Answer:
1. First option.
2. First option.
3. First option.
Step-by-step explanation:
1. You need to remember that the Associative Property of Addition states the following:
[tex](a+b)+c=a+(b+c)[/tex]
Notice that you can group the numbers "a", "b" and "c" in any combination.
In this case, given the statement provided in the exercise:
[tex](2 + 3.4) + 6 = 2 + (3.4 + 6)[/tex]
You can identify that it ilustrates the Associative Property of Addition.
2. Remember that:
- Natural numbers are known as "Counting numbers".
- Whole numbers include positive numbers and zero.
- Integers include the Whole numbers and the negative numbers.
- Rational numbers are those numbers that can be wriitten as a fraction:
[tex]\frac{a}{b}[/tex]
Where "a" is the numerator and "b" is the denominator.
- Integers are a subset of Rational Numbers.
- Irrational numbers cannot be written as a fraction.
Based on this, you can conclude that [tex]\frac{1}{3}[/tex] is a Rational number.
3. The product is the result of a multiplication.
In this case the word "more than" indicates Addition.
Then, the product of 2 more than "y" and 7 can be expressed as:
[tex]7(y+2)[/tex]
The temperature in degrees Celsius is 273.15 less than the temperature in kelvin. Andrew is conducting a science experiment where the temperature must be kept between 13.5°C and 18.5°C. Andrew wants to know the range of the temperature in kelvin.
Select all of the whole number temperatures, in kelvin, at which Andrew can conduct his experiment.
Answer:
The whole number temperatures, in kelvin, at which Andrew can conduct his experiment are 287, 288, 289,290,291.
Step-by-step explanation:
The temperature in degrees Celsius is 273.13 less than the temperature in kelvin; mathematically this means:
[tex]k=c+273.15[/tex]
Where [tex]k[/tex] is the temperature in kelvin and [tex]c[/tex] is the temperature in Celsius.
From this relationship we convert Andrew's temperature range—
13.5°c to 18.5°c—to kelvin:
[tex]k_1=13.5^oc+273.15=286.65[/tex]
[tex]k_2=18.5^oc+273.15=291.65[/tex]
Thus Andrew can conduct his experiment between 286.65 and 291.65 kelvin, and the whole number temperatures between these extremes are 287, 288, 289,290,291.
Thus the whole number temperatures, in kelvin, at which Andrew can conduct his experiment are 287, 288, 289,290,291.
Final answer:
To convert the temperature range from Celsius to Kelvin, add 273.15 to each end of the Celsius range given. The range for Andrew's experiment in Kelvin is from 287 K to 291 K, inclusive.
Explanation:
When converting temperatures from Celsius to Kelvin, one applies the simple formula: K = °C + 273.15. For Andrew's experiment, the temperature must be kept between 13.5°C and 18.5°C. Converting these to the Kelvin scale, we get:
13.5°C + 273.15 = 286.65 K18.5°C + 273.15 = 291.65 KAndrew can conduct his experiment at whole number Kelvin temperatures that fall within this range. Therefore, the range in Kelvin is from 287 K to 291 K, inclusive.
7. Determine if the set of ordered pairs is a relation or a function. Select all that apply.
{(2, 2), (3, 2), (4, 3), (5,4)}
The given relation is a function
Step-by-step explanation:
When a relation is given in the form of ordered pairs, for each ordered pair, the first element of ordered pair represents elements of domain and the second element represents elements of set of range.
In order for a relation to be a function, there should be no repetition in domain i.e. every element should be unique.
Given relation is:
{(2, 2), (3, 2), (4, 3), (5,4)}
As we can see that the domain of given relation is:
{2,3,4,5} i.e. every element is unique
So,
The given relation is a function
Keywords: Relations, functions
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The provided set of ordered pairs {(2, 2), (3, 2), (4, 3), (5,4)} represents both a relation and a function. This holds because each input maps to exactly one output, with no repeating input values.
Explanation:In mathematics, a set of ordered pairs is a relation if input values (also known as the domain or x-values) may have any number of corresponding output values (the range or y-values). A set of ordered pairs is a function if each input value maps to exactly one output value.
Considering the set of ordered pairs: {(2, 2), (3, 2), (4, 3), (5,4)}, we can see that each input (x-value) matches with one corresponding output (y-value) and none of the input values is repeating. Hence, according to the definition, this set of ordered pairs represents both a relation and a function.
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Are the following lines parallel, perpendicular or neither? 5y - x = 5 5y - x = -5 a Parallel b Perpendicular c Neither
Answer:
Parallel lines
Step-by-step explanation:
Parallel lines have equal slopes
The product of the slopes of perpendicular lines equals - 1
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
Rearrange the 2 equations into this form and compare slopes
5y - x = 5 ( add x to both sides )
5y = x + 5 ( divide all terms by 5 )
y = [tex]\frac{1}{5}[/tex] x + 1 ← in slope- intercept form
with slope m = [tex]\frac{1}{5}[/tex]
5y - x = - 5 ( add x to both sides )
5y = x - 5 ( divide all terms by 5 )
y = [tex]\frac{1}{5}[/tex] x - 1 ← in slope- intercept form
with slope m = [tex]\frac{1}{5}[/tex]
Since slopes are equal then the lines are parallel
The sum of 11 and the product of 2 & a number r
Answer:
Step-by-step explanation:
The word "sum" means adding. So, we have 11 + .....
The thing that 11 is being added to is a "product" a product means two things multiplied together. The things being multiplied are the number 2 and the number "r".
-1/3h-2/3=1/7 Do you know the answer?
Answer:
-51/21
The first step in this equation would be to add -2/3 to 1/7
-2/3 and 1/7 need to have the same denominator, which 7 and 3 both go into 21
-2/3 converted to have the denominator, you would have to times top and bottom by 7, so you then get 14/21
Then you want to get the 1/7 with a denominator of 21 also, so you would times top and bottom by 3, so you get 3/21
Now you add 14/21 to 3/21 to get 17/21
-1/3h=17/21
You want to times by the reciprocal of -1/3 which would just be -3/1 so,
17/21*-3/1= -51/21 which is already simplified
So your answer would be -51/21
To check your work you would plug in -51/21 in for h
Step-by-step explanation:
Solve the given equation.
-6. 15*+5 = -75
Answer: -30.75=-75
Step-by-step explanation: Multiply -6.15 by 5.
Hope this helps you out.
Box A holds about
50 marbles. Box B
could hold about
O 5 marbles
O 150 marbles
075 marbles
Answer:
Lack of information.
Step-by-step explanation:
We can't get the answer because this question haven't provide the information enough.
Have a nice day and hope it helps ;)
The diameter of a circular field is 56cm.find the length of wire required to fence it?How many times it can be fenced with 704m of wire.
Final answer:
The length of wire required to fence the circular field is found by calculating the circumference of the field. The number of times the field can be fenced with a given length of wire is found by dividing the total wire length by the circumference.
Explanation:
To find the length of wire required to fence the circular field, we need to find the circumference of the field. The formula to calculate the circumference of a circle is C = πd, where C is the circumference and d is the diameter. So, in this case, the circumference is C = π * 56 cm. Next, to find how many times the field can be fenced with 704m of wire, we divide the total length of wire by the circumference of the field. Therefore, the number of times the field can be fenced is 704 m / (π * 56 cm).
What is the equation of the graph below?
A graph shows a parabola that opens up with a vertex at three comma negative two.
Answer:
[tex]y=(x-3)^2-2[/tex]
Step-by-step explanation:
Given vertex of parabola [tex](3,-2)[/tex]
Where [tex](h,k)[/tex] is the vertex.
[tex](h,k)=(3,-2)\\h=3\ and\ k=-2[/tex]
Also parabola opens up.
The equation of parabola with vertex [tex](h,k)[/tex]
[tex]y= a(x - h)^2 + k[/tex]
If [tex]a>0[/tex] parabola opens up.
[tex]a<0[/tex] parabola opens down.
As the parabola opens up the value of [tex]a[/tex] will greater than zero.
Plugging vertex of parabola in equation [tex]y= a(x - h)^2 + k[/tex]
[tex]y= a(x - 3)^2 -2[/tex]
Let us plug [tex]a=1[/tex]
The equation will be [tex]y= a(x - 3)^2 -2[/tex]
what is the result of subtracting the second equation from the first? x-3y=6 -8x-y=6 (picture included if confusing) please help!! :(
This is the new equation obtained after performing the subtraction.
[tex]\[ 9x - 2y = 0 \][/tex]
When subtracting one equation from another, we subtract the corresponding elements of the equations. Here's the step-by-step process:
Given the two equations:
1. [tex]\( x - 3y = 6 \)[/tex] (First equation)
2. [tex]\( -8x - y = 6 \)[/tex] (Second equation)
We want to subtract the second equation from the first. We do this by subtracting each term of the second equation from the corresponding term in the first equation:
Step 1: Subtract the x-terms:
[tex]\[ x - (-8x) = x + 8x = 9x \][/tex]
Step 2: Subtract the y-terms:
[tex]\[ -3y - (-y) = -3y + y = -2y \][/tex]
Step 3: Subtract the constants:
[tex]\[ 6 - 6 = 0 \][/tex]
So after subtracting the second equation from the first, the result is:
[tex]\[ 9x - 2y = 0 \][/tex]
This is the new equation obtained after performing the subtraction.
6+2+2/3+2/9+...+a6 evaluate
Answer:
8.987 (Approximate)
Step-by-step explanation:
We have to find the sum of a G.P. series up to sixth terms.
The first term of the series is 6 and common ratio is [tex]\frac{1}{3}[/tex].
So, the sum is
[tex]6 + 2 + \frac{2}{3} + \frac{2}{9} + \frac{2}{27} + \frac{2}{81}[/tex]
= [tex]6 \times \frac{1 - (\frac{1}{3})^{6}}{1 - \frac{1}{3} }[/tex]
= 8.987 (Approximate) (Answer)
We know the sum of a G.P.
a + ar + ar² + ar³ + ......... up to n terms = [tex]a\frac{1 - r^{n}}{1 - r}[/tex]
where -1 < r < 1.
6(1) = 16
6(n) = b(n − 1) + 1
Find the 2-term in the sequence.
Answer:
17
Step-by-step explanation:
Given
[tex]b(1)=16\\ \\b(n)=b(n-1)+1[/tex]
Finding the second term of the sequence means to find [tex]b(2).[/tex] To find [tex]b(2)[/tex] substitute [tex]n=2[/tex] into the second expression:
[tex]b(2)=b(2-1)+1\\ \\b(2)=b(1)+1\\ \\b(2)=16+1\\ \\b(2)=17[/tex]
Write a polynomial in standard form with zeroes set at 2i, -2i, 2
The polynomial equation with zeroes 2i, -2i, 2 is [tex]x^3 -2x^2 + 4x - 8 = 0[/tex]
Solution:Given that zeros of polynomial are 2i, -2i, 2
To find: polynomial equation in standard form
zeros of polynomial are 2i, -2i, 2. So we can say,
x = 2i
x = -2i
x = 2
Or x - 2i = 0 and x + 2i = 0 and x - 2 = 0
Multiplying the above factors, we get the polynomial equation
[tex](x - 2i)(x + 2i)(x - 2) = 0\\[/tex] ------- eqn 1
Using a algebraic identity,
[tex](a - b)(a + b) = a^2 - b^2[/tex]
Thus [tex](x - 2i)(x + 2i) = x^2 - (2i)^2[/tex]
We know that [tex]i^2 = -1[/tex]
[tex]Thus (x - 2i)(x + 2i) = x^2 - (2i)^2 = x^2 -4(-1) = x^2 + 4[/tex]
Substitute the above value in eqn 1
[tex](x^2 + 4)(x - 2) = 0[/tex]
Multiply each term in first bracket with each term in second bracket
[tex]x^3 -2x^2 + 4x - 8 = 0[/tex]
Thus the required equation of polynomial is found
if two people agree to pay half of the bills and client a pays $488 one month and client b pays $294 how much is owed to client a
Answer:
$97
Step-by-step explanation:
First, what do we know? Client A payed 488, Client B payed 294. They were supposed to pay equal amounts, but clearly that hasn't happened. If they had been fair, they would have divided the total of each bill equally between them. There is a way for us to do this, simply add the two amounts, and then divide by two.
[tex]488+294=782[/tex]
[tex]\frac{782}{2} =391[/tex]
So, both clients A and B were each supposed to pay 391. How much did client A overpay? We can find this number by looking at the difference between (or subtracting) the amount due (391) and the amount paid (488)
[tex]488-391=97[/tex]
We can verify this is correct by adding 97 to 294, to see if client B will now have paid as much as client A.
[tex]294+97=391[/tex],
which is what client B should have payed, and will have payed once he pays client A the 97 dollars owed.
Thus, client A is owed $97.
Translate
2/3y − 9 < y + 1 into a sentence.
Nine _____ than two-thirds of number is less than the number _____.
Answer:
Nine less than two-thirds of number is less than the number plus one.
Step-by-step explanation:
I jus got it right on edge.
Nine less than two-thirds of the number is less than the number plus one.
What is Algebra?Algebra is the study of mathematical symbols, and the rule is the manipulation of those symbols.
The expression is given below.
2/3y − 9 < y + 1
Then complete the sentence.
Then we have
Nine less than two-thirds of the number is less than the number plus one.
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What is the distance, in feet, across the patch of swamp water?
Answer:
Therefore the distance across the patch of swamp water is 50 ft
Step-by-step explanation:
Given:
VW = 100 ft
WX = 60 ft
XZ = 30 ft
To Find:
ZY = l = ?
Solution:
In Δ VWX and Δ YZX
∠W ≅ ∠ Z …………..{measure of each angle is 90° given}
∠VXW ≅ ∠YXZ ..............{vertically opposite angles are equal}
Δ ABC ~ Δ DEC ….{Angle-Angle Similarity test}
If two triangles are similar then their sides are in proportion.
[tex]\frac{VW}{YZ} =\frac{WX}{ZX} =\frac{VX}{YX}\ \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]
On substituting the given values we get
[tex]\frac{100}{l} =\frac{60}{30}\\\\l=\frac{3000}{60}=50\ ft[/tex]
Therefore the distance across the patch of swamp water is 50 ft
If the domain of the function F = {(x, y) |2x + y = 7} is {1, 2, 3), what is the range?
O {1,2,3}
O (1,3,5)
O {2,5/2, 3)
Answer:
1,3,5
Step-by-step explanation:
The domain is the set of all first elements of ordered pairs (x-coordinates).
The range is the set of all second elements of ordered pairs (y-coordinates).
Answer:
Step-by-step explanation:
y = 7 - 2x
x =1; y = 7 - 2*1 = 7- 2 = 5
x = 2; y = 7 - 2*2 = 7 - 4 = 3
x = 3; y = 7 - 2*3 = 7- 6 = 1
Range = { 1,3,5}
what is the first step in evaluating {[( − )]} ÷ ?
Answer:
Parenthesis
Step-by-step explanation:
The parenthesis are always the first step in the order of operations.
:)
a line intersects the point (-3,-7) and has a slope of -3.What is the slope intercept equation for this line
Answer:
y = -3x -16
Step-by-step explanation:
For problems like this, I like to start with a variation of the point-slope form of the equation of a line:
y = m(x -h) +k . . . . . for a line with slope m through point (h, k)
For your given values, this is ...
y = -3(x +3) -7
y = -3x -9 -7 . . . . eliminate parentheses; next, combine terms
y = -3x -16
Answer:
-3x-16
Step-by-step explanation:
find the value of 2x-yi fx+y=8and4x-y=22
Answer:
10
Step-by-step explanation:
Given
[tex]x+y=8\\ \\4x-y=22[/tex]
Add these two equations:
[tex]x+y+4x-y=8+22\\ \\5x=30\\ \\x=6[/tex]
Substitute it into the first equation:
[tex]6+y=8\\ \\y=8-6\\ \\y=2[/tex]
Then
[tex]2x-y=2\cdot 6-2=12-2=10[/tex]
What is an equation of a line that passes through the points (8 , -3) (8 , 4)
Answer:
Step-by-step explanation:
(8,-3),(8,4)
since both points have the same x value, this means you have a vertical line with an undefined slope...so ur equation would be x = 8....because no matter what y is, x will always be 8
The temperature in Fairbanks, Alasks rose from negative one degrees Fahrenheit to nine degrees Fahrenheit. How many degrees did the temperature change?
Answer:
There was 10° F change in temperature in Fairbanks, Alaska.
Step-by-step explanation:
Given:
Temperature change from = -1° F.
Temperature change to = 9° F
We need to find the change in temperature.
Change in temperature can be calculated by subtracting Temperature change from with Temperature change to.
Framing in equation form we get;
Change in temperature = Temperature change to - Temperature change from
Substituting the values we get;
Change in temperature = [tex]9-(-1)= 9+1=10\° F[/tex]
Hence There was 10° F change in temperature in Fairbanks, Alaska.
Information about how the students at Vista View High School got to school this morning is shown in the table. A 6-column table has 4 rows. The first column has entries Tenth grade, eleventh grade, twelfth grade, Total. The second column is labeled Walk with entries 104, blank, 99, 314. The third column is labeled Bicycle with entries 8, 10, blank, blank. The fourth column is labeled Bus with entries 96, 72, 28, 196. The fifth column is labeled Car with entries blank, 88, blank, 276. The sixth column is labeled Total with entries 282, blank, 252, 815. Out of all 252 twelfth graders, how many rode in a car to school? 11 74 111 114
Answer:
The correct answer is D. 114
Step-by-step explanation:
There are 252 students of twelfth grade at Vista View High School.
99 walked to school
11 went by bicycle
28 used the school bus
To find the amount of twelfth graders that rode in a car, we do this calculation:
Amount of twelfth graders that rode in a car = Total of twelfth graders - those who walked - those who went by bicycle - those who used the bus
Replacing with the real values, we have:
Amount of twelfth graders that rode in a car = 252 - 99 - 11 - 28 = 252 - 138 = 114
The correct answer is D. 114
Answer:
114
Step-by-step explanation:
simplify sqrt (8^17)
a) 8^8 sqrt(8)
b) 8^7 sqrt(8)
c) 2^3 sqrt (8)
d) 2^5 sqrt (8^2)
Answer:
a) [tex]8^8\sqrt{8}[/tex]
Step-by-step explanation:
Given,
[tex]\sqrt{8^1^7[/tex]
We have to simplify the expression by using "The Law of Indices".
[tex]x^m\times x^n=x^m^+^n[/tex]
So we can rewrite the expression as,
[tex]\sqrt{8^1^7[/tex]=[tex]\sqrt{8^1^+^1^6} =\sqrt{8}\times \sqrt{8^1^6}[/tex]
Now according to law of indices, which is;
[tex](x^m)^n=x^m^n[/tex]
So we can rewrite the expression as
[tex]\sqrt{8}\times \sqrt{8^1^6}=\sqrt{8}\times (8^1^6)^\frac{1}{2} \ \ \ \ Or\ \ \ \sqrt{8}\times 8^{16\times\frac{1}{2}} = 8^8\sqrt{8[/tex]
Hence the final Answer is [tex]8^8\sqrt{8[/tex].
what is the equation for a line that passes through the points (3,1) and (4,-1)
Answer:
y-y/x-x
1--1/3-4
1+1/3-4
2/-1
= -2
then you plug in with any one of the points
y=mx+b
1= -2(3) + b
1 = -6 + b
b = 1+6
b = 7
so the equation is: y = -2x+7
What is the product of x(5x + x^2)
Answer:
The product is [tex]x^3+5x^2[/tex]
Step-by-step explanation:
This is because we apply the distributive property of multiplication.
Thus from [tex]x(5x+x^2)[/tex]
we get this:
[tex]x*5x+x*x^2[/tex]
[tex]x*5x[/tex] is [tex]5x^2[/tex] and [tex]x*x^2[/tex] is [tex]x^3[/tex]
in a program designed to help patients stop smoking 232 patients were given sustained care and 84.9% of them were no longer smoking after one month use a 0.05 significance level to test the claim that 80% of the patients. Smoking when given sustained care
Answer:
[tex]z=\frac{0.849 -0.8}{\sqrt{\frac{0.8(1-0.8)}{232}}}=1.869[/tex]
[tex]p_v =2*P(Z>1.869)=0.0616[/tex]
If we compare the p value obtained and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults were no longer smoking after one month is not significantly different from 0.8 or 80% .
Step-by-step explanation:
1) Data given and notation
n=232 represent the random sample taken
X represent the adults were no longer smoking after one month
[tex]\hat p=0.849[/tex] estimated proportion of adults were no longer smoking after one month
[tex]p_o=0.80[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is 0.8.:
Null hypothesis:[tex]p=0.8[/tex]
Alternative hypothesis:[tex]p \neq 0.8[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
3) Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.849 -0.8}{\sqrt{\frac{0.8(1-0.8)}{232}}}=1.869[/tex]
4) Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
[tex]p_v =2*P(Z>1.869)=0.0616[/tex]
If we compare the p value obtained and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults were no longer smoking after one month is not significantly different from 0.8 or 80% .
Given: Rays I and M are bisectors of the angels of triangle ABC . X is the intersection of ray’s I and M, line XD is perpendicular to line AC , line XE is perpendicular to line AB, and line XF is perpendicular to line BC. Prove love XD equals line XE ands is also equal to XF
A. ASA
B. AAS
C. SAS
D. SSS
Line XD equals line XE and is also equal to line XF that proved by using AAS postulate of congruence ⇒ B
Step-by-step explanation:
Let us revise the cases of congruence
SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and including angle in the 2nd Δ ASA ⇒ 2 angles and the side whose joining them in the 1st Δ ≅ 2 angles and the side whose joining them in the 2nd Δ AAS ⇒ 2 angles and one side in the 1st Δ ≅ 2 angles and one side in the 2nd Δ HL ⇒ hypotenuse leg of the 1st right Δ ≅ hypotenuse leg of the 2nd right ΔIn Δ ABC
∵ Ray AL bisects ∠A ⇒ (divides it into two equal angles)
∴ m∠DAX = m∠EAX
∵ Ray BM bisects ∠B ⇒ (divides it into two equal angles)
∴ m∠EBX = m∠FBX
∵ XD ⊥ AC
∴ m∠XDA = 90°
∵ XE ⊥ AB
∴ m∠XEA = 90°
∵ XE ⊥ BC
∴ m∠XFB = 90°
Now lets prove that Δ ADX and ΔAEX are congruent
In Δs ADX and AEX
∵ m∠ADX = m∠AEX ⇒ (their measures are 90°)
∵ m∠DAX = m∠EAX ⇒ proved
∵ AX is a common side in both triangles
- By using the AAS postulate of congruence
∴ Δ ADX ≅ Δ AEX
∴ XD = XE
Let us do the same with Δ BEX and Δ BFX
In Δs BEX and BFX
∵ m∠BEX = m∠BFX ⇒ (their measures are 90°)
∵ m∠EBX = m∠FBX ⇒ proved
∵ BX is a common side in both triangles
- By using the AAS postulate of congruence
∴ Δ BEX ≅ Δ BFX
∴ XE = XF
∵ XE = XD
∵ XE = XF
- If one side is equal two other sides then the two other sides are
equal, that means the three sides are equal
∴ XD = XF
∴ XD = XE = XF
Line XD equals line XE and is also equal to line XF that proved by using AAS postulate of congruence
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Find the value of 3u-8 given that -7u + 9=2
Answer:
-5
Step-by-step explanation:
-7u+9=2
-7u=2-9
-7u=-7
7u=7
u=7/7
u=1
3(1)-8=3-8=-5
The length of a rectangle is three times the width. The perimeter of the rectangle is 32 inches. What is the area of the rectangle (in square inches)?
To find the area of this rectangle, we first solve for the width using the given perimeter, yielding 4 inches. The length, three times this, is 12 inches. Multiplying these values together gives an area of 48 square inches.
Explanation:We are dealing with a rectangle whose length is three times its width. If we call the width of the rectangle 'w', then its length is '3w'. The perimeter of a rectangle is 2 times the sum of its length and width.
So 2*(w+3w) = 32. This simplifies to 8w = 32. Solving for 'w', we find that the width of the rectangle is 4 inches. Then, the length would be three times the width, which is 12 inches.
Having determined these dimensions, we can find the area of the rectangle. The area of a rectangle is its length multiplied by its width. So in this case, it would be 4 inches (width) times 12 inches (length) to give us an area of 48 square inches.
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