determine the orderd pair (8,-3)is a solytion to the linear pair
Answers
To answer this question, we need to evaluate if the ordered pair forms an identity with both equations. We need to substitute the values for x = 8, and y = -3 in both equations:
[tex]\frac{x}{2}+5y=-11\Rightarrow\frac{8}{2}+5(-3)=-11\Rightarrow4-15=-11\Rightarrow-11=-11[/tex]These values result in an equality in this equation. We need to evaluate the other equation:
[tex]6x-\frac{y}{6}=40\Rightarrow6\cdot(8)-(\frac{-3}{6})=40\Rightarrow48+\frac{1}{2}=\frac{97}{2}\ne-11[/tex]In this case, the values do not result in an equality in one of both equations.
Therefore, we have that the correct answer is the option B:
No, the proposed solution does not result in an equality in one of the two equations.
Related Questions
Paulina bought a used car as she was entering college and planned to trade it in when she graduated four years later. She had learned in her high school financial algebra class that the average used car depreciated at an annual rate of 15%. If she had paid $13,900 for her car, how much can she expect to get when it is time for her to trade it in for a new car?
Answers
1st year
depreciable value: $13900
annual depreciation: $13900*15% = $2085
2nd year
depreciable value: $13900 - $2085 = $11815
annual depreciation: $11815*15% = $1772.25
3rd year
depreciable value: $11815 - $1772.25 = $10042.75
annual depreciation: $10042.75*15% = $1506.41
4th year
depreciable value: $10042.75 - $1506.41 = $8536.34
annual depreciation: $8536.34*15% = $1280.45
Final value: $8536.34 - $1280.45 = $7255.89
Please help.
A circle has a diameter of 18 inches. A central angle of 75° intercepts an arc of the circle. What is the intercepted arc length to the nearest tenth of an inch?
A.) 2.08 inches
B.) 3.8 inches
C.) 11.8 inches
D.) 23.6 inches
Answers
Answer:
C.) 11.8 inches===========================
GivenA circle with diameter d = 18 in,Central angle θ = 75°.To findThe length of the given arcSolutionUse arc length formula:
s = πdθ/360Substitute the values and calculate:
s = 3.14 * 18 in * 75°/360° = 11.8 in (rounded)The matching answer choice is C.
if a certain number is added to both the numerator and denominator of the fraction 8/9, the result is 6/7. Find the numer.
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I need some help. Could someone explain it to me?
Answers
Problem
We have the following table given:
x y
0 2
1 6
4 -9
8 8
Solution
We know that the domain correspond to the value of x in the relationship and then the correct answer for this case would be:
2
0
Jusrt 2,9 are the values in the domain of the function
Ary is writing thank you cards to everyone who came to her wedding. It takes her of an hour to write one thank you card. If it took her 8 hours to finish writing all of the cards, how many thank you cards did she write? 48 thank you cards 36 thank you cards 46 thank you cards 40 thank you cards
Answers
The question doesn't specify which fraction of an hour it takes Ary to write a thank you card.
Let's imagine that it takes her 1/4 of an hour to write a thank you card.
In such case, in one hour she will be able to write 4 thank you cards.
and therefore in 8 hours, ishe will be able to write 32 thank you cards (8 times 4 cards).
If it takes her 1/6 of an hour to write a thank you card, then in hone hour she will write a total of 6 thank you cards, and therefore, in 8 hours she will be able to write 8 times 6 thank you cards: 8 x 6 = 48 thank you cards.
If it takes her 1/5 of an hour to write a thank you card, then in hone hour she will write a total of 5 thank you cards, and therefore, in 8 hours she will be able to write 8 times 5 thank you cards: 8 x 5 = 40 thank you cards.
You just use this type of criteria to solve the problem whatever the fraction of the hour it takes to write one card as they specify in the question.
The convex polygon below has 8 sides. Find the value of x.140°11801270153013401561170
Answers
Explanation
The formula for calculating the sum of interior angles in a polygon is ( n − 2 ) × 180 ∘ where is the number of sides.
[tex](n-2)\cdot180=\text{ Sum of internal angles}[/tex]Step 1
find the sum of the internal angles in the given polygon
Let
number of sides = 8
Now, replace
[tex]\begin{gathered} (n-2)\cdot180=\text{ Sum of internal angles} \\ (8-2)\cdot180=\text{ Sum of internal angles} \\ 6\cdot180=\text{Sum of internal angles} \\ 1080=\text{Sum of internal angles}\rightarrow equation(1) \end{gathered}[/tex]Step 2
now, we have the other angles, so
sum of internal angles is:
[tex]\text{angle}1+\text{angle}2+\text{angle}3+\text{angle}4+\text{angle}5+\text{angle}6+\text{angle}7+\text{angle}8=\text{ sum of the internal angles}[/tex]replace
[tex]\begin{gathered} 127+140+118+153+156+117+x+132=\text{ Sum of internal angles} \\ x+943=\text{Sum of internal angles}\rightarrow equation\text{ (2)} \end{gathered}[/tex]hence
[tex]x+945=1080[/tex]subtract 945 in both sides to solve for x
[tex]\begin{gathered} x+945=1080 \\ x+945-945=1080-945 \\ x=135 \end{gathered}[/tex]i hope this helps you
5. Use a number line to find the product: 5 x (-3)=
Answers
First, we solve the expression.
Since it is a negative number we have to place it 15 places to the left ( from zero)
9) solve using substitution method and check your answer:4x - 3y + 2z = 16- 4y - Z = 7= 146x - y
Answers
Given the system of equations, solve the third equation for y, as shown below
[tex]\begin{gathered} 6x-y=14 \\ \Rightarrow y=6x-14 \end{gathered}[/tex]And, solve for z in the second equation,
[tex]\begin{gathered} -4y-z=7 \\ \Rightarrow z=-4y-7 \\ \Rightarrow z=-4(6x-14)-7=-24x+49 \end{gathered}[/tex]Thus, substitute the values of y and z in terms of x into the first equation, as shown below
[tex]\begin{gathered} \Rightarrow4x-3y+2z=4x-3(6x-14)+2(-24x+49)=4x-18x+42-48x+98 \\ \Rightarrow-62x+140=16 \\ \Rightarrow-62x=-124 \\ \Rightarrow x=2 \end{gathered}[/tex]Then, solving for y and z given x=2,
[tex]\begin{gathered} x=2 \\ \Rightarrow y=6*2-14=-2 \\ and \\ z=-24*2+49=-48+49=1 \end{gathered}[/tex]Therefore, the solution to the system of equations is x=2, y=-2, z=1To verify the solutions, substitute the values we found into the three equations of the system, as shown below
[tex]\begin{gathered} x=2,y=-2,z=1 \\ \Rightarrow4x-3y+2z=4*2-3*(-2)+2*1=8+6+2=16\rightarrow correct \\ \Rightarrow-4y-z=-4*(-2)-1(1)=8-1=7\rightarrow correct \\ \Rightarrow6x-y=6*2-1(-2)=12+2=14\rightarrow correct \end{gathered}[/tex]What is the equation for a line passing through (-2,5) perpendicular to y - 3x = 8
Answers
Consider that the equation of a line with slope 'm' and y-intercept 'c' is given by,
[tex]y=mx+c[/tex]Consider the given equation of line,
[tex]\begin{gathered} y-3x=8 \\ y=3x+8 \end{gathered}[/tex]Comparing the coefficient, it is found that the slope of the given line is 3,
[tex]m=3[/tex]Let 's' be the slope of the line which is perpendicular to this line.
Consider that two lines will be perpendicular if their product of slopes is -1,
[tex]\begin{gathered} m\times s=-1 \\ 3\times s=-1 \\ s=\frac{-1}{3} \end{gathered}[/tex]So the slope of the perpendicular line is given by,
[tex]y=\frac{-1}{3}x+c[/tex]Now, it is given that this line passes through the point (-2,5), so it must satisfy the equation of the line,
[tex]\begin{gathered} 5=\frac{-1}{3}(-2)+c_{} \\ 5=\frac{2}{3}+c \\ c=5-\frac{2}{3} \\ c=\frac{13}{3} \end{gathered}[/tex]Substitute the value of 'c' to get the final equation,
[tex]\begin{gathered} y=\frac{-1}{3}x+\frac{13}{3} \\ 3y=-x+13 \\ x+3y=13 \end{gathered}[/tex]Thus, the required equation of the perpendicular line is x + 3y = 13 .
Which equation could be represented by the number line? A. 3 OB.-4 5=1 OC. 1+ -5)= OD. -3+4 -1
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According to the given number line, we have to go back from the second point to the first point 4 spots. In other words, the equation has to include a sum with -4.
Therefore, the answer is A since it's expressing an initial number 3, then the sum with -4.Plot the point given by the following polar coordinates on the graph below. Each circular grid line is 0.5 units apart.230(2.5. -,
Answers
Solution:
Given:
[tex](2.5,-\frac{2\pi}{3})[/tex]In the figure, ∆ABD ≅ ∆CBD by Angle-Side-Angle (ASA). Which segments are congruent by CPCTC? BC ≅ AD CB ≅ AB AB ≅ CD DB ≅ DC
Answers
By CPCTC this is the only valid answer:
CB ≅ AB
Another statement should be AD≅ CD
Corky writes four equations to show each of the properties of equality. Which of Corky's equation is incorrect? Explainwill send image.
Answers
6 + m = 12
A. This IS equivalent
6 + m - m = 12 - m ==> 6 = 12 - m ==> 6 + m = 12
B. This IS NOT equivalent
6 + m - 6 = 12 - 12 ==> m = 0
C. This IS equivalent
6 + m + 2 = 12 + 2 ==> 6 + m = 12
D. This IS equivalent
6 + m - 6 = 12 - 6 ==> m = 6 ==> 6 + m = 12
Answer:
B is not equivalent
You have been tracking an adult female Australian flatback sea turtle who weighs 25 kg. How many kilocalories must she consume each day to maintain her body weight?
Answers
The kilocalories that she must consume each day to maintain her body weight is 6250 kilocalories.
How to calculate the value?From the information, the person has been been tracking an adult female Australian flatback sea turtle who weighs 25 kg.
It should be noted that the requirements is 250kcal per kilograms.
Therefore, the calories will be:
= Weight × Required calories
= 250 × 25
= 6250 kcaloriies
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A newsletter publisher believes that more than 31% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.01 level to substantiate the publisher's claim? State the null and alternative hypotheses for the above scenario. Answer
Answers
The null hypothesis is H0: P = 0.31 and the alternative hypothesis is Ha: P > 0.31.
What is a null hypothesis?The null hypothesis is simply to predict that there is no effect of relationship between the variables.
The alternative hypothesis is to state the research prediction of a relationship or effect. In this case, the newsletter publisher believes that more than 31% of their readers own a Rolls Royce.
The null hypothesis is P = 0.31. while the alternative hypothesis will be that it's greater than 0.31.
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In ABC, B = 51°, b = 35, and a = 36. What are the two possible values for angle A to the nearest tenth of a degree?Select both correct answers.
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Using the law of sines:
[tex]\frac{a}{\sin(A)}=\frac{b}{\sin (B)}[/tex]Solve for A using the data provided:
[tex]\begin{gathered} \sin (A)=\frac{\sin (B)\cdot a}{b} \\ A=\sin ^{-1}(\frac{\sin (51)36}{35}) \\ A\approx53.1 \\ or \\ A\approx126.9 \end{gathered}[/tex]Andrea invites 12 cousins 6 aunts 4 brothers 2 sisters what fraction of her party guests are cousins?
Answers
To determine the fraction of cousins, you have to divide the number of cousins she invited by the total number of guests.
She invited 12 cousins, 6 aunts, 4 brothers, and 2 sisters, a total of 24 guests.
Then:
[tex]\frac{nº\text{cousins}}{\text{total guests}}=\frac{12}{24}[/tex]Both, 12 and 24 are divisible by 12, to simplify the fraction, divide the numerator and denominator by 12
[tex]\frac{12\div12}{24\div12}=\frac{1}{2}[/tex]The fraction
Use a trig equation to solve for x. Round to the nearest tenth.
Answers
Given a right angle triangle
We need to find the measure of the angle x
The opposite side to the angle x = 19
the adjacent side to the angle x = 15
We will find x using the tan function as follows:
[tex]\begin{gathered} \tan x=\frac{opposite}{adjacent} \\ \\ \tan x=\frac{19}{15} \\ \\ x=\tan ^{-1}\frac{19}{15}\approx51.7098^{} \end{gathered}[/tex]Round the answer to the nearest tenth
so, the answer will be x = 51.7
Please step-by-step help me how much of a circle is shaded
Answers
The given data is ratio from the the total are of circle is 1 .
let the shaded area is x then:
All area is equal to one.
[tex]\begin{gathered} \frac{1}{2}+\frac{2}{9}+x=1 \\ \frac{9+4}{18}+x=1 \\ \frac{13}{18}+x=1 \\ x=1-\frac{13}{18} \\ x=\frac{18-13}{18} \\ x=\frac{5}{18} \end{gathered}[/tex]So area of shaded region is
[tex]\frac{5}{18}[/tex]Dr. Hughes instructs her students to solve the equation, 2x - 5y = -20, for y. What is the correct first step?Add +5y to both sides of the equation.O Add -2x to both sides of the equation.Add +2x to both sides of the equation.Divide each term in the equation by -5.
Answers
We have the following expression given:
2x -5y = -20
For this case the correct set in order to begin is add 5y in both sides
Add +5y to both sides of the equation.
Can you explain this math to me please I’ve never seen it before and don’t understand
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For a quadratic function in standard form,
[tex]\begin{gathered} \text{a = coefficient of x}^2 \\ b\text{ = coeffcient of x} \\ c=\text{ the constant term} \end{gathered}[/tex]For the polynomial f(x),
a = 2, b = -3 and c = 4
For the polynomial g(x)
a = 4, b = -6, c = 10
For the polunomial h(x),
a = 7, b = 0, c = 8
For the polynomia p(x),
a = 1, b = -10, c = 0
The variables x and y vary directly. Use values to write an equation that relates x and y. y=25;x=5And y=20;x=12
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A lineal equation has the next form:
[tex]y=mx+b[/tex]where m is the slope and is calculated as follow:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For this case
y1=20
y2= 25
x1=12
x2= 5
so:
[tex]m=\frac{25-20}{5-12_{}}=\frac{5}{-7}=-\frac{5}{7}[/tex]then the equation will be:
[tex]y=(-\frac{1}{7})x+b[/tex]Using one of the points we calculate the b
we are going to use y=25 x=5
[tex]25=(-\frac{5}{7})5+b[/tex]Clearing the b we get:
[tex]25-\frac{25}{7}=b\Rightarrow\frac{200}{7}=b[/tex]b=200/7 or b=28.57
So the final equation is:[tex]y=-\frac{1}{7}x+\frac{200}{7}[/tex]A lineal equation has the next form:
[tex]y=mx+b[/tex]where m is the slope and is calculated as follow:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For this case
y1=20
y2= 25
x1=12
x2= 5
so:
[tex]m=\frac{25-20}{5-12_{}}=\frac{5}{-7}=-\frac{5}{7}[/tex]then the equation will be:
[tex]y=(-\frac{1}{7})x+b[/tex]Using one of the points we calculate the b
we are going to use y=25 x=5
[tex]25=(-\frac{5}{7})5+b[/tex]Clearing the b we get:
[tex]25-\frac{25}{7}=b\Rightarrow\frac{200}{7}=b[/tex]b=200/7 or b=28.57
So the final equation is:[tex]y=-\frac{1}{7}x+\frac{200}{7}[/tex]This question is from a MATH extra credit assignment, so unless I accidentally clicked on a subject other than maths... This question is also not from a test. Please help me if you can. Thank you if you do :)
Answers
Answer
$6,314
Step-by-step explanation
Compound interest formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
• A: final amount, in dollars
,• P: principal, in dollars
,• r: interest rate, as a decimal
,• n: number of times interest is applied per year
,• t: time in years
In this case, the investment is compounded annually, that is, once per year (n = 1). Substituting P = $4,625, r = 0.0352 (=3.52/100), n = 1, and t = 9 years, we get:
[tex]\begin{gathered} A=4,625(1+\frac{0.0352}{1})^{1\cdot9} \\ A=4,625(1.0352)^9 \\ A=\text{ \$}6,314 \end{gathered}[/tex]I need to find the radius and the diameter but I don't understand.
Answers
ANSWER
Radius = 3 yd
Diameter = 6 yd
EXPLANATION
We are given the circle in the figure.
The radius of a circle is defined as the distance between the centre of a circle and its circumference.
Therefore, from the circle given, the radius is 3 yards
The diameter of a circle is defined as the total distance (through the centre) from one end of a circle to another.
It is twice the radius. Therefore, the diameter of the given circle is:
D = 3 * 2
D = 6 yards
The diameter is 6 yards.
If a square has a perimeter of 28 inches, what is its area in square inches?
Answers
Remember that
The formula to calculate the perimeter of a square is
[tex]P=4*b[/tex]where
b is the length side of the square
we have
P=28 in
substitute in the formula
[tex]\begin{gathered} 28=4*b \\ sol\text{ve for b} \\ b=\frac{28}{4}=7\text{ in} \end{gathered}[/tex]The area of a square is
[tex]A=b^2[/tex]substitute the value of b
[tex]\begin{gathered} A=7^2 \\ A=49\text{ in}^2 \end{gathered}[/tex]The area is 49 square inchesoption Cidentify whether each phrase is an expression equation or quantity
Answers
the last one of the right column is a inequality, because it has the sign "<"
the second one of the right column in an expression because it doen't have the sign "="
the first one of the right column is a equation because it has the sign "=".
In December, 64 teams qualify for a basketball tournament. After each round, half of the teams are eliminated.
Which exponential function can be used to find the number of teams left after a rounds, where is a whole number?
O f(x) = (64)
O f(x) =
(x)64
O f(x) = 64 (¹)
○ f(x) = x(¹)
Answers
The exponential function is f(x) = 64·(1/2)ˣ which can be used to find the number of teams left after a round.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
Given that 64 teams qualify for a basketball tournament. After each round, half of the teams are eliminated.
Because it is an exponential function, f(x) will reach 0 as x increases, allowing us to construct the following table of values:
x f(x)
0 64
1 32
2 16
3 8
4 4
5 2
6 1
At that point, 64 teams are in the tournament, and the total number of teams (from this point forward)
Therefore, half of the teams are eliminated after each round and the exponential function is:
f(x) = 64·(1/2)ˣ
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In an office building, 54 office are currently being rented, this represent 30% of the total units. how many offices are in the building
Answers
given that,
54 offices are currently rented
and it represent 30% of the total unit
to get the total offices in the building
let the total offices be x
30% of x = 54
30/100 X x = 54
cross multiply
30x = 5400
dividing both sides by 30
30x/30 = 5400/30
x = 5400/30
x = 180
therefore the total offices in the building is 180
what is the mean of 36,38,39,28,34
Answers
We are to find the mean of
[tex]36,\text{ 38, 39, 28, 34}[/tex]Finding mean
[tex]\begin{gathered} M\text{ean = }\frac{36\text{ + 38 + 39 + 28 + 34 }}{5} \\ Mean\text{ = }\frac{175}{5} \\ M\text{ean = 35} \end{gathered}[/tex]Therefore,
mean = 35
Metric area unit conversion with decimal valuesTammy has a rectangular poster. The poster is 1.2 meters long and 0.9 meters wide. What is the area of the poster in square centimeters? Do not round youranswer.cmcm²cm³
Answers
We are asked to find the final area in square centimeters.
We must first convert the measurements of the poster into centimeters:
1.2m = 120cm
0.9m = 90cm
Area = length * width
= 120*90
= 10800 square centimeters.
