The factors common to 12x and 18xy are 1, 2, 3, 6, and x.
The factors common to 12x and 24y are 1, 2, 3, 4, 6, and 12.
The GCF of the expression is 6.
Answer: Options B, C and E.
Explanation:
Factors are numbers we can increase together to get another number. At the point when we discover the components of at least two numbers, and afterward discover a few variables are the equivalent ("normal"), at that point they are the "basic elements".
These are the factors which are common in the whole expression or are common in any two equations at the time of comparison. The common factor which is the biggest is known as the greatest common factor.
Answer:
B,C,E
Step-by-step explanation:
How do I solve this question
The solution set is x = 3, y = 4 (or) x = 3, y = –4.
Solution:
Given system of algebraic equations are
[tex]y^{2}+(x-8)^{2}=41[/tex] – – – – – (1)
[tex]y^{2}-25=-x^{2}[/tex] – – – – – (2)
Expand equation (1) using algebraic identity: [tex](a-b)^2=a^2-2ab+b^2[/tex]
[tex]y^{2}+x^2-16x+64=41[/tex]
subtract 64 from both sides of the equation
[tex]y^{2}+x^2-16x+64-64=41-64[/tex]
[tex]y^{2}+x^2-16x=-23[/tex] – – – – – (3)
Now, to arrange equation (2) in order, add [tex]x^2[/tex] on both sides.
[tex]y^{2}-25+x^2=-x^{2}+x^2[/tex]
[tex]y^{2}-25+x^2=0[/tex]
Add 25 on both sides of the equation,
[tex]y^{2}+x^2=25[/tex] – – – – – (4)
To solve this subtract equation (4) from equation (3)
[tex]\Rightarrow y^{2}+x^2-16x-(y^{2}+x^2)=-23-25[/tex]
[tex]\Rightarrow y^{2}+x^2-16x-y^{2}-x^2=-23-25[/tex]
[tex]\Rightarrow -16x=-48[/tex]
Divide both sides of the equation by –16,
⇒ x = 3
Substitute x = 3 in equation (4), we get
[tex]\Rightarrow y^{2}+3^2=25[/tex]
[tex]\Rightarrow y^{2}=25-9[/tex]
[tex]\Rightarrow y^{2}=16[/tex]
[tex]\Rightarrow y=\pm 4[/tex]
i. e. y = 4 (or) y = –4
The solution set is x = 3, y = 4 (or) x = 3, y = –4.
Fifty-five and one-half percent of shareholders in a fast food chain are under 40. If 91,00 shareholders, how many are 40 and over?
Final answer:
To determine the number of shareholders aged 40 and over, subtract the number of shareholders under 40 (55.5% of 91,000) from the total, resulting in 40,495 shareholders who are 40 and over.
Explanation:
The question asks how many shareholders are aged 40 and over in a fast food chain given that 55.5% are under 40 and there are a total of 91,000 shareholders.
First, we must find the number of shareholders under 40: 0.555 × 91,000 = 50,505 shareholders. Next, we subtract this from the total number of shareholders to find the number of shareholders aged 40 and over: 91,000 - 50,505 = 40,495 shareholders.
Therefore, 40,495 shareholders are aged 40 and over.
It takes you
3/8 of an hour to walk 9/10 of a mile.
How far can you walk in 1 hour?
a. 0.42
b. 0.3375
c. 2.4
d. 5.25
Answer:
C
Step-by-step explanation:
You can already walk 0.9 of a mile in 3/8 so it cannot be A or B
C is the most reliable because even if you multiple the 0.9 by 3 so it is a little bit over a mile it is still closer to 2.4
Sorin chose a three-digit number and doubled it. Jiao chose a two-digit number. Carlos subtracted Jiao’s number from Sorin’s product. What is the greatest number Carlos can get?
HELP QUICK PLS
Answer:
The number is 1988.Step-by-step explanation:
Carlo's outcome will be the greatest if Sorin's number will be the highest and Jiao's number is the lowest.
Sorin choose a three digit number, the highest three digit number is 999.
After doubled the number, 999, the outcome will be 1998.
Jiao chooses two-digit number, the lowest two-digit number is 10.
Hence, the greatest number that Carlo can get is (1998 - 10) = 1988.
Final answer:
The greatest number Carlos can get is 1988, which is found by doubling the largest three-digit number, 999, to get 1998, and then subtracting the smallest two-digit number, 10.
Explanation:
To find the greatest number Carlos can get, we must consider the largest possible three-digit number that Sorin could double and the smallest possible two-digit number Jiao could choose.
The largest three-digit number is 999. When doubled, it becomes 1998. The smallest two-digit number is 10. Therefore, Carlos' greatest possible number is obtained by subtracting the smallest two-digit number from Sorin's doubled number:
1998 - 10 = 1988
Hence, the greatest number Carlos can get is 1988.
A boat costs $19300 and decreases in value by 5% per year. How much will the boat be worth after 6 years
Answer:
[tex]\$14,187.27[/tex]
Step-by-step explanation:
we know that
In this problem we have a exponential decay function of the form
[tex]y=a(1-r)^x[/tex]
where
y ----> is the value of the boat in dollars
x ---> is the number of years
r ---> is the percent rate of change
a ---> is the initial value or y-intercept
we have
[tex]a=\$19,300\\r=5\%=5/100=0.05[/tex]
substitute
[tex]y=19,300(1-0.05)^x[/tex]
[tex]y=19,300(0.95)^x[/tex]
For x=6 years
substitute the value of x in the exponential function
[tex]y=19,300(0.95)^6\\y=\$14,187.27[/tex]
The sum of two numbers is 35. The greater
number is 1 less than 5 times the smaller number.
What are the two numbers
Answer:
x = 29
y = 6
Step-by-step explanation:
Let the two numbers be represented as x and y
x + y = 35
x = 5y - 1
Substitute x as 5y -1 in equation one
5y -1 + y = 35
5y + y -1 = 35
Add 1 to both sides
6y - 1 + 1 = 35 + 1
6y = 36
Divide both sides by 6
6y/6= 36/6
y = 6
Now substitute y as 6 in any of the equations to get x.
Using equation one ,
We have
x + y = 35
x +6 = 35
Subtract 6 from both sides
x + 6 - 6 = 35 - 6
x = 29
Janelle ate 82% of the pie. What fraction of the pie remained?Janelle ate 82% of the pie. What fraction of the pie remained?
Answer:
It remained 9/50 of the pie
Step-by-step explanation:
If Janelle ate 82% of the pie, now it remains:
100 - 82 = 18%
Let's convert 18% to fraction:
18% = 0.18 = 18/100
Let's simplify 18/100:
18/100 = 9/50 (Dividing by 2 the original fraction)
It remained 9/50 of the pie
Find the value of x so that f(x)= -9 if f(x) =3x+4
Answer:
f(-9) = -23
Step-by-step explanation:
Step 1: Identify the function
f(x) = 3x + 4
Step 2: Set x to -9 in the function
f(-9) = 3(-9) + 4
Step 3: Multiply
f(-9) = -27 + 4
Step 4: Add
f(-9) = -23
Answer: f(-9) = -23
Examine this information carefully.
Angles Sides
30 degrees 4 cm
60 degrees 3 cm
90 degrees 5 cm
What kind of triangle would these measurements make?
A. acute scalene triangle
B. right scalene triangle
C. right isosceles triangle
D. acute isosceles triangle
Answer:
B. right scalene triangle
i am sure about this answer as 90 degree tells us that it is a right angle triangle and as all the measure of angles as well as sides are different it is a scalene triangle.
Your answer should be polynomial standard form polynomial in standard form (c+8)8c+2)=
Answer:
8c² + 66c + 16
Step-by-step explanation:
Given
(c + 8)(8c + 2)
Each term in the second factor is multiplied by each term in the first factor, that is
c(8c + 2) + 8(8c + 2) ← distribute both parenthesis
= 8c² + 2c + 64c + 16 ← collect like terms
= 8c² + 66c + 16
The data depicted in a histogram show approximately a normal distribution if the distribution
bunches up on either end and tapers off toward the center
bunches up in the middle and tapers off symmetrically at either end
is relatively even from one end to the other
bunches up on one end and tapers off toward the other end
Answer:
bunches up in the middle and tapers off symmetrically at either end
Step-by-step explanation:
By definition a normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
Because the data towards the mean is more frequent in occurrence, the graph peaks at the center. The data occurs less frequently at the tail ends of the distribution, thus the shape of the distribution is a bell shape that peaks at the center and tapers off towards the tails. The key characteristic is that the distribution of data is perfectly symmetrical.
This is why the answer is:
The data depicted in a histogram show approximately a normal distribution if the distribution bunches up in the middle and tapers off symmetrically at either end.
Mike has baseball cards and football cards. The ratio of baseball cards to football cards is 5:7 He has 40 baseball cards. How many football cards does he have?
Answer:
56 football cards
Step-by-step explanation:
If 5 baseball cards multiplied by 8 is 40, then you multiply the 7 football cards by 8 as well.
7x8=56
What is 7/`15 divided by 3/4?
Answer:
28/45
Step-by-step explanation:
Solve using cross multiplication.
(7/15) / (4/3) =
28/45
The fraction is already in simplest form
answer:
[tex] \frac{7}{20} [/tex]
explanation:
[tex] \frac{7}{15} \times \frac{3}{4} = \frac{7 \times 3}{15 \times 4} = \frac{21}{60} = \frac{7 \times 3}{20 \times 3} = \frac{7}{20} [/tex]
Complete this statement 0.743 mL = ?L
A 743
B 74.3
C 0.000743
D 0.0743
Answer:
0.743ml=0.000743
Step-by-step explanation:
Consider this function for cell duplication where the cells duplicate every minute.
f(x) = 75(2)x
Determine what each parameter in the function represents.
A) The 75 is the initial number of cells, and the 2 indicates that the number of cells doubles every minute.
B) The 75 is the initial number of cells, and the 2 indicates that the number of cells increases by 2 every minute.
C) The 75 is the number of cells at 1 minute, and the 2 indicates that the number of cells doubles every minute.
D) The 75 is the number of cells at 1 minute, and the 2 indicates that the number of cells increases by 2 every minute.
Answer:
A) The 75 is the initial number of cells, and the 2 indicates that the number of cells doubles every minute
Step-by-step explanation:
When x=0 (no minutes have elapsed), the value of the function is ...
f(0) = 75(2^0) = 75(1) = 75 . . . . the initial number of cells
As x increases by 1 (minute), the number of cells is multiplied by 2, so the 2 is the multiplier each minute. It indicates the number doubles. ("double" = "multiply by 2")
x is not defined, but for the function to make any sense, it must represent elapsed minutes.
In trapezoid PQRS, PQ is parallel to RS. Let X be the intersection of diagonals PR and QS. The area of triangle PQX is 20 and the area of triangle RSX is 45. Find the area of trapezoid PQRS.
Answer:
The area of trapezoid PQRS is 125 square units
Step-by-step explanation:
The picture of the question in the attached figure
we know that
If trapezoid PQRS with parallel sides PQ and RS is divided into four triangles by its diagonals PR and QS , intersecting at X, then the area of triangle PSX is equal to that of triangle QRX, and the product of the areas of triangle PSX and triangle QRX is equal to that of triangle PQX and triangle RSX
Let
A_1 ----> the area of triangle PSX
A_2----> the area of triangle QRX
A_3 ---> the area of triangle PQX
A_4 ---> the area of triangle RSX
[tex]A_1*A_2=A_3*A_4[/tex]
[tex]A_1=A_2[/tex]
so
[tex]A_1^2=A_3*A_4[/tex]
we have
[tex]A_3=20\ units^2\\A_4=45\ units^2[/tex]
substitute
[tex]A_1^2=(20)(45)\\A_1^2=900\\A_1=30\ units^2[/tex]
The area of trapezoid is equal to
[tex]A=A_1+A_2+A_3+A_4[/tex]
substitute
[tex]A=30+30+20+45=125\ units^2[/tex]
Final answer:
The area of trapezoid PQRS is found by adding the areas of triangle PQX (20 square units) and triangle RSX (45 square units) together, which equals 65 square units.
Explanation:
The area of trapezoid PQRS can be found by summing up the areas of triangle PQX and triangle RSX. Since diagonals PR and QS intersect at point X, both triangles share the same height, which is the perpendicular distance from point X to the bases PQ and RS. Thus, the area of trapezoid PQRS is simply the sum of the areas of the two triangles.
To calculate the area of trapezoid PQRS, we add the area of triangle PQX, which is given as 20, to the area of triangle RSX, which is given as 45. Therefore, the area of trapezoid PQRS is:
Area of trapezoid PQRS = Area of triangle PQX + Area of triangle RSX = 20 + 45 = 65
So, the area of trapezoid PQRS is 65 square units.
a triangle is reduced. What is the perimeter of the reduced triangle, in inches.
Answer:
the perimeter is 36
Step-by-step explanation:
Answer:
The correct answer is 36
Step-by-step explanation:
Edg. 2020
Wich expression represents 5/34 in rational exponent form
Option C:
[tex]$\sqrt[5]{34} =34^{\frac{1}{5} }[/tex]
Solution:
Given expression is [tex]\sqrt[5]{34}[/tex].
To write the given expression in rational exponent form.
Using rational exponent rule:
[tex]$\sqrt[n]{a^m} =a^{\frac{m}{n} }[/tex]
i. e. [tex]$\sqrt[\text{root}]{a^\text{power}} =a^{\frac{\text{power}}{\text{root}} }[/tex]
Given [tex]\sqrt[5]{34}[/tex]
Here, root is 5 and power is 1.
Write it using the rational exponent rule,
[tex]$\sqrt[5]{34} =34^{\frac{1}{5} }[/tex]
Therefore option C is the correct answer.
Hence [tex]$\sqrt[5]{34} =34^{\frac{1}{5} }.[/tex]
Answer: 34^1/5
Step-by-step explanation:
how do I write the sum of 6x and 2x is at least 39 ?
Step-by-step explanation:
We have,,
6x and 2x
To find, the value of x = ?
According to question,
The sum of 6x and 2x is at least 39
∴ 6x + 2x = 39
⇒ 8x = 39
⇒ x = [tex]\dfrac{39}{8}[/tex]
∴ The value of x = [tex]\dfrac{39}{8}[/tex]
Thus, put x = [tex]\dfrac{39}{8}[/tex] I write the sum of 6x and 2x is at least 39 .
Pleaseeeeeeee help !
Answer:
answer is a
look at picture
1. In right triangle ABC, C is the right angle. Given m2. In right triangle ABC, C is the right angle. Which of the following is cos B if sin A=0.4?
Answer:
[tex]\cos B=0.4[/tex]
Step-by-step explanation:
Given
[tex]\Sin A=0.4=\frac{4}{10}=\frac{2}{5}\\\\In\ right\ triangle\\\\\sin A=\frac{Perpendicular}{Hypotenuse}=\frac{BC}{AB}=\frac{2}{5}\\\\Then\ \ \cos B=\frac{Base}{Hypotenuse}=\frac{BC}{AB}=\frac{2}{5}=0.4[/tex]
Answer:
Part a)
[tex]c=9.3\ units\\b=7.2\ units[/tex]
Part b) [tex]cos(B)=0.4[/tex] see the explanation
Step-by-step explanation:
The correct question is
In right triangle ABC, C is the right angle. Given measure of angle A = 40 degrees and a =6
Part a) which of the following are the lengths of the remaining two side, rounded to the nearest tenth?
Part b) Which of the following is cos B if sin A=0.4?
see the attached figure to better understand the problem
Part a)
step 1
Find the length of side c
Applying the law of sines
[tex]\frac{a}{sin(A)}=\frac{c}{sin(C)}[/tex]
we have
[tex]a=6\ units\\A=40^o\\C=90^o[/tex]
substitute
[tex]\frac{6}{sin(40^o)}=\frac{c}{sin(90^o)}[/tex]
solve for c
[tex]c=\frac{6}{sin(40^o)}=9.3\ units[/tex]
step 2
Find the length of side b
In the right triangle ABC
[tex]tan(40^o)=\frac{BC}{AC}[/tex] ----> by TOA (opposite side divided by the adjacent side)
substitute the values
[tex]tan(40^o)=\frac{6}{AC}[/tex]
[tex]AC=\frac{6}{tan(40^o)}=7.2\ units[/tex]
therefore
[tex]b=7.2\ units[/tex]
Part b) we know that
If two angles are complementary, the cofunction identities state that the sine of one equals the cosine of the other and vice versa
In this problem
Angle A and angle B are complementary
therefore
the sine of angle A equals the cosine of angle B
we have
sin(A)=0.4
so
cos(B)=0.4
I am a fraction equivalent to 6/8 my numerator is 16 less than my denominator what fraction am i
Answer:
The answer is
[tex] \frac{48}{64} [/tex]
Step-by-step explanation:
Equivalent fractions are set of fractions which have the same value when simplified.
The equivalent fraction to 6/8 whose numerator is 16 less than its denominator can be obtained through two basic methods below.
Method 1
Multiply the numerator and denominator by 8 respectively.
[tex] \frac{6}{8} = \frac{6 \times 8}{8 \times 8} = \frac{48}{64} [/tex]
The numerator being 16 less than the denominator is:
[tex]48 - 64 = - 16[/tex]
Method 2
Find the equivalent fraction to 6/8 whose numerator is 16 less than its denominator by continuous multiplication approach. In other words, multiply 6/8 till you arrive at an equivalent fraction whose numerator is 16 less than its denominator. Simply multiply 6/8 by 2, 3, 4, 5, 6, 7, 8. Thus:
[tex] \frac{6}{8} = \frac{12}{16} = \frac{18}{24} = \frac{24}{32} = \frac{30}{40} = \frac{36}{48} = \frac{42}{56} = \frac{48}{64} [/tex]
The difference between the numerator and denominator of the equivalent fractions are: -2, -4, -6, -8, -10, -12, -14, -16
Hence, 48/64 is the equivalent fraction to 6/8 whose numerator and denominator difference is less than 16.
That is,
[tex] \frac{6}{8} = \frac{48}{64} [/tex]
Such that 48 - 64 = -16.
The fraction equivalent to 6/8 with a numerator 16 less than the denominator is 48/64, which simplifies to 3/4.
Explanation:To find an equivalent fraction to 6/8 where the numerator is 16 less than the denominator, we use an equation to represent the relationship between the numerator (N) and the denominator (D): N = D - 16. Since 6/8 can be simplified to 3/4 by dividing both the numerator and denominator by 2, we set up the following equation: N/D = 3/4.
By substituting N with (D - 16), we get (D - 16)/D = 3/4. To find the value of D, we cross multiply: 4(D - 16) = 3D. Solving for this, we have 4D - 64 = 3D, and therefore D = 64. Since N is 16 less than D, N = 64 - 16, which gives us N = 48. So, the fraction we are looking for is 48/64.
We can check that 48/64 is indeed equivalent to 3/4 by simplifying. Dividing both numerator and denominator by 16, we get 48/64 = 3/4. Thus, the student's fraction is 48/64 which simplifies to 3/4.
A tree casts a 12 foot shadow while the sun is at an angle of elevation of 58º. Use
this information to approximate the height of the tree to the nearest tenth of a foot.
The height of tree is 32 meter
Solution:
Given that, The sun is at an angle of elevation of 58 degree
A tree casts a shadow 20 meters long on the ground
The sun, tree and shadow forms a right angled triangle
The figure is attached below
ABC is a right angled triangle
AC is the height of tree
AB is the length of shadow
AB = 20 meters
Angle of elevation, angle B = 58 degree
By definition of tan,
[tex]tan \theta = \frac{opposite}{adjacent}[/tex]
In this right angled triangle ABC,
opposite = AC and adjacent = AB
Therefore,
[tex]tan\ 58 = \frac{AC}{AB}\\\\tan\ 58 = \frac{AC}{20}\\\\1.6 = \frac{AC}{20}\\\\AC = 1.6 \times 20\\\\AC = 32[/tex]
Thus height of tree is 32 meter
write 3.005 using words
first person is the brainliest
Answer:
three and five hundreths
Answer:
three and five thousandths
Step-by-step explanation:
3 counts as one and the decimal is said as "and" and the spaces after the decimal are tenths,hundredths and thousandths
Solve -2.5(4x - 4)=-6
Final answer:
To solve the equation -2.5(4x - 4) = -6, distribute -2.5 to the terms inside the parentheses, isolate the variable, and solve for x.
Explanation:
To solve the equation -2.5(4x - 4) = -6, we can start by distributing -2.5 to the terms inside the parentheses:
-10x + 10 = -6
Next, we can isolate the variable by subtracting 10 from both sides:
-10x = -16
Finally, we can solve for x by dividing both sides by -10:
x = -16/-10
Therefore, x = 1.6.
The circumference of a circle is about 37.7 cm and the diameter is about 12 cm. What expression best represents the value of π ? Question 3 options: 6/37.7 12/37.7 37.7/6 37.7/12
Answer:
Step-by-step explanation:
Circumference of a circle means the perimeter of a circle and it is given be
Perimeter=2πr
P=2πr
Though π is a constant
But this question want us to find π
Make π the subject of the formula
Then, divide both side by
π=P/2r
Given that P=37.7cm
And diameter =12
And radius is half of diameter.
Therefore, radius =12/2=6cm
Then
π=P/2r
π=37.7/2×6
π=37.7/12.
Then, the last option is the correct option
Compute 5e^2 - 4g + 7 where e = 4 and g = 6 ? (Not sure how to type a squared number where e^2 = “e squared”)
Answer:
63
Step-by-step explanation:
The given expresion is
[tex]5 {e}^{2} - 4g + 7[/tex]
We want to find the value of this expression when e=4 and g=6.
We substitute these values to get:
[tex]5( {4}^{2} ) - 4(6) + 7[/tex]
We evaluate to obtain:
[tex]5(16) - 4(6) + 7[/tex]
Let us multiply out to get:
[tex]80 - 24 + 7[/tex]
This simplifies to 63
Geometry 8.6.3 - Equations of Parallel and Perpendicular Lines and Proofs
Option B: [tex]\frac{1}{25}[/tex]
Solution:
Slope of the perpendicular lines:
If two lines are perpendicular then their slopes are negative reciprocals of each other.
[tex]$m_1=\frac{-1}{ m_2}[/tex]
Slope of the parallel lines:
If two lines are parallel then they have the same slope.
i.e their slopes are equal.
[tex]m_1=m_2[/tex]
Given line m and p are parallel.
Slope of the line m = [tex]\frac{1}{25}[/tex]
Using slope of the parallel lines definition,
Slope of the line p = slope of the line m
Slope of the line p = [tex]\frac{1}{25}[/tex]
Option B is the correct aswer.
Hence the slope of the of line p is [tex]\frac{1}{25}[/tex].
plz hurry 19 points will mark brainliest
which is a measurment of an angle that is supplementary to an angle that measures 80?
10
90
100
260
Good evening,
Answer:
100°
Step-by-step explanation:
Two angles are supplementary if the sum of their measures is equal to 180°
then the measurement of an angle that is supplementary to an angle that measures 80° is :
180 - 80 = 100°
3. A bicycle is pedaled at a constant speed of 2 m/s. Find the time taken to cover a distance of
300m.
Answer:
2.5 minutes or 150 seconds
Step-by-step explanation:
Time = Distance / speed
300/2 = 150.
150 seconds, or 2 and a half minutes