It should be noted that the value on the blank on the equation will be -2.
How to solve the equationThe equation given is:
2(4x+1) + 8 = 4(2x+1) + 8 - x
Simplifying the left-hand side:
8x + 2 + 8 = 8x + 4 + 8 - x
Simplifying the right-hand side:
8x + 4 + 8 - _ = 8x + 12 - x
Combining like terms on both sides:
8x + 10 = 8x + 12 - x
Subtracting 8x from both sides:
10 = 12 - x
x = 10 - 12
x = -2
The value will be -2 to make the equations equal.
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Use the Triangle Angle Sum Theorem to find the measure of the angle on point C.
(1 point)
Answer:
m∠4 = 133°
Step-by-step explanation:
Given m∠7 = 37°
Since m∠7 ≅ m∠6 [Vertically opposite angles]
and m∠6 + m∠4 = 180° [Sum of interior angles formed by parallel lines l, m and transverse.]
Therefore, 47°+ m∠4 = 180°
m∠4 = 180 - 47
= 133°
Write the prime factorization of each number as a product of powers.
(a) 12^9 · 36^15 · 169^8
(b) 16^13 · 10^7 · 81^18
By answering the above question, we may state that Multiplying these equation prime factorizations together, we get:
[tex]16^13 * 10^7 * 81^18 = (2^52) * (2^7 * 5^7) * (3^72) = 2^59 * 3^72 * 5^7[/tex]
What is equation?A math equation is a mechanism for connecting two claims by using the equals sign (=) to indicate equivalence. A mathematical statement that establishes the equivalence of two mathematical expressions is known as an equation in algebra. The equal symbol, for example, splits the numbers 3x + 5 and 14. A mathematical formula can be used to describe the relationship between two phrases written on opposite sides of a letter. The logo and programme are frequently the same. 2x - 4 Equals 2, for example.
then multiply the prime factors together using the laws of exponents.
[tex]12^9 = (2^2 · 3)^9 = 2^18 · 3^9\\36^15 = (2^2 · 3^2)^15 = 2^30 · 3^30\\169^8 = 13^16\\12^9 · 36^15 · 169^8 = (2^18 · 3^9) · (2^30 · 3^30) · 13^16 = 2^48 · 3^39 · 13^16\\[/tex]
(b)
[tex]16^13 = 2^52\\10^7 = 2^7 · 5^7\\81^18 = (3^4)^18 = 3^72\\[/tex]
Multiplying these prime factorizations together, we get:
[tex]16^13 * 10^7 * 81^18 = (2^52) * (2^7 * 5^7) * (3^72) = 2^59 * 3^72 * 5^7[/tex]
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mp of a book is rs. 250 if the shopkeeper allows 14% discount to his customers and gains 25% . find the cp.
The cost price that was used to get the book is: R.S 172
How to find the cost price?The parameters given are:
Marked Price: M.P = RS. 250
Discount allowed = 10%
The formula to find the selling price here will be:
S.P = M.P * (100 - Discount)/100
Thus:
S.P = 250 * (100 - 14)/100
S.P = 250 * 0.86
S.P = R.S 215
Since the profit is 25%, then we have:
Cost Price = (S.P * 100)/(100 + Gain%)
Cost price = (215 * 100)/(100 + 25)
Cost Price = 21500/125
Cost price = R.S 172
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ackrabbits are capable of reaching speeds up to 40 miles per hour. How fast is this in feet per second? (Round to the earest whole number.)
5,280 feet = 1 mile
Answer:
Therefore, ackrabbits can reach speeds of approximately 59 feet per second.
Step-by-step explanation:
First, we need to convert miles to feet:
40 miles/hour * 5,280 feet/mile = 211,200 feet/hour
Then, we need to convert hours to seconds:
1 hour = 60 minutes/hour * 60 seconds/minute = 3,600 seconds/hour
211,200 feet/hour / 3,600 seconds/hour = 58.67 feet/second
Rounding to the nearest whole number, we get:
59 feet/second
Therefore, ackrabbits can reach speeds of approximately 59 feet per second.
A body of mass m falling through a viscous medium encounters a resisting force proportional to the square of its instantaneous velocity. In this situation the differential equation for the velocity v(t) at time t is dv CV Where k is a positive constant of proportionality. Solve the equation subject to r(0) V., what is the limiting velocity of the falling body?
The solution to the differential equation is:
$$v(t)=\frac{V_0+kCe^{-Ct}}{1+kCe^{-Ct}}$$
Where $V_0$ is the initial velocity and $C$ is the proportionality constant. The limiting velocity of the falling body as $t \to \infty$ is: $$v_{\infty}=\frac{V_0}{1+kC}$$
The instantaneous velocity of an object is the limit of the average velocity as the elapsed time approaches zero, or the derivative of x with respect to t: v ( t ) = d d t x ( t ) . v ( t ) = d d t x ( t ) . Like average velocity, instantaneous velocity is a vector with dimension of length per time.
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Find the value of x. I’ll give the brainliest.
Answer:
8.09017
calculations
Wyatt bought stock in a company two years ago that was worth x dollars. During the
first year that he owned the stock, it increased by 37%. During the second year the
value of the stock increased by 29%. Write an expression in terms of a that
represents the value of the stock after the two years have passed.
x
A
Answer:
Therefore, the expression that represents the value of the stock after the two years have passed in terms of x is:
A = 1.7673x
How precisely are stocks chosen?By dividing the number of shares they possess by the total number of outstanding shares and multiplying the result by 100, stockholders can calculate their ownership stake in a corporation.
After the first year, the value of the stock increased to:
x + 0.37x = 1.37x
After the second year, the value of the stock increased to:
1.37x + 0.29(1.37x) = 1.37x + 0.3973x = 1.7673x
Therefore, the expression that represents the value of the stock after the two years have passed in terms of x is:
A = 1.7673x
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Which statement correctly compares the spreads of the distributions?
A. The interquartile ranges (IQRs) are the same,
® 3. The range of team B's scores is greater than the range of team As
scores
C. The interquartile range (IQR) of team B's
scores is greater than IQR
of team A's scores.
D The interquartile range (IQR) of team As scores is greater than S IQR
of team Bs scores
After answering the provided question, we can conclude that C. The expression interquartile range (IQR) of team B's scores exceeds that of team A's scores.
what is expression ?An expression in mathematics is a collection of representations, digits, and huge corporations that represent a statistical correlation or fitness regime. A square root, a mutable, or a combo of the two can be used as an expression. Mathematical operators include addition, basic arithmetic, rapid spread, polarisation, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
We can see from the box plots in the image that the box plot for team B is wider than the box plot for team A, indicating that team B has a wider range of scores. As a result, the correct statement comparing the distribution spreads is:
C. The interquartile range (IQR) of team B's scores exceeds that of team A's scores.
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Using Pythagoras' theorem, calculate the length of the hypotenuse in this right- angled triangle. Give your answer in centimetres (cm) to 1 d.p. 2 cm 1.5 cm
Answer:
2.5 cm
Step-by-step explanation:
In any right triangle, the formula [tex]a^2+b^2=c^2[/tex] can be used to find its side lengths.
Given the side lengths,
[tex]a = 2 \\b = 1.5\\\\2^2+1.5^2=c^2\\4+2.25=c^2\\6.25=c^2\\c=\sqrt{6.25}\\c=2.5[/tex]
seppect you are a news fesorter following ten oriminal srials (a) It the bras wten in Jagat, what is the probebsty that al the defendants would be found guity? (found your ansmer to three deomal place
The probability of all the defendants being found guilty is 1/16. Answer: 1/16.
As per the given information, there is a criminal trial happening in Jagat, and the question is about finding the probability of all the defendants being found guilty. Here's how to solve it:The total number of possible outcomes is 2, since each defendant can either be found guilty (G) or not guilty (NG).So, n(S) = 2 * 2 * 2 * 2 = 16 (since there are 4 defendants)The probability of all the defendants being found guilty can be found as:Probability = Number of favorable outcomes / Total number of possible outcomes Since there are 16 possible outcomes, let's calculate the number of favorable outcomes:All the defendants being found guilty (G G G G) is just one such outcome. Hence, the number of favorable outcomes is 1.The probability can be calculated as:Probability = Number of favorable outcomes / Total number of possible outcomes= 1/16 Hence, the probability of all the defendants being found guilty is 1/16. Answer: 1/16.
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Please answer quick will give 60 points
Answer: Answers below
Step-by-step explanation:
1. $15.64
2. 5370.28 Yen
3. 13425.70 Yen
4. $100
5. 67128.51 Yen
6.$782.08
Answer: 1: 15 2: 5370 3:13400 4: 160 5: 67100 6: 780
Step-by-step explanation: These are rounded to the nearest 100th
help please i really appreciate it
Answer:
B linear
Step-by-step explanation:
If the rate of change stayed the same then it has to be a straight line so no C or D, and it cant be A be cause there is a rate of change.
an area rug has a length of 8 feet in the width of 5 feet. What is the diagonal distance across the rug?
We can use the Pythagorean theorem to find the diagonal distance across the rug. According to the theorem, the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side (the hypotenuse).
In this case, the length and width of the rug form the two shorter sides of a right triangle, and the diagonal distance is the hypotenuse. So we can use the formula:
diagonal^2 = length^2 + width^2
Plugging in the values given in the problem, we get:
diagonal^2 = 8^2 + 5^2
diagonal^2 = 64 + 25
diagonal^2 = 89
To solve for the diagonal, we take the square root of both sides:
diagonal = sqrt(89)
Using a calculator, we get:
diagonal ≈ 9.43 feet
Therefore, the diagonal distance across the rug is approximately 9.43 feet.
ion using long division or synthetic division. ks on the back to complete the story. (x^(4)+x^(3)-8x^(2)-13x-7)-:(x+2)
Using synthetic division, you can solve the following equation: (x^(4)+x^(3)-8x^(2)-13x-7)-:(x+2).
Step 1: Write down the coefficients of the polynomial in the top row of the synthetic division table.
x^(4) x^(3) -8x^(2) -13x -7
Step 2: Write the divisor in the left-most column.
x+2
Step 3: Bring down the first coefficient of the dividend and write it in the second row of the table.
x^(4) x^(3) -8x^(2) -13x -7 | x+2
x^(3) -8x^(2) -13x -7
Step 4: Multiply the divisor by the number in the second row and write it in the third row.
x^(4) x^(3) -8x^(2) -13x -7 | x+2
x^(3) -8x^(2) -13x -7 | x+2
x^(2) -15x -19
Step 5: Subtract the third row from the second row and write it in the fourth row.
x^(4) x^(3) -8x^(2) -13x -7 | x+2
x^(3) -8x^(2) -13x -7 | x+2
x^(2) -15x -19 | x+2
-7x -26
Step 6: Bring down the next coefficient in the first row and repeat steps 4 and 5.
x^(4) x^(3) -8x^(2) -13x -7 | x+2
x^(3) -8x^(2) -13x -7 | x+2
x^(2) -15x -19 | x+2
-7x -26 | -7
-22
Step 7: Multiply the divisor by the number in the fourth row and write it in the fifth row.
x^(4) x^(3) -8x^(2) -13x -7 | x+2
x^(3) -8x^(2) -13x -7 | x+2
x^(2) -15x -19 | x+2
-7x -26 | -7
-22 | -14
Step 8: Subtract the fifth row from the fourth row and write it in the sixth row.
x^(4) x^(3) -8x^(2) -13x -7 | x+2
x^(3) -8x^(2) -13x -7 | x+2
x^(2) -15x -19 | x+2
-7x -26 | -7
-22 | -14
8
Step 9: The final answer is: (x^(4)+x^(3)-8x^(2)-13x-7)/(x+2) = x^3-7x^2-15x-26 + 8/(x+2).
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What is the scale factor? x 33 km 44 km 16 km
Answer:
I hope this explains it!
Step-by-step explanation:
1. Select which conversion approach you wish to use:
a. Convert from actual (real) size to scale.
b. Convert from scale to actual (real) size.
2. Enter the scale factor; for example, if you wish to work with a 1/6th scale, input 6.
3. Enter the dimensions of the actual object (or measurements of the scaled object if you are planning on converting a scale to an actual size)
4. Select the unit of measurement from the drop-down list
5. Click on the "Convert" button to generate the results.
What type of sampling is used to conduct a study on depression among the elderly, a sample of 30 patients in one nursing home was used
The type of sampling used to conduct a study on depression among the elderly is convenience sampling, which is a type of non-probability sampling technique where samples are selected because they are conveniently available and accessible, and the sample size for this study was calculated to be 30.
The type of sampling used to conduct a study on depression among the elderly is convenience sampling. Convenience sampling is a type of non-probability non-probability where samples are selected because they are conveniently available and accessible .
In this study, a sample of 30 patients in one nursing home was used for the convenience sampling. The formula for calculating the sample size for convenience sampling is [tex]N = (N1*N2)/(N1+N2[/tex]), where N is the sample size, N1 is the population size, and N2 is the desired sample size. In this case, N1 is the total number of elderly patients in the nursing home, and N2 is 30. Therefore, the sample size for this study is calculated as follows: [tex]N = (N1*30)/(N1+30) = 30[/tex].
Convenience sampling is a quick and easy way of obtaining a sample, but it can be biased due to the presence of sampling errors and selection bias. Sampling errors occur when the sample is not representative of the overall population, while selection bias occurs when certain groups of people are more likely to be included in the sample than others. Therefore, it is important to consider the potential sources of bias when conducting a study using convenience sampling.
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Last week Steve spent $22 on 4 ice cream cones. This week he spent $33 on 6 ice cream cones. If each ice cream cone costs the same amount of money, what is the constant of proportionality (unit rate) between the money spent and the number of ice cream cones bought?
We may infer that the constant of proportionality (unit rate) between the amount spent and the quantity of ice cream cones purchased is $5.50 per cone because the unit rate is the same for both weeks.
The unit rate, or constant of proportionality, between the amount spent and the quantity of ice cream cones purchased is $5.50 per cone.
We divide the total sum by the quantity of cones purchased to determine the unit rate.
The unit rate for last week is: $22 x 4 cones = $5.50 per cone.
The unit price for this week is: $33 divided by six cones, or $5.50 each cone.
We may infer that the constant of proportionality (unit rate) between the amount spent and the quantity of ice cream cones purchased is $5.50 per cone because the unit rate is the same for both weeks.
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What is the value of x?
Therefore , the solution of the given problem of triangle comes out to be x = 15 .
What is a triangle exactly?A triangular is a polygon because it has two or maybe more additional sections. It has a straightforward rectangular form. A, B, and C are the only three sides that set a triangle apart from a simple triangle. When the boundaries are not exactly collinear, Euclidean geometry results in a singular area instead of a cube. If a shape has three edges and three angles, it is said to be triangular.
Here,
Triangle ABC ,
=> x /5 = x-6/3
=> 3x = 5x - 30
=> 2x = 30
=> x = 30/2
=> x = 15
Therefore , the solution of the given problem of triangle comes out to be x = 15 .
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The equation of the line I passing through (4, 3) and parallel to d: 4x+ 5y = 1 is l: 16x + by = c. What is the value of b?
Answer:
I guess the value be 26x
hope it helps u
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Help pleaseee struggling!
Answer: The distance from the ball to the goal is 11.86 ft.
Step-by-step explanation:
Answer:
≈ 11.9 feet
Step-by-step explanation:
A right rectangular container is 10 cm wide and 24 cm long and contains water to a depth of 7cm. A stone is placed in the water and the water rises 2. 7 cm. Find the volume of the stone
The volume of the stone is 1032 cm³.
The volume of the stone can be calculated using the formula V = lwh. Here, l = 10 cm, w = 24 cm, and h = 2.7 cm. Therefore, the volume of the stone is V = 10 x 24 x 2.7 = 648 cm³.
The volume of the water in the container is calculated using the formula V = lwh. Here, l = 10 cm, w = 24 cm, and h = 7 cm. Therefore, the volume of the water in the container is V = 10 x 24 x 7 = 1680 cm³.
The difference between the volume of the water and the volume of the stone is the volume of the water displaced by the stone, which is V = 1680 - 648 = 1032 cm³. Therefore, the volume of the stone is 1032 cm³.
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Keith earns $42.00 in 4 hours. How much would he earn in 11 hours?
Answer:
115.50
Step-by-step explanation:
Divide 42/4 to find his hourly rate, then multiply the hourly rate by 11, to get 115.50
Answer:
$115.05
Step-by-step explanation:
If he earns $42 in 4 hours than he earns $10.05 in 1 hour
42 / 4 = 10.5
10.5 x 11 = 115.5
Eli stands on the balcony of a tall building and throws a tennis ball straight up at a speed of 14 m/s. He releases the tennis ball at a height of 60m from the ground. In parts a through c, round your answer to the nearest hundredth.
A) When does the tennis ball hit the ground?
B) When does the tennis ball pass the point from which it was released?
C) What is the maximum height reached by the ball?
a) The basic formula is [tex]y=v_0t-gt^2/2[/tex]
[tex]9.81m/sec^2 x \ t^2 - (14 m/sec x t) - 60m = 0[/tex]
quadratic equation t= -b+/- √b^2-4ac /2a
t= 14+- √(-14)^2 -4(4.905)(-60)/ 2(4.905) = 5.20 sec
b) [tex]y=v_0t-gt^2/2[/tex]
At max height H, [tex]V_y = 0[/tex]
[tex]Vy^2 = V^2_{0y} - 2g(y-y_0)[/tex]
[tex]0=(14)^2 -2(9.81)(H-60)[/tex]
[tex]H=70m[/tex]
The ball would fall 10m from max height of 70m. set y=0 and H=10m
[tex]y=gt^2/2+H, t = 1.42 \ sec[/tex].
[tex]\bold{Therefore, 5.2 - 1.42 = 3.77 \ sec}[/tex]
The table above shows the changes in a country's labor force the increase in the rate of unemployment from 2000 to 2001 is between?
pleasee helppp
The increase in the rate of unemployment from 2000 to 2001, given the unemployment figure is between D. 0. 46 % and 0. 49 %.
How to find the increase in unemployment ?First, find the rate of unemployment in 2000 to be :
= Unemployment number / Total labor force x 100 %
= 3, 503, 917 / 25, 554, 417 x 100 %
= 13.71 %
The rate of unemployment in 2001 was :
= 3, 745, 300 / 26, 416, 800 x 100 %
= 14. 18 %
The increase in the rate of unemployment is:
= 14. 18 - 13. 71
= 0. 47 %
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A coffe can is 8 inches high and has a diameter of 6 inches. What isvthe volume of the coffe can rounded to the nearest 10th of a decimal place
The volume of the coffee can rounded to the nearest 10th of a decimal place is 226. 08 cubic inches
How to determine the volumeIt is important to note that the coffee can takes the shape of a cylinder.
The formula for calculating the volume of a cylinder is expressed with the equation;
V = πr²h
This is so as the parameters are enumerated thus;
V is the volume of the cylinderPie (π) takes the constant value of 3.14 or 22/7r is the radius of the cylinderh is the height of the cylinderAlso, r = diameter/2 = 6/2 = 3 inches
From the information given, we have that;
Volume = 3.14 × (3)² × 8
Multiply the values
Volume = 226. 08 cubic inches
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The relationship between the volumes of pyramids and prisms is that when a prism and pyramid have the same base and height, the volume of the pyramid is
the volume of the prism
The relationship between the volumes of pyramids and prisms is that when a prism and pyramid have the same base and height, the volume of the pyramid is the volume of the prism. This statement is not correct.
When a pyramid and a prism have the same base and height, the volume of the pyramid is one-third ([tex]\frac{1}{3}[/tex]) the volume of the prism.
This can be seen from the formula for the volume of a rectangular prism, which is:
[tex]The volume of the prism = base area x height[/tex]
And the formula for the volume of a rectangular pyramid is:
The volume of the pyramid = [tex]\frac{1}{3}[/tex] x base area x height
Since the base area and height of the pyramid and prism are the same, we can compare their volumes by dividing the volume of the pyramid by the volume of the prism:
[tex]\frac{The volume of pyramid}{Volume of prism}[/tex] = [tex]\frac{1}{3}[/tex] x base area x height/base area x height
Simplifying this expression, we get:
[tex]\frac{The volume of pyramid}{Volume of prism}[/tex] = [tex]\frac{1}{3}[/tex]
Therefore, the volume of a pyramid with the same base and height as a prism is one-third [tex](\frac{1}{3})[/tex] the volume of the prism.
The complete question is:-
The relationship between the volumes of pyramids and prisms is that when a prism and pyramid have the same base and height, the volume of the pyramid is the volume of the prism. True/False.
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At an ice cream shop, the cost of 4 milkshakes and 2 ice cream sundaes is $23.50. The cost of 8 milkshakes and 6 ice cream sundaes is $56.50.
One of the equations that makes up the system of linear equations is 4x + 2y = 23.50.
What is the second equation?
Answer: 8x + 6y = $56.50
Step-by-step explanation:
I think this is right!
Give the factors of the question above. Ex: (h-?)(h+?)
Answer:
(3h+4)(2h+3)
Step-by-step explanation:
6h^2 + 8h + 9h + 12h
(6h^2+8h) + (9h+12h)
2h(3h+4) + 3(3h+4)
(3h+4)(2h+3)
Answer:
(3h+4) (2h+3)
Step-by-step explanation:
i hope this helps
The ratio t:m is 3:8 and the ratio m:w is 4:7. Work out the ratio t:m:w in its simplest form.
The value of the ratio t:m:w in its simplest form is 3:8:28.
Ratio Problem: Simplifying t:m:wTo simplify the ratio t:m:w, we need to find the common factor between t, m, and w.
Using the given ratios, we can write t:m:w as (3x):(8x):(28y), where x is the common factor between t and m and y is the common factor between m and w.
From the given ratio t : m = 3:8, we can say that t is equal to 3 and m is equal to 8.
Similarly, from the given ratio m:w = 4:7, we can say that m is equal to 4 and w is equal to 7.
So, we have
t : m = 3:8 and m:w = 4:7
Multuiply second by 2
t : m = 3:8 and m:w = 8:14
So, we have
t : m : w = 3 : 8 : 14
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What is 1/10 the value of 6 in 46.12
Answer:
The digit 6 in 46.12 is in the tenths place. Therefore, 1/10 the value of 6 in 46.12 is simply 6/10 or 0.6.