The Parabola is a locus of points equidistant from a single point called focus and a line called Directrix. The correct option is C.
What is a Parabola?A parabola is a U-shaped figure, all the point on the parabola is equidistant from the focus, and a line called Directrix.
The Parabola is a locus of points equidistant from a single point called focus and a line called Directrix.
Therefore, The correct option is C.
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show that,t for any triangle abc, even if b or c is an obtuse angle, a = b cos c + c cos b. use the law of sines to deduce the "addition formula" sin (b + c) = sin b cos c + sin c cos b.
For the triangle ABC, if B or C is an obtuse angle, then a = b cos C + c cos B according to the law of sines and the addition formula.
What is the law of sines states?For a triangle ABC with angles ∠A, ∠B, and ∠C and with sides a, b, and c
Thus, we can write,
sinA/a = sinB/b = sinC/c
or
a/sinA = b/sinB = c/sinC
Calculation:It is given that in a ΔABC,
The ∠B or ∠C is an obtuse angle.
So, ∠A = 180° - (B + C)
⇒ sin A = sin (180° - (B + C))
⇒ sin A = sin (B + C) (since we know that sin(180° - θ) = sinθ)
From the addition formula,
sin (B + C) = sin B cos C + sin C cos B
⇒ sin A = sin (B + C)
⇒ sin A = sin B cos C + sin C cos B
From the law of sines,
a/sinA = b/sinB = c/sinC = K
⇒ aK =sin A, bK = sin B, cK = sin C
On substituting,
⇒ sin A = sin B cos C + sin C cos B
⇒ aK = bK cos C + cK cos B
⇒ K(a) = K(b cos C + c cos B)
∴ a = b cos C + c cos B
Hence it is proved.
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Three equivalent ratios are shown on the graph
To plot more the points, we move up one and right two.
How to plot more the points?The ratios are given as:
(1, 0.5), (2, 1), and (5, 2.5)
Calculate the slope (m) using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{1 - 0.5}{2 - 1}[/tex]
Evaluate
[tex]m = \frac{0.5}{1}[/tex]
This gives
[tex]m = \frac{1}{2}[/tex]
The above means
Vertical : Horizontal = 1 : 2
This means a vertical movement of 1, followed by an horizontal movement of 1
Hence, to plot more the points, we move up one and right two.
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Complete question
Three equivalent ratios are shown on the graph. On a coordinate plane, points (1, 0.5), (2, 1), and (5, 2.5) are plotted. Starting on one of the plotted points, how can you plot more equivalent ratio points?
help me please n^2, when n = 3
Answer: 9
Step-by-step explanation:
Given:
n², n = 3
Plug-in:
(3)²
Square 3:
3 * 3 = 9, so (3)² = 9
Simplify:
9
What is the logarithmic form of 13² = 169?
The logarithmic form of 13² = 169 is ㏒₁₃ 169 = 2
How to determine the logarithmic formUsing the logarithmic rule , we have that
㏒ₙn = bⁿ
Given 13² = 169
It is important to note that it can be written either in the logarithmic form or in the index form.
In this case, we have written in the index form as .
㏒₁₃ 169 = 2
Thus, the logarithmic form of 13² = 169 is ㏒₁₃ 169 = 2
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PLEASE HELP, kinda forgot how to do it
Answer:
20
Step-by-step explanation:
Rise over run
Answer:
m = 20
Step-by-step explanation:
Two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle. Which congruence theorem can be used to prove that the triangles are congruent?
SSS
AAS
SAS
HL
Answer: Option 2 or B. AAS
Step-by-step explanation: B. AAS
Trust me!
If you are working on Edge the answer is correct. The proof is down below. I hope someone finds this helpful.
If you found any of my answers helpful please like and subscribe I mean "heart", friend me and/or choose my answer as Brainliest. I would appreciate it! Good luck everyone! :)
When two angles and the non-included side of one triangle are congruent to other triangle the by AAS congruency they are congruent. Therefore, option B is the correct answer.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
AAS, two angles and one side of a triangle are equal to two angles and one side of another triangle then they are congruent.
Therefore, option B is the correct answer.
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Select the correct answer from each drop-down menu.
Given: UX=WZ VW=XY
Prove: UV=YZ
The reason in line __ does not justify the statement because ___. Instead, the reason should be ___.
OPTIONS:
1:
A.)4
B.)5
C.)6
D.)3
2:
A.) Values were not added to each side
B.) Values were not subtracted from each side
C.) More than two segments were added.
3:
A.) The substitution property of equality
B.) Segment addition
C.) Given
The answers are D.)3, B.) Values were not subtracted from each side, and A.) The substitution property of equality
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
We have;
UX=WZ
VW=XY
In line 3 the statement does not justify.
Because values were not subtracted from each side.
The reason should be substitution property of equality.
Thus, the answers are D.)3, B.) Values were not subtracted from each side, and A.) The substitution property of equality
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Answer:
I just got it right on the test
Step-by-step explanation:
A researcher who wishes to study the effects of a prenatal breastfeeding education program on the length of time African-American inner-city women breastfeed infants learns that 70% of women in the target population are unmarried. To achieve stratified random sampling in a sample of 50 subjects, the researcher will:
Select a random sample of 35 unmarried and 15 married subjects
A researcher who wishes to study the effects of a prenatal breastfeeding education program on the length of time African-American inner-city women breastfeed infants learns that 70% of women in the target population are unmarried.
To achieve stratified random sampling in a sample of 50 subjects, the researcher will:
Select a random sample of 35 unmarried and 15 married subjects.
hence, Select a random sample of 35 unmarried and 15 married subjects.
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fully simplify 7c - 4h - 2c - 5h
Answer:
5c-9h
Step-by-step explanation:
1) 7c-4h-2c-5h
2) 5c-4h-5h
3) 5c-9h
What else would need to be congruent to show that triangle ABC is congruent to DEF by AAS?
Answer:
B
Step-by-step explanation:
In order the angles <C and <F are shared, then <B and <E, then the side equaling 10. This together proves that this triangle is congruent because of AAS (angle,angle,side) a triangle congruency rule.
Briefly explain how multiple regression enhances the two primary purposes of regression analysis.
The statistical goal of multiple regression analysis is to build a linear equation model that identifies the optimal weighted linear combination of independent variables in the study in order to optimally predict the reference variable.
Regression analysis is usually performed for one of two purposes. Predicting the value of the dependent variable of a person whose information about the explanatory variable is available, or estimating the effect of the explanatory variable on the dependent variable.
In multiple regression analysis, researchers can determine the strength of the relationship between the outcome (dependent variable) and multiple predictors, and the importance of each predictor in the relationship, often the effect of other predictors. It can be evaluated by statistically eliminating it.
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Write at least 1 full sentence explaining the steps you would take to evaluate an expression.
The step you would take to evaluate an expression is to follow the order of operation
What are expressions?Expressions are mathematical statements that involve variables, terms, coefficients and mathematical operators
How to determine the steps?Different expressions require different ways of solving
However, the general guide is that the order of operation must be followed
The order of operation is represented by the acronym BEDMAS
Which means
Bracket
Exponent
Division
Multiplication
Addition
Subtraction
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If I went to bed at around 1:20 AM, and woke up at 8 AM, around how many hours of sleep did I get?
Answer:
you would get about 6:20 of sleep
you would have gotten at least 6 hours of sleep and 20 mins
Step-by-step explanation:
Can someone write me a paragraph proof for this problem
Answer:
Step-by-step explanation:
ur mother
y=3x + 4
x=3y + 4
x-4= 3y
how do divide x-4 by 3?
Answer:
x = 3y + 4
Step-by-step explanation:
add 4 to both sides
simplify
select all the con
Choose the graphs that indicate equations with no solution.
+
3x + 2 = −6(-ª)
y
A
4 -2
4+
2
-2-
2 4
4
+x+
8(-a)
-4 -2
HE
H
у
14
2.
2.
-2-
-4-
-4 -2
-2x + 4
4
4 =
y
4
2
2
+x
A
2
4
+2
3+1=
-4 -2
4
2.
12
x +
4
++++
-4
2
52 + 1 = 7(-z)
y
-2
5(-) + 2
4
TE
t
4
2-
14
+
+X
2
4
Hx
Answer:
Top leftBottom rightStep-by-step explanation:
For there to be no solution, the graphs must never intersect.
An equation is formed of two equal expressions. The graphs that indicate that the equation has no solution are the first graph from the top row and the last graph from the second row.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of a pair of equations is the point at which the graph of the two functions intersects each other. The number of times the two graphs intersect is the number of solutions to the pair of equations.
Since there are only two graphs where the graphs do not intersect.
Thus, the graphs that indicate that the equation has no solution are the first graph from the top row and the last graph from the second row.
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117 Mr. Turtle, Mrs. Squirrel and Ms. Pigeon work at the Magic Forest's post office. Mr. Turtle can
deliver a package from the Southern Glade to the Northern Glade in 3 days, while Ms. Pigeon can
deliver it in 30 minutes. How much time will the same job take Mrs. Squirrel, if the ratio of Mr.
Turtle's time to the Mrs. Squirrel's time is the same as the ratio of Mrs. Squirrel's time to Ms.
Pigeon's time?
The proportion shows that the time taken to do the same job by Mrs. Squirrel is 6 hours.
How to calculate the value?From the information given, the ratios are:
Turtle / Squirrel = Squirrel / Pigeon
3/x = x/(1/48)
x² = 1/16
x = 1/4
The number of days will be:
= 1/4 × 24
= 6 hours.
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What is a disadvantage of debt consolidation?
OA. You can have payments that are lower.
B. You can spread payments over a longer time.
о C. You can have a lower interest rate.
о D. You can pay more money in the long term.
A disadvantage of debt consolidation is you can pay more money in the long term.
What is debt consolidation?
Debt consolidation is when a person takes out a new loan in order to pay off an existing loan. Debt consolidation increases the money you pay in the long term because you would still have to pay for the new debt incurred.
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Help me pleaseee!!! :(
Find the area of the triangle
Answer:
12 yd^2 (c)
Step-by-step explanation:
A=1/2bh
= 1/2 x 8 x 3
=12 yd^2
Hope it helps!!!
Answer: 12 yd^2
Step-by-step explanation:
Area=[tex](1/2) *base*height\\[/tex]
here
base= 8yd
height =3 yd
putting values
area=(1/2)*(8)*(3)
area=12 yd^2
Which function has zeros at x = -2 and x = 5?
O f(x) = x2 + 2x - 10
• f(x) = x2 - 2x - 10
O f(x) = X2 + 3x - 10
® f(x) = x2 - 3x - 10
Answer:
f(x)=x²-3x-10
Step-by-step explanation:
\begin{gathered}f(x) = x {}^{2} - 3x - 10 \\ to \: find \: x \: intercept \:o r \: zero \: substitute \: f(x) = 0\: \\ 0 = x {}^{2} - 3x - 10 \\ x {}^{2} - 3x - 10 = 0 \\ x {}^{2} + 2x - 5x - 10 = 0 \\ x(x + 2) - 5x - 10 = 0 \\ x(x + 2) - 5(x + 2) = 0 \\ (x + 2).(x - 5) = 0 \\ x + 2 = 0 \\ x - 5 = 0 \\ x = - 2 \\ x = 5\end{gathered}
f(x)=x
2
−3x−10
tofindxinterceptorzerosubstitutef(x)=0
0=x
2
−3x−10
x
2
−3x−10=0
x
2
+2x−5x−10=0
x(x+2)−5x−10=0
x(x+2)−5(x+2)=0
(x+2).(x−5)=0
x+2=0
x−5=0
x=−2
x=5
therefore the zeros of the equation are x₁=-2,x₂=5
Michell is making a sign for her sister's birthday. The sign says "HAPPY BIRTHDAY" in all capital letters. If each letter is 4/5 inches long estimate the length needed to spell out “HAPPY BIRTHDAY."
ps.also add 4/5 for the space between the two words..................... Thanks
Answer:
5/4 is the correct answer for this question
6.Find by suitable rearrangement
a)4x2984x250
b) 495+114+205
factor of 13965
The solutions by suitable arrangement are:
2984000814How to find the suitable arrangementa)4x2984x250
By suitable arrangement, we would arrange this as
(4 x 250) x 2984
= (1000 * 2984)
= 2,984,000
b. b) 495+114+205
By suitable arrangement we would have:
(495 + 205) + 114
= 814
c. The factors of 13965 are all of the numbers that can divide this number.
They are: 1, 3, 5, 7, 15, 19, 21, 35, 49, 57, 95, 105, 133, 147, 245, 285, 399, 665, 735, 931, 1995, 2793, 4655, and 13965
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Find the equation of the line perpendicular to y = - 1/2 x − 5 that passes through the point ( 2 , 7 ) . Write this line in slope-intercept form.
The equation of the perpendicular line as required is; y = 2x -3.
What is the equation of the perpendicular line?Since the line in discuss is perpendicular to the given line whose slope is; -1/2. It therefore follows that the slope of the line to be determined is;
m = -1/(-1/2) = 2.
The equation of the required line can therefore be written as;
2 = (y-7)/(x-2)
2x -4 = y -7
Hence, y = 2x -3 is the equation of the line.
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The amount of water in a leaky bucket is given by the linear function , where y is in ounces and x is in minutes. Find and interpret the slope and y-intercept of the linear equation.
The y-intercept = 127 and the slope = -10
How to determine the y-intercept and the slope?The function is given as:
y = 127 - 10x
A linear function is represented as:
y = c + mx
Where
c = the y-intercept
m = slope
This means that:
y-intercept = 127
slope = -10
The y-intercept implies that, the initial amount of water is 127 ounces and the slope implies that the water leaks by 10 ounces per minute
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Complete question
The amount of water in a leaky bucket is given by the linear function y = 127 - 10x, where y is in ounces and x is in minutes. Find and interpret the slope and y-intercept of the linear equation.
Can someone help me out on these geometry fill in the blanks questions? Just questions 2,3,4.. it’s urgent
Which graph shows a system of equations with a solution at (2, -1)?
Graph fourth shows a system of equations with a solution at (2, -1) option fourth is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is
Which graph shows a system of equations with a solution at (2,-1)?
The graph is in the picture, please refer to the attached picture.
As we can see in the graph there are two graphs of a function shown.
The first one is a parabola and the second one is a linear graph.
From the graph, the intersection point of the two groups is at (2, -1)
The intersection point is shown in graph fourth.
Thus, graph fourth shows a system of equations with a solution at (2, -1) option fourth is correct.
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Answer:
Graph 4
Step-by-step explanation:
Circle a is centered at point p, and point q lies on the circle. what other points also lie on circle a?
All the points which are at the distance of PQ from the center of the circle will be located on the circle.
What is a circle?A circle is a closed shape created by following a moving point on a plane while maintaining a constant distance from another point.
According to the given question, the circle named A has it's center at the point P and has a point Q on the circumference of the circle, so any point at the distance of PQ from the center of the circle will lie on the circumference of the circle.
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Answer:
Points S, T, and W
Hope this helps!
Step-by-step explanation:
an=−2+32(n−1)
What is the 21st term of the sequence?
Answer:
a₂₁ = 638
Step-by-step explanation:
substitute n = 21 into the explicit formula
a₂₁ = - 2 + 32(21 - 1) = - 2 + 32(20) = - 2 + 640 = 638
PLEASE HELPPPP
An expression is shown below:
2x3 + 10x2 − 4x2y − 20xy
Part A: Re-write the expression by factoring out the GCF
Part B: Factor the entire expression completely
Show your work
The complete factor of the given expression is 2x(x-2y)(x+5)
Factoring of expressionGiven the following expression shown below
2x^3 + 10x^2 − 4x^2y − 20xy
Factor out the GCF
2x^2(x+5)-4xy(x+5)
Group
(2x^2-4xy)(x +5)
2x(x-2y)(x+5)
Hence the complete factor of the given expression is 2x(x-2y)(x+5)
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