Given:
In triangle DEF, [tex]DE = EF[/tex] and [tex]m\angle 98^\circ[/tex].
To find:
The measure of angle EFD.
Solution:
In triangle DEF,
[tex]DE = EF[/tex] (Given)
It means triangle DEF is an isosceles triangle.
[tex]m\angle EDF=m\angle EFD[/tex] (Base angles of an isosceles triangle are equal)
Using angle sum property in triangle DEF, we get
[tex]m\angle DE F+m\angle EFD+m\angle EDF=180^\circ[/tex]
[tex]98^\circ +m\angle EFD+m\angle EFD=180^\circ[/tex]
[tex]2m\angle EFD=180^\circ-98^\circ[/tex]
[tex]2m\angle EFD=82^\circ[/tex]
Divide both sides by 2.
[tex]m\angle EFD=\dfrac{82^\circ}{2}[/tex]
[tex]m\angle EFD=41^\circ[/tex]
Therefore, the measure of angle EFD is 41 degrees.
Write the expanded form of the expression 5(2x - 4 )
[tex]5(2x-4)=10x-20[/tex]
Hope this helps.
Step-by-step explanation:
Write 5
(2
x−
4)
as an equation.y
=
5
(2x−4)
(i) 3 (a + 5b) + a (a + 4) (ii) y (10 - y) + 3 (y - 2) (iii) 2 (8a - 5b) + 3 (5a - 12) (iv) 3 (y - 3) + ( 8 - 6y + x) (v) a (a - 2b) + b (b + 2a - c) (vi) 5 (x - y + z) + (4x + 3y) plzz solve
Answer:
[tex]3 (a + 5b) + a (a + 4) = a^2 + 7a + 15b[/tex]
[tex]y (10 - y) + 3 (y - 2) = - y^2+13y - 6[/tex]
[tex]2 (8a - 5b) + 3 (5a - 12) = 31a -10b - 36[/tex]
[tex]3 (y - 3) + ( 8 - 6y + x) = -3y + x-1[/tex]
[tex]a (a - 2b) + b (b + 2a - c) =a^2 + b^2 - bc[/tex]
[tex]5 (x - y + z) + (4x + 3y) =9x - 2y +5z[/tex]
Step-by-step explanation:
Solving (i):
[tex]3 (a + 5b) + a (a + 4)[/tex]
Open brackets
[tex]3 (a + 5b) + a (a + 4) = 3a + 15b + a^2 + 4a[/tex]
Collect like terms
[tex]3 (a + 5b) + a (a + 4) = a^2 + 4a+3a + 15b[/tex]
[tex]3 (a + 5b) + a (a + 4) = a^2 + 7a + 15b[/tex]
Solving (ii)
[tex]y (10 - y) + 3 (y - 2)[/tex]
Open bracket
[tex]y (10 - y) + 3 (y - 2) = 10y - y^2 + 3y - 6[/tex]
Collect like terms
[tex]y (10 - y) + 3 (y - 2) = - y^2+10y + 3y - 6[/tex]
[tex]y (10 - y) + 3 (y - 2) = - y^2+13y - 6[/tex]
Solving (iii)
[tex]2 (8a - 5b) + 3 (5a - 12)[/tex]
Open bracket
[tex]2 (8a - 5b) + 3 (5a - 12) = 16a -10b + 15a - 36[/tex]
Collect like terms
[tex]2 (8a - 5b) + 3 (5a - 12) = 16a+ 15a -10b - 36[/tex]
[tex]2 (8a - 5b) + 3 (5a - 12) = 31a -10b - 36[/tex]
Solving (iv)
[tex]3 (y - 3) + ( 8 - 6y + x)[/tex]
Open bracket
[tex]3 (y - 3) + ( 8 - 6y + x) = 3y - 9 + 8 - 6y + x[/tex]
Collect like terms
[tex]3 (y - 3) + ( 8 - 6y + x) = 3y - 6y + x- 9 + 8[/tex]
[tex]3 (y - 3) + ( 8 - 6y + x) = -3y + x-1[/tex]
Solving (v):
[tex]a (a - 2b) + b (b + 2a - c)[/tex]
Open bracket
[tex]a (a - 2b) + b (b + 2a - c) =a^2 - 2ab + b^2 + 2ab - bc[/tex]
Collect like terms
[tex]a (a - 2b) + b (b + 2a - c) =a^2 + 2ab- 2ab + b^2 - bc[/tex]
[tex]a (a - 2b) + b (b + 2a - c) =a^2 + b^2 - bc[/tex]
Solving (vi)
[tex]5 (x - y + z) + (4x + 3y)[/tex]
Open brackets
[tex]5 (x - y + z) + (4x + 3y) =5x - 5y +5z+4x +3y[/tex]
Collect like terms
[tex]5 (x - y + z) + (4x + 3y) =5x +4x +3y- 5y +5z[/tex]
[tex]5 (x - y + z) + (4x + 3y) =9x - 2y +5z[/tex]
Ayuda es para un examen
3. A line contains the points P (1,1) and Q (7,10) what is the slop of the line
Answer:
9/6 is the slope but that simplifies to 3/2
Step-by-step explanation:
y2-y1
x2-x1
10-1=9
7-1=6
In a certain Algebra 2 class of 30 students, 8 of them play basketball and 10 of them
play baseball. There are 18 students who play neither sport. What is the probability
that a student chosen randomly from the class plays both basketball and baseball?
Please help me with the question I asked I’m doing a text please.
Answer:
Wait, what question?? I can try to do it.
can anyone help??? will give best answer brainliest!!
Answer:
5xy = 2
Step-by-step explanation:
This is the only one that has two (x & y) letters/integers on one single number.
Solve the right triangle. Round decimal answers to the nearest tenth. what is angle a and angle b
Answer:
b = 12.6
Step-by-step explanation:
a*2 + b*2 = c*2
6*2 + b*2 = 14*2
36 + b*2 = 196
Subtract 36 from both sides
36 + b*2 = 196
-36 -36
b*2 = 160
Find the square root of both
b = 12.64911064 or 12.6
Can you guys please help me I already got two wrong I can’t get anymore please!?
Answer:
B. x-5
Step-by-step explanation:
Sister's height: x
Gavin's height: 5 in. less than his sister's height.
UM, math question on area
Answer:
whats the question
Step-by-step explanation:
Answer:
multiply width and length, for rectangles, parallelograms, and rhombuses
If a triangle divide by two
if a trapezoid, take the average of the two length and multiply by height
hope this helps
comment if you need calculation for the area of other shapes!
❗️❗️❗️HELP❗️❗️❗️
Use f(x) and g(x) to answer the question.
f(x) = x +4
g(x) = x – 2
What is the product (fºg)(x)?
Answer:
Correct answer is the first one x^2 + 2x - 8
because (x + 4) (x - 2)
= x ^2 + 4x - 2x - 8
= x^2 + 2x - 8
Car A travels 20 mph faster than Car B. In the same time that Car A travels 208 mi, Car B travels 156 mi. Find their speeds. The speed of Car A is and the speed of Car B
Step-by-step explanation:
Assuming the speed of car B to be x and the speed of car A to be x+20
156 = 208
x. x+20
156(x+20)= 208x
156x+3120=208x
3120=208x-156x
3120=52x
x=60
The speed of car A is (x)= 60
The speed of car B is(x+20)= 80
Answer:
[tex]\huge\colorbox{red}{Car\: A=80}\colorbox{blue}{Car B=60}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:equationPEMDASlet's solve:let the speed of car A be A
let the speed of car B be B
according to the first condition:
[tex]\quad A=B+20[/tex]
according to the second condition:
[tex]\quad 156(A)=208B[/tex]
[tex]\text{substitute the value of A into the equation:}\\ \sf \implies 156(B+20)=208(B)[/tex][tex]\sf distribute:\\ \implies 156B+3120=208B[/tex][tex] \sf \: substract\: 156B \: from \: both \: sides : \\ \implies \: 156 B -156 B + 3120 = 208 B - 156 B \\ \implies \: 3120 = 52 B[/tex][tex] \sf divide \: both \: sides \: by \: 52 : \\ \implies \frac{52B}{52} = \frac{3210}{52} \\ \therefore \: B = 60[/tex]therefore
[tex]\text{the speed of car A is 60+20=80}[/tex]
36.Simplify: 5 – {3 – (x - 8) }
Answer:
x-10
Step-by-step explanation:
you have to do what is in the parenthesis first. Do distributive property to
-(x-8)
-(x)-(-8)= -x+8
now you have 5-(3-x+8)
Do distributive property again
5-3+x-8
x-8+2
x-10
hope this helps ~D~
Answer:
your answer will be X−6
Step-by-step explanation:
hope it helps
have a nice day/night ^_^
Get as many people to answer this question will give brainiest for free!!!!
Answer:
huh?
Step-by-step explanation:
Lula is planting her spring garden. It takes nineteen giant bags of soil to fill five flower beds. How much soil is in each flower bed?
Answer:
19/5 = 3 4/5 soils for each flower bed.
Step-by-step explanation:
Answer is 3 4/5 soils in each flower bed.
if f and g are two functions defined by f(x)=3x+5 and g(x)=x^2+1 then g(f(x)) is
the answer is A. fggggggggtggg
2% of the ducks in a pond have a fluffy tail. If 4 ducks have a fluffy tail, how many ducks are in the pond. Please answer best answer gets brainliest.
Answer:
200
Step-by-step explanation:
just look up 2% of 4 is what and you will get the same answer
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
The polygons are similar, but not necessarily drawn to scale. Find the value of x.
The value of x is given from proportion and x = 9
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the first polygon and second polygon be similar
So , the ratio of their corresponding sides will also be similar
Substituting the values in the equation , we get
( x -1 ) / 6 = 16 / 12 be equation (1)
On simplifying the equation , we get
Multiply by 6 on both sides of the equation , we get
( x - 1 ) = ( 16 x 6 ) / 12
( x - 1 ) = 16 / 2
On simplifying the equation , we get
x - 1 = 8
Adding 1 on both sides of the equation , we get
x = 9
And ,
( y + 1 ) / 21 = 32 / 24 be equation (2)
On simplifying the equation , we get
Multiply by 21 on both sides of the equation , we get
( y + 1 ) = ( 4 x 21 ) / 3
y + 1 = 4 x 7
y + 1 = 28
Subtracting 1 on both sides of the equation , we get
y = 27
Hence , the value of x is 9
To learn more about proportion click :
https://brainly.com/question/7096655
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factories the following: x^2 - 3x + 2
Answer:
(x-2)(x-1)
Step-by-step explanation:
Answer:
(x-2)(x-1)
Step-by-step explanation:
[tex]x^{2} -3x+2\\\\(x-2)(x-1)[/tex]
Helppppp what is the answerrrr????
Joanne deposits $4,300 into a one-year CD at a rate of 2.3%, compounded daily.
What is her ending balance after the year?
How much interest does she earn?
What is her annual percentage yield to the nearest hundredth of a percent?
Answer:
5k
Step-by-step explanation:
The interest accrued on the principal is $100.
Using the formula;
A = P( 1 + r/n)^nt
A - amount
P - Principal
r = rate
n = Number of times the interest is compound
t = time in years
Substituting values;
A = 4,300( 1 + 0.023/365)365 × 1
A = $4400
Interest = $4400 - $4,300 = $100
The annual percentage yield is obtained from;
APY=100 (1 + r/n )n – 1
APY=100 (1 + 0.023/365)^n - 1
APY= 100(0.023)
APY= 2.3 %
Learn more: https://brainly.com/question/14283892
How will the graph of the function f(x) = 3x translate when the function is changed to f(x) = 3(x-2)
Answer:
Step-by-step explanation:
Subtracting from the x value shifts the graph to the right that many units. In this case the graph is shifted to the right by 2 units.
Answer:
It moves to the right 2
Step-by-step explanation:
:)
3(x+2)^2+7 in standard form
Answer:-2x^2+3x-7=0
Step-by-step explanation:
A linear sequence (i.e. where the 1st difference is always the same) has 5th term 6 and 92nd term 354. What is the 57th term?
Answer:
I dont know xDDDDDDDDDD
Answer:
a₅₇ = 214
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₅ = 6 and a₉₂ = 354 , then
a₁ + 4d = 6 → (1)
a₁ + 91d = 354 → (2)
Subtract (1) from (2) term by term to eliminate a₁
0 + 87d = 348
87d = 348 ( divide both sides by 87 )
d = 4
Substitute d = 4 in (1) and solve for a₁
a₁ + 4(4) = 6
a₁ + 16 = 6 ( subtract 16 from both sides )
a₁ = - 10
Then
a₅₇ = - 10 + (56 × 4 ) = - 10 + 224 = 214
Hugo cut 15 short strips of paper then he cut 14 long strips how many strips of paper did he go cut in all
A.1 strip of paper
B.28 strip of paper
C.2 strip of paper
D.29 strips of paper
Answer:
D.) 29
Step-by-step explanation:
Add 15 and 14
A number between 1 and 20 and has exactly 4 factors
Answer:
6, 8, 10, 14, 15
Step-by-step explanation:
6(1,2,3,6)
8(1,2,4,8)
10(1,2,5,10)
14(1,2,7,14)
15(1,3,5,15)
Yesenia buys milk to make milkshakes for all her friends. She buys 1 quart of milk and
1/2 gallon of milk. How many cups of milk does she buy?
Answer:
12 CUPSExplanation:
1 quart = 4 cups
1 gallon = 16 cups
Yesenia buys 1 quart -> 4 cups
AND 1/2 a gallon -> 8 cups
4 cups from quart + 8 cups from 1/2 gallon = 12 cups total!
PLEASE NEED HELP WILL CHOOSE BRAINLIEST
Answer Choices:
2
3
-9
7
4
Answer:
9
WILL CHOOSEBRAINLIEST
Answer:
-9
Step-by-step explanation:
-9x^-(-9)=-9x^9
2.In ABC, BD is perpendicular to AC. The dimensions are shown in centimeters.
What is the length, in centimeters, of AC?
ASAP BEFORE TOMORROW 11
Answer:
AC = 12
Step-by-step explanation:
From the question, we have that BD is perpendicular to AC
This means that it is at 90 degrees to the base
so we have two similar right triangles
Let us use Pythagoras’ theorem to get the measure of one of the legs (AD and DC)
Let us call the leg x
We have the Pythagoras’ theorem stating that the square of the hypotenuse (the side facing the right angle; 10 here) is equal to the sum of the squares of the two other sides
10^2 = x^2 + 8^2
100 = x^2 + 64
x^2 = 100-64
x^2 = 36
x = √36
x = 6
AD = DC = 6
AC = 2 * AD
AC = 2 * 6
AC = 12
Does anyone know the answer