The graph of x = 3 is a line parallel to the y-axis, which passes through the point (3, 0). This means that x = 3 for every value of y.
"You are solving a system of equations of two linear equations in two variables, and you discover that there are no solutions to the system"
"You are solving a system of equations of two linear equations in two variables, and you discover that there are no solutions to the system"
So, it will mean the lines are parallel
so, the graph which describe the system is pink
The answer is option D
What angle will make a rotational symmetry?A. 8B. 50C. 45D. 60
To find the angle, we will simply divide 360 by the number of sides
Number of sides = 8
That is;
Angle = 360 / 8 = 45 degree
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
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
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.
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
Hello everybody! Can anyone help me with this? I just need to know if it's a Direct variation, a inverse variation, or neither? (Look at the photo) Thanks!
Remember that
A relationship between two variables, x, and y, represent a proportional variation (direct variation) if it can be expressed in the form y=Kx
An equation of the line that passes through the origin
A relationship between two variables, x, and y, represents an inverse variation if it can be expressed in the form y=1/x
There is a vertical asymptote at x=0
therefore
Looking at the graph
we have an inverse variationanswer is IEvaluate log3/8 91 using the change of base formula. Round your answer to one decimal place.
We have to apply the change of base formula:
[tex]\log _b(a)=\frac{\log _x(a)}{\log _x(b)}[/tex]We can apply this to our expression as:
[tex]\log _{\frac{3}{8}}(91)=\frac{\ln(91)}{\ln(\frac{3}{8})}=\frac{\ln (91)}{\ln (3)-\ln (8)}\approx\frac{4.511}{1.099-2.079}=\frac{4.511}{-0.980}\approx-4.6[/tex]Answer: -4.6
William bought 3 pizzas for himself and 6 friends. Each pizza has m slices. Select all of the following expressions that represent the number of slices of pizza per person. Al (m + m + m) 7 m7 3m 7
12
From the information given,
Wiliam bought 3 pizzas and each had m slices. This means that the total number of slices in the 3 pizzas is 3 * m = 3m
He bought the the pizzas for himslef and 6 friends. This means that the total number of people that shared 3m slices of pizzas is 1 + 6 = 7
Thus, the expression that represent the number of slices of pizza per person are
c) 3m/7
can you find the domain of a piecewise functuon
a piecewise function
x+ 4 , if -4 ≤x <3
. 3 ≤ x < 6
Then ,answer is [ -4,6)
A spring is attached to the ceiling and pulled 17 cm down from equilibrium and released. After 3 seconds the amplitude has decreased to 13 cm. The spring oscillates 14 times each second. Find a function that models the distance, D the end of the spring is below equilibrium in terms of seconds, t, since the spring was released.
The end of the spring is below equilibrium in terms of seconds, t, since the spring was released is D(t) = 17([tex]0.957^{t}[/tex])cos(28πt)
What is equilibrium?A state of balance between opposing forces or actions that is either static (as in a body acted on by forces whose resultant is zero) or dynamic (as in a reversible chemical reaction when the rates of reaction in both directions are equal).
Given that, a spring is attached to the ceiling and pulled 17 cm down from equilibrium and released. After 3 seconds, the amplitude has decreased to 13 cm. The spring oscillates 14 times each second.
Amplitude begins at 17 cm, [tex]A_{0}[/tex] = 17 cm
The amplitude decreases by 13/3 = 4.33 per second = 0.043%
The amplitude function can be then modelled as =
A(t) = [tex]A_{0}[/tex][tex](1-0.043)^{t}[/tex]
A(t) = [tex]A_{0}[/tex][tex]0.957^{t}[/tex]
The spring oscillates 14 times each second, therefore,
T = 1/14
2π/B = 1/14
B = 28π
The graphical equation is;
D(t) = [tex]A_{cos}[/tex](Bt-C)+D
Horizontal shift = 0
Vertical shift = 0
Hence, The end of the spring is below equilibrium in terms of seconds, t, since the spring was released is D(t) = 17([tex]0.957^{t}[/tex])cos(28πt)
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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.
Attached is my question, thank you. And x^2=squared i just can’t find the button to do it.
From the question we are given
[tex]\text{Profit }=Total\text{ Revenue }-total\text{ cost}[/tex]Annual total cost in $ is given by
[tex]C(x)=3600+100x+2x^2_{}[/tex]And an Annual total revenue in $ is given as
[tex]R(x)=500x-2x^2[/tex]Where x is the number of pairs of boots sold
We are to find the profit function
Using the detains given we have
Profit function P(x) is
[tex]P(x)=R(x)-C(x)[/tex]Therefore,
[tex]\begin{gathered} P(x)=500x-2x^2-\lbrack3600+100x+2x^2\rbrack \\ P(x)=500x-2x^2-3600-100x-2x^2 \\ P(x)=-4x^2+400x-3600 \end{gathered}[/tex]Therefore, the profit function is
[tex]P(x)=-4x^2+400x-3600[/tex]Next we are to find determine the number of pair of boots that will maximize annual profit
Plotting the graph of the Profit function we have
Hence, at maximum we have the points (50, 6400)
Therefore, x = 50
This implies that the number of boots that will maximize the annual profit is 500
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 1/729Write the following equation x2 +9y2 + 10x – 18y + 25 = 0 in vertex form.Identify the type of conic section and its direction.
The equation of the conic section is:
[tex]x^2+9y^2+10x-18y+25=0[/tex]Square terms are positive and have different coefficients. Then, we can say it is an ellipse.
To find the vertex form, we need to group x and y:
[tex](x^2+10x)+(9y^2-18y)+25=0[/tex]The grouped terms of y can be factored:
[tex](x^2+10x)+9(y^2-2y)+25=0[/tex]It will be convenient to group the 25 with the group of x, since we can have a perfect square trinomial (since the square root of 25 is 5, which is half ten):
[tex](x^2+10x+25)+9(y^2-2y)=0[/tex]We can factor the first goup:
[tex](x+5)^2+9(y^2-2y)=0^{}[/tex]Now, we can try to make another perfect square trinomila from the second term. We need a number whose square root multiplied by 2 gives us 2 (the coefficient of y) This number will be one. Then, we can sum 1 inside the parenthesis, but we need to substract 9 outside it in order not to alter the equation. (it is 9 because we added 1 inside a parenthesis that is multiplied by 9).
[tex](x+5)^2+9(y^2-2y+1)-9=0^{}[/tex]Now, we can factor the second group of terms and reorganize:
[tex](x+5)^2+9(y-1)^2=9^{}[/tex]Now, to get the equation in the vertex form, we need a 1 in the right side of the equation. Then, we can divide everything (both sides) by 9:
[tex]\frac{(x+5)^2}{9}+(y-1)^2=1[/tex]The equation of the ellipse is now on its vertex form. Since the number dividing the x term (9) is higher than the number dividing the y term (1) we can say that the direction of the ellipse is horizontal. It´s longer axis is parallel to the x axis of the plane.
6) Identifyas amonomial, binomial, or trinomial.4x2 – y + 0z4 binomial monomial Trinomial
For this problem we have the following expression given:
[tex]4x^2-y+0z^4[/tex]Since any number multiplied by 0 is 0 then our expression becomes:
[tex]4x^2-y[/tex]And since we have two terms we can categorize the expression as a binomial.
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 yearsThe table below shows the probability distribution of a random variable Z. Z P(Z) -11 0.06 -10 0.36 -9 0.43 -8 0.03 -7 0.02 -6 0.1 What is the mean of the probability distribution? Write your answer as a decimal. Submit
The mean (μ) of a discrete random variable (z) is calculated as follows:
[tex]\mu=\Sigma z\cdot P(z)[/tex]Substituting with data:
[tex]\begin{gathered} \mu=-11\cdot0.06-10\cdot0.36-9\cdot0.43-8\cdot0.03-7\cdot0.02-6\cdot0.1 \\ \mu=-0.66-3.6-3.87-0.24-0.14-0.6 \\ \mu=-9.11 \end{gathered}[/tex]Can you please help me with this question from math? A) He will receive a refund of $435.B) He will receive a refund of $442.C) He will pay $435.D) He will pay $442.
ANSWER:
A) He will receive a refund of $435.
STEP-BY-STEP EXPLANATION:
According to the table for your income and marital status you must pay a total of $4091
If you already paid a total of $4,526, then:
[tex]\begin{gathered} t=4526-4091 \\ \\ t=435 \end{gathered}[/tex]Which means, they owe you a total of $435 back.
Therefore, the correct answer is A) He will receive a refund of $435.
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]Using the explicit formula, find the 3rd term f(n)=5+4(n-1)
Answer:
13
Explanation:
The explicit formula of a sequence is given below:
[tex]f\mleft(n\mright)=5+4\mleft(n-1\mright)[/tex]When n=3
[tex]\begin{gathered} f\mleft(3\mright)=5+4\mleft(3-1\mright) \\ =5+4(2) \\ =5+8 \\ =13 \end{gathered}[/tex]The 3rd term of the sequence is 13.
Solving a proof I know how to start it just confused how to put it all together
Given that ABCD is a parallelogram, prove that
[tex]\begin{gathered} \bar{AB}\cong\bar{CD} \\ \bar{BC}=\bar{DA} \end{gathered}[/tex]step 1: Sketch the parallelogram
step 2: The diagonal AC, divides the parallelogram into two triangles
[tex]\begin{gathered} \Delta ADC\text{ and }\Delta ABC \\ Note\text{ that,} \\ \angle DAC=\angle ACB\text{ ( the angles are alternate)} \\ \angle DCA=\angle BAC\text{ (the angles are alternate)} \\ side\text{ AC = AC (common sides for both triangles)} \end{gathered}[/tex]step 3: By the ASA (Angle-Side-Angle) congruency theorem,
[tex]\begin{gathered} \Delta ADC\cong\Delta ABC \\ (The\text{ two triangles are congruent)} \end{gathered}[/tex]Hence, by CPCT (corresponding parts of congruent triangles)
[tex]\begin{gathered} \bar{AB}\cong\bar{CD}\text{ } \\ \bar{BC}\cong\bar{DA} \end{gathered}[/tex]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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Which of the follwoing shows the area of circle with a diameter of 8 km? a. 16 km2 50.27km2 X b. 4tkm? ~ 12.57km? c.21km? ~ 6.28km? d. Akm? ~ 3.14km2
The formula of the area of a circle is
[tex]A=\pi r^2[/tex]where r is the radius
in this case, we have the length of the diameter, the diameter is twice the radius
d= diameter
d=2r
therefore
r=d/2
r=8/2
r=4
we substitute the value of the radius in the formula
[tex]A=\pi r^2=\pi(4)^2=16\pi=50.27\operatorname{km}^2[/tex]the area of a circle with a diameter of 8km is 16pi km^2 or 50.27km^2
Abc is isosceles triangle and right angled at C then TanA
When we have a right angled triangle, it means the triangle has a right angle and two acute angles all equally summing up to 180 degrees.
When we have an isosceles triangle, it means there are two equal acute angles.
Therefore, by combining these two statements, we can get the value of the acute angles. A plot is given below.
[tex]\begin{gathered} 90+x+x=180 \\ 90+2x=180 \\ \text{Subtract 90 from both sides to get:} \\ 2x=90 \\ \text{Divide both sides by 2 to get:} \\ x=45^o \end{gathered}[/tex]Next step is to get Tan A.
We can use trigonometric ratios and Pythagoras theorem to get:
[tex]\begin{gathered} AB^{}=\sqrt[]{AC^2+BC^2} \\ AB=\sqrt[]{1^2+1^2} \\ AB=\sqrt[]{2} \end{gathered}[/tex]For Tan A, we employ the Soh Cah Toa to get:
[tex]\begin{gathered} \tan A=\frac{\text{opposite}}{\text{adjacent}} \\ \tan A=\frac{1}{1}=1 \end{gathered}[/tex]Therefore, Tan A = 1
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]How does graphing the line help us represent the value of k (constant of proportionality)?
Answer:
The graph of the line shows that the value of k is the y-coordinate of the point where the x-coordinate is equal to 1.
k = 2.5
1 seagull eats 2.5 pounds of garbage.
Explanation:
First, we need to draw the point (4, 10) on the graph because 4 seagulls eat 10 pounds of garbage. Then, we need to draw a line that passes through this point, and through (0, 0). Finally, we need to identify the number of pounds of garbage when the number of seagulls is 1 or identify the point (1, k). So, we get:
Therefore, the value of k = 2.5 is the constant of proportionality and tell us the number of pounds of garbage that each seagull eat.
So, the graph of the line shows that the value of k is the y-coordinate of the point where the x-coordinate is equal to 1. Also, k represents the slope of the line.
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.
write each fraction in simplest form 3/12
3/12 is 1/4 in its simplest form
Ming prepared three chemical solutions with temperatures -5, -4, and -3. what is the correct compares of the three temputures?
So we will like to compare the three numbers -5, -4 and -3. We will like to compare the three temperatures. To know wich numbers is less than the other we can draw the real line
The more to the left the number are the lesser it is therefore
[tex]-5<-4<-3[/tex]