Using Cramer's Rule, the value of x in the given system of linear equations is 1.
Explanation:We can solve the given system of equations using Cramer's Rule. Cramer's Rule states that in a system of linear equations, if the determinant of the coefficient matrix is non-zero, then the system has a unique solution.
First, let's find the determinant of the coefficient matrix:
| 1 3 |
| 3 1 |
Det = (1*1) - (3*3) = -8
Since the determinant is non-zero (-8 ≠ 0), the system has a unique solution.
Next, let's find the determinant of the x-column matrix:
| 16 3 |
| 8 1 |
Det(x) = (16*1) - (3*8) = -8
Finally, we can find the value of x by dividing the determinant of the x-column matrix by the determinant of the coefficient matrix: x = Det(x) / Det = (-8) / (-8) = 1.
the prime factorization of a certain number is 2 to the 3rd power times 3 times 5 to the second power what is the number and how did you get it
The number that corresponds to the prime factorization '2 to the 3rd power times 3 times 5 to the 2nd power' is 600. Calculate this by resolving each component then multiply the results.
Explanation:The question revolves around finding the result of a number given its prime factorization, specifically when the prime factorization is '2 to the 3rd power times 3 times 5 to the 2nd power'. Let's start by resolving each of those components:
2 to the 3rd power, also known as cubing, would give us 8 because we multiply 2 three times (2*2*2).3 remains as it is because it is a prime number and is not raised to any power.5 to the 2nd power, also known as squaring, would give us 25 because we multiply 5 by itself (5*5).So, with these resolved components, we only have to multiply the results, which is 8 (from 2 cubed) times 3 times 25 (from 5 squared).
This would give us the answer: 8 * 3 * 25 = 600.
Therefore, the number that corresponds to the prime factorization '2 to the 3rd power times 3 times 5 to the 2nd power' is 600.
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Jose can spend no more than 24$ to buy oranges and apples. He will pay 3$ per pound for oranges and $4 per pound for apples. Draw a graph that represents the number of pounds of oranges as the number of pounds of apples Jose can buy.
Hint First, write an inequality. Then, find the x and y intercepts to draw your line. Consider whether you need a solid or dotted line. Do not forget to shade.
Let x = price of a standard ticket, y = price of a matinee ticket, and z = price of a senior ticket. 150x + 80y + 12z = 2,466 380x + 95y + 48z = 5,419 210x + 130y + 60z = 3,960 220x + 225y = 4,445 540x + 270y = 8,370 → y = −2x + 31 x = 11 Finish solving the system using. What are y and z?
Answer: y = 9, z = 8
Step-by-step explanation:
Here, the given equations are,
150x + 80y + 12z = 2,466 ---------(1)
380x + 95y + 48z = 5,419 ---------(2)
210x + 130y + 60z = 3,960 --------(3)
4 × equation (1) - Equation (2),
220x + 225y = 4,445 ------------(4)
5 × equation (1) - equation (3),
540x + 270y = 8,370
⇒ 270 y = 8370 - 540 x
⇒ y = 31 - 2 x
Substituting the value in equation (4),
220 x + 225 ( 31 - 2 x ) = 4445
220 x + 6975 - 450 x = 4445
- 230 x = - 2530
x = 11
By putting this value in equation (5),
we get, y = 31 - 22
y = 9
By putting the value of x and y in equation (1),
1650 + 720 + 12 z = 2466
2370 + 12 z = 2466
12 z = 96
z = 8
Answer:
Y=9
Z=8
For the next one, the solution can be expressed as 11,9, and 8
Step-by-step explanation:
Just did it on edg!
20 is 25% of what number
20 is 25% of 80. so the number is 80.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
We need to find 20 is 25% of what number
Let x be the number which we have to find.
Convert 25% to decimal number.
25/100=0.25
Now multiply 0.25 with x which results 20
0.25x=20
Divide both sides by 0.25
x=20/0.25
x=80
Hence, 20 is 25% of 80. So 80 is the required number.
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what is the vertex of -3x^2 - x + 12
ABCD is a rhombus. If m<1=122, then what is the measure of <2 and <3
Tomas bought 3 software apps and 2 e-books for a total of $21. The two e-books cost $12. If s represents the cost of each app, the total cost of all 5 items is represented by mc021-1.jpg. Which statement about verifying the solution for s is true?
Answer:
s=3
Step-by-step explanation:
A geometric sequence is defined recursively by an = 4an-1 . The first term of the sequence is 0.5. Which of the following is the explicit formula for the nth term of the sequence?
A. 0.5 4n-1
B. 0.5 4n
C. 4 0.5n
D. 4 0.5n-1
E. 0.5 4n+1
please help with question 3!!! And A 2 please!!!
The decimal .087 can be written as A) 8.7 10 B) 87 10,000 C) 87 1,000 D) 87 100
Answer:
it's c
Step-by-step explanation:
because for .087 you move the decimal 3 times
so the decimal is going to end up 08.7
here
We can write 0.87 as 87 / 100.
Option D is the correct answer
Given,
0.087
We have to see the other form it can be written.
What are decimal numbers?The numbers which have a decimal point.
Example: 23.4
It can be written in fractions aswell.
23.4 = 234/10
We have,
0.87
Since there are two numbers after the decimal point we can write it as:
= 0.87
= 087 / 100
= 87 / 100
Thus we can write 0.87 as 87 / 100.
Option D is the correct answer.
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3/4x= -12 What does "x" equal?
Travis had a box of 68 french fries. He gave 13 french fries to each of f friends. Which expression shows how many french fries he had left after giving some to his friends? A. 68 - f × 13 B. (68 + f) × 13 C. 68 + f × 13 D. (68 - f) × 13
Find the vertex of the graphed function. f(x) = |x − 4| + 3 vertex of function The vertex is at ( , ).
Answer: For the second part it is B on edgu
Step-by-step explanation:
The solution is P ( 4 , 3 )
The vertex of the function is given by the coordinates P ( 4 , 3 )
What is a Parabola?
A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k – p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
Let the equation be represented as A
Now , the parabola is
f ( x ) = | x − 4 | + 3 be equation (1)
Now ,
The vertex of f ( x ) = | x | is located at the origin, (0,0)
So , in the form f ( x ) = a | x - h | + k, the h-value translates the graph left/right and the k-value translates the graph up/down
And ,
In the function, f(x) = | x - 4 ) | + 3 , the h-value is 4, and the k-value is 3
So , the vertex of the function moves from the origin, (0,0) and translates 4 units right and 3 units up.
Therefore , the vertex is located at P ( 4,3 )
Hence , the vertex of equation is at P ( 4 , 3 )
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Lionel is buying a computer that notmally sells for $890. The state sales tax rate is 6%. What isvthe total cost ofvthe computer including sales tax?
A video rental store charges $4 to rent a movie and $3 to rent a video game. During one summer, Tony paid a total of $140 to rent movies and video games from this store. If he rented 7 more video games than movies, how much did he spend on movie rentals during the summer?
the answer is 68
if you like at the other persons answer, they explain
but all i know is that its 68
thxs: to the person that answered this question first
The sides of a triangle are 7, 4, n. If n is an integer, state the largest and smallest possible values of n.
Solve the quadratic equation. (x - 4)2 = 36
The solutions to the quadratic equation (x - 4)² = 36 are
x = 10 and x = -2.
We have,
To solve the quadratic equation (x - 4)² = 36, we can start by taking the square root of both sides of the equation.
However, we need to consider both the positive and negative square roots because squaring a number eliminates the sign.
Taking the square root of both sides, we have:
√[(x - 4)²] = √36
Simplifying further:
|x - 4| = 6
Now, we can set up two separate equations to consider both the positive and negative square roots:
x - 4 = 6 or x - 4 = -6
Solving the first equation:
x - 4 = 6
Adding 4 to both sides:
x = 10
Solving the second equation:
x - 4 = -6
Adding 4 to both sides:
x = -2
Therefore,
The solutions to the quadratic equation (x - 4)² = 36 are
x = 10 and x = -2.
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7^18/7^5 simplifies to 7^p is the value of p 3?
If 30 cents out of every 1 dollar goes to taxes and the rest is net income, what's the ratio of taxes to net income? A. 3 : 10 B. 30 : 1 C. 3 : 7 D. 30 : 7
If 30 cents out of every 1 dollar go to taxes, the remaining 70 cents is the net income. Therefore, the ratio of taxes to net income is 3:7.
Explanation:The question asks for the ratio of taxes to net income if 30 cents out of every 1 dollar go to taxes. This question is asking for a mathematical comparison between the amount of money that goes to taxes and the remaining amount of money, which is the net income.
If 30 cents go to taxes out of 1 dollar, that means 70 cents (or $0.70) is the net income because 1 dollar minus 30 cents equals 70 cents. To arrive at the ratio, we compare the amount that goes into taxes to the net income. This would be 0.30 (taxes) to 0.70 (net income).
When we express this as a ratio in simplest form, we do not usually use decimals. Instead, we can convert the decimal into a whole number. Think of the 0.30 and the 0.70 as 30 and 70. The greatest common divisor of 30 and 70 is 10. If we divide both numbers by 10, we get 3 and 7. So, the ratio of taxes to net income is 3:7. Thus, the correct option is C. 3 : 7.
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In the figure. d=4 yd, h=6 yd, and H=8 yd. What is the approximate volume of the figure? Use 3.14 to approximate
Answer: 84yd
Step-by-step explanation:
Vcylinder=πr2h
=π(2)2(6)
=24π
≈24(3.14)
≈75.36 yd
_____________________
The height of the cone is the height of the figure minus the height of the cylinder:
8 yd−6 yd=2 yd
Vcone=13πr2h
=13π(2)22
=223π
≈223(3.14)
≈8.37 yd3
Add the volumes.
75.36 yd3+8.37 yd3=83.73 yd3
To the nearest cubic yard, the volume is 84 yd3.
Evaluate the indefinite integral: 1/( t^2 − 6t + 45) dt
a human usually has 20 baby teeth, which are replaced by 32 adult teeth. Raul lost 8 of his baby teeth . Raul said he lost 4/10 of his baby teeth. Ana said Rual lost 2/5 of his teeth. which of these conjectures are true? Construct an argument to justify your your answer
Final answer:
Ana's conjecture that Raul lost 2/5 of his teeth is correct, as it simplifies from Raul's stated 4/10 after losing 8 out of the total 20 baby teeth.
Explanation:
Raul has said he lost 4/10 of his baby teeth, while Ana said Raul lost 2/5 of his teeth. To figure out which conjecture is true, we must consider Raul's claim first. Since a human usually has 20 baby teeth and Raul has lost 8 of those, we calculate the fraction of teeth he has lost by dividing the number of lost teeth by the total number of baby teeth: 8 ÷ 20 = 2/5. This simplifies to the fraction 2/5, which means Ana's conjecture is indeed the correct one. Both fractions actually represent the same value, because when you simplify 4/10 by dividing the numerator and the denominator by 2, you get 2/5.
A cup of rolled oats (
x
x) provided
310
310 calories. A cup of wheat flakes (
y
y) provided
290
290 calories. A new breakfast cereal combines wheat and oats to provide
302
302 calories per cup. How much of each grain does
1
1 cup of the cereal contain?
Bradley is making fruit salad for each bowl of fruit salad he needs 3/4 cup of grapes how many cups of grapes will he use if he makes 24 bowls of fruit salad
Answer:3/4 i think
Step-by-step explanation:
The fruit salad requires 32 cups of grapes.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Bradley is making fruit salad for each bowl of fruit salad he needs 3/4 cup of grapes.
He makes 24 bowls of fruit salad.
Number of cups of grapes = Total number of bowls ÷ Number of cups of grapes in each bowl
= 24 ÷ 3/4
= 24 × 4/3
= 32
Therefore, the fruit salad requires 32 cups of grapes.
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Please help me out ?
Which linear inequality is represented by the graph?
y < 3x + 2
y > 3x + 2
y < x + 2
y > x + 2
Answer: The graph is represented by the inequality y>3x+2
Step-by-step explanation:
Linear inequality is like linear equation just we have inequality signs (<,>,≤,≥) instead of equal sign(=).
In the given question we have the linear inequality represented by graph
We can see the line in the graph passing through the point (-3,-7)
Let's check which option satisfy the point
1) y<3x+2 for this the line should be y=3x+2
⇒ -7=3(-3)+2
⇒-7= -9+2⇒-7=-7,which is true.
2) y>3x+2 which similar as first.
3) y<x+2 for this the line should be y=x+2
⇒ -7= -3+2
⇒-7=-1 which is not true.
4) y > x + 2 is similar to third.
Option 3) and 4) cannot be the required linear inequality.
Now from 1) and 2) , 2) should be the required linear inequality as the graph is shaded above the line and that must be for y (>) greater than inequality. [ for y (<) less than inequality the graph must be shaded below the line]
Therefore, 2) y > 3x + 2 is the required linear inequality which is represented by the graph.
The linear equality represented by the graph is [tex]\boxed{{\mathbf{y>3x+2}}}[/tex] and it matches with [tex]\boxed{{\mathbf{OPTION B}}}[/tex] .
Further explanation:
It is given that a line passes through points [tex]\left({0,2}\right)[/tex] and [tex]\left({-3,-7}\right)[/tex] as shown below in Figure 1.
The slope of a line passes through points [tex]\left({{x_1},{y_1}}\right)[/tex] and [tex]\left( {{x_2},{y_2}}\right)[/tex]is calculated as follows:
[tex]m=\frac{{{y_2}-{y_1}}}{{{x_2}-{x_1}}}[/tex] ........(1)
Here, the slope of a line is denoted as [tex]m[/tex] and points are [tex]\left({{x_1},{y_1}}\right)[/tex] and [tex]\left({{x_2},{y_2}}\right)[/tex].
Substitute [tex]0[/tex] for [tex]{x_1}[/tex] , [tex]2[/tex] for [tex]{y_1}[/tex] , [tex]-3[/tex] for [tex]{x_2}[/tex] and [tex]-7[/tex] for [tex]{y_2}[/tex] in equation (1) to obtain the slope of a line that passes through points [tex]\left({0,2}\right)[/tex] and [tex]\left({-3,-7}\right)[/tex] .
[tex]\begin{aligned}m&=\frac{{-7-2}}{{-3-0}}\\&=\frac{{-9}}{{-3}}\\&=3\\\end{aligned}[/tex]
Therefore, the slope is [tex]3[/tex] .
The point-slope form of the equation of a line with slope [tex]m[/tex] passes through point [tex]\left({{x_1},{y_1}}\right)[/tex] is represented as follows:
[tex]y-{y_1}=m\left({x-{x_1}}\right)[/tex] .......(2)
Substitute [tex]0[/tex] for [tex]{x_1}[/tex] , [tex]2[/tex] for [tex]{y_1}[/tex] and [tex]3[/tex] for [tex]m[/tex] in equation (2) to obtain the equation of line.
[tex]\begin{aligned}y-2&=3\left({x-0}\right)\\y-2&=3x\\y&=3x+2\\\end{aligned}[/tex]
Therefore, the value of [tex]y[/tex] is [tex]3x+2[/tex] .
Since the shaded part in Figure 1 is above the equation of line [tex]y=3x+2[/tex], therefore, greater than sign is used instead of is equal to.
Thus, the linear inequality is [tex]y>3x+2[/tex] as shown below in Figure 2.
Now, the four options are given below.
[tex]\begin{aligned}{\text{OPTION A}}\to &y<3x+2\hfill\\{\text{OPTION B}}\to &y>3x+2\hfill\\{\text{OPTION C}}\to &y<x+2\hfill\\{\text{OPTION D}}\to &y>x+2\hfill\\\end{aligned}[/tex]
Since OPTION B matches the obtained equation that is [tex]y>3x+2[/tex] .
Thus, the linear equality represented by the graph is [tex]\boxed{{\mathbf{y>3x+2}}}[/tex] and it matches with [tex]\boxed{{\mathbf{OPTION B}}}[/tex].
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Answer Details:
Grade: Junior High School
Subject: Mathematics
Chapter: Coordinate Geometry
Keywords: Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics, inequality
catrina used 25 square green tiles to form a square in the middle of her floor.How many rows did she make?How many tiles did she put in each row?
Final answer:
Catrina used 25 tiles to create a square, which means she made 5 rows with 5 tiles in each row, as the square root of 25 is 5.
Explanation:
Catrina used 25 square green tiles to form a square in the middle of her floor.
To find out how many rows she made and how many tiles she put in each row, we need to think about the properties of a square.
A square has equal sides, so the number of tiles in each row must be the same as the number of rows. Since the total number of tiles is a perfect square (25), we find the square root of 25 to determine the size of each side of the square.
The square root of 25 is 5, so Catrina created 5 rows with 5 tiles in each row. This forms a perfectly square area on her floor with green tiles.
Noah makes ceramic pots for the market. On the weekends he makes 11 more pots than he does during the week. Noah represented the number of pots he makes on weekends using the expression p + 11. Which expression represents the total mumber of pots Noah made one weekend if he made 14 more than his usual number?
Rita makes and sells necklaces. The materials to make each necklace cost $2.75. Last week she made 8 necklaces and wants to make a total profit of $78. Using the equation 8(x+2.75)=78, Rita determined that she needs to sell each necklace for $7 to make a total profit of $78. Which error did Rita make?
Answer:
Rita made a sign error.
Step-by-step explanation:
Let x be the selling price of each necklace.
We are told that the materials to make each necklace cost $2.75.
Since profit is the difference between selling price and cost.
[tex]\text{Profit}=\text{Selling price- Cost}[/tex]
So profit of Rita from selling one necklace will be:
[tex]\text{Profit of Rita from 1 necklace}=x-2.75[/tex]
To find the profit of Rita from selling 8 necklace we will multiply 8 by profit of 1 necklace.
[tex]\text{Profit of Rita from 8 necklaces}=8(x-2.75)[/tex]
As Rita wants to make a total profit of $78 from selling 8 necklaces, so we will substitute 78 as profit of 8 necklaces.
[tex]78=8(x-2.75)[/tex]
Upon comparing our equation with the given equation we can see that Rita made a sign error as she added the cost with the selling price instead of subtracting the cost from selling price.
Let us find the selling price.
[tex]78=8x-22[/tex]
[tex]78+22=8x[/tex]
[tex]100=8x[/tex]
[tex]\frac{100}{8}=x[/tex]
[tex]12.5=x[/tex]
We can see that the selling price of each necklace will be 12.5, therefore, Rita made a sign error.
Given this arithmetic sequence, find d 4,_,_,_,_,179