these two bars | | mean absolute value
here's how to find x
| x - 7| = 2
first apply the absolute rule
x - 7 = 2 x - 7 = -2
in both equations add 7 on both sides
x - 7 + 7 = 2 + 7 x - 7 + 7 = -2 + 7
then simplify the expressions
x = 9 x = 5
now combine these two solutions to get your answer
x = 9 or x = 5
hopefully my explanation helps
Use the ingredients from the food bank’s recipe for vegetable bean soup shown below.
AlternativeText
Anna makes a pot of the soup. She is using a 14-cup measuring cup.
Part A
How many times will Anna need to fill the measuring cup to measure 78 cup of turnips? Show your work.
Anna can only fill the measuring cup a whole number of times, she will need to fill it 6 times to measure 78 cups of turnips.
What is division in mathematics?
Division is the process of splitting a number or an amount into equal parts.
To find the number of times Anna will need to fill the measuring cup, divide the number of cups of turnips by the size of the measuring cup:
78 cups/14 cups:
= 78/14
=5.57 measures
Hence, Anna can only fill the measuring cup a whole number of times, she will need to fill it 6 times to measure 78 cups of turnips.
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Solve for x:-
\(\sf 5 + 2x = 2x + 6\)
Answer:
No solution (0 = 1)
Step-by-step explanation:
Given equation,
→ 5 + 2x = 2x + 6
Then the value of x will be,
→ 5 + 2x = 2x + 6
→ 2x = 2x + 6 - 5
→ 2x - 2x = 1
→ 0 = 1
Hence, there is no solution.
\(\boxed{\begin{array}r \large{ \tt solution \: : } \: \: \: \: \: \\ \\ { \longrightarrow5 + 2x = 2x + 6} \\ \\ \\ ( \sf 2x \: \: present \: \: on \sf\: \: both \: \: \\ \sf sides \: \: of \: \: equality \: \: \: \\ \sf \: \: gets \: \: \sf canceled\: \: out) \\ \\ \sf \longrightarrow5 \neq6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \tt \: \: therefore \: \: there \: \: is \\ \tt no \: \:solution \: \: for \: \: x \: \: \\ \\ \tt that \: \: is \: \: no \: \: value \: \: \: \: \\ \tt \: of \: \: x \: \: that \: \: satisfies \\ \tt the \: \: given \: \: equation\end{array} }\)
the product of a rational and irrational number is always
The product of a rational and an irrational number can be either rational or irrational, depending on the specific numbers involved.
To illustrate this, let's consider an example:
Let's say we have the rational number 2/3 and the irrational number √2.
Their product would be (2/3) * √2.
In this case, the product is irrational.
The square root of 2 is an irrational number, and when multiplied by a rational number, the result remains irrational.
However, it's also possible to have a product of a rational and an irrational number that is rational. For example, if we consider the rational number 1/2 and the irrational number √4, their product would be (1/2) * 2, which equals 1. In this case, the product is a rational number.
Therefore, we cannot make a definitive statement that the product of a rational and an irrational number is always rational or always irrational. It depends on the specific numbers involved in the multiplication.
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Which of the following is/are correct? (Select all that apply. You have only one submission for this question.) If u and v are parallel, then either u.v=jul lvl or u. V-lul lvl. The vector projuv is parallel to v If u and v are orthogonal, then u xv = 0. The expression u. (vw) is meaningful and the result is a scalar. Suppose u: O. If u xv=uxw, it follows that vw. If u and v are parallel, then u xv = 0. The expression u u can be negative
The correct statements are If u and v are orthogonal, then u × v = 0. The vector proj_v u is parallel to v. If u and v are parallel, then u × v = 0.
The statement "If u and v are parallel, then either u · v = |u||v|" is incorrect. The correct statement is "If u and v are parallel, then u · v = |u||v|".
The statement "The expression u.(vw) is meaningful and the result is a scalar" is incorrect. The expression u.(vw) is not meaningful because the dot product is only defined for vectors of the same dimension.
The statement "Suppose u: O. If u × v = u × w, it follows that v = w" is incorrect. The correct statement is "Suppose u ≠ 0. If u × v = u × w, it follows that v - w is parallel to u".
Finally, the statement "The expression u · u can be negative" is incorrect. The dot product u · u is always non-negative, and is only equal to zero if and only if u = 0
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What is the equation of y = x^3 with the given transformations?
vertical compression by a factor of 1/7, horizontal shift 8 units to the left, reflection across the x-axis
(Note) Please include valid step-by-step explanation.
Based on Transformation of functions the transformed equation is \(y=x^3\) is \(y=\frac{-1}{7}(x+8)^3\).
How to transform functions?There are two different translations we can apply to a function graph. In addition, they are scaling. If you count reflections, there are three, but reflections are really a specific instance of the second translation.
Transformations:
Reflecting a function on X-axis : Change y in function to -y.
Reflecting aa function on Y-axis : Change x in function to -x.
Shifting right by a: Replace x by (x-a)
Shifting left by a: Replace x by (x+a).
Shifting up by a: Replace y by (y-a).
Shifting down by a: Replace y by (y+a).
Scaling up by n times: Multiply n
Calculation:Step1: Vertical compression by a factor of \(\frac{1}{7}\), we need to multiply the function by \(\frac{1}{7}\) .
So, we have:
\(y=\frac{1}{7}x^3\);
Step2:Horizontal shift by 8 units to the left, we need to add 8 to x.
So, we have:
\(y=\frac{1}{7}(x+8)^3\);
Step3:Reflection over the x-axis, we need to Replace y by -y.
So, we have:
\(y=-\frac{1}{7}(x+8)^3\)
Based on Transformation of functions the transformed equation is \(y=x^3\) is \(y=\frac{-1}{7}(x+8)^3\).
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1) In the market for apartment housing, the quantity of available apartments is observed to be less than the number of renters who are willing and able to pay the market price of an apartment. In this scenario, the market is said to be _____.(1 point)
A in equilibrium because there is a surplus of apartments on the market
(B) in equilibrium because there is a shortage of apartments on the market
C in disequilibrium because there is a shortage of apartments on the market
D in disequilibrium because there is a surplus of apartments on the market
1) B
2) For a given market, the equilibrium quantity of the good or service will decrease if _____.(1 point)
A demand increases and supply decreases
B demand decreases and supply increases
(C) demand decreases and supply decreases
D demand increases and supply increases
2)C
3) Price Quantity Supplied Quantity Demanded
$10 1,000 2,500
$20 2,000 2,000
$30 3,000 1,500
$40 4,000 1,000
The equilibrium price for this market is _____.
(1 point)
A $10
(B) $20
C $30
D $40
3) B
4) In a given market, the market equilibrium price and quantity are $120 and 5 million units, respectively. At a price of $100, 4.8 million units are supplied, and 5.2 million units are demanded. It can be said that at a price level of $100 there is a _____.(1 point)
A a surplus of 0.4 million units
(B) a shortage of 0.4 million units
C a shortage of 0.2 million units
D a surplus of 0.2 million units
4) B
5)The supply and demand curves for a market are graphed below with price in dollars and quantity in thousands.
Two intersecting lines are graphed. The horizontal axis labeled Quantity goes from 0 to 70 in increments of 10. The vertical axis labeled Price goes from 0 to 50 in increments of 10. A line with a negative slope is labeled D and a line with a positive slope is labeled S. The lines intersect at approximately left parenthesis 33.7 comma 30 right parenthesis. A horizontal dashed line extends from left parenthesis 0 comma 30 right parenthesis to the point of intersection.
Which of the following would result from an increase in the supply curve?
(1 point)
(A) a market equilibrium price less than $30
B a market equilibrium quantity less than $30
C a market equilibrium quantity greater than $30
D a market equilibrium price greater than $30
5) A
5/5 Good job
Answer:
Hey
Step-by-step explanation:
Hey did you find the answers to this? i really need it. im desperate!
1. The market is said to be in disequilibrium because there is a shortage of apartments on the market
2. The equilibrium quantity of the good or service will decrease if demand decreases and supply decreases
3. The equilibrium price for this market is $20
4. It can be said that at a price level of $100 there is a a shortage of 0.4 million units
Equilibrium is the point at which quantity demanded equal quantity supplied
The price at this point is referred to as the equilibrium price.
Above equilibrium, there is a surplus - quantity supplied exceeds quantity demanded. As a result of the surplus, price would fall until equilibrium is reached.
Below equilibrium, there is a shortage - quantity demanded exceeds quantity supplied. As a result of the shortage, price would rise until equilibrium is reached.
A decrease in demand would lead to a leftward shift of the demand curve. As a result, quantity and price decreases. A decrease in supply would lead to a leftward shift of the supply curve. This leads to a decrease in quantity and an increase in price. Taking these two effect together, equilibrium quantity would decrease and there would be an indeterminate effect on equilibrium price
Equilibrium price is $20. This is because this is the price at which quantity demanded exceeds quantity supplied
There is a shortage because quantity supplied is less than quantity demanded
Shortage = 5.2 million - 4.8 million = 0.4 million
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If the population of center ills in 1910 was 4,200 and 5,000 in 1920 assuming exponential growth, what would the population be in 2020?
Use a function in the form of y=Pe^rt
The population of the center ills in the year 2020 will be 16882.32 .
In the question ,
it is given that ,
the the population of the center ills in the year 1910 is = 4200
the population of the center ills in the year 1920 is = 5000
So , the time period = 1920 - 1910 = 10 years
the exponential growth formula is given as
y = P*\(e^{r \times t}\)
5000 = 4200*\(e^{r \times 10}\)
\(e^{r \times 10}\) = 5000/4200
\(e^{r \times 10}\) = 1.19
taking \(ln\) both the sides , we get
10×r ㏑(e) = ㏑(1.19)
10r = 0.1739
r = 0.01739
So , the population in the year 2020 means time = 2020 - 1920 = 80 .
y = 4200 × \(e^{0.01739 \times 80}\)
y = 4200 × \(e^{1.3912}\)
y = 4200 × 4.0196
y = 16882.32
Therefore , The population of the center ills in the year 2020 will be 16882.32 .
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find the value of x so that the function has the given value.
q(x)=12x−3; q(x)=−4
Answer:
\( - \frac{1}{ 12} \)
Step-by-step explanation:
since q(x)=-4
substitute
hence
-4=12x-3
take -3 to the other side where it becomes positive
therefore
-1=12x
divide by 12
you will get the above answer
The following data displays ages in which people started wearing braces. Use the data
below to answer questions 1-4:
14, 14, 15, 15, 16, 16, 16, 18, 19, 57
1. Calculate the following:
a. Mean
b. Median
c. Mode
2. What is the best measure of center for this data? Why?
3. Create a boxplot using the data.
4. Create a stem and leaf plot using the data.
Answer:
Step-by-step explanation:
how big is yo toes?
How many integer solutions are there to the equation for which How many integer solutions are there to the equation for which and are all positive
The number of integer solutions to the equation x + y + z = 20, where x, y, and z are all positive integers, is 18.
To find the number of integer solutions to the equation x + y + z = 20, where x, y, and z are positive integers, we can use a combinatorial approach known as "stars and bars."
Imagine representing the sum 20 as a row of 20 stars: ***************.
Now, we need to divide these stars into three groups (representing x, y, and z) using two bars (|). For example, ||****|*****| represents x = 2, y = 5, and z = 13.
To determine the number of integer solutions, we need to count the number of distinct arrangements of 20 stars and 2 bars. The stars can be placed in any of the 22 positions (20 + 2), and the bars can be placed in any of the 2 available positions. Thus, the number of arrangements is given by the binomial coefficient C(22, 2) = 231.
However, we need to exclude the cases where one or more variables (x, y, or z) equals zero. Since all variables must be positive, we need to subtract the number of solutions where one variable is zero. If we fix x = 0, we are left with the equation y + z = 20, which has C(21, 1) = 21 solutions. Similarly, fixing y = 0 or z = 0 yields 21 solutions each.
Therefore, the total number of integer solutions to the equation x + y + z = 20, with x, y, and z as positive integers, is 231 - 21 - 21 - 21 = 168 - 63 = 105.
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What is the total surface area??
Answer:
790 units^2
Step-by-step explanation:
Take the area of each side and add them all up. Remember each side is there twice.
Formula: SA = 2(15*5 + 15*16 + 5*16)
SA = 2(75 + 240 + 80)
SA = 2(395)
SA = 790
Please help I will give brainliest.
Answer:
c = 9
Step-by-step explanation:
You're looking for a number so that when you use that number in place of x, you end up with 20.
f(x) = 3x - 7
f(c) = 3c - 7
20 = 3c - 7
Add 7
27 = 3c
Divide by 3
9 = c
The price of an item has dropped to $57 today. Yesterday it was $95. Find the percentage decrease.
WHAT IS IT
Answer:
40%
Step-by-step explanation:
(95 - 57) / 95 * 100% = 40% decrease
if you can solve this that would be great
Answer:
I wish you luck
Step-by-step explanation:
please help me with this
Answer:
Step-by-step explanation:
if f(x) is the height in cm of a sunflower plant that is x days old which of the following statements best describes the meaning of f(60) = 210
Help what is this ? Lol help
Answer:
a
Step-by-step explanation:
Mode: 1; since most of the numbers are 1, the mean takes a while to add up and divide but its 1.76, and the middle number (median) is also 1. Hope this helps!! <33
what is an equation of the tangent line at x = 2, assuming that y(2) = 4 and y'(2) = 5?
Therefore, the equation of the tangent line at x = 2 is y = 5x - 6.
The equation of the tangent line at x = 2 can be found using the point-slope formula: y - y1 = m(x - x1), where (x1, y1) is the given point on the curve and m is the slope of the tangent line at that point.
In this case, we are given that y(2) = 4 and y'(2) = 5. This means that the point on the curve at x = 2 is (2, 4) and the slope of the tangent line at that point is 5.
Using the point-slope formula, we can plug in these values and simplify:
y - 4 = 5(x - 2)
y - 4 = 5x - 10
y = 5x - 6
Therefore, the equation of the tangent line at x = 2 is y = 5x - 6.
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A boat is heading towards a lighthouse, whose beacon-light is 113 feet above thewater. From point A, the boat's crew measures the angle of elevation to the beacon,10°, before they draw closer. They measure the angle of elevation a second time frompoint B at some later time to be 21°. Find the distance from point A to point B.Round your answer to the nearest foot if necessary.
The following picture represents an explanation to the given question:
CD represents the beacon
We need to find the distance AB
The measure of the angle C = 90
At the triangle BCD,
The measure of the angle CDB = 90 - 21 = 69
Using the sine law, we will find the length of BD
So,
\(\begin{gathered} \frac{BD}{\sin90}=\frac{CD}{\sin 21} \\ BD=CD\cdot\frac{\sin90}{\sin21}=\frac{CD}{\sin 21} \end{gathered}\)At the triangle ABC
The measure of the angle CDA = 90 - 10 = 80
So, the measure of the angle ADB = angle CDA - angle CDB = 80 - 69 = 11
At the triangle ADB, using sin law:
\(\begin{gathered} \frac{AB}{\sin D}=\frac{BD}{\sin A} \\ \\ AB=BD\cdot\frac{\sin D}{\sin A}=BD\cdot\frac{\sin 11}{\sin 10} \end{gathered}\)substitute with the value of BD and CD s
So,
\(AB=\frac{CD}{\sin21}\cdot\frac{\sin11}{\sin10}=\frac{113\cdot\sin 11}{\sin 21\cdot\sin 10}=346.4798\)Rounding the answer to the nearest foot
So, the answer will be AB = 346 ft
in a sample of 1000 adults, the proportion of people with diabetes is 25%. what is the 95% confidence interval for the percentage of people with diabetes? group of answer choices you cannot solve this problem with the information given (22.32%, 27.68%) (22.75%, 27.25%) (24.69%, 25.31%)
The 95% confidence interval for the percentage of people with diabetes is equals to the (0.335, 0.1652).
We have, a sample of adults with
Sample size = 1000
Sample proportion, p = 25% = 0.25
We have to determine 95% confidence interval for the percentage of people with diabetes.Confidence interval formula for known value of sample proportion is written as CI = p ± Z ( √(p(1 - p)/n)
Now, for the 95% of confidence level or significance level, α = 1- 0.95 = 0.05 or α/2 = 0.25.
Using the normal distribution table, Z₀.₀₂₅ is 1.96. From above formula, confidence interval, CI = 0.25 ± 1.96( √0.25× 0.75/1000)
= 0.25 ± 1.96 ( 0.0433)
= 0.25 ± 0.0848
= ( 0.335, 0.1652)
Hence, required confidence interval is (0.335, 0.1652) .
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Captain Gabriela has a ship, the H.M.S. Khan. The ship is two furlongs from the dread pirate Daniel and his merciless band of thieves. The Captain has probability \dfrac{1}{2} 2 1 start fraction, 1, divided by, 2, end fraction of hitting the pirate ship. The pirate only has one good eye, so he hits the Captain's ship with probability \dfrac{1}{3} 3 1 start fraction, 1, divided by, 3, end fraction. If both fire their cannons at the same time, what is the probability that both the Captain and the pirate miss?
Answer:
1 /3
Step-by-step explanation:
Given that :
Probability that Captain hits pirate = 1/2 ;
P(captain hits) = 1/2
P(captain misses) = 1 - p(captain hits) = 1 - 1/2 = 1/2
Probability that Pirate hits Capitan = 1/3
P(pirate hits) = 1/2
P(pirate misses) = 1 - p(pirate hits) = 1 - 1/3 = 2/3
P(both pirate and captain miss)
P(captain miss) * P(pirate miss)
1/2 * 2/3
(1 *2) / (2*3)
= 2/6
= 1/3
Answer:
it's 1/10
Step-by-step explanation:
khan
The mason will build a wall that uses 36 bricks in each row. The wall will be 140 rows high. Each brick weighs 4 pounds. What is the total weight of all the bricks?
Answer:
20,160 pounds
Step-by-step explanation:
bricks in each row * number of rows * pound of each brick
Answer:
20160 lbs
Step-by-step explanation:
To find the amount of bricks, multiply 36 by 140 which equals 5040. Then, multiply 5040 by the weight: 4. 5040×4=20160
Solve for x. 5 x − 29 > − 34 OR 2 x + 31 < 29
Answer:
x > -1
x < -1
Step-by-step explanation:
5x - 29 > - 34
5x > - 34 + 29
5x > -5
x > -1
2x + 31 < 29
2x < 29 - 31
2x < -2
x < -1
what is the solution to the graph system graphed below
Answer:
(-4, -1)
General Formulas and Concepts:
Algebra I
Solving systems of equations by graphingStep-by-step explanation:
Where the 2 lines intersect would be the solution set of the systems of equations.
determine the area under the standard normal curve that lies between (a) z=−0.24 and z=0.24, (b) z=−1.47 and z=0, and (c) z=0.13 and z=0.62.
The area under the standard normal curve between (a) z = -0.24 and z = 0.24 is 0.1886, (b) z = -1.47 and z = 0 is 0.4292, and (c) z = 0.13 and z = 0.62 is 0.1800.
To determine the area under the standard normal curve between two z-values, we can use a standard normal distribution table or a statistical software. The standard normal distribution is a continuous probability distribution with a mean of 0 and a standard deviation of 1. The area under the curve represents the probability of a random variable falling within a certain range.
Steps to calculate the area under the standard normal curve:
(a) Area between z = -0.24 and z = 0.24:
To calculate the area between these two z-values, we need to find the cumulative probability for each z-value and then subtract the smaller cumulative probability from the larger one. The cumulative probability represents the area under the curve to the left of a given z-value.
Using a standard normal distribution table or a statistical software, we find:
P(z < -0.24) = 0.4052
P(z < 0.24) = 0.5938
The area between z = -0.24 and z = 0.24 is:
P(-0.24 < z < 0.24) = P(z < 0.24) - P(z < -0.24) = 0.5938 - 0.4052 = 0.1886
(b) Area between z = -1.47 and z = 0:
Using the same approach, we find:
P(z < -1.47) = 0.0708
P(z < 0) = 0.5
The area between z = -1.47 and z = 0 is:
P(-1.47 < z < 0) = P(z < 0) - P(z < -1.47) = 0.5 - 0.0708 = 0.4292
(c) Area between z = 0.13 and z = 0.62:
Again, using the same approach, we find:
P(z < 0.13) = 0.5524
P(z < 0.62) = 0.7324
The area between z = 0.13 and z = 0.62 is:
P(0.13 < z < 0.62) = P(z < 0.62) - P(z < 0.13) = 0.7324 - 0.5524 = 0.1800
Therefore, the area under the standard normal curve between (a) z = -0.24 and z = 0.24 is 0.1886, (b) z = -1.47 and z = 0 is 0.4292, and (c) z = 0.13 and z = 0.62 is 0.1800.
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Consider the following function:
f(x)=25-x2/x2-4x-5
Answer:
Step-by-step explanation: wap to print the sum of the square of odd numbers in QBasic
Answer:
Look at the Screenshot
Step-by-step explanation:
Edge 2022
Consider the following sample data values. 7 4 6 12 8 15 1 9 13 a) Calculate the range. b) Calculate the sample variance. c) Calculate the sample standard deviation. a) The range is 14 b) The sample variance is (Round to two decimal places as needed.) c) The sample standard deviation is (Round to two decimal places as needed.)
a) The range is 14.
b) The sample variance is 20.78.
c) The sample standard deviation is 4.56.
a) Range
The range of a given set of data values is the difference between the maximum and minimum values in the set. In this case, the maximum value is 15 and the minimum value is 1. So, the range is:
Range = maximum value - minimum value
Range = 15 - 1
Range = 14
b) Sample variance
To calculate the sample variance, follow these steps:
1. Calculate the sample mean (X). To do this, add up all of the data values and divide by the total number of values:
n = 9
∑x = 7 + 4 + 6 + 12 + 8 + 15 + 1 + 9 + 13 = 75
X = ∑x/n = 75/9 = 8.33
2. Subtract the sample mean from each data value, square the result, and add up all of the squares:
(7 - 8.33)² + (4 - 8.33)² + (6 - 8.33)² + (12 - 8.33)² + (8 - 8.33)² + (15 - 8.33)² + (1 - 8.33)² + (9 - 8.33)² + (13 - 8.33)² = 166.23
3. Divide the sum of squares by one less than the total number of values to get the sample variance:
s² = ∑(x - X)²/(n - 1) = 166.23/8 = 20.78
Therefore, the sample variance is 20.78 (rounded to two decimal places).
c) Sample standard deviation
To calculate the sample standard deviation, take the square root of the sample variance:
s = √s² = √20.78 = 4.56
Therefore, the sample standard deviation is 4.56 (rounded to two decimal places).
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When can we use the SAS theorem?
According to the SAS theorem, two triangles are equal if their two sides and the angle between them are both equal. The included angle is another name for the angle formed by the two sides. The side angle side is referred to as SAS.
More about SAS(Side Angle Side) theorem:
This geometric theorem gave rise to the SAS area formula, which is used in trigonometry. If you know the length of two triangle sides and the included angle, you can use the SAS area formula to determine the triangle's area. In particular, if the included angle is designated as A and the sides of the included angle are denoted by the letters b and c, then
Triangle ABC's area is (b*c*sin A) / 2.
It is crucial that the angle you use to calculate the area of the object lies between the two sides that you utilize.
So basically when the two sides and the angle between them are both equals then the SAS theorem can be used to determine whether the two triangles are also equal.
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State the additional congruency statement needed to prove ABC FGH for the given theorem
ANSWERS
A. AB ≅ FG
B. ∡C≅ ∡H
EXPLANATION
A. To use SAS theorem, we have to know if one more side is congruent to the corresponding side of the other triangle. SAS is side-angle-side. The angle must be included between the two sides. Therefore the missing side is AB congruent to FG:
B. To use ASA Theorem we have to know one more angle. Since ASA is angle-side-angle, the side must be between two angles. Therefore, the missing angle is angle C congruent to angle H:
Which equation has infinite solutions?
3(x – 1) = x + 2(x + 1) + 1
x – 4(x + 1) = –3(x + 1) + 1
2x + 3 = 2 x plus 3 equals StartFraction one-half EndFraction left-parenthesis 4 x plus 2 right-parenthesis plus 2.(4x + 2) + 2
StartFraction one-third EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals 3 left-parenthesis x plus 1 right-parenthesis minus x minus 2.(6x – 3) = 3(x + 1) – x – 2
The equation that has an infinite number of solutions is \(2x + 3 = \frac{1}{2}(4x + 2) + 2\)
How to determine the equation?An equation that has an infinite number of solutions would be in the form
a = a
This means that both sides of the equation would be the same
Start by simplifying the options
3(x – 1) = x + 2(x + 1) + 1
3x - 3 = x + 3x + 2 + 1
3x - 3 = 4x + 3
Evaluate
x = 6 ----- one solution
x – 4(x + 1) = –3(x + 1) + 1
x - 4x - 4 = -3x - 3 + 1
-3x - 4 = -3x - 2
-4 = -2 ---- no solution
\(2x + 3 = \frac{1}{2}(4x + 2) + 2\)
2x + 3 = 2x + 1 + 2
2x + 3 = 2x + 3
Subtract 2x
3 = 3 ---- infinite solution
Hence, the equation that has an infinite number of solutions is \(2x + 3 = \frac{1}{2}(4x + 2) + 2\)
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Complete question
Which equation has infinite solutions?
3(x – 1) = x + 2(x + 1) + 1
x – 4(x + 1) = –3(x + 1) + 1
\(2x + 3 = \frac{1}{2}(4x + 2) + 2\)
\(\frac 13(6x - 3) = 3(x + 1) - x - 2\)