Edna says that when (x - 2)2 = 9, that x - 2 = 3. Use complete sentences to explain whether Edna is correct. Use specific details in your explanation.
Answer:x=5,-1
Step-by-step explanation:
Edna says that when \left ( x-2\right )^2=9[/tex]
then x-2=3
such that x=5
but this is not true as when we put the value of x in equation then it will not satisfy the equation.
It can be solved by taking the terms either on LHS or RHS
[tex]\left ( x-2\right )^2-9=0[/tex]
[tex]x-2=\pm 3[/tex]
x=5
x=-1
1. which function is shown on the graph?
f(x)=1/2cosx
f(x)=−1/2sinx
f(x)=−1/2cosx
f(x)=1/2sinx
2. (picture)
3.(picture)
4.(which equation represents the function on the graph?
5. what is the period of the funtion f(x)=cos2x?
Which of the following fractions is in simplest form?
9/16
8/14
6/20
15/35
The correct fraction in simplest form is 9/16. Hence option 1 is true.
Used the concept of the fraction that states,
A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction.
Ask about the simplest form of a fraction.
When a fraction is in the simplest form then the GCD of numerators and denominators would be 1.
From (i);
9/16
Clearly, GCD (9, 16) = 1
Hence this shows the simplest form of a fraction.
Therefore, option 1 is true.
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A new car is purchased for 20300 dollars. The value of the car depreciates at 9.5% per year. What will the value of the car be, to the nearest cent, after 11 years?
Answer:
6670.65
Step-by-step explanation:
After 11 years, the value of the car will be $1,913.50.
Explanation:To find the value of the car after 11 years, we need to calculate the depreciation of the car each year.
The value of the car depreciates at a rate of 9.5% per year, meaning that each year the value of the car will decrease by 9.5% of its current value.
Let's calculate the value of the car after 11 years:
Step 1: Find the depreciation of the car each year.
Depreciation = 9.5% of $20,300 = $1,928.50
Step 2: Calculate the value of the car after 11 years.
Value after 11 years = $20,300 - (11 * $1,928.50)
Value after 11 years = $20,300 - $21,213.50
Value after 11 years = $1,913.50
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Maria has three children. there is two years age difference between each child. the total ages of all three children is 36 years. tina is the youngest child. how old is tina? let t = the age of tina. which formula will calculate tina's age?
t= Tina's age
t+2= second child
t+4= third child
36= age of all children
Add the ages of all children equal to 36 years. Add 2 to each age because there is 2 years age difference between each child.
t + (t+2) + (t+4)= 36
combine like terms
3t + 6= 36
subtract 6 from both sides
3t= 30
divide both sides by 3
t= 10 Tina's age
t+2= 12
(10)+2= 12 age of second child
t+4= 14
(10)+4= 14 age of third child
ANSWER: The formula that will calculate Tina's age is t + (t+2) + (t+4)= 36.
Hope this helps! :)
HELP!!! What is the slant height x of the square pyramid? Express your answer in radical form.
To find the slant height of a square pyramid, we can use the Pythagorean theorem. The theorem should be applied as follows: A² = (y² + h²), to solve for A which is the slant height. Radical form implies that the answer will include the square root symbol.
Explanation:The question asks to find out the slant height x of a square pyramid. In order to do that, we have to invoke the Pythagorean theorem (x² + y² = h²). Here, x represents the slant height, y could be the half of the side of the base of the pyramid and h is the height from the base to the tip of the pyramid. Assuming that the pyramid is a right pyramid, the Pythagorean theorem applies.
So, the equation becomes A² = y² + h², where A is the slant height we are looking for. We solve for A to get, A = √(y² + h²). This is your slant height in radical form.
Please note you would need specific values for y and h to compute the numerical value of A.
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4(x − 3) − 5(x + 1) = 3 Which of the following algebraic properties is not needed to solve this equation?
PLEASE MATH HELP WILL GIVEBRAINLIEST AND 20 POINTS!!!
1.What is the area of a regular hexagon with a side length of 12 cm?
Enter your answer in the box.
Round only your final answer to the nearest hundredth.
2.In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 5 cm?
3.
What is the exact value of sin 30° ?
Enter your answer, as a simplified fraction, in the box.
Which is a true statement about any two congruent chords in a circle? A.They are parallel. B.They are perpendicular. C.They form an angle. D.They are equidistant from the center of the circle.
They are equidistant from the center of the circle because two congruent chords have the same length, angles, and radii meaning the answer would be D.
Please vote Brainliest, thanks.
The statement (D) "They are equidistant from the center of the circle" is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have a statement:
Which is a true statement about any two congruent chords in a circle?
As we know, due to the similar length, angles, and radii of two congruent chords, they are equally spaced from the circle's center.
Thus, the statement (D) "They are equidistant from the center of the circle" is correct.
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CAN SOME ONE HELP ME WITH THIS HURRY PLEASE
If f(x) = 2x - 7, what is the value of f(2)?
A.-3
B.-5
C.5
D.3
What is the image of the point (4,-2) after a rotation 270 degree clockwise about the origin?
Answer:
The image of the point (4, -2) is (2, 4).
Step-by-step explanation:
Since, the rule of rotation 270 degree clockwise about the origin is,
[tex](x,y)\rightarrow (-y,x)[/tex]
Where, (-y,x) is the image of the point (x,y),
Thus, by the above rule,
[tex](4,-2)\rightarrow (-(-2), 4)[/tex]
Hence, the image of the point (4, -2) is (2, 4).
10 POINTS!!! FULL ANSWER WITH FULL STEP BY STEP SOLUTION PLEASE. DO BOTH PARTS OF 3 AND ALL OF 4.
what ones are relatively prime?
A) 11 & 121
B) 35 & 125
C) 39 & 75
D) 34 & 49
Answer:
it is 34 and 49
Step-by-step explanation:
because i'm big smart
1. Use the above figure to answer the following questions.
a. What is the intersection of plane P and plane R?
b. Name three points that are collinear
c. Name plane R in two more ways
d. Name four coplanar points
e. Name a point that lies on both plane P and plane R
The Polynomial Remainder Theorem
The Polynomial Remainder Theorem in mathematics states that the remainder of dividing a polynomial P(x) by (x - a) is P(a). This theorem is linked to the Binomial theorem for series expansions and is useful in graphing and solving polynomials and quadratic equations.
Explanation:The Polynomial Remainder Theorem is a concept in mathematics associated with series expansions and equation graphing. This theorem states for a given polynomial P(x) and a number a, when P(x) is divided by the binomial (x - a), the remainder is P(a). This is a crucial concept when graphing polynomials, as understanding the remainder can assist in predicting the behavior of the polynomial curve. The theorem is tied to the Binomial theorem which provides a series expansion for expressing powers of a sum of terms (a + b)^n in terms of a and b.
To solve quadratic equations, which are second-order polynomials, the Polynomial Remainder Theorem can also be utilized. It can further clarify the solutions of quadratic functions when they are graphed. Furthermore, in the realm of function graphing, the theorem aids in visualizing how different terms contribute to the shape of the polynomial curve.
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kat had 2 3/5 bags of carrots.she gave 3/4 of a bag of carrots To her sister which shows how many bags of carrots kat had left
Which sentence is an example of the distributive property
The distributive property of multiplication is a very useful property that lets you simplify expressions in which you are multiplying a number by a sum or difference. The property states that the product of a sum or difference, such as 6(5 – 2), is equal to the sum or difference of the products – in this case, 6(5) – 6(2).
Remember that there are several ways to write multiplication. 3 x 6 = 3(6) = 3 • 6.
3 • (2 + 4) = 3 • 6 = 18.
Distributive Property of Multiplication over Addition
The distributive property of multiplication over addition can be used when you multiply a number by a sum. For example, suppose you want to multiply 3 by the sum of 10 + 2.
3(10 + 2) = ?
According to this property, you can add the numbers and then multiply by 3.
3(10 + 2) = 3(12) = 36. Or, you can first multiply each addend by the 3. (This is called distributing the 3.) Then, you can add the products.
The multiplication of 3(10) and 3(2) will each be done before you add.
3(10) + 3(2) = 30 + 6 = 36. Note that the answer is the same as before.
You probably use this property without knowing that you are using it. When a group (let’s say 5 of you) order food, and order the same thing (let’s say you each order a hamburger for $3 each and a coke for $1 each), you can compute the bill (without tax) in two ways. You can figure out how much each of you needs to pay and multiply the sum times the number of you. So, you each pay (3 + 1) and then multiply times 5. That’s 5(3 + 1) = 5(4) = 20. Or, you can figure out how much the 5 hamburgers will cost and the 5 cokes and then find the total. That’s 5(3) + 5(1) = 15 + 5 = 20. Either way, the answer is the same, $20.
The two methods are represented by the equations below. On the left side, we add 10 and 2, and then multiply by 3. The expression is rewritten using the distributive property on the right side, where we distribute the 3, then multiply each by 3 and add the results. Notice that the result is the same in each case.
p[x]=5b exponent x what do the a and b in exponential function represent
Vonda works between 30 and 32 hours per week at a hair salon. she pays a one time $250 chair rental fee, and earns $40 per hour that she works. the hours she works are rounded to the nearest quarter hour. the function p(h)=40h−250 represents vonda's weekly pay as a function of hours worked. what is the practical domain of the function?
The practical domain of the function p(h) = 40h - 250 for Vonda's weekly pay is between 30 and 32 hours, inclusive, with increments of 0.25 hours. These values represent all the possible hours Vonda can work in a week.
To determine the practical domain of the function p(h) = 40h - 250, we need to consider the range of hours that Vonda works. The problem states that Vonda works between 30 and 32 hours per week, and her hours are rounded to the nearest quarter hour. Therefore, the possible values for h (in hours) are:
30.0030.2530.5030.7531.0031.2531.5031.7532.00Hence, the practical domain of the function p(h) is all the values between 30 and 32, inclusive, measured in quarter-hour increments.
HEY THERE
please help me in math>>>
One of the parking lot lights at a hospital has a motion detector on it, and the equation (x+10)2+(y−8)2=16 describes the boundary within which motion can be sensed.
What is the greatest distance, in feet, a person could be from the parking lot light and be detected?
Eighty percent of a roof, or 2800 square feet of the roof, has been re-shingled. What is the total area of the roof? a. 22,400 sq ft b. 2240 sq ft c. 3500 sq ft d. 35000 sq ft
Given that "80% of the roof" is same as "2800 square feet of the roof".
Let's consider total area of roof = X square feet.
Then "80 percent of X" = "2800 square feet".
[tex] 80\% \;of X = 2800 \;square \;feet \\\\\frac{80}{100} *X = 2800 \;square \;feet \\\\\frac{4}{5} *X = 2800 \;square \;feet \\\\X = \frac{5}{4}* 2800 \;square \;feet \\\\X = \frac{14000}{4} \;square \;feet \\\\X = 3500 \;square \;feet \\\\ [/tex]
So total area of the roof would be 3500 square feet.
Hence, option C is correct i.e. 3500 square feet.
Some people say that more babies are born in september than in any other month. to test this claim, you take a simple random sample of 150 students at your school and find that 21 of them were born in september. you are interested in whether the proportion born in september is higher than 1/12—what you would expect if september was no different from any other month.
Final answer:
To test whether the proportion of babies born in September is higher than the expected proportion of 1/12, we can use hypothesis testing. Given a sample of 150 students, with 21 of them born in September, we calculate the test statistic, compare it to the critical value, and make a decision.
Explanation:
To test whether the proportion of babies born in September is higher than the expected proportion of 1/12, we can use hypothesis testing. Let's set up the hypotheses:
Null Hypothesis (H0): The proportion of babies born in September is equal to 1/12.
Alternative Hypothesis (Ha): The proportion of babies born in September is greater than 1/12.
We can use a one-sample proportion test to test these hypotheses. Given that we have a simple random sample of 150 students at your school and 21 of them were born in September, we can calculate the sample proportion: 21/150 = 0.14.
Next, we calculate the test statistic using the formula: test statistic = (sample proportion - null proportion) / standard error. The null proportion is 1/12 = 0.0833, and the standard error is √[(null proportion * (1 - null proportion)) / sample size]. Calculating the test statistic gives us: test statistic = (0.14 - 0.0833) / √[(0.0833 * (1 - 0.0833)) / 150] = 2.92 (rounded to two decimal places).
Finally, we compare the test statistic to the critical value(s) at a chosen significance level to make a decision. The critical value(s) depend on the significance level and the direction of the alternative hypothesis. If the test statistic falls in the rejection region (i.e., it is greater than the critical value), we reject the null hypothesis and conclude that the proportion of babies born in September is higher than 1/12.
What transformations change the graph of f(x) to the graph of g(x)? f(x)=x^2 g(x)=(x+3)^2-7
The graph of g is the graph of f translated to the right 3 units and up 7 units
The graph of g is the graph of f translated to the left 3 units and down 7 units
The graph of g is the graph of f translated up 3 units and to the left 7 units
The graph of g is the graph of f translated down 3 units and to the right 7 units
Answer:
The graph of g is the graph of f translated to the left 3 units and down 7 units
Step-by-step explanation:
As you can see, the F(X) graph has its origin on (0,0) since when X is equal to 0, Y will be equal as 0 as well, so having both quadratic graphs, we just have to see how the graph is translated, in this case you just have to make x=0, when X is equal to 0 on g(x) Y=-7, so the graph will be translated 7 units down, the only option you have that has the graph tranlated 7 units down is option 2:"The graph of g is the graph of f translated to the left 3 units and down 7 units"
And that is your correct answer.
Sam is walking to Joe’s house at a rate of 2 miles per hour. Joe left his house at the same time and is walking at a rate of 1.5 miles per hour. If Sam and Joe live 7 miles apart, how long will it take for Sam and Joe to meet?
Can someone check my answer?
For y = x2 − 4x + 3,
Determine if the parabola opens up or down.
State if the vertex will be a maximum or minimum.
Find the vertex.
Find the x-intercepts.
Describe the graph of the equation.
Show all work and use complete sentences to receive full credit.,
Triangle ABC is translated on the coordinate plane below to create triangle A'B'C':
If parallelogram EFGH is translated according to the same rule that translated triangle ABC, what is the ordered pair of point H'?
The new coordinates of Point H' will be (6, -5) after the translation.
Triangle ABC is translated on the coordinate plane below to create triangle A'B'C':
If parallelogram EFGH is translated according to the same rule that translated triangle ABC.
How to find the point after translation?In the triangle, point A is moved 5 units to the right side and down 6 units.
If we count the same amount of space right side and down from point H, we will end up on a point (6, -5).
Therefore, The new coordinates of Point H' will be (6, -5) after the translation.
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What is the length of DD'?
Answer:
The length of DD' is [tex]\sqrt{29}[/tex] or 5.39 units.
Step-by-step explanation:
The distance formula is
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
From the given figure it is clear that the coordinates of D are (2,0) and coordinates of D' are (7,2).
Using distance formula we get
[tex]DD'=\sqrt{(7-2)^2+(2-0)^2}[/tex]
[tex]DD'=\sqrt{25+4}[/tex]
[tex]DD'=\sqrt{29}[/tex]
[tex]DD'\approx 5.39[/tex]
Therefore the length of DD' is [tex]\sqrt{29}[/tex] or 5.39 units.
Whole numbers are written on cards and then placed in a bag. Pilar selects a single card, writes down the number, and then places it back in the bag. She repeats this 46 times.
Pilar calculates the relative frequency of each number card.
Outcome 1 2 3 4 5
Relative Frequency 0.05 0.35 0.26 0.13 0.21
Which statement about Pilar's experiment is true?
The outcomes do not appear to be equally likely, so a uniform probability model is not a good model to represent probabilities in Pilar's experiment.
The outcomes appear to be equally likely, so a uniform probability model is not a good model to represent probabilities in Pilar's experiment.
The outcomes do not appear to be equally likely, so a uniform probability model is a good model to represent probabilities in Pilar's experiment.
The outcomes appear to be equally likely, so a uniform probability model is a good model to represent probabilities in Pilar's experiment.
Answer:
Option 1
The outcomes do not appear to be equally likely, so a uniform probability model is not a good model to represent probabilities in Pilar's experiment.
Step-by-step explanation:
Given :
The outcomes are : 1 2 3 4 5
The Relative Frequency : 0.05 0.35 0.26 0.13 0.21
To find : Which statement about Pilar's experiment is true?
Solution :
We can see the outcomes do not appear to be equally likely.
Since 0.05 and 1 are not close in number range along with the other options.
So, The outcomes do not appear to be equally likely.
Uniform probability model - A model in which every outcome has equal probability.
But in given case, Probabilities in Pilar's experiment does not support a uniform probability model.
So, A uniform probability model is not a good model to represent probabilities in Pilar's experiment.
Therefore, Option 1 is correct.
The correct statement about Pilar's experiment is: A) The outcomes do not appear to be equally likely, so a uniform probability model is not a good model to represent probabilities in Pilar's experiment.
To determine whether a uniform probability model is appropriate, we need to assess if each outcome has the same likelihood of occurring. In a uniform probability model, if there are 'n' possible outcomes, each outcome has a probability of 1/n.
In Pilar's experiment, she selects a card 46 times, and we are given the relative frequencies of the outcomes 1 through 5. If the outcomes were equally likely, we would expect each number to have a relative frequency of approximately 1/5, since there are 5 different numbers.
Let's calculate the expected relative frequency for each number if the outcomes were equally likely:
Expected relative frequency for each number = 1/5 = 0.2.
Now, let's compare this with the given relative frequencies:
Number 1 has a relative frequency of 0.05 Number 2 has a relative frequency of 0.35 Number 3 has a relative frequency of 0.26 Number 4 has a relative frequency of 0.13 Number 5 has a relative frequency of 0.21These relative frequencies are not close to the expected relative frequency of 0.20 for a uniform distribution. Since the relative frequencies vary significantly from one another, the outcomes do not appear to be equally likely. Therefore, a uniform probability model, which assumes equal likelihood for all outcomes, would not be a good fit for Pilar's experiment.
Hence, the correct conclusion is that the outcomes do not appear to be equally likely, and thus a uniform probability model is not suitable for representing the probabilities in Pilar's experiment.
The complete question is Whole numbers are written on cards and then placed in a bag. Pilar selects a single card, writes down the number, and then places it back in the bag. She repeats this 46 times.
Pilar calculates the relative frequency of each number card.
Outcome 1 2 3 4 5
Relative Frequency 0.05 0.35 0.26 0.13 0.21
Which statement about Pilar's experiment is true?
A) The outcomes do not appear to be equally likely, so a uniform probability model is not a good model to represent probabilities in Pilar's experiment.
B) The outcomes appear to be equally likely, so a uniform probability model is not a good model to represent probabilities in Pilar's experiment.
C) The outcomes do not appear to be equally likely, so a uniform probability model is a good model to represent probabilities in Pilar's experiment.
D) The outcomes appear to be equally likely, so a uniform probability model is a good model to represent probabilities in Pilar's experiment.