Final answer:
The slope of a line parallel to the line 4x - 7y = -14 is determined by converting the equation to slope-intercept form, revealing that the slope is 4/7. Thus, any line parallel to it will have the same slope of 4/7.
Explanation:
The slope of a line parallel to the line 4x - 7y = -14 is first determined by rewriting the given line in slope-intercept form (y = mx + b), where m represents the slope. For the line 4x - 7y = -14, we can solve for y to find the slope:
Add 7y to both sides: 4x = 7y - 14.
Then add 14 to both sides: 4x + 14 = 7y.
Finally, divide every term by 7 to solve for y: (4/7)x + 2 = y.
The slope of the line is 4/7. Since parallel lines have equal slopes, any line parallel to the given line will also have a slope of 4/7.
Which number should replace the question mark in the number grid below?
6b^2-13+6=0 Quadratic equations by factoring
An angle is 5 times the measure of its complement. find the measure of the larger angle
Answer:
75°
Step-by-step explanation:
The angle is our unknown, so we will call it x. If x is the angle, then its complement is 90 - x (complementary angles add up to 90). The word "is" means "equals", and "5 times" is multiplying the complementary by 5:
x = 5(90 - x) so
x = 450 - 5x
Combine like terms to get
6x = 450 so
x = 75
The other angle, the complement to that angle, is 90 - 75 = 15
The larger angle is 75°
Writing equation in slope intercept form
What is the slope of line represents by the equation y=-1/2x+1/4
what is the simplified form of the following expression 7m2+6.5n-4n+2.5m2-n
Answer:
The simplified form of the provided expression is [tex]9.5m^2+1.5n[/tex].
Step-by-step explanation:
Consider the provided expression.
[tex]7m^2+6.5n-4n+2.5m^2-n[/tex]
Arrange the like terms together.
[tex]7m^2+2.5m^2+6.5n-4n-n[/tex]
Add and subtract the like terms as shown below:
[tex]9.5m^2+1.5n[/tex]
Thus, the simplified form of the provided expression is [tex]9.5m^2+1.5n[/tex].
if a line is tangent to a circle,then it is perpendicular to the radius drawn to that point of tangent.
using multiplication property of equality solve x/2=6
Answer:
x=12
Step-by-step explanation:
↓↓↓↓↓↓↓↓↓↓↓↓
Multiplication property of equality is multiply both sides of an equation by the same number does not change the equation.
[tex]\frac{x}{2}=6[/tex]
multiply two both sides
[tex]\frac{2x}{2}=6*2[/tex]
simplify
[tex]6*2=12[/tex]
[tex]12/2=6[/tex]
[tex]12/6=2[/tex]
[tex]2*6=12[/tex]
[tex]x=12[/tex]
Hope this helps!
Christa went shopping for back-to-school clothes. Before the tax was added on, her total was $176. If the sales tax is 6%, what was the total amount she paid?
Answer:
$176·1.06 = $186.56
Therefore, the total amount that Christa paid was $186.56.
Angle bisectors of the angles ∠A and ∠B of a triangle ∆ABC intersect each other at point M. Find m∠AMB, if m∠A = 58°, m∠B = 96°.
Answer:
103 degrees
Step-by-step explanation:
Bisectors means you make a line in the middle splitting the angle in half. So you divide A by 2 to get 29 and B to get 48. Then you add them to get 77. And now you only need point m's angle. 180-77 is 103 so the answer they are looking for is 103.
I have another math question
Suppose a college student pays $700 for tuition fees. However, she also has to pay $400 for her textbooks (ouch!). What percent of her total education costs does she pay for her books? Write your answer to the nearest tenth of a percent, but in decimal form.
The student spends approximately 40% of her total education costs on her books, represented as 0.4 in decimal form.
Explanation:The student's total education costs are the sum of the tuition fees ($700) and the cost of her books ($400). This comes to a total of $700 + $400 = $1100. The percent of the total education cost that is spent on books is then given by the cost of the books divided by the total cost, or $400 / $1100. When expressed as a decimal, this works out to be approximately 0.36 or 36%, but since we want to the nearest tenth of a percent in decimal form, it becomes 0.4 or 40% to the nearest tenth. Therefore, the student spends 40% of her total education costs on her books.
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What is the area of a triangle with vertices at (−2, 1) , (2, 1) , and (3, 4) ?
1. The price of a set of luggage was reduced by $35 for a pre-holiday sale. After the holiday, the set's price tag was marked with an additional discount of 35% of the price during the pre-holiday sale. Let P represent the price of the set of luggage before the sale Which of the following gives an expression representing the price of the set of after the holiday and the final price of the set, if it's original price P was $200?
a) P-0.35*(P-35); $107.25
b) 0.65*(P)-35; $107.25
c) 0.65*(P-35; $107.25
d) 0.65p-22.75; $95.00
Choose the point slope form of the equation below that represents the line passing through the point (-6,4) and (2,0)
Answer: [tex]y=\dfrac{-1}{2}(x-2)[/tex]
Step-by-step explanation:
The equation of a line passing through points (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
Given : The points from which line is passing : (-6,4) and (2,0)
Then , the equation of the line, in point slope form, that passes through (-6,4) and (2,0)will be :-
[tex](y-(0))=\dfrac{4-0}{-6-2}(x-2)\\\\\Rightarrow\y=\dfrac{4}{-8}(x-2)\\\\\Rightarrow\ y=\dfrac{-1}{2}(x-2)[/tex]
1 under typical conditions, 1 feet of snow will melt to 2 inches of water. 2 1 to how many inches of water will 2 feet of snow melt?
you can find the ______ parts of two congruent triangles by aligning them perfectly on top of each other.
A. corresponding
B. similar
C. complementary
D. supplementary
You can find the corresponding parts of two congruent triangles by aligning them perfectly on top of each other.
What are Congruent Triangles?Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
Let the first triangle be ΔABC
Let the second triangle be ΔDEF
Now , when the triangles are aligned perfectly on top of each other ,
They are corresponding and the and the measures of the angles are same
And , the measure of the legs of the triangles will also be congruent
Hence , the corresponding parts are same
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There is no answer choices. I really need help with this! prime factorize (expand) the expression 12a^3bd^5
a piggy bank contains $2.40 in nickels and dimes. if there are 33 coins in all, how many nickels are there
Mr. Miller owns two hotels and is ordering towels for the rooms. He ordered 27 hand towels and 48 bath towels for a bill of $540 for the first hotel. He ordered 50 hand towels and 24 bath towels for a bill of $416 for the other hotel. What is the cost of one hand towel and one bath towel?
This question is based on the concept of solving a two linear equation.
Thus, the cost of one bath towel is $9 and one hand towel is $4.
Given:
Number of ordered of hand towels is 27 and bath towels is 48 and for a bill of $540 for the first hotel.
Number of ordered of hand towels is 50 and bath towels is 24 and for a bill of $416 for the other hotel.
We need tom determined the cost of one hand towel and one bath towel.
According to the question:
Let the hand towels be h and bath towels be b.
Therefore, equation of first hotel is
27h + 48b = 540........(1)
Equation of second hotel is
50h + 24b = 416.........(2)
Now, solving both equation for h and b.
Equation (2) multiplying by -2.
-100 h -48 b = - 832..................(3)
Now, solve equation (1) and (3)
27h + 48b = 540 and -100h - 48b = - 832
⇒ -73 h = - 292
⇒ h = -292 / -73
⇒ h = 4
Therefore, the cost of 1 hand towel is $4.
Now, putting the value of h = 4 in equation (1).
⇒ 27(4) + 48b = 540
⇒ 108 + 48b = 540
⇒ 48b = 540 - 108
⇒ 48b = 432
⇒ b = 432/48
⇒ b = 9
Therefore, the cost of 1 bath towel is $9.
Thus, the cost of one bath towel is $9 and one hand towel is $4.
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Find the equation perpendicular to the line y=−3x+5 that passes through point (2, 6).
Hey there! :)
Perpendicular to y = -3x + 5 ; passes through (2, 6).
Our slope is -3. We know this because it is in the "m" position from slope-intercept form. However, since our equation we're looking for is perpendicular to our given one, we must find the negative reciprocal of -3.
A negative reciprocal is simply a number that is flipped and either given a negative or gets a negative removed.
So the negative reciprocal of -3 is 1/3. This means that our new slope is 1/3.
Now, using point-slope form ( y-y₁=m(x-x₁) ), our new slope (1/3) & (2, 6) , let's find our new equation!
y-y₁=m(x-x₁) y - (6) = 1/3(x - 2)
Simplify.
y - 6 = 1/3x - 2/3
~Hope I helped!~
There are 11 books on a shelf. 5 of these books are new. (a) What is the ratio of new books to used books? (b) What is the ratio of used books to all books?
a) The ratio of new books to used books 5:6.
b) The ratio of used books to all books is 6:11.
What is the ratio?The ratio is defined as the representation of one number with respect to the other number or one number is how many times the other number.
The ratio will be calculated as follows:-
a) Since 5 of the books are new, that means that the other books are used. So, there are 11-5=6. The ratio would be 5:6.
b) We know that the number of used books is 6. The ratio is 6:11.
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The equation for perimeter of square p=4s . what is the formula solved for p
f(x)=3^x and x=-5 help
A) 1/729
B) -15
C) 1/243
D) -125
Three friends were born in consecutive years. The some of their birth years is 5982.find the year in which each person was born
You buy 8 gallons of gasoline at p dollars per gallon and pay $23.20. Write an equation to find the price of one gallon of gasoline. Then find the price of one gallon of gasoline.
Answer:
The price of 1 gallon of gasoline is $2.90.
Step-by-step explanation:
You buy 8 gallons of gasoline at p dollars per gallon and pay $23.20.
We get the expression:
[tex]8p=23.20[/tex]
We can find one gallon as: p=[tex]\frac{23.20}{8}[/tex]
=> p = $2.90
Hence, the price of 1 gallon of gasoline is $2.90.
4[(6 - 1) + 3(5 - 2)] 44 46 56
The numerical expression 4[(6 - 1) + 3(5 - 2)] evaluates step-by-step following the order of operations. Operations within the parentheses are performed first, followed by multiplication, resulting in a final answer of 56
The student's question involves evaluating a numerical expression, which is a concept in mathematics. We have the expression 4[(6 - 1) + 3(5 - 2)] and want to calculate its value step by step following the order of operations:
First, perform the operations inside the parentheses: (6 - 1) = 5 and (5 - 2) = 3.Next, multiply by 3 within the parentheses: 3(5 - 2) becomes 3 * 3 = 9.Now, add the results within the square brackets: 5 + 9 = 14.Finally, multiply the result by 4: 4 * 14 = 56.Hence, the correct answer to the expression is 56
How to solve an expression with variables in the exponents?
Answer:
use logarithms
Step-by-step explanation:
Taking the logarithm of an expression with a variable in the exponent makes the exponent become a coefficient of the logarithm of the base.
__
You will note that this approach works well enough for ...
a^(x+3) = b^(x-6) . . . . . . . . . . . variables in the exponents
(x+3)log(a) = (x-6)log(b) . . . . . a linear equation after taking logs
but doesn't do anything to help you solve ...
x +3 = b^(x -6)
There is no algebraic way to solve equations that are a mix of polynomial and exponential functions.
__
Some functions have been defined to help in certain situations. For example, the "product log" function (or its inverse) can be used to solve a certain class of equations with variables in the exponent. However, these functions and their use are not normally studied in algebra courses.
In any event, I find a graphing calculator to be an extremely useful tool for solving exponential equations.
To solve an expression with variables in the exponents, you apply the rules of exponents.
Explanation:When solving an expression with variables in the exponents, you need to apply the rules of exponents. Here are the key rules:
For example, (27x^3)(4x^2) can be simplified to 108x^5.
On Monday, 490 students went on a trip to the zoo. All 8 buses were filled and 10 students had to travel in cars. How many students were in each bus?
Simplify 2x^4y^5 * 3x^5y^7z^3