What is the line of symmetry for the parabola whose equation is y = x2 + 10x + 25? x = -10 x = -5 x = 5
Answers
Answer:
[tex]y=x^2 + 10x + 25\\\\y=(x+5)^2[/tex]
Used the identity, [tex](a+b)^2=a^2+2ab+b^2[/tex]
The given parabola is of the form , [tex](x+a)^2=y[/tex], having vertex at ,which can be obtained by
x+a=0
x= -a
(-a,0).
So, vertex of the given parabola is , at (-5,0).
The Meaning of term line of symmetry,is that line which divides the parabola in two equal halves.
Drawing the parabola,and finding the line of symmetry,which can be obtained by drawing a line parallel to y axis, passing through (-5,0).
So, the equation of line is : x= -5
Related Questions
Larry wants to inscribe an equilateral triangle in a circle using only a compass and straightedge. He will first construct a circle and locate its center. He will then perform the following steps.
Step 1: Set the width of the compass to the diameter of the circle.
Step 2: Plot a point on the circle. Place the compass on this point and draw two arcs to cut the circle. These two points of intersection between the arcs and the circle represent two of the vertices.
Step 3: Draw a segment between the two vertices. Adjust the width of the compass to the length of the segment. Place the compass on one vertex and draw an arc to construct the third vertex.
Step 4: Draw a line from one vertex to the next to form an equilateral triangle.
What is the error in Larry's construction?
A. He did not draw a pair of perpendicular bisectors to construct two diameters of the circle.
B. He drew only two arcs.
C. He set the width of the compass to the diameter of the circle.
D. He did not ensure that the length of the sides of the triangle was the same as the diameter of the triangle.
Answers
He set the width of the compass to the diameter of the circle. The step 1 should be: Set the width of the compass to the radius of the circle.
The error in Larry's construction is:
C. He set the width of the compass to the diameter of the circle.
Step-by-step explanation:The steps for the construction of an inscribed equilateral triangle is as follows:
Step 1: Draw a circle on a piece of paper.Take a point anywhere on the circumference of the circle and take that point as a starting point.Step 2: Now without changing the span of the circle we have draw two arcs to cut the circle.These two points of intersection between the arcs and the circle represent two of the vertices. Step 3: Draw a segment between the two vertices. Adjust the width of the compass to the length of the segment. Place the compass on one vertex and draw an arc to construct the third vertex. Step 4: Draw a line from one vertex to the next to form an equilateral triangle.Hence, the error he that he set the width of compass equal to the diameter of circle.
Instead he should have set the width of the compass equal to the radius of the circle.
A lamp manufacturer has daily production costs of C = 0.25n2 – 10n + 800, where C is the total cost in dollars for n lamps produced.
What is a reasonable domain for this function, given the problem's context?
A) all integers
B) all real numbers
C) all positive integers
D) all positive real numbers
Answers
The reasonable domain for the given cost function, considering the context of lamp production, is all positive integers (C) because lamps can only be produced in whole, positive quantities.
The lamp manufacturer's daily production costs are given by the function C = 0.25n2 - 10n + 800, where C represents the total cost in dollars and n is the number of lamps produced. Considering the context of the problem, where production numbers must be whole and non-negative, the reasonable domain for this function is all positive integers, which represents the count of lamps that can be produced. This is because the manufacturer cannot produce a fraction of a lamp, nor can they produce a negative number of lamps. Hence, the correct choice for the domain is (C) all positive integers.
35 POINTS!!
The scatter plot shows the relationship betweeen the number of hours students spend watching television and the numer of hours they spend playing outdoor sports each week.
A graph is titled Television and Sport. On the x axis, the label is Weekly Hours of
What is the y-intercept of the line of best fit and what does it represent?
A 10.4 hours; the number of hours students play outdoor sports in a week when they do not watch television
B 7.2 hours; the number of hours students play outdoor sports in a week when they do not watch television
C 10.4 hours; the number of hours students watch television in a week when they do not participate in any outdoor sports
D 7.2 hours; the number of hours students watch television in a week when they do not participate in any outdoor sports
Answers
Answer:
D 7.2 hours; the number of hours students watch television in a week when they do not participate in any outdoor sports
Step-by-step explanation:
Given is a scatter plot which shows the relationship betweeen the number of hours students spend watching television and the numer of hours they spend playing outdoor sports each week.
From the graph showing the regression line, the regression line has y intercept as 7.2
(When x=0, y =7.2)
Hence correct answer is
D 7.2 hours; the number of hours students watch television in a week when they do not participate in any outdoor sports
Your school raise 125% of its fundraising goal. The goal raised $6,750. What was the goal?
Answers
100/x = 125 / 6750
100% is to x and 125 is 6750
100/x = 125/6750 Cross multiply.
100 * 6750 = 125x Divide by 125
100 * 6750 / 125 = x
x = 5400 was the initial goal.
What is the solution set of x/4≤9/x?
Answers
Answer:
x≤-6 or 0<x≤6.Option D.
Step-by-step explanation:
Given:
[tex]\frac{x}{4} \leq \frac{9}{x}.[/tex]
Subtract [tex]\frac{9}{x}[/tex] from both sides,
[tex]\frac{x}{4}-\frac{9}{x} \leq[/tex] 0
Simplifying by taking common denominator:
[tex]\frac{x^2-36}{4x}\leq[/tex]0
Factoring numerator:
[tex]\frac{(x+6)(x-6)}{4x}\leq[/tex]0
Computing the signs and selecting that one satisfies ≤ 0:
x≤ -6,0<x≤6.
Option D is the right answer.
An object with reflectional symmetry can be created by reflecting it about an axis called the _____.
A. Point of symmetry
B. Line of symmetry
C. Symmetrical half
D. Equator of symmetry
Answers
Reflection symmetry is a symmetry with respect to the reflection and is also know as mirror symmetry, line symmetry or mirror-image symmetry.
When a figure undergoes a reflection and does not change , then the figure is said to has the reflectional symmetry.
An object with reflectional symmetry can be created by reflecting it about an axis called the Line of Symmetry.
Hope this helps ..!!
Thank you :)
What type of number results when a negative number is multiplied by a positive number and vice versa?
A. A negative number
B. Zero
C. A positive number
Answers
A positive number results
when a negative number is multiplied by a positive number and vice versa.
This means your answer is option C.
Hope this helps you.
Have a great day! (:
Donnie is solving the equation 2x2=27+3x with the quadratic formula. Which values could he use for a, b, and c? a = 2, b = −3 , c = −27 a = 2, b = −27, c = −3 a = 2, b = 3, c = 27 a = 2, b = 27, c = 3
Answers
a= 2
b= -3
c= -27
The given equation is :
[tex] 2x^{2} =27+3x [/tex]
Now let us write it in standard form:
[tex] 2x^{2} -3x-27=0 [/tex]
Comparing it with general standard form:
[tex] ax^{2} +bx+c=0 [/tex]
So we have a=2, b=-3 and c=-27
First option is correct answer .
5. An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5 cm long. A second side of the triangle is 6.9 cm long. Find the longest and shortest possible lengths of the third side of the triangle. Round answers to the nearest tenth of a centimeter. (1 point)
A. 41.4 cm, 8.3 cm
B. 30 cm, 5.8 cm
C. 41.4 cm, 4.3 cm
D. 8.3 cm, 5.8 cm
Answers
https://answers.yahoo.com/question/index?qid=20120518194118AAhi738
Answer:
Option D -8.3 cm, 5.8 cm
Step-by-step explanation:
Given : An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5 cm long. A second side of the triangle is 6.9 cm long.
To find : The longest and shortest possible lengths of the third side of the triangle?
Solution :
First we create the image of the question,
Refer the attached figure below.
Let a triangle ABC , where angle A has a bisector AD such that D is on the side BC.
The theorem is stated for angle bisector is
"Each angle bisector of a triangle divides the opposite side into segments proportional in length to the adjacent sides".
So, according to question,
Let BD=6 cm, DC=5 cm, AB=6.9 cm
and we have to find AC.
Applying the theorem,
[tex]\frac{BD}{DC}=\frac{AB}{AC}[/tex]
[tex]\frac{6}{5}=\frac{6.9}{AC}[/tex]
[tex]AC=\frac{6.9\times 5}{6}[/tex]
[tex]AC=\frac{34.5}{6}[/tex]
[tex]AC=5.75[/tex]
[tex]AC=5.8 cm[/tex]
If we let AC=6.9 cm, find AB
Then,
[tex]\frac{BD}{DC}=\frac{AB}{AC}[/tex]
[tex]\frac{6}{5}=\frac{AB}{6.9}[/tex]
[tex]AB=\frac{6.9\times 6}{5}[/tex]
[tex]AB=\frac{41.4}{6}[/tex]
[tex]AB=8.28[/tex]
[tex]AB=8.3 cm[/tex]
Therefore, The shortest possible length is 5.8 cm and longest possible is 8.3 cm.
Hence, Option D is correct.
What is the ratio of x to y?
3x = 8y
Answers
3x= 8y
x 8
-- = ---
y 3
Final answer:
The ratio of x to y, given the equation 3x = 8y, is 8:3. This is found by dividing both sides of the equation by 3y and simplifying.
Explanation:
To find the ratio of x to y, given the equation 3x = 8y, you can divide both sides of the equation by 3 to solve for x in terms of y, or vice versa.
Dividing both sides by 3y yields:
x/y = (8y)/(3y)
Assuming y is not zero, the y terms cancel out on the right side of the equation, giving us:
x/y = 8/3
Method 2: Using fraction notation:
Rewrite the equation with x isolated:
x = (8/3) × y
This also shows that the ratio of x to y is 8:3.
Both methods lead to the same answer: x : y = 8 : 3.
Thus, the ratio of x to y is 8:3.
Quadrilateral ABCD is inscribed in a circle.
What is the measure of angle A?
Enter your answer in the box.
m∠A=
°
Answers
x + 2 + 3x + 6 = 180
4x + 8 = 180
4x = 172
x = 43
Now solve for A
3(43) + 6 = A
129 + 6 = A
135 = A
The measure of angle A is 135 degrees.
Hope this helps =)
The answer is m∠A= 135°
Classify the model as exponential growth or exponential decay. Identify the growth or decay factor AND the percent of increase or decrease per time period.
y=2(1/2)^t
Plz help!
Answers
The decay factor is 1/2.
The change is (1/2 -1)*100% = -50% per period. Negative indicates a decrease of 50% per period.
For each babysitting job, ashley charges $2.50 for bus fare plus $8 per hour for each hour she works. she charged $30.50 for her last babysitting job.
a. write a linear equation to represent the problem. be sure to define the variable you choose. __________
Answers
Variable: h = hours worked
linear equation: 30.50 = 2.50 +8h
pleaseeeeeee answer!!!!!!!!!!!!
There are eight planets in our solar system. Venus is the hottest planet, with an average temperature of 460°C. The average temperatures of some other planets are given in the table.
Venus 460°C
Earth 14°C
Mars -60°C
Neptune -214°C
The net change in temperature from Neptune to Mars is _______°C.
The net change in temperature from Earth to Neptune is ________°C.
The net change in temperature from Venus to Earth is _________°C.
Answers
The net change of temperatures between the planets is required.
Neptune to Mars is [tex]154^{\circ}\text{C}[/tex]
Earth to Neptune is [tex]228^{\circ}\text{C}[/tex]
Venus to Earth is [tex]446^{\circ}\text{C}[/tex]
The net change value is the distance of the net change from zero.
So, the absolute value of the change will be the net change.
Difference in temperature of Neptune and Mars
[tex]|-214-(-60)|=154^{\circ}\text{C}[/tex]
Difference in temperature of Neptune and Earth
[tex]|-214-14|=228^{\circ}\text{C}[/tex]
Difference in temperature of Venus and Earth
[tex]|460-14|=446^{\circ}\text{C}[/tex]
Learn more:
https://brainly.com/question/11953855?referrer=searchResults
Answer:
154 for neptune to mars is correct. The 228 and 446 is wrong.
Step-by-step explanation:.
A farmer has 300 ft of fencing with which to enclose a rectangular pen next to a barn. The barn itself will be used as one of the sides of the enclosed area.
What is the maximum area that can be enclosed by the fencing?
Enter your answer in the box.
ft²
Answers
Answer
Maximum area A_max = 11250 ft^2
Step-by-Step Explanation
Declaring Variables:-
The length of the rectangle = y
The width of the rectangle = x
Solution:-
- The perimeter of a rectangle can be expressed using the above two variables as follows:
Perimeter (P) = 2*Length + 2*Width
= 2* ( x + y )
- Since the barn is used as one of the sides (let's say y) we can subtract y
we don't need fencing for this side. The length of the fence required L is:
Length (L) = P - y
= 2*x + y
- We are given 300 feet of fencing. So we equate the length equal to 300 and develop a linear relationship between width and length of the barn.
300 = 2x + y
y = 300 - 2x
- The area (A) of the rectangle is given by the following expression:
A = Length*width
A = x*y
- Substitute the relationship developed between x and y in the Area (A) expression above. Then we have:
A = x*(300 - 2x)
A = 300x - 2x^2
- We will take first derivative of the expression of area (A) developed with respect to x and find the critical point of the area function by setting the first derivative A'(x) = 0.
A(x) = 300x - 2x^2
A'(x) = 300 - 4x
0 = 300-4x
x = 300 / 4 = 75 ft
- The critical point of the given function lies for the width (x) of 75 ft. We will plug in the critical value x = 75 ft back into the original function of Area and find the maximum area.
A(x) = 300x - 2x^2
A(75) = 300 (75) - 2(75)^2
A_max = A(75) = 11250 ft^2
- The maximum area that can be enclosed by the fencing is 11250 ft²
Answer:11250
Step-by-step explanation:
There are 454 grams in a pound. There are 16 ounces in a pound. How many grams are in an ounce?
Answers
Answer: There are 28.375 grams in an ounce.
Step-by-step explanation:
Given: Total grams in a pound =454 grams
Total ounces in a pound = 16 ounces
Therefore, 16 ounces = 454 grams
To find grams in an ounce, we need to divide 454 grams by 16, we get
The total grams in an ounce=[tex]\frac{454}{16}=28.375\ grams[/tex]
∴The total grams in an ounce= 28.375 grams
Hence, there are 28.375 grams in an ounce.
28.375 grams in an ounce.
To calculate how many grams are in an ounce, divide 454 (grams in a pound) by 16 (ounces in a pound) to get 28.375 grams in an ounce.
To find out how many grams are in an ounce:
Given: 1 pound = 454 grams and 1 pound = 16 ounces.Since 1 pound = 454 grams and 1 pound = 16 ounces, divide 454 by 16 to find out how many grams are in an ounce.454 grams ÷ 16 = 28.375 grams in an ounce.an elephant in an african wildlife perserve is 59.3 years old the table shows some students estimates for the elephants age who correctly rounded the age of the elephants to the nearest year
Answers
Hope i helped:)
Have a nice day!
~Luis~
Anybody got the answer to this?
Answers
s = R * teta
Where,
Radio
Teta: arc angle measured in radians.
We have then that the length of the arc in this case is:
s = (7.9) * (180-66.4)) * (pi / 180)
s = 15.7 cm
Answer:
The length of the AD arc is:
s = 15.7 cm
You sell lemonade for $2 per cup and orange juice for $3 per cup. you sell a total of 100 cups for $240. write and solve a system of linear equations to find the number of cups and the number of lemonade and the number of cups of orange juice you sold. answer
Answers
2L + 3OJ = 240
-2L + -2OJ = -200
2L + 3OJ = 240
1OJ = 40
L + OJ = 100
L + 40 = 100
L = 60
Therefore : 60 cups of lemonade and 40 cups of orange juice.
To solve a linear equation in two variables, at least two equations are required. There are 60 lemonade and 40 orange juice cups.
What is Linear equation in two variable ?A linear equation in two variable can be written as ax + by = 0 where a and b are not equal to zero. It is used to represent a straight line.
Given that, rate of lemonade per cup = $2.
And, rate of orange juice per cup = $3.
Total number of cups sold = 100.
Total earning = $240.
Suppose the number of lemonade cup be x,
And, the number of orange juice cup be y.
Then, as per the question two equations can be formed given as,
x + y = 100 -------------------------(1)
2x + 3y = 240 -------------------------(2)
To find x and y, multiply equation (1) by 2 and substract it from equation (2),
2x + 3y - 2(x + y) = 240 - 2×100
=> y = 40
Substitute y =40 in equation (1) to get x as,
x + 40 = 100
=> x = 60.
Hence the number of lemonade cups are 60 and orange juice cups are 40.
To know more about Linear equation in two variable refer to,
https://brainly.com/question/24085666
#SPJ2
TWO QUESTION MUST ANSWER BOTH TO RECEIVE POINTS (PLEASE TAKE IT SERIOUSLY)
1) Line IJ has an equation of a line y = −3x − 8. Which of the following could be an equation for a line that is parallel to line IJ?
A) y = 3x + 7
B) y = 1 over 3x + 7
C) y = −3x + 7
D) y = −1 over 3x + 7
2) Find the perimeter of the shape below:
A) 12.4 units
B) 13.4 units
C)15.1 units
D) 16.8 units
Answers
which of these is the best definition of an ellipse
Answers
therefore
the answer is the option D)
the set of all points in a plane for which the sum of the distances to two fixed points equals a certain constant
A wedding planner purchased small and large lanterns for a wedding reception. The small lanterns cost $25 each, and the large lanterns cost $40 each. The planner purchased a total of 40 lanterns for a total of $1180.
Answers
Explanation:
x=Amount of Small Lanterns y=Amount of Large Lanterns
25x+40y=1180
x+y=40
x=40-y
25(40-y)+40y=1180
1000-25y+40y=1180
1000+15y=1180
15y=180
y=12
x+12=40
x=28
Answer:
The wedding planner must have purchased 28 small lanterns and 12 large lanterns.
Step-by-step explanation:
Let the number of small and large lanterns purchased be S and L respectively.
S + L = 40 ........ Equation 1
L = 40 - S
25S + 40L = 1180 ....... Equation 2
25S + 40(40 - S) = 1180
25S + 1600 - 40S = 1180
-15S = 1180 - 1600
-15S = -420
S = 28
L = 40 - S
L = 40 - 28
L = 12
The wedding planner must have purchased 28 small lanterns and 12 large lanterns.
Samuel has a collection of toy cars. his favorites are the 272727 red ones which make up 60\%60%60, percent of his collection.how many toy cars does samuel have?
Answers
1 % = 27 ÷ 60 = 0.45
100% = 0. 45 x 100 = 45
Samuel has 45 cars.
Answer:
Khan Academy said 45 hope it helps! :)
What is the value of e^In7x a.1 b.7e c.7x d.7
Answers
Just took the test!
Which type of transformation maps trapezoid PQRS onto trapezoid P'Q'R'S'?
reflection
rotation
translation
dilation
Answers
Answer is DILATION
Answer: Dilation.
Step-by-step explanation:
From the given picture , it can be seen that the size of trapezoid P'Q'R'S' is decreased from trapezoid PQRS .
Reflection , rotation and translation are rigid motions that produces congruent images and do not change the size of the shapes.
But dilation is not a rigid motion because it changes the size of the shape by using a scale factor.
Hence, the transformation maps trapezoid PQRS onto trapezoid P'Q'R'S' is "Dilation".
Write a real world problem that you would represent with the equation 4x+5=37.
Answers
x=8
37-5=32
32/4=8.
HELP HELP HELP PLEASE!!!!!
What is the area of this polygon?
Answers
Answer: 35.5 [tex]unit^2[/tex]
Step-by-step explanation:
For finding the area of this polygon we can divide it into triangles and rectangle,
By the below diagram,
The area of this polygon = Area of rectangle having dimension 4× 3 + Area of triangle having base 4 unit and height 3 unit +Area of triangle having base 7 unit and height 3 unit + Area of triangle having base 7 unit and height 2 unit,
=[tex]12 + \frac{1}{2}\times 4\times 3 + \frac{1}{2}\times 7\times 3 + \frac{1}{2}\times 7\times 2[/tex]
= [tex]12 + 6 + 10.5 + 7[/tex]
= [tex]35.5\text{ square unit}[/tex]
PLEASE HELP ASAP!!! 42 POINTS
Answers
Answer:Yes, since the slopes are the same and the y-intercepts are different.
HELP FAST!!!
What is the value of x? Enter your answer in the box. x = Triangle with angles labeled x minus 4 degrees, 3 x degrees, and 100 degrees.
Answers
[tex](x-4) +3x + 100 =180 combine like terms 4x + 96 = 180 subtract 96 from both sides 4x = 84 divide both sides by 4 x = 21 [/tex]
To find the value of x in the triangle, set up an equation using the triangle angle sum theorem and solve for x. The value of x is 21 degrees.
The problem involves finding the value of x in a triangle with given angle measures. According to the triangle angle sum theorem, the sum of the angles in any triangle is always 180 degrees. In this case, we are given two expressions for the angles in terms of x: x - 4 degrees and 3x degrees, plus a given angle of 100 degrees.
To solve for x, set up an equation using the given angles:
x - 4 + 3x + 100 = 180
Combine like terms to solve for x:
4x - 4 + 100 = 180
4x + 96 = 180
4x = 180 - 96
4x = 84
x = 84 / 4
x = 21
Which expression has an equivalent value to x^2 + 9x + 8 for all values of x?
(x + 1)(x + 8)
(x + 2)(x + 6)
(x + 4)(x + 4)
(x + 5)(x +4)