For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
Where:
[tex](x_ {1}, y_ {1})\ and\ (x_ {2}, y_ {2})[/tex]are two points through which the line passes.
According to the statement we have:
[tex](x_ {1}, y_ {1}) :( 10,1)\\(x_ {2}, y_ {2}) :( a, -5)\\m = \frac {1} {3}[/tex]
Substituting we have:
[tex]\frac {1} {3} = \frac {-5-1} {a-10}\\\frac {1} {3} = \frac {-6} {a-10}\\a-10 = \frac {-6} {\frac {1} {3}}\\a-10 = -18\\a = -18 + 10\\a = -8[/tex]
Thus, the value of a is -8.
Answer:
[tex]a = -8[/tex]
Which sign makes the inequality true?
60.00 ___ (56. 28 + 3.42)
3x + 4x = 5y + 2x
This is hard what is the answer
Answer:
x = y
Step-by-step explanation:
7x = 5y + 2x
Subtract 2x from both sides
5x = 5y
x = y
Variables and Inequalities
Answer:
-5x - 6x ≤ 8 - 8x - x
-11x ≤ 8 - 9x
-2x ≤ 8
x ≥ -4
(12345678), X=(1357), Y=(158) find (1)X' n Y
(2) (X' u Y)'
Hope it helps u............
Earl Pumpernickel owns and operates The Earl of Sandwiches, a profitable catering business in Logic Town. Recently, Earl was lucky enough to land a lucrative contract that will enable him to supply food for the Big Corporation for an entire month of lunch conferences. For the upcoming week, for example, he knows that Friday’s meeting will require 12 more sandwiches than Tuesday’s meeting, which will require six fewer sandwiches than Monday’s, which will require 20 more sandwiches than Wednesday’s, which will require five fewer sandwiches than Thursday’s. If the number of sandwiches ordered for the conference that calls for the fewest is 50, how many sandwiches will Earl need to make for the Big Corporation each day next week?
Answer:
Monday: 70
Tuesday: 64
Wednesday: 50
Thursday: 55
Friday: 76
Step-by-step explanation:
Equations
Let's call x to the number of sandwiches ordered for Thursday's meeting. We know that for Wednesday’s, we'll need x-5 sandwiches, for Monday's, we'll need 20 more, i.e. (x-5+20)=x+15 sandwiches. For Tuesday's it will be 6 fewer than x+15, or x+9. Finally, for Friday's, it will be 12 more than x+9 or x+21. Summarizing:
Monday: x+15
Tuesday: x+9
Wednesday: x-5
Thursday: x
Friday: x+21
The fewest of them all is x-5 and is must be equal to 50
[tex]x-5=50[/tex]
[tex]x=55[/tex]
The number of sandwiches per day is
Monday: x+15=70
Tuesday: x+9=64
Wednesday: x-5=50
Thursday: x=55
Friday: x+21=76
How are the two angles related?
Answer:
They are supplementary
Step-by-step explanation:
Two Angles are Supplementary when they add up to 180 degrees.
Arnold’s entire workout consisted of 10 minutes of warm-up exercises, 25 minutes of lifting weights, and 15 minutes on the treadmill. What was the ratio of the number of minutes he lifted weights to the total number of minutes of his entire workout?
Answer:
1:2
Step-by-step explanation:
Find the ratio of the ratio of the number of minutes he lifted weights to the total number of minutes of his entire workout and simplify it
25:10+25+15
25:50
1:2
Answer:
1 to 2
1:2
1/2
Step-by-step explanation:
Ratios can be written in three forms:
A to B
A:B
A/B
Ratios are also simplified by reducing to lowest terms like fractions are.
This problem's ratio is:
minutes lifted weights to total minutes workout
The number of minutes lifting weights is in the question: 25.
To find the total minutes of his workout, add the number of minutes he spent for all of the activities:
Total minutes = warm-up + lifting weights + treadmill
Total minutes = 10 + 25 + 15
Total minutes = 50
The ratio before simplifying is 25/50.
This ratio can be reduced to lowest terms. Both sides are divisible by 25.
25/25 = 1
50/25 = 2
The ratio in lowest terms is 1/2.
It can also be written as 1 to 2 or 1:2.
Find the total number of unit cube that fill the entire prism
Answer:
72 cubes
Step-by-step explanation:
Attached is the picture drawn (though not great one), showing 6 cube on length of prism, 3 cubes on width and 4 cubes on height of prism.
Given: Length of prism= 6
Width= 3
Height= 4
To know the number of cubes, which can fill the entire prism, we need to find volume of prism.
∴ Volume of prism= [tex]length\times width\times height[/tex]
Volume of prism= [tex]6\times 3\times 4= 72[/tex]
∴ 72 units of cube can fill the entire prism.
Adam got 56 out of 84 correct in his test. What fraction of the marks did he get correct
56/84 or 2/3
Hope this helped!
Answer:
56/84
Step-by-step explanation:
Adam had 84 questions, and out of 84, he got 56 right.
Out of just indicates a fraction.
You would then translate:
x/84
If x is how many he got right, you would then substitute in 56:
56/84
:)
The average person's speed when riding a bike along a street is 18 kilometers per hour. What conversion factor can be used to
convert this speed to meters per hour?
A 1 kilometer/
1.000 meters
B 1 meter/
1.000 kilometers
C 1,000 meters/
1 kilometer
D 1.000 kilometers/
1 meter
The conversion factor used to convert kilometer per hour to meter per hour is [tex]1 \text{ meter } = \frac{1}{1000} kilometer[/tex]
Solution:
Given that average person's speed when riding a bike along a street is 18 kilometers per hour
To find: conversion factor used to convert the given speed to meters per hour
Given average speed = 18 km per hour
From the conversion parameters:
1 km = 1000 meters
or
[tex]1 \text{ meter } = \frac{1}{1000} kilometer[/tex]
So, we can use the above conversion factor to convert average speed into meters per hour
18 km per hour = 18000 meter per hour
So the conversion factor used to convert kilometer per hour to meter per hour is [tex]1 \text{ meter } = \frac{1}{1000} kilometer[/tex]
Thus option C is correct. 1000 meters for 1 kilometers
Answer:
its c
Step-by-step explanation:
The sum of two consecutive numbers is 77. The difference of half of the smaller number and one-third of the larger number is 6. If x is the smaller number and y is the larger number, which two equations represent the sum and difference of the numbers? x - y = 6 and 1/2 x + 1/3 y = 77 x + y = 77 and 1/2 x - 1/3 y = 6 x - y = 77 and 1/2 x + 1/3 y = 6
The required equations that represent the sum and difference of numbers are: x + y = 77 and [tex]\frac{x}{2} - \frac{y}{3} = 6[/tex]
Solution:
Let the two consecutive numbers be "x" and "y"
Where "x" is the smaller number and "y" is the larger number
Given that sum of two consecutive numbers is 77
Therefore we frame a equation as:
x + y = 77
Also given that The difference of half of the smaller number and one-third of the larger number is 6
Therefore we frame a equation as:
half of the smaller number - one-third of the larger number = 6
half of x - one third of y = 6
[tex]\frac{1}{2}x - \frac{1}{3}y = 6\\\\\frac{x}{2} - \frac{y}{3} = 6[/tex]
Therefore the required equations that represent the sum and difference of numbers are:
x + y = 77
[tex]\frac{x}{2} - \frac{y}{3} = 6[/tex]
Find the value of x and y
Answer:
x = 25
y = 60
Step-by-step explanation:
Angles with meauseres 80° and 4x° are the same-side interior angles when two parallel lines are cut by transversal. This means the sum of the measures of these angles is equal to 180°.
[tex]80^{\circ}+4x^{\circ}=180^{\circ}\\ \\4x=180-80\\ \\4x=100\\ \\x=25[/tex]
Angles with measures 4x° and (2y - 20)° are vertical angles, so they are congruent:
[tex]4x^{\circ }=(2y-20)^{\circ}\\ \\4\cdot 25=2y-20\\ \\2y-20=100\\ \\2y=100+20\\ \\2y=120\\ \\y=60[/tex]
Write the ratio 3 to 10 in two different ways.
Answer:
3/10, 3:10
Step-by-step explanation:
3 to 10 : 3/10, 3:10
Anna baked 3 batches of cookies with c cookies in each batch.She than ate 8 cookies
Answer:
3c-8
Step-by-step explanation:
at an office supply store emilio bought 3 notebooks and 5 pens for $13.75 if a notebook costs $1.25 more than a pen how does one notebook cost?
Answer:
One notebook costs $2.50
Step-by-step explanation:
The cost of notebook is $2.50.
what is algebra?Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions.
Given:
let the number of pen be x
let the number of notebooks be y.
So, the equation can be written as
3x + 5y= 13.75....(1)
x - y = 1.25
3x- 3y = 3.75 ....(2)
Solving above 2 equation we get
8y = 10
y= 10/8
y= 5/4
y= 1.25
and, x= 1.25+1.25=2.50
Hence, the notebook costs $2.50.
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25 subtracted from the product of a number and 7 is less than -39
Solving the inequality [tex]7x-25<-39[/tex] we get [tex]x<-2[/tex]
Step-by-step explanation:
We need to solve 25 subtracted from the product of a number and 7 is less than -39
Translating into mathematical form
Let the number be x
[tex]7x-25<-39[/tex]
Solving the inequality to find the value of x
[tex]7x-25<-39[/tex]
Adding 25 on both sides
[tex]7x-25+25<-39+25[/tex]
[tex]7x<-14[/tex]
Divide both sides by 7
[tex]x<-2[/tex]
Solving the inequality [tex]7x-25<-39[/tex] we get [tex]x<-2[/tex]
Keywords: Solving inequalities
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The inequality representing the scenario '25 subtracted from the product of a number and 7 is less than -39' is solved by first setting up the inequality 7x - 25 < -39, then isolating x to find x < -2. Here, x represents the unknown number.
Explanation:The student's question involves writing an inequality to represent the given scenario: 25 subtracted from the product of a number and 7 is less than -39. To express this in mathematical terms, let's denote the unknown number as x. The product of this number and 7 is written as 7x. Now, according to the question, when you subtract 25 from this product, the result should be less than -39.
So, the inequality becomes: 7x - 25 < -39. To solve this inequality, you would add 25 to both sides, resulting in 7x < -14. Then, dividing both sides by 7 gives us x < -2. This means that for the inequality to be true, the unknown number x must be less than -2.
What are the intercepts of the graphed function?
x-intercept = (-1,0)
y-intercept = (-3,0)
x-intercept = (0, -1)
y-intercept = (0, -3)
x-intercept = (0, -1)
y-intercept = (-3,0)
x-intercept = (-1, 0)
y-intercept = (0, -3)
Answer:
x-intercept = (-1,0)
y-intercept = (0,-3)
Explanation:
x-intercepts are points where the line crosses the x-axis.
y-intercepts are points where the line crosses the y-axis.
Answer:
D
Step-by-step explanation:
Janessa bought for 4 stamps for $1.48 at this rate how much would 10 stamps cost
Answer:
$3.70
Step-by-step explanation:
divide 1.48 by 4 = .37
multiply by 10
Equation of the line that passes tjrougj the points of (0,-3) (1,-5)
Answer:
y=-2x-3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-5-(-3))/(1-0)
m=(-5+3)/1
m=-2/1
m=-2
y-y1=m(x-x1)
y-(-3)=-2(x-0)
y+3=-2(x)
y+3=-2x
y=-2x-3
Mo’s farm stand sold a total of 165 pounds of apples and peaches. She sold apples for $1.75 per pound and peaches for $2.50 per pound. If she made $337.50, how many pounds of peaches did she sell?
Final answer:
Using a system of equations, it's found that Mo's farm stand sold 65 pounds of peaches, with the total sales of apples and peaches being 165 pounds and revenue $337.50.
Explanation:
To determine how many pounds of peaches Mo's farm stand sold, we can set up a system of equations based on the given information about total weight and revenue from apples and peaches. The weight equation can be written as A + P = 165, where A is the weight of apples sold and P is the weight of peaches sold. The revenue equation is 1.75A + 2.50P = 337.50.
Let's solve for A using the weight equation: A = 165 - P. Substitute A in the revenue equation: 1.75(165 - P) + 2.50P = 337.50. Upon solving, we get: 288.75 - 1.75P + 2.50P = 337.50, which simplifies to 0.75P = 48.75. Therefore, P, the weight of peaches sold, is 65 pounds.
What is m
Enter your answer in the box.
Answer:
Angle M = 98 degrees
Step-by-step explanation:
All triangle angles add up to 180.
Set up equation like this:
(x+6)+(3x-16)+(x)=180
Combine like terms.
5x-10=180
Add on both sides.
5x=190
Divide 5 both sides.
x=38
Solve for angle M.
3(38)-16=98
Which expression is equivalent to 13 - (-21)13−(−21)13, minus, left parenthesis, minus, 21, right parenthesis?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
-21-13−21−13minus, 21, minus, 13
(Choice B)
B
-21+13−21+13minus, 21, plus, 13
(Choice C)
C
-13+21−13+21minus, 13, plus, 21
(Choice D)
D
13+2113+21
The expression 13 - (-21) simplifies to 34.
Explanation:The expression 13 - (-21) can be simplified as follows:
The minus sign before the parentheses means that we need to change the sign of every term inside the parentheses.-(-21) is equivalent to +21, since the negative sign cancels out another negative sign.Therefore, 13 - (-21) simplifies to 13 + 21, which is equal to 34.So, the expression 13 - (-21) is equivalent to 34.
To find the equivalent expression for \(13 - (-21)\), you can simplify the subtraction of a negative number, which is the same as adding its positive counterpart. Therefore:
\[ 13 - (-21) \]
is equivalent to:
\[ 13 + 21 \]
Among the given choices, the expression that matches this result is:
\[ \text{(Choice D) } 13 + 21 \]
Final answer:
The expression 13 - (-21) is equivalent to 13 + 21 because we change the subtraction of a negative number to addition. The final result is 34.
Explanation:
The expression 13 - (-21) involves subtracting a negative number from a positive number. According to the rules for subtracting integers, we change the sign of the number being subtracted and then follow the rules for addition as follows:
Change the sign of the number after the minus sign. So, -(-21) becomes +21.Then, add 21 to 13, which gives us 13 + 21.The sum of 13 and 21 is 34.Therefore, the expression 13 - (-21) is equivalent to 13 + 21, which simplifies to 34.
Which situation can be modeled using the equation 5x+3=27
Answer:
x=4.8
Step-by-step explanation:
5x+3=27
-3 -3
5x=24
/5 /5
x = 4.8
Answer:
Sam has 27 pencils. He has 3 loose pencils and 5 packs of pencils with x pencils in each pack.
Step-by-step explanation:
Suppose that E and F are two events and that P(E)=.8 and P(F/E)=.6 What is P(E and F)?
Lets turn E into x and F into y.
We already know that x is 0.8. And if y/x = 0.6, we have to figure that out.
y/x = 0.6
y/0.8 = 0.6
Multiply by 8 to get y = 0.48.
So we have to find P(xy)
So if we know that x = 0.8 and y = 0.48 then all we have to do is multiply 0.48 and 0.8.
0.48 * 0.8 = 0.384
P(E and F) is 0.384.
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1. Jada measured the height of a plant in a science experiment and finds that, to the 1/4 nearest of an inch, it is 3/4 inches.
a. What is the largest the actual height the plant could be?
b. What is the smallest the actual height the plant could be?
c. How large could the percent error in Jada's measurement be?
The largest possible height of the plant is 1 inch, the smallest possible height is 0 inches, and the largest possible percent error in Jada's measurement is -25%.
Explanation:To find the largest possible height of the plant, we need to round up the measurement of 3/4 inch to the nearest whole inch. In this case, that would be 1 inch. Therefore, the largest the actual height of the plant could be is 1 inch.
To find the smallest possible height of the plant, we need to round down the measurement of 3/4 inch to the nearest whole inch. In this case, that would be 0 inches. Therefore, the smallest the actual height of the plant could be is 0 inches.
The percent error in Jada's measurement can be found by calculating the difference between the approximate measurement and the actual measurement, dividing it by the actual measurement, and then multiplying by 100. In this case, the approximate measurement is 3/4 inch and the actual measurement could be between 0 and 1 inch. So, the largest possible percent error would be (3/4 - 1) / 1 * 100 = -25%, and the smallest possible percent error would be (3/4 - 0) / 1 * 100 = 75%.
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SOMEONE HELP PLEASEEE.I NEED HELP WITH 12TH GRADE TRIG.
Answer:
x = 13.7
Step-by-step explanation:
This is a right triangle so we use the trig ratios. We need an angle of reference (not the right angle) and any side (which is given, hypotenuse = 47).
We can either find the angle at the top or the right to be the angle of reference, Θ (theta).
Angle at the top:
The two angles, 17° and the unknown interior angle add to 90° because they are complementary.
∠Θ = 90° - 17° = 73°
Now use the trig ratio cosine.
cosΘ = adjacent ÷ hypotenuse
cos(73°) = x / 47
x = 47cos(73°)
x = 13.74147..... Round down the exact answer to nearest tenth
x ≈ 13.7 Answer
The value of x is the same as the side adjacent to the angle of reference I chose.
If I chose the other missing angle to be the angle of reference, I would use sine and x would be opposite.
Factor the polynomial.
x²+6x+5
Answer: (x + 1 )(x+5)
Step-by-step explanation:
Given :
[tex]x^{2}[/tex] + 6x + 5
Compare with the general quadratic equation:
a[tex]x^{2}[/tex] + bx + c
To factorize , you are to find two numbers that multiply to give ac , and add to give b.
After which you will re - write the middle number with those numbers.
From the given question , ac = 5[tex]x^{2}[/tex] , we are to find two numbers that will multiply to give 5[tex]x^{2}[/tex] and add to give 6x.
The numbers are 1x and 5x.
We will then replace the middle number by the two numbers , that is
[tex]x^{2}[/tex] + x + 5x + 5
x(x+1) +5( x +1)
(x+1)(x+5)
The quotient of four times a number and nine in an algebraic expression
Answer:
4x/9
Step-by-step explanation:
The quotient of four times a number and nine in an algebraic expression can be represented as (4x/9).
Explanation:The quotient of four times a number and nine in an algebraic expression can be represented as (4x/9). Here, 'x' represents the unknown number. To calculate the value of this expression, you would multiply 4 with 'x' and then divide the result by 9. For example, if the unknown number is 6, the expression would evaluate to (4 * 6)/9 = 24/9 = 2.67.
In the realm of algebraic expressions, the quotient derived from four times an unspecified number divided by nine takes on the simple yet versatile form of (4x/9), with 'x' standing in as the variable denoting the unknown quantity. The computation entails a straightforward process wherein you multiply the value of 'x' by 4 and subsequently divide the outcome by 9. For instance, if 'x' were to represent the value 6, the expression's evaluation would unfold as follows: (4 * 6)/9 = 24/9 = 2.67. This straightforward algebraic framework empowers us to efficiently compute the result based on the specific value attributed to 'x,' facilitating various calculations and problem-solving endeavors.
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Plz plz plz plz plz help
Ok, so 27 is >, 30 is <, 13/5 is 2 3/5, 5 2/7 is 37/7, 9 3/4 is 39/4, and 23/3 is 7 2/3
I did not do #27 and #30, just did the table.
The ratio of boys to girls in history class is 4 to 5. How many girls are in the class if there are 12 boys in the class.
Answer:
15 girls
Step-by-step explanation:
Answer:
15 girls
Explanation:
You first set up the ratio of boys to girls (4/5) as a fraction. Then you look. You make another fraction next to the 4/5 fraction to figure out how many girl are in the class. You know that you are trying figure out how many GIRLS are in the classroom if their are 12 boys. So on the other fraction the DENOMONATER is going to have an x on it because you don't know how many girls their are and girls (according to the fraction boys to girls (4/5) are on the bottom. So, now you cross multiply. 12x5 is 60 and 60/4 is 15. Therefore, you get 15 as your answer.