[tex]6x-14=2-10x\qquad\text{add 14 to both sides}\\\\6x=16-10x\qquad\text{add 10x to both sides}\\\\16x=16\qquad\text{divide both sides by 16}\\\\\boxed{x=1}[/tex]
[tex]Check:\\\\6x-14=6(1)-14=6-14=-8\\\\2-10x=2-10(1)=2-10=-8\\\\CORRECT[/tex]
Answer:
x=1
Step-by-step explanation:
6x-14=2-10x
First step is to add 10x to each side
6x+10x-14=2-10x+10x
16x-14=2
Now add 14 to each side
16x-14+14=2+14
16x=16
Divide each side by 16 to isolate x
16x/16 =16/16
x =1
how do you solve -3y-8=25
Jay is 4 years younger than three times Tamia's age. Jay is 20 years old. How old is Tamia?
Final answer:
To find Tamia's age, an equation was set up based on the relationship between Jay and Tamia's ages. Jay is 20 years old and 4 years younger than three times Tamia's age. Solving the equation shows that Tamia is 8 years old.
Explanation:
Jay is 4 years younger than three times Tamia's age. Given that Jay is 20 years old, we can use this information to find out how old Tamia is. Let's denote Tamia's age as T. The relationship between their ages can be represented by the equation: Jay's age = 3 × Tamia's age - 4. Since Jay's age is 20, we can substitute this into the equation, giving us 20 = 3T - 4.
To solve for T, we first add 4 to both sides of the equation, which gives us 24 = 3T. Next, we divide both sides by 3 to find Tamia's age, resulting in T = 8. Therefore, Tamia is 8 years old.
This problem was solved by setting up an equation based on the relationship described between Jay and Tamia's ages, then using basic algebraic steps to solve for Tamia's age.
Given the equation y = 3x − 4, what is the value of y when x = 4?
A) 2
B) 4
C) 8
D) 10
Answer:
C) 8
Step-by-step explanation:
y = 3x-4
Substitute x=4 into the equation
y = 3*4 -4
y = 12-4
y=8
Put the value of x = 4 to the equation y = 3x - 4:
[tex]y=3(4)-4=12-4=8[/tex]
Answer: C) 8find the area of washers whose external and internal diameter are 1.2m and 0.9m
Answer:
0.49 m²
Step-by-step explanation:
The area (A) is calculated using A = πr² ( r is the radius )
A = external area - internal area
external radius = [tex]\frac{1.2}{2}[/tex] = 0.6
internal radius = [tex]\frac{0.9}{2}[/tex] = 0.45
A = π(0.6² - 0.45²)
= π(0.36 - 0.2025) = 0.1575π ≈ 0.49 m²
Final answer:
The area of the washers is 0.49m².
Explanation:
To find the area of the washers, we need to find the areas of the outer and inner circles and then subtract the smaller area from the larger one. The area of a circle is given by the formula A = πr², where r is the radius of the circle. In this case, the external diameter is 1.2m, so the radius is half of that, or 0.6m. The area of the outer circle is A₁ = π(0.6)² = 1.13m². Similarly, the radius of the inner circle is 0.45m, and the area of the inner circle is A₂ = π(0.45)² = 0.64m². Finally, the area of the washer is the difference between the two areas: A = A₁ - A₂ = 1.13m² - 0.64m² = 0.49m².
What is the unit price of 3 gallons of juice for 6.99
Answer:
The unit price is $2.33 per gallon
Step-by-step explanation:
To find the unit price, we take the price and divide by the amount
$6.99 / 3 gallons
$2.33 per gallon
The unit price is $2.33 per gallon
What multiplication sentence does the model represent?????
Answer:
I Think It Is 0.12*2
Because I See Both Of The Shadings Colored Differently And Each One Has 12 That Is The Reason For Me Thinking This.
convert angle 180° to radians
Answer:
180 degrees in radians is π
Step-by-step explanation:
0° = 0 radians
90°= π/2
180 °= π
270°= 3π/2
360° = 2π
and so on
Waterworld properties to rewrite each expression as an expression that does not use parentheses (b + 3) + 6
Answer:
b+9
Step-by-step explanation:
(b + 3) + 6 = b + (3 + 6) = b + 9
Multiply. Express your answer in simplest form. 7/10 × 2/5
Answer:
7/10 x 2/5 = 14/50 = 7/25
Step-by-step explanation:
mutipily 7 and 2 that gives you 14 and mutilpily 10 and 5 that gives you 50 = 14/50. In simplest form the answer is 7/25.
Answer:
7/10 x 2/5 = 14/50 = 7/25
Step-by-step explanation:
mutipily 7 and 2 that gives you 14 and mutilpily 10 and 5 that gives you 50 = 14/50. In simplest form the answer is 7/25.
Can someone please help
Suppose 6 quarts of milk cost $5.10. Use the unit price (price per quart) to determine how much 5 gallons of milk cost?
A $17.00
B $34.00
C $8.50
D $0.85
E $4.25
Answer:
Answer is: A
Step-by-step explanation:
Because it is.
Answer:
A. $17.00
Step-by-step explanation:
$5.10 for 6 quarts.
Unit cost: ($5.10)/(6 qt) = $0.85/qt
Price for 5 gallons:
1 gallon = 4 quarts
5 gallons = 5 * 4 quarts = 20 quarts
Price for 5 gallons = unit price * number of quarts
Price for 5 gallons = $0.85/qt * 20 qt = $17.00
Answer: A. $17.00
45 POINTS!
PLEASE HELPPPPPPPPPPPPPP!
Answer:
This is a direct variation where the constant of variation is 5/9
Step-by-step explanation:
The equation for direct variation is y = kx
5x-9y =0
Lets try to get this equation in the above form
Add 9y to each side
5x-9y +9y = 9y
5x = 9y
Divide each side by 9
5/9 x = 9y/9
5/9x = y
This is in the form y = k x where k =5/9
Bradley wanted a blue gumball and a green gumball from a vending machine. There were 15 blue gumballs, 12 yellow gumballs, 2 green gumballs, and 16 purple gumballs. How many times would you expect to get a blue gumball or green gumball if a gumball was taken out 250 times?
Answer: Bradley would expect 94 times to get a blue or green gumball.
Step-by-step explanation:
Since we have given that
Number of blue gumballs = 15
Number of yellow gumballs = 12
Number of green gumballs = 2
Number of purple gumballs = 16
Total number of all gumballs = 45
Probability of getting either a blue gumball or green gumball be
[tex]\frac{15}{45}+\frac{2}{45}=\frac{17}{45}[/tex]
So, Expectation of getting a blue gumball or green gumball if a gumball was taken out 250 times :
[tex]\frac{17}{45}\times 250=94.4[/tex]
Since we know that it must be less than 94.4.
So, the nearest smallest integer will be 94 times .
Hence, Bradley would expect 94 times to get a blue or green gumball.
Laura borrows 10000 for 5 years at 6.5% rate. How much will the interest be after 3 years?
SUPER EASY AND REALLY URGENT!!
Answer:
is your answer $3250
Step-by-step explanation:
so we dont know our I (interest) but :
P (principal) = 10000
R (rate) = 6.5% we'll have to turn it into the decimal which is 0.065
T (time) = 5 years
and our basic formula of finding I is I = PxRxT so :
I = 10000 x 0.065 x 5
I = 3250
Three geometric sequences are given below.
Sequence A: 160,40,10,2.5,...
Sequence B: -21,63,-189,567,...
Sequence C: 8,12,18,27,....
Order the sequences from least common ratio to the greatest common ratio.
Answer:
A C B
Step-by-step explanation:
In sequence A. the numbers are being divided by 4.
In sequence B. the numbers are being multiplied by -3
In sequence C. the numbers are being add by 4
So the ratio from least to greatest would be A C B
Answer:
Sequence B, Sequence A, Sequence C
Step-by-step explanation:
Common ratio of a geometric sequence is the ratio of a term and its previous term of the sequence.
Thus, the common ratio of the sequence A: 160,40,10,2.5,...
[tex]r_1=\frac{40}{160}=\frac{1}{4}[/tex]
The common ratio of the sequence B: -21,63,-189,567,...
[tex]r_2=\frac{63}{-21}=-3[/tex]
The common ratio of the sequence C : 8,12,18,27,....
[tex]r_3=\frac{12}{8}=\frac{3}{2}[/tex]
Since, -3 < [tex]\frac{1}{4}[/tex] < [tex]\frac{3}{2}[/tex]
Thus,
[tex]r_2 < r_1 < r_3[/tex]
Hence, the order the sequences from least common ratio to the greatest common ratio is,
Sequence B, Sequence A, Sequence C
suppose that there are two types of tickets to a show: advance and same day. Advance tickets cost $20 and same-day tickets cost $25. For one performance, there were 75 tickets sold in all, and the total amount paid for them was $1700. how many of each type were sold?
SOS HURRY
The vertices of a square are (-5,-4) (-2,-8) (1,-4) (-2,0) What is the area of the square?
First, by using the distance formula for just one side, we can find the length of all sides (a square has 4 equal sides.) Then, we can apply the area of a square formula, which is a^2.
Distance formula:
[tex]\sqrt{(x.2 - x.1)^{2} + (y.2 - y.1)^{2}}[/tex]
√((-2 + 5)^2 + (-8 + 4)^2)
√((3)^2 + (4)^2)
√9 + 16
√25
5
The side lengths of the square are each equal to 5, and by applying the formula for area, we can find the area of the square.
5^2 = 25
The area is 25.can some one help me. Solve this equation.
[tex]\bold{Given : 2^2^x^-^2 - 2^x^-^1 = 2^x - 2}[/tex]
[tex]\bold{\implies (2^2^x) (2^-^2) - (2^x)(2^-^1) = 2^x - 2}[/tex]
[tex]\bold{\implies \frac{(2^2^x)}{(2^2)} - \frac{(2^x)}{(2^1)} = 2^x - 2}[/tex]
[tex]\bold{\implies \frac{(2^2^x)}{4} - \frac{(2^x)}{2} = 2^x - 2}[/tex]
[tex]\bold{\implies \frac{[2^2^x - (2^x)(2)]}{4} = 2^x - 2}[/tex]
[tex]\bold{\implies [2^2^x - (2^x)(2)] = (4)(2^x) - 8}[/tex]
[tex]\bold{\implies 2^2^x - (2^x)(2) - (4)(2^x) + 8 = 0}[/tex]
[tex]\bold{\implies (2^x)^2 - (2^x)(6) + 8 = 0}[/tex]
[tex]\bold{Let\;us\;take : (2^x) = Z}[/tex]
[tex]\bold{\implies Z^2 - 6Z + 8 = 0}[/tex]
[tex]\bold{\implies Z^2 - 4Z - 2Z + 8 = 0}[/tex]
[tex]\bold{\implies Z(Z - 4) - 2(Z - 4) = 0}[/tex]
[tex]\bold{\implies Z = 4\;\;(or)\;\;Z = 2}[/tex]
[tex]\bold{But : Z = 2^x}[/tex]
[tex]\bold{\implies 2^x = 4\;\; (or) \;\; 2^x = 2}[/tex]
[tex]\bold{\implies 2^x = 2^2\;\; (or) \;\; 2^x = 2^1}[/tex]
[tex]\bold{\implies x = 2\;\;(or)\;\; x = 1}[/tex]
Leonard paid $35 registration fee to join the gym. He pays $10 each month.
How much will he pay to use the gym for 6 months?
Say that you own property with a market price of $74,000. The state tax assessors have given it an assessed value of 48% of that amount. If your state’s property tax rate is 0.031, how much do you owe in property tax, to the nearest dollar? a. $1,101 b. $2,294 c. $35,520 d. $1,193
Answer:
A
Step-by-step explanation:
74,000 x .48 = 35520. 35520 is the amount of property you have to pay for.
35520 x 0.031 = 1,101.12. 1.101.12 is the amount you owe in property tax.
The amount owed in property tax to the nearest dollar is $1,101
What is the market price of a property?In real estate management, the market price is the price at which a buyer is willing to pay and which the seller is as agreed to receive at the present time.
From the parameters given:
The market price = $74000The state tax on the property = 48% = 0.48From the property, the required amount of property to be paid for is:
= $74000 × 0.48
= $35520
If the state property tax rate is 0.31, the amount owe in property tax is:
= $35520 × 0.031
= $1,101
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A motorcycle can travel 70 miles per gallon. Approximately how many gallons of fuel will the motorcycle need to travel 60 km?
[1 mile = 1.6 km]
a- 0.2
b- 0.5
c- 0.8
d- 1.4
Answer:
We have the following given
mileage = 70 miles per gallon
distance = 60 km
Required: amount of fuel in gallons
First, we must convert the distance to miles, so
60 km (1 mi/1.6 km) = 37.5 mi
So, the amount of fuel is
37.5 mi / (70 mi/gal) = 0.54 gallon
Answer:
B
Step-by-step explanation:
70 miles * [1.6 km/mile] = 112 km
Notice when you multiply by km/mile by miles the miles cancel out.
1 gallon will get 112 km
x gallon will get 60 km
1/x = 112/60 cross multiply1 * 60 = 112 * x divide by 11260/112 = x switchx = 60/112 Do the divisionx = 0.54 Which rounds to 0.5find the square root of -36
[tex]i=\sqrt{-1}-\text{the imaginary number}\\\\\sqrt{-36}=\sqrt{(36)(-1)}=\sqrt{36}\cdot\sqrt{-1}=\boxed{6i}[/tex]
Caroline ran 15 miles in 5 days. She ran the same distance each day. Write and solve an equation to determine the number of miles she ran each day
Answer:
15/5= x. x=3.
Step-by-step explanation:
Miles ran in total divided by days spent running equals miles ran each day.
A large container has a maximum capacity of 64 ounces The container is filled with 8 ounces less than its maximum capacity
The percentage of its capacity is the large container filled will be 87.5%.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
A large container has a maximum capacity of 64 ounces.
And, The container is filled with 8 ounces less than its maximum capacity.
Now,
Calculate the percent of its capacity is the large container filled as;
Percent = (64 - 8) / 64 x 100
= 56/64 x 100
= 87.5%
Thus, The percentage of its capacity is the large container filled will be 87.5%.
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The complete question is this;
A large container has a maximum capacity of 64 ounces. The container is filled with 8 ounces less than its maximum capacity. To what percent of its capacity is the large container filled?
Mrs Wong is going on a trip. She has 14 books that she hasn’t read yet but she wants to bring only 2 on the trip. In how many ways can she choose 2 books to bring on the trip
In combinatorics, we use the combination formula to calculate the number of ways Mrs. Wong can choose 2 books out of 14. The result is 91 ways.
Explanation:The subject of this question is combinatorics, a topic in mathematics dealing with combinations of objects belonging to a finite set in accordance with certain constraints, such as those specified in this question. In this case, Mrs. Wong has 14 special objects (books) and wants to choose 2 out of them.
We use the combination formula in this scenario. The combination formula is given by C(n, r) = n! / [(n-r)!*r!], where n represents the total number of objects, r is the number of objects to choose, and '!' denotes factorial.
Substituting n as 14 and r as 2 into the formula, we get: C(14,2) = 14! / [(14-2)!*2!] = 91.
Therefore, Mrs. Wong can choose 2 books out of 14 in 91 different ways.
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The question is about combinations in mathematics. Using the formula for combinations, we find that Mrs. Wong can choose 2 books out of 14 in 91 different ways.
Explanation:This is a problem of combinations in mathematics. Mrs. Wong can choose two out of 14 unread books in a certain number of ways, and we're tasked to find that number.
Considering that order of selection does not matter, we can use the formula for combination: nCr = n! / r!(n-r)!. Here, 'n' is the total number of items, 'r' is the items to be chosen.
So the combinations she can make, denoted as 14C2, can be calculated like this:
14C2 = 14! / 2!(14-2)! = (14*13) / (2*1) = 91 ways
Therefore, Mrs Wong can choose 2 books out of 14 in 91 ways.
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There are 225 dozen cookies in the bakery. How many cookies are there?
Answer:
2700 cookies.
Step-by-step explanation:
A dozen is a grouping of twelve, that is a dozen = 12.
If there are 225 dozen cookies in the bakery, then there are
[tex]225\cdot 12=2700[/tex] cookies in the bakery.
there are 2700 cookies in total
Since there are 225 dozen cookies in the bakery, we need to determine the total number of cookies.
To convert dozen to individual units, we multiply the number of dozens ( 225 ) by 12, as there are 12 cookies in each dozen :
225 dozen * 12 cookies / dozen = 2700 cookies
Therefore, there are 2700 cookies in total. By multiplying the number of dozens by 12, we account for the fact that each dozen contains 12 cookies. This calculation allows us to determine the precise quantity of cookies in the bakery.
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Brian rented a book from the book shop.The shop charges $2 for the first day and $3 from the second day onwards.Brian took more then 2 days to return the book and he paid $35 while returning the book.How many days did he keep the book with him?
Brian rented the book for 12 days.
Brian rented a book with the condition that the shop charges $2 for the first day and $3 from the second day onwards. He paid a total of $35 upon returning the book. To determine how many days he kept the book, we must calculate the cost for each day and subtract the initial $2 from the total amount paid.
Steps to Calculate the Number of Days:
Subtract the first day's charge from the total amount: $35 - $2 = $33.Divide the remaining amount by the daily charge starting from the second day: $33 / $3 = 11 days.Add the first day to the result: 11 days + 1 day = 12 days.Therefore, Brian kept the book with him for 12 days.
Which graph is the graph of y - 1 = 0 ?
Answer:
The answer is A because if you subtract the 1 you get y=1 and the line of A is at the point 1 on the y-axis
Step-by-step explanation:
In 1983 the composition of pennies in the United States was changed due, in part, to the rising cost of copper. Pennies minted after 1983 weigh 2.50 grams while the earlier copper pennies weigh 3.11 grams. a. A roll of pennies contains 50 pennies. If a particular roll of pennies weighs 138.42 grams, how many of the earlier copper pennies and how many of the after 1983 pennies does this roll contain? b. Suppose you measure a roll of pennies on a scale which only reads the weight to the nearest gram. The scale says that the roll of pennies weighs 131 grams. What can you conclude about the pennies in this roll? What if the roll weights 134 grams? Explain.
Answer:
Solution for (a)
Earlier Copper pennies are 22.
After 1983 pennies are 28.
Step-by-step explanation:
Pennies minted after 1983 weigh 2.50g
Earlier copper pennies weigh 3.11g
A roll of pennies contains 50 pennies.
A particular roll of pennies weighs 138.42g
Let the number of pennies minted after 1983 be x and;
Earlier copper pennies be 50 - x
2.50x + 3.11(50 - x) = 138.42
Opening the brackets gives;
2.5x + 155.5 - 3.11x = 138.42
Solving like terms together gives;
-0.61x = -17.08
Dividing through gives;
x = 28
So there are 28 after 1983 pennies and;
50 - 28 = 22 earlier pennies.
Question: 1. What is the value of x? Show your work to justify your answer. (2 points) 2. What is the value of the exterior angle? Show your work to justify your answer. (2 points)
Answer:
x=56 and the exterior angle is 116
Step-by-step explanation:
We will call the unknown angle in the triangle y. Angle y and the angle (2x +4) form a straight line so they make 180 degrees.
y + 2x+4 =180
Solve for y by subtracting 2x+4 from each side.
y + 2x+4 - (2x+4) =180 - (2x+4)
y = 180-2x-4
y = 176-2x
The three angles of a triangle add to 180 degrees
x+ y+ 60 = 180
x+ (176-2x)+60 = 180
Combine like terms
-x +236=180
Subtract 236 from each side
-x+236-236 = 180-236
-x = -56
Multiply each side by -1
-1*-x = -56*-1
x=56
The exterior angle is 2x+4. Substitute x=56 into the equation.
2(56)+4
112+4
116
Find the value of x in this figure.
A) 43
B) 47
C) 53
D) 57
Answer: 47 (choice B)
x+43 = 90
x = 90 - 43
x = 47
This works because triangle PQR is a right triangle (with angle Q as the 90 degree angle). We say that that P and R are complementary angles. I added point R to be located where the angle x is written.
Answer:
47
Step-by-step explanation: