The graph of g(x) compare to the graph of the function[tex]f(x)=x^2[/tex] is; identical.
What is a solution to a system of equations? (SOLUTION GRAPHICALLY)For a solution to be the solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, the solution to a system is the intersection of all its equation at a single point.
We are given that;
[tex]g(x)=(x-3)^2+9[/tex] and [tex]f(x)=x^2[/tex]
The vertex form of a quadratic function is given by:
[tex]g(x) = a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola.
Now Comparing [tex]g(x)=(x-3)^2+9[/tex] to [tex]f(x)=x^2[/tex]we can see that g(x) is the result of translating the graph of f(x) horizontally by 3 units to the right and vertically by 9 units upward.
The vertex of g(x) is (3, 9), that is obtained by shifting the vertex of f(x) at the origin (0, 0) to the right by 3 units and up by 9 units.
Since the coefficient is positive in both functions, both parabolas open upwards.
The shape of the parabolas is the same since both have the same coefficient [tex]x^2[/tex].
Therefore, the graph of g(x) is identical to the graph of f(x), its shape, but it is shifted horizontally and vertically with respect to f(x).
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PLS HELP ONLINE SCHOOL!! I DONT GET IT
Answer:
1:1
Step-by-step explanation:
They look exactly the same so they would equal each other
The government of India declared Rhinoceros as an endangered species. They put tags on 32 rhinoceros and released them. Later, they caught 160 rhinoceros, 12 of them were tagged. Find the best estimate for the rhinoceros population? *
Answer:
Step-by-step explanation:
city X has a population of 3 times 10^5 and city Y has a population of 6 times 10^6. Which statement correctly describes the relationship between the population of city X and city Y
Answer:
The population of city Y is 20 times than that of city X.
Step-by-step explanation:
Given:
City X has a population of 3 times 10^5
City Y has a population of 6 times 10^6.
Question asked:
Which statement correctly describes the relationship between the population of city X and city Y?
Solution:
If we will be able to find the number of times the population of city Y more than that of city X, it will be the best and easy to understand relationship between the population of these two towns:
And we can easily calculate by dividing the population of city Y by population of city X.
[tex]=\frac{6\times10^{6} }{3\times10^{5}} \\ \\ =\frac{6\times10^{6-5} }{3}\ (\frac{a^{m} }{a^{n} }= a^{m-n} )[/tex]
[tex]=\frac{6\times10^{1} }{3} \\ \\ =\frac{60}{3} \\ \\ =20\ times[/tex]
Thus, the population of city Y is 20 times than that of city X.
City Y's population is 20 times larger than that of city X. This is determined by dividing City Y's population by City X's.
Explanation:The relationship between the populations of city X and city Y can be understood by comparing the numbers provided: 3 times 10^5 (or 300,000) for city X and 6 times 10^6 (or 6,000,000) for city Y. It's clear that city Y has a significantly larger population. In fact, city Y's population is 20 times larger than that of city X.
This is calculated by dividing city Y's population (6,000,000) by city X's population (300,000), getting the result 20.
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J+j-60=80 solve for j
Answer:
j=70
im sure of it
Answer:
j = 70
Step-by-step explanation:
j + j - 60 = 80
=> 2j - 60 = 80
=> 2j = 80 + 60
=> 2j = 140
=> j = 140/2
=> j = 70
Kevin is 3 years older then Daniel. Two years ago, Kevin was 4 times as old as Daniel. How old is Kevin now
Answer:
Step-by-step explangghdhc6vyation:
Hhyvvh
Answer:
The answer to your question is Kevin is 6 years old.
Step-by-step explanation:
Process
1.- Assign a letter to Daniel and another letter to Kevin
Daniel = d
Kevin = k
2.- Write equation that help to solve this problem
k = d + 3 equation l
k = 4d equation ll four years ago
3.- Solve the system by substitution. Substitute equation ll in equation l
4d = d + 3
-Solve for d
4d - d = 3
3d = 3
d = 1
-Find k
k = 1 + 3
k = 4
4.- Calculate the age Kevin has now
Kevin's age = 4 + 2
= 6
please hurry I am doing the test right now
The intersection of two streets forms a parallelogram. One street is 40 feet wide. The height of the parallelogram formed is 25 ft. What is the area of the intersection?
A parallelogram has a base of 40 feet and a height of 25 feet.
500 sq ft
560 sq ft
1,000 sq ft
1,120 sq ft
Answer:
The answer is 1,000 sq ft
Step-by-step explanation:
i just finished with 100% on the topic test/quiz
Louis is constructing the perpendicular bisector of GH¯¯¯¯¯¯. He has already constructed an arc as shown.
What should Louis do for his next step?
Place the point of the compass on point G and draw an arc, using GP as the width for the opening of the compass.
Place the point of the compass on point P and draw an arc, using GP as the width for the opening of the compass.
Place the point of the compass on point G and draw an arc, using the same width for the opening of the compass as the first arc.
Place the point of the compass on point G and draw an arc, using GH as the width for the opening of the compass.
Answer:
c. Place the point of the compass on point G and draw an arc, using the same width for the opening of the compass as the first arc.
Step-by-step explanation:
I took the k12 test and it was correct.
To construct the perpendicular bisector of GH, Louis should place the point of the compass on point G and draw an arc using the same opening as the first arc. The intersecting point of these arcs is the midpoint of GH, which separates GH into two equal halves.
Explanation:Louis should place the point of the compass on point G and draw an arc, using the same width for the opening of the compass as the first arc. This is a required step in constructing a perpendicular bisector. After Louis has created this arc, the intersection of the two arcs is the midpoint of GH. If a line is drawn from this point to GH, it will create two equal halves, creating the perpendicular bisector.
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What is the radian measure of an angle whose measure is −420°
Answer:
-7/3 pi radians
Step-by-step explanation:
To convert from degrees to radians, multiply by pi/180
-420 * pi/180
-42/18 *pi
Divide by 6 on the top and bottom
-7/3 pi
Cole plays a bass drum that has a radius of 4 inches. What is the drum’s circumference? Use 3.14 for π.
The circumference of Cole's bass drum is 25.12 inches.
The formula to find the circumference (C) of a circle is C = 2πr, where r is the radius and π is approximately 3.14.
Since Cole's bass drum has a radius of 4 inches, we substitute the values into the formula to get
C = 2 × 3.14 × 4 inches.
So, the circumference of Cole's drum is C = 2×3.14 × 4 = 25.12 inches.
Eight percent of all college graduates hired by companies stay with the same company for more than five years. The probability that in a random sample of 12 such college graduates hired recently by companies, exactly two will stay with the same company for more than five years is
Answer:
0.1835
Step-by-step explanation:
This question can be solved by way of binomial distribution.
Let’s have the probability of success as p which is the probability that they stay with the company for more than five years;
p = 8/100 = 0.08
probability of failure, meaning not staying is q = 1-p = 1-0.08 = 0.92
Now let’s write the expression for the binomial distribution. That would be;
probability = 12C2 * 0.08^2 * 0.92^10
= 0.1835
Probabilities are used to determine the chances of an event.
The probability that exactly two stays more than 5 years is 0.1835
The given parameters are:
[tex]\mathbf{n = 12}[/tex] ---- sample
[tex]\mathbf{x = 2}[/tex] --- selected
[tex]\mathbf{p = 80\%}[/tex] --- sample proportion
So, the probability that exactly two stays more than 5 years is calculated using the following binomial probability:
[tex]\mathbf{P(x) = ^nC_x p^x (1 - p)^{n -x}}[/tex]
So, we have:
[tex]\mathbf{P(x) = ^{12}C_2 (8\%)^2 (1 - 8\%)^{12 -2}}[/tex]
[tex]\mathbf{P(x) = ^{12}C_2 (8\%)^2 (92\%)^{10}}[/tex]
Solve 12C2 using a calculator
[tex]\mathbf{P(x = 2) = 66 \times (8\%)^2 \times (92\%)^{10}}[/tex]
[tex]\mathbf{P(x = 2) = 0.1835}[/tex]
Hence, the probability that exactly two stays more than 5 years is 0.1835
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A circle with center on the origin and point on (4,-2)
The equation of the circle is x² + y²=20
Step-by-step explanation:
The equation of circle is written as
(x-h)² +( y-k)²=r²
x² + y²=r²
The circle passes through (0,0) and (4, -2)
The equation of the circle is x² + y²=20
I have attached the document for the explanation part
What number should Rhianna use for the height of the parallelogram if she uses 28 inches for the base?
Answer:
7
Step-by-step explanation:
But lets not quote me on that. :]
1) On Wednesday 62% of the customers who bought gas at a gas station made additional purchases. There were 350 customers who bought gas. How many of these 350 customers made additional purchases?
Answer:
cant
Step-by-step explanation:
Answer:
Correct answer: x = 217
Step-by-step explanation:
Given:
N = 350 customers
62% made additional purchases
x = ? the number of customers that is made additional purchases
Solution is:
x = (62 / 100) · 350 = 217
x = 217
God is with you!!!
the delivered price of leah st clairs new car is 22450. she makes a 2800 down payment and pays the balance in 36 monthly payments of 612. what total amount did leah pay for the car? how much was the finance charge?
Answer:
Total amount paid for the Car=$24,832
Finance Charge=$2,382
Step-by-step explanation:
Down payment on the Car=$2800
Number of Monthly Installments=36
Amount Paid Per Installment=$612
Total Monthly Installment Paid=36*$612=$22032
Therefore, the Total Amount Paid for the Car=Down Payment+Total Installmental Payment=2800+22032=$24,832
Next, we determine the finance charge.
Finance Charge=Total Amount Paid for the Car - Delivered Price of the Car
=24832-22450
=$2,382
Therefore:
Total amount paid for the Car=$24,832
Finance Charge=$2,382
BRAINLIEST!!!
Which best describes the relationship between the two triangles below?
Triangle M L N is similar to Triangle F G H because of the third angle theorem, Angle M is congruent to angle F, Angle L is congruent to angle G, and Angle N is congruent to angle H.
Triangle M L N may or may not be similar to Triangle F G H because the third angle is unknown.
Triangle M L N is similar to Triangle F G H because of the angle-angle criterion, Angle M is similar to angle F, Angle L is similar to angle G, and Angle N is similar to angle H.
Triangle M L N may or may not be similar to Triangle F G H because the side lengths are unknown.
Given:
In the given ΔLMN, ∠M = 51° and ∠L = 36°
And,
In ΔFGH, ∠F = 51° and ∠G = 36°
To find the suitable option from the given options.
Formula
By Third angle theorem, we have,
If two angles in one triangle are congruent to two angles in another triangle, then the third pair of angles must also congruent.
In given two triangles
ΔLMN and ΔFGH
∠M = ∠F = 51° and
∠L = ∠G = 36°
So, it satisfies the condition of third angle theorem.
Hence,
We can conclude that, Triangle M L N is similar to Triangle F G H because of the third angle theorem, Angle M is congruent to angle F, Angle L is congruent to angle G, and Angle N is congruent to angle H.
Thus, Option a is the correct answer.
Answer:
Triangle M L N is similar to Triangle F G H because of the third angle theorem, Angle M is congruent to angle F, Angle L is congruent to angle G, and Angle N is congruent to angle H.
Step-by-step explanation:
i just took the quiz and i got it right
find the value of x in the given right triangle
Step-by-step explanation:
Given
it is a right angled triangle so
with reference angle x
hypotenuse (h) = 12
base (b) = 5
Now
cos x = b / h
cos x = 5 / 12
x = cos ^-1 ( 5/12)
Therefore x = 65.4°
Hope it will help :)
Answer:
Step-by-step explanation:
The box plot represents the number of math problems on the quizzes for an algebra course. A number line goes from 0 to 16. The whiskers range from 5 to 15, and the box ranges from 8 to 14. A line divides the box at 10. What is the range of the data?
Answer:
D
Step-by-step explanation:
The range of the data is 10.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The range of the data can be determined by finding the difference between the maximum and minimum values.
The maximum value is given by the upper whisker, which is 15, and
the minimum value is given by the lower whisker, which is 5.
Therefore, the range of the data is:
Maximum value - Minimum value = 15 - 5 = 10
So, the range of the data is 10.
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The wheels on the bicycle are circles.The diameter of the large wheel is 3 times longer than the small wheel.How many times greater is the area of the larger circle than the area of the smaller circle
Answer:
The area of the larger circle is 9 times greater than that of the smaller circle.
Step-by-step explanation:
Let d be the diameter of the smaller circle and d be the diameter of the larger circle. If d₁ = 3d
Since Area of a circle A = πd²/4 ⇒ A ∝ d²
Let A be the area of the smaller circle and A₁ be the area of the larger circle.
So, A₁/A = d₁²/d² = (3d)²/d² = 9
A₁/A = 9
A₁ = 9A
So the area of the larger circle is 9 times greater than that of the smaller circle.
Answer:
9 times greater
Step-by-step explanation:
Let radius of small circle b r
radius of big circle = 3×(r) = 3r
Area of small circle = πr²
Area of big circle = π(3r)² = 9πr²
How many times area of big circle is larger = 9πr²/ πr² = 9
Can you please answer this question
Answer: 34.25
Step-by-step explanation:
Answer:
34.3 the real answer is 34.25 but rounded it is 34.3
The radius of a large balloon after it is punctured is represented by the following table:
Time (seconds)
Radius (cm)
401
352
10
302
250
15
20
199
149
Which model for R(t), the radius of the balloon t seconds after it's punctured, best fits the data?
Choose 1 answer:
Answer:
R(t)=401−10t
Step-by-step explanation:
Given the data, there appears to be a negative linear relationship between time and radius as the balloon deflates. This suggests a model of the form R(t) = a - bt best fits the data.
Explanation:The subject matter here is a Mathematical topic related to model fitting - a statistical method that estimates the relationship between variables. In this case, the variables are Time (t) and radius (R). From the given data, it seems that the radius is reducing as the time increases, which likely indicates a negative linear relationship.
We can also observe that the data points reduce at a constant rate (e.g., it goes down by 50 cm every 5 seconds initially), which further supports the idea of a linear model.
Therefore, considering this rate of change and the mathematical relationship between the variables, a linear model of the form R(t) = a - bt (where a is the initial radius and b is the rate of decrease) would likely be the best option.
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The river boat, Delta Duchess, paddled upstream at 12 km/h, stopped for 2 hours of sightseeing, and paddled back at 18 km/h. How far upstream did the boat travel if the total time for the trip, including the stop, was 7 hours?
Answer:
36 km
Step-by-step explanation:
Let time taken by upstream=x hours
Upstream speed=12 km/h
Time spend for sightseeing=2 hours
Total time=7 hours
Traveling time=7-2=5 hours
Time taken by downstream=5-x
Downstream speed=18km/h
Distance=[tex]speed\times time[/tex]
Using the formula
Distance traveled when Delta Duchess paddled upstream=12 x
Distance traveled when Delta Duchess paddled back=18(5-x)
According to question
[tex]12x=18(5-x)[/tex]
[tex]12x=90-18x[/tex]
[tex]12x+18x=90[/tex]
[tex]30x=90[/tex]
[tex]x=\frac{90}{30}=3 hours[/tex]
Substitute the values
Distance traveled when Delta Duchess paddled upstream=[tex]12\times 3=36 km[/tex]
Bargain buy is having an internet sale on electronics a 60 inch television is on sale for $798 the television is regularly priced for 1,050 by what percent did the price of the television decrease
Answer:
Price decrease = 24 %
Step-by-step explanation:
Given:
Initial price of the 60 inch television = $ 1050
Final price of the same television = $ 798
We have to find by what percent did the price of the television decrease.
Let the percent decrease be "x".
Formula to be used:
⇒ [tex]Percent\ decrease =\frac{(Initial\ price) - (Final\ price)}{Initial\ price}\times 100[/tex]
Using the above formula:
And plugging the values.
⇒ [tex]\%\ decrease =\frac{(Initial\ price) - (Final\ price)}{Initial\ price}\times 100[/tex]
⇒ [tex]\%\ decrease =\frac{(1050) - (798)}{1050}\times 100[/tex]
⇒ [tex]\%\ decrease =\frac{252}{1050}\times 100[/tex]
⇒ [tex]\%\ decrease =0.24\times 100[/tex]
⇒ [tex]\%\ decrease =24[/tex]
By 24 percent did the price of the television decreases.
Find the area of the circle given the diameter is 8. Use 3.14 for pi
Answer:
50.27
Step-by-step explanation:
Answer:
50.27
Step-by-step explanation:
A=1 /4 πd squared
A≈50.27
Hope this helps
Analyze the map below and answer the question that follows.
A map of population density in South and Southeast Asia. Darker areas have higher population density. Higher population density areas are Indonesia, the coast of Vietnam, the northern border of India, the eastern coast of India, and Bangladesh.
Areas with higher population density are shown in solid, dark green on the map above. Which of the following areas in India has the highest population density?
A.
the Deccan Plateau
B.
the island of Java
C.
the Ganges Plain
D.
the border region near Pakistan
Answer:
the answer is a
Step-by-step explanation:
i got the question right. please mark me brainliest. look at a population density map of southeast Asia
Answer:
a
Step-by-step explanation:
i did the test
A person sights a boat from 235 feet above sea-level as shown. If the angle of depression from the man to the boat is 21 , then determine the boat's distance to the edge of the cliff to the nearest ten feet.
Answer:
B = 612.2 ft
Step-by-step explanation:
Solution:-
- The elevation of person, H = 235 ft
- The angle of depression, θ = 21°
- We will sketch a right angle triangle with Height (H), and Base (B) : the boat's distance to the edge of the cliff and the angle (θ) between B and the direct line of sight distance.
- We will use trigonometric ratios to determine the distance between boat and the edge of the cliff, using tangent function.
tan ( θ ) = H / B
B = H / tan ( θ )
B = 235 / tan ( 21 )
B = 612.2 ft
Answer:
The distance of the boat from the edge of the cliff is 655.75 ft
Distance of the boat from the base of the cliff is 251.72 ft
Step-by-step explanation:
Height of person above sea level = 235 ft
Angle of depression of sight to the boat from the person = 21°
Therefore, based on similar angle between person and angle of depression and the boat with angle of elevation we have,
Angle of elevation of the location of the person as sighted from the boat θ = 21°
Distance from the edge of the cliff of the boat is then given by;
[tex]Sin\theta = \frac{Opposite \, side \, to\, angle}{Hypothenus\, side \, of\, triangle} = \frac{Height\, of\, person\, above \, ses \, level}{Distance\, of\, boat\, from \, edge\, of \, cliff}[/tex]
[tex]Sin21 =\frac{235}{Distance\, of\, boat\, from \, edge\, of \, cliff}[/tex]
[tex]Distance\, of\, boat\, from \, edge\, of \, cliff=\frac{235}{Sin21 } = \frac{235}{0.358} = 655.75 \, ft[/tex]
Distance of the boat from the base of the cliff is given by
[tex]Distance\, of\, boat\, from \, base\, of \, cliff=\frac{235}{cos21 } = \frac{235}{0.934} = 251.72 \, ft[/tex].
Set 1: 8, 15, 13, 7, 11, 17, 13
Median = 13
Lower quartile = 8
Upper quartile = 15
Range = 10
Interquartile range = 7
Set 2: 8, 15, 13, 7, 11, 17, 13, 100
Median = 13
Lower quartile = 9.5
Upper quartile = 16
Range = 93
Interquartile range = 6.5
Which set contains an outlier?
Which measure of spread was most impacted by the outlier?
The set 2 contains an outlier.
The range measure of spread was most impacted by the outlier.
What is the box-and-whisker plot?A box and whisker plot displays a "box" with its left edge at Q₁, right edge at Q₃, "center" at Q₂ (the median), and "whiskers" at the maximum and minimum.
Given:
Set 1: 8, 15, 13, 7, 11, 17, 13
Median = 13
Lower quartile = 8
Upper quartile = 15
Range = 10
Interquartile range = 7
And Set 2: 8, 15, 13, 7, 11, 17, 13, 100
Median = 13
Lower quartile = 9.5
Upper quartile = 16
Range = 93
Interquartile range = 6.5
Set two contains the value 100 as an outlier.
The range is the component of spread that was most adversely affected by the outlier.
This is due to the fact that set two's median, quartiles, and interquartile range are all closely clustered together, but the range is 93, which is extremely disproportional high compared to any of those other numbers.
Therefore, set 2 contains an outlier.
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30 pts if correct and will mark brainliest
Answer:
{HR H O HY HG TR TO TY TG}
2600
Step-by-step explanation:
We can either get heads or tails on the coin and red yellow green or orange on the spin
HR H O HY HG
TR TO TY TG
There are 26 letters for the first space and 10 digits (0-9) for the second space and 10 digits (0-9) for the 3 space
26 * 10 * 10
2600
Answer:
Option 1
Step-by-step explanation:
A sample space is a collection of all possible outcomes
{Coin,colour}
{H R, H Y, H G, H O, T R, T Y, T G, T O}
find the measure of
Answer:
∠ ABC ≈ 137.9°
Step-by-step explanation:
Using the Cosine rule in Δ ABC
cos B = [tex]\frac{a^2+c^2-b^2}{2ac}[/tex]
with a = 89, b = 144, c = 65
cos B = [tex]\frac{89^2+65^2-144^2}{2(89)(65)}[/tex] = [tex]\frac{7921+4225-20736}{11570}[/tex] = [tex]\frac{-8590}{11570}[/tex] , thus
B = [tex]cos^{-1}[/tex] ( - [tex]\frac{8590}{11570}[/tex] ) ≈ 137.9° ( to the nearest tenth )
At the supermarket, peppers cost $2.19 per pound. Christina buys 2 pounds
of peppers. She pays with a $5.00 bill. How much change does she receive?
Answer:
0.62
Step-by-step explanation:
2*4.19=4.38
5-4.38=0.62
please help and explain too
Answer:
Radius = 5inch
CD = 2.75 cm
Step-by-step explanation:
A) isosceles triangles AC = AD BC = BD BC = AC you join lines up and then do Pythagoras. AC ² = 1/2 * 8 ² + 1/2 6²
AC² = 4sq + 3sq
25sq = 16sq + 9sq
AC² = 25sq = 5inch
Radius = 5inch
B) AB = 8inch CD = 6inch radius = 5 ratio = 4 : 3 : 2.5
AB = 24cm CD = 18 radius = 13cm ratio = 4 : 3 : 2.1
4- 2.1 = 1.9 1.9 distributed = 1.30 + 0.65 + 1 =2.75
so ratio must be 4: 2.75 : 2.1 = 4 : 3 : 2.5
Therefore CD = 2.75 cm
Just to get you started.