Answer:
y = 2x - 7
Step-by-step explanation:
(1,-5) (2,-3)
y2 - y1 / x2 - x1 -3 - (-5) / 2 - 1 2/1 = 2
y = 2x + b
-3 = 2(2) + b
-3 = 4 + b
-7 = b
Use a half-angle identity to find the exact value of Sin/8
a.
√2 + √2
√2+ √2
2
b. V2-E
d. √2-√2
2
Please select the best answer from the choices provided
Answer:
To solve this problem, we need to use the following two facts:
1) If a quadratic equation has integer coefficients only, and if one of the roots is a + √b (where a and b are integers), then a - √b is also a root of the equation.
2) If r and s are roots of a quadratic equation, then the equation is of the form x^2 – (r +s)x + rs = 0.
Since we know that 1 - √2 is a root of the quadratic equation, we can let:
r = 1 + √2
and
s = 1 - √2
Thus, r + s = (1 + √2) + (1 - √2) = 2 and rs = (1 + √2)(1 - √2) = 1 – 2 = -1.
Therefore, the quadratic equation must be x^2 – 2x – 1 = 0.
Answer: D
Step-by-step explanation:
What is the equation, In factored form, of the quadratic function shown in the graph?
Given:
The graph of a quadratic function.
To find:
The equation of the quadratic function in factored form.
Solution:
From the given graph it is clear that the graph of the function intersect the x-axis at point (-3,0) and (2,0).
Since -3 and 2 are the zeros of the function, therefore (x+3) and (x-2) are the factors of the required quadratic function.
Now, the function can be written as:
[tex]f(x)=a(x+3)(x-2)[/tex] ...(i)
The graph of the function intersect the y-axis at (0,-6). Substituting [tex]x=0,f(x)=-6[/tex] in (i), we get
[tex]-6=a(0+3)(0-2)[/tex]
[tex]-6=a(3)(-2)[/tex]
[tex]-6=-6a[/tex]
[tex]\dfrac{-6}{-6}=a[/tex]
[tex]1=a[/tex]
Substituting [tex]a=1[/tex] in (i), we get
[tex]f(x)=1(x+3)(x-2)[/tex]
Therefore, the required function is [tex]f(x)=1(x+3)(x-2)[/tex].
Which of the following statements must be true about a rhombus?
The consecutive sides of a rhombus are parallel.
The diagonals of a rhombus are perpendicular.
The diagonals of a rhombus are congruent.
The opposite angles of a rhombus are supplementary.
Answer:
Step-by-step explanation:
The diagonals of a rhombus are perpendicular
Answer: Choice B) The diagonals of a rhombus are perpendicular
=============================================================
Explanation:
Let's go through the answer choices to see which are true statements, and which are false.
A) This is false because consecutive sides must meet up at a vertex point, or else they won't be next to each other. Consecutive sides can never be parallel (regardless what type of quadrilateral we're dealing with, or any polygon for that matter). In other words, consecutive sides share a common point on both segments, which is why they're not parallel. Instead, it should be phrased as "opposite sides of a rhombus are parallel" which is a true statement. B) This is true. If the diagonals are perpendicular, then we could have either a kite or a rhombus. C) This is false. If the diagonals are congruent, then we have a rectangle. We could have a square (which is both a rhombus and a rectangle at the same time), but that's only for specific cases. In a more general sense, we could have a non-square rectangle that isn't a rhombus. D) This is false. A rhombus is a type of parallelogram. For any parallelogram, the opposite angles are always the same measure. The only time the angles are supplementary is when we have a rectangle; otherwise, the angles won't add to 180.There are 18 girls in a class and the ratio of the number of girls and boys in the class is 3:2. Find the number of boys.
Answer:
12
Step-by-step explanation:
Multiply to get the number of girls they've given you.
3 x 6 = 18 girls.
2 x 6 = 12 boys.
Answer:
Number of boys = 12
Step-by-step explanation:
Let the total number of children in the class be x
Number of girls = 18
Number of boys = x - 18
Ratio of girls and boys = 3 : 2
Sum of the ratio = 5
Find the value of x
[tex]\frac{3}{5 } \times x = 18\\\\3 \times x = 18 \times 5\\\\x = \frac{90}{3} = 30[/tex]
Therefore, total number of children in the class = 30
Hence number of boys = x - 18 = 30 - 18 = 12
Which equation will solve the following word problem? There are 36 tables and 7 booths in the family restaurant. Each table seats 4 people. If the restaurant can seat up to 184 people, what is the capacity of each booth?
(B * 7 ) - (36 * 4) = 184
7B + (36 * 4) = 184
184 - (36 * 4) = B/7
184/4 = B * 7
Answer:
7B + (36 * 4) = 184
Step-by-step explanation:
In a family restaurant there are 36 tables and 7 booths.
Each table can seat 4 people.
Let the number of people who can be seated in a booth be represented by B.
Total seating capacity of the restaurant is 184 people.
Expressing this as an equation:
Among the given options, this relation is expressed in the second option, namely, 7B + (36 * 4) = 184
If a car is moving on a straight line with a velocity of 40 m/s and it changes its velocity to 60 m/s in 4 seconds, calculate its acceleration.
Answer:
5m/s²
Step-by-step explanation:
Given :-
Initial Velocity = 40m/s Final velocity = 60 m/sTime = 4sTo Find :-
The acceleration .Solution :-
We know that the rate of change of velocity is called acceleration. Therefore ,
[tex]\sf\implies a = v - u / t \\ [/tex]
[tex]\sf\implies a = 60m/s - 40m/s/ 4 \\ [/tex]
[tex]\sf\implies a = 20m/s \div 4 \\[/tex]
[tex]\bf\implies a = 5m/s^2[/tex]
Which of the following inequalities matches the graph?
Answer:
the answer is C, comment if you need explanation
Step-by-step explanation:
What is the solution to |x + 2| < 1?
Answer:
-3 <x <-1
Step-by-step explanation:
|x + 2| < 1
There are two solutions, one positive and one negative ( remember to flip the inequality for the negative)
x+2 <1 and x+2 > -1
Subtract 2 from each side
x+2-2 < 1-2 and x+2-2 > -1-2
x < -1 and x >-3
-3 <x <-1
What is the slope of a line that runs parallel to y= x + 14
Answer:
m=1
Step-by-step explanation:
y= x + 14
This equation is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope for the line is 1
Parallel lines have the same slope
m=1
Find the value of x line 1 and m are parallel
Helppp
Answer:
The angle ACB = 50 degree.
Step-by-step explanation:
Given that angle E = 40 degree
Angle D = 90 degree
Triangle ABC is congruent to triangle DEC.
Now Angle ACB = Angle ECD = 90 -40 = 50 degree
So, angle ACB = 50 degree.
(a+1)(b+2)
please help me!!!
Answer:
(a + 1) (b + 2 ) = 2a + b + ab + 2
Step-by-step explanation:
[tex](a +1 )(b + 2) \\\\= a( b+ 2) + 1 (b +2) \\\\= ab + 2a + b + 2\\\\=2a + b + ab + 2[/tex]
[tex](a + 1)(b + 2) \\ = a(b + 2) + 1(b + 2) \\ = ab + 2a + b + 2[/tex]
Answer ↦ [tex]\boxed{\tt{ab + 2a + b + 2}}[/tex]
Method Used:↦ Distributive Property.
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
Work out the area of the shaded shape.
Hi there!
[tex]\large\boxed{77m^2}}[/tex]
We can divide the figure into 3 rectangles.
Area of top rectangle:
5 × 5 = 25m²
Long rectangle:
14 × 3 = 42m²
Bottom rectangle:
2 × 5 = 10m²
Add up the areas:
10 + 42 + 25 = 77m²
Find the coefficient of x^4 in the expansion of (x−9)^8
Please I need help!!
Answer:
459270
is the coefficientAccording to the general equation for conditional probability, if P(A n B) = 3/4 and P(B) = 4/5 what is P ( A|B)?
A. 35/36
B. 15/16
C. 8/9
D. 24/25
Given:
[tex]P(A\cap B)=\dfrac{3}{4}[/tex]
[tex]P(B)=\dfrac{4}{5}[/tex]
To find:
The [tex]P(A|B)[/tex].
Solution:
Conditional probability:
[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)}[/tex]
Substituting the given values, we get
[tex]P(A|B)=\dfrac{\dfrac{3}{4}}{\dfrac{4}{5}}[/tex]
[tex]P(A|B)=\dfrac{3}{4}\times \dfrac{5}{4}[/tex]
[tex]P(A|B)=\dfrac{16}{16}[/tex]
Therefore, the correct option is B.
2. (04.02 MC)
The polygons below are similar. Find the value of y. (5 points)
B
8
C
6
در این
مساب
F 6
G
10
A
Z
E 12
H
0 4.5
07.5
12
16
Answer:
polygens
Step-by-step explanation:
A plane gets an average of 25 miles per gallon when it is traveling 500 miles per hour. The plane has 15,000 gallons of gas at the beginning of a trip and travels at an average speed of 500 miles per hour. Which of the following functions f models the number of gallons of gas remaining in the tank t hours after the trip begins?
(A) f = 15000 + (25t/500)
(B) f = 15000 - (25t/500)
(C) f = 15000 - (500t/25)
(D) f = 15000 - 25t
(E) f = 25t
Answer:
D; f = 15,000 - 25t
Step-by-step explanation:
From the question;
per gallon, the number of miles traveled is 25, given traveling speed is 500 miles per hour
So after t hours, if traveling at 500 miles per hour, the amount of fuel expended will be 25 * t = 25t gallons
So, to get the amount remaining, we subtract 25t from what we have at the start of the trip
Mathematically, we have this as;
f = 15,000 - 25t
need help please thanks
Answer:
C
Step-by-step explanation:
All angles in a triangle add up to 180°.
63 + 52 = 115°.
180 - 115 = 65°, so part of the answer is done, y = 65°.
The angle next to y is a vertical angle.
61 + 65 = 126°.
180 - 126 = 54°.
So, x = 54°, y = 65°.
Find the area of this parallelogram.
13 cm
15cm
h
20cm
Answer:
260 square centimeters
Step-by-step explanation:
The formula for the area of a parallelogram is:
b x h
Where the base (b) is multiplied by the height (h) perpendicular to it.
The base here is 20 cm
The height perpendicular to the base is 13 cm
20 x 13 = 260
Or you can decompose and rearrange it into a rectangle. You will get 20 cm as the length and 13 cm as the width. The answer will be just the same!
Hope this helps!
Answer: 260 cm²
Step-by-step explanation: A parallelogram is a
quadrilateral with two pairs of parallel sides.
The formula for the area of a parallelogram is A = bh.
Since the base of the parallelogram is 20 cm and the height
of the parallelogram is 13 cm, we can plug this information into the formula
to get (20 cm)(13 cm) which gives us 260 cm².
So the area of the parallelogram shown is 260 cm².
Simplify:
a.5³×5‐²×5⁴.
b.a⁴×a‐²×x³.
c.(x⁵)²×(y⁵)³
__________
(x³)³×(y²)²
Answer:
a. 125 * 0.04 * 625 = 5 * 625 = 3125
b. a^2 * x^3
c. x^10 * x^ y^15
Last one: x^9 * y^4
Step-by-step explanation:
Because yes.
I am trying to figure this question:
1 + tan^2A = Sec^2A
Answer:
see explanation
Step-by-step explanation:
Using the Pythagorean identity
cos²A + sin²A = 1 ( divide terms by cos²A )
[tex]\frac{cos^2A}{cos^2A}[/tex] + [tex]\frac{sin^2A}{cos^2A}[/tex] = [tex]\frac{1}{cos^2A}[/tex] , that is
1 + tan²A = sec²A ← as required
find the value of the given equation (-155)+(-20) + (-14) + (-133) + (190) + (170) +(-73)
Answer:
-37
Step-by-step explanation:
-155-20-14-133-73=-395
190+170=360
-395+360=-37
What is the answer to this question?
Answer:
yeah,I think it's 16 ...
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Which relation is a function?
Answer:
the function is the solution is done using the operation
Question 12 (5 points)
Determine the value of x
0.28 units
0.98 units
3.58 units
1.12 units
Answer:
1.12 Units
Step-by-step explanation:
1. Use cos(56°) = x/2
Make sure your calculator mode is in deg (degree) not rad(radians)
2. 2(cos(56°)) = x
3. x = 1.118385807
4. Round up to get 1.12 Units
What is the equation of the line graphed below?
5
-5
5
(1, -3)
-5
O A. y = 3x
B. y=-3x
c. y=-5
D. y =
-X
Answer: y = -3x this is the answer.
ILL GIVE BRAINLIEST PLZ ANSWER
Answer:
-6
Step-by-step explanation:
y = -6x - 5
The equation is put in slope intercept form
( y = mx + b )
Where m = slope and b = y intercept
-6 is in the spot of "m"
Meaning that the slope would be -6
Answer:
slope is -6
Step-by-step explanation:
y = mx+b
m is slope :)
b is the point, where the line intersects the y axis
Determine the measure of <0
20.21°
0.005
73.74°
16.26°
Answer:
16.26°
Step-by-step explanation:
1. tanΘ= 7/24
2.[tex]tan^-1(\frac{7}{24} ) =[/tex]Θ
3. Θ = 16.26°
step by step how to solve ? 16x^2-10.3x+10=
Answer:
it is not possible result is not given so it is not possible
Solve for x. Round to the nearest tenth of a degree, if necessary
Answer:
29°
Step-by-step explanation:
cos x = 84/98
x = cos-1(84/98)
x = 28.9