The volume of the rectangular solid is: 11,960 units³.
How to Find the Volume of a Rectangular Solid?The formula to find the volume of a rectangular solid is: (length)(width)(height).
Given the dimensions as:
Length = 20 unitsWidth = 23 unitsHeight = 26 unitsVolume = (20)(23)(26)
Volume of the rectangular solid = 11,960 units³.
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How many interior angles does a 2D shape right arrow have and explain the answer?
The number of interior angles in a 2D shape right arrow is 8 because , the number of sides is also 8
How to determine the interior anglesIt is important that a 2D shape arrow is a shape with 8 sides
Sum of angles of a polygon = (n - 2) × 180
⇒ ( 8 - 2) × 180
⇒ 6 × 180
⇒ 1080
The number of interior angles are 8 and this is so because of the number of sides in the 2D shape right arrow
Thus, the number of interior angles in a 2D shape right arrow is 8 because , the number of sides is also 8
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Please Evaluate C(6,3)
The value of the expression C(6,3) is 20
How to evaluate the expression?The expression is given as:
C(6, 3)
This means 6 combination 3.
And it can be written as:
[tex]^6C_3[/tex]
Apply the combination formula
[tex]^6C_3 = \frac{6!}{3!3!}[/tex]
Evaluate the expression
[tex]^6C_3 = 20[/tex]
Hence, the value of the expression C(6,3) is 20
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Shayla is 3 years older than Todd. If t represents Todd’s age, which expression represents Shayla’s age?
Answer:
t + 3
Step-by-step explanation:
adding 3 years onto t amount of years
Find all primes p, q such that p^2-p=37q^2-q
The pairs of prime numbers (p,q) such that p^2-p=37q^2-q is (43, 7)
How to determine the pairs of numbers?The expression is given as:
p^2 - p=37q^2 - q
The boundary or range of numbers of p and q is not given.
So, we make use of numbers between 2 (because 1 is not a prime number) and a very large number (say 1000000)
i.e. 2 ≤ p ≤ 1000000 and 2 ≤ b ≤ 1000000
Using the above range, we have the following program to determine the pairs of prime numbers (p, q).
for a in range(2,1000000):
for b in range(2,1000000):
if ((a* *2) - a) == (37 * (b* *2) - b):
print(str(a)+","+str(b))
The output of the above program is:
(43, 7)
The above represent all pairs of prime numbers (p,q) such that p^2 - p=37q^2 - q
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is {{-12,8),(-15,8),(-5,8),(-12.8}} a function
Answer:
Yes. {(-12, 8), (-15, 8), (-5, 8)} is function because there is no overlap in the x values.
The table shows the multiplication of two linear expressions.
A 2-column table with 5 rows. First column is labeled Reason with entries Given, Step 1, Step 2, Step 3, Step 4. Second column is labeled Step with entries three-fourths x (negative 8 x + 6), (three-fourths x) (negative 8 x) + (three-fourths x) (6), three-fourths times (negative 8) times x times x + three-fourths times 6 times x, (three-fourths times (negative 8)) times (x times x) + (three-fourths times 6) times x, negative 6 x squared + 9 over 2 x.
What is the mathematical reasoning for Step 3?
associative property
commutative property
distributive property
simplify
The mathematical reasoning for Step 3 is a distributive property.
What is distributive property?It should be noted that the distributive property is the multiplication of the sum of two to more addends by a number that will give same result.
In this case, the mathematical reasoning for Step 3 is a distributive property.
Therefore, the correct option is C.
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Answer: C. Distributive Property
What is the standard form equation of an ellipse that has vertices (18,1) and (−10,1) and co-vertices (4,14) and (4,−12)?
Answer: [tex]\frac{(x-4)^2}{196} +\frac{(y-1)^1}{169} =1[/tex]
Step-by-step explanation:
You first need to determine if the ellipse is horizontal or vertical, which can be found by the length of the major axis.
The vertices are at (18,1) and (-10,1). The distance is 28 units. (horiz)
The co-vertices are at (4,14) and (4,-12) The distance 26 units (vert)
The major axis is horizontal, so the standard form of the ellipse is
[tex]\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2} =1[/tex] where (h,k) are the coordinates of the center.
To find the center, find the midpoint of the major axis [tex](\frac{x1+x2}{2} ,\frac{y1+y2}{2} )[/tex]
The center is at (4,1)
Since the major axis is 2a, a would be 28 divided by 2=14 squared : 196
The minor axis is 2b, so b would e 26/2=13 squared: 169
Inserting the center and a,b values into the standard form eq:
[tex]\frac{(x-4)^2}{196} +\frac{(y-1)^1}{169} =1[/tex]
hope this helps.
A store is having a sale on chocolate chips and walnuts. For 5 pounds of chocolate chips and 3 pounds of walnuts, the total cost is $25 . For 7 pounds of chocolate chips and 9 pounds of walnuts, the total cost is $53 . Find the cost for each pound of chocolate chips and each pound of walnuts.
Answer:
one pound of chocolate chips = $2.75
one pound of walnuts = $3.75
Step-by-step explanation:
we can solve this by first making an equation
let's write the number of chocolate chips in c
and the number of walnuts in w
5c + 3w = 25
7c + 9w = 53
let's first solve for c by multiplying the top equation by 3 and subtracting the bottom equation from it
(15c + 9w = 75) - (7c + 9w = 53)
8c = 22
c = $2.75
Let's now start to solve for w by inputting c into one of the equations.
(2.75)7 + 9w = 53
19.25 + 9w = 53
9w = 53 - 19.25
9w = 33.75
w = $3.75
a pound of chocolate chips = 2.75
a pound of walnuts = 3.75
give me brainliest, please!
Hope this helps :)
Answer:
each pound of chocolate chips costs $2.75
each pound of walnuts costs $3.75
Step-by-step explanation:
let c be the cost of a pound of chocolate chips
and w be the cost of a pound of chocolate chips
For 5 pounds of chocolate chips and 3 pounds of walnuts,
the total cost is $25 means 5c + 3w = 25
For 7 pounds of chocolate chips and 9 pounds of walnuts,
the total cost is $53 means 7c + 9w = 53
Now we have to solve the system:
[tex]\begin{cases}5c+3w=25&\\ 7c+9w=53&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}15c+9w=75&\\ 7c+9w=53&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}15c+9w=75&\\ 8c=22&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}15c+9w=75&\\ c=\frac{11}{4} &\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}9w=75-15 \times \frac{11}{4} &\\ c=\frac{11}{4} &\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}9w=\frac{135}{4} &\\ c=\frac{11}{4} &\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}w= \frac{15}{4} &\\ c=\frac{11}{4} &\end{cases}[/tex]
A theater sells 2 types of fixed-price tickets - orchestra and balcony. Peter pays $50 for 1 orchestra and 4 balcony tickets. Justine pays $150 for 3 orchestra and 12 balcony tickets. А B The cost of 1 balcony ticket. The cost of 1 orchestra ticket. The quantity under A is greater than the quantity under B. The quantity under B is greater than the quantity under A. The quantities under A and B are equal. The information given is insufficient to make the comparison.
Using a system of equations, it is found that:
The cost of an orchestra ticket is of $10.The cost of a balcony ticket is of $10.The quantities are equal.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable a: Cost of an orchestra ticket.Variable b: Cost of a balcony ticket.Peter pays $50 for 1 orchestra and 4 balcony tickets, hence:
a + 4b = 50 -> a = 50 - 4b.
Justine pays $150 for 3 orchestra and 12 balcony tickets, hence:
3a + 12b = 150.
a + 4b = 50 -> a = 50 - 4b.
The equations are equal, hence we suppose that the costs are equal, that is:
a + 4b = 50 -> 5a = 50 -> a = 10.
Hence:
The cost of an orchestra ticket is of $10.The cost of a balcony ticket is of $10.The quantities are equal.More can be learned about a system of equations at https://brainly.com/question/24342899
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Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100
The equations that can be used to find the lengths of the legs of the triangle are as follows:
100 = (x + 2)² + x²24 = 0.5 × (x + 2)(x)x² + 2x - 48 = 0How to find the equation of a right triangle?The equation that can be used to find the length of the leg of the right triangle uses Pythagoras theorem,
Therefore,
c² = a² + b²
where
c = hypotenuse sidea and b are the other legsTherefore,
10² = (x + 2)² + x²
100 = (x + 2)² + x²
Therefore, using the area of a triangle,
area of a triangle = 1 / 2 bh
where
b = baseh = heightTherefore,
area of the triangle = 1 / 2 × (x + 2)(x)
24 = 0.5 × (x + 2)(x)
24 = x² + 2x / 2
cross multiply
48 = x² + 2x
x² + 2x - 48 = 0
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plsss right away will be amazing
Which is the graph of f(x)=√/-x?
Graph 3
Because
y=³√xThe graph is like the first graph
When x approaches+oo y approaches+oo
But when x is negative the reverse thing happens
Hence Graph C is correct
Answer:
Graph 3
Step-by-step explanation:
Given function:
[tex]f(x)=\sqrt[3]{-x}[/tex]
Therefore, the parent function is:
[tex]f(x)=\sqrt[3]{x}[/tex]
(The graph of the parent function is the first graph in the answer options).
The transformation that takes the parent function to the given function is:
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Therefore, the graph of the given function is the third graph in the given answer options (see attached).
solve the inequality
x-2>15
Answer:
Inequality Form: x > 17
Interval Notation: (17, ∞)
Which of the following statements is TRUE about rectangle ABDC.
The statement that is TRUE of the rectangle is AB + BD > AD. Option A
Facts about the rectangleWE have that a diagonal divides the rectangle into two equal triangles
line AD is the length of the diagonal
With the diagonal drawn, we have
AD = hypotenuse
AB and BD are the two other sides
From the Pythagorean theorem, we have that the square root of the square sum of the other two sides fives the hypotenuse. This mean that their sum is greater than the hypotenuse
Thus, the statement that is TRUE is AB + BD > AD. Option A
The complete question is;
Which of the following statements is TRUE about rectangle ABDC.
a. AB + BD > AD
b. AB + BD < AD
c. AB + BD = AD
d. (AB) (BD) = AD
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In London today, twice the high temperature was more than five times the high temperature minus eighty-seven. In interval form, what are the possible temperatures?
The possible temperatures are represented by (-∝, 29)
How to determine the possible temperatures?Let the high temperature be x
So, the statement can be represented as:
2x > 5x - 87
Subtract 5x from both sides
-3x > -87
Divide both sides by -3
x < 29
In interval form, we have (-∝, 29)
Hence, the possible temperatures are represented by (-∝, 29)
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Find the missing side of the triangle.
pythagorean 4
A. 337‾‾‾‾√ km
B. 5‾√ km
C. 193‾‾‾‾√ km
D. 112‾√ km
Applying the Pythagorean theorem, the missing side of the triangle is: C. √193 km.
How to Apply the Pythagorean Theorem?To find the missing side (x) in the right triangle, based on the Pythagorean theorem, we would have the following equation:
x = √(12² + 7²)
x = √(144 + 49)
x = √193
The missing side of the triangle is: C. √193 km
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Answer:
C.) 193√ km
Step-by-step explanation:
I got it right on founders edtell
Which phrase best describes the translation from the graph y = 6x² to the graph of y = 6(x + 1)²?
O6 unit left
O6 unit right
O 1 unit left
O 1 unit right
Answer:
1 UNIT LEFT best describes the translation from the graph y = 6x² to the graph of y = 6(x + 1)².
Which of the following lists is in order from smallest to largest? 5/8, 0.6, 6.2%, 2/3, 2/3, 5/8, 0.6, 6.2% 6.2%, 0.6, 5/8, 2/3, 0.6, 6.2%, 5/8, 2/3
Answer:
6.2%, 0.6, 5/8, 2/3
Step-by-step explanation:
For some reason, you have written the same numbers over and over. It looks like there are only really 4 numbers.
I changed each number into a decimal and then compared them.
6.2% to change a percent to a decimal, move the decimal 2 places to the left so 6.2% equals 0.062.
0.6 is already in decimal form
5/8 you divide 5 by 8. Put in your calculator 5 the division symbol and then 8 to get 0.625.
2/3 is 0.6 repeating or 0.66666 forever.
Now compare:
62% = 0.62
0.6
5/8 = 0.625
2/3 = 0.66666...
Find the surface area of the square pyramid below if the length of the sides of the base are 10 cm, and the slant height is 15 cm.
The surface area of the square pyramid if the length of the sides of the base are 10 cm, and the slant height is 15 cm is 416.2 cm²
Surface areaSurface area of the square pyramid
= a² + 2a√a²/4 + h²
where,
a = sides of base = 10 cmh = slant height = 15 cmSurface area of the square pyramid
= a² + 2a√a²/4 + h²
= 10² + 2(10)√10²/4 + 15²
= 100 + 20√100/4 + 225
= 100 + 20√25 + 225
= 100 + 20√250
= 100 + 20(15.81)
= 100 + 316.2
= 416.2 cm²
Therefore, the surface area of the square pyramid if the length of the sides of the base are 10 cm, and the slant height is 15 cm is 416.2 cm²
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What is the range of possible sizes for side xxx?
Answer:
1.6 < x < 9.6
Step-by-step explanation:
given 2 sides of a triangle then the third side x is in the range
difference of 2 sides < x < sum of 2 sides , that is
5.6 - 4 < x < 5.6 + 4
1.6 < x < 9.6
Write the equation of a parabola whose directrix is
y
=
−
1.5
y
=
-
1.5
and has a focus at
(
−
4
,
−
2.5
)
(
-
4
,
-
2.5
)
.
Answer:
y=0.5x²-4x-10.
Step-by-step explanation:
1) according to the definition of parabola:
d1=d2, then
[tex]2) \ |y+1.5|=\sqrt{(x+4)^2+(y+2.5)^2} ;[/tex]
3) after evolution:
-(2y+4)=(x+4)²; ⇔
[tex]y=-\frac{1}{2}x^2-4x-10.[/tex]
1. The correlation coefficient on a scatter plot representing the variables for the amount of weight a body builder can lift in a gym and the amount of protein the body builder takes each day is 0.76. Describe the meaning of this correlation coefficient.
A
very Strong positive linear relationship between the two variables
B
very Strong negative linear relationship between the two variables
C
moderate positive linear relationship between the two variables
D
no relationship between the two variables
A correlation coefficient of 0.76 indicates a very strong positive linear relationship between the two variables.
What does the correlation coefficient mean?Correlation is a statistical measure used to measure the linear relationship that exists between two variables.
If the sign of the correlation coefficient is positive, it means that the two variables exhibits a positive correlation. The closer to 1, the correlation coefficient is, the stronger the linear relationship.
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Thomas took 3h to paint a room. Brian could paint the same room in 6h. How long would it take for both of them to finish painting the same room together?
please help !! no algebra please
Answer:
2 hours
Step-by-step explanation:
If Thomas can paint 1/3 = 2/6 of the room in a hour and Brian can paint 1/6 of the room in an hour. Which means in an hour they can collectively paint 3/6 = 1/2 of the room. Now you need to find how long it would take then to paint 2/2 of the room. Knowing that 1/2+1/2 = 2/2, it would take them 2 hours to paint the room together
Solve the following system of equations.
{y=x−5
−x−3y=7
Write your answer as an ordered pair in the form (x,y).
Answer:
(2,-3)
Step-by-step explanation:
I am not sure if you meant the first equation to be y or -y. I solved it as y.
y = x-5 -x -3y =7
I am going to take the second equation and write it as x =
-x - 3y = 7 Give equation
-x = 3y +7 Add 3y to both sides
x = -3y-7 Multiplied each term in the equation by -1 so that x could be positive
I am going to substitute -3y-7 for x in the first equation up above
y = x - 5
y = -3y -7 - 5 Substitute -3y-7 for x
y = -3y -12 Combined -7-5
4y = -12 Added 3y to both sides
y = -3 Divided both sides by 4.
I now know that y is -3, I will plug that into x = -3y-7 to solve for x
x = -3(-3) -7
x = 9-7 A negative times a negative is a positive
x = 2
look at the pictures
Answer:
A
Step-by-step explanation:
9|x-8|<36
|x-8|<4
-4<x-8<4
add 8
-4+8<x-8+8<4+8
4<x<12
56m² = ____________ GCF =
68m² = ____________ GCF =
The greatest common factor of the expression is 4m⁴.
What is GCF?GCF simply means the greatest common factor.
The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.
Hence,
56m⁵
68m⁴
The greatest common factor of the expression is the largest positive expression that divides evenly into all numbers with zero .
Hence, the greatest common factor is 4m⁴
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select the correct answer which graph is defined by f(x)= |x^2 -x-2|
The graph of the absolute value function can be seen below.
How to get the graph of f(x)?Here we have the absolute value function:
[tex]f(x) = |x^2 - x -2|[/tex]
Notice that the argument of the absolute value function is a quadratic equation, then the graph of the function f(x) will be the graph of the quadratic equation, but such that the part below the horizontal axis is reflected.
Then the graph of the function is the one you can see below:
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Please help me with this problem. Seriously desperate again !!
The dimensions are 7 inches by 17 inches.
What is the area of rectangle?
Let the length be l inches
Let the breadth be b inches
Area = l*b
We can find dimensions as shown below:
Let the length be x inches
Let the width be y inches
Area = 119 square inches
x=3+2y (1)
Area = l*w
119 = x*y
Putting value of x
119 = (3+2y) *y
119 = 3y+2y^2
2y^2+3y-119=0
2y^2-14y+17y-119=0
2y(y-7) +17(y-7) =0
(y-7) (2y+17) =0
y=7, -17/2
y cannot be negative
so, y = 7
Putting in equation (1)
x=3+2(7)
= 3+14
= 17
Hence, the dimensions are 7 inches by 17 inches.
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If f(x) =2ײ+2 and g(x) =x² -1, find (f-g) (x)
Answer:
[tex]\boxed {(f-g)(x) = x^{2}+3}[/tex]
Step-by-step explanation:
Given :
f(x) = 2x² + 2g(x) = x² - 1Now, this problem can be used using a simple formula.
[tex]\fbox {(f - g)(x) = f(x) - g(x)}[/tex]
Let's solve.
(f - g)(x) = 2x² + 2 - (x² - 1)(f - g)(x) = 2x² - x² + 2 + 1(f - g)(x) = x² + 3∴ The answer will be x² + 3.
Sets A, B, and C are subsets of the universal set U. These sets are defined as follows.
U= {f,g,h,p,q,r,x,y,z}
A={f,g,p,q}
B={g,h,q,x,y}
C={p.q.x.y.z}
Find (C ∪ B) ∩ A'.
Write your answer in roster form or as Ø.
Answer:
(C U B )=(q,x,y)
(C U B )n A=q
Which number has a repeating decimal form?
A. √15
B. 11/25
C. 30
D. 2/6