Parallel lines maintain the exact slope but different y-intercepts. Perpendicular lines have to oppose, reciprocal slopes like 1/2 and -2 or 8/7 and -7/8.
What was the relationship between the lines with equations 4x − 8y = 9 and 8x − 7y = 9?Given: 4x - 8y = 9 ............(1)
8x - 7y = 9 ............(2)
To be the same line, the equations have to be multiples of each other.
Multiplying (1) by 2, we get
2(4x - 8y = 9) = 8x - 16y = 18
From (1) solve the value of y, we get
4x - 8y = 9 ............(1)
-8y = -4x + 9
The value of y = (1/2)x - 9/8
From (2),
8x - 7y = 9
solve the value of y, we get
-7y = -8x + 9
The value of y = (8/7)x - 9/7
To be the exact line, the equations would be exact. Parallel lines maintain the exact slope but different y-intercepts. Perpendicular lines have to oppose, reciprocal slopes like 1/2 and -2 or 8/7 and -7/8.
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please help! look at the photo linked
Answer:
3; 1
Step-by-step explanation:
when there are six spots we can see that there are 2 eyes
so
divide both sides by 2
6:2
6 / 2 : 2 / 2
3 : 1
that is your answer
The exterior surface of a farm silo needs to be painted. if one gallon of paint covers 224 square feet, what is the minimum number of gallons needed to paint the silo? keep in mind that the bottom of the silo is not painted. use π = 3.14
The gallons needed to paint the silo is 10.
How many gallons is needed to paint the silo?A cylinder is a three-dimensional object. It is a prism with a circular base. The total surface area of cylinder can be determined by adding the area of all its faces.
Total surface area of the cylinder excluding its base = 2πrh +πr²
Where:
r = radius h = heightTSA = (2 x 3.14 x 10 x 30) + (3.14 x 10²)
314 + 1884 = 2198 ft²
Number of gallons needed = 2198 / 224 = 9.81 = 10 gallons
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what is the solution to this equation 7x-3(x-6)=30
Hi there,
please see below for solution steps :
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
⨠ use the distributive property
[tex]\sf{7x-3(x-6)=30}[/tex]
[tex]\sf{7x-3x+18=30}[/tex]
⨠ combine like terms
[tex]\sf{4x+18=30}[/tex]
⨠ subtract both sides by 18
[tex]\sf{4x=30-18}[/tex]
[tex]\sf{4x=12}[/tex]
⨠ divide both sides by 4
[tex]\boxed{\sf x=3}[/tex]
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
A gardener uses 1/3 of a liter of water to water 2/7 of a garden.
Answer:
[tex]\boxed{\sf 1\dfrac{1}{6}\ liters \ of \ water}[/tex]
Explanation:
Let the total water required water the entire ground be g
Equation:
[tex]\sf \dfrac{2}{7}\:g = \dfrac{1}{3} \ liters \ of \ water[/tex]
rearranging
[tex]\sf g = \dfrac{7(1)}{3(2)}[/tex]
simplify
[tex]\sf g = \dfrac{7}{6} \ liters \ of \ water[/tex]
rewrite in mixed fraction
[tex]\bf g = 1\dfrac{1}{6}\ liters \ of \ water[/tex]
The water required to water the entire ground is 1 1/6 liters.
A clock has a diameter of 16 inches. How far does the hour hand travel during 5 hours? Use 3.14 for pi.
Therefore the hour hand travels 40.192in in 5 hours
A sector is said to be a part of a circle made of the arc of the circle along with its two radii.
The formula for calculating the area of a sector is expressed as;
A = r²β/2
where
r is the radius of the circle
β is the angle subtended
Since the the hour hand travel during 5 hours, the subtended angle by the sector will be;
β = 360/5
β = 72 degrees
Given the following parameters
r = 16/2
r = 8in
Substitute into the formula
A = 8²(72π)/360
A = 40.192in
Therefore the hour hand travels 40.192in in 5 hours
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to set up a model linear equation to fit real world applications, what should always be the first step?
Answer:
Define the variables.
Step-by-step explanation:
Define the variables, then set up the equations, and finally solve the system using graphing, substitution, or elimination method.
To set up or model a linear equation to fit a real-world application, First, we have to determine the known amounts or quantities before defining the unknown quantity as a variable.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
To set up a model linear equation to fit real-world applications
In the first step determine known amounts or quantities.
Then, assign the unknown amount to a variable.
Now, find a method or approach to express the second unknown in terms of the first if there are many unknown quantities.
Create an equation that translates the words into mathematical functions.
Complete the equation. Make certain that the solution, including the system of measurement, can be expressed in words.
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If g(x)=-2x), which graph is the graph of function g?
Answer:
The graph of g(x) has a y-intercept at (0,0) and a slope of -2.
Amal used the tabular method to show her work dividing –2x3 11x2 – 23x 20 by x2 – 3x 4.
The true statement is (c) Amal's work is incorrect because it includes a positive two instead of a negative two in the answer
How to determine the true statement?The complete question is added as an attachment
From the table, we have
Divisor = x^2 - 3x + 4
Quotient = 2x + 5
Dividend = -2x^3 + 11x^2 - 23x + 20
See that the signs of the leading coefficients of the dividend and the divisor are different
This means that the leading coefficient of the quotient must be negative
From the question, we have:
Quotient = 2x + 5
The expression 2x + 5 has a positive leading coefficient
Hence, the true statement is (c) Amal's work is incorrect because it includes a positive two instead of a negative two in the answer
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use the compound interest formulas A=P e^rt to solve the problem given. round answers to the nearest cent.
Find the accumulated value of an investment of $15,000 for 6 years at an interest rate of 5.5% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously.
Answer:
a) $20,771.76
b) $20,817.67
c) $20,484.80
d) $20,864.52
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedPart (a): semiannually
Given:
P = $15,000r = 5.5% = 0.055n = 2t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=15000\left(1+\frac{0.055}{2}\right)^{2 \times 6}[/tex]
[tex]\implies \sf A=15000\left(1.0275}{2}\right)^{12}[/tex]
[tex]\implies \sf A=20771.76[/tex]
Part (b): quarterly
Given:
P = $15,000r = 5.5% = 0.055n = 4t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=15000\left(1+\frac{0.055}{4}\right)^{4 \times 6}[/tex]
[tex]\implies \sf A=15000\left(1.01375}\right)^{24}[/tex]
[tex]\implies \sf A=20817.67[/tex]
Part (c): monthly
Given:
P = $15,000r = 5.5% = 0.055n = 12t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=15000\left(1+\frac{0.055}{12}\right)^{12 \times 6}[/tex]
[tex]\implies \sf A=15000\left(1+\frac{0.055}{12}\right)^{72}[/tex]
[tex]\implies \sf A=20484.80[/tex]
Continuous Compounding Formula
[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]
where:
A = Final amountP = Principal amounte = Euler's number (constant)r = annual interest rate (in decimal form)t = time (in years)Part (d): continuous
Given:
P = $15,000r = 5.5% = 0.055t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=15000e^{0.055 \times 6}[/tex]
[tex]\implies \sf A=20864.52[/tex]
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How to do this question. First to answer this question will be marked as brainlist.
Answer:
10
Step-by-step explanation:
Every number with exponent zero is equal to 1
(7³×8)⁰ = 1
5⁰ = 1
then:
(3² + 5⁰) / (7³×8)⁰
= (3² + 1) / 1
= (9+1) / 1
= 10
3^2 = 9
3^2 = 95^0 =1
(7^3 x 8)^0 is 1
(anything to power of zero is one)
9 + 1 / 1 gives us the fraction 10/1
10/1 + 1/3 => make denominator the same, so I'll multiply 10/1 by 3
We get : 30/3 + 1/3 => 31/3
Thus answer is 31/3
Hope this helps!
An interior angle of a regular polygon has a measure of 108°. What type of polygon is it?
The polygon is
Answer:
a polygon with an interior angle of 108 is a pentagon
Using the graph of the function g(x) = log3 (x – 4), what are the x-intercept and asymptote of g(x)?
The x-intercept is when y=0, but since [tex]\log_{3}(x-4) \neq 0 \text{ } \forall x[/tex], there is no x-intercept.
The asymptote is when the argument equals 0, which is at x=4.
Evaluate the expression for f = -6 and g = -1.
fg - f =
Answer:
7
Step-by-step explanation:
Given the information from the question:
[tex]fg - f = f \times g - f[/tex]
Next we can use the order of operations to find the value of the expression.
[tex]fg - f = - 6 \times - 1 - ( - 1) \\ = 6 - ( - 1) \\ = 6 + 1 \\ = 7[/tex]
A rental truck company charges a flat fee of $30 to rent a truck in addition to $0.25 per miles how much would it cost to rent a van for 80 miles
Answer:
$50
Step-by-step explanation:
x is distance and y is cost because the cost is dependent on the distance which makes the distance the independent variable. you can always use y=mx+b for these problems!!
Given the following information, calculate the perimeter of triangle RST. Assume triangle RZX is similar to triangle RST.
RZ = 21, RY = 24, RX = 42, ZY = 9, and SW = 15.
Check the picture below.
Find the domain and range of all parts.
For the given functions, the domains are:
1) All real numbers.
2) D: x≥ -3
3) D: set of all real numbers such that x ≠ 0
4) D: 7 ≥ x ≥-7
5) All real numbers.
How to get the domain of the given functions?
For any function, we assume that the domain is the set of all real numbers, and then we remove all the values of x that generate problems (like a denominator equal to zero or something like that).
1) f(x) = x^2 - 4
This is just a quadratic equation, the domain is the set of all real numbers.
2) f(x) = √(x + 3)
Remember that the argument of a square root must be equal to or larger than zero, so here the domain is defined by:
x + 3 ≥ 0
x≥ -3
The domain is:
D: x ≥ -3
3) f(x) = 1/x
We can assume that the domain is the set of all real numbers, but, we can see that when x = 0 the denominator becomes zero, then we need to remove that value from the domain.
Thus, we conclude that the domain is:
D: set of all real numbers such that x ≠ 0
4) f(x) = √(49 - x^2)
Here we must have:
49 - x^2 ≥ 0
49 ≥ x^2
√49 ≥ x ≥-√49
7 ≥ x ≥-7
The domain of this function is:
D: 7 ≥ x ≥-7
5) f(x) = √(x^2 + 1)
Notice that x^2 is always a positive number, then the argument of the above square root is always positive, then the domain of that function is the set of all real numbers.
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A shipment of inexpensive digital watches, including that are defective, is sent to a department store. The receiving department selects 10 at random for testing and rejects the whole shipment if 1 or more in the sample are found defective. What is the probability that the shipment will be rejected?.
0.8926 percent of the time, the shipment will be rejected.
What is Probability?The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
According to the given information:A delivery of 50 cheap digital watches, 10 of which are flawed.
A digital watch's likelihood of malfunctioning
P = 10/50
= 0.2
Size of sample: n = 10
Additionally, if they find one or more samples to be defective, they reject the entire cargo.
Making use of the binomial probability formula:
[tex]P(x)={ }^{n} C_{x} p^{x}(1-p)^{n-x}[/tex]
The random variable x should stand in for the quantity of defective watches.
The chance that the delivery will be refused is:
[tex]\begin{aligned}&P(x \geq 1)=1-P(0) \\&=1-{ }^{10} C_{0}(0.2)^{0}(0.8)^{10}\end{aligned}[/tex]
= 1 - (0.8)
= 0.8926
As a result, 0.8926 percent of the time, the shipment will be rejected.
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I understand that the question you are looking for is:
A shipment of 50 inexpensive digital watches, including 10 that are defective, is sent to a department store. The receiving department selects 10 at random for testing and rejects the whole shipment if 1 or more in the sample are found defective. What is the probability that the shipment will be rejected
write the expression as the sine or cosine of an angle
The expression, written as the sine of an angle is sin (7π/10)
Trigonometry IdentitiesFrom the question, we are to write the given expression as the sine or cosine of an angle.
The given expression is
sin(π/5)cos(π/2) + sin(π/2)cos(π/5)
Let A = π/5
and
B = π/2
Thus, we get
sinA cosB + sinB cosA
From the given information, we have that
sin(A ± B) = sinA cos B ± cosA sinB
∴ sin(A + B) = sinA cos B + cosA sinB
Now,
sinA cosB + sinB cosA = sinA cosB + cosA sin B
∴ sinA cosB + sinB cosA = sin (A + B)
Put A = π/5
and
B = π/2
sinπ/5 cosπ/2 + sinπ/2 cosπ/5 = sin (π/5 + π/2)
sinπ/5 cosπ/2 + sinπ/2 cosπ/5 = sin (7π/10)
Hence, the expression, written as the sine of an angle is sin (7π/10)
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Given the linear regression equation, y^=134. 63−2. 79x. What is the predicted value of y^ when x=45? (round answer to two decimal places, example: 3. 45)
Answer:
9.08
Step-by-step explanation:
To find the predicted value of y, put the x-value where x is in the equation and do the arithmetic.
Substitution[tex]\hat{y}=134.63-2.79x\qquad\text{given}\\\\\hat{y}=134.63-2.79(45) = 134.63-125.55\qquad\text{use 45 for x}\\\\\boxed{\hat{y}=9.08}\qquad\text{simplify}[/tex]
Simplify the expression:
-2(-1 + 2w) =
Submit please
[tex]-2(-1+2w)[/tex]
distribute
[tex]2-4w[/tex]
put in standard form
[tex]-4w+2[/tex]
Find the value of x.
50°
(5x + 30)%
21⁰
What is the solution to the
system of equations graphed below?
y = x- 2
y = 3x - 2
Answer:
(0, -2)
Step-by-step explanation:
The solution to a system of equations is the point on the graph where the lines intersect.
SolutionHere, both lines have a y-intercept of -2, so intersect there. The solution is ...
(x, y) = (0, -2)
Zoey read a novel in 30 days she made it a habit to read 13 pages everyday for the first 20 days. if in the last 10 days she reads 6 pages everyday how many pages are in the book?
Answer:
320 pages.
Step-by-step explanation:
We can simply multiply and add to find how many pages are in the book.
So we have (13 pg * 20 d) + (6 pg * 10 d) = 260 + 60 = 320.
Another way of solving is to set up a proportion for both the 20 and 10 days, find how many pages are read on these days, and add:
[tex]\frac{13pg}{1d}=\frac{xpg}{20d}\\ x=260pages\\\\\frac{6pg}{1d} =\frac{xpg}{10d}\\ x=60pg\\260+60=320[/tex]
A research wants to examine the grams of fat in milk. They separate the milk into the groups: Whole Milk, 2% Fat, and Low Fat. Then randomly select cartons from each of the groups to measure grams of fat. This is an example of ____________ sampling.
if there was a random selection of cartons from each of the groups to measure grams of fat. This is an example of stratified sampling
What is stratified sampling?Stratified sampling can be defined as a method of sampling that involves division of a population into smaller groups or items, these are called strata.
This groups or strata are then arranged or organized based on the shared characteristics or attributes of the members in the group of the given population.
Stratification is the process of classifying the population into groups.
Features of stratified sampling are;
It is a precise metric It provides for a better representation of the overall populationIt can be time-consuming, and potentially expensiveFrom the information given, we can see that it is an example of stratified sampling.
Thus, if there was a random selection of cartons from each of the groups to measure grams of fat. This is an example of stratified sampling
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The ratio is: 450g to 1kg
In it's simplest form
Answer:
9:20
Step-by-step explanation:
1kg is 1000g grams and in order to simify we need the units to be equal . 450:1000 would simplify to
45: 100 by divinding both the number by 10 then divide both number by 5 which would give 9: 20
hopefully this helped . if you need any more explanation pls ask
pls give brainliest if you like my answer :) thanks
Answer:
9: 20
Step-by-step explanation:
First, we have to convert both figures into the same unit.Here we can convert both into grams.As 450g is already given in grams, let us convert 1kg into grams.To convert kilograms into grams we have to multiply kilograms by 1000.Therefore,1kg × 1000 = 1000g
Now let us write those as a ratio.450 : 1000g
450 : 1000
To write the ratio in the simplest form we can divide both by 50.9: 20
As this cannot be simplified anymore, the simplest form of 450: 1000 is 9: 20.Find the polar equation of an ellipse with its focus at the pole and vertices at (−1,0) and (3,0).
The polar equation of an ellipse is [tex]r=-\frac{3}{1+2cos\theta}[/tex].
The vertices of ellipse are (−1,0) and (3,0).
The polar equation of an ellipse can be represented as
[tex]r=\frac{ep}{1+ecos\theta}[/tex]
where e is the eccentricity.
Eccentricity, e = [tex]\frac{c}{a}[/tex]
c is the distance from the center to the focus and a is the distance from the center to the vertex
[tex]c=\frac{3-(-1)}{2}[/tex]
⇒ [tex]c=\frac{4}{2}[/tex]
⇒ c = 2
[tex]a=\frac{3+(-1)}{2}[/tex]
⇒ [tex]a=\frac{2}{2}[/tex]
⇒ a = 1
Then, e = [tex]\frac{2}{1}[/tex]
⇒ e = 2
Now, the polar equation of an ellipse becomes as,
⇒ [tex]r=\frac{2p}{1+2cos\theta}[/tex] ------- (1)
Now plug in a vertex point such as (-1,0) and solve for p,
⇒ [tex]-1=\frac{2p}{1+2cos0}[/tex]
⇒ [tex]-1=\frac{2p}{1+2(1)}[/tex] [∵ cos 0 = 1]
⇒ [tex]-1=\frac{2p}{3}[/tex]
⇒ [tex]-3=2p[/tex]
⇒ [tex]p=-\frac{3}{2}[/tex]
Thus the polar equation of an ellipse (1) becomes as,
⇒ [tex]r=\frac{2(-\frac{3}{2} )}{1+2cos\theta}[/tex]
⇒ [tex]r=-\frac{3}{1+2cos\theta}[/tex]
Hence we can conclude that the polar equation of an ellipse is [tex]r=-\frac{3}{1+2cos\theta}[/tex].
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Given the functions k(x) = 2x2 − 5 and p(x) = x − 3, find (k ∘ p)(x). (k ∘ p)(x) = 2x2 − 6x 4 (k ∘ p)(x) = 2x2 − 12x 13 (k ∘ p)(x) = 2x2 − 12x 18 (k ∘ p)(x) = 2x2 − 8
[tex](k \circ p)(x)=k(p(x))=k(x-3) \\ \\ =2(x-3)^2-5 \\ \\ =2(x^2 - 6x+9)-5 \\ \\ =\boxed{2x^2 - 12x+13}[/tex]
For instance, f[g (x)] exists the composite function of f(x) and g(x). The composite function f[g (x)] exists read as “f of g of x”.
The composite function exists [tex]$k(p(x))=2 x^{2}-12 x+13$[/tex]
Therefore, the correct answer is option b. [tex]$k(p(x))=2 x^{2}-12 x+13$[/tex].
What is the composite of a function?A composite function exists generally as a function that exists written inside another function. The composition of a function exists done by replacing one function with another function.
Given function exists, [tex]$k(x)=2 x^{2}-5[/tex] and p(x) = (x - 3)
To find composite function k(p(x)).
k(p(x)) = k(x-3)
[tex]$&k(p(x))=2(x-3)^{2}-5 \\[/tex]
simplifying the above equation, we get
[tex]$&k(p(x))=2\left(x^{2}+9-6 x\right)-5 \\[/tex]
[tex]$&k(p(x))=2 x^{2}+18-12 x-5 \\[/tex]
[tex]$&k(p(x))=2 x^{2}-12 x+13[/tex]
The composite function exists [tex]$k(p(x))=2 x^{2}-12 x+13$[/tex]
Therefore, the correct answer is option b. [tex]$k(p(x))=2 x^{2}-12 x+13$[/tex].
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2. A football team plays 28 games and wins 4 out of every 7 games played. No match ended in a draw. 20 (a) How many times has this football team lost?
Given f of x is equal to the quantity 8x plus 1 end quantity divided by the quantity 2x minus 9 end quantity, what is the end behavior of the function?
Answer:
Step-by-step explanation:
Equation
f(x) = (8x + 1) / (2x + 9)
Notice the brackets. They are necessary to show what comes before the division sign, and what comes after.
Behavior
The best way to state the behavior is to get something like a graphing program to show you what the curve looks like -- where it's critical points are for example. I use Desmos for this kind of question, Just do a search for Desmos and bookmark it. You will use it quite often.
So you want to know the behavior.
Right Curve
Crosses the x axis at (-0.125, 0)
Crosses the y axis at (0,0,111)
The right curve has a domain of -∞ < x < ∞
The right curve has a range of -∞ < x < ∞
The range is going to have to go out quite a ways before you see any dramatic decrease in the way it is drawn.
Left Curve.
The right hand curve never crosses either the x or y axis. Nor does it just touch the x or y axis.
The domain is -∞ <x < 0
The range is 0<x<∞
Refer to the figure to the right.
A. If RV RT, name two congruent angles.
B. If RSSV, name two congruent angles.
C. If LSRT LSTR, name two congruent segments.
D. If LSTV= LSVT, name two congruent segments.
R
T
Answer:
c if lsrt lstr name two congruent segments
