Look at the figures. How can you prove these triangles are congruent?
Answers
By SAScongruence rule Triangles DFE and ACB are Congruent.
What is Congruency?
Twoangles and a non-included side of a triangle are said to be congruent when they are equivalent to the corresponding angles and sides of another triangle.
The measurements of the sides and angles of two or more triangles determine their congruence. A triangle's size is determined by its three sides, and its shape is determined by its three angles. Two triangles are said to be congruent if the pairings of their respective sides and angles are equal.
We have Two Triangles DFE and ACB.
Now, from the triangles we have
AC = DF
BC = EF
< ACB = < DFE
and, the angle which is congruent is in between two congruent sides.
So, by SAS congruence rule Triangles DFE and ACB are Congruent.
Learn more about congruence rule here:
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Answer:
You can use the Side-Angle-Side Postulate.
Step-by-step explanation:
The Side-Angle-Side (or SAS) Postulate basically states that if two sides of two triangles and the included angle are congruent, the two triangles are congruent.
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Jake and his brother, Rob, built triangular kites for the Beach Cities Kite Festival and covered them with fabric. Jake's kite is 5.5 feet long and 6 feet tall. Rob's kite is 3.5 feet long and 4 feet tall. The fabric they used costs $2.50 per square foot.How much more money did Jake spend on fabric than Rob?
Widget wonders produces widgets. they have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.....the company also discovered that it costs $103. to produce 3 widgets, $163 to produce 7 widgets, and $328 to produce 12 find the total cost of producing 2 widgets
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A.) The average rate of change is $0.50, meaning that for each minute of talk time, the monthly bill increases by $0.50.
B.) The average rate of change is $0.50, meaning that for every ten minutes of talk time, the bill increases by $0.50.
C.) The average rate of change is $0.05, meaning that for each minute of talk time, the monthly bill increases by $0.05.
D.) The average rate of change is $0.05, meaning that for every ten minutes of talk time, the bill increases by $0.05.
Answers
For this case, the first thing we must do is find the average rate of change for the mentioned interval.
By definition we have to:
Substituting values we have:
Rewriting we have:
Answer:
C.) The average rate of change is $0.05, meaning that for each minute of talk time, the monthly bill increases by $0.05.
Answers
The algebraic expression for two-fifths of the square of a number will be (2/5)x².
What is Algebra?
The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The square of the number means the number is multiplied by itself.
The algebraic expression for two-fifths of the square of a number will be
Let the number be x.
Then the square of the number will be
⇒ x²
And the two-fifth number is expressed as,
⇒ 2/5
The algebraic expression for two-fifths of the square of a number will be
⇒ (2/5)x²
Thus, the algebraic expression for two-fifths of the square of a number will be (2/5)x².
More about the Algebra link is given below.
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(2/5)x^2
Answers
Answers
Answer:
£39
Step-by-step explanation:
Let Gavyn's share = x
Since, Sarah gets £26 more than Gavyn.
Sarah's Share = x+26
Equating the Ratio of their Shares and the actual sum received
x+26 : x = 5:3
Converting to Fractions
Cross multiply
5x=3(x+26)
5x=3x+78
5x-3x=78
2x=78
Divide both sides by 2
x=39
Therefore: Gavyn's share x = £39
Answers
56
Step-by-step explanation:
to get 56 u have to flip it then mutiplie
2k(7-5k)+11=6k+3(k^2-1)
with work please.
Answers
⇒ (2k)* 7 - (2k)* (5k) +11= 6k+ 3* k^2- 3*1 (distributive property)
⇒ 14k -10k^2 +11= 6k+ 3k^2 -3
⇒ (14k -14k) +(-10k^2 +10k^2)+ (11-11) = (6k-14k)+ (3k^2+10k^2)+ (-3-11)
⇒ 13k^2- 8k- 14= 0
⇒ 13 (k^2- 8/13k- 14/13)=0
⇒ (k- ((4+3*sqrt(22))/13))* ((k- ((4-3*sqrt(22))/13))= 0
⇒ k= (4+3*sqrt(22))/13 or k= (4-3*sqrt(22))/13).
Hope this helps~
Answer:
k= (4+3*sqrt(22))/13 or k= (4-3*sqrt(22))/13).
Step-by-step explanation:
2k(7-5k)+11=6k+3(k^2-1)
We move all terms to the left:
2k(7-5k)+11-(6k+3(k^2-1))=0
We add all the numbers together, and all the variables
2k(-5k+7)-(6k+3(k^2-1))+11=0
We multiply parentheses
-10k^2+14k-(6k+3(k^2-1))+11=0
We calculate terms in parentheses: -(6k+3(k^2-1)), so:
6k+3(k^2-1)
We multiply parentheses
3k^2+6k-3
Back to the equation:
-(3k^2+6k-3)
We get rid of parentheses
-10k^2-3k^2+14k-6k+3+11=0
We add all the numbers together, and all the variables
-13k^2+8k+14=0
a = -13; b = 8; c = +14;
Δ = b2-4ac
Δ = 82-4·(-13)·14
Δ = 792
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
k1=−b−Δ√2ak2=−b+Δ√2a
The end solution:
Δ−−√=792−−−√=36∗22−−−−−−√=36−−√∗22−−√=622−−√
k1=−b−Δ√2a=−(8)−622√2∗−13=−8−622√−26
k2=−b+Δ√2a=−(8)+622√2∗−13=−8+622√−26