7. A rectangular prism measures 7 1/2 cm by 12 cm by 15 1/2 cm. a. Calculate the number of cubes with edge length cm that fit in this prism. b. What is the volume of the prism in cm3? Show your reasoning. If you are stuck, think about how many cubes with -cm edge lengths fit into .
Answer:
a.The number of cubes with edge length 1/2 cm that fit in this prism= 2520
b. Volume of the prism= 315 cm³
Step-by-step explanation:
Volume of the rectangular prism = length *width * height
= 7 1/2 * 12 * 15 1/2
= 7 * 6* 15 1/2
= 7*3*15
= 315 cm³
Volume of the cube = length *width * height
= 1/2 *1/2 *1/2
= 1/8 cm³
Now number of cubes that would fit in the rectangular prism is given by
= Volume of the prism/ Volume of the cubes
= 315/1/8
= 2520
The number of cubes with edge length cm that fit in this prism= 2520
Find all the zeroes of polynomial 2x4
– 9x3 + 5x2 + 3x – 1 ,if two of its zeroes are 2 + √3 & 2 - √3
9514 1404 393
Answer:
x ∈ {-1/2, 1, 2-√3, 2+√3}
Step-by-step explanation:
The given zeros mean that one of the quadratic factors of the given polynomial is ...
(x -2)^ -3 = x^2 -4x +1
When that is factored out (see first attachment), the remaining quadratic is ...
2x^2 -x -1
This can be factored as ...
= (2x +1)(x -1)
which has roots that make these factors zero: x = -1/2, x = 1.
So, all of the zeros of the given polynomial are ...
-1/2, 1, 2-√3, 2+√3 . . . all zeros
__
A graphing calculator can often point to the zeros of the function quite nicely.
_____
Additional comments
When p is a zero of a polynomial, (x-p) is a factor of it. The given zeros mean that factors are (x-2-√3) and (x-2+√3). The product of these factors is the difference of the squares (x-2)^2 and (√3)^2, so is (x -2)^2 -3.
Using the pattern for the square of a binomial, we see this is ...
(x-2)^2 = x^2 -2·2x +2^2 = x^2 -4x +4
The product of the given factor is then 3 subtracted from this square. The given zeros mean there is a quadratic factor of ...
(x-2-√3)(x-2+√3) = (x-2)^2 -3 = x^2 -4x +4 -3 = x^2 -4x +1
Shana plans to borrow $1,300 to buy a guitar. One bank is offering a simple interest rate of 5% per year on borrowed amounts. Another bank is offering a simple interest rate of 4%. Shana plans to repay the loan in 3 years. In dollars, how much can she save by borrowing from the bank with the lower interest rate? Record your answer in the box.
Answer:
5% times 3=15%
4% times 3=12%
15-12=3
1300 times 0.03= $39
39 dollars.
what is the probability that you will fail a test (pass or fail), draw a red ace, and then roll a 6?
Answer:
0.7890176%
Step-by-step explanation:
First, there is a 64% chance of failing a test.
Then there are 54 cards in a deck. There are two colors, red and black. There are two red aces and two black aces. You have a 50% chance that the card is red. Then there are 27 cards of each color. Since there are 2 aces in those 27, there is a 2/27 or ~7.4%.
Lastly there are 6 sides on a die. Each side has the same chance of landing. So this gets you 16.66%
Now we need to multiply each chance of something happening by one another
64% × 7.4% = 0.04736%
4.736% × 16.66% = 0.7890176%
So there is a 0.7890176% of all of these happening
The probability that you will fail a test, draw a red ace, and then roll a 6 is 0.7890176%
We have given that,
First, there is a 64% chance of failing a test.
We have to determine the probability
What is the probability?
Probability is an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
Then there are 54 cards in a deck. There are two colors, red and black. There are two red aces and two black aces.
You have a 50% chance that the card is red. Then there are 27 cards of each color. Since there are 2 aces in those 27, there is a 2/27 or ~7.4%.
Lastly there are 6 sides on a die. Each side has the same chance of landing. So this gets you 16.66%
Now we need to multiply each chance of something happening by one another
64% × 7.4% = 0.04736%
4.736% × 16.66% = 0.7890176%
So there is a 0.7890176% of all of these happening
Therefore the probability that you will fail a test, draw a red ace, and then roll a 6 is 0.7890176%.
To learn more about the probability visit:
https://brainly.com/question/25870256
#SPJ2
Find the area of the trapezoid
A. 168 in^2
B. 94.5 ft^2
C. 72 ft^2
D. 84 ft^2
Answer:
D. 84 ft^2
Step-by-step explanation:
Formula for area of a trapezoid:
[tex]A=\frac{a+b}{2} h[/tex]
where a and b = bases and h = height
The trapezoid shown has the following dimensions
base 1 = 9ft
base 2 = 12ft
height = 8ft
Using the following information we plug in the values into the formula
[tex]A=\frac{9+12}{2} \\9+12=21\\\frac{21}{2} =10.5\\10.5*8=84[/tex]
Hence, the area of the trapezoid is 84ft² and your answer is D
What is the difference between the two rates of
change?
Function A
Function B.
7
14
21
Y
3
10
17
Answer: ben dover
Step-by-step explanation:
touch your toes ill show you where the wild goose goes
The base area of cube is 64 square cm. Find its volume.
Answer:
a cube has 8 sized
Step-by-step explanation:
64 ×8 equal 512.
Which of the following represents the factorization of the trinomial below?
x² - 8x - 48
A. (X-6)(x-8)
B. (X+6) (x-8)
C. (x-4)(x-12)
D. (x+4)(x-12)
-7 2/3 + (-5 1/2) + 8 3/4 = ????
Answer:
-52/12 or -4 5/12
Step-by-step explanation:
hope this help there 2 ways
Answer:
-53/12 same as -4 4/12 same as -4,416
Step-by-step explanation:
convierte el numero mixto a una fracción impropia
-23/3 + (-5 1/2) + 8 3/4
cuando se encuentren un + en frente de una expresión dentro de un paréntesis, la expresión se mantiene igual
-23/3 - 5 1/2 + 8 3/4
convierte el numero mixto a una fracción impropia
-23/3 - 5 1/2 + 35/4
convierte el numero mixto a una fracción impropia
-23/3 - 11/2 + 35/4
calcula la suma o resta
-53/12
Jameson puts $4,000 in graduation money in an account for 10 years. The interest rate is 4.2%. If he withdraws all of the money after 10 years, how much
does he take out?
Answer:
2,320
Step-by-step explanation:
4.2% gets taken every year and there is 10 year,so 4.2% s uqual to 0.042,so just mutiply 4000 by 0.042 which is 168,then times 168 by 10 which brings you to 1680 and 4000 subtracyed by 1680,which equals 2,320
A jogger is running around a 3/4 mile track and is 2/3 of the way around the track. How far has the jogger traveled
Answer:
im literally doing the same exact thing right now
Step-by-step explanation:
Which equation represents a line which is parallel to the line y=7/2x-4
Answer:
y=-(7)/(2)x-5
Step-by-step explanation:
to make a parallel equation, you must make an equation that has the same slope, but different b intercepts. so, the equation must have 7/2x, and the b part can be any number.
Answer:
y = 7/2x + 2
Step-by-step explanation:
to make a parallel equation, you must make an equation that has the same slope, but different b intercepts. so, the equation must have 7/2x, and the b part can be any number.
What is h?
Im so confused on this question
Answer:
i think h stands for height. I dont see it standing for any thing else
Step-by-step explanation:
Solve the system of equations:
y = x + 2
y = x2 + 5x + 6
A.
(0, 2) and (2, 4)
B.
(–2, 0) and (–3, 0)
C.
(–2, 0)
D.
(0, 2)
Answer: C
Step-by-step explanation:
Since both equations are set equal to y, it follows that
[tex]x+2=x^2 + 5x+6\\\\x^2 +4x+4=0\\ \\ \\(x+2)^2 = 0\\\\x=-2\\\\\implies y=-2+2=0[/tex]
So, the solution is (-2, 0).
3) Using the picture, find the measure of side J.
A) 28√3
B)28
C)56
4) Using the same picture, find the measure of side K.
A) 28√3
B)28
C)56
Answer:
solution is in attachment
hope it helps
Which equation shows the quadratic formula used correctly to solve 7x^2 = 9 + x for x?
Answer:
Step-by-step explanation:
We must rewrite 7x^2 = 9 + x in standard form first: 7x^2 - x - 9 = 0.
The coefficients are 7, -1 and -9, and so the discriminant b^2 - 4ac is
(1)^2 - 4(7)(-9) = 253.
The roots are:
-(-1) ± √253 1 ± √253
x = --------------------- = --------------------
2(7) 14
The lengths of the sides of the triangle are 3, 8, and 10. Is the triangle a right triangle, acute triangle, or an obtuse triangle?
Answer:
Obtuse
Step-by-step explanation:
You have to make sure it is a triangle by adding the smallest and the medium sides, if the result is greater than the bigger side then it is a triangle. you then use the Pythagorean theorem to check if the triangle is a right triangle, acute, or obtuse. If [tex]c^{2}[/tex] = [tex]a^{2} +b^{2}[/tex] then it is a right triangle. If [tex]c^{2} >a^{2} + b^{2}[/tex] then it is an obtuse triangle. if [tex]c^{2} < a^{2} +b^{2}[/tex] then it is an acute triangle. [tex]10^{2}[/tex] _ [tex]3^{2} + 8^{2}[/tex] 9+64_100 70_100 70<100in this case [tex]c^{2}[/tex] is greater than [tex]a^{2} +b^{2}[/tex] therefore, is it an obtuse triangle.
I just need help with the graphing!
Answer:
solution is in attachment
hope it helps
In a circle, an angle measuring 2π radians intercepts an arc of length 14π. Find the radius of the circle in simplest form.
Answer:
7 radians
Step-by-step explanation:
In a circle, an angle measuring 2π radians intercepts an arc of length 14π. Find the radius of the circle in simplest form.
Since our Angle in in radians
The formula for Arc length = S = rθ
S = 14π
θ = central angle = 2π radians
Hence
r = S/θ
r = 14π/2π radians
r = 7 radians
Radius = 7 radians
HELP ME NOWWWWWW. thanks.
Answer:
LETTER C. PO 40 ang sagot
I don’t know how to answer this
Answer:
EII
Step-by-step explanation:
43,5% of this skeleton's body is his mermaid tail.
Write the percent as a decimal.
Answer:
0.435
Step-by-step explanation:
43.5*0.01=0.435
Solve the inequality for t.
11 ≤ t + 4
Simplify your answer as much as possible.
Answer:
t≥7
Step-by-step explanation:
11≤t+4
4 moves to the other side hence its sign changes
11-4≤t
7≤t
they change sides
t≥7
the sign was facing t so this does not change
Answer:
Step-by-step explanation:
Here are some steps to help you
Step 1
11 ≤ t + 4 We are gonna simplify
Step 2
11 ≤ t + 4 simplify
t+4≥11
Step 3
t+4≥11 Subtract 4 from the sides
t≥7
So therefore, your answer will be t≥7
Hope this helps
Please help me with this math question.
Answer:
275 m^3
Step-by-step explanation:
The volume of a triangular pyramid is V=(1/3)Ah, where A is the area of the triangular base and h is the height.
First, let's find A, the area of the base. The area of a triangle is bh/2, where b is the base and h is the height.
In this question, 5 is the base and 15 is the height, so A=5*15/2=75/2.
Now we know A is 75/2, so let's go back to the formula for the volume of a pyramid. We are given h is 22, so
V=(1/3)(75/2)*22=275
Please help, due soon. Use the information provided to write the standard form equation of each circle
Answer:
D
Step-by-step explanation:
The equation of a circle centred at the origin is
x² + y² = r² ( where r is the radius ) , then
x² + y² = ([tex]\sqrt{249}[/tex] )² , that is
x² + y² = 249 → D
Answer 15 points
( don’t answer if you don’t the answer )
Answer:
V=1/3hπr². Basically, 1/3 x height x 3.14 (pi) x radius squared.
Step-by-step explanation:
The formula of figure 2 would be 1/3 x 15 x 3.14 x 8 squared. The volume of figure 2 would be 1005.30965
the formula for figure 3 would be 1/3 x 15 x 3.14 x 4 squared. The volume of it would be 251.32741
hope this helps! (Also please make me brainliest if this helps u :) )
A business shipped 106 packages one day. Customers are charged 4.50 for each standard delivery and 7.50 for each express delivery
The question is incomplete:
A business shipped 106 packages one day. Customers are charged 4.50 for each standard delivery and 7.50 for each express delivery. Total shipping charges for the day were $600.00. How many of each kind of package were shipped?
Answer:
The business shipped 65 standard delivery packages and 41 express delivery packages.
Step-by-step explanation:
Since the business shipped 106 packages one day you can say that:
x+y=106, where:
x is the number of standard delivery packages
y is the number of express delivery packages
Also, you can say that the result of multiplying the price per each type of package for its amount and adding those would be equal to the total shipping charges for the day, which is:
4.50x+7.50y=600
So, you have the following equations:
x+y=106 (1)
4.50x+7.50y=600 (2)
Now, you can solve for x in (1):
x=106-y (3)
Then, you can replace (3) in (2) and solve for y:
4.50(106-y)+7.50y=600
477-4.50y+7.50y=600
3y=600-477
3y=123
y=123/3
y=41
Finally, you can replace the value of y in (3) to be able to find the value of x:
x=106-41
x=65
According to this, the answer is that the business shipped 65 standard delivery packages and 41 express delivery packages.
HELP! I’LL GIVE BRAINLIEST ANSWER
Answer:
d. 20°
Step-by-step explanation:
First, we need to solve for m<Q
m<Q+m<R+m<S=180°
where m<R=90° and m<S=70°
m<Q+90°+70°=180°
m<Q=20°
Since m<Q=m<M
Then, m<M=20°
Determine the volume of the rectangular prism.
Answer:
132in
Step-by-step explanation:
Answer:
hi
Step-by-step explanation:
[tex]v = 4 \times 6 \times 5 \frac{1}{2} \\ v = 24 \times \frac{11}{2} = 132[/tex]
hope it helps
have a nice day
a line with a slope of 1 passes through the point (5,10). what is the equation in this slope-intercept form?
Answer:
y=x+5
Step-by-step explanation:
So first you need to plug everything into the point-slope formula which is
y-y1=m(x-x1)
m being the slope and y1 and x1 being the point (5,10)
So once you plug it in it should look like this: y-10=1(x-5)
Now you solve it
First you need to distribute 1 in 1(x-5) which is (x-5)
Now you have y-10=x-5
Then you add 10 to both sides which is y=x+5
Your answer is y=x+5