When working with unknowable numbers, we can simplify equations by using the distributive property. If the equation be 10x² - (9x + 4x²) + 7 + (5x - 8) then we get 6x² - 4x - 1.
What is meant by distributive law?The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.
Let the equation be 10x² - (9x + 4x²) + 7 + (5x - 8)
Apply rule: a +(b + c) = a + b + c
7 + (5x - 8) = 7 + 5x - 8
= 10 x²- (9 x + 4 x²) + 7 + 5x - 8
simplifying the above equation, we get
= -(9x + 4x²) + 10x² + 5x + 7 - 8
Subtract the numbers: 7 - 8 = -1
= -(9x + 4x²) + 10x² + 5x - 1
Apply the distributive law: -(a + b) = -a - b = 0
-(9x + 4x²) = - 9x - 4x²
= -9x - 4x² + 10x² + 5x - 1
Add similar elements:
-4x² + 10x² = 6x² = -9x + 6x² + 5x - 1
simplifying the above equation, we get
= 6x² - 9x + 5x - 1
Add similar elements: -9x + 5x = -4x
= 6x² - 4x - 1
Therefore, by simplifying the equation, we get 6x² - 4x - 1.
The complete question is:
Simplify 10x² - (9x + 4x²) + 7 + (5x - 8)
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I need help I’m stuck on this
question
x-c/2=d , for x
Answer:
I will answer this asap give me a few mins
Step-by-step explanation:
nun yet
Answer:
x = c/2 + d
Step-by-step explanation:
33-(2c+4)=2(c +7)+c
what is C?
Answer:
x=4.6
Step-by-step explanation:
Because we are finding C, first use the distributive property.
33-(2c+4)=2(c+7)+c can turn into:
33-2c+4=2c+14+c
Now, combine like terms.
33+4=37
2c+c=3c
Now you are left with:
37-2c=3c+14
Now, add 2c on both sides.
37=5x+14
Next, subtract 14 on both sides.
37-14=23
23=5x
Finally, divide by 5 on both sides
x=4.6
For what value of x is sin ( x ) = cos 62, where 0 < x < 90?
Answer:
x = 28°
Step-by-step explanation:
using the cofunction identity
cos x = sin(90 - x) , then
cos62° = sin(90 - 62)° = sin28°
Which of the following combinations could
be three sides of a triangle?
Answer:
C
D
1,2,3,4,5,6 And 7
Step-by-step explanation:
1. By the nature of triangles, the sum of the two sides has to be greater than the third and the difference between two sides has to be less than the third side.
A. 5+6=11 Wrong
B. 1+3<5 Wrong
C. 5+16>20 Right
16-5<20
D.7+7=14 Wrong
2. Two sides of a Triangle are 15 and 8
A. 8+9>15 15-8<9 Can
B. 8+13>15 15-8<13 Can
C. 15+8>21 21-8<15 Can
D. 15+8<25 Cannot
3. According to the Trilateral Relation of Triangle
Let's say the length of the third side is X (X≠Z)
i. 4-4<x x>8 0<X>8 (X≠Z)
4-4>x x<8
i. In 0,1,2,3,4,5,6,7,8,9,10
X could be 1,2,3,4,5,6, and 7
TRIANGLE
A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon.
Each triangle has three sides and three angles, with some of the angles being the same.
In the case of a right triangle, the side opposite the right angle is known as the hypotenuse, while the other two sides are known as the legs.
Trilateral Relationship of Triangle
A trilateral is a shape with three sides in geometry. 'Of trilateral figures, an equilateral triangle is one with three equal sides, an isosceles triangle is one with two equal sides, and a scalene triangle is one with three unequal sides.'
Triangle Inequality
The triangle inequality asserts that the sum of the lengths of any two sides of a triangle must be larger than or equal to the length of the remaining side in mathematics.
The condition of the triangle's sides
According to the triangle inequality, the lengths of any two triangle sides must be more than or equal to the length of the third side. Only a degenerate triangle with collinear vertices can have that total equal to the length of the third side.
If and only if the side lengths satisfy the triangle inequality, a triangle with three given positive side lengths exists.
PLEASE HELP MEEE !!!!!!!!!!!!!!!!!!
Answer:
x=20 degrees
I did what your teacher did down there; I added all the exterior angles and set them equal to 360°
Just combined the like terms and got the answer!
*3x + 4x + 3x = 10x
12 - 10 - 2 = 0
90 + 70 = 160
Put them "as an equation": 10x + 160 = 360
Get rid of what's surrounding the x, so subtract 160 from both sides.
10x = 200
To get rid of whats beside the x *again*, divided 10x by 10 on both sides.
x = 20
Hi I need help ASAP please and thank you
Answer: what’s the question? :D
Step-by-step explanation:
Kelly used a calculator to multiply large numbers. How can she write the number on her calculator screen in standard form? 3.15 E15
Kelly multiplied big number with a calculator. 3.15e-15 number on calculator means or 3.15e-15 in standard form is: 0.00000000000000315.
Given that,
Kelly multiplied big number with a calculator.
We have to find the standard form of 3.15e-15.
3.15e-15 is written in scientific notation, often called standard form. used to express big or tiny numbers differently.
3.15 = coefficient
e = 10 to the power of
-15 = exponent
We get, The standard form as
= 3.15e-15
= 3.15 × [tex]10^{-15}[/tex]
= 0.00000000000000315
Therefore, 3.15e-15 number on calculator means or 3.15e-15 in standard form is: 0.00000000000000315
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Answer:3,500,000,000,000,000
Step-by-step explanation:
3.5x10^15=3,500,000,000,000,000
a card is drawn randomly from a standard 52-card deck. find the probability of the given event. (a) the card drawn is 3 the probability is : (b) the card drawn is a face card (jack, queen, or king) the probability is : (c) the card drawn is not a face card. the probability is :
A card is drawn randomly from a standard 52-card deck. then the probabilities are a) 1/13 b) 3/13 and c) 10/13
There are four 3's in the deck. This means that, from 52 possible cards to drawn, we have 4 chances of drawing a 3. This means that the probability will be:
p = 4/52
p= 1/13
b.
For every suit, there are three face cards, J, Q and K. There are 4 suits, so, the total number of face cards its:
4*3 =12
The total possible cards are, still, 52, so, the probability will be
p= 12/52
p=3/13
c.
We know that the card drawn must be a face card, o not being a face card. There is no third choice here. So, the probability of drawing a face card OR not drawing a face card its:
p=52/52
p=1
so
p( the card is a face card ) + p( the card is not a face card) =1
but, we know that
p( the card is a face card ) =3/13
so
p( the card is not a face card) =1- 3/13
= 10/13
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Mr. rodriguez is packing bags of snacks for his children’s lunchboxes. he plans to use 20 blueberries and 30 grapes. each snack bag will have the same number of blueberries and grapes. how many bags can he make if each bag needs to be the same? 5 bags 10 bags 50 bags 60 bags
The number of bags of blueberries and grapes that Mr. Rodriguez can make is 10.
How many bags can he make?If the number of blueberries and grapes in the bags of snacks would be the same, the common factor of 20 and 30 have to be determined.
A factor is a number that divides another number evenly. For example, a factor of 200 is 10. A common factor is a factor that two or more number share. For example, a common factor of 10 and 20 is 5.
Factors of 20 = 1, 2, 4, 5, 10, 20
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Common factors = 1, 2, 3, 10
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Answer:10 bag thank i m smart
Step-by-step explanation:
if x= 6 and y= -4, evaluate: 3x + x/y - y^2
Answer:
71/2 just
Step-by-step explanation:
just like that
ANSWER
Step-by-step explanation:
if x= 6 and y= -4, evaluate: 3x + x/y - y^2
we will just substitute for the values
3(6) + 6/-4 - (-4)²
=18 + 6/-4 - (16)
=18 + 6/-4 - 16
L.C.M=-4
= -72+6-(64)/-4
= -72-64+6/-4
=-136+6/-4
= -130/-4
=32.5 or 32 2/5
I hope I helped
What is the equation for the linear model in the scatter plot obtained by choosing
the two points closest to the line? Please enter an exact answer (use a simplified
fraction or whole number instead of a decimal).
A. -2x +4
B. 2x+ 4
C. Y= -7/6x + 3
D. Y= 1/2x +4
The equation for the linear model in the scatter plot obtained by choosing
the two points closest to the line is y = - 2x + 4
How to find the equation for a linear model?The equation for the linear model in the scatter plot obtained by choosing
the two points closest to the line can be solved as follows:
The two point closest to the line are as follows:
(2, 0)(1, 2)
Using the linear equation,
y = mx + b
where
m = slopeb = y-interceptHence,
m = 2 - 0 / 1 - 2
m = 2 / - 1
m = -2
Therefore, the y-intercept using (2, 0) will be as follows:
0 = -2(2) + b
b = 4
Hence, the equation for the linear model is y = - 2x + 4
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Apply all relevant properties of
Recall that, when two terms are being multiplied and they have the same number we can add the exponents:
[tex]x^nx^m=x^{n+m}.[/tex]Applying the above property to the given expressions, we get:
[tex]\begin{gathered} 6^{\frac{9}{5}}6^{\frac{1}{5}}=6^{\frac{9}{5}+\frac{1}{5}}, \\ x^{\frac{10}{3}}x^{\frac{11}{3}}=x^{\frac{10}{3}+\frac{11}{3}}, \\ y^{\frac{7}{2}}y^{\frac{1}{2}}=y^{\frac{7}{2}+\frac{1}{2}}. \end{gathered}[/tex]Simplifying the above results, we get:
[tex]\begin{gathered} 6^{\frac{9}{5}}6^{\frac{1}{5}}=6^2, \\ x^{\frac{10}{3}}x^{\frac{11}{3}}=x^7, \\ y^{\frac{7}{2}}y^{\frac{1}{2}}=y^4. \end{gathered}[/tex]Answer:
[tex]\begin{gathered} 6^{\frac{9}{5}}6^{\frac{1}{5}}=6^2, \\ x^{\frac{10}{3}}x^{\frac{11}{3}}=x^7, \\ y^{\frac{7}{2}}y^{\frac{1}{2}}=y^4. \end{gathered}[/tex]y^2-10+30 Prove that the value of the expression must be positive.
Answer:
Step-by-step explanation:
[tex]y^2-10y+30=\\y^2-2(y)(5)+5^2-5^2+30=\\(y-5)^2-25+30=\\(y-5)^2+5[/tex]
[tex](y-5)^2\geq 0\\\Rightarrow\ (y-5)^2+5 > 0\\Thus,\ y^2-10y+30 > 0[/tex]
SUPER URGENT WILL GIVE BRANLIEST AND ALL THE POINTS I HAVE
line a is parallel to line b. if the measure of∠7 is 144° what is the measure of∠4
Answer:
140
Step-by-step explanation:
Remove parentheses by using distributive property -2(3x - 4)
Answer:
-6x+8
Step-by-step explanation:
-2(3x-4)
-2(3x)-2(-4)
-6x+8
The diagonal of a square is 6√3. Find the perimeter
Using the formulas
P=4a
d=2a
Solving forP
P=22d=2·2·6≈16.97056
What is the slope of a line perpendicular to the line whose equation is
2x + 3y = 21. Fully simplify your answer.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]2x+3y=21\implies 3y=-2x+21\implies y=\cfrac{-2x+21}{3} \\\\\\ y=\cfrac{-2x}{3}+\cfrac{21}{3}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{3}}x+7\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
well then, that simply means that
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-2}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-2}\implies \cfrac{3}{2}}}[/tex]
Write 2.01 × 105 in standard form.
The correct answer in the standard form or notation of the given number is 2.1105 x 10^6.
How to write the standard notation?
In mathematics, the standard form or the standard notation of a number can be written as the power of ten by putting the decimal in the calculated number. And these numbers can be written in certain rules.
According to the question, to convert the decimal number to standard form by removing the decimal from the given number.
The required expression can be written as"
2.01 x 105 = 201 x 100 x 105 = 21105 x 10²
Hence, the correct answer in the standard form or notation of the given number is 21105 x 10².
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Please help, hurry... This lesson is called "Distance and Midpoint Formula" in Basic Geometry
Answer:
g(x) = x - 3
Step-by-step explanation:
An inverse function undoes a function meaning (x - 3) is the only function that undoes (x + 3).
Copy down the calculation below and insert one pair of brackets so that the
answer is correct.
12 + 24 divided by 2²+ 8 = 14
Answer:
12+24÷(2^2+8)
Step-by-step explanation:
that should be the answer
if you struggle with questions that are like this use trial and error
What is an equation of the line that passes through the points (-5,7) and (5,5)?
If the area of a rectangular sign is 3752 sq ft, and the width is approximately 56 ft, what is the height of the sign?
Answer: l=67ft
Using the formula
A=wl
Step-by-step explanation:
Solving
l=A
w=3752
56=67ft
4 term in the sequence 3,9,15,21
The nth term in the sequence 3,9,15,21 will be 3 + 6(n - 1).
What is a sequence?It should be noted that a sequence simply means the order in which a particular thing happens or takes place.
From the information, four term in the sequence are given as 3,9,15,21 and we want to find the nth term. It should be noted that this is an arithmetic sequence.
The formula is illustrated as:
= a + (n - 1)d
where a = first term = 3
common difference = 9 - 3 = 6
The nth term will be:
= 3 + (n - 1)6
= 3 + 6(n - 1).
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Four term in the sequence 3,9,15,21. Find the nth term
25percent of what number is 18
Answer:
72%
Step-by-step explanation:
25percent of what number is 18
find unity18 : 25 = 0.72
find percent0.72 * 100 =
72%
OR25% = 1/4 so18 * 4 =
72%
Describe how to transform the quantity of the sixth root of x to the fifth power, to the seventh power, into an expression with a rational exponent. Make sure you respond with complete sentences.
Please only CORRECT ANSWER. Don't answer if you don't know.
The quantity [tex](6\sqrt{x^5})^7[/tex] is transformed, into an expression with a rational exponent.
[tex]x^5 * 7 = 35[/tex]
This is further explained below.
What is the rational exponent. ?Exponents are said to be rational if they are able to be represented in the form of p/q, where the value of q is less than 0.
The notation for rational exponents is often written as xm/n, where x represents the base (a positive integer) and m/n is the rational exponent. Exponents may also be represented as xmn=nxm x m n = x m n.
This is another way to express rational exponents.
Generally, the equation is mathematically given as
[tex](6\sqrt{x^5})^7[/tex]
By bearing this in mind, we can make this process easier.
[tex](a^m)^n = a^m * n[/tex]
Therefore
[tex]x^5 * 7 = 35[/tex]
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Confused about the dimensions. If anyone can help me it's much appreciated.
Answer:
Its C
Step-by-step explanation:
I got it right on USA TEST PREP
Answer:
78m^3
Step-by-step explanation:
basically you have to split it into two rectangles and add the volumes
so think of it like this (first picture)
- looking at the bigger rectangle (blue rectangle) the 6 and the 4 are there as hints to the smaller rectangle so just kind of disregard them
- basically the bottom length is 6 but the top length is 5 and this is because the bottom length includes the other rectangle (smaller/pink rectangle), meaning the extra length from the other rectangle (smaller/pink rectangle) is 1.
- then height is given as 4 and 5. the height of 4 is caused by the line stopping when it meets the pink/smaller rectangle, meaning that the height from the other rectangle (smaller/pink rectangle) is 1.
- so using the correct measurements, the height is 5, the length is 5, and the width is 3 so:
5 • 5 • 3 = 75
~ so as stated above from evaluating the different measurements and how the rectangles “intersect” or meet:
the height is 1, the width is 1, and the length is then given as 3 so:
1 • 1 • 3 = 3
so then 75 + 3 = 78
so the full volume is 78 m^3
hope this helps :)
find the constant of the variation y=-12/11 x
By understanding the definition of a direct variation model, the constant of variation of the expression y = - (12 / 11) · x is - 12 / 11.
What is the constant of variation of a direct variation model?
In the statement we find a linear model of the form y = r · x, which represents a linear variation model, that is, a model where the variable x is directly proportional to the variable y and r is the constant of variation.
Graphically speaking, linear variation model represents a line whose intercept is at the origin. A representation of the expression y = - (12 / 11) · x is shown in the image attached below.
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-c+8x evaluated please help m with this math problem
Answer:0.5
Step-by-step explanation:
A cookbook originally cost $13.00. Yesterday, Marta bought it at 40% off.
How much was deducted from the original price?
Answer:£7.80p
Step-by-step explanation:
To find 10% you would divide 13.00 by 10 which would give you 1.30.You then times that by 4 and the answer (£7.80)would be 40% off
Hope that Helps!!
20% of a saline solution was mixed into saline solution with a concentration of 48% saline. How much of each solution be mixed together to obtain a solution of 8 milliliters with a 32% saline concentration
Answer:
Below in bold.
Step-by-step explanation:
Let x be the amount of 20% saline solution then the amount of 48% will
8 - x milliliters.
So,
0.20x + 0.48(8 - x) = 0.32* 8
0.20x + 3.84 - 0.48x = 2.56
-0.28x = -1.28
x = -1.28/-0.28
= 4.57 milliliters.
8 - x = 3.43 milliliters
The answer is:
4.57 milliliters of 20% solution and 3.43 milliliters of the 48% solution.