Answer:
[tex]x \approx 729[/tex]
Step-by-step explanation:
Given
Let the number be x
So:
[tex]x + 10\sqrt x = 1000[/tex]
Required
Using trial and improvement, find x
This implies that we keep guessing the values of x until we get a value that match the equation.
Let
[tex]x = 625[/tex]
So, we have:
[tex]x + 10\sqrt x = 1000[/tex]
[tex]625 + 10 *\sqrt{625}[/tex]
Take the square root of 625
[tex]625 + 10 *\sqrt{625} = 625 + 10 *25[/tex]
[tex]625 + 10 *\sqrt{625} = 625 + 250[/tex]
[tex]625 + 10 *\sqrt{625} = 875[/tex]
Let
[tex]x = 729[/tex]
So, we have:
[tex]x + 10\sqrt x = 1000[/tex]
[tex]729 + 10 * \sqrt{729}[/tex]
Take the square root of 729
[tex]729 + 10 * \sqrt{729} = 729 + 10 * 27[/tex]
[tex]729 + 10 * \sqrt{729} = 729 + 270[/tex]
[tex]729 + 10 * \sqrt{729} = 999[/tex]
At this point, we can conclude that x is approximately 729 because
[tex]999 \approx 1000[/tex]
So:
[tex]x \approx 729[/tex]
The value of y varies directly with x. If x = 3, then y = 4. What is the value of x when y = 120 ?
Answer:
x = 90
Step-by-step explanation:
If x = 3 and y = 4 then when y = 120 just find out what times 4 = 120
which is 30.
so just multiply 30 for x = 3, then the answer will be 90
x = 90
Answer:
x=90
Step-by-step explanation:
x is directly proportional to y
Therefore, if the initial y value was 4 and the final y value is 120. This means that y initial had been multiplied 120/4 times, which is 30.
Same goes for x. If x initial is 3, then the final x value would be x/3=30. This means that x=3×30, which is equal to 90.
Just do the second one…
The L.C.M. defines the least number that is exactly divisible by two or more numbers, whereas the G.C.F. defines the greatest factor present between any given pair of two or more numbers.
What is the difference between LCM and GCF?LCM is also known as the Least Common Multiple (LCM), and HCF is also known as the Greatest Common Factor (GCF).
The highest common factor (HCF) between two or more numbers is two or more. The LCM, on the other hand, is the lowest common multiple that exactly divides these two figures. The greatest common factor between any two numbers is also known as HCF. Between two or more numbers, LCM is also known as Least Common Divisor.
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Given that K is the midpoint of segments RM and JL, and prove Δ RKJ ≅ Δ MKL.
Statements
Reasons
1. K is the midpoint of segments RM and JL
1. Given
2.
2.
3. and
3.
4. RK = MK and JK = LK
4. Definition of Congruent Segments
5. Δ EGF ≅ Δ EGH
5.
What is Reason #3?
a
Given
b
Definition of Midpoint
c
CPCTC
d
SSS Congruence Postulate
The complate table is,
Statement Reasons
1) K is the midpoint of segments Given
RM and JL.
2) RJ ≅ ML SSS Congruence Postulate
3) RK ≅ MK , JK ≅ LK Definition of Midpoint
4) RK = MK , JK = KL Definition of Congruence
Segments
5) Δ EGF ≅ Δ EGH CPCTC
What is Line segment?A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.
Given that;
K is the midpoint of segments RM and JL.
Now,
Since, K is the midpoint of segments RM and JL.
Hence, We get;
Statement Reasons
1) K is the midpoint of segments Given
RM and JL.
2) RJ ≅ ML SSS Congruence Postulate
3) RK ≅ MK , JK ≅ LK Definition of Midpoint
4) RK = MK , JK = KL Definition of Congruence
Segments
5) Δ EGF ≅ Δ EGH CPCTC
Thus, The complete table is shown above.
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Find BC. AB=24 AC=24 BD=15
Answer:
b) BC = 30
Step-by-step explanation:
triangle ACD is equal to ABC so BC = 2xBD = 30
Which body part is approximately 3 "heads" down from the top of the head
O Shoulder
B Belly Button
O Knees
O Ankles
B. Belly button
Step-by-step explanation:
It can't be knees or ankles because they are too far down, and shoulders are at head level
Isabella has already baked 4 pies, and she can bake 2 pies with each additional cup of sugar she buys. Write an equation that shows the relationship between the additional cups of sugar x and the number of pies y.
Answer:
It would be y = 2x+4
Step-by-step explanation:
This is because Isabella has started with 4 baked pies and is gaining additional pies with in amounts of 2 pies.
With this, 4 would be by itself and 2 would be attached to the variable x for the unknown amount of additional pies.
Lastly, you would have this all equaling y, as y is the total amount of pies.
Shelia works at the ice cream shop and makes $8.00 an hour during the day, and one and a half times that rate in the evening. Last week she worked 12 hours during the day and 6 hours at night. How much was her paycheck?
2. A jet travels 540 miles in 4.5 hours. At this
rate, how far could the jet travel in 11 hours?
a. 1,320 miles
b. 1,500 miles
c. 1,450 miles
de none of the above
Answer:
a
Step-by-step explanation:
Divide distance by time for speed per hour, that is
speed = 540 ÷ 4.5 = 120 mph
Then distance travelled in 11 hours
= 11 × 120 = 1320 miles → a
The brain volumes ?( cm cubed cm3?) of 20 brains have a mean of 1083. 9 1083. 9 cm cubed cm3 and a standard deviation of 122. 2 122. 2 cm cubed cm3. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such? data, would a brain volume of 1348. 3 1348. 3 cm cubed cm3 be significantly? high?
Therefore , the solution of standard deviation is because the value of 1452.2 cm3 does not fall between the range of 917.4 cm3 and 1422.2 cm3.
what is the standard deviation?Standard deviation, often known as variance in a set of data, is a statistical measure of variation. A low standard deviation indicates that the values are more likely to be near the mean of the collection, whereas a high standard deviation indicates that the values are widely distributed. How far the data depart from the mean is expressed by the standard deviation, abbreviated as.
Here,
Considering the details here,
The average brain volume is 1169.8 cm3, while the standard deviation is 126.2 cm3.
The much lower results are u-2 = 11169.8-2(126.2) => 917.4.
Reason: According to the range rule of thumb, the required incredibly low values are 91.7 cm3 or less.
Hint: Use the algorithm to identify values that are at least considerably high.
Step: 2
Considering the data supplied,
The average brain volume is 1169.8 cm3, while the standard deviation is 126.2 cm3.
Significantly higher values include,
u-2α = 11169.8+ 2(126.2)
=> 1422.2
Justification: According to the range rule of thumb, the necessary significantly high values must be 1422.2 cm3 or higher.
Hint: To determine whether the value 1452.2 cm3 is very high, use the findings of steps (1) and (2).
Step: 3
Using step 1 and step (4),
917.4 is among the significantly low numbers or less.
The significantly high values are 1422.2 or higher.
Yes, 1452.2 cm3 is a noticeably high value.
The apt response is choice (B).
Reason: The value is much higher than expected based on the range rule of thumb because the value of 1452.2 cm3 does not fall between the range of 917.4 cm3 and 1422.2 cm3.
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lemme know ——————————-
Answer:
121
Step-by-step explanation:
180 - (56 + 65) = 59
180 - 59 = 121
what are the missing lengths?
Answer:
U can find it using Cos 60 degree
Pleas help me with #2, thanks
Stefan sells Jin a bicycle for $146 and a helmet for $19. The total cost for Jin is 150% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Stefan spend price $110 and made price $60 by selling bicycle and helmet to Jin.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Here, given that,
Selling price of bicycle = $146
Selling price of helmet = $19
Total = 146+19= $165
Let,
x represents the original cost Stefan to buy the bike and helmet.
150% of x = $165
1.5x=$165
Dividing both sides by 1.5
we get ,
x=$110
Stefan bought bicycle and helmet for $110.
Profit made by Stefan = Selling price - buying price
Profit made by Stefan = 165-110= 55
Hence, Stefan spend price $110 and, made $55 by selling bicycle and helmet to Jin.
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PLEASE HURRY!!
Find the value of x
Answer:
Step-by-step explanation:
3x=24
x=8
Riley's dentist has an aquarium in his office with the dimensions 16 in. By 8.5 in. By 10.5 in. What is the volume of the aquarium?
Answer:
1428
Step-by-step explanation:
I did 16 times 8.5 times 10.5. Good Luck!
Jessica has eaten 3 1/2 hot dogs of the 10 hot dogs she
recently found in her freezer. What percent of the hot
dogs has she eaten?
Answer:
65%
Step-by-step explanation:
100%-> 10
1%->0.1
----------------------------
10 - 3 1/2 = 6 1/2
6 1/2 ÷ 0.1 = 65
Dale has $1,000 to invest. He has a goal to have $2,400 in this investment in 12 years. At what annual rate compounded continuously will Dale reach his goal?
Answer:
7.29%
Step-by-step explanation:
Given data
Principal= $1,000
Final amount= $2,400
TIme= 12 years
The expression for the compound interest is given as
A= P(1+r)^t
Make r subject of fomula
r = ln(A/P) / t
r= ln(2400/1000)/12
r= ln(2.4)/12
r= 0.875/12
r= 0.0729
Hence the rate is 7.29%
For what value of a the system of equations Ax Y 2 and 6x 2y 3 has a unique solution?
A = 1, y = -2/3, The value of a for which the system of equations has a unique solution is a = -3.
1. Set the first equation equal to 0:
2x + ay = 2
2. Subtract 2x from both sides of the equation to get:
ay = -2
3. Divide both sides of the equation by a to get:
y = -2/a
4. Substitute this value of y into the second equation to get:
6x + 3(-2/a) = 3
5. Multiply both sides of the equation by a and simplify to get:
6ax - 6 = 3a
6. Add 6 to both sides of the equation to get:
6ax = 3a + 6
7. Divide both sides of the equation by 6 to get:
x = (3a + 6)/6
8. The value of a for which the system of equations has a unique solution is a = -3.
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Mila cuts a sphere with a 13-inch radius in half. Whats the area of the cross section of the sphere in square inches in terms of pi
The area of the cross-section of the sphere in square inches in terms of pi will be 169π inch^2.
The area of a two-dimensional shape created when a three-dimensional object, like a cylinder, is cut perpendicular to a predetermined axis at a point is known as the cross-sectional area.
An area is projected onto the plane when a plane slices through a solid object. The axis of symmetry is then perpendicular to that plane. The cross-sectional area refers to its projection.
The cross-section of a sphere is a circle. Hence the area of the cross-section is the area of a circle with a radius of 13, which is given by π*r^2
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Nick mowed about 3.5 of the school lawn yesterday. He mowed another 1/4 of the lawn this morning. How much is left to mow? Answer if you can.
The portion left to mow is 3x+3.5 /4
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here:Nick mowed about 3.5 of the school lawn yesterday. He mowed another 1/4 of the lawn this morning. Let the whole lawn be x then on the first day portion left to be mowed is x-3.5 and on the second day he moved 1/4 of this quantity thus portion of lawn left to be mowed is
x-x-3.5/4
=3x+3.5 /4
Hence, The portion left to mow is 3x+3.5 /4
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Please enter the missing number: 4, 8, 14, 22, ?
A. 26
B. 28
C. 32
D. 36
E. 40
Answer:
C) 32
Explanation:
it's adding by 4, 6, 8, and then 10; 22 + 10 = 32, so C will be the answer.
Hope this helps!
Activity 1.1 Simplify Me Simplify by removing perfect nth powers: 1. √20 2. √300 3. √128 3 4. √ 5 3 5. √50 3
Answer:
[tex](a)\ \sqrt{20}=2\sqrt{5}[/tex]
[tex](b)\ \sqrt{300} = 10 \sqrt{3}[/tex]
[tex](c)\ \sqrt{128} = 8 \sqrt{2}[/tex]
Step-by-step explanation:
Required
Simplify
[tex](a)\ \sqrt{20}[/tex]
Express 20 as 4 * 5
[tex]\sqrt{20}=\sqrt{4 * 5}[/tex]
Split
[tex]\sqrt{20}=\sqrt{4} * \sqrt{5}[/tex]
This gives:
[tex]\sqrt{20}=2 * \sqrt{5}[/tex]
[tex]\sqrt{20}=2\sqrt{5}[/tex]
[tex](b)\ \sqrt{300[/tex]
Express as 100 * 3
[tex]\sqrt{300} = \sqrt{100} * \sqrt{3}[/tex]
This gives:
[tex]\sqrt{300} = 10 * \sqrt{3}[/tex]
[tex]\sqrt{300} = 10 \sqrt{3}[/tex]
[tex](c)\ \sqrt{128}[/tex]
Express as 64 * 2
[tex]\sqrt{128} = \sqrt{64*2}[/tex]
Split
[tex]\sqrt{128} = \sqrt{64} * \sqrt{2}[/tex]
[tex]\sqrt{128} = 8 * \sqrt{2}[/tex]
[tex]\sqrt{128} = 8 \sqrt{2}[/tex]
Questions 4 and 5 are not clear
Follow the steps in 1 - 3 to solve 4 and 5
Which of the following numbers is closest to 7?
Answer:
B. √50
Step-by-step explanation:
[tex]7^{2}[/tex] is 49 so √49 is 7
So,
since the closest number to 49 is 50, that is the answer.
[tex]\sqrt{51}[/tex] is the closest square root to 7.
What is square root?The square root of a number is defined as the value, which gives the number when it is multiplied by itself. The radical symbol √ is used to indicate the square root. If a number is a perfect square, we can easily find the square root of the number. If the given number is not a perfect square number, the square root can be found using the long division method.
[tex]\sqrt{51} = 7.141\\\sqrt{50} = 7.071\\ \sqrt{46} = 6.782\\ \sqrt{47} =6.855[/tex]
(using calculator)
Absolute distance from 7 :
|7.141 - 7| = 0.141
|7.071 - 7| = 0.71
|6.782 - 7| = 0.218
|6.855 - 7| = 0.145
(The absolute value of a number refers to the distance of a number from the origin of a number line. It is represented as |a|, which defines the magnitude of any integer ‘a’. The absolute value of any integer, whether positive or negative, will be the real numbers, regardless of which sign it has. It is represented by two vertical lines |a|, which is known as the modulus of a.)
Since, 0.141 is the least distance. [tex]\sqrt{51}[/tex] is the closest square root to 7.
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What is the measure, in degrees, of ZA?
Answer:
28
Step-by-step explanation:
2x + 3x + 40 =180
5x= 180 - 140
5x=140
x= 28
Answer:
Step-by-step explanation:
We know that the sum of interior angles of a triangle is 180° so we can say:
40 + 2x + 3x = 180°
40 + 5x = 180°
5x = 140°
x = 28°
Now substitute in 28 for the value of x in Angle A:
=> 2x would become 2(28)
=> 56° = ∠A
Hope this helps!
In ΔOPQ, the measure of ∠Q=90°, the measure of ∠P=76In ΔOPQ, the measure of ∠Q=90°, the measure of ∠P=76°, and PQ = 4. 1 feet. Find the length of OP to the nearest tenth of a foot. °, and PQ = 4. 1 feet. Find the length of OP to the nearest tenth of a foot
The length of OP to the nearest tenth of a foot is 16.9 ft
What is a right-angle triangle?
It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
ΔOPQ is right triangle
Tan (p) = opposite/adjacent = OQ/PQ
Tan (76) = OQ/4.1
4.010 = OQ/4.1
OQ = 4.010 * 4.1 = 16.441
OP² = OQ² + PQ² = 16.441 ² + 4.1² = 287.116
=> OP = √ 287.116 = 16.944
OP≅ 16.9 ft
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A school plans to spend twice the amount it did last year on its winter dance, less the cost of the disco ball which was $150, since they have it from last year. A total of $1,500 is being spent this year. Fill in the blanks to write an equation that will determine the amount of last year’s budget, a.(2 points)
__(a −__) = __
Equation that will determine the amount of last year’s budget
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that a school plans to spend twice the amount it did last year on its winter dance , less the cost of the disco ball which was $150 since they have it from last year
A total of $1,500 is being spent this year.
We need to find the equation which determine the amount of last year’s budget
2a-150=1500
When a is the amount of last year’s budget
Hence, 2a-150=1500 is the equation that will determine the amount of last year’s budget
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PLEASE HELP ME ASAP!!!!!!!
At a carnival, Diana sees a balloon shooter game. The ticket cost is $3. The rule is that the first person to shoot 10 balloons from a total 30 balloons wins $10. What is the expected payoff for the winner?
Answer:
$13
Step-by-step explanation:
The expected payoff for the winner would be the ticket cost, $3, plus the prize money, $10, which totals $13. This is the expected value of playing the game. However, it's important to note that this does not guarantee that the winner will receive exactly $13, as the outcome of the game is dependent on chance and the player's skill. There is always a chance that the player could win more or less than the expected value.
(sin 9x)'
what is the derivative of sin 9x
Answer:
[tex]\displaystyle \frac{d}{dx}[\sin(9x)] = 9 \cos(9x)[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \sin(9x)[/tex]
Step 2: Differentiate
Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = \cos(9x)(9x)'[/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle y' = 9 \cos(9x)(x)'[/tex]Basic Power Rule: [tex]\displaystyle y' = 9 \cos(9x)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
What is the area of the first triangle?
Answer:
1/2 foot
Step-by-step explanation:
1 x 1 = 1
1/2 = 1/2
Write the explicit formula for the sequence below:
The explicit formula for the sequence will be an = 10 + 5n. The correct option is C.
What is arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed as the arithmetic progression.
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.
Given series is 15,20,25,30,...,
The common difference is d = 20 - 15 = 5
First term is, 15
The formula can be written as,
an = a₁ + d(n-1)
an = 15 + 5 ( n - 1 )
an = 15 + 5n - 5
an = 10 + 5n
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