A SHADED REGION IS DESCRIBED BY THE FOLLOWING INEQUALITIES:X> OR EQUAL 0 , Y> OR EQUAL 0 , X+2Y< OR EQUAL TO 4 , X-Y< OR EQUAL 1 WHAT ARE ITS CORNER POINTS?
Its corner points (0, 0), (2, 1), (0, 2), (1, 0)
From the question, we have
All the points should be positive, as we can see after carefully examining the equation.
There are two approaches to approach this problem. The first is to solve the equations, create a graph, and make a decision.
The alternative is to just plug the points into the equations and check to see if the conditions are met; this method is quicker for tests with MCQs.
As a result, option B is correct.
Inequalities:
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than. The different inequality symbols, properties, and methods for resolving linear inequalities in one variable and two variables will all be covered in this article along with examples.
Complete question: A shaded region is described by the following inequalities: x 20, y 20, x + 2y s 4, X y sl. What are its corner points? a. (0, 0), (1, 0), (0; 1), (0, 2) b. (0, 0), (2, 1), (0, 2), (1, 0) c. (0, 0), (4, 0), (0, 2), (2, 1) d. (0, 0), (1, 0), (2, 1), (0, 1) e. (0, -1), (2, 1), (0, 2)
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Solving a percent mixture problem using a linear equationSamantha VEspañolTwo factory plants are making TV panels. Yesterday, Plant A produced twice as many panels as Plant B. Two percent of the panels from Plant A and 3% of thepanels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 490 defective panels?
We are given a question about factory plants making TV panels. The following information holds.
Plant A produces twice as many panels as plant B. This can be expressed mathematically as:
[tex]A=2B[/tex]Also, 2% and 3% of the TV panels from Plant A and Plant B are defective, and both plants produced a total of 490 defective panels. This can be expressed mathematically as:
[tex]\frac{2A}{100}+\frac{3B}{100}=490[/tex]We can clearly see that we have derived two equations. We will substitute the first equation in the second equation to get the number of panels Plant B produced.
[tex]\begin{gathered} \frac{2(2B)}{100}+\frac{3B}{100}=490 \\ \frac{4B}{100}+\frac{3B}{100}=490 \\ \frac{7B}{100}=490 \\ \text{Cross multiply} \\ 7b=490\times100 \\ B=\frac{490\times100}{7} \\ B=70\times100 \\ B=7000 \end{gathered}[/tex]Therefore, the number of panels that plant B produced is:
ANSWER: 7000
alternate interior alternate exterior correspondinglinear pairsame side interiorsame side exterior verticalcomplimentarysupplementarycongruent
The relationship of the angles are:
1. ∠5 and ∠6 are linear pairs.
2. ∠3 and ∠2 are vertically opposite angles.
3. ∠4 and ∠8 are corresponding angles.
Given that,
In the picture there are parallel lines with a transversal.
We have to find the relation between,
1. ∠5 and ∠6?
2. ∠3 and ∠2?
3. ∠4 and ∠8?
Take the 1st angles.
∠5 and ∠6 are linear pairs.
A linear pair of angles is formed when two lines intersect at a single point. If the angles follow the spot where the two lines come together in a straight line, they are said to be linear. In a pair of linear equations, the sum of the angles is always 180°.
Take the 2nd angles.
∠3 and ∠2 are vertically opposite angles.
When two straight lines collide at a particular vertex, they create angles that are perpendicular to one another vertically. Angles that are perpendicular to one another vertically are equal. These are occasionally referred to as vertical angles.
Take the 3rd angles.
∠4 and ∠8 are corresponding angles.
The angles that meet two other straight lines in the same vicinity. If the two lines are parallel, the comparable angles are also equal.
Therefore, The relationship of the angles are:
1. ∠5 and ∠6 are linear pairs.
2. ∠3 and ∠2 are vertically opposite angles.
3. ∠4 and ∠8 are corresponding angles.
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how do u know if an equation has rational, irrational or complex solution
We have the equation:
[tex]49a^2-16=0[/tex]We can factorize this equation as:
[tex]\begin{gathered} 49a^2-16=0 \\ (7a)^2-4^2=0 \\ (7a-4)(7a+4)=0 \end{gathered}[/tex][tex]\begin{gathered} 7a-4=0\longrightarrow a_1=\frac{4}{7} \\ 7a+4=0\longrightarrow a_2=-\frac{4}{7} \end{gathered}[/tex]In this case, we have 2 rational solutions.
If the solution implies the square root of -1, then we would have 2 complex solutions.
If the solution implies a square root that does not have a rational solution, then we have 2 irrational solutions.
We can see it when we apply the quadratic formula:
[tex]x=-\frac{b}{2a}\pm\frac{\sqrt[]{b^2-4ac}}{2a}[/tex]The term with the square root defines what type of solution we have:
If b^2-4ac<0, then we have complex solutions.
If the square root of b^2-4ac does not have a rational solution (b^2-4ac is not a perfect square), then we have irrational solutions.
If b^2-4ac is a perfect square (its square root have a rational solution), we will have rational solutions.
Nintendo previously projected that it would sell 19 million units of the console for the year ending in March. If it ended up selling 26.5 million after several upward versions to the forecast. How many selling off were their estimate
A population of bacteria is growing according to the equation P(t) = 1850e ^ (0.09t). Estimate when the population will exceed 2402t=Give your answer accurate to one decimal place.
We will have the following;
[tex]\begin{gathered} 2402=1850e^{0.09t}\Rightarrow\frac{2402}{1850}=e^{0.09t}\Rightarrow\frac{1201}{925}=e^{0.09t} \\ \\ \Rightarrow ln(\frac{1201}{925})=0.09t\Rightarrow t=\frac{ln(1201/925)}{0.09} \\ \\ \Rightarrow t=2.901289829...\Rightarrow t\approx2.9 \end{gathered}[/tex]So, the population will exceed 2402 bacteria after 2.9 units of time.
At a particular restaurant, each mozzarella stick has 100 calories and each slider has
200 calories. A combination meal with mozzarella sticks and sliders is shown to have
1500 total calories and 9 more mozzarella sticks than sliders. Determine the number
of mozzarella sticks in the combination meal and the number of sliders in the
combination meal.
There are
mozzarella sticks and
sliders in the combination meal.
The 1,500 calories in the combination meal and the amount of calories per mozzarella stick and per each slider gives an equation with the following solution;
There are 11 mozzarella sticks and 2 sliders in the combination meal.
What is a mathematical equation?An equation in mathematics is a statement that two mathematical expressions are equal.
The number of calories in each mozzarella stick = 100
Number of calories in each slider = 200
Number of calories in the combination meal = 1,500
Number of mozzarella sticks in the combination meal = 9 + The number of sliders
Let s represent the number of sliders in the combination meal, we have;
Number of mozzarella in the combination meal = s + 9
The equation that gives the amount of calories in the meal is therefore;
200·s + 100·(s + 9) = 1,500
200·s + 100·s + 900 = 1,500
300·s = 1,500 - 900 = 600
s = 600 ÷ 300 = 2
The number of sliders in the combination meal, s = 2
The number of mozzarella in the meal = 2 + 9 = 11
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I need help with this question please. This is non graded.
To determine the factor of the given polynomial, first, we rewrite it as follows:
[tex](16x^2+4x)+(-20x-5).[/tex]Now, notice that:
[tex]\begin{gathered} 16x^2+4x=4x(4x^+1), \\ -20x-5=-5(4x+1). \end{gathered}[/tex]Factoring out the 4x+1, we get:
[tex](16x^2+4x)+(-20x-5)=(4x-5)(4x+1).[/tex]Answer: [tex](4x+1).[/tex]40 model A cars were sold that week. what else can you say about this bar model?
From the diagram
Ratio of model A car to model B car = 4:6
Ratio of model A to model B = 4:6
Ratio of model B to model A = 6:4
Ratio of model A to total = 4:10
Ratio of model B to total = 6:10
If 40 model A cars sold
I know that 60 model B cars was sold.
in a cave a stalactites gets 4 millimeters longer each year.this year it is 72 centimeters longhow many years until it is 1 meter long
in a cave a stalactites gets 4 millimeters longer each year.this year it is 72 centimeters long
how many years until it is 1 meter long
we have that
the linear equation that represent this situation is equal to
y=4x+720
where
y ------> length in mm
x ----> number of years
Remember that
72 cm=720 mm
so
For y=1 m ------> y=1,000 mm
substitute in the equation
1,000=4x+720
4x=1,000-720
4x=280
x=70 years
therefore
answer is 70 years5. Simplify this expression. (1 point)
(-4)-6(-4)7
Answer:
syntax error. .
Step-by-step explanation:
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32 mm 15 mm 14 mm Find the area of the triangle shown?
Area of triangle = 105 mm²
Explanation:Area of triangle = 1/2 × base × height
base = 14 mm
height = 15 mm
Area of triangle = 1/2 × 14mm × 15mm
[tex]\begin{gathered} \text{Area = }\frac{14\times15}{2} \\ Area\text{ = }7\times15 \\ Area\text{ = }105 \end{gathered}[/tex]Area of triangle = 105 mm²
Solve for the missing side lengths.45°5A. O57057666, yB.O57224,357245,122 -2, y522D. x = 5/2, y = 5/2
The missing sides, x, and y can be obtained using the sine rule
Step 1: Get the angle at A
The angle at A is obtained below:
[tex]180-90-45=45^0[/tex]Step 2: Use the sine rule
[tex]\frac{\sin A}{y}=\frac{\sin B}{x}=\frac{\sin C}{5}[/tex][tex]\begin{gathered} \text{where A=45}^0 \\ B\text{=45}^0 \\ C=90^0 \end{gathered}[/tex]To get y
[tex]\frac{\sin45}{y}=\frac{\sin 90}{5}[/tex]cross multiply
[tex]y=\frac{5\times\sin 45}{\sin 90}=\frac{5\sqrt[]{2}}{2}[/tex]To get x
[tex]\frac{\sin45}{x}=\frac{\sin 90}{5}[/tex][tex]x=\frac{5\times\sin 45}{\sin 90}=\frac{5\sqrt[]{2}}{2}[/tex]Therefore, the answer is option C
In scientific notation, what is the product of 5.78 x 10^5 and 8.04 x 10^-2
The given numbers are
5.78 x 10^5 and 8.04 x 10^-2
We would simplify the exponents by applying one of the laws of exponents which states that
a^b x a^c = a^(b + c)
By applying this law, the expression becomes
5.78 x 8.04 x 10^(5 + - 2)
46.4712 x 10^(5 - 2)
46.4712 x 10^3
The product in scientific notation is
46.4712 x 10^3
If the ones digit in a two-digit number is even, the number is a composite number. Which odd ones digit also tells you the number must be a compositenumber? Explain.
Okay, here we have this:
Considering that a composite number is a number that is not prime, the only number one of the units that tells us that a two-digit number is composed is 5, since every number ending in 5 is a multiple of 5.
Please Help me solve I know I am supposed to use the quadratic formula But I’m still not getting the right answers
To find the maximum profit we need to maximize the function.
First we need to find the critical points, to do this we need to find the derivative of the function:
[tex]\begin{gathered} \frac{dy}{dx}=\frac{d}{dx}(-2x^2+105x-773) \\ =-4x+105 \end{gathered}[/tex]now we equate it to zero and solve for x:
[tex]\begin{gathered} -4x+105=0 \\ 4x=105 \\ x=\frac{105}{4} \end{gathered}[/tex]hence the critical point of the function is x=105/4.
The next step is to determine if the critical point is a maximum or a minimum, to do this we find the second derivative:
[tex]\begin{gathered} \frac{d^2y}{dx^2}=\frac{d}{dx}(-4x+105) \\ =-4 \end{gathered}[/tex]Since the second derivative is negative for all values of x (and specially for x=105/4) we conclude that the critical point is a maximum.
Hence the function has a maximum at x=105/4. To find the value of the maximum we plug the value of x to find y:
[tex]\begin{gathered} y=-2(\frac{105}{4})^2+105(\frac{105}{4})-773 \\ y=605.125 \end{gathered}[/tex]Therefore the maximum profit is $605
Sketch one cycle of the graph of each function 16. y= -2 sin 8x
Answer:
• Amplitude = 2
,• Period = π/4
Explanation:
Given the function:
[tex]y=-2\sin(8x)[/tex]In order to sketch the graph of y, we need to find its amplitude and period.
Comparing the function with the general sine function:
[tex]y=a\sin(bx+c)+d[/tex]We have that:
[tex]\begin{gathered} Amplitude=|a|=|-2|=2 \\ Period=\frac{2\pi}{|b|}=\frac{2\pi}{8}=\frac{1}{4}\pi \end{gathered}[/tex]Next, using these values, we sketch one cycle of the graph below:
1-38. Given f(x)=2x-7, complete parts (a) through (C). HomeworkHelpa. Compute f(0).b. Solve f(x)=0.c. What do the answers to parts (a) and (b) tell you about the graph of y=f(x)?
the Part a. Compute f(0). We have to evaluate the function for x = 0.
[tex]f(0)\text{ = 2(0) - 7 = 0 - 7 = -7}[/tex]Therefore, f(0) = -7.
Part b. Solve f(x) = 0.
[tex]f(x)=\text{ 2x - 7 }=\text{ 0}[/tex]To solve the equation 2x - 7 = 0, we have to add 7 to both sides of the equation, and then dividing the equation by 2:
[tex]2x\text{ - 7 + 7 = 7 }[/tex][tex]2x\text{ = 7 }\Rightarrow x\text{ = }\frac{7}{2}[/tex]So, x = 7/2.
Part c.
Part a tells us that the graph of the function is evaluated in zero, the value for the function is -7. When x = 0, the value for y = -7. This is the intercept of the linear function.
Part b tells us that when y = 0, the value for x = 7/2.
The line passes through points (0, -7) and (7/2, 0). These are the points on y-axis and x-axis, respectively.
Example 1: Choose a point in Quadrant 2, 3, or 4 to be on the terminal arm of an angle in standard position. Determine the principal angle in radians. Include a sketch.Example 2: Using a different quadrant than in Example 1 (but still not Quadrant 1), choose a reciprocal trig ratio. Determine all of the primary and reciprocal ratios for that angle, as well as the principal angle in radians.
Example 1:
The quadrants with their numbering (I, III,III, and IV) are shown below.
Now let us draw an angle in quadrant II.
We have drawn the angle above such that its measure from the positive x-axis is 135° . The angle 135° in radians is 3π/4.
Example 2:
Let us now choose an angle in the 3rd quadrant.
Simplify using exponential notation. 5a^6 x 7a^7
Given:
[tex]5a^6\times7a^7[/tex]Let's simplify using exponential notation.
To simplify, multiply the the base, then use law of indicies to add the exponents
We have:
[tex]undefined[/tex]Help please this is a practice question for points-The other options are $18 and $27
Let the y value for brand A = Y₁
when x = 2 y = 24
[tex]\begin{gathered} Y_1\text{ =}\frac{24}{2}=12 \\ Y_1\text{ = 12x} \end{gathered}[/tex]A kitty in a tuxedo walks into a bank deposit of $4000 in an investment account. the account earns 8% interest, compounded monthly. after 10 years how much money will the fancy kitty have?
Answer:
The amount of money Kitty would have is;
[tex]\text{ \$}8,878.56[/tex]Explanation:
Given that Kitty invested $4000 into an account that earns 8% interest compounded monthly for 10 years;
[tex]\begin{gathered} \text{ Principal P = \$4000} \\ \text{ Rate r = 8\% = 0.08} \\ \text{ Time t =10 years} \\ \text{ number of times compounded per time n = 12} \end{gathered}[/tex]Applying the formula for compound interest;
[tex]F=P(1+\frac{r}{n})^{nt}[/tex]Substituting the given values;
[tex]\begin{gathered} F=4000(1+\frac{0.08}{12})^{12(10)} \\ F=4000(1+\frac{0.08}{12})^{120} \\ F=4000(2.2194) \\ F=\text{ \$}8,878.56 \end{gathered}[/tex]Therefore, the amount of money Kitty would have is;
[tex]\text{ \$}8,878.56[/tex]TODAY!! Help plss I’m confused giving branliest to the best answer!! Thank you!!
3.8 x[tex]10^3[/tex] is 169 times smaller than 6.422x [tex]10^5[/tex].
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq[/tex] a < 10. Scientific notations have some of the profits as:
Better readability due to compact representation Its value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.
We need to find out how many times 3.8 x 10^5 is greater than 3.8 x 10^-7.
To do that, we have to divide 3.8 x 10^5 by 3.8 x 10^-7 and then find the answer.
Let us do that:
[tex]\begin{gathered} \frac{3.8\cdot10^3}{6.422\cdot10^{5}}\text{ = }\frac{3.8}{6.422}\cdot\text{ }\frac{10^3}{10^{5}} \end{gathered}[/tex]
= 169
According to the division law of indices states that if a numerator and a denominator have the same base (e.g. 10), then the power of the numerator can subtract of the denominator.
Therefore, 3.8 x[tex]10^3[/tex] is 169 times smaller than 6.422x [tex]10^5[/tex].
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27, 9, 3, 1, 1/3,1/9....What is the value of the 10th term in the sequence?
1. Identify if the sequence has a common difference or a common ratio.
Common difference: subtract each term from the next term:
[tex]\begin{gathered} 9-27=-18 \\ 3-9=-6 \\ 1-3=-2 \end{gathered}[/tex]There is not a common difference.
Common ratio: Divide each term into the previous term:
[tex]\begin{gathered} \frac{9}{27}=\frac{1}{3} \\ \\ \frac{3}{9}=\frac{1}{3} \\ \\ \frac{1}{3}=\frac{1}{3} \\ \\ \frac{\frac{1}{3}}{1}=\frac{1}{3} \\ \\ \frac{\frac{1}{9}}{\frac{1}{3}}=\frac{3}{9}=\frac{1}{3} \end{gathered}[/tex]The common ratio is 1/3; it is a geometric sequence.
2. Use the next fromula to write the formula to find the nth term in the sequence:
[tex]\begin{gathered} a_n=a_1*r^{n-1} \\ \\ r:common\text{ }ratio \end{gathered}[/tex][tex]a_n=27*(\frac{1}{3})^{n-1}[/tex]Evaluare the formula above for n=10 to find the 10th term:
[tex]\begin{gathered} a_{10}=27*(\frac{1}{3})^{10-1} \\ \\ a_{10}=27*(\frac{1}{3})^9 \\ \\ a_{10}=27*\frac{1}{3^9} \\ \\ a_{10}=27*\frac{1}{19683} \\ \\ a_{10}=\frac{27}{19683} \\ \\ a_{10}=\frac{1}{729} \end{gathered}[/tex]Then, the 10th term is 1/729Solve (x+2<5) u ( x-7>6)
You have the following opeartion between sets:
(x + 2 < 5) U (x - 7 > 6)
In order to find the solution to the previoues expression, you first find the solutionof each inequality, just as follow:
x + 2 < 5 subtract 2 both sides
x < 5 - 2
x < 3
The solution interval is (-∞,3)
x - 7 > - 6 add 7 both sides
x > - 6 + 7
x > 1
The solution interval is (1, ∞)
Then, you have:
(-∞,3) U (1,∞)
which is the same that:
{x| x<3 or x>1}
A department store sells a pair of shoes with an 87% markup if the store sells the shoes for 193.21 then what is their non-markup price
Answer:
103.32
Step-by-step explanation:
p = non-markup price of shoes
0.87p = amount of markup
selling price = p + 0.87p = 193.21
1.87p = 193.21
p = 103.32
check: p + 0.87p = 193.21?
103.32 + 89.89 = 193.21? YES
40. Circle A has a radius 4 inches. Is each statement about circle A true?
The first statement is about the diameter of the circle.
The diameter of a circle is always the double of its radius.
So if circle A ras a radius of 4 inches, its diameter is:
[tex]\text{diameter}=2\cdot\text{radius}=2\cdot4=8\text{ inches}[/tex]So the first statement is true (YES)
The second statement is about the area of the circle. The area of a circle is given by the following equation:
[tex]Area=\pi\cdot r^2[/tex]If the radius of the circle is 4 inches, we have:
[tex]\text{Area}=\pi\cdot4^2=16\pi[/tex]So the second statement is also true (YES)
The third statement is about the volume of a cylinder with a height of 6 inches and the circle A as the base. The volume of a cylinder is given by the equation:
[tex]\text{Volume}=\pi\cdot r^2\cdot h[/tex]Using the radius = 4 inches and the height = 6 inches, we have:
[tex]\begin{gathered} \text{Volume}=\pi\cdot4^2\cdot6 \\ \text{Volume}=\pi\cdot16\cdot6=96\pi \end{gathered}[/tex]The volume is not 64pi, so this statement is false (NO).
find the slope of the line that passes through these two points (0, -2) (5, 3) slope= ?
Find the slope of the line that passes through these two points
P1 = (0, -2)
P2 = (5, 3)
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{3-(-2)}{5-0} \\ m=\frac{3+2}{5} \\ m=\frac{5}{5} \\ m=1 \end{gathered}[/tex]The slope would be 1
Practice questions to use for study guide/ my notes please help want to Ace test!
We have, From the graph it can be seen that when x tends to zero on the right, y
I need help I’m super confused and don’t have much time
ANSWER AND EXPLANATION:
Given:
To be able to determine the distance between the moon and the sun, we'll need to divide the length of side y by the sine of angle x using the below formula;
[tex]Distance\text{ between the moon and the sun}=\frac{y}{\sin x}[/tex]