The number is -4
[tex]x \times[/tex]4+4= 2[tex]x[/tex]-4
[tex]$$x \times 4+4=2 x-4$$[/tex]
Subtract 4 from both sides[tex]$x \times 4+4-4=2 x-4-4$[/tex]
Simplify
[tex]$$x \times 4=2 x-8$$[/tex]
Subtract [tex]$2 x$[/tex] from both sides [tex]$x \times 4-2 x=2 x-8-2 x$[/tex]
Simplify
[tex]$$2 x=-8$$[/tex]
Divide both sides by 2
[tex]\frac{2 x}{2}=\frac{-8}{2}$$[/tex]
Simplify
[tex]$$x=-4$$[/tex]
A strategy for teaching division is by repeated subtraction. It involves repeatedly subtracting the same integer from a big number until the result is zero. It is a fantastic approach to teach kids about division. A technique called repeated subtraction, commonly referred to as division, removes an equal amount of items from a group.
Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
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The difference between 4 and the sum of a number and is equal to twice that number. The number is -4.
Given that,
The difference between 4 and the sum of a number and is equal to twice that number.
Repeated subtraction is a method for teaching division. Until the result is zero, the same integer must be repeatedly subtracted from a large number. Repeated subtraction, sometimes known as division, is a method that takes an equal number of elements out of a group.
Division's opposite is multiplication. If 3 groups of 4 total up to 12, then 4 are in each group when 12 is divided into 3 equal groups. The fundamental goal of division is to produce equal groups or to determine how many individuals are in each group following a fair distribution.
x×4+4=2x-4
Subtracting 4 on both sides
4x+4-4=2x-4-4
4x=2x-8
Now, substracting 2x from both sides
4x-2x=2x-8-2x
2x=-8
x=-4
Therefore, The number is -4.
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A recipe for oatmeal cookies calls for 5 cups of flour for every 8 cups of oatmeal. How much flour is needed for a big batch of cookies that used 16 cups of oatmeal?
Answer:
10 cups
Step-by-step explanation:
Since 16 cups is twice 8 cups, it needs twice 5 cups of flour which is 10 cups.
We can also use a proportion.
5/8 = x/16
8x = 5 × 16
x = 5 × 2
x = 10
Answer: 10 cups
22647 inches to miles, please show work
Answer: 0.3574 miles
Step-by-step explanation:
22647 inches = 0.3574 miles
Find each sum 5/7+1/2
Answer: 17/14 or 1 3/14 simplified
Step-by-step explanation:
14 is the least common multiple of denominators 7 and 2. Use it to convert to equivalent fractions with this common denominator.
Convert the polar equation to rectangular form and identify the graph. Support your answer by sketching the graph. Show and explain your work.
The polar equation r = - 4 · cos θ is equivalent to the equation of the circle (x + 2)² + y² = 2², whose radius is 2 and center is (h, k) = (- 2, 0).
How to transform a polar expression into its rectangular formPolar and rectangular forms are related by this relation: (x, y) → (r · cos θ, r · sin θ), where r is the radial distance with respect to the origin and θ is the angle in standard position. We can use this fact to change the given expression into its rectangular form:
r = - 4 · (x / r)
r² = - 4 · x
x² + y² = - 4 · x
y² = - (x² + 4 · x)
y² - 4 = - (x² + 4 · x + 4)
y² - 4 = - (x + 2)²
(x + 2)² + y² = 4
(x + 2)² + y² = 2²
In a nutshell, the polar equation r = - 4 · cos θ is equivalent to the equation of the circle (x + 2)² + y² = 2², whose radius is 2 and center is (h, k) = (- 2, 0).
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(4x+2)+(x-2) can someone tell me its procedure
[tex] \green\star\:{\underline{\underline{\sf{\orange{Answer:}}}}}[/tex]
¡Hello :D!
To solve the similar terms we must eliminate the parentheses and then put the parentheses back but this time it would be like this: (4 x + x) + ( 2 - 2)
Once we have done that we must restore the ones on the right side which gives us the result of 1 then as we see that there is + in the Parenthesis and another + outside the Parenthesis we do not care + since we are using the law of signs .
We proceed to solve:
[tex]\: \: \: \: \: \: \bold \: \bold \: \bold \: ( \bf4x+2)+(x-2)[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \bf \bold4x + 2 + x - 2[/tex]
[tex] \: \: \: \: \: \: \: \: \bf\tt( \bf4x + x) + (2 - 2)[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf5x[/tex]
So the result is 5x
I hope I've helped XD
The capacities at which U.S. nuclear power plants are working are shown in table for various years.
Year Percent
1975 56
1980 59
1985 58
1990 70
1995 76
2000 88
2004 89
Let
f
(
t
)
be the capacity (in percent) at which U.S. nuclear power plants are working at t years since 1970. A model of the situation is
f
(
t
)
=
0.027
t
2
+
0.216
t
+
53.296
.
Use a graphing calculator to draw the graph of the model and, in the same viewing window, the scattergram of the data. Does the model fit the data well?
The function is not a good model for the data
The function is a good model for the data.
Estimate at what capacity U. S. nuclear power plants were working in 2014.
% Round to the nearest whole percent.
Predict when U. S. nuclear power plants will be working at full (100%) capacity.
Enter the year this occurs.
The function is a good model for the data, capacity U. S. nuclear power plants were working in 2014 is 115% and the year when nuclear power plant working with full capacity is 2008.
Given that the table which shows the capacities at which U.S. nuclear power plants are working and a model of the situation is f(t)=0.027t²+0.216t+53.296.
The Scatter plot for our function and points is shown in attached image and the point are highly related to the curve .
So the function is good model.
The year 2014 means t=2014-1970=44
So to get the population,put t=44 in equation
f(t)=0.027(44)²+0.216(44)+53.296
f(t)=0.027(1936)+0.216(44)+53.296
f(t)=52.272+9.504+53.296
f(t)=115.072
And on rounding it we get 115%.
Now, to find year at which capacity is 100% ,put f(t)=100 and solve for t
f(t)=0.027t²+0.216t+53.296=100
0.027t²+0.216t+53.296=100
0.027t²+0.216t+53.296-100=0
0.027t²+0.216t-46.704=0
Now, we will solve this using quadratic formula for f(x) =ax²+bx+c=0
[tex]\begin{aligned}x&=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\end[/tex]
for our function a= 0.027 , b=0.216 ,c=-46.704 substitute this value and we get
[tex]\begin{aligned}t&=\frac{-0.216\pm \sqrt{(0.216)^2-4\times 0.027\times (-46.704)}}{2\times 0.027}\\ &=\frac{-0.216\pm \sqrt{0.046656+5.044032}}{0.054}\\ &=\frac{-0.216\pm \sqrt{5.090688}}{0.054}\\ &=\frac{-0.216\pm 2.256}{0.54}\\ &=37.78, -45.78\end[/tex]
As we all know time cannot be negative so t=-45.78 will be rejected.
So, t=37.78=38
Now, we will find the corresponding year
1970+38=2008
Hence, from the given table the function is a good model for the data, capacity U. S. nuclear power plants were working in 2014 is 115% and the year when nuclear power plant working with full capacity is 2008.
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5. Kerry McCarthy is a news traffic reporter with an annual gross
pay of $44,500. He is single and is paid on a monthly basis.
How much is withheld monthly for state taxes?
$3,708.33 is withheld monthly for state taxes.
Some states have a graduated income tax that involves a different tax rate for each of several levels of income. The tax rate increases as income increases.
Tax Withheld per Pay Period = Annual Tax Withheld/ Number of Pay Periods per Year
Here, we are given that Kerry McCarthy is a news traffic reporter with an annual gross pay of $44,500.
Thus, the Annual Tax Withheld = $44,500.
He is paid on a monthly basis ⇒ Number of Pay Periods per Year = 12
Hence, we get-
Tax Withheld per Pay Period = 44,500/ 12
= 3,708.33
Thus $3,708.33 is withheld monthly for state taxes.
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K
Monica's car will go 455 miles on 17.5 gallons of gasoline in highway driving.
a) How many gallons will it take to drive 2629 miles from her house to a friend's house?
b) How far can the car be driven on 139 gallons of gasoline?
***
Pie/Circle Graph: As a wildlife biologist, one of your duties is to catch, tag, and
release different species of mammals found in Oak Mountain, Alabama. Use
the data provided below to determine the percentage of each mammal
species caught and then label the different sections found in the pie graph
provided. During a 24 hour period, six cotton mice were caught, nine Norway
rats, 17 pine voles, and two eastern chipmunks.
Six cotton mice has 64%, nine Norway rats has 95%, 17 pine voles has 180%, and two eastern chipmunks has 21% were taken in a 24-hour period from the pie chart.
Given that,
In the figure there is a chart pie chart with 4 parts and 4 colors.
Six cotton mice, nine Norway rats, 17 pine voles, and two eastern chipmunks were taken in a 24-hour period.
We have to find by use the information below to calculate the percentage of each species of captured mammal, and then use that information to name the various pie-shaped sections.
Each value must be converted into a circle's angle for the pie chart.
Total=6+9+17+2=34
Cotton mice=(6/34)×360°=64°
Norway rats=(9/34)×360°=95°
Pine voles=(17/34)×360°=180°
Eastern chipmunks=(2/34)×360°=21°
Therefore, Six cotton mice has 64%, nine Norway rats has 95%, 17 pine voles has 180%, and two eastern chipmunks has 21%.
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[(10-9+8)-7] + [6-((5+4] ÷ 3)] ² - 1
Answer:
10
Step-by-step explanation:
1 Simplify 10-910−9 to 11.
1+8-7+{(6-(5+4)\div 3)}^{2}-1
1+8−7+(6−(5+4)÷3)
2
−1
2 Simplify 5+45+4 to 99.
1+8-7+{(6-9\div 3)}^{2}-1
1+8−7+(6−9÷3)
2
−1
3 Simplify 9\div 39÷3 to 33.
1+8-7+{(6-3)}^{2}-1
1+8−7+(6−3)
2
−1
4 Simplify 6-36−3 to 33.
1+8-7+{3}^{2}-1
1+8−7+3
2
−1
5 Simplify {3}^{2}3
2
to 99.
1+8-7+9-1
1+8−7+9−1
6 Simplify 1+81+8 to 99.
9-7+9-1
9−7+9−1
7 Simplify 9-79−7 to 22.
2+9-1
2+9−1
8 Simplify 2+92+9 to 1111.
11-1
11−1
9 Simplify.
10
One number is six less than three times another number. If the sum of the numbers is 38, find the numbers
Answer:
consider the two number as x and y
first given condition
x-6 = 3y
i.e. x= 3y + 6 eqn 1
second given condition
x+ y = 38
i.e. x= 38-y eqn 2
solving eqn 1 and 2
3y + 6 = 38-y
3y + y = 38-6
4y = 32
y = 8
substituting the value of y in eqn 2
x = 38 - y
x= 38-8
x= 30
hence the required numbers are 8 and 30
can anyone write out step-by-step directions and end up with the solution for this equation
2(3b - 2) = 2(2b + 12)
One way to solve is to follow these steps
2(3b - 2) = 2(2b + 12)
2*3b - 2*2 = 2*2b + 2*12
6b - 4 = 4b + 24
6b-4b = 24+4
2b = 28
b = 28/2
b = 14
Final answer: b = 14write the function whose graph is the graph of y=x^2 but is translated 9 units to thre left
Answer:
y= (x+9)^2
Step-by-step explanation:
If h<0 ( negative) then it shifts to the right, if it is is h>0 ( positive number) then it shift to the left!
y = x2
Shift 2 units left: y = (x+2)2
Then, shift up 9 units: y = (x+2)2 + 9
Then, reflect in the x-axis: y = -(x+2)2 - 9
7 divide 161 step by step
this is what you need?if yes than look and write
Create a formula for a function f (x) that has f (9 )= 10. Do not give a simple constant function (like f (x) = 10 ) as your answer.
f(x)=x+1 is a formula for a function f(x) that has f(9)=10
What is a simple definition for function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input
a constant function is a function whose (output) value is the same for every input value. For example, the function y(x) = 10 is a constant function because the value of y(x) is 10 regardless of the input value x
if we take f(x)= x+1
then put x=9 we get f(9)= 10
Hence , f(x)=x+1 is a formula for a function f(x) that has f(9)=10
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Taylor and Alex are looking for a daycare for their child. They want to make sure the daycare is midway between their jobs. Taylor works at the Rogers Middle School located at (4, -5), and Alex works at St. Philip's located at (2, 5). Where should the daycare be located?
Step-by-step explanation:
(5 ,_4) it the location this is the answer
Which graph is a parabola?
Step-by-step explanation:
THE THIRD GRAPH IS THE PARABOLA!
HOPE THIS HELPS!
Use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below.
f(-2) = ? f(2) = ?
The domain is ___. (use interval notation)
From the graph of the function, we have that:
a) The domain is all real values.
b) The range is y ≤ 4.
c) The x-intercepts are x = -4 and x = 1.
d) The y-intercept is y = 3.
e) f(-2) = 3, f(2) = -5.
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input. In a graph, the domain is composed by the values of x.The range of a function is the set that contains all the values of the output. In a graph, the domain is composed by the values of y.Hence, for this problem:
a) The domain is all real values.
b) The range is y ≤ 4.
What are the intercepts of a function?The x-intercepts of a function are the values of x when f(x) = 0, that is, the values of x for which the function crosses the x-axis.The y-intercept of a function is the values of f(x) when x = 0, that is, the value of y for which the function crosses the y-axis.Hence:
c) The x-intercepts are x = -4 and x = 1.
d) The y-intercept is y = 3.
What are the numeric values?For the graph, when x = -2 y = 3 and when x = 2 y = -5, hence:
f(-2) = 3, f(2) = -5.
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The width of a rectangle measures (10p - 9p) centimeters, and it’s length measures (7p + 8p) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answer:
c
Step-by-step explanation:
The real solutions to the equation 3x5 + 25x4 + 26x3 – 82x2 + 76x = 48 are shown on the graph. What are the nonreal solutions? StartFraction 1 + i StartRoot 5 EndRoot Over 3 EndFraction, StartFraction 1 minus i StartRoot 5 EndRoot Over 3 EndFraction. StartFraction negative 1 + i StartRoot 5 EndRoot Over 3 EndFraction, StartFraction negative 1 minus i StartRoot 5 EndRoot Over 3 EndFraction. StartFraction negative 1 + StartRoot 5 EndRoot Over 3 EndFraction, StartFraction negative 1 minus StartRoot 5 EndRoot Over 3 EndFraction. StartFraction 1 + StartRoot 5 EndRoot Over 3 EndFraction, StartFraction 1 minus StartRoot 5 EndRoot Over 3 EndFraction.
Using the Factor Theorem, the non-real solutions are given as follows:
[tex]\frac{1 + \sqrt{5}i}{3}, \frac{1 - \sqrt{5}i}{3}[/tex]
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
For this problem, the function is:
f(x) = 3x^5 + 25x^4 + 26x³ - 82x² + 76x - 48.
The function can be written as:
f(x) = g(x)h(x).
In which:
g(x) is the polynomial with the real solutions.h(x) is the polynomial with the non-real solutions.Using a calculator, as the graph is not given, the real solutions are given as follows:
[tex]x_1 = -6, x_2 = -4, x_3 = 1[/tex]
Hence:
g(x) = (x + 6)(x + 4)(x - 1)
g(x) = (x² + 10x + 24)(x - 1)
g(x) = x³ + 9x² + 14x - 24.
f(x) is of degree 5, g(x) of degree 3, hence h(x) is of degree 2 and:
f(x) = g(x)h(x)
3x^5 + 25x^4 + 26x³ - 82x² + 76x - 48 = (x³ + 9x² + 14x - 24)(ax² + bx + c)
Hence:
ax^5 = 3^5 -> a = 3.-24c = -48 -> c = 2.-24bx + 14cx = 76x
-24b + 28 = 76
-24b = 48
b = -2.
Then the equation with the non-real solutions is:
h(x) = 3x² - 2x + 2.
Which is a quadratic equation with coefficients a = 3, b = -2 and c = 2, thus:
[tex]\Delta = b^2 - 4ac = (-2)^2 - 4(3)(2) = -20[/tex][tex]x_1 = \frac{2 + \sqrt{-20}}{6} = \frac{2 + 2\sqrt{5}i}{6} = \frac{1 + \sqrt{5}i}{3}[/tex][tex]x_2 = \frac{2 - \sqrt{-20}}{6} = \frac{2 - 2\sqrt{5}i}{6} = \frac{1 - \sqrt{5}i}{3}[/tex]Hence the non-real solutions are:
[tex]\frac{1 + \sqrt{5}i}{3}, \frac{1 - \sqrt{5}i}{3}[/tex]
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Candace bought a laptop for x dollars. She decided to sell it, after adding an $875 markup amount to the original price. If the markup rate used was 20%, then how much did she originally purchase the laptop for? Round your answer to the nearest dollar.
The original amount for the laptop that Candace bought when the markup rate is 20% will be $4375.
How to calculate the value?It should be noted that she added 875 markup amount to the original price and the markup rate used was 20%,
Therefore, 20% of x = 865
0.2x = 875
Divide
x = 875 / 0.2
x = 4375
Therefore, the original amount for the laptop is $4375.
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Joy is going to solve the equation below which of the following represents the equation after just distributing and combining like terms
The correct option is b. -30x + 32 = 182.
After combining the like terms, the equation that represents -8x + 23 - 22x + 9 = 182 is -30x + 32 = 182, where x = -5.
What is defined as equation?In its most basic form, an equation is a statement that demonstrates that 2 mathematical expressions have been equal.
3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are 2 expressions separated by a 'equal' sign.An equation is a formula in mathematics that conveys the equality of two expressions by linking them with the equal sign =.Now, as per the given question;
The stated equation in the question is is,
-8x + 23 – 22x + 9 = 182
Considering like terms together;
-8x – 22x + 23 + 9 = 182
Further simplifying;
– 30x + 32 = 182
Subtracting 32 from the both sides.
– 30x + 32 - 32 = 182 - 32
On solving;
– 30x = 150
⇒ x = -5
Therefore, the expression which defined the equation after taking alike terms is -30x + 32 = 182 for which the value of 'x' comes to be -5.
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The complete question is;
Joy is going to solve the equation below which of the following represents the equation after just distributing and combining like terms?
-8x + 23 – 22x + 9 = 182
a. 14x + 32 = 182
b. -30x + 32 = 182
c. 14x + 14 = 182
d. -30x + 14 = 182
Just 16 and 17 please!
Answer:
1(7-6)1/6
Step-by-step explanation:
Need help with this asap
Answer: x=21, y=8
Step-by-step explanation:
18y+5=10x-61 ==> 18y+5 and 10x-61 are congruent angle, so they're equal
x+10+10x-61=180 ==> x+10 and 10x-61 are supplementary angles since they're on a straight line(a straight line measures 180 degrees and is called a straight angle), so they add up to 180 degrees.
x+10x+10-61=180
11x-51=180
11x=231
x=21
18y+5=10(21)-61
18y+5=210-61
18y+5=149
18y=144
y=8
A coffee company surveyed 40 potential customers to see where they would like the company's new organic coffee sold. Respondents were given the following four locations and asked to choose as many as they liked: grocery stores, drugstores, health food stores, and big box stores. The results are summarized in the bar graph below, with the number of times each location was chosen noted above the corresponding bar.
As per given data of respondents of four locations in the bar graph per40 potential customers , the average number of location chosen per potential customer is equal to 2.5.
As given,
Total number of potential customers =40
Number of respondents from bar graph
At grocery stores= 40
At drugstores respondents =32
At health food stores =8
At big box stores =20
Average number=(40 +32+8+20)/40
= 100 /40
=2.5
Therefore, as per given data of respondents of four locations in the bar graph per40 potential customers , the average number of location chosen per potential customer is equal to 2.5.
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Round 67536 to the nearest hundred
Answer:
67,500
Step-by-step explanation:
i think this is the answer.
Answer: 67500
This is because 536 is closer to 500 than it is to 600
The Taj Mahal is an enormous ivory-white marble monument in India that is known for
its architecture. More than 2 x 104 workers were involved in building the Taj Mahal.
Which number shows another way to express 2 x 10¹?
Answer:the iconic Indian building named Taj Mahal
Step-by-step explanation:
Determine whether the given situation is best described by a linear model or an exponential model. What function models the situation?
The population of rabbits in a forest is tripling every month.
At 0 months (the starting point) there was only one rabbit.
The model that best described the statement is an exponential model and the function that models the situation is A(t) = 4^t
How to determine whether the given situation is best described by a linear model or an exponential model.The statement is given as:
The population of rabbits in a forest is tripling every month.At 0 months (the starting point) there was only one rabbit.The above statement is a population function
Population functions are best represented by an exponential function
Hence, the model that best described the statement is an exponential model.
What function models the situation?Here, we have
Initial value, a = 1
Rate, r = 3
The function is represented as
A(t) = A * (1 + r)^t
So, we have
A(t) = 1 * (1+3)^t
Evaluate
A(t) = 4^t
Hence, the function that models the situation is A(t) = 4^t
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On a map , 1 inch represents 50 miles. You measure the distance on the map between two towns as 3 1 2 inches. How many miles apart are the towns?
The towns are 15600 miles apart.
WHAT IS MAP SCALE ?The term "map scale" refers to the proportion between a distance on a map and its corresponding distance on the ground. Lets see an example like, On a map with a scale of 1:100,000, one kilometer on the ground is equivalent to one centimeter. The scale of a map refers to the proportion between a distance on a map and its actual distance on the ground. This simple concept is complicated by the fact that scale must vary across a map due to the curvature of the Earth's surface. The concept of size is now important in two different ways as a result of this development.
The size of the producing globe is compared to the size of the Earth in the first technique. a theoretical globe known as the generating globe, upon which the map is projected and the Earth is compressed. The ratio of the size of the Earth to that of the generating globe is known as the nominal scale, also known as the major scale or representative fraction.
CALCULATION∵ 1 inch = 50 miles on the map
∴ 312 inches = 312 * 50 = 15600 miles .
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6x + 4y = 36 when x = 3 and y = 4
Answer:
No solution.
Explanation:
Given expression:
6x + 4y = 36when x = 3, y = 4
Substitute these values inside expression:
6(3) + 4(4) = 36
18 + 16 = 36
34 = 36
As the statement "34 = 36" not true. The solution is false or no solution.
Answer:
The given values are wrong.
Step-by-step explanation:
Given information,
→ x = 3
→ y = 4
Solving the given equation,
→ 6x + 4y = 36
→ (6 × 3) + (4 × 4) = 36
→ 18 + 16 = 36
→ 34 ≠ 36
Hence, there is no solution.