To solve the system of equations, rewrite them in standard form, eliminate x, solve for y, and substitute the value of y into the equations to solve for x. The solution to the system of equations is x = 4 and y = 2.
Explanation:To solve the system of equations:
Rewrite the equations in the form Ax + By = CMultiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of x in both equations the same.Subtract the resulting equations to eliminate x.Solve for y.Substitute the value of y into either of the original equations to solve for x.The solution to the system of equations is x = 4 and y = 2.
To solve the provided system of linear equations, the elimination method can be used. The solution to the equations 3x - 2y = 14 and 5x + 6y = 42 is x = 6 and y = 2.
Explanation:The student has provided two linear equations which form a system of equations:
3x - 2y = 145x + 6y = 42To solve this system, we can use either the substitution method, the elimination method, or graphical method. In this case, the elimination method may be more straightforward. Here's a step-by-step explanation:
Multiply the first equation by 3 to make the coefficients of y opposites: 9x - 6y = 42.Now, add the new equation from step 1 to the second equation, 5x + 6y = 42.This results in: 14x = 84.Divide both sides by 14 to find x: x = 6.Substitute x back into the first original equation to find y:3(6) - 2y = 14 results in 18 - 2y = 14.Subtract 18 from both sides: -2y = -4.Divide both sides by -2 to get y: y = 2.Therefore, the solution to the system of equations is x = 6, y = 2.
15. TRIANGLES Find the dimensions of a triangle if the base is 2/3 the measure of the height and the area is 12 square centimeters. (Lesson 4-3)
The dimensions of the triangle with a base that is 2/3 of its height and an area of 12 square centimeters are a base of 4 centimeters and the height of 6 centimeters.
Explanation:The question asks for the dimensions of a triangle. We are given that the base is 2/3 of the height and the area is 12 square centimeters. The formula for the area of a triangle is 1/2 * base * height. Since we know that the base is 2/3 of the height, we can denote the height as 'h' and the base as (2/3)h. From here, we can set up the equation 12 = 1/2 * (2/3)h * h, which simplifies to 12 = 1/3 * h². Solving for 'h', we find the height is √36 or 6 centimeters. Given the base is 2/3 of the height, the base, therefore, is 4 centimeters.
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ryan makes 6 backpacks he uses 3/4 of cloth to make each backpack what is the total amount cloth ,in yards ryan use to make all 6 backpacks
Answer:
Ryan use 4. 50 yards of cloth to make 6 backpack.
Step-by-step explanation:
Given : ryan makes 6 backpacks he uses 3/4 of cloth to make each backpack.
To find : what is the total amount cloth ,in yards ryan use to make all 6 backpacks.
Solution : We have given that
Ryan make a backpack to use = [tex]\frac{3}{4}[/tex] of a cloth.
Ryan make such 6 backpack = [tex]6*\frac{3}{4}[/tex]
= [tex]\frac{18}{4}[/tex] .
= 4. 50 yards.
Therefore, Ryan use 4. 50 yards of cloth to make 6 backpack.
Triangle ABC is a right triangle with leg lengths of 5 and 12 inches. Find the length of the hypotenuse. Round answer to the nearest hundredth if necessary.
So here is a theoretical question. Let L1 and L2 be linear transformation from a vector space V into Vector space W. Let {v1,v2,....,vn} be a basis for V. Show that if L1(vi)=L2(vi) for i=1,2,....,n then L1(v)=L2(v) for any v in V. ...?
What happened to the little boy who swallowed a silver dollar?
The manager of a convenience store wishes to determine how many cartons of eggs are damaged in shipment and delivery. For ten shipments of 1000 cartons of eggs, she examines every 50th carton to see how many cartons contain cracked eggs.
How large is the sample?
a.200 cartons
b.the 50th carton
c.1000 cartons
d.cannot determine from this information
Answer:
Option a is correct
200 cartons is the sample size
Step-by-step explanation:
As per the statement:
For ten shipments of 1000 cartons of eggs, she examines every 50th carton to see how many cartons contain cracked eggs.
First examine how many cartons are examined per shipment.
For every 50th cartons, 1 are examined
For every 100th cartons, 2 are examined
then;
For 1000 cartons , we have 20 are examined.
Examined per shipment = 20 cartons
We have to find how large is the sample.
Since, there are total 10 shipment
then;
For 10 shipment, we have
[tex]20 \times 10 = 200[/tex] cartons
Therefore, 200 cartons is the sample size
Please help 3 questions will Upvote
1.Write the equation of a line with a slope of 3 and a y-intercept of 1.
y = x + 3
y = 3x + 1
3x + y = 1
x + 3y = 1
2.Write the equation of the line that passes through (1, 3) and has a slope of 2 in point-slope form.
y – 1 = 2(x – 3)
y – 3 = 2(x – 1)
x – 1 = 2(y – 3)
x – 3 = 2(y – 1)
3.Write the equation of the line that passes through (–2, 6) and (2, 14) in slope-intercept form.
y = 2x – 2
y = 2x + 10
y = 0.5x + 7
y = 0.5x – 4
Fill in the missing number to complete the factorization:
x 3 + x 2 - 21x - 45 = (x + 3)(x - 5)(x +
Missing number to complete the factorization is 3.
What is factorization?Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number. These numbers are broken down into factors or divisors.
Given expression
[tex]x^{3}+x^{2} -21x-45=(x+3) (x-5) (x+a)[/tex]
Let a be the missing number
(x + 3) (x - 5) (x + a)
= [tex](x^{2} -5x+3x-15)(x+a)[/tex]
= [tex](x^{2} -2x-15)(x+a)[/tex]
[tex]x^{3}+x^{2} -21x-45=x^{3} +x^{2} a-2x^{2} -2xa-15x-15a[/tex]
By comparing the expressions
-2xa - 15x = -21x
⇒ -2xa = -6x
⇒ a = 3
[tex]x^{2} (a-2) = 1x^{2}[/tex]
⇒ a - 2 = 1
⇒ a = 3
-15a = -45
⇒ a = 3
Hence, missing number to complete the factorization is 3.
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Which of the following are quadratic functions?
Check all that apply.
a. y=2(x-3x^2+1)
b. y=5+2x
c. y=1/2x^2-13x+4
d. y= x/x-1 Which of the following are quadratic functions?
Check all that apply.
a. y=2(x-3x^2+1)
b. y=5+2x
c. y=1/2x^2-13x+4
d. y= x/x-1
Final answer:
The quadratic functions are: y = 2(x - 3x² + 1), y = 1/2x² - 13x + 4, and y = 1.
Explanation:
A quadratic function is a polynomial function of degree 2, which means its highest power of x is 2. The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.
Out of the given options, the quadratic functions are:
a. y = 2(x - 3x² + 1)
c. y = 1/2x² - 13x + 4
d. y = x/x - 1 (this can be simplified to y = 1)
The options b. (y = 5 + 2x) is not a quadratic function because it only has a linear term (power of x is 1).
Lana cuts 2 pieces for every 5 inches from a dowel for a craft project, for a total of 6 pieces.
what is 999 divided by 3
Determine the x values that cause the function to be (a) Zero, (b) Positive and (c) Negative, then d) sketch a graph of the function.
Which of the following changes gives no evidence that a chemical reaction has taken place?
A cube of solid forms a puddle of liquid.
A certain liquid is added to a solid, and bubbles of gas form.
Two liquids are mixed, and a precipitate forms.
Heating a blue solid turns the solid white.
How many solutions x 2x 7 = 3x - 7?
A trail mix has 4 cups of raisins, 3 cups of chocolate, 6 cups of peanuts, and 2 cups of cashews. Which ingredients are in the same ratio as cashews to raisins?
Line segment AB has a length of 4 units. It is translated 2 units to the right on a coordinate plane to obtain line segment A'B'. What is the length of A'B'?
Answer:
it 2 units
Step-by-step explanation:
Erica bought 3 1/2 yards of fabric. If she uses 2/3 of the fabric to make a curtain, how much will she have left?
Final answer:
Erica will have 1 1/6 yards of fabric left after using 2/3 of the 3 1/2 yards she purchased to make a curtain.
Explanation:
The student's question is about how much fabric Erica will have left after using 2/3 of the 3 1/2 yards she bought to make a curtain. To solve this problem, we first need to convert the mixed number of yards of fabric to an improper fraction. We start by multiplying the whole number, 3, by the denominator of the fraction, 2, and then adding the numerator, 1. This gives us (3 × 2) + 1 equals 7, so Erica has 7/2 yards of fabric.
Next, we determine how much fabric she uses by multiplying 7/2 yards by 2/3. Doing the multiplication, (7/2) × (2/3), we can cancel out the common factor of 2 to simplify the calculation. The result is 7/3 yards of fabric used for the curtain.
To find out how much fabric is left, we subtract the used fabric from the total amount Erica originally had, which is 7/2 yards. So, we calculate 7/2 - 7/3 yards. To subtract these fractions, they need to have a common denominator. Multiplying 7/2 by 3/3 and 7/3 by 2/2 gives us equivalent fractions with a common denominator of 6. We now have (21/6) - (14/6) yards, and subtracting these gives us 7/6 yards of fabric remaining. This can also be represented as 1 1/6 yards, which is how much Erica will have left after making the curtain.
what is the answer to 8y - 1 = 31
Factor the GCF first and then factor the trinomial: 2x2 + 20x + 50
A. 2(x + 5)(x + 5)
B. 2(x + 5)(x + 10)
C. 2(x + 2)(x + 25)
D. prime Factor the GCF first and then factor the trinomial: 2x2 + 20x + 50
A. 2(x + 5)(x + 5)
B. 2(x + 5)(x + 10)
C. 2(x + 2)(x + 25)
D. prime
For f(x) = 2x + 1 and g(x) = x2 – 7, find (f – g)(x).
A. –x2 + 2x – 6
B. 2x2 – 15
C. x2 – 2x – 8
D. –x2 + 2x + 8
HELP!! give me the correct answer
For the function, f(x) = 2x + 1 and g(x) = x² – 7, (f – g)(x) will be D. –x² + 2x + 8
How to calculate the functionTo find (f - g)(x), we need to subtract the function g(x) from the function f(x).
f(x) = 2x + 1
g(x) = x² - 7
(f - g)(x) = f(x) - g(x)
Substituting the given functions:
(f - g)(x) = (2x + 1) - (x² - 7)
Now let's simplify:
(f - g)(x) = 2x + 1 - x² + 7
Combining like terms, we have:
(f - g)(x) = -x² + 2x + 8
Therefore, the answer is D. -x² + 2x + 8.
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Straight-line depreciation is a method of calculating an asset’s value by subtracting its salvage value from its acquisition or purchase price divided by the estimated useful life of the asset. suppose a manufacturing robot cost $1.5 million in 2005 and is sold in 2010 for $50,000. what is the linear equation representing the value of the robot?
Answer:
Linear equation is V(t) = 1500 - 290t
Step-by-step explanation:
To find the linear equation representing the value of the robot we will calculate per year depreciation in the cost of the robot.
Rate of depreciation = [tex]\frac{\text{(Manufacturing cost in 2005-selling price in 2010)}}{5}[/tex]
= [tex]\frac{[(1.5)(10^{6})-50000]}{5}[/tex]
= [tex]\frac{(1500000-50000)}{5}[/tex]
= [tex]\frac{1450000}{5}=290000[/tex]
If depreciation is represented by V(t) (in $000) then equation will be
V(t) = 1500 - 290t
How do u simplify 2/5 x 6/7? and what the answer?
(X-27)/[(X^1/3)-3] find the limit as X approaches 27
Evaluate BC for A = 5, B = -4, and C = 2
Will calculators or computers be needed to perform some calculations?
Answer:
yes
Step-by-step explanation:
When performing certain statistical calculations, finding roots, or working with powers, calculators or computers are necessary for the calculations; otherwise, more traditional methods will be sufficient.
Tina has to pay 4 percent of the purchase price toward closing costs for her mortgage. If the purchase price is $275,000, what is the closing cost amount?
Answer:
Proportion states that two fractions or ratios are equal.
Let x be the closing cost amount.
As per the statement:
Tina has to pay 4 percent of the purchase price toward closing costs for her mortgage. If the purchase price is $275,000.
Purchased Price = $275,000
then, by definition of proportion :
[tex]\frac{4}{100}=\frac{x}{275000}[/tex]
By cross multiply we have;
1,100,000 = 100x
Divide both sides by 100 we have;
11,000 = x
or
x = $ 11,000
Therefore, the closing cost amount is, 11,000
Multiply. (x – 4)(x2 – 3x + 5) ...?
Answer:
Answer is
[tex]x^3-7x^2+17x-20 \\ [/tex]
Step-by-step explanation:
We need to find
[tex](x-4)(x^2-3x+5) \\ [/tex]
Using distribution rule.
[tex](x-4)(x^2-3x+5)=x^3-4x^2-3x^2+12x+5x-20\\\\(x-4)(x^2-3x+5)=x^3-7x^2+17x-20 \\ [/tex]
So the answer is
[tex]x^3-7x^2+17x-20 \\ [/tex]
The school’s guidance department compares the grade-point averages and standardized state test scores for 10 students in each grade. The table below shows the correlation coefficient for each data set.
Grade Level and Correlation Coefficient
9th grade 0.3
10th grade –0.1
11th grade 0.2
12th grade –0.8
For which data set(s) is a linear regression model reasonable?
~ 9th grade and 11th grade data sets
~ 10th grade data set
~ 10th grade and 12th grade data sets
~ 12th grade data set
Answer:
12th grade data set
Step-by-step explanation:
What is the lcm of 21, 84, 126?
Write the decimal 0.063 as a percent. Answer choices: 0.0063 0.063 0.63 6.3 MY ANSWER: 0.063
The decimal 0.063 can be represented as 6.3% in the percent form.
Thus, option (D) is correct.
Given decimal: 0.063.
As, to convert any decimal into the percentage then multiply the the decimal with 100.
So, to convert 0.063 to a percent multiply it by 100:
= 0.063 x 100
= 6.3
Therefore, 0.063 as a percent is 6.3%.
Thus, option (D) is correct.
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