Answer: [tex]\frac{25}{6} a^{9} b^{10}[/tex]
Step-by-step explanation:
Assuming the described expression is:
[tex]\frac{(5ab)^{3}}{30 a^{-6} b^{-7}}[/tex]
And knowing the condition [tex]a \neq 0[/tex] and [tex]b \neq 0[/tex]
We cansimplify it following the rules related to the exponents with the same base:
[tex]\frac{25}{6} a^{3} b^{3} a^{6} b^{7}[/tex]
Finally:
[tex]\frac{25}{6} a^{9} b^{10}[/tex]
Answer:
Answer: \frac{25}{6} a^{9} b^{10}
Step-by-step explanation:
100% on ed
simplify -2/5 + 4/3
Answer:
14/15
Step-by-step explanation:
find common denomerator 15
giving you -6/15 + 20/15
add
278.63 is 39% of what base
Answer:
The base is 714.436.
Step-by-step explanation:
Given:
Percentage of the base = 39%
Let the base be 'x'.
39 percent of base = 278.63
We need to find the base.
We now that Percentage of the base multiplied by the base is equal to 39 percent of base.
framing in equation form we get;
[tex]39\%x= 278.63\\\\\frac{39}{100}x=278.63\\[/tex]
Now multiplying both side by 100 we get;
[tex]\frac{39}{100}\times 100 \times x=278.63\times 100\\\\39x = 27863[/tex]
Now Dividing both side by 39 we get;
[tex]\frac{39x}{39}=\frac{27863}{39}\\\\x=714.436[/tex]
Hence the base is 714.436.
Jasmine can decorate 37 cakes every 5 minutes. She works for 7 hours a day. Estimate the total number of cakes she can decorate one day.
Answer:
3108
Step-by-step explanation:
number of 5-min segments in 1 hour
= 1 hour ÷ 5 min
= 60 min ÷ 5 min
= 12
number of 5-min segments in 7 hours
= 12 x 7
= 84
given that during each 5 min segment, jasmine decorates 37 cakes
i.e
1 (5-min) segment -----> decorates 37 cakes
84 (5-min) segments -----> decorates 37 x 84 = 3108 cakes
In this question, we're trying to find how many cakes Jasmine can decorate in 1 day.
We know that she can decorate 37 cakes everyone 5 minutes.
We also know she works 7 hours a day.
First, we need to find how much she makes it an hour.
To find this, multiply 37 by 12.
37 · 12 = 444
This means that she can decorate 444 cakes in an hour.
Now, multiply 444 by 7 to see how much she can decorate in a day.
444 · 7 = 3,108
This means that she can decorate 3,108 cakes in a day.
Answer:
3,108 cakes
use synthetic division and the remainder theorem to find P ( a).
P(x)= x^3+2 x^2-3x+5, a=3
Answer:
For given polynomial [tex]P(a)=a^3+2a^2-3a+5=41[/tex] and when a=3 is
[tex]P(3)=41[/tex]
Step-by-step explanation:
Given polynomial is [tex]P(x)=x^3+2x^2-3x+5[/tex]
Remainder Theorem:
To evaluate the function f(x) for a given number "a" you can divide that function by x - a and your remainder will be equal to f(a). Note that the remainder theorem only works when a function is divided by a linear polynomial, which is of the form x + number or x - number.
By using synthetic division for given polynomial [tex]P(x)=x^3+2x^2-3x+5[/tex] and factor is (x-a) (here x-3 is a factor given)
_3| 1 2 -3 5
0 3 15 36
___________________
1 5 12 | 41
Given polynomial can be written as
[tex]P(a)=a^3+2a^2-3a+5[/tex]
To find P(a):
[tex]P(a)=a^3+2a^2-3a+5[/tex]
put a=3
[tex]P(3)=3^3+2(3)^2-3(3)+5[/tex]
[tex]P(3)=27+18-9+5[/tex]
[tex]P(3)=41[/tex]
Therefore for given polynomial [tex]P(a)=a^3+2a^2-3a+5=41[/tex] when a=3 is [tex]P(3)=41[/tex]
Ready-mixed concrete is sold for $92 per cubic yard. Lance wants to pour a new driveway that is 45 yards long, 5 yards wide, and 1/3 yard thick. How much would a new driveway cost?
Answer:
$6900
Step-by-step explanation:
Given:
Length = 45 yards
Width = 5 yards
thickness = 1/3 yard
Volume,
= Length x Width x Thickness
= 45 x 5 x (1/3)
= 75 yards³
Costs:
1 cubic yard = $92
75 cubic yards = $92 x 75 = $6900
PLZ help super fast thanks
Answer:
B. [tex]\frac{1}{x^2y^7}[/tex]
Step-by-step explanation:
Given:
[tex](x^3y^{-2}z)(x^{-5}y^{-5}z^{-1})[/tex]
Hence Solving the given expression we get;
By Law of Indices which states;
[tex](a^xb^yc^z)(a^pb^qc^r) = a^{x+p}b^{y+q}c^{z+r}[/tex]
Hence we get;
[tex]x^{3+(-5)}y^{(-2)+(-5)}z^{1+(-1)}\\\\x^{3-5}y^{-2-5}z^{1-1}\\\\x^{-2}y^{-7}[/tex]
Also We know that
[tex]a^{-6} =\frac{1}{a^6}[/tex]
So,
[tex]\frac{1}{x^2y^7}[/tex]
Factor: x^2 - 100y^2 plz
Answer:
(X-10y)(x+10y)
Step-by-step explanation:
Write in exponential form , calculate the product & factor !
Answer:
Step-by-step explanation:
x² - 100y² = x² - (10y)²
=(x + 10y) (x - 10y)
Hint: a² - b² = (a + b) (a - b)
PLEASE HELP PLEASE I DONT UNDERSTAND THIS
Problem 1
The exterior angles sum to 360
9v+(19v-21)+45+(v+48)+7v = 360
36v+72 = 360
36v+72-72 = 360-72
36v = 288
36v/36 = 288/36
v = 8
Answer: v = 8===============================================
Problem 2
Answer: D) perpendicular bisectorWhy is this? because TW is perpendicular to VS (the right angle marker shows this). At the same time, TW cuts VS into two equal pieces, ie VW = WS. The tickmarks indicate the segments are the same length.
Olive Oil costs $8.70 per liter. A restaurant owner buys 5.6 liter of olive oil. How much does the owner pay?
Answer:
$48.72
Step-by-step explanation:
5.6 liters x $8.70 per liter= $48.72 total cost
Final answer:
To determine the total cost of the olive oil, multiply the quantity of 5.6 liters by the price per liter, which is $8.70. The total cost for the restaurant owner is $48.72.
Explanation:
The question asks us to calculate the total cost for a restaurant owner who buys 5.6 liters of olive oil at a price of $8.70 per liter. To find the total cost, we multiply the quantity of olive oil by the price per liter.
Calculation: Total cost = Quantity x Price per liter
Total cost = 5.6 liters x $8.70 per liter
Total cost = $48.72
Therefore, the restaurant owner will pay $48.72 for 5.6 liters of olive oil.
A team gained 5 yards on their first play of the game. Then they lost 6 yards. Find the total change in yardage
Answer:
The total change in yardage of the team is by - 1 yards.
Step-by-step explanation:
Let us assume that the initial yardage of the team was x yards.
Now, the team gained 5 yards on their play of the game.
Hence, the team now has (x + 5) yards on their play of the game.
Next, the team lost 6 yards and finally, the team will have [(x + 5) - 6] = (x - 1) yards in total.
Therefore, the total change in yardage of the team is by - 1 yard. (Answer)
Answer:
The total change in yardage of the team is by - 1 yards.
Step-by-step explanation:
The total change in yardage of the team is by - 1 yards.
Line L is mapped onto the line t by a dilation centered at
the origin with a scale factor of 3. The equation of line l is
2x - y = 7. What is the equation for line t?
The equation of line T is 2x - y = 7 ⇒ (6x - 3y = 21)
Step-by-step explanation:
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size
If the equation of a line is ax + by = k is dilated, with center origin and scale factor k, then the equation of the image of the line is kax + kby = kcThe line and its image are parallelThe coordinates of a general point on the image is (kx , ky)Line L is mapped onto the line T by a dilation centered at the origin and a scale factor of 3.
That means lint T is the image of line L after dilation
∵ The equation of line L is 2x - y = 7
∵ Line L is dilated by scale factor 3 and centered at origin
- That means multiply the equation of line L by 3 to find the
equation of line t
∵ Line T is the image of line L after dilation
∴ The equation of line T is (3)(2x) - (3)(y) = (3)(7)
∴ The equation of line T is 6x - 3y = 21
Very important note:
The equation of line T is the same with equation of line L but multiplied by the scale factor 3 ⇒ L and T are coincide lines (same line)
That means the equation of lines T and L is 2x - y = 7
The equation of line T is 2x - y = 7 ⇒ (6x - 3y = 21)
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How much surface area would be lost if you glued three 4-cm cubes together to make a rod that is three cubes long and one cube wide?
Answer:
Part 3) [tex]SA=288\ cm^2[/tex]
Part 4) [tex]64\ cm^2[/tex]
Step-by-step explanation:
Part 3) Calculate the total surface area of three 4 cm cubes
we know that
The surface area of a cube is equal to the area of its six square faces
[tex]SA=6b^2[/tex]
so
The surface area of three cubes is equal to the area of its 18 square faces
[tex]SA=18b^2[/tex]
where
b is the length side of the square face
In this problem
[tex]b=4\ cm[/tex]
so
The surface area of three cubes is
[tex]SA=18b^2[/tex]
substitute the given value
[tex]SA=18(4)^2[/tex]
[tex]SA=288\ cm^2[/tex]
Part 4) How much surface area would be lost if you glued three 4-cm cubes together to make a rod that is three cubes long and one cube wide?
In this case the total surface area of the three glued 4-cm cubes is equal to the area of its 14 square faces
so
The surface area lost is equal to
[tex]18b^2-14b^2=4b^2[/tex]
substitute
[tex]4(4)^2=64\ cm^2[/tex]
Gluing three 4-cm cubes together to form a rod results in a loss of 64 cm²of surface area because the areas of the glued faces are no longer exposed.
Each individual cube has 6 faces, so the surface area of one cube is 6 times the area of one face. With a side length of 4 cm, the area of one face is 4 cm imes 4 cm = 16 cm². Thus, the total surface area for one cube is 6 imes 16 cm²= 96 cm². For three separate cubes, this would be 3 imes 96 cm² = 288 cm².
When the three cubes are glued together side by side to form a rod, they share faces. Each glue contact removes two faces worth of area (one from each cube). As there are two glue contacts, a total of 4 faces are lost. Therefore, the lost surface area is 4 imes 16 cm2 = 64 cm².
The original total surface area was 288 cm², so the new surface area after gluing is 288 cm² - 64 cm² = 224 cm². Hence, gluing the cubes together results in a loss of 64 cm² of surface area.
write an equation of a line in slope -intercept form thag is parallel to the line 3x-2y=8
For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
By definition, if two lines are parallel then their slopes are equal.
We have the following equation of the line:
[tex]3x-2y = 8[/tex]
We manipulate algebraically:
[tex]-2y = -3x + 8\\y = \frac {3} {2} x-4[/tex]
Thus, a parallel line will have an equation of the form:
[tex]y = \frac {3} {2} x + b[/tex]
Answer:
[tex]y = \frac {3} {2} x + b[/tex]
How do I explain and show the work for a math word problem of If the baby was 8 lbs. 9 oz. and doubled her weight the first six months
Answer:
5 lb 11⅓ oz
Step-by-step explanation:
First, convert the weight at birth from pound and ounces to just ounces.
8 lb × 16 oz/lb + 9 oz = 137 oz
The baby doubles its weight in the first six months. That means its weight increases by 137 oz over 6 months. To find how much weight was gained in 4 months, write a proportion.
137 / 6 = x / 4
6x = 548
x = 91 ⅓
The baby gained 91 ⅓ oz in 4 months, or 5 lb 11⅓ oz.
What is the value of -2xy if x = -1 and y = 6?
12
-12
26
8
The solution is Option A.
The measure of the equation A = -2xy is A = 12
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = -2xy be equation (1)
Now , when x = -1 and y = 6
Substituting the values of x and y in the equation , we get
A = -2 ( -1 ) ( 6 )
On simplifying the equation , we get
A = 2 ( 6 )
A = 12
Therefore , the value of A is 12
Hence , the equation is A = 12
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how much more is 1/8 than 5/8?
Answer:
About the square root of 24 cubic centimeters
Answer: Its actually not. (maybe a typo)? The real bigger one is 5/8
Step-by-step explanation: So your question is "how much more is 1/8 than 5/8?" . The answer is its not. Lets do a example to help clarify. This is the butterfly method. this is by far the simplest way to compare fractions. Lets say your problem is " which is more, 5/8 or 3/4." the first thing you need to do is line them up like so:
5 3
_ _
8 4
The second thing to do is multiply the opposites.
5 3
_ _
8 4
You would be multiplying 8*3 and 5*4 so like across or whatever.
put the answers on the equation like so,
20 24 <- Which ever in the top is bigger that would be 24. Which is 3/4
5 3 ______________________________/
_ _
8 4
3/4 is bigger in this problem.
Hope I helped!
:)
Find the Surface Area of a cone with a slant height of 7 and a radius of 2. Leave your answer in terms of LaTeX: \piπ.
Group of answer choices
14 π
28/3 π
i 18 π
: 56\pi
Surface area of cone is [tex]18 \pi[/tex] square units
Solution:
Given that cone with a slant height of 7 and a radius of 2
To find: surface area of cone
The surface area of a cone is equal to the curved surface area plus the area of the base
The surface area of cone is given by formula:
[tex]S. A=\pi r^{2}+\pi r l[/tex]
Where "r" is the radius and "l" is the slant height of cone
Substituting r = 2 and l = 7 in above formula,
[tex]\begin{array}{l}{S A=\pi\left(r^{2}+r l\right)=\pi\left(2^{2}+2(7)\right)} \\\\ {S A=\pi(4+14)=18 \pi}\end{array}[/tex]
Thus surface area of cone is [tex]18 \pi[/tex] square units
1. When Jason was 16 years old, he deposited $200 in an account that camned 2-% interest compounded daily. If he makes
no other deposits or withdrawals, what is Jason's balance at age 20?
a. $218.66
b. $222.51
c. $306.42
d. $340.91
Answer:
D. $340.91
Step-by-step explanation:
2.5 gallons of water are poured into 5 equally sized bottles . How much water is in each bottle
Answer:
0.5
Step-by-step explanation:
divide 2.5 and 5 since they are equal sized bottles.
Answer:.5
Step-by-step explanation:2.5 divided by 5 = 0.5
one number is 4 more than another. the sum of the numbers is 20. Find the numbers.
explanation needed
x + (4 + x) = 20
2x + 4 = 20
2x = 16
x = 8
Proof
x + (4 + x) = 20
8 + 4 + 8 = 20
12 + 8 = 20
20 = 20
The numbers are 8 and 12.
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A home alarm system randomly assigns a five-character code for each customer. The code will not repeat a character. The characters are 1, 2, 3, 4, 5, E, M, T, G, Y, and R. What is the total number of codes that can be randomly assigned?
A.) 1,320
B.) 95,040
C.) 9,540
D.) 11,880
Answer:
The total number of codes which can be assigned is, 55440 .
Step-by-step explanation:
According to the question, the home alarm system randomly assigns a five-character code for each customer.The code will not repeat a character and there are 11 distinct characters.
So, the total number of codes that can be randomly assigned is given by,
[tex]^{11}{P}_{5}[/tex]
= [tex]\frac {11!}{6!}[/tex]
= [tex]11 \times 10 \times 9 \times 8 \times 7[/tex]
= 55440
what is 90 ft equal to in centimeters
Answer: 2743.2
Step-by-step explanation:
A formula to try is to multiply the length value by 30.48
2. What is the minimum of the sinusoidal function? Please help thank you
Answer: 1
Step-by-step explanation:
It will be the smallest value for f(x).
The minimum of a sinusoidal function is the lowest point on the graph that is 1.
The minimum of a sinusoidal function is the lowest point on the graph. Looking at the image you provided, the minimum point is the lowest y-coordinate the curve reaches.
Since the graph is a sine wave, it oscillates between a maximum and a minimum value. For a standard sine function, which this graph appears to resemble, these extrema occur at points where the sine of the angle is either 1 or -1.
The minimum value of sine is -1, but the actual minimum value of the function on the graph will depend on any vertical shift and amplitude changes.
To find the exact minimum value from the graph, you'd look for the lowest point on the y-axis that the graph reaches. From the image, it's not perfectly clear, but it looks like the minimum value is around -2 on the y-axis.
This would be the case if the function has no vertical shift from the standard sine wave. If there's a vertical shift, the minimum would be the standard minimum value of sine (-1) plus the vertical shift.
NOTE: Angles not necessarily drawn to scale. PLEASE HELP
Answer:
150 degrees
Step-by-step explanation:
Angles FED and CEG are congruent to one another because opposite angle theorem. That makes angle CEG equal to 130. Same applies for angles DEB and AEC, making angle AEC 20 degrees.
Your variable x is a combination of these two angles, AEC + CEG. 130 + 20 = 150
Therefore x = 150 degrees.
150 degrees is the measure of the value of x from the figure.
Line geometryThe given diagram is a line geometry with the following parameters;
<FED = 130 degrees
<DEB = 20 degrees
Determine the measure of x
x = <FED + <DEB
Substitute the given parameters
x = 130 + 20
x = 150 degrees
Hence the measure of the value of x from the figure is 150 degrees.
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First I will build the envelope. For this, I am using a rectangular piece of material 28m long and 12m wide. Out of this material, I have to cut patches that are 1/12 the length and 2/15 the width of the whole material. What is the area of a patch and how many such patches can I make out of the whole material?
Answer:
3.728 cm²
90
Step-by-step explanation:
To built the envelope I am using a rectangular piece of material 28 m long and 12 m wide.
Out of this material, I have to cut patches that are 1/12 the length and 2/15 the width of the whole material.
So, the length of the patches is [tex]28 \times \frac{1}{12} = 2.33[/tex] m and the width of the patches is [tex]12 \times \frac{2}{15} = 1.6[/tex] m.
Therefore, the area of the patches is (1.6 × 2.33) = 3.728 m² each. (Answer)
Now, the area of the rectangular piece of material is (28 × 12) = 336 m²
Hence, [tex]\frac{336}{3.728} = 90.37[/tex] ≈ 90 such patches can be made out of the whole material. (Answer)
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The true statement is : D. The boiling point decreases by 1.8 degrees as the altitude increases by 1000 feet. True statements are : A,D & E
Step-by-step explanation:
5.
The equation is given as : T(a)= -0.0018a +212 where T (a) is the boiling point of water measured in degrees at altitude a measured in feets.
From the equation , when the altitude is increased by 1000 feets, a=1000, the equation will be
T(1000) = -1.8 + 212, which means that the boiling point decreases by 1.8 degrees as the altitude increases by 1000 feet
6.
The values given can be taken as coordinates and plotted on a graph tool as shown in the attached figure.
Finding the slope of the graph'
m=Δy/Δx
Taking points (14,73) and (9,51.75) the slope of the linear graph will be;
Δy=73-51.75 = 21.25
Δx=14-9 =5
m= 21.25/5 = 4.25
The equation of the linear graph taking m=4.25 and point (14,73)
m=Δy/Δx
4.25 = y-73/x-14
4.25(x-14) = y-73
4.25x - 59.5 =y-73
4.25x - 59.5 + 73 =y
y=4.25x+13.5
From the graph,
The price in 2005 will be $77.25
The predicted average change in ticket price per year is $4.25
The y -intercept is the price of ticket in 1990
True statements are : A,D & E
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Let log_(b)A=3; log_(b)C=2; log_(b)D=5 what is the value of log_(b)((A^(5)C^(2))/(D^(6)))
Answer:
-11
Step-by-step explanation:
Given
[tex]\log_bA=3\\ \\\log_bC=2\\ \\\log_bD=5[/tex]
Use properties:
[tex]\log_b(A\cdot C)=\log_bA+\log_bC\\ \\\log_b\dfrac{A}{C}=\log_bA-\log_bC\\ \\\log_bA^k=k\log_bA[/tex]
Thus,
[tex]\log_b\dfrac{A^5\cdot C^2}{D^6}\\ \\=\log_b(A^5\cdot C^2)-\log_bD^6\\ \\=\log_bA^5+\log_bC^2-\log_bD^6\\ \\=5\log_bA+2\log_bC-6\log_bD\\ \\=5\cdot 3+2\cdot 2-6\cdot 5\\ \\=15+4-30\\ \\=-11[/tex]
5x-83 greater than or equal to -73
write the fact family for 1,4,and 4
Answer:
For 1 is 1
For 4 is 1,2,4
Step-by-step explanation:
A fact family for 1, 4, and 4 can be created using addition and subtraction. The addition equations are 1 + 4 = 5 and 4 + 1 = 5. The subtraction equations are 4 - 1 = 3 and 4 - 3 = 1.
Explanation:In mathematics, a fact family is a set of three numbers that can be used to create four different addition and subtraction equations. In this case, the numbers given are 1, 4, and 4. To create the fact family, we can use the numbers and their corresponding operations.
The addition equations would be: 1 + 4 = 5 and 4 + 1 = 5.
The subtraction equations would be: 4 - 1 = 3 and 4 - 3 = 1.
Therefore, the fact family for 1, 4, and 4 is: 1, 4, and 5 (addition) and 4, 1, and 3 (subtraction).
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write the equation of the line that passes through the point (-1,-6) and is perpendicular to a line that passes through the points (-2,5) and (-4,8)
Answer:
[tex]y=\frac{2}{3}x-\frac{16}{3}[/tex]
Step-by-step explanation:
step 1
Find the slope of the given line
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
(-2,5) and (-4,8)
substitute the values in the formula
[tex]m=\frac{8-5}{-4+2}[/tex]
[tex]m=\frac{3}{-2}[/tex]
[tex]m=-\frac{3}{2}[/tex]
step 2
Find the slope of the perpendicular line to the given line
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
so
[tex]m_1*m_2=-1[/tex]
[tex]m_1=-\frac{3}{2}[/tex] ----> slope of the given line
therefore
[tex]m_2=\frac{2}{3}[/tex] ---> slope of the perpendicular line to the given line
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{2}{3}[/tex]
[tex]point\ (-1,-6)[/tex]
substitute
[tex]y+6=\frac{2}{3}(x+1)[/tex]
step 3
Convert to slope intercept form
[tex]y=mx+b[/tex]
isolate the variable y
[tex]y+6=\frac{2}{3}x+\frac{2}{3}[/tex]
[tex]y=\frac{2}{3}x+\frac{2}{3}-6[/tex]
[tex]y=\frac{2}{3}x-\frac{16}{3}[/tex]