Answer:
Reasonable domain is [1.375,3].
Step-by-step explanation:
Given function is [tex]f\left(t\right)=-16t^2+44t+12[/tex].
Now we need to find about what is the reasonable domain of the graph of the function [tex]f\left(t\right)=-16t^2+44t+12[/tex] when the basketball falls from its maximum height to the ground.
Compare with [tex]at^2+bt+c[/tex], we get a=-16 and b=44
then t-coordinate of vertex [tex]t=-\frac{b}{2a}=-\frac{44}{2\left(-16\right)}=1.375[/tex]
Then that means maximum height of the ball occurs when time t=1.375 seconds.
Now let's find time when ball falls on ground so set f(t)=0
[tex]f\left(t\right)=-16t^2+44t+12[/tex]
[tex]-16t^2+44t+12=0[/tex]
[tex]4t^2-11t-3=0[/tex]
[tex]\left(4t+1\right)\left(t-3\right)=0[/tex]
[tex]4t+1=0[/tex] or [tex]t-3=0[/tex]
[tex]4t=-1[/tex] or [tex]t=3[/tex]
[tex]t=-0.25[/tex] or [tex]t=3[/tex]
Time can't be negative so we use t=3 only
Hence reasonable domain is [1.375,3].
Solve for m -3+m/9=10
-3+m/9=10
Add 3 to both sides:
m/9 = 13
Multiply both sides by 9:
m = 13 * 9
m = 117
Answer:
The proportional relationship between the number of pages (p) and the number of hours (h) is represented by the equation
. Write the equation in standard form with a constant of proportionality greater than 1.
Step-by-step explanation:
Miguel and Grace started collecting rare coins at the same time. Back then, they had the same number of rare coins. Miguel has been collecting 5 coins each week and he now has 38 coins. Grace has been collecting 3 coins each week and she now has 24 coins. How many rare coins did they have altogether when they started collecting?
A) 3
B) 6
C) 7
D) 14
The correct answer is 6
Answer:
Option B is the correct answer
Step-by-step explanation:
Both collections follow arithmetic progression.
Back then, they had the same number of rare coins, which means their first term of AP is same. Let it be a.
Miguel's AP have a common difference 5 and Grace's AP have a common difference 3.
Let the number of weeks completed be n.
We have
a + ( n-1 )x 5 = 38 -------- eqn 1
a + ( n-1 )x 3 = 24 -------- eqn 2
eqn 1 - eqn 2
a + ( n-1 )x 5 - (a + ( n-1 )x 3) = 38 - 24
( n-1 )x 2 = 14
n-1 = 7
n = 8
Substituting in eqn 1
a + ( 8-1 )x 5 = 38
a = 38 - 35 =3
So at starting they both have 3 rare coins.
Total rare coins = 3 + 3 = 6
Option B is the correct answer
Evaluate -4a + 8z if a=8 and z=3.
Answer:
-8
Step-by-step explanation:
-4a + 8z
= -4(8)+8(3)
= -32+24
= -8
use the substitution method
-4a+8z
-4(8)+8(3)
-32+24 Negative number times (*) and positive number=negative number
=-8
Answer is -8
Find the 29th term of the following sequence. 2, 13, 24, 35,....
321
Look for a pattern: The term is 11 more than the number before. this means 11 is added each time.
Since you start with 2 and the number goes up by 11 per term, the equation you would use to find the nth term would be 11n+2
To find the 29th term, simply plug in 29
11n+2
11(29)+2
321
The 29th term is 321.
First you have to find the rate of change. It would be 11 because 35 - 24 = 11, 24 - 13 = 11 and 13 - 2 = 11.
These are the first 4 terms so just keep adding on 11 until you get 29 terms.
2, 13, 24, 35, 46, 57, 68, 79, 90, 101, 112, 123, 134, 145, 156, 167, 178, 189
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
200, 211, 222, 233, 244, 255, 266, 277, 288, 299, 310
19 20 21 22 23 24 25 26 27 28 29
Your final answer would be 310.
Can you guys please help me
Answer: A?
Step-by-step explanation:
Three boys and four girls enter a contest at the local movie theater. A randomly chosen winner will be awarded a free movie ticket, a collectible poster, or free popcorn. What is the probability that a girl will win free popcorn?
Answer:
4/21
Step-by-step explanation:
⇒This question is on probability
⇒Number of boys=3
⇒Number of girls=4
⇒P(S)= 4+3=7
Probability for a girl to win is= 4/7
We have 3 awards a free movie ticket, a collectible poster, or a free popcorn
P(S)= 3
Probability of being awarded a free popcorn = 1/3
The probability that a girl will win free popcorn =
[tex]\frac{4}{7} * \frac{1}{3} = \frac{4}{21}[/tex]
Answer:
4/21
Step-by-step explanation:
Frank, Carl, and Vinny started a lawn mowing business over the summer. This table shows how many lawns each worker mowed during the summer months.
Display the data in matrix W with rows indicating workers. What is element w13?
a.22
b.29
c.21
d.19
Answer:
A.22
Step-by-step explanation:
Answer:
d. 19
Step-by-step explanation:
A matrix is an array of rectangular shape which consists of numbers, symbols, or expressions, arranged in rows and columns.
[tex]\begin{bmatrix}28&21&19\\17&24&15\\22&29&17\end{bmatrix}[/tex]
[tex]w_{1,3}[/tex] means element in first row third column. First row means Frank and third column means August.
So, the number of lawns mowed by Frank in August is
[tex]w_{1,3}=19[/tex]
if cosec theta = 3/2, then find the value of 2 ( cosec2 theta + cot2 theta )
Answer:
7
Step-by-step explanation:
Using the trigonometric identity
• 1 + cot²x = cosec²x, then
2(cosec²Θ + cosec²Θ - 1 )
= 2(2cosec²Θ - 1)
= 4cosec²Θ - 2
= 4 × ([tex]\frac{3}{2}[/tex] )² - 2
= 4 × [tex]\frac{9}{4}[/tex] - 2
= 9 - 2
= 7
What is the reflection of point P(−1, 6) across the line y = x?
ANSWER
P'(6,-1)
EXPLANATION
The mapping for a reflection in the line y=x is
The line y=x is the mirror line for a function and it's inverse.
[tex](x,y)\to (y,x)[/tex]
The x and y coordinates swap position.
The reflection of point P(−1, 6) across the line y = x is
P'(6,-1)
If a triangle has an angle of 20 and an angle of 40 what is the other angle
Answer:
120
Step-by-step explanation:
A triangles angles always add to 180 degrees.
180=20+40+x
180-20=160
160-40=120
120=x
Answer:
120
Step-by-step explanation:
20+40=60
180-60
120
Given: BD is a diameter
m 1 = 100°
m BC= 30°
m ADB=
160
280
330
Answer:
280
Step-by-step explanation:
<1=100 <4=150 <3=30
mADB=100+150+30=280
Answer with explanation:
Given
m∠1=100°
[tex]m \widehat{BC}=30 ^{\circ}[/tex]
To Find:---m∠A D B
Solution
In Δ A OD
Represent the center of circle by O.
→ m∠1=100°
→OD=O A----------Radii of Circle
→∠ADO=∠D A O--------If opposite sides are equal angle opposite to them are equal.
In ΔA OD, Using Angle Sum property of Triangle
→∠ADO+∠D A O+∠A OD=180°
→2 ∠ADO+100° =180°-------------------[∠ADO=∠D A O]
→2∠ADO=180° -100°
→2∠ADO=80°
Dividing both sides by , 2 we get
⇒∠ADO=40°
⇒⇒⇒∠A DB=40°
≡⇒If you are asking about
[tex]m \widehat{ADB}=180 ^{\circ}[/tex]
Because Angle in a semicircle is Right Angle.Diameter B D divides the circle into two equal arc measure of each arc being 180 degree.
⇒⇒If you are asking about Angle made by Major arc ADB, then
[tex]m \widehat{ADB}=\angle AOD + \widehat{BOD}\\\\=100 ^{\circ}+180 ^{\circ}=280 ^{\circ}[/tex]
Option B
2 Ella, James, and Ray's grandmother gave them $24 to divide equally. They spent the
money during a 4-day vacation. They spent the same amount of money each day.
How much did each person spend each day?
A $1
B $2
C $4
D $8
3 kids and $24 will give each 24/3=$8 each
$8 for 4days is 8/4=$2 a day they spent
Jonathan conducted a survey among random boys in his grade to learn their shoe sizes. He found that the mean shoe size of the sample was size 10 and the median was size 8. Which statement is true based on the results of Jonathan’s survey?
Answer: his shoe size was 11
Step-by-step explanation:
Answer:
I hope this helps
Step-by-step explanation:
What is the value of x?
Check the picture below.
graph from liner standard form 3x+2y=12?
Answer:
See picture below.
Answer:
Graph??
Step-by-step explanation:
I can't really graph, but the answer to this is...
[tex]3x+2y=12\\\\2y=3x+12\\\\y=\frac{3}{2} x+6[/tex]
I divided all by 2 to get y
[tex]y=\frac{3}{2} +6\\\\(2,9) -- (x,y)[/tex]
Which function represents g(x), a reflection of f(x) = (3)x across the y-axis?
g(x) = 2(3)x
g(x) = −(3)x
g(x) = (3)−x
g(x) = 2(3)−
Answer: [tex]g(x)=(3)^{-x}[/tex]
Step-by-step explanation:
We know that if a figure is reflected across y axis then its y coordinate remains same but the x coordinate changes its polarity.
i.e. the function [tex]f(x)[/tex] will become [tex]f(-x)[/tex] .
Now, the given function :[tex]f(x)=(3)^x[/tex]
Then , after reflection across y axis the new function will become:
[tex]g(x)=f(-x)=(3)^{-x}[/tex]
Find Kara’s percent grade if she answered 94 questions correctly on the test that had 100 questions
Answer:
94%
Step-by-step explanation:
Since there are 100 questions, it's like 1% for each question. If she answers 94 questions right, then it is 94%.
the inequality 1/2x+3<2x-6 is equivalent to) A. x<-5/6 B. x<6 C. x>-5/6 D. x>6 explain and show work please
Answer:
D. x > 6Step-by-step explanation:
[tex]\dfrac{1}{2}x+3<2x-6\qquad\text{multiply both sides by 2}\\\\2\!\!\!\!\diagup^1\cdot\dfrac{1}{2\!\!\!\!\diagup_1}x+2\cdot3<2\cdot2x-2\cdot6\\\\x+6<4x-12\qquad\text{subtract 6 from both sides}\\\\x<4x-18\qquad\text{subtract 4x from both sides}\\\\-3x<-18\qquad\text{change the signs}\\\\3x>18\qquad\text{divide both sides by 3}\\\\x>6[/tex]
Find the range and interquartile range of the data. Round to the nearest tenth.
183, 339, 284, 111, 134, 344, 133
A. Range=211; interquartile range= 206
B. Range=233; interquartile range= 206
C. Range= 233; interquartile range= 156
D. Range= 211; interquartile range= 156
Answer:
It's B.
Step-by-step explanation:
The range is 344 - 111
= 233.
Arranging the data in ascending order:
111 133 134 183 284 339 344
The lower quartile = 133 and the upper quartile = 339.
So the interquartile range = 339 - 133
= 206.
We first need to list the following Data Set:
111, 133, 134, 183, 284, 334, 339
Range = highest value - lowest value =
Range = 339 - 111 = 228
Interquartile range = upper quartile - lower quartile =
(or IQR = interquartile range, another term)
Interquartile range = 334 - 133 = 201
Let f(x) = -4x - 2 and g(x) = 5x - 6. Find f×g and state its domain
Answer:
see explanation
Step-by-step explanation:
f(x) × g(x)
= (4x - 2)(5x - 6) ← expand factors
= 20x² - 24x - 10x + 12 ← collect like terms
= 20x² - 34x + 12
This is a polynomial of degree 2 and is defined for all real values of x
domain : x ∈ R
what is the value of t=1
Answer:
B. 7
Step-by-step explanation:
When you solve the series for each term, you get 4 + 2 + 1 = 7
Answer:
A
Step-by-step explanation:
Buying shares in a company is one way to invest money.
This statement is true.
When you buy a share in a company, you are investing your money, and you may earn more money if the share’s value rises, or you may lose money if the share’s value falls.
Investing in a company by buying shares makes you a shareholder, with potential income from dividends and stock appreciation. However, it carries risk as there is no guarantee for profits. Diversification is a key strategy when investing in stocks to mitigate risks.
Buying shares in a company is a common method of investment, wherein you become a shareholder and own a part of the company's equity. As a shareholder, you have a claim to the company's assets and profits proportional to the amount of stock you own. There are two primary ways that shareholders can earn money from their investments. One way is through dividends, which are payments distributed from the company's profit to shareholders. The other way is through appreciation in the stock's value, as the company grows and becomes more profitable; this increases the stock's market price, and you can sell your shares for a profit. It's important to understand that purchasing stock does involve risk, as there is no guarantee of dividends or stock appreciation. However, for many, owning stock is preferred over other investments like bonds because of the potential for higher returns. Lastly, when buying stock, especially that of your employer, it's advisable to follow general rules of portfolio investing, such as diversification, not to expose yourself to undue risk.
flip your phone sideways to view the question
Answer:
- 160 I think
Step-by-step explanation
I think i'm right but there are
200 blocks and there are 40 left out so then i did 40 - 200 = -160
ILL GIVE BRAINLIEST HELPP
What is the solution to the equations of lines A and B?
A graph is shown with x- and y-axes labeled from 0 to 6 at increments of 1. A straight line labeled A joins the ordered pair 2, 6 with the ordered pair 6, 2. Another straight line labeled B joins the ordered pair 0, 3 with the ordered pair 4.5, 6.
Answer:
The solution is the point (3,5)
The graph in the attached figure
Step-by-step explanation:
step 1
Line A ----> (2,6),(6,2)
Find the equation of the line A
Find the slope
m=(2-6)/(6-2)
m=-1
Find the equation of the line into point slope form
The equation is equal to
y-y1=m(x-x1)
we have
m=-1
point (2,6)
substitute
y-6=-1(x-2)
y=-x+2+6
y=-x+8 ------> equation of the line A
step 2
Line B ----> (0,3),(4.5,6)
Find the equation of the line B
Find the slope
m=(6-3)/(4.5-0)
m=(2/3)
Find the equation of the line into point slope form
The equation is equal to
y-y1=m(x-x1)
we have
m=(2/3)
point (0,3)
substitute
y-3=(2/3)(x-0)
y=(2/3)x+3 ------> equation of the line B
step 3
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both lines
The solution is the point (3,5)
see the attached figure
Its DE and ik its too late but the points is good. oof
Let f(x)=x^2−10x−11 .
Enter the x-intercepts of the quadratic function in the boxes.
ANSWER
The y-intercept is (0,-11)
The x-intercepts are:
(-1,0) and (11,0)
EXPLANATION
The given function is
[tex]f(x) = {x}^{2} - 10x - 11[/tex]
To find the y-intercept, we put x=0 into the function.
[tex]f(0) = {0}^{2} - 10(0) - 11[/tex]
[tex]f(0) = - 11[/tex]
The y-intercept is (0,-11)
To find the x-intercepts, we put f(x)=0.
[tex]{x}^{2} - 10x - 11 = 0[/tex]
[tex](x + 1)(x - 11) = 0[/tex]
This implies that,
[tex]x = - 1 \: or \: x = 11[/tex]
The x-intercepts are:
(-1,0) and (11,0)
For Future Reference____
-1 & 11 are the X Intercepts
Find the median of the data set: 475, 500, 450, 450, 500
Answer:
475
Step-by-step explanation:
Answer:
450
Step-by-step explanation:
Use the relation to answer the following questions. Graph the relation. State the domain of the relation. State the range of the relation. Is the relation a function? How do you know? Answer:
Answer:
All answers in the pic attached
Simplify
[tex] {x}^{5} \div {y}^{2} \times {x}^{3} \times {y}^{5} [/tex]
And animexcartoons209 please don't use PHOTOMATH...
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^5\div y^2\times x^3\times y^5\implies \cfrac{x^5}{y^2}\cdot x^3\cdot y^5\implies x^5\cdot y^{-2}\cdot x^3\cdot y^5 \\\\\\ x^{5+3}y^{-2+5}\implies x^8y^3[/tex]
Answer:
x⁸y³
Step-by-step explanation:
x⁵ ÷ y² × x³ × y⁵
It will be easier to solve this problem if you first rearrange the expression to associate like terms.
(x⁵ × x³) × (y⁵ ÷ y²)
Now, you can use the rules of exponents: When multiplying, you add exponents; when dividing, you subtract exponents.
x⁵ × x³ = x⁵⁺³ = x⁸
y⁵ ÷ y² = y⁵⁻² = y³
Thus,
(x⁵ × x³) × (y⁵ ÷ y²) = x⁸y³
What is the value of x in this figure?
14√3
28√3
28√2
28
Answer:
x=28 (Yup you're correct)
Step-by-step explanation:
As this problem is involving the Opposite angle and the Hypotenuse, we can use the sin function in order to solve this. The setup is as follows
[tex]sin(30)=\frac{14}{x}[/tex]
Now we can solve for x
[tex]sin(30)=\frac{14}{x}\\\\x=\frac{14}{sin(30)}[/tex]
Now we can plug it into a calculator to get
[tex]x=28[/tex]
Answer:
28Step-by-step explanation:
(Look at the picture)
We have the triangle 30° - 60° - 90°. The sides are in ratio 1 : √3 : 2.
We have a = 14. Therefore x = 2a ⇒ x = 2(14) = 28
the product of -5 and x
Answer:
-5x
Step-by-step explanation:
you multiply them together
(-5)(x)= -5x
Answer:
-5x
Step-by-step explanation:
-5 * X =