Answer:
(a) 40 m
(b) 4 seconds
(c) 1 second, 45 m
(d) 1 second
Step-by-step explanation:
The given height as a function of height is
[tex]h= -5t^2+10t+40[/tex]
where t is the time in seconds and h is the height, in meters.
(a) At the starting time, t=0, the arrow is at the platform.
So, putting t=0, to get the height of the platform
[tex]h= -5(0)^2+10(0)+40 = 40[/tex] m
(b) For determining the length of time the arrow is in the air, first t determining the value of t for which h=0, we have
[tex]-5t^2+10t+40=0 \\\\-t^2+2t+8=0 \\\\-t^2+4t-2t+8=0 \\\\-t(t-4)-2(t-4)=0 \\\\(-t-2)(t-4)=0 \\\\[/tex]
t=-2, t=4
Mathematically, the value of t for which the arrow is in the air is the time from -2 to 4 seconds.
But the arrow was at the platform at time t=0. So, neglecting the negative time, the time for which the arrow was in the air is the time from 0 to 4 seconds, i.e 4 seconds.
(c) Mathematically, the value of t for which the arrow is in the air is the time from t=-2 to t=4 seconds. So, in the middle of time, i.e at t=1 second the arrow will reach the maximum height.
Putting t=1 to get the maximum height, we have
[tex]h=-5(1)^2+10(1)+40[/tex]
h=-5+10+40
h=45 m
Therefore, the maximum height is 45 m at t=1 second.
(d) Referinf option (c), at the time, t=1 second, the arrow has a height of exactly 45m above the ground
What is the missing step in this proof?
What type of number is v64?
Choose all answers that apply:
A)Whole number
B) Integer
c Rational d) irrational
The correct answers are A) Whole number, B) Integer, and C) Rational.
The number √64 is equal to 8. It satisfies the condition √64 = 8 because 8 multiplied by itself (8 x 8) equals 64.
Based on the options provided, the correct answers are:
A) Whole number: Yes, √64 is a whole number. Whole numbers are non-negative integers, and 8 is a non-negative integer.
B) Integer: Yes, √64 is an integer. Integers are numbers that can be positive, negative, or zero without any fractional or decimal parts. In this case, 8 is a positive integer.
C) Rational: Yes, √64 is a rational number. Rational numbers can be expressed as a fraction p/q, where p and q are integers, and q is not zero. The square root of 64 can be written as 8/1, which is a fraction where both the numerator and denominator are integers.
D) Irrational: No, √64 is not an irrational number. Irrational numbers cannot be expressed as fractions and have an infinite non-repeating decimal expansion. However, √64 is a terminating decimal, as it equals 8, which means it is not an irrational number.
Therefore, the correct answers are A) Whole number, B) Integer, and C) Rational.
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f (x) = -x² + 6x - 18
Find f (-3)
Answer:
-45Step-by-step explanation:
Given
f (x) = -x² + 6x - 18To find f (-3) substitute x with -3
f(-3) = -(-3)² + 6(-3) - 18 = - 9 - 18 - 18 = -45f(-3) = -45Step-by-step explanation:
[tex]f(x) = - {x}^{2} + 6x - 18 \\ f( - 3) = - {( - 3)}^{2} + 6( - 3) - 18 \\ = - 9 - 18 - 18 \\ = - 45[/tex]
-45 is the right answer.If x = 3 (y + 2) minus 1 what is the value of w in terms of x and y?
A.) w = StartFraction x minus 3 y Over 3 EndFraction
B.) w = StartFraction x minus 3 y + 1 Over 3 EndFraction
C.) w = x minus 3 y + 1
D.) w = StartFraction x + 1 Over 9 y EndFraction
Answer:
B!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equation x = 3y + 3w - 1 can be written as in terms of x and y by making the subject w is w = (x - 3y + 1)/3 option (B) is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
The question is incomplete.
The complete question is:
If x = 3 (y + w) -1 what is the value of w in terms of x and y?
A.) w = StartFraction x minus 3 y Over 3 EndFractionB.) w = StartFraction x minus 3 y + 1 Over 3 EndFractionC.) w = x minus 3 y + 1D.) w = StartFraction x + 1 Over 9 y EndFractionWe have an expression:
x = 3 (y + w) -1
To find the value of w in terms of x and y.
By using the distributive property:
x = 3y + 3w - 1
By arranging the equation:
3w = x - 3y + 1
Divide by 3 on both the side:
w = (x - 3y + 1)/3
Thus, the equation x = 3y + 3w - 1 can be written as in terms of x and y by making the subject w is w = (x - 3y + 1)/3 option (B) is correct.
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Translate the following phrase into an expression:
“ the sum of an unknown number and 12”
Answer:
French: la somme d'un nombre inconnu et 12
Spanish: la suma de un número desconocido y 12
Latin: XII numerus ignotus est et summa
Step-by-step explanation:
what is the answer of 18x 2 and 3
y = x-1
y= x-2
show work
Answer:
for y=x-1 y=-1 and for y=x2 y=0
Step-by-step explanation:
to find the y intercept substitute x=0 so you have your answer y=-1 and y=0
SOLVE THIS PLEASE, ITS GOT SOMETHING TO DO WITH SOH, CAH, TOA
Answer:
x ≈ 36.9°
Step-by-step explanation:
Using the sine ratio in the right triangle, that is
sinx = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{6}{10}[/tex] , then
x = [tex]sin^{-1}[/tex] ([tex]\frac{6}{10}[/tex] ) ≈ 36.9° ( to 1 dec. place )
Kai marked up the new Kobe Grinch by 35% .She sole them for $168.75 . What was the original price
Answer: 109.69
Step-by-step explanation:
100-35=65
168.75 • 65= 10,968.75/ 100= 109.69
Explain what happens when you divide a fraction by itself.
Answer:
you will get 1
Step-by-step explanation:
because it can only go into its self one time
A furniture manufacturer produces chairs and sofas. Each chair requires 10 yards of fabric, and each sofa requires 20 yards of fabric. The manufacturer has 300 yards of fabric available. To fulfill orders, the number of sofas must be at least twice the number of chairs. The manufacturer earns a profit of $50 on each chair and $80 on each sofa. Let x represent the number of chairs and y represent the number of sofas. Choose the function that represents the manufacturer's profit, P.
Given:
Fabric required for each chair = 10 yards
Fabric required for each sofa = 20 yards.
Total available fabric = 300 yards.
The number of sofas must be at least twice the number of chairs.
Profit on each chair = $50
Profit on each sofa = $80.
To find:
The function that represents the manufacturer's profit, P.
Solution:
Let P represents the manufacturer's profit, x represent the number of chairs and y represent the number of sofas.
Profit on 1 chair = $50
Profit on x chairs = $50x
Profit on 1 sofa = $80
Profit on y sofas = $80y
Total profit = Profit on x chairs + Profit on y sofas
[tex]P=50x+80y[/tex]
Therefore, the required profit function is [tex]P=50x+80y[/tex].
Answer:
B on edge
Step-by-step explanation:
Read the excerpt from Heart of a Samurai.
The water was so clear, he could see straight to the bottom. A snail was making a path like a shiny ribbon slowly unfurling on the sand.
What does the author use the most precise words to describe in the excerpt?
A. the water’s movement
B. the water
C. the snail
D. the snail’s path
Answer: D. the snail’s path
Step-by-step explanation: because The author uses the most precise words to describe the snail's path.
This excerpt has been taken from Heart of a Samurai, a historical novel written by Margi Preus in 2010. Precise words such as 'shiny', 'ribbon' and 'unfurling' have been used in the second sentence to describe the path of the snail, which is a small animal that has a wet body and moves very slowly. In other words, the author describes the way the path looks by establishing a comparison between the path and a shiny ribbon.
Hope this help
Answer:
the snails path
Step-by-step explanation:
Element X decays radioactively with a half life of 13 minutes. If there are 830 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 20 grams?
Answer:
26.92 min
if I'm not wrong!
4. Is the relation shown in the table a function? Use the graph
to justify your answer.
2
4
8
y
3
2
0
y
8
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8
Answer:
67
Step-by-step explanais the bigges number taht u could find
Select all the numbers that show 4% as an equivalent fraction, decimal, or percent.
[] 0.04
[] 40%
[] 10
[] 4
[] 100
[] 0.4
Answer:
Step-by-step explanation:
0.04
All the numbers that show 4% as an equivalent fraction, decimal or percent from the listed options are:
In fraction: [tex]4\% = \dfrac{4}{100}[/tex]In decimal: [tex]4\% = 0.04[/tex]How to convert percent to fraction and decimal?Percent counts the number compared to 100.
So, if we have a%, that means for each 100, there are 'a' parts. If we divide each of them with 100, we get:
For each 1, there are a/100 parts.
Thus, 50% = 50/100 = 0.50 (in decimal)
For this case, the percent we have is 4%
That shows that for each 100 items, we have 4 of them. This can be written in fraction as 4/100
Solving this division, we get the result in decimal as 0.04
Thus, all the numbers that show 4% as an equivalent fraction, decimal or percent from the listed options are:
In fraction: [tex]4\% = \dfrac{4}{100}[/tex]In decimal: [tex]4\% = 0.04[/tex]Learn more about fractions and percent here:
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I forgot what a multiple is. Can someone please tell me.
Answer:
a number that can be divided by another number without a remainder.
Answer:
A multiple is a number that basically can be a number that can be divided by another number without a remainder.
What is the area of a right triangle 6 centimeters
high with a base of 2 centimeters?
The area of the triangle enclosed by 3 sides of a triangle is 6 cm²
What is the area of a triangle?The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. To find a triangle's area, use the formula area = 1/2 * base * height.
Given here: The dimensions of a triangle as 6 cm and base 2 cm
We know the area of the triangle is equal to half of the base times height,
A=1/2×6×2
=6 cm²
Hence, The area of the triangle enclosed by 3 sides of a triangle is 6 cm²
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In the figure below, what is the value of x
Answer:
x = 49°
Step-by-step explanation:
Angles in a Triangle
The sum of the internal angles in any triangle adds up to 180°.
The figure shows a triangle that includes two angles with the same tick mark. This means they are congruent, i.e. they measure the same.
The larger triangle has three defined angles: 43°, 39°, and 2x. Since the sum of them is 180°:
43° + 39° + 2x = 180°
Operating:
82° + 2x = 180°
Subtracting 82°:
2x = 180° - 82° = 98°
x = 98°/2 = 49°
x = 49°
Simplify the algebraic expression.
–9(–8p + 12) – 6p
Answer:
66+12
Step-by-step explanation:
simplified answer
Step-by-step evaluation:
-9(-8p + 12) - 6p
-9 x -8p = 72p -9 x 12 = -108
(72p + -108) - 6p
72p + -108 - 6p
(72p + −6p) + (−108)
66p + −108
Answer:
66p−108
Jo Beth organizes 63 party favors into gift bags.
She places the same number of favors in each
bag. How could she arrange the favors?
Answer:
She had 9 gift bags
Step-by-step explanation:
if we divide 63 by 7 we get 9
now, if we take 9 and call that our bags that means there will be 7 party favors in each bag
F R E E P O I N T S ! !
Answer:
thank you
Step-by-step explanation:
happy holidays have a good day
Answer:
thank you
Step-by-step explanation:
answer this maths question.
Answer:
IM NOT ABLE SEE THE QUESTION
Step-by-step explanation:
PLEASE TYPE AND SEND IT
Answer:
jwjwjowowowowowoowow
How to solve using Substitution or Elimination??? Help!!
y=3x-1
y=2x+2
Answer:
Step-by-step explanation:
Since both equations equals y, then both equations equal each other.
3x - 1 = 2x + 2
Subtract 2x from both sides
x - 1 = 2
Add 1 to both sides
x = 3
Plug x = 3 into one equation(doesn't matter which)
y = 3x - 1
y = 3(3) - 1
y = 9 - 1
y = 8
Answer:
[tex]x=3[/tex]
[tex]y=8[/tex]
Step-by-step explanation:
From these two equations, we can substitute the first equation into the second equation (or the other way round). This gives us:
[tex]3x-1=2x+2[/tex]
[tex]3x-2x=2+1[/tex] (minus [tex]2x[/tex] and add [tex]1[/tex] on both sides)
[tex]x=3[/tex]
To solve for [tex]y[/tex], we can use substitution again:
[tex]y = 3(3)-1[/tex] (using the first equation given)
[tex]y=8[/tex]
Hope this helps :)
A small airplane can hold 44 passengers.fifteen passengers board the plane a. Identify an inequality that represents the additional number of passengers,p, that can board the plane. •15+p<= 44•p—44<=15 • 15+p>=44•15+p<=44. Solve the inequality, the solution is: B. Which best explains whether or not 30 more passengers can board the plane. Please solve this
Answers:
Inequality is [tex]15 + p \le 44[/tex]
Choice A) 30 more passengers cannot board the plane. Only 29 more passengers can board the plane
===============================================
Explanation:
15 people are already on the plane.
p is a placeholder for a positive whole number representing the additional number of people that can get on the plane.
In total, the plane holds 15+p individuals.
This expression's largest possible value is 44. Think of it as the ceiling. In terms of math, we call it the maximum. Since at most 44 people can be on the plane, this means the inequality we'll set up is [tex]15+p \le 44[/tex]
This says "15+p is less than or equal to 44". It's the same as saying "15+p is 44 or smaller".
---------------------------
To isolate p, we subtract 15 from both sides
Doing so leads to...
[tex]15+p \le 44\\\\15+p-15 \le 44-15\\\\p \le 29[/tex]
We can see that the largest p can get is 29, meaning that at most 29 more people can board the plane. There's no way that 30 people can board. That unfortunate 30-29 = 1 person must wait for another plane.
This all shows why choice A is the answer.
----------------------------
As a way to check the answer, we can note how p = 29 leads to 15+p = 15+29 = 44. We've filled the plane to full capacity.
If p = 30, then 15+p = 15+30 = 45, and we've gone 1 seat overboard.
What property is represented?
40 + 0 = 40
• identity
• inverse
• associative
• commutative
Identity property!
Because the identity property for addition tells us that zero added to any number is the number itself. Zero is called the "additive identity." In this case, 0 is being added to 40.
Find the products in simplest form. 12 25 • 15 16 =
Answer:
9/20
Step-by-step explanation:
12 * 15
---------
25 x 16
180/400
To reduce, find the greatest common factor of 180 and 400.
180 / 20
-----------
400 / 20
Your answer would simplify to 9/20.
Round your answer to the nearest hundredth AB=
Step-by-step explanation:
[tex] \sin(20) = 3 \div x[/tex]
Multiply both sides with x :
[tex] x \times \sin(20) = 3[/tex]
And divide both sides with sin(20) :
[tex]x = 3 \div \sin(20) = 8.771[/tex]
Which gives us x=8,771
Answer:
AB = 6
Step-by-step explanation:
sin 20° = 3/?
[tex]\frac{1}{2}[/tex] = [tex]\frac{3}{x}[/tex]
cross-multiply: x = 6
(this is a rhombus btw) for what value of x is the figure the given special parallelogram? HELP PLS, show work.
Answer:
x = 2 or 3
Step-by-step explanation:
Diagonal of a rhombus bisects the vertex angles. So,
[tex]x^{2} =5x-6[/tex]
[tex]=> x^{2} -5x + 6 = 0[/tex]
Lets factorise the eqn.
[tex]=> x^{2} - 2x - 3x + 6 = 0[/tex]
[tex]=> x (x - 2) -3(x-2)[/tex]
[tex]=> (x-2)(x-3) = 0[/tex]
Here x will have 2 values.
1) [tex]x-2=0[/tex]
[tex]=> x =2[/tex]
2) [tex]x - 3 = 0[/tex]
[tex]=> x = 3[/tex]
HELP PLSS
Solve the equation 17−(3x+5)=3x−6
Answer:
x = 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
17 - (3x + 5) = 3x - 6
Step 2: Solve for x
Distribute negative: 17 - 3x - 5 = 3x - 6Add 3x on both sides: 17 - 5 = 6x - 6Combine like terms: 12 = 6x - 6Isolate x term: 18 = 6xIsolate x: 3 = xRewrite: x = 3Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 17 - (3(3) + 5) = 3(3) - 6Multiply: 17 - (9 + 5) = 9 - 6Add: 17 - 14 = 9 - 6Subtract: 3 = 3Here we see that 3 does indeed equal 3.
∴ x = 3 is the solution to the equation.
Answer:
x = 3
Step-by-step explanation:
17 - 1(3x + 5) = 3x - 6
17 − 3 − 5 = 3x − 6
12 - 3x = 3x - 6 subtract five
-3x + 12 = 3x - 6 rearrange terms
-3x = 3x - 18 subtract twelve
-6x = 18 subtract negative three
divide by negative six
x = 3
Complete the flow proof
Answer:
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
1. ∠V ≅ ∠Y [tex]{}[/tex] Given
2. [tex]\overline {WZ}[/tex] bisects ∠VWY [tex]{}[/tex] Given
3. ∠VWZ = ∠YWZ [tex]{}[/tex] Definition of bisection of angle
4. [tex]\overline {WZ}[/tex] ≅ [tex]\overline {ZW}[/tex] [tex]{}[/tex] Reflexive property
5. ΔWVZ ≅ ΔWYZ [tex]{}[/tex] Angle-Angle-Side congruency postulate
6. [tex]\overline {VZ}[/tex] ≅ [tex]\overline {YZ}[/tex] [tex]{}[/tex] CPCTC postulate
Step-by-step explanation:
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
1. ∠V ≅ ∠Y [tex]{}[/tex] Given
2. [tex]\overline {WZ}[/tex] bisects ∠VWY [tex]{}[/tex] Given
3. Given that ∠VWY is bisected by [tex]\overline {WZ}[/tex], therefore ∠VWY is split into two equal angles, ∠VWZ and ∠YWZ, from which we have ∠VWZ = ∠YWZ [tex]{}[/tex] by the definition of bisection of angle ∠WXY by [tex]\overline{WZ}[/tex]
4. By reflexive property, a line is congruent to itself, therefore, [tex]\overline {WZ}[/tex] ≅ [tex]\overline {ZW}[/tex]
5. Given that two adjacent angles and a side adjacent to the two angles in ΔWVZ are congruent to the corresponding two adjacent angles and adjacent side in ΔWYZ, ΔWVZ is congruent to ΔWYZ by the Angle-Angle-Side (AAS) congruency postulate
6. Given that ΔWVZ ≅ ΔWYZ, and side [tex]\overline {VZ}[/tex] of ΔWVZ is the corresponding side to side [tex]\overline {YZ}[/tex] of ΔWYZ, therefore, [tex]\overline {VZ}[/tex] is congruent to [tex]\overline {YZ}[/tex] by the Congruent Parts of Congruent Triangle are Congruent (CPCTC) postulate.