Ashur solves the following system of linear equations.
Which statement about the solution to this system can he say is true?
The values of a and b are both equal to –4.
The values of a and b are both equal to 4.
The value of a is equal to 4, and b is equal to –4.
The value of a is equal to –4, and b is equal to 4.
Answers
The values of a and b are both equal to –4.
The given equations that make up the systems are:
-3a+7b=-16...................(Equation 1)
-9a+5b=16...................(Equation 2)
To find the values of a and b we will have to solve the two equations. To solve the equations let us employ the method of elimination.
Let us multiply (Equation 1) by -3. This will give us:
[tex] -3\times (-3a+7b=-16)=9a-21b=48 [/tex]...........(Equation 3)
Let us now add (Equation 2) to (Equation 3) to eliminate a. This will give us:
-16b=64
[tex] \therefore b=-4 [/tex]
Plugging this value of b in any of the equations we will get the value of a. Let us plug it in (Equation 1). This gives:
[tex] -3(-4)+7b=-16 [/tex]
[tex] 12+7b=-16 [/tex]
[tex] \therefore b=\frac{-28}{7}=-4 [/tex]
Thus, out of the given options, the first option is the correct one. The values of a and b are both equal to –4.
Related Questions
Use common sense to determine whether the given event is impossible; possible, but very unlikely; or possible and likely. A solar eclipse occurs on your birthday.
Answers
-Kaylah
PLEASE HELP ASAP
Find a solution of the linear inequality.
7>(or equal to)4x-5
(3, 4)
(1, 1)
(3, 0)
(2, 1)
Answers
Using your knowledge of circles, label the following on the given diagram: chord, tangent, radius, secant, point of tangency and diameter. Name a minor arc and a major arc.
Answers
A tangent is a line that only touches one point on the circle. The purple line on top of the circle is a tangent line.
A radius is a line from the center to any point on the circle. The red line is a radius.
A secant is like a chord, except it is a line and keeps going. The cyan (sky blue) line is a secant line.
A point of tangency is the point that the tangent line touches. The yellow point on the purple line is the point of tangency.
A diameter is a straight line that crosses the center and two points on the circle. You can say it’s two radii put together. Line segment BD (green) is a diameter.
Hope this helps!
In geometry, a chord, radius, diameter, tangent, secant, and the point of tangency are all parts related to a circle. A radius can also be an axis, a minor arc is the smaller arc between two points on a circle, and a major arc is the larger one. These terms help in understanding the properties and relations of lines to a circle.
In the context of circles in geometry, various terms define specific parts or aspects of a circle. Here's what each term represents:
A chord is a straight line segment whose endpoints both lie on the circle.The radius is a straight line from the center of the circle to any point on the circle. In other cases, it can form an axis which bisects a chord (as per a geometry theorem).A diameter is a chord that passes through the center of the circle, and it is also twice the length of the radius. Two radii forming a straight line constitute a diameter.A tangent is a straight line that touches the circle at just one point, this point is known as the point of tangency. A tangent is perpendicular to the radius drawn to the point of tangency.A secant is a straight line that intersects the circle at two points.A minor arc is the shortest arc connecting two endpoints on a circle, and a major arc is the longer arc connecting the same two endpoints. The length of an arc is proportional to the size of its associated angle at the center of the circle.
When drawing or labeling the parts of a circle, it's important to note these definitions. For instance, if given a diagram with a point on the circle labeled 'A' and the center labeled 'O', the segment OA would be a radius. If there's a straight line that touches the circle at point A and doesn't cross through it, that would be your tangent, and point A is the point of tangency. Any straight line through A that crosses through another point on the circle, say, point B, would be a secant, and the line OAB (if extended through O) would be a diameter. The arc's size determines if it is a minor or major arc, depending on whether it is more or less than half the circle's circumference.
Which of the following fractions is not in simplest form?
3/4
7/10
9/12
4/15
Answers
it's simplest form is 3/4
First, let's try simplifying all the fractions. . .
3/4: 3 cannot be divided and equal a whole number (only 4 can) This is in simplest form.
7/10: 7 cannot be divided and equal a whole number (only 10 can) this is in simplest form.
(correct answer) 9/12: 9 divided by 3 = 3 and 12 divided by 3 = 4 so this fraction in simplest form is 3/4.
4/15: 15 cannot be divided and equal a whole number (only the 4 can) this fraction is in simplest form.
Final answer:
9/12
Hope this helps you.
Have a great day!
HELP ASAP PLEASE!!!!
Answers
recall pythagorean theorem
[tex]a {}^{2} + b {}^{2} = c {}^{2} [/tex]
where and and b are the legs of the right triangle and c is the hypotenuse
[tex]4 {}^{2} + 4 {}^{2} = d {}^{2} [/tex]
apply Pythagorean theorem
[tex] \sqrt{16 + 16 } = d[/tex]
square each 4 and take the square root of both sides
[tex] \sqrt{32} = d[/tex]
simplify
reduce the radical
FINAL ANSWER
[tex]4 \sqrt{2} = d[/tex]
or you can simply see that it's a 45 45 90 triangle and know that the hypotenuse d equal one of the legs times the square root of 2
The midpoint of a line segment with end points as (-10, y1) and (-6, 7) is (-8, 6). What is the value of y1?
Midpoint formula is (x1 + x2)/2 , (y1 + y2)/2 but I keep getting a wrong answer.,
Answers
M ( (x₂-x₁)/2 , (y₂-y₁)/2 )
You need to invert these to get x₁ and y₁:
x₁ =2xm - x₂
y₁ =2ym - y₂
Try with the x to prove the formulae are correct:
x₁ =2·(-8) - (-6) = -16 + 6 = -10 which is what we have!
Then, use the other formula for y:
y₁ =2 ·(6) - (7) = 12 - 7 = 5
Therefore y₁ = 5
the product of two rational numbers
Answers
Answer:
'The product of two rational numbers is rational'
Step-by-step explanation:
Statement 'The product of two rational numbers'.
We know that, 'The product of two rational numbers is rational'.
We can prove it,
Let [tex]\frac{a}{b}[/tex] and [tex]\frac{p}{q}[/tex] are two rational number.
Where, a,b,p,q are integers and [tex]b,q\neq 0[/tex]
Now, Product the two rational number
[tex]\frac{a}{b}\times \frac{p}{q}=\frac{ap}{bq}[/tex]
Since, ap and bq are integers and [tex]bq\neq 0[/tex]
Thus, [tex]\frac{ap}{bq}[/tex] is an fraction with integers in the numerator and denominator making it a rational number.
Therefore, 'The product of two rational numbers is rational' is true.
Find all solutions in the interval [0, 2π).
2 sin2x = sin x
x = pi divided by three. , two pi divided by three.
x = pi divided by two. , three pi divided by two. , pi divided by three. , two pi divided by three.
x = 0, π, pi divided by six , five pi divided by six
x = pi divided by six , five pi divided by six
Answers
Final answer:
The solutions to the equation 2sin^2x = sinx in the interval [0, 2π) are x = 0, π, π/6, 5π/6 and x = π/6, 5π/6.
Explanation:
The given equation is: 2sin^2x = sinx.
To solve this equation, we can first factor out sinx:
sinx(2sinx - 1) = 0.
Setting each factor equal to zero, we get two equations:
sinx = 02sinx - 1 = 0Solving for x, we find:
x = 0, π, π/6, 5π/6x = π/6, 5π/6Which transformation could not map trapezoid 1 to trapezoid 8?
reflection
translation
rotation
Answers
Answer:
A rotation
Explanation:
A reflection across the y-axis would map trapezoid 1 to trapezoid 8.
A horizontal translation would also map trapezoid 1 to trapezoid 8.
However, a rotation would map trapezoid 1 to trapezoid 7; it would not map it to trapezoid 8.
Answer: The answer is (c) rotation.
Step-by-step explanation: We are given a figure where 8 trapezoid are drawn on the coordinate plane. We are to select from the given option the transformation that will not map trapezoid 1 to trapezoid 8.
We can easily check that by reflecting and translating that both these transformations will definitely map trapezoid 1 to trapezoid 8.
Only the rotation will not work here. If we rotate trapezoid 1 by 180° taking origin as the centre of rotation, the the image will be opposite of trapezoid 8. Therefore, rotation will not map trapezoid 1 to trapezoid 8.
Thus, (c) is the correct option.
The pressure P (in pounds per square foot), in a pipe varies over time. Ten times an hour, the pressure oscillates from a low of 40 to a high of 280 and then back to a low of 40. The pressure at time t = 0 is 40. Let the function P = f(t) denote the pressure in pipe at time t minutes. Find the formula for the function P=f(t),
Answers
To model the pressure function in the pipe that oscillates between 40 and 280 ten times an hour, we can use a sine function. The formula is P = f(t) = 120 sin(π/3 t) + 160.
Explanation:The pressure in the pipe oscillates between 40 and 280 ten times an hour, this is a trigonometric function scenario. Assuming the oscillation is sinusoidal, we can use a sine function to model the pressure in the pipe. The oscillation's period is 6 minutes because the pressure changes happen 10 times per hour. Thus, the function modelling this pressure will be of the form
P = a sin(b(t - c)) + d.
Given that the middle value of the pressure (between the max of 280 and the minimum of 40) is 160, this makes
'd' = 160.
The amplitude 'a' is half the total swing of the pressure which is 120.
To find 'b', we use the fact that the period of a sinusoid in this form is (2π/b).
As our period is 6 minutes, that makes 'b' = π/3.
The pressure is at a minima at t=0 so the phase shift 'c' = 0
Hence the formula P = f(t) = 120 sin(π/3 t) + 160.
Learn more about Oscillating Pressure here:https://brainly.com/question/4116396
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Find the volume of the composite space figure to the nearest whole number.
Answers
Answer:
The volume is 180 cube cm.
Step-by-step explanation:
By the given diagram,
The composite figure is made by the two cuboids,
First having dimensions, 2 cm × 5 cm × 6 cm,
And second having dimensions, 8 cm × 5 cm × 3 cm,
So, the volume of the given composite figure = the volume of first cuboid + the volume of second cuboid
= 2 × 5 × 6 + 8 × 5 × 3,
= 60 + 120
= 180 cube cm
The volume of the composite space figure to the nearest whole number is: 180 cube cm.
Here, we have,
from the given information, we get,
By the given diagram,
The composite figure is made by the two cuboids,
First having dimensions, 2 cm × 5 cm × 6 cm,
And second having dimensions, 8 cm × 5 cm × 3 cm,
So, the volume of the given composite figure
= the volume of first cuboid + the volume of second cuboid
= 2 × 5 × 6 + 8 × 5 × 3,
= 60 + 120
= 180 cube cm
Hence, the volume of the composite space figure to the nearest whole number is: 180 cube cm.
To learn more on volume click :
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For customers purchasing a refrigerator at a certain appliance store, let A be the event that the refrigerator was manufactured in the U.S., B be the event that the refrigerator had an icemaker, and C be the event that the customer purchased an extended warranty. Relevant probabilities are below.
P(A) = 0.80 P(B | A) = 0.94 P(B | A' ) = 0.79
P(C | A ∩ B) = 0.76 P(C | A ∩ B' ) = 0.56
P(C | A' ∩ B) = 0.68 P(C | A' ∩ B' ) = 0.33
(c) Compute P(B ∩ C).,
Answers
P(A)=0.75
P(B|A)=0.9
P(B|A′)=0.8
P(C|A∩B)=0.8
P(C|A∩B′)=0.6
P(C|A′∩B)=0.7
P(C|A′∩B′)=0.3
Which table identifies points on the line defined by the equations y-5x=-9
Answers
The equation y - 5x = -9 defines a line that none of the given points (1,5), (2,10), (3,7), and (4,14) lie on, as substituting their x-values in the equation doesn't yield the corresponding y-values.
Explanation:The question involves identifying points on a line described by the equation y - 5x = -9. To verify which points belong to this line, we can substitute the x-values of the given points into the equation and see if the resulting y-values match those in the points. We solve for y in the equation to get y as a function of x (dependence of y on x): y = 5x - 9.
Now, let's examine the points (1,5), (2,10), (3,7), and (4,14) to see if they satisfy this equation:
For (1,5): y = 5(1) - 9 = -4 which does not equal 5, so (1,5) is not on the line. For (2,10): y = 5(2) - 9 = 1 which does not equal 10, so (2,10) is not on the line. For (3,7): y = 5(3) - 9 = 6 which does not equal 7, so (3,7) is not on the line. For (4,14): y = 5(4) - 9 = 11 which does not equal 14, so (4,14) is not on the line.
None of these points lie on the line defined by y = 5x - 9. For a point to be on the line, plugging its x-coordinate into the equation must result in its corresponding y-coordinate.
someone help me please!
Answers
Hope this helps :)
Answer:
hudadagra what does a say im sorry for putting this in answer but it wont let me comment.
Step-by-step explanation:
i cant see the pic
Milena's take-home pay is $1200 a month. She spends 12% of her take-home pay on her cable bill. How much is Milena's monthly cable bill?
Answers
Answer:
$144
Step-by-step explanation:
Just did test
A basket contains 4 green marbles and 8 blue marbles. a marble is drawn without replacement. then another marble is drawn. what is the probability that both marbles will be green?
Answers
Final answer:
The probability of drawing two green marbles consecutively without replacement from a basket of 4 green marbles and 8 blue marbles is 0.1, or 10%.
Explanation:
The question involves calculating the probability of drawing two green marbles in succession without replacement from a basket containing 4 green marbles and 8 blue marbles. For the first draw, the probability of drawing a green marble is 4 out of 12, which reduces to 1/3 or about 0.3333. Once that marble is drawn, there are 3 green marbles left and 7 blue marbles, making a total of 10.
Therefore, the probability of drawing another green marble is 3 out of 10, or 0.3. To find the probability of both events happening consecutively, we multiply the two individual probabilities: (1/3) * (3/10) = 1/10 or 0.1. Hence, the probability that both marbles will be green is 0.1, or 10%.
PLEASE HELP WILL GIVE 20 POINTS MARK BRAIN~LEST 5 STAR RATTING FOR ONE QUESTION
Answers
[tex]( \frac{x^-^4y^2}{yx^2*x^2y^-^4} )^3[/tex]
The first step has been done correctly.
Leaving us with:
[tex] \frac{x^-^1^2y^6}{y^3x^6*x^6y^-^1^2} [/tex]
The second step, however, has been done incorrectly.
Why?
Because what has been applied on the exponent is product rule, where the exponents should get added and not multiplied
So, we should have an answer like this:
[tex] \frac{x^-^1^2y^6}{y^-^1^2^+^3x^6^+^6} = \frac{x^-^1^2y^6}{y^-^9x^1^2} [/tex]
So your answer will be the second option:
Step 2, the exponents in the denominator are multiplied
7 eighty percent of all california drivers wear seat belts. if three drivers are pulled over, what is the probability that all would be wearing their seat belts? worksheet
Answers
64/125
Solve the system of linear equations by elimination. 3x−2y=4 3x−2y=4 6x−2y=−2
Answers
y = -5
You can get this by multiplying the first equation by -1 and then combining. That will get your y values to cancel out.
Using the following equation, find the center and radius of the circle by completing the square.
x2 + y2 + 6x − 6y + 2 = 0
center: (−3, 3), r = 4
center: (3, −3) r = 4
center: (3, −3), r = 16
center: (−3, 3), r = 16
Answers
To complete square to a quadratic equation in its standard form we have:
ax2 + bx + c
Completing squares:
P (x) = (x + b / 2) ^ 2 - b ^ 2/4 + c
Keeping this in mind, we can complete square then:
x2 + y2 + 6x - 6y = -2
(x2 + 6x) + (y2 - 6y) = -2
((x + b / 2) ^ 2 - b ^ 2/4 + c) + ((y + b / 2) ^ 2 - b ^ 2/4 + c) = -2
((x + 6/2) ^ 2 - 6 ^ 2/4 + 0) + ((y + (-6) / 2) ^ 2 - (-6) ^ 2/4 + 0) = -2
((x + 3) ^ 2 - 9) + ((y - 3) ^ 2 - 9) = -2
((x + 3) ^ 2) + ((y - 3) ^ 2) - 9 - 9 = -2
((x + 3) ^ 2) + ((y - 3) ^ 2) - 18 = -2
((x + 3) ^ 2) + ((y - 3) ^ 2) = -2 + 18
((x + 3) ^ 2) + ((y - 3) ^ 2) = 16
((x + 3) ^ 2) + ((y - 3) ^ 2) = 4 ^ 2
Answer:
center: (-3, 3), r = 4
y = 2/3 x + 20
when x = 21 PLEASE EXPLAIN FUNCTION AND SOLUTION
Answers
In this problem, you are asked to compute for the value of y when x = 21. The function shows how the value of y changes with the given value of x.
Y = 2/3x + 20
Y = 2/3 (21) + 20
Y = 14 + 20
Y = 34
Answer:
5
Step-by-step explanation:
just trust me
what is the midpoint of a segment in the complex plane with endpoints at 6 -2i and -4 + 6i
Answers
Answer:
Midpoint of a segment in the complex plane with endpoints at 6 -2i and -4 + 6i is:
1+2i
Step-by-step explanation:
The midpoint of a segment in the complex plane with endpoints at 6 -2i and -4 + 6i is:
[tex]\dfrac{6-2i-4+6i}{2} \\\\=\dfrac{2+4i}{2}\\ \\=1+2i[/tex]
Hence, midpoint of a segment in the complex plane with endpoints at 6 -2i and -4 + 6i is:
1+2i
Answer: 2 + 4 i
Step-by-step explanation:
Hi, to solve this we have to apply the next expression:
(a1 +a2)/ 2 + (b1 +b2 )/2 i=
Where a is the real part, and b is the imaginary part (with i)
For example, for our case:
6 -2i , 6 is the real part (2) and -2 is the imaginary part (b)
Replacing with the values given
(6 -4) /2+ (-2 +6) /2 i = 2 + 4 i
Feel free to ask for more if needed or if you did not understand something.
It rained 2/8 inch in one hour. If rained 4/8 inch in the next hour.find the total amount of rain.wrote in simplest form
Answers
Simplify the rational expression. state any restrictions on the variable. n^4-11n^2+30/n^4-7n^2+10
Answers
To simplify the given rational expression, we factor both the numerator and the denominator, cancel out the common factor, and express the result as (n^2 - 6) / (n^2 - 2), with restrictions on n that it can't equate to the square roots of 5 or 2.
Explanation:The question involves simplifying the rational expression n^4 - 11n^2 + 30 divided by n^4 - 7n^2 + 10, and stating any restrictions on the variable. To simplify this, we first factor both the numerator and the denominator.
Numerator: (n^2 - 5)(n^2 - 6)
Denominator: (n^2 - 5)(n^2 - 2)
After factoring, we can cancel out the common factor (n^2 - 5) from both the numerator and the denominator. This leaves us with (n^2 - 6) / (n^2 - 2).
However, we must state the restrictions on the variable n. The original denominator cannot be equal to zero, thus n^2 cannot be equal to 5 or 2, leading to restrictions of n != sqrt(5) and n != sqrt(2).
if 10% of x is 20, what is 23% of x?
Answers
----------
then x = 200.what is 23% of x?
----------
23% = (23/100)*200 = 46
Sal bought 35 feet of window trim at a hardware store. The trim cost $1.75 per foot, including sales tax. If Sal paid with a $100.00 bill, how much change should he have received?
Answers
The correct answer is:
$38.75
Explanation:
35 feet of trim at $1.75 per foot would give us a cost of
35(1.75) = 61.25.
Paying with a $100 bill, he would receive
100-61.25 = $38.75 in change.
Graph the information presented in the table. Use that graph to predict the week that revenue will equal expenses for this small company.
Note: Revenue and Expenses are drawn on the vertical axis and Month is on the horizontal axis.
Week 6
Week 7
Week 5
Week 8
Answers
Answer:
Step-by-step explanation:
We plot the points on a graph with months on x-axis and Revenue/expenses on y-axis.
A straight line shows the decrease in expenses and another line showing increase in revenue.
The point of intersection shows the common point where the revenue and expenses become equal. This point of intersection we get at 6.5 months as shown in the graph attached.
Answer:
Week 7
Step-by-step explanation:
You can solve this problem by graphing the revenue and the expenses and it's asking on which week the lines intersect.
Spray from a lawn sprinkler makes a circle 40 feet and radius what are the approximate diameter circumference and area of the circle of the lawn watered
Answers
The approximate diameter of the circle is 80 feet, the circumference is approximately 251.327 feet, and the area is approximately 5026.548 square feet.
To find the diameter, circumference, and area of the circle watered by the lawn sprinkler, we can use the formulas:
1. **Diameter [tex](\(d\)) = \(2 \times \text{radius}\)[/tex]
2. **Circumference [tex](\(C\)) = \(2 \times \pi \times \text{radius}\)[/tex]
3. **Area [tex](\(A\)) = \(\pi \times \text{radius}^2\)[/tex]
Given:
Radius[tex](\(r\)) = 40 feet[/tex]
1. Diameter:
[tex]\[d = 2 \times r\]\[d = 2 \times 40 \text{ feet}\]\[d = 80 \text{ feet}\][/tex]
2. Circumference:
[tex]\[C = 2 \times \pi \times r\]\[C = 2 \times \pi \times 40 \text{ feet}\]\[C \approx 2 \times 3.14159 \times 40 \text{ feet}\]\[C \approx 251.327 \text{ feet}\][/tex]
3. Area:
[tex]\[A = \pi \times r^2\]\[A = 3.14159 \times 40^2 \text{ square feet}\]\[A = 3.14159 \times 1600 \text{ square feet}\]\[A \approx 5026.548 \text{ square feet}\][/tex]
Answer:
The approximate diameter of the circle is 80 feet, the circumference is approximately 251.327 feet, and the area is approximately 5026.548 square feet.
How long will it take the ball to reach the ground
Answers
We set the height function equal to zero and solve for t, the time.
h = -16t^2 + 250
-16t^2 + 250 = 0
16t^2 - 250 = 0
[tex] (4t + \sqrt{250})(4t - \sqrt{250}) = 0 [/tex]
[tex] 4t + \sqrt{250} = 0 [/tex] or [tex] 4t - \sqrt{250} = 0 [/tex]
[tex] 4t = -\sqrt{250} [/tex] or [tex] 4t = \sqrt{250} [/tex]
[tex] t = -\dfrac{\sqrt{250}}{4} [/tex] or [tex] t = \dfrac{\sqrt{250}}{4} [/tex]
We discard the negative solution since time must be positive.
The positive solution is
[tex] t = \dfrac{\sqrt{250}}{4} \approx 4.0 [/tex]
Answer: 4.0 seconds
WILL GIVE BRAINLIEST FOR CORRECT ANSWER
7. Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale.
Answers
.7=x/12
12*.7=x
x=8.4
Answer:
x = 8.4 cm
Step-by-step explanation:
Here we have to use the tan ratio to find the value of x.
tan = opposite/adjacent
tan 35 = x/12
Multiplying both sides by 12, we get
x = 12 tan 35 [tan 35 = 0.7]
x = 12*0.7
x = 8.4
Therefore, the value of x = 8.4 cm
Hope this will helpful.
Thank you.