Answer:
Let y=ax^2+bx+c be the equation of the parabola. Set up equations.
Using (0,5). 5=a(0)2+b(0)+c
5
=
a
(
0
)
2
+
b
(
0
)
+
c
Using (2,15), 15=a(2)2+b(2)+5
15
=
a
(
2
)
2
+
b
(
2
)
+
5
4a+2b=10
2a+b=5
Using (4,9)
9=a(4)2+b(4)+5
9
=
a
(
4
)
2
+
b
(
4
)
+
5
16a+4b=4
4a+b=1
Subtract each side of (1) and (2) to eliminate b and solve for a: -2a=4
a=-2
Solve for b using (1): 2(-2)+b=5
-4+b=5
b=9
So, the equation is y=−2x2+9x+5
Step-by-step explanation:
solve similar triangles (advanced)
Answer:
x = 9/4
Step-by-step explanation:
Locate point G on segment DE so that DG = 1 and GE = 4. CG is parallel to AD, so ΔCGE ~ ΔABC. Corresponding sides are proportional.
AB/BC = CG/GE
x/1 = 9/4
x = 9/4
_____
Additional comment
Using the given triangles, you can write the proportion statement as ...
(9+x)/x = 5/1
We judge this to take more steps to solve, so we prefer the method shown above.
How many factors does 60 have? A)10 B) 8 C) 12 D) 4
Answer:
60 have 12 factors :1,2,3,4,5,6,10,12,15,20,30,60
write the equation of the line with slope -3/2 passes through the point (-12,16)
Answer:
Step-by-step explanation:
You have two pieces if information: the slope of a line and a point on the line. So you can use the "point-slope" formula in order to write the equation of this line. It is a fill-in-the-blank type of formula.
y - y1 = m(x - x1)
In this fill-in-the-blank formula the y1, the m, and the x1 will be filled in with the numbers you were given.
The problem gave the slope as -3/2 , this is your m. On these linear equation problems and formulas, m always stands for the slope.
So fill that in:
y - y1 = -3/2 (x - x1)
They also gave you a point, that is the (x1, y1) that you need to fill in the formula. The point was (-12, 16), so -12 will be your x1 and 16 will be your y1. Fill it in!
y - 16 = -3/2 (x - -12)
Simplify that ugly 'minus a negative' in the parenthesis.
y - 16 = -3/2 (x + 12)
If you were never told what form of equation to write, or they said "any form of the equation", then you're done!
This is in "point-slope" form.
y - 16 = -3/2(x+12) Ta-da!
If you need to change it to "slope-intercept' form then there are a few more steps.
y - 16 = (-3/2)x + (-3/2)12
y - 16 = (-3/2)x - 18
+16 +16
y = -3x/2 - 2 This is y=mx+b (called slope-intercept form)
A bird leaves its nest and travels 20 miles per hour downwind for x hours. On the return trip, the bird travels 4 miles per hour slower and has 6 miles left after x hours.
a. What is the distance of the entire trip?
miles
b. How long does the entire trip take?
hours
minutes and
seconds
Answer:
The correct answers are:
A) 60 miles; and B) 3.375 hours.
Explanation:
We will use the equation d = rt for this.
For the first leg of the trip, the bird travels 20 miles per hour for x hours. This gives us the equation
d = 20x
For the return trip, the bird travels 4 miles per hour slower, so 20-4 = 16 miles per hour. He also travels 6 miles less than the return distance, for x hours:
d-6 = 16x
To isolate d, we will add 6 to each side:
d-6+6 = 16x+6
d = 16x+6
We will set the two equations equal to one another, since they both equal d:
20x = 16x+6
Subtract 16x from each side:
20x-16x = 16x+6-16x
4x = 6
Divide both sides by 4:
4x/4 = 6/4
x = 1.5
He travels for 1.5 hours both times.
The first time, 1.5 hours at 20 miles per hour is:
d = 1.5(20) = 30 miles
The original trip is 30 miles. This makes the entire trip 30(2) = 60 miles.
On the return trip, he travels 30-6 = 24 miles at 16 miles per hour:
24 = 16x
Divide both sides by 16:
24/16 = 16x/16
1.5 = x
If he goes 24 miles in 1.5 hours at 16 miles per hour, we can use a proportion to find the time it takes for the entire return trip:
24/1.5 = 30/x
Cross multiplying,
24*x = 1.5(30)
24x = 45
24x/24 = 45/24
x = 1.875
This gives him a total time of 1.5+1.875 = 3.375 hours
Step-by-step explanation:
Task-1:
1. Which of the following are in proportion?
a) 21, 35, 24, 40 b) 75, 21, 18, 6
Answer:
1
Step-by-step explanation:
PLS HELP WILL MARK YOU BRAINLIEST!!
No fake answers pls
Answer:
The first one is true, also the second one. Third one as well and the forth also. They all are solutions of the equations. Weird but true.
Answer:
1) x= -6 isn't the correct solution.
2) x=15 is the correct solution.
3) x= -1 isn't the correct solution.
4) x= -4/5 is the correct solution.
Step-by-step explanation:
1) 2x=9+3
2x=12
x=6
2) x=17-2
x=15
3) (multiply both members per 12)
3x-4x=-1
-x=-1
x=1
4) -3x-15=2x-11
-3x-2x=15-11
-5x=4
x= -4/5
Points A, B and C lie on a circle, centre O.
Angle AOC = 142°.
Find the value of y.
The value of the angle [tex]y[/tex] within the quadrilateral [tex]OABC[/tex] inscribed the circle is 142°.
Let suppose that quadrilateral [tex]OABC[/tex] is a parallelogram. Then, the following conditions must be fulfilled:
[tex]\overline {OA} \cong \overline {BC}[/tex] [tex]\overline{AB} \cong \overline{OC}[/tex] [tex]\angle AOC \cong \angle ABC[/tex]In addition, if we have a rhombus we have the additional condition as A, B and C lie on the circle:
[tex]\overline{OA} \cong \overline {AB} \cong \overline {BC} \cong \overline{OC}[/tex] (4)
If we know that [tex]\angle AOC = 142^{\circ}[/tex], then the value of [tex]\angle ABC = y = 142^{\circ}[/tex].
Based on all these finding, we conclude that the value of the angle [tex]y[/tex] within the quadrilateral [tex]OABC[/tex] inscribed the circle is 142°.
To learn more on parallelograms, we kindly invite to check this verified question: https://brainly.com/question/555469
What is the number of solutions to the system of
equations?
Infinitely Many
Solutions
No Solution
One Solution
Two Solutions
Answer:
infinitely many solutions
Step-by-step explanation:
The lines over lap
Find the values of the variable and the lengths of the sides.
Answer:
See answers below
Step-by-step explanation:
2x - 7 = x + 1 sides are equal
x - 7 = 1
x = 8
Find the length of each side
AD = 2x -7 BC = x + 1 AB = 2x - 2 DC = x - 1
AD = 2(8) - 7 BC = 8 + 1 AB = 2(8) - 2 DC = 8 - 1
AD = 16 - 7 BC = 9 AB = 16 - 2 DC = 7
AD = 9 AB = 14
what is the answer in simplest form?
[tex]\\ \sf\longmapsto 2m^2=-200[/tex]
[tex]\\ \sf\longmapsto m^2=-100[/tex]
[tex]\\ \sf\longmapsto m=√-100[/tex]
[tex]\\ \sf\longmapsto m=√100i[/tex]
[tex]\\ \sf\longmapsto m=10i[/tex]
Help please!! Due today
Answer:answer is x=15=20
Step-by-step explanation:i did it before in class and got an A
if a = 3y + 4z and b = z - 2y, then what is the value of a + b?
Answer:
y + 5z
Step-by-step explanation:
Hope this helps!
please help me asapppppp
ty :)
Answer:
2x + 7y = 35
Step-by-step explanation:
Multiply the equation with 7
7 ( y = -2x/7 + 5 )
7y = -2x + 35
2x + 7y = 35
The question is in the picture pls help!!!!!
Answer:
I believe its (B.)
The map shows two biking trails that meet at a park, located at the coordinate (1, 9). Each unit on the map represents 0.5 mile.How many miles longer is Trail A than Trail B?
The length of the trails can be determined be using a formula related to
Pythagorean theorem, which makes use of the rise and run of a trail.
The number of miles longer Trail A is than Trail B is 4 milesReasons:
The location of the park = (1, 9)
The stating point of Trail A = (-7, -6)
Starting point of Trail B = (6, -3)
The length of a trail is adapted from the formula for the distance between points which is a form of Pythagorean theorem as follows;
[tex]Length \ of \ a \ trail, \ L = \mathbf{\sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}}[/tex]
Therefore;
[tex]Length \ of \ trail, \ A = \sqrt{\left (1-(-7) \right )^{2}+\left (9-(-6) \right )^{2}} = \mathbf{17}[/tex]
[tex]Length \ of \ trail, \ B = \sqrt{\left (1-6 \right )^{2}+\left (9-(-3) \right )^{2}} = \mathbf{13}[/tex]
The difference between the lengths of the trails = 17 mi - 13 mi = 4 miles
Therefore;
Trail A is 4 miles longer than Trail B
Learn more about finding the distance between two points on a graph here:
https://brainly.com/question/9917504
A t-shirt shop bought a total of 24 t-shirts (t) and hats (h) combined. They bought t-shirts for $12.50 each and hats for $8 each. The store spent a total of $259.50, which system of equations could be used to find the number of hats and t-shirts bought?
Answer:
12.5t + 8h = 259.5
t + h = 24
Step-by-step explanation:
Write one equation to deal with the costs and one equation to deal with the numbers of shirts and hats.
12.5t + 8h = 259.5
t + h = 24
Evaluate and simplify without a calculator:
−35+23
Pleasee helpp
Answer:
The answer would be -12, I'm not to sure what simplify means
Solve the system of linear equations by substitution
6x-9=y
y=-3x
Answer:
x=1, y=-3. (1, -3).
Step-by-step explanation:
6x-9=y
y=-3x
-----------
6x-9=-3x
6x-(-3x)=9
6x+3x=9
9x=9
x=9/9
x=1
y=-3(1)
y=-3
Lillian invests money in an account paying a simple interest of 6.6% per year. If she invests $160 and no money will be added or removed from the investment, how much will she have in one year, in dollars and cents?
Answer:
Lillian will have $170.56 in one year
Step-by-step explanation:
First we have to figure out what is 6.6% of 160.
160 * 6.6% = 10.56
Now we just add 160 with the 6.6% to figure out the answer.
160 + 10.56 = 170.56
So, the answer is 170.56 dollars.
Hope this helps! :)
૮ ・ﻌ・ა
What are the values of a1 and r of the geometric series? 2 â€"" 2 2 â€"" 2 2.
The values of [tex]a_1[/tex] is 2 and r are -1 of the geometric series and it can be determined by using geometric summation operation.
Given that,
The geometric series is,
2 – 2 + 2 – 2 + 2
We have to determine
What are the values of a1 and r of the geometric series?
According to the question,
Geometric series;2 – 2 + 2 – 2 + 2
The geometric series [tex]a_1[/tex] is the first term of the geometric sequence and r is the common ratio of the geometric series.
The first term of the given geometric series is 2.
And the common difference in the given geometric series is,
[tex]\rm r = \dfrac{a_2}{a_1}[/tex]
Where [tex]a_1[/tex] is the first term of the geometric sequence and [tex]a_2[/tex] is the second term of the geometric sequence.
Then,
The common difference in the given geometric series is,
[tex]\rm r = \dfrac{-2}{2}\\\\r = -1[/tex]
The common ratio in the given geometric series is -1.
Hence, the values of [tex]a_1[/tex] is 2 and r is -1 of the geometric series
For more details about Geometric progression refer to the link given below.
https://brainly.com/question/25959517
what is the order from least toe greatest with the numbers 0.75,0.3215,2/8,9/16
Answer:2/8, 0.3215, 9/16, 0.75
Step-by-step explanation:
2/8 = 0.25 0.3215 is higher then 9/16 =0.5625 next is 0.75
WILL GIVE BRAINLY,5 STARS, THANKS
4,800/60 = 480 tens / 6 tens = ___
Answer:
80
Step-by-step explanation:
Answer:
800 = 80 tens
Step-by-step explanation:
4800 / 60 = 800
Solve for HL hypotenuse leg theorem
-GEOMETRY
[tex]\huge \bf༆ Answer ༄[/tex]
The Additional information needed to prove the Triangles congruent by HL criteria is ~ D
[tex] \sf ST \cong SE \: \: or \: \: US \cong FS[/tex]ST = SE or US = FS
===========================================
Explanation:
As you mentioned, HL stands for hypotenuse leg. The sides EF and UT marked with triple tickmarks are congruent, and they are the congruent hypotenuses. That takes care of the "H" part of "HL". So we can cross off choice C because it mentions TU = EF, which is already taken care of.
The "L" part can involve either leg of the triangles. So we could involve the legs ST and SE (they appear to be the shorter legs), or we could involve the longer legs US and FS. We only need to pick one of those options to handle the "L" portion. If we knew all three aspects, then we could easily refer to the SSS (side side side) congruence theorem.
The HL theorem only applies to right triangles.
Help me with this pleassssseeeedeeeeeeee..
A line passes through (-5, -3) and is parallel to -3x - 7y = 10. The equation of the line in slope-intercept form is _____.
Answer: y = -(3/7)x - (36/7)
Step-by-step explanation:
Let's convert -3x - 7y = 10 to standard slope intercept form: y=mx + b, where m is the slope and b is the y-intercept (the value of y when x=0).
-3x - 7y = 10
-7y = 3x + 10
y = -(3/7)x - (10/7)
This line has a slope of -(3/7). Any line that is parallel will have the same slope, so we can write y = -(3/7)x + b to start our new line.
We want a value of b that forces the line to go trough point (-5,-3). Use this point in the partial equation and solve for b:
y = -(3/7)x + b
-3 = -(3/7)(-5) + b
-3 = (15/7) + b
b = -3 - (15/7)
b = -(21/7) - (15/7)
b = -(36/7), or -5 1/7
y = -(3/7)x - (36/7)
what 2+2 x10+2X2+10=
Answer:
36
Step-by-step explanation:
Use PEMDAS:
2*10 is 20
2*2 is 4
So the equation is now
2+20+4+10=
Now add:
36
Thus the solution is 36
Hope this helps!
solve: 8+ x/2= 1/4 (x-4)-1
A. X = -40
B. X = 40
C. There are infinitely many solutions.
D. X = -24
-185 = -5 - 9b
How to find the answer to this problem above?
Answer:
b=20
Step-by-step explanation:
-185-5=9b
-180=9b
=>b= -20
anybody help please again •_•
Answer:
i am not to sure but i think its 5/13 or 5/40
A rectangular piece of metal is 5 in longer than it is wide. Squares with sides 1 in long are cut from the four corners and the flaps are folded upward
to form an open box. If the volume of the box is 594 in,what were the original dimensions of the piece of metal?
What is the original width in inches?
The width of the piece of metal will be 24 inches while the length will be 29 inches.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Let's say the width of metal w then the length will be w + 5
Now if we cut 1 inch square from the corner of the metal and then fold then the resultant cuboid will have;
Length = w+5 - 2 -= w + 3
Width = w - 2
Height = 1
So,
Volume = (w+3)(w-2)1
594 = w² + 2w + 3w - 6
w² + w - 600 = 0
By solving this
w = 24 so width will be 24 and length will be 24 + 5 = 29.
Hence "The width of the piece of metal will be 24 inches while the length will be 29 inches".
For more about rectangles,
https://brainly.com/question/15019502
#SPJ2