Answer:
the percentage increase is 35%
A driver starts a trip with 30 gallons of gasoline in the tank of his car. The car
burns 4 gallons for every 80 miles. Assuming that the amount of gasoline in the tank decreases linearly, write a linear function that relates the number of gallons G left in the tank after a journey of "d" miles.
Answer:
Step-by-step explanation:
We have to look at this as something as basic as combining like terms. We know that the driver starts with 30 GALLONS of gas and loses x GALLONS while driving, giving us an equation that says
Gallons of gas used = Gallons in car - gallons used; in other words, if everything is in the same label, you can subtract. We start off with 30 gallons, thus:
Gallons of gas used = 30 G
That's a start, at least. Now we need to figure out how much is burned. Remember, in order to do any subtraction at all we have to have like labels, so we need what goes after that subtraction sign to also be a label in gallons, G. The driver burns 4 gallons per 80 miles times how many miles he drives, so the expression for that is
[tex]\frac{4G}{80mi}*dmi[/tex] and what happens here is that the label of miles cancels out, leaving us with just G, which is what we're after. The whole equation then is
[tex]G=30-\frac{4}{80}d[/tex], choice 1
Function below, choose the correct description of its graph.
vertical
line
horizontal
line
line with a
negative
slope
line with a parabola
positive opening
slope down
O
O
O
O
O
h(x)=0
k(x) = 4x2 +312
f(x) = x-1
O
o
o
O
O
O
Step-by-step explanation:
I think something went wrong with the answer options you provided. and maybe with the problem statement itself.
I see 3 function definitions.
I can tell you what they are and use the provided option phrasing as closely as possible :
h(x) = 0 is a horizontal line (in fact the x-axis)
k(x) = 4x² + 312 is a parabola with the opening upwards
f(x) = x - 1 is a line with positive slope (going from left to right the line goes up)
Which graph represents the function f (x) = StartFraction 1 Over x + 3 EndFraction minus 2?
Given:
The function is:
[tex]f(x)=\dfrac{1}{x+3}-2[/tex]
To find:
The graph of the given function.
Solution:
We have,
[tex]f(x)=\dfrac{1}{x+3}-2[/tex]
It can be written as:
[tex]f(x)=\dfrac{1-2(x+3)}{x+3}[/tex]
[tex]f(x)=\dfrac{1-2x-6}{x+3}[/tex]
[tex]f(x)=\dfrac{-2x-5}{x+3}[/tex]
Putting [tex]x=0[/tex] to find the y-intercept.
[tex]f(0)=\dfrac{-2(0)-5}{(0)+3}[/tex]
[tex]f(0)=\dfrac{-5}{3}[/tex]
So, the y-intercept is [tex]\dfrac{-5}{3}[/tex].
Putting [tex]f(x)=0[/tex] to find the x-intercept.
[tex]0=\dfrac{-2x-5}{x+3}[/tex]
[tex]0=-2x-5[/tex]
[tex]2x=-5[/tex]
[tex]x=\dfrac{-5}{2}[/tex]
[tex]x=-2.5[/tex]
So, the x-intercept is [tex]-2.5[/tex].
For vertical asymptote, equate the denominator and 0.
[tex]x+3=0[/tex]
[tex]x=-3[/tex]
So, the vertical asymptote is [tex]x=-3[/tex].
The degrees of numerator and denominator are equal, so the horizontal asymptote is the ratio of leading coefficients.
[tex]y=\dfrac{-2}{1}[/tex]
[tex]y=-2[/tex]
So, the horizontal asymptote is [tex]y=-2[/tex].
End behavior of the given function:
[tex]f(x)\to -2[/tex] as [tex]x\to -\infty[/tex]
[tex]f(x)\to -\infty[/tex] as [tex]x\to -3^-[/tex]
[tex]f(x)\to \infty[/tex] as [tex]x\to -3^+[/tex]
[tex]f(x)\to -2[/tex] as [tex]x\to \infty[/tex]
Using all these key features, draw the graph of given function as shown below.
Answer:
The Answer Is A.
Step-by-step explanation:
Which missing piece of information would allow the triangles in the figure to be proven congruent by AAS?
A) ∠A ≅ ∠A′
B) BC with a line on top ≅ BC with a line on top of it
C) ∠C ≅ ∠C′
D) AC with a line on top of it ≅ AC with a line on top of it
9514 1404 393
Answer:
C) ∠C ≅ ∠C′
Step-by-step explanation:
The figures show a marked angle and side. To use AAS, we need another angle that is not adjacent to the marked side. That angle is C (or C'), so we require ...
∠C ≅ ∠C′
Equation?
Slope?
Y-intercept?
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (4, 2) ← 2 points on the line
m = [tex]\frac{2-(-3)}{4-0}[/tex] = [tex]\frac{2+3}{4}[/tex] = [tex]\frac{5}{4}[/tex]
The line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = [tex]\frac{5}{4}[/tex] - 3 ← equation of line
The triangles are similar.
What is the value of x?
Enter your answer in the box.
x =
Answer:
x=12
Step-by-step explanation:
each side of the smaller triangle, we can multiply by 4 to get the side of the larger triangle
ex: 8*4=32 and 17*4=68
so we can assume that 15*4= 4x+12
60=4x+12
48=4x
x=12
Answer:
x = 12
Step-by-step explanation:
The triangles are similar so we can use ratios
4x+12 32
------- = ------------
15 8
Using cross products
(4x+12) *8 = 15 * 32
(4x+12) *8 = 480
Divide each side by 8
(4x+12) *8/8 = 480/8
4x+12 = 60
Subtract 12 from each side
4x+12 -12 = 60-12
4x = 48
Divide by 4
4x/4 = 48/4
x = 12
-1/2(6x-10)=1/3(6x+9)
Answer:
x = 2/5
General Formulas and Concepts:
Pre-Algebra
Distributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
-1/2(6x - 10) = 1/3(6x + 9)
Step 2: Solve for x
[Distributive Property] Distribute parenthesis: -3x + 5 = 2x + 3[Subtraction Property of Equality] Subtract 2x on both sides: -5x + 5 = 3[Subtraction Property of Equality] Subtract 5 on both sides: -5x = -2[Division Property of Equality] Divide -5 on both sides: x = 2/5triangle ABC is reflected about the line Y equals negative X to give triangle ABC with vertices A (-1, 1), B (-2, -1), C (-1,0). What are the vertices of triangle ABC?
9514 1404 393
Answer:
A'(-1, 1)B'(1, 2)C'(0, 1)Step-by-step explanation:
Reflection across the line y = -x is accomplished by the transformation ...
(x, y) ⇒ (-y, -x)
Then the images of the given points are ...
A(-1, 1) ⇒ A'(-1, 1) . . . . this point is on the line of reflection, so doesn't move
B(-2, -1) ⇒ B'(1, 2)
C(-1, 0) ⇒ C'(0, 1)
Hans rented a truck for one day. There was a base fee of $15.95, and there was an additional charge of 77 cents for each mile driven. Hans had to pay
$207,68 when he returned the truck. For how many miles did he drive the truck?
Answer: 249 miles
Step-by-step explanation:
First write a function that represents the amount paid for renting a truck:
Set x as each mile driven.Set y as the total amount paid.$15.95 is the base fee paid no matter the mile, meaning the rent start at $15.95, not 0.Function: y = mx + b
m = slope = amount paid for each mile driven = 77¢ = $0.77b = y-intercept = amount paid when 0 miles driven = base fee = $15.95y = 0.77x + 15.95
He paid a total of $207.68, therefore y = 207.68:
207.68 = 0.77x + 15.95
Solve the equation for x:
207.68 - 15.95 = 0.77x
191.73 = 0.77x
x = 249 miles driven
What is the volume of a cylinder of radius 4cm and length of 8cm. famula π=3.14
Answer:
401.92 cm^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
V = (3.14) (4)^2 *8
V= 401.92
A car travels 70.5 miles on 3 gallons of gas find the distance the car travels on 14 gallons of gas
Answer:
329 miles
Step-by-step explanation:
Create a proportion where x is the distance the car can travel on 14 gallons of gas:
[tex]\frac{70.5}{3}[/tex] = [tex]\frac{x}{14}[/tex]
Cross multiply and solve for x:
3x = 987
x = 329
So, the car can travel 329 miles on 14 gallons of gas
Answer:
329 miles
Step-by-step explanation:
We can write a ratio to solve
70.5 miles x miles
--------------- = ------------
3 gallons 14 gallons
Using cross products
70.5 * 14 = 3x
987=3x
Divide each side by 3
987/3 = 3x/3
329=x
329 miles
The midpoint of a segment is (6,−4) and one endpoint is (13,−2). Find the coordinates of the other endpoint.
A. (-1, -6)
B. (-1, 0)
C. (20, -6)
D. (20, 0)
Answer: A. (-1, -6)
Step-by-step explanation:
Use the midpoint formula:
Endpoint #1 = (x₁, y₁) = (13, -2)Endpoint #2 = (x₂, y₂)[tex]midpoint = (\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}) \\\\(6, -4) = (\frac{13+x_{2}}{2}, \frac{-2+y_{2}}{2})\\\\\frac{13+x_{2}}{2} =6\\\\13+x_{2}=6*2\\\\x_{2}=12-13=-1\\\\ \\ \frac{-2+y_{2}}{2}=-4\\\\-2+y_{2}=(-4)*2\\\\y_{2}=-8+2=-6\\\\\\\left \{ {{x_{2}=-1} \atop {y_{2}=-6}} \right.[/tex]
A market surveyor wishes to know how many energy drinks teenagers drink each week. They want to construct a 98% confidence interval for the mean and are assuming that the population standard deviation for the number of energy drinks consumed each week is 1.1. The study found that for a sample of 1027 teenagers the mean number of energy drinks consumed per week is 5.9. Construct the desired confidence interval. Round your answers to one decimal place.
Answer:
The 98% confidence interval for the mean number of energy drinks consumed per week by teenagers is (5.8, 6).
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.327\frac{1.1}{\sqrt{1027}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 5.9 - 0.1 = 5.8 drinks per week.
The upper end of the interval is the sample mean added to M. So it is 5.9 + 0.1 = 6 drinks per week.
The 98% confidence interval for the mean number of energy drinks consumed per week by teenagers is (5.8, 6).
Solve for x and y…….
The shapes are the same size. Match the sides.
3x -1 = 17
Add 1 to both sides:
3x = 18
Divide both sides by 3:
X = 6
2y = 16
Divide both sides by 2
Y = 8
Answer: x = 6, y = 8
A. 12
B. 8
C.3
D.6
Please please help
Answer:B
Step-by-step explanation:
B
11) 161.3 is what percent of 177.2?
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Answer:
it's 91.027%
Step-by-step explanation:
I hope i helped
Which word phrases represent the variable expression m – 11? Choose all answers that are correct. A. 11 more than a number B. the difference of a number and 11 C. the quotient of a number and 11 D. 11 less than a number
Answer: D
Step-by-step explanation:
m – 11
A. 11 more than a number ( m+11 )
B. the difference of a number and 11 ( 11/m )
C. the quotient of a number and 11 ( m/11 )
D. 11 less than a number ( m-11 )
A laptop was originally sold for $975. The laptop is now on sale for $828.75.The percent markdown must have been...
Answer:
15% markdown
Step-by-step explanation:
To find the percent markdown
Take the original price minus the new price
975-828.75
146.25
Divide by the original price
146.25/975
.15
Change to percent form
15% markdown
In 5 days she made 80 sandcastles. Each day she made 4 fewer castles than the day before. How many castles did she make each day?
Answer:
Castles made: N day 1
N - 4 day 2
N - 8 day 3
N - 12 day 4
N - 16 day 5
Total 5 N - 40 = 80
N = 24 total castles day 1
Total castles = 24 + 20 + 16 + 12 + 8 = 80
Evaluate the given expression for x = 5 and y=5. 6x2 + 7xy + 3y?
Step-by-step explanation:
Given, x = 5
y = 5
= 6(5)^2 +7(5)(5) +3(5)
= 6(25)+7(25) +15
= 150+175 + 15
= 150 + 190
=340
Answer:
x = 12 y = 7
Step-by-step explanation:
6x^2 + 7xy + 3y
6(5)^2+ 7(5) + 7(8)y
6(5+5)+25+35 + 7(8)-7y
60+25+35+ 56-7y
y - 5 = 120 + 35 - 5 (+49y)
sqrt 150 + sqrt 49
x = 12 y = 7
Please Help!! much appreciated! :D
Find the value of y.
In the largest triangle, the missing side has length
√((11 + 5)² - x ²) = √(256 - x ²)
But it's also the hypotenuse of the triangle with side lengths 11 and y, so that its length can also be written as
√(11² + y ²) = √(121 + y ²)
so that
√(256 - x ²) = √(121 + y ²)
or, by taking the squares of both sides,
256 - x ² = 121 + y ²
y ² = 135 - x ²
In the smallest triangle, you have
5² + y ² = x ² ==> x ² = 25 + y ²
Substitute this into the previous equation and solve for y :
y ² = 135 - (25 + y ²)
y ² = 110 - y ²
2y ² = 110
y ² = 55
y = √55
REVISED 2/3/
the following using the picture below.
4
a) Two pairs of supplementary angles:
b) A pair of complementary angles:
Please explain this! Thank you!
Supplementary angles are those angles which make a sum of 180°.
Complementary angles are those angles which make a sum of 90°.
The supplementary angles are given by the straight lines making angles of 180°.
There are two straight lines CB and DE
The angles DAF and FAE are the two angles making a straight line DE
The angles CAF and FAB are the two angles making a straight line CB
The complementary angles are given by angles formed between the perpendicular lines making angles of 90°.
Angle BAF is formed by angle BAE and angle AEF
Supplementary Angle given by the straight line DE is formed by the angles DAF and FAE.
Complementary Angle BAF is formed by angle BAE and angle AEF.
https://brainly.com/question/12919120
You are interested in finding out whether middle-aged men who have premature heartbeats are at greater risk of developing a myocardial infarction (heart attack) than men whose heartbeats are regular. Electrocardiogram (ECG) examinations are performed on all male office employees 35 years of age or older who work for oil companies in Houston. The ECG tracings are classified as irregular or regular. Five years later, myocardial infarction rates are compared between those with and those without baseline ECG irregularities. What kind of study is this?
a. Cross-sectional study
b. Case-control study
c. Prospective cohort study
d. Retrospective cohort study
e. Clinical trial
f. Community trial
Answer:
The answer is "Option C".
Step-by-step explanation:
This study looks after results including such illness growth during the trial time, and this includes additional elements such as suspected risk or source of protection (s). The study usually consists of taking and looking at such a cohort of subjects for a long time. The main advantage of these studies is knowledge accumulation and higher efficiency. Systematic reviews may suffer from choice distortion, in addition to the potential indication misinterpretation.
Which one is greater 4.5% or 0.045
Answer:
They are equal
Step-by-step explanation:
4.5% is 0.045 in decimal form
Answer: They are equal
Step-by-step explanation:
I always remember by taking the two o's in percent and moving them two spots to the left and vise versa if you want to make a decimal into a percent (move it two spots to the right).
Is the answer right?
Answer:
one solution.. your answer is correct
Step-by-step explanation:
discriminate = 900 - (4*9*25) = 0
thus only one solution
How many counting numbers have three distinct nonzero digits such that the sum of the three digits is 7?
Answer:
6
Step-by-step explanation:
You have 2 conditions.
1. The digits must be different.
2. The digits must add to 7.
There aren't very many
124
142
214
241
412
421
That's it. That's your answer. There are 6 of them
Last year, the CDC claimed there were 1700 different strains of a virus around the
world. Since then, numbers have increased by 9.7% more than what the scientists
originally estimated. How many strains are estimated currently? Round to the nearest
number.
Answer: 1865
Step-by-step explanation:
Given
Claimed strains of virus is 1700
If it is increased by 9.7%
Estimated value can be given by
[tex]\Rightarrow 1700+1700\times 9.7\%\\\Rightarrow 1700(1+0.097)\\\Rightarrow 1700\times 1.097\\\Rightarrow 1864.9\approx 1865[/tex]
Thus, the estimated number is [tex]1865[/tex]
A triangular patch of grass in a park is bordered by walking paths. The longest path bordering the patch of grass measures 110 feet. The smallest path bordering the patch of grass measures 55 feet. The smallest angle formed by the paths bordering the patch of grass measures 29º.
What is the measure of the largest angle of the triangular patch of grass? Round your answer to the nearest
degree. Show all your work.
Answer:
76 degrees
Step-by-step explanation:
First, we can draw a picture. Two of the sides are 110 feet and 55 feet. In a triangle, the smallest angle is opposite the smallest side and vice versa. Therefore, if I have my triangle arranged in the way shown, the smallest angle of 29 degrees will be opposite of the smallest side of 55 feet.
The law of sines states that a/sinA=b/sinB=c/sinC , with corresponding angles being opposite of its corresponding side. Therefore, we can say that
55 feet/ sin(29 degrees) = 110 / sin(largest angle).
If we say that the largest angle is equal to x, we can say
55 / sin(29°) = 110/sin(x)
multiply both sides by x to remove a denominator
55 * sin(x)/ sin(29°) = 110
multiply both sides by sin(29°) to remove the other denominator
55 * sin(x) = 110 * sin(29°)
divide both sides by 55 to isolate the sin(x)
sin(x) = 110 * sin(29°) / 55
For an angle, if sin(x) = y, we can say that arcsin(y) = x. Therefore, we can say
x = arcsin(110 * sin(29°)/55)
x ≈ 76 degrees
a tree 15m high casts a shadow 8m long. To the nearest degree what is the angle of elevation of the sun?
Answer:
Answered March 20, 2021
This is a right angle triangle where the hypotenuse a^2 = b^2 + c^2
= 15^2 + 8^2 = 225+64= 289
289= 17^2
17 = hypotenuse
The sine of an angle is the ratio of the shortest side to the hypotenuse
= 8/17= 0.4705
sine^-1 0.4705 = 28°
A manager records the repair cost for 14 randomly selected dryers. A sample mean of $88.34 and standard deviation of $19.22 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the dryers. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
Hence the 90% confidence interval estimate of the population mean is [tex](79.24 , 97.44)[/tex]
Step-by-step explanation:
Given that,
Point estimate = sample mean = [tex]\bar x[/tex] = 88.34
sample standard deviation = s = 19.22
sample size = n = 14
Degrees of freedom = df = n - 1 = 13
Critical value =[tex]t\alpha /2,[/tex] df = 1.771
Margin of error
[tex]E = t\alpha/2,df \times (\frac{s}{\sqrt{n} } )\\= 1.771 \times (19.22 / \sqrt 14)[/tex]
Margin of error = E = 9.10
The 90% confidence interval estimate of the population mean is,
[tex]\bar x - E < \mu < \bar x + E\\\\88.34 - 9.10 < \mu < 88.34 + 9.10\\\\79.24 < \mu < 97.44\\(79.24 , 97.44)[/tex]
