Answer:
Absolute value is the distance away from zero, so if x is a rational number and y is opposite, they would both be the same distance away from zero, regardless of their sign.
Step-by-step explanation:
Absolute value is the distance of a number away from zero. For example, if x is equal to the rational number -2, the absolute value of -2 is just 2, given that both 2 and -2 are only a distance of 2 away from the number zero. Think of it as your walk or drive to school. If you live 4 miles from school, you drive a distance of 4 miles there and 4 miles back. That distance is not calculated as a positive 4 miles there and a negative 4 miles back, but rather just 4 miles there and 4 miles back, for a total distance of 8 miles. So, if x=4 and y=(-4), the absolute value of both would be 4.
Hello, I have a question about quadratic equations. I don’t know how to slove these:
1. (x-6)(2x-6)=20
2. (x+3) ² = 8x+12
3. (3x-1)(x+5)=3x ²
can somebody help me?
Answer:
Step-by-step explanation:
Answer:
1.X= 8 or 1
2.X= 3 or -1
3. X = 5/14
Step-by-step explanation:
1. Expanding your original equation (x-6)(2x-6)=20) , you get 2x^2-18x+36=20. Then, subtract 20 from both sides. You get 2x^2-18x+16=0. Now this is a standard Quadratic equation. Use the quadratic Formula to solve this, you get X= 8 or 1.
2. 1. Expand : x²+6x+9-8x-12=0 2. Simplify : x^2-2x-3=0 3. Solve as a quadratic equation : x= 3 or -1.
3. Same thing as the first one!
Hope I helped! <3
A shoreline is eroding at a rate of 1/3 foot per 3 months.how many feet are eroding per year
Answer:
1 1/3 feet per year
Step-by-step explanation:
Steps:
1. How many months per year? 12.
2. 12 divided by 3 (number of months) =4
3. multiply 1/3 and 4.
4. Your answer is 4/3 or 1 1/3 feet per year.
The shoreline is eroding at a rate of 4/3 feet per year, which is approximately 1.33 feet per year, calculated by multiplying the 3-month erosion rate of 1/3 foot by 4.
The question is about calculating the annual rate of shoreline erosion given the erosion rate for a specific shorter period. If a shoreline is eroding at a rate of 1/3 foot per 3 months, we can find the yearly erosion rate by multiplying that rate by the number of 3-month periods in a year, which is 4 (since there are 12 months in a year).
To calculate:
Multiply the 3-month erosion rate by 4:
(1/3 foot per 3 months) x 4 (3-month periods in a year) = 4/3 feet per year
Therefore, the shoreline is eroding at a rate of 4/3 feet, or approximately 1.33 feet, per year.
6 painters can paint the fence in 15 hours. How long would it take 5 workers to do the same job?
Answer:
12.5 hours
Step-by-step explanation:
15/6 is 2.5. 2.5 is how many hours per worker. 5 times 2.5 is 12.5 hours
complete the following statement given: QXR=NYC a.QX= ? b. Y=?
Answer:
Step-by-step explanation:
The given congruent triangles △QXR and △NYC mean that corresponding sides and angles are equal. Hence, line segment QX equals NY and angle Y equals angle X.
The symbols △QXR and △NYC stand for two triangles which are mentioned to be congruent. Congruency in triangles means they have the same size and shape. This implies that the corresponding sides and angles of the two triangles are equal.
a) As per the congruency of the triangles, line segment QX in triangle △QXR would be congruent to corresponding segment in triangle △NYC, which is NY. Hence, line segment QX = NY.
b) Referring to the same principle, angle Y in triangle △NYC should be equal to its corresponding angle in triangle △QXR. Considering the order of the letters in triangles, angle Y would correspond to angle X. Hence, angle Y = angle X.
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point a has the coordinates(2,5) point B has the coordinates (6,17) how long is segment ab in simplified radical form
Answer:
[tex]4\sqrt{10}[/tex]
Step-by-step explanation:
We have been given that point A has the coordinates(2,5) point B has the coordinates (6,17).
To find the length of segment AB we will use distance formula.
[tex]\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Upon substituting coordinates of point A and point B in distance formula we will get,
[tex]\text{Distance between point A and point B}=\sqrt{(6-2)^2+(17-5)^2}[/tex]
[tex]\text{Distance between point A and point B}=\sqrt{(4)^2+(12)^2}[/tex]
[tex]\text{Distance between point A and point B}=\sqrt{16+144}[/tex]
[tex]\text{Distance between point A and point B}=\sqrt{160}[/tex]
[tex]\text{Distance between point A and point B}=4\sqrt{10}[/tex]
Therefore, the length of segment AB is [tex]4\sqrt{10}[/tex].
How do you do this
Help please
Thanks
It's a linear function. We need only two points to the plotting of the graph.
[tex]5x-y=5\qquad\text{subtract 5x from both sides}\\\\-y=-5x+5\qquad\text{change the signs}\\\\y=5x-5\\\\for\ x=0\to y=5(0)-5=0-5=-5\to(0,\ -5)\\\\for\ x=1\to y=5(1)-5=5-5=0\to(1,\ 0)[/tex]
What does the t represent at the end of the vector?
The uppercase T means "transpose". A matrix transpose is where you swap the rows and columns. Anything that is row becomes a column, and vice versa. What this means is that instead of a row vector, you end up with a column vector. The dimensions are important so you can properly multiply matrices.
Determine the maximum value of the objective function, P.
P= 15x+12y
6x+4y≤2000
2x+4y≤1000
x≥0
y≥0
Answer:
Maximum (250,125) Answer
Step-by-step explanation:
This is more of a graphing problem than it is anything else.
Begin by graphing all 4 given equations.
When you do that, mark the intersection points of at least 2 lines. In this case it is exactly 2 lines for each intersecting point.
6x + 4y <= 2000 and 2x + 4y <= 1000 intersect at (250,125)
x=>0 and y=>0 intersect at (0,0)
6x + 4y <=2000 and x => 0 intersect at 333.333
2x + 4y <=1000 and y>=0 intersect at 0,250.
Any other intersection points fall outside the range of the givens. The shaded part we are interested in is sort of a very dark green/blue. It is the interior of the quadrilateral determined by the 4 vertices that are marked.
Now all you have to do is determine the maximum point using P=15x + 12y
For 0,0 P = 15*0 + 12,0 = 0
For 0,250 P = 15*0 + 12*250 = 3000
For 333.3333,0 P = 15*333.3333 + 12*0 = 5000 rounded.
For 250,125 P = 15*250 + 12*125 = 5250 Which is the maximum
Answer (250,125) produces the maximum value Answer
To determine the maximum value of the objective function P in a linear programming problem, one must graph the constraints to find the feasible region and then use the corner-point method to evaluate P at each vertex of this region.
Explanation:The problem presented is a linear programming problem where we need to find the maximum value of the objective function P, given by P = 15x + 12y, subject to certain constraints involving x and y which must both be non-negative. To solve this problem, we will graph the constraints to find the feasible region and then use the corner-point method to evaluate the objective function at each vertex of this region to determine which gives the maximum value.
Step-by-Step Solution:Graph the constraints:6x + 4y ≤ 20002x + 4y ≤ 1000x ≥ 0y ≥ 0Identify the feasible region. It is the area where all the inequalities overlap and where x and y are both non-negative.Find the vertices of the feasible region. This can be done by solving the constraints as equations.Calculate the value of the objective function P at each vertex.Determine the maximum value of P from the evaluated vertices.From net earnings of 740 per month Lisa Jones must spend 200 for her portion of the rent on an apartment she shares with two friends what percent of her net income is her rent payment
Answer:
27% of her net income is her rent payment
Step-by-step explanation:
Net earnings = $740
Lisa spend $200 for rent payment
We need to find out what percent of net earning is her rent payment
Let x be the percentage
x% of net income = rent
x% * 740 = 200
[tex]\frac{x}{100} * 740 = 200[/tex]
Multiply both sides by 1004
740x = 20000
divide both sides by 740
x=27.02702703
So its approximately 27%
PLEASE HELP!
If food costs $520.00 and your total budget is $2,100.00, what percent of your budget is spent on food?
<3 Please explain how to do it. :)
Answer:
24.7619048 %
Step-by-step explanation:
The percent spent on food
food/total
520/2100
.247619048
This is in decimal form
Multiply by 100 to change it to percent
24.7619048 %
The letter X shown above has which type of symmetry?
1. Line Symmetry only
2. Point Symmetry only
3. Point and Line Symmetry
4. No Symmetry
The letter X shown ''Point and Line Symmetry''.
What is Line segment?
Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
Given that;
The letter is X.
Now,
We know that;
A point symmetry is defined as a type of symmetry in which a geometrical figure is divided into two equal and symmetrical parts by a central point.
Thus, Letter X has Point symmetry.
And, The line symmetry is defined as a type of symmetry that divides a geometrical figure into two equal and symmetrical parts.
Thus, Letter X has Line symmetry.
Therefore, The letter X shown ''Point and Line Symmetry''.
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a boat can travel 176 kilometers on 88 liters of gasoline. How much gasoline will it need to go 250 kilometers
Answer:
176 km/88 liters = 2 km/liter
(250 km)(1 liter/2 km) = 125 liters
Your closet has 5 shirts for every 2 sweaters. Your closet has 30 shirts.How many sweaters are in your closet
Answer:
12
Step-by-step explanation:
So the ratio is 5:2, so we can set up a proportion! So there are 12 sweaters.
How to study for Hesi exam
Given: ∆ABC is isosceles m∠ACB = 120° M ∈ AB , CM = 12 m∠BMC = 60° Find: AB
Look at the picture.
This is isosceles triangle. Therefore, the angles at the base are congruent.
m∠ BAC = m∠ABC.
We know, the sum of the measures of the angles in a triangle is equal 180°.
Therefore:
m∠BAC + m∠ABC + m∠ACB = 180°
2m∠ABC + 120° = 180° subtract 120° from both sides
2m∠ABC = 60° divide both sides by 2
m∠ABC = 30°
m∠MCB = 90° → ΔMCB is a right triangle (30 - 60 - 90).
The sides of that triangle are in proportion: 1 : √3 : 2.
Therefore MC : BC : MB = 1 : √3 : 2
MC = 12 → BC = 12√3 and MB = 2 · 12 = 24
ΔCDB is the right triangle (30 - 60 - 90) too.
Therefore CD : BD : BC = 1 : √3 : 2
CD = 1/2 BC → CD = 1/2(12√3) = 6√3
BD = CD√3 → BD = 6√3(√3) = 6(3) = 18
AB = 2BD therefore your answer is:
AB = 2(18) = 36AB length is 24 cm
Further Explanation The first step, find the length of BM
Given length CM = 12 cm
and length CB = 12 sqrt 3
sin 60 ° = CB / BM
1/2 sqrt 3 = 12 sqrt 3 / BM
BM = 1/2 sqrt 3 * 12 sqrt 3
BM = 18 cm
Then find the length of the MA
sin 30 ° = CM / MA
1/2 = 12 / MA
MA = 1/2 * 12
MA = 6 cm
So, the length of AB is BM + MA = 18 cm + 6 cm = 24 cm
A triangle is the name of a shape made from three sides in the form of a straight line and three angles. The mathematician Euclid who lived around 300 BC found that the sum of the three angles on a triangle on a flat plane was 180° degrees. This allows us to calculate the magnitude of one angle when the other two angles are known.
Classification of triangles
According to the length of the sides:
The equilateral triangle is a triangle whose sides are the same length. As a result, all angles are equal, which is 60 °. Isosceles triangle is a triangle whose two sides are the same length. This triangle has two equal angles. An arbitrary triangle is a triangle whose sides have different lengths. Big all the angles are also different.According to the biggest angle:
A right triangle is a triangle whose angle is equal to 90°. The side in front of the 90° angle is called the hypotenuse or the hypotenuse. An acute triangle is a large triangle, all angles <90° An obtuse triangle is a large triangle with an angle of> 90°
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Details
Class: Middle/High School and College
Subject: Mathematics
Keyword: degrees, angles, triangle
All of my points to anyone who can help me with these..! Marking Brainliest as well
Answer:
Question one 186
Question two 240
Step-by-step explanation: You multiply the variable (the letter) by the number that the person is using
Answer:
1. 186
2. 240
Step-by-step explanation:
1. D =3w+60
D =3(42)+60
D =186
2. I =48t
I =48(5)
I =240
A car rental agency advertised renting a car for $ 23.95$23.95 per day and $ 0.34$0.34 per mile. If TrevorTrevor rents this car for 22 days, how many whole miles can he drive on a $ 100$100 budget?
Answer:
see below PLEASE GIVE BRAINLIEST
Step-by-step explanation:
$23.95 x 2 = $47.90
$100 - $47.90 = $52.10
$52.10 ÷ .34 = 153.23 miles can be driven
If you need to round the number will be 153 miles
If f(x)=x2-2x and g(x) = 6x+4, for which values of x does (f+g)(x)=0
[tex]f(x)=x^2-2x;\ g(x)=6x+4\\\\(f+g)(x)=f(x)+g(x)\\\\(f+g)(x)=0\Rightarrow(x^2-2x)+(6x+4)=0\\\\x^2+(-2x+6x)+4=0\\\\x^2-4x+4=0\\\\x^2-2x-2x+4=0\\\\x(x-2)-2(x-2)+0\\\\(x-2)(x-2)=0\iff x-2=0\\\\\boxed{x=2}[/tex]
Jay is letting her bread dough rise. After three hours, her bread dough is 11/5 of its original size.
What percent of its original size is Jay's bread dough?
Answer:
original size of Jay's bread dough is raised to 220%
Step-by-step explanation:
Let 1 be the original size of the bread
her bread dough is 11/5 of its original size.
[tex]1* \frac{11}{5} = 2.2[/tex]
The original size of the bread is raised to 2.2
To get percentage we multiply by 100
2.2*100 = 220%
original size of Jay's bread dough is raised to 220%
15PTS!!
What is the best approximation of the solution to the system to the nearest integer values?
(−2, 6)
(7, −2)
(6, −2)
(−2, 7)
Answer:
(-2,6)
Step-by-step explanation:
The solution to a system of equations is where the two graphs intersection. By looking at the graph we can see that they cross at an x coordinate of approximately -2.4 and at a y coordinate of just above 6. We do not have to be too specific since we just have to be to the nearest integer.
(-2,6)
Please help with the figure below
Answer:
<1 =33
<2 = 147
<4 = 147
Step-by-step explanation:
Angle 1 equals angle 3 because they are vertical angles. Vertical angles are opposite angles made by two intersecting lines.
<1 = <3
<1 = 33
Angle 2 and <3 are supplementary angles because they form a straight line. The add to 180 degrees
<2 + <3 = 180
<2 + 33 = 180
Subtract 33 from each side
<2 +33-33 = 180-33
<2 = 147
Angle 2 equals angle 4 because they are vertical angles
<2 = <4
<4 = 147
6x-14=2-10x what is the x
[tex]6x-14=2-10x\qquad\text{add 14 to both sides}\\\\6x=16-10x\qquad\text{add 10x to both sides}\\\\16x=16\qquad\text{divide both sides by 16}\\\\\boxed{x=1}[/tex]
[tex]Check:\\\\6x-14=6(1)-14=6-14=-8\\\\2-10x=2-10(1)=2-10=-8\\\\CORRECT[/tex]
Answer:
x=1
Step-by-step explanation:
6x-14=2-10x
First step is to add 10x to each side
6x+10x-14=2-10x+10x
16x-14=2
Now add 14 to each side
16x-14+14=2+14
16x=16
Divide each side by 16 to isolate x
16x/16 =16/16
x =1
In ΔABC, m∠A = 40°, m∠B = 60°. Find m∠C. (Hint: Draw the auxiliary line BD parallel to the line segment AC and take a look at the same side and the alternate interior angles)
Answer:
The measure of angle C is 80 degree.
Step-by-step explanation:
Given information: In ΔABC, ∠A = 40° and ∠B = 60°.
Draw the auxiliary line BD parallel to the line segment AC.
If a transversal line intersects the pair of parallel line, then the alternate interior angles are same.
The angle 1 and 2 are alternate interior angles of angle A and B respectively. Therefore angle 1 is equal to angle A and angle 2 is equal to angle C.
Angle 1,2 and B are supplementary angles because they lie on a straight line, therefore their sum is 180 degree.
[tex]\angle 1+\angle B+\angle 3=180^{\circ}[/tex]
[tex]\angle A+\angle B+\angle =180^{\circ}[/tex]
[tex]40^{\circ}+60^{\circ}+\angle C=180^{\circ}[/tex]
[tex]\angle C=180^{\circ}-100^{\circ}[/tex]
[tex]\angle C=80^{\circ}[/tex]
The angle sum property is another way to solve this problem.
According to the angle sum property, the sum of interior angles of a triangle is 180 degree.
Therefore the measure of angle C is 80 degree.
If the odds against an event are 2:7 ,then the pobability that the event will fail to occur is__?
Answer:
The probability will be 2/7.
Hope this helps :D
The probability that the event will fail to occur is 7:9 .
How to calculate the probability that event will fail to occur having given odds against -Given that the odds against an event is 2:7 or 2/7.
The meaning of odds against an event is the ratio of the number of times the respective event does not happen compared to the number of times the event occur .
So for the given problem, it refers that for every 2 occurrences that the event does not occur there will be 7 occurrences that it will happen.
Thus the total number of occurrences of the event is (2 + 7) = 9
This means that the event will occur definitely 2 times in every 9 times total outcome.
The probability that the event will occur is 2/9 or 2:9 .
Therefore the probability that the event will fail to occur is 1 - 2/9 = 7/9 or 7:9 .
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Josh has five-eighths of a foot of plywood. To finish building the deck, he needs five times that amount. How many feet of plywood does Josh need?
A. 3 feet
B. 3 one-half feet
C. 3 one-eighth feet
D. 3 two-ninths feet
Josh needs 3 and one-eighth feet of plywood to finish building his deck. This conclusion is derived from multiplying the amount of plywood he currently has (5/8 feet) by 5.
Explanation:The problem stated tells us that Josh has five-eighths of a foot of plywood and he needs five times that amount to finish building the deck. We can solve this problem by performing a simple multiplication operation. The method to solve it would be: 5/8 (amount of plywood Josh has) * 5 (amount of plywood required) = 25/8 = 3 1/8 feet. Therefore, Josh needs 3 and one-eighth feet of plywood to finish building his deck.
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Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule A(n)=-3+(n-1)(-2.2)
[tex]A(n)=-3+(n-1)(-2.2)=-3+(n)(-2.2)+(-1)(-2.2)\\\\A(n)=-3-2.2n+2.2=-0.8-2.2n\\\\\text{Substitute n = 1, n = 4, n = 10}:\\\\A(1)=-0.8-2.2(1)=-0.8-2.2=-3\\\\A(4)=-0.8-2.2(4)=-0.8-2.2(4)=-0.8-8.8=-9.6\\\\A(10)=-0.8-2.2(10)=-0.8-22=-22.8[/tex]
In college math class of 50 student are 23 are boys 27 are girls on the final exam 15 boys and 14 girls made an A. What is the probability of choosing a boy or an girl A student is choosen at random from the class
Answer:
The probability of choosing an A student is 58% (0.58 or 29/50)
Step-by-step explanation:
The fact that 23 students are boys and 27 are girls is irrelevant to the question so we can ignore that.
There are 50 students in all and out of these students 15 boys and 14 girls made an A.
We can first add 15+14 which equals 29. So 29 students out of 50 made in A on the exam.
29/50 equals 0.58 or 58%.
Really need help please Quadratic Equation?
A model rocket is launched with an initial upward velocity of 30 m/s. The rockets height h ( in meters) after t seconds is givenby the following.
h=30t-5t^2
Find all values of t for which the rockets height is 10 meters.
Round your answers to the nearest hundredth
Answer:
t = 0.35, t = 5.65
Step-by-step explanation:
You are given h = 30t - 5t^2. Put this in standard form order (ax^2 + bx + c) by switching the two terms.
h = -5t^2 + 30t
Now you want to find all the values of t for which the rocket's height is 10 meters, so your equation will be equal to 10 instead of h, because 10 is the height you are solving for.
10 = -5t^2 + 30t
Make the entire equation equal to 0 by subtracting 10 from both sides.
0 = -5t^2 + 30t - 10
To solve this quadratic equation, the easiest way would be to use the quadratic formula: [tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Identify your a, b, and c values in the standard form equation (a = -5, b = 30, c = -10) and substitute these values into the quadratic formula.[tex]\frac{-(30)\pm\sqrt{(30)^2-4(-5)(-10)} }{2(-5)} \rightarrow \frac{-30\pm\sqrt{900-200=700} }{-10} \rightarrow \frac{-30\pm\sqrt{700} }{-10}[/tex]
We have (-30 ± sqrt 700)/-10.
Use a calculator to input the two solutions and solve for them; (-30 + sqrt 700)/-10 and (-30 - sqrt 700)/-10.
[tex]\frac{-30+\sqrt{700} }{-10} = 0.35[/tex]
[tex]\frac{-30- \sqrt{700} }{-10} =5.65[/tex]
The quadratic formula is used to solve the equation h = 30t - 5t^2 when h is set to 10 meters, yielding two times at which the rocket's height is 10 meters: approximately 0.59 seconds and 3.41 seconds.
10 = 30t - 5t2
Moving all terms to one side we get:
5t2 - 30t + 10 = 0
To simplify, we divide the entire equation by 5:
t2 - 6t + 2 = 0
Now we can apply the quadratic formula:
t = √ (62 - 4*1*2) )/ (2*1)
Calculating under the square root, we get:
t = (6 √ (36 - 8) )/ 2
t = (6 ± √28) / 2
Thus, the two solutions for t are:
t = (6 + √28) / 2 and t = (6 - √28) / 2
Rounded to the nearest hundredth, the values of t are approximately 0.59 s and 3.41 s. The rocket reaches a height of 10 meters at these two instances during its flight - once when ascending and once when descending.
cindy can bake 36 cupcakes in 1 hour. she needs a total of 144 cupcakes. she has already made 18 cupcakes. how many hours will it take cindy to bake the rest? write and solve the equation.
Answer:
The answer would be 4 more hours.
Step-by-step explanation:
Since she can make 36 cupcakes in 1 hour,
144 divided by 36 is 4, so it would take four more hours to make the rest.
Hope I helped! God bless you :-)
5x-6=19 what is the variable
Answer:
x=5
Step-by-step explanation:
5x-6=19
first you add 6 to both sides now you have 5x=25 then you divide by 5 on both sides then you get x=5
Question
5x-6=19 what is the variable
Answer:
5Step-by-step explanation:
5x - 6 = 19
5x = 19 + 6
5x = 25
x = 25 : 5
x = 5