Answer:
The volume of the pyramid is 867 inch^3
Step-by-step explanation:
Here in this question, we are interested in calculating the volume of a square based pyramid.
Mathematically, we can use the formula below to calculate the volume V of a square based pyramid.
V = a^2h/3
where a represents the length of the side of the square and h is the height of the pyramid
From the question, the length of the side of the square is 17 in while the height is 9 in
Plugging these values, we have ;
V = (17^2 * 9)/3 = 17^2 * 3 = 867 cubic inch
Special right triangles
Answer: please find the attached files
Step-by-step explanation:
A unit circle formula and special triangle of 45, 30 and 60 degrees can be used to solve the problem.
Please find the attached files for the solution
A customer owes a balance of $400 on their lease. They have a $75 payment due each month. What will be their remaining balance after their next 2 monthly payments are made?
Answer:
Step-by-step explanation:
2(75)=150 that's the amount due in total for two months so
400-150= 250 they will owe $250 after two months payment
2e - 3f = 4
2e - 5f = 8
solve this linear equation by the elimination method
please show your working ✨✨THANK YOU
Answer:
The value of e is -1 and f is -2.
Step-by-step explanation:
The steps are :
[tex]2e - 3f = 4 - - - (1)[/tex]
[tex]2e - 5f = 8 - - - (2)[/tex]
[tex]2e - 3f - 2e - ( - 5f) = 4 - 8[/tex]
[tex]2f = - 4[/tex]
[tex]f = - 4 \div 2[/tex]
[tex]f = - 2[/tex]
[tex]substitute \: f = - 2 \: into \: (1)[/tex]
[tex]2e - 3( - 2) = 4[/tex]
[tex]2e + 6 = 4[/tex]
[tex]2e = 4 - 6[/tex]
[tex]2e = - 2[/tex]
[tex]e = - 2 \div 2[/tex]
[tex]e = - 1[/tex]
To solve this system of equations by addition, our first goal is to cancel
out one of the variables by adding the two equations together.
However, before we add, we need to cancel out a variable.
I would choose to cancel out the e's.
To do this, we need a 2e and a -2e and
here we have a 2e in both equations.
If we multiply the second equation by -1 however,
that will give us the -2e we are looking for.
So we have (-1)(2e - 3f) = (4)(-1).
So rewriting both equations, our first equation stays the same
but our second equation becomes -2e + 3f = -4.
Notice that every term in the second
equation has been multiplied by -1.
2e - 3f = 4
-2e + 5f = -8
Now when we add the equations together,
the e's cancel and we have 2f = -4 so f = -2.
To find e, plug -2 back in for f in the
first equation to get 2e - 3(-2) = 4.
Solving from here, e = -1.
Note that e comes before f in our final answer, (-1, -2).
To determine which variable should go first
in your answer, use alphabetical order.
Find the difference of functions s and r shown
below.
r(x) = -x2 + 3x
s(x) = 2x + 1
(s - r)(x) =
Answer:
[tex]\displaystyle (s-r)(x) = x^2 - x + 1[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]\displaystyle r(x) = -x^2 + 3x \text{ and } s(x) = 2x + 1[/tex]
And we want to find:
[tex]\displaystyle (s-r)(x)[/tex]
This is equivalent to:
[tex]\displaystyle (s-r)(x) = s(x) - r(x)[/tex]
Substitute and simplify:
[tex]\displaystyle \begin{aligned}(s-r)(x) & = s(x) - r(x) \\ \\ & = (2x+1)-(-x^2+3x) \\ \\ & = (2x+1)+(x^2-3x) \\ \\ & = x^2 +(2x-3x) + 1 \\ \\ & = x^2 - x + 1 \end{aligned}[/tex]
In conclusion:
[tex]\displaystyle (s-r)(x) = x^2 - x + 1[/tex]
When solving (x + 35) = −7, what is the correct sequence of operations?
Answer:
x= -42
Step-by-step explanation:
put the liketerms together
x+35= -7
x=-35-7
note*the operation sign changes after crossing the equal sign
x= -42
Juan works as a tutor for $12 an hour and as a waiter for $7 an hour. This month, he worked a combined total of 110 hours at his two jobs.
Let t be the number of hours Juan worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month.
Answer:
12t+7w=D
t+w=110
Step-by-step explanation:
12t= $12 made every tutor hour
7w= $7 made every waiter hour
D= total dollars made
t+w=110 is the tutor hour and the waiter hour adding together
Answer:
12t + 7y = x
or
5t + 770 = x
Step-by-step explanation:
12t + 7y = x
t = number of hours he worked as a tutor
y = number of hours he worked as a waiter
x = the total amount of money he earned
t + y = 110
=> y = 110 - t
=> 12t + 7(110 - t) = x
=> 12t + 770 - 7t = x
=> 5t + 770 = x
Before 8 A.M., there were 64 trucks and 24 cars in a parking lot. Between 8 A.M. and 9 A.M., more cars entered the parking lot and no trucks entered or exited the lot. At 9:00 A.M., the number of trucks represented 1/5 of the parking lot's vehicles. How many cars entered between 8 A.M. and 9 A.M? A. 56 B. 112 C. 148 D. 192 PLZ EXPLAIN
Answer:
232 cars
Step-by-step explanation:
Let's say the number of cars that entered is c.
At 9:00 am, there are a total of 24 + c cars and 64 trucks. We know that this value of 64 represents 1/5 of the total number of vehicles. The total number of vehicles is (24 + c) + 64 = 88 + c. So, we have:
64/(88 + c) = 1/5
Cross-multiply:
88 + c = 64 * 5 = 320
c = 320 - 88 = 232
Thus, the answer is 232 cars.
Note: as 232 doesn't show up in the answer choices, it's possible that the problem was copied correctly.
~ an aesthetics lover
Answer:
232 cars entered between 8 and 9
Step-by-step explanation:
at 9 am there are 64 x 5 vehicles total = 320
320 - 64 - 24 = 232
All the edges of a cube have the same length. Tony claims that the formula SA = 6s, where s is the length of
each side of the cube, can be used to calculate the surface area of a cube.
a. Draw the net of a cube to determine if Tony's formula is correct.
b. Why does this formula work for cubes?
Frances believes this formula can be applied to calculate the surface area of any rectangular prism. Is
she correct? Why or why not?
d. Using the dimensions of Length, Width and Height, create a formula that could be used to calculate the
surface area of any rectangular prism, and prove your formula by calculating the surface area of a
rectangular prism with dimensions L = 5m, W = 6m and H=8m.
Answer:
Here's what I get
Step-by-step explanation:
a. Net of a cube
Fig. 1 is the net of a cube
b. Does the formula work?
Tony's formula works if you ignore dimensions.
There are six squares in the net of a cube.
If each side has a unit length s, the total area of the cube is 6s.
c. Will the formula work for any rectangular prism?
No, because a rectangular prism has sides of three different lengths — l, w, and h — as in Fig. 2.
d. Area of a rectangular prism
A rectangular prism has six faces.
A top (T) and a bottom (b) — A = 2×l×w
A left (L) and a right (R) — A = 2×l×h
A front (F) and a back (B) — A = 2×w×h
Total area = 2lw + 2lh + 2wh
If l = 5 m, w = 6 m and h = 8 m,
[tex]\begin{array}{rl}A &=& \text{2$\times$ 5 m $\times$ 6 m + 2$\times$ 5 m $\times$ 8 m + 2 $\times$ 6 m $\times$ 8 m}\\&=& \text{60 m}^{2} + \text{80 m}^{2} + \text{96 m}^{2}\\&=& \textbf{236 m}^{2}\\\end{array}[/tex]
A restaurant wanted to track how much of a quart of soda customers drank at a meal. The line plot displays the data collected by the restaurant. How much more soda did the customers who drank 3/4 of a quart drink than the customers who drank 1/4 of a quart?
Answer:
C
Step-by-step explanation:
13/4 simplified---->3and 1/4
What are the zeros of the polynomial function? f(x)=x^3+x^2−9x−9
Answer:
1: x = -1
2: x = 3
3: x = -3
Step-by-step explanation:
f(x)=x^3+x^2−9x−9
f(x)=x^2(x+1) −9x−9
f(x) = x^2(x+1) - 9(x+1)
f(x)= (x+1)(x^2-9)
f(x) =(x+1)(x-3)(x+3)
Answer:
[tex]\boxed{x=-1, \ x=-3, \ x=3}[/tex]
Step-by-step explanation:
The zeros of a function are the values of x when f(x) = 0.
[tex]x^3 +x^2-9x-9=0[/tex]
Factor left side of the equation.
[tex]x^2(x +1)-9(x+1)=0[/tex]
Take (x+1) common.
[tex](x^2-9)(x+1)=0[/tex]
Set factors equal to 0.
First possibility:
[tex]x^2 -9=0[/tex]
[tex]x^2 =9[/tex]
[tex]x=\± \sqrt{9}[/tex]
[tex]x=\± 3[/tex]
[tex]x=-3 \ \mathrm{or} \ x=3[/tex]
Second possibility:
[tex]x+1=0[/tex]
[tex]x=-1[/tex]
Please answer this question now
Answer:
V = 60 m³
Step-by-step explanation:
Volume of Triangular Pyramid: V = 1/3bh
Area of Triangle: A = 1/2bh
b = area of bottom triangle (base)
h = height of triangular pyramid
Step 1: Find area of base triangle
A = 1/2(8)(5)
A = 4(5)
A = 20
Step 2: Plug in known variables into volume formula
V = 1/3(20)(9)
V = 1/3(180)
V = 60
expand (x-4)^4 with binomial theorem or pascal's triangle
Answer:
(x-4)^4=x⁴+4x³(-4)¹+6x²(-4)²+4x¹(-4)³+(-4)⁴
=x⁴-16x³+96x²-256x+256
Match each expression with its greatest common factor. 4a + 8 2a2 + 8a 12a2 − 8a 4 − 6a Greatest Common Factor Expression 4 : 2 : 2a : 4a :
Answer:
see explanation
Step-by-step explanation:
4a + 8 4
2a² + 8a 2a
12a² - 8a 4a
4 - 6a 2
Match each expression with its greatest common factor as follows;
4a + 8 4
2a² + 8a 2a
12a² - 8a 4a
4 - 6a 2
What is the greatest common factor?The largest number that is found in the common factors is called the greatest common factor.
The given expression are;
4a + 8
2a² + 8a
12a² - 8a
4 - 6a
The greatest common factor of the expression are as follows;
4a + 8 = 4(a+2) = common factor = 4
2a² + 8a = 2a(a+4a) = common factor = 2a
12a² - 8a = 4a(3a-2) = common factor = 4a
4 - 6a = 2(2-3a) = common factor = 2
Learn more about the greatest common factor here;
https://brainly.com/question/15333869
#SPJ2
What is the volume of the composite figure?
Answers:
192ft^3
96ft^3
76ft^3
152ft^3
Answer:
68 ft³
Step-by-step explanation:
Take the above figure to be 2 rectangular prism. A smaller prism on top, and a bigger one under.
Volume of the smaller rectangular prism on top:
[tex] Volume = whl [/tex]
Where,
w = 2 ft
h = 4 ft
l = 4 ft
[tex] Volume = 2*4*4 = 32 ft^3 [/tex]
Volume of bigger Rectangle prism under:
w = 2 ft
h = 3 ft
l = 6 ft
[tex] Volume = 2*3*6 = 36 ft^3 [/tex]
Volume of composite figure = 32 + 36 = 68 ft³
Answer:
Step-by-step explanation:
The correct answer is 76
Big prism: 4x8x2=64
What's Left: (6-4)x2x3=12
64+12=76
The length of the shadow of a pole on level ground increases by 90m when the angle of elevation of the sun changes from 58° to 36°.Calcule the height of the pole
===================================================
Work Shown:
x = starting length of the shadow
y = height of the pole
tan(angle) = opposite/adjacent
tan(58) = y/x
1.6003345 = y/x
1.6003345x = y
x = y/1.6003345
x = (1/1.6003345)y
x = 0.62486936y
-------------------------
When the angle changes, the adjacent side gets 90 meters longer
tan(angle) = opposite/adjacent
tan(36) = y/(x+90)
0.72654253 = y/(0.62486936y+90)
0.72654253(0.62486936y+90) = y
0.453994166y + 65.3888277 = y
65.3888277 = y-0.453994166y
65.3888277 = 0.546005834y
0.546005834y = 65.3888277
y = 65.3888277/0.546005834
y = 119.758478075162
y = 119.76
The height of the pole is about 119.76 meters.
find the value of 3m-2, if m =7.
Answer:
37-2=35 or 3^7-2=2185
Christine's gross monthly salary at her job
is $5,250. She has the following
deductions from her paycheck.
What is Christine's net take-home pay per
month?
Answer:
$2587.87 per month
Step-by-step explanation:
The listed deductions are ...
25% withheld for federal income tax9.3% withheld for California state income tax6.2% withheld for Social Security tax1.45% withheld for Medicare Tax0.9% withheld for SDI- Disability Insurance5% goes into her retirement 401K account$150 goes to health insurance/ dental for her familyThe percentages have a total of ...
25 +9.3 +6.2 +1.45 +0.9 +5 = 47.85 . . . percent
So, Christine's take-home pay is ...
$5250(1 -0.4785) -150 = $2587.87 . . . per month
Can you please help me on add and subtract fractions level 1 9/8-11/8
Answer:
7/8
Step-by-step explanation:
1. Make 1 9/8 into an improper fraction
1 = 8/8
8/8 + 9/8 = 17/8
2. Subtract
17/8 - 11/8 = 7/8
what is the value of x ?
Answer:
65dg.
Step-by-step explanation:
Triangles are 180dg.
So 68dg + 47dg = 115dg.
-180dg - 115dg = 65dg.
So the missing length is 65 degrees.
Answer: 65
Step-by-step explanation:
Add both of the numbers on there. Then do 180- that number.
68+47=115
180+115=65
This is because in a triangle all the angles together equal 180.
Please help! Explanation please!
Answer:
11 meters.
Step-by-step explanation:
The important thing to note here is that the backyard is a square. Since it's a square, all of its sides all equivalent in length. Thus, let's find the length of the sides. To do this, we use the area formula.
The formula for the area of a square is:
[tex]A=n^2[/tex]
Where n is a side. Since we know the area already, we can find n. Find n:
[tex]121=n^2\\n=11[/tex]
Since every side in a square are equivalent, all sides are 11 meters in length.
Therefore, each section of the fence should be 11 meters long.
A cube whose edge is 20 cm 1 point
long, has circles on each of its
faces painted black. What is the
total area of the unpainted
surface of the cube if the
circles are of the largest
possible areas?(a) 90.72 cm2 (b)
256.72 cm² (c) 330.3 cm² (d)
514.28 cm?
Answer:
Unpainted surface area = 514.28 cm²
Step-by-step explanation:
Given:
Side of cube = 20 Cm
Radius of circle = 20 / 2 = 10 Cm
Find:
Unpainted surface area
Computation:
Unpainted surface area = Surface area of cube - 6(Area of circle)
Unpainted surface area = 6a² - 6[πr²]
Unpainted surface area = 6[a² - πr²]
Unpainted surface area = 6[20² - π10²]
Unpainted surface area = 6[400 - 314.285714]
Unpainted surface area = 514.28 cm²
Chantal is driving on a highway at a steady speed. She drives 55 miles every hour. Let d be the total distance in miles and let h be the number of hours.
Write an equation that represents the situation. I'll give out the brainliest if you get it right.
Answer:
[tex] d = 55h [/tex]
Step-by-step explanation:
We are given that Chantal drives at a constant speed of 55 miles per hour.
If, d represents the total distance in miles, and
h represents number of hours, the following equation can be used to express the given situation:
[tex] d = 55h [/tex]
For every hour, a distance of 55 miles is covered.
Thus, if h = 1, [tex] d = 55(1) = 55 miles [/tex]
If h = 2, [tex] d = 55(2) = 110 miles [/tex].
Therefore, [tex] d = 55h [/tex] , is an ideal equation that represents the situation given in the question above.
The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number?
Answer:
The original number could be 85.
Step-by-step explanation:
Let the 2 digits be x and y.
Let the number be xy then, assuming that x is the larger digit:
x - y = 3.
x = y + 3
Also
10y + x + 10x + y = 143
Substituting for x:
10y + y + 3 + 10(y + 3) + y = 143
22y + 33 = 143
22y = 110
y = 5.
So x = y + 3 = 8.
Answer:
Let the unit digit be x and tens digit be x + 3Therefore, the original number = 10(x + 3) + xOn interchanging, the number formed = 10x + x + 3❍ According to Question now,➥ 10(x + 3) + x + 10x + x + 3 = 143
➥ 10x + 30 + 12x + 3 = 143
➥ 22x + 33 = 143
➥ 22x = 143 - 33
➥ 22x = 110
➥ x = 110/22
➥ x = 5
__________________...Therefore,The unit digit number = x = 5
The tens digit number = x + 3 = 5 + 3 = 8
__________________...The original number = 10(x + 3) + x
The original number = 10(5 + 3) + 5
The original number = 50 + 30 + 5
The original number = 85
Hence,the original number is 85.
You own a farm and have several fields in which your livestock grazes. You need to order barbed-wire fencing for a small pasture that has a length of 5 yards and a width of 3 yards. The barbed wire must be long enough to be placed on all four sides of the outside pasture. How many yards of barbed-wire should you order?
Answer:
16 yards of barbed wire
Step-by-step explanation:
Length=5 yards
Width=3 yards
Perimeter of the pasture=2(length + width)
=2(5 yards +3 yards)
=2(8 yards)
=16 yards
You should order 16 yards of barbed wire for fencing the pasture
Determine the minimum rotation (in degrees) which will carry the following figures onto itself (where all sides and verticles will match up). Assume this is a regular polygon. Round to the nearest tenth if necessary.
Answer:
60°
Step-by-step explanation:
A full rotation is 360°. The figure has six sides.
1. Divide
360 ÷ 6 = 60
Each angle of the polygon is 60°. Therefore, the polygon must be rotated at least 60° for the figure to match all sides and vertices.
The focus of a parabola is (3,-7) and the directrix is y = -4.
What is an equation of the parabola?
Answer:
(a) (x -3)^2 = -6(y +5.5)
Step-by-step explanation:
The equation of a parabola can be written as ...
(x -h)^2 = 4p(y -k)
where (h, k) is the vertex, and p is the distance from the focus to the vertex.
The vertex is half-way between the focus and directrix, so is ...
(h, k) = (1/2)((3, -7) +(3, -4)) = (3, -5.5)
The focus is at y=-7, and the vertex is at y=-5.5, so the distance between them is ...
-7 -(-5.5) = -1.5
Then the equation for the parabola is ...
(x -3)^2 = 4(-1.5)(y -(-5.5))
(x -3)^2 = -6(y +5.5) . . . . matches the first choice
Solve. 4x−y−2z=−8 −2x+4z=−4 x+2y=6 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. x= y= z=
Answer:
(-2, 4, 2)
Where x = -2, y = 4, and z = 2.
Step-by-step explanation:
We are given the system of three equations:
[tex]\displaystyle \left\{ \begin{array}{l} 4x -y -2z = -8 \\ -2x + 4z = -4 \\ x + 2y = 6 \end{array}[/tex]
And we want to find the value of each variable.
Note that both the second and third equations have an x.
Therefore, we can isolate the variables for the second and third equation and then substitute them into the first equation to make the first equation all one variable.
Solve the second equation for z:
[tex]\displaystyle \begin{aligned} -2x+4z&=-4 \\ x - 2 &= 2z \\ z&= \frac{x-2}{2}\end{aligned}[/tex]
Likewise, solve the third equation for y:
[tex]\displaystyle \begin{aligned} x+2y &= 6\\ 2y &= 6-x \\ y &= \frac{6-x}{2} \end{aligned}[/tex]
Substitute the above equations into the first:
[tex]\displaystyle 4x - \left(\frac{6-x}{2}\right) - 2\left(\frac{x-2}{2}\right)=-8[/tex]
And solve for x:
[tex]\displaystyle \begin{aligned} 4x+\left(\frac{x-6}{2}\right)+(2-x) &= -8 \\ \\ 8x +(x-6) +(4-2x) &= -16 \\ \\ 7x-2 &= -16 \\ \\ 7x &= -14 \\ \\ x &= -2\end{aligned}[/tex]
Hence, x = -2.
Find z and y using their respective equations:
Second equation:
[tex]\displaystyle \begin{aligned} z&=\frac{x-2}{2} \\ &= \frac{(-2)-2}{2} \\ &= \frac{-4}{2} \\ &= -2\end{aligned}[/tex]
Third equation:
[tex]\displaystyle \begin{aligned} y &= \frac{6-x}{2}\\ &= \frac{6-(-2)}{2}\\ &= \frac{8}{2}\\ &=4\end{aligned}[/tex]
In conclusion, the solution is (-2, 4, -2)
Answer:
x = -2
y =4
z=-2
Step-by-step explanation:
4x−y−2z=−8
−2x+4z=−4
x+2y=6
Solve the second equation for x
x = 6 -2y
Substitute into the first two equations
4x−y−2z=−8
4(6-2y) -y -2 = 8
24 -8y-y -2z = 8
-9y -2z = -32
−2(6-2y)+4z=−4
-12 +4y +4z = -4
4y+4z = 8
Divide by 4
y+z = 2
z =2-y
Substitute this into -9y -2z = -32
-9y -2(2-y) = -32
-9y -4 +2y = -32
-7y -4 = -32
-7y =-28
y =4
Now find z
z = 2-y
z = 2-4
z = -2
Now find x
x = 6 -2y
x = 6 -2(4)
x =6-8
x = -2
Given that T{X: 2<x ≤ 9} where x is an integer. what is n(T)
Answer:
n(T) = 7Step-by-step explanation:
Given the set T{X: 2<x ≤ 9} where x is an integer, the element of the set T will be {3, 4, 5, 6, 7, 8, 9}. note that from the inequality set 2<x ≤ 9, x is not equal to 2 but greater than 2. The inequality can be divided into two as shown;
If 2<x ≤ 9 then 2<x and x≤9
If 2<x, this means x>2 but not equal to 2. This is the reason why 2 is not contained in the set T.
Similarly if x≤9, this shows that x can not be greater than 9 but less than or equal to 9.
Since the set T = {3, 4, 5, 6, 7, 8, 9}, we are to find n(T). n(T) means cardinality of the set T and cardinality of a set is defined as the total number of element in a set.
Hence n()n(T) = 7 (since there are 7 elements in the set T)
Demerol 45mg and atropine 400mcg/ml give how much per ml to total volume to inject demerol contains 50mg/ml, atropine contains 400mcg/ml how much volume to inject
Answer:
Volume injected = 1.65 ml
Step-by-step explanation:
mass of Demerol =45 mg.
density of pre-filled in syringe = 50 mg/ml
Volume = 45/50 = 0.9 ml
For atropine mass = 0.3 mg
density= 400 mcg/ml [ Note : 1 mcg = 0.001 mg]
volume filled = 0.3/400(0.001) = 0.75 ml
So, the total volume filled = 0.75+0.9 = 1.65 ml
hey help me with this question plzzzz
Look at where we don't have repeating x values. This happens with function C and function D. All the x values are unique for each choice mentioned.
In choices A, B, and E, the value x = -3 repeats itself. So we don't have a function for either of these. A function is only possible if any input (x) leads to exactly one output (y).
