The equation that models the amount of gas left in the car as Phan drives is [tex](g = 18 - 2h)[/tex] and the total amount of gasoline does it take to fill her tank is 18 gallons.
Given :
The table below shows the amount of gas left in her tank as she drives.Number of Hours Spent Driving (h) 3 5 7 9 Amount of Gas Left in Tank, in gallons (g) 12 8 4 0The following steps can be used in order to determine the equation that models the amount of gas left in the car as Phan drives and the total amount of gasoline:
Step 1 - The two-point form of the line can be used in order to determine the equation that models the amount of gas left in the car as Phan drives.
[tex]\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Step 2 - Now, substitute the value of [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the above expression.
[tex]\dfrac{g-12}{h-3}=\dfrac{8-12}{5-3}[/tex]
Step 3 - Simplify the above equation.
[tex]\begin{aligned}\\(g - 12)&=-2(h-3)\\g - 12&=-2h+6\\g &= 18-2h\\\end{aligned}[/tex]
Step 4 - Now, substitute the value of (h = 0) in the above equation.
[tex]g = 18-2(0)\\g = 18 \; {\rm gallons}[/tex]
Therefore, the correct option is A).
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Answer:
g = 18 – 2h; 18 gallons
Step-by-step explanation:
The answer above is correct.
I need help with this
Answer:
5 + 5 = 10
10 + 10 = 20
20 + 20 = 40
40 + 40 = 80
80 is the answer.
PLZ HELP
If a triangle has one interior angle measuring 102°, what is a possible pair of measurements for the other two
interior angles?
Answer:
39
Step-by-step explanation:
There is a possibility that this triangle is isosceles. Angles in triangles add up to 180. 102-180=78. Since we are assuming this triangle is isosceles, we can just divide 78 by 2 and get 39 which might be the other two angles. They might both be 39 degrees.
Since triangle angles must add up to 180 degrees, the other angles must add up to 78 degrees. One possible pair could be if you divided 78 in half, which is 39. There could also be tons of more I can provide a list of below:
39,39
40,38
35,43
What is 0.27 as a percent?
A)0.27%
B)27%
C)2.7%
D)270%
Answer:
B.
Step-by-step explanation:
to turn a decimal into a percentile you have to move the decimal point over two spaces to the right.
Answer:
B
Step-by-step explanation:
Move the decimal 2 places to the left to find a percent.
Evaluate -1 - [-z] where z = -2
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\huge\textsf{-1 - [-z]}\\\\\huge\textsf{= -1 - [- -2]}\\\\\huge\textsf{= -1 - - 2}\\\\\huge\textsf{= -1 + (-2)}\\\\\huge\textsf{= -1 - 2}\\\\\huge\textsf{= -3}\\\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{-3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
-3
Step-by-step explanation:
Evaluate - 1 - ( - z ) where z = -2
you can find this out because when there are two minuses by each other it equals a positive but then z = -2 so that adds another minus so it narrows it down to -1+-2 which equals 3
A freight ship has been moving at 19 miles per hour for the past 2 days. Hugo recorded that the ship moved 155 miles yesterday and 92 miles today. For how many hours has Hugo been keeping track of the ship?
Answer:
13 hours
Step-by-step explanation:
155 + 92 = 247
247 / 19 = 13
what cubed is equal to 1000?
Answer:
10
Step-by-step explanation:
Classify the following triangle
(Chose multiple)
-Equilateral
-Isosceles
-Scalene
-Acute
-Equiangular
-Obtuse
-Right
Answer:
Scalene
Acute
Obtuse
Step-by-step explanation:
≠ Equailateral because all the sides in the given triangle are not equal nor are the three angles 60°
≠ Isosceles because the triangle doesn't have two equal sides nor two equal angles
= Scalene as all the sides are of different lengths and so are all the angles with different degrees.
= Actue because QPO and PQO are less than 90°, thus they are acute angles
≠ Equiangular because none of the given angles are of the same degree.
= Obtuse as POQ is greater than 90°
≠ Right because the given triangle does not have a right angle
What is the following sum? 2 (RootIndex 3 StartRoot 16 x cubed y EndRoot) 4 (RootIndex 3 StartRoot 54 x Superscript 6 Baseline y Superscript 5 Baseline) 4 x (RootIndex 3 StartRoot 2 y EndRoot) 12 x squared y (RootIndex 3 StartRoot 2 y squared EndRoot) 8 x (RootIndex 3 StartRoot x y EndRoot) 12 x cubed y squared (RootIndex 3 StartRoot 6 y EndRoot) 16 x cubed y (RootIndex 3 StartRoot 2 y squared EndRoot) 48 x cubed y (RootIndex 3 StartRoot 2 y EndRoot).
Equivalent expressions are expressions that have the same value, and can be used interchangeably.
The result of the sum [tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5})[/tex] is [tex]4x\sqrt[3]{2y} + 8x^2y\sqrt[3]{2y^2})[/tex]
The expression is given as:
[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5})[/tex]
Rewrite the expression as:
[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 2 (\sqrt[3]{2^4x^3y}) + 4 (\sqrt[3]{3^3 \times 2x^6y^5})[/tex]
Evaluate the roots
[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 2 (2x\sqrt[3]{2y}) + 4 (3x^2y\sqrt[3]{2y^2})[/tex]
Open the brackets
[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 4x\sqrt[3]{2y} + 12x^2y\sqrt[3]{2y^2})[/tex]
The above expression cannot be further simplified.
Hence, the result of the sum [tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5})[/tex] is [tex]4x\sqrt[3]{2y} + 8x^2y\sqrt[3]{2y^2})[/tex]
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The sum of the expression is [tex]4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\[/tex].
We have to determine, the sum of the given expression.
According to the question,
Expression; [tex]2(\sqrt[3]{16x^3y} +4(\sqrt[3]{56x^6y^5})[/tex]
To determine the sum of the given expression following all the steps given below.
Rewrite the expression term in the form of their cubes,
[tex]\rm = 2(\sqrt[3]{16x^3y} +4(\sqrt[3]{56x^6y^5})\\\\ = 2(\sqrt[3]{2^4x^3y} +4(\sqrt[3]{3^3 \times 2 \times x^6y^5})\\\\= 2\times 2(\sqrt[3]{x^3y} +4\times 3(\sqrt[3]{ 2 \times x^6y^5})\\\\= 4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\\\=4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\[/tex]
Hence, The sum of the expression is [tex]4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\[/tex].
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A cylindrical, wooden table top has a density of 0.42 g cm 3 and a mass of 0.25 kg.
The table top has a depth of 6 cm.
Find the radius of the table top, rounded to 1 dp.
The radius of the table top, rounded to 1 dp is 5.6 cm
From the question,
We are to determine the radius of the table top
First, we will determine the volume of the cylindrical wooden table
From the given information
Density = 0.42 g/cm³
Mass = 0.25 kg = 250 g
Using the formula
[tex]Volume = \frac{Mass}{Density}[/tex]
∴ [tex]Volume = \frac{250}{0.42}[/tex]
Volume = 595.238 cm³
Now, for the radius of the table top
Using the formula for volume of a cylinder
[tex]V = \pi r^{2}h[/tex]
Where V is the volume
r is the radius
and h is the height or depth
From the given information
h = 6cm
Putting the parameters into the formula
[tex]595.238 = \pi r^{2} \times 6[/tex]
∴ [tex]r^{2} = \frac{595.238}{6\pi }[/tex]
[tex]r^{2} =31.57835667[/tex]
[tex]r =\sqrt{31.57835667}[/tex]
r = 5.6 cm
Hence, the radius of the table top, rounded to 1 dp is 5.6 cm
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Peter says, "If you subtract 16 from my number and multiply the difference by - 2, the result is
- 34." What is Peter's number?
Answer:
33
Step-by-step explanation:
Let the number be x,
=> (x - 16) -2 = - 34
=> -2x + 32 = -34
=> -2x = - 34 - 32 (by transposing)
=> -2x = -66
=> x = -66/-2 = 33
Peter's number is 33.
Hope you understood.
For any two numbers a and b, the product of a − b times itself is equal to a^2 − 2ab + b^2. Does this familiar algebraic result hold for dot products of a vector u − v with itself? In other words, is it true that (u − v) • (u − v) = u • u − 2u • v + v • v? Justify your conclusion, trying not to express vectors u and v in component form.
Answer:
yes; the distributive property applies to dot products
Step-by-step explanation:
The product of (a-b) with itself is ...
(a -b)·(a -b) = a² -2ab +b²
because the commutative and distributive properties apply to multiplication.
(a -b)·(a -b) = a(a -b) -b(a -b) = a² -ab -ba +b² = a² -ab -ab +b² = a² -2ab +b²
__
The same expansion works for the dot product operation, because the commutative and distributive properties hold for that operation, as well.
(u −v)•(u −v) = u•(u -v) -v•(u -v) = u•u -u•v -v•u +v•v
= u•u -u•v -u•v +v•v = u•u -(u+u)•v +v•v = u•u -2u•v +v•v
_____
Additional comment
The proof of any of the properties of the dot product relies on expressing the vectors in component form. The distributive property is no exception.
For homework Tina is asked to write down the opposite value for each number listed which comparison did Tina write incorrectly
In writing down the opposite value of each number, the comparison Tina wrote incorrectly is: Comparison X
Recall:
Opposite values of a number are numbers that are of the same distance from point zero on a number line.For example, if a is a number, the opposite of a is -a. Or if -3 is a number, the opposite of -3 is 3 because -3 and 3 are both 3 units away from point zero on a number line.Thus, Tina's comparison is given in the diagram attached below.
The comparison labelled X is incorrect because -(-9) = 9. Opposite of 9 is -9.
Therefore, in writing down the opposite value of each number, the comparison Tina wrote incorrectly is: Comparison X
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please answer!!!!!!!!!
Answer:
C. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 5.
Step-by-step explanation:
a swimming pool is drained at a rate of 50 gallons per hour. How many pints per minute is this?
Answer:
8
Step-by-step explanation:
Edward deposited $10,000 into a savings account 3 years ago. The simple interest rate is 4%. How
much money did Edward earn in interest?
Substitute the values into the equation.
Interest = $_• • years
Answer: 10,400
Step-by-step explanation:
I= ? P= 10,000 R= 4% T= 3 yrs
To make pink paint you need 2 pints of white paint and 1 pint of red paint. How many pints of red paint is needed for 10 pints of white paint? *plz i neeeed help
Answer:
5 pints is needed
Step-by-step explanation:
2 pints of white paint for pink
1 pint of red for pink
10 pints of white paint = 5 pints of red
Can someone please take the time out of their day and help me with this question
Answer:
76, 76 104
Step-by-step explanation:
Angle 3 is vertical so it is congruent to Angle 2.
Angle 6 is corresponding, so it is congruent to Angle 2.
Angle 8 is linear to Angle 6, so they add to 180
Answer:
see explanation
Step-by-step explanation:
(a)
∠ 2 and ∠ 3 are vertically opposite angles and are congruent , then
∠ 3 = 76°
(b)
∠ 3 and ∠ 6 are corresponding angles and are congruent , then
∠ 6 = 76°
(c)
∠ 2 and ∠ 8 are same- side exterior angles and sum to 180° , that is
∠ 8 + 76° = 180° ( subtract 76° from both sides )
∠ 8 = 104°
Task-1:
1. Which of the following are in proportion?
a) 21, 35, 24, 40 b) 75, 21, 18, 6
Answer:
1
Step-by-step explanation:
What is 2 plus 55?
........................
Answer:
57
Step-by-step explanation:
...........................
If you add 2 to 55 it’s going to equal 57
what is 3.95 rounded to the nearest whole number
Answer:
4
Step-by-step explanation:
Answer:
3.95 ≈ 4
Step-by-step explanation:
A whole number refers to a whole integer, meaning there can be no decimals or fractions. Follow the rule 4 and below to round down, and 5 and above to round up.
An art teacher divided her students into two groups of equal size.
25 of the first group prefers acrylic paint over watercolor paint.
60% of the second group prefers acrylic paint over watercolor paint.
What fraction of the students prefers watercolor paint over acrylic paint?
Answer:
67.5% or 68%
Step-by-step explanation:
Say each group has 100 students. 25% of 100, is 25 students.
25 students of group 1 prefers acrylic. That leaves 75 students that prefer watercolor.
60% of group 2, or 60 students, prefer water color. That leave 40 students that prefer acrylic.
25+40=65
60+75=135
That is true, since there are 200 students in total.
Now set up a ratio, with watercolor over acrylic.
135:65
135 is 67.5% of 200.
I really don't know if that is a choice, so maybe 68%?
-hope it helps
go follow its datgurlmaribel
Step-by-step explanation:
what is this........???
What value(s) of x will make x2 = 25 true?
A. 5 and -5
B. 5
C. 5
D. 12.5 and -12.5
x^2 = 25
x = -5, 5
Check your work!
(-5)^2 = 25
(5)^2 = 25
Hope this helps! :)
Which function defines the sequence
simplified - 6, -10, -14, -18, ...,
where f (1) = -6 ?
Choose:
An = n - 26
An = 4n - 2
An = -n + 32
An = -4n - 2
What are coordinate of (2,-3) when it is reflected over X axis.
Answer:
the asnwer is (2,3)
Step-by-step explanation:
1085/7 show your work
Answer:
155
Step-by-step explanation:
3(x+3/4+5-x/4-x/6)=10
3(x+3-4+5-x-4-x-6)=10
-3x/-3= -28/3
x= -28/3
The base of a triangle is v245 cm and its height is V20 cm. Find its area.
The given information of the base length and the height of the
rectangle are sufficient to find the area of the triangle.
Correct response:
The area of the triangle is 35 cm.²Methods used for finding the areaGiven that the parameters are;
The base of the triangle = [tex]\sqrt{245}[/tex] cm
The height of the triangle = [tex]\mathbf{\sqrt{20}}[/tex] cm
Required:
To find the area of the triangle
Solution:
[tex]Area \ of \ a \ triangle = \mathbf{ \dfrac{1}{2} \times base \times height}[/tex]Therefore, the area, A, of the given triangle is given as follows;
[tex]A = \dfrac{1}{2} \times \sqrt{245} \ cm \times \sqrt{20} \ cm= \dfrac{1}{2} \times \sqrt{4,900} \ cm^2= \dfrac{1}{2} \times 70 \ cm^2 = 35 \ cm^2[/tex]
The area of the triangle, A = 35 cm²Learn more about the area of plane shapes here:
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You must write your answer in fully simplified form.
8a= 5
Answer:
x = 5/8
Step-by-step explanation:
[tex]\frac{8x}{8} = \frac{5}{8}[/tex]
x=[tex]\frac{5}{8}[/tex]
Someone please help no need to show work just answer (I will give brainliest)
Answer:
image 1 : 3.78
image 2 : 10.20
Step-by-step explanation:
I haven't done geometry in a bit but I'll try to help!