Answer:
m<T = 60°
m<U = 60°
TS = 13
SU = 13
Step-by-step explanation:
Triangle TSU is an equilateral triangle.
All interior angles has equal measures and each = 60° since the sum of interior angles in a triangle is equal to 180 and this divided by 3 = 60
all side lengths are also equal to one another, TU is given as 13 cm so the length of TS and SU is also = 13
A trader old a writ watch for h.3150 after giving a 10% dicount.Find the marked price of the watch
The marked price of the wrist watch after the trader sold a wrist watch for $3150 after giving a 10% discount is $3500.
First, let us understand the percentage:
A percentage is a fraction of a whole expressed as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent.
To determine a percentage, we need to divide the portion of the whole by the whole itself and multiply by 100.
Let the marked price be x.
So,
According to the question;
x - x * 10% = 3150
x - x * 10/100 = 3150
100x - 10x / 100 = 3150
90x = 3150 * 100
x = 3150 * 100 / 90
x = 3500
So, the marked price is $3500.
Thus, the marked price of the wrist watch after the trader sold a wrist watch for $3150 after giving a 10% discount is $3500.
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Find 7 5/12−(−3 3/4) . Write your answer as a mixed number in simplest form.
The simplified expression is 11 (1/6).
What is a fraction?A fraction is a part of the whole represented by a/b, where a and b are any integers.
The given expression is 7 (5/12) - (-3 (3/4)).
Simplify the expression as follows:
7 (5/12) - (-3 (3/4))
= 89/12 +15/4
= (89+45)/12
= 134/12
= 11 (1/6)
Hence, the simplified expression is 11 (1/6).
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suppose 1,608 of 2,400 registered voters sampled said they planned to vote for the republican candidate for president. using the 0.95 degree of confidence, what is the interval estimate for the population proportion (to the nearest 10th of a percent)?
Using the concepts of confidence interval, we got that is he interval estimate for the population proportion if we suppose 1,608 of 2,400 registered voters sampled said they planned to vote for the republican candidate for president.
We know that population proportion is given by the fraction of number of positive results to the total number of results
Therefore, Population Control(P)=1608/2400
=>P =0.67
Now, we are given that confidence interval is 0.95 degree or 95%
For 95%,confidence interval is given by =P±√[P×(1-P)]/n
where n is the total number of registered voters, and P is the population control.
confidence interval=0.67±√[0.67×(1-0.67)]/2400
=0.67±√(0.67×0.33)/2400
=0.67±√0.2211/2400
=0.67±(0.47/48.98)
=0.67±0.0095
=0.660 and 0.679
Hence, if we suppose 1,608 of 2,400 registered voters sampled said they planned to vote for the republican candidate for president. using the 0.95 degree of confidence, the interval estimate for the population proportion is (0.660,0.679)
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8. What is the value of point x? X -4 -3
Answer:
x = -9
Step-by-step explanation:
(x1, y1) = (-4, 3) & (x2, y2) = (x, 4)
m = (y2 - y1)/(x2 - x1)
-1/5 = (4 - 3)/(x - (-4) = 1/(x+4)
-(x + 4) = 5
-x - 4 = 5
-x = 5 + 4 = 9
HELP MEEE PLEASE TYYYYYY
Answer:
45mi/h
Step-by-step explanation:
4 to 8 = 4 hours
v = space / time
v = 180/4 = 45 mi/h
1. Which ordered pair does NOT belong to any quadrant?
(-1,-3)
(1, 3)
(1, -3)
(0, 3)
The point(0,3) is not a part of any quadrant. option D is the correct answer
The points on the x-axis and the y-axis are not a part of any quadrant.
From the question, we have
The point(0,3) is not a part of any quadrant.
Cartesian Coordinate System:
A point in a plane can be found using the coordinate system by connecting two perpendicular lines. In two dimensions, points are represented as coordinates (x, y) with respect to the x- and y-axes. We will study the Cartesian Coordinate System in this article. Axes and quadrants make up a plane. The coordinate axes are the name of the axes. Axes and quadrants make up a plane. The coordinate axes are the name of the axes. A rectangular system's reference lines, the vertical and perpendicular axes, are used to measure distances.
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I will love some help so if you can help that will be wonderful the question is Given the equation k over 34.2 equals 8.7, determine the value of k.
25.5
297.54
3.93
42.9
Answer:
k=297.54
Step-by-step explanation:
i can't really explain it
The value of k that satisfies the equation k/34.2 = 8.7 is approximately 297.54. So, correct option is B.
To determine the value of k in the equation k/34.2 = 8.7, we can solve for k by isolating it on one side of the equation.
We can start by multiplying both sides of the equation by 34.2 to eliminate the denominator:
k/34.2 * 34.2 = 8.7 * 34.2
This simplifies to:
k = 8.7 * 34.2
Evaluating the right side of the equation:
k ≈ 297.54
The correct option from the given choices is 297.54. So, correct option is B.
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given p(a) = 0.90, p(b) = 0.96, p(c) = 0.05 and that events a, b, and c are independent, what is p(a, b, and c).
The P(a, b and c) is 0.0432 when P(a) = 0.90, p(b) = 0.96, p(c) = 0.05.
From the given question, we know that
Probability of event 'a' occurring, P(a) = 0.90
Probability of event 'b' occurring, P(b) = 0.96
Probability of event 'c' occurring, P(c) = 0.05
We have been told that these three events are independent.
Thus, we can use the multiplication rule of probability, which states that the probability of three independent events a, b, and, c occurring is equal to the products of the probability of each individual event occurring.
p(a, b and c) = p(a) × p(b) × p(c)
= 0.90 × 0.96 × 0.05
= 0.0432
Hence, the probability(a, b, and c) is 0.0432.
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at 99% confidence, how large a sample should be taken to obtain a margin of error of 0.027 for the estimation of a population proportion? assume that past data are not available for developing a planning value for p*. round up to the next whole number.
2276 large a sample should be taken to obtain a margin of error of 0.027 for the estimation of a population proportion.
Given:
At 99% confidence, how large a sample should be taken to obtain a margin of error of 0.027 for the estimation of a population proportion.
Error e = 0.027
z score at 99%:
z = 2.576.
sample size n = p(1-p)(z/e)^2
= 0.5(1-0.5)(2.576/0.027)^2
= 0.5*0.5*9102.573
= 0.25*9102.573
= 2275.64
≈ 2276
Therefore 2276 large a sample should be taken to obtain a margin of error of 0.027 for the estimation of a population proportion.
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Evaluate. 7^4 Responses 28 28 343 343 2401 2401 16,384
The exponential number 7⁴ we get expression as 2401.
Given that,
The exponential number is 7⁴.
We have to find the expression.
A number's exponent tells us how many times it has been multiplied by itself.
Exponent-related issues are resolved utilising exponentiation rules or exponentiation attributes.
How many times we must multiply the reciprocal of the base is indicated by a negative exponent is the exponential with negative symbol
A fractional exponent is one where the exponent of a number is a fraction.
Take the exponential number.
7⁴
7×7×7×7
2401
Therefore, The exponential number 7⁴ we get expression as 2401.
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one of euler's conjectures was disproved in the 1960s by three american mathematicians when they showed that there is a positive integer such that find the value of .
It quickly becomes apparent that 174 is much too large, so n must be 144.The value of the n is 144.
Taking the given equation modulo 2,3, and 5, respectively, we have
n⁵≡(mod 2)
n⁵≡(mod 3)
n⁵≡( mod 5)
By either Fermat's Little Theorem (FLT) or inspection, we get
n≡(mod 2)
n≡(mod 3)
n≡( mod 5)
By either the Chinese Remainder Theorem (CRT) or inspection, we get n≡ 24 ( mod 30)
It is clear that n>133, so the possible values for n are 144,174,204,...Note that
n⁵ = 133⁵ + 110⁵ + 84⁵ + 27⁵
n⁵ < 133⁵ + 110⁵ +( 84 + 27)⁵
n⁵ =133⁵ + 110⁵ + 111⁵
n⁵ < 3.133⁵
From which (n/133)⁵ < 3
If n>= 174 then,
(n/133)⁵ > 1.3⁵
(n/133)⁵ = 3
which arrives at a contradiction. Therefore, we conclude that n=144
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7. Write an equation for the line in slope-
intercept form.
Ay
2
4-2 O
2
-4
2
4
X
Answer: y= -2/4x - 3
Step-by-step explanation:
b=y-intercept
Equation for slope-intercept form: y=mx+b
Locate the y-int/b: -3=b
Identify the slope/m: -2/4= 2 down, 4 to the right
Insert slope and y-int into slop-intercept form: y= -2/4x - 3
Volume please help due today!
The new volume of the container will be 120 ft³
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
Given a container with dimensions 3ft by 4ft by 5ft
Its volume need to be twice.
Volume of container = length*width*height
Original volume = 3*4*5 = 60 ft³
After doubling = 60*2 = 120 ft³
New dimensions are = 4ft by 5ft by 6ft
Hence, The new volume of the container will be 120 ft³ and New dimensions are 4ft by 5ft by 6ft
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The tiger at the zoo ate 133 pounds of food in
7 days Find the average change in the zoo's
tiger food supply each day.
Answer:
133/7 = 19
Step-by-step explanation:
"Find the average change in the zoo's tiger food supply each day."
And what does that have to do with anything? It's not like there is a change in diet that we can then easily calculate using derivatives.
Mario invested $6,000 in an account that pays 5% annual interest compounded annually. Using the formula a = p(1 + r)t, what is the approximate value of the account after 2. 5 years? $6,075 $6,118 $6,456 $6,778.
The approximate value of the account after 5 years will be $6778.
Given that,
Mario put $6,000 into a savings account that accrues interest at a rate of 5% per year.
The amount is given by,
A= p(1 + r)^t
P = 6000
R = 5%
T= 2.5 years
R = Rate of Interest
T= Time
P = Principal Amount
By substituting we get,
A= p(1 + r)^t
A = 6000(1 + 0.05)^2.5
A = 6000(1.05)^2.5
A = 6000 * 1.129
A = 6778.35
As a result, the account will roughly be worth $6778 after five years.
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I need help. I was absent for 2 weeks, and I have no idea how to do this.
a) no solution
b) only one solution
c) only one solution
d) infinite many solution.
e) only one solution
f) no solution
g) infinite many solution.
h) infinite many solution.
i) no solution
j) only one solution
k) infinite many solution.
What is 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. LHS = RHS is a common mathematical formula.
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:
We know depending upon the types of lines there are different type of solution
if there are two equations
[tex]a_1 x+ b_1 y+ c_1= 0[/tex] and [tex]a_2 x+ b_2 y+ c_2= 0[/tex]
For Intersecting Lines
[tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]
and, have only one solution
For parallel lines:
[tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]
and, have no solution
For co- incident line
[tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]
and, have infinite many solution.
a) y= -5x + 4 --> 5x + y = 4
5x+y= -3
So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]
and, have no solution
b) y=3/4 x+5
y= 4/3 x + 5
so, [tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]
and, have only one solution
c) y= -3/4x+5
y=3/4x+5
[tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]
and, have only one solution
d) y= 3/4 x + 5
y= 5+ 3/4x
So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]
and, have infinite many solution.
e) y= 3/4x +5
y= x + 2
So, [tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]
and, have only one solution
f) y= 3/4x + 5
y= 3/4x + 2
So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]
and, have no solution
g) 6x -y = 5
-6x + y= -5
So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]
and, have infinite many solution.
h) 2x- y +5 =0
2x- y+ 5 =0
So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]
and, have infinite many solution.
i) 4x- y+ 5 =0
4x- y +3 = 0
So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]
and, have no solution
j) 3x- y +5 = 0
2x -y +5 =0
So, [tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]
and, have only one solution
k) 2x+ y -1 = 0
2x + y- 1= 0
So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]
and, have infinite many solution.
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suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. a study was then done to see if the mean time has increased in the new century. a random sample of 27 first-time convicted burglars in a recent year was picked. the mean length of time in jail from the survey was four years with a standard deviation of 1.9 years. suppose that it is somehow known that the population standard deviation is 1.4. conduct a hypothesis test to determine if the mean length of jail time has increased. assume the distribution of the jail times is approximately normal. calculate the following. (enter exact numbers as integers, fractions, or decimals.) (a) x
Using Z- distribution it is found that the mean length of jail time has increased because the test statistics is greater than the critical value.
Z- distribution: It is a special normal distribution where the mean is 0 and standard deviation is 01.
z = (x -μ) / σ
At the Null hypothesis, it is tested if the mean length of jail time is still of 2.5 years.,
i.e., H₀ :μ = 2.5
Null hypothesis : It refers to a hypothesis that states that there is no relationship between two population parameters.
At the alternative hypothesis, it is tested if it has increased
i.e., H₁ :μ>2.5
Alternative Hypothesis: The alternative hypothesis states the research prediction of an effect or relationship.
we have the standard deviation for population thus the z- distribution is used. The test statistics is :
z= ⁻ₓ -μ /σ /√n
where, x is the sample mean
μ is the value tested at the null hypothesis.
σ is the standard deviation of sample.
n is the sample size.
For this problem the values of parameter are:
x= 5 ,σ =1.4 ,μ = 2.5 and n = 27
hence the value is :
z= ⁻ₓ -μ /σ /√n
= 5 - 2.5 / 1.4 ÷ √27
= 2.5 × √27 /1.4
= 9.27
The critical value for a right tailed test as we are testing if the mean is greater than a value with a significance level of 0.05 is of 2*= 1.645.
since, the test statistics is greater than the critical value, it can be concluded that the mean length of jail time has increased.
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2) A cuboid has sides of length 10 cm, 6cm and 7 cm.
Find the total surface area of the cuboid.
6 cm
10 cm
7cm
The total surface are of cuboid is 304 cm square.
What is total surface area of cuboid?
The area of a cuboid refers to the surface area as the cuboid is a three dimensional solid. Thus, the area of cuboid can be calculated using the formula of area of rectangle, since the faces of a cuboid are in a rectangular shape.
The Total surface area of a cuboid (TSA) is equal to the sum of the areas of it’s 6 rectangular faces, which is given by:
Total Surface Area of a Cuboid (TSA) = 2 (lw + wh + lh) square units
The above formula gives the total surface area of a cuboid having all six faces.
Given, length = 10cm , width = 6 cm , height = 7cm
Total surface area = 2[10(6)+6(7)+10(7)]
=2(60+42+70)
=2(152)
=304.
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DEFG has been dilated to D'EF'G'. Use a pair of corresponding sides to determine the scale factor.
a 2/1=2
b 3/2
c1/2
d2/3
The scale factor for a a pair of corresponding sides will be;
⇒ 3 / 2
What is Proportional?
The equality between two ratio is called Proportional.
Given that;
DEFG has been dilated to D'EF'G'.
Now,
Let the coordinates of DEFG are for side DG are;
D = (- 6, 3)
G = (- 3, 3)
And, The coordinates of D'E'F'G' are for side D'G' are;
D' = (- 4, 2)
G' = (- 2, 2)
So, The length of side DG is;
DG = √ (- 3 - (-6))² + (3 - 3)²
= √ 3²
= 3
And, The length of side D'G' is;
D'G' = √ (- 2 - (-4))² + (2 - 2)²
= √ 2²
= 2
Thus, The scale factor for a a pair of corresponding sides will be;
⇒ DG / D'G' = 3 / 2
Therefore, The scale factor for a a pair of corresponding sides will be;
⇒ 3 / 2
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Plans for a new apartment building call for apartments directly across the hall from each other to be congruent. This computer printout shows Apartment D. If the vertices of Apartment E are located at (-2X1, Y1), (-2%2, Y/2), (-2X3, y3), and (-2%4, y4), will Apartment E be congruent to Apartment D?
Answer:
Step-by-step explanation:
no because (-2X1, Y1), and-2X3, y3), arent congruent so the whole problem is not congruent
Use a quadratic equation to find two real numbers with a sum of 2 and a product of −24. Write the answers in the decreasing order of their values.
_____ and ______
The two numbers whose sum is 2 and product is -24 are 6 and -4
What is a quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x
a[tex]x^{2}[/tex]+bx+c=0
with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
Let the two numbers be x and y
so that
x + y = 2 ----------------1
xy = -24 -----------------2
from equation 1 make x the subject of the equation, so that it becomes
x = 2 - y ---------------3
substitute x in equation 3 in equation 2
y(2-y) = - 24
multiply out the bracket
2y - [tex]y^{2}[/tex] = -24
taking all terms to one side of the equation, it becomes
[tex]y^{2}[/tex] -2y -24 = 0
factorizing the equation
[tex]y^{2}[/tex] -6y + 4y - 24 = 0
y(y - 6) +4(y - 6) = 0
taking the terms outside bracket and putting them in a new bracket we have
(y + 4) (y - 6) = 0
so y + 4 = 0 or y - 6 = 0
y = -4 or y = 6
using y = -4 and substituting in equation 3
x = 2 - - 4
x = 6
In conclusion the two numbers are 6 and -4
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Determining if the inverse is a function
Answer:
I'm not sure, but it could be "inverse"
Step-by-step explanation:
What is the equation of the graph below?
Oy=-(x-2)²+3
Oy=(x + 2)²+3
Oy=-(x+3)²+2
Oy=(x-3)²+2
The equation of the graph is given by y = ( x + 2 )² + 3
What is Equation of Graph of Polynomials?Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Identify the even and odd multiplicities of the polynomial functions' zeros.
Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.
The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities
Given data ,
Let the equation be represented as A
Now , the value of A is
y = ( x + 2 )² + 3
The given equation is in the standard vertex form of a parabola:
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
By comparing the given equation with the standard vertex form, we can see that:
a = 1, h = -2, and k = 3
Hence , the vertex of the parabola is at the point (-2, 3) and the graph is plotted
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A restaurant owner wants to attract more customers by getting enough ratings to appear on a popular social media site. The owner can generate 10% more business by reaching an additional 100 reviews. He knows that he provides one hundred 50% off coupons for meals, he can get 100 reviews. How much will it cost to increase business by 10% if each coupon is likely to cost $15?
Answer:
25%
Step-by-step explanation:
cause i did marh
Parker went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 50 grams of sugar and each bottle of juice has 10 grams of sugar. Parker purchased a total of 14 bottles of juice and soda which collectively contain 300 grams of sugar. Graphically solve a system of equations in order to determine the number of bottles of soda purchased,x, and the number of bottles of juice purchased, y.
The number of bottles of soda purchased are 4 and the number of bottles of juice purchased are 10.
Given,Parker went to the grocery store and bought bottles of soda and bottles of juice.
Each bottle of soda has 50 grams of sugar and each bottle of juice has 10 grams of sugar.
Parker purchased a total of 14 bottles of juice and soda which collectively contain 300 grams of sugar.
we are asked to determine the number of bottles of soda purchased,x, and the number of bottles of juice purchased, y.
So, the total number of bottles:x+y=14
x=14-y ...eq(1)
As, Each bottle of soda has 50 grams of sugar and each bottle of juice has 10 grams of sugar.
50x+10y=300
Substituting the value of x from eq(1)
⇒ 50(14-y) + 10y = 300
⇒ 700 - 50y + 10y = 300
⇒ -40y = 300 - 700
⇒ -40y =-400
y = 400/40
y = 10
The number of juice bottles = 10.
Now, to get the number of bottle of soda by substituting the value of y in equation (1):
x = 14-y
x = 14 - 10
x = 4
The number of soda bottles = 4.
Therefore, the number of bottles of soda purchased are 4 and the number of bottles of juice purchased are 10.
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solve for y
18-5x= -9y
Answer:
y= [tex]\frac{5}{9}[/tex]x - 2
Step-by-step explanation:
You want to get y alone so divide both sides by -9 to get: y = [tex]\frac{5}{9}[/tex]x- 2
this is because 2 negatives (-5x and -9) make a positive
I need help with this please
Answer:
Only the third one is incorrect. First 2 and last 1 are correct.
12x−x+8+3x= ______x + _______ Complete the equation so that it has infinitely many solutions.
Answer:
14x + 8 for the first column and the second one is i think its 2 (7x + 4)
Step-by-step explanation:
sorry if this is not what your looking for
Leo reads 11 pages in one third 1/3 hour. What is the unit rate for hours per pages?
Answer: 33 pages in 1 hour
Step-by-step explanation:
You could cross multiply
[tex]\frac{11}{1/3}[/tex] = [tex]\frac{x}{1}[/tex]
11=1/3x
x=33
Select the correct answer. What is the solution for x in the equation 5/3x + 4= 2/3x? A. B. C. D.
[tex]\boldsymbol{\sf{\dfrac{5}{3}x+4=\dfrac{2}{3}x }}[/tex]
Subtract 2/3x on both sides.
[tex]\boldsymbol{\sf{\dfrac{5}{3}x+4-\dfrac{2}{3}x=0 }}[/tex]
Combine 5/3x and -2/3x to get x.
[tex]\boldsymbol{\sf{x+4=0 }}[/tex]
Subtract 4 from both sides. Any value subtracted from zero results in its negative value.
[tex]\boldsymbol{\sf{x=-4 }}[/tex]
Answer:
x = - 4
Step-by-step explanation:
[tex]\frac{5}{3}[/tex] x + 4 = [tex]\frac{2}{3}[/tex] x ( multiply through by 3 to clear the fractions )
5x + 12 = 2x ( subtract 2x from both sides )
3x + 12 = 0 ( subtract 12 from both sides )
3x = - 12 ( divide both sides by 3 )
x = - 4