Using a proportional relationship, it is found that she would be able to drive 240 miles on 8 gallons of gasoline.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
Researching the problem on the internet, it is found that she drives 30 miles per gallon, hence the function for the distance driven considering the number of gallons in the tank is given by:
D(n) = 30n.
She has n = 8 gallons, hence the distance is given by:
D(8) = 30 x 8 = 240 miles.
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What is 5 x -1 =
Doing summer homework
Answer:
x=1/5
Step-by-step explanation:
You have to isolate x. First, add the one to the sider to give you 5x=1. In order to get the x by itself, you have to divide the 5 into both sides. In the end, this gives you x=1/5.
Write x^2+5x-7 in the form (x+a)^2+b.
Answer: −x2+
5
x
=
7
Move
7
to the left side of the equation by subtracting it from both sides.
−
x
2
+
5
x
−
7
=
0
Once the quadratic is in standard form, the values of
a
,
b
, and
c
can be found.
a
x
2
+
b
x
+
c
Use the standard form of the equation to find
a
,
b
, and
c
for this quadratic.
a
=
−
1
,
b
=
5
,
c
=
−
7
Step-by-step explanation:
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The sum of the angle 5 and angle 6 is 180 degrees. Then the correct option is C.
What is Supplementary angle?When two angles are said to be supplementary angles if their sum is 180 degrees.
A triangle is shown with its exterior angles.
The interior angles of the triangle are angles 2, 3, 5.
The exterior angle at angle 2 is angle 1.
The exterior angle at angle 3 is angle 4.
The exterior angle at angle 5 is angle 6.
We know that the sum of interior and exterior angle of the triangle is 180 degrees.
∠1 + ∠2 = 180°
∠3 + ∠4 = 180°
∠5 + ∠6 = 180°
Then the correct option is C.
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16t^2 + 48t + 160 =0
Answer:
Simplifying -16t2 + 48t + 160 = 0
Reorder the terms: 160 + 48t + -16t2 = 0
Solving 160 + 48t + -16t2 = 0 Solving for variable 't'.
Factor out the Greatest Common Factor (GCF), '16'. 16(10 + 3t + -1t2) = 0
Factor a trinomial. 16((5 + -1t)(2 + t)) = 0 Ignore the factor 16.
hope it helps.
It is known that 10 workers take 30 days to complete a project. They start working and the next day one quits. the next another, the third day another, and so on until the sixth day when they are left alone 5 workers. How many days will it take those 5 workers to finish the job?
Answer:
5 workers finish this work in 60 daysStep by step explanation:
The problem tells us that at the end of the day, there are only 5 workers left, which we must find how many days it takes to finish said work.
We start by finding the type of proportionality we have.
In this case, we have that the more workers there are, they will finish that work in less time, and the fewer workers there are, the longer it will take to finish the work. This is the inverse proportionality, to more less, to less more.
We have only 5 workers left.
In the first case there are 10 workers, and in the second case there are 5 workers left. We find the relationship between the workers in the second case among the workers in the first case.
Ratio = 5 workers / 10 workers = 1/2We see that the time is found by dividing the number of days in which the 10 workers finish the work, by 1/2.
As we know, dividing two fractions is the SAME as multiplying by the inverse fraction.
[tex]\rm 30 * 2/1 \: = 60 \: days[/tex]
By so
5 workers finish this work in 60 dayswhich of the followiing is not a function
Answer:
i think B i don't know but i only guess
Which rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C'?
The rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C' is (x, y) → (x + 7, y - 6).
What is translation?When a line is translated, it means the line is moved from one position to another. The coordinate for triangle ABC are A(-3 ,4) , B(-4,1) and C(-2,1).
The coordinate of triangle A'B'C' is A'(4,-2), B'(3,-5), and C'(5,-5).
From above, it can be seen that the image A'B'C' is obtained from the pre-image ABC by translating the vertices of the image by 7 units to the right and 6 units down.
Therefore, the rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C' is (x, y) → (x + 7, y - 6)
Hence, the rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C' is (x, y) → (x + 7, y - 6).
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Solve using a formula. Please don't guess, I would like professionals to take a look
Let's take this problem step by step:
What we know:
[tex]x+y=4\\xy=-2[/tex]
Before we solve, let's do one thing that will help us out greatly later down the road:
[tex]x+y=4\\(x+y)^2=4^2\\x^2+2xy+y^2=16\\x^2+2(xy)+y^2=16\\x^2+2(-2)+y^2=16\\x^2+4+y^2=16\\x^2+y^2=20[/tex]<--- useful equation
Let's rearrange the problem a little bit:
[tex]x+\frac{x^3}{y^2}+\frac{y^3}{x^2} +y=\frac{x^3}{x^2} +\frac{x^3}{y^2}+\frac{y^3}{x^2}+\frac{y^3}{y^2}[/tex]
Combine fractions of common denominators:
[tex]\frac{x^3+y^3}{x^2} +\frac{x^3+y^3}{y^2} =(x^3+y^3)*(\frac{1}{x^2}+\frac{1}{y^2} )[/tex]
Now's let factor everything apart:
[tex](x^3+y^3)=(x+y)(x^2-xy+y^2)\\\\\frac{1}{x^2}+\frac{1}{y^2} =\frac{x^2+y^2}{x^2y^2}[/tex]
Let's use what we know and our useful equation:
[tex](x+y)*(x^2-xy+y^2)*(\frac{x^2+y^2}{x^2y^2} )\\=4*(x^2+y^2-xy)*(\frac{20}{(xy)^2} )\\=4*(20-(-2))*\frac{20}{(-2)^2} \\=4*22*5\\=440[/tex]
The value is 440
Answer: 440
Hope that helps!
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Find the area of the kite. ) 210m ^ 2 ) 140m ^ 2; 420m ^ 2; 224m ^ 2
Answer:
from the image above
Triangle ABE = Triangle ADE
AE = AE ( common).
angle AEB = angle AEO ( each 90°)
AB = AD ( given).
by side angle side criteria
so area of ABE = area of ADE
similarly,
BC = DC ( given)
BEC = DEC ( 90°)
EC = EC ( 9m each)
so area of BEC = Area of DEC
Area of Kite = 210 m²Indira makes a box-and-whisker plot of her data. she finds that the distance from the minimum value to the first quartile is greater than the distance between the third quartile and the maximum value. which is most likely true?
The statement that is most likely true is , The mean is less than the median because the data is skewed to the left.
Option E is the correct answer.
What is a Box and Whisker Plot ?The method of representing the variation in a data set is called a Box and Whisker Plot .
A data distribution in which the data is skewed to the left
the mean is less than the median.
A data distribution in which the data is skewed to the right
the mean of the data is greater than the median.
It is given in the question that
The distance from the minimum value to the first quartile is greater than the distance between the third quartile and the maximum value.
this means data is skewed to the left,
Therefore, the statement that is most likely true is , The mean is less than the median because the data is skewed to the left.
Option E is the correct answer.
The complete question is
Indira makes a box-and-whisker plot of her data. She finds that the distance from the minimum value to the first
quartile is greater than the distance between the third quartile and the maximum value. Which is most likely true?
The mean is greater than the median because the data is skewed to the right.
The mean is greater than the median because the data is skewed to the left.
The mean is less than the median because the data is skewed to the right
The mean is less than the median because the data is skewed to the left.
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Triangle EFG is isosceles.Find the measure of angles
As angles opposite congruent sides in a triangle are congruent, and also since the interior angles of a triangle add to 180 degrees, if we let angle EFG have a measure of x, then angle GEF also measures x, and thus:
82+x+x=180
2x=98
x=49
Thus, angle EFG is 49 degrees.
So, by the exterior angle theorem, angle DEG measures 82+49=131 degrees
Write down six numbers that have a median of 8, a mean of 9 and a range of 13.
Hurry please!
Answer:
5 ,6,8,8,9,18
Step-by-step explanation:
5 ,6,8,8,9,18
Range:
18-5=13
Median:
8
Mean:
5+6+8+8+9+18=54
54÷6=9
Identify angles with terminology
I need help I’ve been stuck for hours
Mark ran a mean distance of 13.2 km in five days. The next day, Mark ran 20 km.
Find the mean distance Mark ran in the six days.
Answer:
16.6
Step-by-step explanation:
Add the numbers together.
13.2+20=33.2
Now divide the number by 2.
33.2/2=16.6
Hope this helps!
If not, I am sorry.
Evaluate − 5 x 2 + 4 y 3 when x = − 2 and y = 2
Answer:
hope this is helpful.
putting values of X and y in the equation
Answer is 12
Answer:
answer is 39
Step-by-step explanation:
So, we start with the original problem:
3
x
2
−
4
y
2
Then we substitute the given
x
and
y
values into the expression:
3
(
5
)
2
−
4
(
3
)
2
Now, according to the order of operations, we simplify the exponential powers first, thus, reducing the expression to this:
3
(
25
)
−
4
(
9
)
Then, we use the order of operations again and do the multiplication next:
75
−
36
We then use the order of operations a final time and finish off the expression with subtraction:
39
Which ordered pair word form a proportional relationship with the point graph below
a. (10,10)
b. (25,35)
c. (70,50)
d. (90,60)
Answer:
D. (90, 60)
Step-by-step explanation:
A proportional relationship is a relationship in which the ratios of two variables are equivalent.
If we take two points on the graph such as (45, 30) and (30, 20), we can see that they can both be simplified to the ratio 3:2. Using this we can find the correct answer. From looking at all the points we can see that only (90,60) would also form a ratio of 3:2, thus d would be the correct answer.
Find x and y. please help ty!! :)
answer:
x=74 y=27
steps:
triangle in the middle is
180-126 = 54
180-85 = 95
180-149 = 31
126=2x+1+31
126=2x+32
2x=94
x=74
126+2y=180
2y=54
y=27
What is the inverse of f(x)=5x/3+5
Answer:
f^-1(x)=8x/5
Step-by-step explanation:
The inverse of f(x)=5x/3+5 is 8x/5
The inverse function of f(x)=5x/3+5 is f-1(x) = 3x/5 - 15
How to determine the inverse?We have:
f(x)=5x/3+5
Rewrite as:
y=5x/3+5
Swap x and y
x = 5y/3 + 5
Subtract 5 from both sides
5y/3 = x - 5
Multiply through by 3
5y = 3x - 15
Divide through by 5
y = 3x/5 - 15
Rewrite as:
f-1(x) = 3x/5 - 15
Hence, the inverse function of f(x)=5x/3+5 is f-1(x) = 3x/5 - 15
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Find the difference quotient f(x)−(3)−3 when ()=1+4−5^2. Simplify the expression fully as if you were going to compute the limit as →3. In particular, cancel common factors of −3 in the numerator and denominator if possible. (Use symbolic notation and fractions where needed.)
The difference quotient of the expression will be 4.
How to find the quotient?f(x) = 5 + 5x + 4x²
f(3) = 5 + 5(3) + 4(3)³
= 56
Now [f(x) - f(3)]/(x - 3) will be:
= (4x² + 5x + 5 - 56)/(x - 3)
= (4x² + 5x - 51)/(x - 3)
= (4x² + 17x - 12x - 5)/(x - 3)
= (4x + 17)(x - 3)/(x - 3)
= 4x + 17
The difference quotient will be:
g(x + h) = 4(x + h) + 17
= [g(x + h) - g(x)]/h
= (4x + 4h + 17 - 4x - 17)/h
= 4h/h
= 4
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how many triangles are in a 18 sided polygon
Answer:
18Step-by-step explanation:
how many triangles are in a 18 sided polygon
An 18 sided polygon, sometimes also called an octakaidecagon, it has 18 sides and therefore is made up of 18 triangles and has 18 vertices.
(look at the picture)
last Saturday, 1750 people attended an event at fairway gardens. the admission fee was $3.50 for children and $8.00 for adults. if the total money collected at the event was $9,860, how many children and how many adults attended the event?
Step-by-step explanation:
I don't know on my mommy that Is the answer
Answer:
There were 920 children and 830 adults.
Step-by-step explanation:
Let C be the number of children and A be the number of adults. Set up equations. Using the attendance of 1750 people, we can write:
c+a=1750
Using the total money collected of 9860, we can write:
3.50c+8.00a = 9860
Solve by substitution. Using (1), we solve for a to obtain (3): a=1750—c
Substutute (3) to (2) and solve for c:
3.50c + 8.00(1750 — c) = 9860
3.50e+ 14000 — 8.00c = 9860
—4.50e= —4140
c=920
Solve for a using (3):
a=1750 — 920
a=830
So, there were 920 children and 830 adults. (They better have been 6 ft apart)
In a basket, there are 52 apples or pears. The number of apples is 8 more than the number of
pears. How many numbers of apples and pears in the box?
Answer:
44 pears and 52 apples
Step-by-step explanation:
pears are 8 more than apple so 52-8 = 44
Number of apples and pears in a box is equals to [tex]30[/tex] and [tex]22[/tex] respectively.
What is number?" Number is defined as the count of any given quantity as per given condition."
According to the question,
Given,
Total number of apples [tex]= 52[/tex]
[tex]'x'[/tex] represents the number of pears
[tex]'x+ 8'[/tex] represents the number of apples
As per the given condition required equation we get,
[tex]x + x + 8 = 52\\\\\implies 2x = 52-8\\\\\implies x = \frac{44}{2} \\\\\implies x = 22[/tex]
number of pears [tex]= 22[/tex]
number of apples [tex]= 22+8[/tex]
[tex]=30[/tex]
Hence, number of apples and pears in a box is equals to [tex]30[/tex] and [tex]22[/tex] respectively.
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Two number cubes are rolled for two separate events:
Event A is the event that the sum of numbers on both cubes is less than 10.
Event B is the event that the sum of numbers on both cubes is a multiple of 3.
Find the conditional probability of B given that A occurs first.
Answer:
You are right...........
What is the average rate of change for this exponential function for the
interval from X.= 0 to x = 2?
Answer:
1.5
Step-by-step explanation:
The average rate of change is 1.5
when x=0 , the value of y =1
when x=2 the value of y = 4
average rate of change formula = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
a= 0 , f(a)=1
b=2, f(b)= 4
4 - 1 / 2 - 0 = 3/2 = 1.5
Triangle A C D is shown. A line is drawn from point D to point B on side A C to form a right angle. Line A D is labeled s. The length of A B is 8, the length of B C is 5, and the length of B D is 15.
What is the value of s in units?
Answer:
s = 17units
Step-by-step explanation:
For this problem, we are trying to find a specific unknown side length.
We're actually given some extraneous information (information that is not needed to solve the problem): It isn't necessary to know that BC is 5.
If the side AD with the unknown length is part of a right triangle (the triangle in red in the attached diagram), we can use the Pythagorean Theorem to solve for AD.
It isn't clear if the diagram you were provided gives ∠ABD as a right angle, if it only gives ∠CBD as a right angle, or if it gives both as a right angle. Below, we prove that it doesn't matter, because regardless, both must be right angles.
Is Triangle ABD a "right triangle"?
Since B is between A and C, then the two angles ∠ABD & ∠CBD form a linear pair, and by the linear pair postulate are supplementary. Since they are supplementary, their measures add to 180°. Using the fact that all right angles are 90°, substitution, the subtraction property of equality, arithmetic, the measure of ∠ABD is also 90°, and thus must be a right angle. Thus, based on the given information, both ∠ABD & ∠CBD must be right angles.
Consequently, triangle ABD is a right triangle, by definition (it is a triangle that has a right angle).
Pythagorean Theorem
Since triangle ABD is a right triangle, the Pythagorean Theorem can be applied.
The Pythagorean Theorem states that [tex]a^{2} +b^{2} =c^{2}[/tex] where "c" is the hypotenuse (the side across from the right angle) and "a" and "b" the the lengths of the two other sides (called legs) of the right triangle. (Aside: Because of the commutative property of addition, it doesn't matter which of the two legs' lengths is used for a, and which is used for b. The only thing that is required is that "c" be the length of the hypotenuse)
In our triangle, side AD, with unknown length "s" is the length of our hypotenuse, and sides AB and BD are the two legs. Substituting values into the Pythagorean Theorem equation, we can solve for the unknown "s":
[tex]a^{2} +b^{2} =c^{2}[/tex]
[tex](8)^{2} +(15)^{2} =(s)^{2}[/tex]
[tex]64 +225 =s^{2}[/tex]
[tex]289 =s^{2}[/tex]
Applying the square root property...
[tex]\pm \sqrt{289} =\sqrt{s^{2}}[/tex]
[tex]s=17 \text{ or } s=-17[/tex]
Final Solution
We discard the negative solution we obtained, since s represents the length of the side of a triangle.
s = 17units
Answer:
17
Step-by-step explanation:
The graphs below have the same shape. What is the equation of the red
graph?
Answer:
g(x) = x^2+4
Step-by-step explanation:
The graph of f(x) = x^2 is translated up 4 units to become g(x) = x^2+4
If L (-5,4),M(2,2), N(0,-3), S(-7,-1), what is the length of diagonal LN
The length of the diagonal LN would be 8.60 units.
To find the distance between the two coordinates, We use distance formula ;
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
Lets put the values of L and N,
d= [tex]\sqrt{(0 - -5)^2 + (-3-4)^2}[/tex]
d =[tex]\sqrt{25+49}[/tex]
d= [tex]\sqrt{74}[/tex]
d= 8.60 units
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Select the correct answer.
Which value of n makes the equation true?
-1/2n=-8
OA. -16
OB. - -4
OC. 4
O D. 16
ответ: д
-1/2 * 16 = -8
или 16/(-2) = -8
Answer: by rewriting equation in the form, / 1\2 16 X 4X 4 f=~1_~) (Do-2)2=g=~
Step-by-step explanation: hope this helps
I really could use help with this
Answer:
B. [tex]\mathsf {\frac{1}{13}(26x-169)=\frac{1}{12}(-156+24x) }[/tex]
Step-by-step explanation:
[tex]\mathsf {\frac{1}{13}(26x-169)=\frac{1}{12}(-156+24x) }[/tex]
2x - 13 = -13 + 2x
2x - 13 = 2x - 13
As both sides are equal, any value can be substituted for x, and hence it has infinitely many solutions.
Answer:
B. 1/13(26x - 169) = 1/12(-156 + 24x)
Step-by-step explanation:
When looking for an equation with infinetly many solutions, we are looking for an equation that is true when simplified
such as: 3c = 3c
or x - 10 = - 10 + x
this is because any value that we put in for x will simplify to a true equation (will be a solution)
so, let's examine the options:
A. if we combine like-terms on both sides, we will end up with 23 + 32x = 32x + 26
which is false, for any value that we put in for x
B. this statement is true--regardless of the value for x.
1/13 · 26 is the same as 1/12 · 24 (both equal 2; so both sides would distribute to 2x)
1/13th of -169 is -13; and 1/12th of -156 is -13
so, for all values of x, option B is true
(all values of x are a solution; and "x" could be any value)
C. by distributing the 2 (6 - 4x = -5x + 7), we find an equation that is not true for all values of x [we don't even have to find the solution, we just know that there will only be a/a few solution ]
D) because the variable, x, is only on one side (and when distributed, is not cancelled by any other x), we know that it cannot be true for infinetly many solutions
(the only true solution will be when the equation is simplified to 4/18 = 4/18)
hope this helps!!
Which is true about the solution to the systems of inequalities shown?
Answer:
There are no solutions
Step-by-step explanation:
If y is greater or equal to 3x+1 it can not be less than 3x-3 since 3x-3 is 4 less than 3x+1. Therefore, there can not be any solutions for the system of inequalities.
