The resulting equation on using the completing the square is y = (x+5)² - 25
Completing the square methodThe quadratic equation has a leading degree of 2. Given the equation below;
y = x^2+10x
Add the square of the half of coefficient of x to have;
y = x^2+10x + (10/2)²- (10/2)²
y = x^2 + 10x + 5² - 5²
y = x^2 + 10x + 25 - 25
y = (x+5)² - 25
Hence the resulting equation on using the completing the square is y = (x+5)² - 25
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What is the area of Jack’s patio?
Answer:
62m^2
Step-by-step explanation:
From the figure above, we have two rectangles
For one rectangle,
Lenghts= 7m
Width = 6m
Area = lenght× width = 7×6= 42m^2
For the sect rectangle
Lenght = 5cm
Width = 4cm
Area = 5×4 = 20cm^2
Area of jack patio = 42+20= 62m^2
Which exponential equation is equivalent to this logarithmic equation? (2)
Answer:
A. e⁴=xStep-by-step explanation:
Log x=4 ➡️ e⁴=x or x= e⁴
Hope it helps
Find the greatest common factor of these two expressions.
28y^7x^2 and 8y^8v^4x^6
Answer:
4y⁷x²
Step-by-step explanation:
Finding GCF:Prime factorize each expression.
28y⁷x² = 2 * 2 * 7 * y⁷ * x²
8y⁸v⁴x⁶ = 2 * 2 * 2 * y⁸ * v⁴ * x⁶
GCF = 2 * 2 *y⁷*x²
= 4y⁷x²
Which sequence of transformations would yield a trapezoid similar to the original trapezoid but not congruent?A)reflection and dilationB)reflection and rotationC)rotation and reflectionD)translation and rotation help please
The sequence of transformations will be relection and dilation. Then the correct option is A.
What is a transformation of geometry?A spatial transformation is each mapping of feature shapes to itself and it maintains some spatial correlation between figures.
The sequence of transformations would yield a trapezoid similar to the original trapezoid but not congruent.
Reflection does not change the size and shape of the geometry.
Rotation does not change the size and shape of the geometry.
Translation does not change the size and shape of the geometry.
Dilation does not change the shape but changes the size of the geometry.
Then the correct option is A.
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Find the half line in days of Co-60. ROUND YOUR ANSWER TO THE NEAREST TENTH
The half life in days is 1924.0245 days.
What is half life?Half life is the time taken for the radioactivity of a substance to fall to half its original value.
Given:
N= 8
N[tex]_0[/tex]= initial mass
t= in days
So, N= [tex]N_0e^{-kt}[/tex]
Putting the values we get
half value = 5.2713 years or 1924.0245 days
Hence, the half-life is 1924.0245 days.
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PLEASE HELP PLEASEEEE!! 100 PTS!
Answer:
R
H
S
= cos
2
x
Step-by-step explanation:
Hope this helped!
Let a be a matrix with 4 columns. What are the possible values for rank(a)?
The complete question says: Let v, w, be vectors of [tex]\mathbb{R}^4[/tex]. Let A be a matrix with 4 columns v, w, 2v+w, v-w. What are the possible values for rank(A)?
The possible values for rank A = 2
What is a vector space?A vector space is a space that contains vectors as well as the associative including the commutative operation of vector addition and the associative, as well as, distributive operations of vector multiplication by scalars.
From the information given:
If v,w be the vectors in a [tex]\mathbb{R}[/tex]where;
A = matrix with 4 columns v, w, 2v+w, v-w, which are non-independent vectors.However, the vectors 2v+w and v-w can be expressed as a linear combination of the given values of v and w(independent vectors).
We can conclude that the maximum no. of independent rows = 2. Hence, the possible rank of matrix A is 2.
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f(x) = 3x + 6, find the ordered pair when x = -1.
(-1,-3)
(-1,3)
(-1,-9)
(-1,9)
Answer:
(-1 ; 3)
Step-by-step explanation:
when they say find the ordered pair they simply mean find the corresponding y value when x = -1
* where you see x substitute-1 *
f(-1) = 3(-1) + 6
=3
What is the rate of change of the amount earned with respect to hours worked for this function?
Answer:
72
Step-by-step explanation:
I got to get some bread for you guys
Answer:
I'll do it the answer is truthfully 72 if you don't think go check my page
Describe the shape of the distribution for the following and justify your answer:
a. The distance people travel to work on a typical day - The horizontal axis is the distance traveled in a person's daily commute. The vertical axis is frequency (number of people with that distance for their daily commute). Shape of distribution:
uniform
symmetric
skewed left
skewed right
Justification:
b. Number of hours of sleep for each night of the week (weekdays only) - The horizontal axis is the day of the week (Monday to Friday) and the vertical axis is the amount of sleep in hours for that night. Shape of distribution:
symmetric
skewed left
skewed right
uniform
Justification:
c. Age of first heart attack - The horizontal axis is age. The vertical axis is frequency (number of people who had their first heart attack at that age). The population is people in the US who have had at least one heart attack. Shape of distribution:
skewed left
symmetric
skewed right
uniform
Justification:
d. Scores on the Graduate Requirement Exam - This is a standardized test for people entering graduate school. The horizontal axis would be the person's total score. The vertical axis would be frequency (number of people with that score). The population would be all GRE test takers for a given year. Shape of distribution:
skewed left
symmetric
skewed right
uniform
Justification:
As the travelling distance to work increases, number of such people decreases. Therefore this distribution shape will be skewed right.
How to depict the shape?On each weekday, the number of sleeping hours generally remains the same. So the shape of the distribution will be uniform.
In general, most people will have their first heart attack at a higher age. So the shape of the distribution will be skewed left.
Scores of GRE will have a normal distribution in general. So the shape of the distribution will be symmetric.
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Where would 1.84 be on a number line?
Answer:
It is located to the right of the 0 on the line,
Step-by-step explanation:
the numbers are increasing going from left to right. 1.84 is located 1.84 from 0.
PLS HELP ASAP FIRST CORRECT ANSWER GETS BRAINLEIST
Answer: 55[tex]m^{2}[/tex]
Step-by-step explanation:
First find the area of the trapezoid: [tex]\frac{b1 +b2}{2}[/tex](h) : (base 1 + base 2) ÷ 2 x height
base 1 is 5m and we know the other base is parallel to the base of the rectangle so base 2 is 9m.
Since the total height is 7 m and the height of the rectangle is 5 m, subtract to get the height of the trapezoid: 7m - 5m = 2m
put the three values into the equation and solve:
(5m + 9m) ÷ 2 x 2m
(14m) ÷ 2 x 2m
7m x 2m
14[tex]m^{2}[/tex]
Find area of the rectangle which is just base x height
Which is 9m x 5m = 45[tex]m^{2}[/tex]
To find the total area, add the area of the trapezoid and the area of the rectangle. 14[tex]m^{2}[/tex] + 45[tex]m^{2}[/tex] = 55[tex]m^{2}[/tex]
Hope this helps
A trader bought 30 baskets of pawpaw and 100 baskets of mangoes for 2450. she sold the pawpaw at a profit of 40% and the mangoes at a profit of 30%. if her profit on the entire transaction was 855, find the cost price of a basket of pawpaw and the selling price of 100 baskets of mangoes.
The cost price of pawpaw is 40 and the cost if the basket of mangoes is 1250.
How to calculate the price?Based on the information given, the equations to solve the question will be:
30p + 100m = 2450 .... i
1.3 × 40p - 30 p + 1.3 × 100m = 855 ..... ii
30p + 100m = 2450
12p + 30m = 855
Solving simultaneously, the price of pawpaw is 40 and the price of mango is 12.5.
Therefore, the cost of 100 basket of mangoes will be:
= 12.5 × 100
= 1250
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If x+y=4 and x-y=k, what does x equal?
If x+y-z=8 and x-y+z=12 then x=
If x=3b and y=2/6b+4, what is x in terms of y?
The values of x are (4+k)/2 and 10. The value of the variable x in terms of y is x = y -4
System of equationsThese are equations that contains several equations and unknowns.
Given the following system of equation
x+y=4
x-y=k
Add both equation
x + x = 4 + k
2x = 4+k
x = (4+k)/2
For the equation
x+y-z=8
x-y+z=12
Add both equations
2x = 8 + 12
2x = 20
x = 10
The value of x from the equation is 10
Given the equations
x=3b
y = 2/6b+4,
______________
b = x/3
Substitute
y = 2/6(x/3)+4
y = x + 4
x = y - 4
Hence the value of the variable x in terms of y is x = y -4
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Describe the transformations of the graph of y=5 times 2^x-2+3 as compared to the graph of y=2^x
the transformations used are:
Dilation of scale factor 5.Shift of 2 units to the right.Shift of 3 units up.Which transformations are used?
We start with the function:
[tex]f(x) = 2^x[/tex]
And we have the transformed function:
[tex]g(x) = 5*2^{x-2} + 3[/tex]
Bow, let's start with the original function f(x). If first we apply a vertical dilation of scale factor 5, then we have:
g(x) = 5*f(x).
Then we apply a shift of 2 units to the right, so we have:
g(x) = 5*f(x - 2)
Then we apply a shift of 3 units up, so we have:
g(x) = 5*f(x - 2) + 3
Replacing f(x) by the actual function:
[tex]g(x) = 5*2^{x-2} + 3[/tex]
Then the transformations used are:
Dilation of scale factor 5.Shift of 2 units to the right.Shift of 3 units up.If you want to learn more about transformations:
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what's a frustum and what's the formula of the Almighty Formula
Answer:
the portion of a solid that lies between one or two parallel planes cutting it
Step-by-step explanation:
can anybody help me?
f(-2) = 2(-2)² - 8(-2) + 6 = 30
f(-1) = 2(-1)² - 8(-1) + 6 = 16
f(0) = 2(0)² - 8(0) + 6 = 6
f(1) = 2(1)² - 8(1) + 6 = 0
f(2) = 2(2)² - 8(2) + 6 = -2
What is the area of a sector with measure of arc equal to 90° and radius equal to 1 foot?
Answer:
0.7855 square feet
Step-by-step explanation:
90/360×3.142×1 squared
=0.7855
Consider the following graph.
Which statement best describes Cheryl's commute?
A. Cheryl accelerated to 65 mph, made a stop for 5.5 minutes, and then decelerated to 45 mph.
B. Cheryl accelerated to 65 mph, drove at a constant speed for 5.5 minutes, and the decelerated to 45 mph.
C. Cheryl drove at a speed of 65 mph for 1 minute, drove at a constant speed for 5.5 minutes, and then drove at a speed of 45 mph for 2.5 minutes.
D. Cheryl drove at a speed of 65 mph for 1 minute, made a stop for 5.5 minutes, and then drove at a speed of 45 mph for 2.5 minutes
The statement best describes Cheryl's computer is option C. Cheryl accelerated to 65 mph, drove at a constant speed for 5.5 minutes, and then decelerated to 45 mph.
How to find the function which was used to make graph?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
If we know that the function crosses the x-axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
Let's assume the graph of Cheryl's commute was like the one below.
We can see that she started at 0 mph.
One minute later, she was up to 65 mph, so she had accelerated (increased her speed).
At 6.5 min (5.5 min later) her speed was still 65 mph therefore, she was driving at a constant speed.
Over the next 2.5 min, her speed dropped to 45 mph, therefore she was decelerating.
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NEEP HELP ASSAP IF YOU COULD PLEASE
Kyle claimed that the given quadrilaterals are similar because the ratio of their corresponding sides is equal. Is Kyle's claim Incorrect or correct? In two or more complete sentences, Justify your answer.
In square, all angles are of 90°, but in rhombus, opposite angles are equal, but adjacent angles are not equal. Kyle's claim is Incorrect.
What is a quadrilateral?It is a polygon with four sides. The total interior angle is 360 degrees.
Kyle claimed that the given quadrilaterals are similar because the ratio of their corresponding sides is equal.
Kyle's claim is Incorrect. Because the shapes are square and rhombus.
In square, all angles are of 90°, but in rhombus, opposite angles are equal, but adjacent angles are not equal.
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Select the true statement about triangle ABC.
13
5
12
A. sin C = sin A
B. sin C = cos B
C. sin C = tan A
D. sin C = cos A
Answer:
sin C = cos A
Step-by-step explanation:
sinC = opp/hyp
=12/13
cosA = adj/hyp
12/13
Determine the measure of each indicated angle. Show all necessary steps!
a)
We know that a 4-sided polygon's angles add up to 360 degrees
so to find x:
360-(69+118+84)=89 degrees
b)
For a 4-sided polygon we also know that the outside angles add up to 360 degree.
so to find p:
360-(100+62+106)=92 degrees
Hope it helps!
The first term of an arithmetic progres- sion is 3 and the last term is 9. Find the number of terms in the progression if the common difference is 3/2
Answer:
5 terms
Step-by-step explanation:
The numbers will be 3, 4 1/2, 6, 7 1/2, and 9.
Does someone mind helping out with this ?
This circle is centered at the origin, and the length of its radius is 10. What is
the circle's equation?
O A. x² +2²=100
OB. x+y=10
O C. x¹0 + 10 = 100
O D. x² + y² = 10
a
5
10
Answer:
[tex] {x}^{2} + {y}^{2} = 100[/tex]
The equation of the circle is x² + y² = 100.
Option A is the correct answer.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2pir.
The area of a circle is πr².
We have,
The circle's equation is:
x² + y² = r²
where r is the length of the radius.
In this case, r = 10, so the equation becomes:
x² + y² = 10²
Simplifying:
x² + y² = 100
Therefore,
The equation of the circle is x² + y² = 100.
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please help i dont know how to do this
The average monthly temperature of a city can be modeled by a
cosine graph. Melissa has been living in Phoenix, Arizona, where the
average annual temperature is 75°F. She would like to move, and live
in a location where the average annual temperature is 62°F. When
examining the graphs of the average monthly temperatures for
various locations, Melissa should focus on the
The average monthly temperature of a city can be modeled by a cosine graph, Melissa should focus on the Midline. This is further explained below.
What is Melissa's focus on the Midline.?Generally, The average temperature would be indicated somewhere along the curve, most likely near the middle.
In conclusion, Melissa should concentrate on the Midline, which can be used to model the average monthly temperature of a city.
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By the distributive law 49 x 17 + 49 x 3=
Answer:
49(17 + 3)
Step-by-step explanation:
The Distributive Law says [tex]a(b+c)=ab+ac[/tex]. But it can be used in the other direction, [tex]ab+ac=a(b+c)[/tex]. That way, you look at ab and ac to find the common factor a. What's playing the role of a in the expression 49 x 17 + 49 x 3? It's 49, the factor that shows up twice. That's the factor that can be taken outside the parentheses.
49 x 17 + 49 x 3 = 49(17 + 3)
Which solution set matches the equation on the graph?
Answer: C, {(1, -4), (4, -1)}
Step-by-step explanation: Where the two graphs meet are their solutions, and the points where they meet are {(1, -4),(4,-1)}.
