Using the matrix equation, the value of x and y are 5 and 2 respectively.
Consider the 2 by 2 matrix equations,
1/2 [ 4 8 ( x + 3 ) - 4 ] - 3[ 1 y+1 -1 - 2 ] = [ - 1 -5 7 4 ]
[ 2 4 (x+3)/2 -2] + [ - 3 -3y -3 +3 + 6] = [ - 1 - 5 7 4]
[ -1 -3y + 1 (x + 9)/2 + 4] = [ - 1 - 5 7 4]
Therefore,
- 3y + 1 = - 5
Subtracting 1 from each side of the equation,
- 3y + 1 - 1 = - 5 - 1
- 3y = - 6
Dividing each side of the equation by - 3,
y = 2
And;
( x + 9 )/2 = 7
Multiplying each side by 2,
x + 9 = 14
Subtracting 9 from each side of the equation,
x + 9 - 9 = 14 - 9
x = 5
Therefore, the value of x and y is 5 and 2 respectively.
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Factor 12x² + 19x - 21.O (6x + 7)(2x − 3)—O (4x - 3)(3x + 7)O(6x-7)(2x + 3)(4x + 3)(3x7)
given the expression
[tex]12x^2+19x-21[/tex]we are loking 2 numbers whose multiplication is equal to 12
and other 2 number whose multiplication is equal to 21
the sum of the cross multiplication is equal of 19, as follows
[tex](4x*3x)+((4x*7)+(3x*-3))+(-3*7)[/tex]factor is
[tex]\left(4x-3\right)\left(3x+7\right)[/tex]correct answer option B
5000 + 300 + 8 in standard form
The given arithmetic expression is:
5000 + 300 + 8
This sum can be computed as shown below:
Therefore, 5000 + 300 + 8 = 5308
Convert 5308 to standard form
[tex]5308\text{ = 5.308 }\times10^3[/tex]
What’s eight less than four times a number in algebraic expression
Answer:
4x - 8, 4x just means four of x, and eight less means to subtract 8.
Step-by-step explanation:
Answer:
The answer is 4x - 8 and it equals -32
A pancake recipe asked for one and 2/3 times as much milk as flower if two and one half cups of milk is used what quantity of flower would be needed according to the recipe?
Let x be the quantity of flour used
Let y be the quantity of milk used
A pancake recipe asked for one and 2/3 times as much milk as flour:
[tex]y=1\frac{2}{3}x[/tex]If two and one half cups of milk is used what quantity of flower would be needed according to the recipe?
Find x when y=2 1/2:
[tex]2\frac{1}{2}=1\frac{2}{3}x[/tex]Write the quantities as fractions;
[tex]\begin{gathered} 2+\frac{1}{2}=(1+\frac{2}{3})x \\ \\ \frac{4}{2}+\frac{1}{2}=(\frac{3}{3}+\frac{2}{3})x \\ \\ \frac{5}{2}=\frac{5}{3}x \end{gathered}[/tex]Solve x:
[tex]x=\frac{\frac{5}{2}}{\frac{5}{3}}=\frac{15}{10}[/tex]Write the answer as a mixed number:
[tex]\frac{15}{10}=\frac{10}{10}+\frac{5}{10}=1+\frac{5}{10}=1+\frac{1}{2}=1\frac{1}{2}[/tex]Then, for 2 1/2 cups of milk would be needed 1 1/2 cups of flourAnswer: 1 1/2A If y = x + 2 and y = -2x + 8, what do you know about x + 2 and -2x + 8?
If y = x + 2 and y = -2x + 8, what do you know about x + 2 and -2x + 8?
we have
y=x+2
y=-2x+8
Solve the system of equations
equate both equations
x+2=-2x+8
x+2x=8-2
3x=6
x=2
Find the value of y
y=(2)+2
y=4
the solution is (2,4)
that means
(2,4) is a common point , that satisfy both equations
Tyrone's car can travel about 30 miles for each gallon
of gas.
Using d for distance traveled in miles and g for
gallons of gas, write two different equations relating d
and g.
The equation can be written as d=30g
What is an equation?
An equation can be compared to a scale on which objects are weighed. When the two pans are filled with the same amount of anything (like grain), the scale will balance and the weights will be considered equal. To maintain the scale in balance, if any grain is taken out of one of the balance's pans, an equal amount must be taken out of the other pan. More broadly, if the identical operation is carried out on both sides of an equation, the equation remains in balance. Equations are used to describe geometric shapes in Cartesian geometry. The goal has changed since the equations under consideration, such as implicit equations or parametric equations, contain an unlimited number of solutions.
Tyrone's car can travel about 30 miles for each gallon
So, the equation can be written as d=30g, where d is distance travelled and g is gallons of gas used.
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Please help with #4. The directions are with the pic below.
sphere: 12 pounds
cylinder: 108 pounds
Explanation:
Data:
. From balance A:
3 cubes + 1 sphere = 1 cylinder + 2 spheres
. From balance B:
3 cubes = 5 spheres
Since 1 cube = 20 pounds
=> From balance B:
3 cubes * 20 pounds = 5 spheres
60 pounds = 5 sphere
60 / 5 = 5 / 5
12 pounds = 1 sphere
=> From balance A:
3 cubes + 1 sphere = 1 cylinder + 2 spheres
3 spheres * 20 pounds + 1 sphere * 12 pounds = 1 cylinder + 2 spheres * 12 pounds
120 pounds + 12 pounds = 1 cylinder + 24 pounds
132 pounds = 1 cylinder + 24 pounds
132 pounds - 24 pounds = 1 cylinder + 24 pounds - 24 pounds
108 pounds = 1 cylinder
Jamal buys a water heater online for $861. If shipping and handling area additional 11% of the price, how many shipping and handling will Jamal pay?
solve the following equation for pp/r+s=q
the initial equation is:
[tex]\frac{p}{r}+s=q[/tex]To solve for p we can rest s in bout sides so:
[tex]\begin{gathered} \frac{p}{r}+s-s=q-s \\ \frac{p}{r}=q-s \end{gathered}[/tex]Now we can multiply by r so:
[tex]\begin{gathered} \frac{p\cdot r}{r}=(q-s)\cdot r \\ p=(q-s)\cdot r \end{gathered}[/tex]the figure below has a point marked with a large. First translate to figure 4 units up then give the coordinates of the mark point in the original figure in the final figure.:
Large point coordinates (original)= (1,-4)
To obtain the coordinates of the new point, add 4 to the y coordinate.
(1,-4+4) = (1,0)
I'm trying to simplify negative 5/8 divided by negative 3/4 how do I do that?
Slope The first two sets of points are 9,-24 and 13,-21
We need to find the slope using the points (9, -24) and (13 , -21)
so, the slope = 3/4
Passing through (- 4,-7) and (1,3) What is the equation of the line in point-slope form
To calculate the equation of the line passing through the points ( -4. -7) and (1, 3):
[tex]\begin{gathered} \text{ Equation of the line can be calculated by the formula } \\ y-y_1=m(x-x_1) \end{gathered}[/tex]where m = slope
(x1, y1) = any of the points given; say points (-4, -7). That is x1= -4, y1 = -7
To calculate the slope, m:
[tex]\begin{gathered} \text{ m = }\frac{y_2-y_{1_{}}}{x_2-x_1}_{} \\ \text{ where }(x_2,y_2)\text{ = (1, 3)} \\ m\text{ = }\frac{3\text{ - (-7)}}{1-(-4)} \\ m=\text{ }\frac{3+7}{1+4}\text{ = }\frac{10}{5} \\ m=2 \end{gathered}[/tex][tex]\begin{gathered} \text{ substituting m = 2, x}_1=-4,y_1=-7\text{ into the formula }y-y_1=m(x-x_1) \\ we\text{ have} \\ y-(-7)=2(x-(-4)\text{ )} \\ y+7=\text{ 2(x+ 4)} \end{gathered}[/tex]The equation of the line in point slope form is y + 7 = 2(x + 4)
What is the reference angle for 289°? A. 71° B. 19° C. 11° D. 89°
Given:
Angle θ=289°.
For angles from 270° to 360°, the reference angle can be calculated by subtracting the given angle from 360° .
The reference angle of θ can be calculated as:
[tex]\begin{gathered} 360\degree-\theta=360\degree-289\degree \\ =71\degree \end{gathered}[/tex]Therefore, reference angle of 289° is 71°.
I need help with part b, c ii, and d
Recall that:
[tex]\text{average speed=}\frac{total\text{ distance}}{total\text{ time}}.[/tex](b) Since Marcos traveled for 2 hours and 17 minutes a distance of 155 miles, then Marco's average speed for the 155 miles trip is:
[tex]\frac{155mi}{(2+\frac{17}{60})h}=\frac{155mi}{\frac{137}{60}h}=\frac{9300}{137}miles\text{ per hour}\approx67.89miles\text{ per hour.}[/tex](c ii) Since Devon also traveled the 155 miles in 2hours and 17 minutes but at a constant speed, then the constant speed at which he traveled is equal to his average speed, which is equal to:
[tex]\frac{155mi}{(2+\frac{17}{60})h}=\frac{155mi}{\frac{137}{60}h}=\frac{9300}{137}miles\text{ per hour}\approx67.89miles\text{ per hour.}[/tex](d) Marco needs to drive 2 miles in 5 minutes to be able to complete the 155 miles trip in 2 hours and 17 minutes, then he must drive at a constant speed of:
[tex]\frac{2mi}{5\min }=\frac{2mi}{\frac{5}{60}h}=\frac{120mi}{5h}=24\text{miles per hour.}[/tex]Answer:
(b) 67.89 miles per hour.
(c ii) 67.89 miles per hour.
(d) 24 miles per hour.
A focus group of 12 people is to be chosen randomly from among 24 right-handed people and 5 left-handed people. In order to find the probability that 3 of the people chosen are right-handed, you should use
Let 1 and 2 mean that a person is right-handed or left-handed, respectively.
Consider the probability space as the different groups of 12 people that can be formed with the 29 total people. {(1,1,1,1,1,...1),(2,1,1,1,1,...,1),...}
We need to use the binomial distribution in order to find the answer.
Consider X to be the number of right-handed people in the group.
The probability of X=3 is then:
[tex]Pr(X=3)=\text{ binomial coefficien(}12,3\text{)}(\frac{24}{29})^3(1-\frac{24}{29})^{12-3}[/tex]We used the formula
[tex]\begin{gathered} Pr(X=k)=\text{ binomial coefficient(n,k)}\cdot p^k(1-p)^{n-k} \\ \text{where } \\ k=3 \\ n=12 \\ p=\frac{24}{29} \end{gathered}[/tex]Finally, we need to simplify the expression, as shown below
[tex]\Rightarrow P(X=3)=220(\frac{24}{29})^3(\frac{5}{29})^9=0.0000167[/tex]This is the answer one obtains using the binomial distribution; nevertheless, the actual probability is equal to zero because it is not possible to form a group of 12 people that only contains 3 right-handed people as there are only 5 left-handed people (3+5=8).
Consider the triangles ADB and EDC. Explain how they are similar.
Example: Triangles like ABC and EDC are similar by SAS similarity, because angle C is congruent in each triangle, and AC/EC = BC/DC = 2. By the definition of similarity, it follows that AB/DE = BC/EF = AC/DF = 2.
5. Infer from the problem: What is the y-intercept of the line y=3x-5 ?
the given expression is
y = 3x - 5
y +5 = 3x
y - (-5) = 3(x - 0)
so the y-intercept is -5.
Write an equation for the inverse variation represented by the table.x -3, -1, 1/2, 2/3y 4, 12, -24, -18
By definition, Inverse variation equations have the following form:
[tex]y=\frac{k}{x}[/tex]Where "k" is the Constant of variation.
Given the values shown in the table, you can find the value of "k":
- Choose a point from the table. This could be:
[tex](-3,4)[/tex]Notice that:
[tex]\begin{gathered} x=-3 \\ y=4 \end{gathered}[/tex]- Substitute these values into the equation and solve for "k":
[tex]\begin{gathered} 4=\frac{k}{-3} \\ \\ (4)(-3)=k \\ k=-12 \end{gathered}[/tex]Knowing the Constant of variation, you can write the following equation:
[tex]y=\frac{-12}{x}[/tex]The answer is:
[tex]y=\frac{-12}{x}[/tex]Please help me come you just tell me the answer I don’t really need you to explain
Given:
[tex]\begin{gathered} \angle JKL=65 \\ \angle KJL=50 \end{gathered}[/tex]Sum of the angle of any triangle is 180
So:
[tex]\begin{gathered} \angle JKL+\angle KJL+\angle KLJ=180 \\ 65+50+\angle KLJ=180 \\ \angle KLJ=180-(65+50) \\ \angle KLJ=180-115 \\ \angle KLJ=65 \end{gathered}[/tex]Then two sides are also equal.
[tex]\begin{gathered} 3x-2=x+10 \\ 3x-x=10+2 \\ 2x=12 \\ x=\frac{12}{2} \\ x=6 \end{gathered}[/tex]So the value of x is 6.
x+y+z=12x+4y+2z = -6-x+9y-3z=-49 Can someone please help me solve this system of equation?
Let's begin by listing out the information given to us:
[tex]\begin{gathered} x+y+z=1 \\ 2x+4y+2z=-6 \\ -x+9y-3z=-49 \end{gathered}[/tex]To solve this 3 variable equation, let's eliminate one of the variables
add equation 1 & 3, we have:
[tex]\begin{gathered} x-x+y+9y+z-3z=1-49 \\ 10y-2z=-48 \\ Make\text{ z the }subject,we\text{ have:} \\ -2z=-10y-48 \\ divide\text{ through by -2} \\ z=5y+24 \end{gathered}[/tex]Substitute z into equation 1, 2 & 3
[tex]\begin{gathered} x+y+5y+24=1 \\ x+6y=1-24 \\ x+6y=-23 \end{gathered}[/tex][tex]\begin{gathered} 2x+4y+2\left(5y+24\right)=-6 \\ 2x+4y+10y+48=-6 \\ 2x+14y=-6-48 \\ 2x+14y=-54 \end{gathered}[/tex][tex]\begin{gathered} -x+9y-3\left(5y+24\right)=-49 \\ -x+9y-15y-72=-49 \\ -x-6y=-49+72 \\ -x-6y=23 \end{gathered}[/tex]Solve as a simultaneous equation, we have:
[tex]\begin{gathered} x+6y=-23 \\ 2x+14y=-54 \\ \text{Multiply the top equation by 2 \& subtract it from the bottom equation} \\ 2\cdot(x+6y=-23)\Rightarrow2x+12y=-46 \\ 2x+14y=-54-(2x+12y=-46) \\ 2x-2x+14y-12y=-54-(-46) \\ 2y=-8 \\ y=-4 \end{gathered}[/tex]Substitute y = -4 into x + 6y = -23, we have:
[tex]\begin{gathered} x+6\left(-4\right)=-23 \\ x-24=-23 \\ x=-23+24 \\ x=1 \end{gathered}[/tex]Substitute y = -4 into z = 5y + 24, we have:
[tex]\begin{gathered} z=5\left(-4\right)+24 \\ z=-20+24 \\ z=4 \end{gathered}[/tex]identify the rate, base and portion.What percent of 126 is 44.1
In this problem, we have that
Base=126 (represents the 100%)
Portion=44.1
Find out the percentage
100/126=x/44.1
solve for x
x=(100/126)*44.1
x=35%
The percentage is 35%
Determine whether point (4, -3) lies on the line with equation y = -2x + 5 by using substitution and by graphing.
The equation of the line is:
[tex]y=-2x+5[/tex]And we need to find if the point (4,-3) lies on the line.
To solve by using substitution, we need to remember that an ordered pair always has the form (x, y) --> the first number is the x-value, and the second number is the y-value.
In this case (4,-3):
x=4
and
y=-3
So now, we substitute the x value into the equation, and if the y-value we get in return is -3 --> the point lies on the line. If not, the point does not lie on the line.
[tex]\begin{gathered} y=-2x+5 \\ \text{Substituting x=4} \\ y=-2(4)+5 \\ y=-8+5 \\ y=-3 \end{gathered}[/tex]We do get -3 as the y-value which matches with the indicated y value of the point.
Thus, by substitution, we confirm that the point lies on the line.
To check the result by graphing, we need to graph the line. The graph of the line is shown in the following image:
In the image, we can see that the marked point on the line is the point we were looking for (4,-3). So we confirm by the graphing method that the point lies on the line.
Answer: It is confirmed by substitution and graphing that the point (4,-3) lies on the line.
The Ferris wheelThe community loves the Ferris Wheel because when they are at the top of the wheel they can look for their house and it has long been a family favorite. The company sent you a Ferris wheel that has a radius of 40 ft. and each car is 5 ft. tall. The people can’t start to look for their houses until they get above the tents of the carnival and those tents are 20ft tall. The Ferris wheel has 20 passenger cars and it takes 12 minutes to have all the cars filled. Once all cars are filled the Ferris wheel runs at 1 rotation for every 2 minutes for a total of 8 minutes.Once someone has boarded the Ferris wheel, how long will it take for them to be able to start looking for their house?How long will they have to search for their house?
Given:
radius of Ferris wheel = 40 ft
height of a car = 5 ft
height of a tent = 20 ft
no. of passenger cars = 20
time to load all cars = 12 minutes
time for 1 rotation = 2 minutes
time for all rotations = 8 minutes
What we want to know is how many degrees the car will have to travel along the circle before it reaches a height of 20 ft.
We can draw a triangle to represent the unknown and find the angle.
The total height from the ground to the center of the Ferris wheel is 45 ft (5ft car height + 40 ft radius). We deduct the 20ft height of the tent so we get the side of the right triangle we're using to solve for the missing angle. That height is 25 ft.
The radius also serves as the hypotenuse of the triangle.
We can then use the following to solve for the angle theta:
[tex]\begin{gathered} \cos\theta=\frac{adjacent}{hypotenuse} \\ \\ \cos\theta=\frac{25}{40} \\ \\ \cos^{-1}(\cos\theta)=\cos^{-1}(\frac{25}{40}) \\ \\ \theta=51.3\degree \end{gathered}[/tex]Now we know that the car must travel 51.3 degrees along the circle before it gets to a height where it can see above the tents. If one rotation is 360 degrees and it takes 2 minutes to complete one round, then to find the time it will take to travel 51.3 degrees, we use the following equation:
[tex]\begin{gathered} \frac{360\degree}{2minutes}=\frac{51.3\degree}{x\text{ }minutes} \\ \\ x=\frac{51.3(2)}{360} \\ \\ x=0.285\text{ minutes or }17.1\text{ seconds} \end{gathered}[/tex]It will take them 17.1 to be able to start looking for their house.
Now every time the car goes around the path of the Ferris wheel, for 17.1 going up and another 17.1 seconds going down, they will not be able to look for their house.
17.1 seconds x 2 x 4 turns = 136.8 seconds
8 minutes - 136.8 seconds = 480 - 136.8 = 343.2 seconds or 5 minutes and 43.2 seconds
They have 5 minutes and 43.2 seconds to look for their house.
20g of radioactive substance decays by 1/2 of it's original
amount every 30 days. How much is left after 10 days.
The amount of radioactive after 10 days with the same rate of change of decay will be 16.67 g.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
For example the speed 3meter/second.
As per the given,
Radioactive decays by 1/2 of its original in 30 days.
1/2 of original → 30 days.
Divide both sides by 3
1/6 of original → 10 days
Therefore, in 10 days amount of decays will be,
1/6 of 20 ⇒ 20/6 = 3.33
The amount left = 20 - 3.33 = 16.67.
Hence "The amount of radioactive after 10 days with the same rate of change of decay will be 16.67 g".
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Consider the equation cos(2t) = 0.8. Find the smallest positive solution in radians and round your answer to 2 decimal places.
Given:
cos(2t) = 0.8
Take the cos⁻' of both-side of the equation.
cos⁻' cos(2t) = cos⁻'(0.8)
2t = cos⁻'(0.8)
Calculate the value of the right- hand side with your calculator in radians.
2t =0.6435
Divide both-side of the equation by 2
t ≈ 0.32
Simplify the expression -3n-8-7n + 17
We simplify by combining like terms
therefore
[tex]\begin{gathered} -3n-8-7n+17 \\ =-3n-7n-8+17 \\ =-10n+9 \end{gathered}[/tex]an environmental scientists is conducting research on a particular type of air pollutant. She collects air samples over time and determines the average number of micrograms (ug) of the pollutant in a cubic meter (m^3). Her data are shown in the table below.Which Function models the scientists data?A. F(×)=1.12t +50B. F(×)=50 · 1.12tC. F(×)=50 - 6tD. F(×)=50 · 0.88^t
If we graph the points of the table in a coordinate system we'll see that they line up like a line function, so option D is not possible.
If we also add the graphs for the other 3 options, we get:
The points don't line up perfectly but they are much closer to the line in blue than the red or black lines.
Therefore answer is option C f(t) = 50 - 6t
Find the distance between the (3,3) and (10,3) coordinates and write the result in the empty box. plsss helppppppppppp
Answer: 7
Step-by-step explanation:
Distance (d) = √(10 - 3)2 + (3 - 3)2
=√(7)2 + (0)2
=√49
=7
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43524
[tex]\frac{d32423657565\mod{43242}}{dx}_{564564}[/tex]4tet
54
