To find the equation of a parabola given the vertex and one point, use the vertex form of a parabola equation: y = a(x - h)² + k.
Explanation:To find the equation of a parabola given the vertex and one point, you can use the vertex form of a parabola equation: y = a(x - h)² + k. Here's how:
Determine the values of h and k from the given vertex.Use the given point to substitute the values of x and y in the vertex form.Solve for a to find the equation of the parabola.For example, if the vertex is (2, 3) and the point is (4, 5), the equation of the parabola would be y = 1(x - 2)² + 3.
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The flag of a country contains an isosceles triangle. (Recall that an isosceles triangle contains two angles with the same measure.) If the measure of the third angle of the triangle is 35° more than three times the measure of either of the other two angles, find the measure of each angle of the triangle. (Recall that the sum of the measures of the angles of a triangle is 180°.)
During the 2005 football season, Team Tackle beat Team Sack by 5 points. If their combined scores totaled 89, find the individual team scores.
What is the length of the hypotenuse of an isosceles right triangle with an area of 32?
A female grizzly bear weighs 500 pounds. after hibernating for 6 months, she only weighs 200 pounds. what is the mean change in weight per month
Mean change is the average change over an entire data set.
The mean change in weight per month is 50 pounds.
What is mean change?Mean change is the average change over an entire data set.
We have,
The weight of the bear = 500 pounds
After 6 months the weight of the bear = 200 pounds
The change in weight of the bear in 6 months = 300 pounds
We can write it as:
6 months = 300 pounds
We need to find the weight change in one month so we need to make 6 months into 1 month by dividing both sides by 6.
So,
6/6 month = 300/6 pounds
1 month = 50 pounds
Thus the mean change in weight per month is 50 pounds.
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WHAT IS THE EQUATION OF POINT SLOPE FORM
y-y2= m(x-x2)
hope that helped
If w= the weight of trout. Which algebraic expression represents the phrase below?
Product means multiplication.
Given w= weight of a trout.
So, we need to convert "product of 16 and weight of trout: w " into an algebraic expression.
So, product of 16 and w can be written as 16*w or simply 16w.
Hence, B is the correct choice.
Answer:
B
Step-by-step explanation:
Hope this helps!
How to solve nonlinear equations using iteration method?
Vectors...
Let u = <-3, -5>, v = <-3, 1>. Find u + v.
Answer:
u + v = <-3 + -3, -5 + 1> = <-6 , -4>
u + v = <-6 , -4>
Step-by-step explanation:
I hope this helped you.
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A hexadecimal number is a number written in the base 16 number system.â
a. True
b. False
A hexadecimal number is a number written in the base 16 number system which is true.
What is the number system?A way of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It describes the mathematics and algebraic structure of the numbers and gives each number a distinct representation.
The types of the number system are as follows:
Decimal Number System - There are only ten numbers and the base is 10.Binary Number System - There are only two numbers and the base is 2.Octal Number System - There are only eight numbers and the base is 8.Hexadecimal Number System - There are only sixteen numbers and the base is 16.A hexadecimal number is a number written in the base 16 number system which is true.
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PART A: Maria rented a coat at $285 for 3 days. If she rents the same coat for 60 days, she has to pay a total rent of $510. Write an equation in standard form to represent the total rent (y) that Maria has to pay for renting the coat for x days.
PART B: Write the equation obtained in Part A using function notation.
PART C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.
the length of a rectangle is 2 cm less than 7 times the width.the perimeter is 60 cm. find the width and length
4 and 26 are the width and length
Which postulate or theorem proves that △ RNM and △ QNP are congruent?
A) HL congruence theorem
B) SAS congruence postulate
C) AAS congruence theorem
D) SSS congruence postulate
Answer:
B) SAS congruence postulate
Step-by-step explanation:
We have marked that RN and NQ are congruent. We also have marked that MN and NP are congruent.
∠MNR≅∠QNP because they are vertical angles. Vertical angles are opposite angles that share only a vertex; these are vertical angles so they are congruent.
This gives us two sides and an included angle; this is SAS.
B) SAS congruence postulate proves that △ RNM and △ QNP are congruent
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know two triangles are congruent when we have at least three respective sides or angles or both that are same as the other sides or angles of a triangle.
We also know that vertically opposite angles have the same measures.
here the vertically opposite angles are ∠RNM and ∠PNQ.
It is given that side RN is congruent to side NQ and side PN is congruent to side MN.
∴ It is proven by SAS congruence postulate.
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A bakery makes donuts at the rate of 225 per hour. How long will it take the bakery to fill an order of 500 donuts?
solve for v
160=11-v
If ABC DEC, what is the value of x?
x = 8
x = 5
x = 4
x = 1
x = 2
Answer:
Option D. x = 1
Step-by-step explanation:
If the two triangles Δ ABC and ΔDEC are similar then there corresponding sides will be in the same ratio.
Now using this theorem in these triangles
[tex]\frac{AB}{DE}=\frac{BC}{EC}[/tex]
Now it has been given
AB = (4x - 1)
BC = 4
EC = 4
DE = x + 2
By putting these values in the formula
[tex]\frac{4x-1}{x+2}=\frac{4}{4}=1[/tex]
We cross multiply on both the sides
(4x - 1) = (x + 2)
4x - x = 1 + 2
3x = 3
x = 1
Option D. x = 1 is the answer.
What would '6 meters to 60 meters' be in a ratio
Which point is an x-intercept of the quadratic function
f(x) = (x – 8)(x + 9)?
If Dominik completes a project by himself, it will take him 8 hours. Working with Katarina, it will take them 5 hours. If they work together, what is the missing value from the table that represents the part of the project Dominik will complete? 8r 8(5) r (5)
Answer:
answeerits (D) on ed
Step-by-step explanation:
Evaluate the expression -6×2×(-2)×(-5)×(-3)
Doris put $4000 in a 2-year CD paying 6% interest, compounded monthly. After 2 years, she withdrew all her money. What was the amount of the withdrawal?
a. 4000.00
B. $4214.41
C. $4508.64
D. $4448.13
A triangle has three different integer side lengths and a perimeter of 20 units. What is the max length of any one side?
Final answer:
Using the Triangle Inequality Theorem and given a perimeter of 20 units for a triangle with integer side lengths, the maximum length of one side is found to be 15 units.
Explanation:
To determine the maximum length of one side of a triangle with integer side lengths and a perimeter of 20 units, we must apply the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Given a perimeter of 20 units, if we denote the longest side as x, and the other two sides as y and z, we must satisfy two conditions:
x + y + z = 20 (perimeter condition)
x < y + z (Triangle Inequality Theorem)
Since the triangle has different integer side lengths, the largest x can be is when y and z are consecutive integers because this allows for the largest possible x. If we try the smallest integers, 1 and 2, for y and z, their sum is 3. To satisfy the triangle inequality, the largest possible integer for x would be 20 - 1 - 2 = 17. However, this does not satisfy the inequality x < y + z, because 17 is not less than 3.
Next, we increase y and z to 2 and 3, respectively, which sums up to 5. Thus, for x, we have 20 - 2 - 3 = 15. Since 15 is less than 2 + 3, it satisfies the condition required by the Triangle Inequality Theorem. Therefore, the maximum length of any one side of the triangle is 15 units.
Which number produces a rational number when added to 1/5?
Jasmine has $15 dollars and saves $2.50 every month. Radha has $0 and saves $3.50 every month. Jasmine’s savings after x months can be represented by the function f(x) = 2.5x + 15. Radha’s savings after x months can be represented by the function g(x) = 3.5x. a. After how many months will they both have the same amount in savings? Find the values of x for which f(x) = g(x). b. Explain how to check your work. c. Explain what the graph of the two functions would look like.
2.5x+15 = 3.5x
subtract 2.5x from both sides
15 =x
15 months
Complete the equation of the line through (4,-8) and (8,5).
Use exact numbers.
y=_______ Topic:
Slope-intercept from two points.
The equation of the line that passes through (4, -8) and (8, 5) in slope intercept form is y = 13 / 4 x - 21
Slope intercept form of a lineThe slope intercept form of a line is represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore,
(4, -8) and (8, 5)
m = 5 + 8 / 8 - 4
m = 13 / 4
Therefore, using (8, 5)
5 = 13 / 4(8) + b
5 = 26 + b
b = 5 - 26
b = -21
Hence, the equation is as follows:
y = 13 / 4 x - 21
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A rectangle has length x+9 and width 2x-1 what are the areas of the rectangle
In beijing in 2008 the womens 3,000 meter steeplechase became an olympic event what is the distence in kilometer
Explain how to write and evaluate an algebraic expression that represents the situation. The blueberries were divided equally into six bowls. Evaluate when b = 210.
The variable is the number of blueberries, the operation is division, and the constant is 6. Write the division expression as the fraction, b/6 . To evaluate, substitute 210 in for the variable, b, and simplify. 210 divided by 6 is 35. So each bowl has 35 blueberries.
The algebraic expression can be written in terms of the variable b and and evaluated as b/6 = 210/6 = 35
According to the question;
The blueberries were divided equally into six bowls;Hence, the algebraic expressions is;
b/6where, b = total number of blueberries
Hence, when b= 210
The number of blueberries in each bowl is; 210/6 = 35
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Karen's penny bank is 1/3 full. After she removes 240 pennies, it is 1/9 full. How many pennies can Karen's bank hold?
The difference between the bank being 1/3 and 1/9 full equals 240 pennies, so 1/9 of the bank's capacity equals 120 pennies. So, Karen's bank can hold a total of 1080 pennies.
Explanation:This is a mathematics problem dealing with fractions and subtraction. From the problem, we understand that after Karen removes 240 pennies, the bank is 1/9 full from previously being 1/3 full. So, the difference between 1/3 and 1/9, which is 2/9, accounts for the 240 pennies that were removed.
To find out the total capacity of the penny bank, you need to consider that 1/9 (the fraction representing the bank's fill level after removal of the 240 pennies) is equivalent to 120 pennies (half of 240, as 2/9 of the capacity is 240 pennies). This means that the total capacity of the bank (comparable to 9/9 of the fraction) is 120 pennies times 9, which equals to 1080 pennies.
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The admission fee at an amusement park is $2.00 for children and $5.60 for adults. On a certain day, 352 people entered the park, and the admission fees collected totaled 1280 dollars. How many children and how many adults were admitted?
What is the value of X
180 - 70 - 42 = 68
x = 68 degrees