I need help on nine and 10 instructions say to solve these equations by cross multiplying
Answers
Answer:
9. a = -1
10. b = 20
Step-by-step explanation:
The term "cross multiplying" is used to describe the appearance of the result of multiplying both sides of the equation by the product of the denominators. The result is the left numerator is multiplied by the right denominator, and the right numerator is multiplied by the left denominator. The property of equality that supports this is the multiplication property of equality, which tells you the values of the variables are unchanged if you multiply both sides by the same thing. That multiplier is chosen so that it cancels the denominators.
__
9.[tex]\dfrac{2a-5}{3a-4}=\dfrac{2a-3}{3a-2}\\\\(3a-2)(2a-5)=(3a-4)(2a-3)\qquad\text{"cross multiply"}\\\\6a^2 -19a +10=6a^2-17a+12\qquad\text{expand}\\\\-2=2a\qquad\text{add $19a-6a^2-12$}\\\\\boxed{a=-1}\qquad\text{divide by 2}[/tex]
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10.[tex]\dfrac{b-2}{b-6}=\dfrac{b+2}{b-4}\\\\(b-4)(b-2)=(b-6)(b+2)\qquad\text{"cross multiply"}\\\\b^2-6b+8=b^2-4b-12\qquad\text{expand}\\\\20=2b\qquad\text{add $6b+12-b^2$}\\\\\boxed{b=20}\qquad\text{divide by 2}[/tex]
_____
Additional comments
Here are the answer checks:
9. (2(-1) -5)/(3(-1)-4) = (2(-1)-3)/(3(-1)-2) ⇒ -7/-7 = -5/-5 . . . yes
10. (10 -2)/(10 -6) = (10 +2)/(10 -4) ⇒ 8/4 = 12/6 . . . yes
__
Sometimes this method of solving the problem will result in extraneous solutions. Those will generally be values of the variable that make one or more of the denominators be zero. You must be careful to exclude those values from any possible solution set.
Related Questions
x^2-8x+16=3 solve using square roots
Answers
Answer:
x = 4 ± [tex]\sqrt{3}[/tex]
Step-by-step explanation:
x² - 8x + 16 = 3 ← the left side is a perfect square
(x - 4)² = 3 ( take square root of both sides )
x - 4 = ± [tex]\sqrt{3}[/tex] ( add 4 to both sides )
x = 4 ± [tex]\sqrt{3}[/tex]
PLEASE HELP!! I'LL GIVE YOU BRAINLIEST
What is the value of x in the figure?
Enter your answer in the box.
x =
Answers
Answer:
29 is the correct answer because subtract 90 from 61 we get 29
Step-by-step explanation:
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASEAnswer:
29°
Step-by-step explanation:
We know that both angle x and angle "61°" add up to a sum of 90° because it is a right angle.
So, we would have to subtract 61 from 90 to find the missing value.
90 - 61 = 29
Therefore, x equals 29°
-kiniwih426
2m · 2n would be the same as _____.
A) 4 mn
B) 2 m + n
C) 2 mn
D) 2 m - n
Answers
Answer:
A) 4mn
Step-by-step explanation:
2m × 2n = 4mn
I hope this helps!
Ok i promise last question today guys number 24 and 26 pls ur reason for awnsering this correctly is bc ur gonna earn my 50 last points! Thank u hope its clear to read (dont mind my crusty fingers)
Answers
59.9-5 = 54.9
54.9/2 = 109.8
26)
2* 8.45 = 16.9 for two cartridges
35-16.9 = 18.1 amount left after buying cartridges
18.1 / 5.99 = 3.16
so, 3 disk packs.
The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
8 8 8/3 8/3
Answers
Answer:
Step-by-step explanation:
Making late payments on credit card bills has what kind of effect on a person's credit score?
a
Late payments have a negative effect on a person's credit score.
b
Late payments have a positive effect on a person's credit score.
c
Late payments do not affect a person's credit score.
Answers
Answer:
A. Late payments have a negative effect on a person's credit score.
Step-by-step explanation:
Hope this Helps!
Answer:
A late payments have a negative effect on a persons credit score
Step-by-step explanation:
A credit score is basically the trust banks have with you or the potentiality that you will pay them back. Making late payments will obviously lower the banks reliability on you to pay your bill ontime and in full.
Use DeMoivre's Theorem to find the square roots of 4(cos90+ i sin 90). Show your work.
Answers
Answer:
Procedure 6.3. 1:Finding Roots of a Complex Number
Express both z and w in polar form z=reiθ,w=seiϕ. ...
Solve the following two equations: rn=s. ...
The solutions to rn=s are given by r=n√s.
The solutions to einθ=eiϕ are given by: nθ=ϕ+2πℓ,forℓ=0,1,2,⋯,n−1. ...
Using the solutions r,θ to the equations given in (6.3.
Step-by-step explanation:
Answer:-1.79229446 + 3.57598665 i
Step-by-step explanation:
I will honest this how much I can help you
PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Explanation. 1 + 2= 3 and 1/6+2/6=3/6. 3/6 is equivalent to 1/2. So the answer is 3 1/2
Answer:
The Answer is 3 1/2 or C
Step-by-step explanation:
2+1=3
1/6+2/6=3/6
3/6 = 1/2
3 + 1/2 = 3 1/2
Draw the graph of the equation x+5y=6
Answers
Answer:
Step-by-step explanation:
What is the slope of the line whose equation is -2y = -4x + 5
Answers
Answer:
2
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
-2*y-(-4*x+5)=0
STEP 1:
Pulling out like terms
1.1 Pull out like factors :
-2y + 4x - 5 = -1 • (2y - 4x + 5)
Equation at the end of step 1:
STEP 2:
Equation of a Straight Line
2.1 Solve -2y+4x-5 = 0
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line -2y+4x-5 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 5/-2 so this line "cuts" the y axis at y=-2.50000
y-intercept = 5/-2 = -2.50000
Calculate the X-Intercept :
When y = 0 the value of x is 5/4 Our line therefore "cuts" the x axis at x= 1.25000
x-intercept = 5/4 = 1.25000
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -2.500 and for x=2.000, the value of y is 1.500. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 1.500 - (-2.500) = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 2
Geometric figure: Straight Line
Slope = 2
x-intercept = 5/4 = 1.25000
y-intercept = 5/-2 = -2.50000
Answer:
2
Step-by-step explanation:
y=mx+b where m is the slope
to get y by itself you divide both sides by -2 resulting in
y= 2x+(-5/2)
2=m
What is the purpose of the QUADRATIC FORMULA?
N
A Determine the distance between two points
B Determine the zeros of a quadratic function
Calculate the axis of symmetry of a quadratic function
Calculate the y-coordinate of the vertex of a parabola
Answers
Hope this helps
helpppppppppppppppppppppppppppppppppp pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
.... thank you <3
Answers
Answer:
39.9
Step-by-step explanation:
Pls give brainlest if correct.
*Answer*:39.9
Reasoning:Say you wanted to round the number 838.274. Depending on which place value you'll round to, the final result will vary. Rounding 838.274: Rounding to the nearest hundred is 800 Rounding to the nearest ten is 840 Rounding to the nearest one is 838 Rounding to the nearest tenth is 838.3 Rounding to the nearest hundredth is 838.27
**Helping to solve**:When you "round to the nearest _____" regardless of what goes in the blank the steps are nearly always the same: Identify which place value you are rounding to. The smaller the place value, the more accurate the final result will be. Look to the next smallest place value, the digit to the right of the place value you're rounding to.
Therefore, the answer is C. 39.9
This has been..~NatLikesAnime
#LearningWithBrainly
Please give brainliest, a thanks, and a 5 start rating if helpful :)
Please help me with this please and thank you
Answers
Answer:
Nnnnnnnnnnnn
Step-by-step explanation:
L bozo
a. Complete the table.
х
f(x) = 2(2)*
=
-2 -1
0
1
2
1
Answers
Answer:
1/2,1,2,4,8 in order
Step-by-step explanation:
Given:
[tex]\displaystyle \large{f(x)=2(2)^x}[/tex]
The function can be simplified to:
[tex]\displaystyle \large{f(x)=2^{x+1}}[/tex] via law of exponent.
Recall:
[tex]\displaystyle \large{a^m\cdot a^n=a^{m+n}}[/tex]
Next, substitute given x-values in:
[tex]\displaystyle \large{f(-2)=2^{-2+1}=2^{-1}=\dfrac{1}{2}}\\\displaystyle \large{f(-1)=2^{-1+1}=2^0=1}\\\displaystyle \large{f(0)=2^{0+1}=2^1=2}\\\displaystyle \large{f(1)=2^{1+1}=2^2=4}\\\displaystyle \lage{f(2)=2^{2+1}=2^3=8}[/tex]
Therefore, the solution is 1/2,1,2,4,8
An arithmetic sequence is given by 20, 17, 14, 11, ...
(a) Write down the value of the common difference, d.
(b) Find a100
(c) Find s100
Answers
Answer:
The common difference equals:
[tex]-3[/tex]
The sum of the sequence equals:
[tex]62[/tex]
The explicit formula of this sequence is:
[tex]a_n=20+(n-1)*(-3)[/tex]
The recursive formula of this sequence is:
[tex]a_n=a_((n-1))-3[/tex]
The nth terms:
[tex]20,17,14,11,8,5,2...[/tex]
Step-by-step explanation:
An arithmetic sequence, or arithmetic progression, is a set of numbers in which the difference between consecutive terms (terms that come after one another) is constant. This difference is called the common difference.
1. Find the common difference.Find the common difference by subtracting any term in the sequence from the term that comes after it.
[tex]a_2-a_1=17-20=-3\\a_3-a_2=14-17=-3\\a_4-a_3=11-14=-3[/tex]
The difference of the sequence is constant and equals the difference between two consecutive terms.
[tex]d=-3[/tex]
2. Find the sum.Calculate the sum of the sequence using the sum formula:
Formula
[tex]Sum=\frac{(n(a_1+a_n))}{2}[/tex]
Plug in terms
[tex]Sum=(4*(a_1+a_n))/2[/tex]
[tex]Sum=(4*(20+a_n))/2[/tex]
[tex]Sum=(4*(20+11))/2[/tex]
Simplify the expression
[tex]Sum=(4*(20+11))/2[/tex]
[tex]Sum=(4*31)/2[/tex]
[tex]Sum=124/2[/tex]
[tex]Sum=62[/tex]
The sum of this sequence is [tex]62[/tex].
This series corresponds to the following straight line [tex]y=-3x+20[/tex]
3. Find the explicit form.The formula for expressing arithmetic sequences in their explicit form is:
Formula: [tex]a_n=a_1+(n-1)*d[/tex]
Plug in the terms.
[tex]a_1=20[/tex] (this is the 1st term)
[tex]d=-3[/tex] (this is the common difference)
[tex]a_n[/tex] (this is the nth term)
[tex]n[/tex] (this is the term position)
The explicit form of this arithmetic sequence is:
[tex]a_n=20+(n-1)*(-3)[/tex]
4. Find the recursive form.The formula for expressing arithmetic sequences in their recursive form is:
Formula: [tex]a_n=a_((1-n))+d[/tex]
Plug in the d term.
[tex]d=-3[/tex](this is the common difference)
The recursive form of this arithmetic sequence is:
[tex]a_n=a_((n-1))-3[/tex]
5. Find the nth element.[tex]a_1=a_1+(n-1)*d=20+(1-1)*-3=20[/tex]
[tex]a_2=a_1+(n-1)*d=20+(2-1)*-3=17[/tex]
[tex]a_3=a_1+(n-1)*d=20+(3-1)*-3=14[/tex]
[tex]a_4=a_1+(n-1)*d=20+(4-1)*-3=11[/tex]
[tex]a_5=a_1+(n-1)*d=20+(5-1)*-3=8[/tex]
[tex]a_6=a_1+(n-1)*d=20+(6-1)*-3=5[/tex][tex]a_7=a_1+(n-1)*d=20+(7-1)*-3=2[/tex]
Terms and topics:
Artithmetic SequencesAABC is equilateral.
AB = 22x-33 and AC = 7x + 57.
=
B
A
A
с
x = [?]
Answers
Answer:
Answer is 6
Step-by-step explanation:
See it is equilateral so AB=AC=BC
Now we are given values of AB and AC, but they are equal so,
22x-33 = 7x+5722x-7x = 57+3315x = 90x= 15 / 90x=6Hope it helps
BYE
Which expression represents the area of the base of the pyramid? startfraction 3 v over h endfraction units2 (3v – h) units2 (v – 3h) units2 startfraction v over 3 h endfraction units2
Answers
The expression that represents the area of the base of the pyramid(right pyramid) is given by: Option A: 3v/h unit²
What is a right rectangular pyramid?A right rectangular pyramid is a pyramid, with four slant sides, and a rectagular base, such that all the sides are congruent and the vertex is atop of the midpoint of the base rectangle.
How to find the volume and base's area of a right rectangular pyramid?Suppose the base of the pyramid has length = l units, and width = w units.
Suppose that the height of the pyramid is of h units, then:
[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex] is the volume of that pyramid.
The base is a rectangle with length = L units, and width = W units, so its area is:
[tex]b = l \times w\: \rm unit^2[/tex]
Thus, we can express the area of its base in terms of its volume as:
[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3 = \dfrac{b\times h}{3}\\\\3v = b\times h\\\\\\b = \dfrac{3v}{h} \: \rm unit^2[/tex]
Thus, the expression that represents the area of the base of the pyramid (right pyramid) is given by: Option A: 3v/h unit²
Learn more about right rectangular prism here:
https://brainly.com/question/3712320
Answer:
3V/h units^2
Step-by-step explanation:
Solve this equation, 2.5y = 13.75 Explain pleaseeeee
I'll give 25 points i'm desperate...
Answers
Answer:
5.5
Step-by-step explanation:
13.75 divided by 2.5 = 5.5
Miguel scored 74 points in his first 5 games this season. how many points has he scored per game?
Answers
14.8
Step-by-step explanation:[tex]\frac {74}{5}[/tex]____________________________________________________
Evaluate the equation/expression:[tex]14.8[/tex]
I hope this helps you
:)
Answer:
You can divided 74 by 5. 5 fits into 7 once so you subtract 5 and you are left with 2. Then bring down the 4 and you have 24. 5 fits into 24 only 4 times so you would subtract 20 from 24 and be left with 4. Then add a decimal point and a 0. Bring down the 0 and you'll have 40. 5 fits into 40 exactly 8 times so 40 - 40 = 0. The answer is 14.8
Step-by-step explanation:
Select the correct answer.
A rubber gasket has a circumference of 3.2 cm. When placed in service, it expands by a scale factor of 2. What is the circumference of the gasket when in service?
A.
1.6 cm
B.
3.2 cm
C.
6.4 cm
D.
13.2 cm
Answers
3.2x2=6.4 cm
The required circumference of the gasket after dilation with scale factor 2 is 6.4 cm. Option C is correct.
A rubber gasket with a circumference of 3.2 cm is given. After expansion by scale factor 2 the circumference of the gasket is to be determined.
The circumference is defined as the boundary length of any circular shape.
Here,
Circumference of gasket = 3.2 cm
After dilation with scale factor 2, the circumference became.
Dilated circumference of gasket = 2*3.2 = 6.4 cm
Thus, the required circumference of the gasket after dilation with a scale factor of 2 is 6.4 cm.
Learn more about circumference here:
https://brainly.com/question/9319321
#SPJ5
what is john locke's ideas that affected government?
Answers
John Locke's ideas related to government focus on the separation of powers and respect for the individual rights of citizens.
Who was John Locke?John Locke (1632-1704) was a British philosopher who stands out as one of the most important thinkers in history in the field of political philosophy, English empiricism, and classical liberalism.
What were his outstanding ideas?Some of the most popular and important postulates of John Locke were:
The State's main mission is to protect the three natural rights: life, liberty and private property.Individuals have a fourth right, the right to defend these rights, as well as any other individual freedom of citizens.The citizen cedes some rights to the State through a written consensus or constitution.The government must be made up of a king and a parliament. Parliament is where popular sovereignty is expressed and where laws are made that must be followed by both the king and the people.He described the separation of legislative and executive power.The authority of the State is sustained by the principles of popular sovereignty and legality.Power is not absolute but must respect human rights.Learn more about John Locke in: https://brainly.com/question/13346823
please give me complete working and explanation and I will mark you as brainliest!
Answers
Stove cost $4,999
Amount spent on fridge more than the stove = costof fridge - cost of stove
= $10,535 - $4,999
= $5,536
Answer:
she spent 5,536 more dollars π
Step-by-step explanation:
10,535 - 4,999= 5,536
thats how much more money it cost than the stove.
A person invests 7000 dollars in a bank. The bank pays 7% interest compounded
quarterly. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 12400 dollars?
Answers
what is the difference in the length between the longest meter in the shortest meter
Answers
Answer:
1 5/8 inches
Step-by-step explanation:
Hey there!
The question is asking what the difference in the length between the longest meteor and the shortest meteor is.
In the chart, the smallest measurment is 2/8 and the largest is 1 7/8
So in order to solve this you need to subtract these two values
we can convert 1 7/8 to 15/8 to make the subtraction more simple
15/8-2/8=13/8 which is 1 5/8
So the difference between the longest and shortest meteor is 1 5/8 inch
Answer: 1 5/8.
Step-by-step explanation: The longest one is 1 7/8 and the shortest one is 2/8. Both are circled below. To figure this problem out, we need to find the difference of the longest and shortest meteors, also known as a subtraction problem. The work is done below:
1 7/8 - 2/8 = 1 5/8.
Hope this helps! :)
why is this not working
-2^2
Answers
Answer:
-4
Step-by-step explanation:
(-2)^2=4 because a negative number squared is always positive
-(2)^2=-4
please help me please
Answers
Answer:
its 17
Step-by-step explanation:
do 2 step Equation
Find the area of the shaded region
Answers
Answer:
Step-by-step explanation:
Remark
There are many ways you can do this. I think the simplest way is to find the area of the rectangle enclosing the winged shape and take away the area of the three unshaded triangles.
Area of enclosed rectangle
Area = L * w
L = 26 in
w = 15 in
Area = 26 * 15
Area = 390 square inches.
Find the area of the triangle on the right.
Area = 1/2 * b * h
base = 26 inches
height = 15 - 6 = 9
This is a little tricky. What you need to do to get the height of the triangle is realize that it is made from a line that goes from the base of the triangle to its peak. This line is perpendicular to the base. The line you just drew is 15 inches tall, same as the width of the enclosing rectangle.
Substitute values into the formula
Area = 1/2 * 26 * 9
Area = 117 square inches.
Find the area of the top and bottom triangles.
These 2 triangles are the same sort of thing only the base requres a bit of manipulation
height = 15 inches
base = (26 - 14)/2
base = 12/2
base = 6
Again, this requires a little bit of thought. You have 2 bases making up each of the right triangles. To find the sum of both of them, you take 26 and subtract 14 from it. That's where the 12 comes from. Now you divide 2 to get the base of each of the triangles. That gives you 6.
Find the area of one of the triangles.
Area = 1/2 * b * h
Area = 1/2 * 6 * 15
Area = 45 square inches
Find the area of both triangles.
Area of triangles at the top and bottom = 2*45 = 90
Finally find the area of the shaded area.
Area = enclosed rectangle - top triangle and bottom triangle - the triangle on the right.
Area shaded area = 390 - 45 - 45 - 117 = 183
Answer: Area shaded region = 183 square inches.
If you want to identify the mode of a set of data, which of the following graphical displays is best?
Answers
Answer:
Histogram (Please tell me if you disagree, Have a great day:)
Solving systems of linear equations by substitution y= 2x-1 y = 3x +2
Answers
Answer:
(x,y)=(-3,-7)
Step-by-step explanation:
step 1
y=2x-1
y=3x+2
=
2x-1=3x+2
Instructions: Given the figure, what is the angle of rotational symmetry?
Answers
Answer:
180°
Step-by-step explanation:
The Angle of Rotational Symmetry is the degree of rotation required to make the shape look like the original.
If you rotate it once by 90°, it will look completely different.
However, if you rotate it again by 90°, it looks identical to the original.
90° + 90° = 180°
