The ways the system of equations 9x - 2y = 43x+8y=12can be solved are:
A) Multiply the first equation by 4, then add the equations.
D) Multiply the second equation by 3, then subtract the equations.
How can the system of equations?From the given equations,9x - 2y = 43x+8y=12we need to use wyas of solving simultaneous equation to solve it.
Then if we Multiply the first equation by 4, thge we can then perform addition to the second equation like
9x - 2y = 4
36x - 8y = 4
3x+8y=12
then if we add to equation 2 we have
39x =12
then we can solve x = 12/39
The same can be done with equation D .
Therefore, option A and D are correct.
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Answer:
Step-by-step explanation:
To solve the system of equations:
9x - 2y = 4 ...(1)
3x + 8y = 12 ...(2)
We can use elimination method by adding or subtracting the equations in a way that one variable is eliminated.
Here are the possible ways to solve the system:
A) Multiply the first equation by 4, then add the equations.
Multiplying the first equation by 4 gives:
36x - 8y = 16
Adding the resulting equation to the second equation gives:
36x - 8y + 3x + 8y = 16 + 12
Simplifying the equation:
39x = 28
x = 28/39
Substituting x in equation (1) gives:
9(28/39) - 2y = 4
Solving for y gives:
y = -155/78
Therefore, the solution is (x,y) = (28/39, -155/78).
B) Multiply the second equation by 3, then add the equations.
Multiplying the second equation by 3 gives:
9x + 24y = 36
Adding the resulting equation to the first equation gives:
9x - 2y + 9x + 24y = 4 + 36
Simplifying the equation:
18x + 22y = 40
Dividing the equation by 2 gives:
9x + 11y = 20
Substituting 9x from equation (2) gives:
3x + 8y = 12
Solving for x gives:
x = (12 - 8y)/3
Substituting x in equation (3) gives:
9[(12-8y)/3] + 11y = 20
Solving for y gives:
y = 16/39
Substituting y in equation (2) gives:
3x + 8(16/39) = 12
Solving for x gives:
x = 28/39
Therefore, the solution is (x,y) = (28/39, 16/39).
C) Multiply the first equation by 3, then add the equations.
Multiplying the first equation by 3 gives:
27x - 6y = 12
Adding the resulting equation to the second equation gives:
27x - 6y + 3x + 8y = 12 + 12
Simplifying the equation:
30x = 24
x = 4/5
Substituting x in equation (1) gives:
9(4/5) - 2y = 4
Solving for y gives:
y = -23/10
Therefore, the solution is (x,y) = (4/5, -23/10).
D) Multiply the second equation by 3, then subtract the equations.
Multiplying the second equation by 3 gives:
9x + 24y = 36
Subtracting the second equation from the first equation gives:
6x - 26y = -8
Solving for x gives:
x = (26y - 8)/6
Substituting x in equation (2) gives:
3[(26y-8)/6] + 8y = 12
Solving for y gives:
y = 16/39
Substituting y in equation (1) gives:
9x - 2(16/39) = 4
Solving for x gives:
x = 28/39
Therefore, the solution is (x,y) = (28/39, 16/39).
express 2x^2 + 8x in the form a(x + b)^2 + c
The vertex form equivalent to the given expression; 2x² + 8x as required to be determined in the task content is; 2 (x + 2)² + 8.
What is the vertex form equivalent of the expression?The vertex form equivalent of the given expression can be determined as follows;
2x² + 8x
2 (x² + 4x)
2 ( (x + 2)² + 4)
= 2 (x + 2)² + 8.
Ultimately, the vertex form equivalent of the given expression as required is; 2 (x + 2)² + 8.
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the state narcotics bureau must form a 5-member investigative team. if it has agents from which to choose, how many different possible teams can be formed?
the number of different possible teams that can be formed is equal to nCr, or n!/(r!(n-r)!).
Assuming that the state narcotics bureau has more than 5 agents from which to choose, the number of different possible teams that can be formed is equal to the number of combinations of 5 agents out of the total number of agents the bureau has. This can be calculated using the formula nCr (n choose r), where n is the total number of agents and r is the number of agents in each team, which in this case is 5.
Therefore, the number of different possible teams that can be formed is equal to nCr, or n!/(r!(n-r)!).
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State how the triangles are congruent using SSS, SAS, ASA, AAS, or
HL. If they are not congruent, type NOT.
Answer:
ASA
Step-by-step explanation:
There are two pairs of congruent angles, and the pair of congruent sides is included between the angles.
what is the order of processes that support the central dogma?
The order of processes that support the central dogma are:1.DNA replication: the process by which DNA makes a copy of itself.
2.Transcription: the process by which RNA is synthesized from a DNA template.
3.Translation: the process by which proteins are synthesized from RNA templates.
The central dogma of molecular biology describes the flow of genetic information within a biological system. The method by which DNA instructions are translated into useful products is known as the "Central Dogma." Francis Crick, who discovered the structure of DNA, first put up the idea in 1958.
The order of processes that support the central dogma are:
1.DNA replication: the process by which DNA makes a copy of itself.
2.Transcription: the process by which RNA is synthesized from a DNA template.
3.Translation: the process by which proteins are synthesized from RNA templates.
In summary, the central dogma can be described as follows: DNA is replicated to make more DNA, DNA is transcribed into RNA, and RNA is translated into proteins.
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This is the correct answer
Answer: yes
Step-by-step explanation:
-12,1 and x,7 when m = 1/8
The x has a value of 36. The line's two points are (-12, 1) and (36, 7).
The purpose of slope calculation?The slope of a line frequently represents the steepness and direction of the line. The slope of a straight line between the two locations, (x1,y1) and (x2,y2), can be easily determined by calculating the difference between their coordinates.
We can apply the slope formula to determine the value of x:
m is the slope and (x1, y1) and (x2, y2) are two points on the line, with m = (y2 - y1) / (x2 - x1).
We are given the point (x1, y1) = (-12, 1) and the slope m = 1/8. We are also given the y-coordinate of the other point as y2 = 7.
Plugging in the known values, we get:
1/8 = (7 - 1) / (x - (-12))
Simplifying and solving for x, we get:
1/8 = 6 / (x + 12)
1 = 48 / (x + 12)
x + 12 = 48
x = 36
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A and be are both negative integers with a>b. Classify these are true or false. A) b
The statement "sum of a and b integers is a negative integer" is true given that A and B are both negative integers and A is greater than B.
When we add two negative integers, the sum is always negative. This is because adding a negative number is the same as subtracting its absolute value. Therefore, if A and B are negative integers, then A + B will be negative as well.
Since A > B, the sum A + B will be closer in value to A than to B. However, it will still be negative because A and B are both negative integers.
So, the sum of A and B is a negative integer, and the statement is true.
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____ The given question is incomplete, the complete question is given below:
A and B are both negative integers with a>b. Classify this are true or false. sum of a and b integers is a negative integer.
25kg= blank lb i need help plese i have 2 min left
Answer: 25,000 grams
Step-by-step explanation:Really sorry if im wrong.
n the manufacturing of a plastic material, it is be- lieved that the cooling time has an influence on the impact strength. therefore a study is carried out in which plastic material impact strength is determined for 4 different cooling times cooling time in second : 15 25 35 40 impact strength in kj/m2 : 42.1 36.0 31.8 28.7 a) find explanatory and response variable? b) find equation of linear model that describes re- lationship between predicted value of response and explanatory variable? c) based on r2, what you can say about response and explanatory variable?
Explanatory variable: Cooling time in seconds
Response variable: Impact strength in kj/m2
To find the equation of the linear model that describes the relationship between the predicted value of the response and the explanatory variable, we can use linear regression analysis. Using a statistical software or a calculator, we can find the slope and intercept of the line that best fits the data.
The equation of the linear model is:
Impact strength = -1.23 * Cooling time + 62.61
R-squared (R2) is a statistical measure that represents the proportion of the variance in the dependent variable (impact strength) that is explained by the independent variable (cooling time). It ranges from 0 to 1, with higher values indicating a better fit of the model.
Based on the value of R2, we can say how much of the variation in impact strength can be explained by cooling time. The closer R2 is to 1, the better the model fits the data, and the more likely it is that the impact strength is affected by cooling time. A value of 1 would indicate that all the variation in impact strength is explained by cooling time, while a value of 0 would indicate that cooling time has no effect on impact strength.
Without knowing the actual value of R2, we cannot say for sure what the relationship is between the explanatory and response variables. However, if the value of R2 is high (close to 1), we can conclude that cooling time has a significant effect on impact strength. If the value of R2 is low (close to 0), we cannot conclude that cooling time has a significant effect on impact strength.
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If five people share three cartons of chow mein what is each person’s share
Answer:
1.66
Step-by-step explanation:
hope this helps
Answer:
3/5 or 0.8
Step-by-step explanation:
3 Cartons, divided by 5 people =
3/5 or 0.8
One way of writing 75 as the sum of consecutive whole numbers is 24 + 25 + 26. How many other ways are there?
Answer:
None. [tex]24+25+26[/tex] is the only valid answer
Step-by-step explanation:
We can create an expression for the sum of 3 consecutive numbers.
[tex]S=x+(x+1)+(x+2)[/tex]
Which we can simplify to
[tex]S=x+x+1+x+2[/tex]
[tex]S=3x+3[/tex]
In this example we are given a sum of 75.
[tex]75=3x+3[/tex]
Lets solve for [tex]x[/tex].
Subtract 3 from both sides.
[tex]72=3x[/tex]
Divide both sides by 3.
[tex]24=x[/tex]
To find out what the 3 numbers are we can plug in 24 for x
[tex]x+(x+1)+(x+2)[/tex]
[tex]24+(24+1)+(24+2)[/tex]
[tex]24+25+26[/tex]
Answer:
4 other ways (5 ways, total).
Step-by-step explanation:
You want to know how many other ways 75 can be written as the sum of consecutive whole numbers other than 24+25+26.
SolutionIf 75 is written as the sum of an odd number of integers, the middle integer of the set will be 75 divided by the number of integers. The divisors of 75 are {1, 3, 5, 15, 25, 75}. If the numbers in the sum are non-negative, the number of integers involved cannot be more than √(2·75) ≈ 12. Then allowed odd numbers of integers in the sum are 3 and 5.
If 75 is written as the sum of an even number of integers, the quotient when 75 is divided by the number of integers must be 1/2 more than a whole number. Such integer divisors are 2, 6, and 10.
Sums37 + 38 = 75 . . . . 2 integers
24 + 25 + 26 = 75 . . . . 3 integers (the given sum)
13 + 14 + 15 + 16 + 17 = 75 . . . . 5 integers
10 + 11 + 12 + 13 + 14 + 15 = 75 . . . . 6 integers
3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 75 . . . . 10 integers
There are 4 other ways to use consecutive non-negative integers to make a sum of 75.
A repeated-measures research study and a separate independent-measures research study both produced a t statistic with df = 10. How many individuals participated in each research study?
Group of answer choices
a.)n = 12 for a repeated-measures research study and n = 11 for an independent-measures research study
b.)n = 12 for a repeated-measures research study and n = 12 for an independent-measures research study
c.)n = 11 for a repeated-measures research study and n = 11 for an independent-measures research study
d.)n = 11 for a repeated-measures research study and n = 12 for an independent-measures research study
By applying repeated and independent measures concepts, it can be concluded that there are 11 individuals participated in the repeated-measures research study and 12 individuals participated in the independent-measures research study (option D).
In a repeated-measures research study, the degree of freedom (df) is calculated by subtracting 1 from the number of individuals in the study (n). Therefore, if df = 10, then the number of individuals in the study is 10 + 1 = 11.
Whilst, in an independent-measures research study, the degree of freedom (df) is calculated by subtracting 2 from the number of individuals in the study (n). Therefore, if df = 10, then the number of individuals in the study is 10 + 2 = 12.
Therefore, it can be concluded that there are 11 individuals participated in the repeated-measures research study and 12 individuals participated in the independent-measures research study (option D).
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The vertices of △JKL are J(−3, −2), K(1, 4), and L(4, 2). Find the vertices of the image of △JKL under the dilation centered at the origin with scale factor 5.
The coordinate pairs of vertices D₅ (△JKL) of are J'(-15,-10), K'(5,20) and L'(20,10).
What does a math definition of a coordinate plane mean?
A surface with two dimensions known as the coordinate plane is created by two number lines. The x-axis is a single number line that runs horizontally. The y-axis is the name given to the vertical number line that is the other number line.
A place known as the origin is where the two axes collide. To graph points, lines, and other things, we can utilize the coordinate plane.
We know that, D₅ (△JKL) means triangle JKL dilated by scale factor 5 with origin as center of dilation.
If a figure is dilated by factor k and origin is the center of dilation, then
( x, y ) ⇒ ( kx , ky )
From the given problem, the rule of dilation is
( x , y ) ⇒ ( 5x , 5y )
Now
J( -3 , -2 ) ⇒ J'( 5(-3), 5(-2)) = J'( -15 , -10 )
K( 1,4 ) ⇒ K'(5(1) , 5(4)) = K'( 5,20 )
L( 4,2 ) ⇒ L'(5(4), 5(2)) = L'( 20,10 )
Therefore, the coordinate pairs of vertices D₅ (△JKL) of are J'(-15,-10), K'(5,20) and L'(20,10).
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The equation 7(2W + 3) = 14W + 20 has no solutions. Change one term in the original equation to create a new equation with infinitely MANY solutions.
One term in the original equation that needs to be changed to create a new equation with infinitely many solutions is 20 to 21.
What is an equation?An equation is a mathematical or algebraic statement that shows that two or more mathematical expressions are equal or equivalent.
Equations are depicted using the equal symbol (=), unlike mathematical expressions, which consist of variables, constants, numbers, and values.
7(2W + 3) = 14W + 20 does not have a solution because the first expression is unequal to the second expression and cannot be said to be an equation.
7(2W + 3) = 14W + 21 have many solutions for W.
Thus, changing 20 to 21 gives the original equation an indefinite number of solutions for W.
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What is the area of this compound figure?
the answer is 66
its easy... you posted this as high-school... this is 6th grade work
Area is 69 km2
………..,……….
a researcher records the following data: 4, 4, 4, 4, and 3. how would you describe the variability of these data? group of answer choices it is negative because 3 is less than the other scores in the distribution. it is very small (close to 0) because scores are approximately the same. it is very large (much greater than 0) because 3 is an outlier in the data. it is equal to zero because scores are approximately the same.
The variability of the data is very small (close to 0) because all the scores are approximately the same.
The variability of these data can be calculated using the variance formula, which is the average squared difference from the mean. In this case, the mean is 3.8 (the sum of 4, 4, 4, 4, and 3 divided by 5). Therefore, the variance is 0.08 (the sum of the squared differences [4-3.8, 4-3.8, 4-3.8, 4-3.8, 3-3.8] divided by 5). This indicates that the variability of the data is very small (close to 0) because all the scores are approximately the same.
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Tanner is 2 years younger than his
brother. Tanner's age t in years is 2
less than his brother's age b.
dependent variable:
independent variable:
equation:
The equation will be:
t = b - 2
And we can see that:
independent variable = brother's age.dependent variable = Tanner's age.How to identify the variables?Here we have two variables:
t = taner's age
b = age of Tanner's brother.
The independent variable is the one that does not depend on the other, in this case (for how it is worded) is the brother's age.
The dependent variable depends on the other, on this case, Tanner's age.
Now let's write the equation, we know that Taner's age is 2 years less than his brother, then:
t = b - 2
That is the equation.
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Please Help will mark Brainliest!!!
Answer: Neither
3, 5, 9,17
+ 2 +2
They are not the same #'s. For example, if you add 5 and 2 together you get 7. 9 does not equal 7. Not arithmetic, or geometric sequence.
5. People Population The country of Elbonia was established in 2012. Its population at the time was 5
million and is growing at an annual rate of 3.2%. The neighboring country of Neecapia was established
at the same time. Its population was 4.1 million and is growing at an annual rate of 6.5%.
Answer:
Step-by-step explanation:
yes because the montly rate is 6.5%
A ladder leans against the side of a house. The angle of elevation of the ladder is 68° when the bottom of the ladder is 7 ft from the
is the top of the ladder from the ground? Round your answer to the nearest tenth.
Check
68°
O
X
Save-
©2023 McGraw Hill LLC. All Rights Reserved
T
Answer:
17.3 feet
Step-by-step explanation:
We can use the tangent function to evaluate the height of the building.
The definition of the tangent function is
[tex]\tan x=\frac{O}{A}[/tex]
Where
[tex]A[/tex] is the side adjacent to the angle
[tex]O[/tex] is the side opposite to the angle
In this example we are given values of the adjacent side and the angle.
Knowing that we can evaluate the side opposite to the angle.
Numerical Evaluation
We are given
[tex]x=68\\A=7[/tex]
Substituting these values into the equation for the tangent function yields[tex]\tan 68=\frac{O}{7}[/tex]
Lets solve for [tex]O[/tex].
Multiply both sides by [tex]7[/tex].
[tex]O=7*\tan 68[/tex]
Evaluate [tex]\tan 68[/tex].
[tex]O=7*2.47508685[/tex]
[tex]O=17.325608[/tex]
Rounding to the nearest tenth gives us
[tex]O=17.3[/tex]
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which of the ordered pairs (18,8) , ( 8,18) , (9,4) or (4,9) is a solution to the system of equations
When we solve the provided question, the equations will be - > x = 1/2 y + 5
What exactly is an equation?A mathematical equation is a formula that joins two statements and indicates equality with the equal symbol (=). In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the relationship between the two sentences on either side of a letter. There is commonly only one parameter, which also provides as the symbol. For instance, 2x - 4 = 2.
Here, the equations will be -
x = 1/2 y + 5
2x + 3y = 14
2(1/2y + 5) +3y = -14
y = -6
and x 2
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Anshumann wants to paint the wall shown in the diagram below. In order to buy the paint, he will need to know the area of the wall. What is the area of the wall?
1 point
Answer: 240 ft²
Step-by-step explanation:
Break the diagram into a rectangle and triangle:
Area of Rectangle + Area of Triangle = Total area of Wall
(20x10) + 1/2(20 x 4) = Area of wall
200 + 40 = Area of wall
240 ft² = Area of wall
Hare Krishna :)
a theater charges $8 for main floor seats and $5 for balcony seats. for a full house, the ticket income is $4,200. at one show, only 25% of the main floor seats and 40% of the balcony seats were sold for a total of $1,200. how many main floor tickets and how many balcony tickets were sold for this show?
By solving a system of equations we can see that there are 400 main-floor seats and 200 balcony seats.
Let x = number of seats on the main-floor
y = number of balcony seats
We know that if all the seats are sold, then the total income is $4,200, we can write the equation:
x*8 + y*5 = $4,200
And if 25% of the main-floor and 40% of the balcony seats are sold, then we get an income of $1200, then we can write:
0.25*x*8 + 0.4*y*5 = $1,200
x*2 + y*2 = $1,200
2(x + y) = $1200
x + y = $600
x = 600 - y
putting the value of x in equation1)
8(600-y) + 5y = 4200
4800 - 8y + 5y = 4200
3y = 600
y = 200
and x = 600 - 200 = 400
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The side length of a square is( 2/3g+1) cm. Use this information to complete parts (a) and (b)
The perimeter of a square with length of a side given as 2/3g + 1 cm is 8/3g + 1 cm.
Let's call the length of a side of the square "s". According to the information given, s = 2/3g + 1 (in cm).
The perimeter of a square is equal to the sum of the lengths of all four sides, so we can write an expression to represent the perimeter as follows:
P = 4s
Substituting the expression for s from above, we get:
P = 4(2/3g + 1)
So, the expression for the perimeter of the square in terms of g is:
P = 4(2/3g + 1)
Therefore, P = 8/3g + 1.
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Complete question: the length of a square is( 2/3g+1)cm use this information to write an expression to represent the perimeter of the square.
8. Gianna is making bows for her cheerleading squad. She has 4 yards of ribbon to make the
bows. If each bow requires 1/5 a yard of ribbon, will she have enough ribbon to make 18 bows?
Using the concept of proportion, Gianna will have enough yards to make 18 bows
Will she have enough ribbon to make 18 bowsTo solve this problem, we need to apply the concept of proportions.
In order to make 1 bow, she needs 1/5 yard of ribbon
Representing this in an equation form will be;
1 bow = 1/5 yard
18 bow = x yard
cross multiply both sides and solve for x
x * 1 = 18 * (1/5)
x = 3.6 yards
From the above, there will be enough yards to make 18 bows.
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Suppose we want to choose 2 colors, without replacement, from the 5 colors red, blue, green, purple, and yellow.
(a) How many ways can this be done, if the order of the choices matters?
(b) How many ways can this be done, if the order of the choices does not matter?
If the order of choices matter, then;
Number of ways = 20
Also, if order of choices does not matter, then;
Number of ways = 10
Total number of choices = 5
Object choices = 2
By method of permutation
Number of ways = 5! / (5-2)!
Number of ways = 5! / 3!
Number of ways = 5 x 4
Number of ways = 20
Total number of choices = 5
Object choices = 2
By method of combination
Number of ways = 5! / (5-2)! 2!
Number of ways = 5! / 3! 2!
Number of ways = 5 x 4 / 2
Number of ways = 20 / 2
Number of ways = 10
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what value represents the number of ways in which the expected classes are free to vary in the chi‑square goodness‑of‑fit test?
In the chi-square goodness-of-fit test, the number of ways in which the expected classes are free to vary is represented by the degrees of freedom (df) of the test.
The degrees of freedom for the chi-square goodness-of-fit test are calculated as df = k - 1, where k is the number of categories or classes being compared.
In this test, we compare the observed frequencies in each category with the expected frequencies, assuming that the null hypothesis is true. The null hypothesis is that there is no significant difference between the observed and expected frequencies, and any deviation between the two is due to chance.
The degrees of freedom are the reflection of the number of independent pieces of information that are available to estimate the expected frequencies.
The more degrees of freedom, the more likely it is that the observed frequencies could be due to chance, and the less significant the test result will be. Conversely, fewer degrees of freedom means that the observed frequencies are more likely to be significantly different from the expected frequencies, and the test result will be more significant.
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Please answer ASAP What is the value of x? Enter your answer, as a decimal, in the box. Enter the numerical value only.
In the similar triangle, x = 67.5 ft
What are similar triangles?Similar triangles are triangles in which the ratio of their sides are equal.
How to find the value of x?Given the similar triangles, ΔMNP and ΔMAB
By the ratio of similar triangles, we have that
MP/MN = MB/MA
We observe that MN = MA + AN
So, MA = MN - AN
So, MP/MN = MB/MA
MP/MN = MB/(MN - AN)
Given that
MP = 97.5 FT, MN = 71.5 FT, AN = 22 FT and MB = xWe have that
MP/MN = x/(MN - AN)
Making x subject of the formula, we have that
x = (MN - AN)MP/MN
So, substituting the values of the variables into the equation, we have that
x = (MN - AN)MP/MN
x = (71.5 ft - 22 ft)97.5 ft/71.5 ft
x = 49.5 ft × 97.5 ft/71.5 ft
x = 4826.25 ft²/71.5 ft
x = 67.5 ft
So, the value of x = 67.5 ft
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If m∠HZJ = 38°, what is m∠HZG?
Answer:
142 degrees
Step-by-step explanation:
since line GJ is a straight line, its angle measure is 180 degrees. The measure of angle HZJ is 38. Angle HZJ and angle HZG are supplementary, which means their angle measures add up to 180 degrees. So,
180-38=142.
Hope this answer helps!! :D
what do i do if there is a word problem with x but there isnt a number for x
You might need to utilise algebra to answer for the variable x in a word problem if there isn't a particular number provided for it.
Create an equation involving x using the information provided.
For instance, if the question is, "What is the value of x if x is 5 more than twice y and y is 3?" you may write up an equation like this:
x = 5 + 2y
x = 5 + 2(3) (3) (Replace y = 3)
x = 11
By changing the supplied value of y, you can answer for x in this situation by first solving the ensuing equation.
You might need to utilise many equations and algebraic techniques like substitution, elimination, or graphing to solve for x if the issue is more complicated. It could be beneficial to divide the problem into smaller steps and work through each step methodically if you are unclear of how to proceed.
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