x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.
What is, axis of symmetry, vertex and x - intercept?
A vertical line that splits the parabola into two equal half is the axis of symmetry. The equation x = - b/2a tells us where the line of symmetry lies. The parabola's vertex, which is a point (x, y), is where it crosses its axis of symmetry.
A line's x-intercept is the location at which the x-axis is crossed.
Consider, the given equation,
[tex]f(x) = \frac{1}{4}(x - 1)(x + 7)[/tex]
Let,
[tex]y = \frac{1}{4}(x - 1)(x + 7)[/tex] ..(1)
To find x - intercept, plug y = 0 in above equation,
[tex]\frac{1}{4}(x - 1)(x + 7) = 0\\ (x - 1)(x + 7) = 0\\(x - 1) = 0, (x + 7) = 0\\x = 1, x = -7[/tex]
Therefore, x = 1 and x = -7 are the x - intercepts.
Since, the x-coordinate of the vertex is at the midpoint of the x-intercepts.
So,
[tex]x = \frac{-7+1}{2} = \frac{-6}{2} = -3[/tex]
Plug x = -3 in equation (1)
[tex]y = \frac{1}{4}(-4)(4) = -4[/tex]
Therefore, the vertex is, (-3, -4).
The x - coordinate of the vertex is the axis of symmetry.
Therefore, axis of symmetry is x = -3.
Hence, x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.
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Which expression shows the distance you would travel from the gym to your science class in this hallway?
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.
The complete question is given below.
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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|
Find the slope and reduce.
P=(-8, 3) Q=(-6, 2)
Slope
=
Answer:
2-3/-6-(-8)
= -1/2
I need help with this question please help
Question 1 options:
70
180
67
40
140
143
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.
J.5 unit rates
96 kilometers in 3 hours = ?
The unit rate for 96 kilometers in 3 hours is 32 kilometer per hour.
What is unit rate?
A unit is one of a particular object. An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.
Given in the question,
96 kilometer in 3 hours,
In order to find unit rate we have to change given values in kilometers per hour.
Do, 96 kilometer = 3 hours
96/3 kilometer = 1 hour
Therefore, unit rate is 32 kilometer per hour.
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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?
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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Given the equation negative 28 equals y over 7, solve for y.
196
4
−4
−196
please help me.
The linear equation:
-28 = y/7
Can be solved by multiplying both sides by 7, to get y = -196
How to solve the equations?Here we want to solve the equation:
-28 = y/7
And we want to solve this for the variable y.
To do so, we need to isolate said variable in one side of the equation, now remember that we can multiply both sides of the equation by the same number.
Then we can multiply both sides by 7 so we get:
-28*7 = (y/7)*7
-196 = y
The correct option is the last one.
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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.)
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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kumiko decides to buy the same number of apps and games, and she decides to spend as much of the $50 as possible. how many apps and games does she buy? how much money does she have left on her gift card?
The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].
Expressions using linear inequalities compare any two values using inequality symbols like "," ">," "," or "."
The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].
What is Inequality?Expressions using linear inequalities compare any two values using inequality symbols like "," ">," "," or "." These values might be either numerical, algebraic, or both.
The number of apps Kumiko buy is a and the number of games she can buy is g.
The gift card has 50$.
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.
Trapezoid G is a scaled copy of trapezoid F.
Answer:
yes it is???
Step-by-step explanation:
HELP
(2, -1); m = 5/4
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:
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?
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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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.)
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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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
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
(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
what is y=6x+20? Stemscopes
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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-9 (9x -6) = 3 (4x+6)
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]
if three sides of a trapezoid are 10 inches long, how long should the fourth side be if the area is a maximum?
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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Can someone please help me
The proof that show show how ΔTRS ≅ ΔQRP by SAS congruence theorem is explained below.
What is the SAS Congruence Theorem?The SAS congruence theorem states that if two triangles have one pair of corresponding included angles that are congruent, and two pairs of corresponding sides that are also congruent, then both triangles are congruent to each other.
Using the SAS, the proof that shows both triangles are congruent is explained below.
Statements Reasons
1. SR ≅ PR 1. Given
2. SP bisects TQ 2. Given
3. TR ≅ QR 3. Definition of bisection
4. ∠TRS ≅ ∠QRP 4. Vertical ∠s theorem
5. ΔTRS ≅ ΔQRP 5. SAS congruence theorem
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the probability of spinning a1 is the same for both spinners ture or false
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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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.
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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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0.38 in expanded form
Answer:
0 + 0.30 + 0.08
Step-by-step explanation:
hope it helps :)
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
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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. 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.
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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Find m/ABD.
D
с
A
20°
B
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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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?
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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can anyone help?????
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
Pls Help BrainliestBegging u PlsPLS!!!!!!!!!!!!
How many positive three-digit integers have at least one digit that is a 5 or a 7?
Answer:
452 integers------------------------
Three-digit integer in the form of abc.
Possible numbers for each digit
a - 1 to 9, nine options,b and c - 0 to 9, ten optionsLet a = 5 or 7, then for a we have 2, for b and c 10 options:
5bc or 7bc2*10*10 = 200Let b = 5 or 7, then for a we have 9 - 2 = 7, for b 2 and for c 10 options
a5c or a7c7*2*10 = 140Let c = 5 or 7, then for a we have 9 - 2 = 7, for b 10 - 2 = 8 and for c 2 options
ab5 or ab77*8*2 = 112Total options200 + 140 + 112 = 452Write an equation perpendicular to y =− 3x + 2 and passes through the point (0, 8).
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
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
