To find a linear function h(x) given two points, we can use the formula for the slope of a line:
m = (y2 - y1) / (x2 - x1)
Where m is the slope, (x1, y1) and (x2, y2) are the two points.
In this case, the two points are (-3, -4) and (-9, -5). Plugging in the values into the formula, we get:
m = (-5 - (-4)) / (-9 - (-3))
m = (-1) / (-6)
m = 1/6
Now that we have the slope, we can use the point-slope form of a linear equation to find the function h(x):
y - y1 = m(x - x1)
Plugging in the slope and one of the points, we get:
y - (-4) = (1/6)(x - (-3))
y + 4 = (1/6)(x + 3)
y = (1/6)x + 3/6 - 4
y = (1/6)x - 21/6
Simplifying the equation, we get:
y = (1/6)x - 7/2
Therefore, the linear function h(x) is:
h(x) = (1/6)x - 7/2
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The University of Iowa, prompted by a student who died while intoxicated, conducted an investigation of student drinking by randomly selecting 10 different classrooms and interviewing all the students in each of these groups. The type of sampling used is et vered ked out of A) Simple random sampling Flag B) Stratified random sample C) Cluster sampling isthion D) Systematic sampling
The type of sampling used by the University of Iowa in their investigation of student drinking is C) Cluster sampling.
Cluster sampling is a method where the population is divided into groups, or clusters, and a random sample of these clusters is selected for the study. In the case of the University of Iowa's investigation, the population was the entire student body and the clusters were the different classrooms. By randomly selecting 10 classrooms and interviewing all the students in each of these groups, the University of Iowa was using cluster sampling.
Therefore, the correct answer is C: cluster sampling.
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Figure 1 and figure 2 are right triangles. two right triangles labeled figure 1 and figure 2, where the legs of figure 1 are 3 units long and the legs of figure 2 are 7 units long What scale factor was used to produce Figure 2 from Figure 1? 7 over 3, 3 over 7, 7 or 3
The scale factor used to produce Figure 2 from Figure 1 is given as follows:
7/3.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The side lengths are given as follows:
Figure 1: 3 units.Figure 2: 7 units.Hence the scale factor of the dilation is given as follows:
7/3.
(the scale factor is the division of the side length of the dilated figure by the equivalent side length of the original figure).
Missing InformationThe problem asks for the scale factor used from figure 1 to figure 2.
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Answer:
C 7/3 because i got it right
A man received a 2% discount for paying his bill on time. If the discount amounts to Php 160 , how much was the original bill?
The original bill of the man can be calculated using the formula for discount, which is:
Discount = Original Price × Discount Rate
Given that the discount is Php 160 and the discount rate is 2%, we can rearrange the formula to solve for the original price:
Original Price = Discount ÷ Discount Rate
Original Price = Php 160 ÷ 2%
Original Price = Php 160 ÷ 0.02
Original Price = Php 8,000
Therefore, the original bill of the man was Php 8,000 before the 2% discount was applied.
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Feb 28,
Watch help video
Gabriel went to the store to buy some coffee. The price per pound of the coffee is
$4.50 per pound and he has a coupon for $2 off the final amount. With the coupon,
how much would Gabriel have to pay to buy 4 pounds of coffee? Also, write an
expression for the cost to buy p pounds of coffee, assuming at least one pound is
purchased.
Answer:
The original cost for 1 pound of coffee is $4.50, and Gabriel wants to buy 4 pounds, so the total cost without the coupon would be:
4 pounds x $4.50/pound = $18
With the coupon, Gabriel can subtract $2 from the final amount, so the total cost with the coupon would be:
$18 - $2 = $16
Therefore, Gabriel would have to pay $16 to buy 4 pounds of coffee with the coupon.
To write an expression for the cost to buy p pounds of coffee, we can use the formula:
cost = price per pound x number of pounds - coupon
If Gabriel buys at least one pound of coffee, then the expression would be:
cost = $4.50p - $2
So the cost to buy p pounds of coffee can be calculated by plugging in the desired value for p into this expression.
what is P{event }.Can you gave examples
P(event) represents the probability of an event occurring.
What is probability?Probability is a branch of mathematics that deals with the study of random events or experiments. It is the measure of the likelihood or chance that a particular event will occur. Probability is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to happen.
What are events?An event is a set of outcomes of a random experiment, and the probability of an event is the measure of how likely it is to occur.
Here are some examples:
Rolling a fair six-sided die: P(rolling a 3) = 1/6, since there is one outcome (rolling a 3) out of six possible outcomes.Flipping a fair coin: P(flip heads) = 1/2, since there is one outcome (flipping heads) out of two possible outcomes.Drawing a card from a standard deck of 52 cards: P(drawing a heart) = 13/52, since there are 13 hearts out of 52 cards.Selecting a random student from a class: P(selecting a male student) = number of male students / total number of students, where the probability depends on the gender balance of the class.Choosing a number from 1 to 10: P(choosing an even number) = 5/10 = 1/2, since there are five even numbers out of ten possible numbers.To know more about Probability,visit:
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A person invested $3,600 in an account growing at a rate allowing the money to double every 8 years. Write a function showing the amount of money in the account after t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year, to the nearest hundredth of a percent.
A(t) = $3,600(1.125)t is the function that displays the balance of the account after t years, rounded to four decimal places.
Do you mean invested or vested?The definition of the word "invest" is to "expend money with the idea of attaining a profit or material consequence by putting it into financial plans, etc." A person is "vested" when they are "secured in their possession or allocated to a person," on the other hand. It can also imply outfitted with a vest, although that is unimportant just now.
A(t) = P(1 + r)t
where:
A(t) represents the balance of the account after t years.
P is the initial investment, $3,600, and r is the growth rate per year.
The number of years is t.
A(t) = $3,600(1 + 0.125)t
A(t) = $3,600(1.125)t
We can take the growth rate and subtract 1 to get the annual growth percentage, which we can then translate to a percentage as follows:
Percentage growth rate = (1.125 - 1) * 100% = 12.5%
So the account grows by approximately 12.5% per year.
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A survey of 50 young professionals found that they spent an average of $21.37 when dining out, with a standard deviation of $12.67. Can you conclude statistically that the population mean is greater than $23? Use a 95% confidence interval.
The 95% confidence interval is _____,_____. As $23 is _______ of the confidence interval, we ________ conclude that the population mean is greater than $23.
options for second blank space --> below the lower limit, within the limits, above the upper limits.
options for third blank space --> cannot, can.
The 95% confidence interval is (17.77, 24.97). As $23 is within the limits of the confidence interval, we cannot conclude that the population mean is greater than $23.
The 95% confidence interval can be calculated using the formula:
CI = x ± t(s/√n), where x is the sample mean, t is the t-score for the desired confidence level, s is the sample standard deviation, and n is the sample size.
For a 95% confidence level and a sample size of 50, the t-score is 2.009. Plugging in the given values, we get:
CI = 21.37 ± 2.009(12.67/√50) = 21.37 ± 3.60 = (17.77, 24.97)
Since $23 is within the limits of the 95% confidence interval (17.77, 24.97), we cannot conclude that the population mean is greater than $23.
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If log_x y = 4 which of the following is true?
Please
The equation log_x y = 4 can be written as y = x⁴ and the true, correct option is 1.
What is logarithmic rule?A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number. that is, b raised to x = n, in which case one writes x = log base b n. Scientists embraced logarithms immediately because of a number of advantageous characteristics that made complicated, time-consuming computations simpler. In specifically, by searching up each number's logarithm in a special database, adding the logarithms together, and then rechecking the table to discover the number with that computed logarithm, scientists could find the product of two integers m and n.
Given that, log_x y = 4 .
Using the logarithmic rule we have:
log_x y = 4
y = x⁴
Hence, the equation log_x y = 4 can be written as y = x⁴ and the correct option is 1.
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The diagram shows a shape made from two semicircles
The radius of the larger semicircle is 8 cm
8 crn
D
Work out the perimeter of the shape.
Give your answer in terms of .
Answer
Not drawn
accurately
cam
[3 marks]
Answer:
Step-by-step explanation:
big semicircle circumference=1/2*3.14*64
100.48cm
small semicircle circumference=1/2*3.14*16=25.12cm
total perimeter=125.6cm
Using a formula estimate the body surface area of a person whose height is 166cm and weighs 100kg. A. 2.29m^(2) B. 2.15m^(2) C. 55.9m^(2) D. 5.44m^(2)
The correct answer is B. 2.15m^(2). The estimated body surface area of the person is 2.15m^(2).
To estimate the body surface area of a person, we can use the Mosteller formula:
BSA = square root of [(height in cm x weight in kg)/3600]
Plugging in the given values for height and weight:
BSA = square root of [(166cm x 100kg)/3600]
BSA = square root of 1660000/3600
BSA = square root of 461.11
BSA = 2.15m^(2)
Therefore, the estimated body surface area of the person is 2.15m^(2). Hence, B is the correct answer.
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A rectangular prism is shown below. What is the LATERAL surfa
area?
11 cm
5 cm
2 cm
The surface area of the rectangular prism is 174 cm^2
What is a Rectangular Prism?Rectangular Prism is a three-dimensional shape, having six faces, where all the faces (top, bottom, and lateral faces) of the prism are rectangle such that all the pairs of the opposite faces are congruent.
To determine the surface area of Rectangular prism
SA = 2(LH + LW + WH)
Where W = Width = 2 cm
L = Length = 5 cm
H = Height = 11 cm
SA = 2[(5*11) + (5*2) + (11*2)]
SA = 2(55 + 10 + 22)
SA = 2(87)
SA = 2 * 87
SA = 174
Therefore, the surface area of rectangular prism is 174 cm^2
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1. Rewrite the following without negative exponents and simplify: (a)−(34)−4
(b)(6y−53xy2)3
(c)x−9y−14x2x−8
(d)u−2u2u0u3
`u−2u2u0u3 = u^3`
(a) 1 / 34 * 4 = 4 / 34
(b) 6y * (1 / (53xy2))3 = 6y / 53xy2
(c) x * (1 / 9y) * (1 / 14x2) * (1 / (x−8)) = x / (9y * 14x2 * (x−8))
(d) (u−2 * u2) / (u0 * u3) = u−4 / u3
(a) Rewrite the given expression without negative exponents and simplify:(a)- (34)- 4Let us first use the law of exponents that says `(a^m)^n = a^(m*n)`The negative exponent `−4` means the denominator, so we can move the base `3` to the denominator and change the exponent to `+4`.Thus, `(a)−(34)−4 = a*(3^4) = 81a`Therefore, `(a)- (34)- 4 = 81a`(b) Rewrite the given expression without negative exponents and simplify:(b)(6y-5/3xy2)3Let us first use the law of exponents that says `(a^m)^n = a^(m*n)`We have to remove the negative exponent from `y^-5`, we can write it as `1/y^5`.Thus, `(6y-5/3xy2)3 = 6^3 * y^-15 * x^3 * y^6`Moving the base `y` with the negative exponent to the denominator and change the exponent to `+15`.Therefore, `(6y-5/3xy2)3 = 216x^3/ y^9`(c) Rewrite the given expression without negative exponents and simplify:(c) x-9y-14x2x-8We can rewrite `x^-9` as `1/x^9` and `x^-8` as `1/x^8`. Therefore, we get `(1/x^9 * y^-14 * x^2 * 1/x^8)`.Simplifying the above expression we get `(y^-14/x^15)`Therefore, `x-9y-14x2x-8 = y^-14/x^15` (d) Rewrite the given expression without negative exponents and simplify:(d) u−2u2u0u3Here we can observe that `u^0 = 1`. Hence, `u−2u2u0u3 = u^-2*u^2*1*u^3`We can simplify the expression by multiplying the coefficients and adding the exponents. Thus, `u^-2*u^2*1*u^3 = u^(2-2+3) = u^3`Therefore, `u−2u2u0u3 = u^3`
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estion 10 ate the answer choice Simplify each expressi (x^(2)-25x-24)/(6x+2x^(2))*(5x^(2))/(8-x)
Simplified each expression of (x²-25x-24)/(6x+2x²)*(5x²)/(8-x) is (-5x(x-24)(x-1))/(2(3+x)(x-8)).
To simplify the expression (x²-25x-24)/(6x+2x²)*(5x²)/(8-x), we need to factor the polynomials in the numerator and denominator and then cancel out any common factors.
First, let's factor the polynomials:
(x²-25x-24) = (x-24)(x-1)
(6x+2x²) = 2x(3+x)
(5x²) = 5x*x
(8-x) = -(x-8)
Now, let's plug these back into the expression and cancel out any common factors:
((x-24)(x-1))/(2x(3+x))*(5x*x)/(-(x-8))
= ((x-24)(x-1)*5x*x)/(2x(3+x)*-(x-8))
= ((x-24)(x-1)*5x)/(2(3+x)*-(x-8))
= (5x(x-24)(x-1))/(-2(3+x)(x-8))
Finally, let's simplify the expression by multiplying the constants:
= (-5x(x-24)(x-1))/(2(3+x)(x-8))
So the simplified expression is (-5x(x-24)(x-1))/(2(3+x)(x-8)).
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About 72 % of the residents in a town say that they are making an effort to conserve water or electricity. 110 residents are randomly selected.
2. What is the probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80%?
The probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80% is 0.0107.
To find the probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80%, use the formula for the standard error of a proportion:
SE = √(p(1-p)/n)
Where p is the proportion of the population that is making an effort to conserve water or electricity, and n is the sample size.
In this case, p = 0.72 and n = 110. Plugging these values into the formula gives:
SE = √(0.72(1-0.72)/110) = 0.0347
Next, we need to find the z-score for the proportion of 0.80. The z-score is given by:
z = (P - p)/SE
Where P is the sample proportion and p is the population proportion. In this case, P = 0.80 and p = 0.72. Plugging these values into the formula gives:
z = (0.80 - 0.72)/0.0347 = 2.30
Finally, we can use the z-score to find the probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80%. This is given by:
P(z > 2.30) = 1 - P(z < 2.30) = 1 - 0.9893 = 0.0107
Therefore, the probability is 0.0107 or 1.07%.
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The cold drink you usually buy is on special offer today. The price has been reduced by R2 per can. This means that you can get 14 cans for the same price that you usually pay for 10. What is the usual price per can?
The price per can has been lowered by R2, making the standard can cost R7.
what is equation ?A mathematical assertion that establishes the equivalence of two expressions is known as an equation. It is made up of two sides, a left and a right side, separated by the equal sign (=). The equation, which is typically used to determine an unknown variable's value, requires that the values on both sides be equal. Exponents, logarithms, multiplication, division, addition, subtraction, and other mathematical operations can all be used in equations.
given
Let's say that the standard price per can is "x" Rand.
The revised price is (x-2) Rands if the price is decreased by R2.
The issue is that 14 cans are being offered for the customary price of 10 cans. Thus, we can construct the equation:
10x = 14(x-2) (x-2)
After finding x, we obtain:
10x = 14x - 28
-4x = -28
x = 7
The price per can has been lowered by R2, making the standard can cost R7.
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Use long division, define each quotient
(3x^2- 3x + 5) ÷ (x - 6)
Answer:
(x - 6)(3x + 15) + 95
Step-by-step explanation:
Here's the long division of (3x^2 - 3x + 5) ÷ (x - 6):
3x + 15
--------------
x - 6 | 3x^2 - 3x + 5
- (3x^2 - 18x)
--------------
15x + 5
- (15x - 90)
------------
95
Therefore, the quotient is 3x + 15, and the remainder is 95.
The quotient represents the result of the division of the polynomial (3x^2 - 3x + 5) by the divisor (x - 6). In particular, the quotient 3x + 15 represents the linear polynomial that, when multiplied by the divisor x - 6, gives the dividend 3x^2 - 3x + 5.
In other words, we have:
(3x^2 - 3x + 5) = (x - 6)(3x + 15) + 95
The remainder 95 indicates that the division is not exact, and that there is a "leftover" term of 95 when we try to divide the polynomial (3x^2 - 3x + 5) by (x - 6).
Given a circle with center (– 3, 6) and radius 5, what is an equation of the circle?
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-3}{h}~~,~~\underset{6}{k})}\qquad \stackrel{radius}{\underset{5}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-3) ~~ )^2 ~~ + ~~ ( ~~ y-6 ~~ )^2~~ = ~~5^2\implies (x+3)^2+(y-6)=25[/tex]
Can somebody help please I’ll give you brainliest and 30 points!!!!!
Answer:
$512.17
$286.48
$1,958.40
$1,628.85
$56.37
$324.24
$135.55
Note: These calculations were made assuming simple interest. If the interest is compounded, the final amounts will be slightly different.
Step-by-step explanation:
how to solve 3 divided by 561 long division
Answer:
187
Step-by-step explanation:
how to do long division, you know how to start im assuming. then you then bring down and Divide, Multiply, Subtract, with the first number then bring the next number down and repeat that.
Answer:
187
Step-by-step explanation:
I personally just do multiplication whenever I can, but that's just me. Like for example I know 100 x 3 = 300 and 200 x 3 = 600. SO it has to be between 100 and 200.
150 x 3 = 450. So know it narrows it down to between 150 and 200.
175 x 3 = 525
180 x 3 = 540
185 x 3 = 555
190 x 3 =570
So now it's between 185 and 190.
Now I just need to do the following.
186 x 3 = 558
187 x 3 = 561
And there we have the answer.
Precipitation for the month of march was 6 1/2 inches less than average. In April the precipitation was 2 3/8 inches less than average. How many inches below average was the precipitation for both march and April?
For both march and April the precipitation is [tex](4\frac{7}{16})[/tex] inches below the average.
Define Average?The term "average" refers to a central value that represents a set of numbers. There are different types of averages, such as the mean, mode and median.
Let's denote the average precipitation as "a".
In March, the precipitation was [tex]6\frac{1}{2}[/tex] inches less than the average. This can be expressed as:
March precipitation = [tex]a-6\frac{1}{2}[/tex]
In April, the precipitation was [tex]2\frac{3}{8}[/tex] inches less than the average. This can be expressed as:
April precipitation = [tex]a-2\frac{3}{8}[/tex]
To find the total precipitation below average for both March and April, we can add the two expressions:
March precipitation + April precipitation = [tex](a-6\frac{1}{2})[/tex] + [tex](a-2\frac{3}{8})[/tex]
Simplifying the expression, we get:
March precipitation + April precipitation = [tex](2a-8\frac{7}{8})[/tex]
So, after dividing by 2 in result the value will be, [tex](a-4\frac{7}{16})[/tex]
Therefore, the total precipitation below average for both March and April was [tex](4\frac{7}{16})[/tex] inches.
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Choose the formula that expresses the described relationship. A varies inversely as h.
Therefore, the formula that expresses the described relationship where A varies inversely as h is A = k/h.
The formula that expresses the described relationship where A varies inversely as h is A = k/h, where k is the constant of proportionality.
In an inverse relationship, one variable increases as the other variable decreases. In this case, as h increases, A decreases, and as h decreases, A increases. The constant of proportionality, k, remains the same throughout the relationship.
To find the value of k, you can use the formula and plug in known values for A and h. For example, if A = 4 and h = 2, you can plug these values into the formula and solve for k:
4 = k/2
k = 8
Once you know the value of k, you can use the formula to find the value of A or h, given the value of the other variable. For example, if you know that h = 3 and k = 8, you can plug these values into the formula and solve for A:
A = 8/3
A = 2.67
Therefore, the formula that expresses the described relationship where A varies inversely as h is A = k/h.
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Can someone solve this for me please 6x+2y=26,3x-2y=10
Answer:
Step-by-step explanation: point form: (4,1)
x=4 , y=1
364683-5794+8679*4/86.99
some1 pls answer this pt.2 will give brainlist thingy
Answer: 8
Step-by-step explanation: (9-7)^3= 8
Answer: ? = 8
Step-by-step explanation: 2 x 2 x 2 = 8
exact value of sec(sin^(-1)((3)/(10))) o enter EXACT values ed to simplify any radicals
The exact value of sec(sin-1(3/10)) is 1.049988251.
The exact value of sec(sin-1(3/10)) can be found using the following steps:
Step 1: Enter the value of sin-1(3/10) into a calculator to get the angle measure in radians. This will give you an angle measure of 0.304692654.
Step 2: Take the cosine of this angle measure using a calculator. This will give you a value of 0.952424403.
Step 3: The value of secant is the reciprocal of the value of cosine. So, to find the exact value of sec(sin-1(3/10)), take the reciprocal of 0.952424403. This will give you an exact value of 1.049988251.
Step 4: Simplify any radicals if necessary. In this case, there are no radicals to simplify.
Therefore, the exact value of sec(sin-1(3/10)) is 1.049988251.
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I NEED HELP ON THIS ASSAP!
Based on the information, we can infer that the second plan is the best for the bicycle company because it will cost less and will earn more.
How to identify the best alternative for the bicycle company?To identify the best alternative for the bicycle company, we must take into account the information on the cost of design and construction of the bicycles and the cost of labor and production.
In accordance with the above, we can infer that in alternative one the design and construction of the bicycle would be more expensive than alternative two. However, the production of each bicycle would be less.
Therefore, the best alternative would be option two because it requires less initial research and the product will cost more, so it would have a higher retail value, so the investment could be recovered much faster. .
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are 8,192 players in a Rock Paper Scissors tournament. In each round half the players ar d to find the number of players remaining in the tournament at the end of x rounds? f(x)=8192(0.05)^(x) B
Therefore, there would be 1024 players remaining in the tournament at the end of 3 rounds.
The function f(x) = 8192(0.05)^x represents exponential decay, where the number of players is decreasing by a factor of 0.05 in each round. However, in this tournament, the number of players is decreasing by a factor of 0.5 (half the players) in each round. Therefore, the correct function should be f(x) = 8192(0.5)^x.
To find the number of players remaining in the tournament at the end of x rounds, simply plug in the value of x into the function and solve.
For example, if we want to find the number of players remaining at the end of 3 rounds, we would plug in x = 3 and solve:
f(3) = 8192(0.5)^3
f(3) = 8192(0.125)
f(3) = 1024
Therefore, there would be 1024 players remaining in the tournament at the end of 3 rounds. Similarly, you can plug in any value of x to find the number of players remaining at the end of x rounds.
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If the equation is true for all real numbers enter "All -4(6y+4)+19=12(-2y+5)-55
True. All real numbers satisfy the equation -4(6y+4)+19=12(-2y+5)-55.
The statement "If the equation is true for all real numbers enter 'All'" has been used to indicate that the given equation is true for all real numbers.
Given equation: -4(6y + 4) + 19 = 12(-2y + 5) - 55
Using distributive property, simplify both sides of the equation.
-24y - 16 + 19 = -24y + 60 - 55-24y + 3 = -24y + 5
By transposing -24y from the right-hand side of the equation to the left-hand side of the equation, we can simplify it as follows:
3 = 5
Since the above equation is always false for all real numbers, there is no solution. Therefore, we conclude that the given equation has no solution.
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Simplify the expression (yz)⁶
Answer:
[tex]y^{6} z^{6}[/tex]
Step-by-step explanation:
(yz)^6 is the same as:
yz * yz * yz * yz * yz * yz
which is the same as
[tex]y^{6} z^{6}[/tex]
What is 1/5 x 11 because I don’t know
Answer: 2 1/5
Step-by-step explanation:
11= 11/1 x 1/5= 11/2= 2 1/5