Final answer:
The slope of the line passing through (0, 5) and (-12, 2) is calculated using the slope formula and is found to be 1/4.
Explanation:
The slope of the line passing through the points (0, 5) and (-12, 2) can be calculated using the formula slope (m) = (rise)/(run), where 'rise' is the change in the y-values and 'run' is the change in the x-values. To find the slope, we subtract the y-value of the second point from the y-value of the first point and divide by the subtraction of the x-value of the second point from the x-value of the first point: m = (5 - 2) / (0 - (-12)) = 3 / 12 = 1/4. Therefore, the slope of the line is 1/4.
which expression is equal to 1/36? A 1/3 x 1/6 B 1/4 x (1/3)^2 C (1/2)^2 x (1/3) ^2 D 1/2 x 1/3 x 1/3 x 1/3
Answer:
B is the correct answer
Step-by-step explanation:
use your calculator and or in the problem and it should give you a decimal just go to math. and click 1 and click enter again and it should give you a fraction
y=-4x+2 y=6x-8 in substitution
Answer:
(1, - 2 )
Step-by-step explanation:
Given the 2 equations
y = - 4x + 2 → (1)
y = 6x - 8 → (2)
Substitute y = 6x - 8 into (1)
6x - 8 = - 4x + 2 ( add 4x to both sides )
10x - 8 = 2 ( add 8 to both sides )
10x = 10 ( divide both sides by 10 )
x = 1
Substitute x = 1 into (2) for corresponding value of y
y = 6(1) - 8 = 6 - 8 = - 2
Solution is (1, - 2 )
the relationship between the distance run and the time for kofi can be represented by the equation y= 15.55x , where he ran y yards in x seconds which two equations could be used to represent this relationship for bella and elsie
Answer:
D
Step-by-step explanation:
The line representing Bella has a steeper slope than Kofi's, so the slope of that line must be greater than 15.55.
Similarly, the line representing Elsie has a shallower slope than Kofi's, so the slope of that line must be less than 15.55.
The only option that fits is D.
What is the expression that are equivalent to 5(2x+3)
Answer:
10x+15
Step-by-step explanation:
5(2x+3)=10x+15
Answer:
10x+15.
Step-by-step explanation:
Its just simplified.
5 times 2x is 10x
5 times 3 is 15.
Put it together 10x+15.
a direct variation function contains the points
range values y=3x+1 if the domain is -1,0,1,4
Answer:
Range = {-2, 1, 4, 13}
Step-by-step explanation:
Domain is the set of x-values that are allowed for the function. The values for which the function is defined.
Range is the set of y-values that are allowed for the fucntion. The values for which the function is defined.
Since domain is given as:
Domain = {-1, 0, 1, 4}
We have to plug in each of the 4 values and find the corresponding 4 values for the range. Lets do this below:
y = 3x + 1
y = 3(-1) + 1
y = -2
y = 3x + 1
y = 3(0) + 1
y = 1
y = 3x + 1
y = 3(1) + 1
y = 4
y = 3x + 1
y = 3(4) + 1
y = 13
So, the range would be:
Range = {-2, 1, 4, 13}
During the first month of sales, a company sold 1,300,000
units of a certain type of smartphone. During the same
month, 15% of the units sold were returned. If sales and
the return rate remain the same for each of the next 5
months, about how many units of this smartphone will be
returned to the company during this 6-month period?
Answer:
1,170,000
Step-by-step explanation:
The returns are 15% of 1,300,000.
15% of 1,300,000 = 15% * 1,300,000 = 0.15 * 1,300,000 = 195,000
In 1 month, 195,000 smartphones were returned.
In 6 months, 6 times as many smartphones were returned.
6 * 195,000 = 1,170,000
Answer: 1,170,000
Answer:
1,170,000 Smartphones were returned over a 6-month period.
Step-by-step explanation:
Ok, so to start off, 15% of 1,300,000 is 195,000. Now if everything remains the same over the next 5 months, you just need to multiply the 195,000 by 6 to get the 6 month return rate. This results in the number of 1,170,000 Smartphones Returned over a 6-month period.
the local bakery uses 1.75 cups of flour in each batch of cookies. the bakery usee 5.25 cups of flour this morning. How many batches of cookies did the bakery make? if there are 5 dozon cookies in each batch, how many cookies did the bakery make?
The bakery made 3 batches of cookies and a total of 180 cookies.
To determine the number of batches of cookies the bakery made, we divide the total amount of flour used by the amount of flour used in each batch. The bakery used 5.25 cups of flour in total, and each batch requires 1.75 cups of flour. Therefore, the number of batches made is:
[tex]\[ \text{Number of batches} = \frac{\text{Total flour used}}{\text{Flour per batch}} = \frac{5.25}{1.75} \][/tex]
[tex]\[ \text{Number of batches} = 3 \][/tex]
Since there are 5 dozen cookies in each batch, we multiply the number of batches by the number of cookies per batch to find the total number of cookies made:
[tex]\[ \text{Total number of cookies} = \text{Number of batches} \times \text{Cookies per batch} \][/tex]
[tex]\[ \text{Total number of cookies} = 3 \times (5 \times 12) \][/tex]
[tex]\[ \text{Total number of cookies} = 3 \times 60 \][/tex]
[tex]\[ \text{Total number of cookies} = 180 \][/tex]
Thus, the bakery made 3 batches of cookies, resulting in a total of 180 cookies."
x^2=3x+3 in standard form
Answer:
x^2-3x-3=0
Step-by-step explanation:
x^2=3x+3
x^2-3x-3=0
if 2cm represents 9m on a scale drawing how many meters do 15 cm represent
Which congruence theorems can be used to prove ΔABR ≅ ΔACR? Select three options.
Triangles A B R and A C R share side A R. Angles A B R and A C R are right angles. Sides A B and A C are congruent. Sides B R and C R are congruent.
HL
SAS
SSS
ASA
AAS
Answer:
1. HL
2. SAS
3. SSS
Step-by-step explanation:
Triangles ABR and ACR share side AR (hypotenuse of two right triiangles).
Angles ABR and ACR are right angles.
Sides AB and AC are congruent.
Sides BR and CR are congruent.
1. You can use HL theorem, because two triangles have congruent pair of legs and congruent hypotenuses.
2. You can use SAS theorem, because two triangles have two pairs of congruent legs and a pair of included right angles between these legs.
3. You can use SSS theorem, because two triangles have two pairs of congruent legs and congruent hypotenuses.
Answer
1. HL
2. SAS
3. SSS
Step-by-step explanation:
just took the test aced it
help me out
Give the correct answer
1+2=21
2+3=36
3+4=43
4+5=?
1 + 2 = 21 (reversing numbers)
2 + 3 = 32 (reversing numbers) + 4 = 36
3 + 4 = 43 (reversing numbers)
4 + 5 = 54 (reversing numbers) + 4 =58
Answer:
58Step-by-step explanation:
This is a sequence using reversed numbers, and alternating a summing fixed amount.
In the first one you can see that it's only numbers being reversed.
The second one is also reversing numbers but adding 4 units, 32+4=36.
The third one has the same pattern in the first one, just numbers being reversed.
The fourth has the same pattern than the second one, reversed numbers and add 4 units. So, it would be 54+4=58.
Therefore, the answer is 58.
Find values of a and b that make the following equality into identity:
x−1/(x+1)(x−4) = a/x+1 + b/x−4
The value of a and b in given expression must be [tex]\frac{2}{5} \text { and } \frac{3}{5}[/tex] respectively so that given equality becomes identity.
Solution:Need to find the value of a and b in following expression so that following equality will become identity.
[tex]\frac{(x-1)}{(x+1)(x-4)}=\frac{a}{(x+1)}+\frac{b}{(x-4)}[/tex] ------- eqn 1
Lets Simplify Right hand Side first,
[tex]\frac{a}{(x+1)}+\frac{b}{(x-4)}=\frac{a(x-4)+b(x+1)}{(x+1)(x-4)}[/tex]
[tex]\begin{array}{l}{=\frac{a x-4 a+b x+b}{(x+1)(x-4)}} \\\\ {=\frac{a x+b x-4 a+b}{(x+1)(x-4)}} \\\\ {=\frac{(a+b) x-4 a+b}{(x+1)(x-4)}}\end{array}[/tex]
[tex]=>\frac{a}{(x+1)}+\frac{b}{(x-4)}=\frac{(a+b) x-4 a+b}{(x+1)(x-4)}[/tex]
[tex]\text {On substituting } \frac{a}{(x+1)}+\frac{b}{(x-4)}=\frac{(a+b) x-4 a+b}{(x+1)(x-4)} \text { in equation } 1 \text { we get }[/tex]
[tex]\frac{(x-1)}{(x+1)(x-4)}=\frac{(a+b) x-4 a+b}{(x+1)(x-4)}[/tex]
On multiplying both sides by (x+1)(x-4) we get
[tex]\frac{(x-1)}{(x+1)(x-4)} \times(x+1)(x-4)=\frac{(a+b) x-4 a+b}{(x+1)(x-4)} \times(x+1)(x-4)[/tex]
[tex]\Rightarrow x-1=(a+b) x-(4 a-b)[/tex]
On comparing coefficient of x and constant term separately, we get
a + b = 1 and 4a - b = 1
On adding the two equations we get
a + b + 4a - b = 1 + 1
=> 5a = 2
=> [tex]a = \frac{2}{5}[/tex]
[tex]\text {Substituting } \mathrm{a}=\frac{2}{5} \text { in equation } a+b=1, \text { we get }[/tex]
[tex]\begin{array}{l}{\frac{2}{5}+b=1} \\\\ {\Rightarrow b=1-\frac{2}{5}=\frac{3}{5}}\end{array}[/tex]
So the value of a and b in given expression must be [tex]\frac{2}{5} \text { and } \frac{3}{5}[/tex] so that given equality becomes identity.
You need at least $535 to go on a trip to California. You have already saved $200.
You decide to save an additional $25 per week. Which inequality shows the number of
weeks, w, you need to save to be able to go on the trip?
The inequality which shows the number of weeks, w, you need to save to be able to go on a trip is 25w + 200 ≥ 535.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Total amount needed to go for a trip to California = $535
Already saved amount = $200
You decide to save an additional $25 per week.
Let w be the number of weeks needed to save $25 to get the amount needed to go for trip.
These saved amounts must be at least $535 to go for trip.
The amount saved after w weeks is 25w
Total saved amount = 200 + 25w
This saved amount must be ≥ 535.
So the inequality is 200 + 25w ≥ 535.
Hence the inequality which represents the amount need to save to go for trip is 200 + 25w ≥ 535.
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11. A biologist tracked the growth of a strain of bacteria, as shown in
the graph.
a. Explain why the relationship represented by the graph is a
function.
There are no repeated
hamber
b. What If? Suppose there was the same number of bacteria for two consecutive hours. Would the graph still represent a Function? Explain...
In a function, each "x" can only have one "y" number. A relation can still be a function if a y-value has more than one x-value.
Answer:
11. a)
The relationship represented by the graph is a function because it passes the vertical line test (VLT). Any vertical line you pass through the graph, it only "hits" one spot on the graph. For a relation to be a function, each x-value can only have one y-value. This means no hour can have two different amounts of bacteria.
b)
If there were the same number of bacteria for two consecutive hours, the graph would still represent a function. In this case, two values for "y" will have more than one value for "x". Although, each x-value still only has one y-value, so it's still a function.
How many solutions does the following have: 14(z+3) = 14z + 21
Answer: this equation has no solutions ,I just got it correct
Step-by-step explanation:
Answer:
No solutions
Step-by-step explanation:
Khan Academy says its right
Franco read 3/8 of a chapter of his history book in 1/5 of an hour. At this rate, how many chapters of his history book can he read in 1 hour?
Answer:
1 and 7/8 chapter
Step-by-step explanation:
1 ÷ 1/5 = 5
3/8 x 5 = 15/8 or 1 7/8
Answer:
1 7/8 chapters
Step-by-step explanation:
I had a test with this question.2 Points
Which of the items below is not an example of a fixed cost?
O
A. Packaging costs
O
B. Internet access fee
O
C. Monthly rent
O
D. Weekly fixed electricity costs
STI
Answer:
A. packaging costs
Step-by-step explanation:
Packaging costs woupd change based on how many products are being shipped. The other payments are fixed because they are the same amount paid regularly. Packaging would be considered a variable cost.
Internet access fee is not an example of a fixed cost.
What is Fixed Cost?The fixed cost definition states that businesses incur a cost that does not change positively or negatively with the number of goods sold or services given.
A fixed cost is a cost that remains constant regardless of production or sales volume.
Examples of fixed costs include monthly rent, packaging costs, and weekly fixed electricity costs.
Internet access fee is not an example of a fixed cost since it fluctuates based on usage.
The cost of internet access fee will increase or decrease depending on the amount of data used or the duration of usage.
Hence, Internet access fee is not an example of a fixed cost.
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-(2x+2)-1= -x -(x+3)
Answer:
[tex]x \in \mathbb \: R[/tex]
Step-by-step explanation:
The given equation is:
[tex] - (2x + 2) - 1 = - x - (x + 3)[/tex]
We expand to get:
[tex] - 2x - 2 - 1 = - x - x - 3[/tex]
We group like terms to get:
[tex] - 2x + x + x = - 3 + 1 + 2[/tex]
We combine the like terms to obtain:
[tex] - 2x + 2x = - 3 + 3[/tex]
[tex] 0 = 0[/tex]
This is always true therefore the solution is infinite.
A store sells rope by the meter. The equation p=0.8L represents the price p(in dollars) of a piece of nylon rope that is L meters long.
A. How much does the nylon cost per meter?
B. How long is a piece of nylon rope that costs $1.00?
The cost of the nylon rope is $0.8 per meter. For $1, you can purchase 1.25 meters of nylon rope.
Explanation:The given equation is p=0.8L. Here, 'p' stands for the price in dollars and 'L' is the length of the nylon rope in meters.
A. To determine the cost per meter, we look at the coefficient in front of 'L' in our equation. Here, it is 0.8, signifying that the nylon rope costs $0.8 per meter.
B. To find out the length of rope that could be bought for $1, we use the equation by setting 'p' equal to 1 and solving for 'L'. Doing this gives us 'L' = 1 / 0.8 which equals to 1.25 meters.
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given a system of equations, list three ways that we can write new equations that can be used to create equivalent systems
New equations for a system can be written by interacting (adding or subtracting) the given equations, using substitution to insert an equation into another, or scaling an equation by multiplying it by a constant.
Explanation:When working with a system of equations, there are multiple ways in which we can write new equations that create equivalent systems. Here are three methods:
Interaction: This involves adding or subtracting the given equations in a way that eliminates one of the variables, forming a new equation. For example, if we have 2x + 3y = 9 and 4x + 6y = 18, adding the equations will give another valid equation for the system: 6x + 9y = 27. Substitution: In this method, one of the equations is solved for one variable (if possible), then that expression is substituted into the other equation, giving a new equation. For instance, from x = 3y - 2, substituting x into the second equation in the system will result in a new equation. Scaling: This involves multiplying an entire equation by a constant to form a new equation. If we multiply the equation 2x + 3y = 9 by 2, we obtain 4x + 6y = 18, which is valid for the system. Learn more about System of Equations here:
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Final answer:
To create equivalent systems of equations, one can use scaling to multiply an equation by a non-zero constant, substitution to replace variables with equivalent expressions, or elimination through addition or subtraction to reduce the number of variables.
Explanation:
When dealing with a system of equations, there are several methods to create equivalent systems, which effectively means rewriting the equations without changing the solution set. One common approach to achieve this is by using the following techniques:
Scaling: Multiplying an entire equation by a non-zero constant. This changes the coefficients but not the solutions.
Substitution: Replacing one variable with an equivalent expression derived from another equation in the system.
Elimination (Addition or Subtraction): Adding or subtracting equations from each other to eliminate one of the variables, effectively reducing the number of variables to solve for.
These methods allow us to simplify complex systems or prepare them for other solving techniques, such as matrix inversion or graphical representation.
I need a word problem of 5 * 8 equals 40
Word problem - Jose played soccer for 5 hours every afternoon for 8 days. How many hours did Jose play soccer in all?
So this problem is about Jose and the amount of time he spends playing soccer.
Next, let's pick out what we know and what we want to find out.
We know that Jose played soccer for 5 hours every afternoon for 8 days. We want to find out how many hours of soccer he played in all so we need to multiply.
We multiply the amount of time he spent playing soccer each afternoon which is 5 hours by the number of days which is 8 days.
(8) (5) = 40
This means that Jose played 40 hours of soccer in all.
write a polynomial function, p(x) with degree 3 that has p(7)=0
Answer:
[tex]p (x) = x^{3} - 21x^{2}+ 147x - 343[/tex]
is the required polynomial with degree 3 and p ( 7 ) = 0
Step-by-step explanation:
Given:
p ( 7 ) = 0
To Find:
p ( x ) = ?
Solution:
Given p ( 7 ) = 0 that means substituting 7 in the polynomial function will get the value of the polynomial as 0.
Therefore zero's of the polynomial is seven i.e 7
Degree : Highest raise to power in the polynomial is the degree of the polynomial
We have the identity,
[tex](a -b)^{3} = a^{3}-3a^{2}b +3ab^{2} - b^{3}[/tex]
Take a = x
b = 7
Substitute in the identity we get
[tex](x -7)^{3} = x^{3}-3x^{2}(7) +3x(7)^{2} - 7^{3}\\(x -7)^{3} = x^{3}-21x^{2} +147x - 343[/tex]
Which is the required Polynomial function in degree 3 and if we substitute 7 in the polynomial function will get the value of the polynomial function zero.
p ( 7 ) = 7³ - 21×7² + 147×7 - 7³
p ( 7 ) = 0
[tex]p (x) = x^{3} - 21x^{2}+ 147x - 343[/tex]
A polynomial function with degree 3 and P(7)=0 can be written as p(x) = a(x - 7)(x - r2)(x - r3), where r2 and r3 can be any real number and a is any non-zero real number.
Explanation:The student has asked for a polynomial function with a degree of 3 such that P(7) equals 0. By definition, a polynomial function of degree n with given roots can be written as:
p(x) = a(x - r1)(x - r2)... (x - rn)
Since we have been given that P(7)=0 , we can choose 7 as one root, but the other roots can be chosen arbitrarily. So, we can create a polynomial function like below:
p(x) = a(x - 7)(x - r2)(x - r3)
Where r2 and r3 can be any real number and a is any non-zero real number. For example, if we choose r2=1, r3=2 and a=1. The function would be:
p(x) = 1*(x - 7)(x - 1)(x - 2) = ([tex]x^3 - 10x^2[/tex] + 29x - 14)
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Marco needs $57 to buy new basketball shoes. If Marco earns $3 per day working and already has $12 saved, which equation shows how many days Marco must work before he can afford the shoes?
Answer:
57=12+3d
d=number of days worked
Answer:
(57-12)3/x=15 days
x=57-12
Write the equation of the line in slope intercept form that contains the point (-2,-1) and is perpendicular to the graph of y=-2x-3
The required equation of line is:
[tex]y = \frac{1}{2}x[/tex]
Step-by-step explanation:
Given equation of line is:
y=-2x-3
The coefficient of x is the slope of line as the equation is in slope intercept form
Let m1 be the slope of given graph of line
So,
[tex]m_1=-2[/tex]
The product of slopes of perpendicular lines is -1
Let m2 be the slope of required line
Then
[tex]m_1.m_2 = -1\\-2 . m_2 = -1\\m_2 = \frac{-1}{-2}\\m_2 = \frac{1}{2}[/tex]
the slope-intercept form of line is:
[tex]y=m_2x+b[/tex]
Putting the value of slope
[tex]y=\frac{1}{2}x+b[/tex]
To find the value of b, putting the given point (-2,-1) in equation
[tex]-1=\frac{1}{2}(-2)+b\\-1 = -1 +b\\-1+1 = b\\b = 0[/tex]
Hence,
The required equation of line is:
[tex]y = \frac{1}{2}x[/tex]
Keywords: Equation of line, slope-intercept form
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Lester needs to add 2/3 of a cup of flour. He only has a 1/3 cup measure. How many scoops of flour does Lester need to add
Answer:
2 scoops
Step-by-step explanation:
Lester needs to add 2 scoops of flour of 1/3 cup measure.
We have Lester who needs to add 2/3 of a cup of flour but he only has a 1/3 cup measure.
We have to find out how many scoops of flour does Lester need to add.
A guy named Bruce wants a total of 100 grams of Protein powder in the bowl. He only has a 10 grams cup to measure and add. How many scoops of powder he need to add?Assume the number of scoops = x
Then -
10x = 100
x = 10
According to question, we have -
Amount of flour needed by Lester = 2/3
Size of Cup measure = 1/3
Assume that the the number of scoops of protein powder be y.
Then -
[tex]\frac{y}{3} = \frac{2}{3} \\\\y = \frac{2}{3} \times 3\\\\[/tex]
y = 2
Hence, Lester needs to add 2 scoops of flour 1/3 cup measure.
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What is the volume of a cone with diameter 12 centimeters and height 4 centimeters?
Answer:
48pi or about 150.8 cm^3
Step-by-step explanation:
volume of cone = 1/3 * pi * r^2 * h
r = 12/2 = 6
1/3 (6^2) (4) pi = 48pi
48pi ~= 150.8 cm^3
Answer: 150.8 cm^3
Step-by-step explanation: The volume formula is V=πr^2(h/3). Once you plug in the radius (half the diameter) and the height, you solve the equation and get the answer of 150.8 cm^3
Simplify (x − 4)(3x2 − 6x + 2). 3x3 + 6x2 − 22x + 8 3x3 − 18x2 + 26x − 8 3x3 − 18x2 − 22x − 8 3x3 + 6x2 + 22x + 8
Answer:
3x^3-18x^2+26x-8
Step-by-step explanation:
(x-4)(3x^2-6x+2)
3x^3-6x^2+2x-12x^2+24x-8
3x^3-18x^2+26x-8
Answer:
3x^3-18x^2+26x-8
Step-by-step explanation:
(x-4)(3x^2-6x+2)
3x^3-6x^2+2x-12x^2+24x-8
3x^3-18x^2+26x-8
What is equivalent to 5/9
Answer:
10/18
Step-by-step explanation:
U only asked for what is equivalent
Answer:
10/18, 15/27, 20/36, 25/45, 30/54, 35/63, 40/72, 45/81, 50/90, 55/99, 60/108.
Step-by-step explanation:
The universal gas law, pV = nRT, describes the relationship among the pressure, volume, and temperature of a gas.
Answer:
R = 8.31
Step-by-step explanation:
From the table choose a corresponding amount for Volume and pressure. Plug it into the equation and solve for R.
Choosing the second row V = 16.62 and p = .5
p = R/V
.5=R/16.62
multiply both sides by 16.62 to isolate R
16.62(.5) = R
R = 8.31
Answer:8.31
Step-by-step explanation: