Graph the solution to the following system of inequalities.ys-2x-3y> 4x + 710-8-4-Х?10
Answers
Explanation
[tex]\begin{gathered} y\leq-2x-3 \\ y>4x+7 \end{gathered}[/tex]Step 1
First, graph the inequality 1
[tex]y\leq-2x-3[/tex]the related equation is
[tex]y=-2x-3[/tex]now, get 2 coordinates of the line
a) when x=1
[tex]\begin{gathered} y=-2x-3 \\ y=-2(1)-3 \\ y=-2-3 \\ y=-5 \\ so,\text{ the coordinate is (1,-5)} \end{gathered}[/tex]b)when x=0
[tex]\begin{gathered} y=-2x-3 \\ y=-2\cdot0-3 \\ y=0-3 \\ y=-3 \\ \text{coordinate P2}\Rightarrow(0,-3) \end{gathered}[/tex]now, draw a line that pases trought the coordinates we found.
Since the inequality is ≤ , not a strict one, the border line is solid
Step 2
Now, do the same for inequality 2
so
[tex]y>4x+7[/tex]the related equation is
[tex]y=4x+7[/tex]find 2 coordinates of the line
a)when x=0
[tex]\begin{gathered} y=4x+7 \\ y=4\cdot0+7 \\ y=0+7 \\ y=7 \\ so,\text{ the coordinate 3 is (0,7)} \end{gathered}[/tex]b) when x=-2
[tex]\begin{gathered} y=4x+7 \\ y=4\cdot-2+7 \\ y=-8+7 \\ y=-1 \\ so,\text{ the coordinate 4 is (-2},-1) \end{gathered}[/tex]now, draw the line 2, this lines passes trougth the coordiantes 3 and 4
Since the inequality is >, a strict one, the border line is dotted
Step 3
Graph:
in inequality (1) we need the values smaller r than -2x-3, it measn all values under the line,
and in Inequality 2 we need the values greater than 4x+7, it means all values over the line
so, the solution is the dark purple zone
I hope this helps you
Related Questions
Which of the following statements are true of this equation select all that apply. 5 1/6 ÷ 2 5/12 = 2 4/29
Answers
The left hand side of the equation is equal to right hand side.
What is an equation? What is a coefficient?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. In a equation say : ax + b, [a] is called coefficient of [x] and [b] is independent of [x] and hence is called constant.
We have a equation :
5 1/6 ÷ 2 5/12 = 2 4/29
We can write -
5 1/6 ÷ 2 5/12 = 2 4/29
31/6 ÷ 29/12 = 62/29
31/6 x 12/29 = 62/29
62/29 = 62/29
Therefore, the left hand side of the equation is equal to right hand side.
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How would you describe the graphs of the sine and cosine functions? The sine and cosine functions are periodic functions. What does it mean to be a periodic function?
Answers
The sine and cosine functions are wave-like functions that repeat themselves on the plane an infinite number of times. The fundamental difference between the two functions is that the valley of the sine function is intersected by the y-axis. In contrast, the crest of the cosine function intersects the y-axis.
Given a function f(x)
[tex]f(x)=\sin (ax)[/tex]We can find its period using the formula below
[tex]\text{period}=\frac{2\pi}{a}[/tex]where the 2pi term is in radians.
The period of the function is the x-distance needed for the function to complete a cycle.
A periodic function is a function that repeats its values at regular intervals (2pi/a as we found above)
Hello can you assist me please i need to solo e and Identity sine cosine or tangent and identify opposite hypnose or adjeact #12
Answers
Solution (12):
Given the triangle;
The opposite side is labelled as x and the adjacent side is 17.
Using the tangent trigonometry ratio, we have;
[tex]\tan\theta=\frac{opposite}{adjacent}[/tex]Thus;
[tex]\begin{gathered} \tan(51^o)=\frac{x}{17} \\ \\ x=17\tan(51^o) \\ \\ x=20.99 \\ \\ x\approx21 \end{gathered}[/tex]the circle graph shown above represents the distribution of the grades of 40 students in a certain geometry class. How many students received Bs or Cs?
Answers
Given:
Total number of students = 40
From the circle graph given, let's determine the number of students that received Bs or Cs.
Given:
Percentage of students that received Bs = 30%
Percentage of students that received Cs = 40%
Percentage of student that received Bs or Cs = 40% + 30% = 70%
Thus, to find the number of students who received Bs or Cs, we have the equation below:
No of students who received Bs or Cs = (% of students who received Bs or Cs) x (Total n0 of students)
[tex]\text{ No of student who received Bs or Cs = 70\% of 40}[/tex]Thus, we have:
[tex]\begin{gathered} \text{ No of students who received Bs or Cs = }\frac{70}{100}\ast40 \\ \\ =0.70\ast40 \\ \\ =28 \end{gathered}[/tex]Therefore, the number of students who received Bs or Cs are 28
ANSWER:
C. 28
May I please get help finding this. I can’t seem to get the correct solution for the length.
Answers
Triangle ABE is similar to traingle ACD; in similar triangles, corresponding sides are always in the same ratio:
[tex]\frac{DC}{EB}=\frac{AC}{AB}[/tex]Use the equation above to find the length of x:
[tex]\begin{gathered} \frac{x}{4}=\frac{6+9}{6} \\ \\ \frac{x}{4}=\frac{15}{6} \\ \\ x=4\cdot\frac{15}{6} \\ \\ x=\frac{60}{6} \\ \\ x=10 \end{gathered}[/tex]Then, the length of x is 10got a square thats 23cm and 57cm .what is the perimeter
Answers
The perimeter of the shape is obtained by summing up all its 4 sides
=> 23 + 23 + 57 + 57
Perimeter = 46 + 114
perimeter = 160 cm
Don José es un conocido comerciante. Al inicio de la semana tenía una suma de dinero, de la cual invirtió 2,000 pesos en mercancía. Al término de la semana, ingresó por ventas tres veces el capital con que contaba después de comprar la mercancía; de modo que su capital llegó al doble del inicial. Determina cuál es el capital inicial de Don José.
Seleccione una:
O a. 4,000
O b. 10,000
O c. 6,000
Answers
Answer:
The Initial capital is 6000 pesos
Step by step explanation:
x: initial capital of Don José
Start of the week:
I buy merchandise in 2000 pesos
At the end of the week:
Sales income twice the capital you had after buying the merchandise: 2(x-2000)
Income - purchases = Profit
Capital + Profit = Final capital
Capital + Income - purchases = Final Capital
x+ 2(x-2000) - 2000 = 2x
x+2x-4000-2000 = 2x
3x-6000 = 2x
x = 6000
The Initial capital is 6000 pesos
See more in Brainly - brainly.lat/tarea/10835657
Step-by-step explanation:
3 x 1 + 4 x 1/100 + 7 x 1/1000 as a decimal number
Answers
Answer:
3.047
Step-by-step explanation
In a group of 60 students, the probability that at most 30 of them like to swimis 56%. What is the probability that at least 31 of them like to swim?
Answers
Answer= 44%
P(A)= the probability that at most 30 of them like to swim
P(B)= the probability that at least 31 of them like to swim
Notice that P(A)+P(B) have to add up 100%
P(A)+P(B)=100% then solving for P(B)
P(B)= 100% - 56%= 44%
juan is mailing a box like the one pictured below to his sister
Answers
Given:
Given a rectangle with
[tex]\begin{gathered} h=5cm \\ l=12cm \\ w=6cm \end{gathered}[/tex]Required:
To find the volume.
Explanation:
The formula for surface area is
[tex]SA=2lw+2lh+2wh[/tex]Here
[tex]\begin{gathered} =2(12)(6)+2(12)(5)+2(6)(5) \\ =144+120+60 \\ =324 \end{gathered}[/tex]Final Answer:
[tex]324cm^2[/tex]5.) The elements of f(x) are (-7,3).(-1, 6) and (8,-3). What is the range of the function?
Answers
The range of a function is all values of y the function have.
So, looking at the elements (-7, 3), (-1, 6) and (8, -3), the y-coordinates of these points are 3, 6 and -3.
So the range of f(x) is:
[tex]\text{range}=\mleft\lbrace-3,3,6\mright\rbrace[/tex]which answer shows the correct ratios for the problem? in the forest, the ratio of elm trees to oak trees is 5/7. of the 120 trees, how many are elms? a. 40...b. 85....c..50...d...60
Answers
Answer:
The number of elms tree in the forest is;
[tex]50[/tex]Explanation:
Given that the ratio of elm trees to oak trees is 5:7.
And there are 120 trees in total in the forest.
For the ratio of the elms tree to the total number of trees is;
[tex]=\frac{5}{5+7}=\frac{5}{12}[/tex]Let's now calculate the number elms tree in the forest;
[tex]\begin{gathered} n=\frac{5}{12}\times120\text{ tr}ees \\ n=50\text{ tre}es \end{gathered}[/tex]Therefore, the number of elms tree in the forest is;
[tex]50[/tex]Graph x + 4y = 8The y-intercept is ___ (I got this already its 8)
Answers
Answer
The y-intercept = 2
Explanation
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
So, we just have to write the given equation in this form and the y-intercept will become apparent.
x + 4y = 8
4y = -x + 8
Divide through by 4
(4y/4) = (-x/4) + (8/4)
y = -0.25x + 2
Comparing this with y = mx + b
We can see that
b = y-intercept = 2
Hope this Helps!!!
8 А 400 11 1200 С Which triangle can be proven congruent to AABC shown above? (G.6)(1 point) O A. 11 200 400 O B. 22 11 28 C. 1200 200 40° O D. 11 400 28
Answers
Answer:
Triangle A.
Explanation:
We need to look for a triangle which has the same angle measures and same side measurement of corresponding side lengths.
Now in the original triangle we know two angles and one side length; therefore, by AAS another triangle which has two angles and one side length given and they are congruent to that of the corresponding measurements of the first triangle, then the two triangles are congruent.
Now for choice A the problem is that we are given angle measurements different from those given in the original triangle. However, we can use the fact that the angles must sum to 180 degrees to find the third angle and it turns out to be 120.
Hence, at this point triangle A has the same angle and side length measurements as the original triangle; therefore, by AAS the two triangles are congruent.
mr. emmer gave a test in his chemistry class. the scores were normally distributed with a mean of 82 and a standard deviation of 4. what percent of students would you expect to score between 78 and 36?
Answers
Where:
[tex]\begin{gathered} X1=36 \\ X2=78 \\ \mu=82 \\ \sigma=4 \end{gathered}[/tex]So:
[tex]\begin{gathered} P(36\le X\le78)=P(\frac{78-82}{4}\le Z\le\frac{86-82}{4}) \\ P(36\le X\le78)=P(-1\le Z\le1) \\ P(36\le X\le78)=0.6827\approx0.68 \end{gathered}[/tex]As a percentage: 68%
13. Graph the inequality. xs-3 X>8 10 9
Answers
You have teh following inequality:
x ≤ -3
consider that the previous inequality includes all number lower and equal to -3, that is, -3,-4,-5,.., until - infinity.
Then, the graph is:
For the following inequality:
x > 8
consider that the solutions are all numbers greater than 8 without including it.
Then, for the graph, you have:
There are gallon of orange juice and gallon of cranberry juice in the refrigerator. How many gallons of juice are there in all? A 8 10 B. 112/2 C 8 12 17/12
Answers
Answer:
2 gallons of juice
Step-by-step explanation:
your welcome
find the value of x in the figure given then find the measure of angle y
Answers
Answer:
x = 33
Angle Y = 105°
Explanation:
The sum of the interior angles of a polygon with 5 sides is equal to 540°. So, we can write the following equation:
4x + 113 + (3x+8) + (2x + 9) + 113 = 540
So, solving for x, we get:
4x + 113 + 3x + 8 + 2x + 9 + 113 = 540
9x + 243 = 540
9x + 243 - 243 = 540 - 243
9x = 297
9x/9 = 297/9
x = 33
Then, using the value of x, we can calculate the value of the angle with measure (2x + 9) as:
(2x + 9) = 2(33) + 9
(2x + 9) = 75
Finally, this angle and the angle Y are supplementary, the sum of them is equal to 180°, so the measure of angle Y can be calculated as:
(2x + 9) + Y = 180°
75° + Y = 180°
Y = 180° - 75°
Y = 105°
So, x is equal to 33 and the measure of angle Y is 105°
geometry special parallelogramsSide LK = Side KO =Side OL = Side KM = Side NL =
Answers
KLMN is a square
NM = 8
Side LK = 8
Side KO = 8 * sqrt(2)/2 = 4 * sqrt(2)
Side OL = 8 * sqrt(2)/2 = 4 * sqrt(2)
Side KM = sqrt(KN² + NM²) = sqrt(8² + 8²) = sqrt(64 + 64) = sqrt(128) = sqrt(64*2) = 8 * sqrt(2)
Side NL = 8 * sqrt(2)
45°
90°
45°
90°
Answers in BOLD
The area of a square backyard is 79 ft?. The owner is looking to get fencing to enclose the yard, so they need to find the approximate length of each side of the backyard AND what is the perimeter of the backyard?
Answers
According to the given question we have the following:
The area of a square backyard is 79 ft
Therefore if the area of a square backyard is 79 ft that means that length of each side would be the following:
length of each side=area of a square backyard/2
length of each side=79 ft/2
length of each side=39.5
Therefore if 39.5 is lenght of each side, the perimeter of the backyard would be calculated as follows:
perimeter of the backyard=l+l+l+l
perimeter of the backyard=39.5+39.5+39.5+39.5
perimeter of the backyard=158
graph the slope connecting (2,3) and (4,0)
Answers
SOLUTION
STEP 1: Write the given points
[tex](2,3)\text{ }and\text{ }(4,0)[/tex]STEP 2: Find the slope
[tex]\begin{gathered} \mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1} \\ \left(x_1,\:y_1\right)=\left(2,\:3\right),\:\left(x_2,\:y_2\right)=\left(4,\:0\right) \\ m=\frac{0-3}{4-2} \\ m=-\frac{3}{2} \end{gathered}[/tex]The graph of the slope is seen below:
whats the absolute value between the points -45 and -11
Answers
For two real numbers u and v, |u-v| is the absolute value between the points:
|-45-(-11)|=|-34|=34
I need help with homework I got the picture with the questions and will send it to you
Answers
3a.
DVA + AVB = 180 (straight line), so
75 + Angle AVB = 180
Angle AVB = 180 - 75
Angle AVB = 105 degrees
3b.
Angle DVC and Angle BVA are vertical angles.
Vertical angles form when we have a geometrical "X".
Vertical angles are equal so,
DVC = BVA
60 = 60
BVA = 60 degrees
3c.
BVC and CVD are in a straight line, so
BVC + CVD = 180
2x + 35 + 3x + 45 = 180
Let's solve for x:
5x + 80 = 180
5x = 100
x = 100/5
x = 20
Angle BVC = 2x + 35 = 2(20) + 35 = 40 + 35 = 75 degrees
Angle CVD = 3x + 45 = 3(20) + 45 = 60 + 45 = 105 degrees
show how the quadratic formula can be used to rewrite : f(x) = 9x^2 - 149x - 234IN FACTORED FORM
Answers
To factor the function using the quadratic formula we equate it to zero and solve for x:
[tex]\begin{gathered} 9x^2-149x-234=0 \\ x=\frac{-(-149)\pm\sqrt[]{(-149)^2-4(9)(-234)}}{2(9)} \\ x=\frac{149\pm\sqrt[]{30625}}{18} \\ x=\frac{149\pm175}{18} \\ \text{then} \\ x=\frac{149+175}{18}=18 \\ or \\ x=\frac{149-175}{18}=-\frac{26}{18}=-\frac{13}{9} \end{gathered}[/tex]Now we write the function as:
[tex]f(x)=(x-a)(x-b)[/tex]where a and b are the roots we found above, then we have:
[tex]\begin{gathered} f(x)=(x-18)(x-(-\frac{13}{9})) \\ f(x)=(x-18)(9x+13) \end{gathered}[/tex]Therefore:
[tex]f(x)=(x-18)(9x+13)[/tex]Find the degree of the polynomial – 3x + x² +3.
Answers
The degree of the polynomial is the largest power of the variable
The degree of the polynomial is 2
Triangle 1 has a 50 degree angle, a 60 degree angle and one side that is 15 cmlong. Triangle 2 has a 50 degree angle, a 60 degree angle, and one side that is 15cm long. Are the triangles guaranteed to be congruent? No Yes
Answers
Congruent triangles have exactly the same three sides and three angles. The triangles may be rotated to see the congruency between them. In other words congruent triangles has corresponding sides equal and corresponding angles equal.
The 2 triangles have equal corresponding
Find an equation of variation in which y varies directly as x and y=28 when x=7. Then find the value of y when x=16.
Answers
Learn A STORY OF UNITS Lesson 4 Homework Helper 4.2 5. Mikal's backpack weighs 4,289 grams. Mikal weighs 17 kilograms 989 grams more than his backpack. How much do Mikal and his backpack weigh in all?
Answers
We have that the backpack weighs 4,289 grams = 4.289 kg.
Since Mikal weigh 17.989, we have that the total weight is:
[tex]17.989+4.289=22.278[/tex]therefore, Mikal and his backpack weigh 22.278 kg
What integer value of b would make this not factorable
Answers
Answer:
Any integer other than -14 or 14.
[tex](x - 1)(x - 3) = {x}^{2} - 14x + 13[/tex]
[tex](x + 1)(x + 3) = {x}^{2} + 14x + 13[/tex]
Find the missing side or angle.Round to the nearest tenth.b=15a=30c=29A=[ ? 1°
Answers
STEP 1
The given parameters are a=30, b=15 and c=29
The corresponding cosine rule needed to find the angle A is denoted below
[tex]A=\cos ^{-1}\mleft[\frac{b^2+c^2-a^2}{2bc}\mright]^{}[/tex]STEP 2
Substitute the given parameters into the equation.
[tex]\begin{gathered} A=\cos ^{-1}\mleft\lbrace\frac{15^2+29^2-30^2}{2\times15\times29}\mright\rbrace \\ A=\cos ^{-1}\mleft\lbrace\frac{225+841-900}{870}\mright\rbrace \\ A=\cos ^{-1}\mleft\lbrace\frac{166}{870}\mright\rbrace \\ A=\cos ^{-1}0.1908 \\ A=79.0^0 \end{gathered}[/tex]