Answer:
(B)3 seconds.
Step-by-step explanation:
The object will be on the ground when its height is zero.
Therefore given the height function:
[tex]h(t)=144-16t^2\\$When h(t)=0\\144-16t^2=0\\16t^2=144\\$Divide both sides by 16\\t^2=9\\t=3$ sec[/tex]
The object will be on the ground afyer 3 seconds.
It will take 3 seconds for the object to reach the ground from a height of h(t) = 144 - 16t²
What are word problems involving the use of algebraic expressions?Word problems involving the use of algebraic expression require a good step-by-step interpretation with the use of variables to effectively solve the problem and arrive at a valid answer.
From the given information:
The height of an object that is allowed to drop from freefall to the ground is:
h(t) = 144 - 16t²At the time when h(t) = 0
0 = 144 - 16t²
16t² = 144
t² = 144/16
t² = 9
t = √9
t = 3 seconds
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Complete the statement about this table.
The A:B ratio in the table that is not equivalent to the
others is
20:27
10:14
15:21
25:35
Answer:
20:27
Step-by-step explanation:
Find the value of x in the following
a) x:2 = 10:4 b) 3:x= 6:8
Answer:
a) x = 5
b) x = 4
Step-by-step explanation:
a) x:2 = 10:4
Product of extremes = Product of means
=> x*4 = 10*2
=> 4x = 20
Dividing both sides by 4
=> x = 5
b) 3:x = 6:8
Product of extremes = Product of Means
=> 3*8 = 6*x
=> 24 = 6x
Dividing both sides by 6
=> x = 4
Answer:
a. X= 5b. X= 4Solution,
[tex]a. \: \: \frac{x}{2} = \frac{10}{4} \\ \: \: or \: x \times 4 = 10 \times 2 \: ( \: cross \: multiplication) \\ \: \: or \: 4x = 20 \\ or \:x = \frac{20}{4} \\ \: \: \: x = 5[/tex]
[tex]b. \: \frac{3}{x} = \frac{6}{8} \\ or \: 6 \times x = 3 \times 8 \: ( \: cross \: multiplication) \\ or \: 6x = 24 \\ \: or \: x = \frac{24}{6} \\ x = 4[/tex]
Hope this helps...
Good luck on your assignment
Aiden built a cone shaped volcano for a school science project. The volcano has a base diameter of 32 cm and a slant height of 45 cm
a) Whats the lateral area to the nearest tenth of a square?
b) the paint for the volcanos surface costs $1.99/jar, and one jar of paint covers 400cm^2. How much will the paint cost?
Answer:
a) About 2261.95
b) $11.94
Step-by-step explanation:
a) The lateral area of a cone can be calculated via A=πrl
b) Simple do 2261.95/400 and round to the nearest 1 to get 6. Then multiply 6 by 1.99 to get 11.94
Hope it helps <3
Some pupils were asked which their favourite school subject was, from a choice of maths, english and science. Soe of the results are shown in the table. How many pupils in total chose English as their favourite subject?
Answer:
[tex]\boxed{26 pupils}[/tex]
Step-by-step explanation:
Girls for English:
20 + English + 12 = 36
English + 32 = 36
English = 36-32
English = 4 (For girls)
Total for Science:
12+7 = 19
Total for English:
25 + English + 19 = 70
English + 44 = 70
English = 70-44
English = 26 pupils
There are 26 pupils (20 Boys and 6 Girls) who chose English as their favorite subject.
The table shows data about the favorite subject of some of the students.
The following things can be observed from the given table:
Girls who like maths are 20, who like science are 12 and total girls are 38. So, the number of girls who like English will be [tex]38-20-12=38-32=6[/tex]. So. 6 girls like English subject.Out of 25 students who like maths, 20 are girls. So, 5 students are boys who like maths.Total students who like science are 12 girls and 7 boys. So, the sum of students will be 19.Total number of students participated in the survey is 70.So, the total number of students of English subject can be calculated as,
[tex]70-25-19=70-44\\=26[/tex]
So, out of 26 students, 6 are girls and 20 will be boys who love English subject.
Therefore, there are 26 pupils (20 Boys and 6 Girls) who chose English as their favorite subject.
For more details, refer to the link:
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Determine the measure of the interior angle at vertex D.
Answer:
162°
Step-by-step explanation:
This is a hexagon, so the sum of the angle measures will be 720°
Add up the measures
40x=720
Divide
X=18
Multiply by 9 to find angle of D
9*18=162
The measure of the interior angle at vertex D is 162°. Hence, option B. is the right choice.
What are polygons?Polygons are closed plane figures formed by the intersection of 3 or more non-collinear line segments.
What is the sum of all interior angles of a polygon?The sum of interior angles of an n side polygon = (n-2)180°.
How do we solve the given question?We are given a 6 side polygon ABCDEF.
∴ n = 2.
The sum of interior angles of polygon ABCDEF = (6-2)180° = 4*180° = 720°.
The angles are 2x, 9x, 2x, 9x, 9x, and 9x.
Their sum = 2x + 9x + 2x + 9x + 9x + 9x = 40x.
This sum = The obtained sum
or, 40x = 720°
or, x = 720°/40 = 18°.
∴ Interior angle at vertex D = 9x = 9*18° = 162°. Hence, option B. is the right choice.
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Please help ASAP: Factorise the following
Answer:
Step-by-step explanation:
Slide 1:
A) (x+2)(x+8)
B) (x+3)(x+4)
C) (x+1)(x+12)
Slide 2:
A) (x-1)(x+4)
B) (x+1)(x-3)
C) (x-2)(x+4)
Hope this helps!
The time (in minutes) taken for a dose of a certain drug to be effective as a sedative on lab animals is normally distributed with mean =1 and variance 2=0.01. What is the proportion of animals for which the time taken is between 1 and 1.1 minutes?
Answer:
Step-by-step explanation:
Let x be the random variable representing the time (in minutes) taken for a dose of a certain drug to be effective as a sedative on lab animals. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 1
σ = √variance = √0.01 = 0.1
the probability that the time taken for a randomly selected animal is between 1 and 1.1 minutes is expressed as
P(1 ≤ x ≤ 1.1)
For x = 1,
z = (1 - 1)/0.1 = 0
Looking at the normal distribution table, the probability corresponding to the z score is 0.5
For x = 1.1
z = (1.1 - 1)/0.1 = 1
Looking at the normal distribution table, the probability corresponding to the z score is 0.84
Therefore,
P(1 ≤ x ≤ 1.1) = 0.84 - 0.5 = 0.34
The the proportion of animals for which the time taken is between 1 and 1.1 minutes is 0.34
Maria claims that any fraction between 1/5 and 1/7 on a number line must have a denominator that is 6.Enter a fraction that shows Maria's claim is incorrect A. 6/35 B.13/70 C. 9/35 D.16/70 please help me
Answer
A or B
Step-by-step explanation:
the lowest is 1/7 = 5/35 = 10/70
the highest is 1/5 = 7/35 = 14/70
so answer A and B are OK
C and D are out of range
Please. Can anyone help me.
Answer:
correct option is A: [tex]\frac{4}{10} \neq \frac{6}{14}[/tex]
Step-by-step explanation:
If the segment DE was parallel to the segment BC, we could use the Thales' theorem, where the ratio of one segment created in one side of the triangle over the whole side is the same ratio of one segment created in the other side over the whole side:
[tex]\frac{AD}{AB} = \frac{AE}{AC}[/tex]
Using the values given (AD = 4, AB = 6+4=10, AE = 6, AC = 8+6=14), we would have:
[tex]\frac{4}{10} = \frac{6}{14}[/tex]
[tex]4*14=6*10[/tex]
[tex]56=60[/tex]
This sentence is false, therefore the segments DE and BC are not parallel.
The inequation to prove this is the first one we used, using the "not equal" symbol:
[tex]\frac{4}{10} \neq \frac{6}{14}[/tex]
So the correct option is: A
Find the area of the shape shown below.
Answer:
12 [tex]units^{2}[/tex]
Step-by-step explanation:
First Figure: 1/2*2*2 = 2
Second Figure: 2*2 = 4
Third Figure: 1/2*6*2 = 6
2+4+6 = 12
So the area is 12 [tex]units^{2}[/tex]
could someone please answer the questions in the photo
Answer:
10. A dice has 6 sides each from 1-6, rolling each time can give 6 different possible results, hence the chances of rolling a 2, 3, and 5 will be 1/6 respectively.
To roll a 2, 3, and 5 in order, which are independent events,
the required probability will be
= 1/6 x 1/6 x 1/6
= 1/216
11. Using Pythagoras theorem,
8² + B² = 15²
B =√161
=12.689
13. Area of trapezoid= (upper base+ lower base)(height)/2
= (16+23)(3)/2
= 58.5 m²
Answer:
Answers:
Question #10:
Rolling a die three times gives 6 · 6 · 6 possibilities this makes 216 possibilities in total. Rolling the die in the order 2, 3, 5 is only one so the answer is: [tex]\frac{1}{16}[/tex].
Question #11:
Since the triangle is a right triangle we can use the pythagorean theorem:
[tex]B^{2}[/tex] + [tex]8^{2}[/tex] = [tex]15^{2}[/tex]
Working backwards we get that B is equal to 225 minus 64 which gets the square root of 161 or [tex]\sqrt{161}[/tex].
Question #12:
First we can start with finding the area of the rectangle in the trapezoid:
3 · 16 = 48
Next the two right triangles. 21 - 16 = 5 That is the length of the additional two triangles. Dividing 5 by two gets the base of one of them, but if we don't divide it by two we will be able to solve for both at the same time:
3 · 5 = 15
[tex]\frac{15}{2}[/tex] = 7.5
7.5 + 48 = 55.5
Complete the table of values below: x -3 -2 -1 0 1 2 3 How the graph relates to y=2x y=2x Answer Answer Answer Answer Answer Answer Answer Not applicable y=-2x Answer Answer Answer Answer Answer Answer Answer multiplied by Answer y=(3)(2x)
Answer:
The values of x are:
x : -3, -2, -1, 0, 1, 2, 3
Let's solve each by putting each value of x into each equation:
a [tex]y = 2^x[/tex]
> x = -3
=> y = 2^(-3) = 1/8
> x = -2
=> y = 2^(-2) = 1/4
> x = -1
=> y = 2^(-1) = 1/2
> x = 0
=> y = 2^0 = 1
> x = 1
=> y = 2^1 = 2
> x = 2
=> y = 2^2 = 4
> x = 3
=> y = 2^3 = 8
b. [tex]y = -2^x[/tex]
> x = -3
=> y = -2^(-3) = -1/8
> x = -2
=> y = -2^(-2) = -1/4
> x = -1
=> y = -2^(-1) = -1/2
> x = 0
=> y = -2^0 = -1
> x = 1
=> y = -2^1 = -2
> x = 2
=> y = -2^2 = -4
> x = 3
=> y = -2^3 = -8
c. [tex]y = (3)(2^x)[/tex]
> x = -3
=> y = 3 * 2^(-3) = 3 * 1/8 = 3/8
> x = -2
=> y = 3 * 2^(-2) = 3 * 1/4 = 3/4
> x = -1
=> y = 3 * 2^(-1) = 3 * 1/2 = 3/2
> x = 0
=> y = 3 * 2^0 = 3 * 1 = 3
> x = 1
=> y = 3 * 2^1 = 3 * 2 = 6
> x = 2
=> y = 3 * 2^2 = 3 * 4 = 12
> x = 3
=> y = 3 * 2^3 = 3 * 8 = 24
Input these values into the table.
Answer:
a y = 2^x
> x = -3
=> y = 2^(-3) = 1/8
> x = -2
=> y = 2^(-2) = 1/4
> x = -1
=> y = 2^(-1) = 1/2
> x = 0
=> y = 2^0 = 1
> x = 1
=> y = 2^1 = 2
> x = 2
=> y = 2^2 = 4
> x = 3
=> y = 2^3 = 8
b. y = -2^x
> x = -3
=> y = -2^(-3) = -1/8
> x = -2
=> y = -2^(-2) = -1/4
> x = -1
=> y = -2^(-1) = -1/2
> x = 0
=> y = -2^0 = -1
> x = 1
=> y = -2^1 = -2
> x = 2
=> y = -2^2 = -4
> x = 3
=> y = -2^3 = -8
c. y = (3)(2^x)
> x = -3
=> y = 3 * 2^(-3) = 3 * 1/8 = 3/8
> x = -2
=> y = 3 * 2^(-2) = 3 * 1/4 = 3/4
> x = -1
=> y = 3 * 2^(-1) = 3 * 1/2 = 3/2
> x = 0
=> y = 3 * 2^0 = 3 * 1 = 3
> x = 1
=> y = 3 * 2^1 = 3 * 2 = 6
> x = 2
=> y = 3 * 2^2 = 3 * 4 = 12
> x = 3
=> y = 3 * 2^3 = 3 * 8 = 24
Step-by-step explanation:
What is the area of the square adjacent to the third side of the triangle?
Answer:
The area of the square adjacent to the third side of the triangle is 11 units²
Step-by-step explanation:
We are given the area of two squares, one being 33 units² the other 44 units². A square is present with all sides being equal, and hence the length of the square present with an area of 33 units² say, should be x² = 33 - if x = the length of one side. Let's make it so that this side belongs to the side of the triangle, to our convenience,
x² = 33,
x = [tex]\sqrt{33}[/tex] .... this is the length of the square, but also a leg of the triangle. Let's calculate the length of the square present with an area of 44 units². This would also be the hypotenuse of the triangle.
x² = 44,
x = [tex]\sqrt{44}[/tex] .... applying pythagorean theorem we should receive the length of a side of the unknown square area. By taking this length to the power of two, we can calculate the square's area, and hence get our solution.
Let x = the length of the side of the unknown square's area -
[tex]\sqrt{(44)}^2[/tex] = [tex]x^2[/tex] + [tex]\sqrt{33}^2[/tex],
x = [tex]\sqrt{11}[/tex] ... And [tex]\sqrt{11}[/tex] squared is 11, making the area of this square 11 units².
Answer:
11 units²Step-by-step explanation:
If the triangle is right then area of square adjacent to the longest side is equal to sum of areas of squares adjacent to its other sides. (As in Pythagorean theorem)
So:
33 units² + ? = 44 units²
? = 44 units² - 33 units²
? = 11 units²
I need this ASAP! When David was asked how old he was, he said: "I'm three times younger than my dad, but twice as old as Rebecca." Then little Rebecca ran up to him and declared "I am 30 years younger than my dad." How old is David?
Answer:
David is 12 years old.
Step-by-step explanation:
Let r = Rebecca's age
Let d = David's age
let p = Dad's age
David is 3 times as younger than his dad:
d = [tex]\frac{p}{3}[/tex]
David is 2 times older than Rebecca:
d = 2r
Rebecca is 30 years younger than the dad:
r = p-30
All three equations can be solved by a system
2r = [tex]\frac{p}{3}[/tex]
r = p-30
multiplying r = p-30 by negative 2 and adding it to 2r = [tex]\frac{p}{3}[/tex]
0 = (-2p + p/3) + 60
multiplying new equation by 3
0 = (-6p + p) + 180
5p = 180
p = 36
d = 36/3 = 12
PLEASE HELP! ! ! PLEASEEE!!
Answer:
4^2
Step-by-step explanation:
4^4 times 4^3 is equal to 4^7 since you just add the exponents. Then, when dividing, you subtract the exponents, so 4^7/4^5 is 4^2. I hope this is helpful!
Answer:
the answer is
Step-by-step explanation:
4 to the power of 2
you add 4 and 3 which is 7
and 7 subtract 5 which is
4 to the power of 2
Determine which postulate or theorem can be used to prove that
APQS= ARQS.
Answer:
sss
Step-by-step explanation:
as you seen your puestion it says they are similar by side if you ask me by what because your given is side
On a piece of paper, graph this system of equations.
y = x - 10
y = x2 - 2x - 3
Then determine which answer choice matches the graph you drew and
identify the solution(s) to the system.
Answer:
No solution
Step-by-step explanation:
If you graph this system of equations, they do not intersect in any way and therefore there is no solution.
Please answer this question now
Answer:
61
Step-by-step explanation:
Definition of conguency
*figure on the right is rotated a bit
Subtract (4x^2+6) - (2x-5) thanks for the help btw :)
Answer:
C
Step-by-step explanation:
The only like terms are 6 and -5. 6 - (-5) = 11 so the answer is 4x² - 2x + 11.
Answer:
C. 4x² -2x + 11
Step-by-step explanation:
(4x² + 6) - (2x - 5)
→ Remember the minus outside the (2x - 5) means the minus inside changes to a plus
(4x² + 6) - (2x + 5)
→ Remove the brackets
4x² + 6 - 2x + 5
→ Add the whole numbers together
4x² + 11 - 2x which is equivalent to the option c 4x² -2x + 11
What is the measure of ZA?
What is the measure of ZB?
Answer:
[tex] m\angle A = 72\degree \\
m\angle B = 108\degree [/tex]
Step-by-step explanation:
ABCD is a parallelogram.
Since, opposite angles of a parallelogram are congruent.
[tex] \therefore m\angle A = m\angle C\\
\therefore (5y-3)\degree = (3y+27)\degree \\
\therefore 5y - 3= 3y +27\\
\therefore 5y-3y = 27+3\\
\therefore 2y = 30\\\\
\therefore y = \frac{30}{2} \\\\
\therefore y = 15\\
\because m\angle A = (5y-3)\degree \\
\therefore m\angle A = (5\times 15-3)\degree \\
\therefore m\angle A = (75-3)\degree \\
\huge{\red {\boxed {\therefore m\angle A = 72\degree}}} \\\\
\because m\angle A + m\angle B = 180\degree(opposite \: \angle 's\: of\:a\: \parallel ^{gm}) \\
\therefore m\angle B = 180\degree - 72\degree \\
\huge{\purple {\boxed {\therefore m\angle B = 108\degree}}} [/tex]
HELP PLEASE ASAP PLEASE HELP ASAP
Answer:
angle 3 and angle 4 are equal because the diagonals/2 are equal. Angle 4 equals angle 1 due to opposite interior angles thereom. 90 degrees minus 37=53 degrees which is angle 2. Since angle 2 is equal to the angle GKH, 53+53=106 and 180-106=74 degrees, and due to vertical angles, angle 7 is 74 degrees.
I am between 8 o clock in the morning and 3:00 in the afternoon .My number of minutes is odd i am more than half an hour away from the next o clock i am closer to 5pm than to 5am what time am i ?
Answer:
1:00 PM
Step-by-step explanation:
According to the conditions given in the question, i confirm that the time time asked here is 1:00 PM.
at 1:00 PM, its 5 minutes (odd), clearly, more than half an hour away from the next o clock. It is closer to 5 PM than 5 AM.
Farmer Hanson is putting together fruit baskets. He has 240 apples and 150 pears. What is the largest number of baskets he can put together so that he can have the same number of apples and same number of pears in each basket considering no fruit is left out?
Answer: 30 baskets.
Step-by-step explanation:
You need to find the Greatest Common Factor (GCF).
240 (apples) = 2 x 2 x 2 x 2 x 3 x 5
150 (pears) = 2 x 3 x 5 x 5
GCF (240, 150) = 2 x 3 x 5
= 30
You can make 30 baskets containing 240/30 = 8 apples and 150/30 = 5 pears.
Answer:
30 baskets
Step-by-step explanation:
Please help me get the right answer
Answer:
A
Step-by-step explanation:
When multiplying numbers with exponents, the exponents add together. This means that the correct answer is letter A.
PLEASE HELP!!!
What is the third quartile for this data set?
Answer:
38
Step-by-step explanation:
Using the five number summary it is 38 since it is 75 percent of the sample
You have the correct answer. Nice work
==========================================================
Explanation:
If the values aren't sorted, then list them from smallest to largest. The values are already sorted for us, so we move onto the next step.
That next step is to find the median. The median is 29 because four values are smaller than it, and four values are larger than it. The value 29 is right in the middle. This value is in slot 5.
Next, split the data into two halves where L = {21,24,25,28} is the lower half and U = {35,37,39,42} is the upper half. As you can see, any value in set L is smaller than the median. While any value in set U is larger than the median.
The third quartile is the median of set U. We have four values in this set, so the median will be between slots 3 and 4 (between 37 and 39)
Average 37 and 39 to get (37+39)/2 = 38. We see that 38 is the midpoint of 37 and 39.
Therefore, the third quartile is 38.
Please help with this❤️❤️Please plz
Answer:
Step-by-step explanation:
the first answer is D
the second is B
A rectangle has an area of 524.4m2. One of the sides is 6.9m in length. Work out the perimeter of the rectangle. PLEASE ANSWER!!! SOON ASAP
Answer:
165.8 mSolution,
Area of rectangle= 524.4 m^2
Length(L)= 6.9 m
Breadth(B)=?
Now,
[tex]area = length \times breadth \\ or \: 524.4 = 6.9 \times b \\ or \: 524.4 = 6.9b \\ or \: b = \frac{524.4}{6.9} \\ b = 76 \: m[/tex]
Again,
Perimeter of rectangle:
[tex]2(l + b) \\ = 2(6.9 + 76) \\ = 2 \times 82.9 \\ = 165.8 \: m[/tex]
Hope this helps...
Good luck on your assignment.....
Answer:
The perimeter of the rectangle is 165.8cm
Step-by-step explanation:
Area of a rectangle = length × width
Area = 524.4m²
length = 6.9m
524.4 = 6.9 × width
width = 524.4 / 6.9
width = 76m
Perimeter of a rectangle =
2(length ) + 2(width)
length = 6.9m
width = 76m
Perimeter = 2( 6.9) + 2(76)
= 13.8 + 152
The final answer is
= 165.8cm
Hope this helps you
Please I need help with this question
Answer:
Step-by-step explanation:
2/3(6y + 9)
2/3(6y) = 4y
2/3(9) = 6
=4y + 6 (A)
Combine like terms: ab-a2+42-5ab+3a2+10
Answer:
-4AB+2A2+52
Step-by-step explanation:
1. FIRST WE PUT THE LIKE TERMS TOGETHER (REARRANGE THE PROBLEM)
AB-5AB-A2+3A2+42+10
2. SIMPLIFY ALL LIKE TERMS
-4AB+2A2+52
YOUR DONE!!!!!!
HOPE I HELPED
CAN I GET BRAINLIEST PLS? (DESPERATELY TRYING TO LEVEL UP)
-ZYLYNN JADE
Make this into an expression s% of 1/r
Answer:
[tex] \frac{s}{100r} [/tex]
Step-by-step explanation:
s% of 1/r
=
[tex] \frac{s}{100} \times \frac{1}{r} [/tex]
[tex] \frac{s}{100r} [/tex]