Answer:
The value of a is 4. This can be determined by multiplying both sides of the equation by 10, which yields 5√10 = 4√10 + 6√10. Subtracting 4√10 from both sides yields a√10 = 6√10, and dividing both sides by 6 yields a = 4.
I need another answer asap! Please and thank you if you answer this and you will get 15 points! So what is the answer to this question? Dax is buying coffee for 5
people in his office. He also leaves a $2.00
tip for the barista.
If his total, with tip, is $18.25,
how much is each cup of coffee, not including the tip?
Enter your answer as a decimal, like this: 42.53
Answer:
3.25
Step-by-step explanation:
total 18.25 - 2.00 tip = 16.25
16.25/5=3.25
help please i need help im not smart
Step-by-step explanation:
The objective Felipe had was to solve for x. The first step to do is to try to balance each side. He subtracted 3x from 2x which got him -x+6=-8 , since 2x - 3x equals -1x and the 3x minus the 3x cancels out. I hope this helps!
You made it onto the game show Let's Make a Deall You are chosen for the opportunity to win some cash! You are
presented with a bag that contains 5 $100 bills, 9 $20 bills, 17 $5 bills, and 42 $1 bills. (write probabilities in
simplified fraction / ratio form)
Wayne says you can draw three bills randomly from the bag for your prize (you keep each bill you draw). What is
the probability of winning $300?
Unfortunately, you draw three $1 bills! Wayne feels for you and says you can put two of the bills back into the bag
(replace the bills). What is the probability of winning $201?
2x-5/ x^2-6x-7< 1/x-3
The solution is x^2-5x+22<0.
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
here, we have,
2x-5/ x^2-6x-7< 1/x-3,
so, we get,
⇒2x-5/x^2-7x+x-7 < 1/x-3
⇒2x-5/(x-7)(x+1) < 1/x-3
⇒2x-5 * x-3 < (x-7)(x+1)
⇒2x^2-11x+15 < x^2-6x-7
⇒x^2-5x+22<0
Hence, The solution is x^2-5x+22<0.
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notice how using one significant digit would not be graded as correct. given to two significant figures, the current is 2.2 a. does this fall within the 2% tolerance range?
If the current is 2.2 A, it falls within the 2% tolerance range of 2.156 A to 2.244 A and would be considered correct.
To determine if 2.2 A falls within the 2% tolerance range, we first need to establish what the expected current value is. If the expected current value is not specified, it's best to use the maximum rated current value as the expected value.
Once we have the expected current value, we can calculate the tolerance range. Tolerance is expressed as a percentage of the expected value, and in this case, it's 2%.
So the tolerance range is:
(Expected Value) * (Tolerance Percentage) = Tolerance Range
For example, if the expected value is 2.2 A, then the tolerance range would be:
2.2 * 0.02 = 0.044
The tolerance range represents the amount by which the actual current can deviate from the expected value and still be considered acceptable. In this case, the tolerance range is 0.044 A, so the acceptable range for the current would be:
(Expected Value - Tolerance Range) to (Expected Value + Tolerance Range)
2.2 - 0.044 to 2.2 + 0.044 = 2.156 to 2.244
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ANSWER PLEASE 10 POINTS!!! EXPLANATION INCLUDED TOO PLS!
There are red tiles and blue tiles in a box. the ratio of red tiles to blue tiles is 3:5. There are 12 more blue tiles than red tiles in the box. How many red tiles are in the box?
Ty!
r = red tiles
b = blue tiles
b = r + 12 , whatever "r" is, "b" is 12 more than that
[tex]\stackrel{red}{3}~~ : ~~\stackrel{blue}{5}\qquad \implies \cfrac{r}{b}=\cfrac{3}{5}\implies \cfrac{r}{r+12}=\cfrac{3}{5}\implies 5r=3r+36 \\\\\\ 2r=36\implies r=\cfrac{36}{2}\implies r=18[/tex]
Answer:
18
Step-by-step explanation:
Because there are 12 more blue tiles than red, that means that we can write the equation 3x + 12 = 5x. By simplifying, the equation is boiled down to 12=2x. By dividing, we see that x=6. This means that we can multiply 3 by 6 to get 18 red tiles. To check our answer, we just multiply 6 by 5 to get 30, and the ratio 18:30 is equivalent to 3:5. Also, 30-18=12, so this must be correct.
Find each exact value if 0
Tan (x - y) if csc x = 13/5 and cot y = 4/3
Using trigonometry formulas, the value of tan(x-y) = -16/63
What is trigonometry?In the field of mathematics known as trigonometry, correlations between angles and length ratios are studied. Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric identities are frequently employed to rewrite trigonometrical expressions.
Given
cot y = 4/3
1/tan y = 4/3
Cross multiply
tan y = 3/4
Also since csc x = 13/5
1/sin x = 13/5
sin x = 5/13
Since sin x = opp/hyp
opp = 5
hyp = 13
Get the adjacent
hyp² = opp²+adj²
13² = 5²+adj²
adj² = 13² - 5²
adj² = 169 - 25
adj² = 144
adj = 12
cos x = adj/hyp
cos x = 12/13
tan x = sin x/ cos x
tan x = (5/13)/(12/13)
tan x = 5/13 * 13/12
tan x = 5/12
tan(x-y) = tan x - tan y/1 + tan x * tan y
tan(x-y) = (5/12 - 3/4) / 1 + (5/12) (3/4)
tan(x-y) = (5-9/12) / 1 + 5/16
tan(x-y) = -4/12/(21/16)
tan(x-y) = -1/3 * 16/21
tan(x-y) = -16/63
the value of tan(x-y) is -16/63
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2. There are 6 children that each want to eat half of a chocolate bar. If they buy a package of 4 chocolate bars, how many chocolate bars will be left over after they've eaten?
Answer:
1
Step-by-step explanation:
6 children that each want to eat half of a chocolate bar (0.5)
6 * 0.5 = 3 - chocolate bars will be eaten
They bought a package of 4 chocolate bars
4 - 3 = 1 - chocolate bar will be left
Landon is buying jerseys for his baseball team. He will pay $11 for each shirt, plus a one-time fee of $30 for the design. Which equation can be used to find y, the total cost to buy x shirts?
Answer:
The equation to find the total cost for buying x shirts would be y = 11x + 30
Step-by-step explanation:
The equation y = 11x + 30 represents the total cost of buying x jerseys, where x is the number of jerseys and y is the total cost. The $11 represents the cost of each jersey and the $30 is the one-time fee for the design. So, for every jersey purchased, the cost goes up by $11, and the $30 fee is added on top of that.
A train consists of 36 carriages. There were 1,400 passengers on the train. In every ten consecutive carriages, there will be 398 passengers How many passengers occupy 4 middle carriages of the train ?
Answer:
4 middle carriages have 162 passengers
Step-by-step explanation:
Since every 10 consecutive carriages have 398 passengers, then each carriage has 398/10 = 39.8 passengers.
Since there are 36 carriages in the train, then there are 36 * 39.8 = 1428 passengers in the train.
Therefore, there are 1400 - 1428 = -28 passengers missing.
This means that each carriage has 39.8 - (-28/36) = 39.8 + 0.78 = 40.58 passengers.
So, the 4 middle carriages have 4 * 40.58 = 162.32 passengers.
Rounding to the nearest whole number, we can say that 4 middle carriages have 162 passengers.
Answer:
192
Step-by-step explanation:
If a train with 36 carriages holds 1400 passengers, 398 in any 10 consecutive carriages, you want to know the number in the 4 middle carriages.
ModelThe first 30 carriages will hold 3·398 = 1194 passengers, so there must be 1400 -1194 = 206 in the remaining 6 carriages. The same would be true counting carriages from the other end.
Then the 10 +6 carriages at either end of the train must hold 398 +206 = 604 passengers. That leaves 1400 -2·604 = 192 passengers in the middle 4 carriages.
Math Journal At a county fair, a strip of 20 ride tickets costs $13. The manager thinks they should also sell a strip of 8 ride tickets. Describe how the manager can use a unit rate to decide on a fair price for the strip of 8 tickets.
Answer:
20/13=1.54
1.54*8=12.32
The manager can use the unit rate, the price of one ticket to find the price of 8 tickets by doing the steps above.
Step-by-step explanation:
Sam's biweekly paycheck is $1500. 1/2 of his paycheck is used to pay bills. 1/5 of his paycheck is deposited into his savings account. The remainder of his paycheck is used for food and entertainment. How much money does Sam have available for food and entertainment?
[tex]\stackrel{\textit{for bills}}{1500\cdot \cfrac{1}{2}}~~ + ~~\stackrel{\textit{for savings}}{1500\cdot \cfrac{1}{5}}~~ + ~~\stackrel{\textit{food and ET}}{x}~~ = ~~\stackrel{total}{1500} \\\\\\ 750+300+x=1500\implies 1050+x=1500\implies x=450[/tex]
Six percent commission on first $10,000. Eight percent commission over $10,000. Find the total graduated commission on $13,200.
An amount of $ 13,200 has a total comission of 856.
How to determine the total comission for an amount of money
Herein we find the case of the calculation of a comission for an amount of money, where an interest rate of six percent is applied for first $ 10.000 and an interest rate of eight percent is applied for the excedent above $ 10.000. The total comission is determined by following mathematical equation:
C = 10,000 · (6 / 100) + (13,200 - 10,000) · (8 / 100)
C = 856
The graduate must pay a total comission of $ 856 for an amount of $ 13,200.
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Jayden folded a 66 \text{ cm}66 cm66, start text, space, c, m, end text strip of paper into 666 equal parts to model a honeycomb cell. Each part was one side of the model.
What is the length of one side of the model?
The length of one side of the model is 0.099cm/part.After Jayden folded a 66 cm strip of paper into 666 equal parts to model a honeycomb cell.
Jayden created a model of a honeycomb cell by folding a 66 cm strip of paper into 666 equal corridor. By dividing the total length of the strip by the number of corridor.
The length of one side of the model can be calculated as follows:
66 cm / 666 = 0.099 cm/part
Thus,it means each side of the honeycomb cell model is roughly 0.099 cm long. This length was determined by Jayden by dividing the total length of the strip into 666 equal corridor, each part representing one side of the honeycomb cell.
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A group of students formed a circle during a game. The circumference of the circle was about 43.96 feet, and the diameter of the circle was 14 feet.
Which expression best represents the value of pi
In a case whereby A group of students formed a circle during a game. The circumference of the circle was about 43.96 feet, and the diameter of the circle was 14 feet the expression that best represents the value of pi is 43.96 feet/ 14 feet.
How can the value of pibe calculated?The concept that will be use here is Circumference. we were given Circumference of the circle as 43.96 feet
where the Diameter of the circle is 14 feet, then we can find the Circumference of the circle as( πd)
Then ( πd) = 43.96 feet
π= 43.96 feet/ 14 feet
Therefore, option C is correct.
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Tuga has 2⅔ pounds of sweet potatoes. She needs 40 ounces of sweet potatoes to make chili. Which statement explains if Tuga has enough sweet potatoes to
make chili? (1 pound = 16 ounces)
Answer:
Step-by-step explanation:
Convert pounds to ounces:
2[tex]\frac{2}{3}[/tex] = 2.667
2.667 lb x 16 oz/lb = 42.7 oz
42.7 > 40, therefore Tuga has enough sweet potatoes to make chili
Find the area of the triangle below. Be sure to include the correct unit in your answer. 24 ft 6 ft 15 ft
Answer:
72 [tex]ft^{2}[/tex]
Step-by-step explanation:
a = 1/2(24)(6)
a = 72
Stacy was a stay-at-home mom for most of her adult life. At age 46, she started working outside the home. Each year she earns the maximum number of Social Security credits. Until what age must she work to qualify to receive Social Security benefits when she retires?
The age that she must work till she is qualified to receive Social Security benefits when she retires is: 56 years
What is the timeframe for Social Security benefits?Social Security benefits provide partial replacement income for retired beneficiaries and disabled persons, as well as their spouses, children and survivors.
To be eligible for Social Security benefits, you must be enrolled in the Social Security program and accumulate 40 credits while employed.
Benefits are based on your income history, year of birth, and age at which you began applying for Social Security.
If your spouse is unemployed or has not reached the required number of credits, you can receive benefits according to your spouse's work performance.
Benefits may likely be taxed based on the specific income and tax return status.
She will be required to earn a total of 40 credits in order to qualify to be able to receive social security benefits, due to the fact that she earns the maximum number of 4 credits per year, she therefore has to work for at least a minimum of ten years or until at least she is 56.
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Solve this problem:
㏒₅₄168=?
If:
a = ㏒₇12
b = ㏒₁₂24
Answer:
㏒₅₄168 = (1+ab)/(8a-5ab)
Step-by-step explanation:
You want ㏒₅₄168 written in terms of a and b, where ...
a = ㏒₇12b = ㏒₁₂24Log expressionsThe rules of logarithms are relevant here:
[tex]\log_b(a)=\dfrac{\log(a)}{\log(b)}\\\\\log(ab)=\log(a)+\log(b)[/tex]
In order to simplify the writing in what follows, we want to define ...
p = log(2)q = log(3)r = log(7)Now, we can write the equations ...
a = log(12)/log(7) = (2p+q)/r . . . . . . . . . [eq1]
b = log(24)/log(12) = (3p+q)/(2p+q) . . . [eq2]
Using these, we can solve for p and q:
2p +q = ar . . . . . . . . . . . . . [eq3], from [eq1]
(3 -2b)p +(1 -b)q = 0 . . . . . [eq4] from [eq2]
Using your favorite solution method for linear equations, you find ...
p = ar(1 -b)/(2(1 -b) -(3 -2b)) = ar(1 -b)/(2 -2b -3 +2b) = ar(b -1)
q = (-ar(3 -2b)/(-1) = ar(3 -2b)
Desired logarithmSubstituting these expressions into ...
[tex]\log_{54}{168}=\dfrac{\log{(2^3\cdot3\cdot7)}}{\log{(2\cdot3^3)}}=\dfrac{3p+q+r}{p+3q}\\\\=\dfrac{3ar(b-1)+ar(3-2b)+r}{ar(b-1)+3ar(3-2b)}=\dfrac{3ab-3a+3a-2ab+1}{ab-a+9a-6ab}\\\\=\boxed{\log_{54}{168}=\dfrac{1+ab}{8a-5ab}}[/tex]
__
Additional comment
The calculator confirms the result.
If a² + a -½= 5 and a½ - a½ >0, calculate the value of (1) a+a¹
Answer:
we can find a + a^(1/2) by substitution:
a + a^(1/2) = 6/5 + √(6/5)
Step-by-step explanation:
We have the equation:
a² + a - 1/2 = 5
Adding 1/2 to both sides:
a² + a = 5 1/2
Factoring out a from the left-hand side:
a(a + 1) = 5 1/2
Taking the square root of both sides:
a + 1/2 = ±√(5 1/2 / a)
Since a^(1/2) - a^(1/2) > 0, we know that a is positive, so we can discard the negative root. Then we have:
a + 1/2 = √(5 1/2 / a)
Squaring both sides:
a² + a + 1/4 = 5 1/2 / a
Substituting the expression for a² + a from the first equation:
5 1/2 - 1/2 + 1/4 = 5 1/2 / a
Multiplying both sides by a:
5 1/2 a - 1/2 a + 1/4 a = 5 1/2
Simplifying:
5a - 1/2 = 5 1/2
Adding 1/2 to both sides:
5a = 6
Dividing by 5:
a = 6/5
Finally, we can find a + a^(1/2) by substitution:
a + a^(1/2) = 6/5 + √(6/5)
simplify
[tex]\frac{x^\frac{1}{5}x^\frac{2}{5} }{x^\frac{4}{5} }[/tex]
Answer:
Step-by-step explanation:
Since the base x is consistent with all terms of this complex fraction, all you need to do is add the two exponents found in the numerator and from that, subtract the exponent in the denominator.
This gives us x^(3/5) divided by x^(4/5), which is x^(-1/5). This gives 1/x^(1/5), which is 1 divided by the fifth root of x.
WILL MARK BRAINLIEST !!! please help and show work !!
Find the equation of the line passing through (1,5) and parallel to y = 3x - 1.
Answer:
Step-by-step explanation:
Finding an equation of a line can be condensed into 2 easy steps. Step one is to establish the basic form of the equation, including it's slope.
1) Lets use y=mx + b as the basic form, where m is the slope and b is the y-intercept (the value of y when x is zero). We are told the line is parallel to y = 3x - 1, which is a line with a slope (m) of 3. Parallel lines have the same slope, so our kline will also have a slope of 3, bringing us to:
y = 3x + b.
2) The second step is finding the value of b. We are told the line must go through point (1,5), so we need a value of b that will shift the line to (1,5). Easy: just enter this point in the equation we have so far: y = 3x + b:
y = 3x + b
5 = 3*(1) + b for point (1,5)
b = 2
The equation becomes y = 3x + 2
See the attached graph. [Extra credit]
The lines are parallel, and the y-intercept for the second line (b) is (0,2).
what percent of 3,000,000 is equal to 3,600,000?
Answer:
120%
Step-by-step explanation:
3,600,000 divided by 3,000,000, times 100 = 120%
So, 120% of 3,000,000 is equal to 3,600,000
Answer:
120 %
Step-by-step explanation:
To solve for this percentage problem, we set up an equation:
[tex]3,000,000 * \frac{x}{100} = 3,600,000[/tex]
[tex]30,000 * x = 3,600,000[/tex]
x = 120
A house is 32 feet wide and has a gable with rafters 22 feet long, excluding the part which projects below the eaves. Find the pitch of the roof, or the angles between the rafter and the horizontal.
The pitch of the roof is roughly 35.3 degrees, and the middle height of the roof is 19.3 feet.
What is Pythagoras theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship in Euclidean geometry between the three sides of a right triangle. It indicates that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides.
Here,
To find the pitch of the roof, we need to use the Pythagorean theorem to determine the height of the roof at the center. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).
In this case, the height of the roof at the center is the hypotenuse, and the two shorter sides are the width of the house (32 feet) and half of the length of the rafter (22 feet / 2 = 11 feet). So, using the Pythagorean theorem, we can set up the following equation:
h² = (32 / 2)² + 11²
h² = 16² + 11²
h² = 256 + 121
h² = 377
h = √377
h = 19.3 feet
Next, we use the tangent function to find the pitch of the roof. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the roof (19.3 feet), and the adjacent side is half of the rafter length (11 feet). So, we can set up the following equation:
tan(pitch) = 19.3 / 11
We can use the inverse tangent function (tan^-1) to find the angle, which will give us the pitch of the roof in degrees.
pitch = tan^-1(19.3 / 11)
The pitch of the roof is approximately 35.3 degrees and height of the roof at the center is 19.3 feet.
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i need help
solve for a
x = 4
-- All angles of a triangle add up to 180° --
-- the inverse of a trianglenis equal to its opposite angle of intersection--
1) build equation
180° = 20° + (4 + 6x) + (32x + 4)
2) solve
180-20 = 4 + 6x + 32x + 4
160 = 8 + 38x
152 = 38x
152/38 = x
x = 4
verify
180 = 20 + (4 + 6x) + (32x + 4)
180 = 20 + (28) + (132)
180 = 180 so x = 4
A truck that can carry no more than 5600 pounds is being used to transport refrigerators an upright pianos it refrigerator weighs 300 pounds in each piano weights 425 pounds write and graph an inequality to show how many refrigerators and how many pianos the truck carry. will nine refrigerators and eight pianos overload the truck?explain.
Since 6100 is greater than 5600, nine refrigerators and eight pianos would overload the truck.
What is linear inequality?
A linear inequality is an equation that represents a linear relationship between two variables and is used to describe a region of the coordinate plane that satisfies a given set of conditions.
Let "x" be the number of refrigerators and "y" be the number of pianos. The total weight of the refrigerators is 300 pounds per refrigerator, so the total weight of the refrigerators is 300x pounds. The total weight of the pianos is 425 pounds per piano, so the total weight of the pianos is 425y pounds. The total weight of the load must be less than or equal to 5600 pounds, so we can write an inequality as follows:
300x + 425y ≤ 5600
To graph this inequality, we can use the coordinates of points that satisfy the inequality and shade the region that represents the solutions.
To determine if nine refrigerators and eight pianos would overload the truck, we can substitute these values into the inequality and see if it still holds:
300 × 9 + 425 × 8 = 2700 + 3400 = 6100
Since 6100 is greater than 5600, nine refrigerators and eight pianos would overload the truck.
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What is the slope of the line shown below?
A. -2
B. -6
C. 2
D. 6
Answer:
Step-by-step explanation:
a-2
What is the inverse of the function f(x)=5x+7−−−−−√3?
Answer:
The inverse function can be written as:
g(x) = (x - 7 + √3) / 5
Step-by-step explanation:
Starting with the equation y = 5x + 7 - √3, we switch the roles of x and y to get x = 5y + 7 - √3.
Next, we isolate y by subtracting 7 and adding √3 to both sides, which gives x - 7 + √3 = 5y.
Finally, we divide both sides by 5 to get g(x) = (x - 7 + √3) / 5.
This is the inverse function g(x) of f(x) = 5x + 7 - √3. The inverse function is useful in solving problems where the original function is not explicitly invertible.
solve In (2x-3) = 1/2
Justice rents a car for a deposit of $50 and $20 a day. When he turns it in he owes $490. How many days did he have the car?
Justice had the rented car for 22 days, when the rent per day is $20 with $50 deposit.
What do we mean by rent?Rent is a periodic payment made by a tenant to a landlord in exchange for the use of land, building, apartment, office, or other property. A payment or series of payments made by a lessee to an owner in exchange for the use of machinery, equipment, etc.
According to the information in the question:
Deposit = $50
Rent cost per day for the car = $20
Total amount that Justice has to pay = $490
∴ Total number of days that Justice kept the car = (490 - 50)/20
= 440/20
= 22 days
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The number of days did he have the car are 22.5 days.
Explain about rent.a set monthly fee that you pay to utilise someone else's space, including their home, car, television, etc. Because my room is larger than the other renters', I pay a higher rent or more rent.
According to question:Justice rented a car for a deposit of $50 and a daily rate of $20. When he returned the car, he owed $490.
To find out how many days he had the car, we can set up an equation:
$50 + (number of days x $20) = $490.
Solving for the number of days: number of days = ($490-$50)/$20 = 22.5 days.
So Justice had the car for approximately 22.5 days.
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