The height of the rectangular pyramid will be 5 centimeters.
What is volume?The volume of any solid body is defined as the space covered by the object in the three-dimensional space. For a rectangular pyramid, the volume will be the space covered by a pyramid in a three-dimensional space.
Given that the volume of 70 cubic centimeters, length of 7 centimeters, and width of 6 centimeters.
The height of the rectangular pyramid is calculated by using the formula:-
V = ( l w h ) / 3
70 = ( 7 x 6 x h ) / 3
h = 70 / 14
h = 5
Therefore, the height of the rectangular pyramid will be 5 centimeters.
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Find each composition of functions. Simplify your answer.
Let f(x)=1/x . Find f(f(f(x))) .
A composite function exists as a function that depends on another function. A composite function exists formed when one function exists substituted into another function.
The value of f(f(f(x))) is 1/x
What is meant by composition function?In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.
Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.
A function that depends on another function is referred to as a composite function. When one function is inserted into another, a composite function is produced. For instance, f(g(x)) is the composite function created when x in f is replaced with f(x). f(g(x)). You can interpret f(g(x)) as "f of g of x."
Let the given function be f(x) = 1/x
f(f(x)) = f(1/x) = 1/(1/x)
simplifying the above equation, we get
f(f(x)) = f(1/x) = x
f(f(f(x))) = f(x) = 1/x
Therefore, the value of f(f(f(x))) = f(x) = 1/x
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Solve each equation. Round to the nearest ten-thousandth. Check your answers.
4x=19
After solving the equation, x = 19/4 Is the value of x in 4x = 19
⇒ 4x = 19
⇒ x = 19/4
How to solve an equation?
To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Diego evaluated 2 3/11−4/5. Each statement below is a way for Diego to check his answer. Use the drop-down menus to complete each statement. If his answer is the sum of 2 3/11 and 4/5, Diego's answer is too high or too low, or correct. If the sum of his answer and 4/5 is 1, Diego's answer is too high or too low, or correct. If the difference of 2 3/11 and his answer is 4/5, Diego's answer is too high or too low, or correct.
Simply solve the given equation and then evaluate according to the given situations. The answer is
a) Too high
b) Too high
c) Too low
Diego evaluated 2 3/11−4/5
Addition in math is a process of combining two or more numbers. Addends are the numbers added, and the result or the final answer we get after the process is called the sum. It is one of the essential mathematical functions we use in our everyday activities.
Subtraction is an operation used to find the difference between numbers. When you have a group of objects and you take away a few objects from it, the group becomes smaller
2 3/11 - 4/5 = 81/55 = 1.47
a) 2 3/11 + 4/5 = 169/55 = 3.07 (Too high)
b) (2 3/11 - 4/5) + 4/5 = 125/55 = 25/11 = 2.27 (Too high)
c) 2 3/11 - (2 3/11 - 4/5) = 25/11 - 81/55 = 44/55 = 4/5 = 0.8 (Too low)
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Simply answer the supplied equation, then make a judgment call based on the scenarios. The response is
a) Excessive
b) Excessive
• Too little
Diego scored a 2 3/11/4/5.
In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation. It is one of the fundamental mathematical operations we employ on a daily basis.
The operation of subtraction is used to calculate the difference between two numbers. If you remove a few items from a collection of things, the group will get smaller.
2 3/11 - 4/5 = 81/55 = 1.47
a) 2 3/11 + 4/5 = 169/55 = 3.07 (Too high)
b) (2 3/11 - 4/5) + 4/5 = 125/55 = 25/11 = 2.27 (Too high)
c) 2 3/11 - (2 3/11 - 4/5) = 25/11 - 81/55 = 44/55 = 4/5 = 0.8 (Too low)
Brian bought 4 CDs that were each the same price. Including sales tax, he paid a total of $59.20. Each CD had a tax of $0.70. What was the price of each CD before tax?
The total number of earrings in my drawer after I purchase 8 new pairs of
earrings, write an equation to model the situation
An auto repair shop records how far each vehicle they receive has been driven. The data for their
most recent 23 vehicles is shown in the histogram below.
What interval contains the 83rd percentile for this data?
The 83rd percentile contains intervals which are 50 and 100 thousand kilometers.
What is a histogram ?
A histogram is a representation of statistical data that makes use of rectangles to illustrate the frequency of data items in a series of equal-sized numerical intervals.
It is given that , data for most recent 23 vehicles is shown in the histogram.
On the x-axis distance driven in thousands of kilometers and on the y-axis frequency is represented in the histogram.
For 23 vehicles , we have different ranges of distance driven i.e., 0 - 50 , 50 - 100 , 150 - 200 . 200 - 250 , 250 - 300.
We know that the 83rd percentile meant the distance driven is greater than or equal to 83 %.
i.e.,
Here , 83 lies between 50 - 100 , so , 83rd percentile contains intervals which are 50 and 100 thousand kilometers.
Therefore , 83rd percentile contains intervals which are 50 and 100 thousand kilometers.
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Simplify the following:
Simplified answer to the given expression are :
a) 3/5
b) 2
c) 2.236
What is an mathematical expression?
Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
a) given expression is : [tex]\sqrt{\frac{9}{25}}[/tex]
Now, to simplify it we write the factors of 9 and 25 as 3 x 3 and 5 x5 and then take the root of them to get 3/5 as answer.
[tex]\sqrt{\frac{9}{25}}[/tex] = √(3 x 3)/ √(5 x 5 ) = 3/5
b) given expression is : [tex]\sqrt{\frac{12}{3}}[/tex]
Now, to simplify it we first divide 12 with 3 that is 4 and then take the root of 4 to get 2 as answer :
[tex]\sqrt{\frac{12}{3}}[/tex] = √4 = 2
c) given expression is : [tex]\frac{\sqrt{15}}{\sqrt{3}}[/tex]
Now, to simplify it we first divide 15 with 3 that is 5 and then take the root of 5 to get 2.236 as answer :
[tex]\frac{\sqrt{15}}{\sqrt{3}}[/tex] = √15/3 = √5 = 2.236
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Lesson Check (5.NBT.B.5)
1. There are 198 students in the soccer league.
There are 11 players on each soccer team. How
many soccer teams are there?
2
8 ײ + 3× -10 - 2ײ +8 × + 10 please solve and give a solution thankyou..
Answer:
6x2 + 11x
Step-by-step explanation:
First collect like terms:
8x2 - 2x2 + 3x + 8x - 10 + 10 (Ps: x2 and x are not the same!)
Combine them:
6x2 + 11x (the -10 and 10 cancel out)
and this is your polished answer!
Choose the correct term to complete each sentence.
A radical expression can always be rewritten using a(n) (rational exponent/inverse relation).
A radical expression can always be rewritten using a rational exponent .
Radicals : The expressions which include a root ( [tex]\sqrt[n]{x}[/tex] ) are called radicals . For ex . [tex]\sqrt{2}[/tex] , [tex]\sqrt[3]{3}[/tex] , [tex]\sqrt[7]{5}[/tex] , and so on .
Rational Exponent : Numbers of the form ( [tex]a^{m}[/tex] ) are called rational exponents . For ex . [tex]7^{2}[/tex] , [tex]11^{3}[/tex] , [tex]5^{5}[/tex] and so on .
A radical can be converted into a rational exponent . This can be done by keeping the no . inside root as it is and reciprocating the index and raising it to the power of exponent .
( [tex]\sqrt[n]{x}[/tex] ) = ( [tex]x^{1/n}[/tex] ) where x is the base and 1 / x is the power of the exponent .
Hence , a radical expression can always be rewritten using a rational exponent .
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Solve each equation.
4 x+16=34 x
After solving, the factors of equation 4x²+16=34x are:
(x-8) and (4x-2)What is an equation, exactly?A mathematical statement made up of two representations joined by an equal sign is known as an equation.3x - 5 = 16 is an example of an equation.We obtain the value for the variable x as x = 7 after solving this equation.So,
Given equation: 4x²+16=34x
Then,
4x²+16=34x4x²-34x+164x²-x( + )+164x²-x(32+2)+164x²-32x-2x+164x(x-8)-2(x-8)Factors are: (x-8) and (4x-2)
Therefore, after solving, the factors of equation 4x²+16=34x are:
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The correct question is given below:
Solve each equation.
4x²+16=34x
Jim received a gift card for 100 dollars for a pizza restaurant the restaurant charges 15 dollars per pizza. Yoko received a gift card of 70 dollars for a different pizza restaurant. The restaurant changes 10 dollars per pizza. Write an equation to show when two cards would have the same amount of money left in them.
The equation when both cards would have the same amount of money left is 30 = 5p.
When would both cards have the same amount of money?An equation is an algebraic expression that has an equal to sign. A linear equation is an equation that has a single variable that is raised to the power of one. When drawn on a graph, a linear equation is a straight line
Amount left on the gift card = value of the gift card - (amount spent on pizza x number of pizzas bought)
Amount left on Jim's gift card = 100 - ($15 x p)
100 - 15p
Amount left on Yoko's gift card = 70 - (10 x p)
70 - 10p
When both cards have the same amount of money left, the two above expressions would be equal
100 - 15p = 70 - 10p
Combine similar terms:
100 - 70 = 15p - 10p
Add similar terms:
30 = 5p
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The points (0, 0) and (1, 3) fall on a particular line. What is its equation in slope-intercept
form?
Answer:
y = 3x
Step-by-step explanation:
Slope-intercept form of an equation is a shortcut, fill-in-the-blank form you can use to write the equation of a line.
Slope-intercept eq:
y = mx + b
You fill in slope where the m is. And you fill in the y-intercept for the b.
In your problem they gave you two points. You can calculate slope with two points. Subtract the y's, 3-0, put that on top of a fraction. And subtract x's, 1-0, put that on the bottom of the fraction. The slope, m, is 3/1, which is 3.
slope:
m = 3-0 / 1-0 = 3/1 =3
The y-intercept is actually given in your problem. The y-intercept is the point where the line crosses the y-axis. The y-intercept is the point where the x is 0. They gave you the point (0,0) that is the y-intercept. So b = 0.
Fill the m and b in with the given numbers!
y = 3x + 0 Simplify.
y = 3x
yron is cooking meat. The double number line shows that he needs 121212 hours to cook 555 kilograms of meat. A double number line with 6 equally spaced tick marks. The line labeled Meat, kilograms, reads from left to right: 0, four unlabeled tick marks, 5. The line labeled Time, hours, reads from left to right: 0, four unlabeled tick marks, 12. A double number line with 6 equally spaced tick marks. The line labeled Meat, kilograms, reads from left to right: 0, four unlabeled tick marks, 5. The line labeled Time, hours, reads from left to right: 0, four unlabeled tick marks, 12. Based on the ratio shown in the double number line, how long does Myron need to cook 333 kilograms of meat?
Myron would need 7.2 hours to cook 3 kilograms of meat.
time = 12 hours
cook = 5 kilograms of meat.
i.e. For 5 kilograms of meat, it takes 12 hours to cook.
Thus, for 3 kilograms of meat,
Multiple 12 by 3 and divided by 5
= 12/5 * 3
= 12 * 3/5
= 36 / 5
= 7.2 hrs.
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Answer: 12 hours
Step-by-step explanation: 5 kilo grams of meet
What’s the amplitude and the period of this function?
The amplitude and the period of the function are 3 and 2, respectively.
What are the amplitude and the period of a sinusoidal function?
Sinusoidal functions are periodic bounded functions whose form is described below:
y = A · sin (2π · t / T + Ф) + y'
Where:
y' - MidpointA - Amplitudet - TimeФ - PhaseT - PeriodThe period is the horizontal distance between two consecutive peaks or two consecutive bottoms and the amplitude is equal to the half of the distance between a peak and a consecutive bottom. Hence, the amplitude and the period are, respectively:
Amplitude
A = 0.5 · [2 - (- 4)]
A = 3
Period
T = 2 · [0.75 - (- 0.25)]
T = 2
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f(x)=b x and g(x)=logbx are inverse functions. Explain why each of the following is true.
b. The inverse of f₁(x)=b x-h is equivalent to a translation of g .
If b^{h} < 1 then it will be a vertical stretch.
What authority possesses a power rule?
When a base is raised to a power and then the entire expression is raised to another power, the power of a power rule in exponents is used to simplify the algebraic statement.
A translation of function f is f₁ (x) = bˣ⁻h . It is equivalent to a vertical stretch or vertical compression of function f.
[tex]f_{1} (x) = b^{x - h}[/tex]
If we used the rules of powers, we know that when we have a subtraction in the power of an exponential, it can be split into a division. So the function can be rewritten as
[tex]f_{1} (x) = \frac{b^{x} }{b^{h} }[/tex]
Remember the original function was
f(x) = bˣ
therefore
[tex]f_{1}(X) = \frac{f(x)}{b^{h} }[/tex]
this means that if [tex]b^{h} < 1[/tex] then it will be a vertical stretch.
If b^{h} < 1 then it will be a vertical stretch.
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Luke gets pizza delivered from the same local pizza parlor every Thursday. This week, he ordered 3 pizzas for his family and spent $32.75. Last week he ordered 4 pizzas and spent $41.50. Assume the price for each pizza is the same.
a) Does the pizza parlor charge a delivery fee? Explain.
b) Write an equation describing the total amount Luke spends, d, to get p pizzas delivered.
Yes, the pizza parlor charges a delivery fee and the equation describing the total amount Luke spends, d, to get p pizzas delivered is d = 10.60p.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
Luke gets pizza delivered from the same local pizza parlor every Thursday. This week, he ordered 3 pizzas for his family and spent $32.75.
Last week he ordered 4 pizzas and spent $41.50.
Each pizza costs when ordered 3 pizzas
= 32.75/3 = $10.91
Each pizza costs when ordered 4 pizzas
= 41.50/4 = $10.37
Yes, the pizza parlor charges a delivery fee.
= (41.50+32.75)/(3+4) = 10.60
d = 10.60p
Thus, yes, the pizza parlor charges a delivery fee and the equation describing the total amount Luke spends, d, to get p pizzas delivered is d = 10.60p.
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A frame around a rectangular family portrait has a perimeter of 102 inches. The length of the frame is 9 inches less than twice the width. Find the length and width of the frame.
Given the perimeter, the length and width of the rectangular family portrait are 20 inches and 31 inches respectively.
What is the length and width of the rectangular frame?The perimeter of a rectangle is expressed mathematically as;
P = 2( l + w )
Given the data in the question;
Let "x" represent the width of the rectangle.
Width w = xLength l = 2x - 9Perimeter P = 102 inchesTo determine the width and length of the rectangle, plug the given values into the formula above and solve for x.
P = 2( l + w )
102 = 2( ( 2x - 9 ) + x )
102 = 2( 2x - 9 + x )
102 = 2( 3x - 9 )
Apply distributive property
102 = 2(3x) + 2(-9)
102 = 6x - 18
102 + 18 = 6x
120 = 6x
6x = 120
x = 120/6
x = 20
Now, the numerical length and with of the rectangular frame will be;
Width w = x = 20 inches
Length l = 2x - 9 = 2(20) - 9 = 40 - 9 = 31 inches.
Given the perimeter, the length and width of the rectangular family portrait are 20 inches and 31 inches respectively.
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What is the slope of the line represented by the points in the table?
Negative 0.05
Negative .005
0.005
0.05
Applying the slope formula, the slope of the line is determined as: 2.
What is the Slope of a Line Represented by a Table?The slope of a line represented by a table of values can be calculated using any two set of ordered pairs form the given table, and applying the slope formula below:
Slope (m) = y2 - y1/x2 -x1
Using any two points of the line, (0, -0.25) and (1, -0.2), as represented in the table, let:
(0, -0.25) = (x1, y1)
(1, -0.2) = (x2, y2)
Plug in the values
Slope (m) = (-0.2 -(-0.25))/(1 - 0)
Slope (m) = 0.05/1
Slope (m) = 0.05
Thus, the slope of the line as represented by the table of values is calculated as: 0.05.
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What is the factored form of x² + 6x + 8?
O(x + 5)(x + 3)
O(x + 4)(x + 2)
O(x + 7)(x + 1)
O(x + 3)(x + 3)
The factored form of the equation x² + 6x + 8 is (x + 4) (x + 2), that is, option B.
Here, we are given a quadratic equation x² + 6x + 8
We can factorize this equation using the splitting the middle term method.
Here the coefficient of x is 6, hence, we need to spilt 6 in such a manner that the product of the split terms is 8.
6 can be written as 4 + 2 and we can see that 4 × 2 = 8
Hence, we can write the given equation as-
x² + 4x + 2x + 8
= x (x + 4) + 2 (x + 4)
= (x + 4) (x + 2)
Hence, the factored form of the equation x² + 6x + 8 comes out to be (x + 4) (x + 2), that is, option B.
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Question 17 of 25
Which of the following values are in the range of the function graphed below?
Check all that apply.
Answer:
B, C, E
Step-by-step explanation:
Given a graph, you want to know the set of listed values that is included in the range of the graph.
RangeThe range of a function is its vertical extent, the set of output values the function may have. The graph shows a function with a range of ...
-6 ≤ y ≤ 0
Listed values that fall in that range are ...
-1 (B), -2 (C), and -6 (E)
Find m
a. 24
b. 58
c. 37
d. 19
Answer:
24
Step-by-step explanation:
Lydia wants to ride her bicycle 34 miles this week. She has already ridden 7 miles. If she rides for 5 more days, which equation could be used to determine xx, the average number of miles she would have to ride to meet her goal?
Answer: Well i tried doing 7x5 but it is 35 and she has to ride her bike 34 miles so hope this helps if not then sorry
Step-by-step explanation:
The equation to determine the average number of miles she would have to ride to meet her goals is
5x = 34 - 7
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total miles = 34 miles
Number of days to ride = 5
The equation to determine the average number of miles.
5x + 7 = 34
Now,
Solve for x.
5x = 34 - 7
5x = 27
x = 27/5
x = 5.4 miles
Thus,
The average number of miles is 5.4 miles.
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What polynomial, when divided by 2x², yields 7x6 - 6x4 + 8x² as a quotient
Answer:
14x⁸ - 12x⁶ + 16x⁴
Step-by-step explanation:
To find the required polynomial, multiply 2x² and the quotient.
Multiply each term of (7x⁶ - 6x⁴ + 8x²) by 2x².
2x² * 7x⁶ = (2*7) *x²⁺⁶ = 14x⁸
Required polynomial =2x² *(7x⁶ - 6x⁴ + 8x²)
= (2x²*7x⁶) - (2x²*6x⁴) + (2x²*8x²)
= 14x⁸ - 12x⁶ + 16x⁴
Solve each equation in the interval from 0 to 2π . Round your answer to the nearest hundredth.
cos2t = 1/2
Greetings from Brasil...
Is 2.738 a rational or irrational number
Answer: It is a rational number.
Hence, [tex]2.738[/tex] a rational number.
What is the rationa number?
A rational number is a type of real number, which is in the form of [tex]\frac{p}{q}[/tex] where [tex]q[/tex] is not equal to zero. Any fraction with non-zero denominators is a rational number.
Here [tex]2.73[/tex] acn be written as
[tex]2.73=\frac{2.73}{1}[/tex]
Now, we multiply numerator and denominator by [tex]100[/tex].
So, it would be
[tex]\frac{2.73(100)}{1(100)}\\\\=\frac{273}{100}[/tex]
So, the fraction is written as [tex]2.73[/tex].
Hence, [tex]2.738[/tex] a rational number.
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Solve the system of equations 8x- 3y =9 4x -4y=-8
Answer:
x = 3, y = 5.
Step-by-step explanation:
8x - 3y = 9
4x - 4y = -8
multiply the second equation by 2:
8x - 8y = -16
Subtract this from the first equation:
5y = 25
y = 5.
Substitute for y in equation 2:
4x - 4(5) = -8
4x = -8 + 20 = 12
x = 12/4 = 3.
Answer:
2
Step-by-step explanation:
1=1=2
find the distance bd on the number line below.
Answer:
4
Step-by-step explanation:
B= 1
D= -3
Distance between the two? 4 points
1 - (-3) = 4
Select all the equations by that have the same solution as 2x-5=15
Answer:
2x=20 i guess
Step-by-step explanation:
2x -5= 15
add 5 to both sides
you should get 20
it's 2x=20
A triangle has vertices A(-2, 3), B(0, 0), and C(1, 2). What are the coordinates of the vertices if the triangle is reflected over the y-axis and then dilated by a scale factor of 2?
A'(4, 6), B'(0, 0), C'(-2, 4)
A'(-4, -6), B'(0, 0), C'(2, -4)
A'(-4, -6), B'(2, 2), C'(2, -4)
A'(4, 6), B'(2, 2), C'(-2, 4)
The the vertices if the triangle is reflected over the y-axis and then dilated by a scale factor of 2 wii be A'(4, 6), B'(0, 0) and, C'(-2, 4).
According to the given question.
The vertices of a triangle ABC are A(-2, 3), B(0, 0), and C(1, 2).
As we know that,
The rule for reflecting a triangle over the y axis is to negate the value of x-coordinate of each point, but leave the y-value the same.
Therefore, the vertices of triangle ABC when it is reflected over y-axis are
A'(2,3)
B'(0, 0)
C'(-1, 2)
Also, when the triangle is dialated by a scale factor 2 then the vertices will be
A'(4, 6)
B'(0, 0)
And, C'(-2, 4)
Hence, the the vertices if the triangle is reflected over the y-axis and then dilated by a scale factor of 2 wii be A'(4, 6), B'(0, 0) and, C'(-2, 4).
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