Answer:
Rocket will hit the ground in 10.55 seconds.
Step-by-step explanation:
Let be [tex]y = -16\cdot x^{2}+157\cdot x +124[/tex], where [tex]x[/tex] and [tex]y[/tex] are time after launch and the height of the rocket, measured in seconds and meters, respectively. To find the time that the rocket will hit the ground, we need to equalize height to zero and solve the resulting expression:
[tex]-16\cdot x^{2}+157\cdot x + 124 = 0[/tex]
The quadratic function can be solved analitically by Quadratic Formula, that is to say:
[tex]x = \frac{-157\pm \sqrt{157^{2}-4\cdot (-16)\cdot (124)}}{2\cdot (-16)}[/tex]
Roots of the polynomial are, respectively:
[tex]x_{1} \approx 10.55\,s[/tex], [tex]x_{2}\approx -0.74\,s[/tex]
Only first root offers to us a reasonable solution. Hence, we conclude that rocket will hit the ground in 10.55 seconds.
NEED HELP ASAP!!!!!!!!!!!!!!!!!!!!!!
What is the value of the missing divisor in the equation 1,872 divided _____=234
Answer: 8
Step-by-step explanation: You can test 234 by multiplying it by random numbers like i did on a calculator and from there i tested 8 and it fit 1874 so i knew that was the answer
The recipe says it serves 8 people. By what number should jenny multiply each ingredient to make enough meatloaf for 40 people?
Answer:
5
Step-by-step explanation:
8*5=40 so you multiply the ingredients by 5
what is the least common multiple of 31 and 46?
Amber worked 2.2 hours on Monday and 5.9 hours on Tuesday. Her pay rate is $9.50 per hour. How much will Amber be paid for two days?
Answer:
$76.95
Step-by-step explanation:
Amber worked for 2.2 hours on Monday and she makes $9.50 per hour, so that means you multiply 9.50 x 2.2 and it equals 20.9, then it says she works 5.9 hours on Tuesday, so that means you multiply 9.50 x 5.9 and it equals 56.05, so in total you add 20.9 from Monday and 56.05 from Tuesday and it equals 76.95, which means $76.95 is how much Amber will be paid.
Answer:
76.95
Step-by-step explanation:
What is the equation of the line that passes through the point (-5,7) and has a slope of -2/-5
this should be it y=-2/5x+5
much they will have left over. (a) If a package of curtains cost $21.50, what is the cost of the 3 packages of curtains in the cart? it in the cart
64.5 is the answer.
I HOPE THIS HELPS HAVE A GREAT DAY!
Answer:
64.50
hope this helps!!!
A truck can be rented from Company A for $80 a day plus $0.40 per mile. Company B charges $40 a day plus $0.60 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
At____miles, the rental costs are the same from either company.
Answer:
200 milesStep-by-step explanation:
Let the required miles be x
Rental for Company A
80 + 0.4xRental for Company B
40 + 0.6xRental costs are equal when:
80 +0.4x = 40 + 0.6x0.6x - 0.4x = 80 - 400.2x = 40x = 40/0.2x = 200 miles
Find f(g(x)) when f(x) = 3x2 + x - 8, and g(x) = 4x + 5.
A) f(g(x)) = 12x2 + 4x - 27
B) f(g(x)) = 48x2 + 84x + 25
C) f(g(x)) = 48x2 + 124x + 72
D) f(g(x)) = 144x2 + 124x + 30
Answer:
Its C.
Step-by-step explanation:
what's the area for 8 in 6 in 4 in in a irregular polygon
Answer:
192
Step-by-step explanation:
8x6x4
Answer:
192
Step-by-step explanation:
because it is
-6(7) + 36 + (-12)
Helpppppp
Answer:
-18
Step-by-step explanation:
Answer:-18
Step-by-step explanation:
Identify the percent of change as an increase or a decrease.
16 centimeters to 44.2 centimeters
Increase
Decrease
Question 2
Find the percent of change.
Answer:
Increase
Step-by-step explanation:
The number gets larger. Increase means it gets larger, but decrease means it gets lower.
Find the coordinates of the point (x,y) at the given angle θ on a circle of radius r centered at the origin. Show all work. Round decimal to three places. (5 points) θ=215° and r=4 Type equation here. Type equation here. (5 points) θ=-30° and r=1 Type equation here. Type equation here.
Answer:
(i) The equivalent coordinates in rectangular form are [tex](x, y) = (-3.277,-2.294)[/tex].
(ii) The equivalent coordinates in rectangular form are [tex](x, y) = (0.866, 0.5)[/tex].
Step-by-step explanation:
In this exercise we must find the equivalent coordinates in rectangular form from polar form. That is:
[tex](x, y) = (r\cdot \cos \theta, r\cdot \sin \theta)[/tex]
Where:
[tex]r[/tex] - Norm of vector, dimensionless.
[tex]\theta[/tex] - Direction of vector with respect to +x semiaxis, measured in sexagesimal degrees.
(i) ([tex]r = 4[/tex], [tex]\theta = 215^{\circ}[/tex])
[tex](x. y) = (4\cdot \cos 215^{\circ}, 4\cdot \sin 215^{\circ})[/tex]
[tex](x, y) = (-3.277,-2.294)[/tex]
The equivalent coordinates in rectangular form are [tex](x, y) = (-3.277,-2.294)[/tex].
(ii) ([tex]r = 1[/tex], [tex]\theta = 30^{\circ}[/tex])
[tex](x. y) = (1\cdot \cos 30^{\circ}, 1\cdot \sin 30^{\circ})[/tex]
[tex](x, y) = (0.866, 0.5)[/tex]
The equivalent coordinates in rectangular form are [tex](x, y) = (0.866, 0.5)[/tex].
there were m balloons at the beginning of a party. by the end of the party, 6 of them had popped. using m, write an expression for the number of balloons that were left.
Answer:
m-6=x
Step-by-step explanation:
Find f (−3) for the function f (x) = -5/-3 x -2
A) 3/5
B) -7
C) − 5/3
D) 3
E) −2
plug in -3 for x and get -5-2 which is -7 so b
What’s -6y + 4x=5 in ymx+b
Answer:
[tex]\boxed {y = \frac{2}{3}x - \frac{5}{6}}[/tex]
Step-by-step explanation:
First you need to solve the expression in order to get the expression in Slop-Intercept Form:
[tex]y = mx + b[/tex]
-The following equation:
[tex]-6y + 4x = 5[/tex]
Solve:
[tex]-6y + 4x = 5[/tex]
[tex]-6y + 4x - 4x = 5 - 4x[/tex]
[tex]-6y = 5 - 4x[/tex]
[tex]\frac{-6y}{-6} = \frac{5 - 4x}{-6}[/tex]
[tex]y = \frac{5 - 4x}{-6}[/tex]
[tex]\boxed {y = \frac{2}{3}x - \frac{5}{6}}[/tex]
Therefore, the expression in Slope-Intercept Form is [tex]y = \frac{2}{3}x - \frac{5}{6}[/tex].
*Two buses were coming from two different places situated just in the opposite
direction. The average speed of one bus is 5 km/hr more than that of another on
and they had started their journey in the same time. If the distance between
places is 500 km and they meet after 4 hours, find their speed.
Answer: 60 km/hr and 65 km/hr
Step-by-step explanation:
o-----------------------------------←500→-------------------------------------o
Bus 1: rate = r + 5 Bus 2: rate = r
time = 4 time = 4
distance = d distance = 500 - d
Use distance = rate x time
Bus 1: d = 4(r + 5) Bus 2: 500 - d = 4(r)
d = 4r + 20 -d = 4r - 500
d = 500 - 4r
Solve the System of Equations using the Substitution method:
4r + 20 = 500 - 4r
8r + 20 = 500
8r = 480
r = 60
Bus 1: rate = r + 5 Bus 2: rate = r
= 60 + 5 = 60
= 65
Distance between both buses = 500km
Time taken by them to meet each other = 4hr
Let speed of bus A be v km/hr.
ATQ, speed of bus B is 5km/ hr more than that of bus A.
∴ Speed of bus B will be (v + 5) km/hr.
★ Diagram :
[tex]\boxed{\setlength{\unitlength}{1cm}\begin{picture}(6,2)\thicklines\put(1,1){\circle*{0.2}}\put(5,1){\circle*{0.2}}\put(1,1){\vector(1,0){1}}\put(5,1){\vector(-1,0){1.5}}\put(0.2,0.9){A}\put(5.5,0.9){B}\put(1.4,1.2){v}\put(3.85,1.2){v+5}\put(2.35,0.4){\sf{500\;km}}\put(2.2,0.5){\vector(-1,0){1.3}}\put(3.55,0.5){\vector(1,0){1.5}}\end{picture}}[/tex]
★ As we know that,
Speed = Distance/Time ... (I)Assuming both buses as point masses,
Relative speed of object A wrt object B when the object B moves in the opposite direction of A is given by
[tex]\boxed{\bf{v_{AB}=v_A+v_B}}[/tex]Relative speed of bus A wrt B :
[tex]:\implies\:\sf{v_{AB}=v_A+v_B}[/tex]
[tex]:\implies\sf\:v_{AB}=v+(v+5)[/tex]
[tex]:\implies\bf\:v_{AB}=2v+5[/tex]
By substituting values in (I), we get
[tex]\leadsto\sf\:v_{AB}=\dfrac{d}{t}[/tex]
[tex]\leadsto\sf\:2v+5=\dfrac{500}{4}[/tex]
[tex]\leadsto\sf\:2v+5=125[/tex]
[tex]\leadsto\sf\:2v=120[/tex]
[tex]\leadsto\sf\:v=60\:kmph[/tex]
Speed of bus A = 60 kmphSpeed of bus B = (v + 5)
Speed of bus B = 65 kmphHope It Helps!What is 3.4 x 10^-6 in standard notation?
Answer:
The answer is 0.0000034
Step-by-step explanation:
13.8___13.80 < > = Complete the inequality statement with the symbol that makes it true
Answer:
=
Step-by-step explanation:
because 13.80 equal 13.8 . Because how we know we need to delite 0 snd it will be 13.8
Answer:
13.8 = 13.80
Step-by-step explanation:
13.8 and 13.80 are the same values.
Hope it helped!
-5/7*1/6
What's the answer?
Answer:
-5/42
Step-by-step explanation:
Answer: -0.11
Step-by-step explanation:
Which equation can be used to solve the problem?
750 is 150 percent of what?
Answer:
it would be 750/500
Step-by-step explanation:
150% of 500 is 750
Please help me solve this!! If you do think yu so much and have a nice day or night
Answer:
5668
Step-by-step explanation:
Which expression is equivalent to 36 + 54?
A=4(8 + 14)
B=9(4 + 54)
C=12(3 +4)
D=18(2 +3)
Sara owns a tree farm. Variety A of a pine tree is shipped to her at 12 inches tall and grows at a rate of 14 inches per year. Variety B of a pine tree is shipped to her at 2 inches tall and grows at a rate of 16 inches per year.
Which equation can be used to determine the number of years, x, at which the trees will be an equal height?
14 + 12x = 16 + 2x
14 + 12, x, = 16 + 2, x
16 + 12x = 14 + 2x
16 + 12, x, = 14 + 2, x
12 + 16x = 2 + 14x
12 + 16, x, = 2 + 14, x
12 + 14x = 2 + 16x
12 + 14, x, = 2 + 16, x
Answer:
Step-by-step explanation:
X=5
Select the construction that guarantees A' is a reflection of point A across line BC
Answer:
Construction B
Step-by-step explanation:
A' is the reflection of point A across line BC
Line BC is the mirror, the distance from point A to line BC and from BC to point A' is same and is the shortest distance.
This is achieved by constructing perpendicular line from the point A to BC and extending same line by same distance from BC.
How many solutions does the following equation have?
-6(x + 7) = -4x – 2
Choose 1 answer:
A.No solutions
B.Exactly one solution
C.Infinitely many solutions
Answer:
B. Exactly one solution
Step-by-step explanation:
What’s there answer for this 4.5x10^-5
Answer:
0.000045
Step-by-step explanation:
-3a+7=22 solve for a show work
Answer:
a = -5
Step-by-step explanation:
-3a + 7 = 22
Subtract 7 from both sides.
-3a = 15
Divide both sides by -3.
a = -5
Answer:
- 5
Step-by-step explanation:
Step 1:
- 3a + 7 = 22 Equation
Step 2:
- 3a = 15 Subtract 7 on both sides
Step 3:
a = 15 ÷ - 3 Divide
Answer:
a = - 5
Hope This Helps :)
HELP WILL MARK BRAINLIEST!!!
A quadratic function for a parabola has axis of symmetry x = -2, points (-3, 2) and (0,11) and opens upward. What is the value of a? What is the vertex?
Answer:
Let's see what to do buddy..
Step-by-step explanation:
_________________________________
STEP (1)
We know that the quadratic functions form are like this :
[tex]y = a \: {x}^{2} + b \: x + c [/tex]
The quadratic function opens upward so ;
[tex]a > 0[/tex]
The axis of parabolic symmetry passes through the vertex of the parabolic.
So we know that x vertex is equal to -2.
The vertex's x is finding from this equation:
[tex]x = - \frac{b}{2a} \\ [/tex]
So we have :
[tex] - 2 = - \frac{b}{2a} \\ [/tex]
Multiply the sides of the equation by 2a :
[tex]b = 4a[/tex]
_________________________________
STEP (2)
A quota passes through points (-3,2) and (0,11) , so points (-3,2) and (0,11) must be true in the quota equation.
[tex]y = f(x) = a{x}^{2} + bx + c \\ \\b = 4a \\ \\ y = f(x) = a {x}^{2} + 4ax + c [/tex]
[tex]f( - 3) = 2 \\ \\ a ({ - 3})^{2} + 4a( - 3) + c = 2 \\ \\ 9a - 12a + c = 2 \\ \\ - 3a + c = 2 \\ \\ \\ \\ f(0) = 11 \\ \\ a ({0})^{2} + 4a(0) + c = 11 \\ \\ c = 11 [/tex]
[tex] - 3a + c = 2 \\ \\ c = 11 \\ \\ - 3a + 11 = 2 \\ 11 \: goes \: to \: the \: other \: side \: \\ \\ - 3a = 2 - 11 \\ - 3a = - 9 \\ divided \: the \: sides \: of \: the \: equation \: by \: - 3 \\ a = 3[/tex]
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
Can someone please help
Not sure what does "Zero" mean. But I'll move with y-intercept, slope and slope intercept form.
The y-intercept is (0,4) because the graph passes through (0,4)
For the slope, look at the grid and the line, it's -2. Or we can solve this by using the ordered pairs.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
(0,4) and (3,-2) both are the part of the graph, therefore.
[tex]m=\frac{-2-4}{3-0} \\m=-\frac{6}{3}\\m=-2[/tex]
So the slope is -2 and for the slope intercept form, it must be the equation.
We know that m = -2 and b = 4 because b is the y-intercept from y = mx+b where m is the slope and b is the y-intercept.
Thus, [tex]y=-2x+4[/tex] from the y = mx + b.