Answer:
Step-by-step explanation:
To solve this problem you have to complete the square. To do that, set the quadratic equal to 0, then move the constant over to the other side. That's 2 steps in one, but they're simple ones:
[tex]-5t^2+10t=-65[/tex]
The first picky rule that completing the square has to follow is that the coefficient on the squared term has to be a 1. Ours is a -5, so we factor it out:
[tex]-5(t^2-2t)=-65[/tex] . Now it gets even pickier. To create a perfect square binomial on the left, we take half the linear term, square it, and add it in to both sides. Our linear term is a -2. Half of -2 is -1, and -1 squared is 1, so we add 1 into the set of parenthesis. BUT the -5 out front is a multiplier and refuses to be ignored. To offset the addition of the 1 inside the parenthesis, we have to multiply it by the -5 out front to get -5:
[tex]-5(t^2-2t+1)=-65-5[/tex]
The perfect square binomial on the left side and simplifying the right:
[tex]-5(t-1)^2=-70[/tex] . Now we'll move the 70 over and set the quadratic back equal to y:
[tex]-5(t-1)^2+70=y[/tex]
That's the quadratic in vertex form. The vertex here is (1, 70) which serves to answer 2 questions for us: the max height of the ball along with the time it was at that max height. For us, the ball reached a max height of 70 m after 1 second in its travels.
You could also do it the "calculus way" which is to find the derivative of the position function, which is
-10t + 10 = 0 and solve for t:
-10t = -10 so
t = 1. That's the time that the ball is at its highest point, and to find the highest point, sub that value in for t in the position function:
[tex]h(t)=-5(1)+10(1)+65[/tex] which comes to 70 m. I'm not sure what class you're taking so I did both! Calculus is way easier.
Combine like terms.
3p2q2-3p2q3+4p2q3-3p2q2+pq
Answer:
104
Step-by-step explanation:
:D
Find the value of x if 12x=34^2 - 26^2
Answer:
40
Step-by-step explanation:
[tex] 12x = 34^2 - 26^2 \\
12x = (34+26)(34-26)\\
12x = 60\times 8\\\\
x = \frac{60\times 8}{12}\\\\
x = 5\times 8\\
x = 40[/tex]
A cylinder has a volume of 390 cm³. If a cone has the same dimensions as the cylinder then what is the volume of the cone.
Answer: The volume of the cone is 130 cubic centimeters.
Step-by-step explanation:
We know that to find the volume of a cylinder you will use the formula
V= [tex]\pi[/tex][tex]r^{2} *h[/tex] Where r is the radius and h is the height.
And to find the volume of a cone you will use the formula
V= [tex]\pi[/tex][tex]r^{2}[/tex]*h /3
So if they have the same dimensions which is the height and the radius then we will just divide the volume of the cylinder by 3 to find the volume of the cone.
V = 390/3
V = 130 cm^3
(Algebra || is Soo hard!) Please someone help me:)
Answer:
B
Step-by-step explanation:
B is the correct answer
2+i/5= i=5 +=-
have a nice day
Answer:
[tex]\boxed{\sf B) \ 2-i}[/tex]
Step-by-step explanation:
[tex]\sf \frac{2+i}{5}[/tex]
Reciprocal the fraction.
Switch the denominator with the numerator.
[tex]\sf \frac{5}{2+i }[/tex]
Multiply the numerator and the denominator with the conjugate [tex]\sf 2-i[/tex].
[tex]\sf \frac{5(2-i)}{(2+i)(2-i)}[/tex]
[tex]\sf \frac{10-5i}{(2+i)(2-i)}[/tex]
Apply rule to solve for the denominator:
[tex]\sf (a+bi)(a-bi)=a^2 +b^2[/tex]
[tex]\sf a=2\\b=1[/tex]
[tex]\sf \frac{10-5i}{2^2 +1^2 }[/tex]
[tex]\sf \frac{10-5i}{4+1}[/tex]
[tex]\sf \frac{10-5i}{5}[/tex]
Simplify the fraction.
[tex]\sf \frac{10}{5}-\frac{5i}{5}[/tex]
[tex]\sf 2-i[/tex]
GIVING BRAINIEST (open attachment)
Answer:
1/19
Step-by-step explanation:
Let's say there are x yellow cubes.
That means there are 3x blue cubes.
Therefore, there must be 15x green cubes.
In total: we have 19x cubes.
Therefore the probability of a cube being yellow is x / 19x
which simplifies to 1/19
Answer:
1/19
Step-by-step explanation:
Solution:-
- First we will define the distribution of colors in the bag.
- We will use variable:
x: the number of yellow cubes in bag
- The following color distribution can be made by using the data given in the question:
Color Number of cubes
Yellow x
Blue 3*x = 3x
Green 3x*5 = 15x
======================================
Total 19x
======================================
- Sarah is to draw a cube from the bag. We are to determine the probability that the randomly picked cube would be yellow. We will denote our event as randomly picking a yellow cube from the bag with a defined finite distribution.
p ( Picks Yellow cube ) = [ Number of yellow cubes ] / [ Total cubes ]
p ( Picks Yellow cube ) = [ x ] / [ 19x ]
p ( Picks Yellow cube ) = 1 / 19 .... Answer
Lea's car travels an average of 303030 miles per gallon of gas. If she spent \$20.70$20.70dollar sign, 20, point, 70 on gas for a 172.5172.5172, point, 5 mile trip, what was the approximate cost of gas in dollars per gallon? Choose 1 answer: \$1.45
The question was not written properly above.
Complete Question :
Lea's car travels an average of 30 miles per gallon of gas. If she spent $20.70 on gas for 172.5 mile trip, what was the approximate cost of gas in dollars per gallon?
Answer:
$3.6
Step-by-step explanation:
From the above question, we have the following information:
For
30 miles = 1 gallon of gas
We are also told she travelled,
$20.70 on gas for 172.5 miles
Step 1
Find how many gallons of gas was issued in the 172.5 miles
30 miles = 1 gallon of gas
172.5 miles = y
Cross multiply
30 × y = 172.5 miles × 1
y = 172.5 miles/30
y = 5.75 gallons
Therefore, for 172.5 miles she used 5.75 gallons of gas
Step 2
For step 2 we find the approximate cost of gas in dollars per gallon
$20.70 = 172.5 miles = 5.75 gallons of gas
Hence,
5.75 gallons of gas = $20.70
1 gallon of gas = $X
Cross Multiply
5.75 gallons × $X = $20.70 × 1 gallon
$X = $20.70 × 1 gallon/ 5.75 gallons
$X = $3.6
X = $3.6
Therefore, the approximate cost of gas in dollars per gallon = $3.6
I don't understand how to do this problem.
Answer:
First blank: 6a
Second blank: 2/3
Third blank: 21.6
Fourth blank: 3.9
Step-by-step explanation:
Basically, all you need to do is distribute the 2/3 to the stuff inside the parentheses. That means in the first blank, write 6a inside since you're multiplying 2/3 and 6a, and then in the second blank you write 2/3 since you're multiplying 2/3 and 9 together.
2/3*6a+2/3*9 = 21.6 is what you should have.
Now, just solve for a.
4a+6 = 21.6
4a=15.6
a=3.9
Answer:
2/3 * 6a+ 2/3 +9 = 21.6
a = 3.9
Step-by-step explanation:
2/3 ( 6a+9) = 21.6
Distribute
2/3 * 6a+ 2/3 +9 = 21.6
4a + 6 = 21.6
Subtract 6 from each side
4a = 15.6
Divide each side by 4
4a/4 = 15.6/4
a =3.9
Solve y^2-7=2xy ; 2x^2+3=xy
with explanation and proper steps!
Answer:
what does ; resemble
Step-by-step
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
A) Let's solve for x. [tex]y^2-7=2xy[/tex]
Step 1: Flip the equation.
[tex]2xy = y^2 - 7[/tex]
Step 2: Divide both sides by 2y.
[tex]\frac{2xy}{2y} = \frac{y^2- 7}{2y}[/tex]
[tex]x = \frac{y^2- 7}{2y}[/tex]
Answer : [tex]x = \frac{y^2- 7}{2y}[/tex]
~~~~~~~~~~~~~
B) Let's solve for y. [tex]2x^2+3=xy[/tex]
Step 1: Flip the equation.
[tex]xy = 2x^2 + 3[/tex]
Step 2: Divide both sides by x.
[tex]xy = \frac{2x^2 + 3}{x}[/tex]
[tex]y = \frac{2x^2 + 3}{x}[/tex]
Answer : [tex]y = \frac{2x^2 + 3}{x}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
Find the coordinates of P so that P partitions the segment AB in the ratio 3:1 if A(0,7) and B(−4,2).
Answer:
(-3, 3.25)
Step-by-step explanation:
3. The diagram shows a piece of rectangular tile
PQRS. A kite shape TUVW is inscribed in the
rectangle. Given that the perimeter of PQRS is
120 cm, find the area of TUVW.
Answer:
432cm²
Step-by-step explanation:
If the Perimeter is 120cm, PT=8 (120-28-12-12-28-12-12)/2
This means the rectangle is 24x36.
area of a kite is the diagonals divided by 2 (or half of the rectangle).
24x36=864
864/2=
432 cm²
can I help someone with math
Answer:
please mark my answer brainliest
Step-by-step explanation:
can you tell me a subscript n =sin to the power theta +cosec to the power n theta...and a subscript 1 =2...then prove that a subscript n =2...
A(n)=-5+6(n-1).. what’s the 12th term?
Answer:
The answer is 61
Step-by-step explanation:
To find each n term replace the n with term u need to find .
A(12)= -5+6(12-1)
=-5+6(11)
=61
Answer:
61
Step-by-step explanation:
A(n)=-5+6(n-1)
Let n = 12
a(12) = -5 + 6(12-1)
-5+6(11)
-5+66
61
Please answer it in two minutes
Answer:
0.9
I guess.
If yes
.. Follow me..
Can someone please tell me the answer! THANK YOU
Answer: approximately 24 square units in the shaded areas
Step-by-step explanation:
The area of the entire dark circles will be for each πr², then divided by 2 to get the area of the semicircles created on the sides of the triangles:
16π + 9π = 25π Half that times value for pi
≈ 39.2699 is the area of the dark semicircles. Round to 39.27
Now the fun! Find the area of the parts subtracted by the light semicircle:
The area of the entire circle is 25π or about 78.54. The triangle is half of an inscribed rectangle, 6×8, so 48. Subtracted from the circle leaves about 30.54 in the four slices between the arcs of the circumference and the perimeter of the rectangle. We are concerned with only half of the slices, so we will subtract 15.27
Area of the dark semicircles minus the area of the light slices will leave the area of the shaded crescents:
39.27 - 15.27 = 24 square units . Voila!Meryl needs to cut down 10.5 trees for every 5 cabins she builds. How many trees will she need to cut down if she builds 7 cabins?
Answer:
14.7 TreesStep-by-step explanation:
[tex]10.5 \:trees = 5 \:cabins\\x \: trees\:\:\:\:\:\:=7\:cabins\\\\5x = 73.5\\\frac{5x}{5} = \frac{73.5}{5}\\ x = 14.7 \: trees[/tex]
The surface area of a cube is 24 square inches What us the side length of the cube ?
A=24in² this th ans because the side of cube is 24 cm
n the kite, AC = 10 and BD = 6. What is the area of kite ABCD? 15 square units 30 square units 45 square units 60 square units
Answer:45
Step-by-step explanation:
Answer:
B. 30 square units
Step-by-step explanation:
Edge 2021
Please answer this question now
Answer:
66 degrees
Step-by-step explanation:
WV is the radius and WX is a tangent, so angle W is 90 degrees. So, 90+24=114 and 180-114 is 66.
Hope this is helpful! :)
7th grade-Post-test Summer Sc...
Show all steps
ܝ
Which of the following pairs are like terms? Select all that apply.
11a and 13a power of 2
18k and 18b
7x and 16x
17yz and 12y
9pq and 8qp
Answer:
9pq, 8qp, and 7x, 16y
Step-by-step explanation:
these pairs have the same variable and exponent. To be a like term, you have to have same variables and same exponents, so therefore 11a and 13a^2 can't be like terms.
Find the value.
9x+6 when x=-2/3
Answer:
0Step-by-step explanation:
Given,
[tex] - \frac{2}{3} [/tex]
Now, let's find the value of 9x + 6
[tex]9x + 6[/tex]
plug the value of X
[tex] = 9 \times (- \frac{2}{3} ) + 6[/tex]
Multiplying a positive and negative equals a negative
[tex]( + ) \times ( - ) = ( - )[/tex]
[tex] = - 9 \times \frac{2}{3} + 6[/tex]
Reduce the number with Greatest Common Factor 3
[tex] = - 3 \times 2 + 6[/tex]
Multiply the numbers
[tex] = - 6 + 6[/tex]
The sum of two opposites equals 0
[tex] = 0[/tex]
Hope this helps..
best regards!!
A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $20 per square meter. Material for the sides costs $12 per square meter.
Answer:
$ 327.08
Step-by-step explanation:
Let x = width of the container,
Then Length of the container = 2x
Let h = height of the container,
volume of the container can be calculated as length × width × height
= 2x × x × h
= 2x² h
Then we can say Volume =
= 2x² h=10
If we simplify inorder to get h
We have h= 5/x²
Then the area= (2L×h) +(2xh)
Where L is lenght
x= wish
h= height
= 2× 2x × h+ x× h
= 4x× 5/x + 2x × 5/x
Area = 30/x
Now, the area of the base = length × width
But from question, for the base costs $20 per square meter. Material for the sides costs $12 per square meter
Then the cost C(x)= 2x²× 20+30/x ×12
C(x)= 40x²+35/x²
If we differenciate wrt x we have
C(x)= 80-360/x²
If we equate C(x)=0the
80=360/x²
x= 1.651
If substitute to C(x)= 40x²+35/x²
C(x) = 40(1.651)² + 35/(1.651)²
We have cost= 327.08
A quarterback throws a football to a teammate. The football is 6.5ft above the ground when it leaves the quarterback's hand. His teammate catches it 3.5s later, at a height above the ground of 5 ft. Which quadratic model
Answer:
y = - 16t² + 55.6t + 6
Step-by-step explanation:
Using y - y₀ = vt - 1/2gt² where g = 32 ft/s², and v the velocity of the football
So y = y₀ + vt - 1/2 × (32 ft/s²)t²
y = y₀ + vt - 16t² where y₀ = 6.5 ft
y = 6 + vt - 16t²
Now, when t = 3.5 s, that is the time the teammate catches the ball after the quarterback throws it, y = 5 ft. Substituting these into the equation, we have
5 = 6.5 + v(3.5 s) - 16(3.5 s)²
5 = 6.5 + 3.5v - 196
collecting like terms, we have
5 - 6.5 + 196 = 3.5v
194.5 = 3.5v
v = 194.5/3.5 = 55.57 ft/s ≅ 55.6 ft/s
So, substituting v into y, our quadratic model is
y = 6 + 55.6t - 16t²
re-arranging, we have
y = - 16t² + 55.6t + 6
Determine the number of solutions for each quadratic.
1.) 4x^2-3x+4=0
2.)9x^2-12x+4=0
Answer:
1. Technically 2, but might be 0 in your teacher's opinion.
2. 1
Step-by-step explanation:
Solving problem one.
So I don't know if you have learned about imaginary numbers, but if you have, then you would end up with two answers if you plugged in the quadratic formula.
If you haven't learned about imaginary numbers, then I would say your best option would be to write 'No real solution' since there are technically 2 solutions.
Solving problem two.
Turns out this quadratic has a special property and it's actually a square of one equation. You can find out by just factoring the equation.
It's (3x-2)^2. Since it's squared, that means that only 2/3 would work as x in this equation.
Which of the following options have the same value as 40% of 84?
Choose 2 answers:
40•84
0.41/84
40
100 • 84
84/40
0.4 • 84
Answer:
0.4.84
Step-by-step explanation:
you divide the 40 by 100
Help to answer the questions..
Answer:
See Below
Step-by-step explanation:
The relation is :
=> {(-5,0)(2,8)(2,15)(4,16)}
Domain => x inputs of the relation
Domain = { -5 , 2, 4}
Range => y inputs of the relation
Range = { 0 , 8 , 15 , 16}
PLEASE HELP!!!
In a survey, 250 adults and children were asked whether they know how to
swim. The survey data are shown in the relative frequency table.
Answer:
82% Add .34+.48.
Step-by-step explanation:
The question is asking how many people CAN swim. This is why the answer is 82. But if the question asks how many people CANT swim the answer will be 18. This is why some people might get confused.
please help me to understand how this problem was solved. if you aren't going to explain don't even bother. no trolling :0
Answer:
see below
Step-by-step explanation:
In the first step, they added 28 to both sides of the equation to get rid of the -28 on the left side. Next, they subtracted 4x from both sides to get rid of the 4x on the left side. They are doing this so that they can isolate y on one side. Isolating y basically means that you need to get all of the y terms on one side and all of the non-y terms on the other side. Next, they divided the entire equation by 8 to get rid of the 8 in 8y. Finally, since y and f(x) are the same thing, they simply substituted f(x) for y.
Which is the heaviest of these weight : 1/2 kg , 0.6kg, 125g, 475g
Answer:
0.475 kg
Step-by-step explanation:
1/2 kg = 0.5 kg
125g = 0.125kg
475g = 0.475kg
grams are lighter than kg and 0.5kg,0.125g, and 0.6kg are all lighter than 0.475kg
hope this helps!
Answer:
0.6 kg
Step-by-step explanation:
The easy way to find out the answer is to bring all into same unit:
1/2 kg= 1/2*1000 g= 500 g0.6 kg = 0.6*1000 g= 600 g125 g475 gComparing all four we see the greatest number is 600, so the answer is :
600 g or 0.6 kg is the heaviest weightJenny has some tiles in a bag. The tiles are of three different colors: purple, pink, and orange. Jenny randomly pulls a tile out of the bag, records the color, and replaces the tile in the bag. She does this 50 times. The results are recorded in the given table: Color of Tile Number of times the tile is drawn
i
6 purple, 18 pink, 26 orange
i
What is the experimental probability that Jenny will pull out a purple tile?
Answer:
6/50
Step-by-step explanation:
Jenny pulled out 6 purple tiles out of the 50 trials
Answer: The experimental probability of Jenna pulling a purple tile is 6/50.
Step-by-step explanation:
In her experiment, Jenna pulled out 6 purple tiles out of the 50 total tiles she pulled. This would make the experimental probability of her pulling out a purple tiles 6/50.
suppose for an angle theta in a right triangle cos theta = C. Sketch and label this triangle, and then use it to write the other five trig functions of theta in terms of C.
Answer:
[tex]sin\theta = \sqrt{1-C^2}[/tex]
[tex]tan\theta = \dfrac{\sqrt{1-C^2}}{C}[/tex]
[tex]cot\theta = \dfrac{C}{\sqrt{1-C^2}}[/tex]
[tex]sec\theta = \dfrac{1}{C}}[/tex]
[tex]cosec\theta = \dfrac{1}{\sqrt{1-C^2}}[/tex]
Step-by-step explanation:
Given that:
[tex]\theta[/tex] is an angle in a right angled triangle.
and [tex]cos\theta = C[/tex]
To find:
To draw the triangle and write other five trigonometric functions in terms of C.
Solution:
We know that cosine of an angle is given by the formula:
[tex]cosx =\dfrac{Base}{Hypotenuse}[/tex]
Here, we are given that [tex]cos\theta = C[/tex] OR
[tex]cos\theta = \dfrac{C}{1}[/tex]
i.e. Base = C and Hypotenuse of triangle = 1
Please refer to the right angled triangle as per given statements.
[tex]\triangle PQR[/tex], with base PR = C units
and hypotenuse, QP = 1 unit
[tex]\angle R[/tex] is the right angle.
Let us use pythagorean theorem to find the value of perpendicular.
According to pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}[/tex]
[tex]1^{2} = C^{2} + QR^{2}\\\Rightarrow QR = \sqrt {1-C^2}[/tex]
[tex]sin\theta = \dfrac{Perpendicular}{Hypotenuse}\\\Rightarrow sin\theta = \dfrac{\sqrt{1-C^2}}{1}\\\Rightarrow sin\theta = \sqrt{1-C^2}[/tex]
[tex]tan\theta = \dfrac{Perpendicular}{Base}\\\Rightarrow tan\theta = \dfrac{\sqrt{1-C^2}}{C}[/tex]
[tex]cot\theta = \dfrac{Base}{Perpendicular}\\\Rightarrow cot\theta = \dfrac{C}{\sqrt{1-C^2}}[/tex]
[tex]sec\theta = \dfrac{Hypotenuse}{Base}\\\Rightarrow sec\theta = \dfrac{1}{C}}[/tex]
[tex]cosec\theta = \dfrac{Hypotenuse}{Perpendicular}\\\Rightarrow cosec\theta = \dfrac{1}{\sqrt{1-C^2}}[/tex]