Answer:
A' (0, -1)
B' (0, 1)
C' (4, 1)
D' (4, -1)
Step-by-step explanation:
We have the following points of a quadrilateral ABCD:
A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2)
and the rule of the translation is given by:
(x, y) ---> (x + 2, y − 3)
which means that each point will move means 3 units to the left and 4 units upwards.
So the points after transformation will be:
A(−2, 2) ---> (-2+2, 2-3) ---> A' (0, -1)
B(−2, 4) ---> (-2+2, 4-3) ---> B' (0, 1)
C(2, 4) ---> (2+2, 4-3) ---> C' (4, 1)
D(2, 2) ---> (2+2, 2-3) ---> D' (4, -1)
If we plot these points on a graph and join the corresponding vertices with line segments, then we will see that all the the lines will be parallel to each other since they followed the same rule of transformation.
The new coordinates of the transformed vertices A', B', C', and D' are:
A' (0, -1)
B' (0, 1)
C' (4, 1)
D' (4, -1)
To find the new coordinates of the transformed vertices A', B', C', and D', you need to apply the transformation rule (x + 2, y - 3) to the original coordinates of A, B, C, and D.
A' = (x + 2, y - 3)
A' = (-2 + 2, 2 - 3)
A' = (0, -1)
B' = (x + 2, y - 3)
B' = (-2 + 2, 4 - 3)
B' = (0, 1)
C' = (x + 2, y - 3)
C' = (2 + 2, 4 - 3)
C' = (4, 1)
D' = (x + 2, y - 3)
D' = (2 + 2, 2 - 3)
D' = (4, -1)
So, the new coordinates of the transformed vertices A', B', C', and D' are:
A' (0, -1)
B' (0, 1)
C' (4, 1)
D' (4, -1)
Now, let's describe the characteristics of the quadrilateral ABCD and its image A'B'C'D' when the corresponding vertices are connected with line segments:
Quadrilateral ABCD:
A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2)
ABCD is a trapezoid with two parallel sides (AB and CD) and two non-parallel sides (BC and AD).
The trapezoid is located in the first quadrant.
Image A'B'C'D':
A'(0, -1), B'(0, 1), C'(4, 1), and D'(4, -1)
A'B'C'D' is also a trapezoid with two parallel sides (A'B' and C'D') and two non-parallel sides (B'C' and A'D').
A'B'C'D' is located in a different position due to the transformation. It has been shifted 2 units to the right and 3 units down.
The transformation (x + 2, y - 3) has effectively shifted the entire quadrilateral 2 units to the right and 3 units down in the coordinate plane. The basic shape and characteristics of the trapezoid are preserved, but its position in the plane has changed.
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What is the solution to the system of equations? Use the substitution meathod to solve. 6=-4x+y and -5x-y=21
6+4x=y or y=4x+6
Plug in to second equation: -5x-(4x+6)=21
-9x-6=21
-9x=27
x=-3
Plugging in, you get that y=-12+6 or -6.
Therefore, the solution is (-3,-6)
Find measure angle BCA
m∠BCA = 57 degrees.
The sum of the exterior angles of a triangle is 360 degrees.
So,
[tex](5x+12)+(9x+1)+(10x-37)=360\\24x-24=360\\24x=384\\x=16[/tex]
So the exterior angle corresponds to ∠BCA is = 10x - 37 = 10(16) - 37 = 123.
So the interior angle ∠BCA is = 180 - 123 = 57 degrees.
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Faye can sort 150 recyclable items in 3 minutes.How many recyclable items can Faye sort in 4 minutes?
Answer:
200
Step-by-step explanation:
150/3=50 so she sorts 50 items per minute, then 50*4=200
Answer:
Number of recyclable items sort in 4 minutes by Faye = 200
Step-by-step explanation:
Given that Faye can sort 150 recyclable items in 3 minutes.
Number of recyclable items sort in 3 minutes = 150
[tex]\texttt{ Number of recyclable items sort in 1 minute =}\frac{150}{3}=50[/tex]
Number of recyclable items sort in 4 minutes = 4 x Number of recyclable items sort in 1 minute
Number of recyclable items sort in 4 minutes = 4 x 50 = 200
Number of recyclable items sort in 4 minutes by Faye = 200
What is the simplified form of the complex fraction?
Answer:
[(x+3)(x+2)] /[(2x+3)(x-3)]
Step-by-step explanation:
[(2x²+x-6)/(x²-x-6)]/[(4x²-9)/(x²+5x+6)]
= (2x²+x-6)/(x²-x-6) × (x²+5x+6) /(4x²-9) Factor
= [(2x-3)(x+2)]/[(x-3)(x+2] × [(x+3)(x+2)] /[(2x+3)(2x-3)] Cancel terms
= (2x-3)/(x-3) × [(x+3)(x+2)] /[(2x+3)(2x-3)] Cancel terms
= [(x+3)(x+2)] /[(2x+3)(x-3)]
[tex]\dfrac{\frac{2x^2+x-6}{x^2-x-6}}{\frac{4x^2-9}{x^2+5x+6}}=(*)\\---------------------\\2x^2+x-6=2x^2+4x-3x-6=2x(x+2)-3(x+2)=(x+2)(2x-3)\\-----------\\x^2-x-6=x^2+2x-3x-6=x(x+2)-3(x+2)=(x+2)(x-3)\\-----------\\x^2+5x+6=x^2+2x+3x+6=x(x+2)+3(x+2)=(x+2)(x+3)\\-----------\\4x^2-9=(2x)^2-3^2=(2x-3)(2x+3)\\----------------------[/tex]
[tex](*)=\dfrac{(x+2)(2x-3)}{(x+2)(x-3)}\cdot\dfrac{(x+2)(x+3)}{(2x-3)(2x+3)}=(**)\\----------------------\\(x+2)-canceled\\(2x-3)-canceled\\----------------------\\(**)=\dfrac{(x+2)(x+3)}{(x-3)(2x+3)}\\\\Answer:\ \boxed{\boxed{\dfrac{(x+2)(x+3)}{(2x+3)(x-3)}}}[/tex]
A box has a volume of 128 feet. The length is twice the width and the height is the same as the width. What are the dimensions of the box?
Answer: width = 4 ft, length = 8 ft, height = 4 ft
Step-by-step explanation:
width (w): w
length (L): 2w
height (h): w
Volume (V) = w * L * h
128 = w(2w)(w)
128 = 2w³
64 = w³
∛64 = ∛w³
4 = w
width (w): w = 4
length (L): 2w = 2(4) = 8
height (h): w = 4
In the process of proving that opposite sides of a parallelogram are congruent, Ross drew a diagonal of the parallelogram and determined that the two triangles formed are congruent. He then concluded that opposite sides must be congruent, because corresponding parts of congruent triangles are congruent.
Using his markings in the diagram, which postulate allowed him to determine that the two triangles formed are congruent?
A) AAS
B) ASA
C) SAS
D) SSS
Answer:
(B) ASA
Step-by-step explanation:
we will verify each options
option-A:
we can see that there is no consecutive two angles
so, this postulates can not be true
so, this is FALSE
option-B:
We can see that
one angle and then side and another angle are equivalents
so, this is TRUE
option-C:
We can see that
one side and two angles are equivalents
so, this is FALSE
option-D:
we can see that
one side and two angles are equivalents
so, this is FALSE
Answer:
B
Step-by-step explanation:
A tourist starts to walk up a mountain path that is 31 miles long at the rate of 4 miles per hour. After walking for a while, he gets tired and decides to get a taxi. The taxi gets him to the top travelling at a constant speed of 50 mph. If the tourist reaches the destination 2 hours after he started, what distance does he have to pay the cab driver for?
Let the Distance traveled by the tourist by walking be : D miles
Given : Tourist walks at a rate of 4 Miles per Hour
[tex]\mathsf{\implies Tourist\;travels\;D\;Miles\;in : \frac{D}{4}\;Hours}[/tex]
Given : The Total Distance of Mountain Path = 31 Miles
Distance traveled by the tourist by hiring a Taxi is : (31 - D) Miles
Given : The Taxi travels at a constant speed of 50 miles per hour
[tex]\mathsf{\implies Tourist\;travels\;(31 - D)\;Miles\;in : (\frac{31 - D}{50})\;Hours}[/tex]
Given : The Tourist reaches the destination 2 Hours after he started
Time taken by Walking + Time Taken by travelling in Taxi = 2 Hours
[tex]\mathsf{\implies \frac{D}{4} + \frac{31 - D}{50} = 2}[/tex]
[tex]\mathsf{\implies \frac{D}{2} + \frac{31 - D}{25} = 4}[/tex]
[tex]\mathsf{\implies (\frac{25D + 2(31 - D)}{50}) = 4}[/tex]
[tex]\mathsf{\implies (\frac{25D + 62 - 2D}{50}) = 4}[/tex]
[tex]\mathsf{\implies ({23D + 62}) = 200}[/tex]
[tex]\mathsf{\implies 23D = 200 - 62}[/tex]
[tex]\mathsf{\implies 23D = 138}[/tex]
[tex]\mathsf{\implies D = 6}[/tex]
⇒ Distance traveled by the tourist by walking = 6 Miles
⇒ Distance traveled by the tourist by hiring a taxi = (31 - 6) = 25 Miles
⇒ The Distance for which tourist has to pay for cab driver is 25 Miles
The distance traveled by taxi = 25 miles
Further explanationLinear motion consists of 2: constant velocity motion with constant velocity and uniformly accelerated motion with constant acceleration
• At constant velocity motion:
the speed of vo = v = constant
acceleration = a = 0
Δx = vt or x = xo + vtAn equation of constant velocity motion
[tex]\large {\boxed {\bold {x = v \times \: t}}}[/tex]
x = distance = m
v = speed = m / s
t = time = seconds
x1, x2 = distance traveled
t1, t2 = travel time
1 = tourist, 2 = taxi
[tex]\rm x1=v1.t1=4t1\\\\x2=v2.t2=50.t2\\\\t1+t2=2~hours\\\\t1=2-t2[/tex]
Total distance = x1 + x2
[tex]\rm 31~miles=4t1+50t2\\\\31=4(2-t2)+50t2\\\\31=8-4t2+50t2\\\\23=46t2\\\\t2=0.5[/tex]
then:
[tex]\rm x2=v2.t2\\\\x2=50\times 0.5\\\\x2=\boxed{\bold{25~miles}}[/tex]
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The distance of the elevator
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resultant velocity
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the average velocity
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I need help on this, please hurry and thank you!
Answer:
[tex]A.\ a_n=n^2+1[/tex]
Step-by-step explanation:
[tex]Check:[/tex]
[tex]a_n=n^2+1\\\\a_1=1^2+1=1+1=2\qquad CORRECT\\\\a_2=2^2+1=4+1=5\qquad CORRECT\\\\a_3=3^2+1=9+1=10\qquad CORRECT\\\\a_4=4^2+1=16+1=17\qquad CORRECT\\\\a_5=5^2+1=25+1=26\qquad CORRECT[/tex]
Used PEMDAS:
P Parentheses first
E Exponents (ie Powers and Square Roots, etc.)
MD Multiplication and Division (left-to-right)
AS Addition and Subtraction (left-to-right)
First Power, next Addition
Answer: A.
Step-by-step explanation:
2, 5, 10, 17, 26
First, check the difference between each term:
2 → 5 = +3
5 → 10 = +5
10 → 17 = +7
17 → 26 = +9
Since the difference (d) is not the same, this is not an arithmetic sequence.
Now, check the second tier {3, 5, 7, 9}
3 → 5 = 2
5 → 7 = 2
7 → 9 = 2
The difference (d) of the second tier is the same, so it is an exponential sequence.
--> the only option that is an exponential sequence is option A.
the elves were working when the head elf came in and there was only 2 weeks left until christmas. what percentage of the month was left before christmas?
Answer:
45 %
Step-by-step explanation:
Time left until Christmas = 2 weeks
= 2 * 7 days [since 1 week = 7 days]
= 14 days
Number of days in December = 31
Percentage of the month left before Christmas = [tex]\frac{Time left until Christmas}{Number of days in December} * 100[/tex]
= [tex]\frac{14}{31} * 100[/tex]
= 0.45 * 100
= 45 %
Answer:
what the other person said.
Step-by-step explanation:
A mountain bike originally priced at $965.00 is up for sale at a discount of 11%. What is the price of the mountain bike after the discount?
Select all of the values that are solutions of x2 + 20 = 12x. x = -10 x = -2 x = 2 x = 10
Answer:
2, and 10
Step-by-step explanation:
Let's work through each one.
First, plug -10 into the equation:
-10² + 20 = 12 x -10?
-10² = 100
100 + 20 = 120
12 x -10 = -120
120 = -120? False!
But, using these same calculations, we can see that 10 is a correct answer.
Because everything's the same up to 12 x 10 = 120.
120 = 120
Same with 2 and -2
-2 does not work, but 2 does.
2² + 20 = 12 x 2?
4 + 20 = 24?
24 = 24? True!
The solution of the given quadratic equation is x = 2 and x = 10.
What is a quadratic equation?A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared.
Given a quadratic equation, x²+20 = -12x
x²-12x+20 = 0
On factorizing the equation,
x²-10x-2x+20 = 0
x(x-10)-2(x-10) = 0
(x-10)(x-2) = 0
x = 10 or x = 2
Hence, the solution of the given quadratic equation is x = 2 and x = 10.
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Rectangle ABCD has vertices A(3, 5), B(5,5), C(5, 1) and D(3, 1). Drag and drop the coordinates of each vertex when rectangle ABCD is rotated 90° counter-clockwise around the origin.
Answer:
Given the coordinates of rectangle ABCD are;
A = (3, 5)
B = (5,5)
C = (5, 1) and
D = (3, 1)
The rule of rotation 90 degree counter-clockwise around the origin is given by;
[tex](x, y) \rightarrow (-y, x)[/tex]
Now, the coordinates of each vertex when rectangle ABCD is rotated 90 degree counter-clockwise around the origin are;
[tex]A(3, 5) \rightarrow A'(-5, 3)[/tex]
[tex]B(5, 5) \rightarrow B'(-5, 5)[/tex]
[tex]C(5, 1) \rightarrow C'(-1, 5)[/tex]
[tex]D(3, 1) \rightarrow D'(-1, 3)[/tex]
The art club at a school raised $248 at a car wash. They spent $206 to set up an art show, and raised $316 at the art show by selling artwork the members had made. How much money did the club have after the show?
Answer:
Money club have after the show is $358 .
Step-by-step explanation:
As given
The art club at a school raised $248 at a car wash.
They spent $206 to set up an art show, and raised $316 at the art show by selling artwork the members had made.
Than
Money club have after the show = school raised money at a car wash + Raised money at the art show - spent money to set up an art show.
Money club have after the show = 248 + 316 - 206
Money club have after the show = 564 - 206
Money club have after the show = $358
Therefore money club have after the show is $358 .
Answer:
It is 358.
Step-by-step explanation:
The club started with $248, and then spent $206.
248−206=42
The club had $42, left after they spent for the art show.
Then, they raised another $316, at the show.
42 + 316 = 358
Answer: 358
in parallelogram ABCD diagonals AC and BD intersect at Point E, BE = 2x^2 -3x + D = x^2 + 10 what is BD
Answer
Given the statement: In parallelogram ABCD, diagonals AC and BD intersects at point E.
Given that ABCD is a parallelogram.
As, we know that in a parallelogram diagonals bisect each other.
Since AC and BD intersect at E, and we get E is the mid point of both diagonals AC and BD.
⇒ BE = DE .....[1]
Substitute the given values of [tex]BE = 2x^2 -3x[/tex] and [tex]DE = x^2+10[/tex] in [1] we have;
[tex]2x^2-3x = x^2+10[/tex]
Subtract [tex]x^2[/tex] on both sides we get;
[tex]2x^2-3x-x^2 = x^2+10-x^2[/tex]
Simplify:
[tex]x^2-3x =10[/tex]
Subtract 10 on both sides we get;
[tex]x^2-3x-10 =0[/tex]
or
[tex]x^2-5x+2x-10 =0[/tex]
[tex]x(x-5)+2(x-5)=0[/tex]
[tex](x-5)(x+2)=0[/tex]
equate these factors equal to zero we get;
(x-5) = 0 and (x+2) = 0
we have;
x = 5 and x = -2
Since, x cannot be negative.
So, x =5
[tex]BE = DE = x^2+10 = (5)^2+10 = 25+10 = 35 units[/tex]
Diagonals BD = BE + DE = 35 + 35 =70 units.
Therefore, the value of BD = 70 units.
The radius of a cylindrical construction pipe is 2ft. If the pipe is 19ft long, what is its volume?
Use the value 3.14 for π, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:
239 ft³
Step-by-step explanation:
Multiply the squared radius by π:
2*2*3.14=12.56 ft².
Multiplying the height:
12.56*19≅239 ft³.
1 liter = 4.23 cups
1 cup = 8 ounces
Convert 2 liters to ounces (round to the nearest whole ounce).
A) 8 ounces
B) 34 ounces
C) 48 ounces
D) 68 ounces
Answer:
(D)68
Step-by-step explanation:
If 1 litre =4.23 cups
and 1 cup = 8 ounces
Therefore: 1 litre = 4.23 X 8 Ounces = 33.84 Ounces
2 litres = 2 x 33.84 Ounces
=67.68 Ounces
=68 Ounces (To the nearest whole number)
The number of ounces in 2 liters will be 68 ounces. Thus, the correct option is D.
Given that:
1 liter = 4.23 cups
1 cup = 8 ounces
Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.
The number of cups in 2 liters is calculated as,
⇒ 2 x 4.23
⇒ 8.46 cups
The number of ounces in 8.46 cups is calculated as,
⇒ 8.46 x 8
⇒ 67.68 or 68 ounces
Thus, the correct option is D.
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Stacy is attending music festival the tickets for the festival cost $87.96. Staci plans to purchase $30 T-shirts from the event for close friends. She's taking $200 to the festival. What is the maximum number of T-shirts Staci can purchase
Classify the series as arithmetic or geometric then determine whether the series is convergent or divergent
Answer: Arithmetic , Divergent
Step-by-step explanation:
Given sequence is
{aₙ} = { 4 , 10/3 , 8/ 3 , 2 , . . . }
To check whether the sequence is geometric or not , we divide second term by first term to find the common ratio . Then we again divide third term by second term to get common ratio .
The common ratio we get would same , then it is geometric .
10/3 10 5
r₁ = ----------- = ------ = ------
4 12 6
8/3 8 3 4
r₂= ---------- = ---------- * ------------ = -----
10/ 3 3 10 5
Thus the common ratio are not same . So the sequence is not geometric .
Now we check for arithmetic .
We take difference of second and first term and then difference of third and second term . If it will be same then it is arithmetic . This is called common difference , d .
10 - 2
d₁ = ------ - 4 = -------
3 3
8 10 - 2
d₂ = ------ - -------- = ---------
3 3 3
Thus the common difference is same .
So the given sequence is arithmetic .
To find whether it is convergent or divergent , we need to write sum of n terms first .
Formula for finding sum of n terms of arithmetic sequence is
n
sₙ = ----- [ 2a + ( n - 1 ) d]
2
We have a = 4 , d = - 2/3 .
Plug in this formula we get
n n 2 2
sₙ = ------- [ 2 * 4 + ( n - 1 ) ( -2/3) ] = ------ [ 8 - ----- n + ------ ]
2 2 3 3
n 26 2
sₙ = ------ [ ------ - ------- n ]
2 3 3
To check whether it is convergent or divergent , we take limit sₙ approaches to infinity .
n 26 2
lim sₙ = lim { --- [ --- - ------ n ] } = - ∞
n → ∞ n→∞ 2 3 3
As the sequence diverge , thus the series is divergent .
Thus given series is arithmetic , divergent .
Second is the correct option .
Sixteen students in a drama club want to attend a play . The ticket price is $35 for each student, and the transportation and meal for everyone will cost $960. To pay for the trip the students design sweatshirt to sell for a profit $19 per sweatshirt . If each student sells the same number of sweatshirt how may sweatshirts must each students sell so that there will be enough money to pay for the entire cost of the trip
So firstly, we need to find how much the entire trip will cost. To do this, add the product of 16 and 35 (since tickets are 35 per student, and there are 16 students) with 960:
[tex](35*16)+960\\560+960\\\\\$ 1520[/tex]
The total cost of the trip is $1520. Next, we know that the sweatshirts will be making a profit of $19 per article sold so divide 1520 by 19:
[tex]1520\div 19=80[/tex]
The students need to sell 80 sweatshirts total to get enough money for the trip. Now, to know how many sweatshirts each student needs to sell individually, divide 80 by 16 (since there are 16 students):
[tex]80\div 16=5[/tex]
AnswerIn short, each student must sell 5 sweatshirts to pay for the entire trip.
Will someone please explain this to me? I'm not looking for an answer, just an explaination.The quotient of a number and 2 is the same as the difference of the number doubled and 3. What is the number?
Answer:
2
Step-by-step explanation:
let the number be n then
[tex]\frac{n}{2}[/tex] = 2n - 3 ( myltiply both sides by 2 )
n = 4n - 6 ( subtract 4n from both sides )
- 3n = - 6 ( divide both sides by - 3 )
n = 2
check
[tex]\frac{2}{2}[/tex] = 1 and (2 × 2 ) - 3 = 4 - 3 =1
can some one help me with this please and thank you
Lets hope i'm right.
Triangle formula: 1 / 2 b x h
y:
Half one of them. Lets do 4 since 5 would result in a decimal.
(4) = 2 x 5 = 10.
y (10) + 1 = 11
x:
Half one.
(2) = 1 x 3 = 3
Answers:
y = 11
x = 3
Hope this helps! Wait for another answer to make sure i'm right. ;) ~Pooch ♥
Mrs. Gustafsson's English class is taking an exam that is made up of short-response questions and essay questions. There are 22 questions that are worth 100 points in total. Each short-response question is worth 4 points, and each essay question is worth 10 points. How many short-response question are on the exam? Select one: A. 14 B. 2 C. 18 D. 2
I need help with this ASAP, 99 points
Answer:
Short-response question = 20.
Step-by-step explanation:
Let x be number of short response questions and y be the number of essay questions.
We have been given that there are 22 questions that are worth 100 points in total. Each short-response question is worth 4 points, and each essay question is worth 10 points. Using our given information we can form a system of equations as:
[tex]x+y=22...(1)[/tex]
[tex]4x+10y=100...(2)[/tex]
Now we will solve our system of equations using substitution method.
From equation 1 we will get,
[tex]y=22-x[/tex]
Upon substituting [tex]y=22-x[/tex] in equation 2 we will get,
[tex]4x+10(22-x)=100[/tex]
[tex]4x+220-10x=100[/tex]
[tex]4x-10x=100-220[/tex]
[tex]-6x=-120[/tex]
[tex]x=\frac{-120}{-6}[/tex]
[tex]x=20[/tex]
Therefore, there are 20 short-response questions on the exam.
Answer:
D. 20
Step-by-step explanation:
I got it right on prepworks
What is the inverse of the function? g(x)=-4/3x+2
The correct answer is A.
The inverse function of your problem is [tex]g^{-1}[/tex] (x) = -[tex]\frac{3}{4}[/tex] x + [tex]\frac{3}{2}[/tex] .Hope this helps,
Davinia.
The inverse of the function g(x)=-4/3x+2 is
[tex]g^{-1}(x) = -\frac{3}{4}x+\frac{3}{2}[/tex]
The given function is:
[tex]g(x) = -\frac{4}{3}x + 2[/tex]
To find the inverse of the function g(x), follow the steps below
Make x the subject of the formula
[tex]g(x) = -\frac{4}{3}x+2\\\\ -\frac{4}{3}x = g(x) - 2\\\\-4x=3g(x)-6\\\\x = -\frac{3}{4}g(x)+\frac{6}{4} \\\\x = -\frac{3}{4}g(x)+\frac{3}{2}[/tex]
Replace x by [tex]g^{-1}(x)[/tex] and replace g(x) by x
The inverse function therefore becomes:
[tex]g^{-1}(x) = -\frac{3}{4}x+\frac{3}{2}[/tex]
The inverse of the function g(x)=-4/3x+2 is [tex]g^{-1}(x) = -\frac{3}{4}x+\frac{3}{2}[/tex]
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What is the value of X?
Enter your answer in the box.
Answer:
x = 5
Step-by-step explanation:
in ΔABC , AB = BC , hence triangle is isosceles, thus
∠A = ∠C = 73° ( base angles are equal )
the sum of the 3 angles in a triangle = 180°
subtract the sum of the base angles from 180 for ∠B
∠B = 180° - (73 + 73)° = 34°
⇒ 6x + 4 = 34 ( subtract 4 from both sides )
6x = 30 ( divide both sides by 6 )
x = 5
complex roots problem
Answer:
b^2-4ac >0 the roots are real
Step-by-step explanation:
b^2-4ac >0 the roots are real
b^2-4ac = 0 there is 1 root
b^2 -4ac <0 the root are complex
Angel and robert want to hike a trail that goes from main to georgia the trail is 2050 miles long if they hike 12 miles a day for 30 days how man milea do they have left to hike?
Answer:
They have 1,690 miles left.
Step-by-step explanation:
12 x 30 = 360 miles
2050 - 360 = 1690 miles
Last one lol Thanks Bro...
The only solution of the equation x2 + bx + 16 = 0 is x = 4. What is the value of b?
b = –16
b = –8
b = 8
b = 16
[tex]\heartsuit[/tex] If x = 4 is the Only Solution of the Equation x² + bx + 16 = 0
[tex]\heartsuit[/tex] Then the Value x = 4 should satisfy the Given Equation
⇒ (4)² + b(4) + 16 = 0
⇒ 16 + 4b + 16 = 0
⇒ 4b + 32 = 0
⇒ 4b = -32
⇒ b = -8
16. A company spends $100 per day on fixed expenses such as electricity, rent, and the like. It also spends $35 per day on each employee working that day. Find a linear equation relating the total daily cost, C, with the number of employees working on any particular day, x.
Answer:
C = $100+$35x
Step-by-step explanation:
Given :
A company spends $100 per day on fixed expenses such as electricity, rent, and the like.
It also spends $35 per day on each employee working that day.
To Find : a linear equation relating the total daily cost, C, with the number of employees working on any particular day, x.
Solution :
A company spend $100 per day on fixed expenses
No. of employees working on a particular day = x
Company spend on each employee per day = $35
It spends on x employee = $35x
Since total daily cost = C
Thus C = $100+$35x
Hence , a linear equation relating the total daily cost, C, with the number of employees working on any particular day, x. : C = $100+$35x
Angle dfg and angle fkl are complementary angles, m angle dfg= x+4, and m anlge jkl = x+10 . Find the measure of each angle
Answer:
42° and 48°
Step-by-step explanation:
Complementary angles sum to 90°, hence
x + 10 + x + 4 = 90
2x + 14 = 90 ( subtract 14 from both sides )
2x = 76 ( divide both sides by 2 )
x = 38
x + 10 = 38 + 10 = 48° and x + 4 = 38 + 4 = 42°
what is 4/7*3/4??? NEED HELP
Answer
3/7 - three sevenths
Step-by-step explanation:
Multiply both numerators and both denominators
4*3=12 and 7*4=28
first one is your numerator
second one is your denominator
12/28
Then simplify
12/4=3 and 28/4=7
3/7