Given:
Car uses 1.6 gallons to go 32 miles
Let's find the amount of gallons of gas the car needs to travel 420 miles.
Here, the relationship between the miles driven and the amount of gas needed is direct variation.
Since it is a direct variation, we have the variation equation when y varies directly with x:
y = kx
Where k is the constant of variation.
Hence, we have:
32 = 1.6k
Let's solve for k.
Divide both sides by 1.6:
[tex]\begin{gathered} \frac{32}{1.6}=\frac{1.6k}{1.6} \\ \\ 20=k \\ \\ k=20 \end{gathered}[/tex]The constant of variation is 20.
The equation that represents this situation is:
y = 20x
Therefore, to find the amount of gallons of gas needed if the car travels 420 miles, substitute 420 for y and solve for x.
420 = 20x
Divide both sides by 20:
[tex]\begin{gathered} \frac{420}{20}=\frac{20x}{20} \\ \\ 21=x \\ \\ x=21 \end{gathered}[/tex]Therefore, the car needs 21 gallons of gas
Find the height of a cylinder with a volume of 36pie cm with an exponent of 3 and a base with a radius of 3 cm.h = ???cmv \: is \: 36\pi \: cm ^{3}vis36πcm3r \: is \: 3cmris3cm
Data
Volume = 36 cm3
radius = 3 cm
Formula
Volume of a cylinder = pi x r2 x h
Solve for h
h = Volume / (pi x r2)
Substitution
h = 36 / (3.1416 x (3)2)
Simplification
h = 36 / (3.1416 x 9)
h = 36 / 28.2744
Result
height = 1.27 cm
Find the next two terms in this
sequence.
20, 32, 42, 50, 56, [ ? ], [ ? ]
The next two digits in the sequence are 60 and 62 and the sequence looks like this: 20, 32, 42, 50, 56, 60, 62
What do we mean by sequence?Sequences are ordered collections of numbers, also known as "terms," such as 2,5,8. There are some sequences that adhere to a particular pattern that allows for an endless extension. For instance, 2,5,8 adheres to the "add 3" pattern, so we can now continue the sequence. There are formulas for sequences that show us where to find any given term. You should be familiar with the following four main categories of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences.So, the next to numbers will be:
20, 32, 42, 50, 56, [ ? ], [ ? ]We can observe that:
20 + 12 = 3232 + 10 = 4242 + 8 = 5050 + 6 = 56Similarly,
56 + 4 = 6060 + 2 = 62Therefore, the next two digits in the sequence are 60 and 62 and the sequence looks like this: 20, 32, 42, 50, 56, 60, 62
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14. Pick the corner point below that maximizes the following objective function: p=22x+14y (6,5)(0,0)(0,12)(15,0)(11,13)
Okay, here we have this:
Considering the provided function, we are going to replace the coordinate pairs one by one in the function, to observe which of the pairs maximizes the function, so we obtain the following:
(6, 5):
p=22x+14y
p=22(6)+14(5)
p=132+70
p=202
(0,0):
p=22x+14y
p=22(0)+14(0)
p=0+0
p=0
(0, 12):
p=22x+14y
p=22(0)+14(12)
p=0+168
p=168
(15, 0):
p=22x+14y
p=22(15)+14(0)
p=330+0
p=330
(11, 13):
p=22x+14y
p=22(11)+14(13)
p=242+182
p=424
Finally we obtain that the corner point that maximizes the function p=22x+14y is the last option (11, 13).
no solution one solution infinitely many solutions 3x + 7 = 14 + 3x 22x + 11 = 4x - 7 3(x + 2) = 3x + 6
no solution one solution infinitely many solutions
3x + 7 = 14 + 3x
22x + 11 = 4x - 7
3(x + 2) = 3x + 6
Part 1
we have
3x + 7 = 14 + 3x
solve for x
3x-3x=14-7
0=7 -----> is not true
that means
No solution
Part 2
we have
22x + 11 = 4x - 7
solve for x
22x-4x=-7-11
18x=-18
x=-1
so
One solution
Part 3
we have
3(x + 2) = 3x + 6
solve for x
Divide by 3 both sides
x+2=x+2 -----> its a identity
that means
infinitely many solutions
Patrick rolls a die. What is the probability that he rolls an 1, 3 or 5?
The total possible outcomes of a dice are: 1,2,3,4,5 and 6.
There are 6 possible outcomes, all with equal probability.
Then, as all the outcomes have the same probability, we have to calculate what is the probability of having one ot three specific outcomesout of the possible 6 outcomes.
We can calculate this as:
[tex]P=\frac{\#\text{success outcomes}}{\#\text{possible outcomes}}=\frac{3}{6}=\frac{1}{2}=0.5=50\text{ \%}[/tex]Answer: P(1,3, or 5) = 1/2 = 0.5 = 50%
please help me out quickly
Answer:
take the first 1 an flip it to the other side and with the second row put that 1 on the other side an switch the other two the same way
V is the midpoint of UW. If UV = 2x and VW = x + 8,what is UV?
Please explain and show work
Based on the definition of the midpoint of a line segment, the length of UV is determined as: 16 units.
What is the Midpoint Definition of a Segment?The midpoint of a segment is defined as the point on a line segment where the line segment is bisected into two equal smaller segments. The length of the smaller segments formed will be equal to each other.
Given that V is the midpoint of segment UW, it means that V divides segment UW into two equal smaller segments, UV and VW.
UV = 2x
VW = x + 8
Therefore:
UV = VW
Substitute
2x = x + 8
2x - x = x + 8 - x [subtraction property of equality]
x = 8
Find the length of UV:
UV = 2x
Plug in the value of x
UV = 2(8)
UV = 16 units.
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I'm kind of confused on this one I got some help but I'm still struggling to figure it out
Explanation
Step 1
the standard form of a quadratic equation is given by
[tex]f(x)=ax^2+bx+c[/tex]then, by the table, we have:
[tex]y=f(x)[/tex][tex]\begin{gathered} f(x)=ax^2+bx+c \\ f(-4)=a(-4)^2+b(-4)+c \\ f(-4)\rightarrow30=16a-4b+c\rightarrow\text{Equation}(1) \\ f(-3)=a(-3)^2+b(-3)+c \\ f(-3)=9a+-3b+c \\ f(3)=0=9a+-3b+c\rightarrow\text{Equation}(2) \\ \end{gathered}[/tex]now, we have 2 equations, and 3 variables ( a, b and c, so we need one more equation)
when x= 2
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ f(2)=0=a2^2+b\cdot2+c \\ f(2)=0=4a+2b+c\rightarrow Equation\text{ (3)} \end{gathered}[/tex]Step 3
solve the equations
[tex]\begin{gathered} 30=16a-4b+c\rightarrow\text{Equation}(1) \\ 0=9a-3b+c\rightarrow\text{Equation}(2) \\ 0=4a+2b+c\rightarrow Equation\text{ (3)} \end{gathered}[/tex][tex]\begin{gathered} 0(eq2)=0(eq3) \\ \text{9a-}3b+c=4a+2b+c \\ \text{subtract c in both sides} \\ \text{9a-}3b+c-c=4a+2b+c-c \\ \text{9a-}3b=4a+2b \\ \text{subtract 4a in both sides} \\ \text{9a-}3b-4a=4a+2b-4a \\ 5a-3b=2b \\ \text{add 3b in both sides} \\ 5a-3b+3b=2b+3b \\ 5a=5b \\ \text{divide both sides by 5} \\ \frac{5a}{5}=\frac{5b}{5} \\ a=b \end{gathered}[/tex]Now, replace a=b in equation (1) and equation (2)
[tex]\begin{gathered} 30=16a-4b+c\rightarrow\text{Equation}(1) \\ 30=16a-4a+c \\ 30=12a+c\rightarrow\rightarrow equation\text{ (4)} \\ 0=9a-3b+c\rightarrow\text{Equation}(2) \\ 0=9a-3a+c \\ 0=6a+c\rightarrow\rightarrow equation(5) \end{gathered}[/tex]Step 3
use equations (4) and (5) to find a and c
[tex]\begin{gathered} 30=12a+c\rightarrow\rightarrow equation\text{ (4)} \\ 0=6a+c\rightarrow\rightarrow equation(5) \end{gathered}[/tex]a)isolate c in both equations and equal the expressions to find a
[tex]\begin{gathered} 30=12a+c\rightarrow\rightarrow equation\text{ (4)} \\ 30-12a=c \\ c=30-12a \\ 0=6a+c\rightarrow\rightarrow equation(5) \\ -6a=c \\ c=c \\ 30-12a=-6a \\ \text{add 6a in both sides} \\ 30-12a+6a=-6a+6a \\ 30-6a=0 \\ \text{subtract 30 in both sides} \\ 30-6a-30=0-30 \\ -6a=-30 \\ \text{divide both sides by -6} \\ \frac{-6a}{-6}=\frac{-30}{-6} \\ a=5 \end{gathered}[/tex]we have a= 5,
now, replace in equation (4) to find x
[tex]\begin{gathered} 30=12a+c\rightarrow\rightarrow equation\text{ (4)} \\ 30=12\cdot5+c \\ 30=60+c \\ \text{subtrac 60 in both sides } \\ 30-60=60+c-60 \\ -30=c \\ c=-30 \end{gathered}[/tex]Therefore we have
a=5 b=5 c=-30
Step 4
finally, rewrite the equation
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ f(x)=5x^2+5x-30 \end{gathered}[/tex]I hope this helps you
The graph of a piecewise function, f x( )is plotted in Figure 1. Discuss the continuity of f x( )at x =−1using the continuity test
the graph is not continuous at x=-1
[tex]\lim _{x\rightarrow-1^-}f(x)\ne\lim _{x\rightarrow-1^+}f(x)\ne f(-1)[/tex]Cooper, Sha'NiyaThe sum of three consecutive integers is 177. What is the largest of the integers, and why?
We can represent the sum of the three consecutive integers as:
[tex]n+(n+1)+(n+2)=177[/tex]Then, we need to solve the equation for n, then:
[tex]3n+3=177_{}\Rightarrow3n=177-3\Rightarrow3n=174\Rightarrow n=\frac{174}{3}\Rightarrow n=58[/tex]Then, the largest of the integers is n + 2 or 58 +2 = 60.
The reason is that the other integers are 58, 58 + 1 = 59, that is, 58 and 59.
We can check that:
58 + 59 + 60 = 177.
find AB 15 8 A-3 and - 1:03:36:13 : C12
Given :
[tex]\begin{gathered} A=\begin{bmatrix}1 & {2} & {} \\ {3} & {4} & \end{bmatrix} \\ B=\begin{bmatrix}{6} & {7} & {} \\ {5} & {8} & \end{bmatrix} \end{gathered}[/tex]So,
[tex]AB=\begin{bmatrix}{1} & {2} & {} \\ {3} & {4} & {}\end{bmatrix}\begin{bmatrix}{6} & {7} \\ {5} & {8}\end{bmatrix}=\begin{bmatrix}{c11} & {c12} \\ {c21} & {c22}\end{bmatrix}[/tex]c11 = row 1 column 1 = 1 * 6 + 2 * 5 = 6 + 10 = 16
c12= row 1 column 2 = 1 * 7 + 2 * 8 = 7 + 16 = 23
c21 = row 2 column 1 = 3 * 6 + 4 * 5 = 18 + 20 = 38
c22 = row 2 column 2 = 3 * 7 + 4 * 8 = 21 + 32 = 53
What is the range of this function?O A. ys-9OB. y2-9C. All real numbersD. x 1
Given the function:
[tex]y=x^2-2x-8[/tex]The function above is a quadratic function, the graph is a parabola
The standard form of a quadratic function is given by:
[tex]\begin{gathered} ax^2+bx+c=0 \\ \text{for a parabola with }a\text{ vertex (h, k)} \\ If\text{ a<0},\text{ the range is y}\leq k \\ \text{if a>0},\text{ the range is y}\ge k \end{gathered}[/tex]From the given graph and function,
[tex]\begin{gathered} The\text{ vertex (h, k) = (}1,\text{ -9)} \\ a\text{ =1} \\ \sin ce,\text{ a>0, the range is y}\ge-9 \end{gathered}[/tex]Therefore, the range of the function is:
[tex]undefined[/tex]My math teacher has the answer as -1/4. I got 1/4 and cannot figure out the negative part.
To find the limit we need to rationalize the function, we achieve this by multiplying by a one written in an appropiate way:
[tex]\begin{gathered} \lim_{h\to0}\frac{2-\sqrt{4+h}}{h}=\lim_{h\to0}\frac{2-\sqrt{4+h}}{h}\cdot\frac{2+\sqrt{4+h}}{2+\sqrt{4+h}} \\ =\lim_{h\to0}\frac{(4-(\sqrt{4+h})^2)}{h(2+\sqrt{4+h})} \\ =\lim_{h\to0}\frac{4-(4+h)}{h(2+\sqrt{4+h})} \\ =\lim_{h\to0}\frac{4-4-h}{h(2+\sqrt{4+h})} \\ =\lim_{h\to0}\frac{-h}{h(2+\sqrt{4+h})} \\ =\lim_{h\to0}\frac{-1}{2+\sqrt{4+h}} \\ =-\frac{1}{2+\sqrt{4+0}} \\ =-\frac{1}{2+\sqrt{4}} \\ =-\frac{1}{2+2} \\ =-\frac{1}{4} \end{gathered}[/tex]Therefore:
[tex]\lim_{h\to0}\frac{2-\sqrt{4+h}}{h}=-\frac{1}{4}[/tex]A sprinkler waters a circular region in Jason's yard that has a radius of 15 feet. Rounded to the nearest square foot, what is the area of the circular region that is watered by the sprinkler?
A sprinkler waters a circular region in Jason's yard that has a radius of 15 feet. Rounded to the nearest square foot, what is the area of the circular region that is watered by the sprinkler?
the area of the circular region is
A=pi*r^2
we have
pi=3.14
r=15 ft
substitute
A=3.14*(15^2)
A=707 ft2Oliver puts 600.00 into an account to use for school expenses the account earns 3% interest compounded annually how much will be in the account after 6 years
$600.00
3% interest = 0.03
compund anually
How much in 6 years
P = 600
r = 0.03
n = 1
t = 6
[tex]A\text{ = 600(1 + }\frac{0.03}{1})^{(1)(6)}=600(1.03)^{6\text{ }}\text{ = 600(1.1940) = 716.40}[/tex]Answer:
$716.40
hi, I nee help with this, I don't know if my answer is correct! it would be helpful if you told me which one it is and than do your explaination if that's possible, it's just more convenient for me!
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion. In other words, similar triangles are the same shape, but not necessarily the same size.
therefore, in this case we can see that the triangles have an equal angle and their sides are similar.
We can find s , the slant height using Pythagorean theorem , and since this solid is made of parts of simple solids , we can combine the formulas to find surface area and volume
EXPLANATION
Given that the slant represents the diagonal side of a solid, we can use the Pythagorean Theorem as shown as follows:
Thus, if we know the height and the base, we can compute the slant height by the Pythagorean as explained above.
The Pythagorean Theorem says:
Therefore, we can substitute the radius and the height in the Pytagorean Equation to obtain the slant height.
[tex]\text{radius}^2+\text{height}^2=\text{slant height\textasciicircum{}2}[/tex][tex]r^2+h^2=s^2[/tex]Pluggin in the given values into the equation:
[tex]5^2+7^2=s^2[/tex]Isolating the slant height:
[tex]\sqrt[]{5^2+7^2}=s[/tex]Now, if we need to compute the Surface Area, we need to combine the formulas for all the solids that form the figure.
Figure:
Thus, the surface area is:
[tex]Total\text{ Surface Area=}\frac{SurfaceArea_{\text{sphere}}}{2}+Surface\text{ Area of the Cone}-\text{ Surface Area of the Base}[/tex]Replacing terms:
[tex]=\frac{4\cdot\pi\cdot r^2}{2}+(\pi rs+\pi r^2)-\pi r^2[/tex]We can apply the same reasoning to the Volume:
[tex]Total\text{ Volume}=\frac{Volume\text{ Sphere}}{2}+Volume\text{ of the cone}[/tex][tex]=\frac{\frac{4}{3}\pi r^3}{2}+\frac{1}{3}\pi r^2h[/tex]Finally, just replacing the corresponding values, give us the appropiate surfaces and volumes.
What is the equation of the line that passes through the point (-6,5) and has a slope of -\frac{1}{6}
?
HELP
The equation of the line with point (-6,5) and slope as -1/6 in slope intercept form is y=-1x/6+6
Given, the equation of the line passes through the point (-6,5)
and has a slope of -1/6.
point (-6,5) = (x₁,y₁)
slope (m)= -1/6
equation of the line is :
y-y₁=m(x-x₁)
substitute the values in the above formula:
y-5=(-1/6)(x-(-6)
y-5=-1x/6+6/6
y-5=-1x/6+1
y=-1x/6+1+5
y=-1x/6+6
Hence the equation of the line is y=-1x/6+6.
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A small tabletop is 3/4 ft by 3 1/2 ft. Rita solves 3/4⋅3 1/2 to find the area of the tabletop in square feet. Choose numbers to complete Rita's calculations for the area.
Number which represents the area of table top which has measures of 3/4 ft by 3 1/2 ft is equal to 21/8 square feet.
As given,
Measures of a small tabletop is equal to 3/4 ft by 3 1/2 ft
length=3 1/2 ft
=7/2 ft
Width=3/4 ft
Formula used to measure area of the small tabletop is equal to
=Length ×width
Substitute the values in formula to get a number which represents the area of small tabletop :
Area=(3/4) × (7/2)
=21/8 square feet
Therefore, number which represents the area of table top which has measures of 3/4 ft by 3 1/2 ft is equal to 21/8 square feet.
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Bud Graham owns property in Salinas assessed at $250,000 and pays a property tax rate of $1.96 per $100 of assessed value. He also owns property in Modesto assessedat the same $250,000 and pays property tax at a rate of $21.50 per $1,000 of assessed value. What is Bud's total property tax bill for properties in both towns?$10,275$9,965$11,045$10,996None of these choices are correct.
Ok so first we are gonna calculate the tax bill for each town independently and then we are gonna add their values. The tax rate in Salinas is $1.96 per $100 of assessed value and we know Mr. Graham's property is assessed at $250000 so we can use the rule of three:
$100-----------$1.96
$250000----------x
Where x represents his property tax bill for Salinas. According to the rule of three:
[tex]x=\frac{250000\cdot1.96}{100}=4900[/tex]So he has to pay $4900 in taxes for that property. Now we make the same process for his property on Modesto:
$1000-----------$21.5
$250000----------x
[tex]x=\frac{250000\cdot21.5}{1000}=5375[/tex]So he has to pay $5375 for his property in Modesto. Adding the two bills we know the total property bill: $4900 + $5375 = $10275
Lisa used [tex] \frac{1}{4} [/tex]cup of milk in her muffin recipe. How can you write I as a decimal? 0 A. 0.2 B. 0.25 C. 0.4 OD 1.4
Answer:
1/4 = 0.25
Option B
Step-by-step explanation:
To write 1/4 as a decimal, we use a division, dividing 1 by 4.
So
1/4 = 0.25
Divide (41°48') = 4.
The division of 41°48' by 4 gives the result 10°27'.
What is termed as the division?Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 divided into 3 equal portions adds up to 4 in each group in division. Each component of a division eqn has its own name.Dividend: A dividend is indeed the number divided during the division process.Divisor: The divisor is the number in which the dividend is divided.Quotient: A quotient is an outcome of the division process.Remainder: We can't always divide things exactly. There could be an extra number. The leftover number is known as the remainder.The following describes the relationship between such four parts:
Dividend = Divisor x Quotient + Remainder
For the given expression,
(41°48') divided by 4.
= 41°48' / 4
= 10°27'.
Thus, the division of the expression 41°48' by 4 gives 10°27'.
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There are two parts ill send the second part after the first part is answered. Please!
Which number line shows the solution of 5x-25>-15
The solution to the inequality 5x - 25 > -15 in inequality and interval notation form are x > 2 and (2,∞)
How to solve linear inequality problems?A linear inequality is simply an expression where two values are compared by the inequality symbols <, >, ≤ or ≥.
Given the data in the question;
5x - 25 > -15
To solve for x, bring all terms containing the variable to the left side of the equation and the terms without variables to the right side of the equation.
5x - 25 > -15
Add 25 to both sides
5x - 25 + 25 > -15 + 25
5x > -15 + 25
5x > 10
Divide each term in 5x > 10 by 5 and simplify.
5x > 10
5x/5 > 10/5
x > 2
Therefore, the solution to inequality is x > 2.
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which values are solution to the inequality below. Check all applyX^2<64A. 65B. 64C. 7D. -8E> 0F. NO SOLUTION
Answer:
[tex]C\text{ and E.}[/tex]Step-by-step explanation:
[tex]x^2<64[/tex]Take the square root of both sides:
*A positive number has two square roots, one positive, and one negative, which are opposite to each other.
[tex]\begin{gathered} x<\pm\sqrt[]{64} \\ -8Therefore, 0 and 7 are solutions to inequality.A sphere has a diameter of 4ft . what is its surface area ?The surface area of the sphere is _ ft 2(Type an exact answer in terms of pie .)
The formula of the surface area of an sphere is
[tex]SA=4\pi r^2[/tex]where r is the radius
the radius is half of the diameter
r=4/2
r=2 ft
we substitute the values
[tex]SA=4\pi(2)^2=4\cdot\pi\cdot4=16\pi ft^2[/tex]the surface area is 16pi ft^2
The indoor climbing gym is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans, v, and 3 buses, b, with 242 students. High School B rented and filled 2 vans and 6 buses with 260 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry?
Solution:
We would start by analyzing the statements;
High School A rented and filled 8 vans, v, and 3 buses, b, with 242 students. Mathematically;
[tex]8v+3b=242.........equation1[/tex]High School B rented and filled 2 vans, v, and 6 buses, b, with 260 students. Mathematically;
[tex]2v+6b=260...............equation2[/tex]Now, we would solve equation 1 and equation 2 simultaneously.
From equation 2;
[tex]\begin{gathered} 2v+6b=260 \\ \\ \text{ Divide through by 2;} \\ \frac{2v}{2}+\frac{6b}{2}=\frac{260}{2} \\ \\ v+3b=130 \\ \\ v=130-3b..........equation3 \end{gathered}[/tex]Substitute equation 3 in equation 1;
[tex]\begin{gathered} 8(130-3b)+3b=242 \\ \\ 1040-24b+3b=242 \\ \\ 1040-242=24b-3b \\ \\ 798=21b \\ \\ b=\frac{798}{21} \\ \\ b=38 \end{gathered}[/tex]Substitute the value of b in equation3;
[tex]\begin{gathered} v=130-3(38) \\ \\ v=16 \end{gathered}[/tex]ANSWERS:
[tex]\begin{gathered} \text{ High School A: }8v+3b=242 \\ \\ \text{H}\imaginaryI\text{gh School B: 2}v+6b=260 \\ \\ \text{ Van: \$}16 \\ \\ \text{ Bus: \$}38 \end{gathered}[/tex]i have a hard time in school can some one pls tell me what this is
Answer: 17 1/3
Step-by-step explanation: hope this helps!
A few days later, the American tourist went to a bank in Plymouth and exchanged 150 American dollars for British pounds. How many pounds did she receive? (Round your answer to two decimal places.)
The amount of money that the American tourist will receive will be 132.74 pounds.
What is money?It should be noted that money is the medium of exchange. In this case, it should be noted that 1 pound = 1.13 dollar
The American tourist went to a bank in Plymouth and exchanged 150 American dollars for British pounds, the pound received will be:
= Amount / rate
= 150 / 1.13
= 132.74 pounds.
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Using the imagine below, find the measure of angle y.
y+ (5x-10)= 180 º
Due to the lines are parallels
[tex]\alpha=\beta[/tex]So then
(5x-10)= (x+86)
5x - x = 86 + 10
4x = 96
x = 24
__________________
Checking
(5x-10= 5*24-10= 110º
(x+86) = 24+ 86= 110º
__________________________
y+ (5x-10)= 180 º
y+ 110º = 180 º
y= 180-110º
y= 70º
