1.Given: Triangle PQR with m∠P=(2x)° , m∠Q=(4x)° , and m∠R=(6x)° .
Prove: x = 15
By the triangle sum theorem, the sum of the angles in a triangle is equal to 180°. Therefore, m∠P+m∠Q+m∠R=180° . Using the ,__________ (2x)°+(4x)°+(6x)°=180° . Simplifying the equation gets 12x = 180. Finally, using the division property of equality, .___________
answer to each box to complete
substitution property, distributive property, angle addition postulate, x=12 x=15 x=30
we have
m∠P=[tex](2x)\°[/tex]
m∠Q=[tex](4x)\°[/tex]
m∠R=[tex](6x)\°[/tex]
1) By the triangle sum theorem, the sum of the angles in a triangle is equal to [tex]180\°[/tex]
therefore
m∠P+m∠Q+m∠R=[tex]180\°[/tex]
we know that
Substitution Property of Equality, states that If the values of two quantities are known to be equal, you can replace the value of one quantity with the other
so
2) Using the Substitution Property of Equality
[tex](2x)\°+(4x)\°+(6x)\°=180\°[/tex]
Simplifying the equation gets
[tex](12x)\°=180\°[/tex]
3) using the division property of equality
The Division Property of Equality states that if you divide both sides of an equation by the same nonzero number, the sides remain equal
[tex](12x)\°/12=180\°/12[/tex]
[tex]x=15\°[/tex]
therefore
the answer is
Part a) Substitution Property of Equality
Part b) [tex]x=15\°[/tex]
Answer:
Part a) Substitution Property of Equality
Part b) x=15
Step-by-step explanation:
Given triangle PQR with
[tex]m\angle P=(2x)^{\circ}[/tex]
[tex]m\angle Q=(4x)^{\circ}[/tex]
[tex]m\angle R=(6x)^{\circ}[/tex]
By the triangle sum property, the sum of the angles of a triangle is equal to [tex]180^{\circ}[/tex]
∴ m∠P+m∠Q+m∠R=180°
Substitution Property of Equality, states that If the values of two quantities are known to be equal, one can replace the value of one quantity with the other
[tex](2x)^{\circ}+(4x)^{\circ}+(6x)^{\circ}=180^{\circ}[/tex]
Simplifying the equation we get
[tex](12x)^{\circ}=180^{\circ}[/tex]
Using the division property of equality
The Division Property of Equality states that division with the same non zero number results that both sides remain equal
[tex]\frac{(12x)^{\circ}}{12}=\frac{180^{\circ}}{12}[/tex]
[tex]x=15[/tex]
Hence, the answer is
Part a) Substitution Property of Equality
Part b) x=15
Two bags had 100 kilograms of sugar each. after taking out 3 times as much sugar from bag one than bag two, bag one had half as much sugar left as bag two. how much sugar is left in each bag?
According to the given statement, we can get the equation:
50 - 3x = 1/2 (50-x)
where x = amount removed from bag two, 3x removed from bag one
Then we multiply both sides by 2 (to eliminate the ½)
100-6x= 50-x
Add 6x to both sides
100= 50-5x
Then subtract 50 from both sides
50=5x
Lastly, divide by 5
10=x
Therefore 10 kg of sugar was removed from bag 2
further, 3x= 30, so 30 kg of sugar was removed from bag 1.
50-30=20 kg remaining in bag 1.
50-10=40 kg remaining in bag 2.
Answer:
40 kg in the first bag, 80 in the second
Step-by-step explanation:
A has $32 more than B, and B has five times as much money as C. If C has d dollars, how much does A have? Answer:
A = B+32
B = 5C
A = 5C+32
C has d dollars so replace d for c
A = 5d+32
Classify each number as a Natural number, Whole Number, Integer, Rational Number, or Irrational. (Write all that apply)
a)-40 b)5 c) -14/11 d)√34 e) -√16
Which statement is true with respect to the Euclidean approach to geometry?
Answer:
I would think the answer is "axioms are used to prove theorems"
Step-by-step explanation:
A recipe calls for 12 ounces of flour, but your scale shows only pounds. The recipe requires __________ pounds of flour. Enter your answer as the decimal number that correctly fills in the blank in the previous sentence. If necessary, round to the nearest hundredth, like this: 42.56 Hint: 1 pound=16 ounces 67 pts
A fabric store sells two types of ribbon. One customer buys 3 rolls of the lace ribbon and 2 rolls of the satin ribbon and has a total of 120 yards of ribbon. Another customer buys 2 rolls of the lace ribbon and 4 rolls of the satin ribbon and has a total of 160 yards of ribbon. How many yards are on one roll of lace ribbon and one roll of satin ribbon?
Answer:
20 and 30. that's your answer.
Step-by-step explanation:
It takes 1.25 seconds for light to travel from the moon to the earth how many miles away is the moon
If Joan read 75 pages in 4 hours how long will it take her to read 250 pages
A student has some $1 and $5 bills in his wallet. he has a total of 1919 bills that are worth $5959. how many of each type of bill does he hav
Is -5 an irrational number?
Is this right? It's geometry
Which choice shows a true conditional with a correctly identified hypothesis and conclusion?
A. If next month is January, then this month is the last of the year. Hypothesis: This month is the last of the year. Conclusion: Next month is January.
B. Next month is February, so this month is the last month of the year. Hypothesis: Next month is February. Conclusion: This month is the last of the year.
C. Next month is February, so this month is the last month of the year. Hypothesis: This month is the last of the year. Conclusion: Next month is February.
D. If next month is January, then this month is the last of the year. Hypothesis: Next month is January. Conclusion: This month is the last of the year.
The correct choice is D, where 'If next month is January' is the hypothesis, and 'then this month is the last of the year' is the conclusion, demonstrating the proper format and identification of a true conditional statement.
The question is concerning a true conditional statement and the identification of its hypothesis and conclusion. To form a proper conditional, we use the format 'If... then...' where the 'if' part represents the hypothesis and the 'then' part represents the conclusion. The hypothesis is the supposed condition, while the conclusion is the result or outcome that follows from the hypothesis.
Let's analyze the choices:
Choice A has the conclusion and hypothesis reversed.
Choice B is an incorrect format for a conditional because it uses 'so' instead of 'if... then...'.
Choice C has the same issue as choice B.
Choice D is in the correct format and has the hypothesis and conclusion properly identified. If next month is January is the hypothesis, and then this month is the last of the year is the conclusion.
Therefore, the answer is Choice D.
The difference of two positive numbers is 5 and the sum of their squares is 125. find the numbers.
The two positive numbers are 10 and 5.
Given that,
The difference between two positive numbers is 5.
And the sum of their squares is 125.
Let us assume that,
The numbers are x and y.
Here, the difference between two positive numbers is 5.
x - y = 5
x = 5 + y .. (i)
And, the sum of their squares is 125.
That is,
x² + y² = 125
Substitute the value of x from (i);
(5 + y)² + y² = 125
25 + y² + 10y + y² = 125
2y² + 10y + 25 = 125
2y² + 10y - 100 = 0
2 (y² + 5y - 50) = 0
y² + 5y - 50 = 0
y² + (10 - 5)y - 50 = 0
y² + 10y - 5y - 50 = 0
y (y + 10) - 5 (y + 10) = 0
(y - 5) (y + 10) = 0
This gives,
y = 5
y = - 10
Since the numbers are positive.
Hence, y = - 10 is not possible.
From (i);
x = 5 + y
Put y = 5;
x = 5 + 5
x = 10
Hence,
The two positive numbers are 10 and 5.
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What you s 50 percent of 2.98
Answer:
1.49
Step-by-step explanation:
50% of 2.98 is 1.49
What is the value of the expression, 3 1/4 - 1 7/8 in simplest form? Someone please help!
Compound interest question :
Elle invests some money into a bank which pays 5% compound interest per year. She wants it to be worth £8000 at the end of 3 years. What is the smallest amount, to the nearest £, that she can invest?
How do i solve this for x
x + y = 0 x - y = 8 What is the solution of the system shown?
A; (-8, 12)
B; (8, -12)
C; (8, 12)
As a group, are sellers better or worse off with the price ceiling compared to trade in a market with no price controls? That is, do they capture more or less gain with the ceiling?
what is the answer for 13=4x-9
The solution of the given equation is 5.5.
What is an equation?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The given equation is 13=4x-9.
The collection of values used to replace the unknowns in an equation to make it true is known as the solution.
Here, add 9 on both the sides of an equation.
That is, 13+9=4x-9+9
4x=22
Divide 4 on both the sides of an equation.
4x/4 =22/4
x=5.5
Therefore, the value of x is 5.5.
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the slope of the line passing through the points (-6,3)and(-6,39) is
The slope of the line passing through points is undefined.
What is slope of a line?The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.
For the given situation,
The line passing through points (x1, y1) is (-6, 3) and (x2,y2) is (-6, 39)
The formula of slope of line is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
⇒ [tex]m=\frac{39-3}{-6-(-6)}[/tex]
⇒ [tex]m=\frac{39-3}{-6+6}[/tex]
⇒ [tex]m=\frac{39-3}{0}[/tex]
⇒ [tex]m=\infty[/tex]
Since x1 = x2, there is no horizontal change. The line passes as a straight line.
Hence we can conclude that the slope of the line passing through points is undefined.
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A customer ordered fourteen zingers. zingers are placed in packages of four, three, or one. in how many different ways can this order be filled?
The number of different ways this order can be filled is:
13 ways.
Step-by-step explanation:A customer ordered fourteen zingers.
zingers are placed in packages of four, three, or one.
Case-1
If the number of packages of four are: 3
Then 4×3=12 zingers.
a)
So, there will be zero packet of 3.
and 2 packs of 1.
Since, 12+2×1=14
Case-2
If the number of packages of four are: 2
i.e. 4×2= 8 zingers.
a)
If number of packages of 3 are: 2
i.e. 3×2=6
then number of package of 1 have to be 0.
b)
If number of packages of 3 are: 1
i.e. 3×1=3 zingers
Number of packages of 1 zinger will be: 3
i.e. 8+3+3=14
c)
If number of packages of 3 are: 0
Then number of packets of 1 will be: 6
Case-3
If the number of packages of four are: 1
a)
If number of packages of 3 are: 3
i.e. 3×3=9 zingers.
Hence, number of packets of 1 have to be: 1
b)
If number of packages of 3 are: 2
i.e. 3×2=6 zingers
Then number of packets of 1 have to be: 4
c)
If number of packages of 3 are: 1
i.e. 3×1=3 zingers
Then number of packets of 1 have to be: 7
d)
If number of packages of 3 are: 0
i.e. 3×0=0 zingers
Then number of packets of 1 have to be: 10
Case-4
If the number of packages of four are: 0
a)
If number of packages of 3 are: 4
i.e. 3×4=12 zingers
Then number of packets of 1 have to be: 2
b)
If number of packages of 3 are: 3
i.e. 3×3=9 zingers
Then number of packets of 1 have to be: 5
c)
If number of packages of 3 are: 2
i.e. 3×2=6 zingers
Then number of packets of 1 have to be: 8
d)
If number of packages of 3 are: 1
i.e. 3×1=3 zingers
Then number of packets of 1 have to be: 11
e)
If number of packages of 3 are: 0
i.e. 3×0=0 zingers
Then number of packets of 1 have to be: 14
There are total 13 ways of doing so.
( 1 from case-1
3 from case-2
4 from case-3
and 5 from case-4
i.e. 1+3+4+5=13 ways )
The order can be filled in 5 different ways by using packages of 4, 3, or 1 zingers.
Explanation:To find the number of different ways the order can be filled, we can use the concept of permutations and combinations. Since zingers can be placed in packages of 4, 3, or 1, we need to find all the possible combinations of these packages that add up to 14.
For packages of 4, we can have 1 package of 4 and 2 packages of 5, for a total of 2 combinations.For packages of 3, we can have 1 package of 3 and 3 packages of 5, for a total of 2 combinations.For packages of 1, we can have 7 packages of 1, for a total of 1 combination.Therefore, the total number of different ways the order can be filled is 2 + 2 + 1 = 5.
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Write log3 6 as a logarithm of base 2
a. log base 2 of 3 over log base 2 of 6
b. log base 2 of 6 over log base 2 of 3
c. log base 3 of 2 over log base 6 of 2
d. log base 6 of 2 over log base 3 of 2
Final answer:
The expression log3 6 can be converted to a logarithm of base 2 using the change of base formula, which results in log2 6 / log2 3. So the correct option is b.
Explanation:
The student asked how to express log3 6 as a logarithm with a base of 2. To perform this conversion, we can use the change of base formula, which states that logab = logcb / logca for any positive numbers a, b, and c, where a and c are not equal to 1. In this formula, 'c' can be any base, but in our case, we will use base 2 since that's what the question requires.
So, by applying the change of base formula, we can write:
log₃6 = log₂6 / log₂3Therefore, the correct option that represents log3 6 as a logarithm of base 2 is:
(b) log₂6 / log₂3Define a variable and write an equation for each situation. Solve each equation to answer the question.
A plumber finished three jobs on Tuesday. The first two only cost the owner $45 trip fee because they took very little time to complete. For the third job, the plumber charged the trip fee plus 6 times his hourly rate. If the plumber received a total of $303 for the day, what is the hourly rate?
H = Hourly Rate
for my Equation I made,
5(45)+6h=303
but cant figure out how to solve it
(9th Grade ALG 1)
Plz work out the problem, thnx :-)
Can anyone help me please? I would really appreciate it! Thank you :D
An equation that is true for all real numbers for which both sides are defined is called a(n)
An equation that is true for all real numbers for which the operations are defined is called an identity. It is always true no matter the values of its variables. An example is sin²(x) + cos²(x) = 1
Explanation:An equation that is true for all real numbers for which both sides are defined is called an identity. An identity equation is always true, no matter what values are substituted for its variables. For example, the equation sin²(x) + cos²(x) = 1 is an identity because it is valid for all real numbers x.
Identity equations commonly appear in branches of math such as algebra and trigonometry.
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-3x+2y=25
19x+3y=-33
A mountain climber ascends 800 feet per hour from his original position. After 6 hours, his final position is 11,600 feet above sea level. Find the climber's position.
Find the common ratio for the following sequence
27,9,3,1
Answer:
The common ratio is [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Given sequence,
27, 9, 3, 1
Since,
[tex]\frac{9}{27}=\frac{3}{9}=\frac{1}{3}[/tex]
Hence, in the given sequence the ratio of a term to its previous term is [tex]\frac{1}{3}[/tex]
Therefore, we can say that,
The common ratio of the given sequence is [tex]\frac{1}{3}[/tex]