In the equation f(x) = -3(2), reflected about x - axis is : f(x) = 3.2
According to the question, given that
equation f(x) = -3(2)
the equation reflected x - axis is f(x) = 3.2
Therefore, Reflected about the x-axis in the equation f(x) = -3(2) is f(x) = 3.2
The graph of the parent function is either "moved," "resized," or "reflected" by a function transformation. The three primary categories of function transformations are as follows:
- Translation
- Dilation
- Reflection
The only one of these transformations, dilation, alters the size of the original shape; the other two, however, just affect the shape's location.
By comparing the original and converted graphs, you can quickly determine which one has changed because you can tell by by glancing at the graph that it has moved up 2 units, left 3 units, etc. However, it can be challenging to graph the function transformation when a graph is provided. The next few steps make it much simpler to graph transformations. Here, the function y = f(x) is changed to y = a f(b (x + c)) + d.
Step 1: Write down some of the original curve's defining coordinates. Thus, we are aware of the previous x and y coordinates.
Step 2: Simply put "b (x + c) = old x-coordinate" and solve for x to determine the new x-coordinate of each location.
Step 3: Simply apply all outside operations (of brackets) on the old y-coordinate to determine the new y-coordinate of each point. To determine each new y-coordinate, find ay + d, where 'y' is the old y-coordinate.
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Write an equation in slope - intercept form for the line that passes through the given paint andis parallel to the given equation.(9, 12), y = 13x-4
The equation of a line is given by
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope of the line and (x1,y1) is a point where the line passes through.
In our case we have a point but we don't have the slope yet, so we have to find it. To do this we have to remember that two lines are parallel if and only if their slopes are equal, that is
[tex]m_1=m_2[/tex]We know that the line we are looking for is parallel to the line
[tex]y=13x-4[/tex]we notice that this line in written in the slope-intercept form
[tex]y=mx+b[/tex]then its slope is 13.
Since the line is parallel to the one we are looking for, our slope is also 13.
Using the point (9,12) and the slope the equation of the line is
[tex]y-12=13(x-9)[/tex]now we have to write in the slope-intercept form
[tex]\begin{gathered} y-12=13x-117 \\ y=13x-117+12 \\ y=13x-115 \end{gathered}[/tex]Therefore the line is
[tex]y=13x-115[/tex]Find the length of the diameter of the circle
with the following equation: (x-4)^2+(y-2)^2=5
The length of the diameter of the circle is found as the 2×(√5).
What is termed as the equation of the circle?The equation of circle offers an algebraic method for describing a circle given its center and radius length. The equation of a circle differs from the formulas used to calculate a circle's area or circumference. The standard equation for a circle with a radius r and a center at (x1,y1) is: (x−x1)²+(y−y1)²=r².,
For the given question;
The equation of the circle is given as;
(x-4)^2+(y-2)^2=5
Comparing the equation of the circle with the standard form.
Radius r² = 5
Then, r = √5
Now, the diameter is the twice of the radius.
Diameter = 2×radius
Diameter = 2×(√5)
Thus, the length of the diameter of the circle is found as the 2×(√5).
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which of the following polynomials is in standard form?y^12-y^15+y^10-4yz^5+z^3-z^2-42z^3+z^5-9x+x^2+x^3+x^4
For a polynomial to be in standard form, the terms are arranged from the highest exponent to the lowest exponent.
Thus, from the polynomials given, the polynomial in standard form is:
[tex]z^5+z^3-z^2-4[/tex]This is because the term with the highest exponent is the first term, the next exponent is 3, followed by the term with an exponent of 2, then the last term is the term with the least exponent.
ANSWER:
[tex]z^5+z^3-z^2-4[/tex]Write the equation of a line that passes through the points (-1, 3)and (2,6)
The equation of a line in 2 point form is
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]So, inputting the points, we have
[tex]\begin{gathered} \frac{y-3}{x+1}=\frac{6-3}{2+1} \\ \frac{y-3}{x+1}=\frac{3}{3}=1 \\ \text{cross multiply} \\ y-3=x+1 \\ y=x+4 \end{gathered}[/tex]So, the equation of our line is y = x + 4
help me please
thank you
Answer:
Domain: A, [tex)(-\infty, \infty)[/tex]
Range: [tex][4, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Albert is in a hot air balloon that has just taken off and is now floating 20 meters above its
launching point Isabelle is standing on the ground, 21 meters away from the launching point.
How far apart are Albert and Isabelle?
meters
Albert floating in hot air balloon and Isabelle standing at ground are 29 meters far apart from each other.
What is hot air balloon?
A hot air balloon is a lighter in weigh than air. It is an object made up of an envelope-like bag that holds heated air. A wicker basket, gondola, or capsule suspended below transports people and a heat source, typically an open flame produced by burning liquid propane. A capsule also carries passengers in some long-distance or high-altitude balloons.
Lets understand with the help of a right angle triangle, The point from where the hot air balloon taken off be point A, and the point where Isabelle is standing is point B, and the point where the balloon is point C.
The AB= distance between Isabelle and the point from where hot air balloon taken off = base of the imagined triangle,
AC = height at which hot air balloon is floating = perpendicular of the imagined triangle
BC = distance between Isabelle and hot air balloon = Hypotenuse of the imagined triangle
Applying Pythagoras theorem,
(BC)² = (AC)² + (AB)²
(BC)² = (20)² + (21)²
BC = 29
Hence Albert and Isabelle are 29 meters far apart.
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. how many 1/4s are in 6
Let us divide 6 by 1/4
6/1 ÷ (1/4)
6/1*4/1 (Turning the second fraction upside down and multiplying it by the first fraction)
24 (Multiplying)
The answer is 24.
Answer:
Step-by-step explanation:
Since there are four 1/4 in 1 then you have to multiple 6*4= 24!
SET A
15 points
Hi to everyone I just need an answer for my activity one of my subject
thank you:)
Answer:
8 points for solving 6 questions?? Nah thats worth 25 points
Step-by-step explanation:
Classify the following polynomials as: Constant MonomialLinear MonomialQuadratic MonomialCubic MonomialFourth Degree MonomialLinear BinomialQuadratic BinomialCubic BinomialQuadratic TrinomialFourth Degree BinomialFifth Degree Monomial
Solution:
Given the expressions;
[tex]\begin{gathered} -11z \\ -23 \\ 9x^4+9 \\ 2h^2-1,000 \end{gathered}[/tex]A linear monomial is a polynomial whose degree is one and has one terms.
A constant monomial is a term with only a number.
A fourth degree binomial is a polynomial whose degree is 4 and has two terms.
A quadratic binomial is a polynomial whose degree is 2 and has two terms.
ANSWERS:
[tex]\begin{gathered} -11z\ldots\ldots\ldots.....\ldots\ldots....\text{ Linear monomial} \\ -23\ldots\ldots\ldots.....\ldots..\ldots...Cons\tan t\text{ monomial} \\ 9x^4+9\ldots\ldots\ldots.....\ldots\text{.. Fourth degree binomial} \\ 2h^2-1,000\ldots.\ldots..\ldots..\ldots..Q\text{uadratic binomial} \end{gathered}[/tex]481,462 rounded to the nearest hundred thousand
Answer: 500,000
Step-by-step explanation: To round the numbers their nearest hundred thousand, first we have to make the first five digits into the lower number that ends with zero
Example: 52437 is rounded to the nearest hundred thousand is 52000
Sorry if you don't understand I'm just bad at explaining :) T^T
çok acill çözüm lütfeen
Answer: it is yes
Step-by-step explanation:
When the crate folow top botom nuberto
Factorise fully the following
9x^2+3x^3
Answer:
[tex]3x^2\left(3+x\right)[/tex]
Step-by-step explanation:
Look for common factor: [tex]3x^{2}[/tex] since we take the least exponent
and between numbers (3,9) the common factor is 3.
Thefore, we need to divide [tex]3x^2[/tex] by the equation.
[tex]3x^2(3+x)[/tex].
Step-by-step explanation:1. Write the expression.[tex]9x^2+3x^3[/tex]
2. Find a common denominator for both expressions, based on the x variable.[tex]\frac{9x^2}{3x^2} +\frac{3x^3}{3x^2} \\ \\3x^2(3+x)[/tex]
3. Express your result.[tex]9x^2+3x^3=3x^2(3+x)[/tex].
The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the triangle is increasing at a rate of 4 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 7 centimeters and the area is 91 square centimeters?
____ cm/min
.
The floor of an elevator shaft is a square with an area of 42.25 square feet. Find the length of
a side of the floor.
Chapter 2 Expor
Answer:
6.5ft
Step-by-step explanation:
[tex]A=s^{2} \\42.25=s^{2} \\\sqrt[2]{42.25}=\sqrt[2]{s} \\6.5=s[/tex]
Answer:
6.5ft
Step-by-step explanation:
Use slope to determine if lines AB and CD are parallel, perpendicular, or neither. 2. A(0,2), B(5, 4), C(1.8).D(3,3)m(TABm(CD)Types of Lines
A (0,2) B (5,4)
C(1,8) D( 3,3)
Apply the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]For AB
[tex]m=\frac{4-2}{5-0}=\frac{2}{5}[/tex]For CD
[tex]m=\frac{3-8}{3-1}=-\frac{5}{2}[/tex]So both slopes are negative reciprocals of each other.
They are perpendicular lines.
Match the pairs of angles formed by the parallel lines and transversal to their correct vocabulary identification
The angles that are formed by the parallel lines and the transversal are:
1. Vertical Angles
2. Same-side Exterior Angles
3. Corresponding Angles
4. Alternate Interior Angles
5. Alternate Exterior Angles
6. Same-side Interior Angles
7. Adjacent Angles
What are Special Angle Pairs that are Formed by Parallel Lines and Transversal?The following are special angle pairs that are formed when a transversal intercepts two parallel lines:
1. Vertical Angles: These are nonadjacent angles that share the same vertex and are directly opposite each other. An example of such angle pair is angle 6 and angle 7.
2. Same-side Exterior Angles: These are exterior angles that lie on the same side of a transversal but on sperate parallel lines. Example include angle 2 and angle 8.
3. Corresponding Angles: These angles are located on each parallels lines that are cut across by a transversal and lie relatively in the same corner to each other. An example is, angle 1 and angle 5.
4. Alternate Interior Angles: an example of such pair of interior angles that lie on opposite side of a transversal is, angle 3 and angle 6.
5. Alternate Exterior Angles: An example of a pair of alternate exterior angle is angle 2 and 7.
6. Same-side Interior Angles: These pair of angles are interior angles on the same side of a transversal. Example of such pair of angles is, angle 4 and angle 6.
7. Adjacent Angles: These are angles that share a common side and a vertex, an example is: angle 1 and angle 2.
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0.25(8+x)=14 I understand just not fully
25(8+ x)=14
25*8+ 25x =14
200+ 25x= 14
25x=14-200
25x = -186
x = -186/25
x= -7.44
QUESTION 3 Round the following to the most appropriate whole number. The ratio of children to adults at an amusement park is typically 5 to 3. 201 adults are in the park. How many children should be in the park?
335 children should be in the park, if the ratio of children to adults at an amusement park is typically 5 to 3 and 201 adults are in the park.
What is ratio?A ratio is the comparison of two similar quantities or the proportion of one similar quantity to another. With the same meaning, ratios can be expressed in three different ways using words or symbols. In other words, ratios can be expressed by sandwiching a fraction bar, the word "to," or the ratio symbol ":" between the two values being compared.
The ratio of ninth-graders to tenth-graders can take on any of the three forms listed below, using the previous example of comparing the two groups of students in Ms. Jones' class:
10 /20
10 to 20
10 : 20
Given ratio of children to adults is 5:3
5 + 3 = 8
5/8 are children and 3/8 are adults
Let the total no. of people be x
3/8 = 201/x
x = 201 × 8/3
= 536
Now. no. of children is
5/8 × 536
= 335
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Here’s the question. Let me know when u have the answer. Also, this is just apart of a homework practice
Let f(x) be a function; thus, the reflection across the y-axis of f(x) is given by f(-x).
Therefore, in our case,
[tex]g(x)=f(-x)=-(-x)^3-8(-x)^2-9(-x)+11[/tex]Simplifying,
[tex]\Rightarrow g(x)=x^3-8x^2+9x+11[/tex]Thus, the answer is g(x)=x^3-8x^2+9x+11, the first option (top to bottom).
evaluate the expression 2x + 3 when x = 1.6
Given the following expression:
[tex]2x+3[/tex]You need to follow the steps shown below in order to solve the exercise:
1. Since you know the value of "x", you must substitute it into the given equation:
[tex]2x+3=2(1.6)+3[/tex]2. Now you must solve the multiplication:
[tex]=3.2+3[/tex]3. Finally, you need to solve the addition in order to find the value of the expression. Therefore, you get that the result is the following:
[tex]=6.2[/tex]The answer is:
[tex]=6.2[/tex]The domain for the relation below is {x| -6
We need to find the point given the domain and range of the relation:
For domain and range, the result includes the number. Hence, the end values are given by the points.
For point C:
(-6,4)
Because point c is on quadrant two, where x is negative and y is positive.
Also, it takes the higher y value.
For point D:
(6,3)
Because point D is on quadrant 1, where x is positive and y is also positive.
Given f(x) = 4x -5; what is f(4)?
Statistics questions pictured in attachment.
Using the normal distribution, it is found that:
a) The variable used in this problem is: The time (in hours) a 4-year old spends unsupervised per day.
b) The distribution is: X ~ N(3, 1.8).
c) The probability is P(X < 1) = 0.1335, and is given by the bottom left graph.
d) The percentage of children who spend over 10 hours a day unsupervised is of 0.01%.
e) 90% of the children spend at least 0.7 hours unsupervised.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the following rule:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X.The variable used in this problem is:
The time (in hours) a 4-year old spends unsupervised per day, as the distribution involves only 4-year old children, and the mean and the standard deviation are measured in hours.
The mean and the standard deviation of the distribution are given, respectively, by:
[tex]\mu = 3, \sigma = 1.8[/tex].
Hence the distribution can be described approximately as follows:
X ~ N(3, 1.8).
The probability that a person spends less than 1 hour a day unsupervised is the p-value of Z when X = 1, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (1 - 3)/1.8
Z = -1.11
Z = -1.11 has a p-value of 0.1335.
The bottom left graph shows this probability, as the number in hours cannot be less than 0(there is no negative number of hours).
The proportion of children who spends over 10 hours a day unsupervised is one subtracted by the p-value of Z when X = 10, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (10 - 3)/1.8
Z = 3.89
Z = 3.89 has a p-value of 0.9999
1 - 0.9999 = 0.0001, hence the percentage is of 0.01%.
For item e, the measure is the 10th percentile, which is X when Z = -1.28, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
-1.28 = (X - 3)/1.8
X - 3 = -1.28 x 1.8
X = 0.7 hours.
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i have to solve for x and i dont know how to
The value of x is 9.
Given:
The length of the tangent lines are given as, 5x and 7x-18.
The objective is to find the value of x.
The two tangents of a circle drawn from a point outside a circle will always be equal.
Then, the value of x can be solved by,
[tex]\begin{gathered} 5x=7x-18 \\ 5x-7x=-18 \\ -2x=-18 \\ x=-\frac{18}{-2} \\ x=9 \end{gathered}[/tex]Hence, the value of x is 9.
Find the radius of the piñata in feet. near to nearest hundredth.
Explanation:
The formula is given below as
[tex]\begin{gathered} S=4\pi r^2 \\ where, \\ S=surfacearea=60ft^2 \\ r=radius \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} S=4\pi r^{2} \\ 60=4\pi r^2 \\ r^2=\frac{60}{4\pi} \\ r^2=\frac{15}{\pi} \\ square\text{ root both sides } \\ r=\sqrt{\frac{15}{\pi}} \\ r=2.19 \end{gathered}[/tex]Hence,
The final answer to the nearest hundredth is
[tex]2.19[/tex]From a hot-air balloon, Guadalupe measures a 31 degree angle of depression to a landmark thats 316 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary
We will first sketch the problem
Let x be the vertical distance above the ground
Using the trigonometric ratio;
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex][tex]\tan 31=\frac{x}{316}[/tex]cross-multiply
[tex]x=316\tan 31^o[/tex][tex]x\approx189.9[/tex]Find the equation of a line with given slope and containing given point. Write the equation in sole-intercept m= -7/2, point (-8,-4)
Given:
There are given that the slope and the point:
[tex]\begin{gathered} m=-\frac{7}{2} \\ point:\left(-8,-4\right) \end{gathered}[/tex]Explanation:
To find the equation, first, we need to see the formula for slope-intercept form:
So,
From the slope-intercept formula;
[tex]y=mx+b[/tex]Where,
[tex]\begin{gathered} m=-\frac{7}{2} \\ \lparen x,y)=\left(-8,-4\right) \end{gathered}[/tex]Now,
We need to find the value of b by using given information:
So,
Put all the given values into the given slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ -4=-\frac{7}{2}\left(-8\right)+b \\ -4=28+b \\ b=-32 \end{gathered}[/tex]Then,
Put the value of b and m into the slope-intercept form;
So,
[tex]\begin{gathered} y=mx+b \\ y=-\frac{7}{2}x+\left(-32\right) \\ y=-\frac{7}{2}x-32 \end{gathered}[/tex]Final answer:
Hence, the equation of a line is shown below;
[tex]y=-\frac{7}{2}x-32[/tex]The graph of f is given below. Use the graph to determine the following items.
• The z-values, if any, where f has a relative maximum.
• The value(s), if any, of the relative maximum(s) of f.
• The z-values, if any, where f has a relative minimum.
• The value(s), if any, of the relative minimum(s) of f.
Part 1
Relative maxima are where the function changes from increasing to decreasing.
No x-values satisfy this.Part 2
None, see above.
Part 3
Relative minima are where the function changes from decreasing to increasing.
No x-values satisfy this.Part 4
None, see above.
Which of the following side lengths would create a right triangle? Select all
that apply.
5, 5, 10
3,4,7
12, 16, 20
4.5, 6, 7.5
11, 60, 61
6,9, 10
3, 4, 12
8, 15, 17
Answer:
5,12,13
Step-by-step explanation:
first you write out a^2 or a squares + b^2=C ^2 You plug in for a and b the smaller numbers then for c you put the biggest number. Now square everything. And you should get 25 for a. 144 for b. 169 for c. Now add a and b which is25+144 and that equals 169. So 5,12,13 is your answer.
A family creates a monthly budget based on their combined wages and expenses for one month. Complete the budget by choosing the correct option for each cell labeled A through E.
Budgeted Income $ Actual Income $ Difference
Wages $2,500.00 Wages $2,650.00 $150.00
Total Budgeted Wages $2,500.00 Total Actual Income $2,650.00 $150.00
Budgeted Expenses $ Actual Expenses $ Difference
Food $525.00 Food $500.00
A.
Credit Card $100.00 Credit Card $100.00 $0.00
Field Trips $0.00 Field Trips $15.00 -$15.00
Gas $150.00 Gas $120.00 $30.00
Clothing $0.00 Clothing $80.00
B.
Gifts $100.00 Gifts $20.00 $80.00
Entertainment $100.00 Entertainment $65.00
C.
Mortgage Payment $1,080.00 Mortgage Payment $1,080.00 $0.00
Utility Bills $160.00 Utility Bills $140.00 $20.00
Car Payment $225.00 Car Payment $225.00 $0.00
Car Insurance $157.00 Car Insurance $157.00 $0.00
Total Budgeted Expenses $2,597.00 Total Actual Expenses $2,502.00 $95.00
Surplus/Shortage D. Surplus/Shortage E. $245.00
$
$
$
$
$
Step-by-step explanation:
A. 525 - 500 = 25
B. 0 - 80 = -80
C. 100 - 65 = 35
D. 2,500 - 2,597 = 97 shortage
so: -97
E. 2,650 - 2,502 = 148 surplus
so: 148
