Answer:
A Rigid Motion is a transformation that preserves length (distance preserving) and angle measure (angle preserving). Another name for a rigid motion is an isometry. A direct isometry preserves distance and orientation. Translations and Rotations are direct isometries.
Step-by-step explanation:
The ratio of caretakers to childeren is _:_. If 24 more children are added, they should hire _ more caretakers to maintain the ratio of caretakers to children.
Answer:
The first is 1:6 and the second one is 4
Step-by-step explanation:
What is the effect on the graph of f(x) = x² when it is transformed to
h(x) = 3x²-7?
A. The graph of f(x) is horizontally compressed by a factor of 3 and
shifted 7 units to the right.
B. The graph of f(x) is vertically stretched by a factor of 3 and shifted
7 units down.
C. The graph of f(x) is vertically stretched by a factor of 3 and shifted
7 units to the right.
D. The graph of f(x) is horizontally stretched by a factor of 3 and
shifted 7 units down.
The effect on the graph of f(x) = x² when it is transformed to h(x) = 3x² - 7 is described by option B. The graph of f(x) is vertically stretched by a factor of 3 and shifted 7 units down.
The original function f(x) = x² represents a parabola with its vertex at the origin (0, 0). The graph opens upward and has a general U-shape.The transformation h(x) = 3x² - 7 indicates that the function has been multiplied by 3, resulting in a vertical stretch. This means that the points on the graph are now vertically spread out, making the U-shape more elongated.Additionally, the transformation includes subtracting 7 from the function, shifting the entire graph downward by 7 units. This means that each y-coordinate of the original function has been reduced by 7 units.The combination of the vertical stretch by a factor of 3 and the downward shift of 7 units results in a new graph h(x) that is vertically stretched and shifted downward. The overall shape of the graph remains a U-shaped parabola, but it is now wider and lower compared to the original graph.Therefore, option B accurately describes the effect of the transformation on the graph of f(x) = x² to h(x) = 3x² - 7.For more such questions on graph, click on:
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Find an equation of the straight line that is perpendicular to y=2x+1 and passes through the point (-2,5)
Answer:
y = -1/2x + 4
Step-by-step explanation:
to answer this question you need to find the slope and the y-intercept
to find the slope of a line that is perpendicular to another line you take the opposite and reciprocal of the slope of the first line
in this case the slope of the initial line is 2; therefore, the opposite reciprocal is -1/2
knowing slope ('m') = -1/2 and having the point (-2, 5) can give us the y-intercept of the new line; we start with:
y = mx + b and then plug the values in so find the y-intercept ('b')
5 = (-1/2)(-2) + b
5 = 1 + b
b = 4
put it all together: y = -1/2x + 4
An electric company charges each of its customers a monthly fee of $19 to maintain the account and nine cents per kilowatt hour what is an equation that relates the monthly cost c in dollars of power consumed P in kilowatt hours 
Answer:
c = 19 + 0.09P
Step-by-step explanation:
The total cost is the $19 monthly fee plus the amount per hour.
c = 19 + 0.09P
A number is greater than 8. The same number is less than 10. The inequalities x> 8 and x < 10 represent the situation Which best explains the number of possible solutions to the inequality? There is one solution because 9 is the only number between 8 and 10. There are a three solutions because 8, 9, and 10 are possible solutions. There are a few solutions because there are some fractions and decimals betwee There are infinite solutions because there is always another number between any two numbers?
Answer:
there are few solutions
Step-by-step explanation:
because for example 8.1 is between 8 and ten
8.1735282
is between 8 and 9
Please help me solve these 3 math problems
The domain of the rational function h(x) = (x - 3)/(x² - 4) is equal to (-∞, -2) ∪ (-2, 2) ∪ (2, ∞).
The possible points that would lie on h(x) = x² - x + 1 are (3, 7).
True: (1, -1) is a point of the graph of f(x) = -2(x + 1)² + 7.
What is a domain?In Mathematics, a domain is the set of all real numbers for which a particular function is defined.
From the graph of h(x) = (x - 3)/(x² - 4), the domain in interval notation and set builder notation is as follows;
Domain = (-∞, -2) ∪ (-2, 2) ∪ (2, ∞)
Domain = {x|x ≠ 2, -2}.
Next, we would determine possible x-value for the given quadratic function as follows;
h(x) = x² - x + 1
7 = x² - x + 1
7 - 1 = x² - x
6 = x² - x
x² - x - 6 = 0.
x² - 3x + 2x - 6 = 0.
x(x - 3) + 2(x - 3) = 0
(x + 2)(x - 3) = 0
x = 3 or x = -2.
For second quadratic function f(x) = -2(x + 1)² + 7, we have:
f(x) = -2(x + 1)² + 7
-1 = -2(1 + 1)² + 7
-1 = -2(2)² + 7
-1 = -8 + 7
-1 = -1 (True).
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algebra 2........,..
Isolate the radical term by adding 6 to both sides of the equation.
\(\sqrt[]{6x+6}=6\)Square both sides of the equation to eliminate the radical sign.
\(6x+6=36\)Subtract 6 from both sides of the equation.
\(\begin{gathered} 6x=36-6 \\ 6x=30 \end{gathered}\)Divide both sides of the equation by 6.
\(\begin{gathered} \frac{6x}{6}=\frac{30}{6} \\ x=5 \end{gathered}\)Therefore, the solution of the equation is {5}.
Find the vertex and focus of the parabola x^2+14x-8y+65=0
Answer:
heres the graph i don't rly understand this all but mabe it will help
Hope This Helps!!!
what is the answer of 3x+235+237
Answer:
3x + 472
Step-by-step explanation:
Answer:
3x + 472
Step-by-step explanation:
We have the expression 3x + 235 + 237 and are asked to find the answer.
We are not solving for x, neither are we doing anything complicated, we need to focus on like terms, which are certain numbers having different symbols, in which they can only be added with the numbers with the same symbols as them.
In this equation, we have two terms, variables and constant. We can only add the constants because once again, you cannot add two terms that don't have the same symbol.
Therefore :
3x + 235 + 237
235 + 237
472.
The answer is 3x + 472
At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric. What percentage of the player's serves were between 115 mph and 145 mph?
A) approximately 16%
B) at most 34%
C) at most 2.5%
D) at most 13.5%
The percentage of players serves were between 115 mph and 145 mph is approximately 16%.
Given :
The statistician reported that the mean serve speed was 100 miles per hour
the standard deviation of the serve speeds was 15 mph
Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric
To find :
What percentage of the player's serves were between 115 mph and 145 mph?
Solution :
μ =100
σ = 15
P ( 115 < x <145)
= P ( \(\frac{115-100}{15}\) < x-μ /6 <\(\frac{145-100}{15}\) )
= P ( \(\frac{15}{15}\) < z < \(\frac{15}{15}\) )
= p ( 1<z<3)
= p( z<3)-p(z-1)
=0.9987-0.8413
=0.1574
p ( 115<xx<145)= 15.74 %
p( 115<x<145)= approximately 16%
The percentage of players serves were between 115 mph and 145 mph is approximately 16%.
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Use calculator to evaluate the following logarithm accurate to 5 decimal places. If it is undefined, the indicate undefined.
You have the following expression:
log(-15.44)
Take into account that the logarithm of a negative number is not defined.
Then, the answer is Undefined
15. Rachel Teeter has a monthly budget of $3000. She plans
to spend 34% for rent and utilities, 23% for food, 5% for
entertainment, 25% to pay off debt, and the remainder
will go into a savings account.
(a) What percent of the total budget will go into a savings
account?
Answer: 17%
Step-by-step explanation:
If you add up 34%, 23%, 5%, & 25% that would equal 83%, if you subtract the 83% from 100%, you would get 17%.The 17% is equivalent to 510. So Rachel Teeter will have $510 in her savings account.
Don’t mod this look at picture
What is the area of the square that measures 3.1 m on each side
The area of the square with a side length of 3.1 meters is 9.61 square meters.
To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.
Area of a square = side length × side length
Substituting the given side length into the formula:
Area = 3.1 m × 3.1 m
To perform the calculation:
Area = 9.61 m²
It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.
Remember, to find the area of any square, you simply need to multiply the length of one side by itself.
The area of the square with a side length of 3.1 meters is 9.61 square meters.
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Gift are packaged in cylinders
each cylinder is 12cm high with diameter of 8cm
calculate the volume of each cylinder
use 3 as a value for J
Answer:
V = 192π cm³ ≈ 603 cm³
Step-by-step explanation:
V = πR²h
V = π(8/2)²(12)
V = 192π cm³ ≈ 603 cm³
J = 3 Hooray, but why?
Answer:
Step-by-step explanation:
Radius r = 4 cm
Height h = 12 cm
Volume = πr²h = 192π cm³ ≈ 576 cm³
Find the value of 14/8 + 15/12
Answer:
The value of \(\frac{14}{8} + \frac{15}{12}\) = 3
Step-by-step explanation:
Explanation
Given \(\frac{14}{8} + \frac{15}{12}\)
L.C.M 8 , 12 is 24
\(\frac{14}{8} + \frac{15}{12} = \frac{14 X 3 + 15 X 2}{24}\)
= \(\frac{42 +30}{24} = \frac{72}{24} = 3\)
Final answer:-
The value of \(\frac{14}{8} + \frac{15}{12}\) = 3
Noel paid $204 for 8 tickets to a soccer game. Each ticket cost the same amount.
What was the cost of each ticket in dollars and cents?
Answer:
$25.50
Step-by-step explanation:
8 tickets cost $204.
$204 ÷ 8 = $25.50
A researcher is interested in testing to determine if the mean price of a casual lunch is different in the city than it is in the suburbs. The null hypothesis is that there is no difference in the population means (i.e. the difference is zero). The alternative hypothesis is that there is a difference (i.e. the difference is not equal to zero). He randomly selects a sample of 9 lunch tickets from the city population resulting in a mean of $14.30 and a standard deviation of $3.40. He randomly selects a sample of 14 lunch tickets from the suburban population resulting in a mean of $11.80 and a standard deviation $2.90. He is using an alpha value of .10 to conduct this test. Assuming that the populations are normally distributed and that the population variances are approximately equal, the degrees of freedom for this problem are _______.
Answer:
The degrees of freedom for this problem are 21
Step-by-step explanation:
Degrees of freedom:
When testing an hypothesis involving two samples, the number of degrees of freedom is given by:
\(df = n_1 + n_2 - 2\)
In which \(n_1\) is the size of the first sample and \(n_2\) is the sample of the second sample.
In this question:
Samples of 9 and 14, so \(n_1 = 9, n_2 = 14\)
The degrees of freedom for this problem are
\(df = n_1 + n_2 - 2\)
\(df = 9 + 14 - 2 = 21\)
The degrees of freedom for this problem are 21
The required degree of freedom is 21.
Given that,
He randomly selects a sample of 9 lunch tickets from the city population resulting in a mean of $14.30 and a standard deviation of $3.40.
He randomly selects a sample of 14 lunch tickets from the suburban population resulting in a mean of $11.80 and a standard deviation $2.90.
He is using an alpha value of .10 to conduct this test.
We have to find,
The degrees of freedom for this problem are.
According to the question,
Degrees of freedom refers to the maximum number of logically independent values, which are values that have the freedom to vary, in the data sample.
Degrees of freedom are commonly discussed in relation to various forms of hypothesis testing in statistics, such as a chi-square.
When testing an hypothesis involving two samples, the number of degrees of freedom is given by,
\(Degree \ of \ freedom = n_1+n_2-2\)
Where, \(n_1\) is the size of the first sample and \(n_2\) is the sample of the second sample.
\(n_1 = 9 \ and\ n_2 = 14\)
Therefore,
\(Degree \ of \ freedom = 9+14-2\\\\Degree \ of \ freedom = 21\)
Hence, The required degree of freedom is 21.
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Which expression is greater than the exact answer to the problem 2789 x 3.875
A 2800 x 4
B 3000 x3
C2700 x 4
D 2800 x 3
hurry quick pls
Answer:
Answer is A
Step-by-step explanation:
when u multiply 2789 x 3.875 u will get 10807.375 so now u have to figure out which answer give a greater amount of number than that, when you try the first answer which is 2800 x 4 u will get 11200 which is greater than the original equation
What is the expression and value of “six less than nine times the sum of a number and eight” when n = 5? 9 (n + 8) minus 6; when n = 5, the value is 111. 6 minus 9 (n + 8); when n = 5, the value is 111. 9 (n) + 8 minus 6; when n = 5, the value is 47. 6 minus 9 (n) + 8; when n = 5, the value is 47.
Answer:
See below.
Step-by-step explanation:
9(n+8)-6
n=5
9(5+8)-6
9(13)-6
117-6
111
A sum is the answer to an addition expression or equation.
When one refers to "less than", they mean the number is "less than" the entirety of the expression or equation.
-hope it helps
Find the probability that a randomly
selected point within the square falls in the
red-shaded circle.
6
18
18
P =
The probability of landing on the red shaded circle is 6/18
Concept of probabilityProbability simply measures the chances at which an event could occur in a sample or population.
Mathematically, Probability is calculated thus:
P(X) = required outcome/ Total possible outcomesHere ,
Required = red circle = 6Entire circle = 18P(red circle ) = 6/18
Therefore, the probability is 6/18
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pls answer!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: -49
Step-by-step explanation: 7 x 7 = 49, but since it has the (-) symbol it will be -49.
Which of the following ordered pairs is a possible solution to the equation y = 3x - 2?
(-3, 1)
(0, 2)
(2, 0)
(1, 1)
Answer:
(1,1)
Step-by-step explanation:
circumference of circle 132cm find the area of circle is
Answer: 1386 sq.cm.
Step-by-step explanation:
2Pi r= 132
2 * 22/7 * r = 132
r = 21
Area = pi * r * r
= 22/7 * 21 * 21
= 1386 sq.cm.
Hope this helps :))
Write 0.9 repeating as a fraction
A. 1/11
B. 1/7
C. 1/99
D. 1/9
Answer:
The answer is A.
Step-by-step explanation:
What gravitational force does the moon produce on the Earth if their centers are 3.88x108 m apart and the moon has a mass of 7.34x1022 kg?
The gravitational force that the moon produces on the Earth is approximately 1.99x10²⁰ N.
What is Newton's law of gravitation?Every particle in the universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers, according to Newton's rule of universal gravitation.
We can use Newton's law of gravitation to solve this problem:
\($F = G \frac{m_1 m_2}{r^2}$\)
where F is the gravitational force, G is the gravitational constant, \($m_1$\) and \($m_2$\) are the masses of the two objects, and r is the distance between their centers.
Plugging in the given values, we get:
\($F = (6.674\times10^{-11} \text{ N}\cdot\text{m}^2/\text{kg}^2) \frac{(7.34\times10^{22} \text{ kg})(5.97\times10^{24} \text{ kg})}{(3.88\times10^8 \text{ m})^2}$\)
Simplifying the expression, we get:
\($F \approx 1.99\times10^{20} \text{ N}$\)
Therefore, the gravitational force that the moon produces on the Earth is approximately 1.99x10²⁰ N.
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what is (2+3q)(-4) in distributive property
Answer:
-12q - 8
Step-by-step explanation:
Distribute -4 to 2 and 3q
2 * -4 = -8
3q * -4 = -12q
-12q - 8
2 ( 3x + 1 ) = x - 8
Answer:
x=-2
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
6x + 2 = x-8
6x - x = -8 -2
5x=-10
x=-2
A rental car company charges $22 per day to rent a car and $0.08 for every mile driven. Samuel wants to rent a car, knowing that:
He plans to drive 450 miles.
He has at most $80 to spend.
Write and solve an inequality which can be used to determine xx, the number of days Samuel can afford to rent while staying within his budget.
Using the inequality concept, the expression models the number of days Samuel can afford to rent while staying within his budget is 11x + 18 ≤ 40
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
A rental car company charges $22 per day to rent a car and $0.08 for every mile driven
The maximum amount to spend = $80
Fixed charge per day $22
Charge per mile = $0.08
The inequality which represents the number of days Can be expressed thus :
(Charge per day × number of days) + (charge per mile × number of miles) ≤ 80
22x + 0.08× 450 ≤ 80
22x + 36 ≤ 80
Divided by 2 both sides of an inequality,
11x + 18 ≤ 40
Hence, the required inequality expression is 11x + 18 ≤ 40
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If two variables have a negative correlation, you would expect that _____ scores on one variable are generally associated with ____ scores on the second variable.
lower; higher
When two variables move in the opposing directions, there is a negative correlation. Accordingly, when one variable rises, the other falls, and vice versa, when one variable falls, the other rises. For instance, the length of time a student spends studying for an exam and their exam grade. The average exam score often declines as study time increases. As a result, higher scores on the second variable are typically associated with lower scores on the first. This connection can be demonstrated in different contexts, such as the connection between stress levels and income. Stress levels often drop as money rises. This implies that higher stress levels are typically correlated with lower income scores.
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