Use the premises and conclusion to answer the questions.
Premises:
If the sides of a triangle are the same length, then the triangle is an equilateral triangle.
If a triangle is an equilateral triangle, then the measure of each angle is 60°.
Conclusion:
If the sides of a triangle are the same length, then the measure of each angle is 60°.
Is the argument valid? Why or why not?
The argument is not valid because the premises are not true.
The argument is not valid because the conclusion does not follow from the premises.
The argument is valid by the law of syllogism.
The argument is valid by the law of detachment.
Answer: The argument is valid by the law of syllogism.
Step-by-step explanation:
Law of syllogism in geometric arguments is similar to transitive property which tells that that if x=y and y=z then x=z.
Given premises: If the sides of a triangle are the same length, then the triangle is an equilateral triangle.
If a triangle is an equilateral triangle, then the measure of each angle is 60°.
Therefore by law of syllogism we can conclude that "If the sides of a triangle are the same length, then the measure of each angle is 60°."
find the inverse of f(x)=-3x+3
A land developer declared a dividend of Php 10,000,000.00 for its common stock. Suppose there are 600,000 shares of common stock, how much is the dividend per share?
The dividend per share is 16.67 and this can be determined by using the formula of the dividend per share.
Given :
A land developer declared a dividend of Php 10,000,000.00 for its common stock.Suppose there are 600,000 shares of common stock.The formula of Dividend per share can be used to determine the value of dividend per share. The formula of dividend per share is given by:
[tex]\rm Dividend \; per \; share = \dfrac{Dividend }{Total\; number \;of \;shares}[/tex]
Now, substitute the value of the known terms in the above formula:
[tex]\rm Dividend \; per \; share = \dfrac{10000000 }{600000}[/tex]
[tex]\rm Dividend \; per \; share = \dfrac{100 }{6}=16.67[/tex]
So, the dividend per share is 16.67.
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If a person lives to be exactly 100 years old, how many leap years will that person see
Janelle is five years younger than Louisa. In three years, Janelle will be half Louisa’s age. If j represents Janelle’s age now and l represents Louisa’s age now, which matrices represent the situation?
Answer: C
Step-by-step explanation: Got it right
Final answer:
The matrix form representing the given situation with Janelle and Louisa's ages is a system of linear equations derived from the word problem, and can be represented as: [1 -1 | -5] and [0.5 -0.5 | -1.5].
Explanation:
The question involves setting up equations based on the given word problem and representing them in matrix form. The situation describes a relationship between the ages of Janelle and Louisa, with Janelle being five years younger than Louisa. In three years, Janelle will be half of Louisa's age. This can be represented with two equations:
j = l - 5
j + 3 = 0.5 * (l + 3)
These equations can then be represented in matrix form. Matrices are used in mathematics to represent systems of linear equations, and the equations stages can be translated into a matrix where each row represents an equation:
Matrix for the system of equations:
[1 -1 | -5]
[0.5 -0.5 | -1.5]
The first row of the matrix represents the first equation, showing the coefficients of j and l, and the constant term on the right side of the equation. The second row represents the second equation with the respective coefficients and constant term.
Is it possible to draw a triangle with 150cm , 10cm and 10cm
The dimensions of a rectangular bin are consecutive integers. If the volume of the bin is 4896 cubic inches, what are the dimensions of the bin?
cubed root of 4896 = 16.98
round to 17
17-1 = 16
17 +1 = 18
16* 17 *18 = 4896
bin is 16 in x 17 in x 18 in
Answer:
The dimension of the rectangle is [tex]16\times 17\times 18[/tex]
Step-by-step explanation:
Given : The dimensions of a rectangular bin are consecutive integers. If the volume of the bin is 4896 cubic inches.
To find : What are the dimensions of the bin?
Solution :
The dimensions of a rectangular bin are consecutive integers.
Let the consecutive integers are x,x+1,x+2
So let, length, l=x
Breadth b=x+1
Height h=x+2
The volume of the bin is
[tex]V=l\times b\times h[/tex]
[tex]4896=x\times (x+1)\times (x+2)[/tex]
[tex]4896=(x^2+x)(x+2)[/tex]
[tex]4896=x^3+2x^2+x^2+2x[/tex]
[tex]x^3+3x^2+2x-4896=0[/tex]
Plot the equation graphically to find the value of x.
Refer the attached figure below.
The value of x is 16.
So, Length is l=16
Breadth is b=x+1=16+1=17
Height is h=x+2=16+2=18
The dimension of the rectangle is [tex]16\times 17\times 18[/tex]
What is the value of x? 3 /4 x+5− 1 /2 x=3
Fill in the blanks to write an equation in slope-intercept form representing the function shown in the table.
y =
x +
The slope intercept equation which models the data in the table given ls y = 3x + 1
General form of a slope - intercept equation :
y = bx + c ; b = slope ; c = interceptSlope can be calculated thus:
Slope = (y2 - y1) /(x2 - x1)
Slope = (-2 + 8) / (-1 + 3)
Slope = 6/2 = 3
Taking any pair of points, we can calculate the intercept, c :
y = 3x + c
10 = 3(3) + c
10 = 9 + c
c = 10 - 9
c = 1
Therefore, the slope - intercept equation is y = 3x + 1
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A coupon subtracts $17.95 from the price P of a pair of headphones you pay $71.80 for the headphones after using the coupon write and solve an equation to find the original price of the headphones
Answer:
[tex]P-17.95=71.80[/tex]
Original cost: $89.75.
Step-by-step explanation:
Let P represent the original price of the headphones.
We have been given that a coupon subtracts $17.95 from the price P of a pair of headphones.
The cost of headphones after using the coupon would be [tex]P-17.95[/tex].
We are also told that you pay $71.80 for the headphones after using the coupon. We can represent this information in an equation as:
[tex]P-17.95=71.80[/tex]
Let us solve for P.
[tex]P-17.95+17.95=71.80+17.95[/tex]
[tex]P=89.75[/tex]
Therefore, the original cost of headphones is $89.75.
Three collinear point
When you are comparing two sets of data, and one set is strongly skewed and the other is symmetric, which measures of the center and variation should you choose for the comparison?
When comparing two sets of data, choose the median for skewed data and mean with standard deviation for symmetric data.
When comparing two sets of data where one is strongly skewed and the other is symmetric, for the comparison, it is advisable to choose the median as the measure of the center for the skewed data since it is resistant to outliers, and the mean and standard deviation for the symmetric data to give an overall representation of the data.
Kim drives 156 miles from Rotherham to London.
She drives at an average speed of 60 miles per hour.
She leaves Rotherham at 7:30 am.
Does she arrive in London before 10:00 am?
Please show all of your working out.
Answer:
No, she will not arrive London before 10:00 am.
Step-by-step explanation:
It is given that:
Kim drives 156 miles from Rotherham to London.
She drives at an average speed of 60 miles per hour.
i.e. in one hour she drives 60 miles.
Hence she covers 1 mile in 1/60 hours.
Now she has to travel 156 miles.
i.e. it takes her:
156/60 hours=2.6 hours.
i.e. it takes her 2 hours and 36 minutes to reach from Rotherham to London.
(
since 0.6 hours=36 minutes.
As 1 hour= 60 minutes.
so, 0.6 hours=0.6×60=36 minutes ).
Hence, if she start from Rotherham at 7:30 am.
Then she will reach London at:
7:30+2.6=10:06 am.
Hence, she will reach London after 10 am.
Your gross weekly salary is $800.00. Your federal income tax deduction is $53. The Social Security tax is 6.2%. The Medicare tax is 1.45% of gross pay. The state tax is 1.5% of gross pay. Each week you have $28.40 deducted for medical insurance and $12.00 for a health savings account. What is your net pay?
The net weekly pay is $633.4
How to determine the net pay?The gross pay is given as:
Gross = $800.00
The deductions are:
Federal income tax deduction = $53.Social Security tax = 6.2%. Medicare tax = 1.45%State tax = 1.5%Medical insurance = $28.40Health savings account = $12.00The net pay is then calculated as:
Net pay = 800.00 - (53 + 6.2% * 800 + 1.45% * 800 + 1.5% * 800 + 28.40 + 12.00)
Evaluate
Net pay = 633.4
Hence, the net weekly pay is $633.4
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∠A and ∠B are vertical angles with m∠A = x and m∠B = 4x - 30. What is m∠A?
The measure of angle m∠A such that ∠A and ∠B are vertical angles is 10.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
Vertical angles are opposite angles become by the intersection of two straight lines and having the same measure.
Given that ∠A and ∠B are vertical angles
∠A = ∠B
x = 4x - 30
4x - x = 30
3x = 30
x = 10
Hence "The measure of angle m∠A such that ∠A and ∠B are vertical angles is 10".
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How do you write -6.16666666... as a fraction?
d=11/5(p-15) solve for p
At $1.25 per square foot, what is the cost of cleaning a rug with dimensions 9 feet 3 inches by 6 feet 9 inches?
A line contains the points (82, −96) and (87, −86) .
What is the slope of the line in simplified form?
Enter your answer in the box.
1) what is the answer to 5(3x-2y)+2(x+2y)-3(3x-2y)?
a= 8x-12y
b= 8x
c= 8x-8y
d= 8xy
2) what is the answer to 2x-3+3x-5?
a= -x-8
b= 5x-8
c=-x+2
d= 5x+2
Use the listing method to write the following set.
{x | x ∈ N, x < 3}
(A.) {1, 2, 3}
(B.) {0, 1, 2, 3}
(C.) {1, 2}
Karen calculates the volume of cylinder A with a radius of 3 inches, and a height of 6 inches. The volume of this cyliner is 54pi inches cubed. Cylinder B also had a radius of 3 inches, but the height is doubled. What is the relationship between the volumes of the two cylinders?
The coordinates of the points M, N, P, and Q are -11, 32, -15, and 17, respectively. Which point is closest to the origin? M N P Q
need hlp wit these math prob
see attached picture for answer:
for the format you need it would be 1.5x +-y = 12
a baker starts with 4/10 kilogram. of flour to make bread he adds 3/100 kilogram of flour to his bread mixture how much total flour is used to make the bread
Answer:
Total amount of the flour used is [tex]\frac{43}{100}[/tex] kg.
Step-by-step explanation:
Baker starts with [tex]\frac{4}{10}[/tex] kilograms of flour to make bread.
He further adds flour to his bread mixture = [tex]\frac{3}{100}[/tex] kg
Now we have to calculate the amount of flour he used to make the bread.
Total flour = [tex]\frac{4}{10}+\frac{3}{100}[/tex]
= [tex]\frac{40+3}{100}[/tex]
= [tex]\frac{43}{100}[/tex] kg
Therefore, total amount of the flour used is [tex]\frac{43}{100}[/tex] kg
What is the measure of ∠F?
What is the measure of ∠R?
What is the measure of ∠C?
Answer: The measure of ∠F=55°
The measure of ∠R=36°
The measure of ∠C=43°
Step-by-step explanation:
The angle sum property of triangle say that the sum of all the interior angles of a triangle is 180 degrees.Therefore By using angle sum property in Δ RST
∠R+∠S+∠T=180°
⇒∠R+76°+68°=180°
⇒∠R=180°-144°
⇒∠R=36°
In Δ CDE, where ∠C is a right angle.
∠C+∠D+∠E=180°
⇒∠C+90°+47°=180°
⇒∠C=180°-137°
⇒∠C=43°
In ΔDEF
∠D+∠E+∠F=180°
⇒104°+21°+∠F=180°
⇒∠F=180°-125°
⇒∠F=55°
Property of equality states that if LM = 7, and ER + LM = NP, then ___ = NP
a. LM + 7
b. ER + LM
c. ER + 7
d. 7
Answer:
NP
Step-by-step explanation:
−32+(−2)=
whats the answer
please help me with this!!!!!!!!!!
x/(2/9) = 6
x *(9/2) = 6
9x/2=6
9x = 6*2
9x=12
x = 12/9 = 4/3
X = 4/3
Rotating a polygon in Quadrant II 270° clockwise is the same as
A) rotating it 90° clockwise.
B) rotating it 180° clockwise.
C) rotating it 90° counterclockwise.
D) rotating it 270° counterclockwise.
Defined by two lines or rays diverging from a common point.
A) arc
B) angle
C) parallel lines
D) perpendicular lines
What are two lines in the same plane that do not intersect?
A) angle
Eliminate
B) line segment
C) parallel lines
D) perpendicular lines