The domain and the range of the function are {−5, −2, 1 ,5} and {−26, −14, −2} respectively
How to determine the domain and the range?From the question, we have the following parameters that can be used in our computation:
Function: f(x) = 4x - 6
Table of values
x −5 −2 1 5
y −26 −14 −2 −14
The set of x values is the domain
So, we have
Domain = {−5 −2 1 5}
Rewrite as
Domain = {−5, −2, 1 ,5}
The set of y values is the range
So, we have
Range = {−26 −14 −2 −14}
Rewrite as
Range = {−26, −14, −2}
Hence, the range is {−26, −14, −2}
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choose all that correctly estimate where the function is increasing or decreasing.
Notice that the all estimations for each graph are correct.
HELP PLEASE!!
Which one is correct? =/ or = ?
Answer: Not equal to.
Step-by-step explanation: you don't get the same answer to the problem for both.
If point A(-5, -7) lies on the terminal arm of an angle, determine the exact value for the
primary trigonometric ratios of the angle.
Answer:
[tex]sin(a)=\frac{y}{r}=-\frac{7\sqrt{74} }{74}[/tex]
[tex]cos(a)=\frac{x}{r} =-\frac{5\sqrt{74} }{74}[/tex]
[tex]tan(a)=\frac{y}{x} =\frac{7}{5}[/tex]
Step-by-step explanation:
Given the terminal side of an angle we can calculate the distance between the point given and the origin:
[tex]r=\sqrt{x^2+y^2}[/tex]
[tex]r=\sqrt{|(-5^2)+(-7^2)|}[/tex]
[tex]r=\sqrt{74}[/tex]
y = opposite side
x = adjacent side
r = hypotenuse
Now we have
[tex]r=\sqrt{74}[/tex]
[tex]x=-5[/tex]
[tex]y=-7[/tex]
[tex]sin(a)=\frac{y}{r}=-\frac{7\sqrt{74} }{74}[/tex]
[tex]cos(a)=\frac{x}{r} =-\frac{5\sqrt{74} }{74}[/tex]
[tex]tan(a)=\frac{y}{x} =\frac{7}{5}[/tex]
Solve the following inequality, 6 < 3r-45 < 36 Which graph shows the correct solution?
We know that:
6 < 3r-45 < 36
We want to re arrange the inequations:
Step 1: all terms with an unkown value on one side.
We want to let 3r "be alone" in the middle side:
6 < 3r-45 < 36
6 + 45 < 3r < 36 + 45 [adding 45 in each part]
51 < 3r < 81 [6 + 45 = 51 and 36 + 45 = 81]
Step 2: we want to clear r
51 < 3r < 81
51/3 < r < 81/3 [dividing by 3 all sides]
17 < r < 27 [51/3 = 17 and 81 /3 = 27]
Answer: 17 < r < 27GRAPHwhat is .2323... as a fraction
help with this one please
The graph of g(X) = -(x+3)⁴ compares to the parent function of f(x) = x⁴ got shifted 3 units to left and reflected over x-axis.
Translation means shifting , rescaling and reflecting parents function.
Shifting the graph means to move the graph to new location
Scaling means changing it shape
and Reflecting means a mirror image of parent function across either x-axis or y-axis.
here, If we draw graph of both the function you'll see
The parent function f(x) = x⁴ have center as (0,0)
where as Center of function g(x) = -(x+3)⁴ is (-3,0)
means g(x) = -(x+3)⁴ is moves towards the left by 3 units
and also the graph is in downwards which means it has also reflected across x-axis
Hence , the g(x) = -(x+3)⁴ is shifted 3 units to the left and reflected over the x-axis compare to parent function.
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three times the measure of an angle is equal to twice the measure of the angle's supplement. what is the measure of the angle
Answer:
The angle has measure 72°.
Step-by-step explanation:
Definition:
Two angles are supplementary angles if the sum of their measures equals 180°.
Let x and y be the supplementary angles.
According to the definition above, then,
x + y = 180
We can the above equation for y:
x + y = 180
y = 180 - x
The two angles have measures:
x
180 - x
Now we look carefully at this statement:
"three times the measure of an angle is equal to twice the measure of the angle's supplement"
We translate the above statement into an equation, using x for one angle, and 180 - x for the supplement.
3x = 2(180 - x)
Solve the equation for x.
Distribute 2 on the right side.
3x = 360 - 2x
Add 2x to both sides.
5x = 360
Divide both sides by 5.
x = 360/5
x = 72
The angle has measure 72°.
Help me pleaseee i need help fasttt
Answer:
5(−2)−3 y = 5 (- 2) - 3
Step-by-step explanation:
y = 5x − 3 y = 5 x - 3 Substitute −2 - 2 for x x and find the result for y y. y = 5(−2)−3 y = 5 (- 2) - 3
3 (3+4k)=45 can you help me with this one
Given 3 ( 3 + 4k ) = 45
So, divide both sides by 3
3 + 4k = 45/3
3 + 4k = 15
subtract 3 from both sides
3 + 4k - 3 = 15 - 3
4k = 12
divide both sides by 4
k = 12/4 = 3
So, the value of k = 3
What is the equation of the horizontal asymptote for the following exponential graph? Please help I need it
Answer:
y=5
Step-by-step explanation:
The curve stops at the y value of 6. And we need a horizontal line for the asymptote, so we don't need an x value only a y-value. So the y-value is 5 on the y-axis, which means your equation will be y=5.
-Hope this helped
solve -5(3n+4)=40 I need help
Simplify the expression to obtain the value of n.
[tex]\begin{gathered} -5(3n+4)=40 \\ 3n+4=\frac{40}{-5} \\ 3n+4=-8 \\ 3n=-8-4 \\ n=-\frac{12}{3} \\ =-4 \end{gathered}[/tex]Thus value of n is -4.
Share 24 cards between Lacey and Martha in the ratio of 2:6
In the ratio of 2:6 , Lacey will get 6 cards and Martha will get 18 cards
Total number of cards = 24
Let Lacey gets "x" numbers of cards and Martha gets "y" numbers of cards
Ratio of cards given to Lacey to Martha = 2:6
x:y = 2:6
and we also know that total cards are 24
x + y = 24
x = 24 - y
putting value of x in the ratio,
[tex]\frac{24 - y}{y} = \frac{2}{6}\\[/tex]
cross multiplication,
6(24 - y) = 2y
144 - 6y = 2y
8y = 144
y = 18
Substituting value of y ,
x = 24 - 18
x = 6
Hence , Lacey will get 6 cards and Martha will get 18 cards.
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The following box plot represents the average heights of the students in Mr. Taylor's fourth grade math class.
1) In this question, we need to remember that in any boxplot the line in the middle of the box indicates the median.
Based on that, we can tell the Median is 140
2) In the Interquartile Range, we need to find the range between the lower quartile and the upper one, based on that boxplot. We can tell the IQR is:
[tex]IQR=Q_3-Q_1\Rightarrow141-138=3[/tex]Note that the boundaries of the box show us the lower and the upper quartile:
Mia had a board that was 15 1/2 feet long. He cut three pieces off the board that are each 3 7/8 feet long. How much of the board is left?
Answer
The remaining board piece will be 3 (7/8) feet long
Explanation
Mia's board is 15 (1/2) feet long.
He cut three pieces off the board with each board measuring 3 (7/8) feet long.
The key to this is to first convert the values given in mixed fractions as improper fractions.
3 (7/8) = (31/8)
15 (1/2) = (31/2)
Then, the three pieces each had a length of 3 (7/8)
1 piece = 3 (7/8) feet = (31/8) feet
3 pieces = 3 × (31/8) = (93/8) feet
So, taking this out of 15 (1/2) long board will leave
[15 (1/2)] - (93/8)
= (31/2) - (93/8)
To do that, we need to take the LCM of these two denominators
[tex]\begin{gathered} \frac{31}{2}-\frac{93}{8} \\ =\frac{124-93}{8} \\ =\frac{31}{8} \end{gathered}[/tex]The remaining board piece will be
(31/8) = 3 (7/8) feet long
Hope this Helps!!!
A 170-foot tall antenna has 4 guy-wires connected to the top of the antenna, and each guy-wire is anchored to the ground. A side-view of this scenario is shown.One of the guy-wires forms an angle of α=0.33 radians with the antenna and the opposing guy-wire forms an angle of β=0.43 radians with the antenna.What is the horizontal distance between anchor 1 and the base of the antenna? ____feet What is the horizontal distance between anchor 2 and the base of the antenna?_____ feet What is the distance between anchor 1 and anchor 2? ____feet
Let's label the diagram with the information provided. The diagram would look like:
What is the horizontal distance between anchor 1 and the base of the antenna?This is labeled as x.
With respect to angle alpha, the side x is opposite and the antenna is the side adjacent.
Thus, we need the trig ratio tan to solve for "x". Shown below:
[tex]\begin{gathered} \tan \alpha=\frac{x}{170} \\ \tan (0.33)=\frac{x}{170} \\ x=170\times\tan (0.33) \\ x=58.23 \end{gathered}[/tex]Answer: 58.23 feet
What is the horizontal distance between anchor 2 and the base of the antenna?
This is labeled as y.
With respect to angle beta, the side y is opposite and the antenna is the side adjacent.
Thus, we need the trig ratio tan to solve for "y". Shown below:
[tex]\begin{gathered} \tan \beta=\frac{y}{170} \\ \tan (0.43)=\frac{y}{170} \\ y=170\times\tan (0.43) \\ y=77.97 \end{gathered}[/tex]Answer: 77.97 feet
What is the distance between anchor 1 and anchor 2?
The distance between Anchor 1 and Anchor 2 is "x + y". We already found x and y. Let's do the sum:
[tex]\begin{gathered} x+y \\ =58.23+77.97 \\ =136.2 \end{gathered}[/tex]Answer: 136.2 feet
Sandra and Peter share a packet of 30 marshmallow eggs in the ratio of 2:3
Using the given ratio, we will see that we can define the proportions to find that:
Sandra gets 12 marshmallows.
Peter gets 18 marshmallows.
How many marshmallow eggs will get each one?We know that Sandra and Peter share a packet of 30 marshmallow eggs in the ratio of 2:3.
We can find the fractions for each person by doing the following steps:
So if we add the two values in the ratio we get 2 + 3 = 5
The ratio is:
Sandra:Peter = 2:3
Then we can write the fractions as:
The fraction of the total number of eggs that Sandra gets is 2/5
The fraction of the total number of eggs that Peter gets is 3/5
Now remember that the total number of marshmallow eggs is 30, then the number that Sandra gets is:
S = (2/5)*30 = 12
And the number that Peter gets is:
S = (3/5)*30 = 18
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6(3n+10) whats the answer
Problem: 6(3n+10)
Solution:
Applying the distributive law of natural or real numbers, we obtain:
[tex]6(3n+10)\text{ = 6.3n+ 10.6 = }18n+60[/tex]then, the correct answer is:
[tex]6(3n+10)\text{ =}18n+60[/tex]Which of the following determines the range of spectral lines produced during electron transition?
A.
the total number of energy levels the electron can jump to
B.
the lower energy level to which the electron returns
C.
the higher energy level to which the electron jumps
D.
the number of electrons under electron transition at the same time
The range of spectral lines produced during electron transition is determined by the total number of energy levels the electron can jump to.
Spectral lines are bright or dark lines over continuous spectrum which occur due to emission or absorption of energy.
When an electron jumps to or from one energy level to another energy level, spectral lines are produced. The range of spectral lines depends on the number of energy levels available to which the electron can jump. This depends the amount of energy gained/lost by the electron.
Thus, the range of spectral lines produced during electron transition is determined by the total number of energy levels the electron can jump to.
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According to a survey, 62% of Americans go on vacation each year. Two Americans are chosen from a group of 100 Americans what is the probability that one or both of the people chosen does not go on vacation each year?
Answer:
61.56%
Explanation:
Let the first American = A
• P(A goes) = 0.62
,• P(A does not) = 0.38
Let the second American = B
• P(B goes) = 0.62
,• P(B does not) = 0.38
The probability that one or both of the people chosen does not go on vacation each year
=P(A goes and B does not) or P(A does not and B does) or P(both do not)
[tex]\begin{gathered} =P(AB^{\prime})+P(A^{\prime}B)+P(A^{\prime}B^{\prime}) \\ =(0.62\times0.38)+(0.38\times0.62)+(0.38\times0.38) \\ =0.2356+0.2356+0.1444 \\ =0.6156 \end{gathered}[/tex]Therefore, the probability that one or both of the people chosen does not go on vacation each year is 61.56%.
Write a rule to describe a transformation when a triangle hasbeen reflected over the x-axis.(x,y) →Using (-x,-y)
For a transformation that involves a reflection over the x-axis, it means the pre-image is reflected across the horizontal line.
For a reflection over the x-axis, the x coordinate remains the same while the y coordinate changes.
The rule that describes a transformation when an image has been reflected over the x-axis is:
(x, y) ==> (x, -y)
Using the pre-image (-x, -y), we have:
(-x, -y) ==> (-x, y)
For a triangle, we have:
A(-x, -y) ==> A'(-x, y)
B(-x, -y) ==> B'(-x, y)
C(-x, -y) ==> C'(-x, y)
The table shows the rational approximation of several irrational numbers.
Which is the approximate value of √3?
The approximate value of √3 is 1.732 which is an irrational number.
Given that,
We have to find the value of root3.
√3 is an irrational number.
Real numbers that cannot be represented as a ratio are referred to as irrational numbers. Or to put it another way, irrational numbers are actual numbers that defy logic.
Irrational numbers are real numbers that cannot be represented by a straightforward fraction. These can't be stated as ratios, like p/q, where p and q are both integers, q≠0. In terms of statistics, it defies reason.
The approximate value of √3 is 1.732.
Therefore, The approximate value of √3 is 1.732 which is an irrational number.
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-2x-10y=20 D:-10,-5,0,5x=-10x=-5x=0x=5
Given the function
[tex]-2x-10y=20[/tex]First I'll rewrite it in terms of y
[tex]\begin{gathered} -2x-10y=20 \\ -10y=20+2x \\ y=\frac{20}{-10}+\frac{2x}{-10} \\ y=-2-\frac{1}{5}x \end{gathered}[/tex]Next is to determine the values of y (range) for the given values of x
Now you can graph it:
What is the image point of (-8,-5) after a translation right 1 unit and down 5 units?
Answer:
(- 7, - 10 )
Step-by-step explanation:
a translation of 1 unit right means add 1 to the x- coordinate
a translation of 5 units down means subtract 5 from the y- coordinate.
(- 8, - 5 ) → (- 8 + 1, - 5 - 5 ) → (- 7, - 10 )
Zeke wants to build a fence around his backyard with the 200 feet (ft) of fencing he bought at Lowe's. Zeke wants to use all of the fencing he bought. he also wants the length of the fencing to be 10 times the width. the equation A=200w-10w^2 can be used to find the area of the garden, where w is the width of the garden, in ft
Considering the vertex of the quadratic equation, the width that will maximize the area of the garden, and the maximum area, are as follows:
Width: 10 ft.Maximum area: 1000 ft².What is the vertex of a quadratic equation?A quadratic equation is defined as follows:
y = ax² + bx + c.
The vertex can be either a maximum point or a minimum point, depending on the coefficient a, as follows:
Maximum: a < 0.Minimum: a > 0.The coordinates of the vertex are given as follows:
x = -b/2a.y = -(b² - 4ac)/4a.For this problem, the equation is:
A(w) = -10w² + 200w.
Hence the coefficients are:
a = -10, b = 200, c = 0.
The width that will maximize the area is:
w = -200/(2(-10)) = 200/20 = 10 ft.
The maximum area is of:
A = -(200)²/(4(-10)) = 1000 ft².
Missing InformationThe problem is incomplete and could not be found on any search engine, hence we suppose that it asks for the width that will maximize the area of the garden, and the maximum area.
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The radius of the front wheel of Terry's bike is 61cm.
Terry goes for a cycle and travels 60.32km.
How many full revolutions did Terry's front wheel complete?
In linear equation, 157 did Terry's front wheel complete.
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).Terry goes for a cycle and travels 60.32km.
so, 60.32 * 1000 ÷ ( 2 * 3.14 * 61 )
= 60320 ÷ 2 * 3.14 * 61
= 60320 ÷ 6.28 * 61
= 60320 ÷ 383.08
= 6032000/ 38308
= 1508000/9577
= 157
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The slope of a soil line is quarter inch per foot if this drainage line is 50 feet long the difference in elevation from one end to the other is most nearly?
Since the slope of the soil line is a quarter of an inch per foot and the drainage line is 50 feet long, then the difference in elevation is:
[tex]50\text{feet}\times\frac{1}{4}\frac{in}{feet}.[/tex]Simplifying the above expression we get:
[tex]\frac{50}{4}in=12.5in\text{.}[/tex]Recall that:
[tex]1\text{ in=}\frac{1}{12}feet.[/tex]Therefore:
[tex]12.5in\approx1.04\text{feet.}[/tex]Answer: 12.5 inches= 1.04 feet.
Clarissa and Koko solve 3x + 5 = 2x + 4 by graphing the related function. Is either of them correct? Explain your reasoning.
Answer:
clarissa
Step-by-step explanation:
many wholes are in 21 / 5
Divide the numbers:
21/5 = 4.2
9-6 Worksheet: Dilations
Graph the polygon and its image after a dilation with the given scale factor
1. J(2, 4), K(4, 4), P(3, 2); r = 2
5.1-2.
ty
of
X
Answer:
Step-by-step explanation:
it ty
Answer:
٠٠
First write all the points on the graph
second
multiply 2 in all the numbers and write them again
Here is an equation that is true for all values of x: 6(x + 3) = 6x + 18. Londyn saw this equation and says she can tell 18( x + 3) + 32 = 3(6x + 18) + 32 is also true for any value of x. How can she tell? Explain your reasoning.
We need to decide whether the given equations are always or never true for values of x .The given equations are ,
[tex]x - 12 = x + 1[/tex]solve out for x,
[tex]\longrightarrow x -x =12+1\\ [/tex]
[tex]\longrightarrow 0 =13\\ [/tex]
This can never be true. Hence the equation is never true for any values of x.
[tex]x + \frac{3}{4} = x - \frac{3}{4} [/tex]solve out for x,
[tex]\longrightarrow x -x =\dfrac{3}{4}+\dfrac{3}{4}\\ [/tex]
[tex]\longrightarrow 0=\dfrac{3}{2}[/tex]
This can never be true. hence the equation is never true for any values of x.
[tex]4(x + 3) = 8x + 12 - 4x[/tex]solve out for x,
[tex]\longrightarrow 4x +12=8x+12-4x\\[/tex]
[tex]\longrightarrow 4x -8x +4x =12-12\\[/tex]
[tex]\longrightarrow 0=0[/tex]
hence this equation is true for all values of x.
[tex]2x - 8 - x = x - 8[/tex]solve out for x,
[tex]\longrightarrow 2x -x -x =8+8\\ [/tex]
[tex]\longrightarrow 0=0 [/tex]
hence the equation is true for all values of x.
[tex]2(x + 5) + 3x = 5(x - 5)[/tex]solve out for x,
[tex]\longrightarrow 2x +10+3x =5x-25\\ [/tex]
[tex]\longrightarrow 5x -5x =-25-10\\[/tex]
[tex]\longrightarrow 0 =-35[/tex]
This can never be true. hence the equation is never true for any values of x.
and we are done!