Answer:
j = 3
Step-by-step explanation:
Recall the slope formula:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Now, simply substitute the values from the question.
[tex]\frac{1}{3} =\frac{-4+3}{j-6}[/tex]
Now, use the cross-multiplication method. (remember, when subtracting negatives, the negative becomes a positive)
[tex]1(j-6)=3(-4+3)[/tex] Cross Multiplication
[tex]1(j-6)=3(-1)[/tex] Simplify
[tex]j-6=-3[/tex] Distributive Property
[tex]j=3[/tex] Addition Property
Therefore, j = 3.
PQR is similar to WXY. PQ =12 cm and WX=9 cm. The area of WXY is 72 cm2. Find the area of PQR.
If PQR is similar to WXY and PQ=12 cm and WX=9 cm and the area of WXY is 72cm², then the area of PQR is equal to 128 cm².
The area of PQR can be determined by first finding the scale factor. The scale factor in mathematics can be defined as the ratio of the length of a side of one figure (which in this case is a triangle) to the length of the side of a similar figure.
Therefore, the scale factor = 9 / 12
Now by using theorem 61,
area ΔWXY / area ΔPQR = (9/12)²
As the area of WXY = 72cm², therefore;
72 / area ΔPQR = 81 / 144
81 (area ΔPQR) = 144 × 72
81 (area ΔPQR) = 10,368
area ΔPQR = 10,368 / 81
area ΔPQR = 128 cm²
Hence, the area of PQR is calculated to be 128 cm².
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Write each equation in exponential form.
log₆6=1
Answer:
The answer to the given question is 6
Logarithmic scale: A measurement scale in which the position is marked using the logarithm of a value rather than the actual value.
A logarithmic equation includes a logarithm in the variable x.
An exponential equation is one in which the variable is represented by an exponent. A logarithmic equation is one in which the logarithm of a variable-containing expression is used.
For logarithmic equations, log b (x) = y is equivalent to b^y = x such that x > 0, b > 0 and b is not equal to 1.
In the given problem, b = 6, x = 6 and y = 1
b = 6
x = 6
y = 1
Substituting the values of b, x and y into the equation b^y = x;
6^(1) = 6
therefore, the value of the given equation log₆6=1 is 6
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Write each expression as a single logarithm.
log₃4 + log₃y + log₃8 x
The expression log₃4 + log₃y + log₃8x can be written as [tex]log_{3}32xy[/tex] in a single logarithm form.
Given that the expression is log₃4 + log₃y + log₃8 x.
We are told to write the expression as a single logarithm.
Change of base theorem is basically used when we have to find the log values having different bases from 10 as we have tables which tell the log values with base 10. We know that [tex]log_{a}b[/tex]=[tex]log_{x}b/log_{x}a[/tex] and
log mn=log m+log n.
The expression is log₃4 + log₃y + log₃8 x.
log₃4 + log₃y + log₃8x=[tex]log_{3}[/tex] (4*y)+ [tex]log_{3}[/tex] 8x
=[tex]log_{3}[/tex] (4*y*8x)
=[tex]log_{3}[/tex] 32xy
Hence the expression log₃4 + log₃y + log₃8x can be written as [tex]log_{3}32xy[/tex] in a single logarithm form.
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Please help me please help me
Answer:
Step-by-step explanation:
90 degree
Do the math: the price of iron ore can be measured per ton. a ton is about the
weight of a cow. if the price of 1 ton of iron ore starts at $104 per ton with a
quantity demanded of 90 tons, then rises to $211 per ton, what is the new quantity
demanded at this price? assume the slope of the demand curve is -3.2 and the
y-intercept is $392. round your answer to the nearest tenth of a ton.
Answer:
Step-by-step explanation:
56.6 tons.
Based on the slope of the demand curve and the new price of iron ore, the new quantity demanded at the new price of $211 is 49.60 tons
What is the new equilibrium quantity demanded?The equation given will allow us to find the new quantity demanded:
y = Mx + c
y = new quantity demanded
m = slope of the demand curve
x = change in price of iron ore
c = y intercept
Solving for the new quantity demanded at the new price gives:
= -3.2 x (211 - 104) + 392
= -342.40 + 392
= 49.60 tons
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if p and q are the robots of the equation 3x^2 _ 16x + 2 = 0, find the value of p+q(1+ p).
Step-by-step explanation:
3x² - 16x + 2 = 0
ax² + bx + c = 0
a = 3 , b = -16 , c = 2
= p + q.(1 + p)
= p + q + p.q
= -b/a + c/a
= -(-16)/3 + 2/3
= (16 + 2)/3
= 18/3
= 6
5 5/6 divided by 3 1/6
let's firstly convert the mixed fractions to improper fractions and then divide.
[tex]\stackrel{mixed}{5\frac{5}{6}}\implies \cfrac{5\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{35}{6}} ~\hfill \stackrel{mixed}{3\frac{1}{6}}\implies \cfrac{3\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{19}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{35}{6}\div \cfrac{19}{6}\implies \cfrac{35}{6}\cdot \cfrac{6}{19}\implies \cfrac{35}{19}\cdot \cfrac{6}{6}\implies \cfrac{35}{19}\cdot 1\implies 1\frac{16}{19}[/tex]
Choose Yes or No to tell if the equation is true.
I'll give u brainliest and i'll do anything this is really important
Answer:
true,true,false,false
Step-by-step explanation:
true it's the amount of decimal places
true: same with this true
false: if it was 10^5 then yes but it's not
false: there is one too many 10s
Show that k=(4 + 3j)/(5-j) can be rearranged to j =(5k - 4)/(3 + k)
Answer: f(x)=4
f(x)=√3x−4
f(x)=4x−5
Step-by-step explanation:
How to find the Length of a triangle
Answer:
10
Step-by-step explanation:
it us a right triangle so we can use the equation
a^2 + b^2 = c^2
6^2 + 8^2 = c^2
36 + 64 = c^2
100 = c^2
10 = c
A theater wants to take in at least $2,000 for a particular showing of a movie.
Children's tickets cost $5 each and adult tickets cost $10 each. Write an
inequality describing the number of tickets that will allow the theater to meet
their minimum. Let x = the number of children's tickets sold and y = the
number of adult tickets sold.
15xy 2000
5x+10y < 2000
5y + 10x ≥ 2000
5x+10y ≥ 2000
The inequality describing the number of tickets that allows the theater to meet their minimum will be 5x + 10y ≥ 2000. Then the correct option is D.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
A movie theater hopes to make at least $2,000 from a certain showing. Adult tickets are $10 each, while child tickets are $5 each.
Let x be the number of children's tickets sold and y be the number of adult tickets sold. Then the inequality is given as,
5x + 10y ≥ 2000
The inequality describing the number of tickets that allows the theater to meet their minimum will be 5x + 10y ≥ 2000. Then the correct option is D.
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xv plus 6x negative 5 equals 0
After converting the mathematical statement - xv plus 6x negative 5 equals 0 into mathematical equation, we get -
x = 5/(v + 6).
What is linear equation?
An equation of the form ax + b = 0 such that a ≠ 0 is called linear equation in one variable. The graph of this equation represents a straight line.
Given is a linear equation in the form of a mathematical statement -
xv plus 6x negative 5 equals 0.
In order to solve for x, we will first convert this mathematical statement into a linear mathematical equation. The mathematical equation can be written as -
xv + 6x - 5 = 0
We will solve this question using transpose method.
xv + 6x = 5
x(v + 6) = 5
x = 5/(v + 6)
Therefore, after converting the mathematical statement - xv plus 6x negative 5 equals 0 into mathematical equation, we get -
x = 5/(v + 6)
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An elephant charged 13.3 meters on 15 seconds. At this rate, how far would the elephant go in one minute? (20 seconds = 1/3 minute)
Answer: 53.2 meters
Step-by-step explanation:
Since 15 seconds is 1/4 of 1 minute, multiply 13.3 by 4 to get 53.2.
Translate this sentence into an equation. The product of 9 and Victor's height is 162. Use the variable v to represent Victor's height.
Answer: 9v=162
Step-by-step explanation:
If you need the answer, Victors height is 18.
9v = 162
/9 /9
V = 18
Step-by-step explanation:
we are given a variable of victors height as v
according the expression
9 × v = 162
9v = 162
divide both sides by 9
v = 18
30 POINTS! Question is on the attachment below :D
A. 35 in. x 17 in.
B. 36 in. x 18 in.
C. 35 in. x 18 in.
D. 36 in. x 17 in.
Answer:
B
Step-by-step explanation:
35 [tex]\frac{3}{4}[/tex] ≈ 36 ( to the nearest whole number
17 [tex]\frac{5}{6}[/tex] ≈ 18 ( to the nearest whole number )
then 36 in × 18 in
a number is at least 6 and less than 15. Write as inequality and graph.
The inequality expression 6 <= x < 15 to represent the statement "a number is at least 6 and less than 15"
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the expression and the inequality?The mathematical statement is given as
a number is at least 6 and less than 15.
Represent the number with x
So, we have
x is at least 6 and less than 15.
At least 6 means greater than or equal 6
So, we have
x >= 6
Less than 15
So, we have
x < 15
When the above expressions are combined, we have
6 <= x < 15
Next, we plot the inequality expression 6 <= x < 15 to represent the statement "a number is at least 6 and less than 15"
See attachment for the inequality expression
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Please help I need this in an hour
write an expression that represents the phrase "one third the difference of 15 and a number"
Answer: 1/3-5(n)
Step-by-step explanation:
Read each question. Then write the letter of the correct answer on your paper.What is the product of ∛3 and 5√3 ?
(A) 9√3 (B) 8√9 (C) 15√3⁸ (D) 9√3¹⁵
The product of ∛3 and 5√3 is 15√3⁸ (Option C).
This question can be easily solved by using the concept of roots. The two terms mentioned in the question are ∛3 ( cubic root of 3 ) and 5√3 (5th root of 3 ). This question can be solved in 4 easy steps
Step 1 : Identify the power of the root and take LCM of those numbers.
In this case, the powers of root for ∛3 and 5√3 are 3 and 5, respectively. Take LCM of 3 and 5.
LCM = 3 x 5 = 15
=> We get the LCM of 3 and 5 as 15.
Step 2 : Write the given numbers in the form of fractional powers
∛3 = 3¹ˡ³ => The power of 3 = 1/3
5√3 = 3¹ˡ⁵ => The power of 5 = 1/5
Step 3 : Multiply and divide the powers of the base number ( in this case 3 ) with a number such that you get the denominator as the LCM ( in this case 15 )
1/3 can be multiplied and divided by 5 to get the denominator as 15
=> 1 * 5 / 3 * 5 = 5 /15
1/5 can be multiplied and divided by 3 to get the denominator as 15
=> 1 * 3 / 5 * 3 = 3 /15
Step 4 : Find the product of the two terms
15√3⁵ x 15√3³ = 15√3³⁺⁵ = 15√3⁸
Therefore, using the concept of roots and fractions, we get the product of ∛3 and 5√3 as 15√3⁸.
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Rachel earns $6000 less than twice as much as Tom. Their two incomes total $48,000. How much does Rachel earn?
Answer:
30,000
Step-by-step explanation:
Add 6,000 to 48,000, which equals 54,000
You then divide 54,000 by three = 18,000
Multiply 18,000 by 2 = 36,000
Subtract 6,000 frome 36,000 = 30,000
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Question: The sets of numbers 6, 8, 10 and 5, 12, 13 are Pythagorean triples. Use what you know about the Pythagorean Theorem and explain or show why they are Pythagorean triples. Be sure to show your work for each set of triples! (5 points)
We know that 6, 8, 10 and 5, 12, 13 are Pythagorean triples.
The formula to see if a set of three numbers is a pythagorean triple is:
[tex]a^{2} +b^{2} =c^{2}[/tex]
For the first one, we can do
6^2 + 8^2 = 10^2 and see if it is true.
36 + 64 = 100, so this works.
The next one, we can do
5^2 + 12^2 = 13^2
25 + 144 = 169
This also works.
So in conclusion, using the formula, we can prove that they are both Pythagorean triples.
I hope this is clear to you, have a great day! :)
a = y² - x²
b = 2xy
c = x² + y²
where x and y are positive integers y > x
→ In Pythagorean triple number set 6,8,10
c² = a² + b²(10)² = (6)² + (8)²100 = 36 + 64100 = 100→ In Pythagorean triple number set 5,12,13
c² = a² + b²13² = 5² + 12²169 = 25 + 144169 = 169At a baseball game, 35% of people attending were supporting the home team, while 65% were supporting the visiting team. If 735 people attending the game supported the home team, what was the total number of people attending the game?
Answer:
1300
Step-by-step explanation:
455 divided by 35%
= 455 x 100/35
= 455 x 20/7
= 65 x 20
= 1300
The total number of people attending the game is 2100.
Given that, at a baseball game, 35% of people attending were supporting the home team, while 65% were supporting the visiting team.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let the total number of people attending the game be x.
Given, 735 people attending the game supported the home team.
Now, 35% of x=735
⇒ 35/100 × x=735
⇒ 35x=73500
⇒ x=73500/35
⇒ x=2100
Therefore, the total number of people attending the game is 2100.
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PLEASE ANSWER Quick in a game!
Slope of a line passing through
(1, 5) and (7, 9)?
-1/5
5/2
2/3
1/2
Answer:
Choice 3 (2/3)
Step-by-step explanation:
Slope is equal to the change in y over the change in x.
If we look at the two coordinates, we'll see that to get from (1, 5) to (7, 9), you need to move up 4 and to the right 6.
4/6 = 2/3, which matches the 3rd choice
Hope this helps
order the following rational and irrational numbers from least to greatest
1.25,square root of 2,1 3/8, and 1 3/5
The ordering of the numbers will be 1.25, 1 3/8, ✓2, 1 3/5 and 1.875.
How to illustrate the information?It should be noted that ✓2 = 1.414
It should be noted that 1 3/8 = 1.375
It should be noted that 1 3/5 = 1.6
The other numbers given are 1.25 and 1.875
Therefore, the ordering of the numbers will be 1.25, 1 3/8, ✓2, 1 3/5 and 1.875.
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A 117.3 cm²
B 104.8 cm²
C 97.3 cm²
D 71.1 cm²
The Lateral Surface Area of a Right triangular prism is given by:
= (a + b + c) × h
= (ah + bh +ch)
where a, b and c are the dimensions of base and h is the height of the Right triangular prism.
The given dimensions of base are:
a = 5 cm
b = 2.5 cm
c = 5.6 cm
The height of the Right triangular prism is 8 cm.
Now, the Lateral Surface Area of a Right triangular prism will be
= (5 + 2.5 + 5.6) × 8
= (40 + 20 + 44.8)
= 104.8 [tex]cm^{2}[/tex]
Therefore, the Lateral Surface Area of the Right triangular prism is 104.8 [tex]cm^{2}[/tex].
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A tortoise moves
at about 0.05
meters per
second. How
many
centimeters per
second does a
tortoise move?
Answer:
0.05 metrs = 5 cetimeters
Step-by-step explanation:
1 meter = 100 centimeters
0.05 meters = 0.05 * 100 = 5 centimeters
Descartes says 15.7 is less than 15.245 because 15.27 has fewer digits after the decimal point than 15.245 . is he correct ? explain
The statement "15.7 is less than 15.245 because 15.27 has fewer digits after the decimal point than 15.245" is false
How to determine the true statement?The statement is given as
15.7 is less than 15.245 because 15.27 has fewer digits after the decimal point than 15.245
When comparing greater and lesser values, we do not make use of the number of digits in them
Instead, we compare the values
Though, 15.7 is less than 15.245 but the reason is that 15.27 has lesser value than 15.245
Hence, the statement "15.7 is less than 15.245 because 15.27 has fewer digits after the decimal point than 15.245" is false
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Use the Change of Base Formula to evaluate each expression.
log ₁₂20
The value of the expression log ₁₂20 is 4.33.
Given that the expression is log ₁₂20.
We are required to find the value of the expression by using the change of base formula.
The change of base theorem is used by a person when we have been given logarithm values with different bases.
(We know that [tex]log _{a} b[/tex]=log b/ log a)
The expression is log ₁₂20.
log ₁₂20=log 20/log 12
Now we have to use values of log in the above expression to find its value.
=1.30/0.30
=4.33
Hence the value of the expression log ₁₂20 is 4.33.
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Solve each equation. Round to the nearest ten-thousandth. 5x +3=12
the value of the given equation 5x +3=12 Round to the nearest ten-thousandth = 1.8000
What is rounding off?In a given base, a round number is a number that ends with one or more "0s." So, 590 is more round than 592, but less round than 600. A round number is frequently interpreted in both technical and casual language to stand for a value or values close to the nominal value represented.
According to the given data:given:- 5x +3=12
simplifying:
5x +3=12
5x = 12 - 3
5x = 9
x = 9/5
x = 1.8000
the value of the given equation 5x +3=12 Round to the nearest ten-thousandth = 1.8000
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An item is regularly priced at $30. It is now priced at a discount of 70%
off the regular price. What is the price now?
If something is priced at 30$,then 70% off would make it 9.00$!