In order to solve using substitution, we'll need to first isolate one variable in one equation. I will be using 7x - 2y = 3 and solving for y to begin.
7x - 2y = 3
-2y = -7x + 3
2y = 7x - 3
y = 3.5x - 1.5
Next, we'll plug in our value of y (found above) into the equation 3x + 4y = 11 and solve for x.
3x + 4(3.5x - 1.5) = 11
3x + 14x - 6 = 11
17x = 17
x = 1
Finally, we'll plug our value of x in to the first equation (7x - 2y = 3) and solve for y.
7(1) - 2y = 3
7 - 2y = 3
-2y = -4
y = 2
The solution to these equations is (1, 2).
Hope this helps! :)
Which is a factor of x^2-9x+14
Answer:
x =2 or x=7
Step-by-step explanation:
x^2-9x+14= 0
Now splitting the middle term we get,
x^2-7x -2x +14 =0
x(x-7) - 2(x-7) =0
(x-2) (x-7) =0
x-2=0 or x-7 =0
x =2 or x=7
The factors of [tex]x^2-9x+14[/tex] are (x - 7) and (x - 2)
What is an algebraic expression?"It is a mathematical statement which consists of variables and constants, and some algebraic operations."
What is quadratic expression?"It is a polynomial expression with degree 2""The general form is [tex]ax^{2} +bx+c[/tex] where a, b, c are real values with [tex]a\neq 0[/tex] "For given question,
We have been given a quadratic expression [tex]x^2-9x+14[/tex]
We need to factorize given quadratic expression.
[tex]\Rightarrow x^2-9x+14\\\\= x^2-7x-2x+14~~~~~~~~...........(-9x=-2x-7x~~and~14=(-9)\times (-2))\\\\=x(x-7)-2(x-7)\\\\=(x-7)(x-2) ~~~~~~~~~~~~............(Seperate~out~common~terms)[/tex]
Therefore, the factors of [tex]x^2-9x+14[/tex] are (x - 7) and (x - 2)
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Taxicabs downtown charge a flat fee of $3.25, plus a state tax of $0.50, plus $0.50 for each 1/ 5 mile they travel with a passenger. Travis took a taxicab from his office to a meeting on the other side of town. The cab ride cost $14.75, which includes a $3.00 tip. In decimal form, how far is it from his office to the meeting?
Answer:
3.2 miles
Step-by-step explanation:
Initial fee plus state tax first because they are static:
3.25 + 0.5 = 3.75
Remove the initial charge plus tip from total cost:
14.75 - 3 - 3.75 = 8
Divide by 0.5 to get how many 1/5 of a mile he went:
8 / 0.5 = 16
Divide 16 by 5 to get miles:
16 / 5 = 3.2 miles
Answer:
3.2 miles
Step-by-step explanation:
Initial fee plus state tax first because they are static:
3.25 + 0.5 = 3.75
Remove the initial charge plus tip from total cost:
14.75 - 3 - 3.75 = 8
Divide by 0.5 to get how many 1/5 of a mile he went:
8 / 0.5 = 16
Divide 16 by 5 to get miles:
16 / 5 = 3.2 miles
I have 420 apples & its 35% of what I needed how many apples do I need
Answer:
1200 apples.
Step-by-step explanation:
The way I thought about this was, you need to figure out how many apples per percent. Thus, I divided 420 by 35, which gave me 12.
We have deduced that every percent = 12 apples.
Multiply 12 by 100 (apples per percent x total percentage)
12 x 100 = 1200
You are solving 5 – 83 = y3. Which equation will you get if you multiply both sides by 3?
Answer:
15 - 3(8³) = 3y³
Step-by-step explanation:
5 – 8³ = y³
3(5 - 8³) = 3(y³)
15 - 3(8³) = 3y³
Answer:
15-8=y
Step-by-step explanation:
Two of the steps in the derivation of the quadratic formula are shown below.
Step 6: StartFraction b squared minus 4 a c Over 4 a squared EndFraction = (x + StartFraction b Over 2 a EndFraction) squared
Step 7: StartFraction plus or minus StartRoot b squared minus 4 a c EndRoot Over 1 a EndFraction = x + StartFraction b Over 2 a EndFraction
Which operation is performed in the derivation of the quadratic formula moving from Step 6 to Step 7?
subtracting StartFraction b Over 2 a EndFraction from both sides of the equation
squaring both sides of the equation
taking the square root of both sides of the equation
taking the square root of the discriminant
GIVING 20PTS. TO WHOEVER HELPS ALONG WITH 5 STARS
Answer:
C
Step-by-step explanation:
I just guessed and got it right
Answer:
C. taking the square root of both sides of the equation
Credit card A is running a promotion where they will charge 0% interest for the first year, and then 0.8% interest compounded continuously after that. Credit card B has an interest rate of 0.7%, also compounded continuously. If you are going to make a $500 dollar purchase and plan to not make a single payment for 2.5 years, which credit card would you go with? Explain for answer in 1-2 sentences.
Answer:
Since the total amount you have to pay for the purchase on the credit card A is lower, then it's the best option.
Step-by-step explanation:
For credit card A the ammount will only be compounded after 1 year, so the total time elapsed for the laon is 1.5 years, while for the credit card B it'll be the full 2.5 years. To compute the total amount of a interest compounded continuously we must apply the formula:
M = C*e^(r*t)
Where M is the total amount, C is the initial amount, r is the interest rate and t is the time elapsed.
For credit card A:
M = 500*e^(0.008*1.5) = 506.03614
For credit card B:
M = 500*e^(0.007*2.5) = 508.8270
Since the total amount you have to pay for the purchase on the credit card A is lower, then it's the best option.
Answer:
hey
Step-by-step explanation:
what was your answer?
Katarina bought a package of 500 stickers. Each sheet in the package has 20 stickers.
25% of the stickers on each sheet are hearts. The remaining stickers are stars.
The correct options are: B and D. The true statements about stickers are: Katarina has 375 star stickers and 75% of the stickers are stars.
Let's analyze each statement given the information that 25% of the 500 stickers are hearts, and the remaining stickers are stars.
1. Total number of stickers: 500
2. Percentage of heart stickers: 25%
3. Percentage of star stickers: 100% - 25% = 75%
Now, let's calculate the actual numbers:
- Number of heart stickers:
[tex]\[ 25\% \text{ of } 500 = \frac{25}{100} \times 500 = 0.25 \times 500 = 125 \][/tex]
- Number of star stickers:
[tex]\[ 75\% \text{ of } 500 = \frac{75}{100} \times 500 = 0.75 \times 500 = 375 \][/tex]
Now, let's evaluate each statement:
A. Katarina has 100 heart stickers.
- False. Katarina has 125 heart stickers.
B. Katarina has 375 star stickers.
- True. Katarina has 375 star stickers.
C. The package contains 20 sheets of stickers.
- Not enough information is given to determine this. This statement is irrelevant without knowing how many stickers are on each sheet.
D. 75% of the stickers are stars.
- True. 75% of 500 stickers are stars.
E. The number of heart stickers is the same as the number of star stickers.
- False. The number of heart stickers (125) is not the same as the number of star stickers (375).
So, the true statements are:
B. Katarina has 375 star stickers.
D. 75% of the stickers are stars.
The complete question is:
Katarina bought a package of 500 stickers. 25% of the stickers are hearts. The remaining stickers are stars. Select all the statements that are true.
A.Katarina has 100 heart stickers.
B.Katarina has 375 star stickers.
C.The package contains 20 sheets of stickers
D.75% of the stickers are stars.
E.The number of heart stickers is the same as the number of star stickers.
Anthony is running a lemonade stand. He expects to make $108 for the day, but ends up making 204% of that amount. How much money did Anthony make that day?
Answer:
$220.32
Step-by-step explanation:
108 x 2.04 = 220.32
The two angles shown are complementary angles.What is the value of x?
Answer:
complementary angles are angles that sum up to 90 degrees. that is all I can say because I can't see any diagram
Answer:
complementary angles are angles that sum up to 90°
i can't see any diagram
Don has an album that holds 900 hockey cards. Each page of the album holds 9 hockey cards. If 68% of the album is empty, how many pages are filled with hockey cards?
Answer:
The answer is 288 pages are filled with hockey cards
Step-by-step explanation:
First, you need to figure out what percentage of the album is full which is 32% So, with that 32% you figure out how many pages that is. So you would find 32% of 900 which is 288 therefor, that would be your answer.
I hope this helped <3
A walker and a cyclist are 45 miles apart. They move towards each other with speeds of 5 mph and 10 mph respectively. In how many hours will they meet?
Answer: they will meet after 3 hours.
Step-by-step explanation:
Let t represent the number of hours it will take them to meet.
A walker and a cyclist are 45 miles apart. If they move towards each other, in t hours, they would have covered a total of 45 miles
Distance = speed × time
They move towards each other with speeds of 5 mph and 10 mph respectively. It means that the distance covered by the walker in t hours is 5 × t = 5t
Also, the distance covered by the cyclist in t hours is 10 × t = 10t
Since the total distance covered us 45 miles, then
5t + 10t = 45
15t = 45
t = 45/15
t = 3 hours
A can of tomato soup is 4 1
4
inches tall and has a diameter of 3 inches. The company that
makes the cans uses sheets of metal that are 1,000 in2
.
Completely answer the following questions. Show all work.
1. How many whole cans can the company make out of each sheet of metal?
2. Will there be any metal left over? If so, how much
the can of soup is 3 inch wide and 4 1/4in height
Answer:
1. 17 whole cans
2. Yes, 38.65 in2 of metal
Step-by-step explanation:
First we need to find the surface area of the can.
The base and the top of the can have a area of pi*r^2.
If the radius is half the diameter, we have r = 3/2 = 1.5 inches, so:
A1 = pi * 1.5^2 = 7.069 in2
The side of the can has a area of pi*d*h. If the diameter is 3 inches and the height is 4.5 inches, we have:
A2 = pi*3*4.5 = 42.412 in2
So the total area of the can is:
2*A1 + A2 = 56.55 in2
To know how many cans we can make with 1000 in2 of metal, we just need to divide the total metal for the surface area of each can:
number of cans = 1000 / 56.55 = 17.684 cans
We can make 17 cans, and the metal left over is 1000 - 17 * 56.55 = 38.65 in2
Which of the equations below represents the relationship shown in the table?
Answer:
D
Step-by-step explanation:
just check at least two
How can you tell if a fraction is a perfect square?
Answers: A fraction is a perfect square if it's reduced version (of an improper fraction if the number is greater than 1) has both numerator and denominator numbers that are perfect squares. IE: 25/36 is a perfect square because both 25 and 36 are perfect squares.
Step-by-step explanation:
So for example 5/25 is a perfect square but 2/5 wouldn't be a perfect square.
Tell me if this helped you
If a fraction can be expressed as the product of two equal fractions, it may also be expressed in its simplest form as a perfect square.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
A fraction is a perfect square if both the numerator and the denominator of its reduced version, which is an improper fraction if the integer is greater than 1, are perfect squares. To put it another way, 25/36 is a perfect square as 25 and 36 are both perfect squares.
Thus, if a fraction can be expressed as the product of two equal fractions, it may also be expressed in its simplest form as a perfect square.
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A ratio of the number of items within a defined unit of area measures
Answer:
Density
Step-by-step explanation:
Density is the number of items per unit area. It is gotten by dividing the number of items by the area it occupies. It measures the compactness of an item in a given area. The higher the density, the more compact items are per unit area and the lesser the density, the less compact items are per unit area. It is measured in items/m²
The diameter of a circle is 101010 units. What is the radius of the circle?
Answer:
50505 units
Step-by-step explanation:
The radius is the fixed distance from the center of a circle to any point on its circumference. The radius of a circle always equals half of its diameter, so to find the diameter, multiply the radius by two. ( 101010/ 2=50, 505 units)
You want to go on a trip to Disney World with your friends. The trip costs $1450 and they have a special discount of 35% off. The tax rate for the package is 10%. What is the total price of the trip?
Answer: the total price of the trip is
$1087.5
Step-by-step explanation:
The trip costs $1450 and they have a special discount of 35% off. It means that the amount that would be taken off is
35/100 × 1450 = $507.5
The cost of the trip would be
1450 - 507.5 = $942.5
The tax rate for the package is 10%. It means that the amount of tax to be paid is
10/100 × 1450 = $145
Therefore, the total price of the trip would be
942.5 + 145 = $1087.5
6. Calculate Suppose Cory's
blood pressure is 125 at its
highest point. To return his
blood pressure to normal,
Cory must reduce it by what
percentage? (Show your
work.)
Answer:
Let's suppose that the ideal blood pressure is 100 (the ideal values are between 90 and 110, i am taking the middle value)
If 125 is the 100%, and we want to go to 100, then we need to decrease by:
125 - 100 = 25
now, to calculate the percentage that represents the 25, we need to calculate:
(25/125)*100% = 20%
So to reduce his blood pressure to normal, he must reduce it by 20%
To find out by what percentage Cory must reduce his blood pressure to normal, subtract the normal from Cory's blood pressure, divide the result by Cory's initial blood pressure, and then multiply by 100. For instance, if normal blood pressure is 120, Cory must reduce his blood pressure by approximately 4%.
Explanation:To calculate the percentage that Cory needs to reduce his blood pressure, we first need to know the normal blood pressure level. For example, if the normal blood pressure is considered to be 120, then we can proceed as follows:
First find the difference between Cory's actual blood pressure and the normal blood pressure. In this case, it would be 125 - 120 = 5. Then, divide this difference by the initial (Cory's) blood pressure, which is 5 / 125 = 0.04. Multiply the result by 100 to get it in percentage terms: 0.04 * 100 = 4%.
So, Cory would need to reduce his blood pressure by approximately 4% to return to a normal level, assuming normal blood pressure is 120.
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Question
Segments AC and BD are diameters of circle Q.
a. Find the measure of arc AB
b. Find the measure of arc AD
Answer:
Arc AB = 80°
Arc AD= 100°
Step-by-step explanation:
Arc AB
Since AC is the diameter, it would be 180°, and since arc BC is given (100°), arc AB would be 80°
Arc AD
Since BD is a diameter, it would also be 180°. Arc ED is given and previously you found arc AB. So subtract 50 and 80 from 180 and you'll get 50° for arc AE. Add that with arc ED and you'll get 100°
On a coordinate plane, a parabola opens down with solid circles along the parabola at (negative 3, negative 5), (negative 2, 0), (negative 1, 3), (0, 4), (1, 3), (2, 0), (3, negative 5). Use the drop-down menus to identify the values of the parabola. Vertex = Domain = {x| } Range = {y| y ≤ }
Answer:
vertex: (0,4) // domain: x is a real number // Range: 4
Step-by-step explanation:
got a 100%
Answer:
C,D,C in that order
Step-by-step explanation:
100 POINTS if it is wrong i will delete your answer! Calculating Monthly Expenses
The second step to building a family budget is to outline your expenses in greater detail, itemizing fixed and variable expenses.
Suppose the table below shows your family’s monthly expenses by category.
Expense Fixed or Variable Expense? Average Monthly Cost Yearly Cost Percent of Yearly Budget (Rounded)
Income Tax Fixed $400 $4,800 "$4,800" /"$48,900" " = 9.8%"
Housing $950
Food $7,800
Clothing Variable $75
Transportation Fixed $6,000
Insurance & Medical $1,200
Entertainment $100 $1,200
Emergency Fund Fixed $50
Savings for College Fixed $600
Savings for Retirement $100 $1,200
Total $4,075 $48,900 100%
Fixed expenses are expenses that do not change from month to month, and variable expenses are expenses that can fluctuate from month to month. Complete the second column of the chart by determining if each expense is fixed or variable. (10 points – 2 points each)
Choose an example of a fixed expense and an example of a variable expense, and explain why they are classified that way. (4 points)
Answers:
Across->
Housing: Fixed, $950, $11,400, ?
Food: Variable, $650, $7,800,?
Clothing: Variable, $75, $900,?
Transportation: Fixed, $500, $6,000,?
Insurance&medical: Variable, $1,200, $14,400,?
Entertainment: Variable, $100, $1,200,?
Emergency fund: Fixed, $50, $600,?
Saving for C: Fixed, $50, $600,?
Saving for R: Fixed, $100, $1,200,?
Step-by-step explanation:If it is the cost monthly you are looking for, divide the yearly cost by 12. If you are looking for yearly cost, multiply the monthly cost by 12.
And if you would like to know what a variable and fixed expense is, the variable expense is the expense that can change, so say for instance, food isn’t gonna cost at two different places, so it’s variable. A fixed expense is an expense that is regularly paid and always the same cost.
Answer:
Housing: Fixed, $950, $11,400, 23.3%
Food: Variable, $650, $7,800, 16%
Clothing: Variable, $75, $900, 1.8%
Transportation: Fixed, $500, $6,000, 12.3%
Insurance&medical: Variable, $1,200, $14,400, 29.5%
Entertainment: Variable, $100, $1,200, 2.5%
Emergency fund: Fixed, $50, $600, 1.2%
Saving for C: Fixed, $50, $600, 1.2%
Saving for R: Fixed, $100, $1,200, 2.5%
Step-by-step explanation: Added correct percentages...
MAY SOMEBODY HELP ME THANKS!!
A circular plate has circumference 22 inches. What is the area of this plate? Use 3.14 for pi.
IM MARKING BRAINLIEST!!
Answer:
A≈38.52 in²
Step-by-step explanation:
Answer:
Step-by-step explanation:
A car moves at a constant speed of 50 miles per hour. How long does it take the car to go 200 miles?
Answer: 4 hours
Step-by-step explanation: If you take 50 times 4 it will get you 200. Another way to look at it is the car is going 50 miles per hour, so in one hour the car has gone 50 miles, in two hours it’s gone 100, three hours it’s gone 150, so in four hours it’s gone 200 miles
Final answer:
To calculate how long it takes to travel 200 miles at a constant speed of 50 miles per hour, divide the distance by the speed. The car will take 4 hours to cover the distance.
Explanation:
To determine how long it takes a car moving at a constant speed to cover a certain distance, we use the formula time = distance \/ speed. In this case, the car is moving at a constant speed of 50 miles per hour and needs to cover a distance of 200 miles.
We can calculate the time it will take as follows:
Time = Distance \/ Speed
Time = 200 miles \/ 50 miles per hour
Time = 4 hours
Therefore, it will take the car 4 hours to travel 200 miles at a constant speed of 50 miles per hour.
The students put recycling bins for cans for bottles in the cafeteria in the teachers lounge. They split them easily into 3 bags how many pounds were in each bag
Answer:
There were 16.3 pounds in each of the bags
Step-by-step explanation:
The complete question is as follows;
The students put recycling bins for cans and bottles in the cafeteria and teachers lounge. At the end of last week, there was a total of 48.9 pounds of cans and bottles. They split them evenly into 3 bags. How many pounds were in each bag?
Solution;
This is a straightforward question that borders on one of the arithmetic operations which is division.
To properly understand this question, we can reframe it to mean if you have three bags containing cans and bottles with a total weight of 48.9 pounds, what is the weight of each bag if they have the same weight?
we can see we have succeeded in making the question look simpler while meaning the same thing.
To get the weight of each of the bags, what we simply do is to divide the total weight of the bags by 3
Mathematically that would be 48.9/3 = 16.3
This means that each of the bags weigh 16.3 lbs
Triangle A B C is shown. Angle A C B is a right angle. The length of the hypotenuse is 20.
What additional information would be necessary to determine sin(A) without using the Pythagorean theorem? Explain.
The length of AC is needed because it is the side adjacent to ∠A.
The length of AC is needed because it is the side opposite ∠A.
The length of BC is needed because it is the side opposite ∠A.
The length of BC is needed because it is the side adjacent to ∠A.
Answer:
The length of BC is needed because it is the side opposite ∠A.
Step-by-step explanation:
Given the right angles triangle as shown in the attachment, we can get sin(A) without using Pythagoras theorem. Instead we will use SOH CAH TOA trigonometry identity.
According to SOH:
Sin(A) = Opposite/Hypotenuse
Sin(A) = |BC|/|AB|
Opposite side of the triangle is the side facing ∠A.
Based on the formula, we will need to get the opposite side of the triangle which is length BC for us to be able to determine sinA since the hypotenuse is given.
Answer:
Bc is needed because it is opposite of A
Step-by-step explanation:
what is Value of Gummy Bear,Value of Lollipop,Value of Lime Gummy,Value of Ring Pop,Value of the Question Mark
Gummy Bear = 16
Lollipop = 16
Lime = 0
Ring pop = 4
Question mark (total) = 36
Phil is buying a sandwich. He has the following choices. Bread: wheat (W), italian (I), baguette (B) Cheese: grated (G), sliced (S) Meat: chicken (C), turkey (T), fish (F), ham (H) If each sandwich consists of one type of bread, one type of cheese, and one type of meat, which best represents four of his possible sandwich choices?
Answer: c
Step-by-step explanation:
Plzzz help I have to turn this in by 3:30 pm
Answer:
1. 24 2. 12 3. it is a very easy concept
Step-by-step explanation:easy
Find an equation of the hyperbola with center at the origin that satisfies the given condition: A vertex at ( 0,-12) and a focus at (0,-13)
Answer:
c:
Step-by-step explanation:
Which expression is equivalent to (StartFraction (2 a Superscript negative 3 Baseline b Superscript 4 Baseline) squared Over (3 a Superscript 5 Baseline b) Superscript negative 2 Baseline EndFraction) Superscript negative 1?
The expression equivalent to the given expression is [tex]\left[\dfrac{1}{(36a^{4}b^{10})}\right][/tex] and this can be determined by using the arithmetic operations.
Given :
Expression --- [tex]\left[\dfrac{(2a^{-3}b^4)^{2}}{(3a^5b)^{-2}}\right]^{-1}[/tex]
The following steps can be used in order to evaluate the given expression:
Step 1 - The arithmetic operations can be used in order to evaluate the given expression.
Step 2 - Write the given expression.
[tex]\left[\dfrac{(2a^{-3}b^4)^{2}}{(3a^5b)^{-2}}\right]^{-1}[/tex]
Step 3 - Simplify the above expression.
[tex]\left[\dfrac{1}{(3a^5b)^{2}(2a^{-3}b^4)^{2}}\right][/tex]
Step 4 - Open the brackets and square the given terms in the denominator.
[tex]\left[\dfrac{1}{(9a^{10}b^2)\times (4a^{-6}b^8)}\right][/tex]
Step 5 - Multiply the terms present in the denominator.
[tex]\left[\dfrac{1}{(36a^{4}b^{10})}\right][/tex]
Therefore, the correct option is C).
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