Answer:
So the maximum amount of gasoline the tank can contain is 13 gallons and there are already 7 gallons of gasoline in the tank. Therefore, we want to make sure that the amount of gasoline put in the tank doesn't reach any higher than 13 gallon.
The amount of gasoline that Lou bought with x dollars is x/2.50 gallons.
We have the inequality:
x/2.50 + 7 ≤ 13
*If you solve it, x should be smaller or equal to $15.
The math problem can be solved by setting up a compound inequality expressing the range that Lou can spend on gasoline. This factors in the total capacity of his tank, the current amount of gas, and the price per gallon. The result is 0 <= x <= $15.
Explanation:For this problem, Lou needs to fill the remainder of his gas tank, which is 13 gallons total but already has 7 gallons. That means he needs to fill 13 - 7 = 6 gallons more. Gasoline costs $2.50 per gallon, so the total amount of money he spends, represented by x, can be calculated using the inequality $2.50 * number of gallons <= x.
But because Lou can add anywhere from 0 to 6 gallons, we will have a compound inequality. So, the inequality will be: $2.50 * 0 <= x <= $2.50 * 6.
This simplifies to 0 <= x <= $15, meaning Lou can spend anywhere from $0 to $15 on gasoline, depending on how much more he wants to put in his tank.
Learn more about Compound Inequality here:https://brainly.com/question/31904612
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Decide which trigonometric ratio to use. Solve for x in the triangle below. Round your answer to the hundredths place.
Options
4.59
0.07
6.55
5.60
Answer: 4.59
sin(35)=x/8
8*sin(35)=x
x=4.59
The value of x in the given triangle round to the nearest hundredths is:
4.59
Step-by-step explanation:From the given triangle we observe that the side x is the opposite side corresponding to angle 35°.
i.e. we will use sine trignometric ratio in the triangle to get the value of x.
We know that:
[tex]\sin 35=\dfrac{x}{8}ddd[/tex]
Since the sine of an angle is the ratio of opposite side to the hypotenuse of the right angled triangle.
i.e.
[tex]x=8\times \sin 35\\\\i.e.\\\\x=8\times 0.5736\\\\i.e.\\\\x=4.588[/tex]
which is approximately equal to 4.59 units.
Fins the zeros, multiplicity, and effect on the graph of the function in
f(x) = -x (3x-2)^2(x+9)^5
and
f(x) = x^3+10x^2+25x
Answer:
See explanation
Step-by-step explanation:
Zeroe of the function is such velue of x at which f(x)=0.
1. Consider the function [tex]f(x)=-x(3x-2)^2 (x+9)^5.[/tex]
Zeros are:
[tex]-x(3x-2)^2(x+9)^5=0\\ \\x=0\text{ or }x=\dfrac{2}{3}\text{ or }x=-9.[/tex]
Zero [tex]x=0[/tex] has multiplicity of 1, zero [tex]x=\dfrac{2}{3}[/tex] has multiplicity of 2, zero [tex]x=-9[/tex] has multiplicity of 5.
At [tex]x=0[/tex] or [tex]x=-9[/tex] the graph of the function crosses the x-axis, at [tex]x=\dfrac{2}{3}[/tex] the graph of the function touches the x-axis.
2. Consider the function [tex]f(x)=x^3+10x^2+25x=x(x^2+10x+25)=x(x+5)^2.[/tex]
Zeros are:
[tex]x(x+5)^2=0\\ \\x=0\text{ or }x=-5.[/tex]
Zero [tex]x=0[/tex] has multiplicity of 1, zero [tex]x=-5[/tex] has multiplicity of 2.
At [tex]x=0[/tex] the graph of the function crosses the x-axis, at [tex]x=-5[/tex] the graph of the function touches the x-axis.
The period of this function is
2π
π/8
π/4
π/2
I’m not quite sure what the function is but if it’s sine the period is pi/8
ANSWER
The period is
[tex] \frac{\pi}{8} [/tex]
EXPLANATION
The given function completes four cycles on the interval
[tex]
[ - \frac{\pi}{4} , \frac{\pi}{4} ][/tex]
Therefore the period is
[tex] = \frac{ \frac{\pi}{4} - \frac{\pi}{4} }{4} [/tex]
Simplify the numerator:
[tex] = \frac{ \frac{\pi}{2}}{4} [/tex]
Simplify further to get:
[tex]= \frac{\pi}{8} [/tex]
Though it is true I enjoy your writing style, I don't agree with your main point of view about this one. I do delight in your website nevertheless. Gedefkkfdefd
Answer:
34.
Step-by-step explanation:
1. x/5 = 10 *
2. x + 2 = 15 *
3. 5x = 40 *
4. 2y = 44 *
5. r - 15 = 30 *
Answer:
Step-by-step explanation:
1) x/5 = 10
multiply by 5 : x = 50
2) x + 2 = 15
add -2 : x = 13
3) 5x = 40
divid by 5 : x =8
4) 2y = 44
divid by 2 : y = 22
5. r - 15 = 30
add 15 ; 5r =45
divid by 5 : r = 9
Write an algebraic expression to represent the following verbal expression. the cube of the difference of a number and 43
Answer:
(n - 43)³
Step-by-step explanation:
Let the number be n.
Then the desired expression is (n - 43)³
Answer:
Algebraic expression = (x-43)^3
Step-by-step explanation:
Given , the verbal expression is the cube of the difference of a number and 43.
Let x be the number
Now, according to question
Difference means subtraction in which a number is subtracted from the other number
Difference of a number and 43
It means 43 is subtracted from x
Now , the algebraic expression =x-43
Cube of the difference of a number x and 43 =(x-43)(x-43)(x-43)
Cube of a number means multiply a number three times with self .
Therefore, Cube of the difference of a number x and 43=[tex](x-43)\times (x-43)\times(x-43)[/tex]
Cube of the difference of a number x and 43=(x-43)^3
Because in multiply when base same then power of the number added.
Hence,the algebraic expression =(x-43)^3.I
6 / 2 (1 + 2) = 9
PLEASE EXPLAIN HOW IT IS 9!!! I followed PEMDAS, and I keep getting 1
Answer:
9
Step-by-step explanation:
6 / 2 (1 + 2) = 9
PEMDAS
Parentheses first
1+2 =3
Substitute this in
6 / 2 (3) = 9
Multiplication and Division from left to right
Division first
6/2 =3
Substitute this in for 6/2
3 (3) =9
3*3 =9
Max's T-shirt business uses the demand function P = -Q + 28 and the supply function P = Q - 12. According to these functions, what will the equilibrium point be for Max's T-shirt business?
A. (20,8)
B. (12,28)
C. (8,20)
D. (28,12)
A and c —————- Bc 20 +8 is 28
Answer:
The answer is (8,20) on APEX. just did the test. good luck!
The center is a(?,?)
The radius is _____ units.
Answer:
The center is at [tex](2,4)[/tex]
3 units
Step-by-step explanation:
You can observe in the graph a circle.
The x-coordinate and the y-coordinate of the center of the circle shown in the figure are:
[tex]x=2[/tex] and [tex]y=4[/tex]
Therefore, the point of the center of the circle is:
[tex](2,4)[/tex]
You can observe that the diameter goes from -1 to 5, then the diameter is:
[tex]diameter=1units+5units\\\\diameter=6units[/tex]
The radius is half the diameter. Therefore, you can say that the radius of this circle is:
[tex]radius=\frac{diameter}{2}\\\\radius=\frac{6units}{2}\\\\radius=3units[/tex]
ANSWER
The center is (2,4)
The radius is 2√2 units
EXPLANATION
Each of the ticks is 1 unit
Counting two ticks from the origin to the right and 4 units up will land us at the center of the circle.
Hence the center is (2,4)
The circle passes through (0,2).
The radius is
[tex]r = \sqrt{ {(2 - 0)}^{2} + {(4 - 2)}^{2} } [/tex]
[tex]r = \sqrt{8} = 2 \sqrt{2} [/tex]
Point B is the image of point A when point A is rotated about the origin. What is known about point A and B?
A:Point B is the result of a 180° rotation.
B:Point A and B have the same x-coordinate.
C:Point B is the result of a 90° counterclockwise rotation.
D:Point A and point B are the same distance from the origin.
Answer:
D:Point A and point B are the same distance from the origin.
Step-by-step explanation:
hope this helps :)
Answer:
D
Step-by-step explanation:
Hit the THANKS button pls >.<
V
V
V
Use the drop-down menus to identify the key values of the box plot. The median is . The minimum is . The maximum is . The lower quartile (Q1) is . The upper quartile (Q3) is .
ANSWERS:
C
A
E
B
D
Answer: The lower quartile is Q1) is your minimum & your maximum is quartile Q3) bc is the larger one
Step-by-step explanation:
c
a
e
b
d
is none of your answer.
Answer:
person above is correct
Step-by-step explanation:
show them some love
Please help will mark brainliest (answer must be right)
True or false
The points on a line can be paired one to one with real numbers ?
Answer: TRUE
Step-by-step explanation: This is true, because there is an infinite amount of real numbers in both, and they are both countably infinite (so these infinities are equal). Hope this helps!
Which of the following ordered pairs represents an output of 5 and an input of -8?
(-8,-8)
(-8,5)
(5, 5)
(5, -8)
Answer:
(-8,5)
Step-by-step explanation:
The output corresponds to the y-value of an ordered pair while the input corresponds to the x-value of an order pair.
An ordered pair is written like this (x,y)
Determine the area of a sector with a central angle of 90° and a radius of 10 meters.
A. 25 meters2
B. 90π meters2
C. 100π meters2
D. 25π meters2
Area of circle
= 90/360 x π x (10)^2
= 1/4 π x 100
= 25 π meter^2
Final answer:
The area of a sector with a central angle of 90° and a radius of 10 meters is calculated using the formula A = θ/360 × πr². Substituting the given values, the area is found to be 25π m². The correct answer is D. 25π meters².
Explanation:
Finding the Area of a Sector
To find the area of a sector with a central angle of 90° in a circle with a radius of 10 meters, we use the formula for the area of a sector, which is A = θ/360 × πr², where θ is the central angle in degrees, π is the mathematical constant approximately equal to 3.14159, and r is the radius. Since the central angle θ is 90°, and the radius r is 10 meters, we have:
A = 90°/360° × π × (10 m)²
= 0.25 × π × 100 m²
= 25π m².
Therefore, the correct answer is D. 25π meters².
Please help with #5 only
Answer:
1680Step-by-step explanation:
[tex]\sum\limits_{n=1}^{42}2n-3\\\\a_n=2n-3\\\\a_{n+1}=2(n+1)-3=2n+2-3=2n-1\\\\a_{n+1}-a_n=(2n-1)-(2n-3)=2n-1-2n+3=2=constant\\\\\text{Therefore it's an arithmetic sequence with first term}\\\\a_1=2(1)-3=2-3=-1\\\\\text{and common difference}\\\\d=2[/tex]
[tex]\text{The formula of a sum of terms of an aithmetic sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{Substitute:}\\\\n=42,\ a_1=-1,\ d=2:\\\\S_{42}=\dfrac{2(-1)+(42-1)(2)}{2}\cdot42=[-2+(41)(2)](21)=(-2+82)(21)\\\\=(80)(21)=1680[/tex]
Kevin caught some fish. Of them 4/9 were herring, and 2/9 salmon. What was the total amount of fish, amount of herring and amount of salmon if there were 12 flounders?
There were 3 different fish caught, Salmon, Herring and Flounder.
4/9 were Herring, 2/9 were Salmon, 4/9 +2/9 = 6/9
This means 3/9 were Flounders ( 3/9 + 6/9 = 9/9 = 1)
3/9 can be reduced to 1/3.
1/3 of the fish were Flounders.
Divide the amount of flounders by the portion caught:
12 / 1/3 = 12 * 3/1 = 36 total fish.
Now you have total number of fish, multiply the total by each portion for each type of fish.
Total fish = 36
Herring = 4/9 x 36 = 16
Salmon = 2/9 x 36 = 8
Please help me with this pleaseee
Answer:
x = 88.2
Step-by-step explanation:
The angle at the top of the triangle = 90° - 10° = 80°
and the left side of the triangle is x ( opposite sides of a rectangle )
Using the tangent ratio in the right triangle
tan80° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{500}{x}[/tex]
Multiply both sides by x
x × tan80° = 500 ( divide both sides by tan80° )
x = [tex]\frac{500}{tan80}[/tex] ≈ 88.2
At the start of an experiment, the temperature of a solution was -12°C. During the expirament
Answer:
The final temperature of the solution was 5°C
Step-by-step explanation:
we know that
1) At the start of an experiment, the temperature of a solution was -12°C
In this moment the temperature is -12°C
2) During the experiment, the temperature of the solution rose 5°C each hour during 4 hours
so
5°C*4=20°C
In this moment the temperature is -12°C+20°C=8°C
3) The temperature changed by -3°C
In this moment the temperature is 8°C-3°C=5°C
Answer:
The final temperature of the solution was 5°C
Step-by-step explanation:
Which represents the solution(s) of the system of equations, y = x2 – x + 1 and y = x? Determine the solution set by graphing.
Answer:
(1 , 1)
Step-by-step explanation:
Given in the question two equations
Equation 1
y = x² – x + 1
Equation 2
y = x
Equate both equations
x² – x + 1 = x
0 = x² – x + 1 - x
x² – 2x + 1 = 0
x² - x - x + 1 = 0
x(x - 1) -1(x - 1) = 0
(x - 1)(x - 1) = 0
(x-1)² = 0
x - 1 = 0
x = 1
Plug x = 1 in first equation
y = 1² – 1 + 1
y = 1
Answer:
The answer is option A, or (1,1)
Step-by-step explanation:
I just took the test
What is the recursive rule for the sequence?
Answer:
C
Step-by-step explanation:
Since we are dealing with recursive equations, we can use a simple format.
[tex]a_{1}=x \\ \\ a_{n}=a_{n-1}+y[/tex]
x is the starting value and y is the change.
We can see that the change is -5.6 since 5.6 is being subtracted from each term each time.
So the equation would be
[tex]a_n=a_{n-1}-5.6[/tex]
We can check this by plugging in the numbers.
Let's see if -8.3 works, which is the 2nd term in the equation.
[tex]a_2=a_{2-1}-5.6 \\ \\ -8.3=a_{1}-5.6 \\ \\ -8.3=-2.7-5.6 \\ \\ -8.3=-8.3[/tex]
Therefore, the recursive rule is the third one.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
The results of a poll show that the true proportion of students who prefer the new schedule is likely in the interval (0.195,0.245).
What is the point estimate of the proportion of students who prefer the new schedule?
Enter your answer, as a decimal, in the box.
Answer:
0.22
Step-by-step explanation:
The point estimate is the average of the upper and lower bounds of the interval.
Need help
Choices
4
3
2
1
Answer:
1
Step-by-step explanation:
The amplitude is the maximum distance away from the middle of the wave. Here we can see that the middle of the wave is the x axis and the farthest point (largest difference between the y coordinate of the x-axis, or the line y = 0, and the wave) is 1 unit away.
Answer:
1
Step-by-step explanation:
A triangle has side lengths 32, 45 and 18. What type of triangle is it?
A) right
B) acute
C) obtuse
D) none of the above
A triangle has side lengths 44, 36 and 30. What type of triangle is it?
A) right
B) acute
C) obtuse
D) none of the above
Answer:
Part A) Option C. obtuse
Part B) Option B. acute
Step-by-step explanation:
we know that
Applying the Pythagoras Theorem
if [tex]c^{2}=a^{2}+b^{2}[/tex] ----> is a right triangle
if [tex]c^{2}>a^{2}+b^{2}[/tex] ----> is an obtuse triangle
if [tex]c^{2}<a^{2}+b^{2}[/tex] ----> is an acute triangle
where
c is the greater side
Part A) A triangle has side lengths 32, 45 and 18. What type of triangle is it?
we have
[tex]c^{2}=45^{2}=2,025[/tex]
[tex]a^{2}+b^{2}=32^{2}+18^{2}=1,348[/tex]
therefore
[tex]c^{2}>a^{2}+b^{2}[/tex]
Is an obtuse triangle
Part B) A triangle has side lengths 44, 36 and 30. What type of triangle is it?
we have
[tex]c^{2}=44^{2}=1,936[/tex]
[tex]a^{2}+b^{2}=36^{2}+30^{2}=2,196[/tex]
therefore
[tex]c^{2}< a^{2}+b^{2}[/tex]
Is an acute triangle
Please help me with this
Answer:
8.4
Step-by-step explanation:
hope it helped
A rectangular prism is 4 inches long, 6 inches wide, and has a height of 5 inches. What is its volume?
60 in 3
120 in 3
148 in 3
240 in 3
Answer:
Step-by-step explanation:
The volume of a rect. prism is V = (length)(width)(height).
Here the volume is V = (4 in)(6 in)(5 in) = 120 in³ or 120 in^3
Note: Please use " ^ " to indicate exponentiation: 120 in^3
Answer:
120 in 3
Step-by-step explanation:
Solve: 110°20'
PLS TRY to translate degrees and minutes to degrees! BRAINLIEST for 1st answer :)
Answer:
110 1/3 or 100.33 degrees (to the nearest hundredth).
Step-by-step explanation:
There are 60 ' (minutes) in a degree.
So 20' = 20/60 = 1/3 of a degree.
Answer:
110 1/3°
Step-by-step explanation:
Recall that 1° = 60'. Then 20' is 1/3 of 1°, or (1/3)°.
Then 110° 20' = 110° + (1/3)° = 110 1/3°.
The coordinates of Trapezoid EFGH are E(8, 8), F(8,10), G(1, 6), and H(4, 1). The image of EFGH under dilation is E’F’G’H’. If the coordinates of vertex E’ are (4, 4), what are the coordinates of vertex F’? A)(2, 6) B)(4, 6) C)(2, 5) D)(4, 5)
Answer:
D) (4,5)
Step-by-step explanation:
Vertex E was dilated by 1/2 because 8/2 = 4. Thus, you will divide all the other coordinates by the same scale factor.
To angle are supplementary. Measure of one angle is 56 degrees, what is the measure of the second angle
Answer:
124°
Step-by-step explanation:
Supplementary angles add to 180°.
56° + second angle = 180°
Subtract 56° from both sides of the equation:
second angle = 180° - 56° = 124°
Mike spent $7920 on his vacation, which was 11% of his monthly salary. What was his monthly salary
Answer: $72000
7290 divided by 11 = 720 720 times 100 = 72000HELP PLEASE!!! I WILL FIVE STAR!!
Answer:
Step-by-step explanation:
You can't answer c. There is not enough information. Other than there are 14 boys that went, you know nothing about how many went.
Girls going = (3/5) * 20 = 12
Girls not going = 20 - 12 = 8