Answer:
The mass of sunflower seeds in the mixture is 1-pound
The mass of chocolate-covered peanuts in the mixture is 3-pounds
The mass of raisins in the mixture is 2-pounds
Step-by-step explanation:
The given parameters are;
The cost per pound of raisins = $3
The cost per pound of sunflower seeds = $1
The cost per pound of chocolate-covered peanuts = $1.50
The mass of raisings in the mixture = 2 × The mass of sunflower seeds in the mixture
The total cost of the mixture = $11.50
The mass of the mixture = 6-pounds
Let x represent the mass of sunflower seeds in the mixture, and y represents the mass of chocolate-covered peanuts in the mixture, we have;
The mass of raisins in the mixture = 2 × x
The system of equation are;
2·x + x + y = 6...(1)
2·x × 3 + x × 1 + y × 1.5 = 11.50...(2)
Simplifying the above two equations give;
For equation (1), we have;
3·x + y = 6...(1)
For equation (2), we have;
7·x + 1.5·y = 11.50...(2)
Making y the subject of both formulas, gives;
For equation (1), we have;
y = 6 - 3·x
For equation (2), we have;
y = 11.50/1.5 - 7/1.5·x
Equating both equations of y, to find the common solution as follows;
6 - 3·x = 11.50/1.5 - 7/1.5·x
7/1.5·x - 3·x = 11.50/1.5 - 6
14/3·x - 3·x = 23/3 - 6
5/3·x = 5/3
x = 3/5 × 5/3 = 1
x = 1
The mass of sunflower seeds in the mixture = x = 1-pound
y = 6 - 3·x = 6 - 3 × 1 = 3
y = 3
-The mass of chocolate-covered peanuts in the mixture = y = 3-pounds
The mass of raisins in the mixture = 2 × x = 2 × 1 = 2-pounds.
3 − 3k + 7k = 5b find the equation for k
Answer:k=5b/4 - 3/4
Step-by-step explanation:
Answer:
[tex]k=\frac{5}{4}b - \frac{3}{4}[/tex]
Step-by-step explanation:
-3k + 7k = 5b - 3
4k = 5b - 3
[tex]k=\frac{5}{4}b - \frac{3}{4}[/tex]
Consider the following.
cos(x) = x3
A) Prove that the equation has at least one real root.
The equation cos(x) = x3 is equivalent to the equation f(x) = cos(x) − x3 = 0. f(x) is continuous on the interval (0, 1) there is a number c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation cos(x) = x3, in the interval (0, 1).
B) Use your calculator to find an interval of length 0.01 that contains a root.
Answer:
Step-by-step explanation:
Given that:
cos(x) = x³
f(x) = cos (x) - x³
f(x) is continuous on the interval (0, 1)
when;
f(0) = cos (0) - (0)
f(0) = 1 - 0
f(0) = 1 > 0
f(1) = cos (1) - 1³
f(1) = 0.5403 - 1
f(1) = -0.4597
f(1) = - 0.46
f(1) = - 0.46 < 0
Since, 1 > 0 > -0.46, thus there is a number ''c" in (0,1)
such that f(c) = 0
By applying the Intermediate Value Theorem, there is a root of the equation in the interval (0,1)
b) Given that:
The interval length = 0.01; this implies that it is 0.005 length from its root.
f(0.865) = 0.0014
f(0.87) = - 0.013
The solution to the interval lies between 0.865 , 0.87 by using a calculator at length 0.01.
Sal invests $16,000 at age 35. He hopes the investment will be worth $320,000 when he turns 40. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.
59.9%
Sorry I don’t have time to explain in the middle of an exam
The rate of growth needs to be 59.9%.
The formula used to determine the future value of an investment when interest is compounded continuously is:
FV = A x [tex]e^{r}[/tex] x N
A= amounte = 2.7182818 N = number of years r = interest rateFV = future value$320,000 = $16,000 x [tex]e^{r}[/tex] x 5
Divide both sides by $16,000
20 = 5[tex]e^{r}[/tex]
Take the In of both sides
In(20) = 5r
Divide both sides by 5
r = 59.9%
To learn, please check: https://brainly.com/question/14640433
The diagram shows a triangle.
45°
38°
What is the value of s?
Answer:
97 degrees
Step-by-step explanation:
If 45 + 38 = 83
A triangle is 180 always
so 180-83=97
An online streaming service costs $25 to join. Each gigabyte used costs $2.50. Let g represent the number of gigabytes. Would this situation represent a function?
True False
Answer: 10
Step-by-step explanation:
25 ÷ 2.5 = 10
10 gigabytes
please help me!
Decrease £40 by 10%
Answer:
36
Step-by-step explanation:
40 * .10 = 4
40-4 = 36
help im being timed what is the perimeter of this triangle?!
Answer:
AB + BC + CA
Step-by-step explanation:
12b-8 + 12b- 8 + 9b+8
33b - 8
Quiz 3-3 Parallel and Perpendicular Lines on the Coordinate Plane (Gina Wilson All Things Algebra 2014-2019) need these for a quiz please!
Answer:
14. [tex]y = -2x -1[/tex]
15. [tex]y = -\frac{3}{4}x +3[/tex]
16. [tex]y= 4x + 9[/tex]
17. [tex]y = -\frac{5}{3}x -2[/tex]
18. [tex]y= -\frac{2}{3}x -5[/tex]
19. [tex]y = 4x -3[/tex]
20. [tex]y = -3x -7[/tex]
Step-by-step explanation:
Solving (14):
Given
[tex](x_1,y_1) = (-7,13)[/tex]
[tex]Slope (m) = -2[/tex]
Equation in [tex]slope- intercept[/tex] form is:
[tex]y - y_1 = m(x-x_1)[/tex]
Substitute values for y1, m and x1
[tex]y - 13 = -2(x -(-7))[/tex]
[tex]y - 13 = -2(x +7)[/tex]
[tex]y - 13 = -2x -14[/tex]
Collect Like Terms
[tex]y = -2x -14 + 13[/tex]
[tex]y = -2x -1[/tex]
Solving (15):
Given
[tex](x_1,y_1) = (-4,6)[/tex]
[tex]Slope (m) = -\frac{3}{4}[/tex]
Equation in [tex]slope- intercept[/tex] form is:
[tex]y - y_1 = m(x-x_1)[/tex]
Substitute values for y1, m and x1
[tex]y - 6 = -\frac{3}{4}(x - (-4))[/tex]
[tex]y - 6 = -\frac{3}{4}(x +4)[/tex]
[tex]y - 6 = -\frac{3}{4}x -3[/tex]
Collect Like Terms
[tex]y = -\frac{3}{4}x -3 + 6[/tex]
[tex]y = -\frac{3}{4}x +3[/tex]
Solving (16):
Given
[tex](x_1,y_1) = (-5,-11)[/tex]
[tex](x_2,y_2) = (-2,1)[/tex]
First, we need to calculate the [tex]slope\ (m)[/tex]
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{1 - (-11)}{-2 - (-5)}[/tex]
[tex]m = \frac{1 +11}{-2 +5}[/tex]
[tex]m = \frac{12}{3}[/tex]
[tex]m = 4[/tex]
Equation in [tex]slope- intercept[/tex] form is:
[tex]y - y_1 = m(x-x_1)[/tex]
Substitute values for y1, m and x1
[tex]y - (-11) = 4(x -(-5))[/tex]
[tex]y +11 = 4(x+5)[/tex]
[tex]y +11 = 4x+20[/tex]
Collect Like Terms
[tex]y= 4x + 20 - 11[/tex]
[tex]y= 4x + 9[/tex]
Solving (17):
Given
[tex](x_1,y_1) = (-6,8)[/tex]
[tex](x_2,y_2) = (3,-7)[/tex]
First, we need to calculate the [tex]slope\ (m)[/tex]
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{-7 - 8}{3- (-6)}[/tex]
[tex]m = \frac{-7 - 8}{3+6}[/tex]
[tex]m = \frac{-15}{9}[/tex]
[tex]m = -\frac{5}{3}[/tex]
Equation in [tex]slope- intercept[/tex] form is:
[tex]y - y_1 = m(x-x_1)[/tex]
Substitute values for y1, m and x1
[tex]y - 8 = -\frac{5}{3}(x -(-6))[/tex]
[tex]y - 8 = -\frac{5}{3}(x +6)[/tex]
[tex]y - 8 = -\frac{5}{3}x -10[/tex]
Collect Like Terms
[tex]y = -\frac{5}{3}x -10 + 8[/tex]
[tex]y = -\frac{5}{3}x -2[/tex]
18.
Given
[tex](x_1,y_1) = (-6,-1)[/tex]
[tex]y = -\frac{2}{3}x+1[/tex]
Since the given point is parallel to the line equation, then the slope of the point is calculated as:
[tex]m_1 = m_2[/tex]
Where [tex]m_2[/tex] represents the slope
Going by the format of an equation, [tex]y = mx + b[/tex]; by comparison
[tex]m = -\frac{2}{3}[/tex]
and
[tex]m_1 = m_2 = -\frac{2}{3}[/tex]
Equation in [tex]slope\ intercept\ form[/tex] is:
[tex]y - y_1 = m(x-x_1)[/tex]
Substitute values for y1, m and x1
[tex]y - (-1) = -\frac{2}{3}(x - (-6))[/tex]
[tex]y +1 = -\frac{2}{3}(x +6)[/tex]
[tex]y +1 = -\frac{2}{3}x -4[/tex]
[tex]y= -\frac{2}{3}x -4 - 1[/tex]
[tex]y= -\frac{2}{3}x -5[/tex]
19.
Given
[tex](x_1,y_1) = (-2,-11)[/tex]
[tex]y = -\frac{1}{4}x+2[/tex]
Since the given point is parallel to the line equation, then the slope of the point is calculated as:
[tex]m_1 = -\frac{1}{m_2}[/tex]
Where [tex]m_2[/tex] represents the slope
Going by the format of an equation, [tex]y = mx + b[/tex]; by comparison
[tex]m_2 = -\frac{1}{4}[/tex]
and
[tex]m_1 = -\frac{1}{m_2}[/tex]
[tex]m_1 = -1/\frac{-1}{4}[/tex]
[tex]m_1 = -1*\frac{-4}{1}[/tex]
[tex]m_1 = 4[/tex]
Equation in [tex]slope\ intercept\ form[/tex] is:
[tex]y - y_1 = m(x-x_1)[/tex]
[tex](x_1,y_1) = (-2,-11)[/tex]
Substitute values for y1, m and x1
[tex]y - (-11) = 4(x - (-2))[/tex]
[tex]y +11 = 4(x +2)[/tex]
[tex]y +11 = 4x +8[/tex]
Collect Like Terms
[tex]y = 4x + 8 - 11[/tex]
[tex]y = 4x -3[/tex]
20.
Given
[tex](x_1,y_1) = (-10,3)[/tex]
[tex](x_2,y_2) = (2,7)[/tex]
First, we need to calculate the slope of the given points
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{7 - 3}{2 - (-10)}[/tex]
[tex]m = \frac{7 - 3}{2 +10}[/tex]
[tex]m = \frac{4}{12}[/tex]
[tex]m = \frac{1}{3}[/tex]
Next, we determine the slope of the perpendicular bisector using:
[tex]m_1 = -\frac{1}{m_2}[/tex]
[tex]m_1 = -1/\frac{1}{3}[/tex]
[tex]m_1 = -3[/tex]
Next, is to determine the coordinates of the bisector.
To bisect means to divide into equal parts.
So the coordinates of the bisector is the midpoint of the given points;
[tex]Midpoint = [\frac{1}{2}(x_1+x_2),\frac{1}{2}(y_1+y_2)][/tex]
[tex]Midpoint = [\frac{1}{2}(-10+2),\frac{1}{2}(3+7)][/tex]
[tex]Midpoint = [\frac{1}{2}(-8),\frac{1}{2}(10)][/tex]
[tex]Midpoint = (-4,5)[/tex]
So, the coordinates of the midpoint is:
[tex](x_1,y_1) = (-4,5)[/tex]
Equation in [tex]slope- intercept[/tex] form is:
[tex]y - y_1 = m(x-x_1)[/tex]
Substitute values for y1, m and x1: [tex]m_1 = -3[/tex] & [tex](x_1,y_1) = (-4,5)[/tex]
[tex]y - 5 = -3(x - (-4))[/tex]
[tex]y - 5 = -3(x +4)[/tex]
[tex]y - 5 = -3x-12[/tex]
Collect Like Terms
[tex]y = -3x - 12 +5[/tex]
[tex]y = -3x -7[/tex]
What is the equation of the linear function?
= -x + 6
A
y = -2x + 3
y=-3x +3
y = ;& + 3
Done
NEED HELP ASAP WILL GIVE BRAIN
Review the diagram.
On a coordinate plane, a vector labeled 120 meters forms angle 25 degrees with the x-axis. It goes to point mirror 1. Another vector labeled 90 meters goes from point mirror 1 to mirror 2. It forms angle 20 degrees with a horizontal line. Point mirror 2 goes to (0, 0).
A laser beam is aimed 25° from horizontal at a mirror 120 m away. The beam bounces off the mirror and continues for an additional 90 m at 20° above horizontal until it hits a target, mirror 2. What is the distance between the origination point and the target?
approximately 85 m
approximately 122 m
approximately 174 m
approximately 194 m
Answer:
Vectors are usually described in terms of their components in a coordinate system. Even in everyday life we naturally invoke the concept of orthogonal projections in a rectangular coordinate system. For example, if you ask someone for directions to a particular location, you will more likely be told to go 40 km east and 30 km north than 50 km in the direction 37° north of east.
In a rectangular (Cartesian) xy-coordinate system in a plane, a point in a plane is described by a pair of coordinates (x, y). In a similar fashion, a vector
→
A
in a plane is described by a pair of its vector coordinates. The x-coordinate of vector
→
A
is called its x-component and the y-coordinate of vector
→
A
is called its y-component. The vector x-component is a vector denoted by
→
A
x. The vector y-component is a vector denoted by
→
A
y. In the Cartesian system, the x and y vector components of a vector are the orthogonal projections of this vector onto the x– and y-axes, respectively. In this way, following the parallelogram rule for vector addition, each vector on a Cartesian plane can be expressed as the vector sum of its vector components:
Step-by-step explanation:
Answer:
approximately 85 m
Step-by-step explanation:
use the law of cosines
x²=120²+90²-2(120)(90)cos(45)
*120 & 90 are given values
*45 is from 25+20; bcuz of alternate interior angles, the other angle from mirror 1 is 25 degrees, making the total 45 degrees
x=√120²+90²-2(120)(90)cos(45)
x=85, the distance btwn origin point and mirror 2
PLease help me for my homework hahaqhahahahahhahaha please
Answer
Step-by-step explanation:
rise over run so it'd be 3/3 positive or y= 3x-3
Solve for x.
9(x + 1) = 25 + x
O x= 2
O x = 3
0 x = 4
O x = 5
Answer:
Step-by-step explanation:
9(x+1)=25+x
9x+9=25+x subtract x both sides
8x+9=25 subtract 9 both sides
8x=16 divide by 8
x=2
Caylan is making bakes goose for a charity bake sale ha places a tray of scones a tray of muffing and a tray of cookies in the oven the second bake for 15 the muffins bake for 12 minutes and the cookies bake for 10 minutes when one tray is done he removes it a replaces it with another tray of the same item how many minutes after caylan puts the trays in the oven will he first remove the scones muffins and cookies at the same miinutes
Answer:
Step-by-step explanation:
an hour, or 60 minutes
Answer:
60 minutes
Step-by-step explanation:
i d 1 0 t
Help please it’s needed!
Solve for x in the equation: 2x-7=14
Answer: x=10.5
Step-by-step explanation:
To solve for x, we want to use our properties to isolate x.
2x-7=14 [add both sides by 7]
2x=21 [divide both sides by 2]
x=10.5
Now, we know that x=10.5.
Find the area of the shape below
Answer:
????
Step-by-step explanation:
Answer:
where's the shape
Step-by-step explanation:
what's the length and width, maybe I can help
Samantha claims that 4x + 2 is equivalent to the expression x + 17 + 3x − 15. Check whether Samantha’s equivalent expression is correct using x = 2. Samantha is incorrect because when using x = 2, the resulting values in both expressions are different. Samantha is incorrect because the expressions cannot be checked using x = 2. Samantha is correct because when using x = 2, the resulting values in both expressions are equal.
Answer:
The correct answer is c
Answer:
Answer is c
Step-by-step explanation:
Your welcome
PLEASE HELP ME
What is the simplified form of
the quantity of x plus 6, all over 3 − the quantity of x plus 2, all over 3
How do you write 352 in expanded form
Answer:
300+ 50 + 2
Step-by-step explanation:
If you add 300+50+2 you get 352 all you need to do is break down the number to pieces! :)
Explanation:
The number 352 has 3 in the hundreds place, 5 in the tens place, and 2 in the ones place.
So that's why 352 = 300 + 50 + 2
(PLEASEEE HELP) Which graph of which line represents a
proportional relationship?
Graph A
Graph B
Graph C
Graph D
Look carefully at the graph of multiple graphs shown below. Which of the graphs
represents or shows a proportional relationship?
Answer:
B
a proportional relationship in a graph needs to go through the 0.0, and also needs to be a stright line.
Which model represents the product 6×34?
Answer:
204 is the answer
Step-by-step explanation:
204 is the answer
Paki heart nalang po kung nakatulong
Answer:
its the 3rd
Step-by-step explanation:
Can someone help me with 5-6
Answer:
B, C
Step-by-step explanation:
I love slope
What is the answer to this
2(x-5)-6=-18
x=___
Answer:
x= -1
Step-by-step explanation:
Distribute:2(x -5) -6 = -18
2x -10 -6 =-18
Subtract the numbers:2x -10 -6 =-18
2x -16 = -18
Add 16 to both sides of the equation:2x =16 += -18
2x -16 +16 = -18 +16
Simplify:2x = -2
Divide both sides of the equation by the same term:2x/2 = -2/2
Simplify:x=-1
Answer:x = -1
what are the three products of celullar respiration
Answer:
Cellular respiration is this process in which oxygen and glucose are used to create ATP, carbon dioxide, and water. ATP, carbon dioxide, and water are all products of this process because they are what is created.
Step-by-step explanation:
8(-4a + 8b) = 240please
Answer:
= -32a+64b
Step-by-step explanation:
thats the answer
Write the equation of a line that is parallel to y = 6x +1 and that passes through the point (-7,1).
Answer:
[tex]y=6x+43[/tex]
Step-by-step explanation:
We want the equation of a line that is parallel to [tex]y=6x+1[/tex] which also passes through (-7, 1).
Since the new line is parallel, it must have the same slope as the original line.
The slope of the original line is 6.
Hence, the slope of our new line must also be 6.
We know that the slope is 6.
And it passes through the point (-7, 1).
So, we can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
Substitute:
[tex]y-1=6(x-(-7))[/tex]
Simplify:
[tex]y-1=6(x+7)[/tex]
Distribute:
[tex]y-1=6x+42[/tex]
Add 1 to both sides. Hence, our equation is:
[tex]y=6x+43[/tex]
Help!!Find the y-intercept of the line on the graph.
Enter the correct answer.
The y-intercept of the graph is -3
How to find the y-intercept of a graph?The y-intercept is the point where the line intersects the y-axis. This is the value of y when x is equals to zero.
Using slope intercept formula,
y = mx + b
where
m = slopeb = y-interceptNow, let's trace the value of y when x = 0 in the graph.
Therefore,
when x = 0, y = -3
Hence, the y-intercept of the graph is -3
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In Joey's neighborhood the ratio of families with dogs to families with cats is 5 to 2. There are 15 more families with dogs than families with cats. How many families have cats, and how many families have dogs?
Answer:
10 families have cats
25 families have dogs
Step-by-step explanation:
The difference of ratio units is 5-2 = 3. The difference in pet counts is 15, so we can see that each ratio unit stands for 15/3 = 5 pets. Then ...
dogs : cats = 5 : 2 = (5·5) : (2·5) = 25 : 10
There are 10 families with cats and 25 families with dogs.
Answer:
B D and E.
Step-by-step explanation:
What is the slope of 3x-2y=7?
Answer:
The slope is -3/2
Step-by-step explanation:
Hope this helped have a good day!
Every month Michael pays $39.95 for phone service plus $0.10 for every text message over a preset limit. Which equation represents the amount of money Michael pays for phone service each month, y, with x text messages over the limit? what is the equation?