Step-by-step explanation:
subtract 21 from both sides
x2+2x+7-21=21-21
x2+2x+14=0
use quadratic equation
x=(-3+-(b^2-4ac)^1/2)/2a
in our equation a=1,b=2and c=14
(-2+-(14+56)^1/2)/2
x=-1+(60^1/2)/2
there is only one positive answer and it is 2.87
Length of DE is ___
units.
Length of DB is ___
units.
Measure of angle FED is ___
degrees.
Answer:
Length of DE = 7.5 units
Length of DB = 9.2 units
Measure of ∠FED = 82°
Step-by-step explanation:
In ΔABC,
AD ≅ BD and CE ≅ BE [Given]
By the theorem of mid-segments,
DE = [tex]\frac{1}{2}(AC)[/tex]
= [tex]\frac{1}{2}(15)[/tex]
DE = 7.5 units
Since AD ≅ FE ≅ 9.2 [By midpoint theorem in ΔACB]
Therefore, length of DB = 9.2 units
[Although it's not given in the question, but we assume FE║AB]
Since FE║AB and DE is a transverse,
Therefore, m(∠FED) ≅ m(∠BDE) ≅ 82° [Interior alternate angles]
Triangle A C D is shown. Point B is near the center of the triangle. Angle A C D is bisected by line segment C B. Lines are drawn from point B to points A and D to form 3 triangles within the larger triangle. Angle C B D is 125 degrees. The length of line segment A C is 52 centimeters and the length of line segment B D is 29 centimeters. If Line segment C B. bisects ∠ACD, what additional information could be used to prove ΔABC ≅ ΔDBC using SAS? Select three options. m∠ABC = 125° and AB ≅ DB ΔACD is isosceles with base AD ΔABD is isosceles with base AD CD = 52 cm AB = 29 cm
Answer:
it's A B D i don't know why the other person couldn't have just said that and make it look confusing
Answer:
A< B< D
Step-by-step explanation:
Can I please have help
Answer:
A (1,0), B (3,0) Q (2,-1) P(0,3)
Step-by-step explanation:
A(1,0) B (3,0) these are the roots of the current graph so the factors or the x-intercepts.
Q is the minimum so it is halfway between the x-intercepts
halfway = 3+1/2 , x=2
plug x=2 into the equation
y=(2-1)(2-3)
y= -1
therefore Q = (2,-1)
P is the y-intercpet when x=0, so plug x=0 into the equation
y=(0-1)(0-3) = 3
therefore Q =
(0,3)
Write the polynomial which represents the perimeter of a triangle whose sides are represented
by 2x² + 3x, 5x²-1, and 3x² + 7x-1.
Answer:
The polynomial is 10x^2 + 10x -2
Step-by-step explanation:
To get the polynomial which represents the perimeter, what we need to do is to add up all
these values. We use the formula for finding the perimeter of a triangle and that involves adding up all the three sides. That would be;
2x^2 + 3x + 5x^2 -1 + 3x^2 + 7x -1
10x^2 + 3x -1 + 7x -1
10x^2 + 10x -2
Henry places £6000 in an account which pays 4.6% compound interest each year. Calculate the amount in his account after 2 years.
Answer:
6564.696
Step-by-step explanation:
A=6,000×(1+0.046)^(2)
A=6,564.696
I need the answers immediately hw is due in 5 mins!!!!!!!
Which is NOT a solution of the inequality: 5 - 2x ≥ -3 ? *
0
2
4
5
Answer: 5
Step-by-step explanation:
rearrange to make x the subject a= 4x/t -p
Answer:
x = [tex]\frac{t(a+p)}{4}[/tex]
Step-by-step explanation:
Given
a = [tex]\frac{4x}{t}[/tex] - p ( isolate term in x by adding p to both sides )
a + p = [tex]\frac{4x}{t}[/tex] ( multiply both sides by t )
t(a + p) = 4x ( divide both sides by 4 )
[tex]\frac{t(a+p)}{4}[/tex] = x
Why can't you use the product of powers rule to simplify
this expression? Explain.
3^4.2^8
Answer:
You can't use this rule because the two exponents have different bases. In order to use this rule the two exponents must have the same base.
Answer:
It is because both expressions have different base value. For this question, the bases are 3 and 2 where the product rule cannot be applied. Product rule can only be used when both expressions have the same bases.
who can solve ? 9y < -3
Answer:
y< -1/3
Step-by-step explanation:
To solve the inequality, we must get the variable, y, by itself.
9y< -3
Perform the opposite of what is being done to the equation, to both sides.
y is being multiplied by 9. The opposite of multiplication is division. Therefore, divide both sides by 9.
9y/9 < -3/9
y< -3/9
-3/9 can be reduced. 3 can be divided evenly into both the numerator (top number) and denominator (bottom number).
y< (-3/3) / (9/3)
y< -1/3
Find the speed of a car on km/hr that is moving
at speed 144mls
Answer:
Speed in km/hr = 518.4 km/hr
Step-by-step explanation:
Speed = 144 m/s
To convert m/s to km/her, you just need to multiply it by 3.6
Speed in km/hr = 144 × 3.6
Speed in km/hr = 518.4 km/hr
Answer:
518.40km/h
Step-by-step explanation:
144m/s
it means that in 1 sec it does 144m
we are searching how many km it does in 1 hour
1 hour = 60*60=3600 sec
so in 3600 sec (= 1 hour) it does 144*3600 m
and 1 km = 1 000m
so in 1 hour it does 144*3600/1000 = 144*3.6 = 518.40
the speed of the car is 518.40km/hr
hope this helps
What does y=? Also if you cant read that bright red number its 60
Answer:
y = 13.9
Step-by-step explanation:
The triangle is a 30-60-90 triangle, so x is 16 (double 8). Use the pythagorean theorum to find y. 256 - 64 =192. [tex]\sqrt{192}[/tex] is about 13.9
A motorcycle has an initial speed of u m/s. It accelerates to a speed of 1.2u in 10 seconds. The motorcycle then travels at a constant speed of 1.2u m/s for 15 seconds. Assuming that the acceleration is constant, express the total distance, D in metres, traveled by the motorcycle.
Answer:
Step-by-step explanation:
A motorcycle has an initial speed of u m/s. It accelerates to a speed of 1.2u in 10 seconds
V = U + at
1.2u = u + a*10
=> a = 0.02u
S= ut + (1/2)at²
Distance in 1st 10 secs
S = u(10) + (1/2)(0.02)(10)²
=> S = 10u + u
=> S = 11u m
Constant speed 1.2u for 15 secs
S = 1.2u * 15
=> S = 18u m
Total Distance Covered d = 11u + 18u = 29u m
Juana is making a triangular hat for a puppet. If two of the three angles of the hat both measure 30 . what is the measure of the third angle?
Answer:
180 that boy is soo wrong
Step-by-step explanation:
solve 2x^2-4x-18=0 by completing the square. round the solutions to the nearest hundredth
Answer:
1-√10
1+√10
Step-by-step explanation:
2x^2-4x-18=0x^2-2x-9=0x^2-2x+1-10=0(x-1)^2-10=0(x-1+√10)(x-1-√10)=0x=1-√10x=1+√10Question 14 (1 point)
John is collecting vintage baseball cards and has about 25 he got from his dad. He is collecting
about 2 cards per month. Write a function, C(x), that represents how many cards John has
after x months.
N
Answer:
C(x) = 25 + 2x
Step-by-step explanation:
He already has 25 cards.
He is collecting 2 cards per month. In x months, he will have collected:
2 * x = 2x cards
That means that the number of cards he will have after x months will be the sum of the cards he already has and the cards he collects per month:
C(x) = 25 + 2x
PLEASE HELP WILL MARK BRAINLIEST
Find the area of the right triangle.
Answer:
Step-by-step explanation:
This right triangle is on a grid.
The area is the height * base/2
The base is on a line segment parallel to the x axis which is 6 squares.
The height is on a line segment parallel to the y axis which is 2 squares
The area is the height * base /2
Area = 6 * 2 /2 = 12/2 = 6 square units.
THIS QUESTION GOT ME STRESSIN HELPPP A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.
Answer:
14 and 10
Step-by-step explanation:
14x5=70
10x3=30
100=70+30
Jan lost 22 points on her exam. She got 11 questions wrong.
What integer represents the point value of each wrong answer?
Answer:
2
Step-by-step explanation:
22/11=2
(14)+(-11) plz help idk what it is
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
(14)+(-11)=3
How much is one gram into ounces?
Answer:
1 gram is 0.035274 in ounces
Answer:
It would be about 0.035274
Step-by-step explanation:
For an approximate result, divide the mass value by 28.35
Hope this helps
What is the value of the product (3 – 2i)(3 + 2i)?
timed test please help me
Answer:
the answer is 9-4i
Step-by-step explanation:
multiply
what we will call the complete path of the circle
Answer:
True.
Step-by-step explanation:
The circumference is the perimeter of a circle. The complete path around the circle is called the circumference.
Answer:
True
The distance around the circle makes up the circumference.
A committee consisting of 2 faculty members and 4 students is to be formed. Every committee position has the same duties and voting rights. There are 10 faculty members and 11 students eligible to serve on the committee. In how many ways can the committee be formed?
Answer:
14,850 ways
Step-by-step explanation:
Since the order does not matter, the number of possible committees is given by the product of the combination of picking 2 out of 10 faculty members and the combination of picking 4 out of 11 students:
[tex]n= \frac{10!}{(10-2)!2!}* \frac{11!}{(11-4)!4!}\\n=\frac{10*9}{2}*\frac{11*10*9*8}{4*3*2*1}\\n=14,850[/tex]
The committee can be formed in 14,850 ways
Let f(x) = 2x, g(x) = x2 + 2, and h(x) = 4x +3. Find the composite function.
(F*g)
Answer:
(f * g)(x) = 2(x²) + 4
Step-by-step explanation:
Explanation:-
let f(x) = 2 x, g(x) = x² + 2, and h(x) = 4 x +3
(f * g)(x) = f(g(x)) = f(x² + 2)
= 2(x² + 2)
= 2(x²) + 4
final answer:-
(f * g)(x) = 2(x²) + 4
Joe needs to replace the carpet in his living room and hallway with laminate flooring. A floor plan is shown below. Can you help him to find the total area of floor that needs to be covered?
*diagram of floor plan is attached below
Answer:
30m²
Step-by-step Explanation:
From the floor plan shown in the attached diagram, the hall way and the living room both takes the shape of a rectangle.
To find the total area of floor to be covered, we can use the formula of the area of a rectangle to find the area of the hall way + the area of the living room.
Area of rectangle = L*B
For the hall way, L = 3.2m, B = 1.5m
Area of hall way = 3.2*1.5 = 4.8m²
For the living room, L = 6m, B = 4.2m
Area of Living room = 6*4.2 = 25.2m²
Therefore, area of floor to be covered = 4.8m² + 25.2m² = 30m²
Answer:
30m²
Step-by-step explanation:
4 Student is 20% of ____ students
I need the answer please help me I don't want to fail my math class
Answer:
4 Student is 20% of 20 students
Step-by-step explanation:
if 4 = 20% then 1 = 5% to get a hundred percent then you need to multiply by 20
so 20
4 Student is 20% of 20 students
Answer:
4 Student is 20% of _20___ students
Step-by-step explanation:
20% of x = 4
20% = 0.20
of means multiplication so
0.2 * x = 4
x = 4 / 0.2 = 40 /2 =20
The total cost of a pair of jeans and three shirts is $114. The shirts each cost the same amount, and the jeans are $45.
What is the price per shirt?
a.) $69
b.) $23
c.) $53
d.) $159
Answer:
23
Step-by-step explanation:
j = jeans
s = shirt
j + 3s = 114
jeans = 45
45+ 3s = 114
Subtract 45 from each side
45-45+3s = 114-45
3s =69
Divide each side by 3
3s/3 =69/3
s = 23
Each shirt is 23
Answer:
b.) 23
Step-by-step explanation:
114-45=69
69/3=23
What change(s) should Sylvia make to the equation to find the value of t in the above scenario?
Answer:
Option (D).
Step-by-step explanation:
Initial population of the deer [tex]P_{0}[/tex] = 4800
Decrease in the population of the deer after every 8 years = [tex]\frac{1}{2}\times (\text{Initial population})[/tex]
Decrease in population is an exponential process, so the expression representing population will be,
[tex]P_{t}=P_{0}(1-r)^x[/tex]
Where [tex]P_{t}[/tex] is the population after 'x' slots of 8 years.
r = fraction of decrease in the population
x = [tex]\frac{\text{Number of years}}{8}[/tex]
By substituting the values of r and x in the expression,
[tex]P_{t}=P_{0}(1-\frac{1}{2})^{\frac{t}{8}}[/tex]
[tex]P_{t}=4800(\frac{1}{2})^{\frac{t}{8}}[/tex]
Therefore, Sylvia should do few corrections in her expression.
(8) should be replaced by ([tex]\frac{1}{2}[/tex]) and [tex]\frac{t}{2}[/tex] should be replaced by [tex]\frac{t}{8}[/tex].
Option D. will be the answer.
How much would $100 invested at 6% interest compounded monthly be worth after 20 years? Round to the nearest cent.
Answer:$331.02
Step-by-step explanation:
you got it right on a p e x
The ordered pair (a, b) gives the location of point P on the coordinate plane. The value of aaa is 0, but b is not zero. Where could point P be located on the coordinate plane?
Answer:
On the y-axis line
Step-by-step explanation:
Given the location (a,b) of the point P on the coordinated plane.
If a=0
Then the location of P on the x-axis is at x=0
Since b is not equal to zero, b could be positive or negative.
Therefore, the point P could be located on the positive y-axis or the negative y-axis,
It must be exactly on the line.