#1
[tex]\\ \sf\hookrightarrow -5x+4=-1[/tex]
[tex]\\ \sf\hookrightarrow -5x=-5[/tex]
[tex]\\ \sf\hookrightarrow x=1[/tex]
Incorrect
#2
[tex]\\ \sf\hookrightarrow 4x-3=-7[/tex]
[tex]\\ \sf\hookrightarrow 4x=-4[/tex]
[tex]\\ \sf\hookrightarrow x=-1[/tex]
Correct
#3
[tex]\\ \sf\hookrightarrow 3y-4=5[/tex]
[tex]\\ \sf\hookrightarrow 3y=9[/tex]
[tex]\\ \sf\hookrightarrow y=3[/tex]
Ans not given
#4
[tex]\\ \sf\hookrightarrow -2y+7=12[/tex]
[tex]\\ \sf\hookrightarrow -2y=5[/tex]
[tex]\\ \sf\hookrightarrow y=-5/2[/tex]
Incorrect
#5
[tex]\\ \sf\hookrightarrow 3a-6=18-a[/tex]
[tex]\\ \sf\hookrightarrow 4a=24[/tex]
[tex]\\ \sf\hookrightarrow a=6[/tex]
Incorrect
#6
[tex]\\ \sf\hookrightarrow 5(2t-1)=2[/tex]
[tex]\\ \sf\hookrightarrow 10t=7[/tex]
[tex]\\ \sf\hookrightarrow t=7/10[/tex]
Incorrect
#7
[tex]\\ \sf\hookrightarrow ax-b=0[/tex]
[tex]\\ \sf\hookrightarrow x=\dfrac{b}{a}[/tex]
Correct
Done
Help help help help hep
i think that the answer is 0 because f(2) means that you substitute 2 for x
2(2)=4
4-4=0
LAST ATTEMPT MARKING AS BRAINLIEST!! ( write a rule to describe each transformation)
Answer:
See explanation
Step-by-step explanation:
Dilation of 1.5 about the origin. (Each new point is 1.5 times as far from the origin.)
G (-1, 3) G' (-1.5, 4.5)
F (-2, -2) F' (-3, -3)
G'x / Gx = -1.5/-1 = 1.5
G'y / Gy = 4.5 / 3 = 1.5
F'x / Fx = -3 / -2 = 1.5
F'y / Fy = -3 / -2 = 1.5
when the height of a rectangular prism was halved, the volume was 168 cubic cm. if the original prism had a length, width, and height of consecutive integers, increasing in that order,
(a) write and equation to solve for the length, x, of the original figure,
(b) solve length, x,
(c) show that the equation is unique
show all work.
a) The equation is therefore; x³ + 3x² + 2x = 336
b) Solving for the length, we get the length to be; x = 6.
c) All workings are as shown below;
According to the question;
When the height of a rectangular prism was halved, the volume was 168 cubic cm.In essence, the volume of the original prism is;
Volume = 168 × 2.Volume = 336cm³Since, the original prism had a length, width, and height of consecutive integers, increasing in that order.
Therefore, length = xwidth = (x +1)height = (x +2)Volume = x (x+1) (x+2) = 336a) The equation is therefore;
x³ + 3x² + 2x = 336b) Solving for the length, x is as follows;
(x-6) (x² + 9x + 56) = 0By testing values and checking;
Upon solving the polynomial, x = 6.c) All workings are as shown above.
Read more on cubic equation:
https://brainly.com/question/8878887
How do I find the equation of the perpendicular bisector between (-2,5) and (2,-1)?
Answer:
[tex]y = \frac{2}{3} x + 2[/tex]
Step-by-step explanation:
Start by finding the slope of the given line.
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
Slope of given line
[tex] = \frac{5 - ( - 1)}{ - 2 - 2} [/tex]
[tex] = \frac{5 + 1}{ - 4} [/tex]
[tex] = \frac{6}{ - 4} [/tex]
[tex] = - \frac{3}{2} [/tex]
A perpendicular bisector cuts through the line at its midpoint perpendicularly.
The product of the slopes of two perpendicular lines is -1.
Let the slope of the perpendicular bisector be m.
[tex] - \frac{3}{2} m = - 1[/tex]
[tex]m = - 1 \div ( - \frac{3}{2} )[/tex]
[tex]m = - 1 \times ( - \frac{2}{3} )[/tex]
[tex]m = \frac{2}{3} [/tex]
[tex]y = \frac{2}{3}x + c[/tex], where c is the y-intercept.
To find the value of c, we need to substitute a pair of coordinates that lies on the perpendicular bisector into the equation. Since the perpendicular bisector passes through the midpoint of the given line, we can use the midpoint formula to find the coordinates.
[tex]\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}[/tex]
Midpoint of given line
[tex] = ( \frac{ - 2+ 2}{2} , \frac{5 - 1}{2} )[/tex]
[tex] =( \frac{0}{2} , \frac{4}{2} )[/tex]
= (0, 2)
[tex]y = \frac{2}{3} x + c[/tex]
When x= 0, y= 2,
2= ⅔(0) +c
2= 0 +c
c= 2
Thus, the equation of the perpendicular bisector is [tex]y = \frac{2}{3} x + 2[/tex].
2. The sum of two cubes can be factored by using the formula q3 + b3 = (a + b)(a? - ab + b).
(a) Verify the formula by multiplying the right side of the equation.
(b) Factor the expression 8x3 + 27.
(c) One of the factors of 23 - bºis a - b. Find a quadratic factor of a3 - bº Show your work.
(d) Factor the expression x3 - 1.
Factorization involves breaking down an expression.
The factorized expression of [tex]8x^3 + 27[/tex] is [tex]8x^3 + 27 =(2x + 3)(4x^2 -8x3 +9)[/tex]The other factor of [tex]2^3 - b^3[/tex] is [tex]4+2b+b^2[/tex]The factorized expression of x^3 - 1 is [tex]x^3 - 1^3=(x-1)(x^2+x+1)[/tex]The sum of cubes is given as:
[tex](a^3 + b^3) = (a + b)(a^2 -ab + b^2)[/tex]
(a) Verify the formula
Expand the expression on the right-hand side
[tex](a^3 + b^3) = a^3 -a^2b + ab^2 +a^2b - ab^2 + b^3[/tex]
Collect like terms
[tex](a^3 + b^3) = a^3 -a^2b +a^2b+ ab^2 - ab^2 + b^3[/tex]
[tex](a^3 + b^3) = a^3 + b^3[/tex]
The formula has been verified
(b) Factorized 8x^3+ 27
We have:
[tex]8x^3 + 27[/tex]
Express 27 as 3^3
[tex]8x^3 + 27 =8x^3 + 3^2[/tex]
Express 8 as 2^3
[tex]8x^3 + 27 =2^3x^3 + 3^3[/tex]
Rewrite as:
[tex]8x^3 + 27 =(2x)^3 + 3^3[/tex]
Given that:
[tex](a^3 + b^3) = (a + b)(a^2 -ab + b^2)[/tex]
The expression becomes
[tex]8x^3 + 27 =(2x + 3)((2x)^2 - (2x)3 +3^2)[/tex]
[tex]8x^3 + 27 =(2x + 3)(4x^2 -8x3 +9)[/tex]
(c)The other factor of 2^3 - b^3
By difference of cubes, we have:
[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex]
So, the equation becomes
[tex]2^3 - b^3=(2-b)(2^2+2b+b^2)[/tex]
This gives
[tex]2^3 - b^3=(2-b)(4+2b+b^2)[/tex]
Hence, the other factor of [tex]2^3 - b^3[/tex] is [tex]4+2b+b^2[/tex]
(c) Factor x^3 - 1
We have:
[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex]
Express 1 as 1^3 in x^3 - 1
[tex]x^3 - 1 =x^3 - 1^3[/tex]
[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex] becomes
[tex]x^3 - 1^3=(x-1)(x^2+x+1^2)[/tex]
[tex]x^3 - 1^3=(x-1)(x^2+x+1)[/tex]
Read more about factorization at:
https://brainly.com/question/43919
Please help!!!! Will give brainliest!!!!
Answer:
it is c
Step-by-step explanation:
Understand how to work with negative bases and negative exponents.
5^2 =
5^-2 =
(-5)^2 =
- 5^2 =
(Remember to find the base, then multiply.)
Answer:
[tex]Understand \: how \: to \: work \: with \: negative \: bases \\ \: and \: negative \: exponents. \\
\bold{answer - } \\ {5}^{2} = 5 \times 5 = 25 \\ {5}^{ - 2} = \frac{1}{ {5}^{2} } = \frac{1}{25} = 0.04 \\ {( - 5)}^{2} = ( - 5) \times ( - 5) = 25 \\ - {5}^{2} = ( - 5) \times ( - 5) = 25 \\ \\ \bold \purple{hope \: it \: helps \: ♡}[/tex]
Jackson bought 6 basketballs for 72 dollars what was the price per basket ball
Answer:
the answer would be 12 I say this because 72 divied by 6 would equal 12
Answer:
12 dollars
Set up a proportion.
6/72=1/x
Solve by cross-multiplying (my preferred method) and then you will end up with the final answer of x=12.
12 is the answer :)
PLEASE MARK BRAINLIEST!
THANK YOU & HAVE A WONDERFUL DAY :))
Round 9296 to the nearest hundred?
The answer it 9300 so 9296 round to is 9300
The point (3, 3) is in what quadrant? 2,1,3,4
Answer:
1
Step-by-step explanation:
(3,3) has a positive x value and a positive y value which means it is in the first quadrant
Principal = $ 15000, rate = 10% p.a. and time
21/5 years
PLS HELP ASAP
Answer:
Simple Interest: A=P(1+rt)
A=15000(1+(0.1*4.2))
A=$21,300
Compound Interest:A=P(1+r/n)^nt
A=15000(1+0.1/4.2)^1*4.2
A=$64,500
Step-by-step explanation:
find the angle of rotation that maps point D onto point A
Answer:
A - 144
Step-by-step explanation:
everything else would be too far. thx
After 5 throws in a game of darts, Brent's mean score was 32. Calculate his total score.
1.To know this answer, we need to know some vocabulary that's used in t. Most people don't know how to solve questions if they have hard Vocabulary and what the question is Asking
Mean=The average of all his throws
It's asking us to calculate his total score
2. Find Clues to help you solve word problems
Finding clues in Word Problems is a very important part a lot of people skip but this helps you solve the question easier
5 throws and Mean Score is 32 are the clues
3. Guess and check
The method to this thingy is called guess and check. There is another method which is slightly harder and i just don't want to do it.
Let's just say his scores were... 5, 6, 4, 5,10Add them up and you get 30Then 30/5
Let's try bigger numbers
20+25+20+20
If you like this method, you may try it another method is called work Backwards
5x32=160
Then divide 160 by 5 to double check and you get 32!!
========================================
Therefore, the answer s 160 as his total score
hope this gives you a clue to what we are doing and when you have a question like this, I really hope you understand the concept
Hope this helped (:
Help help help help hep
Answer:
Yes
Step-by-step explanation:
Decrease £110 by 50%
Answer:
£55
Step-by-step explanation:
50% is just another way to say 1/2. This means that 1/2 of £110 is £55.
write an expression that is equivalent to 1/3(24p-33) -iready
Answer:
8p - 11
Step-by-step explanation:
Got the same I-Ready question lol
20 is 25% of what number?
Enter your answer in the box.
Answer:
80
Step-by-step explanation:
25 percent is equal to 1/4
1/4 of 80 is 20
Answer:
80
Step-by-step explanation:
Three boxes are stacked one on top of the other. One box is 4 feet 8 inches tall, one is 3 feet 10 inches tall, and one is 2 feet 7 inches tall. How high is the stack?
Write your answer in feet and inches. Use a number less than 12 for inches.
A rectangle is 8 feet long. Its width is represented by “seven plus x feet.” Which expression represents the area, in square feet, of the rectangle?
56 + 8x
Area of Rectangle = Length x Width
Area of Rectangle = 8(7 + x)
The area of a square pond is 1000m2.A path of uniform width is surrounded outside the pond and its area is 369m2.find the outer length of the path
Answer:
631 m²
Step-by-step explanation:
Outer length of park = Total area - Area of pond
Outer length of park = 1000 - 369
Outer length of park = 631 m²
Answer:
Hope it will help you a lot.
Express the following surds in the simplest form
a)
[tex] \sqrt{128} [/tex]
b)
[tex] \sqrt{48} [/tex]
c)
[tex] \sqrt{300} [/tex]
[tex] \sqrt{128} \\ = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2} \\ = \sqrt{ {2}^{2} \times {2}^{2} \times {2}^{2} } \\ = 2 \times 2 \times 2 \\ = 8[/tex]
[tex] \sqrt{48} \\ = \sqrt{2 \times 2 \times 2 \times 2 \times 3} \\ = \sqrt{ {2}^{2} \times {2}^{2} \times 3 } \\ = 2 \times 2 \sqrt{3} \\ = 4 \sqrt{3} [/tex]
[tex] \sqrt{300} \\ = \sqrt{2 \times 2 \times3 \times 5 \times 5} \\ = \sqrt{ {2}^{2} \times 3 \times {5}^{2} } \\ = 2 \times 5 \sqrt{3} \\ = 10 \sqrt{3} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
In six years Xavier will be 3 times older than Joanne is today. Joanne is 24. How old is Xavier?
Answer:
72
Step-by-step explanation:
Which expression is equivalent to 1/4 (5x + 6)?
The expression which is equivalent to 1/4 (5x + 6) is; Choice A: {5(1/4)x} + {6(1/4)x}.
According to the question:
We are required to determine an expression which is equivalent to 1/4 (5x + 6).In a bid to expand the expression; we must multiply each term in the parenthesis by (1/4);
In essence; we have;
{5(1/4)x} + {6(1/4)x}Read more on multiplication;
https://brainly.com/question/847421
∫(sinxdx)/(sinx^3+cosx^3)
A waitress is filling coffee mugs at a diner. She pours 12 fluid ounces into each of 5 mugs from a full pot of coffee. If her coffee pot holds 8 cups, how many fluid ounces does she have left?
Answer:
4 fluid ounces
Step-by-step explanation:
A waitress is filling coffee mugs at a diner. She pours 12 fluid ounces into each of 5 mugs from a full pot of coffee. If her coffee pot holds 8 cups, how many fluid ounces does she have left?
Remember
8 fluid ounces = 1 cup.
First you need to do find out how many fluid ounces she poured in total.
So do,
5 mugs × 12 fluid ounces.
which is 60 fluid ounces.
Now that you now that you need to convert 8 cups into fluid ounces.
Like I said at the top 8 fluid ounces = 1 cup.
So you need to do,
8 cups × 8 fluid ounces.
Which is 64 fluid ounces she can hold in her coffee pot.
Now you subtract,
64 fluid ounces - 60 fluid ounces.
Which is 4 fluid ounces left in her coffee pot.
The number of fluid ounces she has left is 4 fluid ounces if the waitress is filling coffee mugs at a diner. She pours 12 fluid ounces into each of the 5 mugs from a full pot of coffee.
What is unit conversion?It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.
It is given that:
A waitress is filling coffee mugs at a diner. She pours 12 fluid ounces into each of 5 mugs from a full pot of coffee.
Let x be the number of fluid ounces she has left.
4 fluid ounces
As we know,
8 fluid ounces = 1 cup
The total amount of coffee = 5×12
The total amount of coffee = 60
Total amount = 8 cups × 8 fluid ounces.
x = 64 fluid ounces - 60 fluid ounces.
x = 4 fluid ounces
Thus, the number of fluid ounces she has left is 4 fluid ounces if the waitress is filling coffee mugs at a diner. She pours 12 fluid ounces into each of the 5 mugs from a full pot of coffee.
Learn more about the unit conversion here:
brainly.com/question/14350438
#SPJ2
let f(x)=3x^2-6x+5 what is the leading coefficient
Help pls pls pls and thank you
Answer:
2 feet: $18
4 feet: $36
5 feet: $45
$81 = 4.5 feet
10 feet = $90
Step-by-step explanation:
2 feet: $18
4 feet: $36
18 + 18
5 feet: $45
18 + 18 + 9
$81 = 4.5 feet
81/18
10 feet = $90
18 + 18 + 18 + 18 + 18
PLEASE HELP FOR 100 POINTS AND BRAINLIESTT HELP PLEASE
Kim has fraction 1 over 2 cup of almonds. She uses fraction 1 over 8 cup of almonds to make a batch of pancakes.
Part A: How many batches of pancakes can Kim make with fraction 1 over 2 cup of almonds? (4 points)
Part B: On your own paper, draw a fraction model that shows the total number of batches of pancakes that Kim can make with fraction 1 over 2 cup of almonds. Make sure to label the model. Below, explain your model in detail to describe how this model visually shows the solution for Part A.
Answer:
The total number of batches of pancakes that Kim can make with the model is 4 batches of pancake
Step-by-step explanation:
Number of cups of pancakes = 2/4
Number of cups of almonds to make a batch of pancakes = 1/8
Therefore, the batches of pancakes that she can make will be:
= 2/4 ÷ 1/8
= 2/4 × 8/1
= 4
In conclusion, the number of batches of pancakes that Kim can make with the cup of almonds is 4 batches.
A spherical solid, centered at the origin, has radius 4 and mass density(x,y,z)=6-(x^2+y^2+z^2). Set up the triple integral and find its mass.
I've attached a photo of the question.
There's something very off about this question.
In spherical coordinates,
x² + y² + z² = ρ²
so that
f(x, y, z) = 6 - (x² + y² + z²)
transforms to
g(ρ, θ, φ) = 6 - ρ²
When transforming to spherical coordinates, we also introduce the Jacobian determinant, so that
dV = dx dy dz = ρ² sin(φ) dρ dθ dφ
Since we integrate over a sphere with radius 4, the domain of integration is the set
E = {(ρ, θ, φ) : 0 ≤ ρ ≤ 4 and 0 ≤ θ ≤ 2π and 0 ≤ φ ≤ π}
so that the integral is
[tex]\displaystyle \int_{\phi=0}^{\phi=\pi} \int_{\theta=0}^{\theta=2\pi} \int_{\rho=0}^{\rho=4} (6 - \rho^2) \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi[/tex]
Computing the integral is simple enough.
[tex]\displaystyle = \int_{\phi=0}^{\phi=\pi} \int_{\theta=0}^{\theta=2\pi} \int_{\rho=0}^{\rho=4} (6 \rho^2 - \rho^4) \sin(\phi) \, d\rho \, d\theta \, d\phi[/tex]
[tex]\displaystyle = 2\pi \int_{\phi=0}^{\phi=\pi} \int_{\rho=0}^{\rho=4} (6 \rho^2 - \rho^4) \sin(\phi) \, d\rho \, d\phi[/tex]
[tex]\displaystyle = 2\pi \left(\int_{\phi=0}^{\phi=\pi} \sin(\phi) \, d\phi\right) \left(\int_{\rho=0}^{\rho=4} (6 \rho^2 - \rho^4) \, d\rho\right)[/tex]
[tex]\displaystyle = 2\pi \cdot 2 \cdot \left(-\frac{384}5\right) = \boxed{-\frac{1536\pi}5}[/tex]
but the mass can't be negative...
Chances are good that this question was recycled without carefully changing all the parameters. Going through the same steps as above, the mass of a spherical body with radius R and mass density given by
[tex]\delta(x, y, z) = k - (x^2 + y^2 + z^2)[/tex]
for some positive number k is
[tex]\dfrac{4\pi r^3}{15} \left(5k - 3r^2\right)[/tex]
so in order for the mass to be positive, we must have
5k - 3r² ≥ 0 ⇒ k ≥ 3r²/5
In this case, k = 6 and r = 4, but 3•4²/5 = 9.6.
help , I have like no clue on what I'm doing
Answer:
Step-by-step explanation:
Linear equations can have the form y = mx + b
where m is the slope of the line and equals Δy/Δx
and b is the y intercept.
Just for fun, let's choose the first and last sets of data points.
Δy = (275 - 135) = 140
Δx = (5 - 1) = 4
so slope m = 140/4 = 35 and the units on the slope would be $/month
Answer:
The slope of the line is 35
Step-by-step explanation:
We'll select [tex](1,135)[/tex] and [tex](2,170)[/tex] for this problem.
The slope is defined as the rate of change. Its formula is [tex]Slope=m=\frac{Rise}{Run}=\frac{y_2-y_1}{x_2-x_1}[/tex] where our two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
Therefore, we have [tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{170-135}{2-1}=\frac{35}{1}=35[/tex] as our slope.