Answers
(a) [tex]a+b-c\\-2+-3-4\\-5-4\\-9[/tex]
(b) [tex]b+c^3\\-3+4^3\\-3+64\\61[/tex]
(c)[tex]\frac{3b^2-c^2+a^2}{-3abc} \\\frac{3(-3)^2-(4)^2+(-2)^2}{-3(-2)(-3)(4)} \\\frac{3(9)-16+4}{6(-3)(4)} \\\frac{27-16+4}{-18(4)} \\\frac{11+4}{-72} \\\frac{15}{-72} \\-\frac{5}{24}[/tex]
Answer:
The answer to (A) is -9.
The answer to (B) is 61.
The answer to (C) is [tex]-\frac{5}{24}[/tex] in fraction form or -0.208 in decimal form.
Step-by-step explanation:
For problem (A), which is [tex]a+b-c[/tex], in order to solve for this problem, plug in the information given from the question. The problem will look like [tex](-2)+(-3)-(4)[/tex]. Solve the problem by first adding (-2) + (-3), which equals (-5), and then, solve for (-5) -(4), which equals -9. The final answer for problem (A) will be -9.
For problem (B), which is [tex]b+c^{3}[/tex], start by plugging in the information given from the question. The problem will look like [tex](-3)+(4)^{3}[/tex]. Solve the problem by cubing 4, which equals 64, and then, solve for (-3)+(64), which equals 61. The final answer for problem (B) will be 61.
For problem (C), which is [tex]\frac{3b^{2}-c^{2}+a^{2} }{-3abc}[/tex], start by plugging in the information given from the question. The problem will look like [tex]\frac{3(-3)^{2}-(4)^{2}+(-2)^{2} }{-3(-2)(-3)(4)}[/tex]. Solve the problem by first simplifying the numerator.
To simplify the numerator, raise -3 to the power of 2, which will equal 9, and multiplying 3 by 9, which will look like [tex]\frac{27-(4)^{2}+(-2)^{2} }{-3(-2)(-3)(4)}[/tex]. Next, raise 4 to the power of 2, which equals 16, and multiply -1 by 16, which will look like [tex]\frac{27-16+(-2)^{2} }{-3(-2)(-3)(4)}[/tex]. The next step is to raise -2 to the power of 2, which will look like [tex]\frac{27-16+4 }{-3(-2)(-3)(4)}[/tex]. Then, subtract 16 from 27, which equals 11, and add (11) + (4), which equals 15. The numerator equals 15.
Next, simplify the denominator. First, multiply -3 by -2, which equals 6, and the problem will look like [tex]\frac{27-16+4 }{6(-3)(4)}[/tex]. Then, multiply 6 by -3, which equals -18, and the problem will look like [tex]\frac{27-16+4 }{-18(4)}[/tex]. The next step is to multiply -18 by 4, which equals -72, and the denominator will equal -72.
Then, reduce the expression by cancelling the common factor, and the common factor is 3. The final answer will be [tex]-\frac{5}{24}[/tex] in fraction form or -0.208 in decimal form.
Related Questions
The point-slope form of the equation of the line that passes through (-9,-2) and (1,3) is y-3=1/2(x-1) what is the slope-intercept form of the equation for this line
Answers
Answer:
y = (1/2)x + 2 1/2
Step-by-step explanation:
y - 3 = (1/2)(x - 1)
Distribute the 1/2
y - 3 = (1/2)x - 1/2
Add 3 to both sides
y = (1/2)x + 2 1/2
83 in scientific notation
Answers
Answer:
8.3 x 10^1
hope this helps
have a good day :)
Step-by-step explanation:
Leon verified that the side lengths 21, 28, 35 form a Pythagorean triple using this procedure. Step 1: Find the greatest common factor of the given lengths: 7 Step 2: Divide the given lengths by the greatest common factor: 3, 4, 5 Step 3: Verify that the lengths found in step 2 form a Pythagorean triple: 3 squared + 4 squared = 9 + 16 = 25 = 5 squared Leon states that 21, 28, 35 is a Pythagorean triple because the lengths found in step 2 form a Pythagorean triple. Which explains whether or not Leon is correct? Yes, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple. Yes, any set of lengths with a common factor is a Pythagorean triple. No, the lengths of Pythagorean triples cannot have any common factors. No, the given side lengths can form a Pythagorean triple even if the lengths found in step 2 do not.
Answers
Answer:
Yes, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple
Step-by-step explanation:
The given side lengths are;
21, 28, and 35
From the given side lengths, the greatest common factor = 7
Therefore, we have;
3 × 7, 4 × 7, and 5 × 7
A Pythagorean triple is formed by three numbers, 'a', 'b', and, 'c', which are both positive and integers, that are related as follows;
c² = a² + b²
Therefore, for the three numbers, we get;
3, 4, and 5 is a Pythagorean triple
5² = 3² + 4²
Multiplying both sides by 7² gives;
(5)² × (7)² = (3)² × (7)² + (4)² × (7)²
By the laws of indices, (a·b)ⁿ = aⁿ × bⁿ
Therefore;
(5 × 7)² = (3 × 7)² + (4 × 7)²
Therefore, multiplying every length of the Pythagorean triple by the same whole number results in a Pythagorean triple.
(The relationship can also be shown using similar triangles, as multiplying the side lengths of a triangle by the same whole number, gives a similar triangle, having the same relationship between its sides)
A circle has a circumference of 616 cm.
What is the approximate radius of the circle? (Use 22/7
as an estimate for pi.)
A 14 cm
B. 49 cm
C. 98 cm
D. 196 cm
Answers
Answer:
π =14 cm
Step-by-step explanation:
Given:
circumference of a circle =616 cm
pie(π)=22/7
circumference of a circle=πr^2
616=22/7 *r^2
616*7/22 =r^2
4312/22 =r^2
196=r^2
[tex]\sqrt{196}[/tex] =r
14 =r
Simplify each of the following by rationalizing the denominator.
please do answer my doubt
Answers
Answer:
(47+21√5)/2
Step-by-step explanation:
Given the expression
7+3√5/7-3√5
= 7+3√5/7-3√5 * (7+3√5)/(7+3√5)
= 49+21√5+21√5+9(5)/[7(7)-9(5)]
= 49+42√5+45/49-45
= 94+42√5/4
= 2(47+21√5)/4
=(47+21√5)/2
Hence the required expression is (47+21√5)/2
michelle has three textbooks each way 5/8 pounds what is the total weight of her textbook
Answers
Answer:
1 and 7/8 pounds
Step-by-step explanation:
There are 3 textbooks that each weigh 5/8 of a pound
3*5/8=15/8
1 and 7/8
quadrilateral BANK is a parallelogram. if AB= 10cm and AN= 6cm, what is the length of NK?
guys patulong, thanks!
Answers
Answer:
The length of NK is 10 cm.
Answer:
10 cm
Step-by-step explanation:
In parallelogram, opposite sides are parallel and equal.
AB and NK are opposite sides
So, NK = AB = 10cm
(Trigonometry) Find the values of x and y. Round your answers to the nearest tenth.
Answers
Answer:
[tex]x = 38.1[/tex]
[tex]y = 23.4[/tex]
Step-by-step explanation:
The given triangle is a right triangle. This is indicated by the box around one of the angles, signifying that the angle measure is (9) degrees. By its definition, a right triangle is a triangle with a (90) degree angle, thus the given triangle is a right triangle. In this situation, one can use right-angle trigonometry to find the value of the unknown side. In essence, right triangle trigonometry provides one with a series of ratios to describe the relationship between the sides and angles of the right trinagle. These ratios are the following,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]
Keep in mind that the way a side is named is relative to the angle it is being described from. Thus, the (opposite) and (adjacent) sides acquire different names based on the angle relative to them. However, the (hypotenuse) is the hypotenuse no matter the angle, as the hypotenuse is the side opposite the right angle.
Solve for (y) first. One is given the angle measure and the measure of the side opposite the angle measure. One is asked to find the measure of the side adjacent to the angle. Use the ratio of tangent (tan) to achieve this.
[tex]tan(\theta)=\frac{opposite}{adajcent}\\[/tex]
Substitute,
[tex]tan(52)=\frac{30}{y}[/tex]
Inverse operations,
[tex]y=\frac{30}{tan(52)}[/tex]
Simplify,
[tex]y = 23.4386[/tex]
Now solve for the hypotenuse (x). One could use the Pythagorean theorem to do this, but since this is trigonometry, one might as well use the trigonometric ratios. One is given an angle, as well as the side opposite the angle, one is asked to find the hypotenuse. To do this, one can use the trigonometric ratio of sine (sin).
[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
Substitute,
[tex]sin(52)=\frac{30}{x}[/tex]
Inverse operations,
[tex]x=\frac{30}{sin(52)}[/tex]
Simplify,
[tex]x = 38.0705[/tex]
Which one of the following represents exponential growth?
A: y = (48000)(.05)^x
B: y = (48000)(.95)^x
C: y = 2400(.05)^x
D: y = (48000)(1.05)^x
Answers
Subtract the given polynomials using the vertical format.
Answers
===========================================
Explanation:
The negative out front of the parenthesis will swap the sign of each term. That means -3c^3 becomes +3c^3, or simply 3c^3. The other terms in the parenthesis are handled the same way.
After distributing the negative through, we add straight down.
The 7c^3+3c^3 becomes 10c^3
Then we have -5c^2+(-2c^2) become -7c^2
Finally, 2c+2c simplifies to 4c
Answer:
10C³-7C²+4C
7c³-(-3c³) -5c²-(+2c²) +2c-(-2c)
When factored completely, which is a factor of 6x^3-12x^2-48x?
Answers
Answer: C
Step-by-step explanation:
The solution is Option A.
The value of the equation is 6x³ - 12x² - 48x is A = 6x ( x + 2 ) ( x - 4 )
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = 6x³ - 12x² - 48x be equation (1)
On simplifying the equation , we get
Taking 6x as the common factor , we get
A = 6x ( x² - 2x - 8 )
On simplifying the equation , we get
A = 6x ( x + 2 ) ( x - 4 )
Therefore , the value of A is 6x ( x + 2 ) ( x - 4 )
Hence , the equation is 6x ( x + 2 ) ( x - 4 )
To learn more about equations click :
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What is the solution to the system of equations
Answers
Step-by-step explanation:
[tex]5x + 3y = 13 \\ 7x + 8y = - 16 \\ 5x = 13 - 3y \\ x = \frac{13 - 3y}{5} \\ 7( \frac{13 - 3y}{5} ) + 8y = - 16 \\ 18.2 - 4.2y + 8y = - 16 \\ 3.8y = - 34.2 \\ y = - 9 \\[/tex]
[tex] x = \frac{13 - 3( - 9)}{5} = \frac{13 + 27}{5} = \frac{40}{5} = 8 \\ x = 8 \\ y = - 9[/tex]
Evaluate the following expression at x = -5
-2x-3
Answers
Answer:
7.
Step-by-step explanation:
-5 x -2 = 10 (2 negatives being multiplies = positive)
Then, 10 - 3 = 7.
A regular polygon of (2A+ 1) sides has 140°
as the size of each
interior angle. Find A
Answers
Answer:
Ext angles = 40 degs 360/40 = 9 sides
Step-by-step explanation:
between which 2 square roots does 7 lie
6,7
23,30
32,43
45,60
Answers
Answer:
32, 43
Step-by-step explanation:
Your welcome! :)
Answer:
The answer is 45,60.
Step-by-step explanation:
We can use a square chart to answer this question.
I will zoom in to the particular ones we need.
[tex] {6}^{2} = 36[/tex]
[tex]{7}^{2} = 49[/tex]
[tex] {8}^{2} = 64[/tex]
7 is the square root of 49.
45 lies in between 36 and 49 so its square root is more than 6 but less than 7. It is around 6.708 to the nearest thousandth.
Meanwhile, 60 lies in between 49 and 64 so its square root is more than 7 but less than 8. It is around 7.746 to the nearest thousandth.
Hence, we can say that 7 lies in between the square root of 45 and the square root of 60.
The number of boxes in Warehouse "A" currently totaling 476 is increasing at a rate of 4 boxes per day. The number of boxes in Warehouse "B" currently totaling 986 is decreasing at a rate of 6 boxes per day. In how many days will these two warehouses contain the same number of boxes
Answers
Answer:
These two warehouses will contain the same number of boxes in 51 days.
Step-by-step explanation:
Since the number of boxes in Warehouse "A" currently totaling 476 is increasing at a rate of 4 boxes per day, while the number of boxes in Warehouse "B" currently totaling 986 is decreasing at a rate of 6 boxes per day, To determine in how many days these two warehouses contain the same number of boxes, the following calculation must be performed:
Warehouse A = 476 + 4X
Warehouse B = 986 - 6X
476 + 4 x 50 = 476 + 200 = 676
986 - 6 x 50 = 986 - 300 = 686
476 + 4 x 51 = 476 + 204 = 680
986 - 6 x 51 = 986 - 306 = 680
Therefore, these two warehouses will contain the same number of boxes in 51 days.
A school has 833 students. Of those students, 463 play a sport (A), 52 are in the band (B), and 21 do both(AB). (C) represents neither.
Answers
Answer:
Im sorry but it is kind of confusing
Step-by-step explanation:
data distribution lol
Answers
Answer:
The range of the value of numbers is 8
Step-by-step explanation:
Mathematically, the range refers to the difference between the biggest and the smallest number
From the diagram, the biggest number is 13and the smallest is 5
The difference between this two is the range
we have this as 13 -5 = 8
PLEASE PLEASE I RLY NEED HELP ...... ....... . .. . . . . . . . . .... . . . Pick three Enlightenment thinkers and explain how they inspired America’s founders.
Answers
Answer:
Enlightenment philosophers John Locke, Charles Montesquieu, and Jean-Jacques Rousseau all developed theories of government in which some or even all the people would govern. These thinkers had a profound effect on the American and French revolutions and the democratic governments that they produced.
I am guessing your in the same situation as me sweeping across the internet for help in our summer school history classes well I found this hope it helps
I will give BRAINLIEST to the correct answer
Find the measure of angle 5
Answers
Answer:
84
Step-by-step explanation:
1 is = 84 since its a vertical angle.
5= 84 since its the corresponding angle in this tranversal.
Hoped this helped,
JoeLouis2
what does the scale 1:500 000 mean
Answers
A scale of 1:5000000 means that:
This is mainly used in map or shadow etc. things.
For example in map it is given that the scale is 1mm:5000000mm, then it means that 1mm on the map is equal to 5000000mm in real life. So, you can be asked what does 5mm on map means in real life. So, you have to solve like this:
5 × 5000000 = real life size
25000000mm = real life size
In shadow like question, it can be asked that if 5000000 m of building casts a shadow of 1 m, then how much will be the shadow of a 10000000 m building. So, you have to solve it like this:
(10000000/5000000) × 1 = shadow size
=> 2 × 1 = shadow size
=> 2m = shadow size
You can tell me the specific questions so that I can help.
The scale 1:500 000 means 1 unit on a map represents 500000 in real life
What are scales?Scales are used to represent big or small measurements on a map or graph
How to interpret the scale?The scale is given as:
1:500 000
The above means that:
1 unit on a map represents 500000 in real life
Read more about scale at:
https://brainly.com/question/3457976
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what is the following product ? (sqrt14-sqrt3)(sqrt12+sqrt7)
Answers
Answer:
Step-by-step explanation:
[tex](\sqrt{14}-\sqrt{3})(\sqrt{12}+\sqrt{7})=\sqrt{14}*\sqrt{12}+\sqrt{14}*\sqrt{7}-\sqrt{3} *\sqrt{12}-\sqrt{3} *\sqrt{7}\\\\=\sqrt{14*12} + \sqrt{14*7}-\sqrt{3*12}-\sqrt{3*7}\\\\=\sqrt{2*7*2*2*3} + \sqrt{2*7*7}-\sqrt{3*3*2*2}-\sqrt{3*7}\\\\=2\sqrt{2*7*3}+7\sqrt{2}-3*2-\sqrt{21}\\\\= 2\sqrt{42}+7\sqrt{2}-6-\sqrt{21}[/tex]
The following expressions are factorizations of 60. Which is the prime factorization?
Answers
Answer:
d
Step-by-step explanation:
press 60 on your casio calculator then the equal sign then shift and then 3rd row this button ".,,," which means factorise
Solve the following system by graphing and identify the point of intersection -2x - y=-12 2x-3y=4
Answers
Answer:
{x,y} ={10,-8}
Step-by-step explanation:
hope it help please mark me as brinnelist
1. Suly watched a film that was 90 minutes long. 1/6 of the way through the film, the
doorbell rang. The pizza man had arrived with the order.
How many minutes of the film had she watched before the pizza man arrived?
(3 marks)
a.
Answers
Answer:
15 minutes
Step-by-step explanation:
Suly watched a film that was 90 minutes long. Then, she stopped at the [tex]\frac{1}{6}[/tex]mark. This means that we have to find [tex]\frac{1}{6}[/tex] of 90 minutes to find the amount of time Suly watched before the pizza man arrived. So therefore, the answer is 15 minutes.
Have a nice day. : )
Answer:
15 minutes
Step-by-step explanation:
Given:
The film Suly is watching is 90 minutes longSuly watched 1/6 of the film before the pizza man arrivedSteps:
90/6=15Question
Patrick has 4 green hats, 3 blue hats, and 1 orange hat. If he selects a hat at random, what is the
probability of selecting a green hat?
.
0.4
O 0.5
O 0.8
Answers
Answer:
0.5
Step-by-step explanation:
First we need to find the total number of hats 4 green hats + 3 blue hats + 1 orange hat = 8 hats P( green hat) = green / total
= 4 / 8
= 1/2
does anyone understand this or can anyone explain what i need to do please ?? there’s no instructions
Answers
Answer:
nah man... good luck tho
help me solve this with explanation
Answers
Answer:
x = 19
<6 = 109
<7 = 109
Step-by-step explanation:
Angles 6 and 7 are vertical angles so they are equal
7x -24 = 5x+14
Subtract 5x from each side
7x-5x -24 = 5x-5x+14
2x-24 = 14
Add 24 to each side
2x-24 +24 = 14+24
2x = 38
Divide by 2
2x/2 = 38/2
x = 19
<6 = 7x -24 = 7*19 -24 = 109
<7 = 5(19)+14 = 109
Help!’!!!!!!!!! And thanksss
Answers
5 people are going to a dinner party. Each person at the party will eat 23 pounds of turkey. If you can only buy whole pounds of turkey, how many pounds should you buy?
