A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line will be y =4x+5. Thus, the correct option is C.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
Given the slope of the line is 4 and it goes through (-1,1), therefore, the equation of the line will be,
y = mx + c
y = 4x + c
Substitute the value of points,
1 = 4(-1) + c
1 = -4 + c
5 = c
Hence, the equation of the line will be y =4x+5. Thus, the correct option is C.
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Write the equation using function notation f(x). then find f(0)
2x^2 - 3y = 6
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: f(0) = -2[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 2 {x}^{2} - 3y = 6[/tex]
[tex]\qquad \tt \rightarrow \: 3y + 6 = 2 {x}^{2} [/tex]
[tex]\qquad \tt \rightarrow \: 3y = 2 {x}^{2} - 6[/tex]
[tex]\qquad \tt \rightarrow \: y = \cfrac{2 {x}^{2} - 6 }{3} [/tex]
[tex]\qquad \tt \rightarrow \: y = \cfrac{2 {}^{} }{3} {x}^{2} - 2[/tex]
[ here, y can be replaced with f(x) because y is a function of x ]
[tex]\qquad \tt \rightarrow \: f(x) = \cfrac{2 {}^{} }{3} {x}^{2} - 2[/tex]
[tex] \large\textsf{Find f(0):} [/tex]
[tex]\qquad \tt \rightarrow \: f(0) = \cfrac{2 {}^{} }{3} {(0)}^{2} - 2[/tex]
[tex]\qquad \tt \rightarrow \: f(0) = 0 - 2[/tex]
[tex]\qquad \tt \rightarrow \: f(0) = - 2[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
which law would you use to simplify the expression....
Answer:
power of a power
Step-by-step explanation:
the power of a power law says that, "if a base raised to a power is being raised to another power, the exponents are multiplied and the base remains the same."
for example, for this problem, you would do:
[tex](x^4)^9\\= x^4^*^9\\= x^3^6[/tex]
Help me with this i need steps :c!
Answer:
The area of a triangle is 1/2 × base × height. 24 = 1/2 × 12 × height. Therefore height = 24/6 = 4 .
Answer:
8
Step-by-step explanation:
24=6*h/2
48=6*h
8=h
h is altitude
The length of a rectangle is 44 inches greater than twice the width. If the diagonal is 2 inches more than the length, find the dimensions of the rectangle.
Answer:
18 inches by 80 inches
Step-by-step explanation:
The given relations can be used in conjunction with the Pythagorean theorem to find the rectangle dimensions.
__
setupLet x and y represent the width and length of the rectangle, respectively. One of the relations is that between length and width:
y = 2x +44 . . . . . length is 44 more than twice the width
The other relation is described by the Pythagorean theorem. The square of the diagonal is the sum of the squares of the length and width:
x² +y² = (y +2)²
__
solutionExpanding the second equation, and subtracting y², we find ...
x² +y² = y² +4y +4
x² = 4y +4
Substituting for y using the first equation gives the quadratic ...
x² = 4(2x +44) +4
x² = 8x +180 . . . . . . . eliminate parentheses
x² -8x +16 = 196 . . . . add 16 -8x to make perfect squares
(x -4)² = 14²
We're only interested in the positive solution, so ...
x = 4 +14 = 18 . . . . . . . . square root, add 4
y = 2(18) +44 = 80
The dimensions of the rectangle are 18 inches wide by 80 inches long.
_____
Check
The diagonal is √(18² +80²) = √6724 = 82.
How many square feet of tile is needed for a room of 24 foot x 24 foot
Answer:576
Step-by-step explanation:
24 squared is 576
how do i work this out?
She has 45% of the original amount left
Ratio and proportionsFractions are written as a ratio of two integers
Given the following
Initial amount. = ∈4000
Amount given to her sister = 1/4 * 4000 = 1000
Amount given to her brother = 40% of 3000 = 1200
Amount left = 4000 - (1000+1200)
Amount left = ∈1800
Determine the percentage left
x * 4000 = 1800
x = 1800/4000
x = 0.45
x = 45%
Hence she has 45% of the original amount left
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Geometry question! Please help thanks!
The measure of the angles are Z = 90, X = 90, V = 90, Y = ∠20, W = ∠8 and W = ∠20
How to solve the angles?The sum of angles on a straight line is 180 degrees.
This means that:
Z + 90 = 180
X + 90 = 180
V + 90 = 180
Solve for the variables
Z = 90;
X = 90
V = 90
Also, alternate angles are equal.
This means that:
Y = ∠20
W = ∠8
This is so because the above angles are alternate angles.
Lastly, corresponding angles are equal.
So, we have:
W = ∠20
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For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.21 probability of failure. Complete parts (a) through (c) below.
Would it be unusual to observe one component fail? Two components?
It
▼
would not
would
be unusual to observe one component fail, since the probability that one component fails,
enter your response here, is
▼
less
greater
than 0.05. It
▼
would not
would
be unusual to observe two components fail, since the probability that two components fail,
enter your response here, is
▼
greater
less
than 0.05.
Using the probability concept, we have that:
a) It would not be unusual to observe one component fail, since the probability that one component fails is greater than 0.05.
b) It would be unusual to observe two components fail, since the probability that two components fail is less than 0.05.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes. If a probability is less than 0.05, the event is considered unusual.
In this problem, the probabilities are given as follows:
0.21 probability that one component fails, hence not unusual.(0.21)² = 0.0441 probability that two components fail, hence unusual.More can be learned about probabilities at https://brainly.com/question/14398287
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The function f(x)= –StartRoot negative x EndRoot is shown on the graph.
The range of the required function f(x) = -√-x is all real values less than or equal to 0.
The nature of the function is imaginary because of the negative sign present inside the root. Hence the range of the function exists only and only if the function gives real values in each of its outcomes.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.
As per question
f(x) = -√-x
clearly, for each positive real number the function becomes imaginary.
So the domain of the given function lies (-∞, 0).
and for every x in its domain function has its exists in range of all real values less than and equal to zero.
Thus, the range of the function f(x) ≤ 0.
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Which expression is equivalent to...
What is the simplified form of StartRoot StartFraction 72 x Superscript 16 Baseline Over 50 x Superscript 36 Baseline EndFraction EndRoot? Assume x ≠ 0.
StartFraction 6 Over 5 x Superscript 10 Baseline EndFraction
StartFraction 6 Over 5 x squared EndFraction
Six-fifths x Superscript 10
Six-fifths x squared
The simplification form of the provided expression is 6/5x¹⁰ option first is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
[tex]\rm = \sqrt{\dfrac{72x^{16}}{50x^{36}}}[/tex]
[tex]\rm = \sqrt{\dfrac{72}{50}} \sqrt{\dfrac{x^{36}}{x^{16}}}[/tex]
[tex]\rm = \sqrt{\dfrac{36\times2}{25\times2}} \sqrt{\dfrac{x^{36}}{x^{16}}}[/tex]
[tex]\rm ={\dfrac{6x^{8}}{5x^{18}}}[/tex]
[tex]\rm ={\dfrac{6}{5x^{10}}}[/tex]
Thus, the simplification form of the provided expression is 6/5x¹⁰ option first is correct.
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Answer:
6x3
Step-by-step explanation:
Edge 2023
TIME REMAINING
09:44
On a coordinate plane, a solid straight line has a positive slope and goes through (negative 3, negative 5) and (0, negative 4). Everything to the right of the line is shaded.
Which linear inequality is represented by the graph?
y ≥ One-thirdx – 4
y ≤ One-thirdx – 4
y ≤ One-thirdx + 4
y ≥ One-thirdx + 4
Since everything to the right of the line is shaded, the linear inequality which represents the graph is equal to: A. y ≥ 1/3x - 4.
How to determine the linear inequality?In order to determine the linear inequality which represents the graph, we would find the slope of the given points.
Mathematically, the slope of a straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
[tex]Slope = \frac{-4\;-\;(-5)}{0\;-\;(-3)}\\\\Slope = \frac{1}{3}[/tex]
Slope = 1/3.
From the standard equation, we have:
y - y₁ = m(x - x₁)
y - (-5) = 1/3(x - (-3))
y + 5 = 1/3x + 1
y = 1/3x + 1 - 5
y = 1/3x - 4
y ≥ 1/3x - 4.
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What is the value of x?
E
(2x)°
xº
D
Answer:
30°
Step-by-step explanation:
Since ED = FD, the ∠DEF = ∠EFD
Since ∠DEF = 2x, ∠EFD is also equal to 2x
The sum of the 3 angles of a triangle is 180°
So x + 2x + 2x = 180
6x = 180
x = 30
Russell has been offered positions by two cable companies. The first company pays a salary of $17,000 plus a commission of $20 for each cable package sold. The second pays a salary of $14,300 plus a commission of $30 for each cable package sold. How many cable packages would need to be sold to make the total pay the same?
Russell has to sell 270 cable packages to make the total pay of both the companies as same.
Suppose that Russell sells x cable packages such that the total pay of both the companies is the same.
Then the revenue Russell would make at the first company is $17000+20x
And, the revenue Russell would make at the second company is
$14300+30x
Since, the above two values are equal
so, 17000+20x=14300+30x
⇒17000-14300=30x-20x
⇒10x=2700
⇒x=270
The above problems are called mathematical modelling.
Mathematical modelling is the process of locating such equations to explain actual occurrences.
These formulae are referred to as mathematical models together with the definitions given to the variables.
Therefore, Russell has to sell 270 cable packages to make the total pay of both the companies as same.
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A sample of size 400 was drawn and sample mean was found t
be 99. Test whether this sample could have come from a normal
population with mean 100 and variance 64 at 5%
significance.
Answer:
etrf4f3dvef3rf3rfr2wrgwrf2rg3rf3rgerferferfef I'm
The volume of a can of Pepsi is 0.33liter. There are 12 cans in 1 carton
What is the volume of 5 cartons of Pepsi?
Answer:
19 liters 800 milliliters
Step-by-step explanation:
0.33 * 12 * 5 = 19.8 liters
What is the greatest common factor of 20 and 36?
2
4
5
6
Answer:
GFC = 4
Step-by-step explanation:
Factors of 20 1 2 4 5 10 20
Factors of 36 1 2 3 4 6 9 12 18 36
Answer:4
Step-by-step explanation:nice and simple
Find x and Y pls help
Answer:
Step-by-step explanation:
Comment
The angle supplementary to x and 3x are equal.
Supplementary angles = 180
Solution
x + 3x = 180
4x = 180 Divide by 4
4x/4 = 180/4
x = 45
The angle supplementary to x is 3x
3x = 3*45
3x = 135
This angle is vertically opposite y. Vertically opposite angles are equal. So y = 135
Answer
x = 45
y = 135
y = 4/5 + square root x + 0.2 - 5x
Answer:
5
Step-by-step explanation:
Please answer BOTH the questions tyyyyyysm
C and A
X = at least 45 and more
This means we need to have a full closed dot.
It's A because the question says more than 75 ft meaning only open dots.
he roots of the quadratic function describing the relationship between the number of products produced and overall profit margins are x= 0 and 150. the vertex is (75, 10000).
The question was incomplete. Below you will find the missing parts of the question.
The company actually loses money on their first few products as it costs them more to make them, but once they hit ? they break even again. The worst case scenerio is that they produce ? items, as they will have a profit of ? dollars. The first root tells us that the profit will be 0 when ? products are sold.
Answer: The company actually loses money on their first few products as it costs them more to make them, but once they hit 150 they break even again. The worst case scenerio is that they produce 75 items, as they will have a profit of 10000 dollars. The first root tells us that the profit will be 0 when 0 products are sold.
Because the roots are x = 0 and 150, the vertex is (75, 10000).
So, the function is y = [tex]-\frac{10000}{5625}(x-75)^{2} +10000[/tex]
When, y = 0,
[tex]0=-\frac{10000}{5625} (x-75)^{2} +10000[/tex]
⇒ [tex]\frac{10000}{5625} (x-75)^{2}=10000[/tex]
⇒ [tex](x-75)^{2} = 10000(\frac{5625}{10000})[/tex]
⇒ [tex](x-75)^{2} = 5625[/tex]
⇒ [tex]x-75=75[/tex]
⇒ x = 150
When y=0, then x =150, their income was in balance.
When x = 75, then y=10000, they will have a profit of 10000 dollars.
The first root tells us that the profit will be 0 when 0 products are sold.
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What is the inequality for this verbal description?
Kyle has d dollars to spend at the garden store. He wants to buy one small
tree for $9.00 and s pounds of soil that cost $5.00 per pound. Which
inequality represents this situation?
OA. d≥ 5s +9
OB. d> 5s +9
OC. d<9s +5
O D. d≥ 9s +5
Answer:
A) d [tex]\geq[/tex] 5s + 9
Answer:
A. d ≥ 5s + 9
Step-by-step explanation:
9.00 is fixed cost5.00 is cost per pound of soilHence, equation will be :
d ≥ 5s + 9 (As d must be greater than/equal to this value for Kyle to afford it)Clarinex-D is a medication whose purpose is to reduce the symptoms associated with a variety of allergies. In clinical trials of Clarinex-D, 5% of the patients in the study experienced insomnia as a side effect. As random sample of 20 Clarinex-D users is obtained, and the number of patients who experienced insomnia is recorded. Find and interpret probability that 3 or fewer experienced insomnia as a side effect.
Using the binomial distribution, it is found that there is a 0.9842 = 98.42% probability that 3 or fewer experienced insomnia as a side effect, which means that it is a highly likely event.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
n = 20, p = 0.05.
The probability that 3 or fewer experienced insomnia as a side effect is given by:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{20,0}.(0.05)^{0}.(0.95)^{20} = 0.3585[/tex]
[tex]P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.3774[/tex]
[tex]P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.1887[/tex]
[tex]P(X = 3) = C_{20,3}.(0.05)^{3}.(0.95)^{17} = 0.0596[/tex]
Then:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3585 + 0.3774 + 0.1887 + 0.0596 = 0.9842[/tex]
0.9842 = 98.42% probability that 3 or fewer experienced insomnia as a side effect.
Since this probability is greater than 95%, this is a highly likely event.
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Which of the following is a sum of cubes?
Answer:
x^3 + 8y^6
Step-by-step explanation:
Answer:
the answer is B !!!
Step-by-step explanation:
thank me later lol
Using a graphing calculator (or Desmos), graph the equation y = (x - 5)² + 2, describe the transformation.
Answer:
the graph has a parent function of f(x) = x²
The (x - 5)² tells us that the graph is shifted to the right 5 units.
The +2 tells us that the graph is shifted up 2 units.
Can someone help me? I’ll give brainliest to whoever gets it right first
Answer:
72 Degrees
Step-by-step explanation:
We know that its 72 because of VAT, the vertical angle theorem.
Find how many quarts of 6% butterfat milk and 3% butterfat milk should be mixed to yield 45 quarts of 4% butterfat milk. Find how many quarts of 6 % butterfat milk and 3 % butterfat milk should be mixed to yield 45 quarts of 4 % butterfat milk .
Answer:
See below
Step-by-step explanation:
x = amount of 6% milk.... amount of fat = .06x
45-x = amount of 3% milk ...amount of fat = .03 (45-x)
Amount of fat in final mix of 45 quarts = .04 (45)
Inputs = output
.06x + .03(45-x) = .04(45)
.06x + 1.35 - .03x = 1.8
.03x = .45
x = 15 quarts of 6% then 30 quarts of 3%
How do you solve this question
[tex]a - 4 = ( \sqrt{a} - 2)( \sqrt{a} + 2)[/tex]
[tex] \frac{ \sqrt{a} - 2}{a - 4} = \frac{ \sqrt{a} - 2}{( \sqrt{a} - 2)( \sqrt{a} + 2) } = \frac{1}{ \sqrt{a} + 2 } [/tex]
How to find the a in the equation y=ax^3 + d given the two points (0,10), (2,20)
Answer:
[tex]y=\dfrac{5}{4}x^3+10[/tex]
Step-by-step explanation:
Given information:
[tex]y=ax^3+d[/tex](0, 10)(2, 20)Create two equations by substituting the given points into the given equation:
Equation 1: point (0, 10)
[tex]\implies a(0)^3+d=10[/tex]
[tex]\implies 0+d=10[/tex]
[tex]\implies d=10[/tex]
Equation 2: point (2, 20)
[tex]\implies a(2)^3+d=20[/tex]
[tex]\implies 8a+d=20[/tex]
Substitute Equation 1 into Equation 2 and solve for a:
[tex]\implies 8a+d=20[/tex]
[tex]\implies 8a+10=20[/tex]
[tex]\implies 8a+10-10=20-10[/tex]
[tex]\implies 8a=10[/tex]
[tex]\implies \dfrac{8a}{8}=\dfrac{10}{8}[/tex]
[tex]\implies a=\dfrac{10}{8}[/tex]
[tex]\implies a=\dfrac{5}{4}[/tex]
Finally, substitute the found values of a and d into the original formula:
[tex]\implies y=\dfrac{5}{4}x^3+10[/tex]
Check by substituting the x-values of the two given points into the found equation:
[tex]x=0 \implies y=\dfrac{5}{4}(0)^3+10=10 \leftarrow \textsf{correct}[/tex]
[tex]x=2 \implies y=\dfrac{5}{4}(2)^3+10=20 \leftarrow \textsf{correct}[/tex]
Put(0,10)
10=a(0)³+dd=10Now
Put again (2,20) this time
20=2³a+1010=8aa=10/8a=5/4Abby used the law of cosines for TriangleKMN to solve for k.
k2 = 312 + 532 – 2(31)(53)cos(37°)
Triangle K N M is shown. The length of K N is 53, the length of N M is k, and the length of K M is n.
Law of cosines: a2 = b2 + c2 – 2bccos(A)
What additional information did Abby know that is not shown in the diagram?
mAngleK = 37° and n = 31
mAngleK = 37° and k = 31
mAngleN = 37° and n = 31
mAngleN = 37° and k = 31
Answer:
m∠K = 37° and n = 31
Step-by-step explanation:
A lot of math is about matching patterns. Here, the two patterns we want to match are different versions of the same Law of Cosines relation:
a² = b² +c² -2bc·cos(A)k² = 31² +53² -2·31·53·cos(37°)ComparisonComparing the two equations, we note these correspondences:
a = kb = 31c = 53A = 37°Comparing these values to the given information, we see that ...
KN = c = 53 . . . . . . . . . . matching values 53NM = a = k . . . . . . . . . . . matching values kKM = b = n = 31 . . . . . . . matching values 31∠K = ∠A = 37° . . . . . . . matching side/angle namesAbby apparently knew that ∠K = 37° and n = 31.
__
Additional comment
Side and angle naming for the Law of Sines and the Law of Cosines are as follows. The vertices of the triangle are labeled with single upper-case letters. The side opposite is labeled with the same lower-case letter, or with the two vertices at either end.
Vertex and angle K are opposite side k, also called side NM in this triangle.
