a. in radiansb.in degreesHint:HEARRERANote: You can earn partial credit on this problem.Preview My AnswersSubmit Answers
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EXPLANATIONS:
Given;
We are given the following expression;
[tex]arctan(\frac{1}{\sqrt{3}})[/tex]Required;
We are required to find the angle measure of this in both radians, and degrees.
Step-by-step solution;
For the angle whose tangent is given as 1 over square root of 3, on the unit circle, we would have
[tex]\begin{gathered} tan\theta=\frac{1}{\sqrt{3}} \\ Rationalize: \\ \\ \frac{1}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\ \\ =\frac{\sqrt{3}}{\sqrt{3}\times\sqrt{3}} \\ \\ =\frac{\sqrt{3}}{3} \end{gathered}[/tex]On the unit circle, the general solution for this value as shown would be;
[tex]tan^{-1}(\frac{\sqrt{3}}{3})=\frac{\pi}{6}[/tex]To convert this to degree measure, we will use the following equation;
[tex]\frac{r}{\pi}=\frac{d}{180}[/tex]We now substitute for the value of r;
[tex]\begin{gathered} \frac{\frac{\pi}{6}}{\pi}=\frac{d}{180} \\ \\ \frac{\pi}{6}\div\frac{\pi}{1}=\frac{d}{180} \\ \\ \frac{\pi}{6}\times\frac{1}{\pi}=\frac{d}{180} \\ \\ \frac{1}{6}=\frac{d}{180} \end{gathered}[/tex]We now cross multiply;
[tex]\begin{gathered} \frac{180}{6}=d \\ \\ 30=d \end{gathered}[/tex]Therefore;
ANSWER:
[tex]\begin{gathered} radians=\frac{\pi}{6} \\ \\ degrees=30\degree \end{gathered}[/tex]Related Questions
Instructions: varies indirectly with . If =7 when =−4, find when =2. Use the forward slash (i.e. "/") for all fractions (e.g. -1/2 is the same as −12).
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y varies directly as x
This can be written mathematically as:
y = kx
If y = 7, x = -4
Solve for the constant k
7 = -4k
k = -7/4
The equation is:
y = -7/4 x
When x = 2
substitute x =2 anto the equatio n y = -7/4 x
[tex]\begin{gathered} y=-\frac{7}{4}\times2 \\ \\ y=-\frac{7}{2} \end{gathered}[/tex]Find the missing side. Round to the nearest tenth.
1)
X
1.
2.
21°
16
2)
12
40°
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The sides of a triangle can be determined if the trigonometric ratios and angles are given. The missing sides of the given triangle are 6 and 8 respectively.
What are trigonometric ratios?The trigonometric ratios are defined for a right angled triangle.
The example of these ratios are sin, cos, tan, cosec, sec and cot.
The trigonometric ratios are useful in determining the heights and distances of the large objects.
The diagram for the given triangle is given below,
Since, sin(x) = (The side opposite to angle x) / Hypotenuse
Apply the above trigonometric ratio in triangle 1 to get,
Sin(21°) = x / 16
=> x = 16 × Sin(21°)
=> x = 16 × 0.36
=> x = 5.76
Which is approximately 6 when taken as nearest to tenth.
Similarly for triangle 2, it can be written as,
Sin(40°) = x / 12
=> x = 12 × Sin(40°)
=> x = 12 × 0.64
=> x = 7.68
Which is approximately 8 when taken as nearest to tenth.
Hence, the missing sides for the given triangles are 6 and 8 approximately.
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Solve the equation involving absolute value. Type you answers from smallest to largest. If an answer is not an integer then type it as a decimal rounded to the nearest hundredth. |x^2+2x-36|=12 x=Answer, Answer, Answer and Answer
Answers
Given:
The euqation is,
[tex]|x^2+2x-36|=12[/tex]Explanation:
Simplify the equation.
[tex]\begin{gathered} |x^2+2x-36|=12 \\ x^2+2x-36=\pm12 \end{gathered}[/tex]Solve the x^2 + 2x - 36 = 12 for x.
[tex]\begin{gathered} x^2+2x-36=12 \\ x^2+2x-36-12=0 \\ x^2+8x-6x-48=0 \\ x(x+8)-6(x-8)=0 \\ (x+8)(x-6)=0 \\ x=-8,6 \end{gathered}[/tex]Solve the equation x^2 + 2x - 36 = -12 for x.
[tex]\begin{gathered} x^2+2x-36+12=0 \\ x^2+2x-24=0 \\ x^2+6x-4x-24=0 \\ x(x+6)-4(x+6)=0 \\ (x+6)(x-4)=0 \\ x=-6,4 \end{gathered}[/tex]Thus solution of the equation is x = -8, -6, 4, and 6
in the diagram pq and St find the slope of st
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1) Looking at that diagram, we can see that Point S shares the same x-coordinate from point Q since they are on the same Vertical Line. So, it's safe to say that the x-coordinate of Point S is x=-2
2) And point S is at the same horizontal axis of point P. So for the same principle, we can say that the y-coordinate of point S is y=4
S(-2,4)
3) So let's find the Fourth point of that figure, so let's find the slope of PQ
[tex]\begin{gathered} m_{PQ}=\frac{4-1}{1-(-2)}=\frac{3}{-1+2}=\frac{3}{3}=1 \\ \\ m_{ST}=-1 \end{gathered}[/tex]Since PQ is perpendicular to ST then the slope is the opposite reciprocal of 1, i.e. -1
Write an equation in slope-intercept form for the line that is parallel to y = 3x + 7 and passes through the point (-4, -8).
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The line parallel to y = 3x +7 and passes through the point (-4,-8) is
y=3x+4
What is a slope-intercept form?It gives the graph of a straight line and it is represented in the form
y= mx +c. It is one of the form used to calculate the equation of a straight line. We have to calculate the slope of the line from the equation. The slope calculated can be used in the slope-intercept form. It is the most popular form of a straight line.
We need to find the slope to the line y = 3x +7.
The slope of a line is m
Here, from the equation y=3x+7, m=3
So, m=3
The slope-intercept form is,
y= mx +c
-8 = 3(-4)+c
-8=-12+c
c=4 and m=3
Now, the above equation equation becomes,
y=3x+4
The line parallel to y = 3x +7 and passes through the point (-4,-8) is
y=3x+4
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The following data set represents the ACT scores for students in Mrs. Smith's collegescience class.18 32 16 2319 21 28 2922 30 19 21What ACT score is the mode for the class?
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Recall that in statistics, the mode is the value that appears most frequently in a set of data. You may find it useful to represent the data in statistical graphs such as dot plots or bar charts. In this case, we will use the following chart
As we can see from the image, The most frequently used numbers are 19 and 21. We are dealing with a bimodal data set. The mode is given by 19 and 21.
I will show you the pic
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If it rotates clockwise around the origin. It will be in the following quadrant
[tex]\begin{gathered} 90^{\circ}\rightarrow quadrant\text{ 1} \\ 180^{\circ}\rightarrow quadrant\text{ 4} \\ 270^{\circ}\rightarrow quadrant\text{ 3} \\ 360^{\circ^{\prime}^{\prime}}\rightarrow quadrant\text{ 2} \end{gathered}[/tex]7. The manager of a local restaurant has found that his cost function for producing coffee is C(x) = .097x, where C(x) is the total cost in dollars of producing x cups. (He is ignoring the cost of the coffeepot and the cost labor.) Find the total cost of producing the following numbers of cups of coffee. (a) 1000 cups (b) 1001 cups (c) What is the marginal cost for any cup? Let C(x) be the total cost in dollars to manufacture x items. Find the average cost in exercises 8 and 9.
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To solve for the total cost of producing the following numbers of cups of coffee:
[tex]\begin{gathered} C(x)=0.097x \\ \end{gathered}[/tex]where
[tex]\begin{gathered} x=nu\text{mber of cups of coff}e \\ C(x)=total\text{ cost }in\text{ dollars of producing x cups} \end{gathered}[/tex](a) The total cost of producing 1000 cups =
[tex]\begin{gathered} C(x)=0.097x \\ x=1000 \\ C(x)=1000(0.097)=\text{ \$97} \end{gathered}[/tex](b) The total cost of producing 1001 cups =
[tex]\begin{gathered} C(x)=0.097x \\ x=1001 \\ C(x)=1001(0.097)=\text{ \$97}.097 \end{gathered}[/tex](c) The marginal cost for any cup = $0.097
marginal cost can be found by taking the derivative of the function
[tex]\begin{gathered} C(x)=0.097x \\ C^1(x)=0.097=\text{ \$0.097} \end{gathered}[/tex]pan made a scale drawing of a swimming pool. The diving board is 2 inches long in the drawing. The actual diving board is 18 feet long. What scale did Pam use for the drawing?
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Divide the length of the object on the drawing by its actual size to find the scale:
[tex]\frac{2\text{ inches}}{18\text{ feet}}[/tex]Since each feet has 12 inches:
[tex]\frac{2\text{ inches}}{18\text{ feet}}=\frac{2\text{ inches}}{18\cdot12\text{ inches}}=\frac{2}{216}=\frac{1}{108}[/tex]Therefore, the scale used in the drawing is 1:108 (one inch in the paper equals 108 inches in real life).
11. Determine if the following sequence is arithmetic or geometric. Then, find the 12th term. 2, 6, 18, 54, ... a. arithmetic: 35 b. arithmetic: 354,294 c. geometric: 35 d. geometric: 354,294
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We have the sequence: 2, 6, 18, 54...
If the sequence is arithmetic, there must be a common difference between the terms that remains constant.
This is not the case for this sequence.
We can try by seeing if there is a common factor k such that:
[tex]a_n=k\cdot a_{n-1}[/tex]We can do it by:
[tex]\frac{a_2}{a_1}=\frac{6}{2}=3[/tex][tex]\frac{a_3}{a_2}=\frac{18}{6}=3[/tex][tex]\frac{a_4}{a_3}=\frac{54}{18}=3[/tex]There, we have a geometric sequence, with factor k=3:
[tex]a_n=3\cdot a_{n-1}[/tex]We can relate it to the first term as:
[tex]\begin{gathered} a_2=3\cdot a_1 \\ a_3=3\cdot a_2=3\cdot3\cdot a_1=3^2\cdot a_1 \\ a_4=3\cdot a_3=3\cdot3^2\cdot a_1=3^3\cdot a_1 \\ a_n=3^{n-1}\cdot a_1=3^{n-1}_{}\cdot2 \end{gathered}[/tex]For n=12, we have:
[tex]a_{12}=3^{12-1}\cdot2=3^{11}\cdot2=177,147\cdot2=354,294[/tex]The value of a12 is 354,294.
The answer is d) Geometric, 354,294.
What is the connection between side ratios and angle in a right triangle
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Trigonometric ratios are ratios between any two sides of a right triangle that can then be used to determine the measure of an angle between those two sides. Primary trigonometric ratios (in a right triangle trigonometry) are: sin (x), cos (x) and tan (x)
On the basis of any two side lengths, we may even determine the acute angle measurements in a right triangle. We may get the ratios of the lengths of the triangle's sides to an acute angle in a right triangle by knowing the acute angle's measurement.
What relationship exists between a triangle's side ratios and angle?In a triangle, the longest side is located across from the largest angle, while the shortest side is located across from the smallest angle.
Triangle Unfairness: The lengths of any two sides added together in a triangle always exceed the length of the third side.
Pythagoras Theorem, a²+b²=c² in a right triangle with hypotenuse c.
A triangle is a right triangle if its sides conform to the relationship a²+b²=c²
The right angle, or 90°, is always one angle. The hypotenuse is the side with the 90° angle opposite. The longest side is always the hypotenuse. The other two inner angles add up to 90 degrees.
Remember that the Pythagorean theorem only holds true for right triangles, in which case the converse of the theorem also holds true. In other words, if a triangle's sides satisfy the connection, then it must be a right triangle.
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Consider the functions g(x) = 2x + 1 and h(x) = 2x + 2 for the domain 0 < x < 5 Without evaluating or graphing the functions, how do the ranges compare?
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Without evaluating or graphing the functions, it is obvious that the minimum and maximum values in the range of h(x) is greater than the minimum and maximum values in the range of g(x) by 1.
What is a domain?In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain represents the input values (x-values) to a function.
What is a range?In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range refers to the set of all possible output numerical values (real numbers), which are shown on the y-axis of a graph.
In conclusion, the minimum and maximum values in the range of h(x) differs from those of function g(x) by 1.
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Latrice eamns 5 points for each question she answers correctly. Her grade, g is described by g = 5c, where c is the number of questions answered correctly. What is the dependent variable-Number of points per question-total grade-number of questions missed-number of questions right
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The equation that describe's Latrice grade is given by:
g = 5c
g represen
I'll send you the pic
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1. 5 (3) = 15
2. 4 (8) = 32
3. 6 (3/2) = 9
4. 12 ( ) = ?
Equivalent Linear Expressions MC 2.02
Which expression is equivalent to (-3 1/3d + 3/4) - (3 5/6d + 7/8)
A: 1/2d-1/8
B: 1/2d-1 5/8
C: 43/6d-1/8
D: -43/6d-1/8
Answers
The expression is equivalent to the given expression is -43/6d-1/8.
What is expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
Given an expression [tex]-3\frac{1}{3d} +\frac{3}{4} - (3\frac{5}{6d}+\frac{7}{8} )[/tex]
= -10/3d +3/4 - 23/6d - 7/8
= -10/3d - 23/6d + 3/4 - 7/8
= -43/6d - 1/8
Hence, The expression is equivalent to the given expression is -43/6d-1/8.
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Answer:
- 4/15x + 4
Step-by-step explanation:
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Not homework just review for test not worth any points
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Recall that:
Interest is the monetary gain for lending money to a third party.
Simple interest is applying the interest to the original amount without considering the extra flow of money each time the interest is applied.
Compounded interest is applying the interest to the total amount including the extra flow of money each time the interest is applied.
1) Plan A. From the given information, in 12 months Ari will earn:
[tex]I=500\cdot0.065\cdot12=390.[/tex]dollars, therefore she will have a total of $890.00.
2) Plan B. Now we use the formula for compounded interest to compute the total amount that Ari will have after one year:
[tex]A=500(1+0.065)^{12}=500\cdot2.129096\approx1064.55.[/tex]3) From the above calculations, we conclude that Ari will make more money if she invests in plan B.
4) Ari has to leave the money for another:
Using plan B. Let t be the number of extra months Ari needs to leave the money in the fund, then:
[tex]1100=500\cdot(1.065)^{12+t}\text{.}[/tex]Solving for t, we get:
[tex]\begin{gathered} 1.065^{12+t}=2.2, \\ (12+t)ln(1.065)=\ln (2.2), \\ 12+t=\frac{\ln (2.2)}{\ln (1.065)}=12.52, \\ t=12.52-12=0.52. \end{gathered}[/tex]Then, Ari needs to leave the money for another half a month but since the interest is applied each month she needs to leave the money for another whole month.
Using Plan A: Let t be the number of extra months Ari needs to leave the money in the fund, then:
[tex]1100=500\cdot0.065\cdot(12+t)\text{ +500.}[/tex]Solving for t we get:
[tex]\begin{gathered} \frac{1100-500}{500\cdot0.065}=12+t, \\ t=\frac{600}{32.5}-12, \\ t=6.46. \end{gathered}[/tex]Then, Ari needs to leave the money for another 6.46 months but since the interest is applied monthly she needs to leave the money for another 7 months.
Angel is at a birthday party. There are 12 cupcakes where some are blue and some are green. Out of There are 8 green cupcakes. Express the number of blue cupcakes as a decimal
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12 cupcakes
8 green cupcakes
To find the number of blue cupcakes subtract the green cupcakes (8) to the total cupcakes:
12 -8 = 4 blue cupcakes
To express as a decimal, divide the number of blue cupcakes by the total number of cupcakes:
4/12 = 0.33333
Fourteen more than 4 times a number is 42what is equation?what is solution?
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We have to express this phrase in mathematical terms.
We call the number x.
Then, four times a number is "4x".
Fourtenn more than 4x is "4x+14", and this is equal to 42.
Then, we can write:
[tex]4x+14=42[/tex]And solve as:
[tex]\begin{gathered} 4x+14=42 \\ 4x=42-14 \\ 4x=28 \\ x=\frac{28}{4} \\ x=7 \end{gathered}[/tex]Answer: the equation is 4x+14=42 and the solution is x=7
Which expression represents the simplest factorization of 56st – 21t?
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The expression which represents the simplest factorization of 56st – 21t is 7t(8s - 3).
How to factorise an expression?Factorization is the process of creating a list of factors. It is also an expression listing items that when multiplied together will produce a desired quantity.
Greatest common factor is the largest positive integer or polynomial that is a divisor of several different numbers.
56st - 21t
Factors of
56st = 1, 2, 4, 7, 8, 14, 28,:56, t, s
21t = 1, 3, 7, 21
The common factors of 56st and 21t is 7 and t
56st - 21t
= 7t(8s - 3)
Check:
7t(8s - 3)
= 56st - 21t
In conclusion, the simplest factorization of the expression 56st - 21t is 7t(8s - 3).
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I really don't understand this lesson can you help me please
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Data:
M = Math books
E = Englisg books
TB = Total books
The total of the books is the addition of the math and english books
[tex]TB\text{ = M+ E}[/tex]The Math books are: M= E-9 (Nine less that English books (E))
So replacing this in the expression for Total Books:
[tex]TB=(E-9)+E\text{ }\Rightarrow TB=E-9+E[/tex]The final expression is:[tex]TB=2E-9[/tex]Look at the models below. DO Tell whether each statement is True or False. equivalent to į because à has 2 times as many shaded parts and 2 times as many equal parts as True False 3 b. , is equivalent to because has 2 times as many parts shaded and 2 more equal parts than True 0 False 4 is equivalent to because both models have i shaded part True False d. is equivalent to because á has 2 + 6 = 8 equal parts. True False
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a.
Since:
[tex]\frac{1}{3}\equiv\frac{2}{2}\times\frac{1}{3}=\frac{2}{6}[/tex]The statement is true
b.
Since:
[tex]\frac{2}{2}\times\frac{1}{4}=\frac{2}{8}\ne\frac{2}{6}[/tex]The statement is false
c.
Since:
[tex]\frac{1}{4}\equiv\frac{2}{2}\times\frac{1}{4}=\frac{2}{8}[/tex]The statement is true.
d.
Since:
[tex]\begin{gathered} \frac{2}{6}=\frac{1}{3} \\ \frac{2}{8}=\frac{1}{4} \\ \frac{1}{4}\ne\frac{1}{3} \end{gathered}[/tex]The statement is false.
will you kindly assist me pls. work math step by step answer in numbers pls. to work how you got the answer
Answers
Translating for numbers, we have:
[tex]\frac{1}{5}=0,2\rightarrow3\frac{1}{5}=3,2[/tex]This way, we can make what follows:
[tex]Day_1+Day_2=3\frac{1}{5}+4=3,2+4=7,2_{}[/tex]Calculating now the amount is needed to complete the 9 miles:
[tex]Day_3=9-7,2\text{ = 1,8}[/tex]--------------------------------------------------------------------------------------------------------
And from here, the solution with the fractions.
We can start with the sum of what Shelly has biked in the first two days:
[tex]Day_1+Day_2=3\frac{1}{5}+4=7\frac{1}{5}_{}[/tex]This is the amount of mile she has already biked. But we know she needs to complete all the 9 miles in the third day. So, the difference from 9 and the amount she already did is the amount she needs to bike in the third day.
[tex]\text{Day}_3\text{ = 9 - 7}\frac{1}{5}\text{ = 1}\frac{4}{5}[/tex]claudia earns overtime pay when she works more then 40 hours in a week how many hours of overtime pay did she work for the week of march 4march 4-10march 4 -- 8.5march 5 -- offmarch 6 -- 9.25march 7 -- 8.75march 8 -- 10march 9 -- offmarch 10 -- 7.75A.44.25B. 40.0C. 4.25D. 2.25
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She earns overtime pay when she works more than 40 hours in one week . The number of overtime pay she works for the weeks of march 4 can be calculated below
[tex]\begin{gathered} \text{total hour worked =}8.5\text{ +9.25+8.75+10+7.75=}44.25 \\ \text{The number of overtime pay for the w}eek\text{ of march 4 is 44.25} \end{gathered}[/tex]Find the following values of the function6(-7+8f(x) = 75 - 2.c12-2 < -2– 2 4f(-4)=f(-2) =f(-1) =f(9) =91)Answers in progress)
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Find the following values of the function
6
(-7+8
f(x) = 7
5 - 2.c
12
-
2 < -2
– 2a> 4
f(-4)=
f(-2) =
f(-1) =
f(9) =
9
1)
Write an equation for each scenario, then find the solution.5. You're making a Wawa run for snacks and energy drinks on your bike. It takes you0.4 hours at x miles per hour to make it to Wawa. On your way back you have toride 3 miles per hour slower (you're weighed down by your Wawa goodies) and ittakes you 0.5 hours. How far is it from your house to Wawa?6. Laura retired from her job recently, and she has saved about $500,000 over the
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Let y represent the distance from your house to wawa. This means that the distance from wawa to your house is also y miles.
It takes you 0.4 hours at x miles per hour to make it to Wawa.
Distance = speed * time
Therefore, on your way to wawa, the expression would be
y = 0.4 * x = 0.4x
On your way back you have to ride 3 miles per hour slower. This means that your speed was (x - 3) miles per hour. Since it took you 0.5 hours, the expression for distance would be
y = 0.5(x - 3)
Since the distance is the same, it means that
0.4x = 0.5(x - 3)
0.4x = 0.5x - 1.5
0.5x - 0.4x = 1.5
0.1x = 1.5
x = 1.5/0.1
x = 15
Therefore,
y = 0.4x = 0.4 * 15
y = 6
The distance from your house to wawa is 6 miles
Find the maximum value of the objective function and the values of x and y for which it occurs. F= 2x+y3x+5y ≤45 x ≥0 and y ≥02x+4y ≤32The maximum value of the objective function is ______.
Answers
The objective function is:
[tex]F=2x+y[/tex]We need to find the shaded region where 4 inequalities overlap, then we need to graph the given inequalities:
[tex]\begin{gathered} 3x+5y\leq45 \\ 5y\leq-3x+45 \\ y\leq\frac{-3}{5}x+\frac{45}{5} \\ y\leq-\frac{3}{5}x+9 \end{gathered}[/tex]And the other one:
[tex]\begin{gathered} 2x+4y\leq32 \\ 4y\leq-2x+32 \\ y\leq\frac{-2x}{4}+\frac{32}{4} \\ y\leq-\frac{1}{2}x+8 \end{gathered}[/tex]And x>=0, y>=0
The graph is:
The coordinates of the shaded region are then:
(0,0), (0,8), (10,3) and (15,0)
To obtain the maximum value, let's evaluate the objective function in all the coordinates:
[tex]\begin{gathered} F(0,0)=2\times0+0=0+0=0 \\ F(0,8)=2\times0+8=0+8=8 \\ F(10,3)=2\times10+3=20+3=23 \\ F(15,0)=2\times15+0=30+0=30 \end{gathered}[/tex]Then, the maximum value is the largest value obtained, then it's 30 and it occurs at x=15 and y=0.
What is the solution to the inequality x(x – 3) > 0?Question 8 options:A) x ≤ 0 or x ≥ 3B) x < 0 or x > 3C) x ≤ 0 and x ≥ 3D) 0 < x < 3
Answers
,Inequalities
It's given the inequality:
x(x - 3) > 0
Note the left side is the product of two expressions: x and x-3.
That product must be greater than zero, or positive.
Recall that the product of two numbers is positive in two different cases:
Both are positive, for example 5*4=20
Both are negative, for example (-5)*(-4) = 20
This means that we can provide two different answers to the inequality, both valid:
1. When x >0 AND x - 3 >0 (both positive), or
2. When x <0 AND x - 3 < 0 (both negative).
The first condition leads to:
x>0 AND x>3. If we intersect these conditions, the solution for this part is x>3.
The second condition gives us:
x<0 AND x<3. The intersection of these conditions gives x<0.
Thus, the final solution is the union (OR) both partial intervals above, i.e.
x>3 OR x<0 --> Option B)
Answer:
X < 0 and x > 3.
Step-by-step explanation:
chatgpt.
Solve by using substitution.=−3−3=−4−5
Answers
hdhduxhx, this is the solution to the exercise:
Multiplying by -1 the second equation, we have:
y = -3x - 3
-y = 4x + 5
____________
0 = x + 2
x = -2
_____________
Now we can solve for y in the first equation, this way:
y = - 3x - 3
y = -3 (-2) - 3
y = 6 - 3
y = 3
____________
Finally, let's prove that x = -2 and y = 3 is correct for the second equation, as follows:
y = -4x - 5
3 = -4 (-2) - 5
3 = 8 - 5
3 = 3
___________
We proved that x = -2 and y = 3 is correct.
3. The difference of two-thirds of a number x and6 is at least -24. Which inequality represents allpossible values for x?
Answers
We will solve as follows:
The expression represented in the text is:
[tex]\frac{2}{3}x-6\ge-24[/tex]Now, we solve for x:
[tex]\Rightarrow\frac{2}{3}x\ge-18\Rightarrow2x\ge-54[/tex][tex]\Rightarrow x\ge-27[/tex]So, the solution is x >= 27. [Option D]
What is (6/7)/(2/7)?
Answers
To find the value of;
[tex]\frac{(\frac{6}{7})}{(\frac{2}{7})}[/tex]When dividing fractions, for example a divided by b is equals a times 1/b;
[tex]a\text{ divided by b = a }\times\frac{1}{b}[/tex]note that the divisor which is b is inversed and multiplied.
So, let us apply the same rule to the given question.
The divisor which is the second fraction for the question is 2/7, we need to inverse 2/7 and multiply it by the first fraction.
The inverse of 2/7 is 7/2, So;
[tex]\frac{(\frac{6}{7})}{(\frac{2}{7})}=\text{ }\frac{6}{7}\times\frac{7}{2}=\frac{(6\times7)}{(7\times2)}=\frac{42}{14}[/tex]And finally;
[tex]\frac{42}{14}=3[/tex]Therefore the final answer is 3.
[tex]\frac{(\frac{6}{7})}{(\frac{2}{7})}=\text{ 3}[/tex]