Question:
Solve the following inequality:
[tex]12x+6<17[/tex]Solution:
Consider the following inequality
[tex]12x+6<17[/tex]solving for 12x, we get:
[tex]12x<17-6[/tex]this is equivalent to:
[tex]12x<11[/tex]solving for x, we get:
[tex]x<\frac{11}{12}[/tex]so that, the correct answer is:
[tex]x<\frac{11}{12}[/tex]find the exact values of the six trigonometric functions of the angle 0 shown in the figure(Use the Pythagorean theorem to find the third side of the triangle)
The right angled triangle is given with reference angle theta.
The opposite side (facing the reference angle) is 3, while the hypotenuse (facing the right angle) is 5. The adjacent shall be calculated using the Pythagoras' theorem as follows;
[tex]\begin{gathered} \text{Adj}^2+3^2=5^2 \\ \text{Adj}^2=5^2-3^2 \\ \text{Adj}^2=25-9 \\ \text{Adj}^2=16 \\ \text{Adj}=\sqrt[]{16} \\ \text{Adj}=4 \end{gathered}[/tex]Therefore, the trigonometric functions of angle theta are shown as follows;
[tex]\begin{gathered} \sin \theta=\frac{opp}{hyp}=\frac{3}{5} \\ \cos \theta=\frac{adj}{hyp}=\frac{4}{5} \\ \tan \theta=\frac{opp}{adj}=\frac{3}{4} \\ \csc \theta=\frac{hyp}{opp}=\frac{5}{3} \\ \sec \theta=\frac{hyp}{adj}=\frac{5}{4} \\ \cot \theta=\frac{adj}{opp}=\frac{4}{3} \end{gathered}[/tex]Uptown Tickets charges $7 per baseball game tickets plus a $3 process fee per order. Is the cost of an order proportional to the number of tickets ordered?
The cost of an order is proportional to the number of tickets if the relation between them is constant.
Then, if we order 1 ticket the cost will be $7 + $3 = $10
And if we order 2 tickets, the cost will be $7*2 + $3 = $17
So, the relation between cost and the number of tickets is:
For 1 ticket = $10 / 1 ticket = 10
For 2 tickets = $17/ 2 tickets = 8.5
Since 10 and 8.5 are different, the cost of an order is not proportional to the number of tickets ordered.
Answer: they are not proportional
decide wether the following sides are acute obtuse or a right triangle.
The acute triangle is defined by the condition,
[tex]a^2+b^2The obtuse triangle is defined by the condition, [tex]a^2+b^2>c^2[/tex]Here, we have,
[tex]\begin{gathered} 19^2=361 \\ 12^2=144 \\ 15^2=225 \\ 12^2+15^2>19^2 \end{gathered}[/tex]Thus, the triangle is an obtuse triangle.
A family is traveling from their home to avacation resort hotel. The table below showstheir distance from home as a function of time.Time (hrs)0257Distance(mi)0140375480Determine the average rate of change betweenhour 2 and 7, including the units.
Let
x -------> the time in hours
y -------> the distance in miles
we know that
To find the average rate of change, we divide the change in the output (y) value by the change in the input value (x)
so
For x=2 h ------> y=140 mi
For x=7 h ------> y=480 mi
rate of change=(480-140)/(7-2)
rate of change=340/5=68 mi/h
The average rate of change is equal to the speed in this problem
Geometry Problem - Given: segment AB is congruent to segment AD and segment FC is perpendicular to segment BD. Conclusion: Triangle AEG is isosceles. (Reference diagram in picture)
As the triangle AEF has 2 angles with the same measure, triangle AEF is isosceles.
Graph the system below. What is the x-coordinate of the solution to the system of linear equations?y= -4/5x + 2y= 2/3x + 2A. -4B. 2C. 3D. 0
The solution is (x,y) = (0,2)
Simplify the expression.
the expression negative one seventh j plus two fifths minus the expression three halves j plus seven fifteenths
negative 19 over 14 times j plus 13 over 15
negative 19 over 14 times j minus 13 over 15
negative 23 over 14 times j plus negative 1 over 15
23 over 14 times j plus 1 over 15
The expression is simplified to negative 23 over 14 times j plus negative 1 over 15. Option C
What is an algebraic expression?An algebraic expression can be defined as an expression mostly consisting of variables, coefficients, terms, constants and factors.
Such expressions are also known to be composed or made up of some mathematical or arithmetic operations, which includes;
AdditionSubtractionDivisionBracketMultiplicationParentheses. etcFrom the information given, we have that;
negative one seventh j = - 1/7jtwo fifths = 2/5three halves j = 3/2 jseven fifteenths = 7/15Substitute the values
- 1/7j + 2/5 - 3/2j - 7/15
collect like terms
- 1/7j - 3/2j + 2/5 - 7/15
-2j - 21j /14 + 6 7 /15
-23j/14 + -1/15
Hence, the correct option is negative 23 over 14 times j plus negative 1 over 15
Learn more about algebraic expressions here:
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H D 2 cm 4 cm The two rectangles below are similar. What is the ratio of the perimeters of rectangle ABCD to rectangle EFGH? B А 4 cm E 8 cm F 2:1 8:1 1:4 1:2 2
In order to determine the ratio of the perimeters for the given rectangles, first calcualte their perimeters. Use the following formula:
P = 2w + 2l
w: width
l: length
For the smaller rectangle you have:
w = 2cm
l = 4 cm
P = 2(2cm) + 2(4cm) = 4cm + 8cm = 12cm
For the bigger triangle you have:
w' = 4cm
l' = 8cm
P' = 2(4cm) + 2(8cm) = 8cm + 16cm = 24cm
Then, you have:
P/P' = 12cm/24cm = 1/2
Hence, the ratio is 1:2
An independent third party found the cost of a basic car repair service for a local magazine. The mean cost is $217.00 with a standard deviation of $11.40. Which of the following repair costs would be considered an “unusual” cost?
Given
An independent third party found the cost of a basic car repair service for a local magazine.
The mean cost is $217.00 with a standard deviation of $11.40.
To find: The repair costs which would be considered an “unusual” cost.
Explanation:
It is given that, the mean is 217.00, and the standard deviation is 11.40.
Consider, the distribution as a Normal distribution.
Then, the first range is defined as,
[tex]\begin{gathered} First\text{ }range:mean\pm SD \\ \Rightarrow X_1=mean+SD \\ =217.00+11.40 \\ =228.4 \\ \Rightarrow X_2=mean-SD \\ =217.00-11.40 \\ =205.6 \end{gathered}[/tex]And, the second range is defined as,
[tex]\begin{gathered} Second\text{ }range:mean\pm2SD \\ \Rightarrow X_3=217.00+2(11.40) \\ =217.00+22.8 \\ =239.8 \\ \Rightarrow X_4=217.00-2(11.40) \\ =217.00-22.8 \\ =194.2 \end{gathered}[/tex]Hence, the answer is option a) 192.53 since it does not belongs to the above ranges.
Consider the parabola given by the equation: f ( x ) = − 2 x 2 − 12 x − 9 Find the following for this parabola: A) The vertex: B) The vertical intercept is the point C) Find the coordinates of the two x intercepts of the parabola and write them as a list of points of form (x, y) separated by commas: It is OK to round your value(s) to to two decimal places.
Answer:
it is C) find the coordinated of two x intercept is
Amtrak's annual passenger revenue for the years 1985 - 1995 is modeled approximately by the formulaR = -60|x- 11| +962where R is the annual revenue in millions of dollars and x is the number of years after 1980. In what year was the passenger revenue $722 million?In the years ____ and ___, the passenger revenue was $722 million.
ANSWER
1987 and 1995
EXPLANATION
The revenue is modeled by:
[tex]R=-60|x-11|+962[/tex]To find the years that the revenue was $722 million, we have to solve for x when R is 722.
That is:
[tex]\begin{gathered} 722=-60|x-11|+962 \\ \Rightarrow722-962=-60|x-11| \\ -240=-60|x-11| \\ \Rightarrow|x-11|=\frac{-240}{-60} \\ |x-11|=4 \end{gathered}[/tex]We can split the absolute value equation into two different equations because the term in the absolute value is equal to both the positive and the negative of the term on the other side of the equality.
That is:
[tex]\begin{gathered} x-11=4 \\ x-11=-4 \end{gathered}[/tex]Solve for x in both:
[tex]\begin{gathered} x=11+4 \\ \Rightarrow x=15 \\ x=11-4 \\ \Rightarrow x=7 \end{gathered}[/tex]That is to say 7 and 15 years after 1980.
Therefore, in the years 1987 and 1995, the revenue was $722 million.
Given the diagram below which could be used to calculate AC
Cos a = adjacent side / hypotenuse
Where:
a= angle = 37°
adjacent side = 20
Hypotenuse = x (the longest side , AC)
Replacing:
Cos (37)=20/ x (option B)
the variable y is directly proportional to x. if y equals -0.6 when x equals 0.24, find x when y equals -31.5.
You have that y is proportional to x. Futhermore, you have y = -0.6 when x = 0.24.
Due to y is proportional to x, you have the following equation:
[tex]y=kx[/tex]where k is the constant of proportionality. In order to find the value of x when y = -31.5, you first calculate k.
k is calculated by using the information about y=-0.6 and x=0.24. You proceed as follow:
y = kx solve for k
k = y/x replace by known x and y values
k = -0.6/0.24
k = -2.5
Hence, the constant of proportionality is -2.5.
Next, you use the same formula for the relation between y and x to find the value of x when y = -31.5. You proceed as follow:
y = kx solve for x
x = y/
State which pairs of lines are:(a) Parallel to each other.(b) Perpendicular to each other.
So first of all we should write the three equations in slope-intercept form. This will make the problem easier to solve. Remember that the slope-interception form of an equation of a line looks like this:
[tex]y=mx+b[/tex]Where m is known as the slope and b the y-intercept. The next step is to rewrite the second and third equation since the first equation is already in slope-intercept form. Its slope is 4 and its y-intercept is -1.
So let's rewrite equation (ii). We can begin with substracting 4 from both sides of the equation:
[tex]\begin{gathered} 8y+4=-2x \\ 8y+4-4=-2x-4 \\ 8y=-2x-4 \end{gathered}[/tex]Then we can divide both sides by 8:
[tex]\begin{gathered} \frac{8y}{8}=\frac{-2x-4}{8} \\ y=-\frac{2}{8}x-\frac{4}{8} \\ y=-\frac{1}{4}x-\frac{1}{2} \end{gathered}[/tex]So its slope is -1/4 and its y-intercept is -1/2.
For equation (iii) we can add 8x at both sides:
[tex]\begin{gathered} 2y-8x=-2 \\ 2y-8x+8x=-2+8x \\ 2y=8x-2 \end{gathered}[/tex]Then we can divide both sides by 2:
[tex]\begin{gathered} \frac{2y}{2}=\frac{8x-2}{2} \\ y=\frac{8}{2}x-\frac{2}{2} \\ y=4x-1 \end{gathered}[/tex]Then its slope is 4 and its y-intercept is -1. As you can see this equation is equal to equation (i).
In summary, the three equations in slope-intercept form are:
[tex]\begin{gathered} (i)\text{ }y=4x-1 \\ (ii)\text{ }y=-\frac{1}{4}x-\frac{1}{2} \\ (iii)\text{ }y=4x-1 \end{gathered}[/tex]It's important to write them in this form because when trying to figure out if two lines are parallel or perpendicular we have to look at their slopes:
- Two lines are parallel to each other if they have the same slope (independently of their y-intercept).
- Two lines are perpendicular to each other when the slope of one of them is the inverse of the other multiplied by -1. What does this mean? If a line has a slope m then a perpendicular line will have a slope:
[tex]-\frac{1}{m}[/tex]Now that we know how to find if two lines are parallel or perpendicular we can find the answers to question 4.
So for part (a) we must find the pairs of parallel lines. As I stated before we have to look for those lines with the same slope. As you can see, only lines (i) and (iii) have the same slope (4) so the answer to part (a) is: Lines (i) and (iii) are parallel to each other.
For part (b) we have to look for perpendicular lines. (i) and (iii) are parallel so they can't be perpendicular. Their slopes are equal to 4 so any line perpendicular to them must have a slope equal to:
[tex]-\frac{1}{m}=-\frac{1}{4}[/tex]Which is the slope of line (ii). Then the answer to part (b) is that lines (i) and (ii) are perpendicular to each other as well as lines (ii) and (iii).
in this problem you will use a ruler to estimate the length of AC. afterwards you will be able to see the lengths of the other two sides and you will use the pythagorean theorem to check your answer
Answer:
5.124
Explanation:
Given the following sides
AB = 6.5cm
BC = 4.0cm
Required
AC
Using the pythagoras theorem;
AB^2 = AC^2 + BC^2
6.5^2 = AC^2 + 4^2
42.25 = AC^2 + 16
AC^2 = 42.25 - 16
AC^2 = 26.25
AC = \sqrt{26.25}
AC = 5.124
Hence the actual length of AC to 3dp is 5.124
(Please show your work for question 18.)
It is given that AB = CB from this information we conclude that <A=<C by reason :angles opposite equal sides.
<A+<B+<C=180°(Sum of angles in a triangle)
[tex](4x - 13) + (5x - 2) + (4x - 13) = 180 \\ 4x + 5x + 4x - 13 - 2 - 13 = 180 \\ 13x - 28 = 180 \\ 13x = 180 + 28 \\ 13x = 208 \\ \frac{13x}{13} = \frac{208}{13} \\ x = 16[/tex]
x=6°
ATTACHED IS THE SOLUTION
GOODLUCK
what is 0.09 as a percentage?
I have to create a graph but I need some help and clarification
To complete the table you evaluate the equation by the given value of x to find the corresponding value of y:
[tex]y=x+4[/tex][tex]\begin{gathered} x=4 \\ \\ y=4+4 \\ y=8 \\ \\ (4,8) \end{gathered}[/tex][tex]\begin{gathered} x=8 \\ \\ y=8+4 \\ y=12 \\ \\ (8,12) \end{gathered}[/tex][tex]\begin{gathered} x=12 \\ \\ y=12+4 \\ y=16 \\ \\ (12,16) \end{gathered}[/tex][tex]\begin{gathered} x=16 \\ \\ y=16+4 \\ y=20 \\ \\ (16,20) \end{gathered}[/tex]To put those (x,y) points in the plane;
the frist coordinate x is the number of units you move to the left (if x is negative) or to the right (if x is positive)
the second coordinate y is the number of units you move down (if y is negative) or up (if y is positive)
Then, using the points (0,4), (4,8), (8,12), (12,16) and (16,20) you get the next graph for y=x+4:
The Caldwell family placed a large back-to-school order online. The total cost of the clothing was $823,59 and the shipping weight was 32 lb. 10 oz. They live in the LocalZone (shipping = $5.87, plus $. 11 per lb. for each lb. or fraction of a lb. above 15 lbs.) and the sales tax rate is 7.5%. Find the total cost of the order.$864.43$876.77$893.21o $901.22None of these choices are correct.
The breakdown of fees paid by the Caldwell family are calculated and shown below;
[tex]\begin{gathered} \text{Total cost of clothing = \$823.59} \\ \text{Sales tax = 7.5\% of \$823.59} \\ =\frac{7.5}{100}\times823.59=61.769 \\ \text{Sales tax = \$61.77} \\ \\ \text{Shipping fe}e \\ \text{Total weight of item = 32lb 10oz }\approx\text{ 33lb} \\ \text{The excess weight above 15lbs = 33 - 15=18lbs} \\ \text{Shipping cost on the extra 18lbs = \$0.11}\times18=1.98 \\ \text{Total cost on shipping = \$5.87+\$1.98=\$7.85} \end{gathered}[/tex]The total cost of the order will now be
Total cost of clothing = $823.59
Shipping cost = $7.85
Sales tax = $61.77
TOTAL = $823.59 + $7.85 + $61.77 = $893.21
Therefore, the total cost of the order is $893.21
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Answer:
√52
Step-by-step explanation:
[tex] \sqrt{ {(4 - ( - 2))}^{2} + {(1 - ( - 3))}^{2} } [/tex]
[tex] \sqrt{ {6}^{2} + {4}^{2} } = \sqrt{36 + 16} = \sqrt{52} [/tex]
write the exponential function for the data displayed in the following table
As per given by the question,
There are given that a table of x and f(x).
Now,
The genral for of the equation is,
[tex]f(x)=ab^x[/tex]Then,
For the value of x and f(x).
Substitute 0 for x and -2 for f(x).
So,
[tex]\begin{gathered} f(x)=ab^x \\ -2=ab^0 \\ -2=a \end{gathered}[/tex]Now,
For the value of b,
Substitute 1 for x and -1/3 for f(x),
So,
[tex]\begin{gathered} f(x)=ab^x \\ -\frac{1}{3}=ab^1 \\ ab=-\frac{1}{3} \end{gathered}[/tex]Now,
Put the value of a in above result.
So,
[tex]\begin{gathered} ab=-\frac{1}{3} \\ -2b=-\frac{1}{3} \\ b=\frac{1}{6} \end{gathered}[/tex]Now,
Put the value of a and b in the general form of f(x).
[tex]\begin{gathered} f(x)=ab^x \\ f(x)=-2\cdot(\frac{1}{6})^x \end{gathered}[/tex]Hence, the exponential function is ,
[tex]f(x)=-2(\frac{1}{6})^x[/tex]Solve x^2 - 3x - 10 = 0 by factoring. *Mark only one oval.O {-5,2}O (-2,-5)O {-2,5}○ {-10,1}
In order to solve this quadratic equation by factoring, we can do the following steps:
[tex]\begin{gathered} x^2-3x-10=0\\ \\ x^2-3x-5\cdot2=0\\ \\ x^2+2x-5x-5\cdot2=0\\ \\ x(x+2)-5(x+2)=0\\ \\ (x-5)(x+2)=0\\ \\ \begin{cases}x-5=0\rightarrow x=5 \\ x+2=0{\rightarrow x=-2}\end{cases} \end{gathered}[/tex]Therefore the solution is {-2, 5}. Correct option: third one.
144 grapefruits in 4 boxes, How many grapefruits in 100 boxes?
Problem
144 grapefruits in 4 boxes, How many grapefruits in 100 boxes?
Solution
for this case we can do the following proportional rule:
4/144 = x/100
And solving for x we got:
x= 100 (4/144)= 2.77
So between 2 and 3 grape fruits are expected
The ratio of students polled in 6th grade who prefer lemonade to iced tea is 8:4, or 2:1. If there were 39 students in 6th grade polled, explain how to find the number of students that prefer lemonade and the number of students that prefer iced tea. Be sure to tell how many students prefer each.
Since we know the ratio is 2:1, then to find the number of students who like iced tea we convert the ratio to a fraction:
[tex]\frac{1}{2}[/tex]this means that one of two students preferred iced tea.
To find the number of students who prefer iced tea we multiply the total number of students by the fraction, then:
[tex]39\cdot\frac{1}{2}=\frac{39}{2}=19.5[/tex]Since we can't have a fraction of a student, we conclude that 19 students prefer iced tea and 20 prefer lemonade.
Find the volume of 12 cm
Answer:
1728 cm ^ 3.
Step-by-step explanation:
we are given 12 cm
As we know formula of volume of cube = s ^3 ( side * side * side ) So = 12 * 12* 12 = 1728 cm ^ 3.
Find the Volume cylinder (8cm) (12cm) h = 8cm r = 12cm h = 8 cm r = 12 cm. The volume of a cylinder is equal to the area of the base πr2 π r 2 times the height. π⋅(radius)2 ⋅(height) π ⋅ ( r a d i u s) 2 ⋅ ( h e i g h t) Substitute the values of the radius r = 12 r = 12 and height h = 8 h = 8 into the formula to find the volume of the cylinder
P.s hopes this helps
Quadrilateral HGEF is a scaled copy of quadrilateral DCAB. What is themeasurement of lin EG?
Answer:
14 units
Explanation:
If quadrilaterals HGEF and DCAB are similar, then the ratio of some corresponding sides is:
[tex]\frac{FH}{BD}=\frac{EG}{AC}[/tex]Substitute the given side lengths:
[tex]\begin{gathered} \frac{6}{3}=\frac{EG}{7} \\ 2=\frac{EG}{7} \\ \implies EG=2\times7 \\ EG=14 \end{gathered}[/tex]The measurement of line EG is 14 units.
A local children's center has 46 children enrolled, and 6 are selected to take a picture for the center'sadvertisement. How many ways are there to select the 6 children for the picture?
The question requires us to find how many ways we can select 6 children from a total of 46.
The formula for combinations is given as follows;
[tex]nC_r=\frac{n!}{(n-r)!r!}[/tex]Where n = total number of children, and r = number of children to be selected. The combination now becomes;
[tex]\begin{gathered} 46C_6=\frac{46!}{(46-6)!6!} \\ 46C_6=\frac{46!}{40!\times6!} \\ 46C_6=\frac{5.5026221598\times10^{57}}{8.1591528325\times10^{47}\times720} \\ 46C_6=\frac{5.5026221598\times10^{10}}{8.1591528325\times720} \\ 46C_6=\frac{0.674410967996781\times10^{10}}{720} \\ 46C_6=\frac{6744109679.967807}{720} \\ 46C_6=9,366,818.999955287 \\ 46C_6=9,366,819\text{ (rounded to the nearest whole number)} \end{gathered}[/tex]Put the following equation of a line into slope-intercept form, simplifying all fractions.
4x-3y=9
Answer:
y=4/3x+3
Step-by-step explanation:
we know that slope intercept form is y=mx+b, where m is the slope and b is the y intercept
for 4x-3y=9, we have to isolate y
we subtract 4x to both sides to get
-3y=-4x+9
to get y alone, we divide both sides by -3
y=4/3x+3
Answer:
Y=4/3x-3
Step-by-step explanation:
Y=4/3x-3
the other guy had the right idea but the two negatives make a positive!
Identify all points and line segments in the picture below.Points: A, B, C, DLine segments: AB, BC, CD, AD, BD, ACPoints: A, B, C, DLine segments: AD, AC, DC, BOPoints: A, B, C, DLine segments: AB, AD, AC, DC, BCPoints: A, BLine segments: AB, AC, DC, BC
Option C
Points: A, B, C, D
Line segments: AB, AD, AC, DC, BC
Use a system of equations to solve the following problem.The sum of three integers is380. The sum of the first and second integers exceeds the third by74. The third integer is62 less than the first. Find the three integers.
the three integers are 215, 12 and 153
Explanation:
Let the three integers = x, y, and z
x + y + z = 380 ....equation 1
The sum of the first and second integers exceeds the third by 74:
x + y - 74 = z
x + y - z = 74 ....equation 2
The third integer is 62 less than the first:
x - 62 = z ...equation 3
subtract equation 2 from 1:
x -x + y - y + z - (-z) = 380 - 74
0 + 0 + z+ z = 306
2z = 306
z = 306/2
z = 153
Insert the value of z in equation 3:
x - 62 = 153
x = 153 + 62
x = 215
Insert the value of x and z in equation 1:
215 + y + 153 = 380
368 + y = 380
y = 380 - 368
y = 12
Hence, the three integers are 215, 12 and 153