Answers
Answer: The whole equation is simplified down to -20.
Step-by-step explanation:
Here's how I got my answer:
Equation is 4p^2 + 7q^3
All you need to do is plug in the values they have given you. If you apply them, you get:
4 (-3)^2 + 7 (-2)^3
Which simplifies to:
4 (9) + 7 ( -8)
Simplify furthermore:
36 + (-56)
Which gives you:
-20
Related Questions
Which interval notation represents the set of all numbers from -9 to 0, inclusive?
Answers
Answer:
[-9,0]
Step-by-step explanation:
You use brackets to indicate that the numbers, in this case -9 and 0, are included in the interval.
You use parentheses to indicate that the numbers are excluded from the interval.
Since we want to include the numbers in the interval, we use the brackets.
The answer is [-9,0]
Hope this helps!
If m∠XWZ = 90, what is x?
Right angle X W Z is divided into 2 acute angles labeled 5 x plus 5 degrees and 2 x plus 8 degrees.
Answers
Answer: x=11
Step-by-step explanation:
If m∠XWZ = 90 and is divided into 2 acute angles labeled 5x+5 degrees and 2x+8 degrees then the value of x is 11.
Given,
m∠XWZ = 90.
Right angle ∠XWZ is divided into 2 acute angles labeled as:
- 5x + 5 degrees
- 2x + 8 degrees.
We need to find the value of x.
What is an acute angle?An acute angle means angles that are less than 90 degrees.
If an angle is divided, the sum of the divided angles must be equal to the angle divided.
Find the right angle.
m∠XWZ = 90
Find the acute angles that are being divided.
= 5x + 5° and 2x + 8°
Find x.
Since m∠XWZ is divided we have,
90° = 5x + 5° + 2x + 8°
Now,
Add the like terms.
90 = 7x + 13
Subtract 13 on both sides.
90 - 13 = 7x
77 = 7x
Divide both sides by 7.
11 = x
x = 11
We can crosscheck the angles:
90° = 5x + 5° + 2x + 8°
90 = 5x11 + 5 + 2x11 + 8
90 = 55 + 5 + 22 + 8
90 = 60 + 30
90 = 90
Thus if m∠XWZ = 90 and is divided into 2 acute angles labeled 5x+5 degrees and 2x+8 degrees then the value of x is 11.
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what is repeating .67 as a fraction?
Answers
Answer:
67-100
Step-by-step explanation:
This is the answer because the . is ones the 6 is tens and the 7 is the hundreds
hello please help ASAP thank you!
Answers
Answer:
I believe it is 1.
Step-by-step explanation:
1. because thats half
Which words represent SUBTRACTION
less than
sum
difference
total
Answers
Answer:
I think it's sum and difference
Answer:
less than and difference
Step-by-step explanation:
82, 77, 72, 67, 62 ....... The recursive pattern in the sequence above is latex-_ (be sure to show if it is positive or negative). The 4th term in the sequence is . An explicit formula that I can use to write for this sequence is latex-_ . The value of the 100th term is .
Answers
Answer:
a. It is a negative pattern
b. Fourth term is 67
c. Explicit formula is Tn = 87 - 5n where n is the number of the term.
d. The value of the 100th term is -413
Step-by-step explanation:
1.Firstly, we want to know if the pattern is positive or negative.
Looking at the pattern, we can see our first term as 82, second as 77, third as 72.
What this show is that the pattern is decreasing as we move on from one term to another. So we can say it is a negative recursive pattern.
2. We are asked which term is the 4th.
This is quite obvious from the spelt out pattern.
82 77 72 67
1....2......3.....4
67 is the fourth term.
3. We want an explicit formula for the sequence.
What this question is asking us is a formula such that we can use at any point in time to calculate the value of the term at that point.
Firstly we have the first term as 82.
We need the common difference.
Mathematically this is the second term minus the first term which is same as the third term minus the second term.
That would be; 77-82 = 72-77 = -5
Mathematically the nth term of an arithmetic sequence is;
Tn = a + (n-1) d
Where in this case a is 82 and d is -5
Substituting these values, we have;
Tn = 82 + (n-1)-5
Tn = 82 -5n + 5
Tn = 82 + 5 -5n
Tn = 87 -5n
Where Tn is the term we are looking for while n is the number of the term.
4. Value of the 100th term
Simply substitute the value of 100 for n in the explicit formula.
That would be;
87 -5(100) = 87-500 = -413
15 and 17 pls.. 15 points!!!!
Answers
Step-by-step explanation:
15) 50 ÷ 2 = 25
17) Mean = 301, Mode = 40-50
(10+20) ÷ 2 = 15, (20+30) ÷ 2 = 25, (30+40) ÷ 2 = 35
(40+50) ÷ 2 = 45, (50+60) ÷ 2 = 55, (60+70) ÷ 2 = 65
(70+80) ÷ 2 = 75
• 15×4 = 60, 25×8 = 200, 35×10 = 350, 45×12 = 540
55×10 = 550, 65×4 = 260, 75×2 = 150
Mean = (60+200+350+540+550+260+150) ÷ 7
= 2110 ÷ 7
= 301.4285....
= 301
Mode : the highest frequency
Answer:
15) 50 ÷ 2 = 25
17) Mean = 301, Mode = 40-50
(10+20) ÷ 2 = 15, (20+30) ÷ 2 = 25, (30+40) ÷ 2 = 35
(40+50) ÷ 2 = 45, (50+60) ÷ 2 = 55, (60+70) ÷ 2 = 65
(70+80) ÷ 2 = 75
• 15×4 = 60, 25×8 = 200, 35×10 = 350, 45×12 = 540
55×10 = 550, 65×4 = 260, 75×2 = 150
Mean = (60+200+350+540+550+260+150) ÷ 7
= 2110 ÷ 7
= 301.4285....
= 301
Mode : the highest frequency
In a rectangular field of dimensions 20m x 15m , a triangular park is constructed. If the
dimensions of the park are 5m, 7m and 8m respectively, find the cost of levelling the
remaining field at the rate of Rs 100 per m
m?
Answers
Answer:
My answer is 28,250Rs.
Area of a triangle=1/2b×h.
1/2×7×5=17.5.
Area of a rectangle=l×b.
20×15=300.
Area of rectangle-Area of the triangle=300-17.5=282.5m^2.
If 1m^2=100Rs.
then 282.5m^2=282.5×100=28,250Rs.
Find the distance between the two points. (-6,-10) & (-2,-10)
Answers
Answer:
The answer is 4 unitsStep-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{( {x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-6,-10) & (-2,-10)
The distance between them is
[tex]d= \sqrt{ ({ - 6 + 2})^{2} + ({ - 10 + 10})^{2} } \\ = \sqrt{ ({ - 4})^{2} + 0} \\ = \sqrt{16} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]We have the final answer as
4 unitsHope this helps you
Which expression represents the phrase “twice the quotient of 50 and a sum of a number y and 8
Answers
Answer:
2 * 50/(y + 8)
Step-by-step explanation:
"twice the quotient of 50 and a sum of a number y and 8"
y + 8
"twice the quotient of 50 and a sum of a number y and 8"
50/(y + 8)
"twice the quotient of 50 and a sum of a number y and 8"
2 * 50/(y + 8)
Answer:
2*50/ (8+y)
Step-by-step explanation:
twice the quotient of 50=2*50 divided by something
the sum of a number= y and 8
So... 2*50/ (8+y) is the answer
3) Walt and 23 of his friends are going on a month-long
camping trip. Bags of marshmallows come with about 38
marshmallows per bag. They decide to bring 12 bags of
marshmallows to the trip. How many marshmallows will
each person get if they each eat the same number of
marshmallows and eat all of the marshmallows at camp?
Answers
Answer:
19 marshmallows per person.
Step-by-step explanation:
So, 38 marshmallows per bag and 12 bags were brought.
38 x 12 = 456
Walt and 23 of his friends - 24 people
456/24 = 19 marshmallows
18 cans of soda cost $6.48. What is the cost per can in dollars? Please help, I'm in a hurry
Answers
Answer:
36 cents
Step-by-step explanation:
In order to figure out how much one can cost you need to do 6.48/18 which then gets you 33 cents, the cost of one can.
-6=-2+w solve the equation
Answers
Answer:
w = -4
Step-by-step explanation:
Answer:
w = -4
Step-by-step explanation:
[tex]-6=-2+w\\[/tex]
Switch sides
[tex]-2+w=-6[/tex]
Add 2 to both sides
[tex]-2+w+2=-6+2[/tex]
Simplify
[tex]w=-4[/tex]
Evaluate: 20/ 5·2^-3
Answers
0.125 x 5 = 0.625
20/0.625 = 32
The answer is 32.
Step-by-step explanation:
[tex] = \frac{20}{5} . {2}^{ - 3} [/tex]
[tex] = 4. \frac{1}{ {2}^{3} } [/tex]
[tex] = \frac{4}{2 \times 2 \times 2} [/tex]
[tex] = \frac{4}{8} [/tex]
[tex] = \frac{1}{2} [/tex]
Help Plzzz.........
Answers
Answer:
£7448
Step-by-step explanation:
Simple interest (I) is calculated as
I = [tex]\frac{PRT}{100}[/tex]
P is principle ( amount invested), R is rate of interest and T is time in years.
Here P = £5600, R = 11 and T = 3 , thus
I = [tex]\frac{5600(11)3)}{100}[/tex] = £1648
Value after 3 years = £5600 + £1848 = £7448
1. The subsets of the real numbers can be represented in a Venn diagram as shown. To which subsets of real numbers does 12 belong? A) Integers and Whole Numbers only B) Rational Numbers, Integers, and Whole Numbers C) Rational Numbers and Integers only D) Irrational Numbers, Integers, and Whole Numbers 2. Which statement BEST describes the relationship between whole numbers and natural numbers shown in the diagram? A) The diagram shows that whole numbers are a subset of natural numbers, because all whole numbers are natural numbers. B) The diagram shows that natural numbers are a subset of whole numbers, because all natural numbers are whole numbers. C) The diagram shows that whole numbers are a subset of natural numbers, because some whole numbers are not natural numbers. D) The diagram shows that natural numbers are a subset of whole numbers, because all whole numbers and natural numbers have no numbers in common.
Answers
2. D) The diagram shows that natural numbers are a subset of whole numbers, because all whole numbers and natural numbers have no numbers in c
1. C) Rational Numbers and Integers only
2. D) The diagram shows that natural numbers are a subset of whole numbers, because all whole numbers and natural numbers have no numbers in c.
In mathematics, a rational number is a number such as −3/7 that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Every integer is a rational number: for example, 5 = 5/1
4√2 + √2 with work
8√3 - 4√3 with work
2√3 x √32 with work
Answers
Step-by-step explanation:
4√2 + √2 = 5√2 we add 4 and the invisible 1 in front of √2, the common root stays same
8√3 - 4√3 = 4√3 subtract 4 from 8 the common root stays same
2√3 x √32 ➡ 2√3 x 4√3 too add the expressions we first need to make the roots common then add 4 and 2
Answer:
1. [tex]5\sqrt{2}[/tex]
2. [tex]4\sqrt{3}[/tex]
3. [tex]8\sqrt{6}[/tex]
Step-by-step explanation:
Number 1:
We can treat [tex]\sqrt{2}[/tex] as a variable in which we are multiplying 4 by. Let's call [tex]\sqrt{2}[/tex] x.
This makes our expression [tex]4x + x[/tex]. Combining like terms, we get [tex]5x[/tex]. This means that [tex]4\sqrt{2} + \sqrt{2} = 5\sqrt{2}[/tex].
Number 2:
Again, we can use the same logic as we did in number 1. Let's treat [tex]\sqrt{3}[/tex] as a variable y.
[tex]8y-4y[/tex]
Subtracting a y term from a y term will equal the difference between the coefficients times y. So it's [tex]4y[/tex]. This means that [tex]8\sqrt{3}-4\sqrt{3}=4\sqrt{3}[/tex]
Number 3:
When we multiply radicals, we want to put the radicals in [tex]\sqrt{x}[/tex] form.
[tex]\sqrt{32}[/tex] is already in this form.
However [tex]2\sqrt{3}[/tex] is not.
[tex]2\sqrt{3}[/tex] is the same thing as [tex]\sqrt{3\cdot2^2} = \sqrt{3\cdot4} = \sqrt{12}[/tex].
Now we multiply these radicals by multiply the term inside the square root sign
[tex]\sqrt{32}\cdot\sqrt{12}=\sqrt{32\cdot12} =\sqrt{384}[/tex]
384 is divisible by 64, so:
[tex]\sqrt{384} = \sqrt{64\cdot6} = 8\sqrt{6}[/tex]
Hope this helped!
What is the solution to this equation?
Answers
Answer:
x = -7/2
Step-by-step explanation:
(1/4) ^ (x+1) = 32
Rewriting 32 as 2^5 and 1/4 and 2^-2
2^-2 ^ (x+1) = 2^5
We know that a^b^c = a^ ( b*c)
2 ^ (-2x-2) = 2 ^ 5
Since the bases are the same, the exponents have to be the same
-2x-2 = 5
Add 2 to each side
-2x = 7
Divide by -2
x = -7/2
10k4 ⋅ (−9k3) how to solve this
Answers
Answer:
The product of the terms in the given expression is -90k⁷
Step-by-step explanation:
10k⁴ · (-9k³)
When we multiply exponents, then we are going to add the exponential together. So, we will add 4 and 3 together which is 7. Since our base numbers are different, then we also multiply them together. So, we will multiply 10 by -9 which is -90.
-90k⁷
You want to put a logo on each cell phone holder you make. Sew-on logos cost 2.30 for 10. Stick-on logos cost 9.40 for 100. Divide the cost by the number of logos for both types
Answers
Answer:
[tex]Rate = \$0.23[/tex] and [tex]Rate = \$0.094[/tex]
Step-by-step explanation:
Given
Sew-on logos
Cost = $2.30
Units = 10
Stick-on logos
Cost = $9.40
Units = 100
Required
Divide cost by units, in both cases
When we divide cost by units, it gives the unit rate.
i.e.
[tex]Rate = \frac{Cost}{Units}[/tex]
FOR SEW-ON LOGOS
Substitute $2.30 for Cost and 10 for Units
[tex]Rate = \frac{\$2.30}{10}[/tex]
[tex]Rate = \$0.23[/tex]
FOR STICK-ON LOGOS
Substitute $9.40 for Cost and 100 for Units
[tex]Rate = \frac{\$9.40}{100}[/tex]
[tex]Rate = \$0.094[/tex]
Hence, the solution is
[tex]Rate = \$0.23[/tex] and [tex]Rate = \$0.094[/tex]
Find the value of x in the equation below. 12+x = 16.7
Answers
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 4.7}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{12 + x = 16.7}[/tex]
Move 12 to right hand side and change it's sign
[tex] \dashrightarrow{ \sf{x = 16.7 - 12}}[/tex]
Subtract 12 from 16.7
[tex] \dashrightarrow{ \sf{4.7}}[/tex]
Hope I helped!
Best regards!
Answer:
[tex]\huge\boxed{\sf x = 4.7}[/tex]
Step-by-step explanation:
12 + x = 16.7
Subtracting 12 to both sides
x = 16.7 - 12
x = 4.7
What is the approximate value of this square root?
Answers
Answer:
12.1
Step-by-step explanation:
To approximate this value, we simply need to know some perfect squares. We know that the value 144 is the perfect square of 12. And we know the value 169 is the perfect square of 13.
Note, that our value, 146 is far closer to 144 than to 169, so we know that we will be close to 12 as our approximation.
The distance from 144 to 146 is 2, while the distance from 169 to 146 is 23.
A rough fractional approximation can be found with 2/23 approximately 0.08.
For the solution then, our approximation of sqrt(146) ~= 12.08 ~= 12.1
Cheers.
A lawn company advertises that they can spread 7,500 square feet of grass seed in 2 and a half hours. Find the number of square feet of grass seed that can be spread per hour.
Answers
Answer:
3000 square feet
Step-by-step explanation:
Divide 7,500 by 2.5:
7500/2.5
= 3000
So, 3000 square feet of grass seed can be spread per hour
Isabel need to cut a square piece of wood with the area of 70 in.² approximate the size of the square round to the nearest 10th of a inch
Answers
Answer:
8.4 in by 8.4 in
Step-by-step explanation:
The area of a square is the side length squared.
Let s be the side length:
s^2 = 70
s = \sqrt(70) = 8.4 in
A company needs two loads of sand to make an indoor beach area when employee picnic one load of sand weigh 4 tons and the other load Waze 7500 pounds what is the total weight of sand in pounds
Answers
Answer:
15500 pounds
Step-by-step explanation:
The weight of one load is 4 tons and the weight of other load is 7500 pounds.
We know that, 1 ton = 2000 pounds
4 tons = 8000 pounds
Total weight = 8000 pounds + 7500 pounds
Total weight = 15500 pounds
So, the total weight of sand is 15500 pounds.
The second side of a triangular deck is 3 feet longer than the shortest side, and the third side is3 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 52 feet, what are the lengths of the three sides?
Answers
Answer:
13, 16, 23
Step-by-step explanation:
The first side is x.
The second side is x + 3
The third side is 2x - 3
(x) + (x +3) + (2x - 3) = 4x
4x = 52
x = 13
Consider a rectangle with width of x units and an area of 10 square units. The length l of the rectangle can be modeled by the function l(x)=10/x. Suppose the width of the rectangle increases 1 unit while the area remains constant. Which graph models the length of the new rectangle
Answers
Answer: answer is C
Step-by-step explanation:
The question asks us to find the a graph which represents the width of the rectangle increasing by 1 unit while the area remains constant. The best graph to model this, would be answer choice C
8(7x-2)=96 What is X
Answers
Answer:
x = 2
Step-by-step explanation:
8(7x-2)=96
7x-2 = 96 : 8
7x-2 = 12
7x = 12 +2
7x = 14
x = 14 : 7
x = 2
Answer:
x=2Step-by-step explanation:
[tex]8\left(7x-2\right)=96\\\\\mathrm{Divide\:both\:sides\:by\:}8\\\frac{8\left(7x-2\right)}{8}=\frac{96}{8}\\\\Simplify\\7x-2=12\\\\Add\:2\:to\:both\:sides\\7x-2+2=12+2\\\\Simplify\\7x=14\\\\\mathrm{Divide\:both\:sides\:by\:}7\\\frac{7x}{7}=\frac{14}{7}\\\\Simplify\\x=2[/tex]
Given that a rectangle has a length of 5/2x + 10 with a width of 5/2x + 5, formulate an expression to represents the area of the rectangle.
Answers
Answer:
A = ²⁵/₄x² + ⁷⁵/₂x + 50Step-by-step explanation:
L = ⁵/₂x + 10
W = ⁵/₂x + 5
A = L•W
A = (⁵/₂x + 10)(⁵/₂x + 5)
A = ⁵/₂x•⁵/₂x + ⁵/₂x•5 + 10•⁵/₂x + 10•5
A = ²⁵/₄x² + ²⁵/₂x + ⁵⁰/₂x + 50
A = ²⁵/₄x² + ⁷⁵/₂x + 50
Or if yoy mean:
L = 5/(2x) + 10
W = 5/(2x) + 5
A = [5/(2x) + 10][5/(2x) + 5] = 25/(4x²) + 75/(2x) + 50
rewrite expression in the form k*z^n
Answers
Answer:
9z
Step-by-step explanation:
4th root of z = z^1/4
=> 3 * z^1/4
=> 3z^1/4
3z^1/4 * 3z^3/4
=> 3 x 3 x z^1/4 + 3/4
=> 9z^4/4
=> 9z^1
=> 9z
The expression [tex]3\sqrt[4]{z}~.~3z^{\frac{3}{4} }[/tex] in the form k . [tex]z^{n}[/tex] is 9z.
We are given:
= [tex]3\sqrt[4]{z}~.~3z^{\frac{3}{4} }[/tex]
We need to write this in the form of :
= [tex]k~.~z^{n}[/tex]
What are exponents and powers?We use exponents and powers when we want to write very large numbers or very small numbers in a simplified manner.
Example:
8 = 2 x 2 x 2 = [tex]2^{3}[/tex].
Where 2 is the base and 3 is the exponents.
72 = 8 x 9 = [tex]2^{3} \times3^{2}[/tex].
Here we have two bases 2 and 3 and two exponents 3 and 2.
8 / 9 = [tex]\frac{2^{3} }{3^{2} }[/tex] = [tex]2^{3} \times3^{-2}[/tex].
Here the bases are 2 and 3 and exponents are 3 and -2.
We have
[tex]3\sqrt[4]{z}~.~3z^{\frac{3}{4} }[/tex]
Here,
[tex]\sqrt[4]{z}[/tex] can be written as [tex]z^{\frac{1}{4} }[/tex].
[tex]z^{\frac{1}{4} }~.~z^{\frac{3}{4} }[/tex] can be written as :
[tex]z^{\frac{1}{4} +\frac{3}{4} }\\\\ z^{\frac{4}{4} } \\\\z^{1} = z[/tex]
Now we have,
3 x 3 x [tex]z^{\frac{1}{4} }[/tex] x [tex]z^{\frac{3}{4} }[/tex]
3 x 3 x z
[tex]3^{2}[/tex] x z
9 x [tex]z^{1}[/tex]
So, comparing with k . [tex]z^{n}[/tex]
we have,
k = 9 and n = 1.
The expression [tex]3\sqrt[4]{z}~.~3z^{\frac{3}{4} }[/tex] in the form k . [tex]z^{n}[/tex] is 9z.
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