During a soccer game, a goalie kicks a ball upward from the ground. The equation h(t)=-10t^2+40 represents the height of the ball above the ground in feet as a function of time in seconds. When the ball begins moving downward toward the ground, a player from the other team intercepts the ball with his chest 11 feet above the ground. How long after the goalie kicks the ball does the player intercept the ball?
Answer:
3.98 seconds
Step-by-step explanation:
The given relationship between height, in feet, and the time, in seconds, is
[tex]h(t)=-10t^2+40[/tex]
[tex]\Rightarrow t^2=\frac{40-h(t)}{10}[/tex]
[tex]\Rightarrow t= \pm\sqrt{4-0.1h(t)}\cdots(i)[/tex]
Let at time [tex]t_1[/tex], the ball was at the goalie, so, [tex]h(t_1)=0[/tex], and at the time [tex]t_2[/tex], the ball was intercepted, so, [tex]h(t_2)=11[/tex].
Now, the time to reach the player after the goalie kicks the ball
[tex]\Delta t=t_2-t_1[/tex]
By using equation (i)
[tex]\Delta t=(\pm\sqrt{4-0.1h(t_2)})-\left(\pm\sqrt{4-0.1h(t_1)}\right)\cdots(ii)[/tex]
Now, at the highest point, the slope of the graph must be zero.
So, [tex]\frac {dh(t)}{dt}=0[/tex]
[tex]\Rightarrow -20t=0[/tex]
[tex]\Rightarrow t=0[/tex]
As at the highest point, the time is zero, to before reaching the highest point ( when kikes by the goalie, [tex]t_1[/tex]) take the time with the negative sign and after the highest point (when the ball intercepted, [tex]t_2[/tex]) take the positive sign.
So, from equation (ii) become.
[tex]\Delta t=\sqrt{4-0.1\times 11}-\left(-\sqrt{4-0.1\times 0} \right)[/tex]
[tex]=\sqrt{3.9}-(-\sqrt 4)[/tex]
[tex]=1.98+2[/tex]
= 3.98 seconds
Hence, the time to reach the ball to the player after the goalie kicks the ball is 3.98 seconds.
Help please!!!
Question 6
5 pts
Factor the variable expression:
36X + 8X
0419x-4)
4X (9+2)
9(4X+2x)
8(X+X)
Answer:
4x (9+2)
Step-by-step explanation:
36x+8x
36 and 8 can be divided by 4 and they both have an x
[tex]36x + 8x = 4x(9 + 2)[/tex]
[tex]44x = 36x + 8 x[/tex]
[tex]44x = 44x[/tex]
The Answer is
[tex] \green {\boxed{4x(9+2)}}[/tex]
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how many solutions does a quadratic equation that can be written as the difference of squares have?
Answer:
there are teo solutions that can be written as tge difference of square have.
There are two possible solutions for the quadratic equation that can be written as the difference of squares.
What is a quadratic equation?A quadratic equation is of the form -
y = f(x) = ax² + bx + c
Given is a quadratic equation that can be written as the difference of squares.
A quadratic equation that can be written as the difference of squares is of the form -
(x² - a²)
For the roots, we can write the equation as -
(x² - a²) = 0
x² = a²
x = ± a
Therefore, there are two possible solutions for the quadratic equation that can be written as the difference of squares.
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The figure shown is reflected over the x-axis, then reflected
over the y-axis, and then translated 3 units right.
Which graph best represents the new position of the figure
after the three transformations?
Select one:
Answer:
grapgh?????
Step-by-step explanation:
Tommy and Arnold are playing with water balloons. Arnold is standing by a bush that is 20 feet from where Tommy is standing. Tommy released a water balloon at 5 feet above the ground and hits Arnold’s chest- which is also 5 feet above the ground. The balloon reached a maximum height of 15 feet off the ground. using Tommy’s location as the starting point, help Tommy write an equation that describes the path of the water from the point of release to Arnold's chest. Using the equation y=a(x-h)^2+k
Answer:
The equation that describes the path of the water balloon is:
[tex]y =-\frac{1}{10}\cdot (x-10)^{2}+15[/tex]
Step-by-step explanation:
The motion of the water balloon is represented by quadratic functions. Tommy launches a water balloon from [tex]A(x,y) = (0\,ft, 5\,ft)[/tex] and hits Arnold at [tex]B(x,y) = (20\,ft, 5\,ft)[/tex]. Given the property of symmetry of quadratic function, water ballon reaches its maximum at [tex]C(x,y) = (10\,ft,15\,ft)[/tex], which corresponds to the vertex of the standard equation of the parabola, whose form is:
[tex]y = a\cdot (x-h)^{2}+k[/tex] (Eq. 1)
Where:
[tex]a[/tex] - Vertex parameter, measured in [tex]\frac{1}{ft}[/tex].
[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical components of the vertex, measured in feet.
[tex]x[/tex], [tex]y[/tex] - Horizontal and vertical location of the ball, measured in feet.
If we know that [tex]x = 0\,ft[/tex], [tex]y = 5\,ft[/tex], [tex]h = 10\,ft[/tex] and [tex]k = 15\,ft[/tex], the vertex parameter is:
[tex]5\,ft = a\cdot (0\,ft-10\,ft)^{2}+15\,ft[/tex]
[tex]a = \frac{5\,ft-15\,ft}{(0\,ft-10\,ft)^{2}}[/tex]
[tex]a = - \frac{1}{10}\,\frac{1}{ft}[/tex]
The equation that describes the path of the water balloon is:
[tex]y =-\frac{1}{10}\cdot (x-10)^{2}+15[/tex]
A vet measured the mass of two birds. The mass of the robin was 76.58 grams. The mass of the blue jay was 81.05 grams.
Estimate the difference in the masses of the birds.
The estimated difference in masses of the two birds is grams.
Answer:
a) 4.47
b) 4.47 g
Step-by-step explanation:
The masses of the birds are given as;
The mass of the robin =76.58 grams.
The mass of the blue jay = 81.05 grams.
Difference in the masses of the birds is : 81.05 - 76.58 =4.47
Difference in masses of the two birds is grams is : 81.05g - 76.58g =4.47g
7r - 15/s
When r = 3 and s = 5
Answer:
18
Step-by-step explanation:
7r - 15/s
First step: Substitute
7(3) - 15/5
21 - 3
21 - 3 = 18
a company packages fruit baskets of different weights and ships them to customers. the company charges a flat fee for packaging the baskets. the total packaging and shipping cost in dollars, y, of a fruit basket weighing x pounds is represented by the line on the graph below. (1 point at (3, 10) another at (6, 16))
what is the y intercept of the line on the graph
Answer:
4
Step-by-step explanation:
The y-intercept of any given graph is always the value of the y of the point where the line of the graph intercepts or cut across the y-axis. It is the value of y when x = 0.
In this case, the y-intercept of the line of the graph above is y = 4. At y = 4, x = 0.
It represents the flat fee the company charges for packaging the baskets = $4.
can you ou guys please help me with the first two questions?
please help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
10
Step-by-step explanation:
Brainliest who wants it?? 15 x 15 - 31 + 46 - 5 + 12 =______
Answer:
247
Step-by-step explanation:
Answer: 247
Step-by-step explanation: 247
HELP ME PLEASE!!! this is the recipe.
Answer:
Ok... hmmmmm
So im going to assume that this is an adding fractions question so for a half batch it would be 1 1/4 + 2 2/4 which is 3 3/4 cups and for a double batch it would be 15 cups because 10 + 5 is 15.
The first blank probably is 3 3/4
The second blank probably is 15
<3 I already answered this on the other question but I want points so tysm.
Please help me solve this problem!
Answer:
The line would be a diagonal line that is negative(pointing down).
You can use Desmos Graphing Calculator to help you even more! :)
find three points that solve the equation then plot on the graph -x-2y=8
i gotchu: (-8,0) (0,-4) (4,-6)
Answer:
(-8,0) (0,-4) (4,-6)
Step-by-step explanation:
Frank has been driving at a constant speed for 3 hours, during which time he traveled 195 miles. Frank would like to know how long it will take him to complete the remaining 455 miles, assuming he maintains the same constant speed. Help Frank determine how long the remainder of the trip will take. Include a table or diagram to support your answer
Answer:
10.6 hours
Step-by-step explanation:
What is the range of the function in this table x 1 2 3 4 Y 2 4 3 2
Answer:
(2, 4, 3)
Step-by-step explanation:
Range = Y
how do I do slope? i know nothing about it and i need to learn it.
Answer:
slope is easy it is rise over run.
Step-by-step explanation:
rise/run
rise means up
run means move sideways.
Answer: what do you mean by slope?
Step-by-step explanation:
the game that you have to control a ball and you have power-ups and you have to stay on platforms and you have to avoid the red rectangles?
if you place a 37 foot ladder against the top of a 12 foot building, how many felt will the bottom of the ladder be from the bottom of the building
Answer:
Would it be 25 that’s what I got
Step-by-step explanation:
(GIVING BRAINLIEST TO FIRST CORRECT ANSWER)
What is the equation, in slope intercept form, for the given graph?
Answer:
y=1/2x-1
Step-by-step explanation:
0,-1
2,0
0--1 si 1
2-0 is 2
1/2
anya bought 1.3 pounds of apples. She used 0.28 pound in a pie. How much is left? Use the bar diagram to help you
Answer:
1.02 pounds left
Step-by-step explanation:
Skip the bar graph, just subtract .28 from .30 and voila!
The temperature in Monarch, Wisconsin, was -3° F at 6:00 a.m. The temperature rose 12 degrees in 9 hours. What was the temperature in Monarch at 3:00p.m.?
Answer:
9 degrees
Step-by-step explanation:
The temperatire was -3 and then rose by 12, -3 + 12 = 9
Find the distance between the two points in simplest radical form.
n.
(6, -9) and (1,3)
Help?
[tex]\large\underline{\underline{\red{\sf \blue{\longmapsto} Step-by-step\: Explanation:-}}}[/tex]
Given to points to us are :-
( 6 , -9)( 1 , 3 )Now , we can use Distance Formula , which is :-
[tex]\boxed{\purple{\tt Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}}[/tex]
Here ,
x1 = 6 .x2 = 1.y1 = (-9)y2 = 3.→ Substituting the respective values ,
⇒ Distance = √ [ ( 6 - 1)² + ( 3 +9)² ] .
⇒ Distance = √ 5² + 12²
⇒ Distance = √ 25 + 144
⇒ Distance = √ 169 .
⇒ Distance = 13 units .
Hence the distance between two points is 13u.
Write , or = to make the statement true. 9.008 ___ 9.08
Answer:
9.008 < 9.08
Step-by-step explanation:
9.08 is greater because you compare the number 9 and 9 are the same, 0 and 0 still the same, but then 0 and 8 you know eight is greater. was this helpful enough
Round 23,487 to the nearest ten. PLEASE HELP I WILL BRAINEST ASAP
Answer:
23,490
Step-by-step explanation:
Directions: Graph the lines in standard form.
5. 3x + 2y = 6
Answer:
x=2 y=3
Step-by-step explanation:
3x=6
2y=6
x=2
y=3
please help asapppppppppppppp
If we perform the vertical line test, we can see that every line touches the graph once. This means that the graph is a graph of a function.
Answer choice b is correct.
Someone help please. Its algebra 1.
Select the equation of a line in slope-intercept form that passes through (-2,2) and is perpendicular to the graph of y= 1/2x-3.
A. y= -2x +2
B. y= -2x -2
C. y= 1/2x -2
D. y= 1/2x +2
Answer:
B
Step-by-step explanation:
the line is perpendicular to y=1/2x-3
so its gradient, m, would be -2 (m¹m²= -1)
sub the coordinates and the gradient into this equation to find the equation of line in slope intercept form
y-y¹ = m(x-x¹)
The equation of the line in slope-intercept form that passes through (-2,2) and is perpendicular to the graph of y= 1/2x-3 is; y = -2x - 2
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Where x₁ - x coordinate, y₁ - y coordinate, m - slope
Point (-2,2)
Then the equation of a line perpendicular to the graph of y= 1/2x-3.
its gradient, m, would be; -2 (m¹m²= -1)
Now Write the equation as;
y-y₁ = m(x-x₁)
y - 2= -2(x + 2)
y = -2x - 2
Hence, the equation of the line in slope-intercept form that passes through (-2,2) and is perpendicular to the graph of y= 1/2x-3 is; y = -2x - 2
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luke paid 30 percent less for a used car than its original price of $3,500. how much did luke pay for the car?
Answer:
Im not sure ok
Step-by-step explanation:
Im trying to solve too
Answer:
2450
Step-by-step explanation:
30% of 3500
30÷100×3500
=30×35
=1050
3500-1050
=2450
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
48 yd : 56 yd
Answer:
4/6
Step-by-step explanation:
i am too unmotivated to do any math even if its easy please help :)
Answer:
40% increase
Step-by-step explanation:
First, find the difference:
161-115=46
Then divide by the past price to get the percent increase:
46/115=.4=40%