TRIGONOMETRY if 0 is in the first quadrant and cos 0=3/5 what is sin (1/20)?Where 0 is theta
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Given:
[tex]\cos \text{ }\theta\text{ = }\frac{3}{5}[/tex]Using the trigonometric identity:
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Simplify the following expression by combining liker terms: 4x +9 -6x +610X-1510x+15-2x+152x+15
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We have the expression 4x+9-6x+6 and we have to simplify it.
We can group the terms that are alike. We have two groups of terms: the ones that are multiplied by "x" and the ones that are just numbers alone.
Then, the terms 4x and (-6x) are alike and we can add them, getting (-2x). In this terms, x is the common denominator of both terms.
The other terms that are alike are 9 and 6, that can be added to get 15.
[tex]\begin{gathered} 4x+9-6x+6 \\ (4-6)x+(9+6) \\ -2x+15 \end{gathered}[/tex]The answer is -2x+15.
rick is preparing a roast beef for his family.the roast beef weighs 2 3/4 pounds. if he wants to make each serving to be 1/2 pounds of meat how many servings can he make
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To find the number of roast beef servings that Rick can make, we proceed as follows:
Step 1: Divide the total weight of the roast beef by the amount of weight of meat per serving, as follows:
[tex]\begin{gathered} \text{Total weight of roast beef =}2\frac{3}{4}\text{ pounds=}\frac{11}{4}\text{ pounds} \\ \text{amount of weight of meat per serving = }\frac{1}{2}\text{ pounds} \\ \text{Therefore:} \\ \text{Number }of\text{ servings =}\frac{T\text{otal weight of roast beef}}{A\text{mount of weight of meat per serving}} \\ \Rightarrow\text{ Number }of\text{ servings =}\frac{\frac{11}{4}}{\frac{1}{2}} \\ \Rightarrow\text{Number }of\text{ servings =}\frac{11}{4}\times\frac{2}{1}=\frac{22}{4}=\frac{11}{2}=5.5\text{ } \end{gathered}[/tex]Therefore, the number of roast beef servings that Rick can make is 5.5
What is the surface area of a pyramid if its one triangular face has an area of 20 sq. cm and its square base has a side of 5cm?A. 100 sq.cmB. 105 sq.cmC. 110 sq. cmD. 115 sq.cm
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To solve this problem, we will use the following formula for the surface area of a square pyramid:
[tex]SA=BA+4A_t,[/tex]where BA= base area, and A_t is the area of one of the lateral triangles.
Now, we are given that:
[tex]A_t=20cm^2.[/tex]Recall that the area of a square is given by the following formula:
[tex]A_s=side^2.[/tex]We are given that the side of the base is 5 cm long, therefore, the base area is:
[tex]A_s=(5cm)^2=25cm^2.[/tex]Finally, we get that:
[tex]SA=25cm^2+4(20cm^2)=105cm^2.[/tex]Answer:
[tex]105cm^2.[/tex]A blueprint of a shopping complex shows the bottom edge of the roof to be 68 feet above the ground. If the roof rises to a point 122 feet above the ground over a horizontal distance of 4.5 yards, what is the slope of the roof?41.2128
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SOLUTION
Given:
A blueprint of a shopping complex shows the bottom edge of the roof to be 68 feet above the ground. If the roof rises to a point 122 feet above the ground over a horizontal distance of 4.5 yards, what is the slope of the roof?
[tex]Slope\text{ =}\frac{rise}{run}[/tex][tex]\begin{gathered} Rise\text{ =122-68=54 feet} \\ Run=4.5yards=13.5feet \end{gathered}[/tex][tex]\therefore Slope=\frac{54}{13.5}=4feet[/tex]
Final answer:
rogers father vompares the text plan from two different companies dail up charges $5.00 for 100 text messages and ring ring charges $8 for 200 text messages
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Rogers father compares the text plan from two different companies dial up charges $5.00 for 100 text messages and ring ring charges $8 for 200 text messages
Step 1
find the unit price
Company 1
price= $ 5
number of text messages=100
[tex]\begin{gathered} \text{unit price=}\frac{\text{price}}{\text{number of text messages}} \\ \text{unit price=}\frac{5}{100} \\ \text{unit price=0.05} \end{gathered}[/tex]Company 2
price= $ 8
number of text messages=200
[tex]\begin{gathered} \text{unit price=}\frac{8}{200} \\ \text{unit price=}0.04 \end{gathered}[/tex]Step 2
compare the text plan
[tex]\begin{gathered} \text{price 1 }then, the text message is cheaper in the company 2Which of the following graphs have hamiltonian circuits?
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Answer:
D
Step-by-step explanation:
+10B-10-8-644810Bc8--10and aWe can show that ABC is congruent to AA'BC by a translation ofunits)across the-axis.
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ANSWER
ABC is congruent to A'B'C' by a translation of 2 units and a reflection across the x-axis
EXPLANATION
We want to identify the transformations that were carried out on ABC to obtain A'B'C'.
First, we notice that A'B'C' is not aligned with ABC because the vertex of B' is 2 units behind the vertex of B.
So, we can say that there was a translation of 2 units to the left or -2 units..
Also, we notice that the vertices of ABC were flipped over the x-axis to obtain A'B'C'.
Therefore, we can conclude that there was a reflection across the x axis.
Hence, ABC is congruent to A'B'C' by a translation of 2 units and a reflection across the x-axis.
Determine the equation of a line in point slope that passes through (5, -6) and (-1, 6)?
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First, let's take a look at the point-slope form of a line:
[tex]y-y_0=m(x-x_0)[/tex]Where:
• m, is the ,slope, of the line
,• (Xo,Yo) ,is a point that belongs to the line
Now, let's calculate the slope of our line with the poins given:
[tex]\begin{gathered} m=\frac{6-(-6)}{-1-5}\rightarrow m=\frac{6+6}{-6}\rightarrow m=\frac{12}{-6} \\ \\ \rightarrow m=-2 \end{gathered}[/tex]Using this slope and point (5,-6), we'll get the equation of our line in the point-slope form.
[tex]y-y_0=m(x-x_0)\rightarrow y-(-6)=-2(x-5)\rightarrow y+6=-2(x-5)[/tex]The equation of the line is the following:
[tex]y+6=-2(x-5)[/tex]A 100$ printer cost 44$ less than eight times the cost of a ream of paper. How much is a ream of paper?
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Find the perimeter and area of the figure, rounding to the nearest tent. Use 3.14 for π 7ft 25 ft 4 ft
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Answer:
89.12 ft
Explanation:
The perimeter of the figure is the sum of all the sides. So, we need to find the length of the quarter of the circles. This length can be calculated as:
[tex]\frac{2\cdot\pi\cdot r}{4}=\frac{2\cdot3.14\cdot4ft}{4}=6.28\text{ ft}[/tex]Where r is the radius of the circle.
Then, the perimeter can be calculated as:
Perimeter = 2(7 ft) + 2(25 ft) + 4(6.28 ft)
Perimeter = 14 ft + 50 ft + 25.12 ft
Perimeter = 89.12 ft
Because there are 2 segments of 7 ft, 2 of 25 ft, and 4 corners of 6.28 ft
Therefore, the answer is 89.12 ft
I need help with this question... the correct answer choice
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The given a parallelogram with 4 coordnates in the corner.
The transformation that carries the parallegoram below itself is ,
the rotation of 180 counterclockwise about the origin.
I am trying to find the slope-intercept form of the following equation:Find the equation of a line through (7, -3) that is perpendicular to the line y = -x/3 - 8
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Given:
The equation of line is,
[tex]y=-\frac{x}{3}-8[/tex]As given that the required line is perpendicular to the above line.
It means the slope of required line will be negative reciprocal of above line.
[tex]\begin{gathered} y=-\frac{x}{3}-8 \\ \text{Compare it with y=mx+b} \\ \Rightarrow m=-\frac{1}{3} \end{gathered}[/tex]The slope of the required line will be,
[tex]m_1=-\frac{1}{m}=-\frac{1}{-\frac{1}{3}}=3[/tex]Now, given that the required line passing through point (7,-3) .
[tex]\begin{gathered} y=m_1x+b \\ (x,y)=(7,-3) \\ -3=3(7)+b \\ b=-24 \end{gathered}[/tex]The slope-intercept form is,
[tex]\begin{gathered} y=m_1x+b \\ y=3x-24 \end{gathered}[/tex]3. Which inequality is represented by the graph below?y < 3x + 2y =3x + 2y > 3x + 2y= 3. + 2
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Answer
Option A is correct.
The inequality equation represented by the graph is
y < 3x + 2
Explanation
When plotting the graph of linear inequality equations, the first step is to first plot the graph of the straight line normally, using intercepts to generate two points on the linear graph.
Looking at the graph given, we can tell that the graph without considering the inequality yet is y = 3x + 2
If the inequality sign is (< or >), then the line drawn will be a broken line.
If the inequality sign is (≤ or ≥), then the line drawn is an unbroken one.
For this question, we can see that the lin is a broken line, so, the inequality sign will either be a < or >.
The shaded region now depends on whether the inequality sign is facing y or not.
If the inequality sign is facing y, it means numbers above the line plotted are the wanted region and the upper part of the graph is shaded.
If the inequality sign is not facing y, it means numbers below the line plotted are the wanted region and the lower part of the graph is shaded.
For this question, we can see that the lower part of the line is shaded, so, that means the inequality sign is not facing y.
So, the inequality equation represented by the graph is
y < 3x + 2
Hope this Helps!!!
a rational function with at least one vertical asymptote, and a horizontal asymptote. You will describe the characteristics of your function, and give a numerical example of the function at one of the vertical asymptotes.
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ANSWERS
Function:
[tex]h(x)=\frac{x+1}{(x-1)(x+3)}[/tex]Key features:
• Asymptotes: x = 1, x = -3, (vertical), and ,y = 0, (horizontal).
,• Intercepts: (0, -1/3), (-1, 0)
,• Symmetry: none
,• Example of end behavior: as x → 1⁺, y → infinity,, while, as x → 1⁻, y → -infinity
EXPLANATION
The vertical asymptotes of a rational function are given by the zeros of the denominator. For example, the function,
[tex]h(x)=\frac{x+1}{(x-1)(x+3)}[/tex]Has two vertical asymptotes: one at x = 1, and one at x = -3.
The horizontal asymptote is determined by the degrees of the numerator (n) and denominator (m):
• If n < m then the horizontal asymptote is the x-axis
,• If n = m then the horizontal asymptote is y = a/b, where a and b are the leading coefficients of the numerator and denominator, respectively.
,• If n > m then there is no horizontal asymptote
In the given example, the degree of the numerator is 1, while the degree of the denominator is 2. Thus, function h(x) has a horizontal asymptote that is the x-axis.
Now, we have to find the key features for this function:
• y-intercept:, occurs when x = 0
[tex]h(0)=\frac{0+1}{(0-1)(0+3)}=\frac{1}{-3}=-\frac{1}{3}[/tex]Hence, the y-intercept is (0, -1/3)
• x-intercepts:, the x-intercepts are the x-intercepts of the numerator: ,(-1, 0),.
,• The ,asymptotes, are the ones mentioned above: ,x = 1, x = -3, (vertical), and ,y = 0, (horizontal).
,• The ,symmetry, is determined as follows:
[tex]\begin{gathered} Even\text{ }functions:f(-x)=f(x) \\ Odd\text{ }functions:f(-x)=-f(x) \end{gathered}[/tex]If we replace x with -x in function h(x), we will find that the result is neither h(x) nor -h(x) and, therefore this function is neither even nor odd.
Finally, an example of the end behavior of this function around the asymptote x = 1 is that as x → 1⁺, y → infinity, while as x → 1⁻¹, y → -infinity.
If we take values of x greater than x = 1 - so we will approach 1 from the right, we will get values of the function that show an increasing behavior. Let's find h(x) for x = 4, x = 3, and x = 2,
[tex]\begin{gathered} h(4)=\frac{4+1}{(4-1)(4+3)}=\frac{5}{3\cdot7}=\frac{5}{21} \\ \\ h(3)=\frac{3+1}{(3-1)(3+3)}=\frac{4}{2\times6}=\frac{4}{12}=\frac{1}{3} \\ \\ h(2)=\frac{2+1}{(2-1)(2+3)}=\frac{3}{1\times5}=\frac{3}{5} \end{gathered}[/tex]And we will find the opposite behavior for values that are less than 1 - but greater than -1 because there the function has a zero and its behavior could change,
[tex]\begin{gathered} h(0)=\frac{0+1}{(0-1)(0+3)}=\frac{1}{-1\times3}=-\frac{1}{3} \\ \\ h(\frac{1}{2})=\frac{\frac{1}{2}+1}{(\frac{1}{2}-1)(\frac{1}{2}+3)}=\frac{\frac{3}{2}}{-\frac{1}{2}\times\frac{7}{2}}=\frac{\frac{3}{2}}{-\frac{7}{4}}=-\frac{3\cdot4}{2\cdot7}=-\frac{6}{7} \end{gathered}[/tex]The graph of the function and its key features is,
A student usually saves $25 a month. He would like to reach a goal of saving $400 in 12 months. The student writes the equation 400 = 12(×+ 25) to represent this situation. Solve the equation for x.Show your workWrite your answer as a sentence that describes what the variable x represents
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
$25 / month = monthly savings
$400 = goal
12 months = time
400 = 12 * (x + 25 ) ====> equation
Step 02:
400 = 12 (x + 25)
400 = 12 x + 12(25)
400 = 12 x + 300
400 - 300 = 12 x
100 / 12 = x
8.33 = x
x = $8.33
The answer is:
The variable x represents the amount of additional money the student must save each month to reach the goal.
x = $8.33
Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 30 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 4 months, and the distribution of lifetimes is normal.
A. a) If Accrotime guarantees a full refund on any defective watch for 2 years after purchase, what percentage of total production will the company expect to replace? (Round your answer to two decimal places.)\
B. If Accrotime does not want to make refunds on more than 6% of the watches it makes, how long should the guarantee period be (to the nearest month
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a) The percentage of total production will the company expect to replace is of 6.62%.
b) The guarantee period should be of 23 months.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for the duration of the watches are given as follows:
[tex]\mu = 30, \sigma = 4[/tex]
The proportion of watches that will be replaced are those that last less than 2 years = 24 months, hence it is given by the p-value of Z when X = 24, as follows:
Z = (24 - 30)/4
Z = -1.5.
Z = -1.5 has a p-value of 0.0662.
Hence the percentage is of 6.62%.
For item b, the guarantee period should be the 6th percentile, which is X when Z = -1.555, hence:
-1.555 = (X - 30)/4
X - 30 = -1.555 x 4
X = 23 months.
More can be learned about the normal distribution at https://brainly.com/question/25800303
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Select all of the value below the satisfy the inequality
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Given:
[tex]\frac{1}{2}(x-5)+9>8[/tex][tex]\frac{1}{2}(x-5)>8-9[/tex][tex]\frac{1}{2}(x-5)>-1[/tex][tex]x-5>-2[/tex][tex]x>5-2[/tex][tex]x>3[/tex]Values satisfying the inequality are:
[tex]5\text{ , }\frac{22}{7}\text{ , }3.015[/tex]A water tower tank in the shape of a right circular cylinder is44 meters tall and has a diameter of26 meters. What is the volume of the tank? UseT = 3.14 and round to the nearest hundredth, if necessary.
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We have that the volume of a cylinder is given by the following equation:
[tex]V=\pi\cdot r^2\cdot h[/tex]h is tall and r the radius, the radius is:
[tex]\begin{gathered} r=\frac{d}{2}=\frac{26}{2}=13 \\ \end{gathered}[/tex]replacing:
[tex]\begin{gathered} V=3.14\cdot(13)^2\cdot44 \\ V=23349.04 \end{gathered}[/tex]The volumen of the cylinder is 23349.04 cubic meters
Question 7 Luna's savings increases as a linear function of the number of chores she does, as shown in the table. How much money did Luna have saved before she started doing chores? Chores Savings ($) 1 74 2 78 3 82 4 86 $0 $70 $64 $68
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What is the constant of proportionality in the table below? Hours worked 3 6 9 12 Money Earned $45.75 $91.50 $137.25 $183.00 $ I per hour
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If the "hours worked" and the "Money earned" are proportional, this means that both variables increase and decrease at the same rate. You could say that the more hours you work, the more money you make, and vice-versa.
The constant of proportionality indicates the rate of change of one of the variables with respect to the other.
Let "y" represent the money earned and "x" represent the hours worked, you can express the proportional relationship between both variables as follows:
[tex]y=kx[/tex]Where "k" represents the constant of proportionality and can be calculated by dividing the value of y by the value of x:
[tex]k=\frac{y}{x}[/tex]To determine the said value you have to choose any ordered pair of the table and do as follows:
Using the pair
Hours worked x=3
Money earned y=$45.75
[tex]\begin{gathered} k=\frac{y}{x} \\ k=\frac{45.75}{3} \\ k=15.25 \end{gathered}[/tex]The constant of proportionality is $15.25 per hour.
A line passes through the point (3,-8) and has a slope of -4 . Write an equation in slope-intercept form for this line.
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The slope-intercept form of the line which passes through the point (3,-8) and with a slope of -4 is y = -4x + 4
We know that the equation of a line passing through a given point is as follows:
(y - y1) = m (x - x1) ….. (i)
Here, (x1, y1) ⇒ coordinates of the point
m ⇒ slope of the line
In the given question,
y1 = -8
x1 = 3
m = -4
Putting these values in equation (i),
(y - (-8)) = (-4) (x-3)
(y + 8) = -4x + 12
On rearranging, we get
y = -4x + 12 - 8
y = -4x + 4
Therefore, the slope-intercept form of the line which passes through the point (3,-8) and with a slope of -4 is y = -4x + 4.
Read more about slope intercepts:
brainly.com/question/13959234
A. Translate the verbal phrases into algebraic expressions.3. The square of the quotient of 54 and j
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ANSWER
(54/j)²
EXPLANATION
We have to translate this verbal phrase into an algebraic expression. An algebraic expression is a combination of variables, numbers, and arithmetic operations. For example, the expression (x² + 2) is an algebraic expression.
In this phrase, we have "the square of ...", so we will have an expression in the form (...)².
Then, the square is of a quotient, between 54 and j, where 54 is the numerator and j is the denominator.
Hence, the algebraic expression is (54/j)².
2) Reflection across the line y = x. B(-2, 1), S(-2, 2), R(3, 3), H(2, -2) B'( ) S/ ) R (2) J( )
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Let's begin by identifying key information given to us:
[tex]B\mleft(-2,1\mright),S\mleft(-2,2\mright),R\mleft(3,3\mright),H\mleft(2,-2\mright)[/tex]Reflection is done over the line y = x, we have:
[tex]\begin{gathered} (x,y)\rightarrow(y,x) \\ B\mleft(-2,1\mright)\rightarrow B^{\prime}(1,-2) \\ S\mleft(-2,2\mright)\rightarrow S^{\prime}(2,-2)_{} \\ R\mleft(3,3\mright)\rightarrow R^{\prime}(3,3) \\ H\mleft(2,-2\mright)\rightarrow H^{\prime}(-2,2) \end{gathered}[/tex]Triangles ACD and BCD are isosceles. Angle DBC has a measure of 84 degrees and angleBDA has a measure of 24 degrees. Find the measure of angle BAC.
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The Solution.
The reflex angle DBC can be calculated as below:
[tex]\angle DBC=360-84=276^o\text{ ( angle at a point)}[/tex][tex]So,\text{ }\angle DBA=\angle CBA=\frac{276}{2}=138^o[/tex]Note that: angle BDA = angle BCA = 24 degrees
Thus, considering triangle CBA (which is similar to triangle DBA), we can find angle BAC.
[tex]\angle BAC+138+24=180\text{ (sum of angles in a triangle)}[/tex][tex]\begin{gathered} \angle BAC=180-(138+24) \\ \text{ =180-162} \\ \text{ =18 }^o \end{gathered}[/tex]Therefore, the correct answer is 18 degrees.
Please help with parts (a), (b),and (c).No need much explanation
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Given the Histogram that summarizes the data obtained by Kemala:
(a) The Class Width is the length of the intervals.
In order to find the Class Width, you need to subtract the lowest value of each bar from the lowest value of the previous bar.
In this case, you get:
[tex]\begin{gathered} 5-2=3 \\ 8-5=3 \\ 11-8=3 \end{gathered}[/tex]Therefore:
[tex]Class\text{ }Width=3[/tex](b) You need to identify the number of beaches that had 10 or fewer pregnant turtles. Therefore, you need to add the corresponding number of beaches that correspond to these bars (A, B and C):
Then, you get:
[tex]3+8+4=15[/tex](c) You can identify that the interval of the last bar is from 11 to 13, and the number of beaches that corresponds to that bar is:
[tex]6[/tex]As you can see below
Hence, the answers are:
(a)
[tex]3[/tex](b)
[tex]15[/tex](c)
[tex]6[/tex]7.) A jug of egg nog sells for $5.12One jug holds(128 punces. What is the unit priceper ounce?
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Answer:
The unit price per ounce is;
[tex]\text{\$0.04 per ounce}[/tex]Explanation:
Given that A jug of egg nog sells for $5.12 and One jug holds 128 ounces.
We can derive the unit price per ounce by dividing the price by the number of ounces;
[tex]\begin{gathered} r=\frac{\text{ \$5.12}}{128\text{ ounces}} \\ r=\text{ \$0.04 per ounce} \end{gathered}[/tex]Therefore, the unit price per ounce is;
[tex]\text{\$0.04 per ounce}[/tex]which of the fillowing statements must be true based on the diagram below?
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Answer:
HI is a perpendicular bisector
H is the vertex of a right angle
H is the midpoint of a segment in the diagram
Explanation:
Taking into account the diagram, we can say that the segments GH and HF have the same length. Additionally, HI form an angle of 90° with segment GF.
So, the true statements are:
HI is a perpendicular bisector because it forms a 90° angle and divides the segment GF into two equal segments.
H is the vertex of a right angle because angle FHI is right ( measures 90°)
H is the midpoint of a segment in the diagram because point H divides segment GF into two equal parts.
Therefore, the answers are:
HI is a perpendicular bisector
H is the vertex of a right angle
H is the midpoint of a segment in the diagram
Let’s say that the patient drinks an 8-ounce glass of orange juice. The nurse must convert that to milliliters (mL) or cubic centimeters (cc) in order to record the intake volume in the patient’s fluid input and output chart. (Remember 1 mL = 1 cc.)
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Answer: 8 ounce = 237 ml
Explanation:
From the information given,
volume of drink taken by patient = 8 ounce
We want to convert 8 ounce to ml
Recall,
1 US fluid ounce = 29.57 ml
Thus,
8 ounce = 8 x 29.57 = 236.56
Approximately,
8 ounce = 237 ml
The surface area of a rectangular prism is 60. Which of the following are possible dimensions of the rectangular prism? 1 Pt
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The surface area of a rectangular prism with sides a, b and c is given by the formula:
[tex]S=2(ab+ac+bc)[/tex]Use that formula to find the surface area that a prism with the given dimensions on each option would have.
A. 6, 2, 1 1/2
[tex]\begin{gathered} S=2(6\cdot2+6\cdot1\frac{1}{2}+2\cdot1\frac{1}{2}) \\ =2(12+9+3) \\ =2(24) \\ =48 \end{gathered}[/tex]B. 5, 4, 1 1/4
[tex]\begin{gathered} S=2(5\cdot4+5\cdot1\frac{1}{4}+4\cdot1\frac{1}{4}) \\ =2(20+\frac{25}{4}+5) \\ =2(\frac{125}{4}) \\ =\frac{125}{2} \\ =62.5 \end{gathered}[/tex]C. 3, 4, 1 1/2
[tex]\begin{gathered} S=2(3\cdot4+3\cdot1\frac{1}{2}+4\cdot1\frac{1}{2}) \\ =2(12+3\frac{3}{2}+6) \\ =2(21\frac{3}{2}) \\ =45 \end{gathered}[/tex]D. 6, 3, 1 1/3
[tex]\begin{gathered} S=2(6\cdot3+6\cdot1\frac{1}{3}+3\cdot1\frac{1}{3}) \\ =2(18+8+4) \\ =2(30) \\ =60 \end{gathered}[/tex]Therefore, the only possible dimensions of a rectangular prism with surface area 60 listed on the options, are 6, 3 and 3 1/3. The answer is:
[tex]\text{Option D}[/tex]Select all inputs for which f (x)=2A:x=-7B:x=0C:x=4D:none of the above
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To answer this question, we need to see the graph of the function carefully.
For x = -7, we can see that the function is equal to 2, that is:
[tex]f(-7)=2[/tex]For x = 0, we have that the function is equal to -1, that is:
[tex]f(0)=-1[/tex]For x = 4, we have that the function is equal to -2, that is:
[tex]f(4)=-2[/tex]We need to find the value of x. Then, we have to find the point where we "touch" the function, and then find the y-value of the function.
Therefore, in summary, we have that the only input for which f(x) = 2 is when x = -7 (option A).