Two weather stations are aware of a thunderstorm located at point C. The weather stations A and B are 24 miles apart.
Answers
Assuming the dashed lines are parallel and perpendicular to the base, we can start by draw a third parallel line that passes through C and naming some distances:
Now, we can see that the given angles are alternate interior angles with respect to the angles formed by the new perpendicular line and the lines AC and BC:
Now, we can see that b and the base a + 24 are related with the tangent of 48°:
[tex]\tan 48\degree=\frac{a+24}{b}[/tex]Also, b and a are related with the tangent of 17°:
[tex]\tan 17\degree=\frac{a}{b}[/tex]We can solve both for b and equalize them:
[tex]\begin{gathered} b=\frac{a+24}{\tan48\degree} \\ b=\frac{a}{\tan17\degree} \\ \frac{a+24}{\tan48°}=\frac{a}{\tan17\degree} \\ a\tan 17\degree+24\tan 17\degree=a\tan 48\degree \\ a\tan 48\degree-a\tan 17\degree=24\tan 17\degree \\ a(\tan 48\degree-\tan 17\degree)=24\tan 17\degree \\ a=\frac{24\tan17\degree}{\tan48\degree-\tan17\degree}=\frac{24\cdot0.3057\ldots}{1.1106\ldots-0.3057\ldots}=\frac{7.3375\ldots}{0.8048\ldots}=9.1162\ldots \end{gathered}[/tex]Now, we can relate a and x with the sine of 17°:
[tex]\begin{gathered} \sin 17\degree=\frac{a}{x} \\ x=\frac{a}{\sin17\degree}=\frac{9.1162\ldots}{0.2923\ldots}=31.18\ldots\approx31.2 \end{gathered}[/tex]And x is the distance between A and C, the storm. Thus the answer is approximately 31.2 miles, fourth alternative.
Related Questions
find each percent of change 50.5 and 75
Answers
Answer: 48.5%
Explanation:
The quantity 50.5 incresed to 75. The change in value is:
[tex]75-50.5=24.5[/tex]The change was 24.5, so we need to find what percentage of 50.5 is 24.5.
For this we can use the rule of three.
Quantity Percentage
50.5 ---> 100%
24.5 ---> x
this means that if 50.5 is the 100%, 24.5 is a percentage x. This percentage x is found using the rule of three by multiplying que cross quantities in the last table (24.5 by 100), and then dividing by the remaining amount (50.5).
Thus:
[tex]x=\frac{24.5\cdot100}{50.5}=\frac{2450}{50.5}=48.5[/tex]The percentage change between 50.5 and 75 is 48.5%
what digit is in the
Answers
Explanation:
A.
1. We did not start with 1 because 1 is less than 3. Because of that, we start with 16. 16 divide by 3 = 5.
2. 5 times 3 = 15
3. 16 minus 15 = 1.
B.
1. Since 1 is again less than 3, we brought down another 6. The new dividend is 16. 16 divide by 3 = 5.
2. 5 times 3 = 15
3. 16 minus 15 = 1.
C.
1. Again, 1 is less than 3. We bring down the next number which is 2. The new dividend is now 12. 12 divided by 3 = 4.
2. 4 times 3 = 12.
3. 12 minus 12 = 0
D.
1. Again, zero is less than 3. We bring down the last number 4. The new dividend is 4. 4 divided by 3 = 1.
2. 1 times 3 = 3.
3. 4 minus 3 = 1. Since there is no more number to bring down, 1 is the remainder.
The answer for this division is 5 541 with a remainder of 1.
TRIGfind the following in triangle CAT.lineAT is 16.5angleT is 43degrees how do I solve?
Answers
h= 22.6, CT =47º, CA=15.4
1) We're going to use trig ratios for that. So to find CT, the hypotenuse, and considering the angle 43º as our reference, we can write:
[tex]\begin{gathered} \cos (43)=\frac{adjacent}{\text{hypotenuse}} \\ \cos (43)\text{ =}\frac{16.5}{h} \\ \cos (43)h=16.5 \\ h=\frac{16.5}{\cos (43)} \\ h=22.5609\approx22.6 \end{gathered}[/tex]So the CT is equal approximately to 22.6.
2) Now let's find out the measure of angle C. The simplest way is to consider the fact that every triangle has the sum of its interior angles as 180º
90º +43º + C = 180º
133º + C = 180º
C =180º -133º
C = 47º
3) Let's focus on CA leg.
Concerning that, we can make use of another trig ratio. Since we know the measure of angle C
[tex]\begin{gathered} \tan (47)=\frac{opposite}{\text{adjacent}} \\ \tan (47)\text{ =}\frac{16.5}{CA} \\ CA=\frac{16.5}{\tan (47)} \\ CA\text{ =15.38649}\approx15.4 \end{gathered}[/tex]CA is approximately 15.4
If △STU is similar to △XYZ, the sides of △STU must be congruent to thecorresponding sides of △XYZ.A. TrueB. False
Answers
Similar triangles are triangles that have the same interior angles and the corresponding sides are proportional, that is, for triangles STU and XYZ we have the proportion:
[tex]\frac{ST}{XY}=\frac{TU}{YZ}=\frac{SU}{XZ}[/tex]The corresponding sides are congruent only if the proportion rate is 1, but that is not always true and it's not necessary.
Therefore the correct option is B: False
If the corresponding sides are congruent, the triangles are congruent.
during 24 ow much hours Allan spend lisining music
Answers
spendlisteningSolution
Note: we need to find the time he will be using for listenng to music and playing Tennis and then subtract them
[tex]\begin{gathered} 1)\text{Time use for listening to music : } \\ \frac{12}{100}\times\text{ 24 = }\frac{288}{100}\text{ = 2.88hours} \\ \\ 2)\text{Time spendth in playing Tennis} \\ \frac{10}{100}\times24\text{ = }\frac{240}{100}=\text{ 2.4hours} \\ \\ \text{Difference in time = }2.88\text{ - 2.4} \\ \text{ = 0.48} \\ \text{Answer = 0.48 hour.} \end{gathered}[/tex]Many water bottles contain 16 fluid ounces, or 1 pint, of water. Drink labels often show the number of fluid ounces and the number of milliliters in a container. How many milliliters are in a 16-fluid-ounce drink?29.6 milliliters = 1 fluid ouncesPart A-D
Answers
Answer:
473.6 milliliters
Explanation:
A. One rate is the conversion factor
First, we know that 29.6 milliliters are equivalent to 1 fluid ounce, so the first rate of the conversion factor is:
[tex]\frac{29.6mL}{1\text{ fl oz}}[/tex]B. The other rate relates the known amount to the unknown converted amount
Then, we want to know how many milliliters are in 16 fluid ounces, so the other rate is:
[tex]\frac{x\text{ mL}}{16\text{ fl oz}}[/tex]C. Set the rates equal to one another.
[tex]\frac{29.6\text{ mL}}{1\text{ fl oz}}=\frac{x\text{ mL}}{16\text{ fl oz}}[/tex]D. multiply both parts of the left rate by a number that will make the number of fluid ounces in the two rates the same.
The number that will make the fluid ounces in the two rates the same is 16, so we need to multiply by 16
[tex]\frac{29.6\text{ mL x 16}}{1\text{ fl oz x 16}}=\frac{473.6\text{ mL}}{16\text{ fl oz}}[/tex]Therefore, there are about 473.6 milliliters in 16 fluid ounces.
At basketball tryouts, Jeremiah will shoot a 1-point shot, 2-point shot, and a 3-point shot one after theother. The table below shows Jeremiah's probability of making each shot:ShotProbability of making1-point80%2-point50%3-point30%Assume the outcome of one shot doesn't change the probability of other shots.The coach will record the total points Jeremiah scores from these 3 shots.Which graph represents the theoretical probability distribution of Jeremiah's total points?Choose 1 answer:
Answers
The graph that represents the theoretical probability distribution of Jeremiah's total points is given by:
Graph A.
What is a probability distribution?The probability of an event in an experiment is calculated as the absolute frequency of the desired outcomes in the experiment divided by the total number of outcomes in the experiment.
The probability distribution gives the probability of all possible events in the context of the problem.
For Jeremiah to make zero points, he needs to:
Miss the 1 - point shot: 0.2 probability.Miss the 2 - point shot: 0.5 probability.Miss the 3 - point shot: 0.7 probability.Hence:
P(X = 1) = 0.2 x 0.5 x 0.7 = 0.07 = 7%.
For Jeremiah to make one point, he needs to:
Make the 1 - point shot: 0.8 probability.Miss the 2 - point shot: 0.5 probability.Miss the 3 - point shot: 0.7 probability.Hence:
P(X = 1) = 0.8 x 0.5 x 0.7 = 0.28 = 28%.
For Jeremiah to make two points, he needs to:
Miss the 1 - point shot: 0.2 probability.Make the 2 - point shot: 0.5 probability.Miss the 3 - point shot: 0.7 probability.Hence:
P(X = 2) = 0.2 x 0.5 x 0.7 = 0.07.
For Jeremiah to make three points, he needs to either:
Miss the 1 - point shot: 0.2 probability.Miss the 2 - point shot: 0.5 probability.Make the 3 - point shot: 0.3 probability.Or:
Make the 1 - point shot: 0.8 probability.Make the 2 - point shot: 0.5 probability.Miss the 3 - point show: 0.7 probability.Hence:
P(X = 3) = 0.2 x 0.5 x 0.3 + 0.8 x 0.5 x 0.7 = 0.31.
For Jeremiah to make four points, he needs to:
Make the 1 - point shot: 0.8 probability.Miss the 2 - point shot: 0.5 probability.Make the 3 - point shot: 0.3 probability.Hence:
P(X = 4) = 0.8 x 0.5 x 0.3 = 0.12.
For Jeremiah to make five points, he needs to:
Miss the 1 - point shot: 0.2 probability.Make the 2 - point shot: 0.5 probability.Make the 3 - point shot: 0.3 probability.Hence:
P(X = 5) = 0.2 x 0.5 x 0.3 = 0.03.
For Jeremiah to make six points, he needs to:
Make the 1 - point shot: 0.8 probability.Make the 2 - point shot: 0.5 probability.Make the 3 - point shot: 0.3 probability.Hence:
P(X = 6) = 0.8 x 0.5 x 0.3 = 0.12.
Hence Graph A is correct, as it contains these probabilities.
More can be learned about probabilities at https://brainly.com/question/14398287
#SPJ1
I need to know the sum of the two terms
Answers
Answer: 194 degrees
From the given figure, we can see a transversal forming between the pairs of parallel lines.
Let us focus on the lines n, a, and e. Here, we can see a pair of parallel lines a and e, cut by a transversal n.
We are given a measurement for angle 4, which is 97. Then we are asked to find the sum of angle 2 and angle 4.
One theorem with respect to transversals that we must be familiar with is the Alternate Interior Angles Theorem which states that:
When two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.
With this, we can see from the figure that angle 2 and angle 4 are actually alternate interior angles.
Since they are alternate interior angles, and they are congruent, this would mean that angle 2 also measures 97.
[tex]m\angle4=97;m\angle2=97[/tex]With this, we can now add the two measurements, and that would give us:
[tex]97+97=194[/tex]The sum of angle 2 and angle 4 is 194 degrees.
Jim borrows $300 at 7% per annum compounded quarterly for 7 years. Determine the interest due on the loan.
Answers
Answer:
[tex]I=\text{ \$187.62}[/tex]Step-by-step explanation:
Compounded interest is represented as;
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{where,} \\ P=\text{ principal } \\ r=\text{ interest rate} \\ n=\text{ times compounded per unit time} \\ t=\text{ time in years} \end{gathered}[/tex]Therefore, for a principal of $300 at 7% per annum compounded quarterly;
[tex]\begin{gathered} A=300\cdot(1+\frac{0.07}{4})^{4\cdot7} \\ A=487.62 \\ \text{Then, the interest due would be the subtraction of A-P} \\ I=487.62-300 \\ I=\text{ \$187.62} \end{gathered}[/tex]What is the area, in square feet, of the trapezoid below?8.8 ft4 ft5-3 ft
Answers
We are asked to find the area of the trapezoid.
Recall that the area of the trapezoid is given by
[tex]A=\frac{1}{2}(b_1+b_2)\times h[/tex]Where b₁ is the length of base 1 that is 8.8 ft
b₂ is the length of base 2 that is 5.3 ft
h is the height that is 4 ft
Let us substitute the given values into the above formula
[tex]\begin{gathered} A=\frac{1}{2}(8.8+5.3)\times4 \\ A=\frac{1}{2}(14.1)\times4 \\ A=\frac{1}{2}(56.4)_{} \\ A=28.2ft^2 \end{gathered}[/tex]Therefore, the area of the trapezoid is 28.2 ft²
The area of the parallelogram is 273in squared what’s the height ?
Answers
The formula for determining the area of a parallelogram is expressed as
Area = base x height
Given that
base = 39
area = 273
Then,
273 = 39 x height
height = 273/39
height = 7 ft
Properties of Equality Addition Property of Equality Subtraction Property of Equality For real numbers a, b, and c, if a = b, For real numbers o, b, and c, if a = b, then a +C= then a-c= Multiplication Property of Equality Division Property of Equality For real numbers a, b, andc, if a = b and For real numbers o, b, and c, ifo =b and cz0, C0, then a c then = C
Answers
y = -9
Explanation:
we simplify the expression to get y: 2/3 y + 15 = 9
[tex]\begin{gathered} \frac{2}{3}y\text{ + 15 = 9} \\ \text{Subtract both sides }by\text{ 15} \\ \frac{2}{3}y\text{ + 15 -15 = 9 - 15} \\ \text{This is a subtraction property of equality} \\ \frac{2}{3}y\text{ = -}6 \end{gathered}[/tex][tex]\begin{gathered} \text{Multiply both sides by the inverse of }the\text{ coefficient of y} \\ \text{coefficent of y = 2/3 } \\ inverse\text{ of the }coefficent\text{ of y = 2/3} \\ \frac{2}{3}y\times\frac{3}{2}\text{ = -6}\times\text{ }\frac{3}{2} \\ it\text{ is a Multiplication property of equality: }a\times c\text{ = b}\times\text{ c} \\ y\text{ = -18/2} \\ \end{gathered}[/tex][tex]y\text{ = -9 }[/tex]What is the slope of the line that passes through the points (9, 5) and (21,-5)?
Answers
The equation of the line that passes through points (9, 5) and (21,-5) isy = (-5/6)x - 25/2.
How does the slope intercept form made?The slope-intercept form of an a line is a method of writing the equation of a line so that the slope as well as y-intercept are easily identifiable.The the line's slope represents its steepness, and also the y-intercept is the point at which the line intersects a y-axis.For the given question;
The line passes through points are-
(x1, y1) =(9, 5) and
(x2, y2) = (21,-5)
Slope = m = (y2 - y1)/(x2 - x1)
m = (-5 - 5)/(21 - 9)
m = -10/12
m = -5/6
Equation of the line is found using slope intercept form.
y - y1 = m (x - x1)
y - 5 = (-5/6)(x - 9)
y = (-5/6)x - 25/2
Thus, the equation of the line that passes through points (9, 5) and (21,-5) isy = (-5/6)x - 25/2.
To know more about the slope intercept form, here
brainly.com/question/1884491
#SPJ13
Which point has the coordinates (-2.5, 5.5)? A.point EB.point FC.point GD.point H
Answers
Write equation below matches the following statement?Five more than two times a number,n, is sixteen.
Answers
"Five more than two times n" indicates that you have to multiply n by 2 and add 5, the result of this operation is 16, so the expression is:
[tex]2n+5=16[/tex]3|x + 1| - 9 = 0? Solution set?
Answers
x = (2, -4)
Explanation:Given:
[tex]\begin{gathered} 3|x+1|-9=0 \\ \\ 3|x+1|=9 \\ \\ |x+1|=3 \\ \\ x+1=3 \\ \Rightarrow x=2 \\ \\ OR \\ -(x+1)=3 \\ \\ -x-1=3 \\ \\ -x=3+1 \\ \\ -x=4 \\ \\ x=-4 \end{gathered}[/tex]x = (2, -4)
Evaluate each of the following. Illustrate with a point on the graph g(-2)=g(3)=g(0)=g(7)=
Answers
Solution
From the graph given we have this:
g(-2)= -3
g(3)= 4
g(0)= -3
g(7)= 0
A fruit bowl contains 4 green apples, 7 red apples, and 5 yellow apples. What is the probability that a randomly selected apple will NOT be red?
Answers
Problem
A fruit bowl contains 4 green apples, 7 red apples, and 5 yellow apples. What is the probability that a randomly selected apple will NOT be red?
Solution
For this case we can find the total number of apples like this:
4+7+5= 16 apples
And the number of apples not red are:
4 + 5= 9 apples
Then the probability of being not red would be:
p = 9/16
If you will conduct a research about the poor study habits of Grade 7 students, how will you present your research problem using mathematical function?
Answers
I would define what a poor study habit is, using a parameter like study time in hours or days.
Let a study time of at least 2 hours per day be good, and less than 2 hours per day be poor.
Let f(x) be the study habit of a particular grade, so we write:
Good study time as:
[tex]f(x)\ge2[/tex]Bad study time as:
[tex]f(x)<2[/tex]The last one can represent the study habits of Grade 7 students.
0 2 4 6 8 10 12 14 16 What is the interquartile range of plot A
Answers
The given Data set can be arranged in the ascending order as,
0,2,4,6,8,10,12,14,16.
After paying $7 for a movie ticket Grace still had $3.75 how much money did Grace have before buying the ticket A. $3.25B. $10.25C. $4.52D. $10.75
Answers
D. $10.75
To solve this we have to write an equation:
Movie ticket price: $7
Money left : $3.75
Original amount: x
The original amount (x) minus the price of the ticket(7) must be equal to the money left after the purchase (3.75)
x-7 =3.75
Solving for x:
x = 3.75+7
x = 10.75
Write the equation of the line on the graph.
Answers
Answer:
The correct equation is
[tex]y = - \frac{7}{5} x + 4[/tex]
Choose all of the expressions that are equivalent to 2 1/2 divided by 1 2/6A 5/2 times 6/8B 2/5 times 6/8C 1 2/6 divided by 2 1/2D 5/2 divided by 8/6
Answers
A scatter plot showed a positive correlation for 11 bowlers. As the number of strikes, s, a bowler made in a game increased, the number of points, p, the bowler scores also increased. The equation for the line of best fit for the data is p = 25s + 40. Estimate the number of strikes made by a bowler with 140 points. A) 4B) 6C) 25D) 40
Answers
The model variables the relationship between the strikes (s) and the number of points scored (p)
[tex]p=25s+40[/tex]To determine the number of strikes made, so that 140 points where scored, you have to replace the model with p=140 and solve for s
[tex]140=25s+40[/tex]The first step is to pass "40" to the others side of the equal sing, by performing the inverse operation "-40" to both sides of the expression
[tex]\begin{gathered} 140-40=25s+40-40 \\ 100=25s \end{gathered}[/tex]Then you have to divide both sides of the expression by 25 to determine the value of s
[tex]\begin{gathered} \frac{100}{25}=\frac{25s}{25} \\ 4=s \end{gathered}[/tex]The bowler made s=4 strikes, the correct choice is A.
writing exponential functions (4, 112/81), (-1, 21/2)
Answers
The given points are (4, 112/81) and (-1, 21/2).
To find an exponential function from the given points, we have to use the forms.
[tex]\begin{gathered} y_1=ab^{x_1} \\ y_2=ab^{x_2} \end{gathered}[/tex]Now, we replace each point in each equation.
[tex]\begin{gathered} \frac{112}{81}=ab^4 \\ \frac{21}{8}=ab^{-1} \end{gathered}[/tex]We solve this system of equations.
Let's isolate a in the second equation.
[tex]\begin{gathered} \frac{21}{8}=\frac{a}{b} \\ \frac{21b}{8}=a \end{gathered}[/tex]Then, we replace it in the first equation
[tex]\frac{112}{81}=(\frac{21b}{8})\cdot b^4[/tex]We solve for b.
[tex]\begin{gathered} \frac{112\cdot8}{81\cdot21}=b\cdot b^4 \\ \frac{896}{1701}=b^5 \\ b=\sqrt[5]{\frac{896}{1701}}=\frac{2\sqrt[5]{4}}{3} \\ b\approx0.88 \end{gathered}[/tex]Once we have the base of the exponential function, we look for the coefficient a.
[tex]a=\frac{21b}{8}=\frac{21}{8}(\frac{2\sqrt[5]{4}}{3})=\frac{7\sqrt[5]{4}}{4}[/tex]Therefore, the exponential function is[tex]y=\frac{7\sqrt[5]{4}}{4}\cdot(\frac{2\sqrt[5]{4}}{3})^x[/tex]The image below shows the graph of this function.
19. Which of the following regions represent the points in the solution of the inequality x ≤ 1? a. Left of the line x = 1 b. On and left of the line x = 1 c. On and right of the line x = 1 d. Right of the line x = 1
Answers
ANSWER
b. On and left of the line x = 1.
EXPLANATION
The inequality is x less than or equal to 1. This means that the line x = 1 is included in the solution, which leaves us with options b or c.
To represent the values less than x = 1, we would take the values to the left of the line.
Hence, the region that represents the solutions of x ≤ 1 is on and left of line x = 1.
why aren't 38 and 40 relatively prime
Answers
No they aren't relatively because they don't come from the same prime number
Out of 50 students, 17 want pepperoni pizza, 19 want sausage pizza and the rest want a supreme pizza. What percent of the students want a supreme pizza?
Answers
First, lets find how many students want the supreme pizza. Let 'x' be the number of those students. Then, given the information, we have:
[tex]x+17+19=50[/tex]solving for 'x', we get:
[tex]\begin{gathered} x+17+19=50 \\ \Rightarrow x+36=50 \\ \Rightarrow x=50-36=14 \\ x=14 \end{gathered}[/tex]we have that x = 14 students want a supreme pizza.
Now, if we suppose that the 50 students are the 100%, then, using a rule of three, we get:
[tex]\begin{gathered} 50\rightarrow100\% \\ 14\rightarrow y\% \\ \Rightarrow y=\frac{14\cdot100}{50}=\frac{1400}{50}=28 \\ y=28\% \end{gathered}[/tex]therefore, 28% of the students want a supreme pizza
How many solutions exist for the equation cos 2θ − sin θ = 0 on the interval [0, 360°)?
Answers
We are given the following equation
[tex]\cos 2\theta-\sin \theta=0[/tex]Let us solve the above trigonometric equation.
Using the double angle identity,
[tex]\cos 2\theta=1-2\sin ^2\theta[/tex]So, the equation becomes
[tex]\begin{gathered} \cos 2\theta-\sin \theta=0 \\ 1-2\sin ^2\theta-\sin \theta=0 \end{gathered}[/tex]Now, let us solve the equation by substitution
Let sinθ = u
[tex]\begin{gathered} 1-2\sin ^2\theta-\sin \theta=0 \\ 1-2u^2-u=0 \\ -2u^2-u+1=0 \end{gathered}[/tex]Let us solve the above equation using the quadratic formula
[tex]u=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]The coefficients are
a = -2
b = -1
c = 1
[tex]\begin{gathered} u=\frac{-(-1)\pm\sqrt[]{(-1)^2-4(-2)(1)}}{2(-2)} \\ u=\frac{1\pm\sqrt[]{1+8}}{-4} \\ u=\frac{1\pm\sqrt[]{9}}{-4} \\ u=\frac{1\pm3}{-4} \\ u=\frac{1-3}{-4},\; \; u=\frac{1+3}{-4} \\ u=\frac{-2}{-4},\; \; u=\frac{4}{-4} \\ u=\frac{1}{2},\; \; u=-1 \end{gathered}[/tex]So, the two possible values are u = 1/2 and u = -1
Substitute them back into sinθ = u
[tex]\begin{gathered} \sin \theta=\frac{1}{2},\; \; \sin \theta=-1 \\ \theta=\sin ^{-1}(\frac{1}{2}),\; \; \theta=\sin ^{-1}(-1) \\ \theta=\frac{\pi}{6}\; and\; \frac{5\pi}{6},\; \; \theta=\frac{3\pi}{2}\; \\ \theta=30\degree\; and\; \; 150\degree,\; \; \theta=270\degree \end{gathered}[/tex]Therefore, the two solutions of the given equation are θ = 30°, θ = 150°, θ = 270° on the interval [0, 360°)
Answer:
I got it correct, by graphing on desmos
Step-by-step explanation:
Look at picture
You phone a plumber for a quote on fixing your leaky pipes. You are quoted $190 for the service call and $90 per hour for the work. You are on a budget and can afford no more then $460 . Write an inequality to find the number of hours of work h you can afford. ( assume h greater than or equal 0) then solve the inequality
Answers
We want to find h which represents the number of hours of work that you can afford.
From the information given,
The charge per hour of work is $90. This means that the charge for h hours of work is
90 x h = 90h
The service fee is $190. This is a constant fee that must be paid irrespective of the number of hours. Thus, the total cost of h hours of work is
90h + 190
Again, you are on a budget and can afford no more then $460. This means that the amount that you can spend is less than or equal to $460. the symbol for representing 'less than or equal to' is '≤'
Therefore, the inequality that will be used to find the number of hours of work h you can afford is
90h + 190 ≤ 460
To solve the inequality, we would subtract 190 from both sides of the inequality. We have
90h + 190 - 190 ≤ 460 - 190
90h ≤ 270
We would divide both sides of the inequality by 90. We have
90h/90 ≤ 270/90
h ≤ 3