Answer:
We can simplify the expression log₂8³x using the following logarithmic rule:
logₐb^c = c * logₐb
Using this rule, we can rewrite the expression as:
log₂8³x = 3log₂8 + log₂x
We can further simplify by recognizing that 8 can be expressed as a power of 2:
8 = 2³
Substituting this in, we get:
3log₂8 + log₂x = 3log₂(2³) + log₂x = 3 * 3 + log₂x = 9 + log₂x
Therefore, the simplified expression is:
log₂8³x = 9 + log₂x
Step-by-step explanation:
f(x)=x³+x² - 6x=c then find the X- intercept of f(x)
Therefore , the solution of slope intercept comes out to be X intercept for the function is x = - 1
What does slope intercept mean?In math, the intersection is where the line's slope intersects the y-axis. a point on a line or curve where the y-axis crosses. The formula for the linear line is given as Y = mx+c, whereby m denotes the slope и c the y-intercept. In the intercept form of the equation, the line's slope (m) and y-intercept (b) are highlighted. The slope and y-intercept of an equation with the intercepting form (y=mx+b) are m and b, respectively. There are several equations that can be rewritten to appear to be slope detections. The slope and como are both modified to 1 if y=x is translated as y=1x+0, for example.
Here,
It is the point where a line or curve crosses the X axis
The function f(x) = x³ + x² - 6x = c
Let, y = f(x) = x³ + x²- 6x -c =0
at the X intercept, y = 0,
so, 0 = x³+ x²- 6x -6
x²(x +1) - 6(x +1) =0
(x +1) ( x²-6) = 0
x = -1, x = √6
X intercept is x = -1
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What is the degree of the polynomial? 4x^2y^3-2x^2+7y-8
The degree of the given polynomial is 5.
What is polynomial?A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
Given is a polynomial, 4x²y³-2x²+7y-8
We know that, A polynomial of two variable x and y, like ax^ry^s is the algebraic sum of several terms of the prior mentioned form, where r and s are possible integers.
Here, the degree of the polynomial is r+s where r and s are whole numbers.
Therefore, in the given polynomial, the degree will be
4x²y³
Taking the powers,
2+3 = 5
Hence, the degree is 5
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find the vertices of this hyperbola 36x^2-y^2-216x+10y+261=0
The required vertices of hyperbola is given as (3, 5±√38).
What is an hyperbola?Hyperbola is part of conic section, and its equation is given as,
[tex](x - h)^2/a^2 + (y - k)^2/b^2 = 1[/tex], where h,k is center and a and b are the lengths of the semi-major and the semi-minor axes.
Here,
Given equation of hyperbola,
36x²-y^²-216x+10y+261=0
Equation of hyperbola in vertex form is given as,
(x - 3)²/(19/18) - (y - 5)²/38 = 1
From above equation,
h = 3 k = 5 a = √38/6 and b = √38
Vertices of the hyperbola is given as,
(h, k ± b) = (3, 5±√38)
Thus, the required vertices of hyperbola is given as (3, 5±√38).
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The graph shows the relationship between time and the number of soda bottles a machine can make. Use the points (5,250) and (8,400) to find the numbers of soda bottles the machine can make each minutes.
The graph demonstrates the relationship, and it indicates that the machine can produce 1200 soda bottles every minute.
what is unitary method ?The unitary technique is sometimes useful for multiplying and dividing by fractions because it makes sense immediately and can be done mentally if the numbers add up. This makes it a good method for defending or explaining frequently employed written fractional algorithms, like division by a fraction. The unitary technique has a formula that involves finding the value of a single unit, multiplying it by the quantity of units, and then finding the desired value.
given
y=20x
The total number of bottles produced in the specified amount of time, expressed in seconds, is represented by y.
When x=1 and y=20, the machine can produce 20 soda bottles each second.
There are 60 seconds in a minute, thus when x=60, y=20*60 equals 1200 drink bottles.
The graph demonstrates the relationship, and it indicates that the machine can produce 1200 soda bottles every minute.
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B varies directly as m. A study shows that m= 6 when b = 5.
The value for the proportional constant, for given data, is 5/6.
What is a Linear Function?A linear function is a function that, when plotted, creates a straight line. Typically, it is a polynomial function with a maximum degree of 1 or 0. Nevertheless, calculus and linear algebra are also used to represent linear functions.
Given that b varies directly as m
so b ∝ m
it says b is directly proportional to m,
removing the proportional sign apply a constant k,
b = km
where k is the proportional constant,
and m = 6 and b = 5
5 = 6k
k = 5/6
Hence the value of the constant is 5/6.
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10 POINTS!
This graph shows a proportional relationship.
What is the constant of proportionality?
Answer: The constant of proportionality is 12.
Step-by-step explanation: You can start by dividing 36 by 3 60 divided by 5 then 72 divided by 6 and then 84 divided by 7. All of the division problems have an answer of 12. So the constant of proportionality is 12.
If you have an 54.96 and you take a summative test worth 80% how much will that bring up your grade what will be your new grade
If you have a grade of 54.96 and you take a summative test worth 80%, it would bring up your grade by the following calculation:
New grade = (54.96) + (80/100) * (100 - 54.96)
New grade = 54.96 + (0.8) * (45.04)
New grade = 54.96 + 36.032
New grade = 90.992
So, your new grade would be 90.992
It's worth noting that this calculation assumes that the summative test is worth 80% of your overall grade, and that your previous grade was 54.96 out of 100. If this isn't the case, the result will be different.
Aimee is estimating 315 x 47 by first
rounding to 1 s.f.
Which of these calculations should Aimee
use?
300 × 0
300 × 50
320 × 0
315 × 50
320 × 50
315x0
300 × 47
315x47
320 × 47
For estimation, she have to make calculation as 320x50/
How do I round to the nearest significant digit?Using one significant figure as an example 3692 should be converted to one square foot (s.f.). The number 3 is the first significant digit because it is the first non-zero digit.6 exceeds 5 in number.We round up because 6 is greater than 5 One plus three equals four, and 3692 is four thousand square feet.
How are estimates calculated?each number to the nearest significant figure.Use the 'approximately equal to' symbol to build the new estimated calculation.Consider units when calculating and use the rounded numbers to provide an approximation.
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What value is missing from the table?
Answer: D - 14
Step-by-step explanation:
1 gallon = 2.15
So to find how many gallons is worth 30.10, divide by 2.15
30.10 ÷ 2.15 = 14
Answer:
Step-by-step explanation:
To find the required gallons of gas for 30.10$, you can use the following formula:
Required gallons of gas=Cost of required gallons of gas/cost of one gallon of gas
Here given that, the cost of required gallons of gas is 30.10$ and the cost of one gallon of gas is 2.15$
Now apply the formula:
Required gallons of gas = 30.10$/2.15$ = 14
Therefore, the required gallons of gas = 14
So 14 gallons of gas costs 30.10$
Option D is the correct answer.
whats the answer for
(x+1)(x+5)=(x+3)(x-4) +3
Answer: x = -2
Step-by-step explanation: Divide each side by factors that do not contain the variable to isolate it.
A toy company spends $1800 per day for factory expenses plus $9 to make each teddy bear. They sell the teddy bears for $15 a piece. Create and solve an equation that could be used to find the number of bears, b ,the company has to sell in one day to equal its daily cost.
The number of bears, b is 300 for the company has to sell in one day to equal its daily cost.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
A toy company spends $1800 per day for factory expenses plus $9 to make each teddy bear.
And, They sell the teddy bears for $15 a piece.
Let number of bears for the company has to sell in one day to equal its daily cost = b
Hence, We can formulate the inequality as;
⇒ 15b = 9b + 1800
Solve for b;
⇒ 15b - 9b = 1800
⇒ 6b = 1800
⇒ b = 300
Thus, There are 300 teddy bears has to sell in one day.
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Can someone please tell me how do we solve this? Thank you.
Answer:
C
Step-by-step explanation:
Figure ABCD is a rectangle. Find the
value of x.
B
A
x + 11
E
x = [?]
6x +1
C
D
Enter
Answer:
x=2
Step-by-step explanation:
x+11=6x+1
10=5x
x=2
How much solutions does this equation have
y= 1/4x+1
y=1/4x-1
Answer: No Solution
Step-by-step explanation:
There is no solution.
A set of equations with the same slopes and different y-intercepts have no solution.
A circle is inscribed into a square, find the area of the circle if one side of the square is 15 m
Answer:
follow me if this helped you
Step-by-step explanation:
Area of inscribed square.
A circle is inscribed into a square, find the area of the circle if one side of the square is 15 m
The diameter of the inscribed circle is equal to the length of the square's diagonal, which is equal to the length of one side of the square multiplied by the square root of 2 (since the diagonal of a square is equal to the square root of 2 times the length of one side). Therefore, the diameter of the inscribed circle is 15m * sqrt(2) = 15m * 1.41421356237 = 21.213203435596424m
The area of a circle is given by the formula A = π * r^2, where r is the radius of the circle. Since the diameter of the circle is 21.213203435596424m, the radius is half of that, which is 10.60660171779821m.
So the area of the circle is A = π * r^2 = π * 10.60660171779821^2 = 353.09
Marcella wants to earn a total of at least $4,000 per month. For each company, find the least number of office machines she would need to sell each month in order to meet this goal. Show your work.
Answer:
1540$!$($9$
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Marcella would need to sell at least 40 office machines each month to earn at least $4,000.
To find the least number of office machines Marcella would need to sell each month to earn at least $4,000, we need to know the price of each office machine and the commission she receives for each sale.
We can use following formula:
Total Earnings = (Number of Machines Sold) x (Price of Machine) x (Commission Rate)Rearranging this formula to solve for the number of machines sold, we get:
Number of Machines Sold = Total Earnings / (Price of Machine x Commission Rate)Plugging in the values we know:
Number of Machines Sold = 4000 / (1000 x 0.1)
Number of Machines Sold = 4000 / 100
Number of Machines Sold = 40
Therefore, Marcella would need to sell at least 40 office machines each month to earn at least $4,000.
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Determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance.
In a study of a birth sex selection method used to increase the likelihood of a baby being born female, 2085 users of the method gave birth to 1019 males and 1066 females. There is about a 169
chance of getting that many babies born female if the method had no effect.
Because there is a 16% chance of getting that many babies born female if the method had no effect, the method
procedure that raises the likelihood of a baby born female from the approximately 50% rate expected by chance to the produced by this method.
(Round to the nearest integer as needed.)
So, this method
has statistical significance.
should be used to make conclusions.
has practical significance.
does not have practical significance.
4
%
couples would likely use a
Because there is a 16% chance of getting that many babies born female if the method had no effect, the method has no statistical significance. Hence couples would likely use a procedure that raises the likelihood of a baby born female from the approximately 50% rate expected by chance to the 51.13% produced by this method.
This means that the method has practical significance.
What is the relation between the p-value and the conclusion of the test hypothesis?Depends on if the p-value is less or more than the significance level:
If it is more, the null hypothesis is not rejected, meaning that the research study is not statistically significant.If it is less, it is rejected, meaning that the research study is statistically significant.The p-value for this problem is given as follows:
0.16.
As the p-value is greater than the standard significance level of 0.05, the method has no statistical significance.
The percentage of females born is given as follows:
1066/2085 x 100% = 51.13%.
As this percentage is an increase from the usual 50%, the method has practical significance.
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In the sketchpad, solve 27 x 7 with an area model.
Following is the area model of 27 x 7 = 189.
An area model is a rectangular graphic used in mathematics to multiply and divide two numbers or expressions.
The length and breadth of the rectangle are determined by the factors, also known as the quotient and divisor. In other words, you can divide a large area (in this case, a 23 37 rectangle) into smaller ones, calculate the areas of each separately, and then sum them to determine the overall area.
Which steps comprise the area model?Write the enlarged form of each factor first. Next, sketch your model. To determine the area of each smaller rectangle, multiply next. To find the entire area, add those items last.
20 7
7 140 49
27 × 7 = 140 + 49 = 189
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two functions f and g are defined over the set r of real numbers as follows: f:x > x^2-2x-1 and g:x > x-1. find the value of x for which f(x)=g(x)-2
The values of x for which f(x) = g(x) - 2 are given as follows:
x = 1 and x = 2.
How to solve the equation?The functions for this problem are defined as follows:
f(x) = x² - 2x - 1.g(x) = x - 1.The equation is given as follows:
f(x) = g(x) - 2.
Replacing the values, we have that:
x² - 2x - 1 = x - 1 - 2
x² - 2x - 1 = x - 3
x² - 3x + 2 = 0.
We can factor the equation as follows:
(x - 2)(x - 1) = 0.
Hence the solutions are obtained as follows:
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need explaining with working out
Therefore , the solution of the given problem of triangle comes out to be a=6 and b=17.
A triangle is what exactly?An triangle is a polygon since it has four or more parts. It is a simple geometric shape. A square having angles A, B, and C is referred to as a triangle ABC. When the sides are not collinear, Euclidean geometry generates a single plane and square. If a triangle has three sides and three corners, it is a polygon. The corners of a triangle are where its three sides meet. The sum of the angles in a triangle is 180 degrees.
Here,
Given : A right triangle ,
=> 8²+a²= 10²
=> a² = 100 -64
=> a² =36
=> a =6
For b,
=> b² = 8² + 15²
=> b² = 64 + 225
=> b² = 289
=> b = 17
Therefore , the solution of the given problem of triangle comes out to be a=6 and b=17.
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a florist has 133 roses.she sold 5/7 of them how many roses are left with her
A. 58
B. 38
C. 57
D. 19
At Six Flags, 1,473 people entered the park in 3 hours. At Hershey Park, they had 944 guests
enter the park in 2 hours. If the rates were constant the entire time, which park had more
people enter in the first hour?
Six Flags:
1,473/3 = 491 people per hour.
Hershey Park:
944/2 = 472 people per hour.
Six Flags has more people in the first hour. Six Flags has 19 more people than Hershey Park.
491>472
I hope this helps you!!
What is the measure
Answer:
Angle FSM = 92° OPTION B
Step-by-step explanation:
[tex]5x+32=7x+8[/tex]
[tex]5x-7x=8-32[/tex]
[tex]-2x=-24[/tex]
[tex]x=\frac{-24}{-2} =12[/tex]
Angle FSM:
[tex]FSM=7x+28=7(12)+8=84+8=92[/tex]
Hope this helps
jason paid 12.75 for 5.5 pounds of hamburger. how many dollars per pound
Answer: ≈2.32
Step-by-step explanation: So, we can solve this in 2 ways:
1) 12.75 / 5.5 (easiest way)
= 2.3181818181818183
(Rounded to the nearest hundredth) ≈ 2.32
2) Set up a proportional relationship:
[tex]\frac{12.75}{5.5}[/tex] = [tex]\frac{?}{1}[/tex]
Now, divide 12.75 by 5.5, and get about 2.32
Now, let's check our answer:
2.32 x 5.5 = 12.76
So, he paid about 2.32 per pound.
I hope this helped!
What is the circumference of a circle whose diameter is 15 niches
The circumference of a circle with a given diameter of 15 inches is equal to 15pi which is equal to 47.12 inches.
What is the circumference of a circle?The circumference of a circle is the distance around the edge of the circle.
What is the formula for calculating the circumference of a circle?The formula for calculating the circumference of a circle is given by,
C = 2πr = πd
Where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle and d is the diameter.
It is also known as the perimeter of the circle.
In the question above, we're given,
Diameter of the circle (d ) = 15 inches.
So, using the formula for the circumference of the circle,
Circumference (c) = π d
= π * 15
= 47.12 inches
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The following values are placed on a number line: 170%, one and two over five, and 0.3.
Which of the following images shows the correct placement of the values?
Number line starting at negative 0.4 on the left up to 2.4 on the right. Units are marked every two tenths unit. 0.3 is labeled at 0.3. One and two fifths is labeled at 1.2, and one hundred seventy percent is labeled at 1.6.
Number line starting at negative 0.4 on the left up to 2.4 on the right. Units are marked every two tenths unit. 0.3 is labeled at 0.3. One and two fifths is labeled at 1.4, and one hundred seventy percent is labeled at 1.7.
Number line starting at negative 0.4 on the left up to 2.4 on the right. Units are marked every two tenths unit. 0.3 is labeled at 0.3. One hundred seventy percent is labeled at 0.7, and one and two fifths is labeled at 1.4.
Number line starting at negative 0.4 on the left up to 2.4 on the right. Units are marked every two tenths unit. 0.3 is labeled at 0.3. One and two fifths is labeled at 1.2, and one hundred seventy percent is labeled at 1.5.
Given the number lines (attached) the correct one is Option B) because it represents the right placement of values.
What is a number line?A number line is a depiction of a graded straight line that serves as a visual representation of real numbers in primary mathematics. Every point on a number line is presumed to be a real number, and every real number is assumed to be a point.
We can tell that option B is correct because:
0.3 is placed right after 0.2 and before 0.3;1 2/5 (which is the same as 1.4) is placed right above 1.4; and 170% which is the same as 1.7 is placed right after 1.6 and just before 1.8.Thus, option B is correct in the given number line.
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how can i show m 2 = 2m 1
Answer:
Step-by-step explanation:
m
2
+
2
m
+
1
2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
2
m
=
2
⋅
m
⋅
1
Rewrite the polynomial.
m
2
+
2
⋅
m
⋅
1
+
1
2
Factor using the perfect square trinomial rule
a
2
+
2
a
b
+
b
2
=
(
a
+
b
)
2
, where
a
=
m
and
b
=
1
.
(
m
+
1
)
2
Short RESPONSE
5. To enter an aquarium adult tickets, a cost $15 each and children tickets, c cost $8
each. The expression 15a + 8c can be used to determine the total cost (in dollars)
for a adult tickets and c children.
How much will it cost for 3 adults and 4 children to enter the aquarium
Show your work
Answer: $_.
Answer: $77
Step-by-step explanation:
Using the given expression, we can find the total cost for all the tickets.
The question asks for the cost of 3 adults and 4 children.
Let's substitute the values for the variables(again).
We'll get
15*3+8*4(since there's 3 adults and 4 children)
= 45+32
= 77
Total: $77
Nice airpods, btw
A gear wheel with 9 teeth plays into a gear wheel with 27 teeth. When the smaller wheel has made 42 revolutions, how many
revolutions has the larger wheel made?
A) 14
B) 16
C) 120
D) 126
Show work please
Answer:
A) 14
Step-by-step explanation:
When a small is gear connected to a larger gear, the smaller gear makes more revolutions than the larger gear. Use the ratio of the numbers of teeth to find the ratio of the numbers of revolution.
1 gear has 9 teeth
1 gear has 27 teeth
27/9 = 3
The ratio is 3:1.
The small gear makes 3 revolutions for each revolutuion of the large gear.
The large gear makes 1/3 revolution for each revolution of the small gear.
Here, the small gear makes 42 revolutions.
42/3 = 14
The large gear makes 14 revolutions.
Answer: A) 14
The larger gear has made 14 revolutions when the smaller gear has made 42 revolutions. This is because the ratio of the teeth on the gears is 1:3, which is also the ratio of their revolutions.
Explanation:The ratio of the number of teeth on the two gears is also the ratio of the number of rotations they make. In this case, the smaller gear has 9 teeth and the larger gear has 27 teeth. So, the ratio is 9:27, which simplifies to 1:3.
This means that for every one rotation of the larger gear, the smaller gear will make three rotations.
Since the smaller gear has made 42 rotations, to figure out the number of rotations the larger gear has made, you would divide 42 by 3. (because of the 1:3 ratio). The answer is 14.
Therefore, the larger gear has made 14 revolutions when the smaller gear has made 42 revolutions. So, the correct answer is A) 14.
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Suppose there are two groups of shapes. In Group 1, all of the shapes have four right angles. In Group 2, all of the shapes have four sides that are all the same length. Which of the following shapes can always fit into both groups?
A.
rhombus
B.
rectangle
C.
square
D.
pentagon
Answer:
D
Step-by-step explanation:
all around of side are 360 degree that's why only pentagon has 360 degree