Answer:
The arrow will take 4.19 seconds to hit the ground
The arrow will go 24 feet to reach its maximum height and it takes 2 seconds to reach this height
Step-by-step explanation:
The quadratic function is f(t) = -5t² + 20t + 4, where
f(t) is the height in feet
t is the time in seconds
If the arrow hit the ground that means h(t) = 0
→ Substitute h(t) by 0 and use the quadratic formula to find t
∵ h(t) = 0
∴ 0 = -5t² + 20t + 4
→ Switch the two sides
∴ -5t² + 20t + 4 = 0
→ Multiply all terms by -1 to make the coefficient of t² positive
∴ 5t² - 20t - 4 = 0
→ The quadratic formula is [tex]t=\frac{-b+-\sqrt{b^{2}-4ac}}{2a}[/tex] , where
a is the coefficient of t²b is the coefficient of tc is the numerical term∵ a = 5, b = -20, c = -4
∴ [tex]t=\frac{-5+-\sqrt{(-20)^{2}-4(5)(-4)}}{2(5)}[/tex]
∴ [tex]t=\frac{-5+-\sqrt{400+80}}{10}[/tex]
→ Find the values of t in decimal
∴ t = 4.19 seconds OR t = -0.19 ⇒ refused because it is negative
∴ The arrow will take 4.19 seconds to hit the ground
The graph of this quadratic function is a parabola with maximum vertex (h, k), where
h = [tex]\frac{-b}{2a}[/tex]k = f(h)To find the maximum height and the time taking for this to occur find h and k where k is the maximum height and h is the time for this to occur
∵ f(t) = -5t² + 20t + 4
∵ a = -5 and b = 20
∴ h = [tex]-\frac{20}{2(-5)}=-\frac{20}{-10}=2[/tex]
∴ The time for the maximum height is 2 seconds
→ Now use it to find k
∵ k = f(h)
∴ k = f(2)
∵ f(2) = -5(2)²+ 20(2) + 4
∴ f(2) = -5(4) + 40 + 4
∴ f(2) = -20 + 40 + 4
∴ f(2) = 24
∴ k = 24
∴ The maximum height is 24 feet
The arrow will go 24 feet to reach its maximum height and it takes 2 seconds to reach this height
Raquel can type 63 words every minute. Rick can type 73 words every minute. How many more words can Rick type than Raquel in 135 minutes?
Group of answer choices
Answer:
1350 words
Step-by-step explanation:
8505 is the amount of words raguel can type in 135 minutes. 9855 is the amount Rick can type in 135 min. 9855-8505=1350 which is the answer
help me and do it out please
2x+4=12
Answer:
x=4
Step-by-step explanation:
2x=12-4
2x=8
2x/2=8/2
x=4
4(2x - 2) + 2 = 4(x - 2)
Answer:
X=-1/2
Step-by-step explanation:
Hope this helps. Plz give brainliest.
Answer:
x = -1/2 or -0.5
Step-by-step explanation:
4(2x - 2) + 2 = 4(x - 2)
open the parenthesis
8x - 8 + 2 = 4x - 8
add 8 to both sides of the equation
8x - 8 + 2 + 8 = 4x - 8 + 8
combine like terms
8x + 2 = 4x
subtract 4x from both sides of the equation
8x - 4x + 2 = 0
4x + 2 = 0
subtract 2 from both sides of the equation
4x + 2 - 2 = 0 -2
4x = -2
divide both sides by 4
4x/4 = -2/4
x = -1/2
Helppppppp!!!!!!!!??????
Answer:
5/10
Step-by-step explanation:
Answer −9
x + 1 = −80
Brainlist included
Answer:
x=9
Step-by-step explanation:
-9x+1=-80
To eliminate the one, you subtract one from both sides.
That gives you:
-9x=-81
Then you divide both sides by negative nine to get x by itself.
x=9
Tickets to an amusement park cost $35 for adults and $20 for children. The equation 35x+20y=140 shows how many adults x and children y can visit the amusement park with $140. If no children go, how many adults can go to the amusement park with $140?
A)7
B)5
C)4
D)2
Answer: Four adults
Step-by-step explanation: 4 x 35 = 140. There are no children, so you can just ignore 20y (I hope this helps!)
If no children will go to the amusement park then a total of 4 adults can go to the amusement park for $140. Hence, option C is correct.
What is an equation?Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right is shown to be equal in reference to one another. LHS = RHS (left hand side = right hand side) appears in all mathematical equations.
You can solve equations to determine an unknown variable's value, which corresponds to an unknown quantity. It is not an equation if there is no "equal to" sign in the statement.
The given equation is :
35x + 20y = 140
Cost of adults to go to the amusement park, (x) = $35 and,
Cost of children going to the amusement park, (y) = $20.
If no children are going to the amusement park, then the number of adults who can go to the park is :
35x + 20(0) = 140
35x = 140
x = 140/35
x = 4.
Hence, this concludes that option C is correct.
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What's the fraction of this equation 0.017
The fraction is _______
What is the value of x
Answer:
x = 32 :)
Step-by-step explanation:
20+4x+x=180
5x=160
160/5=32
brainliest pls if correcto
. Which fraction has the greatest value?
5/9. 7/8. 12/17. 8/11
Answer:7/8
Step-by-step explanation:
It is 7/8 because it is the fraction that is closest to a whole number
What is the slope of the line?
Answer:
1/2
Step-by-step explanation:
Slope equals rise over run. To find this use two points that land evenly on the graph then count how ever many spaces up and then to the side. In this case, it goes up 1 and right 2, so put that into fraction form, 1/2, and that is your answer.
Answer:
1/2
Step-by-step explanation:
What is the surface area?
4 ft
10 ft
5 ft
square feet
if f(x)=3x+23, find the value of x so that f(x)=36
with steps please!
Answer: f(36)=131
Step-by-step explanation:
f(x)=3x+23
f(36)=3(36)+23
f(36)=108+23
f(36)=131
Answer:
131
Step-by-step explanation:
f(x)=3x+23 The first thing you do is plug in 36. so replace the X's with 36.
f(36)=3(36)+23 The second step is to multiple 3 times 36.
f(36)=108+23 The last step is to add 108 to 23.
F(36)=131
i am about to SCREAM!!! i need help
For the following inequality, find a solution for the variable. Show all of your work and use complete sentences to explain the solving process that you used to find a solution for the inequality. Be sure to include at least two terms from the word bank.
Word Bank
sum difference product quotient
equal variable solution inverse
add subtract multiply divide
more than less than greater than inequality
greater than or equal to less than or equal to equation negative
x + 4 < 1
Answer:
x<5
Step-by-step explanation:
x+4<1
x<+1-4(in this situation +1-4 is kinda like saying -4+1 so you add them)
{x<5}
(thanks and sorry and welcome)
Answer:
For the inequality statement, x ≤ -3, multiply each side of the inequality by the reciprocal of . The solution is x ≤ -12.
Step-by-step explanation:
[tex]\frac{4}{1}[/tex] · [tex]\frac{1}{4}[/tex]x ≤ -3 · [tex]\frac{4}{1}[/tex]
If x=-1, then which of the following equations makes a true statement?
A.) 4x+9=20
B.) -4x–5=-15
C.) -3x+15=18
D.) -5x–15=-22
Answer:
Option C
Step-by-step explanation:
Option A:[tex]4(-1)+9=20\\\\-4+9=20\\\\\boxed{5\neq 20}[/tex]Option B:[tex]-4(-1)-5=-15\\\\4-5=-15\\\\\boxed{-1\neq -15}[/tex]Option C:[tex]-3(-1)+15=18\\\\3 + 15 = 18\\\\\boxed{18=18}[/tex]
Option C is the correct answer.
Option D:[tex]-5(-1)-15=-22\\\\5-15=-22\\\\\boxed{-10\neq -22}[/tex]
Hope this helps.
For the value of x = - 1, the correct equation is,
⇒ - 3x + 15 = 18
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The value of x is,
⇒ x = - 1
Now, Substitute the value of x in all equations and check the correct equation.
For equation 3;
⇒ - 3x + 15 = 18
Substitute x = - 1 ;
⇒ -3×-1 + 15 = 18
⇒ 3 + 15 = 18
⇒ 18 = 18
Thus, The correct equation is,
⇒ - 3x + 15 = 18
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El radio de la rueda de una bicicleta mide 30cm ¿cuanto avanza la bicicleta en cada vuelta?
pls help me i dont know how to do this pls answer ASAP
Answer:
If it does not pass through the origin, or is anything other than linear, it is not proportional
1.) Non-proportional
2.) Proportional
3.) Non-proportional
4.) Non-proportional
5.) Proportional
6.) Proportional
7.) Non-proportional
10.) Non-proportional
11.) Non-proportional
Answer:
Step-by-step explanation:
N means Non-Proportional
P means Proportional
1.N
2.P
3.N
4.N
5.P
6.N
7.N
10.N
11.N
segment addition postulate
Step-by-step explanation:
for 1:
we know that bc+cd=bd
plug in what we wre given
23+22= bd
add.
for 2:
we know that ef+fg=eg
plug in what we know
4x+3 + 6x+9 = 72
combine like factors
10x+12=72
solve
(subtract 12 on both sides) 10x=60
(divide by 10 on both sides) x=6
Enter the first 4 terms of the sequence defined by the given rule. Assume that the domain of each
function is the set of whole numbers greater than 0.
f(1) = 3, f(n)=(-7).f(n-1)+19
The first 4 terms of the sequence are
and
Answer
1.7
2. -11
3. 43
4. -119
first person to answer gets brainllest A regular hexagon and a rectangle have the same perimeter, P. A side of the hexagon is 4 less than the length, l, of the rectangle. The width of the rectangle, w, is 2 less than the length of the rectangle. What is the perimeter of the hexagon?
Answer:
Perimeter of the hexagon is 36 units
Step-by-step explanation:
if the length is ten using the information provided you will get a perimeter of 36 for both
Answer:
36
Step-by-step explanation:
Hope it helps :)
Brainliest pls?
Solve the following proportion using the multiplication property of equality.
2/35=h/60
h=____ (Type as a interger or simplified fraction)
Use the properties of longarithms to expand log(x^3y)
[tex]\log(x^3y) = \log(x^3) + \log(y) = 3\log(x) + \log(y)[/tex]
If Dan earns $35 for 7 hours of work, what is his unit rate of earning? *
Answer:
$5 an hour
Step-by-step explanation:
refer to image
Which set of points on the graph represents equivalent ratios?
A: points C,D,and F
B: points B,C, and D
C: points B,C, and F
D: A,C, and D
Answer:
I think the answer is B cuz it goes straight to like b,c,d
Answer:
b
Step-by-step explanation:
Evaluate the expression.
2’5 + 2 (12 – 7) x 4 =
Answer:
the answer is 72 to the expression.
The empty gas tank of a motor boat is to be filled. The tank is shaped like a rectangular prism with length 32cm, width 28cm, and height 15cm. Suppose gas is pumped into the tank at a rate of 840cm3 per minute. How many minutes does it take to fill the empty tank?
Solve the inequality.
8(x – 2) + 9 < 3(x – 1) + 5x
Answer:
infinate solution
Step-by-step explanation:
8(x - 2) + 9 < 3(x - 1) + 5x
Distribute
8x - 16 + 9 < 3x - 3 + 5x
Combine like terms
8x - 7 < 8x - 3
Subtract 8x to both sides
-7 < -3
Since -7 is less than -3, there are many infinitely solutions to this equation.
simplify each expressions: 7(5y - 3)
Answer:
35y-21
Step-by-step explanation:
7(5y-3)
7*5y 7*-3
35y-21
some one help me plz asap!!!!!!!!!!!!!!!!!!
Answer:
g+(h+j)+k
(g+h)+ j+k
Step-by-step explanation:
these are the answers
hope it helps
for any question comment me ❤❤❤
What are the missing parts that correctly complete the proof? Given: Point A is on the perpendicular bisector of segment P Q. Prove: Point A is equidistant from the endpoints of segment P Q. Image: A horizontal line segment P Q. A midpoint is drawn on segment P Q labeled as X. A vertical line X A is drawn. A is above the horizontal line. The angle A X Q is labeled a right angle. The line segments P X and Q X are labeled with a single tick mark. A dotted line is used to connect point P with point A. Another dotted line is used to connect point Q with point A. Drag the answers into the boxes to correctly complete the proof. Statement Reason 1. Point A is on the perpendicular bisector of PQ¯¯¯¯¯. Given 2. PX¯¯¯¯¯≅QX¯¯¯¯¯¯ Response area 3. ∠AXP and ∠AXQ are right angles. Response area 4. Response area All right angles are congruent. 5. AX¯¯¯¯¯≅AX¯¯¯¯¯ Reflexive Property of Congruence 6. △AXP≅△AXQ Response area 7. AP¯¯¯¯¯≅AQ¯¯¯¯¯ Response area 8. Point A is equidistant from the endpoints of PQ¯¯¯¯¯. Definition of equidistant Look below me
Answer:
These are the answers in order
Step-by-step explanation:
1. Definition of bisector
2. Definition of perpendicular
3. ∠AXP ≅ ∠AXQ
4. SAS Congruence Postulate
5. Corresponding parts of congruent triangles are congruent
The missing parts that complete the proof are;
2) Definition of a bisector.
3) Perpendicular Definition.
4) ∠AXP ≅ ∠AXQ
6) SAS Congruence Theorem.
7) Corresponding sides of 2 congruent triangles are congruent.
We are given that;Point A is the perpendicular bisector of PQ
Point A is equidistant from the endpoints of PQ.
2) We are told that PX = QX; Since A bisects PQ at X, it means it divides it into 2 equal parts. Thus, this id true because it corresponds with the definition of a bisector.3. ∠AXP and ∠AXQ are right angles; Since perpendicular means right angle or 90°, we can say that this statement is true because it corresponds with the definition of perpendicular.
4. All right angles are congruent; This simply means they are equal. Thus, the two right angles here ∠AXP and ∠AXQ are congruent. We can write this with congruency symbol as; ∠AXP ≅ ∠AXQ
6. △AXP≅△AXQ; This means that △AXP is congruent to △AXQ. From the diagram, we can see that AP = AQ and that QX = PX and that ∠AXP = ∠AXQ. This means 2 corresponding sides and one corresponding angle are equal and the congruence theorem this depicts is SAS Congruence Theorem.
7. AP = AQ; This is true because we are told A is equidistant from both P and Q. Also, from the SAS congruency theorem, we can say that the corresponding sides AP and AQ are congruent.
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