Answer: x = square root of -x + 3 / 2
Step-by-step explanation:
2x^2 + x - 1 = 2
add 1 to both sides
2x^2 + x = 3
subtract x from both sides
2x^2 = -x + 3
square root both sides
2x = square root of -x + 3
divide by 2
x = square root of -x + 3 / 2
Answer:
Step-by-step explanation:
hello :
2x² + X - 1 = 2
2x² + X - 1 -2 = 2-2
2x² + X - 3 =0
(x-1)(2x+3) =0
x-1=0 or 2x+3 = 0
x =1 or x= -3/2
You bought your car for $12500 and it is depreciating at 13% per year. How long until it is only worth half of what you paid for it? What is your answer to the nearest year?
Answer:
5 years
Step-by-step explanation:
We are given;
Initial value of the car = $12,500 Rate of Depreciation = 13% per year New value (after depreciation) = $6,250 (half the initial value)We are required to determine the time taken for the value of the car to depreciate to half the original value.
We need to know the depreciation formula;New value = Initial value ( 1 - r/100)^nTherefore;
$6,250 = $12,500(1 - r/100)^n
0.5 = (1 - 13/100)^n
0.5 = 0.87^n
Introducing log on both sides;
log 0.5 = n log 0.87
Therefore;
n = log 0.5 ÷ log 0.87
= 4.977
= 5 years
Therefore, it takes 5 years for the value of the car to depreciate to half the initial value.
Samantha wants to invest $6800 in a savings account that pays 6% simple interest. How long will it take for
this investment to double in value? Round your answer to the nearest tenth.
Answer:
years
Step-by-step explanation:est $ 6800
Samantha wants to invest $ 6800 in a saving account that pays 6% simple interest .
Let it will be take x year
Principle =$6800
Interest = $ 6800
Rate of interest = 6%
Time = x(let)
According To Problem
6800=[tex]\frac{6800\times x\times 6}{100}[/tex]
⇔x = [tex]\frac{100}{6}[/tex] = 16.67 year
Therefore ,it will take 16.67 year .
Answer:
16.67 years.
Step-by-step explanation:
Samantha wants to invest $6800 in a savings account that pays 6% simple interest.
Let after y years the amount will be double in value.
So, using the formula of simple interest we can write
[tex]2 \times 6800 = 6800(1 + \frac{6\times y}{100})[/tex]
⇒ [tex]2 = 1 + \frac{6y}{100}[/tex]
⇒ 6y = 100
⇒ y = 16.67 years.
Therefore, after 16.67 years the amount will become double in value. (Answer)
Find the length of the midsegment.
Answer:
57
Step-by-step explanation:
The midsegment is one half the length of the third side of the triangle, that is
6x + 3 = [tex]\frac{1}{2}[/tex](3x + 87)
Multiply both sides by 2 to clear the fraction
12x + 6 = 3x + 87 ( subtract 3x from both sides )
9x + 6 = 87 ( subtract 6 from both sides )
9x = 81 ( divide both sides by 9 )
x = 9
Thus
midsegment = 6x + 3 = 6(9) + 3 = 54 + 3 = 57
Brad plans 27 roses and 36 daffodils. He plants an equal number of each type of flower in each row. What is the greatest possible number of roses in each row?
Answer:
3 rows of roses and 9 daffodils each row. (3x9=27)
4 rows of roses, 9 in each row.
(4x9=36)
Hope that helps!
Step-by-step explanation:
Answer:
Step-by-step explanation:
9 roses in the 3 rows. 9 goes into 27, 3 equal times.
Find g(f(4)).
g(f(4)) =
Answer:
what is the equation of f(x)
Step-by-step explanation:
Answer:
9 is the answer
Step-by-step explanation:
Joyce and Haley are running two different bake sales for a school fundraiser. Joyce sold each item for $2 and was given a donation of $7 from a parent. Haley sold each item for $3, but did not have any donations. Who do you expect to make the most money from the bake sale if they sell the same number of items?
solve using the graphing method or the algebraic substitution method.
Joyce: y = 2x + 7
Haley: y = 3x
From looking at these two equations, we can assume that Haley will eventually catch up and pass Joyce because she sells items for $3 whereas Joyce had a head start of $7, but only sells items for $2.
Using substitution, we plug in y = 3x into y in the first equation: 3x = 2x + 7
This leaves us at x = 7.
y = 3(7) or 21.
The point at which Haley's and Joyce's money will be exactly the same is (7, 21). After this point, Haley will have more money.
Find an irrational number between pie and 2pie
Answer:
square root of 13
Step-by-step explanation:
sqrt(13)=3.606...
pi=3.14...
2pi=6.28...
sqrt(13) is between
Add the two expressions,
--4.25r +3 and 2.5r- 6
Enter your answer in the box
Answer:
Please read the answer below.
Step-by-step explanation:
Let's add the two expressions as they are written in the question:
- - 4.25r + 3 and 2.5r - 6 = 4.25r + 3 + 2.5r - 6
= 6.75r - 3
In case it wasn't written accurately and the expressions are (first on the left with just one negative sign):
- 4.25r +3 and 2.5r- 6 = - 4.25r + 3 + 2.5r - 6
= -1.75r - 3
Bob drives a truck for a soft drink company. His truck is filled with 15 oz cans and 70 oz bottles. Let C be the number cans and b be the number of bottles. The truck must be carrying less than 7000 lbs. find the inequality describing this.
Answer:
Using ounces, the inequality should be:
15c + 70b < 112,000
Using pounds, the inequality should be:
0.9375c + 4.375b < 7,000
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Weight of a can of soft drink (c) = 15 ounces
Weight of a bottle of soft drink (b) = 70 ounces
The truck mist be carrying less than 7,000 pounds
2. Find the inequality describing this.
Let's recall that 1 pound = 16 ounces and 1 ounce = 0.0625 pounds
c = Number of cans in the truck
b = Number of bottles in the truck
Upon saying that, we can write the inequality either using ounces or pounds, this way:
Using ounces, the inequality should be:
15c + 70b < 7,000 * 16
15c + 70b < 112,000
Using pounds, the inequality should be:
15 * 0.0625c + 70 * 0.0625b < 7,000
0.9375c + 4.375b < 7,000
2y + 2 = -3x
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Please help me!!! Will give brainliest and 12 points! Topic is Pythagorean identity find values
Answer:
cos θ = -(√3)/2
tan θ = -1/√3
Step-by-step explanation:
[tex]\frac{\pi }{2} <\theta <\pi \ \ \ sin \ \theta = \frac{1}{2} \\[/tex]
Part A: find cos θ:
Using Pythagorean identity
sin²θ + cos²θ = 1
cos²θ = 1 - sin²θ = 1 - (1/2)² = 1 - 1/4 = 3/4
cos θ = ±√(3/4) = ±(√3)/2
∵(π/2) < θ < π ⇒ ∴ cos θ = -(√3)/2
Part B: find tan θ:
sec θ = 1/(cos θ) = -2/√3
Using Pythagorean identity
tan²θ + 1 = sec²θ
tan²θ = sec²θ - 1 = 4/3 - 1 = 1/3
tan θ = ±√(1/3) = ± 1/√3
∵(π/2) < θ < π ⇒ ∴ tan θ = -1/√3
What is 120 degrees in radians?
Answer:2.0994
Step-by-step explanation:
You would want to set up the equation like this
120°×π/180 which will then be 2.094rad
120 degrees is equal to 2π/3 radians. You can convert degrees to radians by using the conversion factor π/180. This method simplifies to 2π/3 for 120 degrees.
Converting Degrees to Radians
To convert an angle from degrees to radians, you can use the conversion factor that 360° is equal to 2π radians. Therefore, 1 degree is equal to π/180 radians. To convert 120 degrees to radians, you can follow these steps:
Write down the conversion factor: 1° = π/180 radians.Multiply 120 by π/180: 120° × π/180.Simplify the expression: 120/180 × π = 2/3π.Therefore, 120 degrees is equal to 2π/3 radians. This method ensures accurate conversion and is useful in various mathematical calculations.
Which of the following is an even function?
f(x) = (x - 1)2
OMX) = 8x
O f(x) = x2-X
Of(x) = 7
Answer:
F(X)=7 is the even function
Step-by-step explanation:
f(x)=(x-1)2 is neither odd or even
f(x)=8x is a odd function
f(x)=x2-x is neither odd or even
and f(x)=7 is EVEN
Addison brought treats to school to share for her birthday. She divided the treats evenly among the 22 students in her class. Every student got 3 treats. Write and solve an equation to determine how many treats she brought. Let t represent the number of treats. Brady loves to go fishing! He goes every weekend. This weekend he caught 4 less fish than he did last weekend. He caught 7 fish this weekend. Write and solve an equation to determine how many fish he caught last weekend. Let f represent the number of fish.
Answer:
1. 22 * 3 = t
2. 4 + 7 = f
Step-by-step explanation:
Addison brought 66 treats to school and Brady caught 11 fish last weekend.
Explanation:To determine how many treats Addison brought to school, we can write the following equation: t/22 = 3, where t represents the number of treats. To solve for t, we can multiply both sides of the equation by 22 to get t = 3 * 22 = 66. Therefore, Addison brought 66 treats to school.
To determine how many fish Brady caught last weekend, we can write the equation: f - 4 = 7, where f represents the number of fish. To solve for f, we can add 4 to both sides of the equation to get f = 7 + 4 = 11. Therefore, Brady caught 11 fish last weekend.
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A cube has a surface area of 100 square inches. Which choice is closest to the length
of an edge of the cube?
A. 1.7 inches
B. 3.3 inches
C. 10 inches
D. 4.1 inches
Answer:
D. 4.1 inches
Step-by-step explanation:
While working at the drugstore, Robbie earns $12 per hour. How many hours will it take Rubbie to earn $48?
Answer:
4 hours.
Step-by-step explanation:
If Robbie earns 12 dollars per hour, it will take him 4 hours to earn 48 dollars. This is because 48/12 = 4.
48/12=hours
12+12+12+12=hours
4 hours
Solve the linear equation.
8x+32=1/5(25x−15)−4x I need help please ill give 100 points
Enter your answer in the box.
Answer:
x = -5
Step-by-step explanation:
8x+32=1/5(25x−15)−4x
8x + 32 = 5x - 3 - 4x
8x + 32 = x - 3
7x = -35
x = -5
Answer:
x = -5
Step-by-step explanation:
Let's expand the parentheses on the right side first:
(1/5) * (25x - 15) = (1/5) * 25x - (1/5) * 15 = 5x - 3
Now put this back in:
8x + 32 = 5x - 3 - 4x
Move all the x terms to one side and all the constants to one side:
8x - 5x + 4x = -3 - 32
Combine like terms:
7x = -35
Divide both sides by 7:
x = -35/7 = -5
Thus, the answer is -5.
Hope this helps!
If AD/DB =AE/EC, then line segment blank is parallel to line segment blank
Answer:DE and BC
Step-by-step explanation:
giving free brainliest to first correct response,
what is 2+2+5+3+6+4+6+2+5+78+2+1?
Answer:
116
Step-by-step explanation:
2+2+5+3+6+4+6+2+5+78+2+1
4+5+3+6+4+6+2+5+78+2+1
9+3+6+4+6+2+5+78+2+1
12+6+4+6+2+5+78+2+1
18+4+6+2+5+78+2+1
22+6+2+5+78+2+1
28+2+5+78+2+1
35+78+2+1
113+2+1
116
Answer:
116
Step-by-step explanation:
5x-3y=-12 in slope-intercept form
Answer:
Subtract 5x from both sides of the equation
-3y = 12 - 5x
Then, divide each term by -3 and simplify.
y = -4 + 5x
------
3
After that, you'll do this
y= 5x
----- - 4
3
Lastly, you put that into slope-intercept form.
y = 5
---- x - 4
3
A truck uses 1 tablespoon of gasoline to drive 125 yards. How many miles can the vehicle travel per gallon?
And hint: there are 256 tablespoons in a gallon
Answer:
18.18 miles.
Step-by-step explanation:
A truck uses 1 tablespoon of gasoline to drive 125 yards.
Now, 1 gallon of gasoline contains 256 tablespoons of gasoline.
So, the truck uses 1 gallon i.e. 256 tablespoons of gasoline to drive (256 × 125) = 32000 yards.
Now, 1-mile distance contains 1760 yards.
Therefore, the truck uses 1 gallon of gasoline to drive [tex]\frac{32000}{1760} = 18.18[/tex] miles. (Answer)
Two sides of a triangle have the same length. The third side measures 2 m less than twice the common length. The perimeter of the triangle is 26 m. What are the lengths of the three sides?
The lengths of the three sides of the triangle are 7m, 7m, and 12m.
Explanation:Let the length of the two equal sides be 'x'.
The third side measures 2m less than twice the common length, so it is (2x - 2)m in length.
Given that the perimeter of the triangle is 26m, we can set up the equation:
x + x + (2x - 2) = 26
Simplifying the equation:
4x - 2 = 26
4x = 28
x = 7
So, the lengths of the three sides are 7m, 7m, and (2x - 2)m = (2 * 7 - 2)m = 12m.
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Final answer:
The triangle with two sides of equal length and a perimeter of 26 m has sides measuring 7 m, 7 m, and 12 m.
Explanation:
To solve for the lengths of the sides of the triangle described in the question, we can set up an equation based on the information given. Since two sides of the triangle have the same length, we can call that common length 'x'. The third side is described as being '2 m less than twice the common length', which can be written as '2x - 2'. The perimeter of the triangle, which is the sum of the lengths of all sides, is given as 26 m.
Therefore, the perimeter equation would be:
x + x + (2x - 2) = 26
This simplifies to:
4x - 2 = 26
Adding 2 to both sides, we get:
4x = 28
Dividing both sides by 4, we find x:
x = 7
Now we know that the two sides of equal length are both 7 m, and the third side is:
2x - 2 = 2(7) - 2 = 12
So the lengths of the three sides of the triangle are 7 m, 7 m, and 12 m.
$925 at 2.3% for 2.4 years what is the interest earned
Answer:
51.06
Step-by-step explanation:
So
P=$925
R=2.3%
T=2.4
So to get the answer we would need to multiply all of these together so first we would do 925 times 2.3% which would be 21.275. Then we would do 21.275 times 2.4 then we would get the answer of 51.06.
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 8 people took the trip. She was able to purchase coach tickets for $290 and first class tickets for $980. She used her total budget for airfare for the trip, which was $5080. How many first class tickets did she buy? How many coach tickets did she buy?
Sarah bought 4 first class tickets and 4 coach tickets for a total of 8 tickets, using her entire budget of $5080.
Explanation:Sarah purchased tickets for a total of 8 people with a mix of coach and first class tickets. The cost for coach tickets was $290 each, and the cost for first class tickets was $980 each. With a total airfare budget of $5080, we need to determine how many of each type of ticket she bought.
Let's denote the number of first class tickets as x and the number of coach tickets as y. The two equations representing the situation are:
x + y = 8 (since there are 8 people including Sarah)980x + 290y = 5080 (the total cost of tickets must equal the budget)From the first equation, we can express y in terms of x: y = 8 - x. Substituting this into the second equation gives us:
980x + 290(8 - x) = 5080
Solving for x will give us the number of first class tickets, and using the value of x, we can find y, the number of coach tickets. After simplifying and solving, we find that:
980x + 2320 - 290x = 5080
690x = 2760
x = 4
Thus, Sarah bought 4 first class tickets. To find the number of coach tickets (y), we substitute x into the first equation:
y = 8 - 4
y = 4
Therefore, Sarah also bought 4 coach tickets.
Solve for x in the diagram below (picture included)
Answer:
34
Step-by-step explanation:
We know the straight line is equal to 180°, and the three angles that make it are (x+12),100°, and x. We can use the equation 180=(x+12)+100+x to find x.
180=(x+12)+100+x
We can remove the parentheses and combine x plus x to 2x.
180=100+2x+12
100+12=112
so
180=112+2x
-112 -112
68=2x
÷2 ÷2
34=x
3 plus 1 1/4 just please help me
Answer:
5.75
Step-by-step explanation:
3 + 11/4
Use BIDMAS to help you
11/4 = 2.75
3+ 2.75 = 5.75
Plz mark brainliest i just need 3 more plz plz plz
A person invests $200 in an account that earns 1.98% annual interest compounded
quarterly. Find when the value of the investment reaches $500.
Answer:
[tex]t=46.4\ years[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=?\ years\\P=\$200\\A=\$500\\ r=1.98\%=1.98/100=0.0198\\n=4[/tex]
substitute in the formula above
[tex]500=200(1+\frac{0.0198}{4})^{4t}[/tex]
[tex]2.5=(1.00495)^{4t}[/tex]
Apply property of exponents
[tex]2.5=[(1.00495)^{4}]^t[/tex]
Apply log both sides
[tex]log(2.5)=log[(1.00495)^{4}]^t[/tex]
[tex]t=log(2.5)/log[(1.00495)^{4}][/tex]
[tex]t=46.4\ years[/tex]
Final answer:
To find when the investment of $200 at a 1.98% annual interest rate compounded quarterly will reach $500, we use the compound interest formula and solve for t, representing time in years.
Explanation:
The subject is Mathematics, specifically focusing on the concept of compound interest. To find out when the investment will reach $500, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^(nt)[/tex]
Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money).
r = the annual interest rate (decimal).
n = the number of times that interest is compounded per year.
t = the time the money is invested for in years.
In the case of the student's question:
P = $200
n = 4 (since the interest is compounded quarterly)
A = $500
We rearrange the formula to solve for t:
t = (log(A/P)) / (n×log(1+r/n))
Substitute the given values:
t = (log(500/200)) / (4×log(1+0.0198/4))
Use a calculator to compute t, which will give us the number of years it takes for the investment to reach $500.
Write an equation for a line perpendicular to Y equals negative 3X -2 and passing through the point (9,7)
The equation for line perpendicular to y = -3x - 2 and passing through the point (9,7) in slope intercept form is:
[tex]y = \frac{x}{3}+4[/tex]
Solution:
Given that we have to write the equation for line perpendicular to y = -3x - 2 and passing through the point (9,7)
Let us first find the slope of line
The equation of line in slope intercept form is given as:
y = mx + c -------- eqn 1
Where, "m" is the slope of line and "c" is the y - intercept
Given equation of line is:
y = -3x - 2
On comparing the above equation with eqn 1
m = -3
We know that product of slope of a line and line perpendicular to it is equal to -1
Therefore,
[tex]-3 \times \text{ slope of line perpendicular to given line } = -1\\\\\text{ slope of line perpendicular to given line } = \frac{1}{3}[/tex]
Now find the equation of line passing through the point (9, 7)
[tex]\text{Substitute } (x, y) = (9, 7) \text{ and } m = \frac{1}{3} \text{ in eqn 1 }[/tex]
[tex]7 = \frac{1}{3} \times 9+c\\\\7=3+c\\\\c = 4[/tex]
[tex]\text{Substitute } m = \frac{1}{3} \text{ and } c = 4 \text{ in eqn 1 }[/tex]
[tex]y = \frac{1}{3}x+4\\\\y = \frac{x}{3}+4[/tex]
Thus the equation of line in slope intercept form is found
Which of the following algebraic equations is equivalent to ?
xn = a
an = x
ax = n
xa = n
Answer:
[tex]a^n=x[/tex]
Step-by-step explanation:
The complete question is in the attachment.
We want to find an expression that is equivalent to: [tex]\sqrt[n]{x} =a[/tex]
Note that: [tex]\sqrt[n]{x} =x^{\frac{1}{n} }[/tex]
This implies that:
[tex]x^{\frac{1}{n}}=a[/tex]
Or
[tex]x^{\frac{1}{n}}=a^1[/tex]
[tex]x^{\frac{1}{n}*n}=a^{1*n}[/tex]
This simplifies to:
[tex]x=a^n[/tex]
Answer: The answer is X^n = a
Step-by-step explanation:
Got it right!
1. Which situation would most likely be
represented by a rational number that is
not an integer?
A number of students in a classroom
B score on a math test
C number of keys on a keyboard
D price of a pencil
Answer:
D Price of a pencil
Step-by-step explanation:
In A the number of students has to be an integer because you can't have part of a student
In B most likely your teacher will give you your score in a whole number form like 95% and not 94.87% because they would round it if it isn't a whole number already
C is similar to A you can't have a part of a computer key
Lastly in D stores very frequently have there prices at something like $1.99 which isn't a integer
The situation that would most likely be represented by a rational number that is not an integer is the price of a pencil.
Explanation:The situation that would most likely be represented by a rational number that is not an integer is D) price of a pencil. A rational number is any number that can be expressed as a fraction, where both the numerator and denominator are integers. The price of a pencil can be a rational number in the form of a decimal, such as 0.99 or 2.50, which are not whole numbers.
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