Answer:
1)The ball hits the ground after 3 seconds.
2)The maximum height of the ball is 49 feet
3)It takes 1.25 seconds to reach its maximum height
Step-by-step explanation:
Height of building = 40 feet
We are given that A ball is thrown straight up from the top of building with an initial speed of 24 feet per second.
So, The height of the ball as a function of time can be modeled by: [tex]h(t)=-16t^2+40t+24[/tex]
1)After how many seconds the ball hit the ground.
Substitute h(t)=0
So,[tex]-16t^2+40t+24=0\\-2t^2+5t+3=0\\2t^2-5t-3=0\\2t^2-6t+t-3=0\\2t(t-3)+1(t-3)=0\\(2t+1)(t-3)=0\\t=\frac{-1}{2} , 3[/tex]
Since time cannot be negative
So,the ball hits the ground after 3 seconds.
2)What is the maximum height of the ball?
It takes maximum height at vertex
Formula : [tex]t = \frac{-b}{2a}[/tex]
[tex]t=\frac{-40}{2(-16)}=1.25 seconds[/tex]
Substitute the value of t in function
[tex]h(1.25)=-16(1.25)^2+40(1.25)+24\\h(1.25)=49 feet[/tex]
So,the maximum height of the ball is 49 feet
3).How long did it take for the ball to reach its maximum height?
It takes 1.25 seconds to reach its maximum height
WILL GIVE BRAINLIEST IF FULL COMPLETE CORRECT ANSWER IS GIVEN.
Sarah has some large, polygon-shaped cardboard cutouts that she needs to sort, because she wants to hang them in her geometry classroom. The first division she needs to make is to divide the regular polygons from the irregular ones. In order to save time measuring all angles and sides of each polygon, and owing to the size and number of sides/angles in each shape, Sarah decides to measure just one angle in each polygon. Consider the following angle measures for polygons A through T, and answer the following questions.
a. If each angle measure represented an exterior measure of its polygon, which of the polygons could be regular? Explain your answers.
b. If each angle measure represented an exterior measure of a regular polygon, name each polygon by using its number of sides. (For any figure with more than 12 sides, just use the number: e.g. 45-gon.)
c. If each angle measure represented an interior measure of its polygon, which of the polygons could be regular? Explain your answers.
d. If each angle measure represented an interior measure of its polygon, which of the polygons do we know are convex? Explain your answers.
Answer:
a. ABCDEFHILO
b. 36- 24- 18- dodeca- nona- octa- hexa- penta- square, triangle
c. HLNOPQ
d. ABCD EFGH IJKL MNOP Q
Step-by-step explanation:
a. The exterior angles of a regular polygon have a measure that is 360° divided by the number of sides. If the angle has an integer value, that value must be a divisor of 360°.
Possible regular polygons are ...
ABCDEFHILO
__
b. A: 36-gon; B: 24-gon; C: 18-gon; D: dodecagon; E: nonagon; F: octagon; H: hexagon; I: pentagon; L: square; O: triangle
__
c. The supplement of a regular polygon's interior angle is equal to 360° divided by the number of sides. That is, the angle's supplement must be a divisor of 360°.
Possible regular polygons are ...
HLNOPQ
__
d. In order for a polygon to be convex, it can have no reflex interior angles. That is, all interior angles must be at most 180°. Only polygons R, S, T cannot be convex.
Possible convex polygons are ...
ABCD EFGH IJKL MNOP Q
Answer:
a. ABCDEFHILO
b. 36- 24- 18- dodeca- nona- octa- hexa- penta- square, triangle
c. HLNOPQ
d. ABCD EFGH IJKL MNOP Q
Step-by-step explanation:
a. The exterior angles of a regular polygon have a measure that is 360° divided by the number of sides. If the angle has an integer value, that value must be a divisor of 360°.
Possible regular polygons are ...
ABCDEFHILO
__
b. A: 36-gon; B: 24-gon; C: 18-gon; D: dodecagon; E: nonagon; F: octagon; H: hexagon; I: pentagon; L: square; O: triangle
__
c. The supplement of a regular polygon's interior angle is equal to 360° divided by the number of sides. That is, the angle's supplement must be a divisor of 360°.
Possible regular polygons are ...
HLNOPQ
__
d. In order for a polygon to be convex, it can have no reflex interior angles. That is, all interior angles must be at most 180°. Only polygons R, S, T cannot be convex.
Possible convex polygons are ...
ABCD EFGH IJKL MNOP Q
If k(x) = 5x-6, which expression is equivalent to (k+k) (4)?
Answer:
5(4) - 6 + 5(4) - 6
Step-by-step explanation:
k(x) = 5x - 6
(k+k)(x) = 5x - 6 + 5x - 6
(k+k)(4) = 5(4) - 6 + 5(4) - 6
=> Option D is correct
Hope this helps!
The expression is equivalent to (k+k) (4) will be 5(4) - 6 + 5(4) - 6. The correct option is B.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The expression will be solved as below:-
k(x) = 5x - 6
(k+k)(x) = 5x - 6 + 5x - 6
(k+k)(4) = 5(4) - 6 + 5(4) - 6
Therefore, the expression is equivalent to (k+k) (4) will be 5(4) - 6 + 5(4) - 6. The correct option is B.
To know more about Expression follow
https://brainly.com/question/723406
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Which expressions are equivalent to x+x+x + 2 ?
Choose 2 answers:
A
3x + 2
B
3 + 2x
C
3(x+2)
D
2(x+1)+x
E
5x
Answer:
A + D
Step-by-step explanation:
Answer A is three x's (same as original) and answer D, when expanded using the distributive property, equals 2x + 2 + x, which is equal to 3x + 2.
Two roots of a 3-degree polynomial equation are 5 and -5. Which of the following cannot be the third root of the equation ?
0
-5i
-5
5i
5
Answer:
- 5i and 5i
Step-by-step explanation:
The Fundamental theorem of Algebra states that a polynomial of degree 3 has 3 roots, real and/ or complex.
Complex roots occur in conjugate pairs.
Given 2 real roots x = 5, x = - 5
There cannot be complex roots as they occur in pairs which would result in the polynomial having 4 roots instead of 3.
Which of the following side lengths are the legs? 6, 14, and 12
Answer:
The side lengths that are the legs are 6 and 12 because the hypotenuse is the largest side length of a triangle (since there are three side lengths shown).
Answer:
6 & 12
Step-by-step explanation:
In a right triangle, the greatest side length belongs to hypotenuse, other 2 numbers represent the legs
so as per the given, 14 is hypotenuse ans 6 & 12 are legs
Sue wants to increase 160 by 4%
She writes down
160 x 1.4 = 224
Sue's method is wrong.
a) Instead of multiplying by 1.4, write down
what she should have multiplied by
Bill wants to decrease 160 by 6%
b) Complete the statement below to show how Bill can decrease 160 by 6%
160 × ___ =___
Answer:
see explanation
Step-by-step explanation:
An increase of 4% = 104% = [tex]\frac{104}{100}[/tex] = 1.04
Sue should have multiplied by 1.04
(b)
A decrease of 6% = 94% = [tex]\frac{94}{100}[/tex] = 0.94 , thus
160 × 0.94 = 150.4
Step-by-step explanation:
NOTE: Increasing x by p% means multiplying x by (1+p%).
4% = 4/100 = 0.04then
increase 160 by 4% means multiply 160 by (1+4%)
in other words:
1+0.04 = 1.04
increase 160 by 4% means 160 by 1.04
160×1.04 = 166.4
160×(1 - 6%) = 160×(1 - 0.06) = 160×0.94 = 150.4Find the area of the shape
What is the value of n ?
Answer:
Your answer would be the letter a
Answer:
Step-by-step explanation:
180 -133 = 47
180-142=38
38+47= 85
180 - 85 = 95
180 - 95= 85
The answer is A
The following list gives the first 4 values of a sequence that follows a numerical pattern.
1,-4,-9,-14...
Which is most likely the 10th value in the sequence?
A) -36
B) -39
C) -42
D) -44
A motorist travelled 300 km
at an average
OF 75 km / h In and returned at an average speed of v km / b . if his average speed for the whole journey is 60km/h, find v?
Answer:
Step-by-step explanation:
Total distance /total time=total speed
600÷60=10hrs
300÷75=4hrs
I0-4=6
V=300÷6=50km/h
brainliest will be given, plz help me
Answer:
200,000 x 0.05 = 10,000
200,000 + 10,000 = 210,000
This will be 2015 (210,000)
210,000 x 0.05 = 10,500
210,000 + 10,500 = 220,500
2016
220,500 x 0.05 = 11250
220,500 + 11,250 = 231,750
231,750 should be the value
Hope this helps
Step-by-step explanation:
What is the price of the Ps5 going to be?
Currently we do not know the price of the PS5 but I believe it will be $550
Find the length of LM. Show your work.
Answer:
20Solution,
<N=180-53-44
=83
Apply sines rule,[tex] \frac{lm}{sin \: 83} = \frac{14}{sin44} \\ lm = \frac{14 \: sin \: 83}{sin \: 44} \\ lm = 20[/tex]
hope this helps..
Good luck on your assignment..
Answer:
LM =20.00356825
Step-by-step explanation:
We will use the law of sines
sin M sin N
-------- = ------------
LN LM
We can find the measure of N since the sum of the angles of triangles is 180
L+ M+ N =180
53+ 44 + N =180
N =180 - 53-44
N =83
sin 44 sin 83
-------- = ------------
14 LM
Using cross products
LM sin 44 = 14 sin 83
LM = 14 sin 83 / sin 44
LM =20.00356825
What is the horizontal asymptote of the graph of f(x) = 4×5^x
options
1.y=0
2.y=20
3.y=4
4.y = 5
Answer:
The horizontal asymptote is y=0
Which of the following polynomial functions is graphed below?
HELP ASAP!!! Plz!!
Answer: C
Step-by-step explanation:
A P E X
Answer:
C
Step-by-step explanation:
Please help!!!!!!!!!!!!!!!
Answer:
C
Step-by-step explanation:
[tex]12x\sqrt{900x^2y^4z^6}= \\\\12x\sqrt{30^2x^2(y^2)^2(z^3)^2}= \\\\12x(30xy^2z^3)= \\\\360x^2y^2z^3[/tex]
Therefore, the correct answer is choice C. Hope this helps!!
Please Help!! Which graph shows the solution to this system of inequalities?
Answer:
A. The first graph
Step-by-step explanation:
When you graph these two equations on a graphing calc, you should be able to see one dotted line and one solid, as well as the solutions being mostly in the 1st quadrant.
If x^2 is added to x, the sum is 56. Which of the following could be the value of x?
Answer:
-8, 7
Step-by-step explanation:
Set up an equation.
x² + x = 56
Set the equation equal to zero and factor.
x² + x - 56 = 0
(x + 8)(x - 7) = 0
Solve for x.
x + 8 = 0
x = -8
x - 7 = 0
x = 7
The possible x values are -8 and 7.
how do i write 7 degrees warmer today than yesterdays temperature t
Which of the following is equivalent to 18 minus StartRoot negative 25 EndRoot? 5i 18 – 5i 18 + 5i 23
Answer:
Step-by-step explanation:
[tex]18-\sqrt{-25}=18-\sqrt{i^{2}*5^{2}}\\\\=18-5i[/tex]
Answer: the answer is b
Step-by-step explanation:
Answer ASAP 84.9 66.2 38.2 33.8
Step-by-step explanation:
You need to use trigonometric stuff here. Since you're given the hypotenuse and an angle you can plug that right into an equation.
Recall that sin is opposite over hypotenuse and cos is adjacent over hypotenuse.
[tex]sin(\theta)=\frac{o}{h} \\sin(30)=\frac{x}{14} \\0.5=\frac{x}{14} \\x=7[/tex]
Now that you know the opposite side (DC) you can use tan, too, but I'm going to use cos.
[tex]cos(\theta)=\frac{a}{14} \\cos(30)=\frac{x}{14} \\\frac{\sqrt{3} }{2} =\frac{x}{14} \\x=7\sqrt{3}[/tex]
This is the adjacent side (BC). I put it in its exact value, but in decimal form it's ≈12.124.
Now you can do the perimeter:
[tex]2l+2w\\2(12.124)+2(7)\\24.248+14\\38.25[/tex]
Your answer is the 38.2
Q5
Below is a triangular prism
14cm
12cm
2 cm
Given that the volume of the prism is 1344cm' work out a
cm go
(2 m
Show me the answer
Answer:
30cm^3
Step-by-step explanation:
Triangular Prism Volume Formula:
V = b x h
b = base
h = height
5 x 6 = 30
30cm^3
50g in the ratio 3:2
Answer:
3+2=5 so the answer is 3/5 multiply by 50
Answer:
Step-by-step explanation:
3+2=5
3/5 x50=30g
2/5 x50=20g
Find the sum of the sequence: 108, 105, 102,...,15
Answer:
1968
Step-by-step explanation:
The given sequence is a finite arithmetic sequence.
Step 1: Determine the number of terms in the sequence
For an arithmetic sequence, the nth term:
A(n)=a+(n-1)d
In the sequence:
First term, a=108Last term, l=15Common difference, d=105-108= -3Therefore, to find which term the number 15 is, we have:
15=108+(n-1)(-3)
15=108-3n+3
15=111-3n
3n=111-15
3n=96
Number of terms in the sequence, n=32
Step 2: Find the sum of the sequence
For an arithmetic sequence with a given first and last term:
[tex]Sum, S(n)=\frac{n}{2}(a+l)\\ =\frac{32}{2}(108+15)\\=16*123\\$Sum of the sequence, S(n)=1968[/tex]
an ostrich is 255 cm.Suppose that you want to make a scale drawing of an ostrich. The scale is 30:1. What height will you make the ostrich in your drawing
Answer:
The height of the drawing should be: 8.5 cm
Step-by-step explanation:
Use the proportion given by the scale in order to find the height "h" that you need to draw:
[tex]\frac{30}{1} =\frac{255}{h} \\30=\frac{255}{h}\\30\,h=255\\h=\frac{255}{30}\\ h=8.5\,\,cm[/tex]
PLSSS HELP WILL BE MARKED BRAINLIEST
Answer:
We need 232 mL of Compound A
Step-by-step explanation:
We know the ratio
A : B : total
4 3 4+3
4 3 7
We want 406
406 /7 =58
Multiply each part by 58
A : B : total
4*58 3*58 7*58
232 174 406
We need 232 mL of Compound A
Pls help will award most brainliest (this is due today)
i) If PQRS is a quadrilateral inscribed in a circle, then the opposite angles of the quadrilateral are supplementary.
ii) The values of x and y are 120 degrees and 120 degrees respectively.
Help me with this math problem please
Answer:
The relative frequency of event "spin a 3" is calculated by:
F = number of elements/total number of elements
= 24/50 = 0.48
Hope this helps!
:)
pls help for brainliest
Answer:
5.8 cm
Step-by-step explanation:
A= 1/2 x b x h
A=1/2 x 4.6 x 2.5
A=5.75 CM=5.8 cm
Answer:
[tex]5.8 {cm}^{2} [/tex]
Step-by-step explanation:
[tex]area \\ = \frac{1}{2} \times base \times height \\ = \frac{1}{2} \times 4.6 \times 2.5 \\ = \frac{11.5}{2} \\ = 5.75 {cm}^{2} [/tex]
round to one decimal.
5.8
hope this helps
brainliest appreciated
good luck! have a nice day!
Are the expressions –0.5(3x + 5) and –1.5x + 2.5 equivalent? Explain why or why not.
Answer:
No.
Step-by-step explanation:
If you distribute the 1st equation out, you will be able to see that it is -1.5x - 2.5 while the other equation is -1.5x + 2.5. Since you have to distribute the negative, they are not equivalent.
Answer:
Both expressions are not equal.
Step-by-step explanation:
-0.5(3x+5) = -1.5x - 2.5
–1.5x+2.5 = -1.5x + 2.5
The first expression results in subtracting 2.5, the second expression results in adding 2.5.