Answer:
f(9) = 15Step-by-step explanation:
In order to find f(9) we substitute the value of x that's 9 into f(X) that's where there's x we substitute it with 9 and calculate.
We have
[tex]f(x) = x + 6[/tex]
[tex]f(9) = 9 + 6 \\ = 15[/tex]
We have the final answer as
f(9) = 15Hope this helps you
Three functions are shown.
Linear
Quadratic
Exponential
Which of the following statements is true?
The correct statement C. Exponential growth will always exceed linear growth.
What is termed as the Exponential growth?Exponential growth is a data pattern that exhibit good increases over time, resulting in the curve of such an exponential function.Whereas exponential growth is frequently used in corporate finance, the actuality is frequently more complex. In the case of a savings account, the implementation of exponential growth did work well because the rate of interest is assured and does not change over time. This isn't the case with the majority of investments.For the given question;
In the end, a "exponential growth function" would always outperform a "linear growth function" because "x-values" tend to increase in continuation, and as such the change rate affiliated with the "exponential function" as well increases in continuation, whereas the "linear function's" change rate is considered constant.
Thus, Exponential growth will always exceed linear growth.
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The complete question is-
Three functions are shown.
A. Linear growth will always exceed exponential growth.
B. Quadratic growth will always exceed exponential growth.
C. Exponential growth will always exceed linear growth.
many wholes are in 21 / 5
Divide the numbers:
21/5 = 4.2
16 oz harbor peanut butter for 2.49 or a 64 oz jar of peanut butter for 6.99 round everything up to the nearest cent or hundreth. yes mam
We have to find the "better buy" between two options:
1) 16 oz jar for $2.49
2) 64 oz jar for $6.99
We can compare this two options with the unit price of each one. The unit price will be expressed in "$ per oz" or "$/oz". The option with the smaller unit price is the "better buy".
We can calculate the unit price as teh quotient between the price and the weight of each option.
Unit price for Option 1:
[tex]u_1=\frac{2.49\text{ \$}}{16\text{ oz}}\approx0.16\frac{\$}{oz}_{}[/tex]Unit price for Option 2:
[tex]u_2=\frac{6.99\text{ \$}}{64\text{ oz}}\approx0.11\frac{\$}{oz}[/tex]As the Option 2 (64 oz jar) has a smaller unit price, the better buy is the 64 oz jar for $6.99.
Answer: the better buy is the 64 oz jar for $6.99.
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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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°.
use the product, quotient, and power rules of logarithms to rewrite the equation as a single logarithm.
We are given the following expression:
[tex]\log a-3\log b+4\log c[/tex]we are asked to simplify this expression. To do that we will first use the following property:
[tex]a\log b=\log ^{}b^a[/tex]we will apply this to the second and third terms, like this:
[tex]\log a-\log b^3+\log c^4[/tex]Now we will use the following property:
[tex]\log a-\log b=\log (\frac{a}{b})[/tex]we will use this property for the first and second terms:
[tex]\log (\frac{a}{b^3})+\log c^4[/tex]Now we will use the following property:
[tex]\log a+\log b=\log ab[/tex]We will use the property in the last two terms, like this:
[tex]\log (\frac{ac^4}{b^3})[/tex]And thus, we have simplified the logarithmic expression into one single logarithm
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]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.
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!
Write the equation of the linear relationship in slope-intercept form, using decimals as needed.
x 25 35 45 55
y 85 77 69 61
The equation that represents this relationship is y =
The equation of the linear relationship in slope-intercept form is y = (-4/5)x + 105.
Given:
x 25 35 45 55
y 85 77 69 61
slope between (25,85) and (35,77) is m = 77-85/35-25
= -8/10
m= -4/5
y=mx+c passes though (25,85)
85 = -4/5*25 + c
85 = -4*5+c
85 + 20 = c
c = 105.
y = mx + c
y = (-4/5)x + 105
Therefore the equation of the linear relationship in slope-intercept form is y = (-4/5)x + 105.
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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:
Nell participated in a 3-day charity walk. Sheraised $0.50 for each 1/3 of mile that she walked. Thefirst day, Nell walked 12 miles. The second day, shewalked 8 miles. The third day, she walked 16 miles.How much money did Nell raise?
the Numbers of days = 3
The second statement(She raised $0.50 for each 1/3 of mile that she walked) means
1/3 miles = $0.50
For first day walk we have:
1/3 miles = $0.50
12 miles = 12 x 0.50 x 3 = $18
For Second day walk we have:
1/3 miles = $0.50
8miles = 8 x 0.50 x 3 = $12
For Third day walk we have:
1/3 miles = $0.50
16miles = 16 x 0.50 x 3 = $24
The amount she raised for the three days becomes
$18 + $12 + $24
=$54
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 .2323... as a fraction
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
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)
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.
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:
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]
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
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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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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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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95% of ____ is 427.5
Answer: Hi! The answer is 406,125.
Step-by-step explanation: You can either go by 1%, meaning you divide 427,5 by 100 and then do x95, which gives you 95%, or you can do 427,5x0,95. Either way you get 406,125!
Answer:
406.125
Step-by-step explanation:
what is the value of the expression y - x?
Answer:
[tex]y-x=-10[/tex]
Step-by-step explanation:
In any trapezoid, the sum of all angles is 360°. Additionally, the sum of both angles on the same side of the trapezoid is 180°. Therefore, we know that:
[tex](7x+40)+(68-6y)=180[/tex]
[tex](17y+73)+(121-4x)=180[/tex]
To solve for [tex]x[/tex] and [tex]y[/tex], we must set up a system of equations and solve by substitution, elimination, or graphing.
To start, simplify the first formula, then isolate the [tex]x[/tex] variable:
[tex](7x+40)+(68-6y)=180[/tex]
[tex]7x-6y+68+40=180[/tex]
[tex]7x-6y+108=180[/tex]
[tex]7x-6y=72[/tex]
[tex]7x=72+6y[/tex]
[tex]x=\frac{72+6y}{7}=\frac{72}{7}+\frac{6}{7}y[/tex]
Next, simplify the second formula, then substitute the value above for [tex]x[/tex]:
[tex](17y+73)+(121-4x)=180[/tex]
[tex]-4x+17y+121+73=180[/tex]
[tex]-4x+17y+194=180[/tex]
[tex]-4(\frac{72}{7}+\frac{6}{7}y)+17y+194=180[/tex] (substituted for [tex]x[/tex] here)
[tex]-\frac{288}{7}-\frac{24}{7}y+17y+194=180[/tex]
[tex]-\frac{288}{7}-\frac{24}{7}y+\frac{119}{7}y+\frac{1358}{7}=\frac{1260}{7}[/tex]
[tex]-288-24y+119y+1358=1260[/tex]
[tex]95y+1070=1260[/tex]
[tex]95y=190[/tex]
[tex]y=2[/tex]
Finally, substitute 2 for [tex]y[/tex] in the first formula as simplified:
[tex]7x=72+6y[/tex]
[tex]7x=72+6(2)[/tex]
[tex]7x=72+12[/tex]
[tex]7x=84[/tex]
[tex]x=12[/tex]
Therefore:
[tex]x=12[/tex] and [tex]y=2[/tex]
And the expression [tex]y-x[/tex] equals:
[tex]y-x=2-12=-10[/tex]
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 )
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 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
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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