Answer:
what red and blue dots?
Step-by-step explanation:
change to Ax+By=c form 2y=3x
We want to write the equation 2y=3x in the form Ax+By=C.
[tex]\begin{gathered} 2y=3x \\ -3x+2y=0 \\ So,\text{ A=-3, B=2 and C=0} \end{gathered}[/tex]Students were asked to prove the identity (tan x)(sin x) = sec x − cos x. Two students' work is given.Student AStep 1: sine x over cosine x times sine x equals secant x minus cosine xStep 2: sine squared x over cosine x equals secant x minus cosine xStep 3: 1 minus cosine squared x over cosine x equals secant x minus cosine xStep 4: 1 over cosine x minus cosine squared x over cosine x equals secant x minus cosine xStep 5: sec x − cos x = sec x − cos xStudent BStep 1: tangent x times sine x equals 1 over cosine x minus cosine xStep 2: tangent x times sine x equals 1 over cosine x minus cosine squared x over cosine xStep 3: tangent x times sine x equals 1 minus cosine squared x over cosine xStep 4: tangent x times sine x equals sine squared x over cosine xStep 5: tangent x times sine x equals sine x over cosine x times sine xStep 6: tan x sin x = tan x sin xPart A: Did either student verify the identity properly? Explain why or why not. (10 points)Part B: Name two identities that were used in Student A's verification and the steps they appear in. (5 points)
The identities used by student A is
1 - sin²x= cos²x
sin x/ cos x = tan x
what is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have to prove (tan x)(sin x) = sec x − cos x.
Now, student A and student B perform the proof.
Student A starts with tan x sin x then approaches to prove sec x - cos x.
So, Student A complete the proof.
But, student B starts with tan x sin x but failed to prove sec x - cos x.
The identities used by student A is
1 - sin²x= cos²x
sin x/ cos x = tan x
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slove using elimination-2x-5y=12x+2y=-10
We have the following:
[tex]\begin{gathered} -2x-5y=1 \\ 2x+2y=-10 \end{gathered}[/tex]solving using elimination:
[tex]\begin{gathered} -2x-5y=1 \\ + \\ 2x+2y=-10 \\ -2x+2x-5y+2y=1-10 \\ -3y=-9 \\ y=\frac{-9}{-3} \\ y=3 \end{gathered}[/tex]Now, for x:
[tex]\begin{gathered} -2x-5\cdot3=1 \\ -2x-15=1 \\ -2x=16 \\ x=\frac{16}{-2} \\ x=-8 \end{gathered}[/tex]Therefore:
x = -8 and y = 3
3 A youth soccer team is planning to attend an out of town tournament and must
stay in a hotel. Each room costs $119. The team will also be charged a flat $25
fee for use of the conference room. The total cost of the hotel can be represented
by the equation f(x) = 119x+25. If the team will use 10 to 16 rooms for the one
night, what is the range of the function for this situation?
A {10, 11, 12, 13, 14, 15, 16}
B {1215, 1334, 1453, 1572, 1691, 1810, 1929}
c {10, 16}
D {1215, 1929}
BE SURE YOU HAVE RECORDED ALL OF YOUR ANSWERS
ON THE ANSWER DOCUMENT.
S
Answer:
Running a sports event involves a lot of moving pieces, and it's the planner's job to keep them all moving in the right direction.
Step-by-step explanation:
A bag with 6 marbles has 1 blue marble, 2 red marbles, and 3 yellow marbles. A marble is chosen from the bag at random. What is the probability that it. Is blue?
the chance to get a yellow marble would be a 1/2 chance or 50%
red would be 1/3 chance or 33.3333% chance
to get a blue marble would be a 1/6 or 0.1666666% chance.
I took a picture of the question
The transformation in the picture is option c Reflection.
Given,
Reflection transformation:
A reflection is a transformation that works similarly to a mirror by switching all pairs of points that are directly across from one another along the line of reflection. A mathematical formula or the two sites it passes through can be used to define the line of reflection.
According to the law of reflection, r = I the angle of incidence and reflection are equal. θ r = θ I . At the point where the ray strikes the surface, the angles are measured in relation to the perpendicular to the surface.
Here,
In the picture the transformation is reflection.
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Determine if it opens up or down and find the axis of symmetry
Statement Problem: Determine if it opens up or down and find the axis of symmetry. Given the function;
[tex]f(x)=-2x^2+12x-15[/tex]Solution:
The graph of the function is;
Thus, from the graph. It shows it opens down.
The axis of symmetry is;
[tex]x=-\frac{b}{2a}[/tex]From the given function;
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ f(x)=-2x^2+12x-15 \\ a=-2,b=12,c=-15 \end{gathered}[/tex]Thus, the axis of symmetry is;
[tex]\begin{gathered} x=-\frac{12}{2(-2)} \\ x=-\frac{12}{-4} \\ x=3 \end{gathered}[/tex]
Compute the value of the discriminant and give the number of real solutions of the quadratic equation.-2x² + 6x - 3=0Discriminant:12Number of real solutions:
The formula for the value of discriminant in a quadratic equation in the form ax^2 + bx + c = 0 is :
[tex]d=b^2-4ac[/tex]Where d is the discriminant and
a, b, c are the coefficients in the quadratic equation.
From the given problem,
[tex]ax^2+bx+c=0\Rightarrow-2x^2+6x-3=0^{}[/tex]a = -2, b = 6 and c = -3
Using the formula above,
[tex]\begin{gathered} d=b^2-4ac \\ d=6^2-4(-2)(-3) \\ d=36-24 \\ d=12 \end{gathered}[/tex]Note that if the discriminant is greater than 0, the number of real solution is 2.
The answer is
discriminant = 12
Number of real solutions = 2
Answer:
[tex]2[/tex]
[tex]x[/tex]
[tex]0 \div - 2[/tex]I am having trouble with this and every time I put it in the answer box it says I am wrong
Let's begin by listing out the information given to us:
[tex]\begin{gathered} 0\div-2 \\ \Rightarrow\frac{0}{-2}=0 \\ \therefore The\text{ ans}wer\text{ is zero (0)} \end{gathered}[/tex]Any number that is dividing zero always gives a result of zero
I need help 0.259 written out as a fraction or mixed number?
1) To write 0.259 as a fraction let's firstly rewrite as
[tex]\frac{259}{1000}[/tex]2) Count the digits the dot has gone to the left. Each digit to the left means divided by ten. Like this:
3) Since it starts with a zero then it can't be a Mixed number. So it is an improper fraction. No further simplification could be done.
Maria is taking a multiple-choice
exam in which
there are five possible answers for each question.
The instructions indicate that she will be rewarded
2 points for each correct response, that she will lose
half a point for each incorrect response and that no
points will be added or subtracted for answers left
blank.
A. If Maria does not know the correct answer to a
question, is it to her advantage or disadvantage to
guess at an answer?
B. If she can eliminate one of the possible choices, is it
to her advantage or disadvantage to guess at the
answer?
Since there is no expected value, there is neither a benefit nor a drawback to making an educated prediction.
Expected value (EV), which is based on a random variable's probability distribution, refers to the long-term overall average of that variable.The expected value of a company or even other investment is a crucial factor in investing and is taken into account while performing scenario analysis.To create optimum portfolios, modern portfolio theory combines anticipated value with the standard deviation of an investment's risk.Correct Probability P(Correct) Equals 1/5 = 0.20
P(Wrong) = 4/5 = 0.80.
Expected Value is equal to P(Correct) * Marks given for Correct Questions plus P(Incorrect) * Marks given for Incorrect Questions.
Value Expected Equals 0.20*2 + 0.80* (-0.50)
Value Expected = 0
Since there is no expected value, there is neither a benefit nor a drawback to making an educated prediction.
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Where are the minimum and maximum values for f(x) = sin x + 1 on the interval [0, 2π]?A. min:z =OB. min:x=OC. min:z =max:x= = 0, 2πOD. min:z = 0, π, 2π max: z =Reset Selectionmax: 1 =2 2max:z = 0, π, 2π
Given the function:
[tex]f(x)=sinx+1[/tex]Let's find the minimum and maximum values over the interval [0, 2π].
Let's first find the derivative of the function:
[tex]f^{\prime}(x)=cosx[/tex]Now set the derivative to 0 and solve for x:
[tex]\begin{gathered} cosx=0 \\ \\ \text{ Take the inverse cosine of both sides:} \\ x=cos^{-1}(0) \\ \\ x=\frac{\pi}{2} \end{gathered}[/tex]The cosine function is positive in quadrants I and IV, to find the reference angle(minimum), subtract the first solution from 2π:
[tex]\begin{gathered} x=2\pi-\frac{\pi}{2} \\ \\ x=\frac{2(2\pi)-\pi}{2} \\ \\ x=\frac{4\pi-\pi}{2} \\ \\ x=\frac{3\pi}{2} \end{gathered}[/tex]Plug in the values in the function to determine the minimum and maximum:
[tex]\begin{gathered} f(\frac{\pi}{2})=sin(\frac{\pi}{2})+1=1+1=2 \\ \\ \\ f(\frac{3\pi}{2})=sin(\frac{3\pi}{2})+1=-1+1=0 \end{gathered}[/tex]Therefore, we have the following:
Minimum occurs at: x = 3π/2
Maximum occurs at: x = π/2
ANSWER:
[tex][/tex]which inequality comparing two of the expressions is false when
From the inequlity 1/3 is less than or equals to x or x is less than or equals to 3/7. This means x range from 1/3 to 3/7 . This means x can be 1/3 or 3/7. Therefore, the inequality comparing two of the expression is false when
[tex]\begin{gathered} \sqrt[]{2x}<5x^3 \\ \sqrt[]{2\times\frac{1}{3}}<5(\frac{1}{3})^3 \\ \sqrt[]{\frac{2}{3}}<5\times\frac{1}{27} \\ \sqrt[]{\frac{2}{3}}<\frac{5}{27} \\ \text{From the last inequality you can notice that }\sqrt[]{\frac{2}{3}}<\frac{5}{27}\text{ is false} \end{gathered}[/tex]HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
is (8, -44) a solution of the eqution y = -7x + 6
Answer:
It is NOT a solution to the equation
Step-by-step explanation:
To solve this, plug (8, -44) into the equation. Remember that 8 is x and -44 is y:
y = -7x
-44 = -7 (8)
-7 x 8 = -56
-44 ≠ -56
HELPPPPThe data is matricesCalculate a) A + B, b) CD
Answer:
Given that,
a)A+B
we get,
b)CD
Evaluate. Write your answer as a
decimal or whole number.
(0.07)² =
Answer:
(0.07)^2
= (7 / 100)^2
= 7^2 / 100^2
= 49 / 10000
= 0.0049
(123*7+38*101)/(90-15*6)
Figure it out ur self
2(x + 4) = - 3(x + 5)
Solving for x:
[tex]\begin{gathered} 2(x+4)=-3(x+5)\rightarrow2x+8=-3x-15 \\ \rightarrow2x+3x=-15-8\rightarrow5x=-23 \\ \rightarrow x=-\frac{23}{5} \end{gathered}[/tex]Solving a word problem with three unknowns using a linear... The sum of three numbers is 104. The first number is 6 less than the second. The third number is 3 times the second. What are the numbers?
Let the unknown numbers be x, y, and z where
• First number = x
,• Second number = y
,• Third number = z
If the sum of the three numbers is 104, then;
[tex]x+y+z=104[/tex]If the first number is 6 less than the second, hence;
[tex]\begin{gathered} x=y-6 \\ \end{gathered}[/tex]Also, if the third number is 3 times the second, then;
[tex]z=3y[/tex]Substitute equations 2 and 3 into equation 1 to reduce the variables to the function of "y" only:
[tex]\begin{gathered} x+y+z=104 \\ (y-6)+y+3y=104 \\ y-6+4y=104 \\ 5y-6=104 \\ 5y=104+6 \\ 5y=110\rbrack \\ y=\frac{110}{5} \\ y=22 \end{gathered}[/tex]Get the first number "x"
[tex]\begin{gathered} x=y-6 \\ x=22-6 \\ x=16 \end{gathered}[/tex]Get the third number "z"
[tex]\begin{gathered} z=3y \\ z=3(22) \\ z=66 \end{gathered}[/tex]Therefore the three numbers are 16, 22, and 66.
Solve the inequality 6x^2 + 5x < 4
Answer: -4/3 < x< 1/2
Step-by-step explanation: inequality form
What is the slope intercept equation for the following line
The equation of the line in slope-intercept form is: y = -1/2x - 3.
How to Write the Equation of a Line in Slope-Intercept Equation?The equation of a line can be expressed as y = mx + b, which is in the slope-intercept form, where m is the slope of the line and b is the y-intercept of the line.
Using two points on the line, (0, -3) and (-2, -2):
Slope (m) = (-2 -(-3))/(-2 - 0)
Slope (m) = (-2 + 3)/(-2)
Slope (m) = 1/-2
Slope (m) = -1/2.
The y-intercept (b) of the line is, -3.
To write the equation of the line, substitute m = -1/2 and b = -3 into y = mx + b:
y = -1/2x - 3
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2 - (32/f) use f = 8
Answer:
f = -2
Step-by-step explanation:
2-(32/8) = -2
-8 I think or -2
This is what I think it is
Consider this scenario and then answer the next three questions: A land owner wants a good approximation of the width of his stream from point D to point C. At high point B, he lays a carpenter’s square (used to make right angles) so that he can sight along BC and BA. AD = 9.3 ft and BD = 15.7 ft.1) State the corresponding proportional sides between similar triangles ABC and ADB. 2) Calculate the length of segment AB. Round the answer to the nearest tenth. (Hint: Use Pythagorean Theorem)3) Answer the following questions about the previous scenario: (a) Write an algebraic expression to represent the length from A to C. (b) Write a proportion to find the distance across the stream. (c) What is the length across the stream?
1) Let's consider both triangles ABC and ADB:
Then the proportional sides between similar triangles is:
[tex]\frac{AB}{AD}=\frac{BC}{BD}=\frac{AC}{AB}[/tex]2)Since we have that AD=9.3 and BD=15.7, using the pythagorean theorem we get the following:
[tex]\begin{gathered} AB^2=AD^2+DB^2 \\ \Rightarrow AB^2=(9.3)^2+(15.7)^2=86.5+246.5=333 \\ \Rightarrow AB=\sqrt[]{333}=18.2 \\ AB=18.2 \end{gathered}[/tex]Therefore, AB=18.2 ft
3)a)the best way to represent the length from A to C is with the pythagorean theorem:
[tex]AC=\sqrt[]{AB^2+BC^2}[/tex]b)The proportion to find the distance across the stream is the segment DC, then:
[tex]\frac{AD}{BD}=\frac{DB}{DC}[/tex]c)We can find the length by using the values for AD, BD and DB that we previously got:
[tex]\begin{gathered} AD=9.3 \\ BD=15.7 \\ \Rightarrow\frac{9.3}{15.7}=\frac{15.7}{DC} \\ \Rightarrow DC\cdot(\frac{9.3}{15.7})=15.7 \\ \Rightarrow DC=\frac{15.7}{(\frac{9.3}{15.7})}=26.5 \\ DC=26.5 \end{gathered}[/tex]Finally, we have that the length across the stream is 26.5 ft
Read the description of a proportional relationship.
In The Tall Tales of Timothy Toad, a witch brews a magical invisibility potion. There is a proportional relationship between the amount of potion the witch drinks (in milliliters), x, and the amount of time she is invisible (in minutes), y.
The equation that models this relationship is y=4x.
How much potion does the witch drink to be invisible for 16 minutes? Write your answer as a whole number or decimal.
Using the equation that models the proportional relationship, the amount of portion the witch drinks to be invisible for 16 minutes is: 64 ml.
What is a Proportional Relationship Equation?The equation that represent a proportional relationship between two variables, x and y, is given as y = kx, where the unit rate of the relationship is represented as k in the equation.
Given the following:
x = amount of portion in milliliters that the witch drinks.y = the amount of time in minutes that the witch is invisible.The equation for this relationship is given as y = 4x.
To find the amount of portion (y) the witch drank to be invisible for 16 minutes (x), substitute x = 16 into y = 4x:
y = 4(16)
y = 64
The witch will drink 64 ml of the portion.
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which of the following ratios has the same ratio value as 4:6
ratio value 4 : 6 is 2/3
therefore the anser is 6 : 9 because the ratio value is 2/3 too
Evaluate.
(jk − 1) ÷ j when j = −4 and k = −0.7
Answer:
-0.45
Step-by-step explanation:
(jk − 1) ÷ j =(-4*-0.7 - 1) ÷ -4(2.8 - 1) ÷ -4 1.8 ÷ -4-0. 45what is 13579 x2468?
to muliply the given number is,
[tex]13579x2468?=33512972[/tex]The answer is 33512972.
the part of Ray and Kelley's roller coaster is a curved pattern that can be represented by a polynomial function. I will upload the complete question. because it is to much to type.
Thus, the answer is Kelsey is the one who is correct. Because the number of intercepts is different from the number of zeroes.
1) Examining the question, we take into consideration that not all intercepts are zeroes of the polynomial.
In a third-degree polynomial function, there is another kind of intercept. The y-intercept.
2) So, we can tell that there is no way for both of them to be correct.
3) Thus, the answer is Kelsey is the one who is correct. Because the number of intercepts is different from the number of zeroes.
Which number line represents the solution to 5x < 30? F t 8 0 2 4 6 10 G =N + 4 H 8 0 6 10 H + 0 + 8 2 4 6 10 J + 2 + 4 0 6 8 10
Answer:
Line H, the third option
Step-by-step explanation:
First, find the value of x
5x < 30Divide both sides by 55x/5 < 30/5x < 6X is strictly less than 6, so the answer cannot include 6
This means the answer needs to have an open circle as an endpointThe less than sign (<) tells you the line should be pointing to the left
The diameter of a circle is 8 meters. What is the circumference?Give the exact answer in simplest form. _____ meters. (pi, fraction)
Answer:
[tex]8\pi\text{ or 25.12 meters}[/tex]Explanation:
The below formula can be used to determine the circumference of a circle;
[tex]C=\pi d[/tex]where pi = 3.14
d = 8 meters
Let's go ahead and substitute the above values into our equation and solve for C;
[tex]C=8\pi=25.12\text{ meters}[/tex]