Therefore , the solution of the given problem of triangle comes out to be the equilateral triangle are is 62.28 cm².
Describe the triangle.In geometry, triangular polygons are ones that have three vertices and a right side. This object in two dimensions has three straight sides. Triangles are examples of three-sided polygons. The sum of a triangle's three angles is 180 degrees. The triangle lies on one plane.
Here,
Given : side = 12cm
Area of an equilateral triangle
=> √3/4 * side²
Side of triangle =12 cm
Area of an equilateral triangle
= > √3/4 * 12²
=>√3/4 * 12*12
=> 62.28 cm²
Therefore , the solution of the given problem of triangle comes out to be the equilateral triangle are is 62.28 cm².
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What i the cartoonit' purpoe in thi cartoon?
to convince people that fungal band are dangerou for beetle
to convince people that beetle are damaging to tree
to make people laugh at a play on word
to make people believe that longhorn beetle hate fungi
The cartoonist's purpose of the given cartoon is C: "to make people laugh at a play on the words".
Though the cartoon in the picture is designed based on the concept that fungal bands are an effective way of the biological control of Asian longhorn beetles, the core purpose of the cartoonist in designing this cartoon is to portray the idea in a comical way, indicating how these fungi actually form a music band called 'the fun guy' and they remove the beetles by playing their music, that awful racket as the beetle says.
Thus, the cartoonist's purpose of this cartoon is to make people laugh at a play on the words.
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Given that startfraction a b over d e endfraction = startfraction b c over e f endfraction = one-half, complete the statements to show that △abc ~ △def by the sas similarity theorem. horizontal and vertical lines are . so, angles are right angles by definition of perpendicular lines. all right angles are . therefore, △abc ~ △def by the sas similarity theorem.
Lines running horizontally and vertically are parallel. So, angles A, B, and C are right angles by definition of perpendicular lines. All right angles are equal. Therefore, △ABC ~ △DEF by the SAS similarity theorem.
Given that startfraction a b over d e endfraction = startfraction b c over e f endfraction = one-half
Step 1: Multiply both sides of the equation by de:
a/b * de = bc/ef * de
Step 2: Simplify the left side of the equation:
ade = bcde
Step 3: Divide both sides of the equation by ad:
a/d = b/e
Step 4: Multiply both sides of the equation by be:
ab/d = be/e
Step 5: Simplify the left side of the equation:
ab = be
Step 6: Divide both sides of the equation by be:
a/b = 1/e
Step 7: Multiply both sides of the equation by ef:
a/b * ef = 1/e * ef
Step 8: Simplify the left side of the equation:
aef = ef
Step 9: Divide both sides of the equation by ef:
a/b = 1/e
Conclusion: startfraction a b over d e endfraction = startfraction b c over e f endfraction = one-half
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Answer:
perpendicular
b and e
congruent
Find the lope-intercept equation of the line that pae through (1,-3) and ha a lope of -1/4
The slope intercept form of the equation is
y = -1/4x -11/4
What is Slope Intercept form ?One of the most popular ways to describe a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula may be used to get the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills.
The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. Any point's coordinates on a straight line must fulfill a certain relation, which is known as the equation of a straight line.
Any location that is not on the line will not fulfill the coordinates.
This equation's solution is simple to find. A straight line's slope, or angle of inclination from the x-axis, and the intercept it makes with the y-axis are both necessary to determine the slope intercept form of the line.
The line passes through (1,-3)
slope = -1/4
The equation of the line
y = mx + c
here m is the slope and c is the intercept.
putting the point and slope in the equation
-3 = -1/4 *1 + c
⇒ c = -11/4
So the slope intercept form of the equation is
y = -1/4x -11/4
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A particle moves along the x-axis so that at time
t
≥
0
t≥0 its position is given by
x
(
t
)
=
t
3
−
6
t
2
−
29.
x(t)=t
3
−6t
2
−29. Determine the total distance traveled by the particle from
0
≤
t
≤
7.
0≤t≤7.
The total distance traveled from 0 ≤ t ≤ 7, considering the position function x(t) = t³ - 6t² - 29, is given as follows:
288.75 units.
How to obtain the total distance traveled?The position function for this problem is defined as follows:
x(t) = t³ - 6t² - 29.
The total distance traveled over an interval [a,b] is given by the definite integral of the function x(t) over the interval from x = a to x = b.
The definite integral in this problem is calculated as follows:
I = 0.25t^4 - 2t³ - 29t, from t = 0 to t = 7.
Applying the Fundamental Theorem of Calculus, the total distance is calculated as follows:
I = 0.25(7)^4 - 2(7)³ - 29(7) - (0.25(0)^4 - 2(0)³ - 29(0))
I = 288.75 units.
(which is the absolute value of the result of the definite integral).
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Find the value of x in the diagram at the right.
Show your work.
In the given diagram beside a coffee, the value of x is 38.
What is diagram?A diagram is a visual, symbolic representation of data. Diagrams have been used on cave walls since prehistoric times, but they became more common during the Enlightenment. The method occasionally employs the projection of a three-dimensional visualisation onto a two-dimensional surface. Sometimes the word "graph" is used in place of the word "diagram."
We know that all angles here add up to 360°
And with the vertical angles theorem we get the equation
2(36°) + 2(78 - x)° + 2(3x - 10) = 360°
2(36 + 78 - x + 3x - 10) = 360°
2(104 + 2x) = 360°
208 + 4x = 360°
4x = 360 - 208
4x = 152
x = 152/4
x = 38
Thus, In the given diagram beside a coffee, the value of x is 38.
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Jess and Brian are playing the following game: Jess thinks of a fraction, and Brian flips a coin. If the coin turns up heads, Jess multiplies the number she's thinking of by $\frac{5}{6}$. If the coin turns up tails, she multiplies the number she's thinking of by $\frac{6}{5}$. Brian flips the coin ten times, and after each flip Jess multiplies the number in her head by either $\frac{5}{6}$ or $\frac{6}{5}$, depending on the coin flip. The ten coin flips turn out to be:\[ \text{THTTHTHTTT}, \]where H means 'heads' and T means 'tails.' What number is Jess thinking of at the end of the game if she starts out with the fraction $\frac{5}{9}$
Starting out with the fraction of 5/9, Jess would be thinking of the fraction 144/125 at the end of the game if the ten coin flips turn out to be {THTTHTHTTT}.
What is the probability of getting H or T in a coin flip?Since both outcomes are equally likely, the probability of getting heads is 0.5 and the probability of getting tails is also 0.5. Alternatively, the probability of getting H or T in a coin flip is 1.
What is the significance of probability?Probability is an important method for comprehending and making judgments regarding uncertain occurrences in many disciplines, including statistics, finance, and science. It aids in quantifying and forecasting the probability of specific events, enabling us to make better educated choices and comprehend the degree of risk involved with various activities. In summary, probability is a key idea in decision-making and risk management because it is a potent instrument for comprehending and managing uncertainty.
Taking the sequence of coin flips in ten tires, i.e THTTHTHTTT , and starting from the fraction 5/9, the fraction that jess would be thinking at the end of the game can be calculated as,
5/9 * (6/5)^7 *(5/6)^3 , since there are 7 Tails and 3 Heads during the whole game. Which is equal to the fraction 144/125.
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Which represents the solution set of 5(x+5) <85?
Ox< 12
O x> 12
O x < 18
O x> 18
Answer: O x<12
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
5x+25<85
Step 2: Subtract 25 from both sides.
5x+25−25<85−25
5x<60
Step 3: Divide both sides by 5.
5x/5 < 60/5
x<12
A band wants to enter a contest that requires traveling expenses. They need at least $1,150 to cover all of the expenses. They have already saved $700. They are selling shirts with a profit of $7. 00 per shirt to earn the remaining money Part Which inequality represents the minimum number of shirts, n, the band must sell to earn the remaining money 1, 150
the number of shirts has to be an integer (you can not sell "part" of a shirt) n >= 65
They need at least $1,150
They have already saved $700
They are selling shirts with a profit of $7.00 per shirt
If they sell n number of shirts, they will earn n times $7.00
Since they have already 700, they will earn a total of 700 + 7n
If this quantity has to be equal or greater to 1,150, we can write:
1150 <= 700 + 7n
if we solve this inequality for n:
1150 <= 700 + 7n
1150 - 700 <= 7n
450 <= 7n
450/7 <= n
64.28 <= n
Since the number of shirts has to be an integer (you can not sell "part" of a shirt)
n >= 65
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The volume of a sphere is given by the equation V = 1/6(square root of 3.14) x 60^3/2
where S is the surface area of the sphere. Find the volume of a water walking ball, to the nearest cubic meter
A cylinder shaped dispenser holds 5,652 cubic centimeters of liquid soap and is now full. The radius of the dispenser is 7.5 centimeters. What is the difference between the height of the soap in the full dispenser and the height when 4,239 cubic centimeters of soap remains in the dispenser
On solving the provided question, we can say that difference of cylinder between the height of the soap 8 cm.
what is cylinder?One of the most fundamental curved geometric forms is the cylinder, which is often a three-dimensional solid. It is referred to as a prism with a circle as its base in elementary geometry. Several contemporary fields of geometry and topology also define a cylinder as an indefinitely curved surface. A three-dimensional object known as a "cylinder" consists of curving surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure that has two bases that are both identical circles joined by a curving surface at the height of the cylinder, which is determined by the distance between the bases from the center. Examples of cylinders are cold beverage cans and toilet paper wicks.
[volume of cylinder]=pi*r²*h- = h=[volume of cylinder]/(pi*r²)
Volume=5652 cm³
r=7.5 cm, so, h= [tex][5652]/(3.14*7.5²) = h=32 cm[/tex]
the height of the soap in the full dispenser is 32 cm
the height when 4,239 cubic centimeters of soap remains in the dispenser is h [tex]=[4239]/(3.14*7.5²) = h=24 cm[/tex]
the difference is [tex]32-24 = 8 cm[/tex]
the answer is
8 cm
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I need some help again:(. My question says "complete the statement with the correct exponent" it shows 5 (blank) = 125 I know that whenever I have a two it's 5 squared but I don't know how to actually find the exponent without it showing 5 x 5 x 5 ( and so on,not what it actually showed just an example )
The value of the exponent based on the information is 3. Therefore, 5³ = 35.
How to illustrate the exponent?It should be noted that the exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
Based on the information given, it should be noted that this can be written as:
5^x = 125
5^x = 5³
Since the base is equal
x = 5.
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find the zeroes of the polynomial and verify the relations between coefficient and zeroes
3x²-x-4
Answer:
(-1) & 4/3
Step-by-step explanation:
Polynomial:3x² - x - 4
Sum = -1
Product = 3*(-4) = -12
Factors = -4 and 3 { (-4)*3 = -12 & (-4) + 3 = -1}
3x² - x - 4 = 3x² + 3x - 4x -4 {Rewrite the middle term using the factors}
= 3x(x + 1) -4(x + 1)
=(x + 1)(3x - 4)
x + 1 = 0 ; 3x - 4 = 0
x = -1 ; 3x = 4
x = 4/3
[tex]\sf Zeroes \ of \ the \ polynomial \ are \ (-1) \ and \ \dfrac{4}{3}[/tex]
Verification:
[tex]\sf 3x^2 - x - 4 = 0\\\\Divide \ the \ entire \ equation \ by \ 3\\\\\\\dfrac{3x^2}{3}-\dfrac{x}{3}-\dfrac{4}{3}=0\\x^2 - \dfrac{x}{3}-\dfrac{4}{3}=0[/tex]
Coefficient of x = sum of the zeroes
[tex]\sf = -1 + \dfrac{4}{3}\\\\=\dfrac{-3}{3}+\dfrac{4}{3}\\\\=\dfrac{1}{3}\\\\[/tex]
Constant = product of the zeroes
[tex]\sf = (-1)*\dfrac{4}{3}\\\\=\dfrac{-4}{3}[/tex]
Thus verified.
What is the gradient of 2x 3y 6?
The gradient of the linear equation 2x + 3y + 6 is (3/2).
The gradient of a linear equation in the form of y = mx + c is m, which represents the slope of the line. The slope is defined as the ratio of the change in y to the change in x. It represents the steepness of the line.
The equation 2x + 3y + 6 is not in the form of y = mx + c. It is in the form of Ax + By + C = 0, which is the general form of a linear equation. To find the gradient of such an equation we need to divide -A/B. In this case, the gradient of the line is -2/3.
The gradient of a line gives us the direction of the line, it is the slope of the line. It tells us how steep the line is and if it is going up or down. A positive gradient means the line is going up and a negative gradient means the line is going down.
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18=0. 125. Which calculation is NOT a way to find 58?
CLEAR CHECK
A. 5÷8
B. 5⋅0. 125
C. 0. 5+0. 125
D. 1−0. 125
The correct option is D. 1 − 0. 125 is NOT the correct way to find the value of fraction 5/8.
Explain the term fraction?a numerical expression in which the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator as well as denominator of a complex fraction. The numerator of a proper fraction is less than every denominator.Consider the given options;
A. 5÷8
5÷8 = 5/8 (correct)
B. 5⋅0. 125
5*0.125 = 0.625
5*0.125 = 5/8 (correct)
C. 0. 5+0. 125
5+0. 125 = 0.625
5+0. 125 = 5/8 (correct)
D. 1−0. 125
1−0. 125 = 0.785
1−0. 125 = 7/8 (not correct)
Thus, option D is not the correct way to solve the equation.
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The correct question is attached.
A watch increased in price by 4/5. After the increase it was priced at £126. What was the original price of the watch?
A watch increased in price by 4/5 is priced at £126, then the original price of the watch was £100.
We know that the price of the watch increased by 4/5. To find the original price of the watch, we can use the following formula:
original price = new price / (1 + increase percentage)
In this case, the new price of the watch is £126 and the increase rate is 4/5. So we have:
original price(1 + 4/5) = 126
original price = 126 / (1 + 4/5)
original price = 126 / (1+ 0.8)
original price = 126/1.8
original price = 70
So, the original price of the watch was £70.
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15 points, see attachment
Answer: HG = CD.
Step-by-step explanation: If you tilt the second triangle so it's flat like the first triangle, you can see that HG is equal to CD.
A function multiplies its input by 3/4 then adds 7 to get its output. Use function notation to represent this function.
f(x)=_____
In function notation, the function is represented as f(x) = (3/4)x + 7.
In function notation, the function is represented by the letter "f" followed by the input value inside parentheses. The input value is typically represented by the letter "x". In this case, the function takes "x" as its input and performs the operation of multiplying it by 3/4 and then adding 7 to get the output. We can represent this function using the equation f(x) = (3/4)x + 7.
It's worth noting that the function notation is a way to express a mathematical relationship between two variables, the input variable (x) and the output variable (f(x)), in which every input value of x corresponds to exactly one output value. This equation represents the same function regardless of the input value, and it can be used to find the output for any input value by simply substituting it in the equation.
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If 3x+14=26, which of these equations is true?
Answer:
x=4
Step-by-step explanation:
3x+14=26
3x=26-14
3x=12
x=12/3
x=4
Answer: x = 4
Let's solve your equation step-by-step:
3x+14=26:
Step 1: Subtract 14 from both sides.
3x+14−14=26−14
3x=12
Step 2: Divide both sides by 3.
3x/3 = 12/3
x=4
The 19th and 15th terms of an AP are- 5 and -7 1/2, respectively. What is the sum of the first 20 terms.
The sum of the first 20 terms of the sequence is - 206.25
What is an Arithmetic Progression?Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence. For example, the series of natural numbers: 1, 2, 3, 4, 5, 6,… is an Arithmetic Progression, which has a common difference between two successive terms (say 1 and 2) equal to 1 (2 -1). Even in the case of odd numbers and even numbers, we can see the common difference between two successive terms will be equal to 2
a + 18d = - 5
a + 14d = -7 1/2
---------------------
4d = -5 + 15/2
8d = -10 + 15
8d = 5
d = 5/8
a + 18(5/8) = -5
8a + 90 = -40
8a = -40 - 90
8a = -130
a = -130/8
The sum of the first 20 will be;
Sum = (20/2) (2(-130/8) + (20-1)(5/8))
Sum = 10 (-260/8 + 95/8)
Sum = 10 (-165/8)
Sum = - 206.25
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Is math hard to study?
Han says that the value of the 7 in 735,208 is 10 times the value of the 7 in 137,342. Do you agree with Han
Han is wrong , we do not agree with him. The value of the 7 in 735,208 is not the 10 times the value of the 7 in 137,342.
The value of 7 here refers to the place value of 7 , in 735,208 7 is at lakhs place whereas in 137,342 , 7 is in thousandth place .
Therefore , Han is wrong as because if we will the 7 in 137,342. when multiplied by 10 will go to the ten thousandth place and not the lakh place.
The place value is a measure which is used to represent the position of each digit in a number . Based on their position in the number, digits are assigned place values such as ones, tens, hundreds, thousands, ten-thousands, and so on. For example, 1 in 512400 has a place value of ten thousands, i.e. 10000.
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The histogram shows the number of items that customers bought during a trip to the grocery story 1 day. 400 customers took a trip to the grocery store that day. Which is the best estimate for the number who bought at least 50 items during their trip
The number of people who bought fewer than 30 items exists 204.
What is meant by histogram?The frequency distribution of a few data points for one variable is represented graphically by a histogram. Heterogeneous "bins" or "range groups" are frequently used in histograms in order to categorize data and count the number of data points that are part of each bin.
Among graphing tools, the histogram is widely used. It is utilized to encapsulate discrete or continuous data that is measured on an interval scale. It is frequently employed as a convenient way to highlight the key characteristics of the data distribution.
As opposed to bar charts, which show categorical variables, histograms visualize quantitative or numerical data. Typically, a histogram's numerical data will be continuous (having infinite values).
Number of people who bought fewer than 30 items
= (0.14 + 0.12 + 0.24)400
= 0.51 x 400 = 204
Therefore, the correct answer is option B) 204.
The complete question is:
The histogram shows the number of items that customers bought during a trip to the grocery store one day. Four hundred customers took a trip to the grocery store that day. Which is the best estimate for the number who bought fewer than 30 items during their trip?
A) 278
B) 204
C) 148
D) 106
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Solve the system of equations.
y = 3x
y=x²-4
A. (-1, -3) and (4, 12)
O B. (-4, 12) and (1, -3)
C. (-1, 3) and (4, -12)
OD. (-4,-12) and (1, 3)
Answer:
A
Step-by-step explanation:
Se them equal to each other
3x = [tex]x^{2}[/tex] - 4
[tex]x^{2}[/tex] -3x -4 = 0
(x + 1) ( x -4)
x + 1 = 0
x = -1
y = 3x
y = 3(-1)
y = -3
(-1,-3)
x - 4 = 0
x = 4
y = 3x
y = 3(4)
y = 12
(4, 12)
What should be the value of a if the value of 2x^2 XA equals to 5 when?
The value of a is -5. All phrases that involve x become zero when we set their value to zero, leaving only constant terms.
The given equation is 2x^2 + x -a = 5.
let's try to understand what is an equation.
An equation can be defined in numerous ways. Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For example,
The two equations 4x + 56 and 14 are joined by the equal sign to get the equation 4x + 56 = 14. Algebraic equations in mathematics frequently have one or more variables.
There are many different kinds of equations, including cubic, quadratic, and linear equations.
There are many distinct sorts of equations, depending on the degree of the equation.
2x^2 + x -a = 5. put x = 0.
2*0 + 0 - a = 5
0 + 0 -a = 5
-a =5
a = -5.
So the value of a is -5.
Given Question is incomplete complete question here:
What should be the value of a if the value of 2x^2+x - a equals to 5
when x = 0?
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the sum of a number b and 24
answer:
b+24
step-by-step explanation:
it’s just asking for the sum so add the two values. there are no other integers given other than 24 so the answer is in expression form. hope that helps!
Coach Brown buys packs of Gummi Bears at $0. 60 and resales them at $1. 0. At what percent did he mark the candy up?
A. 10. 47
B. 3. 59
C. 9
D. 67
E. 69
F. 10. 25
If the coach buys the packs of Gummi Bears at $0.60 and resales them at $1 , then the percent markup for the candy is (d) 67% .
The price for which the Coach buys Gummi Bears is = $0.60 ;
the price at which the Coach resales them is = $1 ;
So , the Markup is the difference in the price of purchase and price of resale of the candy ,
that means ; the [tex]Markup = \$1 - \$0.60[/tex] ;
= $0.4
So , the Percent Markup is = [tex]\frac{0.4}{0.6} \times 100[/tex]
= 66.66666...
≈ 67% .
Therefore , the percent Markup for the Candy is 67% .
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Simplifying algebraic expression
4-6 = -2
x/7-6
Substitute
28/7-6
PEMDAS
28/7 = 4
4-6 = -2
(If you're looking for the expression, it's 4-6. But if straight answer, -2)
Answer:
[tex] \sf \: \frac{x}{7} - 6 = - 2[/tex]
Step-by-step explanation:
Given information,
[tex] \sf \rightarrow \: \frac{x}{7} - 6[/tex]
[tex] \sf \rightarrow \: x = 28[/tex]
Now the value of expression is,
[tex] \sf \rightarrow \: \frac{x}{7} - 6[/tex]
[tex] \sf \rightarrow \: \frac{28}{7} - 6[/tex]
[tex] \sf \rightarrow \: 4 - 6[/tex]
[tex] \sf \rightarrow \: - 2 = > final \: value[/tex]
Therefore, the answer is -2.
Simplify: [tex]\frac{-28cd^3}{-21bd^2}[/tex]
The answer is 4cd/3b
hope it's correct
How do you know if a graph is logarithmic or exponential?
exponential function in the form y=ab^x by identifying the common ratio (b) and y-intercept (a) in the graph and if the log term involved in the given function then it is a logarithmic
How do you identify an exponential function from a graph?
Given a graph of a line, we can write a linear function in the form y=mx+b by identifying the slope (m) and y-intercept (b) in the graph. GIven a graph of an exponential curve, we can write an exponential function in the form y=ab^x by identifying the common ratio (b) and y-intercept (a) in the graph
and if the log term involved in the given function then it is a logarithmic
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2x-(x+5)=-1
Solve for x.
Answer:
x=4
Step-by-step explanation:
2x-(x+5)=-1
Solve for x
Distribute the minus sign
2x-x-5=-1
Combine like terms
x -5 = -1
Add 5 to each side
x-5+5 = -1+5
x=4
[tex]2x-(x+5)=-1[/tex]
Distribute negative sign:
[tex]2x+-1(x+5)=-1[/tex]
[tex]2x+-x+-5=-1[/tex]
Combine Like Terms:
[tex](2x+-x)+(-5)=-11[/tex]
[tex]x-5=-1[/tex]
Add 5 to both sides:
[tex]x-5+5=-1+5[/tex]
[tex]\fbox{x = 4}[/tex]