 units by subtracting 2 from the x-coordinates of the points on the graph of f.
The graph of the function
[tex]\frac{1}{2}f(x+2)[/tex]here
[tex]a=\frac{1}{2}[/tex]So the graph of g has undergone a vertical shrinking by a factor of
[tex]\frac{1}{2}[/tex]The graph of the function
[tex]g(x)=-\frac{1}{2}f(x+2)[/tex]reflect the graph of
[tex]\frac{1}{2}f(x+2)[/tex]across the x-axis by multiplying the y coordinate of the points on the graph of
[tex]\frac{1}{2}f(x+2)[/tex]by -1.
Thus the graph of the function
[tex]g(x)=-\frac{1}{2}f(x+2)[/tex]is as:
Final Answer:
The graph of the function g is attached in the explanation part.
The graph below shows the number of bushels of soybeans a farmer harvested from his field.NUMBER OF ACRES HARVESTEDwhich set of ordered pairs could have been used to make the graph?A. (3, 125), (4, 200), (5, 225)B. (50, 1), (200, 4), (300, 6)C. (100, 2), (250, 5), (350, 7)D. (2, 100), (3, 150), (5, 250)And don't worry this is just a practice :)
From the graph, we can see that the set of ordered pairs which belongs to the line are
D). (2, 100), (3, 150), (5, 250)
Because x-axis is the first coordinate and y-axis is the second coordinate. In options B and C, they are
arranged in the wrong place. In option A, point (3,125) doesn´t belong to the line.
2(q + 4) = 10
Solve for q
Answer:
q=1
Step-by-step explanation:
2(q+4)=10
q+4=5
q=1
:]
Answer:
3
Step-by-step explanation:
2 x 3 6 4 10
Classify the four angles of the quadrilateral. С 750 B 1050 90° 90-
Anlges A and D are right angles becuase they measure 90
Angle C is Acute because it is smaller than 90
Angle B is Obtuse because it is grather than 90
Where ya got 12 from ?
Answer:
12 is the number that comes after 11 and before 13. 12 represents the number between 11 and 13. 12 is a composite number.
Step-by-step explanation:
12 is the number that comes after 11 and before 13.
12 represents the number between 11 and 13. 12 is a composite number.
Use the rule for the order of operations to simplify: 8+6(6-2(5-4))
Given the expression below
[tex]8+6(6-2(5-4))[/tex]Step 1: Using PEMDAS rule
P=> Parenthesis
E=>Exponent
M=>Multiplication
D=>Division
A=>Addition
S=> Subtraction
From the rule above, we will start our simplification with the parenthesis
Step 1: simplify (5-4)
[tex]\begin{gathered} 8+6(6-2(5-4) \\ 8+6(6-2(1)) \end{gathered}[/tex]Step 2: Expand 2(1)=> 2x1, then simplify (6-2(1))
[tex]8+6(6-2(1))\Rightarrow8+6(6-2)\Rightarrow\cdot=8+6(4)[/tex]Step 3: Expand 6(4)=>6 x 4
[tex]8+6(4)\Rightarrow8+6\times4\Rightarrow8+24[/tex]Step 4: Add 8 and 24
[tex]8+24=32[/tex]Hence, the final answer is 32
Answer: your answer would be 32
Step-by-step explanation:
using PEMDAS we would first go by parentheses and use the order by each step.
Rodger biked 30 miles in 2 hours. Write this rate as a unit rate.
Rodger biked 30 miles in 2 hours. Write this rate as a unit rate.
__________________________________
30 miles / 2 hours = 15 miles/hour
_________________________________________
Answer
15 miles/hour
PLEASE HELP WILL MARK BRANLIEST!!!
What is the equation of a line that is parallel to y = x + 2 and passes through the point (5,7)?
Enter your answer with no spaces.
Answer:
See below
Step-by-step explanation:
Slope of given line is 1 y = (1) x + 2
parallel line has same slope
so it will start to look like this y = (1) x + b
sub in the point 5,7 to find b = 2
final answer y=x+2
Please help I was sick today and I don’t understand
Answer:
This is a 30 60 90 triangle. They are saying the hypotenuse is 3x + 6 and the shortest side is 8x - 4. In a 30 60 90 triangle, the hypotenuse is 2 times the short side meaning that/
3x + 6 = 16x - 4
Now we can solve...
10 = 13x
x= [tex]\frac{10}{13}[/tex]
Figures 1 and 2 are shown in the coordinate grid. Which is a true statement?
As per given by the question,
There are given two figure on coordinate grid, figures 1 and 2.
Now,
From concept of similar figure:
Similar figure means, that have the same shape and exactly the same in every way, on the other hand;
The similar figure means they are same shape but not the same size, then these figure is also called similar figure.
Now,
From concept of the congruent figure:
The congruent means, that two figure exactly the same that means, we can say that they are congruent, when both figure have same shape and same size.
So,
According to both concept, similar and congruent;
The given figure 1 and 2 is simililar, because of same shape. But due to different size, both figure have not congruent.
So, the given figures 1 and 2 is similar, but not congruent.
Hence, the option first is correct.
Define a variable, write an inequality, and solve: A number decreased by 7 is at least 15
Inequality: [tex]x-7\ge 15[/tex]
Solution: [tex]x\ge 22[/tex]
Inequality is a mathematical statement which depicts the relation between two or more mathematical variable or quantities which involves in relation which is not equal or inequal.
Given the statement is "A number decreased by 7 is at least 15"
Let the number be the variable x.
Now decreased by 7 = x-7
Suitable inequality sign for at least statement is [tex]\ge[/tex]
So the required inequality is given by,
[tex]x-7\ge15[/tex]
Solving the same we get,
[tex]x-7+7\ge 15+7[/tex]
[tex]x\ge 22[/tex]
Thus the number is [tex]x\ge 22[/tex]
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At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric. What percentage of the player's serves were between 115 mph and 145 mph?
A) approximately 16%
B) at most 34%
C) at most 2.5%
D) at most 13.5%
The percentage of players serves were between 115 mph and 145 mph is approximately 16%.
Given :
The statistician reported that the mean serve speed was 100 miles per hour
the standard deviation of the serve speeds was 15 mph
Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric
To find :
What percentage of the player's serves were between 115 mph and 145 mph?
Solution :
μ =100
σ = 15
P ( 115 < x <145)
= P ( [tex]\frac{115-100}{15}[/tex] < x-μ /6 <[tex]\frac{145-100}{15}[/tex] )
= P ( [tex]\frac{15}{15}[/tex] < z < [tex]\frac{15}{15}[/tex] )
= p ( 1<z<3)
= p( z<3)-p(z-1)
=0.9987-0.8413
=0.1574
p ( 115<xx<145)= 15.74 %
p( 115<x<145)= approximately 16%
The percentage of players serves were between 115 mph and 145 mph is approximately 16%.
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The following expression gives an approximate value of the total average credit card debt in a U.S. household (in dollars)
t
years after 1995.
420
t
+
5750
Use this expression to predict what the total average credit card debt was or will be in the year 2006.
Answer: In the year 2006, the total average credit card debt for a U.S. household will be (or was)
dollars.
In the year 2006, the total average credit card debt for a U.S. household was 10370 dollars.
How to solve Exponential functions?
We are given the expression that gives an approximate value of the total average credit card debt in a U.S. household (in dollars), t years after 1995 as;
420t + 5750
where t represents number of years after the year 1995. Thus, for the year 2006, the value of t is;
t = 2006 - 1995
t = 11 years
Thus;
f(11) = 420(11) + 5750
f(11) = 10370 dollars
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(b) Use the function to predict the average price per square foot in 2032 .
Answer:
1187.49
Step-by-step explanation:
[tex]P(40)=0.023(40)^3-0.289(40)^2+3.068(40)+55.170=1187.49[/tex]
Jordan wants to use the Starz princess hall, the Dynamic DJ's as his music And Roscoe's for his equipment. If Jordan has a total of $800 and wants the music to play for 4 hours, how many people can Jordan party?
The number of people that can attend Jordan's party is 50 people.
How many people can attend Jordan's party?The equation that represents the total amount that would be spent at the party would be a linear equation. A linear equation increases at a constant rate.
The form of the linear equation would be:
Total amount = rental fee + (charge per hour of the Dynamic DJ x number of hours he plays) + (cost per person of Roscoe's rentals x number of people)
$800 = $400 + ($50 x 4) + ($4 x p)
$800 = $400 + $200 + $4p
$800 = $600 + $4p
$800 - $600 = $4p
$200 = $4p
p = $200 / $4
p = 50 people
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differentiate y = (x²-7x)^5 (3x^5-5x)
The given expression is
y = (x²-7x)^5 (3x^5-5x)
To differentiate, we would apply the product rule which is expressed as
(fg)' = f'g + fg'
Let f = (x²-7x)^5 and g = (3x^5-5x)
f' = 5(2x - 7)(x²-7x)^4
g' = 15x^4 - 5
By applying the product rule, it becomes
y' = 5(2x - 7)(3x^5-5x)(x²-7x)^4 + (15x^4 - 5)(x²-7x)^5
Let f(x) = 9x - 8. Find (f o f)(1).
Let f(x) = 9x - 8. Find (f o f)(1).
we know that
(f o f)(1).=f(f(1))
step 1
find f(1)
f(1)=9(1)-8
f(1)=1
substitute
f(f(1))=f(1)=1
therefore
the answer is 1
Homework 4: Trigonometry:Finding Sides and Angle** This is a 2-page document! **x=7.3Directions: Solve for x. Round to the nearest tenth.
Using trigonometric ratio. SOHCAHTOA
[tex]\begin{gathered} \cos 63^{\circ}=\frac{adjacent}{\text{hypotenus}} \\ \cos 63^{\circ}=\frac{x}{16} \\ x=16\cos 63^{\circ} \\ x=16\times0.45399049974 \\ x=7.26384799583 \\ x\approx7.3 \end{gathered}[/tex]can someone help me please ?
The most appropriate choice for HCF of two numbers will be given by -
Maximum number of performers in each row so that all the rows are equal in length = 8
What is HCF?
HCF means Highest Common Factor. HCF of two numbers a and b is the largest number that is divides both a and b.
Number of instruments = 24
Number of flag bearers = 16
Maximum number of performers in each row so that all the rows are equal in length = HCF of 24 , 16
[tex]24 = 2^3 \times 3\\16 = 2^4[/tex]
HCF = [tex]2^3[/tex] = 8
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What are the dimensions, a, b, and c, of the net? 13 cm a = v cm b= cm cm 12 cm 15 cm 6 5 cm a с
Looking at the diagram of the triangular prism and its net, we can see that
a = width of the base = 5 cm
b = the slant height = 13 cm
c = length of the base = 15 cm
Integers greater than -6 and less than 2
IN OTHER WORDS WE ARE LOOKING FOR WHOLE NUMBERS BETWEEN -6 AND 2
[tex] - 5 \\ - 4 \\ - 3 \\ - 2 \\ - 1 \\ 0 \\ 1[/tex]
ATTACHED IS THE SOLUTION
Answer:
1,0,-1,-2,-3,-4,-5
Step-by-step explanation:
What does it mean by non collinear points and another name for angle ABD?
a) Point = could be any point A to D = for example A
b) Line : AD
Could be any line named by the endpoints.
c) Segment: Fragment of a line
AB
d) Ray: part of a line that has a fixed star but no end:
BE
e) Angle : Could be any angle, the middle letter is where the angle rests.
f) 3 collinear points: A,B,C
3 points that are in the same line
g)Opposite rays: same end point but opposite directions
BE and BC
h) Plane: infinite set of points forming a connected flat surface.
ABDC
i) 3 non collinear points: AEC
Three points that aren't on the same line
j) another name for m
what is the value of f(x)=2(0.75)^x when x=3
Answer: f(3) = 0.84375
Step-by-step explanation:
f(3) is asking for the value of the function when x = 3, not multiplying f by 3. (f(x) is basically the output, y)
So we just plug in 3 for x and simplify (use PEMDAS)
f(3) = 2(0.75)^3
f(3) = 2(0.421875)
f(3) = 0.84375
Answer:
[tex]\frac{27}{32}[/tex]
Step-by-step explanation:
It may be a bit easier to represent 0.75 as a fraction, since we can use the following property of exponents: [tex](\frac{a}{b})^x = \frac{a^x}{b^x}[/tex]
We can represent 0.75 as: [tex]\frac{3}{4}[/tex]
And substituting this into the function we get: [tex]f(x)=2(\frac{3}{4})^x[/tex]
calculating the value when x=3, we get: [tex]f(3)=2(\frac{3}{4})^3[/tex]
using the property previously stated we get: [tex]f(3)=2(\frac{3^3}{4^3})[/tex]
Raising each value to the exponent we get: [tex]f(3)=2(\frac{27}{64})[/tex]
When we multiply by two, we can simplify by splitting up 64, into two factors: 2 and 32, to get: [tex]\frac{2*27}{32*2}[/tex]
From here it's easy to see that we can cancel out the values 2, to get: [tex]\frac{27}{32}[/tex]
Which is our answer!
3. Using the diagram below, answer the following questions. Remember, you must
show your work for credit.
LA = 6y+42
ZC
ZD
A. Solve for y. (2 points)
ZA=
y=
I
B. Find the measure of angles A, C and D showing all work. (2 points)
ZC=
LB = 66
ZD =
Using vertical angles, it is found that:
A. The solution for y is of y = 4.
B. The angle measures are given as follows:
<A = 66º.<C = 114º.<D = 114º.Vertical AnglesIf two angles are opposite by the same vertex in crossing segments, these angles are called vertical angles, and they are congruent, that is, they have the same measure.
In the context of this problem, the angles of 6y + 42 and of 66 are vertical, hence the value of y is calculated as follows:
6y + 42 = 66
6y = 24
y = 24/6
y = 4.
Angles A and C are supplementary, meaning that the sum of their measures is of 180º, hence:
<C + 66º = 180º
<C = 180º - 66º
<C = 114º.
Angles C and D are vertical, hence the measure of angle D is calculated as follows:
<D = 114º.
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Classify the triangle with the following angle measure: 20^, 50^, 110^
An acute triangle is a triangle with three acute angles, whereas an obtuse triangle is a triangle with one obtuse angle and two acute angles.
An obtuse angle is a angle which is more than 90°.
In our problem, the triangle has a 110° angle, and 110°>90°; therefore, the answer is obtuse triangle
The admission fee to an amusement park is $18. It costs an additional "c" dollars to rent a locker to hold your belongings. The total cost for 9 people to
enter the amusement park and each rent a locker is $252. How much does it cost for one person to rent a
In AUVW, UW is extended through point W to point X, mZUVW = (3x + 16)°, mZWUV = (2x + 8), and mZVWX= (8x - 18). Find mZWUV.
Let's draw the figure to better understand the problem.
7. Select all the equations that have the same solution as 3x - 6 = 18.
a. 3x = 12
b. 3x = 24
f.
c. 3(x - 2) = 18
d. 6x 12 = 36
e. 3x 12 = 36
18 = 5 - 3x
The equation which satisfied the given expression after simplification are (a) 3x = 24 and (c) 3(x - 2) = 18.
How simplification method work?
In mathematics, the simplification method is used for the equation formation for the problem statements. And it also convert the complicated expression into simpler one to make the calculation easy.
According to the question, the given equation can be simplified by using simplification method and it is written below:
The given equation is: 3x - 6 = 18
3x = 18 + 6 = 24 ⇒ 3x = 24
Similarly, 3x - 6 = 18
3(x - 2) = 18
Hence, the equation which satisfied the given expression after simplification are (a) 3x = 24 and (c) 3(x - 2) = 18.
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Identify the domain and range of the function. y=x−−√−1
The domain of the function is [1, ∞) and the range of the function is [0,∞).
Domain and range:
The domain and range of a function are refers the set of all the inputs and outputs a function can give respectively.
Basically, domain takes all the possible input values from the set of real numbers whereas the range takes all the output values of the function.
Given,
Here we have the function
y = √x - 1
Now, here we need to find the domain and range of the function.
The given function is rewritten as,
√x - 1 > 0
Square both sides then we get,
x - 1 > 0
Add 1 on both sides then we get,
x > 1
Therefore, the domain is [1, ∞).
Similarly, let us consider, y ≥ 0
Therefore, the range is [0,∞).
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