Answer:
[tex]a^{2} (a+3) = 20\\OR\\a^3 +3a^2 -20 = 0[/tex]
Step-by-step explanation:
Given that:
There is a square prism which has height equal to 3 yards longer than that of the base of the prism.
Let the base of prism = [tex]a[/tex] units
As per question statement:
Height, [tex]h = (a+3)[/tex] units
Volume of the prism = 20 cubic yards
Now, we have to find a representative function that will represent the volume of the solid.
First of all, let us have a look at the formula for volume of a prism.
[tex]V = B\times h[/tex]
Where, [tex]B[/tex] is the area of base and
[tex]h[/tex] is the height of prism.
And the base is a square, whose area will be represented as:
[tex]B = Side \times Side[/tex]
Now, putting the values in the formula for Volume:
[tex]V = a^2(a+3) = 20\\OR\\a^3+3a - 20 =0[/tex]
How many terms are there in the following expression:
3x + 2y + 8 - x +7y
there are terms in the expression.
Roscoe hit a ball straight up at a speed of 96 ft/s. His bat hit the ball at a height 3 ft above the ground. After how many seconds did the ball hit the ground? (Give your answer to the nearest hundredth of a second.)
Answer:
t = 6.031 seconds
Step-by-step explanation:
Roscoe hit a ball straight up at a speed of 96 ft/s.
His bat hit the ball at a height 3 ft above the ground.
We need to find how many seconds did the ball hit the ground.
Using equation of motion to find height of the ball.
[tex]h=-16t^2+96t+3[/tex]
When it hits the ground.
h = 0
[tex]-16t^2+96t+3=0[/tex]
It is a quadrctic equation where a = -16, b = 96 and c = 3
[tex]t=\dfrac{-96\pm \sqrt{96^2-4(-16)(3)} }{2(-16)}\\\\t=-0.031\ s, 6.031\ s[/tex]
Neglecting negative value.
So, after 6.031 seconds the ball will hit the ground.
Given :
Roscoe hit a ball straight up at a speed of 96 ft/s.
His bat hit the ball at a height 3 ft above the ground.
To Find :
After how many seconds did the ball hit the ground.
Solution :
When the ball reaches the same height from which it is thrown ( i.e. 3 ft ) its displacement will be zero.
So, using equation of motion :
[tex]s = ut + \dfrac{at^2}{2}\\\\96t - \dfrac{10t^2}{2} = 0\\\\5t^2 - 96t = 0\\\\t( 5t - 96 ) = 0\\\\t = \dfrac{96}{5}\\\\t = 19.2 \ s[/tex]
Now, time taken to reach ground from 3 feet of height is :
[tex]s = ut + \dfrac{at^2}{2}\\\\3 = 96t + 5t^2 \\\\5t^2 + 96t - 3 = 0[/tex]
t = 0.03 s
Therefore, time taken is T = 19.2 + 0.03 = 19.23 seconds.
jazmines dog weights 63 pounds. Her vet told her that a healthy weight for her dog would be less than or equal to 47 pounds. Jazmines dog can lose an average of 6 pounds every week. Write the solution to an inequality that describes all posible number of weeks x for which her dog can be at a healthy weight
Answer:
2 weeks and 4 days
Step-by-step explanation:
she is 63 pounds and she needs to get to 47 so 63-47=16 then if she loses 6 pounds every week then 6+6=12 which make 2 weeks cause we used two 6's so now we have a remainder which makes days 12-16=4 so their ya go
2 weeks and 4 days
UDD Question 6 10 pts Solve for x. Round to the nearest tenth (one decimal place). Just type the number, no unit of measurement. G X 240 DI F 48 Next * Previous
Answer:
The answer is;
54.4
Step-by-step explanation:
The given parameter are;
Triangle ΔFGH = Right triangle
The length of segment [tex]\overline {FH}[/tex] = 48
The measure of ∠HFG = 28°
The measurement required = The measure of segment [tex]\overline {FG}[/tex] = x
The measure of ∠FHG = 90° angle opposite hypotenuse side of a right triangle
Therefore, ∠FGH = 180° - ∠HFG - ∠FHG = 180° - 90° - 28° = 62°
∠FGH = 62°
By sine rule, we have;
[tex]\overline {FH}[/tex]/(sin ∠FGH) = [tex]\overline {FG}[/tex]/(sin(∠FHG)
By substituting the known values, we have;
48/(sin 62°) = x/(sin(90°)
sin(90°) = 1, therefore, we have;
x/1 = x = 48/(sin 62°) = 54.4 (by rounding the answer to the nearest tenth)
x = 54.4
A cyclist travels 18 km from home to the park.
She leaves home at 16:00 and arrives at the park at 16:45.
What is her average speed in km/h?
Answer: 24 km/h
Step-by-step explanation:
She traveled 18 km in 45 minutes, this could be simplified to .4 km/min or 24 km/h
Find the new price after the markdown given. Round to the nearest cent if necessary. $5,250 marked down 15%
Marked down 15% means the new price would be 85% of the original price ( 100%-15% - 85%)
Multiply the original price by 85%:
5250 x 0.85 = 4462.50
The new price is $4,462.50
Which word best describes a parallelogram with diagonals that are congruent and perpendicular?
A. rectangle
B. rhombus
C. square
D. trapezoid
Call the actor spam her she blocked me 3053035819 call her name lauren.
Answer:
so, its 2.34 to the square root of 163
Step-by-step explanation:
you need to find the angle congruent to side 'actor'
times that by your credit card and divide by lauren
hope i get brainliest!!
If the measure of two sides of the triangle are 3 feet's and 7 feet's, which is the least possible whole number measure for the third side
Answer:
5 feet
Step-by-step explanation:
By triangle inequality, the sum of lengths of any two sides has to be strictly greater than the length of the third side.
Let x feet be the length of the third side.
We have 3+x>7, x+7>3 and 3+7>x.
Solving these, we get x > 4, x > -4 and x < 10.
The solution is therefore 4 < x < 10 and the smallest whole number which satisfies the inequality is 5.
Therefore the answer is 5 feet.
The mean of 5 numbers is 6.
The numbers are in the ratio 1 : 3 : 3 : 4 : 4.
Find the numbers.
Answer:
2, 6, 6, 8, 8
Step-by-step explanation:
First, we know that the mean is the sum of the number divided by the amount, so if we take the answer we have, 6, and multiply that by the amount of number, 5, then we get 30.
Now we add the numbers in the ratio, so 1 + 3 + 3 + 4 + 4 = 15
15 x 2 = 30
This means we need multiply the numbers in the ratio by 2 to get
2 + 6 + 6 + 8 + 8 = 30
Answer:
2, 6, 6, 8, 8
Step-by-step explanation:
The mean is calculated as
mean = [tex]\frac{sum}{count}[/tex], thus
[tex]\frac{sum}{5}[/tex] = 6 ( multiply both sides by 5 )
sum = 30
sum the parts of the ratio, 1 + 3 + 3 + 4 + 4 = 15 parts
30 ÷ 15 = 2 ← value of 1 part of the ratio, thus
3 parts = 3 × 2 = 6
4 parts = 4 × 2 = 8
Thus the 5 numbers are
2, 6, 6, 8, 8
15 POINTS!
Please help
Thank you
Answer: 1. 2 x^3 - 13 x + 15
2. 2 x^4 - 12 x^3 + 13 x^2 + 15 x
Step-by-step explanation:
For the expression 15-15z to have a negative value, what must be true about the value of z?
Choose the correct answer.
A. The value of z has to be 0.
B. The value of z has to be less than 1.
C. The value of z has to be greater than 1.
D.The value of z has to be negative.
Answer:
C. The value of z has to be greater than 1
Step-by-step explanation:
[tex]15 - 15z < 0 \\ - 15z < - 15 \\ 15z > 15 \\ z > 1[/tex]
What is a closing balance?"
a. The amount of money you have at the end of the statement period
b. The amount of money you have when you close your account
С The amount of money you owe at the end of the statement period
d The amount of money waiting to be transferred out of your account.
From the top of a lighthouse 160 feet high, the angle of depression of a boat out at sea
is 24. Find, to the nearest foot, the distance from the boat to the foot of the
lighthouse. (The foot of the lighthouse is at sea level.)
Answer:
Lighthouse= 160 ft Theta= 24 We want to find the length so we will dotan(24)= 160/x x= 359 feetThe distance from the boat to the foot of the lighthouse is 359.36 ft
What is height and distance?Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction from a certain location.
Given that, From the top of a lighthouse 160 feet high, the angle of depression of a boat out at sea is 24.
The whole situation is representing a right triangle (refer to figure)
Let the distance from the boat to the foot of the lighthouse be x
We know that, angle of depression = angle of elevation
Then, using formula of height and distance,
tan 24° = 160 / x
x = 160 / tan 24°
x = 359.36
Hence, the distance from the boat to the foot of the lighthouse is 359.36 ft
For more references on height and distance, click;
https://brainly.com/question/15939509
#SPJ2
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Answer:
1 mile = 0.5 cm
Step-by-step explanation:
I hope this helps!
Hey again!
The answer to your question is 2 cm = 1 mile
We can solve this by doing 9/4.5, and we get 2. This means that every 2 centimeters in the scale drawing is equal to 1 mile in the actual.
Hope this helps!
The measures of the acute angles of a right triangle are in the ratio 5:7
Answer:
37.5:52.5
Step-by-step explanation:
5u + 7u = 90
12u = 90
u = 7.5
So the angles are (5x7.5) =37.5 degrees
(7x7.5) = 52.5 degrees.
Anthony and Jesus decide that they want to buy a Playstation 5 together. They each have $225. Ray has a Gamestop coupon that gives him 10% off his order, so they decide to go to Gamestop. The price of the Playstation is $499.00. If tax is 7%, will they be able to buy the console? If not, how much money will they have to borrow from their parents?
Answer:
Yes, they will have enough.
Step-by-step explanation:
1. $499.00 + 7% = $533.93
2. $225 x 2 = $550
3. $550 - $533.93 = $16.07 left to spend
Combine like terms to simplify the expression below.
5y - 8x - y + 12y
Answer:
it will 16y-8x and common 8 is so 2y-x
Mia's office recycled a total of 9 pounds of paper over 3 weeks. After 7 weeks, how many pounds of paper will Mia's office have recycled? Choices: 24 21 15 18
Answer:
After 7 weeks, Mia's office will have recycled 21 pounds.
Step-by-step explanation:
With the information provided, you can use a rule of three to find the pounds of paper that Mia's office will have recycled after 7 weeks given that they recycled 9 pounds over 3 weeks.
3 weeks → 9 pounds
7 weeks → x
x=(7*9)/3
x=21
According this, the answer is that after 7 weeks, Mia's office will have recycled 21 pounds.
Evaluate the expression for the given value of x.
−6x + 5 for x= −6
x3−2=10 help plz i need help
20 points
A large amount of peanuts was divided equally into 6 small bags. The total number of peanuts, p, was 342. Which
statements can be used to write an expression and then find the number of peanuts that ended up in each bag?
Check all that apply.
The operation is division.
The operation is multiplication.
The variable is the number of bags.
342 divided by 6 equals 57.
Write the division expression as a fraction,
To evaluate, substitute 342 for the variable.
Each bag will have 57 peanuts.
The constant is 342.
Answer:
I think the answer is A, D, E, F, and G.
Tell me if i'm right or wrong please.
Answer:
adefg
Step-by-step explanation:
Help meeeeee! plsssssssssssssssssssssssssssss
Step-by-step explanation:
Store a must offer 30%
help me so much rn plz plz
Answer:
5(9+x)
Step-by-step explanation:
5 x 9 = 45
then if do 5 times x it would look like 5x
PLS HELP ill give brainliest im really stuck and its DUE SOON
Answer:
B
Step-by-step explanation:
The length of one leg of an isosceles right triangle is 7 units. What is the length of the hypotenuse?
Evaluate the expression for the given value of x.
3x + 4 for x= 5
Parlings vary directly with mots. If 7.5 mots are worth 37.5 parlings, how many parlings will get you 13 mots?
Answer:
65 parlingsStep-by-step explanation:
Use ratios:
7.5 mots / 37.5 parlings = 13 mots / x parlingsx = 13*37.5/7.5x = 65Solve:
1/3(2x-6/5)=4/9(x+1/3)
[tex] \frac{1}{3} .( \frac{2x - 6}{5} ) = \frac{4}{9} .( \frac{x + 1}{3} )[/tex]
[tex] \frac{2x - 6}{15} = \frac{4x + 4}{27} [/tex]
[tex]54x - 162 = 60x + 60[/tex]
[tex] - 222 = 6x[/tex]
[tex]x = - 37[/tex]
I guess it's right.We learnt this way in Turkey.
{(2,5), (-3, 4), (-4,-4), (x,-5)}
What value of x will make the relation a function?
-3
-4
5
2
Answer:5
Step-by-step explanation:
because idrk my teacher just answered this question and i thought i would share :)
