Answer:
a) The equation of the parabola
[tex]y = \frac{-x^{2} }{4} +5[/tex]
Step-by-step explanation:
Explanation:-
Step(i):-
Given the directrix of the parabola y = 6
Focus of the parabola S(0,4)
The standard equation of the parabola
( x- h)² = 4 a (y-k)
(h,k) is the vertex of the parabola
Axis of the parabola is parallel to y-axis
Given the directrix of the parabola y = 6
The directrix of the parabola y = k -a = 6
k-a =6 ...(i)
The focus of the parabola
S( h , K+a) = (0,4)
so h = 0 and K+a =4
K+a =4 ....(ii)
Step(ii):-
Solving (i) and (ii) equations , we get
Adding (i) and (ii) equations and we get
K-a + k+a = 6 +4
2 K = 10
K =5
Substitute K =5 in equation (i)
K -a =6
5 -a =6
5-6 =a
a = -1
Step(iii):-
we have (h,k) =( 0,5) and a = -1
The equation of the parabola
( x- h)² = 4 a (y-k)
( x- 0)² = 4 (-1) (y-5)
x² = -4 y + 20
-4 y = x² - 20
dividing '-4' on both sides, we get
[tex]y = \frac{x^{2} }{-4} +\frac{-20}{-4}[/tex]
[tex]y = \frac{-x^{2} }{4} +5[/tex]
Final answer:-
The equation of the parabola
[tex]y = \frac{-x^{2} }{4} +5[/tex]
What are the roots of 3x^2+10=4x
All instruments used in the song see you again?
Answer:
Of course Piano,keyboard and guitar.
Holly and Tamar completed the work in the table to determine if a triangle with side lengths of 40, 42, and 58 is a right triangle. Holly’s Work Tamar’s Work (40 + 42) squared = 58 squared. 82 squared = 3,364. 6,724 not-equals 3,364. The triangle is not a right triangle. 42 squared + 40 squared = 58 squared. 1,764 + 1,600 = 3,364. 3,364 = 3,364. The triangle is a right triangle.
Which best describes the accuracy of their solutions?
A. Holly is correct.
B. Tamar is correct.
C. Neither Holly nor Tamar is correct.
D. Both Holly and Tamar are correct.
Answer:
B. Tamar is correct.
Step-by-step explanation:
A triangle can be proven as a right angle triangle if it follows Pythagoras theorem. The pythagoras theorem can be use to know if a triangle is right angled triangle. Therefore, pythagoras theorem is expressed as
c² = a² + b²
where
c = hypotenuse sides
a and b can be any of the opposite or adjacent sides.
The hypotenuse side is the longest side so the triangle with length side of 40, 42 and 58 will have the hypotenuse as 58 . The other sides will be the opposite and adjacent sides
c² = a² + b²
58² = 40 ² + 42²
3364 = 1600 + 1764
3364 = 3364
Therefore, it obeys Pythagoras principle. Tamar's work is correct . The triangle is a right angled triangle.
Answer:
B
Step-by-step explanation:
[tex]x^{3} =216[/tex]
Answer:
x = ±6
Step-by-step explanation:
=> [tex]x^3 = 216\\[/tex]
Taking cube root on both sides
=> x = ±6
don’t really quite understand this question.
Answer:
D.
Step-by-step explanation:
Because its three times as much as 42 so its opposite of multiplication so its division with is also 3x=42 and to solve that you divide 3x by 3 and just get x then you divide 42 and 3 and u get your answer( im not gonna do the math lol)
Kelli does the grocery shopping for her family of four. The net income for the
household is $4,500 a month and she aims to spend 13 percent a month on
groceries. Kelli has decided to begin using a cash system for grocery shopping.
How much cash should Kelli pull out weekly to use at the grocery store?
Answer:
$585
Step-by-step explanation:
simply find 13% of 4500. 0.13 x 4500 is $585
What is the solution to the equation Two-thirds x + 1 = one-sixth x minus 7?
Answer:
x = -16
Step-by-step explanation:
2/3x +1 = 1/6x - 7
Multiply each side by 6 to get rid of the fractions
6(2/3x +1) = 6(1/6x - 7)
4x +6 = x - 42
Subtract x from each side
4x-x +6 = x-x-42
3x +6 = -42
Subtract 6 from each side
3x +6-6 = -42-6
3x = -48
Divide each side by 3
3x/3 = -48/3
x = -16
So the right answer is -16
Look at the attached picture
Hope it will help you
Good luck on your assignment
What is the equation of the line of best fit that Frank drew?
A: Y = -3x + 12
B: Y = -3x + 16
C: Y = 1/3x +12 (/ means fraction)
D: Y = 1/3x + 16
Answer:
The answer is actually not an option here. The answer is y=-1/3x+16
HELPPPP MEEEEE ASAPPP :Which angles are pairs of corresponding angles? Check all that apply.
4 lines intersect to form 16 angles. Clockwise from top left, the angles are 1, 2, 3, 4; 5, 6, 7, 9; 9, 10, 11, 12; 13, 14, 15, 16.
Angle1 and Angle3
Angle2 and Angle14
Angle1 and Angle6
Angle3 and Angle7
Angle8 and Angle9
Angle5 and Angle12
9514 1404 393
Answer:
angle 2 and angle 14 angle 3 and angle 7Step-by-step explanation:
Assuming angles are numbered clockwise at each intersection before moving to the next intersection, corresponding angles will differ in their numbers by a factor of 4.
Among the offered choices, the differences of angle numbers are ...
2, 12, 5, 4, 1, 7
Of those pairs listed, angles 2 and 14, and angles 3 and 7 are corresponding angles.
Which congruence theorem can be used to prove △WXZ ≅ △YZX? Triangles W X Z and Y Z X share side X Z. Angles W X Z and X Z Y are right angles. Angles X W Z and X Y Z are congruent. AAS ASA SAS HL
Answer:
The correct option is AAS.
Step-by-step explanation:
Consider the diagram below.
It is provided that The triangles △ WXZ and △ YZX share a side XZ.Angles ∠WXZ and ∠XZY are right angles.Angles ∠XWZ and ∠XYZ are congruent.If two angles are congruent it implies that they are same in degrees or radians.
So, the angles ∠XWZ and ∠XYZ are equal.
So, in the diagram below, one of the triangles have two angles that are equal to the corresponding angles on the other triangle and the two triangles share a side.
Then according to the Angle-Angle-Side (AAS) statement the triangles △ WXZ and △ YZX are congruent.
Thus, the correct option is AAS.
The congruence theorem that can be used to prove that △WXZ ≅ △YZX is; AAS
We are told that;ΔWXZ and ΔYZX share side XZ
∠WXZ and ∠XZY are right angles
∠XWZ and ∠XYZ are congruent
Now, from the given parameters, we can say that from reflexive property of congruence, XZ is congruent to itself and thus, we have one side of both triangles that is congruent.Secondly, since ∠WXZ and ∠XZY are right angles, it means they are equal and therefore congruent to each other.Lastly, we are told that ∠XWZ and ∠XYZ are congruent.In summary, we have 2 corresponding angles and one corresponding side that are equal but the corresponding side is not with the included angles and as such the triangles are congruent by AAS Congruency.Read more about AAS Congruency at; https://brainly.com/question/7727792
Graph the line that represents a proportional relationship between y and x where the unit rate of change of y with respect to x is 4/3. In other words, a change of 1 unit in x corresponds to a change of 4/3 in y
Answer:
you can do 4/3 x 1 if I get it wrong im sorry
a wooden cylinder beam of length 5 meters has a radius of 210cm. the wood density is 693kg/m
i) calculate the volume of the beam in cubic meters
ii) calculate the mass of the beam in kilograms.
Answer:
Cylinder Volume = π • r² • height
Volume = PI * .210 m^2 * 5
Volume = 0.6927211801 cubic meters
Wood has a mass of 693 / cubic meter
mass = 0.6927211801 * 693 = 480.06 kilograms
Step-by-step explanation:
A pebble drops from a balcony that is 80 feet above the ground. The pebble lands on the top of a sign that is 16 feet high. The function y=80−16t2 represents the height y (in feet) of the pebble t seconds after dropping from the balcony. How many seconds does the pebble drop before hitting the sign?
The pebble hits the sign after ______ seconds.
Answer:
t =2 seconds
Step-by-step explanation:
We have, a function that represents the height y of the pebble after dropping the balcony as follows :
[tex]y=80-16t^2[/tex]
The pebble lands on the top of a sign that is 16 feet high.
It is required to find the time does the pebble drop before hitting the sign. The above equation becomes,
[tex]80-16t^2=16\\\\-16t^2+80=16\\\\-16t^2=64\\\\t^2=4\\\\t=2[/tex]
So, the pebble hits the sign after 2 seconds.
Which of the binomials below is a factor of this
trinomial?
x²+x-12
O A. x + 6
O B. X-6
O C. x+4
O D. X-4
Answer:
C
Step-by-step explanation:
The answer is X+4
Please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Alguien que tenga la caridad de explicarme como se hace esto o que me de la respuesta
Answer:
El angulo mide 150 grados.
Step-by-step explanation:
I have attached the work to your problem // Agregué una foto con tu trabajo.
Please see the attachment below // Mirala abajo.
I hope this helps! // Espero que te ayude mi foto. Saludos de Colombia.
if (-3,-4) is a point on the line y =mx+2 ,find the value of m
Answer:
m = 2
Step-by-step explanation:
Given
y = mx + 2
Since (- 3, - 4) is a point on the line then it satisfies the equation.
Substitute x = - 3 and y = - 4, the coordinates of the point, into the equation and solve for m, that is
- 4 = - 3m + 2 ( subtract 2 from both sides )
- 6 = - 3m ( divide both sides by - 3 )
2 = m
Rory records the percentage of battery life remaining on his phone throughout a day. The graph represents the percentage of battery life remaining after a certain number of hours. A graph titled Phone Battery Life. The horizontal axis shows Elapsed Time (hours) numbered 2 to 20, and the horizontal axis shows Battery Life (%) numbered 10 to 120. A line begins at 100% in 0 hours, to 20% in 8 hours, to 100% from 10 to 12 hours, to 60% in 16 hours, to 100% from 17 to 20 hours. At which times could Rory's phone have been plugged into the charger? Select three options. 6 hours 9 hours 11 hours 14 hours 19 hours
Answer:
9,11,19
Step-by-step explanation:
let x be the hours and y the percentage
x=0 , y=100
x=8 , y=80
x=9 , y=0
x=10 , y=100 , x=11 still charging so it is still plugged in
x=16 , y=60 and so on ....
x=18 , y=20
and it will charged again
the answer is 9,11,19
(a) According to the Ministry of Health, the height of Guinean travellers who were quarantined in Tamale for the novel coronavirus were normally distributed about a mean of 160cm and a standard deviation of 8cm. Find the probability that a traveller selected at random has (a) Height between 148cm and 175cm (b) Height above 164cm (c) Height below 179cm
Answer:
a) [tex]P(148<X<175)=P(\frac{148-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{175-\mu}{\sigma})=P(\frac{148-160}{8}<Z<\frac{175-160}{8})=P(-1.5<z<1.875)[/tex]
[tex]P(-1.5<z<1.875)=P(z<1.875)-P(z<-1.5)= 0.970-0.0668= 0.9032[/tex]
b) [tex]P(X>164)=P(\frac{X-\mu}{\sigma}>\frac{164-\mu}{\sigma})=P(Z>\frac{164-160}{8})=P(z>0.5)[/tex]
[tex]P(z>0.5)=1-P(z<0.5)= 1-0.691= 0.309[/tex]
c) [tex]P(X<179)=P(\frac{X-\mu}{\sigma}<\frac{179-\mu}{\sigma})=P(Z<\frac{179-160}{8})=P(z<2.375)[/tex]
[tex]P(z<2.375)= 0.991[/tex]
Step-by-step explanation:
Let X the random variable that represent the heights of Guinean travels , and for this case we know the distribution for X is given by:
[tex]X \sim N(160,8)[/tex]
Where [tex]\mu=160[/tex] and [tex]\sigma=8[/tex]
Part a
We are interested on this probability
[tex]P(148<X<175)[/tex]
We can ue the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we got:
[tex]P(148<X<175)=P(\frac{148-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{175-\mu}{\sigma})=P(\frac{148-160}{8}<Z<\frac{175-160}{8})=P(-1.5<z<1.875)[/tex]
And we can find this probability with this difference using the normal standard distribution or excel:
[tex]P(-1.5<z<1.875)=P(z<1.875)-P(z<-1.5)= 0.970-0.0668= 0.9032[/tex]
Part b
[tex]P(X>164)=P(\frac{X-\mu}{\sigma}>\frac{164-\mu}{\sigma})=P(Z>\frac{164-160}{8})=P(z>0.5)[/tex]
And we can find this probability with this difference using the normal standard distribution or excel:
[tex]P(z>0.5)=1-P(z<0.5)= 1-0.691= 0.309[/tex]
Part c
[tex]P(X<179)=P(\frac{X-\mu}{\sigma}<\frac{179-\mu}{\sigma})=P(Z<\frac{179-160}{8})=P(z<2.375)[/tex]
And we can find this probability with this difference using the normal standard distribution or excel:
[tex]P(z<2.375)= 0.991[/tex]
Please help me with this!!
Answer: Second picture, B
Step-by-step explanation:
Sine is opposite/hypotenuse. Since this is inverse sine, we are looking for the measure of the angle, but the opposite /hypotenuse still applies to sine. We need to find the figure that has 5 opposite of ∠x and 8.3 is the hypotenuse.
We can eliminate C and D because 8.3 is not the hypotenuse, when it has to be according to sine.
The first picture shows that 8.3 is the hypotenuse, but 5 is not opposite of ∠x. It is adjacent to ∠x. This would actually be cos⁻¹(5/8.3).
The second picture, B, shows that 5 is the opposite of ∠x and 8.3 is the hypotenuse. Therefore, B is correct.
Answer:
C
Step-by-step explanation:
[tex]sin^{-1} x = csc x\\[/tex]
sin = [tex]\frac{opposite}{hypotenuse}[/tex]
[tex]csc = \frac{1}{sin} = \frac{1}{\frac{opposite}{hypotenuse}} = \frac{hypotenuse}{opposite}[/tex]
hypotenuse is 5 and opposite is 8,3 -----> third option
Point A is located at (0, -2) and is rotated 180°. What are the coordinates of point A'?
Answer: The coordinates will be (0,2) after a 180 degrees rotation.
Step-by-step explanation:
90 180
(0,-2) → ( -2,0)→ ( 0,2)
Answer:
(0,2)
Step-by-step explanation:
Rule for a rotation of 180° about the origin: [tex](x,y)\rightarrow(-x,-y)[/tex]
We are given the point (0, -2).
Applying the rule:
[tex](0,-2)\rightarrow(0,2)[/tex]
A' should be at (0,2).
What type of correlation does this graph show?
strong positive correlation
weak positive correlation
strong negative correlation
weak negative correlation
no correlation
Answer:
Weak positive correlation
Step-by-step explanation:
Because it can’t be strong otherwise the points would have been very close to the line of best fit
help plz!!!!!!!!!!!!!!!!!!!!
2: V = 330 m^2
3: V = 144 m^2
Step-by-step explanation:
All the figures shown are rectangular prisms.
You can find the volume of a rectangular prism through this formula:
[tex]V = wlh[/tex], where w is the width, l is the length, and h is the height.
To find the volume of a composite figure, find the volume of each smaller figure, then add them together.
Question 2: 330 m^2
V = 3 * 5 * 6 (smaller prism)
V = 8 * 5 * 6 (larger prism)
smaller prism = 90 m^2
larger prism = 240 m^2
240 + 90 = 330 m^2
Question 3: 144 m^2
V = 3 * 4 * 2 (small prism 1)
V = 3 * 4 * 2 (small prism 2)
V = 12 * 4 * 2 (large prism)
small prisms: 24 m^2
large prism: 96 m^2
24 + 24 + 96 = 144 m^2
The following are the last 10 run scores Colin got in cricket: 23, 20, 4, 19, 28, 35, 25, 0, 1, 30 a) Work out Colin's mean score. b) Colin plays cricket again on Sunday. He gets 35 runs. What is his new mean score? Give your answers as decimals. Anyone help I hate maths lol
Answer:
I have given it step by step below.
Step-by-step explanation:
(i) Mean = sum of observations/total no. of observation
= 23 + 20 + 4 + 19 + 28 + 35 + 25 + 0 +1 + 30/ 10
= 185/10
= 18.5
(ii) additional 35 runs
New Mean
=previous total + 35/10 + 1 (the 1 gets added in denominator because of the additional observation)
= 185 + 35/11
= 220/11
= 20
Hope this helps you!
How would you identify a perfect square trinomial? Give an example.
Answer:
"Perfect square trinomials" are quadratics which are the results of squaring binomials. (Remember that "trinomial" means "three-term polynomial".)
For instance:
(x + 3)2
= (x + 3)(x + 3)
= x2 + 6x + 9
...so x2 + 6x + 9 is a perfect square trinomial.
find the first term 43, 39, 35, 31, 27,
Answer:
23
Step-by-step explanation:
the difference between each number in the sequence is 4. Taking 4 away from 27 gives you 23
Hope this helps!
A parabola has a vertex at (-1,0) and opens down. What is the equation of the parabola?
Answer:
y = -(x + 1)^2
Step-by-step explanation:
I graphed the parabola on the graph below so you can see that it has a vertex at (-1,0) and opens down.
A recipe instructs the cook to use 4 cups of water for each 3 cups of powder. If you used 10 cups of water, how much powder should be added?
Answer:
8 cups
Step-by-step explanation:
hope I could help
Which of the following is the radical expression of 5
a_
7
Answer
[tex]\sqrt[7]{a^{5} }[/tex] is the correct answer to the given question.
Step-by-step explanation:
The given question is incomplete the options are missing also the question is also not well described the question is [tex]a^{5/7}[/tex].
[tex]a^{5/7}[/tex]
There is property when we convert any power number into the radical form the denominator of the power number is shifted to the order of the radical number .Here 7 is denominator in the power of [tex]a^{5/7}[/tex] so 7 is shifted to the order of the radical number .So it can be written as [tex]\sqrt[7]{a^{5} }[/tex] is the correct answer.
The student body has 190
students. In how many ways
can it elect a president, vice-
president, secretary?
Answer:
6751080 different ways
Step-by-step explanation:
President: 190 choices
Vice president 189 choices
secretary: 188 choices
190*189*188 =6751080 different ways
Observa las dimensiones del siguiente portarretrato, y escribe la expresión que determina el área disponible para la fotografía del portarretrato.
Answer:
DStep-by-step explanation:
The dimensions of the portrait are attached.
The total area of the portrait is represented by its width 5+x and its length x+1.
We know by definition that the area of a rectangle is
[tex]A= w \times l[/tex]
Where [tex]w[/tex] is the width and [tex]l[/tex] is the length.
Using the given expressiones, we have
[tex]A=(5+x)(x+1)=5x+5+x^{2} +x=x^{2} +6x+5[/tex]
Therefore, the right answer is D.
