A:
16a^2-24a+9
16a^2-12a-12a+9
4a(4a-3)-3(4a-3)
(4a-3)(4a-3)
(4a-3)^2
(4a-3)^2
B: Use difference of squares method
(3a+5b)(3a−5b)
Part A: The length of each side of the square is (4a - 3) units.
Part B: The dimensions of the rectangle are (3a + 5b) units (length) and (3a - 5b) units (width).
Part A:
The area of a square is given by the formula A = s^2, where "s" is the length of each side of the square. In this case, the area is (16a² - 24a + 9) square units.
To determine the length of each side of the square, we need to factor the area expression completely and set it equal to (s^2).
The area expression is a quadratic trinomial: 16a² - 24a + 9.
To factor the trinomial, we look for two binomials that, when multiplied together, give us the original trinomial. The binomials will have the form: (ma ± b)(na ± c).
To factor 16a² - 24a + 9, we look for two numbers whose product is 16 * 9 = 144, and whose sum is -24 (the middle coefficient).
The two numbers are -12 and -12 because (-12) * (-12) = 144 and (-12) + (-12) = -24.
Now, rewrite the middle term (-24a) using -12a - 12a:
16a² - 12a - 12a + 9
Group the terms and factor by grouping:
(16a² - 12a) - (12a - 9)
Now, factor out the greatest common factor (GCF) from each group:
4a(4a - 3) - 3(4a - 3)
Now, notice that we have a common binomial factor of (4a - 3):
(4a - 3)(4a - 3)
Since both binomials are the same, we can rewrite it as (4a - 3)^2.
Now, set (4a - 3)^2 equal to (s^2):
(4a - 3)^2 = s^2
To find the length of each side (s), take the square root of both sides:
√((4a - 3)^2) = √(s^2)
4a - 3 = s
Therefore, the length of each side of the square is (4a - 3) units.
Part B:
The area of a rectangle is given by the formula A = length * width. In this case, the area is (9a² - 25b²) square units.
To determine the dimensions of the rectangle, we need to factor the area expression completely and identify the length and width.
The area expression is a difference of squares: 9a² - 25b².
To factor a difference of squares, we use the formula: a² - b² = (a + b)(a - b).
In this case, a = 3a and b = 5b:
9a² - 25b² = (3a + 5b)(3a - 5b)
Therefore, the dimensions of the rectangle are (3a + 5b) units (length) and (3a - 5b) units (width).
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If the vertex of a parabola is (2,9), what is the axis of symmetry?
Answer:
x=2
Step-by-step explanation:
The Axis of Symmetry is when a line is put where it splits the parabola in the half perfectly. The vertex is where the parabola starts. The line x=2 is when it splits it into two congruent parts.
Let g be the function given by g(x)=limh→0sin(x h)−sinxh. What is the instantaneous rate of change of g with respect to x at x=π3?
The instantaneous rate of change of g with respect to x at x = π/3 is 1/2.
How to determine the instantaneous rate of change of a given functionThe instantaneous rate of change at a given value of [tex]x[/tex] can be found by concept of derivative, which is described below:
[tex]g(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]
Where [tex]h[/tex] is the difference rate.
In this question we must find an expression for the instantaneous rate of change of [tex]g[/tex] if [tex]f(x) = \sin x[/tex] and evaluate the resulting expression for [tex]x = \frac{\pi}{3}[/tex]. Then, we have the following procedure below:
[tex]g(x) = \lim_{h \to 0} \frac{\sin (x+h)-\sin x}{h}[/tex]
[tex]g(x) = \lim_{h \to 0} \frac{\sin x\cdot \cos h +\sin h\cdot \cos x -\sin x}{h}[/tex]
[tex]g(x) = \lim_{h \to 0} \frac{\sin h}{h}\cdot \lim_{h \to 0} \cos x[/tex]
[tex]g(x) = \cos x[/tex]
Now we evaluate [tex]g(x)[/tex] for [tex]x = \frac{\pi}{3}[/tex]:
[tex]g\left(\frac{\pi}{3} \right) = \cos \frac{\pi}{3} = \frac{1}{2}[/tex]
The instantaneous rate of change of g with respect to x at x = π/3 is 1/2. [tex]\blacksquare[/tex]
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The instantaneous rate of change of g with respect to x at x = π/3 is 1/2.
What is the instantaneous rate of change?The instantaneous rate of change is the change in the rate at a particular instant, and it is the same as the change in the derivative value at a specific point.
The instantaneous rate of change is given by the following formula;
[tex]\rm g(x)=lim_{h\rightarrow 0}\dfrac{f(x+h)-f(x)}{h}[/tex]
The given function is;
[tex]\rm f(x)=sinx[/tex]
The function is also written as;
[tex]\rm g(x)=lim_{h\rightarrow 0}\dfrac{sin(x+h)-sin(x)}{h}\\\\g(x)=lim_{h\rightarrow 0}\dfrac{sinx cosh +cosx sinh-sinx}{h}\\\\g(x)=lim_{h\rightarrow 0}\dfrac{sinh}{h}. \ lim_{h\rightarrow 0} cosx\\\\g(x)=cosx[/tex]
Substitute the value of x in the function
[tex]\rm g(\pi /3)= cos(\pi /3)=1/2\\[/tex]
Hence, the instantaneous rate of change of g with respect to x at x = π/3 is 1/2.
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Kevin is planning a trip. His round-trip train ticket
costs 550 and the hotel costs $200 per night. If
he spends $850 on his train ticket and hotel, how
many nights did he stay?
FIRST TO ANSWRR GETS 30 POINTS!
A jewellery shop is having a sale.
A bracelet is now reduced to £420.
This is 70% of the original price.
a) Work out the original price of the bracelet.
A ring is now reduced to £840.
This is a saving of 40% of the original price.
b) Work out the original price of the ring.
Answer:
a) £600
b) £1400
Step-by-step explanation:
a) Set up a ratio of price to percentage of original price.
Let x = original price
⇒ £420 : 70 = £x : 100%
[tex]\sf \implies 420 : 70 = x : 100[/tex]
[tex]\sf \implies \dfrac{420}{70}=\dfrac{x}{100}[/tex]
[tex]\sf \implies x=100\cdot\dfrac{420}{70}[/tex]
[tex]\sf \implies x=600[/tex]
Therefore, the original price of the bracelet was £600
b) Set up a ratio of price to percentage of original price.
If the ring is reduced by 40% then it is now 60% of the original price, since 100% - 40% = 60%
Let x = original price
⇒ £840 : 60% = £x : 100%
[tex]\sf \implies 840 : 60 = x : 100[/tex]
[tex]\sf \implies \dfrac{840}{60}=\dfrac{x}{100}[/tex]
[tex]\sf \implies x=100\cdot\dfrac{840}{60}[/tex]
[tex]\sf \implies x=1400[/tex]
Therefore, the original price of the ring was £1400
Videos Incorporated charges a membership fee of $4.99 plus $0.99 for each movie you watch. Videos Plus does not charge a membership fee but charges $2.99 per movie. Videos Plus is a better deal than Videos Incorporated. Which inequality represents this situation?
What is the inequality symbol for the situation? Answer Chocies: >, <, =.
Videos Incorporated Expression: Answer choices: 4.99x + 0.99, 4.99 + 0.99x, 4.99 - 0.99x
Videos Plus Expression: Answer Choices: 2.99x, 2.99x + 1, 2.99x - 1.
Which inequality represents this situation?
Videos Incorporated Expression:
-> Starting membership fee of $4.99, and then adding onto the overall cost is $0.99 for every movie watched.
4.99 + 0.99x
Videos Plus Expression:
-> There is no membership fee, but adding to the cost is $2.99 per movie.
2.99x
Which inequality represents this situation?
-> You do not have answer options, so this is a guess.
-> It states that "Videos Plus is a better deal than Videos Incorporated" which means Videos Incorporated costs more than Videos Plus
2.99x < 4.99 + 0.99x
Find the geometric mean between 6 and 21.
Answer:
13.5
Step-by-step explanation:
That is the mean between 6 & 21
Jackson recorded the following data: 2,5, X, 2, 4, 3. If the mean
of the data is 3, what is the value of x? Explain how you found your answer
Answer:
x = 2
Step-by-step explanation:
mean = sum of data / number of data
3 = 2 + 5 + x + 2 + 4 + 3 / 6
3 = 16 + x / 6
18 = 16 + x
2 = x
The missing value of data is 2.
What is arithmetic Mean?The simplest and most popular way to measure a mean or average is the arithmetic mean. It simply entails adding up a collection of numbers, then dividing that total by the total number of numbers in the series.
We have,
Data: 2,5, X, 2, 4, 3
Mean= 3
So, Mean
3 = Sum of data/ Total number of data
3 = (2 + 5 +x + 2 + 4 +3)/ 6
18 = 16 + x
x = 18 - 16
x= 2
So, the missing value of data is 2.
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if u help me and answer correctly ill give brainlest thanks
Answer:
10/4 in simplest form 5/2
Step-by-step explanation:
Since 2 goes into 10 and 5 you divide 2 by those two numbers which gives you 5/2
i dont understand???????????
Answer:
Step-by-step explanation:
We can obtain that the dimensions of the rectangle are 7 by 5.
Since A = lw, the total area is 35.
Two marathon runners start a race at different times. Runner A stars her race first. and then Runner B starts his race 30 minutes later. Runner A runs 4 miles per hour. Runner B runs 6 miles per hour. Which equation can be used to determine the time in hours, t, that the runners will be side by side, the same distance from the starting line?
Answer:
4t = 6(t - 1/2)
Step-by-step explanation:
For Runner A, the expression is 4t since this runner's rate is 4 mph. For Runner B, the expression is 6(t - 1/2) since Runner B starts 1/2 hour after Runner A, and this runner's rate is 6 mph. Set these two expressions equal to each other.
Pls help with this problem
Step-by-step explanation:
every triangle inscribed into a circle with the baseline being a diameter of the circle must be a right-angled triangle.
therefore,
angle XVY = 90°.
for VY we can use Pythagoras
c² = a² + b²
with c being the Hypotenuse (the line opposite of the 90° angle, in our case XY).
XY = 2×ZY = 2×17 = 34.
so,
34² = 30² + VY²
VY² = 34² - 30² = 1156 - 900 = 256
VY = 16
Gavin purchased a stereo speaker in the shape of a triangular pyramid. It has a height of 6 inches. The volume of the speaker is 22 in3.
What is the area of the base of the speaker?
A. 5 in
B. 11 in
C. 66 in
D. 44 in
Answer: 11 in
Step-by-step explanation: To find the surface area of a triangular pyramid, the formula is B = 3v/h, where v is volume and h is height. Plugging this in, 3 * 22 = 66. 66 divided by 6 is 11. Thus, the area of the base is 11 inches.
rent is putting in a sidewalk that is 1/18 yard thick, 9 yards long, and 1 yard wide. how many cubic yards of cement does he need?
Answer:
1/18 x 9 x 1 = .5 cubic yards. Why would you ever waste time asking this....
Step-by-step explanation:
Answer:
Step-by-step explanation:
We have to find the volume. we can use volume of the cuboid formula
l = 1/18 yard
w = 9 yard
h = 1 yard
Volume = l*w*h
[tex]= \dfrac{1}{18}*9*1\\\\\\= \dfrac{1}{2}\\\\\\= 0.5 \ \sf cubic yard[/tex]
0.5 cubic yards of cement is needed
What is the measure of ∠H?
1. 115
2. 65
3. 50
4. 25
Answer:
2
Step-by-step explanation:
Since FG is congruent to FH, angles FGH and FHG are congruent since angles opposite congruent sides in a triangle are congruent.
PLEASE HELP!!!
NO LINKS!!!!
7. A spherical balloon has a circumference of 25 cm.
a.) What is the approximate surface area of the balloon to the nearest square
centimeter?
b.) What is the approximate volume of the balloon to the nearest cubic
centimeter?
8. The volume of a sphere is 2,000pim^3. What is the surface area of the sphere to the nearest square meter?
9. The volumes of two similar solids are 1408 m^3 and 594m^3. The surface area of the smaller solid is 549m^2. What is the surface area of the larger solid?
10. What is the maximum volume of a square pyramid that can fit inside a cube with a side length of 14cm?
Answer:
im lost only because you made this so long
Step-by-step explanation:
This figure represents a ramp for a dollhouse that is being covered with fabric on all sides. How much fabric is needed to cover the ramp? 144 cm² 138 cm² 110 cm² 66 cm²
Answer: 144 cm^2
Step-by-step explanation:
i did the quiz
Answer:
144 cm²
Step-by-step explanation:
I took the K12 test
If the distance between two lines never changes,is it perpendicular,parallel,intersecting lines or rays
Answer:
parallel
Step-by-step explanation:
If the distance between two lines never changes, they are parallel lines.
Answer:
parallel
Step-by-step explanation:
parallel lines never have a distance change between them
The bases of a trapezoid are 11 meters and 14 meters. It’s height is 10 meters. What is the area of the trapezoid?
Answer:
120 m²
Step-by-step explanation:
A = (1/2) · (p + q) · h
A = (1/2)(14 + 10)(10)
A = (1/2)(24)(10)
A = 120
Hope this helps :)
Max made a journey of 700km partly by train and partly by bus.He started his journey at 8.00am. by train which travelled at 50km/hr. After alighting from the train, he took a lunch break of 30 minutes. He then continued his journey by bus which travelled at 75km/hr.The whole journey took 11.75hours. Determine the distance travelled by bus.
I really don't know I'm not big on school subjects
I NEED THAT ANSWER ASAP
Answer:
2064.19 km^3
Step-by-step explanation:
Formula for volume of a sphere
V = 4/3 pi r^3
= 4/3 * 3.14 * 7.9^3 =
Answer:
[tex]2064\ km^3[/tex]
Step-by-step explanation:
Volume of a Sphere: [tex]\frac{4}{3}\pi r^3[/tex]
r (radius) = 7.9 km[tex]V=\frac{4}{3}\pi r^3[/tex]
[tex]V=\frac{4}{3}*3.14*(7.9)^3 \\\\V=\frac{4}{3}*3.14*493.039\\\\V=\frac{4}{3}*1548.142\\\\V=\frac{4}{3}*\frac{1548.142}{1}\\\\V=\frac{6192.568}{3}\\\\V=2064.18933 < == round\ to\ the\ nearest\ whole\ number\\\\V=2064\ km^3[/tex]
Therefore, the volume of the sphere is [tex]2064\ km^3[/tex]
Hope this helps!
Graph the inequality of x>15
Answer:
Hope this helps!
Asad wants to print 500 photos. A shop charges at rate of 0. 20 per photo to print. How much does he pay to print the photos?
Answer:
$100
Step-by-step explanation:
multiply 500 by 0.20
you can also see this as a fraction .20 is also 1/5 so if you take 1/5 of 500 you get 100
A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 feet from the base of the pole. A right triangle with side length 10 feet, hypotenuse of 22 feet, and side of h. What is the height of the pole? Round to the nearest hundredth. 12. 00 feet 19. 60 feet 24. 17 feet 38. 40 feet.
The height of the pole from the ground is 19.60 feet round to the nearest hundredth.
How to find the length of longest side in right angle triangle?To find the lenght of longest side in right angle triangle, the Pythagoras theorem is used.
According to this theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.
A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 feet from the base of the pole.
A right triangle with side length 10 feet, hypotenuse of 22 feet, and side of h. Thus, the length of side of h by the Pythagoras theorem can be given as,
[tex]h^2=22^2-10^2\\h=\sqrt{484-100}\\h=\sqrt{384}\\h=19.60\rm\; ft[/tex]
Thus, the height of the pole from the ground is 19.60 feet round to the nearest hundredth.
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Mr.B called Mrs.A, then called Ms.C. If Mr.B called Ms. C first, then Mrs. A, what property does this mimic? Associative, Commutative, or Distributive property.
Order these from least to greatest 69/10 , 6.99, 7.927, 6 8/9
Answer:
6 8/9 , 69/10 , 6.99 , 7.927
Step-by-step explanation:
[tex]\frac{69}{10} = 6.9[/tex]
[tex]6\frac{8}{9} = 6.8[/tex]
Please help with an explanation of how you found the answer because I am really confused. I will mark brainliest for best answer!
Answer:
The answer is A
Step-by-step explanation:
The minimum is 52 and the maximum is 65 therefore B and C are false.
Data set total number is 13 D medium is 56
so A is the correct answer
Which is the pattern for factoring the sum of cubes
Answer:
a³ +b³ = (a +b)(a² -ab +b²)
Step-by-step explanation:
The patterns for factoring the sum and difference of cubes are similar. The sign of the second term in each factor is reversed from one pattern to the other.
a³ -b³ = (a -b)(a² +ab +b²)
a³ +b³ = (a +b)(a² -ab +b²) . . . . . pattern for factoring sum of cubes
A 50kg ball rolls off a building it is going 5 m/s when it hits the ground. How tall is the building
Answer:
1.25m
Step-by-step explanation:
s=ut+1/2gt^2
Newton's second law of motion
F=ma
50x10
500N
500/50
g/a=10m/s^2
u=0m/s
s= 1/2gt^2
v=u+gt
5=0+(10t)
5=10t
t=0.5s
s=0.5×10×(0.5)^2
=1.25m
Help pls!!!!!!!!!
ddddddddddddddd
A tower that is 166 feet tall casts a shadow 167 feet long. Find the angle of elevation of the sun to the
nearest degree.
Answer:
The angle is approximately [tex]45^\circ[/tex].
Step-by-step explanation:
We should start with a diagram (like the one attached). Notice the length of the tower and the length of the shadow are the legs of a right triangle, and the angle of elevation is an acute angle of that triangle.
Since we are given the opposite and adjacent sides to the angle, we will use the tangent function:
[tex]\tan{\theta}=\frac{\text{opposite side}}{\text{adjacent side}}[/tex]
In this case, the opposite side is the height of the tower, 166 ft. The adjacent side is the length of the shadow, 167 ft. So, we have:
[tex]\tan{\theta}=\frac{166}{167}[/tex]
To get the angle, we need to use inverse tangent:
[tex]\theta=\tan^{-1}(\frac{166}{167})\\\theta \approx 45[/tex]
The angle is approximated [tex]45^\circ[/tex] when rounded to the nearest degree.