2.2 question 7) Which lines are perpendicular? The_____ lines are perpendicular (blue and green) How do you know? The product of their slopes is....
Two families visited an amusement park. The first family bought 2 hot dogs and 3 bottles of waters, which totaled $18. The second family bought 4 hot dogs and 2 bottles of waters, which totaled $28. How much did one hot dog cost?
$2
$4
$5
$6
The answer is 6.
6x4=24
and that leaves the water to =2 per bottle.
so, 24+4=28
Answer:
$6.00
Step-by-step explanation:
To solve this problem, we have to construct two separate equations for each family, and then use any of the methods for solving simultaneous equations.
Let's consider h to represent the cost of 1 hot dog, and w to mean the cost of 1 water bottle.
• For the first family:
[tex]2h + 3w = 18[/tex]
We can rearrange the equation to make w the subject:
⇒ [tex]3w = 18 - 2h[/tex]
⇒ [tex]w = \frac{18 - 2h}{3}[/tex]
• For the second family:
[tex]4h + 2w = 28[/tex]
Since we have previously obtained an expression for w in terms of h, we can substitute that expression for w in the above equation, and then solve for h:
⇒ [tex]4h + 2(\frac{18 - 2h}{3}) = 28[/tex]
⇒ [tex]4h + \frac{36 - 4h}{3} = 28[/tex]
⇒ [tex]12h + 36 - 4h = 84[/tex] [Multiplying both sides of the equation by 3]
⇒ [tex]8h + 36 = 84[/tex]
⇒ [tex]8h = 48[/tex]
⇒ [tex]h = \bf 6[/tex]
∴ The price of one hot dog is $6.00.
The cost of one hot dog at an amusement park is $6.
What are linear and non-linear functions?A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x - 2 depicts a linear function because it is a straight line in the coordinate plane.
Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.
An example of a non-linear function is a quadratic function.
Let, the cost of hot dogs is 'x' and the cost of bottles of water be 'y'.
From the given information the two linear equations can be formed as,
2x + 3y = 18...(i) and 4x + 2y = 28...(ii)
Multiplying equation (i) by 2 and subtracting form (ii) we have,
4x + 2y = 28.
(-) 4x + 6y = 36
_____________
- 4y = - 8.
y = 2.
And hence x is equal to, 4x + 4 = 28 ⇒ 4x = 24 ⇒ x = 6.
So, The cost of one hog dog is $6.
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which of the following ordered pairs make this question true y=2x-4?
Answer:
There is not a single ordered pair which is a solution to y=2x−4 .
MAPS Leila is walking from the park at point P to a restaurant at point R. She wants to stop for a break when the distance she has traveled and the distance she has left to travel has a ratio of 3:5. At which point should Leila stop for her break?
The point at which Leila should stop to take break is (6.25 , 3.75)
Given P(10 , 3) and R (0 , 4)
The ratio is 3:5
Let the break point be point B.
The formula is : (n(x₁) ₊ m(x₂)/ m₊n , n(y₁) ₊ m(y₂)/ m₊n)
P(10,3) = (x₁ , y₁)
R(0,4) = (x₂ , y₂)
m:n = 3:5
B = (5(10) ₊ 3(0)/3₊5 , 5(3) ₊ 3(4)/3₊5)
B = (50₊0/8 , 15₊12/8)
B = (50/8 , 27/8)
B = (6.25 , 3.75)
Hence Leila should stop at point (6.25 , 3.75) for her break.
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a) Work out the value of 23 +52
b) Work out the value of 72-33
c) Work out the value of 82 + √100
Answer:
Step-by-step explanation:
One
23 + 52 = 75 This can be done using columns
2 3
5 2 No carries Add.
7 5
Two
72 - 33 = 39
7 2
3 3 You have to borrow a ten from the 7 to make this work
3 9
Three
82 + sqrt(100)
sqrt(100) = 10
82 + 10 = 92
Under her cell phone plan, Caroline pays a flat cost of $54.50 per month and $5 per gigabyte. She wants to keep her bill at $74 per month. Write and solve an equation which can be used to determine gg, the number of gigabytes of data Caroline can use while staying within her budget.
To stay within budget, she must use 3.9 gigabytes.
Giving the following information:
Under her cell phone plan, Sofia pays a flat cost of $54.50 per month and $5 per gigabyte. She wants to keep her bill at $ 74 per month.
First, we need to establish the total cost formula:
Total cost= 54.5 + 5*x
x= number of gigabytes
Now, we isolate x:
74= 54.5 + 5x
19.5/5= x
3.9= x
To stay within budget, she must use 3.9 gigabytes
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If f (x) = 3x - 1 and g (x) = x²+1, find the following.
a) f(-1) + g (4) =
b) g(2) - g (-3) =
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Your car's gas tank holds 13 gallons, and you expect to get about 25 miles per gallon on this winding road. to be sure you don't run out of gas, you never want to have less than 1 gallon in the tank. you start with a full tank of gas. will you need to stop for gas during the first day's drive? explain how you know, and show your work.
If you had to drive for more than 300 miles for the first day you need to stop for gas fill up.
What is unitary method ?Unitary method is a mathematical tool for finding the value of single unit then deriving the given units according to the question.
According to the given question your car's gas tank holds 13 gallons, and you expect to get about 25 miles per gallon.
Given that you never want to run out of gas to not face this issue you always keep 1 gallon of gas in the tank.
So when you fill your tank completely you fill for 12 gallons of gas because 1 gallon is already there.
Also given that the car can go 25 miles per gallon.
So, for 12 gallons of gas you can go (25 × 12 ) miles which is
= 300 miles.
If you had to drive for more than 300 miles then you need to stop for gas in first day's drive.
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You sold your car for $1,000 which had cost $1,450. How much did you lose expressed as a %?.
Answer:
45%
Step-by-step explanation:
1,450 - 1,000 = 450
the 450 becomes 0.45
to make 0.45 a percent, we multiply it by 100
0.45 x 100 = 45
45%
R, S, and T are collinear. S is between R and T. RS =2w + 1, ST = w - 1, and RT = 18. Use the Segment Addition Postulate to slove for w. Then determine the lenght of RS.
R, S, and T are collinear . Then 13 is the length of RS.
What do collinear points mean?
Collinear points are those that are situated along a single or shared straight line. In Euclidean geometry, two or more points are said to be collinear if they are located on a line either near or far from one another.The question to know
RS + ST = RT
RS = w + 1 , ST = w - 1
RT = 18
2w + 1 + w - 1 = 18
3w = 18
w = 18/3
w = 6
RS = 2 * 6 + 1 = 13
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98÷13=
I need help please...
Answer:
7.538461538
Step-by-step explanation:
PLEASE I ONLY HAVE 15 MINS LEFT, HELP! Find the inverse of the following matrix:
Answer:
The inverse is [-4/3 -5/3 1]
[-4/3 -8/3 1]
[1/3 2/3 0]
Sorry, I didn't know how to type it well.
What is an equation of the line that passes through the point (-4,-6) and is parallel to the line 2x-y=6
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]2x-y=6\implies -y=-2x+6\implies y=\stackrel{\stackrel{m}{\downarrow }}{2} x-6\leftarrow \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is 2 and it passes through (-4 , -6)
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-4)}) \implies y +6= 2 (x +4) \\\\\\ y+6=2x+8\implies y=2x+2[/tex]
which of the following is equivalent to 3^4 ? Which of the following is equivalent to 3^ 4 ?
12
81
7
64
81 is equivalent to 3^4
What Is the Power of a Number?
The power of a number stands for how many multiples of the number there are. The power of a number is represented by something called an exponent
When a number is "raised to the second power," it means that the number is multiplied together twice, for example. When a number is "raised to the fifth power," it means that it is multiplied together five times.
we have to solve 3^4
here 3 raised to the fourth power
then 3 is multiplied together 4 times
3*3*3*3
81
Hence ,81 is equivalent tp 3^4
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I went to a toy shop and bought a toy car which costs $16.80, but there was a 20% discount. how much did I pay?
Step-by-step explanation:
16.80 - 20% of 16.80 = 13.44
you paid 13.44$
Answer:
=13.44
Step-by-step explanation:
0.20×16.80=3.36
16.80-3.36=13.44
Sort the following numbers into the correct category:
If you do this I will do the following: Like, Friend you, (if you want me to.) give you the brainiest, (when two people answers then I will be able to pick the best one.) and I believe that is all! Please do this and if you do not do it correctly like I wanted it and yes, I do want it to be actually “CORRECT.” So please help me complete this.And once you have done this I will say, “Thank you for your help!” :)
Answer:
sqrt of 49 is simplified as 7 so its a rational that can be put in all the rows
Step-by-step explanation:
Rational numbers: -1.3, 2.7777.., 25/2 also known as 12.5, O
Integers: sqrt of 49 also known as 7, 0
Whole numbers: sqrt of 49 also known as 7, 0
Natural numbers: sqrt of 49 also known as 7, 0
Irrational numbers: sqrt of 2, Pi,
Can someone help me please
Answer:
182.5
Step-by-step explanation:
182.5
steps
623420÷3416=
182.5
1. Jake reads the following problem: If the original scale factor for a scale drawing of a square swimming pool is 1/90, and the length of the original drawing is measured to be 8 inches, what is the length on the new scale drawing if the scale factor of the new scale drawing length to actual length is 1/144? He works out the problem: 8 inches ÷ 1/90 = 720 inches 720 inches× 1/144 = 5 inches Is he correct? Explain why or why not.
Yes Jake is correct we the scales are accurately represented.
How to calculate the value?From the information, the original scale factor for a scale drawing of a square swimming pool is 1/90, and the length of the original drawing is measured to be 8 inches.
Therefore, the original length will be:
= 8 ÷ 1/90
= 8 × 90
= 720 inches
Therefore, Jack is correct.
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Which equation represents a linear function? Iready- Understand functions, Level H.
Answer:
y = 4x + 5
Step-by-step explanation:
y = 4x + 5 is the only one that graphs a straight line
Pls help 15 points going out
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4. Liness and t are parallel. Find the value of x.
Answer: The value of X = 50°
Step-by-step explanation:
from diagram:
40° = 40°(vertically opposite angles)
40° + 90° + opposite side of X = 180 °(exterior angle property)
130° + opposite side of X = 180°(linear pair property)
opposite side of X = 180° - 130°
= 50°
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7x ≤3x-24 or 10x-1≥9
Answer:
Im not pretty sure but i think thats the answer ^^
A mother wants to invest $15,000.00 for her son's future education. She invests a portion of the money in a bank certificate of deposit (CD account) which earns 4% and the remainder in a savings bond that earns 7%. If the total interest earned after one year is $900.00, how much money was invested in the CD account?
The total interest earned after one year is $900.00.
How much money was invested in the CD account? $
(Round to the nearest cent, if necessary.)
From the analysis of the above math, the amount she invested in the CD account is 5,000. See the analysis below.
What is the analysis showing the above answer?Let A be the amount invested in the CD.
Let B be the amount invested in the savings bond.
A + B = 15, 000
.04A + .07B = 900
Multiply the first equation by -.04 and add it to the second equation to get rid of the A term.
-.04A-.04B = -600 add this equation to the second equation.
.03B = 300 multiplying by 100. 3B = 30,000
dividing by 3 on both sides: B = 10,000. So A = 5,000
So she invested 5,000 in the CD account
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which of the following situations best descrbies a student engaged in active learing 1. A student uses only one of the resources provided by the teacher 2. A student skips parts of lessons that she find difficult 3. A student records questions to ask the teacher about a concept 4. A student does not discuss math outside of lessons.
Answer:1.c 2.b 3.a
Step-by-step explanation:
Which shows the expression below simplified?
A. 8 × 10-3
B. -1.4 x 10-3
C. 8x10-1
D. 8×104
0.00056+ (7 x 10-²)
Answer:
A.77
B.-17
C.79
D.832
E.0.07056
Step-by-step explanation:
A.=8×10-3
=80-3
=77
B.=-1.4×10-3
=-14-3
=-17
C.=8×10-1
=80-1
=79
D.=8×104
=832
E.=0.00056+(7×10^-2)
=0.00056+0.07
=0.07056
Help !!! With this please !!!
Answer: $48.17
Step-by-step explanation:$148.68-$24.32= $124.36
$124.36-$37.53= $86.83
$135 -$86.83=$48.17
So he needs forty-eight dollars and 17 cents.
How do you write 0.00603 in scientific notation?
Answer: .[tex]306^{-3}[/tex]
Step-by-step explanation:
Answer: +6.03E-3
Step-by-step explanation:
[tex]0.00603=6.03*10^{-3}[/tex]
6.03*10⁻³=+6.03E-3
Which of the following options are examples of how you can name the angle?
Answer:
3rd and 4th
Step-by-step explanation:
Answer:
∠C and ∠DCB and ∠BCD
Step-by-step explanation:
We can name an angle either using one letter that represents it or use all three letters together.
When we use a single letter to represent or point an angle we must choose the center letter, C in this case.
And when we use all three letter to point an angle we must place the center letter, again C in this case, in the middle
Therefore the angle can be named as
∠C or ∠DCB or ∠BCD
what is 1+1?
And hows ur day???
Answer:
The answer is 2, and thanks for asking my day's good :D
How's your day?
Step-by-step explanation:
A cubical die is 3 m long. Find its volume. How much space does it occupy?
Answer:
27 m³
Step-by-step explanation:
Formula we use,
→ V = a³
Let's solve the problem,
→ V = a³
→ V = 3³
→ [ V = 27 m³ ]
Hence, it occupies 27 m³.