Answers
Answer:
D. (CPCTC)
Step-by-step explanation:
Your proof that the triangles are congruent is complete at the 4th step. In Step 5, you are asked to draw a conclusion about corresponding angles in those congruent triangles.
__
what is congruence?Two geometric objects are congruent if they are identical in size and shape by any measure. If they are not labeled, you cannot tell them apart. Every measure of one is identical to the corresponding measure of the other. The location and orientation of congruent figures does not affect their congruence. You can move them, rotate them, flip them over, and they remain congruent.
This property, "corresponding parts of congruent triangles are congruent," is abbreviated "CPCTC." Once you have demonstrated objects are congruent, you can use this fact to relate measures of the objects that may not have been part of the demonstration.
proving congruencegeneral
We generally work with plane geometric figures that are polygons or have well-defined curved edges. Polygon figures are comprised of straight sides of fixed length. At each vertex, where sides meet, an angle is formed. Corresponding sides form corresponding angles.
The sides are generally named by the vertices at either end. The angles may be named by the vertex where it is located, or by the names of the sides that make it up.
In triangle ABC, for example, the vertices have labels A, B, and C. The sides are AB, AC, and BC. And the angles are A, B, and C, or BAC, ABC, ACB. (The vertex of the angle is the middle letter.)
To prove polygons are congruent, you must show corresponding angles are congruent, and corresponding sides are congruent. Generally, the number of sides will put constraints on the size of the angles. (A 6-sided polygon will have 6 angles that total 720°, for example.)
triangles
When the polygon is a triangle, the constraints on side lengths and angles generally mean there are shortcuts to proving congruence. The postulates that tell you what these are have been given mnemonic abbreviations. When we say, "angle" or "side" in this context, we are referring to congruent corresponding angles in the two triangles, or congruent corresponding sides.
AAS -- two consecutive angles and a side adjacent to one of them will prove congruenceASA -- two angles and the side between them will prove congruenceSAS -- two sides and the angle between them will prove congruenceSSS -- three sides will prove congruenceThese can also be applied to right triangles, where one angle is known to be 90°. In addition, there is a theorem that only applies to right triangles:
HL -- the hypotenuse and one leg will prove congruence. (Note that the hypotenuse is opposite the known 90° angle, so this is effectively an SSA congruence statement, only applicable to right triangles.)your proof
The triangles in your figure have a side marked with a single hash mark. This means those corresponding sides in the two triangles are congruent to each other.
There is an angle marked with two (2) arcs in each triangle. This marking means those corresponding angles are congruent. Likewise for the angles marked with three (3) arcs. You will notice the 3-arc angle, 2-arc angle, and 1-hash mark side are in the same order in the two triangles. This means the AAS congruence postulate applies, as is claimed on line 4 of your proof.
using congruenceAs you have seen, we only need to show some parts of a triangle are congruent in order to show all parts of the triangle are congruent. When we make a claim about corresponding parts that weren't an explicit part of the proof, we are essentially relying on the definition of congruent polygons. For triangles, that definition is summarized by the abbreviation CPCTC.
Line 5 of your 2-column proof is making a claim about corresponding angles of the triangle. That claim is supported by CPCTC.
_____
Additional comment
Choices A and C refer to congruence postulates, as discussed above. Those have no relation to the claim regarding angles ACB and XZY.
The "corresponding angles theorem" tells you corresponding angles are congruent where a transversal crosses parallel lines. It has no relation to the angles in this problem.
Related Questions
What is the area of the hexagon?
5m
4 m
4 m
12 m
5m
60 m ²
120 m 2
106 m ²
68 m 2
Answers
Answer:
68 square meters
Step-by-step explanation:
The hexagon is made up of two trapezoids. Use the formula to find the area of each trapezoid then add those two areas together.
Area of a trapezoid (add the two bases together, multiply by the height then divide by 2):
[tex]A = \frac{1}{2} (b_{1}+b_{2})h[/tex]
Top trapezoid:
[tex]A = \frac{1}{2} (5 + 12)4\\A = \frac{1}{2} (17)4\\A= \frac{1}{2} (68)\\A = 34[/tex]
Bottom trapezoid (identical to the top trapezoid):
[tex]A = \frac{1}{2} (5 + 12)4\\A = \frac{1}{2} (17)4\\A= \frac{1}{2} (68)\\A = 34[/tex]
Add the areas together:
34 + 34 = 68
Which expression is equivalent to -1/2 (1/4 x - 3/8). SHOW WORK
Answers
Hey there!
-1/2 (1/4 * - 3/8)
= -1/2(1/4)(-3/8)
= -1/2(-3/32)
= 3 / 64
Therefore, your answer should be:
3/64
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
I really need help with this
Answers
What represents vector t = –5i + 12j in trigonometric form?
t = 13 ❬cos 67.38°, sin 67.38°❭
t = 13 ❬sin 67.38°, cos 67.38°❭
t = 13 ❬cos 112.62°, sin 112.62°❭
t = 13 ❬sin 112.62°, cos 112.62°❭
Answers
The representation of the vector in trigonometry form is t = 13 ❬cos 112.62°, sin 112.62°❭
Complex numberThe representation of complex number in polar form is expressed as;
y = r(cosФ + isinФ)
where;
r is the modulus
Ф is the argument
Given the vector t = –5i + 12j, the modulus of the vector is given as;
r = √(-5)²+(12)²
r = √25 + 144
r = √169
r = 13
Determine the angle between the vectors
Ф = arctan(-12/5)
Ф = -67.38
Since tan is negative in the second quadrant, hence;
Ф = 180 - 67.38
Ф = 112.62°
The representation of the vector in trigonometry form is t = 13 ❬cos 112.62°, sin 112.62°❭
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PLEASE HELP ME. QUAD has coordinates Q(-4, 9), U(2, 3), A(-3, -2), and D(-9, 4). Prove that quadrilateral QUAD is a
rectangle.
Answers
Check the picture below.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ Q(\stackrel{x_1}{-4}~,~\stackrel{y_1}{9})\qquad U(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill QU=\sqrt{[ 2- (-4)]^2 + [ 3- 9]^2} \\\\\\ ~\hfill \boxed{QU=\sqrt{72}} \\\\\\ U(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad A(\stackrel{x_2}{-3}~,~\stackrel{y_2}{-2}) ~\hfill UA=\sqrt{[ -3- 2]^2 + [ -2- 3]^2} \\\\\\ ~\hfill \boxed{UA=\sqrt{50}}[/tex]
[tex]A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad D(\stackrel{x_2}{-9}~,~\stackrel{y_2}{4}) ~\hfill AD=\sqrt{[ -9- (-3)]^2 + [ 4- (-2)]^2} \\\\\\ ~\hfill \boxed{AD=\sqrt{72}} \\\\\\ D(\stackrel{x_1}{-9}~,~\stackrel{y_1}{4})\qquad Q(\stackrel{x_2}{-4}~,~\stackrel{y_2}{9}) ~\hfill DQ=\sqrt{[ -4- (-9)]^2 + [ 9- 4]^2} \\\\\\ ~\hfill \boxed{DQ=\sqrt{50}}[/tex]
now, let's take a peek at that above, DQ = UA and QU = AD, so opposite sides of the polygon are equal.
Now, let's check the slopes of DQ and QU
[tex]D(\stackrel{x_1}{-9}~,~\stackrel{y_1}{4})\qquad Q(\stackrel{x_2}{-4}~,~\stackrel{y_2}{9}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-9)}}} \implies \cfrac{9 -4}{-4 +9}\implies \cfrac{5}{5}\implies \cfrac{1}{1}\implies 1 \\\\[-0.35em] ~\dotfill[/tex]
[tex]Q(\stackrel{x_1}{-4}~,~\stackrel{y_1}{9})\qquad U(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{3 -9}{2 +4}\implies \cfrac{-6}{6}\implies \cfrac{-1}{1}\implies -1[/tex]
keeping in mind that perpendicular lines have negative reciprocal slopes, let's notice that the reciprocal of 1/1 is just 1/1 and the negative of that is just -1/1 or -1, so QU has a slope that is really just the negative reciprocal of DQ, those two lines are perpendicular, thus making a 90° angle, and their congruent opposite sides will also make a 90°, that makes QUAD hmmm yeap, you guessed it.
3. The diagonal of a rectangular field is 169 m. Ifthe ratio of the length to the width is 12:5, find the: (a) (b) dimensions; perimeter of the field.
Answers
The dimensions of the rectangle are length 156 m and a width of 65m, and a perimeter P = 442m
How to find the dimensions of the rectangle?For a rectangle of length L and width W, the diagonal is:
[tex]D = \sqrt{L^2 + W^2}[/tex]
Here we know that the diagonal is 169m.
And the ratio of the length to the width is 12:5
This means that:
W = (5/12)*L
Replacing all that in the diagonal equation:
[tex]169 = \sqrt{((5/12)^2*L^2 + L^2} \\\\169^2 = (25/144)*L^2 + L^2 = ( 25/144 + 1)*L^2\\\\\frac{169}{\sqrt{25/144 + 1} } = L = 156[/tex]
So the length is 156 meters, and the width is:
W = (5/12)*156 m = 65m
Finally, the perimeter is:
P = 2*(L + W) = 2*(156 m + 65m) = 442m
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nate spent 3/8 of his money on clothes .he spent £510 on clothes.calculate how much money he had left over?
Answers
Answer:
£850
Step-by-step explanation:
We can compute the left-over amount by comparing that to the amount spent.
__
setupWritten as ratios, we have ...
spent : left-over = 3/8 : 1 -3/8 = 3/8 : 5/8 = 3 : 5
Writing this using fractions, we have ...
left-over / spent = 5 / 3
solutionSolving for left-over gives ...
left-over = spent × (5/3) = £510×5/3 = £850
Nate had £850 left over.
_____
Additional comment
Nate's money totaled £510 +850 = £1360.
The fraction spent is £510/£1360 = 3/8, as required.
In a recent season in a basketball league, a certain player made 746 field goals, which was 48.9% of the shots he tried. How many shots did he try?
Answers
Answer:
I don't no ok ok ok ok ok ok ok ok ok
help me with this please
Answers
Answer:
1/12 more red rice then white rice
Step-by-step explanation:
3/4 = 0.75
2/3 = 0.666666....
Clearly Red rice is more but it will be difficult to state how much more in decimal form so we must use fraction form :
3/4 = 9/12
2/3 = 8/12
So there is 1/12 more red rice then white rice
Hope this helped and have a good day
Suppose you make $1500 at your summer job and you decide to invest this money in a savings account that
pays interest at an annual rate of 5.5% compounded continuously. How many dollars will be in the account
after 5 years?
Answers
Answer:
$1912.50
Step-by-step explanation:
5.5% of $1500 is 82.50
so 82.50×5(years)
=412.5 + 1500
=1912.50
Answer:
You will need this formula
Total = Principal * e ^ (rate * years)
where 'e' equals 2.718281828459
Total = 1,500 * 2.718281828459 ^ (.055 * 5)
Total = 1,500 * 2.718281828459 ^ (.275)
Total = 1500 * 1.31653067486762
Total = 1,974.80
formula www.1728.org/rate2.htm
Calculator located here: https://www.1728.org/compint.htm
Step-by-step explanation:
A Pythagorean triple is a set of three positive integers a, b, and c that satisfy the equation a² + b² = c².
The numbers 3, 4, and 5 are a Pythagorean triple because 3² + 4² = 5². Pythagorean triples are usually written in parentheses, such as (3, 4, 5) .
You can determine other Pythagorean triples by multiplying every number in (3, 4, 5) by the same positive integer. This creates similar triangles where the number you multiplied every triple by is the scale factor.
To create Pythagorean triples that are not similar to a triangle with side lengths of 3, 4, and 5, follow these steps.
Choose two positive integers, m and n, where m>n .
Determine a using a=m2−n2 .
Determine b using b=2mn .
Determine c using c=m2+n2
.
Write the triple (a, b, c) .
a. What Pythagorean triple results when m = 3 and n = 2? Explain.
b. Determine two other Pythagorean triples by multiplying every triple in part a by the same number.
c. Choose your own values for m and n. What Pythagorean triple results? Explain.
Answers
Answer:
Step-by-step explanation:
(3k,4k,5k)
sea k=2
la terna es:
(6,8,10)
sea k=5
la terna sería:
(15,20,25)
PLSS ANSWER MY QUESTION
IN THE PICTURE
☞ NONSENSE ANSWER REPORT ☜
☞ WRONG ANSWER REPORT ☜
☞CORRECT ANSWER ☜ ➣ brainlist or follow
Answers
Answer:
1) Area of frame: [tex]140cm^2[/tex] ; Area of picture: [tex]40cm^2[/tex] ; Total Area: [tex]180cm^2[/tex].
2) Area 1 = [tex]48cm^2[/tex] ; Area 2 = [tex]12cm^2[/tex] ; total area = [tex]60cm^2[/tex] [first answer line : [tex]60cm^2[/tex]]
Step-by-step explanation:
1. So to answer this question, you have to find the inner photo area first (which you will then subtract from the overall rectangle area to get the photo frame area).
To find area, you multiply length x width. For this question, there are not enough measurements given to initially multiply length and width. So, assuming that the photo is centered on the frame and the frame width is consistent along all sides, you find the difference between the overall length (12) and the picture length (5).
12 - 5 = 7
The leftover area (outside of the picture) is 7 cm (half of seven on both sides), so one side can be assumed to be : 3.5 cm
this means that 15 cm - 3.5 cm of both sides lengths (difference between the two lengths given) is the height of the photo, 15 - 3.5(2) = 8
So, the dimensions/measurements of the photo are 5 cm by 8 cm.
This means that the inner photo area is 40 (5 x 8) cm
The area of the frame will be the area of the total rectangle [12 x 15] - the inner photo area [40]. [ (12)(15) - 40 ]
[180 - 40] = 140 cm
(area is measured in squared units, so the area of the frame should be written as [tex]140cm^{2}[/tex] ; and the area of the photo should be written as [tex]40cm^{2}[/tex])
The total area is the entire area of the rectangle: (12)(15) = 180. (This should be written as [tex]180cm^2[/tex])
--------------------------------------
2) Finding the area of a shape that isn't a simple rectangle is easier if you separate the shape into smaller rectangles. I will separate the two rectangles into 4 x 12 and 2 x 6 [6 cm would be the remaining side length if you remove the length of 4].
{you can separate the shape in multiple ways, so my answer is only one answer to this problem out of other splits.}
as mentioned, the area is length x width.
4 x 12 = 48.
2 x 6 = 12. Once again, you should write area in squared units.
(the area 1 should be written as [tex]48cm^{2}[/tex] ; the area 2 should be written as [tex]12cm^2[/tex])
you can combine the separated areas (add them) to find the total area. 48 + 12 = 60.
(the total area should be written in squared units also, so the total area should be written as: [tex]60cm^2[/tex])
The area of the figure is [tex]60cm^2[/tex]
maxine earns $1250 dollars a month. whats is the maximum amount she should use for budget for housing?
show your work so I know how to do this
Answers
Answer:
The National Housing Act of 1937 established guidelines for maximum rents for low-income families. Originally the maximum rent threshold was set at 20%, however this increased to 30% in 1981 (and has remained at this level ever since). This figure is used to determine how much of your gross monthly income you should spend on rent.
The 28% Rule is used for determining how much of your gross monthly income should be used for a mortgage, however the FHA's threshold is a little higher at 31% of your gross monthly income on a mortgage.
Renting:
30% of $1,250 = 0.3 × 1250 = $375
Mortgage 28% Rule:
28% of $1,250 = 0.28 × 1250 = $350
Mortgage 31% FHA:
31% of $1,250 = 0.31 × 1250 = $387.50
Therefore, discounting the higher FHA's threshold, the maximum amount to budget for housing is:
$375 (if renting)$350 (if buying)PLEASE HELP "What is the value of x in the triangle" (15 Points)
Answers
Answer:
The answer is B.) 3
Step-by-step explanation:
Answer:
jesse got right
Step-by-step explanation:
branliest.
Find the area of a regular polygon with 6 sides that has a side length of 6 inches and an apothem of 4 inches.
Area = [?]in2
Answers
Answer:
see the attachment photo!
SUPER EASY POINTS, i also need some clarification on this question... would i be correct?
Answers
Answer:
[tex]\bf \sf \dfrac{1}{3}[/tex]
Explanation:Take points: (6, 2), (3, 1)
[tex]To \ find \ proportionality = \sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]
Insert values
[tex]\rightarrow \sf \dfrac{1-2}{3-6}[/tex]
Simplify
[tex]\rightarrow \sf \dfrac{-1}{-3}[/tex]
Cancel out the negatives
[tex]\rightarrow \sf \dfrac{1}{3}[/tex]
Answer:
B) [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
When y varies directly with x, the relationship is [tex]y=kx[/tex] where [tex]k[/tex] is the constant of proportionality. Hence, [tex]k=\frac{y}{x}[/tex].
So, your answer would not be correct because you did [tex]\frac{x}{y}[/tex] instead of [tex]\frac{y}{x}[/tex], so the correct option would be the reciprocal, or [tex]\frac{1}{3}[/tex].
Can someone pls help me with this
Answers
The length has [tex]\frac{3.5}{0.5}=\boxed{7}[/tex]
The width has [tex]\frac{2.5}{0.5}=\boxed{5}[/tex]
The height has [tex]\frac{1.5}{0.5}=\boxed{3}[/tex]
What's the most effective method for controlling inventory ? a ) Electronically , by reviewing billing receipts b ) Electronically , by checking recent orders Oc ) Visually , by looking at discarded packaging d ) Visually , by looking at what's on the shelf
Answers
Answer:
a ) Electronically , by reviewing billing receipts
Step-by-step explanation:
The main purpose of controlling inventory is to make sure that the optimal amount of products are being kept.
Therefore, option A is correct.
i need helppp with this question
Answers
Answer:
2
Step-by-step explanation:
g/5 - h is equal to 20/5 - 2
equal to 20 divided by 5 is equal to 4(20÷5=4)
then 4minus h which is 4- 2 =2
therefore the answer is 2
I hope this helps you
The probability of rain on the last day of July is 95 % . If the probability remains constant for the first seven days of August , what is the probability that it will rain at most two of those seven days in August ? Find the Mean , Standard Deviation , and Variance .
Answers
The probability that it rains at most 2 days is 0.00005995233 and the variance is 0.516
The probability that it rains at most 2 daysThe given parameters are:
Number of days, n = 7Probability that it rains, p = 95%Number of days it rains, x = 2 (at most)The probability that it rains at most 2 days is represented as:
P(x ≤ 2) = P(0) + P(1) + P(2)
Each probability is calculated as:
[tex]P(x) = ^nC_x * p^x * (1 - p)^{n - x}[/tex]
So, we have:
[tex]P(0) = ^7C_0 * (92\%)^0 * (1 - 92\%)^{7 - 0} = 0.00000002097[/tex]
[tex]P(1) = ^7C_1 * (92\%)^1 * (1 - 92\%)^{7 - 1} = 0.00000168821[/tex]
[tex]P(2) = ^7C_2 * (92\%)^2 * (1 - 92\%)^{7 - 2} = 0.00005824315[/tex]
So, we have:
P(x ≤ 2) =0.00000002097 + 0.00000168821 + 0.00005824315
P(x ≤ 2) = 0.00005995233
Hence, the probability that it rains at most 2 days is 0.00005995233
The meanThis is calculated as:
Mean = np
So, we have:
Mean = 7 * 92%
Evaluate
Mean = 6.44
Hence, the mean is 6.44
The standard deviationThis is calculated as:
σ = √np(1 - p)
So, we have:
σ = √7 * 92%(1 - 92%)
Evaluate
σ = 0.718
Hence, the standard deviation is 0.718
The varianceWe have:
σ = 0.718
Square both sides
σ² = 0.718²
Evaluate
σ² = 0.516
This represents the variance
Hence, the variance is 0.516
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a 2 gallon container of window cleaner costs $11.52. what is the price per cup?
Answers
Answer:
$0.36
Step-by-step explanation:
To convert between gallons, quarts, pints, and cups it can be helpful to memorize this:
2 Cups in a Pint
2 Pints in a Quart
4 Quarts in a Gallon
We can work backwards using this, finding that there are 4 quarts in a gallon, 8 pints in a gallon, and 16 cups in a gallon.
Since we have 2 gallons, we must multiply the number of cups by 2 to get 32 cups in 2 gallons.
Now we can solve for the price per cup by dividing the cost of all 2 gallons by how many cups are in it (32.)
$11.52 / 32 = $0.36
That is the answer
- Kan Academy Advance
write the equation representing the number of children in your family
Answers
Answer:
0+4
Step-by-step explanation:
Instructions: Given the figure, what is the
angle of rotational
symmetry?
Rotation:
o
Answers
Answer:
The angle of rotational symmetry is 4
Which action will help increase a low FICO score?
A.
reducing credit card balances
B.
holding payment on bills
C.
applying for credit more frequently
Answers
Let me know if you have any other questions, hope this helps!
Lamar is considering two loans
Which loan will have the lowest total payback?
Answers
Answer:
Loan A will have the lowest total paycheck because the total of the principal than the same total for loan B
What is the value of n?
A. 69
B. 20
C. 29
D. 49
Answers
Answer:
[tex] \pink{\boxed{{\colorbox{white}{Answer}}}}[/tex]
C. 29
Step-by-step explanation:
[tex] \pink{\boxed{{\colorbox{white}{- MsTiyana}}}}[/tex]
PLEASE HELP
State the coefficient of the variable and the exponent on the variable for this expression: x/5 (this is supposed to be vertical but I don't know how to do that)
Answers
For the given relation, the coefficient is (1/5) and the exponent is 1.
Which are the coefficient and the exponent of the variable?For a relation of the form:
[tex]y = a*x^n[/tex]
a is the coefficient and n is the exponent.
In this case, we have:
[tex]y = \frac{x}{5}[/tex]
This can be rewritten to:
[tex]y = \frac{1}{5}*x^1[/tex]
So we can see that the coefficient is (1/5), and the exponent is 1.
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If (1, 0) is an ordered pair of the function F(x), which of the following is an
ordered pair of the inverse of F(x)?
Answers
If the ordered pair (1, 0) represents the function F(x), then the ordered pair (0, 1) represents the inverse of F(x). Option A is correct.
What is a function?A connection between independent variables and the dependent variable.is defined by the function.
The complete question is
"If (1,0) is an ordered pair of the function f(x), which of the following is an ordered pair of the inverse of f(x)?
A. (0,1)
B. (0,0)
C. (1,0)
D. (1,1)"
Functions help to represent graphs and equations. A function is represented by the two variables one is dependent and another one is an independent function.
The relation between them is shown as y if dependent and x is the independent variable.
If the ordered pair (1, 0) represents the function F(x), then the ordered pair (0, 1) represents the inverse of F(x).
F(x)∈ (1, 0)
F⁻¹(x)∈(0, 1)
Hence, option A is correct.
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Last month David and Mary saved some money in a ratio of 3:5. This month they saved an additional $154 together, and David now has three times as much money as he had last month and Mary has two times as much as she had last month. How much money did they save last month?
Answers
Answer:
David: $42Mary: $70Step-by-step explanation:
The two relations can be translated to a system of linear equations in two variables. These can be solved in any of the usual ways.
__
setupLet d and m represent the amounts David and Mary saved last month, respectively.
The first relation tells us
d/m = 3/5 ⇒ 5d = 3m ⇒ 5d -3m = 0
The second relation tells us that adding 3 times what David had last month to 2 times what Mary had last month will give a total that is 154 greater than the sum of their funds last month.
d +m + 154 = 3d +2m ⇒ 2d +m = 154
__
solutionWe can add 3 times the second equation to the first to eliminate m.
(5d -3m) +3(2d +m) = (0) +3(154)
11d = 462 . . . . . . . . simplify
d = 42 . . . . . . . . . divide by 11
Using the second equation, we can find Mary's savings:
m = 154 -2d
m = 154 -2(420 = 70
David saved $42 last month; Mary saved $70.
All of the following are irrational except _____.
Answers
The number that is not irrational is [tex]1.\overline{45}[/tex]. The correct option is the second option [tex]1.\overline{45}[/tex]
Irrational numbersFrom the question, we are to determine which of the given options is not irrational
Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q, where p and q are integers.
[tex]1.\overline{45}[/tex] is a repeating decimal and it can be expressed as a fraction
[tex]1.\overline{45} = \frac{144}{99}[/tex]
∴ [tex]1.\overline{45}[/tex] is not an irrational number. It is a rational number
The other options cannot the expressed as a fraction.
Hence, the number that is not irrational is [tex]1.\overline{45}[/tex]. The correct option is the second option [tex]1.\overline{45}[/tex]
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