Answers
9a). The measure of segment GH from the given information can be evaluated as one-fourth of the perimeter; 48/4 = 12 cm.
9b). The measure of <EJF is 90° as the angle EJF is a right angle made at the intersection of the rhombus diagonals.
9c). The measure of <EHG is 60° as the opposite angles in a rhombus are congruent and <EHG = 2 × <EHJ = 2 × 30 = 60°.
10a). The sides labelled in the rectangle are congruent by the rectangle diagonal congruence concept; it therefore follows that the required value of x is; 9x+ 20 = 10x +8; and x = 12.
10b). The angle measures as labelled in the rhombus are congruent as this follows from the fact that the diagonal is an angle bisector. Hence, 2x +15 = 5x +3; and x = 4.
What is congruence?The concept of congruence describes a similarly between 2 or more geometric figures or elements.
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Related Questions
To play the lottery in a certain state, a person has to correctly select 5 out of 45 numbers, paying $1 for each five-number selection. If the five numbers picked are the same as the ones drawn by the lottery, an enormous sum of money is bestowed. What is the probability that a person with one combination of five numbers will win
Answers
Using the combination formula, the probability that a person with one combination of five numbers will win is:
[tex]\frac{1}{1,221,759}[/tex]
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
For this problem, 5 numbers are taken from a set of 45, hence the number of combinations is:
[tex]C_{45,5} = \frac{45!}{5!40!} = 1,221,759[/tex]
Hence the probability is:
[tex]\frac{1}{1,221,759}[/tex]
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Which equation is equivalent to
f(x) = 16x4 -81 = 0?
✓(4x² +9)(4x² - 9) = 0 ✓
COMPLETE
Select all of the zeroes of the function.
O
2/3
DONE
Answers
The given equation is equivalent to (4x²+9)*(4x²-9) or (4x²+9)*(2x-3)*(2x+3). And the zero of the function are: [tex]\pm \frac{3}{2}[/tex] and [tex]\pm \frac{3}{2}i[/tex].
What is a Quadratic Function?The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
For solving a quadratic function you should find the discriminant: D=b²-4ac and after that use this variable in the formula: [tex]x=\frac{-b\pm\sqrt{D} }{2a}[/tex].
FactoringIn math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.
The question gives: [tex]16x^4-81=0[/tex], you can factor this equation. See below.
(4x²+9)*(4x²-9)
(4x²+9)*(2x-3)*(2x+3)
Therefore, you should choose one of options: (4x²+9)*(4x²-9) or (4x²+9)*(2x-3)*(2x+3).
Next step is to solve the given equation. Solving for (4x²+9)*(2x-3)*(2x+3)=0, then:
For 2x-3=0
x=3/2
For 2x+3=0
x= -3/2
For 4x²+9=0
4x²=-9
x²= -9/4
x = [tex]\pm \sqrt{\frac{-9}{4} }[/tex]
x =[tex]\pm \frac{3}{2}*\sqrt{-1 }\\ \\ \pm \frac{3}{2}*i[/tex]
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Find the midpoints of A(-3,-9) and B (-8,-2) graphically
Answers
The midpoints of A(-3,-9) and B (-8,-2) is the coordinate points (-5.5, -3.5)
Midpoint of coordinatesCoordinate points are written in the form (x, y). The midpoint of two points (x1, y1) and (x2, y2) is expressed as:
M(x, y) ={(x1+x2)/2, (y1+y2)/2}
Given the following coordinates A(-3,-9) and B (-8,-2)
M(x, y) = {(-3+(-8))/2, (-9-(-2))/2}
M(x, y) = {(-3-8)/2, (-9+2)/2}
M(x, y) = (-11/2, -7/2)
M(x, y) = (-5.5, -3.5)
Hence the midpoints of A(-3,-9) and B (-8,-2) is the coordinate points (-5.5, -3.5)
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Find the service area of a cylinder with a base diameter of 6ft and height of 4ft
Answers
The service area of the cylinder is 42[tex]\pi[/tex] square fts.
What is cylinder?Two parallel bases joined by a curving surface make up the three-dimensional solid known as a cylinder.
Typically, the bases are shaped like circles. The height "h" of the cylinder stands for the perpendicular distance between the bases, while "r" stands for the cylinder's radius.
The uses of cylinder are-
A popular piece of scientific equipment used to determine the volume of a liquid is a graduated cylinder, sometimes referred to as a measuring cylinder or mixing cylinder. Its form is slender and cylindrical. The measured amount of liquid is shown by each marked line on the graduated cylinder.Total surface area of the cylinder formula:
It is the sum of the base surface area and the lateral surface area;
Total area = base area + lateral area , or
Total area = 2 π r² + (2 π r) h , or
Total area = 2 π r (r + h)
Calculation for the total area of the cylinder;
Base diameter is 6 ft
Radius is 6/2 = 3 ft
Height is 4 ft
Total area = 2[tex]\pi[/tex]3(3 + 4)
= 6[tex]\pi[/tex]×7
= 42[tex]\pi[/tex]
Therefore, the total surface area of the cylinder is 42[tex]\pi[/tex] square fts.
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A spinner has two equal sections, one green and one orange. The spinner is spun three times, resulting in the sample space S
Answers
The graph that is used to represent this probability distribution is the graph of b.
What is probability?In mathematics and the field of statistics, the probability is used tp denote likelihood of an event occurring.
The sample space is given as
S = {GGG, GGO, GOG, OGG, GOO, OGO, OOG, OOO}.
X=0, the Probability of having Orange(O), in GGG is given to be 1/8
X=1, we have to get the probability, in G G O , GOG,and O G G, this gives a total of 3 = 3/8
X=2, Probability of Orange O, in GOO , OGO, oog = 3/8
X=3, Probability of Orange O in all is also given as 1. Hence the probability is = 1/8
Complete questionA spinner has two equal sections, one green and one orange. The spinner is spun three times, resulting in the sample space S = {GGG, GGO, GOG, OGG, GOO, OGO, OOG, OOO}. If the random variable X represents the number of times orange, O, is spun, which graph represents the probability distribution?
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Drag each expression to the correct location on the table. Simplify each exponential expression using the properties of exponents and match it to the correct answer. 3². (33) ².3-8 3 (32) (2-3)-3 2-3 (2-¹)(3- (3-5 1-2) -2)* 3 1 25-35.6-5 (23) (2-3)-¹ 22 113
3 2 1
Answers
The expression has been dragged the correct location on the table.
What is an exponential expression?It should be noted that an exponential expression simply means a way to write Lowe's in short form.
In this case, the expression has been dragged the correct location on the table.
This is attached below.
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Use the diagram to complete the following tasks.
Given: S is the midpoint of QT.
Finish the following statement: AQRS = A_
Identify the congruent Zs.
Justify your answer.
Answers
The given statements:
1) ΔQRS ≅ ΔSTU (according to the ASA axiom)
2) The congruent ∠S: ∠RSQ ≅ ∠UST (Vertical angles)
What does the ASA axiom state?The ASA axiom states that "two triangles are said to be congruent if two pairs of corresponding angles and the sides between these angles are equal".
Finding the given tasks:It is given that,
S is the midpoint of QT.
So, SQ ≅ ST <S>
Since ∠S is at the intersection of two transversal lines, ∠RSQ ≅ ∠UST <A>. This is beacuse they are vertically opposite.
And QT is the transverse line for the parallel lines, QR║UT. So, the alternate angles(interior) are congruent. I.e., ∠SQR ≅ ∠UTS <A>.
From this, the given triangles have two equal corresponding angles and congruent sides in between them.
So, ΔQRS ≅ ΔSTU according to ASA axiom.
Therefore, ΔQRS ≅ ΔSTU and ∠RSQ ≅ ∠UST.
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The fitness center held a weight loss competition in which 128 people participated. The amount of weight loss was normally distributed with a mean of 18 pounds and a standard deviation of 5.4 pounds. Approximately how many people lost at least 15 pounds?
Select one:
a. 72
b. 78
c. 84
d. 90
Answers
Answer:
d. 90
Step-by-step explanation:
z = (x - mean)/SD = (15 - 18)/5.4 = - 3/5.4 = -0.55555555... ≈
≈ -0.56
remember the z-table represents the rounded values.
the z-table at -0.56 gives us the p-value of 0.28774.
that is the probability to the left of 15 pounds, so, the probability to have lost 15 pounds or less.
to have lost at least 15 pounds, we have to get the right side of 15 pounds in the bell curve.
and that is 1 - 0.28774 = 0.71226
so, the probability to have lost at least 15 pounds is therefore 0.71226.
how many people are that ?
well, there were in total 128 people (with the total probability of 1 representing everything).
the number of people that lost at least 15 pounds are the proportionate share of 0.71226 of 1 (the whole) :
128 × 0.71226 = 91.16928...
so, the closest answer option is d. 90
21+21+7+7+7+7+8+8+8+8+9+9
Answers
Answer:
21+21+7+7+7+7+8+8+8+8+9+9
Step-by-step explanation:
amswer is 120
Answer:
Step-by-step explanation:
21+2=42.There are four sevens-which is 7x4=28.There are four eights meaning it is 8x4=32+28=60+42=102+(9+9)=102+18=120
Which term best describes the figure shown below?? WILL MARK BRAINLIEST!!!
Answers
Answer:
Line LM
Step-by-step explanation:
Answer:
A line is a straight path on a plane that extends forever in both directions with no endpoints.
The answer will be lineLM
please help me im in a rush
Answers
Answer:
7.6
Step-by-step explanation:
mean = [weights] / amount of weights
m = 10 + 7 + 6 + 10 + 13 + 10 / 6
m = 46 / 6
m = 7.66666666 (recurring)
m = 7.6
James has $0.50 more than his brother John. The sum of their money is $2.50. how much money does John have
Answers
Answer:
Step-by-step explanation:
John has $1.25
James has $1.75
i think
Answer:
$1.00
Step-by-step explanation:
James has $0.50 more than John.
When they put their money together, they have a combined total of $2.50.
[tex]2.50-0.50=2.00[/tex]
[tex]2.00\div2=1.00[/tex]
[tex]1.00+1.50=2.50[/tex]
[tex]=2.50[/tex]
John has one dollar.
Hope this helps.
Which expression is equivalent to?
3/2
Answers
Answer:
D
Step-by-step explanation:
simplified is 1 1/2, 1.5 or 3/2
Are the triangles similar? If so, state the similarity and postulate or theorem that justifies your answer
Answers
Answer:
Yes
Step-by-step explanation: The answer is Side Angle Side (SAS)
Gavin made a patio area out of square blocks that are by . The area of his patio is and the length is . a) Determine the width of his patio. b) Determine the number of blocks Gavin used to make his patio.
Answers
The width of his patio is 19.5 feet based on the information about the area given.
How to calculate the width?Area = Length × Width
175.5 = 19.5 × w
Width = 175.5/19.5
Width = 9 feet
The width of his patio is 19.5 feet.
The number of blocks that were used will be:
= 175.5/(1.5 × 1.5)
= 175.5/2.25
= 78 blocks
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Complete question
Gavin made the patio area out of square block that are 1.5 by 1.5 feet. The area of the patio is 175.5 ft² and the length is 19.5ft.
a. Determine the width of his patio.
b. Determine the number of blocks Gavin used to make his patio.
A vegetable garden is in the shape of a triangle with a base of b = 25 ft and a height of h = 9 ft. find the area of the vegetable garden.
Answers
Answer:
Step-by-step explanation:
Formula
Area = 1/2 b* h
Givens
b = 25
h = 9
Solution
Area = 1/2 * 25 * 9 Substitute givens into formula
Area = 1/2 * 225 Combine
Answer
Area = 112.5 ft^2
Find the polynomial function in standard form that has the zeros listed. i and -i
Answers
The polynomial function in standard form that has the zeros listed. i and -i is x² +1 = 0.
What is polynomial function?A quadratic, cubic, quartic, and other functions involving only non-negative integer powers of x are examples of polynomial functions.
The values of x that fulfil the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case. The degree of the equation f(x) = 0 determines how many zeros a polynomial has.
Calculation for the polynomial function-
The general two degree/quadratic equation is given by-
ax² + bx + c = 0
Where a ≠ 0
If the two roots of the equation are x1 and x2.
Then the relation between roots and coefficients of the polynomial are -
The sum of the roots = (- coefficient of x)/(coefficient of x²)x1 + x2 = (-b)/a
The multiplication of the roots = constant/coefficient of x²x1.x2 = c/a
From the above two relation the general equation can be written as-
x² -(x1 - x2)x + x1.x2 = 0
Lets say x1 = i and x2 = -i
Substitute the values of x1 and x2 in the general equation
x² -(i - i)x + (i).(-i) = 0
x² - i ² = 0
x² + 1 = 0
Therefore, the polynomial function in standard form that has the zeros listed. i and -i is x² + 1 = 0.
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I need help with cancelling units please
Answers
Answer:
D
Step-by-step explanation:
You are looking for what you would need to cancel the yards in 800 yards.
800 yards (1 mile/ 1760 yards). You have yards in the numerator of your original measurement. You will cross cancel out the yard on the the top and the yards on the bottom.
Helen needs a replacement ball bearing for this part. The surface area of each spherical ball bearing is approximately 452.16 square millimeters. What is the radius of the bearing that Helen needs to buy? Round your answer to a whole number.
Answers
Helen needs a replacement ball bearing whose radius is 5.99mm
A sphere is a perfectly round geometrical 3-dimensional object. It can be characterized as the set of all points located distance r (radius) away from a given point (center). It is perfectly symmetrical, and has no edges or vertices.
The formula of surface area of the sphere is [tex]4\pi r^{2}[/tex] where r represents radius
Given: Surface area of ball = 452.16[tex]mm^{2}[/tex]
Using formula we get,
[tex]4\pi r^{2}[/tex] = 452.16[tex]mm^{2}[/tex]
r^2 = 452.16/4[tex]\pi[/tex]
r = 5.99 mm
Thus Helen needs a replacement ball bearing whose radius is 5.99mm
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what is 1/2y+3.2=20? Does it have no solution?
Answers
Answer:
y = 33.6
Step-by-step explanation:
1/2 y + 3.2 = 20 subtract 3.2 from both sides of the equation
1/2y = 16.8 multiply both sides by 2
y = 33.6
Sophia for the exponential function f left parenthesis x right parenthesis equals 5 times 2 to the power of x, what is the value of f left parenthesis 3 right parenthesis?
Answers
The value of f left parenthesis 3 right parenthesis is 45.
According to the statement
We have given that the F(x) = 5(x)^2
and we have to find the value when Sophia have a 3 right parenthesis.
So, Parenthesis are used in mathematical expressions to denote modifications to normal order of operations.
And now we have to find the value for 3 right parenthesis
And for this purpose we have to put the value X= 3 in the f(x) then
F(x) = 5(x)^2
F(3) = 5(3)^2
F(3) = 5*9
F(3) = 45.
here the value of 3 right parenthesis is 45.
So, The value of f left parenthesis 3 right parenthesis is 45.
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the price of an all access take it to the fair is $42.99 before tax roland bought the all access ticket for 40% off then he pay 7% sales tax on the discounted price part a how much did roland paid in sale tax? part b what is the total amount that roland paid for the ticket ?
Answers
The total amount that roland paid for the ticket is $27.60
Given that the price of an all-access ticket to the fair is $42.99 before tax. Roland bought the all-access ticket for 40% off.
We need to calculate the total amount paid by the roland
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100
The price after 40% off -
= 42.99*60% = $25.794
Sales tax on 25.794
= 25.794*7% = $1.80558
Total amount Paid for the ticket
= 1.80558 + 25.794 = $27.59958
= $27.60
Hence the total amount paid by roland is $27.60
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-2(x-0.5+1) i have this question and i really really really need help in solving it so...yeah!
Answers
Answer:
Step-by-step explanation:
model aeroplane is made to a scale of 1 by two of the size of the real plane the area of the wings of the real plane are 40 m square find the area of the wings of the model in centimetre square
Answers
The area of the wings of the model is 100000 square centimeters
How to determine the model area of the wings?The given parameters are:
Scale factor, k = 1/2
Actual area of wings, A = 40 square meters
The model area is calculated as
Model area = Actual area * k^2
This gives
Model area = 40 * (1/2)^2
Evaluate
Model area = 10 square meters
Convert square meters to square centimeters
Model area = 10 * 10000 square centimeters
Evaluate
Model area = 100000 square centimeters
Hence, the area of the wings of the model is 100000 square centimeters
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The volume of a cube is 36 cm3. What is the surface area of the cube, rounded to the nearest tenth of a cm2
Answers
Answer:
65.4 cm²
Step-by-step explanation:
The volume of a cuboid is calculated by multiplying the length, base, and height together. Since a cube has equal sides, the formula for the volume of a cuboid can be simplified as shown below.
Volume of cube
= side ×side ×side
= side³
Given that the volume is 36 cm³, let's find the length of each side.
side³= 36
Cube root both sides:
side=[tex]\sqrt[3]{36}[/tex]
Total surface area of a cube is the sum of the surface areas of its 6 identical square faces.
Area of a square
= side ×side
= side²
Surface area of 1 face= [tex](\sqrt[3]{36})^2[/tex]
Total surface area
= [tex]6(\sqrt[3]{36} )^2[/tex]
= 65.416 (5 s.f.)
= 65.4 cm² (nearest tenth)
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https://brainly.com/question/2160079920% of a number is 17 . find the number
Answers
Answer:
x = 85Step-by-step explanation:
20% of a number is 17 . find the number
divide 17 by 20 and you find 1%, multiply by 100 and you get 100%
x = 17 : 20 * 100
x = 0.85 * 100
x = 85
A triangle on a coordinate plane has three vertices A(2 , 3), B(5, 4), and C(3, 6). Use this description to do the following transformations (if needed, draw this triangle on a sheet of paper):
a. Dilation 1: What would be the new coordinates if this triangle were dilated to a scale factor of 2 with the center of the dilation at the origin? How did you determine these points?
b. Dilation 2: What would be the new coordinates if this triangle were dilated to a scale factor of 2 with the center of the dilation at the point (6, 8)? How did you determine these points?
c. What series of transformations would carry dilation 1 onto dilation 2? Compare Dilation 1 to Dilation 2. Explain what conclusions you can draw about the scale factor, difference in area, and center of dilation.
d. What is the proportion of the side lengths from Dilation 1 to Dilation 2? What is the proportion of their angle measures? Explain your answer.
Answers
The dilation by a scale factor of 2 of the points A(2, 3), B(5, 4), C(3, 6) gives;
a. A'(4, 6), B'(10, 8), C'(6, 12)
b. A'(-2, -2), B'(4, 0), C'(0, 4)
c. The transformation that would carry dilation 1 onto dilation 2 is T(-6, -8)
The area of dilation 1 and 2 are the sameThe center of dilation does not change the aread. The proportion of the side length of Dilation 1 and Dilation 2 is 1:1
The angle measures are the sameHow can the new coordinates be found?The general formula for finding the coordinates of the image of a point following a dilation is presented as follows;
[tex]D _{(a , \: b)k}(x, \: y) = (a + k \times (x - a) , \: b+ k \times (y - b))[/tex]
Where;
(a, b) = The center of dilation
k = The scale factor of dilation
(x, y) = The coordinate of the pre-image
The given points are;
A(2, 3), B(5, 4), C(3, 6)
a. The scale factor of dilation = 2
The center of dilation = The origin (0, 0)
Therefore;
[tex]D _{(0 , \: 0)2}(2, \: 3) = (0 + 2 \times (2 - 0) , \: 0+ 2 \times (3 - 0)) = (4, \:6)[/tex]
Therefore dilation about the origin, with a scale factor of 2 gives;
A(2, 3) → A'(4, 6)Similarly
B(5, 4) → B'(10, 8)C(3, 6) → C'(6, 12)b. With the center of dilation at (6, 8), we have;
[tex]D _{(6 , \: 8)2}(2, \: 3) = (6 + 2 \times (2 - 6) , \: 8+ 2 \times (3 - 8)) = (-2, \:-2)[/tex]
A(2, 3) → A'(-2, -2)[tex]D _{(6 , \: 8)2}(5, \: 4) = (6 + 2 \times (5 - 6) , \: 8+ 2 \times (4 - 8)) = (4, \:0)[/tex]
B(5, 4) → B'(4, 0)[tex]D _{(6 , \: 8)2}(3, \: 6) = \mathbf{(6 + 2 \times (3 - 6) , \: 8+ 2 \times (6 - 8))} = (0, \:4)[/tex]
C(3, 6) → C'(0, 4)c. The difference between the coordinates of the points on dilation 1 and 2 is a shift left 6 places and a shift downwards 8 places
Using notation, we have;
Dilation 1 T(-6, -8) → Dilation 2The area of the images of dilation 1 and 2 are equal given that the scale factor is the same.
The location of the center of dilation does not change the area of the imaged. From the above calculation, given that the difference between pre-image point and the center is multiplied by the scale factor followed by the addition of the x and y-values, the lengths of the sides of dilation 1 and 2 are the same, such that we have;
The proportion of the side lengths is 1Given that the side lengths are the same, by AAA congruency postulate, we have;
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Answer:
The angle measures are the same.
Step-by-step explanation:
Go to a clothing store with
your parent/guardian and
pick out one item that you
would like to purchase. How
much of a discount would
you have if the item had
25% off sale? What would
a
the sale price be?
Answers
Answer:
original price $75
discount $18.75
sale price $56.25
Step-by-step explanation:
I found a pair of dress pants for $75.
Since the discount is 25%, then the discount is
25% of $75 = 0.25 × $75 = $18.75
The sale price is the original price, $75, minus the discount, $18.75.
$75 - $18.75 = $56.25
Write an equation of a line that goes through (-18,13) and is perpendicular to 6x+4y=-16
Answers
Here,
y=mx+c
the slope of the line 6x+4y= -16 is -20.
if the two lines are perpendicular, the slope of 1st line * slope of second line=-1
the slope of the 2nd line is -1/2
y-y1=m(x-x1)
y-13=-1/2(x- -18)
when you solve, you get the equation of the line as 2y+x=50
In basic geometry, if two geometry objects intersect at right angles (90 degrees or π / 2 radians), they are vertical.
If two lines intersect at right angles, the line is perpendicular to another line. Explicitly (1) if two lines intersect, the first line is perpendicular to the second line. (2) At the intersection, the straight line angle on one side of the first line is cut by the second line into two congruent angles. Verticality can be shown as symmetric. That is, if the first line is perpendicular to the second line, then the second line is also perpendicular to the first line. Therefore, two straight lines can be said to be perpendicular (to each other) without specifying the order.
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Compute a value for t that satisfies the equation below. "-2/3" t - 2 = - 3
Answers
Answer:
t = 3/2
Step-by-step explanation:
Instead of randomly guessing values of "t" that will satisfy the equation, you can easily find the correct value by solving the equation in terms of "t". In other words, you can set the equation equal to "t" to find the final answer.
(-2/3)t - 2 = -3 <----- Original equation
(-2/3)t = -1 <----- Add 2 to both sides
t = 3/2 <----- Divide both sides by -2/3
You can check this value by plugging it into "t" and determining whether both sides of the equations will be equal.
(-2/3)t - 2 = -3 <----- Original equation
(-2/3)(3/2) - 2 = -3 <----- Plug 3/2 into "t"
-6/6 - 2 = -3 <----- Multiply -2/3 and 3/2
-1 - 2 = -3 <----- Simplify -6/6
-3 = -3 <----- Subtract