Final answer:
The rock takes approximately 2.032 seconds to reach the ground.
Explanation:
The height of the rock can be modeled by the equation h(t) = -16t² + 10t + 100, where h(t) is the height of the rock and t is the time in seconds. To find the time it takes for the rock to reach the ground, we need to solve the equation when h(t) is equal to zero. We can do this by setting the equation equal to zero and using the quadratic formula.
Using the quadratic formula, we get: [tex]t = (-b \± \sqrt(b^2 - 4ac))/(2a)[/tex]
Plugging in the values of a, b, and c from the equation, we get: [tex]t = (-10 \± \sqrt{10^2 - 4(-16)(100)/2(-16)[/tex]
Simplifying, we get: [tex]t = (-10 \± \sqrt{100 + 6400/(-32)[/tex]
Continuing to simplify, we get: [tex]t = (-10 \± \sqrt{6500/(-32)}[/tex]
So, it takes approximately 2.032 seconds for the rock to reach the ground.
26. Adrian has a cube that has a volume of 64
cubic centimeters. Which is the surface area of
Adrian's cube?
A. 6 square centimeters
B. 16 square centimeters
C. 32 square centimeter
D. 96 square centimeters
Answer:
Bend down
Step-by-step explanation:
Bebebe
For f(x) = 2x+1 and g(x) = x+14, find (gof)(x).
Answer: OPTION B
Step-by-step explanation:
You can observe that the exercise provides you two Linear functions.
The first Linear function is the function f(x). This is:
[tex]f(x) = 2x+1[/tex]
And the other Linear function is the function g(x):
[tex]g(x) = x+14[/tex]
In order to find [tex](gof)(x)[/tex], you need to follow these steps shown below:
Step 1:
You must substitute the function f(x) into the function g(x); this means that the function f(x) will be in the place of the variable "x" of the function g(x); as you can observe below:
[tex](gof)(x) = (2x+1)+14[/tex]
Step 2:
Finally you must combine the like terms (You can notice that the like terms are 1 and 14; then you must add them). Therefore, you get that [tex](gof)(x)[/tex] is:
[tex](gof)(x) = 2x+1+14\\\\(gof)(x) = 2x+15[/tex]
Make x the subject of the formula 6x+a=5(x+t)
Answer: x = 5t - a
Step-by-step explanation:
6x + a = 5 (x + t)
expanding the bracket
6x + a = 5x + 5t
collecting like terms
6x - 5x = 5t - a
x = 5t - a
Answer:
x = 5t - a
Step-by-step explanation:
in order to make x the subject of formulae from the expression 6x+a=5(x+t)
the first step to do is to open the bracket (BODMAS).
6x+a=5(x+t)
6x + a = 5x + 5t
collect the like terms
6x-5x = 5t - a
x = 5t - a
therefore the value of x in the expression , that is expressing x interms of t and a from the expression 6x+a=5(x+t) is solved to be x = 5t - a
HELP
Find the measure of angle z in the following figure,
Answer:
B
Step-by-step explanation:
so you know that where it around angle c you use supplementry angels. this makes it 180-130=50.
you then know that the triangle is 90degrees plus 50 degrees plus x =180
90+50+z=180
140+z=180
z=40
Answer:
B) ∠z = 40°
Step-by-step explanation:
All three angles of a triangle add up to 180°. In this image, you can see that the angle ∠ACD is 130°. Because ∠ACB and ∠ACD are supplementary angles it means that their angles equal 180° when added together.
If ∠ADC = 130° then:
180° - 130° = 50°
Since we now know that ∠ACB is 50°, we can subtract our two angles from 180° to get the measurement for angle z.
180° - 50° - 90° =
180° - 140° = 40°
~Hope this helps!~
Please Help & Thank You
What is the volume of the prism?
Enter your answer in the box as a mixed number in simplest form.
Answer:
67 [tex]\frac{1}{2}[/tex] [tex]cm^3[/tex]
Step-by-step explanation:
the volume of a rectangular prism is the three sides multiplied together, [tex]h*w*l[/tex]
converting the mixed number to improper fraction to make multiplying easier.
[tex]\frac{9}{2} *6*\frac{5}{2}[/tex] = [tex]\frac{135}{2}[/tex]
converting back to mixed number in simplest form
[tex]\frac{135}{2}[/tex]= 67 R 1
[tex]\frac{135}{2}[/tex]= 67 [tex]\frac{1}{2}[/tex]
Find the exact valued the function f(x)=6•4^x fox x=-2
Answer:
f(-2) = 3/8
Step-by-step explanation:
f(x)=6•4^x
Let x=-2
f(-2) = 6 * 4^-2
The negative in the exponent means it goes to the denominator
f(-2) = 6 * 1/ 4^2
= 6/4^2
=6/16
Simplifying
=3/8
Brianna bought 3 bottles of ketchup and 2 bottles of mustard for $11.85. Logan bought 3 bottles of ketchup and 5 bottles of mustard for $13.73. Find the cost of each.
the cost of ketchup is $3.53 & mustard is $0.63 .
Step-by-step explanation:
Here we have , Brianna bought 3 bottles of ketchup and 2 bottles of mustard for $11.85. Logan bought 3 bottles of ketchup and 5 bottles of mustard for $13.73. We need to find the cost of each. Let's find out :
Let cost of ketchup be x and mustard be y than ,
Brianna bought 3 bottles of ketchup and 2 bottles of mustard for $11.85
We have following equation ,
⇒ [tex]3x+2y=11.85[/tex] ..........(1)
Logan bought 3 bottles of ketchup and 5 bottles of mustard for $13.73
We have following equation ,
⇒ [tex]3x+5y=13.73[/tex] ........(2)
Now , (2) - (1) , i.e.
⇒ [tex]3x+5y-(3x+2y)= 13.73-11.85[/tex]
⇒ [tex]3y= 1.88[/tex]
⇒ [tex]y=0.627[/tex]
Putting value of y in (1) :
⇒ [tex]3x+2(0.627)=11.85[/tex]
⇒ [tex]3x=11.85-1.254[/tex]
⇒ [tex]x=3.532[/tex]
Therefore , the cost of ketchup is $3.53 & mustard is $0.63 .
The cost of each bottle of ketchup is $3.532 and cost of each mustard is $0.626
Explanation:
Given:
3 bottles of ketchup + 2 bottles of mustard = $11.85
3 bottles of ketchup + 5 bottles of mustard = $13.73
Cost of each = ?
Let x be the cost of each bottle of ketchup
Let y be the cost of each bottle of mustard
According to the question:
3x + 2y = $11.85
3x + 5y = $13.73
Substituting both the equation, we get:
3x + 2y = $11.85
3x + 5y = $13.73
________________
-3y = -1.88
y = $0.626
Substituting the value of y = $0.626 in equation 1
3x + 2(0.626) = $11.85
3x + 1.252 = $11.85
3x = 10.598
x = $3.532
Therefore, cost of each bottle of ketchup is $3.532 and cost of each mustard is $0.626
determine whether the quadrilateral is a parallelogram justify your answer.
Step-by-step explanation:
Yes, it is a parallelogram because the opposite angles are congruent
Option C
Answer:
yes opposite angles are congruent.
Step-by-step explanation:
On both sides 36 and 144 are congruent or equal
Which problem solving strategy would be best to solve this problem?
Avelina earned half as much money as Gus. If Gus earned $125.00, how much money did Avelina earn?
Answer:
$62.50
Step-by-step explanation:
125/2=62.5 --> $62.50
Answer:
dude put the whole question so people can answer right .
Step-by-step explanation:
(9. Suppose you deposited $100 in a savings account
4 years ago with a simple interest rate of 2.2%.
The interest that you earned in those 4 years
is $8.80. Which of the following is true? Select
all that apply.
Answer: A and B are true
Step-by-step explanation:
Interest is 0.022, that is 2.2% = 2.2/ 100= 0.022
Principal is %100 as stated in the question
Mark as brainliest
In a class of 50 students,27 are athletes 9 are musicians and 6 of the musicians are athletes . If one student is randomly selected from the class , find the probability of choosing an athlete or a musician
Answer: 0.6
Step-by-step explanation:
Total population of class = 50
There are 27 athletes, and 9 musicians However, 6 of the musicians are also athletes.
Therefore, totals for athletes and musicians are:
27 + 9 -6 = 30
Thus, the probability of choosing an athlete or a musician is 30/50= 0.6
We could also use the formula:
P(A or M) = P(A) + P(M) - P(A and M)
P(A or M)=27/50+9/50-6/50
P(A or M)=30/50=0.6
I hope this helps!
???????????????????????????/
Answer:
B. 5 × 5 × 8
Step-by-step explanation:
Each of the boards have an area of 25. You have 8 of them.
Answer:
b. 5 × 5 × 8
Step-by-step explanation:
"...the total area is five feet × five feet times eight"
Equation:
(5 × 5) × 8
Simply remove brackets:
5 × 5 × 8
Answer the question and make sure it is squared and in meters
Answer:
10,000m²
Step-by-step explanation:
The figure can be divided into a rectangle and a triangle as shown in the attachment.
The area of the rectangular portion is
[tex] = l \times w[/tex]
[tex] = 120 \times 30[/tex]
[tex] = 3600 {m}^{2} [/tex]
The area of the triangular portion is
[tex] = \frac{1}{2} \times 80 \times 160[/tex]
[tex] = 6400 {m}^{2} [/tex]
The area of the figure is therefore
[tex] = 6400 + 3600[/tex]
[tex] = 10000 {m}^{2} [/tex]
The base of the glass house to the right is a rectangle. What’s the perimeter of the base of the house?
Final answer:
The perimeter of a rectangle is found by adding up the lengths of all its sides.
Explanation:
The perimeter of a rectangle is found by adding up the lengths of all its sides. In this case, the base of the glass house is a rectangle.
Let's say the length of the base is 12 meters and the width is 8 meters. To find the perimeter, we add up the lengths of all four sides: 12 + 8 + 12 + 8 = 40 meters.
8.21 Divided by 7.8=19.1
Answer: Not true
Step-by-step explanation:
8.21 /7.8
8.21 × 100 divided by 7.8 ×100
821/780
= 1.05
need help !!!!!!!!!!!
Answer:
d
Step-by-step explanation:
8/root3
Have to find out what the angle x is respond ASAP pls
Answer: Angle x equals 19 degrees
Step-by-step explanation: We have two polygons, one with five sides and the other with eight sides. The question states that the pentagon has exactly one line of symmetry which means the line that runs down from point D to line AB divides the shape into exactly two equal sides. Hence angle A measures the same size as angle B (in the pentagon).
First step is to calculate the angles in the pentagon. The sum of angles in a polygon is given as
(n - 2) x 180 {where n is the number of sides}
= 3 x 180
= 540
This means the total angles in the pentagon can be expressed as
A + B + 84 + 112 + 112 = 540
A + B + 308 = 540
Subtract 308 from both sides of the equation
A + B = 232
Since we have earlier determined that angle A measures the same size as angle B, we simply divide 232 into two equal sides, so 232/2 = 116
Having determined angle A as 116 degrees, we can now compute the value of angle A in the octagon ABFGHIJK. Since the figure is a regular octagon, that means all the angles are of equal measurement. So, the sum of interior angles is given as
(n - 2) x 180 {where n is the number of sides}
= 6 x 180
= 1080
If the total sum of the interior angles equals 1080, then each angle becomes
1080/8
= 135 degrees.
That means angle A in the octagon measures 135, while in the pentagon it measures 116. The size of angle x is simply the difference between both values which is
x = 135 - 116
x = 19 degrees
hi! can anyone help me pls?
Answer:
Option B, -4 and 4
Step-by-step explanation:
Step 1: Subtract 15 from both sides
y^2 - 1 - 15 = 15 - 15
y^2 - 16 = 0
Step 2: Factor
y^2 - 16
(y + 4)(y - 4)
Step 3: Find the solutions
y + 4 - 4 = 0 - 4 and y - 4 + 4 = 0 + 4
y = -4 and y = 4
Answer: Option B, -4 and 4
Answer:
-4 and 4
Step-by-step explanation:
All you need to do is solve for y
[tex]y^{2} - 1 = 15\\[/tex] (plus 1 to both sides)
[tex]y^{2} = 16[/tex] (take square root of 16)
[tex]y = \sqrt{16}[/tex]
[tex]y = +-4[/tex] (whenever you to the root of a perfect square you want the positive and negative root)
To double check if your answer is right: plug in -4 and +4 in as y and see if it equals 15
1. [tex](4)^{2} - 1 =15[/tex]
[tex]16-1 = 15\\15= 15[/tex]
(positive 4 checks out)
2. [tex](-4)^{2} - 1 = 15[/tex]
[tex]16 - 1 = 15\\15 = 15[/tex]
( negative 4 checks out)
A circular walking path has a diameter of 45 yards. What is the circumference of the dinner plate
Answer:
45pi yards
Step-by-step explanation:
C = Pi x D
D = 45 yards
C = Pi x 45 yards
C = 45Pi yards, or 141.3716694 yards
What is the recursive rule for -6,12,-24,48,-96?
Answer:
multiply by -2
$850, 4%, 6 months . Find simple interest, please help ASAP!!!
The required simple interest is given as $17.
Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.
Here,
Principal = $850
Rate = 4%
Time = 6 months
Simple interest = principal × rate/100 × time / 12
= 850 × 4 / 100 × 6/12
= 850 × 0.04 × 1/2
= $17
Thus, the required simple interest is $17.
Learn more about simple interests here:
https://brainly.com/question/26457073
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The cost of your new contact lenses is $200. If you left 25% deposit upon
ordering the lenses, what is your remaining balance?
Answer: Remaining balance is $150
Step-by-step explanation:
Contact lens= $200
25% of the amount was paid
= 25/100 × 200 = $50
Out of $200 of contact lens, $50 was paid as deposit, subtract $200 from $50 to give balance.
$200 - $50 = $150
I hope this helps.
After calculating a 25% deposit on the $200 contact lenses, which is $50, the remaining balance that needs to be paid is $150.
Explanation:If the cost of your new contact lenses is $200, and you left a 25% deposit upon ordering the lenses, we need to first calculate the amount of the deposit and then determine the remaining balance.
To find the deposit amount, we take 25% of the total cost:
Deposit = 25% of $200Deposit = 0.25 × $200Deposit = $50Once we have calculated the deposit amount, we subtract it from the total cost to find the remaining balance owed:
Remaining Balance = Total Cost - DepositRemaining Balance = $200 - $50Remaining Balance = $150So, after leaving a 25% deposit on the contact lenses, your remaining balance would be $150.
What is the value of the expression 3/8 -1/4
Your Answer Is: 0.125
The value of the expression 3/8 - 1/4 is 1/8.
To find this, you must first find a common denominator, which in this case is 8. Multiply 1/4 by 2/2 to get 2/8. Now, you are able to subtract the fractions to find your answer. 3/8 - 2/8 = 1/8. Thus meaning, 1/8 is your answer.
I hope this helps!
Help with this and I’ll mark you as brainliest ❤️
Answer:
The answer is C
Step-by-step explanation:
Because 1 is 90 because it shaped like a L 2 is 45 because its narow, and 3 is the smallest of them all. I also did it before
If you can buy 1/4 pizza for 5 dollars, how much can you purchase for 8 dollars?
Answer: 2/5 pizza
Step-by-step explanation:
Solve for x.
x/6 = 2
x=___________
Answer:
12
Step-by-step explanation:
x/6 = 2
x = 6×2 = 12
Answer:
X=12 (sorry for the handwriting)
Frankie buys some stamps. She
Spends £11.70 on 20 p and 50p,
stamps. She buys twice as many 20p stamps as 50 stamps.how many 20p stamps did she buy ?
Answer:
86'
Step-by-step explanation:
Help me with this math question please.
Answer:
No
Step-by-step explanation:
Write the ratios of erasers to cost (dropping the dollar sign) as fractions:
(number of erasers)/(price): 2/1 and 10/4
The question is if the ratios 2/1 and 10/4 are equivalent.
2/1 = 2
10/4 = 2.5
A proportion is setting two ratios equal. Here, one ratio equals 2, and one ratio equals 2.5.
Since the ratios are not equivalent, the relation is not proportional.
What is the missing denominator?3/4=18/?
Answer:
24
Step-by-step explanation:
The equations just need to be equal so you multiply 3 by 6 to get 8 and then 4 by 6 to get 24
3 / 4 = 18 / 24
-2 (3 x - 9 ) + 5x = 10
Answer: × = 8
Step-by-step explanation:
-2 (3 x - 9 ) + 5x = 10
Step 1: Open the bracket
-6× + 18 + 5x = 10
Step 2: Combine like terms
-6× + 5× = 10 -18
-1× = -8
×= -8/-1
×=8
Answer:
x=8
Step-by-step explanation: