Answer:
x = 5±√31
Step-by-step explanation:
Step 1: Complete the Square
x² - 10x + 25 = 6 + 25
(x - 5)² = 31
Step 2: Solve for x
√(x - 5)² = √31
x - 5 = ±√31
x = 5±√31
And we have our answers!
Answer:
its A on edge
Step-by-step explanation:
Which functions graph is a translation of the graph of f(x)= 3x^2 + 4 seven units down?
A. F(x)= -4x^2 +4
B. F(x)= 10x^2+4
C. F(x)= 3x^2-3
D. F(x)= 3x^2 +11
Answer:
Option C
Step-by-step explanation:
Consider the function f ( x ) = 3x^2 + 4;
[tex]f ( x ) = 3x^2 + 4,\\\\4 = vertex ( y - intercept ),\\\\\\[/tex]
Now if this graph were to be translated 7 units down, considering the function was f ( x ) = 3x^2, the new graph would be f ( x ) = 3x^2 - 7. The same concept is applied to the graph f ( x ) = 3x^2 + 4;
[tex]4 - 7 = - 3,\\f ( x ) = 3x^2 - 3\\\\Solution - Option C[/tex]
* Note that a translation doesn't effect the rate with which the graph changes, it only effect's it's position on the coordinate plane
Hope that helps!
Q4. An 8-sided fair die is rolled twice and the product of the two numbers obtained when the die is rolled two times is calculated.
(a) Draw the possibility diagram of the product of the two numbers appearing on the die in each throw
(b) Use the possibility diagram to calculate the probability that the product of the two numbers is
I) A prime number
ii) Not a perfect square iii)
A multiple of 5 iv)
Less than or equal to 21
v) Divisible by 4 or 6
Answer:
B)
1.) 7/64 (2.) 27/32 (3.)15/64 (4.)5/8 (5.)21/32
Step-by-step explanation:
Given the following :
Two 8 - sided fair die (1, 2, 3, 4, 5, 6, 7, 8)
Total sample space = 8^2 = 64
B1)
Probability = (number of required outcome / number of total possible outcomes)
probability of getting a prime number:
number of prime numbers in possibility diagram = 7
1) P(getting a prime number) = 7/64
11) P(not a perfect square)
Not a perfect square values in the diagram = 54
= 54 / 64 = 27 / 32
111) a multiple of 5:
Multiple of 5 in the diagram = 15
= 15 / 64
IV) Less than or equal to 21:
= 40/64 = 5/8
V) divisible by 4 or 6:
Numbers divisible by four or 6 = 42
= 42 / 64 = 21 / 32
Find the 75th term of the arithmetic sequence -21, -10,1, ...
Answer:
a(75) = 793
Step-by-step explanation:
Arithmetic Explicit Formula: an = a1 + (n-1)d
Step 1: Find equation
d = (1-(-10)) = 11
a1 = -21
an = -21 + 11(n-1)
Step 2: Plug in 75 as n
a(75) = -21 + 11(75-1)
a(75) = 793
And we have our final answer!
What is the sign of the product (–5)(–3)(–8)(–6)? Positive, because the products (–5)(–3) and (–8)(–6) are negative, and the product of two negative numbers is positive Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive Negative, because the products (–5)(–3) and (–8)(–6) are negative, and the product of two negative numbers is negative Negative, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is negative
Answer:
Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive
Step-by-step explanation:
There are an even number of negative factors, so the product is positive:
Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive
A flower shop normally orders 18 3/5 pounds of roses each week. The shop is planning on ordering four times as much during the week of Valentine's Day. For how many pounds of roses should the order be?
Answer:
74 2/5 pounds
Step-by-step explanation:
They usually order 18 3/5 pounds of roses.
They want to order 4 times this amount:
4 * 18 3/5
= 4 * 93/5
= 74 2/5 pounds
They should order for 74 2/5 pounds
Write a quadratic function that has an axis of symmetry of x=7
Answer:
If a function has an axis of symmetry x = a,
Step-by-step explanation:
then f (x) = f (- x + 2a). The following graph is symmetric with respect to the origin. In other words, it can be rotated 180o around the origin without altering the graph. Note that if (x, y) is a point on the graph, then (- x, - y) is also a point on the graph.The graph of a quadratic function is a parabola. The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.
What is the slope of the line in the graph? On a coordinate plane, a line goes through points (negative 2, negative 1) and (0, 1). slope =
Answer:
1
Step-by-step explanation:
The slope is given by
m = (y2-y1)/(x2-x1)
= (1 - -1)/(0- -2)
= (1+1)/(0+2)
2/2
=1
Answer:
1
Step-by-step explanation:
by using rise over run
Simplify 11(2x + 3).Simplify 8(3 - 2x)
Answer:
1. 22x+33
2.24-16x
Step-by-step explanation:
Use the distributive property to multiply the variables
(2x times 11)plus (three times 11)
(8 times 3)plus(eight times -2x)
IS ANYONE HERE GOOD AT CALCULUS?? IF SO, PLEASEEEE HELP ME!!!! An object’s velocity at time t is given by v(t) = –2 sin t. Let s(t) represent the object’s position at time t. If s(0) = 0, then s(t) = A) 2 cos t. B) –2 cos t. C) 2 cos t – 2. D) –2 cos t + 2.
Answer: C
Step-by-step explanation:
Since we are given velocity, which is the first derivative, we have to fidn the antiderivative of velocity to get position.
∫-2sint dt
s(t)=2cos(t)+C
Since we are given s(0)=0, we can plug in the values to find C, constant.
0=2cos(0)+C
0=2(1)+C
0=2+C
C=-2
Now that we know our constant, we can find out position.
s(t)=2cos(t)-2
Answer:
Sorry this is not an answer but it wouldn't let me comment go you friend me or something so we can work on calculus together
Step-by-step explanation:
What is the nth term rule of the quadratic sequence below -4,1,12,29,52,81,116
Step-by-step explanation:
29-12 is a 17 difference
52-29 is a 23 difference (adding 6 to the number 17)
81-52 is a 29 difference (adding 6 to the number 23)
116-81 is a 35 difference (adding 6 to the number 29)
Answer:
29-12 is a 17 difference
52-29 is a 23 difference (adding 6 to the number 17)
81-52 is a 29 difference (adding 6 to the number 23)
116-81 is a 35 difference (adding 6 to the number 29)
Step-by-step explanation:
Evaluate the expression \dfrac{7^2}{x^2-2} x 2 −2 7 2 start fraction, 7, squared, divided by, x, squared, minus, 2, end fraction for x=3x=3x, equals, 3
Answer:
7
Step-by-step explanation:
We want to evaluate the fraction below for x = 3. We will put the value of x to be 3:
[tex]\dfrac{7^2}{x^2-2}\\\\= \dfrac{7^2}{3^2-2}\\\\= \dfrac{49}{9-2}\\\\= \dfrac{49}{7} = 7[/tex]
The answer is 7.
Answer:
7Step-by-step explanation:
goodluck khan academy users
Factorize x^3-10x^2-53x-42
Answer:
(x+1)(x-14)(x+3)
Step-by-step explanation:
The first step in factorising polynomials is to find the smallest factor first. The way to do this is with trial and error. Lets see if x+1 is a factor.
According to the factor theorem, (x-a) is a factor of P(x) if and only when P(a) = 0
In this case we will use f(x) = ((x)^3)-((10x)^2)-53x-42
f(-1) = 0
Therefore (x+1) is a factor of the polynomial.
Now we divide the polynomial with (x+1) via long division to get (x^2)-11x-42.
We now factorise (x^2)-11x-42 using whatever method you would like. I'm going to use the AC method, where we find a number that multiplies to AC and adds to B, In this case AC = -42, and B = -11.
Therefore (x^2)-11x-42 factosied is (x-14)(x+3)
Now merge (x+1) with (x-14)(x+3)
The final answer is (x+1)(x-14)(x+3)
If this has helped, please consider making this the Brainliest answer!
Answer:
(x+1)(x+3)(x-14)
Step-by-step explanation:
=> x³-10x²-53x-42
We'll break 10x² and -53x into parts
=> x³+x²-11x²-11x-42x-42
Taking common
=> x²(x+1)-11x(x+1)-42(x+1)
Taking x+1 as common will make it
=> (x+1)(x²-11x-42)
Using mid term break formula
=> (x+1)(x²-14x+3x-42)
=> (x+1)[x(x-14)+3(x-14)]
Taking (x-14) as common
=> (x+1)(x+3)(x-14)
This is the required factorized form.
Hope it helps :)
On the right triangle shown below, calculate the height of the traffic
light. Round your answer to the nearest whole number. Enter the
value without units.
Answer:
x = 14
Step-by-step explanation:
Tan 25 = [tex]\frac{opposite}{adjacent}[/tex]
Where opposite = x, Adjacent = 30 m
=> 0.466 x 30 = x
=> x = 14
Answer:
[tex]\Huge \boxed{\mathrm{14 \ meters}}[/tex]
Step-by-step explanation:
We can use trigonometric functions to solve for the problem.
[tex]\displaystyle \sf tan( \theta )=\frac{opposite \ side}{adjacent \ side}[/tex]
Plug in the values and evaluate.
[tex]\displaystyle \sf tan( 25\° )=\frac{x}{30}[/tex]
Multiply both sides by 30.
[tex]\displaystyle \sf 30 \cdot tan( 25\° )=x[/tex]
[tex]\sf x=13.98922974...[/tex]
The height of the traffic light is 14 meters (rounded to nearest whole number).
Z^5=-7776i
Find the solution of the following equation whose argument is strictly between 270 and 360 degrees
Answer:
Z=+6
Step-by-step explanation:
Z^5=-7776i
Let's note that i I mathematics means negative one i.e
i = -1
So the equation is equal to
Z^5=-*-(7776)
Z^5 = 7776
Z= 5√7776
Since it's a divisible by 6
It's giving us a clue that 6 it's the answer.
Ok let's check the 5th root of 7776 in our calculator.
Z=+6
+6 is the solution to the equation
Z^5=-7776i
Write the equation of the function y=6/x translated 5 units to the left and 4 units up
Answer:
f(x)= (6/x+5)+4
Step-by-step explanation:
y/x translated 5 units
y/x+5 then 4 units up y/(x+5) +4
how big is New York city
Answer:Land area: 302.6 mi²
Population: 8.399 million
Step-by-step explanation:
New York City can be described as very big and it has actually been ranked as the 24th biggest city in the United States in terms of land area it ...
Answer:
Land area: 783.8 km²
Population: 8.399 million
Step-by-step explanation:
Ashley and Beth drove from city A to city B in exactly 5 hours, not taking rest stops. Ashley drove up to the area located halfway between the two cities at the average speed of 40 miles per hour and then Beth drove the other half at an average speed of 60 miles per hour. How many hours did Beth drive on their trip?
Answer:
2 hours
Step-by-step explanation:
Time= 5 hrs
Ashley's speed= 40 mph
Beth's speed= 60 mph
Beth's time in travel= x
Since they drove the same distance, we have this equation:
60x=40(5-x)60x=200-40x100x=200x=200/100x=2 hoursCan anyone help me i am really confused
Answer:
125 cm³
Step-by-step explanation:
The volume (V) of a cube = s³ ( s is the length of the sides )
Since the shape is a cube then all sides are congruent, thus
V = 5³ = 5 × 5 × 5 = 25 × 5 = 125 cm³
Answer:
v=l×w×h 5×5×5=125cubedcm
Step-by-step explanation:
you see a cube has an equal length, width and height
A line which intersects one of two parallel lines intersects the other also.
A. Always
B. Sometimes
C. Never
(I put always, but that turned out to be incorrect)
Answer:
Sometimes
Step-by-step explanation:
When a line intersects one of two parallel lines, it will sometimes intersect the other also.
Ex. If one of the parallel lines was at y=2, the intersecting line could be y=2.
The correct answer is- B. sometimes
A line which intersects one line need not necessarily intersect other line also , also the two parallel lines never intersect.
What is transversal?
A transversal is a line that passes through two lines in the same plane at two distinct points. Its a line that crosses other lines.
here, in the question its not mentioned about transversal so its not necessary that line which intersects one parallel line also intersect other. Hence, its sometimes either or situation that depends upon the probability of the situation that a line will intersect or not.
hence, the correct answer is- B. Sometimes.
learn more about "transversal" here
https://brainly.com/question/24756209
#SPJ2
What shape best describes the cross section cut at an angle to the base of a right rectangular prism? Trapezoid Parallelogram Square Rectangle
Answer:
Rectangle.
Step-by-step explanation:
The 2 dimensional section would be a rectangle.
Answer:
rectangle
Step-by-step explanation:
Find the equation of a line that passes through the point (3,2) and has a gradient of - 1/3
Leave your answer in the form y=mx + c
Answer:
y = -1/3x +3
Step-by-step explanation:
When given a point and slope, it is convenient to start with a point-slope form of the equation of a line.
y = m(x -h) +k . . . . . line with slope m through point (h, k)
y = (-1/3)(x -3) +2 . . . line with slope -1/3 through point (3, 2)
y = -1/3x +3 . . . . . . . simplified to slope-intercept form
can someone help me please? thanks!
Answer:
V = 11/21
Step-by-step explanation:
Formula: V = 4/3πr³
Simply plug in r to find volume
V = 4/3π(1/2)³
V = 0.52381
And we have our answer!
Two points A (-2, 9) and B (4, 8) lie on a line l. (i) Find the slope of the line l. (ii) Find the coordinates of the midpoint of the points A and B (iii) Find the distance between points A and B.
Answer:
The slope of the line is: [tex]\frac{-1}{6}[/tex]
The midpoint is located in (1, 8.5)
The distance between the points is 2.236
Step-by-step explanation:
The slope of the line can be calculated by:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8-9}{4+2} = \frac{-1}{6}[/tex]
The midpoint can be calculated by:
[tex]midpoint = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})\\midpoint = (\frac{-2 + 4}{2}, \frac{9 + 8}{2})\\midpoint = (1, 8.5)[/tex]
The distance between two points is:
[tex]distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\distance = \sqrt{(-4+2)^2 + (8 - 9)^2}\\distance = \sqrt{(-2)^2 + (-1)^2}\\distance = \sqrt{4 + 1} = \sqrt{5} = 2.236[/tex]
if z (3,-1) is the midpoint of line segment of coordinate x (5,2) and y (a,b) then find the value of a and b. I need it fast if u tell fast I'll mark ur Brainliest. It's a deal
Answer:
the coordinates of y are (1,-4)
Step-by-step explanation:
by using midpoint formula
z(x,y)=([tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex])
putting the values of coordinates
(3,-1)=[tex]\frac{5+a}{2}[/tex],[tex]\frac{2+b}{2}[/tex]
separating the coordinates
3=[tex]\frac{5+a}{2}[/tex] and -1=[tex]\frac{2+b}{2}[/tex]
3×2=5+a and -1×2=2+b
6=5+a and -2=2+b
6-5=a and -2-2=b
1=a and -4=b
so the actual coordinates of y are (1,-4)
i hope it will help you
AC answers are
18.7
15.5
14.3
13.1
[tex]AB=8.391[/tex]
[tex]AC=13.05407[/tex]
Answer:
AB =8.4
AC = 13.1
Step-by-step explanation:
Use SOH CAH TOA, which means Sin= Opposite/Hypotenuse, Cosine= Adjacent/Hypotenuse, and Tangent= Opposite/Hypotenuse.
AB is the opposite compared to the angle, BC is the adjacent compared to the angle, and AC is the hypotenuse.
Write down what you know in the formulas:
theta = 40 degrees
BC = adjacent = 10
Plug them in to solve what you need:
AB is opposite, so use the tangent equation:
tangent (40 degrees) = AB / 10
AB =8.4
AC is the hypotenuse, so use the cosine equation:
cosine (40 degrees) = 10 / AC
AC = 13.1
What is the value of the power a if 5^a = 1/125
Answer:
a = -3
Step-by-step explanation:
5^a = 1/125
The fraction 1/125 can be written as a power with base 5.
5^a = 5^(-3)
Cancel the same bases on both sides.
a = -3
Answer:
a = -3.
Step-by-step explanation:
5^a = 1/125
1/125 = 1 / 5^3
= 5^-3
5^a = 5^-3
so a = -3.
When planning road development, the road commission
estimates the future population using the function
represented in the table, where x is the time in years and
f(x) is the total population.
What is the significance of 160,000 in the function?
the maximum population of the city
the expected population in 5 years
the initial population at the time of the estimation
the amount of increase in the population in years
Answer:
C
Step-by-step explanation:
Got 100% on edge.
Solve the equation 4x2 – 27x – 5 = –10x to the nearest tenth.
Let A = {1, 2, 3, 4, 5} and B = {2, 4}. What is A ∩ B? (1 point)
A. {2, 4}
B. {1, 2, 3}
C. {1, 2, 3, 4}
D. {1, 2, 3, 4, 5}
Answer:
{2, 4}.
Step-by-step explanation:
A = {1, 2, 3, 4, 5} and B = {2, 4}.
A ∩ B?
This means intersection or what is in common
A ∩ B = {2, 4}.
Find the value of x.
Answer:
x= 42
Step-by-step explanation:
(2x +1)°= 85° (vert. opp. ∠s)
2x +1= 85
2x= 85 -1 (bring constant to 1 side)
2x= 84 (simplify)
x= 84 ÷2
x= 42