SOLUTION
TO SHOW THAT;
[tex]1-\frac{1}{4}=\frac{3}{4}[/tex]Step 1:
[tex]\begin{gathered} \frac{1}{1}-\frac{1}{4} \\ \frac{4-1}{4}=\frac{3}{4} \end{gathered}[/tex]TO SHOW THAT;
[tex]1-\frac{1}{3}=\frac{2}{3}[/tex]Step 2:
[tex]\frac{1}{1}-\frac{1}{3}=\frac{3-1}{3}=\frac{2}{3}[/tex]I got stuck with my math homeworkI was trying to figure these equations for 2 HOURS STRAIGHT (i gave up )
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given equation
[tex]1-5\left(x-1\right)=2\left(2x-1\right)-x[/tex]STEP 2: Simplify the equation
Expand the two sides of the equation
[tex]\begin{gathered} 1-5(x-1)=2(2x-1)-x \\ 1-5x+5=4x-2-x \end{gathered}[/tex]STEP 3: Simplify both sides
[tex]\begin{gathered} -5x+6=3x-2 \\ \mathrm{Subtract\:}6\mathrm{\:from\:both\:sides} \\ -5x+6-6=3x-2-6 \\ -5x=3x-8 \\ \mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides} \\ -5x-3x=3x-8-3x \\ -8x=-8 \\ \mathrm{Divide\:both\:sides\:by\:}-8 \\ \frac{-8x}{-8}=\frac{-8}{-8} \\ \\ \therefore x=1 \end{gathered}[/tex]Hence, the value of x is 1
Write a quadratic function in standard form whose graph passes through the given points1. (-1,5), (0,3), (3,9)
The Standard Form of a Quadratic Function:
[tex]\text{ y = ax}^2\text{ + }bx\text{ + c}[/tex]Using the given points (-1,5), (0,3), and (3,9), let's substitute each point to the equation.
At (-1,5):
[tex]\text{ y = ax}^2\text{ + bx + c }\rightarrow5=a(-1)^2\text{ + b(-1) + c}[/tex][tex]\text{ 5 = a - b + c}[/tex]At (0,3):
[tex]\text{ y = ax}^2\text{ + bx + c }\rightarrow3=a(0)^2\text{ + b(0) + c}[/tex][tex]\text{ 3 = c}[/tex]At (3,9):
[tex]\text{ y = ax}^2\text{ + bx + c }\rightarrow9=a(3)^2\text{ + b(3) + c}[/tex][tex]\text{ 9 = 9a + 3b + c}[/tex]We now get these equations:
5 = a - b + c ; 3 =c; 9 = 9a + 3b + c
Let's determine the value of a, b and c. We get,
Substituting 3 = c to 5 = a - b + c,
[tex]\text{ 5 = a - b + c }\rightarrow\text{ 5 = a - b + 3 }\rightarrow\text{ a - b = 2}[/tex][tex]\text{ b = a - 2}[/tex]Let's substitute 3 = c and b = a - 2 to 9 = 9a + 3b + c,
[tex]\text{ 9 = 9a + 3b + c }\rightarrow\text{ 9 = 9a + 3(a-2) + 3}[/tex][tex]\text{ 9 = 9a + 3a - 6 + 3 }\rightarrow\text{ 12a = 9 + 6 - 3 }\rightarrow\text{ 12a = 12}[/tex][tex]\text{ a = }\frac{12}{12}\text{ = 1}[/tex]Since a = 1, let's solve for the value of b which is b = a - 2.
[tex]\text{ b = a - 2 }\rightarrow\text{ b = 1 - 2}[/tex][tex]\text{ b = -1}[/tex]Since we've identified that a = 1, b = -1 and c = 3, let's substitute the values to the standard form of a quadratic function to be able to make the equation.
[tex]\text{ y = ax}^2\text{ + bx + c }\rightarrow y=(1)x^2\text{ + (-1)x + (3)}[/tex][tex]\text{ y = x}^2\text{ - x + 3}[/tex]Therefore, the quadratic function in a standard form whose graph passes through the given points (-1,5), (0,3), (3,9) is y = x^2 - x + 3.
Situation: A 40 gram sample of a substance that's used for drug research has a k-value of 0.1472. N = Noekt No = initial mass (at time t = 0) N = fhass at time t k = a positive constant that depends on the substance itself and on the units used to measure time t = time, in days
t = time, in days
k = 0.1472
N = 40 gram
[tex]40=N_0e^{(0.1472)t}[/tex]What is the equation of the line that is parallel to the line y = x + 4 and passes through the point (6, 5)?y = x + 3y = x + 7y = 3x – 13y = 3x + 5
You have to find a line that is parallel to y=x+4 and passes through the point (6,5)
Parallel lines always have the same slope.
The slope of the line is the coefficient that multiplies the x term, in this case, there is no number multiplying "x" but that does not mean that the line has no slope, turns out that the line has a slope equal to "1" when the variables (letters in an equation) are "alone" the coefficient is 1
So for both lines, the slope is
[tex]m=1[/tex]Using the slope and the known point of the line, you can determine the equation of said line by using the "point-slope" form
[tex]y-y_1=m(x-x_1)[/tex]Where
(x₁,y₁) are the coordinates of a point of the line
m is the slope
Replace the coordinates of the point and the slope in the formula
[tex]y-5=1(x-6)[/tex]Next is to solve for y to express it in slope-intercept form
[tex]\begin{gathered} y-5=1\cdot x-1\cdot6 \\ y-5=x-6 \\ y-5+5=x-6+5 \\ y=x-1 \end{gathered}[/tex]The equation for a line parallel to y=x+4 that passes through point (6,5) is
[tex]y=x-1[/tex]Help mee pleasee!!
thank you <3
As a function, the cost C(x) of publishing the newsletter would be C(x) = 75.00 + 0.25x, where the number of copies printed is x.
What is a function?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
We have been given that the cost of producing a newsletter is an initial charge of $75.00 for formatting and editing plus $0.25 for printing each copy.
Let the number of copies printed x and the cost C(x) of printing the newsletter as a function
As per the given data, the function would be as:
C(x) = 75.00 + 0.25x
Therefore, the cost C(x) of printing the newsletter as a function expressed would be C(x) = 75.00 + 0.25x.
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1 - Determine whether the given function is even, odd, or neither.a. [tex]f(x) = x ^{3} \times x ^{2} - 4[/tex]b. [tex]f(x) = 4x^{2} + x^{4} [/tex]2 - Evaluate the piece wise function at the given value of the independent variable. (picture)
We have a piecewise function that we should evaluate based on the condition of the independent variable
It is the value of the independent variable that will dictate which of the two equations to use
We can see that the value of the independent variable given is -3
Mathematically, -3 is not greater than 3; so this means the value of the independent variable given falls within the domain of the second part of the piece-wise function
Hence, we are to evaluate f(x) = -(x + 1) at the point x = -3
Thus;
f(-3) = -(-3 + 1)
f(-3) = -(-2)
f(-3) = 2
Find the equation of the given line,Find the equation of the line passing through (2, 1) with slope 3.у =
Tori, this is the solution to the exercise:
Step 1: Let's remember that this is a case that we can solve using the following equation form:
y = mx+b, where m is the slope and b is the y-intercept.
Step 2: Solving for b:
y = mx + b
We replace x and y with the coordinates:
1 = 3 * 2 + b
1 = 6 + b
b = 1 - 6
b = - 5
Step 3: Therefore, the equation of the line that passes through the point (2,1) with a slope of 3 is:
y = 3x - 5
Write an equation of the circle with center (6,8) and radius 7
Let’s find the equation of a circle with
radius r = 7 and center (h,k) =(6,8).
By definition, an equation of the circle with center (h,k) and radius r is
[tex](x-h)^2\text{ }+\text{ (}y-k)^2\text{ = }r^2[/tex]This is called the standard form for the equation of the circle. Then, in our case, replacing the data we have, we should have:
[tex](x-6)^2\text{ }+\text{ (}y-8)^2\text{ = 7}^2\text{ = 49}[/tex]so, we can conclude that the equation of the circle with center (6,8) and radius 7 is :
[tex](x-6)^2\text{ }+\text{ (}y-8)^2\text{ }^{}\text{ = 49}[/tex]A new energy drink advertises 177 calories in for 12 ounces. How many calories are in 20 ounces of the drink? _ calories
We can use the rule of three to solve this question, first, we need to build our relation, remeber that we need to put calories on one side and ounces on the other:
[tex]\begin{gathered} 177\rightarrow12 \\ x\rightarrow20 \end{gathered}[/tex]Now we need to solve it for x, we can build it as a fraction
[tex]\frac{177}{x}=\frac{12}{20}[/tex]Now we can solve it for "x", let's do a cross multiplication:
Therefore
[tex]12x=177\cdot20[/tex]We can divide by 12
[tex]x=\frac{177\cdot20}{12}[/tex]Now we can just to the calculus and we will have the value of x, if we do it we get
[tex]x=295\text{ calories}[/tex]Therefore, there are 295 calories in 20 ounces of drink
help meeeeeeeeee pleaseee
Answer:
I think this would convert to (-infinity,-4).
Step-by-step explanation:
Forgive me if I'm wrong, but this is the best i could remember from when I was learning this.
.name three fractions that are equivalent to 2/5
Answer:
4/10, 20/50, and 40/100
Hope this is helpful
the cost of manufacturing and selling x units of a product is c-7x+11 and the corresponding revenue R is R - x^2 - 15 find the number of the units needed to earn below and above the btrak even value
We know:
Profit = Revenue - Cost
When Revenue is equal to Cost, we have the break-even point.
Let's equate revenue and cost:
[tex]\begin{gathered} R=C \\ x^2-15=7x+11 \end{gathered}[/tex]To find the value of x, we can take all terms to LHS (Left-Hand-Side) and use the quadratic formula. The process of finding x is shown below:
[tex]\begin{gathered} x^2-15=7x+11 \\ x^2-15-7x-11=0 \\ x^2-7x-26=0 \\ u\sin g\text{ quadratic formula,} \\ x=-2.7,9.7 \end{gathered}[/tex]We can't have a negative value, so we disregard x = -2.7
What we have is
x = 9.7
So,
For 10 units (and above) sold, we will have a profit.
For 9 units (and below) sold, we will incur a loss.
Randall wants to mix 54 Ib of nuts worth $1 per lb with some nuts worth $5 per Ib to make a mixture worth $4 per lb. How many pounds of $5 nuts must he use?
Let:
x = no. of lb of $5 nuts required.
resulting mixture = x + 54
Hence:
[tex]54\times\text{\$1}+\text{ \$5x}=(x+54)\times\text{\$4}[/tex]Solving for x:
[tex]\begin{gathered} 54+5x=4x+216 \\ 5x-4x=216-54 \\ x=162 \end{gathered}[/tex]ANSWER
Randall must use 162 lb of $5 nuts
try to write an equation to describe the relationship between the stage number N and the number of squares S.
Let's first identify the number of squares in each stage:
Stage 1: 7 squares.
Stage 2: 14 squares.
Stage 3: 21 squares.
If we notice the sequence, we notice that it increases by 7 per stage, therefore:
Stage N: N*S
Where S is always equal to 7.
Foe example, in the stage 4:
Stage 4: 4*7 = 28 squares.
The equation is:
7*N
find the image of P(7,7) under a dilation with scale factor 1/2 and center of dilation (1,3)
Given,
The coodinates of the points are P(7,7).
The scale factor is 1/2.
The coordinates of center of dilation is (1,3).
In the operation described here, it is the vector (center of dilation→ similar point) that will get multiplied by a factor 1/2.
The vector from the centre (1,3) to point (7,7) has coordinates (7,7) - (1,3)
[tex]((7-1),(7-3))=(6,3)[/tex]Now, dilated the coordinates by the scale factor of 1/2 then,
[tex]\frac{1}{2}(6,3)=(3,\frac{3}{2})[/tex]Image of the point is at,
[tex]\begin{gathered} (3,\frac{3}{2})=(3+1,\frac{3}{2}+3) \\ =(4,\frac{9}{2}) \end{gathered}[/tex]Hence, the coordinates of the image is (4,9/2).
Find c if a=2.93 mi,b=3.95 mi and c=40.3 degrees C=Round your answer to 3 decimal places
Using the law of cosines, we have the following relation between the measures of this triangle:
[tex]c^2=a^2+b^2-2ab\cos C[/tex]Plugging the given values, we have:
[tex]c^2=(2.93)^2+(3.95)^2-2(2.93)(3.95)\cos40.3^o[/tex]Solving for c, we have our answer:
[tex]c\approx2.556[/tex]The measure of c is 2.556 miles.
I can find percentages and values using the 68-95-99.7 rule, z-scores, and the standard normal distribution.answer the questions only if you know the answer please
ANSWER and EXPLANATION
1) We want to find the z score for a student who had a GPA of 3.8.
To do this, we have to apply the formula for z score:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where:
x = score/GPA
μ = mean
σ = standard deviation
Therefore, the z score for the student with a GPA of 3.8 is:
[tex]\begin{gathered} z=\frac{3.8-3}{0.6} \\ z=\frac{0.8}{0.6} \\ z=\text{1}.33 \end{gathered}[/tex]2) The z score is a measure of how far away a data point is from the mean, in other words, it is a measure of how many standard deviations a data point is above or below a mean.
We can find how many standard deviations there are in a z score of -2.4 by dividing -2.4 by the standard deviation (0.6):
[tex]\begin{gathered} \frac{-2.4}{0.6} \\ -4 \end{gathered}[/tex]Therefore, since the z score is negative, we can conclude that the student's GPA is 4 standard deviations below the mean value.
This shows a scale drawing of Javier's room. The scale of his room is 1 cm = 2 ft. 5 cm 6.5 cm How much carpet does Javier need to purchase to completely cover his floor? A 130 square feet B. 120 square feet C. 111 square feet
Answer:
A 130 ft²
Step-by-step explanation:
if I understand this right, then the scale is 1 cm on a drawing is 2 ft in reality.
the room in the drawing measures 5 cm × 6.5 cm.
the question about how much carpet is needed is the question about the area of the floor of the rectangle room.
first e need to get the real measurements :
5 cm = 5×1 cm = 5 × 2 ft = 10 ft
6.5 cm = 6 5×1 cm = 6.5×2 ft = 13 ft
so, the real room is 10 ft × 13 ft.
and the area is therefore 130 ft².
Connect the points to form a rectangle. What is the perimeter of the rectangle
The answer is option A 34 units.
We need to count the distance between the points and then add them to get the perimeter.
L and M are 5 units away, as well as X from J
L and X are 12 units away, as well as M from J
Now we can add the distances:
5 + 5 + 12 + 12 = 34
THen the perimeter is 34 units
PLSSS HELPPPPP IM RLYYYYY CONFUSEDDDDDD
Answer:
Top Left: -6
Top Right: -x
Bottom Left: 12x
Bottom Right: 2x^2
Trinomial: 2x^2 + 11x - 6
Step-by-step explanation:
Hello! Let's help you with your question here!
So, box method. From your question, the process is pretty easy. It would require a bit more work when factoring a trinomial.
The equation in question is already factored which is very useful, now it's a matter of the values in the box. I am on the assumption that the two top boxes and the two left boxes are filled in for you and you just need to fill the middle (if that isn't the case, do let me know). To just fill the boxes in the middle, evaluate it like you would multiplying rows and columns. So, it would be as such:
6 x
-1 -6 -x
2x 12x 2x^2
In terms of simplifying, we use FOIL to expand it out into a trinomial and collect like terms. Therefore, it becomes:
[tex](x+6)(2x-1) = (x*2x)+(x*(-1))+(6*2x)+(6*(-1))[/tex]
[tex]= 2x^2 + (-x) + (12x) + (-6)[/tex]
[tex]=2x^2+11x-6[/tex]
Let me know if there are any questions and if it is wrong, do let me know!
list the transformations
Answer:
on what?
Step-by-step explanation:
Help me to answer the second question with a more detailed process, thank you.
Hence the answer is
Quotient is
[tex]x^2+2x-4[/tex]remainder is 9
Question in picture answer correct
The reason for the statements for the algebraic proof is as follows;
Multiplication property of equalityDivision property of equalityHow to solve equation with reasons?The equation given is as follows:
3x / 6 = 4 . This equation is given.
Therefore,
3x / 6 = 4
Using multiplication property of equality, we will multiply both sides of the equation by 6.
3x / 6 × 6 = 4 × 6
3x = 24
The multiplication property of equality states that when we multiply both sides of an equation by the same number, the two sides remain equal.
Hence,
3x = 24
Using division property of equality, we divide both sides by 3.
3x / 3 = 24 / 3
x = 8
The Division Property of equality says that dividing both sides of an equation by the same number does not affect the equation.
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Jennifer made a cake and brownies. Her cake dish was 8 inches long, 5 inches wide and 2 inches deep. Her brownie tin was 9 inches long, 4 inches and 2 inches deep. Which dish has a larger volume? By how much?
Answer:
The cake is larger by 8 in^3
Step-by-step explanation:
The volume equals the product of the length of all 3 sides, or length * height * width
The volume of the cake is 8in*5in*2in which equals 80 in^3
The volume of the brownie tin is 9in*4in*2in which is 72 in^3
Clearly, the cake has more volume since 80 in^3 > 72 in^3
It is greater by the brownie tin by 80 in^3 - 72 in^3, or 8 cubic inches.
Choose the coefficient closest to 0.Choose the coefficient with the least value.
Explanation:
In the given graph f(x) = a |x| .
The coefficient ''a'' increases the graph of the function will shrink and it will goes to zero.
And when coefficient ''a'' decreases the graph will expands.
The graph in the option C represents the graph below x-axis and the coefficient of |x| will be negative so it will be least value.
Answer: Option C.
Raffi has forgotten to multiply numbers that contain decimals. To multiply 0.4 x 1.34, he ignores the decimals
and multiples 4 x 134 = 536. Explain how Raffi could use estimation to determine where the decimal
point should be placed.
Answer:
.536 would be the correct answer. You could estimate by rounding 1.34 to 1 and 0.4 is close to .5 or 1/2. What is 1/2 of 1 1/2 or .5. This would lead me to place the decimal before the 5.
Step-by-step explanation:
The probability the Shane will sink a foul shot is 80%. If Shane attempts 40 foul shots, what is the probability that he sinks at least 28 shots? Round your answer to the nearest whole percenta-96%b-90%c-95%d-80%
For this problem we have to calculate the probability that x is greater or larger than 28
[tex]\begin{gathered} P(x\ge28)=\Sigma P(x=i) \\ i\text{ goes from 28 to }40 \end{gathered}[/tex]For each i, the probability
[tex]P(x=i)=\frac{40!}{28!\cdot12!}\cdot0.8^i\cdot0.2^{40-i}[/tex]Now computing the sum:
[tex]P(x\ge28)=96[/tex]The answer is 96%
If cost of 15 eggs is ? 75, then find out the cost of 4 frozen eggs
Problem:
If the cost of 15 eggs is $75, then find out the cost of 4 eggs?
Solution:
If the cost of 15 eggs is $75, then each egg cost:
[tex]\frac{\text{\$75}}{15}=\text{ \$5 for each egg}[/tex]thus, 4 eggs cost :
$5 x 4 = $20
then, the correct answer is $20
A Web music store offers two versions of a popular song. The size of the standard version is 2.3 megabytes (MB). The size of the high-quality version is 4.1 MB. Yesterday, the high-quality version was downloaded three times as often as the standard version. The total size downloaded for the two versions was 3796 MB. How many downloads of the standard version were there?
The number of downloads of the standard version is 949.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Two versions of a song.
S = Standard version size = 2.3 MB
H = High-quality size = 4.1 MB
Hgh quality size = 3 x Standard quality size
H = 3 x S
H = 3S ____(1)
The total size downloaded for the two versions was 3796 MB.
This can be written as:
H + S = 3796 ______(2)
From (1) and (2) we get,
3S + S = 3796
4S = 3796
S = 3796/4
S = 949
Now,
From (1),
H = 3S = 3 x 949 = 2847
The number of downloads of the standard version is 949
The number of downloads of the High-quality version is 2847
Thus,
The number of downloads of the standard version is 949.
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. When you are translating a number from scientific notation to standard form, what does the
exponent tell you?
O the number of zeroes to add to the end of the original number
O the number to multiply by the first factor
O the number of places to move the decimal point
O the number of times to multiply the first factor by itself?
Answer:
A. The number of zeroes to add to the end of the original number
Step-by-step explanation:
