x = number of months
7*x = 7 times the number of months
7*x = total cost if you ignore the $100 fee
7x+100 = total cost with the fee of $100 included
y = total cost
y = 7x+100
Final Answer: y = 7x+100
note: the slope is 7 and the y intercept is 100
Solve: √81/100
Will mark brainliest for fastest and correct response.
Answer:
[tex]\dfrac{9}{100}=0.09\ or\ \dfrac{9}{10}=0.9[/tex]
Step-by-step explanation:
[tex]\sqrt{a}=b\iff b^2=a\ for\ a\geq0\ and\ b\geq0\\\\\text{We have}\ \sqrt{81}:\\\\\sqrt{81}=9\ because\ 9^2=81.\ \text{Therefore}\\\\\dfrac{\sqrt{81}}{100}=\dfrac{9}{100}\\\\\text{If is}\ \sqrt{\dfrac{81}{100}},\text{then:}\\\\ \text{Use}\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\\sqrt{\dfrac{81}{100}}=\dfrac{\sqrt{81}}{\sqrt{100}}=\dfrac{9}{10}=0.9\\\\\sqrt{81}=9\ because\ 9^2=81\\\sqrt{100}=10\ because\ 10^2=100[/tex]
.......... is the slope zero
Answer:
Step-by-step explanation:
OK... You have to use this formula: Y2 - Y1
X2 - X1
-2 represents X17 represents Y12 represents X2-5 represents Y2Y2 - Y1
X2 - X1
-5 - 7
2 - - 2
-12
-2
Simplify by dividing both -12 & -2 by 2: -6
-1
It's either -6 or it's just -6 by itself... Really sorry if I'm wrong...
-1
Well, a linear equation should look like this: y = ax + b.
So if the slope is 0, then y = a*0 + b = b.
If y = b, then the line is a horizontal line like this: ______________
Now, we look at the points that were given in the question: (-2, 7), (2, -5)
If the slope is 0, then the value of y, should not change, but the value of x will constantly be changing. So it means that as x increases, y is always the same.
If we look at the y place on the points: The y values are the bold numbers:
(-2, 7), (2, -5)
As you can see, 7 is not the same as -5. So the line's slope is not 0. The slope would be a negative number. Why? Well, 7 is above the x-axis and -5 is below the x-axis. For the x values, -2 is smaller than 2, so the point (-2, 7) is located at the top left quadrant and the point (2, -5) is located at the bottom right quadrant.
So to answer your question, the slope is not zero. The slope is negative.
An elevator building code requires at least 2.2 square feet per person. The depth of an elevator box is 7 feet. How wide must the elevator be to legally accommodate 15 people? Round to the nearest tenth if necessary.
Answer:
4.7
Step-by-step explanation:
Multiply 15 by 2.2. And get 33
Divide 33 by 7 and get 4.7
Hope it helps!
Final answer:
To accommodate 15 people, the elevator must be approximately 4.7 feet wide.
Explanation:
The question is asking us to calculate the width of the elevator box that can legally accommodate 15 people, given that the elevator building code requires at least 2.2 square feet per person and the depth of the elevator is 7 feet.
First, we need to find out the total area required for 15 people:
Total area = Number of people × Area per person = 15 × 2.2 square feet
Total area = 33 square feet
As we have the depth of the elevator, we can now calculate the width:
Total area = Width × Depth
Width = Total area / Depth
Width = 33 sq ft / 7 ft
Width ≈ 4.7 feet
Therefore, the elevator must be approximately 4.7 feet wide to accommodate 15 people as per the building code's requirements.
830000 in scientific notation
Answer:
8.3 * 10 ^5
Step-by-step explanation:
830000
To change this to scientific notation, we move the decimal 5 places to the left. The exponent will be positive 5 because we moved it to the left
8.3 * 10^ +5
8.3 * 10 ^5
Please explain in full sentence for full credit
Answer:
The median of the histogram is scores ranging from 70-80
Step-by-step explanation:
Median of a histogram is always the "class interval" in which the MIDDLE NUMBER falls in.
If we add up all the bars (y-axis), we see HOW MANY NUMBERS in total there are. So we have:
[tex]1+2+1+2+6+9+13+5=39[/tex] numbers in total
What is the middle number out of 39 numbers?
It is: [tex]\frac{n+1}{2}[/tex] th number where [tex]n=39[/tex] for this problem
So, the middle number is : [tex]\frac{39+1}{2}=\frac{40}{2}=20[/tex]th number
Which class interval does the 20th number fall into?
First class interval has 1, so total is 1Second class interval has 2, so total is 1+2=3Third class interval has 1, so total is 3+1=4Fourth class interval has 2, so total is 4+2=6Fifth class interval has 6, so total is 6+6=12Sixth class interval has 9, so total is 12+9=21So, definitely, 20th number falls into the sixth class interval which is "70-80".
Hence, the median of the histogram is scores ranging from 70-80.
PLZ HELPP ASAP :))))))
Answer:
x = 91.5
Step-by-step explanation:
for 30.5 miles travelled gas used is 1 gallon ← unit rate
To calculate distance travelled multiply gas used by 30.5
For 3 gallons used
distance travelled = 3 × 30.5 = 91.5 miles
⇒ x = 91.5
In May, 2018 a store had a furniture with a listed price of $550, having a sales tax of 3% on the listed price. Next month the price increased by 33 1/3 %. What sales tax should be paid in dollars on the new price?
Answer: $ 22
Step-by-step explanation:
[tex]\boxed{\$ 22}[/tex] of sales tax should be paidon the new price.
Further Explanation:
Calculation:
The given listed price of furniture in the month of May is [tex]\$550.[/tex]
The sales tax is of [tex]3\%[/tex] on the listed price of the furniture.
The price of the month May is increased by [tex]33\dfrac{1}{3}\%.[/tex]
The increased price of the furniture can be obtained as follows,
[tex]\begin{aligned}{\text{Increased price}} &= 550 + \left( {33\frac{1}{3}\% \times 550} \right)\\&= 550 + \left( {\frac{{33.34}}{{100}} \times 550} \right)\\&= 550 + 0.3333 \times 550\\&= 550 + 183.32\\&= 733.32 \\\end{aligned}[/tex]
The new price of the furniture in dollars is [tex]\$ 733.32.[/tex]
The sales tax is of [tex]3\%[/tex] on the listed price.
The sales tax on the new price can be obtained as follows,
[tex]\begin{aligned}{\text{Sales tax}}&= 3\% {\text{ of new price}}\\&= \frac{3}{{100}} \times 733.32\\&= \$ 22\\\end{aligned}[/tex]
[tex]\boxed{\$ 22}[/tex] of sales tax should be paid in dollars on the new price.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Sales Tax
Keywords: May, 2018, store, furniture, listed, price, listed price, $550, sales, sales tax, 3%, tax on listed price, next month, price increased, increased price, month, 33 1/3%, paid, dollars, new price.
The number 900 has an interesting property in that the only primes that divide into it evenly are 2, 3, and 5. What are the next two numbers after 900 that also have this property?
900 = 2 · 2 · 3 · 3 · 5 · 5
Next numbers:
2 · 2 · 2 · 3 · 3 · 3 · 5 · 5 · 5 = 900 · 15 = 13,500
2 · 2 · 2 · 2 · 3 · 3 · 3 · 3 · 5 · 5 · 5 · 5 = 13,500 · 15 = 202,500
202,500 · 15 = 3,037,500
3,037,500 · 15 = 45,562,500
....
One label on a package of bolts says that each bolt has a diameter of 0.55 inch. To be in the package, the percent error of the diameter must be less than 6%. A test on the production line shows a bolt with a diameter of 0.52 inch. Should this bolt go into the package?
The bolt with a diameter of 0.52 inch has a percent error of approximately 5.45% from the advertised 0.55 inch, which is within the acceptable margin of less than 6%. Therefore, it should be included in the package.
Explanation:The question revolves around determining if a bolt with a diameter of 0.52 inch should be packaged given that the labeled diameter is 0.55 inch and the allowable percent error is less than 6%. To calculate the percent error, we use the formula: Percent Error = (|Actual Value - Theoretical Value| / Theoretical Value) × 100%. Applying the numbers: Percent Error = (|0.52 - 0.55| / 0.55) × 100% = (0.03 / 0.55) × 100% ≈ 5.45%.
Since the percent error of 5.45% is less than 6%, the bolt with a diameter of 0.52 inch should be included in the package. This decision is based on the calculated percent error being within the accepted tolerance level.
Explain why it doesn’t matter what letter or symbol is used to find an unknown number
Answer:
Symbols (or letters) in an equation can be important.
Step-by-Step Explanation:
The symbol [or letter (x, m, n, etc.)] is usually not important because the symbol represents a number. Sometimes it is important because each symbol (or letter) can represent another number.
for example: n+3 = 4-m (the symbol/ letters are different because they represent a different number).
for another example: n+3 = 4 (the symbol/ letter is only one letter).
The choice of letter or symbol to represent an unknown number in mathematics is arbitrary. It doesn't impact the mathematical operation or relationships, as the fundamental principles of algebra apply universally to any symbol.
It doesn't matter what letter or symbol is used to represent an unknown number because the essence of algebra and mathematical expressions is based on abstraction and generality. Mathematical symbols are placeholders for values and can be interchanged without changing the underlying mathematical relationships. Here's why it doesn't matter:
1. Universality of Symbols: Mathematical symbols and variables are universally understood and follow consistent rules. Whether you use "x," "y," "a," "b," or any other symbol, the principles of mathematics remain the same.
2. Abstraction: Algebra allows us to work with general concepts rather than specific numbers. The choice of symbols is arbitrary and doesn't affect the mathematical operations. The symbols represent placeholders for any number that satisfies the given conditions.
3. Flexibility: Different symbols can be used for different contexts or problems. For example, "x" is often used for unknowns in equations, "a" for constants, and "y" for dependent variables in functions. However, this is a convention, and other symbols can be used interchangeably.
4. Consistency: The rules of algebra, such as the commutative, associative, and distributive properties, hold true regardless of the symbols used. Algebraic manipulations and equations remain valid irrespective of the choice of symbols.
In summary, mathematical symbols are versatile and interchangeable because they serve as placeholders for values. The principles of algebra and mathematics are symbol-independent, allowing for flexibility in representation while maintaining the same underlying mathematical relationships.
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kevin correctly answered 75% of his 32 test questions. how many questions would kevin have to answer to get more that 80% correct?
Kevin needs to answer at least 26 questions correctly out of 32 to exceed an 80% success rate, which means he needs to get 2 more questions right than he previously did.
Kevin correctly answered 75% of his 32 test questions, which is 24 questions. To achieve more than an 80% correct rate, Kevin needs to answer more than 80% of 32, which is more than 25.6 questions. Since Kevin can't answer a fraction of a question, he must answer at least 26 questions correctly. To find the number of additional questions he needs to answer correctly to exceed 80% when he has already answered 24 correctly, we subtract 24 from 26, resulting in 2 more questions that Kevin needs to answer correctly to exceed an 80% success rate.
Solve the system of equations using the substitution method. y = 7x – 16, y = 2(2x – 5) What is the solution? (, )
Answer:
Solving the system of equations using the substitution method, the solution is: x=2 and y=-2
Step-by-step explanation:
(1) y=7x-16
(2) y=2(2x-5)
Substituting "y" of the equation (1) in the equation (2)
(2) 7x-16=2(2x-5)
Applying the distributive property to eliminate the parentheses on the right side of the equation:
7x-16=2(2x)-2(5)
Multiplying:
7x-16=4x-10
Solving for x: Subtracting 4x and adding 16 both sides of the equation:
7x-16-4x+16=4x-10-4x+16
3x=6
Adding like terms:
Dividing by 3 both sides of the equation:
3x/3=6/3
x=2
Replacing x by 2 in the equation (1):
(1) y=7(2)-16
y=14-16
y=-2
Solution: x=2 and y=-2
Answer:
Solve the system of equations using the substitution method. y = 7x – 16, y = 2(2x – 5) What is the solution? (, )Step-by-step explanation:
Which equation is a point slope form equation for line AB ? y+1=2/3(x−4) y+1=3/2(x−4) y+1=−2/3(x−4) y+1=−3/2(x−4) A graph with a line running through point A, with coordinates (4, -1), and point B, with coordinates (-2, 3)
Answer:
C) y + 1 = -2/3(x - 4)
Step-by-step explanation:
The given line passes through the points A (4, -1) and B (-2, 3)
Let's find the slope now.
Slope (m) = (y2 - y1)/(x2 - x1)
= (3 - (-1)) / (-2 - 4)
= (3 + 1)/-6
= 4/-6
Slope (m) = -2/3
The equation of line y - y1 = m (x - x1)
y - (-1) = -2/3(x - 4)
y + 1 = -2/3(x - 4)
Answer: C) y + 1 = -2/3(x - 4)
Thank you.
Answer:
answer is c)
Step-by-step explanation:
:)
3y+12=2x in slope-intercept form?
[tex]\bf \stackrel{\textit{solving for \underline{y}}}{3y+12=2x}\implies 3y=2x-12\implies y=\cfrac{2x-12}{3}\implies y=\cfrac{2x}{3}-\cfrac{12}{3} \\\\\\ y=\cfrac{2}{3}x-4\impliedby \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]
A nutrition label states that there are 36g of carbohydrates in each serving. This accounts for 12% of a daily value. How many grams of carbohydrates are recommended per day?
The recommended daily intake of carbohydrates is 300 grams per day based on a daily value of 12%.
To determine how many grams of carbohydrates are recommended per day based on a daily value of 12%, you can use the following calculation:
First, calculate what 1% of the daily value would be:
1% of daily value = 36 grams / 12% = 3 grams
Now, to find the recommended daily intake, simply multiply this by 100 since you want to find the recommended intake for 100% of the daily value:
Recommended daily intake = 3 grams/1% * 100% = 300 grams
So, the recommended daily intake of carbohydrates is 300 grams per day based on a daily value of 12%.
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Which of the following has a translation rule of Move 3 Right and Down 4?
(x+3, y+4)
(x+3, y-4)
(x-3, y-4)
(x-3, y+4)
Answer:
(x-3, y+4) hope this helps.
Answer:
The correct answer option is (x + 3, y - 4).
Step-by-step explanation:
If we are talking about the translation rule with respect to the origin (0, 0), then the correct option will be (x + 3, y - 4).
Since moving to the right on the x axis means a positive addition so moving three units right will mean 'plus 3'.
While moving down means that the value of y is going in negative so it will be (y - 4)
the average u.s. citizen throws away about 1,606 lb of trash each year. find this rate in pounds per month, to the nearest tenth
Answer:
The average U.S. citizen throws away about 133.8 pounds of garbage a month.
Step-by-step explanation:
First take the total amount of trash thrown away in a year (1,606), and divide it by the number of months in a year (12).
1,606 / 12 = 133.833333
You would get 133.833333 and would round it to the nearest tenth and get 133.8.
Answer:
133.83 lb/month, or 133.8 lb/month to the nearest tenth.
Step-by-step explanation:
Here we need to find the unit rate of throwing stuff away.
To do this, divide 1,606 lb by 12 months, since we want the answer in pounds per month:
1,606 lb
------------- = 133.83 lb/month, or 133 5/6 lb/month
12 mos
There are 325 children at the zoo . If 64% of children are boys and the
rest are girls, how many children at the zoo are girls?
Answer:
117 Girls
Step-by-step explanation:
If 64% of the kids are boys, then 36% are girls 64% + 36% = 100%
.36 x 325 = 117 girls
Proof
.64 x 325 = 208 boys
208 + 117 = 325
There are 117 girls at the zoo.
To determine how many children at the zoo are girls, we start by understanding that 64% of the 325 children are boys. Let's go through the steps to find out the number of girls.
Calculate the number of boys by multiplying 64% by 325.
Percentage to decimal conversion: 64% = 0.64. So, 0.64 × 325 = 208 boys.
Subtract the number of boys from the total number of children to find the number of girls: 325 - 208 = 117 girls.
Therefore, there are 117 girls at the zoo.
Can u solve this for me??
Answer:
75 weeks
Step-by-step explanation:
Let the number of weeks be x
10x + 45 = 789 Subtract 45 from both sides
10x = 789 - 45 Combine
10x = 744 Divide by 10
x = 744/10 Divide
x= 74.4 weeks. It will not hurt her to save the extra week to get the phone
River C is 100 miles longer than River D. If the sum of their lengths is 5,570 miles, what is the length of each river?
Let the Length of River D be : P
Given : River C is 100 Miles Longer than River D
⇒ Length of River C = P + 100
Given : The Sum of Both Rivers is 5570 Miles
⇒ P + (P + 100) = 5570
⇒ 2P + 100 = 5570
⇒ 2P = 5570 - 100
⇒ 2P = 5470
⇒ P = 2735
⇒ Length of River D is : 2735 Miles
⇒ Length of River C is : (P + 100) = (2735 + 100) = 2835 Miles
Which fraction is equivalent to [tex]\frac{25}{35}[/tex]
A) [tex]\frac{2}{3}[/tex]
B) [tex]\frac{20}{30}[/tex]
C) [tex]\frac{3}{5}[/tex]
D) [tex]\frac{5}{7}[/tex]
[tex]\dfrac{25}{35}=\dfrac{25:5}{35:5}=\dfrac{5}{7}\to\boxed{D)}[/tex]
please help me with this geo problem
Answer:
x = 1.25y = 1.75Step-by-step explanation:
Find x
8/10 = 5/(5 + x) Cross multiply8*(5 + x) = 10*5 Combine on the right8(5 + x) = 50 Remove the brackets on the left.40 + 8x = 50 Subtract 40 from both sides.40-40 +8x = 50-40 Combine8x = 10 Divide by 88x/8 = 10/8 Dividex = 1.25Find y
7/(7 + y) = 8/10 Cross multiply8*(7 + y) = 10 * 7 Combine the right8(7 + y) = 70 Remove the brackets.56 + 8y = 70 Subtract 56 from both sides56 - 56 + 8y = 70 - 56 Combine8y = 14 Divide by 8y = 1.75Can anyone answer this??
OPTIONS:
1. first, second
2. 3,9,-3,-9
3. first, second
4. is not, is
Unable to determine the subject of the question due to lack of information.
Explanation:The arithmetic operations described pertain to the addition and multiplication of numbers and the result of their signs. For instance:
When two positive numbers add or multiply, the result is also positive (e.g., 3 + 2 = 5 and 2 x 3 = 6).
When two negative numbers add or multiply, the result is negative when adding and positive when multiplying (e.g., -4 + (-2) = -6 and (-4) x (-3) = 12).
For numbers with opposite signs, in addition, subtract the smaller number from the larger number and give the result the sign of the larger number, while in multiplication, the result will have a negative sign (e.g., -5 + 3 = -2 and (-3) x 2 = -6).
Regarding quantum numbers, the sets of quantum numbers provide information about the state of an electron in an atom. Each set of numbers must follow specific rules:
The principal quantum number n must be a positive integer.
The azimuthal quantum number l must be an integer ranging from 0 up to n - 1.
The magnetic quantum number mē must range from -l to +l.
The spin quantum number ms must be either +1/2 or -1/2.
Therefore, for the given quantum numbers a. {4, 2, -2, 1} is not an allowed set because the spin quantum number must be either +1/2 or -1/2, not 1. Similarly, set b. {3, 1, 0, -1/2} is a possible set because it follows all the designated rules for quantum numbers.
A health club charges non-members $5 per day to swim and $9 per day for an exercise class. Members pay a yearly fee of $300 plus $4 per day to attend an exercise class and no swim fee. If Robert swims and takes an exercise class every time he goes to the gym, which equation shows the number of days he must use the gym to make the membership worthwhile?
Answer:
22 days PLEASE GIVE BRAINLIEST
Step-by-step explanation:
Nonmember:
swim: $5
exercise: $9
Per day: 9 + 5 = $14
Member:
$300 per year plus $4 per day for an exercise class. $0 for swimming
300 ÷ 14 = 21.428 21 days x $14 = $294 22 days x $14 = $308
So.... if he goes to the gym at least 22 days he will save money with the membership.
Answer:
The answer is D.) 5d+9d = 300 + 4d
Step-by-step explanation:
The equation states that for each day he attends to the gym to swim and exercise without a membership he has to pay for both, which is $5 and $9 respectively. This is each day that he attends.
However, if he HAS a membership, he only has to pay the $300 yearly fee once, and then $4 everyday he attends afterwards to do both swimming and exercising.
Now, in order to find out when the membership is worth it you need to find out when the membership cost and the non-membership cost is equal. so on one side of the equation you'll need the non-membership costs, and on the other side we'll put the membership cost.
So, for the non-membership cost, every day he goes it'll cost him $5 to swim and $9 to exercise, meaning that one side of the equation is 5d (d represents days) + 9d
And for the membership side we have the $300 initial, one-time fee, and then the $4 a day he has to pay to attend. This is equivalent to 300+4d
Finally, we put both equations together in a way to show that we want both sides to be equal, i.e
5d+9d = 300+4d
Thus our answer is D
1. 5 + 2x - 8
2. (-2x +6)2
3. 7 + 3x + 6x - 4
4. (-4) - (3)(5x + 8)
5. 9x - 7x - 5
6. x - 12x
7. 7 (3x + 6) + 2x
8. (-11x) - 10x
9. 3x - 12 - 5x
10. 13+4x-5
11.
basically all those
Answer:
1. 2x-3
2.-4x+12
3.9x+3
4.-15x-12
5.2x-5
6.-11x
7.23x+42
8.-21x
9.-2x-12
10.4x-8
Step-by-step explanation:
Which of the following shows the situation below in function notation?
The depth of a lake at a certain point, which is a function of the distance of that point from shore, is 30 feet.
A. Distance from shore(depth) = 30 ft
B. Distance from shore(30 ft) = depth
C. Depth(distance from shore) = 30 ft
D. Depth(30 ft) = distance from shore
Answer:
C
Step-by-step explanation:
The general functional notation is:
[tex]f(x)=A[/tex]
Where it means that [tex]f[/tex] is a function of [tex]x[/tex], and the answer is [tex]A[/tex].
From the problem, we know that the depth is a function of distance, and at that specific distance, the depth is 30 ft.
So we see that depth is a function of distance from shore, and the answer is 30 ft.
Matching this to our explanation of functional notation above, we can say that:
Depth(distance from shore) = 30 ft
Answer C is right.
Answer:
Depth distance from shore equals 30 ft
Step-by-step explanation:
Confirmed from pretest
Please help! Will give brainiest
The water level in an inflatable pool decreases by about 6.35×10−16.35×10−1 centimeters each day due to evaporation. There are 8.64×1048.64×104 seconds in a day.
About how many centimeters does the water level in the pool decrease each second?
Express the answer in scientific notation.
___x___cm fill in the blanks with the following 1.5, 2.3, 5.5, 7.3, 10^-6, 10^-5, 10^-4, 10^3
Given : Water Level in the Pool decreases by 6.35 × 10⁻¹ cm each Day
⇒ In One Day : The Level decreases by 6.35 × 10⁻¹ cm
⇒ In [8.64 × 10⁻⁴] Seconds : The Level decreases by 6.35 × 10⁻¹ cm
[tex]\mathsf{\implies In\;One\;Second : The\;Level\;Decreases\;by = (\frac{6.35 \times 10^-^1}{8.64 \times 10^4})}[/tex]
[tex]\mathsf{\implies In\;One\;Second : The\;Level\;Decreases\;by = 0.73 \times 10^-^5}[/tex]
[tex]\mathsf{\implies In\;One\;Second : The\;Level\;Decreases\;by = 7.3 \times 10^-^6}[/tex]
First Blank : 7.3
Second Blank : 10⁻⁶
which best explains why the given lines are or are not perpendicular x=-2,y=8
The given lines 'x=-2' and 'y=8' are indeed perpendicular as they intersect at a right angle of 90 degrees, which defines perpendicularity.
Explanation:In the context of coordinate geometry, the equations 'x=-2' and 'y=8' represent two lines in a 2D space. The line x=-2 is a vertical line that passes through -2 on the x-axis, while y=8 is a horizontal line that passes through 8 on the y-axis.
These lines are indeed perpendicular because they intersect at a right angle, which is a primary characteristic of perpendicular lines. Perpendicularity in 2D space is defined by a 90-degree angle between two lines, and in this case, the vertical line (x=-2) and horizontal line (y=8) do, indeed, intersect perpendicularly.
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Please someone help
Answer:
a. opens: upward
b. a.o.s.: x = 1
c. vertex: (1, -4)
d. x-intercepts: (-1, 0), (3, 0); y-intercept: (0, -3)
Step-by-step explanation:
A:By looking at the graph, we can see that the parabola opens upward. This means that its a-value is positive.
B:The axis of symmetry is the line that passes exactly through the center of the parabola. It always starts with x = __, because it is a vertical line.
The center of this parabola is at the x-value of 1, so we can say that the equation of the axis of symmetry is x = 1.
C:The vertex is at the highest or lowest point of the parabola, also known as the maximum or minimum point. Since this graph opens up, the vertex is at the minimum point.
Look at the graph and find the point where the parabola opens upwards. This point is at the x-value of 1 and the y-value of -4, so the vertex of the parabola is at (1, -4).
D:Again, look at the graph provided to find the x and y-intercepts. On the x-axis, the parabola crosses through at the x-values of -1 and 3, so the x-intercepts are (-1, 0) and (3, 0).
The parabola crosses the y-axis at the y-value of -3, so the y-intercept of the parabola is (0, -3).
Write two equations of lines in slope-intercept form that are parallel to the graph of the line in Part I. y=1/2x+5
Explain why the equations of the lines in Part I and Part II are parallel.
Answer:
The two equations are [tex]y=\frac{1}{2}x+5[/tex] and [tex]y=\frac{1}{2}x[/tex]
Step-by-step explanation:
we have given that : Part I= [tex]y=\frac{1}{2}x+5[/tex] equation of line
slope intercept form is y=mx+c
the slope of the line Part I is m=1/2
taken another equation of line Part II= [tex]y=\frac{1}{2}x[/tex]
whose slope of line Part II is m=1/2
since, both equation have same slope therefore these two equation Part II and Part I are parallel
It is also shown by the graph attached.