The equation is simplified as [tex]x^{16}=x^{16}[/tex].
The given equation is [tex]x^{12} . \ x^{4} = x^{8} . \ x^{8}[/tex].
We need to simplify and explain the equation.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Use the exponent rule [tex]a^m . \ a^n=a^{m+n}[/tex] to simplify the given equation.
Now, [tex]x^{12} . \ x^{4} = x^{8} . \ x^{8}[/tex]
⇒ [tex]x^{12+4}=x^{8+8}[/tex]
⇒ [tex]x^{16}=x^{16}[/tex]
The exponents of both the sides of equation are the same.
Therefore, the equation is simplified as [tex]x^{16}=x^{16}[/tex].
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The cheerleaders want to raise money to go to camp, so they decide to sell spirit ribbons. They will earn 50¢ for each ribbon that they sell. However, they have to purchase the ribbons first for a total cost of $75. Use the table below to figure their total profit from selling ribbons.
What is the total profit after selling 0 ribbons?
Using a linear function, we have that:
The rule is P(x) = 0.5x - 75.The total profit after selling 0 ribbons is of -$0.75.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, when x increases by 10, the profit increases by 5, hence the slope is:
m = 5/10 = 0.5.
Then:
P(x) = 0.5x + b.
When x = 10, P(x) = -70, hence:
-70 = 0.5(10) + b
b = -75.
Hence:
The rule is P(x) = 0.5x - 75.The total profit after selling 0 ribbons is of -$0.75.More can be learned about linear functions at https://brainly.com/question/24808124
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f(x) = 12x + 10 is a function which can used to to calculate a person's daily paycheck.
Which would be a reasonable domain for this function?
A : all real numbers
B : 0
C : 0
D : 0
A : all real numbers
Answer:
A. All real numbers.
Step-by-step explanation:
Justin is evaluating the expression 12.53.8x, when x is 7.9.
12.5+3.847.9)
16.3(7.9)
128.77
What was Justin's error?
Justin should have multiplied 12.5 and 7.9 first.
Justin should have added 12.5 and 7.9 first.
Justin should have multiplied 3.8 and 7.9 first.
O Justin should have added 3.8 and 7.9 first.
Justin should have multiplied 3.8 and 7.9 first
How to evaluate an expression?He is trying to evaluate the expression 12.5 + 3.8x, when x = 7.9.
This was Justin solution to the expression
12.5 + 3.8(7.9)
16.3(7.9)
128.77
Now let's do our own arithmetic,
12.5 + 3.8x
we have to substitute the value of x in the equation.
12.5 + 3.8(7.9)
Using PEMDAS principle, we have to multiply before addition.
Therefore,
12.5 + 3.8(7.9)
12.5 + 30.02
42.52
Hence, Justin should have multiplied 3.8 and 7.9 first
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please help thank youuuu
Answer: 87/100
Step-by-step explanation:
Complete the table of values for f(x) = -3|x+1|-4 using the table of values for g(x) = |x|
f(x)>=-7
Functions:
Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics.
If a variable y is so related to a variable x that whenever a numerical value is assigned to x, there is a rule according to which a unique value of f(x)is determined, then f(x) is said to be a function of the independent variable x
Given :
f(x) = -3|x+1|-4
using the table of values for g(x) = |x|
Solution :
f(x) = -3|x+1|-4
f(x) = -3|g(x)+1|-4
f(x) = -3||x|+1|-4
which means |x| is always positive |x|>0
f(x) = -3||x|+1|-4
f(x) = -3x-3-4
f(x) = -3x-7
f(x)>=-7
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In exercises 21 and 22, find the indicated angle measure. (See photo)
Answer:
42°, 101°
Step-by-step explanation:
These answers come from the angle subtraction postulate.
What is the area of the base of this right circular cone in terms of л?
r = 4 m
h = 6 m
___ л m^2
Answer:
16π m²
Step-by-step explanation:
area of circle = πr²
area = π × (4 m)²
area = 16π m²
PLEASE HELP ASAP!
:))
Answer: The converse of this theorem is also true; that is, if two lines n and m are cut by a transversal so that the alternate interior angles are congruent, then n║m.
Step-by-step explanation:
What does it mean converse in geometry?
The converse of a statement is formed by switching the hypothesis and the conclusion. The converse of "If two lines don't intersect, then they are parallel" is "If two lines are parallel, then they don't intersect." The converse of "if p, then q" is "if q, then p."
So, in the figure below, if we can choose n║m, then ∠1≅∠2
Since n║m , by the corresponding Angles Postulate,
∠1≅∠2.
Therefore, by the definition of congruent angles,
m∠1=m∠2
Since ∠1 and ∠2 form a linear pair, they are supplementary, so
m∠1+m∠2=180°.
Therefore, the converse of this theorem is also true; that is, if two lines n and m are cut by a transversal so that the alternate interior angles are congruent, then n║m.
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Please help due soon.
Answer:
-3x>24
Step-by-step explanation:
-3x-10>14
now we add 10 to both sides, 10+14 is 24
so, the missing step is -3x>24
Options are
A. (-3, -1)
B. (3,1)
C. (6,4)
D. (2,6)
Answer: D
Step-by-step explanation: 2,6
A yard has a perimeter of 190 feet. If four times the length of the yard equals 15 times the width, what are its dimensions
We get the dimensions of the park as length = 75 feet and width = 20 feet.
We are given that:
A yard has a perimeter of 190 feet.
Also, four times the length of the yard equals 15 times the width.
Now,
Let the length of the yard be x.
ATQ, we get the width of the yard as:
15 width = 4 x
Width = 4 / 15 x
Perimeter = 2 ( l + b )
190 = 2( x + 4 / 15 x )
95 = 19 x / 15
19 x = 95 × 15
19 x = 1425
x = 1425 / 19
x = 75 feet.
Length = 75 feet
Width = 4 / 15 x = 20 feet.
Therefore, we get the dimensions of the park as length = 75 feet and width = 20 feet.
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Find a number such that one-half of the number is three more than one-fourth of the number.
The number such that one-half of the number is three more than one-fourth of the number is 12.
It is given in the question that a number is such that one-half of the number is three more than one-fourth of the number.
We have to find the number.
Let the number be x.
According to the question, we can write,
x/2 = x/4 + 3
Solving the linear equation, we get,
x/2 - x/4 = 3
(2x - x)/4 = 3
x/4 = 3
x = 4*3
x = 12
Hence, the number such that one-half of the number is three more than one-fourth of the number is 12.
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select the correct answer. what is the slope of the line that goes through the points (-4,2) and (8,5)?
A. "-4"
B. "-1/4"
C. 1/4
D. 4
Answer: The slope of the line that goes through the points is = ¼
Step-by-step explanation:
Define Slope:
The slope is a numerical value that describes the steepness of a line and is usually determined by calculating the ratio of the vertical distance to the horizontal distance (rise over run) between two points.
The slope of the line that goes through the points (-4,2) and (8,5).
Let, X1=-4
Y1=2
X2=8
Y2=5
We can use m=(y2-y1) / (x2-x1)
replace with x1, y1 and x2, y2 values in this equation
We can write: m=[(5-2) / (8-(-4))]
Solve it: M= 3/12
M=1/4
So, the slope of the line that goes through the points is = ¼.
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#12: m∠GKH = ____
need the answer
Evaluate.
7- 24 ÷ 8 × 4 + 6
Answer:
-35
Step-by-step explanation:
Question =7-24÷8×4+6
=7-192÷4+6
=7-49+6
=-41+6
=-35
Therefore,right answer is (-35)
PLEASE MARK ME AS THE BRAINIEST.
A teacher surveys a random group of students about their preference for doing classwork
online or on paper. The results are shown in the table below.
STUDENT CLASSWORK
PREFERENCE
Preference
Online
Paper
Number of
Students
17
8
Based on the results, how many students out of 350 will most likely have a preference to
do their classwork online?
Show your work.
The number of students those who will most likely have their preference to do their classwork online is 238 out of 350
According to the question statement, A teacher surveys a random group of students about their preference for doing classwork online or on paper.
17 Preferred Online and 8 Preferred on paper.
We are supposed to find the number of students who will most likely have their preference to do their classwork online.
We will be using the concept of Probability for solving this.
[tex]Probability(Event)=\frac{Favourable Outcomes}{Total Outcomes}[/tex]
Probability(Event) = Favorable Outcomes/Total Outcomes
For the survey probability of students preferring online mode of classwork is = [tex]\frac{17}{17+8} =\frac{17}{25}[/tex]
= [tex]0.68[/tex]
Now if we consider a group of 350 students and probability of students preferring online mode of classwork as 0.68
Let the number students preferring online mode of classwork be "x"
so [tex]\frac{x}{350} =0.68[/tex]
or [tex]x=0.68*350\\x =238[/tex]
Therefore, the number of students those who will most likely have their preference to do their classwork online is 238 out of 350
Probability: P(A) = n(A)/n(S)where P(A) is the probability of an event “A”, n(A) is the number of favorable outcomes and n(S) is the total number of events in the sample space.
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Can someone help me please
Answer:
182.5
Step-by-step explanation:
182.5
steps
623420÷3416=
182.5
please help me with this problem
Answer:
The equivalent fraction of 6/9 is 4/6
A random sample of 100 diabetics undergoes genotyping and it was found that 23 of them have the gene. compute the z test statistic needed for this hypothesis test.
The z test statistic needed for this hypothesis test is 0.75 .
Z test is a statistical test that is conducted on data that approximately follows a normal distribution. The z test can be performed on one sample, two samples, or on proportions for hypothesis testing. It checks if the means of two large samples are different or not when the population variance is known.
NOW,
sample proportion = p = x / n = 0.23
Test statistics
z = ( p - p0 ) / [tex]\sqrt{ p0*(1-p0)}[/tex] / n
= ( 0.23 - 0.20) / [tex]\sqrt{ (0.20*0.80) / 100}[/tex]
= 0.75
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how could you use a compass to construct a segment that is twice the length of a given segment?
By taking the measure of the given line segment and making arc on one of the end points from one point of the line segment and joining those three points will be the line as twice as the given segment.
Following are the steps to construct a line segment that is twice the given segment :
Step 1 : Take the compass and measure the length of the given line segment let’s say AB
Step 2 : Now with that measure put one end of the compass on one of the points of a line segment, either point A or point B.
Step 3 : Now mark an arc on the right side of the point if the compass is on point B or mark the arc on the left side if the compass is on point A.
Step 4 : Mark that arc as point C and join the line AC or BC.
Hence AC or BC will be the new line segment which will as twice as the given line segment.
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Is height discrete or continuous data? Give a reason for your answer.
please help
Answer: Continuous data
Step-by-step explanation:
On the first day of class, a statistics professor asked her students to report their grade point averages (gpas) as part of a class survey. for those students who knew their gpas, the histogram was:______.
On the first day of class, a statistics professor asked her students to report their grade point averages (gpas) as part of a class survey. for those students who knew their gpas, the histogram was Left skewed.
The meaning of grade point averages?
You can determine your grade point average (GPA) by dividing the total number of high school credits you have earned by the total of all of your course grades. The majority of secondary and universities record grades on a 4.0 scale.What exactly does a 4.0 GPA mean?
High schools commonly report grade point averages (GPAs) on a 4.0 scale. A 4.0, or the highest grade, is awarded. You can get your total GPA by averaging your grades from all of your classes. This scale is regularly used in the majority of institutions and many secondary schools.Learn more about grade point averages
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Say you are given the graph of a line y=-x. Write an equation that intersects the given line but is not perpendicular to it. PLEASE ANSWER!!! NEED EXTREME HELP!!!
Answer:
fdsjfgdndgnxhñgjxgjxgjx
Consider the expression 4a + (-3b), where bis a negative number and a < b. Is the sum positive or negative?
The sum will be negative.
The product of two negative numbers is always positive and if we add two numbers, the sign of the greater number is used in the result.
Here, we are given an expression 4a + (-3b)
Also we are told that a < b and b is a negative number
Mow, since b is a negative number, (-3b) will always be positive. This is because the product of two negative numbers, here -3 and b, will always be positive.
Now, a can be positive or negative. If a is positive, the sum will always be positive. However, if it is negative, the sum can be either positive or negative.
Here, in fact, since a < b, a will always be negative only
Let us take an example, say a = -3 and b = -2
Then the sum becomes 4(-3) + (-3)(-2)
= -12 + 6
= -6
If we observe closely since a and be are both negative and a < b, in absolute terms a will always be greater than b since for negative numbers higher the value, smaller is the number.
Thus, we can conclude that 4a > (-3b) for all values of a and b
and since 4a will always be negative, the sum will also be negative.
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The equation of line j is y+5=8(x+4). Perpendicular to line j is line k, which passes through the point (4, – 1). What is the equation of line k?
8x+y=31
perpendicular means the slopes are opposite reciprocals of each other. perpendicular to: y +5= 8(x +4) → m = 8 m⊥ = -8
Input the slope (m⊥ = -8) and the point (x₁, y₁) = (4, -1) into the Point-Slope formula: y - y₁ = m(x - x₁)
y - (-1) = -8(x -4)
y + 1 = -8 x + 32 simplified
8x+y =31
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In the word grapefruit the ratio of vowels to consonants is 2:3 .find the ratios of vowels to consonats in the word pineapple and strawberry. give each ratio in its simplest form.
Answer:
48 because of the vowels it became 48 .
Step-by-step explanation:
I Quesliod. Make sure you start new workings. In the word grapefruit, the ratio of vowels to consonants is . Find the ratios of vowels to consonants in the words pineapple and strawberry. Give each ratio in its simplest form. grapefruit Vowels :Consonants Remember: vowels are a, e, i, o, u
Help, Theres a time limit!
Answer:
The answer is 2.72 * 10^8 sec.
Step-by-step explanation:
Distance between Earth and Sirius is 5.062 * 10^13 miles.
Time taken = Distance travelled/speed
5.062*10^13 miles/sec/1.86*10^5 miles.
=2.72 * 10^8 sec.
So this means that the time taken to travel light from Sirius to Earth is 2.72*10^8.
x = 10 g y = 10 kg y + x =
a)10.1 kg
b)100.1 g
c)10.1 kg
d)10.01 g
The correct option is d)10.01 kg; y + x = 10.01 kg.
What is referred as the unit conversion?When converting units, you are generally given one measure but instead asked to convert it to another.
For example, you may be given a volume in "gallons" but also asked to convert it to "fluid ounces." They will have given you (or you will be able to quickly find) the conversion units which are appropriate for the task. In order to complete the conversion, you will be required to multiply or divide by one of the following unit equivalences.For the given values in the question;
x = 10 g and y = 10 kg
As, both the values are of mass.
For adding both values, the unit must be same.
So, convert the value of x in kg from g.
1 kg = 1000 g
Thus, 1 g = 1/1000 kg
10 g = 10/1000 kg
10 g = 0.01 kg
Now add both;
x + y = 0.01 + 10
x + y = 10.01 kg
Thus, the value of x + y is found as 10.01 kg.
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The correct question is-
a)10.1 kg
b)100.1 g
c)10.1 kg
d)10.01 kg
Five sections of fencing around a garden are 7 yards long, 8 3/4 yards long, 12 1/2 yards long, 15 1/3 yards long, and 7 3/4 yards long. What is the total length of the fencing?
Answer: 51.33
Step-by-step explanation:
7+8.75+12.5+15.33+7.75 = 51.33
2
You can also use scientific notation for very small numbers. The
thickness of a dollar bill is about 0.0043 inches. Write this quantity in
scientific notation.
A. First move the decimal point to the right to get a number that is
greater than or equal to 1 but less than 10.
0.0043 The decimal point moves 3
places to the right.
Remove the extra zeros to get the first factor:
B. Since 0.0043 is less than 1, you moved the decimal point to the right,
so the exponent in the power of 10 will be negative.
-3
0.0043 = 4.3
X 10
the thickness in scientific notation is:
4.3* 10⁻³ inches
How to write the thickness in scientific notation?
Here we know that the thickness of a dollar bill is 0.0043 inches.
Now, scientific notation refers to the notation where we have a single digit at the left of the decimal point, and the order of the number is defined by a factor of a power of 10.
To write our number in scientific notation we need to count the number of zeros that we have before the first non-zero decimal, and we can see that it is equal to 3.
Then we can move all the digits 3 units to the left, and add a factor 10⁻³ to correct that, then we will get:
0.0043 = 4.3* 10⁻³
From this, we conclude that the thickness in scientific notation is:
4.3* 10⁻³ inches
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