Given:
There are given that the slope and the point:
[tex]\begin{gathered} m=-\frac{7}{2} \\ point:\left(-8,-4\right) \end{gathered}[/tex]Explanation:
To find the equation, first, we need to see the formula for slope-intercept form:
So,
From the slope-intercept formula;
[tex]y=mx+b[/tex]Where,
[tex]\begin{gathered} m=-\frac{7}{2} \\ \lparen x,y)=\left(-8,-4\right) \end{gathered}[/tex]Now,
We need to find the value of b by using given information:
So,
Put all the given values into the given slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ -4=-\frac{7}{2}\left(-8\right)+b \\ -4=28+b \\ b=-32 \end{gathered}[/tex]Then,
Put the value of b and m into the slope-intercept form;
So,
[tex]\begin{gathered} y=mx+b \\ y=-\frac{7}{2}x+\left(-32\right) \\ y=-\frac{7}{2}x-32 \end{gathered}[/tex]Final answer:
Hence, the equation of a line is shown below;
[tex]y=-\frac{7}{2}x-32[/tex]Find the slope of each line and then determine if the lines are parallel perpendicular or neither.If a value is not an integer type it in as a decimal rounded to the nearest hundredth.
ANSWERS
• Slope of line 1: ,8
,• Slope of line 2: ,-6
,• The lines are ,neither
EXPLANATION
The slope of a line passing through points (x1, y1) and (x2, y2) is,
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]The points given for line 1 are (-8, -55) and (10, 89). The slope of this line is,
[tex]m_1=\frac{-55-89}{-8-10}=\frac{-144}{-18}=8[/tex]The points given for line 2 are (9, -44) and (4, -14). The slope of this line is,
[tex]m_2=\frac{-44-(-14)}{9-4}=\frac{-44+14}{5}=\frac{-30}{5}=-6[/tex]• If two lines are ,parallel, then they have the same slope.
,• If two lines are ,perpendicular, then their slopes are opposite and reciprocal.
The slopes of these two lines are 8 and -6. These slopes are different and they are neither opposite nor reciprocal. Hence, these lines are neither parallel nor perpendicular.
If f (x) = x² − 1 and g (x) = 4x − 3, find [f o g] (3) .
Answer:
(f ￮ g)(3) = 80
Step-by-step explanation:
evaluate g(3) then substitute the value obtained into f(x)
g(3) = 4(3) - 3 = 12 - 3 = 9 , then
f(9) = 9² - 1 = 81 - 1 = 80
The parking fee at a carnival is $1.50 for kids and $3.00 for adults. The day of the event 1700 people showed up and $3,750.00 was collected. How many children and how many adults attended??
There are 900 children and 800 adults in attendance
How to determine the number of children and adults in attendance?The given parameters are:
Kids fee = $1.50 per kidAdult fee = $3.00 per adultNumber of people = 1700Amount collected = $3,750.00Let the kids be x and the adults be y
So, we have
x + y = 1700
1.5x + 3y = 1750
Make y the subject in x + y = 1700
y = 1700 - x
Substitute y = 1700 - x in 1.5x + 3y = 1750
1.5x + 3(1700 - x) = 3750
So, we have
1.5x + 5100 - 3x = 3750
Evaluate the like terms
1.5x = 1350
Divide
x = 900
Recall that
y = 1700 - x
So, we have
y = 1700 - 900 = 800
Hence, the number of children and adults in attendance are 900 and 800 respectively
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Write 243 as a power using the number 3 as the base
Answer:
[tex]3^5[/tex]
Step-by-step explanation:
Hello! Let's help you with your question here!
So, we want to know 243 as a power using the number 3 as the base. Well, there is an easy way in figuring out to what the power would be.
We have the total and we already have the base. In order to figure out what the power number is, we can essentially just divide 243 by our base number 3, until we get to a point where we can't divide the number by 3 without getting a decimal value! So it would look like this!
[tex]243/3=81[/tex]
[tex]81/3=27[/tex]
[tex]27/3=9[/tex]
[tex]9/3=3[/tex]
[tex]3/3=1[/tex]
Now, it's just a matter of counting how many times we divided by 3 and it turns out we divided the number by 3 5 times! Therefore, we can say that:
[tex]3^5=243[/tex]
Which of these are equivalent to 11/4 choose all that apply
Answer: -11 ÷ 4; 11 ÷ (-4); [tex]\frac{-11}{4}[/tex]; [tex]\frac{11}{-4}[/tex]
Step-by-step explanation:
A negative divided by a negative is a positive.
A positive divided by a negative or a negative divided by a positive is a negative.
Similarities and differences between compound event, mutually exclusive event, overlapping event, independent event, dependent event
Difference between Dependent and Independent event:
[tex]\begin{gathered} Dependent\text{ Event:} \\ The\text{ outcome of one event affects the outcome of the other.} \\ \text{If A and B are dependent events},\text{ then the probability of both occuring is:} \\ P(A\text{ and B)=}P(A)\times P(B|A) \end{gathered}[/tex][tex]\begin{gathered} \text{Independent Event:} \\ The\text{ outcome of one event does not affects the outcome of the other.} \\ \text{If A and B are independent events, then the probability }of\text{ both occuring is:} \\ P(A\text{ and B)=}P(A)\times P(B) \end{gathered}[/tex]Find the value of X in the triangle below use the value to determine the value of the angles and labels up accordingly 6x+4x+2x
Answer: 15
Step-by-step explanation:
Triangle = 180 degrees
So, 6x + 4x + 2x = 180
Next, you combine like terms: 6x + 4x + 2x = 12x
Now, your equation should be 12x = 180
Then, you divided 180 by 12 and you get 15
Answer: x = 15
Write an equation and solve. A number y divided by 5.5 is equal to 86
y is divided by 5.5 and is equal to 86, so:
[tex]\frac{y}{5.5}=86[/tex]Solve for y:
Multiply both sides by 5.5:
[tex]\begin{gathered} y=86\cdot5.5 \\ y=473 \end{gathered}[/tex]D
Question 3
If a car is traveling at 85 mph, how fast is the car traveling in feet per second? Round to 2
decimal places. (Reminder: there are 5280 feet in a mile)
1 pts
Answer:
See below
Step-by-step explanation:
85 mi/hr * 1 hr / 3600s * 5280 ft / mi =
85 * 5280 / 3600 = 124 2/3 ft/s
If f (x) = 3x2 + 5x − 4, then the quantity f of the quantity x plus h end quantity minus f of x end quantity all over h is equal to which of the following?
If a function [f(x) = (3x² + 5x - 4)], then the expression [{f(x + h) - f(x)}/h] will be equal to (3h + 6x + 5).
As per the question statement, a function [f(x) = (3x² + 5x - 4)].
We are required to calculate the value of the expression [{f(x + h) - f(x)}/h].
Since, [f(x) = (3x² + 5x - 4)] given,
Then, [f(x + h) = {3(x + h)² + 5(x + h) -4}]...[substituting (x + h) in place of "x" in the equation {f(x) = (3x² + 5x - 4)}]
Or, [f(x + h) = {3(x² + 2xh + h²) + 5x + 5h - 4}]
Or, [f(x + h) = (3x² + 3h² + 6xh + 5x + 5h - 4)]
Or, [f(x + h) = (3x² + 5x + 3h² + 5h + 6xh - 4)]
Therefore, [{f(x + h) - f(x)}/h]
= [{(3x² + 5x + 3h² + 5h + 6xh - 4) - (3x² + 5x - 4)}/h]
= [{(3x² - 3x²) + (5x - 5x) - (4 - 4) + 3h² + 5h + 6xh}/h]
= [(3h² + 5h + 6xh)/h]
= [h(3h + 6x + 5)/h]
= (3h + 6x + 5)
That is, [{f(x + h) - f(x)}/h] will be equal to (3h + 6x + 5).
Function: In Mathematics, a function is an operator, which when fed with particular inputs, will perform a fixed set and sequence of operations on the input, and produce particular outputs.Expression: Expressions are mathematical statements that consist of a minimum of two terms containing numbers or variables, or both, connected by operator(s) in between, and formed as per arithmetic rules.To learn more about Functions and Expressions, click on the link below.
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Kayden walks 4/5 km to a friends house. Then he and friend walk 1 3/5 km more to go fishing at their favorite pond. How far to Kayden walk all together?
PLEASE HELP THIS IS ON KHAN
Can you please help with 8 I need to finish 8 more packets by tonight
Given the expression below
[tex]\frac{1}{2}(10.4x-2q)-2.8(x-7q)[/tex]Using distributive property, we have
[tex]\frac{1}{2}(10.4x)-\frac{1}{2}(2q)-2.8(x)-2.8(-7q)[/tex][tex]5.2x-q-2.8x+19.6q[/tex]collect like terms
[tex]\begin{gathered} 5.2x-2.8x+19.6q-q \\ \rightarrow2.4x+18.6q \end{gathered}[/tex]Hence, the simplest form of the fraction is 2.4x + 18.6q
write equation In standard form
15( y - 1/3 ) =x
The standard form of the linear equation 15( y - 1/3 ) = x is 3x - 45y = -15.
What is the given equation in standard form?The standard form of a linear equation is expressed as;
Ax + By = C
Where A and B are the coefficient of x and y respectively, C is the constant term.
Given the equation in the question;
15( y - 1/3 ) = x
Multiply both sides by 3
3(15( y - 1/3 )) = 3x
First, apply distributive property to remove the parenthesis.
15( 3y - 1 ) = 3x
45y - 15 = 3x
3x = 45y - 15
Now, move all terms containing variables to the left and side of the equation and reorder the equation in form of Ax + By = C
3x - 45y = -15
Therefore, the standard form of the equation is 3x - 45y = -15.
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Find the zeros by using the quadratic formula and tell whether the solutions are real or imaginary. F(x)=x^2+14x+20.
Find the zeros by using the quadratic formula and tell whether the solutions are real or imaginary. F(x)=x^2+14x+20.
we have that
the quadratic formula is equal to
[tex]x=\frac{-b\pm\sqrt[\square]{b^2-4ac}_{}}{2a}[/tex]where
a=1
b=14
c=20
substitute the given values in the formula
[tex]\begin{gathered} x=\frac{-14\pm\sqrt[\square]{14^2-4(1)(20)}_{}}{2(1)} \\ \\ x=\frac{-14\pm\sqrt[\square]{116}_{}}{2} \\ \\ x1=\frac{-14+\sqrt[\square]{116}_{}}{2} \\ \\ x2=\frac{-14-\sqrt[\square]{116}_{}}{2} \end{gathered}[/tex]x1 and x2 are the zeros of the quadratic equation
The solutions are real numbers
6. The water level of a stream has been
rising at a constant rate all day. When
the water depth was measured at noon,
it was 3 inches deep. By 4 P.M., it was 4
inches. If x represents the number of
hours since noon and y represents the
water level in inches, sketch the
relationship between x and y.
The sketch for the equation, y = 1/4x + 3, which represents the relationship between x and y is given in the diagram below.
How to Write the Equation of a Relationship?If x and y represents two variables of a relationship, and the starting value is represented as "b", the unit rate/constant rate as "m", the equation of the relationship between x and y, in slope-intercept form, is: y = mx + b.
From the information, the two points we can derive for the relationship between x and y are:
(0, 3) which is the water level at noon.(4, 4) which is the water level at 4 pm.Thus, we would have the following:
Constant rate/unit rate (m) = change in y / change in x = (4 - 3)/(4 - 0) = 1/4
y-intercept of the equation is the initial depth of water (b) = 3
To write the equation, substitute m = 1/4 and b = 3 into y = mx + b:
y = 1/4x + 3
The sketch for the relationship between x and y is shown in the diagram below.
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The relationship between the depth of water and time can be represented
as y = (1/4)x + 3.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given, The water level of a stream has been rising at a constant rate all day.
When the water depth was measured at noon, it was 3 inches deep.
By 4:00 pm, it was 4 inches.
From this, we can conclude the two points are (0, 3) and (4, 4).
Slope(m) = (y₂ - y₁)/(x₂ - x₁).
slope(m) = (4 - 3)/(4 - 0).
Slope(m) = 1/4.
∴ 3 = (1/4)×0 + b.
b = 3.
So, y = (1/4)x + 3.
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What’s the correct answer answer asap for brainlist
Answer:
Iron
Step-by-step explanation:
Just learned about this
Answer:
C. Hydrogen
Step-by-step explanation:
Carbon, Hydrogen, Oxygen, and Nitrogen are most commonly found in lipids.
if this helps you, pls leave a heart. if it dosent, im so sorry. :(
one pump can empty a pool in 2 days, whereas a second pump can empty the pool in 11 days. How long will it take the two pumps, working together, to empty the pool?It will take the two pumps ___ days to empty the pool together.
Let x be the number of days it will take the two pump to empty the pool together
[tex](\frac{1}{2}+\frac{1}{11})\times x=1[/tex][tex](\frac{11+2}{22})\times x=1[/tex][tex]\frac{13}{22}x=1[/tex]Multiply both-side by 22/13
[tex]x=\frac{22}{13}[/tex][tex]=1.6923[/tex]Give one example of how a learner on level 1 will define a rectangle.
Step-by-step explanation:
Level 1 Analysis: Describe shapes on the basis of their properties. Students learn what properties each shape has. Example: “All rectangles have 4 sides with opposite sides equal and parallel, and 4 right angles.” or “Perpendicular lines form a right angle.”
A learner on basic level one will define a rectangle by four straight lines at right angles.
A rectangle has four straight lines in which any two opposite sides are parallel and equal in length to each other and any two adjacent sides are perpendicular to each other making a right angle in between the sides.
It is a four-sided polygon having four angles in which all the internal angles are of 90 degree each. One can make a rectangle by taking 2 sets of two sticks different in length and arrange the equal sides opposite to each other making an angle of 90 degree between every adjacent side.
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A ball is dropped from a height of 6 feet. With each bounce, the ball rebounds to a height that is three-quarters as high as the previous bounce. Represent the height to which the ball rises after it hits the floor for the nth time using a recursive formula and an explicit formula. Recursive Formulas: anar.an-1 or an+1 =rean Explicit Formula: an = Q .m-1 Represent (using sigma notation) the total vertical distance the ball has traveled when it hits the floor for the fifth time. Calculate this distance. ? Σ ? k=? Sn 4,(1-r") 1-r
We know that each time the ball bounces it travels a distance of 3/4 the original height, that means that for each bounce the ball will rise:
[tex]a_n=\frac{3}{4}a_{n-1}[/tex]where a_n is the height of the nth bounce and a_(n-1) is the bounce n-1 (the previous one).
Now, from this formula we know that:
[tex]a_1=\frac{3}{4}a_0=\frac{3}{4}\cdot6=\frac{9}{2}[/tex]Therefore the explicit formula for the height of the nth bounce is:
[tex]\begin{gathered} a_n=\frac{9}{2}(\frac{3}{4})^{n-1} \\ =\frac{9}{2}\cdot\frac{4}{3}(\frac{3}{4})^n \\ =6(\frac{3}{4})^n \end{gathered}[/tex]Then:
[tex]a_n=6(\frac{3}{4})^n[/tex]Now, to find the total distance it travels by the fifth bounce we follow:
The first time the ball hits the ground it has traveled a distance of 6 ft.
Now, for the second bounce we have:
[tex]6(\frac{3}{4})+6(\frac{3}{4})=12(\frac{3}{4})[/tex](one distance up and one distance down).
For the third bounce we have:
[tex]6(\frac{3}{4})(\frac{3}{4})+6(\frac{3}{4})(\frac{3}{4})=12(\frac{3}{4})^2[/tex]If we continue this process we notice that the ball will travel a total distance of:
[tex]6+12(\frac{3}{4})+12(\frac{3}{4})^2+12(\frac{3}{4})^4+\ldots\text{..}[/tex]but this can be written (for an infinity number of bounces) as:
[tex]\begin{gathered} 6+12\sum ^{\infty}_{n\mathop=0}(\frac{3}{4})^{n+1} \\ =6+12(\frac{3}{4})\sum ^{\infty}_{n\mathop=0}(\frac{3}{4})^n \\ =6+9\sum ^{\infty}_{n\mathop=0}(\frac{3}{4})^n \end{gathered}[/tex]As we said this is for an infinity of bounces if we like only five bounces then we have:
[tex]6+9\sum ^5_{n\mathop=0}(\frac{3}{4})^n[/tex]Now to find the distance in this case we do the sum and we get appoximately 35.5928 feet.
In a survey, 100 people were asked if they smoke and whether or not they exercise regularly ( more than twice a week). The results are summarized in the table below.
Explanation:
a) The % of people that do not smoke, regardless of whether or not they exercise.
= No. of people that dont smoke/total number of people
= 76/100
Answer: 76% of people do not smoke.
b) % of people that do not exercise regularly, regardless of whether or not they smoke:
= 84/100
Answer = 84% do not exercise regularly
Help me plsss I will mark brainliest
Solve for n.
−2(n − 4.5) > 11
n > 1
n < 1
n > −1
n < −1
Answer:
D. n < −1
Step-by-step explanation:
Hope this helps :))
13. Bethany buys a used car for $9,000. She puts $600 down and finances the rest for 4 1/2 years at 5%annual interest. At the end of years, the $9000 car will have cost her $
Answer :
$11,062.40
Explanation :
The formula for the future amount in a compounding interest is :
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where P is the present value
r is the rate of interest
n is the number of compounding in a year
t is time in years
From the given problem,
She puts a downpayment of $600 so the remaining will be :
9000 - 600 = 8400, which she will be financing for 4.5 years
So P = 8400
r = 5% or 0.05
n = 1 (Since it will only be compounding once in 1 year - annually)
t = 4.5 years
Using the formula above :
[tex]\begin{gathered} A=8400(1+\frac{0.05}{1})^{1(4.5)} \\ A=10462.40 \end{gathered}[/tex]The value of the $9000 car after 4.5 years will be the sum of the downpayment and the future amount.
[tex]600+10642.40=\$11,062.40[/tex]The answer is $11,062.40
Jackson and his family are driving to his grandmother's house. They have 5 of the trip left to go. Theyplan to complete the remainder of the trip over the next 3 hours. What fraction of the total trip willJackson's family travel each hour, if they drive at a constant rate?
Given:
The number of the trip =5 trips.
The number of hours = 3 hours
Jackson's family travel each hour
[tex]=\frac{The\text{ number of the trips}}{\text{The number of hours}}[/tex][tex]=\frac{5}{3}[/tex]Hence Jackson's family travel 5/3 trip each hour.
nt-Facing Task StatementHere is a scatter plot that shows the years when some used cars were madeand their prices in 2016, together with the graph of a linear model for therelationship between year and price.
The slope is positive
as the line moves from 2006 to 2016, it also goes up showing an incease in car prices.
A teacher received the following answer to a quiz question in which the student was asked to simplify the expression in Step 1:
Step 1: −5(x − 16y) + 7(−2x − 8y)
Step 2: −5x + 80y − 14x − 8y
Step 3: −5x − 14x + 80y − 8y
Step 4: (−14x − 5x) + (80y − 8y)
Step 5: −19x + 72y
Part A: Identify the step where the student made a mistake and explain the specific error that was made. Support your answer using the correct vocabulary. (6 points)
Part B: How would you correct the mistake? Show all your work.
The student made a mistake and explain the specific error that was made. Support your answer using the correct vocabulary. The mistake has been done in Step 2.
PART A: There is a mistake in Step 2, Distributive Property has been employed incorrectly.
7 has to multiply by both the terms inside the bracket, but it has been multiplied with the first term only.
7(-2 x-8 y)=-14 x-56 y and 7(-2 x-8 y) -14 x-8 y
Hence, -5(x-16 y)+7(-2 x-8 y)=-5 x+80 y-14 x-56 y
PART B :
The given equation is
-5(x-16 y)+7(-2 x-8 y)
Applying distributive property to the above equation that states A(B+C)=AB+AC, we get :
-5 x+80 y-14 x-56 y
Now, Writing the terms with the same variable together, we get
(-5 x-14 x)+(80 y-56 y)
Proceeding with solving terms inside the brackets according to BODMAS, we get,
-19 x+24 y
Hence , −5(x − 16y) + 7(−2x − 8y) = -19x +24y
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Evan has $580 to spend at a bicycle store for some new gear and biking outfits.
Assume all prices listed include tax.
• He buys a new bicycle for $396.95.
• He buys 4 bicycle reflectors for $7.40 each and a pair of bike gloves for $22.94.
• He plans to spend some or all of the money he has left to buy new biking outfits
for $42.10 each.
Required inequality is 47.25x ≤ 194.02.
What is inequality?An inequality is created when two or more algebraic expressions are compared using the symbols <, >, or ≤. They represent mathematical formulas when neither side is equal.
Given Data
Evan has $580 to spend at a bicycle store for some new gear and biking outfits
He buys a new bicycle for $396.95.
• He buys 4 bicycle reflectors for $7.40 each and a pair of bike gloves for $22.94.
• He plans to spend some or all of the money he has left to buy new biking outfits for $42.10 each.
Money spend on reflectors = 4(17.33)
Money spend on reflectors = $69.32
Total money left = (580 -(285.41 + 69.32 + 31.25))
Total money left = $194.02
If she buy x biking outfits:
47.25x ≤ 194.02
Required inequality is 47.25x ≤ 194.02.
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Fill in the missing angle measures. Given: ab and c d and <1 = 32°
hello
from the image given,
angle 1 = 32
[tex]\begin{gathered} \angle1=\angle8 \\ \text{reaon: alternate angles are equal} \end{gathered}[/tex][tex]\begin{gathered} \angle1=\angle3 \\ \text{reason:corresponding angles are equal} \\ \angle3=32^0 \end{gathered}[/tex][tex]\begin{gathered} \angle1+\angle5=180^0 \\ \text{reason: angles on a straight line is equal to 180}^0 \\ \angle1=32 \\ 32+\angle5=180 \\ \angle5=180-32 \\ \angle5=148^0 \end{gathered}[/tex][tex]\begin{gathered} \angle5+\angle6=180^0 \\ reason;\text{ angles on a straight line = 180} \\ \angle5=148 \\ 148+\angle6=180 \\ \angle6=180-148 \\ \angle6=32^0 \\ or\text{ we can simply say } \\ \angle1=\angle6 \\ \text{reason: opposite angles are equal} \end{gathered}[/tex][tex]\begin{gathered} \angle5=\angle2 \\ \text{reason: opposite angles are equal} \\ \angle2=148^0 \\ or\text{ we can say }\angle1+\angle2=180\text{ since they are on a straight line} \end{gathered}[/tex][tex]\begin{gathered} \angle3+\angle4=180^0 \\ \text{reason: angles on a straight line = 180} \\ 32+\angle4=180 \\ \angle4=180-32 \\ \angle4=148^0 \end{gathered}[/tex][tex]\begin{gathered} \angle4=\angle7 \\ \text{reason: opposite angles are equal} \\ \angle7=148 \end{gathered}[/tex][tex]\begin{gathered} \angle1=\angle8 \\ \text{reason; alternate angles are equal} \\ \angle8=38^0 \end{gathered}[/tex][tex]\begin{gathered} \angle1=\angle14 \\ \text{alternate angles are equal} \\ \angle14=32^0 \end{gathered}[/tex][tex]\begin{gathered} \angle5=\angle13 \\ \text{reason;corresponding angles are equal} \\ \angle13=148^0 \end{gathered}[/tex][tex]\begin{gathered} \angle13=\angle10 \\ \text{reason:opposite angles are equal} \\ \angle10=148^0 \end{gathered}[/tex][tex]\begin{gathered} \angle9=\angle14 \\ \text{reason:opposite angles are equal} \\ \angle9=32^0 \end{gathered}[/tex][tex]\begin{gathered} \angle12=\angle13 \\ \text{reason: alternate angles are equal} \\ \angle12=148^0 \end{gathered}[/tex][tex]\begin{gathered} \angle11+\angle12=180 \\ \text{reason:angles on a straight line equal 180}^0 \\ \angle11+148=180 \\ \angle11=180-148 \\ \angle11=32^0 \end{gathered}[/tex][tex]\begin{gathered} \angle12=\angle15 \\ \text{reason : opposite angles are equal} \\ \angle15=148^0 \end{gathered}[/tex][tex]\begin{gathered} \angle11=\angle16 \\ \text{reason: opposite angles are equal} \\ \angle16=32^0 \end{gathered}[/tex]from the calculations above, it's evident we can use several ways to find angles in four parallel lines
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Yesterday a chef used 32 eggs to make 2 chocolate souffles and 6 lemon meringue pies. The day before, he made 2 chocolate souffles and 10 lemon meringue pies, which used 48 eggs. How many eggs does each dessert require? A chocolate souffle requires __ eggs and a lemon meringue pie requires __ eggs.
the system of equations above represent the question, we need to solve the system in order to know the number of eggs necessary for each dessert
x is the number of eggs used to make the chocolate souffle.
y is the number of eggs used to make lemon meringue pies.
First, we need to multiply the second equation with -1 so we have
[tex]-2x-10y=-48[/tex]we will sum the first equation with the equation above
[tex]\begin{gathered} -4y=-16 \\ y=\frac{-16}{-4}=4 \\ y=4 \end{gathered}[/tex]we substitute the value of y in the first equation
[tex]\begin{gathered} 2x+6(4)=32 \\ 2x+24=32 \\ 2x=32-24 \\ 2x=8 \\ x=\frac{8}{2} \\ x=4 \end{gathered}[/tex]A chocolate souffle requires 4 eggs and a lemon meringue pie requires 4 eggs.
A roll of gasket material is 16 in wide. What length is needed to obtain 21 sq ft of the material? the answer has to be as a mixed number
The Solution:
Given:
[tex]\begin{gathered} L=length=? \\ \\ W=width=16in \\ \\ A=area=21ft^2 \end{gathered}[/tex]Step 1:
Convert 21 square feet to square inches.
Recall:
[tex]\begin{gathered} 1\text{ foot}=12\text{ inches.} \\ So, \\ 21ft^2=21\times12=252\text{ }inches^2 \end{gathered}[/tex]Step 2:
Apply the formula for area.
[tex]\begin{gathered} A=L\times W \\ \\ 252=L\times16 \end{gathered}[/tex]Divide both sides by 16.
[tex]L=\frac{252}{16}=\frac{63}{4}=15\frac{3}{4}\text{ }inches[/tex]Therefore, the correct answer is:
[tex]15\frac{3}{4}\text{ inches}[/tex]Subtract the two polynomials 3x^2+7x-1 - x^2+6x-1
The polynomial (3x²+7x-1)-(x²+6x-1). The polynomial after subtraction is 2x²+x.
Given that,
The polynomial (3x²+7x-1)-(x²+6x-1)
We have to subtract the polynomial and find the polynomial.
The polynomial is nothing but algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. Mathematical operations like addition, subtraction, multiplication, and positive integer exponents can be performed on polynomial equations, however division by variables cannot.
Take the polynomial,
=(3x²+7x-1)-(x²+6x-1)
We have to subtract the each terms like x² terms and x terms and constant.
=3x²-x²+7x-6x-1+1
=2x²+x
Therefore, the polynomial after subtraction is 2x²+x.
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