(i) The null hypothesis is that the mean living area of all single-family homes in the county is equal to or less than 2400 square feet. The alternative hypothesis is that the mean living area of all single-family homes in the county is greater than 2400 square feet.
(ii) The test statistic is calculated using the formula: (sample mean - hypothesized mean) / (standard deviation / square root of sample size). In this case, the test statistic is [tex]\frac{(2540 - 2400)}{\frac{472}{\sqrt{50} } } =2.44[/tex]
(iii) The p-value is the probability of obtaining a sample mean as extreme or more extreme than the one observed, assuming the null hypothesis is true. Using a t-distribution with 49 degrees of freedom (since we are using a sample size of 50 and estimating the population standard deviation), we can find the p-value to be 0.009.
(iv) Using a significance level of 0.05, we can conclude that the real estate agent's claim is not true, since the p-value is less than 0.05. We reject the null hypothesis and accept the alternative hypothesis that the mean living area of all single-family homes in the county is greater than 2400 square feet. If we use a significance level of 0.01 instead, we still reject the null hypothesis since the p-value is less than 0.01.
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HELP PLEASE
Solve the right triangle if the hypotenuse is 5 and one acute angle is 34°. Round answers to two decimal places.
Given that the hypotenuse of the right triangle is as given then;
i. α = 56^o
ii. Adjacent = 2.80
iii. Opposite = 4.15
Properties of a right angled triangle.A right triangle is a type of triangle which has only one of its internal angles equal to 90^o. Thus the hypotenuse is opposite to the greatest angle, while the second long side is opposite to the greater angle, and the shortest side opposite to the measure of the least angle.
Applying the Pythagorean theorem to the triangle, we have;
i. The sum of angles in a triangle is 180^o. So that;
α + 34 + 90 = 180
α + 124 = 180
α = 56^o
ii. Let the length of the opposite side be represented by y;
Sin θ = opposite/ hypotenuse
Sin 34 = y/ 5
y = 5 * Sin 34
= 2.796
The length of its opposite side is 2.80.
iii. Let the length of the adjacent side be represented by x;
Cos θ = adjacent/ hypotenuse
Cos 34 = x/ hypotenuse
= x/ 5
x = 5 * Cos 34
= 4.145
The length of its adjacent side is 4.15.
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Select ALL the correct answers. Select the expressions that are equivalent to the expression below. (375/345) 1/3
The equation is given by A = ∛ ( 375/345 ) and A = ( ∛375 ) / ( ∛ 345 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = (375/345) ^ 1/3 be equation (1)
On simplifying the equation , we get
The number raised to the power ( 1/3 ) means it is the cube root of the number ,
So , A = ∛ ( 375/345 )
Now , taking the cube root on both the numerator and denominator ,
A = ( ∛375 ) / ( ∛ 345 )
Hence , the value of A is ( ∛375 ) / ( ∛ 345 )
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eliminate the parameter t to find a Cartesian equation for:
x=t2
y=2+3t
x=Ay2+By+C
Where A=________ B=__________ and C=________
Cartesian equation for x=t2,y=2+3t, x=Ay2+By+C, Where
A=1, B=0, and C=0
To eliminate the parameter t and find a Cartesian equation for the given equation, we need to solve for t in terms of x and substitute it into the equation for y.
We start by solving for t in terms of x:
t = √x
Now, we substitute this into the equation for y:
y = 2 + 3√x
Therefore, the equation for x and y becomes:
x = x
y = 2 + 3√x
Which can be represented as a Cartesian equation:
Ay2 + By + C = 0
where A=1, B=0, and C=0.
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Evaluate the expression when a=−15
and b=−5
a/b
Answer: 3
Step-by-step explanation:
Norman earns $8 for every dog he washes plus25% of the cost of the dog wash. Write an expression that represents the total amount of money Norman earns for one dog wash with a cost, c.
Answer:
y = 0.25c + 8
Step-by-step explanation:
Let's y represent the total cost
We know
25% = 0.25
So, we will write this in the slope-intercept form y= mx +b
So, we have m = 0.25, and b = 8, so our equation is
y = 0.25c + 8
The scores of 10 students on a history test are 85, 79, 65, 72, 86, 66, 90, 98, 78, and 76. Which box plot represents the given data?.
The box will start at 72 and end at 86. At 78.5, a vertical line will be drawn through the box. Arrows will appear at both ends of the box. The one on the left will come to a halt at 65 miles per hour, while the one on the right will come to a halt at 98 miles per hour.
What is box plot?A box plot, often known as a boxplot, is a method in descriptive statistics for graphically displaying the localization, spread, and skewness groups of numerical data through their quartiles. A box plot is a graphical representation of statistical data that uses the lowest, first quartile, median, third quartile, and maximum values. The name "box plot" refers to how the graph resembles a rectangle with lines extending from the top and bottom. Box and whisker plots, often known as box plots, are an excellent graphic for displaying the distribution of data points over a specified metric. These graphs show ranges within variables that have been measured. Outliers, the median, the mean, and where the majority of the data points fall inside the "box" are all included.
Here,
65, 66, 72, 76, 78, 79, 85, 86, 90, 98
Q1 = 72
(78 + 79) / 2 = 78.5 Q2 (median)
Q3 = 86
min = 65
max = 98
So the box plot will look like this:
The box will begin at 72 and conclude at 86. At 78.5, a line will be drawn vertically through the box. Arrows will emerge from both ends of the box. The one on the left will come to a stop at 65, while the one on the right will come to a rest at 98.
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Need help on the question
What is called as factor of polynomial?
Therefore , the leading term 1 and constant 0 in the above function make it a polynomial function.
A polynomial function is what?A polynomial function can be defined in an equation that uses only real number exponents or non-negative integer powers of a variable. Examples of such equations include cubic and quadratic equations. The exponent of the polynomial 2x+5 is 1, for instance.
Here,
For the following polynomial function, exponents all positive integers in this case.
Exponent 1 applies to the positive number 2x.
, 1 where is an integer with positive exponent and and.
Among the coefficients of the function are real values like 5 and 1.
Thus, a polynomial characterizes the function.
It is a polynomials with a degree of five.
When writing a polynomial in standard form, the word with the largest exponent is used as the starting point, and the other terms are written in order of importance of expressions with lesser exponents.
The polynomial is expressed in standard form as f(x)=2x+1.
containing the leading word 1, the constant 0, and
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A rectangle has a width of 15 cm and a length of 25 cm. What is the perimeter of the rectangle?
A. 50 cm
B. 75 cm
C. 100 cm
D. 125 cm
Answer:
The perimeter of a rectangle is the total distance around the outside of the rectangle. To find the perimeter of a rectangle, you add the lengths of all four sides.
In this case, the width of the rectangle is 15 cm and the length is 25 cm. To find the perimeter, we add the lengths of all four sides, which are:
15 cm + 15 cm + 25 cm + 25 cm = 75 cm
Therefore, the perimeter of the rectangle is 75 cm. The answer is B. 75 cm.
Step-by-step explanation:
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 13, 19,25,... Find the 48th term.
The given sequence is 13, 19, 25, ...
What comprises an arithmetic series?
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.
This sequence appears to be increasing by 6 each time, so it is an arithmetic sequence. The common difference is 6. The nth term of an arithmetic sequence is given by the formula:
an = a1 + (n-1)d
where a1 is the first term, d is the common difference and n is the position of the term in the sequence.
We can use this formula to find the 48th term of the sequence:
a48 = a1 + (48-1)d
a48 = 13 + (48-1)6
a48 = 13 + 47*6
a48 = 13 + 282
a48 = 295
So, the 48th term of the sequence is 295.
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Algebra 2, I remember doing this but i’m confused bc I remember like (f)g)(x) something like that so do I multiply or what?
If the function g(t) is -4t + 5 then (g o g)(t) will be 16t - 15.
What is a function?A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain. Originally, functions were the idealization of how a varying quantity depends on another quantity.f(g(x)) means so wherever there is an x in the function f, the function g(x) is substituted.Here given function,
g(t) = -4t + 5
We have to find (g o g) (t)
(g o g)(t) = g(g(t))
= g(-4t + 5)
= -4(-4t + 5)+ 5
= 16t -20 +5
= 16t - 15
Therefore the function (g o g)(t) is 16t - 15.
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Jean sold 32 boxes of
cookies. If this is 40% of
her goal how many boxes
does Jean want to sell?
Answer:
80 boxes of cookies
Step-by-step explanation:
First, we have to find 1% by taking
32 divided by 40 = 0.8
Then we take it times 100%
0.8 x 100 = 80 boxes of cookies
Jean want to sell 80 boxes of cookies
A Question 1 (1 point) Retake question
The ratio of the measures of the three angles in a triangle is 14:5:11.
Find the measures of the angles.
Please helllopppp
The measures of the three angles in a triangle is 84°, 30° and 66° respectively.
How do you calculate a triangle's ratio?α + β + γ = 180° . From this, you can calculate the angles: ax, bx, and cx, as well as the unknown x. We translate these ideas into a detailed procedure for using ratios to locate missing angles in triangles in the following section.
The ratios are:
∠A = 14, ∠B = 5, ∠C = 11
Total ratio = 14 + 5 + 11= 30
The total angle in a triangle = 180°
So,
∠A= 14 / 30 × 180°= 0.46× 180°= 84°
∠B= 5/30 × 180°= 0.16 × 180°=30°
∠C= 11/30 × 180°= 0.366× 180°= 66°
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How do you find the legs of a 30 60 90 triangle given the long leg?
Answer:
A 30-60-90 triangle is a special type of right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. The side opposite the 30 degree angle is called the "short leg", the side opposite the 60 degree angle is called the "medium leg", and the side opposite the 90 degree angle is called the "long leg".
The ratios of the sides in a 30-60-90 triangle are always in the proportion of 1 : √3 : 2 . To find the legs of a 30-60-90 triangle when given the long leg, you can use these ratios.
If the long leg is "x", then the short leg is x/2 and the medium leg is x*√3/2.
For example, if the long leg is 8 cm, you can use these ratios to find the short leg and medium leg:
The short leg is 8 cm / 2 = 4 cm
The medium leg is 8 cm * √3 / 2 = 4 * √3 cm = 4 * 1.732 cm = 6.928 cm (approx)
So, in this example, the short leg is 4cm and the medium leg is 6.928cm (approx).
It's always a good idea to draw a diagram and label the sides to help you visualize the problem and check your answer.
Step-by-step explanation:
Reflection: State if the figure has a reflection that carries onto itself. If so state how many lines of symmetry the figure has.
This refers to objects that can be divided into two identical halves. The line that divides the object into its identical halves is known as the line of symmetry.
Line of symmetry is of three types: vertical symmetry, horizontal symmetry, and diagonal symmetry.
Irregular shapes have no equal sides. Thus, they can not be split into two identical halves.
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Which of the following equations has no real roots?A x 2+4x+3 2=0B x 2 +4x−3 2 =0C x 2 +5x+3 2 =0D 3x2 +4 3x+4=0
The equation x² - 4x + 3√2 = 0 has no real roots.
Roots of Quadratic EquationThe roots of a quadratic equation are the values of variables satisfying the given quadratic equation.
There are three types of roots in quadratic equations, they are:
Real and distinct roots.Real and equal roots.Complex roots.Difference between real and non-real roots
How many roots f(x) has can be seen from the discriminant's value : -
If b2 - 4ac > 0, the quadratic function has two unique real roots.
If b2 - 4ac = 0, then the quadratic function has one repeating real root.
If b2 - 4ac < 0, then the quadratic function has non-real roots.
Discriminant ; D = b² - 4ac
According to the given question, we have to find the nature of the roots of the equation, so finding the nature of the roots of all the equations separately
1. x² - 4x + 3√2 = 0
Here, a = 1, b = -4 and c = 3√2
∵ D = b² - 4ac
∴ D = (-4)² - 4(1)(3√2)
⇒ D = 16 - 12√2
⇒ D = 16 - 12(1.414) = 16 - 16.968
∴ D = -0.968
⇒ D < 0
Consequently, there are no real roots in the equation.
2. x² + 4x - 3√2 = 0
Here, a = 1, b = 4 and c = -3√2
∵ D = b² - 4ac
∴ D = (4)² - 4(1)(-3√2)
⇒ D = 16 + 12√2 > 0
⇒ D > 0
As a result, the equation has two unique real roots.
3. x² + 5x + 3√2 = 0
Here, a = 1, b = 5 and c = 3√2
∵ D = b² - 4ac
∴ D = (5)² - 4(1)(3√2)
⇒ D = 25 - 12√2 = 8.029
⇒ D > 0
As a result, the equation has two unique real roots.
4. 3x² + 4√3x + 4 = 0
Here, a = 3, b = 4√3 and c = 4
∵ D = b² - 4ac
∴ D = (4√3)² - 4(3)(4)
⇒ D = 48 - 48 = 0
⇒ D = 0
As a result, the equation has two roots that are equal.
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What are the 5 steps to solving inequalities?
The five steps to solving inequalities are:
Isolate the inequality symbol by using inverse operations. Simplify the inequality by combining like terms on either side of the inequality. Graph the inequality on a number line. Make a sign analysis of the inequality by determining the sign of the expression on either side of the inequality. Find the solution set of the inequality by identifying the values that make the inequality true.To solve an inequality, one must isolate the inequality symbol, simplify the inequality, graph the inequality on a number line, make a sign analysis of the inequality, and find the solution set of the inequality.
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Solve For Each Variable 17n+8=104+5n
The solution of the expression 17n + 8 = 104 + 5n for the variable n is given as follows:
n = 8.
How to solve the expression?The expression for this problem is defined as follows:
17n + 8 = 104 + 5n
Combining the like terms, the expression is given as follows:
17n - 5n = 104 - 8.
12n = 96.
The inverse operation of the multiplication is the division, hence the value of n is obtained as follows:
n = 96/12
n = 8.
Which is the solution of the expression for the variable n.
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Subtract. Simplify your answer
(-8k^2-6)-(6k^2-5k)
Answer:
-14[tex]k^{2}[/tex] + 5k -6
Step-by-step explanation:
(-8[tex]k^{2}[/tex] -6) - (6[tex]k^{2}[/tex] - 5k) Distribute the negative sign
-8[tex]k^{2}[/tex] - 6 -6[tex]k^{2}[/tex] + 5k Combine like terms
-14[tex]k^{2}[/tex] + 5k -6
Answer: -14k^2+15k-6
Step-by-step explanation:
(-8k^2-6)-(6k^2-5k)
-8k^2-6-6k^2+5k
-14k^2-6+5k
-14k^2+15k-6
What is a residual and how is it used in finding the line of best fit?
Residual is the difference between the expected and actual y values, so r I = y I y i. A negative residual indicates that the anticipated value is excessively high, whereas a positive residual indicates that the projected value was excessively low. The goal of a regression line is to reduce the total amount of residuals.
What is Mcq, or salvage value?
When an item reaches the end of its useful life, its salvage value—or potential market value—is estimated. It can also be described as the asset's book value after depreciation has been taken into account.
What does the depreciation formula's residual value mean?
The asset's final worth is its residual value. To obtain the entire amount, it is therefore deducted from the starting value. Consequently, we are given the depreciation figure. This sum is divided by the usable years of the asset using the straight-line depreciation technique.
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How do I Create a table in form?
Therefore , the solution of the given problem of table comes out to be we can create a table in form by following below steps.
Explain a table.A mathematical list is a list of numbers that represents the results of a calculation with several inputs. organized in rows and columns, data consists of numbers and descriptions. It is simple to recall the table and the 10 pattern. 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30 are the numerals in numerical order. Value mapping are used to illustrate the connections between various data elements.
Here,
Import the layout table by moving the pointer to the desired location on the form template.
Click Insert, followed by Layout Table, in the Tables toolbar.
The number of rows and rows to be included in the table should be entered with in Insert Table dialog box.
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The length of a basketball court is 84 feet, and the perimeter is 268 . What is the width of the basketball court?
Answer: 50 ft
Step-by-step Explanation:
First, subtract the given length from the perimeter:
*268 - (84 x 2) = 100
Then divide this by 2:
100 / 2 = 50
*We multiply the 84 by 2 since the court is assumed to have 4 sides meaning there are two sides with lengths and two sides with widths.
Evaluate. 12/3+3/4÷(−1/3)−1/2
The fraction 12/3+3/4÷(−1/3)−1/2is evaluated to give -114/10
What is a fraction?A fraction can be defined as part of a whole element, variable or number
The several types of fractions in mathematics are;
Mixed fractionsProper fractionsImproper fractionsSimple fractionsComplex fractionsFrom the information, we have that;
12/3+3/4÷(−1/3)−1/2
The fraction given is a mixture of proper fractions and improper fractions
Expand the bracket, we get;
12/3 + 3/4 ÷ -1/3 -1/2
Find the lowest common denominator
48 + 9 /12 ÷ -2 - 3 /6
Add the numerators
57/12 ÷ -5/6
Take the inverse of the divisor and multiply
57/12 × 6/-5
-114/10
Hence, the value evaluated from the fraction is -114/10
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100 POINTS! PLEASE HELP
Given that one of the factors is (x-5), which graph represents the polynomial function?
y=-x^4 +6x^3 +11x^2 -60x -100
The graph on the bottom left represents the polynomial function
y = -x⁴ + 6x³ + 11x² - 60x - 100.
What is graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
Given:
An equation,
y = -x⁴ + 6x³ + 11x² - 60x - 100.
And one of the factors of the equation is (x-5).
That means, x = 5 is one of the roots of the equation.
From the given graphs,
we can eliminate top left graph and bottom right graph.
Because, the graphs of the equation do not touch the x-axis at x = 5.
Let x = -2,
Then,
y = -(-2)⁴ + 6(-2)³ + 11(-2)² - 60(-2) - 100.
y = -16 -48 + 44 + 120 - 100
y = 0
That means,
x = -2 is one of the roots of the equation.
And the graph is given in the attached image.
And the graph is the bottom left graph.
Therefore, the graph in the bottom left is the required graph.
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A factory makes 718 toy trains in one day. The toy trains are placed in boxes of 30
Answer:
23.9
Step-by-step explanation:
15.
Marco is making blueberry muffins. The ratio between flour and blueberries for the recipe being used is shown in the table below.
Cups of Cups of
Flour Blueberries
1-2
24
A.Ocup
2
8
How many cups of blueberries will Marco need if he has 2 cups of flour to use?
B.
cup
D
1
2
3
4
1
c. 11 cups
6 cups
Therefore , the magical ratio for muffins is therefore 2:2:1:1, which is the answer to the ratio problem that was provided.
What is a ratio?An ordered combination of numbers “ a ” and “ b that is stated as just a / b, where b not greater than zero, is referred to as a ratio. A ratio is the result of equating two ratios. If there were one boy and three girls, the ratio could be shown as 1:3. 1/4 are boys, and 3/4 are girls. A part is a number, a proportion of size, or a difference among two or more things.
Here,
Since: Marco To avoid your batter and bakery items acquiring a purple-blue tinge, wash freeze blueberries multiple times in water it until water becomes lighter in color.
The magic muffin ratio is 2:2:1:1, which equals 1-two cups and 2,8 cups.
With a paper towel, dry them off, and then delicately fold it into the batter. Maintaining the lightness of rapid breads is the aim of this process.
The magical ratio for muffins is therefore 2:2:1:1, which is the answer to the ratio problem that was provided.
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2y = 6x + 4
y = -2x + 2
find x and y
The value of x is 0.
The value of y is 2.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 9 is an equation.
We have,
2y = 6x + 4 _____(1)
y = -2x + 2 ______(2)
Substituting (2) in (1).
2 (-2x + 2) = 6x + 4
-4x + 4 = 6x + 4
4 - 4 = 6x + 4x
10x = 0
x = 0
Now,
x = 0 in (2)
y = -2 x 0 + 2
y = 0 + 2
y = 2
Thus,
The value of x and y is 0 and 2.
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A ray , and an angle is two . The measure of an angle related to the length of its sides. So, the measure of an angle the same at all distances from its vertex.
The combination of two rays with the same terminal is called an angle. The vertex of the angle is the common terminal of the rays, which are referred to as the sides of the angle.
What is the relation between angle and rays?A ray is a segment of a line with one endpoint and an endlessly extending end. Two rays can be linked at their starting points to create an angle, and their other ends can stretch indefinitely.
According to the question,
the proportion of an angle's measurement to the width of its sides.
Therefore, an angle's measure is constant regardless of how far it is from its vertex.
Due to the fact that adjacent angles are two angles with a shared vertex, and side, but not interior points.
Therefore,
The combination of two rays with the same terminal is called an angle.
The vertex of the angle is the common terminal of the rays, which are referred to as the sides of the angle.
Hence the measure of an angle is the same at all distances from its vertex.
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Answer:
Step-by-step explanation:
- x/7 − 8 = 17
Show work
And check
Answer:
x = -175
Step-by-step explanation:
Given:
⇒ [tex]-\frac{x}{7}-8=17[/tex]
Solution:
Work:
[tex]-\frac{x}{7}-8=17[/tex]
[tex]-\frac{x}{7}-8+8=17+8[/tex] ⇒ Add 8 to both sides
[tex]-\frac{x}{7}=25[/tex]
[tex]7\left(-\frac{x}{7}\right)=25\cdot \:7[/tex] ⇒ Multiply both sides by 7
-x = 175
[tex]\frac{-x}{-1}=\frac{175}{-1}[/tex] ⇒ Divide both sides by -1
x = -175
Check:
Since, x = -175. We can substitute into the equation to check.
[tex]-\frac{-175}{7}-8=17[/tex]
[tex]-\frac{-175}{7}=25[/tex]
[tex]25-8=17[/tex] ⇒ Statement = True (25 minus 8 is 17.
Hence, x = -175
Lenvy~
∣x−7∣=∣2x−8∣ (there are 2 solutions for the positive one and the negative)
Answer:
x = 1, x = 5
Step-by-step explanation:
|x−7|=|2x−8| ==> there are 2 ways to simplify this equation:
1. x - 7 = 2x - 8
2. -(x - 7) = 2x - 8
Let's first solve equation 1:
x - 7 = 2x - 8
-7 = x - 8 ==> subtract x on both sides
x - 8 + 8 = -7 + 8 ==> add 8 on both sides
x = 1 ==> simplify
Now let's solve equation 2:
-(x - 7) = 2x - 8
-x - (-7) = 2x - 8 ==> distribute the negative sign to x and -7
-x + 7 = 2x - 8 ==> subtracting a negative number is equivalent to adding a
positive number
7 = 3x - 8 ==> add x on both sides
15 = 3x ==> add 8 on both sides
x = 5 ==> divide 3 on both sides
Hence, the answers are x = 1 and x = 5.