Answers
Answer:
Step-by-step explanation:
1. The vertex is where the parabola is changing from increasing to decreasing
2. From the picture, we can see that the vertex is at (1,2)
3. The formula for vertex form is f(x)=a(x-h)^2+k
4. Vertex is (1,2) or (h,k)
5. You can see that the parabola opens upside down like a "n" so it has been reflected in the x axis
6. So, your equaltion is f(x)=-(x-1)^2+2
7. In this cause you can see that a=-1, but if not given you would choose a random point on the parabola and plug it in :). Example:(0,1): 1 = a(0-1)^2+2
a=-1.
8. Your answer: f(x)=-(x-1)^2+2
Related Questions
what is y=6x+20? Stemscopes
Answers
The solution of the given equation [tex]y=6x+20[/tex] is [tex]x = \frac{y + 20}{6}[/tex]
What is linear equation?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.
We have,
[tex]y = 6x + 20[/tex]
Arrange the equation both sides so that all variable terms are on the left hand side.
[tex]6x - 20 = y[/tex]
Add 20 to both sides of the equation.
[tex](6x - 20) + 20 = y + 20[/tex]
[tex]6x = y + 20[/tex]
Divide both sides by 6 we get,
[tex]\frac{6x}{6} = \frac{y + 20}{6}[/tex]
∴ [tex]x = \frac{y + 20}{6}[/tex]
Hence, final solution is [tex]x = \frac{y + 20}{6}[/tex] .
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after sampling a column of water from the surface to a depth of 3000 meters (nearly 10,000 feet), a colleague abroad an oceanographic research vessel tells you that the water column is isopycnal. what does this mean? what conditions create such a situation? what would have to happen in order to create a pycnocline?
Answers
Salinity and density decrease as temperature rises. Salinity and density, therefore, have a negative relationship with temperature. The density rises as salinity rises. As the temperature drops, ocean water becomes denser. Therefore, water becomes denser as it becomes colder. The density of seawater also rises as salinity does.
Water that is less dense floats above water that is denser. The warmer water will float on top of the colder water if there are two layers of water with the same salinity. However, there is a catch! Salinity has less of an impact on water density than temperature does. Therefore, if the layer with higher salinity is considerably warmer than the layer with lower salinity, the layer with higher salinity can actually float on top of the layer with lower salinity.
As you descend to the ocean's bottom, the temperature of the water continues to drop. So, as you descend to the ocean's bottom, the density of the water keeps rising. The deep ocean is divided into layers, with the lightest water at the top and the densest water at the bottom. The ocean's depths have horizontal circulation. In other words, water flows in strata of equal density.
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at a local college, 35.1% of students major in business, 12.3% of students major in economics, and 2.6% of students major in business and economics. what is the probability that a randomly selected student majors in business or economics? (write your answer as a percent rounded to 1 decimal place.)
Answers
The probability that a randomly selected student majors in business or economics is 44.8%.
Describe the union set in probability?A set that contains every element in at least one of two sets is called a union of two sets. The union is denoted by the symbols A∪B or “A or B” A fresh batch that includes every element from both sets is created when two sets intersect. The intersection is denoted by the symbols A∩B or “A and B”.Let 'B' be the students of business.
P(B) = 35.1%
Let 'E' be the students of business.
P(E) = 12.3%
Thus,
P(E ∩ B) = 2.6%
P(E ∪ B) = probability for student majors in business or economics.
P(E ∪ B) = P(B) + P(E) - P(E ∩ B)
Put the values-
P(E ∪ B) = 35.1% + 12.3% - 2.6%
P(E ∪ B) = 44.8%
Thus, the probability that a randomly selected student majors in business or economics is 44.8%.
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potatoes cost $0.85 per pound. Luke bought 2.75 pounds of potatoes. How much did he pay for the potatoes. Round to the nearest cent
Answers
Answer:
$2.34
Step-by-step explanation:
2.75 x 0.85 = $2.3375
Since we are rounding, it will round up to $2.34.
Answer:
Step-by-step explanation:
Cost of 2.75 pounds of potato =.
2.75x0.85
= $2.3375
find the circumference using the formula calculate your answer to the nearest hundredth
Answers
The circumference of the circle to the nearest hundredth is 21.98 inches.
How to find the circumference of a circle?The circumference of a circle is the measure of the boundary or the length of the complete arc of a circle.
The circumference of a circle is the perimeter of the circle. It's the wholes boundary of the circle.
The circumference of the circle can be found as follows:
circumference of a circle = 2πr
where
r = radiusTherefore,
diameter of the circle = 7 inches
radius of the circle = 7 / 2 = 3.5 inches
Hence,
circumference of a circle = 2 × 3.14 × 3.5
circumference of a circle = 21.98 inches
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Write and graph linear equations
Answers
The equation of the line is y = -3/4x + 10, the graph of the equation has been plotted
The slope of the line = -3/4
The slope of the line the change in y coordinate with respect to the change in x coordinate of the function
The line is passing through the point (0,10)
The point slope form is
[tex](y-y_1)=m(x-x_1)[/tex]
Substitute the values in the equation
y-10 = -3/4(x-0)
y - 10 = -3/4x
y = -3/4x + 10
The equation of the line in slope intercept form is
y = -3/4x + 10
Plot the graph using the slope intercept form
Hence, the equation of the line is y = -3/4x + 10, the graph of the equation has been plotted
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I need help with this question please help
Question 1 options:
70
180
67
40
140
143
Answers
Step-by-step explanation:
1. in a parallelogram the opposite angles are equal.
so,
3x - 7 = x + 73
and
angle DAB = angle DCB = z - 3
3x - 7 = x + 73
2x - 7 = 73
2x = 80
x = 40
angle ADC = angle ABC = x + 73 = 40 + 73 = 113°
to get to z we need also to remember, as a quadrilateral shape the sum of all inner angles of a parallelogram is 360°.
so,
2×113 + 2×(z - 3) = 360
226 + 2z - 6 = 360
220 + 2z = 360
2z = 140
z = 70
angle DAB = angle DCB = z - 3 = 70 - 3 = 67°
Answer:
Step-by-step explanation:
By definition of a parallelogram, we know that the opposite angles are equal.
Thus, x+73=3x-7.
We can further use algebra and subtract by 3x and 73 on both sides.
We now have -2x=-80.
If we divide both sides by -2, then we get x=40.
We can plug x=40 back into 3x-7 and x+73, and we get 113 for both angles, which of course makes sense because they should be equal.
By definition of a parallelogram, we know that the angles of a parallelogram add up to 360, and that angle DAB = angle BCD = z-3.
This means that 113+113+z-3+z-3=360.
Combining like terms, we get 220+2z=360.
We can use algebra again, and subtract both sides by 220, getting 2z=140.
Dividing both sides by 2, we get z=70.
Because angle DAB=z-3, and z=70, we can plug in 70 for z, producing the result of angle DAB=67.
(d)
After one year, the value of Annie's car had reduced by 20%.
At the end of the second year, the value of Annie's car had reduced by a further 15% of its value at the
end of the first year.
07
(i) Calculate the overall percentage reduction after the two years.
20
Answers
a yield sign measures 24 inches on each of its three sides. what is the area of the sign? (round your answer to one decimal place.)
Answers
A yield sign measures 24 inches on each of its three sides ( equilateral )then the area of the sign is 249.4
Given,
24 inches on each of its three side. (See in attached picture)
Consider ADB,
As it is an equilateral triangle, BD = BC/2 = 12 inches
By Pythagoras theorem,
AB^2 = BD^2 + AD^2
24^2 = 12^2 + AD^2
24^2 – 12^2 = AD^2
576-144 = AD^2
432= AD^2
20.78= AD
Area = ½ (base * height)
= ½ (24*20.78)
= 249.4
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At the fast food restaurant, an order of fries costs $1.08 and a drink costs $1.09. How
much would it cost to get 5 orders of fries and 4 drinks? How much would it cost to
get f orders of fries and d drinks?
Total cost, 5 orders of fries and 4 drinks:
Total cost, f orders of fries and d drinks:
Answers
Answer: $9.76
Step-by-step explanation: If you multiply f, the order of fries (5) by the cost of it ($1.08) you would get $5.40 & if you multiply d, the order of drinks (4) by the cost of it ($1.09) you would get $4.36. If you add up both the total numbers, you would get a final answer of $9.76.
Answer:
$9.76
Step-by-step explanation:
1.08f + 1.09d= Total
1.08(5)+1.09(4)= Total
5.40+4.36= Total
a small radio transmitter broadcasts in a 20 mile radius. if you drive along a straight line from a city 27 miles north of the transmitter to a second city 24 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?
Answers
To solve the given problem first we need to find the equation for line then we have to find the intersection point on circle.
You will pick up a signal from the transmitter in 29% of the drive.
Given:
The radius is 53 mile.
The origin point of transmitter is .
Calculate the slope of line with point and .
Substitute the value.
Write the general equation of line.
Now we got the equation of line,
Write the transmitter reach the area enclosed by the next circle.
Substitute the value of .
Further solving we get the point and .Please refer the attached figure.Apply the Pythagoras theorem to find the total distance.Apply the Pythagoras theorem to find distance when the signal is picked up.Calculate the percentage of distance covered.Thus, You will pick up a signal from the transmitter in 29% of the drive.
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Surface area of a rectangular prism 2cm 8cm 7 cm
Answers
The surface area of the rectangular prism is 172cm^2
What is a prism?Prism is a three-dimensional solid object in which the two ends are identical. It is the combination of the flat faces, identical bases and equal cross sections. The faces of the prism are parallelograms or rectangles.
The surface area of prism is 2A+ pH
where A is the base area
P is the perimeter of the base
and h is the height
for a rectangular prism, the base area is 2×8=16cm^2
perimeter of a rectangle= 2(l+b)
= 2(8+2)
= 20cm
surface area =( 2× 16) + 20× 7
= 32+ 140
= 172cm^2
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HELP
(2, -1); m = 5/4
Answers
Answer:
part b
y + 1 = 5/4(x - 2)
part c
y - 5 = 3(x - 0) or y - 5 = 3(x)
Step-by-step explanation:
-9 (9x -6) = 3 (4x+6)
Answers
Answer:
[tex]-9 (9x -6) = 3 (4x+6) \\ - 9 \times 9x + 9 \times 6 = 3 \times 4x + 3 \times 6 \\ - 81x + 54 = 12x + 18 \\ -81x - 12x = - 54 + 18 \\ - 93x = - 36 \\ x = \frac{36}{93} \\ x = \frac{18}{46.5} \\ x = 0.3870967742[/tex]
Choose the
system of inequalities that best matches the graph below.
Answers
The system of inequalities that best matches the graph is Option C
Step-by-step explanation:
To find the system of inequalities, we simply need to find the equation of each line.
Thus, let's find the inequality that is represented by each line.
Red Line:
First, let’s determine the slope. To do so, we can use the slope formula:
m = (y₂-y₁) / (x₂-x₁)
We can use any two points that's on the Red Line. Using (3, -2) and (6, -4) and substituting them into the slope formula yields:
m = (-4+2) / (6-3) = -2/3
Therefore, the slope of the red line is 2.
To write the equation of the red line, we can use the slope-intercept form:
y = mx + c
Notice that our y-intercept of our red line is (0, 3). Therefore, b = 3 and we already determined that m = -2/3:
y = ((-2/3)x) + (-3)
y = (-2/3)x -3
Now, we need to determine our sign. Notice that the shaded region is below the red line. Therefore, y is less than our equation.
And since our line is shaded, our sign will be less than or equal to. Therefore:
y ≤ (-2/3)x - 3
Blue line:
Again, let’s first find the slope. We can use the two points (3,0) and (0, -3). Hence:
m = (-3-0) / (3-0) = -3/3 = -1
So, the slope is -1.
We can now use the slope-intercept form. Notice that our y-intercept is (0, 0). Thus, we will substitute -1 for m and 0 for b. This yields:
y = -1x + 0
y = -x
Finally, we will determine our sign. Since the shaded region is above the blue line, our y is lesser than our equation. Therefore, our equation is:
y < -x
Thus, all together, our inequalities are:
y ≤ (-2/3)x - 3
y < -x
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Which expression shows the distance you would travel from the gym to your science class in this hallway?
Answers
The expression that shows the distance you would drive from the gym to the office along this road is b.|-6|+|4|
What is a Distance ?Distance is a numerical or qualitative measurement of the distance between two objects or points. Distance is defined as an object's total movement without regard for direction. The distance can be defined as how much ground an object has covered regardless of its starting or ending point.
To find the distance between two points in a number line we do the absolute value of the points subtracted. That is if we need to find the distance between point a and point b in a number line we do |a-b|.
Now, the Gym is at point -6 in the number line and the office is at point 4 in the number line, then the distance from -6 to 4 is |-6-4| = |-10| = 10.
Now, option a is |-6+4| ≠ |-6-4|.
The option b is |-6|+|4| = 6+4 = 10 =|-6-4|. Then, option b is correct.
Option c is -6+4 ≠ |-6-4|.
The option d is -|6|+|4| = -6+4 ≠ |-6-4|.
Then, the correct answer is b.
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Complete question
Which expression shows the distance you would drive from the gym to the office along this road?
a.|-6 + 4|
b.|-6|+|4|
c.-6+4
d.-|6|+|4|
the probability of spinning a1 is the same for both spinners ture or false
Answers
The probability of spinning a 1 is the same for both spinners: False
How to determine the true statement?The spinners that complete the question are added as an attachment
From the attached figures, we have
Spinner 1
Number of 1 = 1
Sections = 4
Spinner 2
Number of 1 = 2
Sections = 6
The probability of obtaining 1 is calculated as
P(1) = Number of 1/Sections
So, we have
Spinner 1
Number of 1 = 1
Sections = 4
P(1) = 1/4
Spinner 2
Number of 1 = 2
Sections = 6
P(1) = 2/6
By comparison
1/4 and 2/6 do not have the same value
Hence. it is false that the probability of spinning a 1 is the same for both spinners
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. Use the distance formula to find the distance between the points (5,6) and (10,12). You
can leave the answer as a square root if it is not a perfect square.
Answers
The distance between the two points (5,6) and (10,12) is [tex]\sqrt{61}[/tex]
What is the distance between two points formula?
The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a standard formula to calculate the distance between two points. This equation can calculate the separation between any two locations on an x-y plane.
Solution explained:
First, Write the distance formula:
[tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]
Now,
Substitute (5,6) and (10,12) into [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex] :
[tex]\sqrt{(10 - 5)^{2} + (12 - 6)^{2}}[/tex] Calculate
[tex]\sqrt{(5)^{2} + (6)^{2}}[/tex] Calculate
[tex]\sqrt{25 + 36}[/tex] Calculate
Hence. the distance between points (5,6) and (10,12) is [tex]\sqrt{61}[/tex].
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John is in charge of feeding the pigs and cows on the farm. The cow's food costs twice as much as the pig's food. There are 46 cows and 22 pigs on the farm. John has a $860 budget for food a month. How much can John spend on food for each cow per month?
I tried solving this and got some random answer like $7.5432... per pig. Please Help
Answers
The cost of feed for a cow in a month is $15.08
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls)
Similarly the ratio of the cost of cow's food to pig is 2:1
represent the cost of feed of a cow by x and the cost of feed for a pig to be y
therefore x= 2y
there are 46 cows, therefore the cost of feed for 46 cows is 46x
there are 22 pigs, therefore the cost of pig is 22y
46x+22y= 860
representing 2y for x
46(2y)+22y= 860
114y= 860
y= 860/114
y=$ 7.54
recall x=2y
x= 7.54×2= $15.08
therefore $15.08 is spent on a cow in a month
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Sara has a box of markers. In the box are 5 red markers, 3 blue markers, 9 purple markers,
and 3 pink markers. If she reaches into the box and randomly pulls out a marker, what is the
probability that Sara will pick a blue marker?
Answers
The probability that Sara will pick a blue marker is 3/20.
What is probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Math's to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.
Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given,
the box contains red markers = 5
blue marker = 3
purple marker = 9
pink markers = 3
Total number of markers = 20
The probability that she picks blue marker = 3/20
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Suppose the temperature in your town is 88°F and rising 1.5°F every hour, h. In how many hours will the temperature be over 100°F? Write an inequality representing the situation. Solve the inequality.
Answers
Find m/ABD.
D
с
A
20°
B
Answers
The answer of this question can be given by using congruence
Answer is 20°
What is an example of congruence?
Congruent relates to anything that is "exactly equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another.
Given That:
∡DBC = 20°
DC = AD
DB is common on both triangle
As we have hypotenuse common in both triangle and 1 side equal then we can sa it is a congruent triangle by RHS
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The time taken by the rocket to reach its maximum height is 1.25 seconds and the maximum height is 32 feet.
Given equation:
h(t) = -16t^2+40t+7 and initial velocity is 40 feet per second and launching pad is 7 feet tall.
a = 1
t = -b/2a
= -40/2*-16
= -40/-32
= 40/32
= 1.25 seconds
h(2.5) = -16(1.25)^2+40*1.25+7
= -1.5625*16+50+7
= -25+57
= 32 feet.
Therefore The time taken by the rocket to reach its maximum height is 1.25 seconds and the maximum height is 32 feet.
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can anyone help?????
Answers
Answer: 0
Step-by-step explanation:
Since y is 2, and it’s being multiplied by 4, you have 8 - 8 which =0
Y=2
4(2) - 8
8-8
0
Answer:
0
Step-by-step explanation:
4y - 8
Given that,
y = 2
To find the value of given expression, replace y with 2 and solve the expression.
Let us solve it now.
4y - 8
4 × 2 - 8
8 - 8
0
10. Bob buys some games for $13 each. He has a coupon for $5 off the total
price. If he pays $73, how many games did he buy
Answers
He bought 6 games
Explanation:
73+5=78
78/13=6
Also I would appreciate brainiest trying to level up!
Write an equation perpendicular to y =− 3x + 2 and passes through the point (0, 8).
Answers
Answer:
y = [tex]\frac{1}{3}[/tex] x + 8
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 3x + 2 ← is in slope- intercept form
with slope m = - 3
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex]
the line crosses the y- axis at (0, 8 ) ⇒ c = 8
y = [tex]\frac{1}{3}[/tex] x + 8 ← equation of perpendicular line
Trapezoid G is a scaled copy of trapezoid F.
Answers
Answer:
yes it is???
Step-by-step explanation:
kumiko decides to buy the same number of apps and games, and she decides to spend as much of the $50 as possible. how many apps and games does she buy? how much money does she have left on her gift card?
Answers
The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].
Expressions using linear inequalities compare any two values using inequality symbols like "," ">," "," or "."
The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].
What is Inequality?Expressions using linear inequalities compare any two values using inequality symbols like "," ">," "," or "." These values might be either numerical, algebraic, or both.
The number of apps Kumiko buy is a and the number of games she can buy is g.
The gift card has 50$.
Total amount of apps = 1.25a
Total amount of games = 2.5g
So, the linear equality will be [tex]1.25a+2.5g\leq50[/tex].
She can can only games and apps for amount less than and equal to $50.
Therefore, The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].
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The given question is Incomplete. Here is the complete question:
Kumiko has a $50 gift card for a Web site that sells apps and games. Games cost $2.50 each, and apps cost $1.25 each. Write an inequality that represents the number of apps a and the number of games g that Kumiko can buy and describe any constraints.
if three sides of a trapezoid are 10 inches long, how long should the fourth side be if the area is a maximum?
Answers
The area of the trapezoid is maximum when the fourth side be 20 inches.
What is meant by trapezium?Trapezoids are quadrilaterals with two parallel and two oblique sides. It is also known as a trapezium. A trapezoid is a four-sided closed shape or figure with a perimeter that covers some area.
By applying Pythagorean theorem,
[tex]c^2=a^2+b^2[/tex]
[tex]10^2=h^2+x^2[/tex]
[tex]100=h^2+x^2[/tex]
[tex]h^2=100-x^2[/tex]
[tex]h=\sqrt{100-x^2}[/tex]
Area of the trapezoid is,
[tex]A=\frac12 \times h\times (b_1+b_2)[/tex]
By substituting the values of h, b1, and b2 in the above equation,
[tex]A=\frac12 \times \sqrt{100-x^2} \times (10+2\times x+10)[/tex]
[tex]A=\sqrt{100-x^2} \times (x+10)[/tex]
If we take the derivative of both sides of the equation in relation to x, we get
[tex]\frac{dA}{dx}=\frac{d}{dx}[\sqrt{100-x^2} \times (x+10)][/tex]
[tex]\frac{dA}{dx}=\sqrt{100-x^2} \ \frac{d}{dx} (x+10) + (x+10) \ \frac{d}{dx} \sqrt{100-x^2}[/tex]
[tex]\frac{dA}{dx}=\sqrt{100-x^2} - \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]
[tex]\frac {dA}{dx}=0[/tex]
[tex]0=\sqrt{100-x^2} - \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]
[tex]\sqrt{100-x^2} = \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]
100-x²=x²+10x
2x²+10x-100=0
x²+5x-50=0
(x-5)(x+10)=0
If, x+10=0
x=-10
The above value is not accepted because it is a negative value,
If, x-5=0
x= 5
The value is accepted because it is positive value
The length of the trapezium which should be fourth is,
b₂=2x+10
b₂= 2(5)+10
b₂=20
The area of the trapezoid is maximum when the fourth side be 20 inches
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a high school statistics class wants to estimate the average number of chocolate chips in a generic brand of chocolate chip cookies. they collect a random sample of cookies, count the chips in each cookie, and calculate a 95% confidence interval for the average number of chips per cookie (18.6 to 21.3). which interpretation of the 95% confidence interval is valid?
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