The solution to the provided expression using the difference of square formula of algebra is a=1.
What is the difference of squares formula?The difference of square says, the difference of the square of two terms is equal to the product of their sum and difference. It can be given as,
a^2-b^2=(a+b)(a-b)
The given expression in the problem is,
[tex]15(2a - 2) = 5(a^2 -1)[/tex]
From the property of difference of square, the above equation can be written as,
[tex]15(2a - 2) = 5[(a +1)(a-1)]\\15\times[2(a - 1)] = 5[(a +1)(a-1)][/tex]
Divide both side of the equation with (a-1) as,
[tex]5\times2 = 5(a +1)[/tex]
Divide both side of the equation with number 5 as,
[tex]2 = (a +1)\\a=2-1\\a=1[/tex]
Hence, the solution to the provided expression using the difference of square method of algebra is a=1.
Learn more about the difference of square here;
https://brainly.com/question/1148545
The solutions to 15(2a – 2) = 5(a2 – 1) are:
a = 1, a = –1
a = 5, a = –1
a = 5, a = 1
Answer:
C. a = 5, a = 1
Step-by-step explanation:
Can anybody help me please with question 1 please and thank you .I would really appreciate it so much.
Answer:
Given
Step-by-step explanation:
At the beginning it says "Given: AB = CB" so they just gave you that information.
7. a. dilate point c using center d and scale factor 3/4
b. dilate segment ab using center d and scale factor 1/2.
The dilations will give the relations:
C'D = (3/4)CD and A'B' = (1/2)AB
And a sketch of the graph can be seen at the end.
How to dilate C?First, we want to dilate point C using D as the center of dilation with a scale factor = 3/4.
This only means that we will have the new point C', such that:
C'D = (3/4)*CD
Where CD is the distance between points C and D
b) Similarly, we will dilate the whole segment AB into the segment A'B', such that:
A'B' = (1/2)AB.
It is hard to give the exact graph when we don't know the coordinates of the points, but the graph should look something like the one you can see below.
If you want to learn more about dilations, you can read:
https://brainly.com/question/3457976
add [7x] ^2-8, [2x] ^2+1 and 5-x^2. and ^ means power and if you spam i will report you
Answer:
52x2−2
Step-by-step explanation:
=49x2+−8+4x2+1+5+−x2
Combine Like Terms:
=49x2+−8+4x2+1+5+−x2
=(49x2+4x2+−x2)+(−8+1+5)
=52x2+−2
Solve each system of equations 2a+b+c=0 2b+c+a=-4 2c+a+b+4
Answer:
(a, b, c) = (0, -4, 4)
Step-by-step explanation:
Any of a variety of calculators, spreadsheets, or web sites can solve these equations for you. A calculator result is attached. It shows the solution to be ...
(a, b, c) = (0, -4, 4)
__
If you'd like to solve the system by hand, here's one way:
Add the three equations together:
(2a +b +c) +(2b +c +a) +(2c +a +b) = (0) +(-4) +(4)
4a +4b +4c = 0 . . . . simplify
a +b +c = 0 . . . . . divide by 4
Substitute this into each of the other equations:
a +(a +b +c) = 0 ⇒ a +0 = 0 ⇒ a = 0
b +(a +b +c) = -4 ⇒ b +0 = -4 ⇒ b = -4
c +(a +b +c) = 4 ⇒ c +0 = 4 ⇒ c = 4
Solve for x.
z = 6 π x y
Image Below
Answer:
third option
Step-by-step explanation:
Given
z = 6πxy ( isolate x by dividing both sides by 6πy )
[tex]\frac{z}{6\pi y}[/tex] = x
Homework Jim Thompson! Part 1
Problem 1
Answers:
Choice A) CylinderChoice C) Rectangular prismChoice D) Rectangular pyramidReason:
Refer the diagram below to see how rectangular cross sections are possible. The cross sections are marked in red.
For the rectangular prism, we could have a vertical or horizontal plane. For the cylinder, only a vertical cross section is possible. On the flip side, a rectangular pyramid can only have horizontal rectangular cross sections (which are similar to the base).
========================================================
Problem 2
Answer: Approximately 73,280.62908 square feet
Explanation:
Calculate the area of the trapezoid. Ignore the small triangle for now.
A = h*(b1+b2)/2
A = 354*(266+158)/2
A = 75,048
Now calculate the area of the triangle we ignored earlier
Before we do this, we'll need to use the pythagorean theorem to find the missing horizontal piece
a^2 + b^2 = c^2
b = sqrt(c^2 - a^2)
b = sqrt(97^2 - 40^2)
b = 88.368546 which is approximate.
Now we can find the area of the small triangle
Area = base*height/2 = 88.368546*40/2 = 1,767.37092
This is to be subtracted from the area of the trapezoid we found earlier.
75,048 - 1,767.37092 = 73,280.62908
Round the result however you need to.
You poured some 6% alcohol solution and some 8% alcohol solution into a mixing container. Now you have 600 grams of 7.4% alcohol solution. Write and solve a system of equations to find how many grams of 6% solution and how many grams of 8% solution you poured into the mixing container.
You mixed ___ grams of 6% solution with ____grams of 8% solution.
Answer:
180 grams of 6%420 grams of 8%Step-by-step explanation:
Let s and e represent the grams of 6% and 8% solution, respectively. The given relations can be described by ...
s + e = 600 . . . . . you have 600 grams of mixture
0.06s +0.08e = 0.074(600) . . . . grams of alcohol in the mixture
__
The first equation can give an expression for s that substitutes nicely into the second equation:
s = 600 -e
0.06(600 -e) +0.08e = 0.074(600) . . . . substitute for s
0.02e = 0.014(600) . . . . . . subtract 0.06(600)
e = 420 . . . . . . . divide by 0.02
s = 600 -420 = 180
You mixed 180 grams of 6% solution with 420 grams of 8% solution.
Answer: 180 grams of 6% solution with 420 grams of 8% solution.
Step-by-step explanation:
Let x and y be the weight (in grams) of 6% and 8% alcohol solution. Since the total weight is 600 grams, therefore,
[tex]$$\Rightarrow x+y=600 \ldots \text { (1) }[/tex]
Using the statement given, we can write the following equation:
[tex]\Rightarrow 6 x+8 y=(7.4)(600)\\ \Rightarrow 6 x+8 y=4440 \text {... (2) }[/tex]
Substitute the value of y from equation (1) into equation (2), we'll get:
[tex]\begin{gathered}\Rightarrow 6 x+8(600-x)=4440 \\\Rightarrow 6 x+4800-8 x=4440 \\\Rightarrow 2 x=360 \\\Rightarrow x=180\end{gathered}[/tex]
Therefore,
[tex]\Rightarrow y=600-180=420[/tex]
Therefore, you mixed 180 grams of 6% solution with 420 grams of 8% solution.
Which is a factor of x2 8x – 48? (x – 6) (x 4) (x – 16) (x 12)
Answer: D
Step-by-step explanation:
Sony’s wireless bluetooth speaker originally costs $99. Currently it is on sale for 45% off. What is the discount?
Answer:
How much it's worth now - 54.45 Dollars
Discount - 44.55 Dollars
Assessment timer and count
Assessment items
Item 3
A lamp is on sale, and its price is reduced from $80 to $50.
What is the percent of decrease?
Answer:
37.5 percent
Step-by-step explanation:
Finding percent is simple. You want to find percent of the price drop so you subtract 50 from 80 and get 30. Once you get 30 you divide by 80 (your original price). Once you do this you will get 0.375. Multiply this by 100 to get your percent.
100 BRAINLY POINTS!!!
A scatter plot shows a negative linear relationship between the time spent reviewing a writing assignment and
the number of spelling mistakes on it. The following statements describe possible relationships between the
variables.
I. As the review time decreases, the number of spelling mistakes increases.
II. As the review time increases, the number of spelling mistakes increases.
III. As the review time decreases, the number of spelling mistakes decreases.
IV. As the review time increases, the number of spelling mistakes decreases.
Which of these statements are correct?
A. Only IV
B. Only III
C. II And III
D. I And IV
EXPLAIN YOUR ANSWER
SHOW YOUR WORK
PLEASE CUH I NEED HELP
Negative slope
Means sample equation in slope intercept form is
y=-mxSo if you spot 2 mistakes on observing 1 min
then slope is 2
y=-2xPut one by one
(1,-2)(2,-4)Direct variation
Hence
Option 1 and 4 are correctAnswer:
D) I and IV
Step-by-step explanation:
The variable along the x-axis is the independent variable.
The variable along the y-axis is the dependent variable.
It would be fair to determine that the time spent reviewing a writing assignment is dependent upon the number of spelling mistakes, as the more mistakes an assignment has, the longer it should take to review, however we cannot say this for certain, therefore we cannot assign the dependent and independent variables.
If the scatter plot shows a negative linear relationship, then as the x-values increase, the y-values decrease.
Statements I and IV suggest a negative linear relationship only, depending on which variable is dependent and independent.
(FYI Statements II and III describe positive linear relationships)
Statement I
x-axis (independent variable) = number of spelling mistakes
y-axis (dependent variable) = review time
Statement IV
x-axis (independent variable) = review time
y-axis (dependent variable) = number of spelling mistakes
Therefore, as we cannot be sure which is the dependent variable and which is the independent variable, the solution is D.
A box of dried fruit has 52 Calories in 4 servings how many calories are there per serving
Answer:
13 calories per serving
Step-by-step explanation:
52/4 = 13
Answer:
13
Step-by-step explanation:
52 divide 4 equals to 13
Hope this help :)
True or false: When describing range, you should start with the smallest y-value, au
work your way to the largest.
Answer:
true
Step-by-step explanation:
hope this helped!
p.s it would be cool if you gave me brainliest.
Answer:
True
Step-by-step explanation:
To find the range first order the data from the least to greatest. Then subtract the smallest value from the largest value in the set.
someone help please
Answer:
Step-by-step explanation:
Semicircle:
diameter = 6 yd
r = 6/2 = 3 yd
[tex]Area \ of \ semicircle = \dfrac{1}{2}\pi r^{2}\\\\[/tex]
[tex]=\dfrac{1}{2}*3.14*3*3\\\\= 14.13 \ yd^{2}[/tex]
Triangle:
base = b =6 yd
height = h = 4 yd
[tex]Area \ of \ triangle = \dfrac{1}{2}bh\\\\[/tex]
[tex]=\dfrac{1}{2}*6*4\\\\\\= 3*4\\\\= 12 \ yd^{2}[/tex]
Area of composite figure =area of semicircle + area of triangle
= 14.13 +12
= 26.13 yd²
Find the length of the side RT in the triangle above.
In the given ∆RST,
➾Tan 53° = ST/RT
➾ 1.327 = 14/RT
➾ RT = 14/1.327
➾ RT = 10.55 (approx)
➢ Therefore, the length RT = 10.55 cm (approx)
which expression is equivalent to 2(t+1)+(t+3)?
a. 2t + 5
b. 3t + 5
c. 3t + 3
d 4t + 8
Can anyone please help me with this question?
Answer:
Step-by-step explanation:
67 is tyen answer i did the quiz im in 9th grade
Please help :)
It would be really helpful if your formatted your answer like 8b. (Answer)
It’s fine if you can’t answer them all juts say which ones your can :) tysm!
Answer:
36
Step-by-step explanation:
one calculator price =30/5=6
cost price of 6 calculator=6*6=36
Byron earns $11.00 per hour. How many hours will Byron have to work to earn $143.00?
7.7 hours
13.0 hours
14.3 hours
15.7 hours
Answer:
13.0 hours
Step-by-step explanation:
$143 ÷ $11 (how he gets payed per hour) = 13 hours
Byron has to work 13 hours to earn $143 dollars
Answer:
[tex]Byron \: will \: have \: to \: work \: for \\ \: 13\: hrs \: to \: earn \: 143[/tex]
[tex]let \: the \: number \: of \: hrs \: = x \\ then \\ for \: the \: salary \: of \: \: 143 \: \\ the \: earning \: \times \: the \: time \: (x) = 143 \\ so \: 11x \: = 143 \\ x = \frac{143}{11} = 13.[/tex]
Graph the line with the equation y=5/4x-2
Can anyone help me with this?
Answer:
is there an area tho
Step-by-step explanation:
please help!! a circular garden has a diameter of 16 yards. what is the area of the garden. use 3.14 for pi.
A. 50.24 yd2
B. 100.48 yd2
C. 200.96 yd2
D. 803.84 yd2
Answer:
C. 200.96 yd²
Step-by-step explanation:
diameter = 16 yd
radius = diameter/2 = 16 yd / 2 = 8 yd
area = πr²
area = 3.14 × (8 yd)²
area = 200.96 yd²
anyone know this? pleaseee
Answer:
x-4/3
Step-by-step explanation:
the unknown number is the number they think of, you can't read their mind. but you know you have to subtract by 4 and divide by 3.
Can you answer the question on the picture
Answer:
[tex]\huge\boxed{\sf 6x^2-x+16}[/tex]
Step-by-step explanation:
[tex]= (2x-3)(3x+4)\\\\Expand\\\\= 2x(3x+4)-3(3x+4)\\\\Distribute\\\\= 6x^2+8x-9x+16\\\\= 6x^2-x+16\\\\\rule[225]{225}{2}[/tex]
Answer:
6x²-x-12
Step-by-step explanation:
(2x-3)(3x+4)
2x(3x+4) -3(3x+4)
6x²+8x-9x-12
6x²-x-12
Solve for the given variable
ax-bx=3;x
I need help :
Answer:
x = [tex]\frac{3}{a-b}[/tex]
Step-by-step explanation:
Given
ax - bx = 3 ← factor out x from each term on the left side
x(a - b) = 3 ← divide both sides by (a - b)
x = [tex]\frac{3}{a-b}[/tex]
The slope of 5,10 and 2,6 ?
Answer:
4/3
Step-by-step explanation:
We can use the slope formula to find the slope
m = ( y2-y1)/(x2-x1)
= ( 6-10)/(2-5)
= -4/-3
= 4/3
1. Which of the following models is an exponential decay model?
a) y = 12 (3.57)^t
b) y = 4 (1.21)^t
c) y = 1 + 6t
d) y = 7 (0.98)^t
2. Which of the following models is an exponential decay model?
A) y = 2,000 (0.07)^t
B) y = 4,000 (3.84)^t
C) y = 26t^2
D) y = 1 + 17t
3. Exponential decay models have a base between ____ and ____.
Answer:
1. d) [tex]\mathsf{y=7(0.98)^t}[/tex]
2. A) [tex]\mathsf{y=2000(0.07)^t}[/tex]
3. zero and 1
Step-by-step explanation:
General form of an exponential model: [tex]\mathsf{y=ab^x}[/tex]
If 0 < b < 1 then model decays
1. d) [tex]\mathsf{y=7(0.98)^t}[/tex]
2. A) [tex]\mathsf{y=2000(0.07)^t}[/tex]
3. Exponential decay models have a base between 0 and 1
If the area of a rectangle is 12mn^2 and the width is 3m^2n, what would be the length of the rectangle, given that length is found by dividing area by length?
Let's see
Area=Length×Breadth[tex]\\ \rm\rightarrowtail 3m^2n(L)=12mn^2[/tex]
[tex]\\ \rm\rightarrowtail mL=4n[/tex]
[tex]\\ \rm\rightarrowtail L=4n/m[/tex]
Answer:
[tex]\sf length=\dfrac{4n}{m}[/tex]
Step-by-step explanation:
Area of a rectangle = width × length
Given:
[tex]\sf area=12mn^2[/tex][tex]\sf width=3m^2n[/tex]Substituting the given expressions into the equation:
[tex]\sf \implies 12mn^2=3m^2n \times length[/tex]
[tex]\sf \implies length=\dfrac{12mn^2}{3m^2n}[/tex]
Factor 12 to 3 · 4:
[tex]\sf \implies length=\dfrac{3 \cdot 4mn^2}{3m^2n}[/tex]
Cancel the common factor of 3:
[tex]\sf \implies length=\dfrac{4mn^2}{m^2n}[/tex]
Simplify [tex]\sf \dfrac{n^2}{n}=n[/tex] :
[tex]\sf \implies length=\dfrac{4mn}{m^2}[/tex]
Simplify [tex]\sf \dfrac{m}{m^2}=\dfrac{1}{m}[/tex] :
[tex]\sf \implies length=\dfrac{4n}{m}[/tex]
Drag each day to the correct location on the tree drag each estimated measurement next to the correct she not all shapes and measurements will be used.
A tree from a forest with a height of 30 feet is shown below the bottom branches are about 4 feet from the ground and are 10 feet long from left to right.the tree trunk is about 2 feet wide.
what are the appropriate shapes to model the trunk of the tree and the rest of the tree?what are the approximate surface areas of each of the two shapes?
Answer: cone Cylinder
Surface area is 402ft2 and 69ft2
Step-by-step explanation:
I got the answer right
The appropriate shape to model trunk is cylinder, rest of the tree is cone and surface area of trunk is 25.12 [tex]feet^{2}[/tex]and surface area of rest of the tree is 415.58 [tex]feet^{2}[/tex].
What is surface area?It is the space occupied by a two dimensional surface. The area occupied by a three dimensional object by its outer surface area.
How to calculate surface area?The upper part of the tree is similar to the cone and the trunk is of cylindrical shape. So the appropriate shape used to model the entire is cone above the cylinder.
We have been given the height of entire tree=30 feet,
Width of upper part=10 feet.
Height of trunk=4 feet
Width of tree means diameter of upper part or cone. Height of cone means height of cylinder, width of trunk means diameter of cone.
So, The radius of cone ie 5 feer,radius of cylinder is 1 feet, height of cone be 30-4=26 feet.
Surface area of cone is πrl where l is slant height of cone which is equal to [tex]\sqrt{r^{2} +h^{2} }[/tex]
l=[tex]\sqrt{5^{2} +26^{2} }[/tex]
=[tex]\sqrt{701}[/tex]
=26.47 feet.
Surface area of cone=π*5*26.47
=3.14*5.26*26.47
=415,28 [tex]feet^{2}[/tex]
Surface area of cylinder=2πrh
=2π*4*1
=2*3.14*4
=25.12 [tex]feet^{2}[/tex]
Hence cone and cylinder of surface area 415.28 [tex]feet^{2}[/tex] and 25.12 [tex]feet^{2}[/tex] can be used to model out tree.
Learn more about surface area at https://brainly.com/question/16519513
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slope-intercept form, write the equation of the line
that passes through the point (4, 2) with a slope of 5.
Answer:
[tex]y=5x-18[/tex]
Step-by-step explanation:
Given the following question:
Point A = (4, 2) = (x, y)
Slope = 5
To find the answer we are going to have to use the formula for slope intercept, substitute the values, then solve for the variable b to have our answer.
[tex]y=mx+b[/tex]
[tex]y=2[/tex]
[tex]m=5[/tex]
[tex]x=4[/tex]
[tex]2=5(4)+b[/tex]
[tex]5\times4=20[/tex]
[tex]2=20+b[/tex]
[tex]20-20=0[/tex]
[tex]2-20=-18[/tex]
[tex]-18=b[/tex]
[tex]b=-18[/tex]
[tex]y=5x-18[/tex]
Your answer is "y = 5x - 18."
Hope this helps.