Answer: 7
Step-by-step explanation:
Answer:
7 is the GCF of 21 and 28
Step-by-step explanation:
The GCF of 21 and 28 is 7. To calculate the greatest common factor (GCF) of 21 and 28, we need to factor each number (factors of 21 = 1, 3, 7, 21; factors of 28 = 1, 2, 4, 7, 14, 28) and choose the greatest factor that exactly divides both 21 and 28, i.e., 7.
how to find perimeter of a triangle?
Answer:
Just add the 3 sides together
Step-by-step explanation:
if a triangle has the side values of 3, 4, 6. Then you would simply add them together!
3+4+6=13
therefor that triangles perimeter is 13
hope this helps!
The coordinates of the endpoints of
KL
are K(
–
16,10) and L(
–
9,
–
11). Point M is on
KL
and divides it such that KM:LM is 4:3.
What are the coordinates of M?
Write your answers as integers or decimals.
The coordinates M along the directed line segment is (-12, -2)
How to find the coordinates of the point along the directed line segment?The points are given as:
K = (-16, 10)
L = (-9, -11)
The ratio on the segment can be represented as;
KM : LM, m : n = 4 : 3
So, we have the coordinates of the point M that lies along the directed line segment to be
M = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)
So, we have:
M = 1/(4 + 3) * (4 * -9 + 3 * -16, 4 * -11 + 3 * 10)
Evaluate
M = 1/7 * (-84, -14)
Evaluate
M = (-12, -2)
Hence, the coordinates of the point M is (-12, -2)
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Please Help
Find(f+g)(x)if f(x)-/16x4 and g(x)=3x2-3x-5
The function operation (f + g)(x) of the functions f(x) = √( 16x⁴ ) and g(x) = 3x² - 3x - 5 is -5x² + 5x - 7.
What is the function operation (f + g)(x) of the given functions?A function is simply a relationship that maps one input to one output.
Given the functions in the question;
f(x) = √( 16x⁴ )g(x) = 3x² - 3x - 5To determine the function operation (f + g)(x), replace the function designators with the functions and simplify.
(f + g)(x) = f(x) + g(x)
(f + g)(x) = √( 16x⁴ ) + ( 3x² - 3x - 5 )
Replace √( 16x⁴ ) with 4x²
(f + g)(x) = 4x² + 3x² - 3x - 5
Collect and add like terms
(f + g)(x) = 7x² - 3x - 5
Therefore, the function operation (f + g)(x) is 7x² - 3x - 5.
Option A is the correct answer.
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The data to the right represent the cost of living for 20
states. The cost of living is a measure of the average
price paid for housing, utilities, groceries, healthcare,
transportation, and miscellaneous expenses. The
national average cost of living is 100. The data can be
used to compare a state to the national average and
to other states.
T
Use these data to construct a frequency distribution with a first class of 85.0-94.9. Fill in the missing classes and the frequency for each class belo
Cost of living
Number of states
9
85.0-94.9
125.0134.9
8-8
20
(Type integers or decimals. Do not round.)
151.2121.3 99.4 94.5 89.7
138.7120.1 96.7 94.5 89.6
132.1106.5 95.3 90.9 89.4
124.9101.6 95.2 90.1 89.2
The frequency distribution based on the information given is illustrated below.
What is the frequency distribution of table?
A frequency distribution table is the chart that summarizes all the data under two columns - variables/categories, and their frequency.
It should be noted that the distribution table has two or three columns and the first column lists all the outcomes as individual values or in the form of class intervals, depending upon the size of the data set.
Given the above information the frequency distribution table is:
Cost of living[tex]\begin{table}[]\begin{tabular}{ll}Cost of living & Number of States \\85.0 - 94.9 & 9 \\95.0 - 104.9 & 5 \\105.0 - 114.9 & 0 \\115.0 - 124.9 & 2 \\125.0 - 134.9 & 2 \\135.0 - 144.9 & 1 \\145.0 = 154.9 & 1 \end{tabular}\end{table}[/tex] Number of states
85.0 - 94.9 9
95.0 - 104.9 5
105.0 - 114.9 0
115.0 - 124.9 2
125.0 - 134.9 2
135.0 - 144.9 1
145.0 - 154.9 1
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Mr. Olin bought 6 sketchbooks for the students in his art class. Each sketchbook was on sale for $3 oG. If the sketchbooks cost $18 total before tax, what was the original price of each sketchbook
Answer:
i think it is 18
Step-by-step explanation:
because if he brought 6 for $18 and it was in sale for $3 that means there is no tax
List 1 4/5, -7/4, 41%, and -1.3 from greatest to least.
The descending order to the list is 1, 4/5, 41%, -1.3, -7/4.
What us descending order?
When numbers are arranged from greatest to smallest or highest to lowest it is said to be in descending order.
Main Body:
To solve this question we need to convert all numbers into decimal system.
calculate:
1 can be written as 1.00
4/5 can be written as 0.8
-7/4 = -1.75
41% = 41/100 = 0.41
-1.3 can remain as it is because it itself is in decimal form.
Hence the order from greatest to smallest is as
1 > 0.8 > 0.41 > -1.3 > -1.75
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Simon bought a $48 table on sale at 30% off.
Select from the drop-down menu to correctly complete the sentence
0.03(50)
0.3(50)
3(50)
30(50).
Simon bought a $48 table on sale. The price of the table can be estimated by $50.
The sale propose 30% off, then an estimate for the discount can be calculated using proportion:
$50 -- 100%,
$x -- 30%
that is mathematically
Find x:
Answer: correct choice is B
Mike Meier purchased a lawnmower for $328.61, a lawn sprinkler for $13.27, and a hose reel for $27.96. He must pay the state tax of 5.5 percent, the county tax of 1.5 percent, and the city tax of 2 percent. What is the total purchase price?
Answer: $402
Step-by-step explanation: I believe this answer is correct i did all the math
The average December temperature in Salt Lake City, Utah is 10 degrees Farenheit. The actual December
temperture can vary in Salt Lake City by 5 degrees Farenheit either above or below the average. What is the
minimum temperature of Salt Lake City in December?
The minimum temperature in Salt Lake City in December is 5 degrees Fahrenheit.
The average December temperature in Salt Lake City, Utah, is 10 degrees Fahrenheit. The actual December temperature can vary in Salt Lake City by 5 degrees Fahrenheit either above or below the average.
We need to find out the minimum temperature in Salt Lake City in December. Let the temperature be denoted by the variable "M". The minimum temperature is the difference between the average temperature and the variation in the temperature.
M = 10 - 5
M = 5
Hence, the minimum temperature in Salt Lake City in December is 5 degrees Fahrenheit.
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Identify the values of the variables. Give your answers in simplest radical form. Help!
Considering the triangle given the variables are calculated to be
x = (5√6)/3
y = (10√6) / 3
How to calculate the unknown variablesInformation given in the question
right angle triangle
The unknown variables is calculated using SOH CAH TOA
Definition of variables for the right angle triangle
hypotenuse = y
opposite = 5√2
adjacent = x
The variable x is solved using tan, TOA, the angle is 60
tan 60 = Opposite / Adjacent
tan 60 = (5√2) / x
x = (5√2) / tan 60
x = (5√6)/3
The variable y is solved using sin, SOH, the angle is 60
sin 60 = Opposite / Hypotenuse
sin 60 = (5√2) / y
y = (5√2) / sin 60
y = (10√6) / 3
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Two rockets are to be launched at the same time from NASA headquarters in Florida, and are to meet at a space station many miles from Earth. The first rocket is to travel at 19,200 miles per hour and the second rocket will travel at 18,000 miles per hour. If the first rocket is scheduled to reach the space station 0.5 of an hour before the second rocket, how far is the space station from NASA headquarters?
By solving a linear equation, it can be calculated that
The space station is at a distance of 144000 miles from NASA headquarters
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here, a linear equation needs to be solved
Let the space station be d miles from NASA headquarters
Speed of the first rocket = 19200 miles/hour
Speed of the second rocket = 18000 miles /hour
Time taken by the first rocket to reach the space station = [tex]\frac{d}{19200}[/tex]
Time taken by the second rocket to reach the space station = [tex]\frac{d}{18000}[/tex]
By the problem,
[tex]\frac{d}{18000} - \frac{d}{19200} = 0.5\\\\\frac{16d - 15d}{288000} = 0.5\\\\\frac{d}{288000} = 0.5\\\\d = 288000 \times 0.5\\\\d = 144000 \ miles[/tex]
The space station is at a distance of 144000 miles from NASA headquarters
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find the standard form of the equation of the circle with end points of a diameter at the point (2,3) and (-5,5)
Use the following model to answer the question.
3 groups are shown. Each group shows 2 tens rods and 6 ones cubes.
Which division problem is shown by the model?
Which division problem is shown by the model?
Which division problem is shown by the model?
A.
0
.
66
÷
3
=
0
.
22
B.
0
.
66
÷
3
=
0
.
26
C.
0
.
78
÷
3
=
0
.
62
D.
0
.
78
÷
3
=
0
.
26
Answer: 78 ÷ 3 = 26
Step-by-step explanation:
We are given that there are 3 groups shown. This means we will be dividing by 3.
We are given that each group has 2 ten rods (20) and 6 ones cubes (6). This means the answer is 26.
Lastly, 26 * 3 = 78, meaning we are dividing 78 by 3.
This gives us:
78 ÷ 3 = 26
What is the slope of the line that passes through the points (-6, -7) and (-3, -2)?
there are 4 consecutive even integers that sum to 276
The required consecutive even integers are 66, 68, 70, and 72.
We have four integers. The integers are consecutive, that means the integers are one after the other. The integers are even, which means they are all divisible by two. The sum of these four even integers is 276.
Let the first even integer be represented by the variable "n". The next three consecutive integers are (n + 2), (n + 4), and (n + 6). Let the sum be denoted by "S".
S = n + (n + 2) + (n + 4) + (n + 6)
276 = 4n + 12
4n = 264
n = 66
Hence, the required integers are 66, 68, 70, and 72.
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Subtract the linear expressions. Show your work.
(4-3x + 9x) - (-11-7x + 9)
(2 points) Let x³ - 2x²-x+2=0 be a polynomial equation. Find the list of all potential rational solution(s) for the polynomial equation using the
Rational Root Theorem. Then, find the actual rational solution(s).
1. Find all potential rational solution(s).
Answer (separate by commas):
2. Find all distinct actual rational solution(s).
Answer (separate by commas):
Note: You can earn partial credit on this pmblem
Potential rational solution(s) to the above polynomial equation is ±1, ±2.
Actual rational solution are ±1, +2.
What is polynomial equation?
Polynomial equations are those created using exponents, coefficients, and variables. The greater of its possible exponents is referred to as the equation's degree.
Main Body:
Given:
x³ - 2x² - x +2 = 0
We will use the Rational Root Theorem:
If the rational number r/s is a root of a polynomial whose coefficients are integers, then the integer r is a factor of the constant term, and the integer s is a factor of the leading coefficient.
So, if the constant therm is 2 and the leading factor is 1, candidates for roots are:
±1,±2
Dividing x³ - 2x² - x +2 = 0 by x-1, we get
x²-x-2 as quotient.
Splitting the middle term ,
⇒x² - 2x + x - 2
⇒x(x- 2) + 1(x-2)
⇒(x+1)(x-2)
so x= -1 , 2
Hence the rational solution to the equation are ±1, 2.
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On a coordinate plane, the position of two friends can be defined by the points A(1,3) and B(7,6). Their teacher is standing at point C, the teacher’s distance from point A is twice the distance from Point B. What are the coordinates of point C?
A.) (5,5)
B.) (-5,5)
C.) (4, 9/2)
D.) (8/3, 3)
Please show work if possible!
The coordinate of point C will be (5, 5). Then the correct option is A.
What is the section of the line?Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have
x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)
On a direction plane, the place of two companions can be characterized by the focuses A(1,3) and B(7,6). Their instructor is remaining at point C, and the educator's separation from point An is two times the separation from Point B.
The ratio is given as 2:1.
x = (7 × 2 + 1 × 1) / (2 + 1)
x = 15 / 3
x = 5
y = (6 × 2 + 1 × 3) / (2 + 1)
y = 15 / 3
y = 5
The coordinate of point C will be (5, 5). Then the correct option is A.
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or
The equation of line k is y=
–
10x–8. Perpendicular to line k is line , which passes through the point (2,2). What is the equation of line ?
Considering the definition of perpendicular line, the equation of perpendicular line is y= -1/10x + 11/5.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseThe line is y= 10x -8.
The line has a slope of 10. If you multiply the slopes of two perpendicular lines, you get –1:
10× slope perpendicular line= -1
slope perpendicular line= (-1)÷ 10
slope perpendicular line= -1/10
The perpendicular line has a form of: y= -1/10x + b
The line passes through the point (2, 2). Then:
2= -1/10× (2) + b
2= -1/5+ b
2+ 1/5= b
11/5= b
Finally, the perpendicular line is y= -1/10x + 11/5.
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manuel wishes to purchase 25cent and 30 cent stamps. he decides to buy 10 fewer 30 cent stamps. How many of each can he buy for no more than $19.00
Using the simplification, Manuel buy 15 stamps of 25 cents and 5 stamps of 30 cent.
In the given question,
Manuel wishes to purchase 25 cent and 30 cent stamps.
He decides to buy 10 fewer 30 cent stamps.
We have to find how many of each can he buy for no more than $19.00.
Let he buy x stamps of 25 cent.
He want to buy 10 fewer 30 cent stamps.
So he buy x−10 stamps of 30 cent.
But he have to buy total stamps of $19.
So the equation is
x+x−10 = 19
Simplifying
2x−10=19
Add 10 on both side
2x−10+10=19+10
2x=29
Divide by 2 on both side
2/2 x =29/2
x=14.5
x≈15
Hence, he buy 15 stamps of 25 cent.
Now finding the number of 30 cent.
he buy x−10 stamps of 30 cent.
So 15−10=5.
So he buy 5 stamps of 30 cent.
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Lance Whittingham IV specializes in buying deep discount bonds. These represent bonds that are trading at well below par value. He has his eye on a bond issued by the Leisure Time Corporation. The $1,000 par value bond pays 4 percent annual interest and has 18 years remaining to maturity. The current yield to maturity on similar bonds is 12 percent. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods.
a. What is the current price of the bonds?
b. By what percent will the price of the bonds increase between now and maturity? (Round "PV Factor" to 3 decimal places, intermediate and final answers to 2 decimal places. Omit the "%" sign in your response.) Price increases by %
a) The current bond price (present value) is $420.03.
b) The percentage by which the price of bonds will increase between now (current) and maturity (18 years) is 138%.
How is the bond price determined?The current bond price represents its present value.
The present value is the discounted future cash inflows.
We can compute the present value using an online finance calculator as follows:
N (# of periods) = 18 years
I/Y (Interest per year) = 12$
PMT (Periodic Payment) = $40 ($1,000 x 4%)
FV (Future Value) = $1,000
Results:
PV = $420.03
Sum of all periodic payments = $720.00
Total Interest = $1,299.97
Percentage increase in bond price = [(Future value - Present value)/Present value x 100]
= 138% [($1,000 - $420.03)/$420.03 x 100]
Thus, the present value of the bonds $420.03 will grow by 138% at maturity.
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find the value of the ratio (red to blue) of the areas of the similar figures. Write the ratio as a fraction in simplest form. 12 and 8
The ratio of the areas of the similar figures is given as follows:
225/16.
What are similar figures?Similar figures are figures that share these two features:
Congruent angle measures, that is, the same angle measures.Proportional side lengths.The ratio of the side lengths of the similar figures can be represented as follows:
(b/a).
The side length is measured in units, while the area is measured in units squared, hence the ratio of the areas of the similar figures is represented as follows:
(b/a)² = b²/a².
From the image of the right triangle shown at the end of the answer, the ratio of the side lengths is:
15/4.
Hence the ratio of the areas of the figures is given as follows:
(15/4)² = 225/16.
Missing InformationThe figures are given by the image at the end of the answer.
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6 sqrt 44z + sqrt 99z
Answer: 15√11z
Step-by-step explanation:
Graph The any form equation 3(-2x-4y-3) = 5(x - 5y + 10) Build equation with the given information (2) slope = m = -5 point (-3,-2) 3 point 1 (-5,-3) point2 (-7,-9) Build an equation parallel to the given equation and passing through The point 47 y = - ³²/²x-4 point (-7,5)
Here is what i did
I used a graphing calculator
screenshot included with question
Answer:
48 fl oz = 6 c
4 gal = 16 qt
Step-by-step explanation:
4 times 4 is 16
48 divided by 8 is 6
Last year, the student population at Haley Elementary School was 360 students. After rezoning this year, the student population is 10% smaller. HOW MANY STUDENTS ATTEND HALEY ELEMENTARY THIS YEAR?
Answer: 324
Step-by-step explanation: 10% is the same as 1/10
360/10 is 36
360-36= 324
meaning 324 students now attend Haley elementary school <3
hope this helps <33
A house on the market was valued at $355,000 . After several years, the value decreased by 9%. By how much did the house's value decrease in dollars? What is the current value of the house?
Answer: $323,050
Step-by-step explanation:
355,000 over 1 x 9 over 100 = 3195000 over 100 (31950)
355,000- 31,950 = 323,050 which is your answer, hope this helped <3
A letter is chosen at random from the word MATHEMATICS. Find the probability that it will be
a) an H
b) an M
c) a B
d) a vowel,
e) a letter other than an A
Answer:
a) 1/11
b) 2/11
c) 0/11
d) 4/11
e) 9/11
Step-by-step explanation:
'MATHEMATICS' has 11 letters.
a) there is only one H out of the 11 letters meaning the probability is 1/11
b) there are two M s out of the 11 letters meaning the probability is 2/11
c) there is no B in the word meaning the probability is 0/11
d) there are four vowels (2 A s, 1 E and 1 I) out of the 11 letters meaning the probability is 4/11
e) there two A s in the word and 11-2=9 meaning the probability is 9/11
Hope this helps :)
A store pays $114 for a picnic table. The store marks up the price by 28%. What is the
amount of the mark-up?
The markup price on the table would be $32.
What is the markup price?The gross profit of a unit, which is its sales price less its cost to produce or acquire for resale, is divided by the unit's cost to determine the markup %. The markup percentage, which is computed as (12 - 8) / 8, is 50% for an item that costs the business $8 to produce but is priced at $12.So, we have:
Discount = 28%The selling price of the picnic table = is $114Now, calculate the makeup price:
Mark-up price = Discount * Selling Price
Mark-up price = (28/100) * 114
Mark-up price = 31.92
Mark-up price ≈ 32.
Hence, the markup price on the table would be $32.
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The daily production costs for a golf ball manufacturer can be modeled with the function C(x) = 0.1x2 - 7x + 140, where C(x) is the total cost and x is the number of golf balls produced per hour. Use the graph to answer the question.
Graph of function c of x equals 0 point 1 x squared minus 7 x plus 140. The graph has the axis labeled as number of golf balls produced, and the y-axis labeled as cost. The curve begins at (0, 140), decreases to (35, 17.5), and then increases to infinity.
Which statement shows the correct relationship between production cost and number of golf balls produced?
The statement that shows the correct relationship between production cost and the number of golf balls produced is that the minimum production cost of 17.5 occurs when 35 golf balls are produced.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Then the minimum is represented by the formula;
c - b² / 4a
We have given equation C(x) = 0.1x² - 7x + 140
a = 0.1
b = -7
c = 140
Now plugging in values to c - b² / 2a
= 140 - 7² / (4 * 0.1)
= 17.5
The minimum production cost will be; 17.5
Now plugging 35 into the given equation;
C(x) = 0.1x² - 7x + 140
C(x) = 0.1 ( 35)² - 7 (35) + 140
C(x) = 17.5
Therefore, 35 golf balls produce the minimum cost.
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Answer:
that the minimum production cost of 17.5 occurs when 35 golf balls are produced.
Step-by-step explanation: