Answer:
So, the vertex form of your function is f(x)=2*(x+2)^2+7
The vertex is at (-2|7)
This is the graph of your function.
vertex point at (-2|7)
Step-by-step explanation:
f(x)=2*x^2+8*x+15
f(x)=2*(x^2+4*x+15/2) ( Factor out )
f(x)=2*(x^2+4*x+(2)^2+-1*(2)^2+15/2) ( Complete the square )
f(x)=2*((x+2)^2+-1*(2)^2+15/2) ( Use the binomial formula )
f(x)=2*((x+2)^2+1*7/2) ( simplify )
f(x)=2*(x+2)^2+7 ( expand )
A medical helicopter flies about 150 miles per hour. Use the map and the Pythagorean Theorem to determine approximately how long it will take the helicopter to reach the hospital from the crash site.
Assuming the crash site is (3, 4) and the hospital is (7, 8), the distance between the two points is approximately 5.6 miles.
What is miles?Miles is a unit of distance measurement, equal to 5,280 feet, or 1,760 yards. Miles are often used to measure the distance between two points, such as the distance between two cities. Miles are also used to measure the distance traveled, such as the number of miles a car has driven.
Using the Pythagorean Theorem, the distance between the crash site and the hospital can be determined. Assuming the crash site is (3, 4) and the hospital is (7, 8), the distance between the two points is approximately 5.6 miles.
To calculate the time it will take the medical helicopter to reach the hospital, divide the distance (5.6 miles) by the speed (150 miles per hour). This gives a total time of approximately 37.3 minutes.
It is important to remember that this is an approximation, as wind, visibility, and other factors can affect the helicopter's speed. Additionally, the helicopter may need to make adjustments to its course due to obstacles or other factors. As such, the actual time it takes the helicopter to reach the hospital may be longer or shorter than this estimate.
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Joaquin hikes 10 miles in a straight line then makes a left turn and hikes an additional 12 miles in a straight line. What is the shortest distance to where he started?
Answer:
15.6204994
Step-by-step explanation:
Pythagoras Theorem
10^2 + 12^2 = 100 + 144
sqrt 244 = 15.6204994
Ahmad and Wei Xiang receive the same salary. Every month Ahmad saves 7 /9 of his salary while Wei Xiang saves 5 /7 of his salary. Every year Ahmad saves $2016 more than Wei Xiang. Find the monthly salary of Ahmad.
The monthly salary of Ahmed will be $4536.
What is an expression?In mathematics, an expression is a combination of mathematical symbols, such as numbers, variables, and operators, that represents a mathematical quantity or relationship.
Let's say their monthly salary is $x.
Ahmad saves 7/9 of his salary, so he saves (7/9)x each month.
Wei Xiang saves 5/7 of his salary, so he saves (5/7)x each month.
We know that Ahmad saves $2016 more than Wei Xiang each year. In other words:
[tex]\dfrac{7}{9}x\times12 - \dfrac{5}{7}\times 12 = $2016[/tex]
Simplifying this equation, we get:
[tex]\dfrac{28}{63}x = $2016[/tex]
Multiplying both sides by 63/28, we get:
x = $4536
Therefore, their monthly salary of Ahmad is $4536.
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need help with part a part b and par c
Answer:
A 4/15 B 11/15 C 4/15
Step-by-step explanation:
A
1-2/5-1/3
15/15-6/15-5/15
4/15
B 2/5+1/3
6/15+5/15
11/15
C
Answer in part A
What is the domain of the function [tex]f(x)=\frac{2}{5} \sqrt{x}[/tex]
The domain of the function f(x) = 2/5√x is equal to {0, ∞}.
What is a domain?A domain refers to the set of all real numbers (x-values) for which a particular function is defined.
How to identify the domain any graph?In Mathematics, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain:
Domain = {0, ∞}.
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Find the zeros of the function f(x) = - 1.9x squared- 4.3x + 1
Answer:
x = sqrt(2609)/38 - 43/38 or x = -43/38 - sqrt(2609)/38
Step-by-step explanation:
Solve for x:
-1.9 x^2 - 4.3 x + 1 = 0
-1.9 x^2 - 4.3 x + 1 = -(19 x^2)/10 - (43 x)/10 + 1:
-(19 x^2)/10 - (43 x)/10 + 1 = 0
Multiply both sides by -10/19:
x^2 + (43 x)/19 - 10/19 = 0
Add 10/19 to both sides:
x^2 + (43 x)/19 = 10/19
Add 1849/1444 to both sides:
x^2 + (43 x)/19 + 1849/1444 = 2609/1444
Write the left hand side as a square:
(x + 43/38)^2 = 2609/1444
Take the square root of both sides:
x + 43/38 = sqrt(2609)/38 or x + 43/38 = -sqrt(2609)/38
Subtract 43/38 from both sides:
x = sqrt(2609)/38 - 43/38 or x + 43/38 = -sqrt(2609)/38
Subtract 43/38 from both sides:
Answer: x = sqrt(2609)/38 - 43/38 or x = -43/38 - sqrt(2609)/38
Last year, 89 musicians attended a jazz camp, and 15 of them were bassists. What is the experimental probability that the first musician to sign up will be a bassist? Write your answer as a fraction or whole number. P(bassist)=
The experimental probability that the first musician to sign up will be a bassist is 0.1685.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that, last year, 89 musicians attended a jazz camp, and 15 of them were bassists.
Total number of outcomes =89 and the number of favorable outcomes = 15
So, P(bassist)= 15/89
= 0.1685
Therefore, the experimental probability that the first musician to sign up will be a bassist is 0.1685.
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Answer:
15/89
Step-by-step explanation:
Someone help pleaseee
To prove two triangles are congruent, you can use one of the following methods: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), or Hypotenuse-Leg (HL) for right triangles only.
Methods for Proving Triangles CongruentTo prove that two triangles are congruent, there are several methods, including:
Side-Side-Side (SSS) Congruence: If the three sides of one triangle are equal to the three sides of the other triangle, then the triangles are congruent.
Side-Angle-Side (SAS) Congruence: If two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle, then the triangles are congruent.
Angle-Side-Angle (ASA) Congruence: If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the triangles are congruent.
Angle-Angle-Side (AAS) Congruence: If two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of the other triangle, then the triangles are congruent.
Hypotenuse-Leg (HL) Congruence (for right triangles only): If the hypotenuse and one leg of one right triangle are equal to the hypotenuse and the corresponding leg of the other right triangle, then the triangles are congruent.
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PLEASE HELP!! I NEED IT DONE ASAP!!
Write the sentence as an equation:
367 equals the quotient of n and 204
367= n/204 ????? maybe
) how does one unit increase in x1 or x2 change the log odds and odds of the event that y = 1
A one unit increase in x1 will increase the odds by exp(b1) times, and a one unit increase in x2 will increase the odds by exp(b2) times.
One unit increase in x1 or x2 will increase the log odds and odds of the event that y = 1. This is because the log odds and odds are directly related to the values of x1 and x2.
Specifically, if we have a model where the log odds of y = 1 is given by:
log odds = b0 + b1*x1 + b2*x2
Then a one unit increase in x1 will increase the log odds by b1 units, and a one unit increase in x2 will increase the log odds by b2 units.
Similarly, if we have a model where the odds of y = 1 is given by:
odds = exp(b0 + b1*x1 + b2*x2)
Then a one unit increase in x1 will increase the odds by exp(b1) times, and a one unit increase in x2 will increase the odds by exp(b2) times.
In both cases, the increase in the log odds and odds of the event that y = 1 is directly related to the values of b1 and b2, which are the coefficients of x1 and x2 in the model.
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Hannah can rake and fill 9.8 bags of leaves each hour. How many bags of leaves will Hannah rake and fill in 8 hours?
a month is randomly chosen what is the probablitly that the month has 31 days
The probability of choosing a month with 31 days is the number of months with 31 days divided by the total number of months.
What is the probability?
Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.
There are 12 months in a year, and 7 of them have 31 days. Therefore, the probability that a randomly chosen month has 31 days is:
P(month has 31 days) = 7/12
This is because each month is equally likely to be chosen, and there are 7 months with 31 days out of a total of 12 months.
Hence, the probability of choosing a month with 31 days is the number of months with 31 days divided by the total number of months.
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PLS HELP: WILL GIVE BRAINLIEST
(see image)
Answer:i forgott sorry
Step-by-step explanation:
Answer:
Step-by-step explanation: I will have to ask a pro as I am a newbie helper.
A small town's population has been growing at a rate of 3% per year. The initial population of the town was 8,500. A nearby town had an initial population of 12,250 people but is declining at a rate of 2% per year.
Write two equations to model the population of each town. Let pa represents the first town's population and t represents years. Let pb represents the second town's population and t represents years.
Use your equation to predict the number of years when the two towns will have the same population. About how many people will be in each town at that time?
By using natural logarithm, both towns will have about 15,929-15,942 people at that time.
Explain about natural logarithm ?
The natural logarithm, denoted by ln(x), is a mathematical function that is the inverse of the exponential function. It is a logarithmic function with a base of e, where e is a mathematical constant approximately equal to 2.71828.The natural logarithm of a positive number x is the power to which e must be raised to obtain x. In other words, if y = ln(x), then [tex]e^y = x.[/tex]
According to the question :
For the first town, the equation to model the population is:
[tex]pa = 8500(1 + 0.03)^t[/tex]
For the second town, the equation to model the population is:
[tex]pb = 12250(1 - 0.02)^t[/tex]
To find when the two towns will have the same population, we can set pa = pb and solve for [tex]t:8500(1 + 0.03)^t = 12250(1 - 0.02)^t[/tex]
Dividing both sides by 8500:(1 + 0.03)^t = 1.4412
Taking the natural logarithm of both sides:
t ln(1.03) = ln(1.4412)Solving for t:t = ln(1.4412)/ln(1.03) ≈ 16.6 years
Therefore, the two towns will have the same population in about 16.6 years.
To find the population at that time, we can substitute t = 16.6 into either equation.
Using the first equation, we get: [tex]pa = 8500(1 + 0.03)^16.6 = 15,929[/tex]
Using the second equation, we get: [tex]pb = 12250(1 - 0.02)^16.6 ≈ 15,942[/tex]
So, both towns will have about 15,929-15,942 people at that time.
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Scientists researching amphibians put tags on 36 frogs in a wetland area. Later, the scientists captured 100 frogs, of which 15 had tags. To the nearest whole number, what is the best estimate for the frog population
The best estimate for the frog population is 42.
How to estimate the population?We can use a proportion to estimate the frog population based on the number of tagged frogs and the proportion of tagged frogs in the second sample.
If we assume that the proportion of tagged frogs in the second sample is representative of the proportion of tagged frogs in the overall population, then we can set up a proportion:
tagged frogs / total sample = tagged frogs in population / total population
Using the values given in the problem, we can write:
36 / 100 = 15 / total population
Solving for the total population:
Total population = (100 x 15) / 36
Total population = 41.67
Rounding this to the nearest whole number, we get an estimate of 42 frogs in the population. Therefore, the best estimate for the frog population is 42.
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Divide
75 points for answer
On solving the question the provided answer will be as Therefore, the equation quotient is 4x^2 - 8x + 22, and the remainder is -26. So we can write: 4x^3 + 6x + 18 = (x+2)(4x^2 - 8x + 22) - 26
What is equation?The equals sign (=) is used in mathematical equations to denote equality between two assertions. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in mathematics. For instance, the equal sign places a space between the integers in the formula, which is 3x + 5 = 14. The relationship between each line on each side of a character can be expressed mathematically. Frequently, the logo and the specific component of software are the same. such as, for example, 2x - 4 = 2.
4x^2 - 8x + 22
---------------------
x+2 | 4x^3 + 0x^2 + 6x + 18
- (4x^3 + 8x^2)
---------------
-8x^2 + 6x
- (-8x^2 - 16x)
--------------
22x + 18
- (22x + 44)
---------
-26
Therefore, the quotient is 4x^2 - 8x + 22, and the remainder is -26. So we can write:
4x^3 + 6x + 18 = (x+2)(4x^2 - 8x + 22) - 26
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i need so much help please ;-;
Step-by-step explanation:
1) B
2) D
3) C
4) D
5) C
6) C
question 5 might b wrong if they r including the 3 year old then it should have like if not then don't use the line
Answer:
1. A
2. C
3. D
4. C
5. B
6. B
Step-by-step explanation:
A is greater than, B is less than, C is greater than or equal to, and D is less than or equal to. Hope this helps :)
Jerry's Fish Shack claims that 16% of its employees are late to work once a week. The manager surveyed 25 employees and found that actually 20% are late to work once a week. What does the test statistic calculation look like in this situation for an appropriate hypothesis test?
Answer:
Step-by-step explanation:z=.2-.16 / √.156(.84)/25
took the test
Answer:
[tex]z =\frac{0.20 - 0.16}{\sqrt{\frac{0.16 * 0.84}{25}} }[/tex]
This is the correct option.
Have a productive learning day today!
In calcium carbonate the masses of calcium carbon and oxygen are in the ratio 10:3:12.when 200 gram of a coumbond was analysing.it was contain 80 grams of calcium,30gram carbon and 90gram oxygen is it calciumcarbonate
From the given information provided, the 200gm of compound that was analysed is not calcium carbonate.
To determine whether the given compound is calcium carbonate, we need to check whether the ratio of masses of calcium, carbon, and oxygen in the compound is 10:3:12, as it is for calcium carbonate.
Let's first calculate the total mass of the compound using the given masses of calcium, carbon, and oxygen:
Total mass = mass of calcium + mass of carbon + mass of oxygen
Total mass = 80 g + 30 g + 90 g
Total mass = 200 g
The total mass of the compound is indeed 200 g, which matches the given information.
Now, let's calculate the ratio of masses of calcium, carbon, and oxygen in the compound:
Ratio of masses = mass of calcium : mass of carbon : mass of oxygen
Ratio of masses = 80 g : 30 g : 90 g
Ratio of masses = 8 : 3 : 9
We can see that the ratio of masses is not exactly 10:3:12, which is the ratio for calcium carbonate. Therefore, we cannot conclude that the given compound is calcium carbonate.
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if (a) degree and 2a degree are a pair of co interior angles between parallel lines find (a) degree and 2a degree(
The solution is, The function is zero degree.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
We have the following function:
f (x) = 2a ^ 2b + 3a ^ 3b ^ 2 + 2a ^ 2b ^ 4
We note that the function depends on x because it is f (x).
However, there is no variable x in the function.
Therefore we can assume that the function is constant, since:
a = constant
b = constant
Therefore, the degree of the function is zero
Answer:
The function is zero degree.
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The complete question:
Given f(x)=2a^2b+3a^3b^2+2a^2b^4 what is the degree?
PLEASE HELP WITH THIS !! WILL GIVE BRAINLIEST
The table that represents a linear relationship that is also proportional is:
X Y
-10 -5
1 -3
2 -1
What is function?In mathematics, a function is a rule that assigns to each element in a set (called the domain) a unique output value in another set (called the range or codomain). In other words, a function is a relationship between an input (or independent variable) and an output (or dependent variable), where each input corresponds to exactly one output. This relationship can be represented in different ways, such as through an algebraic equation, a graph, or a table of values. Functions are a fundamental concept in mathematics and are used to model and analyze many real-world phenomena. They have a wide range of applications in various fields, including physics, engineering, economics, and computer science.
Here,
To calculate the ratio of Y to X for each pair of values in the table:
For the first pair (-10, -5):
Ratio of Y to X = (-5) / (-10) = 0.5
For the second pair (1, -3):
Ratio of Y to X = (-3) / (1) = -3
For the third pair (2, -1):
Ratio of Y to X = (-1) / (2) = -0.5
As we can see, the ratios are all different, which means that the relationship is not proportional. Therefore, this table does not represent a linear relationship that is also proportional.
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A car left Birdwood at 8:35 am and travelled to Rayville, a distance of 150 km, arriving at 11:05 am. What was the average speed of the trip? pls show working
Answer:
17.96 mph is the answer to this question
The cross-country coach later determines that the length of the football field is 120 yards. All students must run five laps. Using your answer from Part A, determine the actual number of yards that each athlete must run in the tryouts.
In order to make the team, students must complete the laps in 6 minutes. How quickly must they run each lap? I got 4x t 140 for part a
Each athelete have run 340 yards.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
let x be the length of field.
so, width = x - 70
So, length = 120
then width = 120 -70 = 50
So, each athlete have to run
= 2 (120 + 50)
= 2 x 170
= 340 yard
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When the sample mean equals 25 and the sample standard deviation equals 5, the standardized value of 15 equals ______.A. 2.00B. -2.00C. 3.00D. -3.00
The standardized value of 15 is -2.00 which is option B.
The standardized value of 15 when the sample mean equals 25 and the sample standard deviation equals 5 is -2.00.
Standardized value, also known as z-score, is a measure of how many standard deviations a data point is from the mean. It is calculated using the formula:
z = (x - μ)/σ
where z is the standardized value, x is the data point, μ is the sample mean, and σ is the sample standard deviation.
In this case, the sample mean (μ) is 25, the sample standard deviation (σ) is 5, and the data point (x) is 15. Plugging these values into the formula, we get:z = (15 - 25)/5z = -10/5z = -2.00
Therefore, when the sample mean equals 25 and the sample standard deviation equals 5, the standardized value of 15 equals -2.00, i.e., option B
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Find the value of x round the anwser to nearest tenth
Answer:
The value of x of given triangle is 23.77 .
Explain the Subtraction of negative number on number line
Answer:example -17 + -2=21
Step-by-step explanation: plus times minus is minus times minus = plus we use the sign of the larger number
line q has an eqaution of y= -10/9x +2. line r includes the point (9, -3) and is parallel to line q. What is the eqaution of line r.
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of line Q
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{10}{9}}x+2\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is -10/9 and it passes through (9 , -3) for line R
[tex](\stackrel{x_1}{9}~,~\stackrel{y_1}{-3})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{10}{9} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{- \cfrac{10}{9}}(x-\stackrel{x_1}{9}) \implies y +3= -\cfrac{10}{9} (x -9) \\\\\\ y+3=-\cfrac{10}{9}x+10\implies {\Large \begin{array}{llll} y=-\cfrac{10}{9}x+7 \end{array}}[/tex]
Peyton is a sprinter who can run the 40-yard dash in 4.5 seconds. He converts his speed into miles per
hour, as shown below.
402 4:5
(1)
(2)
40 yd
4.5 sec
5280 ft
1 ini
.
3 ft
I yd
Which ratio is incorrectly written to convert his speed?
3 ft
60 sec
1 min
1 yd
5280 ft
1 mi
(3)
60 sec 60 min
1 min
1 hr
60 min
1 hr
●
RELA
3ft
Tyd
The ratio which is incorrectly written to convert the speed is given by the relation ( 5,280 feet / 1 miles )
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the speed of Peyton be represented as A
Now , the value of A is
A = ( 40 / 4.5 ) yards / seconds
Now , to convert the following speed to miles per hour , we use the ratio as
The proportion is A = ( 40 yards / 4.5 seconds ) / x ( 3 feet / 1 yard ) x ( 1 mile / 5280 feet ) x ( 60 second / 1 minute ) x ( 60 minute / 1 hour )
Or the proportion can be simplified as
1 mile = 1760 yard
And , 1 hour = 3600 seconds
So , A = ( 40 / 4.5 ) x ( 3600 / 1760 )
A = 18.18 miles per hour
And , the proportion is A = ( 40 yards / 4.5 seconds ) / x ( 3 feet / 1 yard ) x ( 1 mile / 5280 feet ) x ( 60 second / 1 minute ) x ( 60 minute / 1 hour )
Therefore , the incorrect ratio is ( 5,280 feet / 1 miles )
Hence , the proportion is solved
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In 2002, a group of investors invested $100,000 at 3.5% for 1 year. In 2003, interest rates climbed to 5.5%. How much more money would the investors have made by investing the same amount of money at the 2003 interest rate? $200.00 $2,000.00 $9,000.00 $20,000.00
The investors would have made $2,000 more by investing the same amount of money at the 2003 interest rate. The answer is $2,000.00.
What is the simple interest?
Simple interest is a method of calculating the interest on a loan or investment, where the interest rate is applied only to the initial principal amount.
The interest earned on an investment can be calculated using the formula:
interest = principal x rate x time
where principal is the initial amount invested, rate is the interest rate, and time is the length of time the money is invested.
Using this formula, we can calculate the interest earned on the $100,000 investment at 3.5% for 1 year:
interest = $100,000 x 0.035 x 1 = $3,500
In 2003, the interest rate increased to 5.5%. If the investors had invested the same $100,000 at this rate, the interest earned would be:
interest = $100,000 x 0.055 x 1 = $5,500
The difference in interest earned between the two investments is:
$5,500 - $3,500 = $2,000
Hence, the investors would have made $2,000 more by investing the same amount of money at the 2003 interest rate. The answer is $2,000.00.
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Find the inverse of the function, f(x) = ( x−2)³ − 3.
Please show all work in finding the inverse.
Answer:
f(x)^-1=[tex]\sqrt[3]{x+3}[/tex]+2
Explanation:
f(x) = ( x−2)³ − 3
y=( x−2)³ − 3
y+3= ( x−2)³
[tex]\sqrt[3]{y+3}[/tex]=x-2
x=[tex]\sqrt[3]{y+3}[/tex]+2
f(x)^-1=[tex]\sqrt[3]{x+3}[/tex]+2
