The graph below shows the solution to which system of inequalities?A. x< 1 and y2 xB. ys 1 and y>xC. x≤ 1 and y> xD. y< 1 and y2
Answers
To answer this question let's look at each line first.
The slant line can be express by the equation:
[tex]y=x[/tex]We notice that the shaded part is above this line, then we have that that inequality is written as:
[tex]y\ge x[/tex]Now, the horizontal line is express as:
[tex]y=1[/tex]since the shaded region is below that line and the line is dashed the inequality is:
[tex]y<1[/tex]Therefore, the system of inequalities is:
[tex]\begin{gathered} y\ge x \\ y<1 \end{gathered}[/tex]Related Questions
What is the answer for x?
Answers
By the concept of parallels lines the value of x is 4 .
What are parallels lines?Coplanar, straight lines that don't intersect anywhere are considered parallel lines in geometry. Lines in the same three-dimensional space that never cross one another and are said to be parallel. Curves that are parallel to each other and maintain a setting a minimum distance do not touch or intersect. Lines in a plane that consistently have the same separation are said to be parallel. Nothing can cross a parallel line. Lines that cross at a straight angle of 90 degrees are called perpendicular lines. Two lines in the same plane that are equally spaced apart and never cross each other are referred to in geometry as parallel lines. Both vertical and horizontal can be used. Parallel line examples abound in daily life, such as the rows of notebooks and zebra crossings.
9x - 6 = 6x + 6
3x = 12
x = 4
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if f is defined by the function f(x)=x-4/x-2 then lim f(x) is equivalent to which of the following
Answers
Answer:
The correct answer is the third option:
[tex]\lim_{x\to4}(\sqrt{x}-2)[/tex]Explanation:
We have the function:
[tex]f(x)=\frac{x-4}{\sqrt{x}-2}[/tex]In the numerator, we have x - 4. We can rewrite it as a difference of squares, since:
[tex]\begin{gathered} x=(\sqrt{x})^2 \\ 4=2^2 \end{gathered}[/tex]Thus:
[tex]x-4=(\sqrt{x}-2)(\sqrt{x}+2)[/tex]Then, the limit:
[tex]\begin{gathered} \lim_{x\to4}(\frac{(\sqrt{x}-2)(\sqrt{x}+2)}{(\sqrt{x}-2)} \\ \end{gathered}[/tex]We can cancel out the terms, since we are taking limit, this is, numbers that infinitely close to 4, bt never 4. This way we can cancel the terms, and get:
[tex]\lim_{x\to4}(\sqrt{x}+2)[/tex]
Now finish solving the equation. What is the value of m?-(m - 6) = 3m + 14-m + 6 = 3m + 14-m + 6 - 3m = 3m + 14 - 3m-4m + 6 = 14m=
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D − 37 = 40D =Check your solution.− 37 = 40
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We have to solve this equation:
[tex]D-37=40[/tex]We can solve it for D by adding 37 on both sides of the equation as this won't change the equality:
[tex]\begin{gathered} D-37+37=40+37 \\ D=77 \end{gathered}[/tex]Answer: D = 77
Kyla is filling a water bucket that holds 5 and 1/4 gallons using a container that holds 3/4 of a gallon per container (a) Create a division problem that finds how many containers Kyla will need to use. Evaluate this quotient(b) Check your answer to (a) by using a product. Show your work
Answers
Given a water bucket that holds
[tex]5\frac{1}{4}gallons[/tex]A container with the measurement below was used to fill the water bucket
[tex]\frac{3}{4}\text{gallon}[/tex](a) The division problem that shows how many containers are needed to fill the water bucket is
[tex]\frac{5\frac{1}{4}}{\frac{3}{4}}[/tex]The quotient is as solved below:
[tex]5\frac{1}{4}=\frac{5\times4+1}{4}=\frac{21}{4}[/tex][tex]\begin{gathered} \frac{5\frac{1}{4}}{\frac{3}{4}}=\frac{\frac{21}{4}}{\frac{3}{4}} \\ \frac{21}{4}\frac{\square}{\square}\frac{3}{4} \\ =\frac{21}{4}\times\frac{4}{3} \end{gathered}[/tex][tex]\frac{7\times1}{1\times1}=7[/tex]Hence, the quotient is 7 Containers
(b) Checking the answer using a product as shown below
[tex]\begin{gathered} 7\times\frac{3}{4}=5\frac{1}{4} \\ \frac{7\times3}{4}=\frac{21}{4} \end{gathered}[/tex][tex]\frac{21}{4}=5\frac{1}{4}[/tex]Hence, the product of 7 and 3/4 gallons container will fill 5 1/4 water bucket
1 2 3 At the beginning of the day the temperature was - 17°C. At noon the thermometer read -2°C What is the total change in degrees Celsius?
Answers
The total change in temperature = temperature at noon minus temperature at the beginning of the day
[tex]=-2^0^{}c-(-17^0c)=-2^0c+17^0c=15^0c[/tex]Lynn got a $50 gift card to an online music store she uses the gift cards to buy an album for 9.99 she also wants to use the gift card to buy some songs. Each song cost 1.29. What equality is described the situation where n is the number of songs like monster by
Answers
ANSWER
B. 9.99 + 1.29n ≤ 50
EXPLANATION
The total amount of money she spends at the store has to be at most, the value of the gift card $50. This is the cost of the album, 9.99, and then 1.29 for each song. If the total number of songs is 'n', then for n songs, she'll spend 1.29n. In total she spends: 9.99 + 1.29n at the store. The equation is
[tex]9.99+1.29n\le50[/tex]5. Logan is cooking carrots as part of his dinner. He is in a rush so he wants them to cook as fast as possible. He decides to cut them into small pieces so they cook faster. Will this work? Use the dimensions of two pieces of carrot to justify your answer.
Answers
Let's imagine a piece of carrot that has a shape of a cylinder, and the total surface area of the carrot is S.
If we cut the carrot in half, with a cut parallel to the cylinder base, we will have two smaller cylinders, but the total surface area will increase, since the "internal" part of the bigger cylinder will now be an external area for the new 2 pieces:
In the drawing, the green circles in the right image will add to the total surface area.
If only the base of the cylinder is touching the pan, the surface area will double (from pi*r² to 2*pi*r²), since we will have two pieces of carrot instead of one, with the same base area.
If a bigger surface area is in contact with the pan, the carrots will cook faster. Therefore the answer is YES.
An accountant charges a fee of $100 to complete a company's taxes. The accountant also charges an additional $35 per hour to complete the taxes. Which of the following equations can be used to describe this problem? y = 35 − 100x y = 35 + 100x y = 100 − 35x y = 100 + 35x
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We have that 100 is a fix amount and if x describes the additional charges per hour we have that the equations is 100 + 35x. The answer is y = 100 + 35x
Examine the figure below.If AABC is similar to ADEF, determine the measure of
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We have two similar triangles.
They will have proportional sides and equal measures.
Then, if we have to evaluate Then, we can write:
[tex]\begin{gathered} m\angle A=m\angle D \\ 3x+18=4x+2 \\ 3x-4x=2-18 \\ -x=-16 \\ x=16 \end{gathered}[/tex]Knowing x, we can calculate m[tex]\begin{gathered} m\angle A=3x+18 \\ m\angle A=3\cdot16+18=48+18=66\degree \end{gathered}[/tex]Answer: the measure of A is 66º
Write and solve addition equations3/8 + n = 7/8
Answers
So,
We're going to solve:
[tex]\frac{3}{8}+n=\frac{7}{8}[/tex]For n:
[tex]\begin{gathered} n=\frac{7}{8}-\frac{3}{8} \\ \\ n=\frac{4}{8} \end{gathered}[/tex]Therefore, n=4/8
Find the lateral surface area of the following cylinder:r = 3 cmh = 3 cmLSA = [?]π cm?Leave your answer in terms of pi
Answers
In order to calculate the lateral surface area of the cylinder, we can use the following formula:
[tex]\text{LSA}=2\pi rh[/tex]Where r is the radius and h is the height of the cylinder.
Using r = 3 and h = 3, we have:
[tex]\begin{gathered} \text{LSA}=2\pi\cdot3\cdot3 \\ \text{LSA}=18\pi \end{gathered}[/tex]So the LSA is equal 18π cm², therefore the answer is 18.
Use the point highlighted in the graph below to write the equation in point slope form for the line provided.
Answers
Making the equation of the graph using the Point-Slope Form:
[tex]\text{ y - y}_1=m(x-x_1)[/tex]Since slope was not given, let's compute first for the slope (m) using this formula,
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1_{}}[/tex]From the graph, we have one set of coordinates given: (2, 3)
However, we cannot solve the slope with one point alone, thus let's find another point that's along the line and easier to find. From the graph, we get (0,4).
Let's now compute for the slope (m).
[tex](x_1,y_1)=(0,4);(x_{2,}y_2)=(2,3)_{}[/tex][tex]\text{ m = }\frac{3\text{ - 4}}{2\text{ - 0}}\text{ = }\frac{-1}{2}[/tex]Let's now make the equation using the Point-Slope Form using (2,3) as (x1,y2),
[tex]\text{ y - y}_1=m(x-x_1)[/tex][tex]\text{ y - 3 = (}\frac{-1}{2})(x-\text{ 2)}[/tex][tex]\text{ y - 3 + 3 = -}\frac{1}{2}x\text{ + }\frac{2}{2}\text{ + 3}[/tex][tex]\text{ y = }\frac{-1}{2}x\text{ + 1 + 3 = }\frac{-1}{2}x\text{ + 4}[/tex]Thus, the equation of the line is,
[tex]\text{ y = }\frac{-1}{2}x\text{ + 4}[/tex]hello I am stuck on this problem in need of help please thank you
Answers
First let's do a quick table to help us, when we have S = 0 we cannot make any cookies, then N = 0. When we have one cup of sugar S = 1 we can make 30 cookies, then N = 30. For S = 2, which means, 2 cups of sugar we can make 60 cookies, and so on, then we can do a table like
Then we can see that the relation between N and S is 30, because N = 30.S, for each unit of S that we put we get 30 more cookies, then the equation is
[tex]N=30S[/tex]And if we want to solve it for S
[tex]S=\frac{N}{30}[/tex]Looking at the graph we can see that S is in the y-axis, therefore we are going to use the equation where we have S on the left side, which means, solved for S. Then we are going to plot the equation:
[tex]S=\frac{N}{30}[/tex]This equation is a line, a very simple graph! you can plot two points and then draw a line, for example, use the point (30,1) and (60,2), if we plot these points we get
Now we draw a line that connects these two points, and we have the graph!
Find the exponential function f(x)=Ca^x whose graph is given below.
Answers
Answer:
f(x) = 2[tex](\frac{1}{3}) ^{x}[/tex]
Step-by-step explanation:
exponential in the form
f(x) = C[tex]a^{x}[/tex]
to find C and a use points from the graph
using (0, 2 ) , then
2 = C[tex]a^{0}[/tex] ( [tex]a^{0}[/tex] = 1 ) , so
C = 2
f(x) = 2[tex]a^{x}[/tex]
using (2, [tex]\frac{2}{9}[/tex] )
[tex]\frac{2}{9}[/tex] = 2a² ( divide both sides by 2 )
[tex]\frac{1}{9}[/tex] = a² ( take square root of both sides )
[tex]\sqrt{\frac{1}{9} }[/tex] = a ⇒ a = [tex]\frac{1}{3}[/tex]
f(x) = 2 [tex](\frac{1}{3}) ^{x}[/tex] ← exponential function
Given the following angles of a regular polygon, 120°, (4*x+-3)°, (x+14)°, 45°, 135°, (x-31)°, and (x*6+20)°, what is the value of x?
Answers
Since the polygon has seven angles we deduce it is a heptagon. In that case the sum of the interior angles must be equal to 900°. We can formulate the following equation accordingly.
120°+(4*x-3)°+ (x+14)°+ 45°+ 135°+ (x-31)°+ (x*6+20)° = 900°
120°- 3° +14° + 45° + 135° - 31° + 20 + 4x + x + x + 6x = 900° (Organizing)
300 ° + 12x = 900° (Operating like terms)
12x= 900° - 300° (Transposing 300° to the other side of the equation)
12x= 600° (Subtracting 300° from 900°)
12/12x= 600° / 12 (Dividing by 12 on both sides of the equation)
x= 50°
Answer is: x= 50°
PQR is a right triangle. If PQ=8, what is PR?
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Sine formula
[tex]\sin (angle)=\frac{\text{ opposite side}}{\text{ hypotenuse}}[/tex]Considering angle Q = 60°, the opposite side is PR, and the hypotenuse is PQ = 8. Substituting this information into the formula, we get:
[tex]\begin{gathered} \sin (m\angle Q)=\frac{PR}{PQ} \\ \sin (60\degree)=\frac{PR}{8} \\ \frac{\sqrt[]{3}}{2}=\frac{PR}{8} \\ \frac{\sqrt[]{3}}{2}\cdot8=PR \\ 4\sqrt[]{3}=PR \end{gathered}[/tex]15% of 80 is 60% of what number?
Answers
Let x be the required number.
[tex]15\text{ \% of 80 =}60\text{ \% of x}[/tex][tex]15\text{ \% }\times\text{ 80 =}60\text{ \% }\times\text{ x}[/tex][tex]\frac{15}{100}\text{ }\times\text{ 80 =}\frac{60}{100}\text{ }\times\text{ x}[/tex]
Using the cross-product method, we get
[tex]\frac{15\times80}{100}\times\frac{100}{60}=x[/tex][tex]x=20[/tex]Hence 15% of 80 is 60% of 20.
The answer is 20.
13. A table costs $439. It is on sale for 40%off. a How much do you save? b. What isthe sales price? Solve question#3 parts a &b.a. I saveb. The sales price isу
Answers
A table costs 439, and it is on sale for 40%. That means we shall deduct 40% of 439 from the actual cost as follows;
[tex]\begin{gathered} \text{Sales}=\text{Cost}-\text{Discount} \\ \text{Sales}=439-(439\times\frac{40}{100}) \\ \text{Sales}=439-(439\times0.40) \\ \text{Sales}=439-175.60 \\ \text{Sales}=263.40 \end{gathered}[/tex]Therefore,
The savings is $175.60
The sales price is $263.40
Find the absolute value of -1818-181/18-1/18Find the opposite of -2525-251/25-1/25
Answers
the absolute value of a number does not contain negative sign
so the absolute value of the given expression (-18) is,
= 18
thus, the answer is option A.
3
the opposite of -25 will be,
= -(-25)
= 25
thus the answer is for the second question is option A
I need help with this practice problem, I am struggling to solve It’s from my trigonometry prep guide
Answers
Answer:
Corey stepped 59.71 ft away
Explanation:
The situation is sketched in the following diagram.
The distance from the foot of the tree is y and x for angles 41 and 68 degrees respectively.
Therefore, the distance Corey has to step away is y - x.
Now, from trigonometry, we know that
[tex]\tan (68^o)=\frac{\text{opposite}}{\text{adjacent}}[/tex][tex]\Rightarrow\tan (68^o)=\frac{\text{8}0}{\text{x}}[/tex]We solve for x and get
[tex]\begin{gathered} \Rightarrow x\tan (68^o)=80 \\ \Rightarrow x=\frac{80}{\tan (68^o)} \end{gathered}[/tex]since tan (68) = 2.475.., the above becomes
[tex]x=\frac{80}{2.75\ldots}=32.32[/tex]Now, for angle 41 we have
[tex]\tan (41^o)=\frac{opposite}{\text{adjacent}}[/tex][tex]\tan (41^o)=\frac{80}{y}[/tex]solving for y gives
[tex]y=\frac{80}{\tan (41^o)}[/tex]since tan(41) = 0.869..., the above becomes
[tex]y=\frac{80}{0.869\ldots}[/tex][tex]\Rightarrow y=92.0295\ldots[/tex]Therefore, the distance Corey has to step away from the tree to get a better view is (rounded to the nearest hundredth)
[tex]y-x=92.0295-32.322[/tex][tex]\boxed{y-x=59.71.}[/tex]Find the area of the triangle below.Carry your intermediate computations to at least four decimal places. Round your answer to the nearest tenth.9 ft13 ft6 ft
Answers
The area of the triangle is 27 square feet
Explanation:The area of a triangle is given as:
[tex]A=\frac{1}{2}bh[/tex]Where b and h are the base and height of the triangle respectively
[tex]\begin{gathered} A=\frac{1}{2}(9\times6) \\ \\ =27ft^2 \end{gathered}[/tex]write your own multiple event probability problem and solve it as if you are explaining your reasoning to a friend.
Answers
Problem:
You and your sister have six-sided dice each one. What is the probability that if both roll your dice, you get an even number and your sister get an odd number.
Now, each dice has 6 numbers: 1,2,3,4,5,6
The even numbers are: 2,4,6 (3 options)
The odd numbers are: 1,3,5 (3 options)
Now, the probability of rolling an even number is:
[tex]P(e)=\frac{3}{6}[/tex]And the probability of rolling an odd number is:
[tex]P(o)=\frac{3}{6}[/tex]Then, the probability that you get an even number and your sister an odd number is the product of the probabilities of each event:
[tex]\begin{gathered} P(e\cap o)=P(e)*P(o) \\ \\ P(e\cap o)=\frac{3}{6}*\frac{3}{6} \\ \\ P(e\cap o)=\frac{9}{36}=\frac{1}{4} \end{gathered}[/tex]The probability is 1/4
The graph of f (in blue) is translated a whole number of units horizontally and vertically to obtain the graph of h (in red).Write down the expression for h *(x)The function f is defined * x/-=(x)/^ q
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lax and tip word pr You might need: 3 Calcu The sales tax in your city is 4.4%. and an item costs $3 before tax. How much tax would you pay on that item?
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Tax = $0.13(nearest hundredth)
The engines of a plane are pushing itdue north at a rate of 300 mph, andthe wind is pushing the plane 20°west of north at a rate of 40 mph. Inwhat direction is the plane going?O[?]Round to the nearest tenth.
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STEP - BY - STEP EXPLANATION
What to find?
The direction in which the plane is going.
Given:
From the question given; the engines of a plane are pushing it due north at a rate of 300 mph, and the wind is pushing the plane 20° west of north at a rate of 40 mph.
We know that;
Spread of Data Worksheet
1. Construct the box-and-whisker plot for the number of episodes in each season of the TV show "The
Office.
Season
1
2
3
4
5
6
7
8
9
Number of
Episodes
6
22
25
19
28
26
26
24
25
Answers
The Box and Whisker Plot is shown in the graph below .
Box and Whisker Plot :
It is plotted to display variation in a set of data . In most cases, a histogram analysis provides a sufficient display, but a box and whisker plot can provide additional detail while allowing multiple sets of data to be displayed in the same graph.
How to construct a box and whisker plot ?
The left and right sides show the lower and upper quartiles of the data resp. . The box covers the interquartile interval where half the data is found .The vertical line that split the data in two is the median of data .
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select all the sets of the value that could be the side length of Triangle z.sides are 7,4,10
Answers
We will determine if the sets are proportional, if they are, then those will be the sets of lengths that would belong to triangle z, that is:
a.
[tex]\frac{4}{8}=\frac{7}{11}=\frac{14}{10}\Rightarrow\frac{1}{2}\ne\frac{7}{11}\ne\frac{7}{5}[/tex]So, set a is not one.
b.
[tex]\frac{4}{10}=\frac{7}{17.5}=\frac{10}{25}\Rightarrow\frac{2}{5}=\frac{2}{5}=\frac{2}{5}[/tex]So, set b could be a set of lengths that belong to triangle z.
c.
[tex]\frac{4}{6}=\frac{7}{9}=\frac{10}{11}\Rightarrow\frac{2}{3}\ne\frac{7}{9}\ne\frac{10}{11}[/tex]So, set c is not one.
d.
[tex]\frac{4}{6}=\frac{7}{10.5}=\frac{10}{15}\Rightarrow\frac{2}{3}=\frac{2}{3}=\frac{2}{3}[/tex]So, set d could be a set of lengths that belong to triangle z.
e.
[tex]\frac{4}{8}=\frac{7}{14}=\frac{10}{20}\Rightarrow\frac{1}{2}=\frac{1}{2}=\frac{1}{2}[/tex]So, set e could be a set of lengths that beling to triangle z.
So, the options that could be candidate are: b, d & e.
Question 18 of 30Use the formula below to solve the given problem. In the formula, drepresents the distance an object falls, in meters, and trepresents the timethat an object falls, in seconds. Round to the nearest tenth and do not includeunits in your answer.A screw from the space shuttle in outer space falls from the space shuttle.How far would the screw fall in 11 seconds?ſa=t•2.8Answer here
Answers
SOLUTION
We were asked to find how far the screw will fall in 11 seconds.
How far simply means the distance. So we will find the distance using the formula they gave to us.
[tex]\begin{gathered} So\text{ from the formula }\sqrt[]{d}\text{ = t . 2.8, } \\ \sqrt[]{d}\text{ = t }\times\text{2.8, d = distance that we want to find, t = time = 11seconds} \end{gathered}[/tex][tex]\begin{gathered} \sqrt[]{d\text{ }}\text{ = 2.8t, when we multiply t by 2.8 } \\ \text{Now, we will take the square of both sides to remove the }\sqrt[]{\text{ }}\text{ } \\ (\sqrt[]{d})^2=(2.8t)^2 \\ d=(2.8\times11)^2 \\ d=30.8^2 \\ d\text{ = 948.64} \\ d\text{ = 948.6 to the nearest tenth} \end{gathered}[/tex]Therefore, the answer is 948.6 to the nearest tenth
In New York State, the minimum wage has grownexponentially. In 1966, the minimum wage was$1.25 an hour and in 2015, it was $8.75.Algebraically determine the rate of growth to thenearest percent.
Answers
The Solution.
In 1966, which is the initial year(t); t = 0, and minimum wage(y), y = $1.25
Similarly.
In 2015, t = 49 years , (that is, 1966 to 2015), and y = $8.75
The rate of growth to the nearest percent is
[tex]\text{Rate of growth =}\frac{y_2-y_1}{t_2-t_1}\times100[/tex][tex]\begin{gathered} \text{Where y}_2=8.75,t_2=49\text{ years} \\ y_1=\text{ \$1.25},t_1=0 \end{gathered}[/tex]Substituting into the formula above, we get
[tex]\text{Rate of growth =}\frac{8.75-1.25}{49-0}\times100[/tex][tex]\text{Rate of growth = }\frac{7.5}{49}\times100=15.31\approx15\text{ \%}[/tex]Hence, the correct answer is 15%