Answers
.. 10Ta +25Tb = 220
.. Ta +Tb = 10
It is convenient to solve this by substitution. Use the second equation to write an expression for Tb.
.. Tb = 10 -Ta
Now use this in the first equation.
.. 10Ta +25(10 -Ta) = 220
.. -15Ta +250 = 220 . . . . . . . collect terms
.. -15Ta = -30 . . . . . . . . . . . . . subtract 250
.. Ta = 2 . . . . . . . . . . . . . . . . . divide by the coefficient of Ta
.. Tb = 10 -2 = 8
Selection C is appropriate.
Related Questions
You have an equally likely chance of choosing any number from 1 to 10. What is the probability that you choose a number greater than 6?
Answers
(1/10)+(1/10)+(1/10)+(1/10)=4/10=2/5
Answer is 2/5
Answer:
2/5
Step-by-step explanation:
1 to 10, it is 10 numbers
and there are 4 numbers which are 7,8,9,10 are bigger than 6
so P =4/10=2/5
the second of two numbers is 4 more than the first the sum of the numbers is 56 find the numbers
Answers
Answer:
26, 30
Step-by-step explanation:
If you subtract from the sum the excess of the second over the first, you have a sum that is twice the first.
first number = (56 -4)/2 = 26
The second number is 4 more, so is ...
second number = 26 +4 = 30
_____
Check
Their total is 26 +30 = 56, as required.
Reciprocal of 1/10 = ?
Reciprocal of 16 = ?
Answers
Jenna has 8 pairs of jeans. Three of them are blue. What percentage of her jeans is blue?
= 37.5%
But my question is this:
Jenna bought two more pairs of jeans.
If both of them are blue, what percentage of her jeans is blue now?
If both of them are not blue, what percentage of her jeans is blue now?
Answers
b) blue/total = (3)/(8 +2) = 3/10 = 30%
Consider the diagram and the paragraph proof below. Given: Right △ABC as shown where CD is an altitude of the triangle Prove: a2 + b2 = c2 Because △ABC and △CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA. Likewise, △ABC and △ACD both have a right angle, and the same angle A is in both triangles, so they also must be similar by AA. The proportions and are true because they are ratios of corresponding parts of similar triangles. The two proportions can be rewritten as a2 = cf and b2 = ce. Adding b2 to both sides of first equation, a2 = cf, results in the equation a2 + b2 = cf + b2. Because b2 and ce are equal, ce can be substituted into the right side of the equation for b2, resulting in the equation a2 + b2 = cf + ce. Applying the converse of the distributive property results in the equation a2 + b2 = c(f + e).
Answers
This is because since f + e = c,
then a² + b² = c(f + e)
a² + b² = c(c)
a² + b² = c²
This is the correct answer
Answer:
Because f+e=c
Therefore ,[tex]a^2+b^2=c^2[/tex]
Step-by-step explanation:
Given A right triangle ABC as shown in figure where CD is an altitude of the triangle.
To prove that [tex]a^2+b^2=c^2[/tex]
Proofe: Given [tex]\triangle ABC\; and\; \triangle CBD[/tex] both are right triangle and both triangles have common angle B si same.
Therefore , two angles of two triangles are equal .
Hence, [tex]\triangle ABC \sim\triangle CBD[/tex] by using AA similarity.
Similarity property: when two triangles are similar then their corresponding angles are equal and their corresponding side are in equal proportion.[tex]\frac{a}{f} =\frac{c}{a}[/tex]Similarly , [tex]\triangle ABC \sim \triangle ACD[/tex] by AA similarity property . Because both triangles are right triangles therefore, one angle of both triangles is equal to 90 degree and both triangles have one common angle A is same .
[tex]\therefore[/tex] [tex]\frac{b}{c} =\frac{e}{b}[/tex]
The corresponding parts of two similar triangles are in equal proportion therefore , two proportion can be rewrite as
[tex]a^2=cf[/tex] (I equation)
and [tex]b^2=ce[/tex] (II equation)
Adding [tex]b^2[/tex] to both sides of firs equation
[tex]a^2+b^2=cf+b^2[/tex]
Because [tex]b^2=ce[/tex] and ce can be substituted into the right side of equation wevcan write as
[tex]a^2+b^2=ce+cf[/tex]
Applying the converse of distributive property we can write
[tex]a^2+b^2=c(f+e)[/tex]
Distributive property: a.(b+c)= a.c+a.b
[tex]a^2+b^2=c^2[/tex]
Because f+e=[tex]c^2[/tex]
Hence proved.
A roadway repair crew has fixed 42 mi of the roadway. That number of miles is 30% of the total number of miles that need to be repaired
Answers
Answer:
The answer is 140 miles 100x42 is 4200 divide that by 30= 140Step-by-step explanation:
solve the following system using substitution x+4y=21 4x-y=16
Answers
4x-y=16
Isolate one of the variables
x + 4y = 21
subtract 4y from both sides
x = -4y + 21
Plug that into the other equation
4x - y = 16
4(-4y + 21) - y = 16
-16y + 84 - y = 16
combine like terms
-17y + 84 = 16
subtract 84 from both sides
-17y = -68
divide both sides by -17
y = 4
Plug that into the equation
x+4y=21
x + 4(4) = 21
x + 16 = 21
subtract 16 from both sides
x = 5
Hope this helps!
The circle is centered at the point (-3,4) and has a radius of length 3. What is its equation?
Answers
during the new year celebration there are orange, green purple, and blue fireworks. In how many different orders can the different colors of fireworks appear?
Answers
If they cannot be repeated, there are 24 possible combinations.
There are 24 different orders in which the different colors of fireworks can appear.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
If there are four colors of fireworks (orange, green, purple, and blue), then the number of different orders in which they can appear can be found by calculating the number of permutations of four objects, which is:
4! = 4 x 3 x 2 x 1 = 24
Therefore,
There are 24 different orders in which the different colors of fireworks can appear.
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Which equation represents a nonlinear function?
x(y – 5) = 2
y – 2(x + 9) = 0
3y + 6(2 – x) = 5
2(y + x) = 0
Answers
_____________________________________________________
Consider:
_____________________________________________________
Choice: [A]: " x(y–5) = 2 " ;
Divide each side by "x" ;
" [x(y – 5)] / x = 2/x " ;
→ y – 5 = 2/x ;
Add "5" to each side of the equation:
y – 5 + 5 = 2/x + 5 ;
→ y = 2/x + 5 ; not a line; since one cannot divide by "zero" ; there would be no "point" on the graph at "x = 0". So, this answer choice: [A] is correct.
_______________________________________________________
Choice [B]:
y -2x -18 = 0
y - 2x = 18
y = 18 + 2x ; y = 2x + 18 ; is a line.
_________________________________________________
Choice C) 3y + 12 - 6x = 5 ;
3y = 5 - 12 + 6x ;
3y = -7 + 6x ; 3y = 6x - 7 ; y = 6x/3 - 7/3 ; y = 2x - 7/3 ; is a line.
_________________________________________________
Choice: [D]:
2(y+x) = 0 ;
[2*(y+x)] / 2 = 0/2 ; y + x = 0 ; y = -x ; is a line.
_________________________________________________
Answer:
The correct answer is: A: x(y – 5) = 2
Step-by-step explanation:
edge2021
Please help:
Solve using logarithms. Round the solution to the nearest hundredth. Show your work.
(you will need to use a calculator at some point)
Answers
So, the first thing we are going to do is take natural logarithm, [tex]ln[/tex], to both sides of our equation:
[tex]ln(5^{x+2} )=ln(9^{2x+3} )[/tex]
Now, by the power rule of logarithms:
[tex](x+2)ln(5)=(2x+3)ln(9)[/tex]
[tex] \frac{(x+2)ln(5)}{2x+3} =ln(9)[/tex]
[tex] \frac{x+2}{2x+3}= \frac{ln(9)}{ln(5)} [/tex]
[tex] \frac{x+2}{2x+3} =1.365[/tex]
[tex]x+2=1.365(2x+3)[/tex]
[tex]x+2=2.73x+4.095[/tex]
[tex]-1.73x=2.095[/tex]
[tex]x=- \frac{2.095}{1.73} [/tex]
[tex]x=-1.211[/tex]
Using our calculator we can conclude that [tex]x[/tex] is approximately -1.211
2.7 Q9
The functions f and g are defined by the following tables. Use the tables to evaluate the given composite function.
Answers
Answer: [tex](gof)(-1)=-2[/tex]
Step-by-step explanation:
By definition, a composite function is a function formed by substituing one function into another function.
Given the composite function:
[tex](gof)(-1)[/tex]
You can rewrite it in the following form:
[tex]g(f(-1))[/tex]
In order to evaluate it, follow these steps:
- Based on the table of the function f(x), the ouput value for [tex]x=-1[/tex] is [tex]y=3[/tex]. Then:
[tex]f(-1)=3[/tex]
- This will be the input of the function g(x).
- Notice in the table of the function g(x) that the output value when [tex]x=3[/tex] is [tex]y=-2[/tex]:
[tex]g(3)=-2[/tex]
Therefore:
[tex]g(f(-1))=-2[/tex] or [tex](gof)(-1)=-2[/tex]
Answer:
The value of [tex]\rm{gof(-1)}[/tex] is -2.
Step-by-step explanation:
Given,
The table contains the functional value of f(x) and g(x).
To find: [tex]\rm{gof(-1)}[/tex]
[tex]\rm{fog(-1)}[/tex] is a composite function of f(x) and g(x).
[tex]\rm{gof(-1)}=\rm{g[f(-1)}][/tex]
Clearly from the table, the value of f(x) when [tex]x=-1[/tex] is 3.
Therefore,
[tex]f(-1)=3[/tex]
Now,
[tex]\rm{gof(-1)}=\rm{g[f(-1)}]\\\rm{fof(-1)}=\rm{g(3)}[/tex]
Clearly from the table, the value of g(x) when [tex]x=3[/tex] is -2.
Thus,
[tex]\rm{gof(-1)}=-2[/tex]
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Keisha's boat has a top speed of 9 miles per hour in still water. While traveling on a river at top speed, she went 10 miles upstream in the same amount of time she went 20 miles downstream. Find the rate of the river current.
Answers
The speed is still water is 9 mph.
The speed of the current is c.
Going downstream, the current adds speed, so the sped downstream is 9 + c.
The speed upstream is 9 - c.
9 + c is twice 9 - c.
9 + c = 2(9 - c)
9 + c = 18 - 2c
3c = 9
c = 3
Answer: The speed of the current is 3 mph.
Check:
9 + c = 12
9 - c = 6
By taking into the account the speed of the current, the downstream speed, 12 mph, is indeed twice the upstream sped, 6 mph.
12km is equal to how many meters? (show all work)
Answers
12 kilometers is equal to 12,000 meters.
What is the range of the following set?
28, 45, 12, 34, 36, 45, 19, 20
8
33
45
57
Answers
To find the range of this set, we must subtract the lowest number in the set from the highest number.
In this set, the highest number is 45 and the lowest number is 12. Subtract:
45 - 12 = 33
ANSWER:
The range of this set is B. 33.
Please help me with question 22
Answers
-----------------------------------------------------
Erase line A. For the pair of lines B and C, the marked angles are same side exterior angles. They are supplementary
(2x+18) + (6x+26) = 180
8x + 44 = 180
8x = 180-44
8x = 136
x = 136/8
x = 17
Since x = 17,
smaller angle = 2x+18
smaller angle = 2*17+18
smaller angle = 34+18
smaller angle = 52 degrees
convert the following logarithmic equation to the equivalent exponential equation. Use the caret (^) to enter exponents. y=ln x
Answers
f(x)=a^x
"a" is the base and "x" is the exponent.
2. It is important to know that the logarithmic functions and the exponential functionsare inverse. Then, you have:
y=ln x
e^y=e^(lnx)
e^y=x
3. Therefore, the answer is:
x=e^y
Answer:
To solve this problem, you need to remember that an exponential function has the following form:
f(x)=a^x
"a" is the base and "x" is the exponent.
2. It is important to know that the logarithmic functions and the exponential functionsare inverse. Then, you have:
y=ln x
e^y=e^(lnx)
e^y=x
3. Therefore, the answer is:
Step-by-step explanation:
an artist painted a 6 foot tall painting, then decide to also create a smaller version. if she uses a scale of 4 inches=1.5 feet, what will be the height of the smaller painting
Answers
x----------------- > the height of the smaller painting
y-----------------> the height of the tall painting-----------> 6 ft
the scale factor is-------------- > x/y
(x/y)=(4 in)/(1.5 ft)
x=y*[(4 in)/(1.5 ft)]-------> 6*(4 in)/(1.5 ft)=16 in
the answer is x=16 in
Final answer:
To determine the height of the smaller version of the painting using the scale of 4 inches = 1.5 feet, we first convert the original height to inches (6 feet = 72 inches) and then use a proportion to find that the height of the smaller painting is 16 inches.
Explanation:
The student's question involves using a scale to determine the height of a smaller version of a painting. The scale given is 4 inches = 1.5 feet. To begin, we convert the original height of the painting from feet to inches since the scale is in inches. The original height of 6 feet is equivalent to 72 inches (because 1 foot is equal to 12 inches).
Next, we set up a proportion using the scale:
4 inches / 1.5 feet = x inches / 6 feet
Now we solve for x, which represents the height of the smaller painting in inches:
4 / 1.5 = x / 6
4 / 1.5 * 6 = x
x = 4 * 6 / 1.5
x = 24 / 1.5
x = 16 inches
Thus, the height of the smaller version of the painting will be 16 inches.
A computer program in Shannon’s computer carries out a single mathematical operation in 1.5 × 10-6 seconds. How much time would the program take to complete 2.5 × 103 mathematical operations?
Answers
x = 1.5 * 10^-6 * 2500
x = 0.00375 or 3.75 * 10^-3 second.
Good question.
You forgot A, B, C, and D but the correct answer is option D, 3.75 x 10 ^ -3 seconds
A band that will be the opening act for a concert charges a $500.00 flat fee as well as 10% of all profits from ticket sales. If the band earns $1,200, how much was made in total ticket sales for the show?
Answers
Answer:
The answer is 7,000
Your welcome ;)
Find the longer diagonal of a parallelogram having sides of 10 and 15 and an angle measure of 120° between them. 13.2 18.0 21.8 23.1
Answers
to get the length of the longest diagonal we use the cosine rule which states that----------> c²=a²+b²-2abCos(C)
where a,b and c are the sides and C is the angle.
therefore
a=15,b=10,C=120,c=?
to solve for the length C we shall substitute the values
c²=15²+10²-2*15*10*cos 120
c²=225+100-300*cos120
c²=325-(300*(-0.5))
c²=325-(-150)c²=475
c=√475
c=21.79-------------> c=21.8 units
since this is the opposite side to the largest angle, we therefore conclude that the longer diagonal of the parallelogram is 21.8 units
the answer is 21.8 units
Answer:
21.8
Step-by-step explanation:
Use the chain rule to find ∂z/∂s and ∂z/∂t. z = x5y7, x = s cos(t), y = s sin(t)
Answers
Using the Chain Rule of differentiation, we can solve for ∂z/∂s and ∂z/∂t given the functions for z, x, and y. The Chain Rule is fundamental for calculus by finding the derivative of composite functions.
Explanation:To solve for ∂z/∂s and ∂z/∂t with z = x5y7, x = s cos(t), and y = s sin(t), we'll employ the use of the Chain Rule of differentiation. First, we consider ∂z/∂s. As z is x raised to the power of 5 then multiplied by y to the power of 7, we can express ∂z/∂x and ∂z/∂y. Proceeding using the chain rule, which in simpler terms could be stated as 'the derivative of the outside times the derivative of the inside', we get the values of ∂z/∂s and ∂z/∂t. The chain rule in calculus is an important tool when differentiating composite functions.
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Keshawn is constructing the inscribed circle for △PQR . He has already used his compass and straightedge to complete the part of the construction shown in the figure. Which construction could be his next step? Construct the angle bisector of ∠XQR . Construct the line through points P and X. Construct the perpendicular bisector of PQ¯¯¯¯¯ . Construct the perpendicular to QR¯¯¯¯¯ that passes through point X.
Answers
Answer:
Construct the perpendicular to QR¯¯¯¯¯ that passes through point X.
Step-by-step explanation:
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Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle C?
Enter your answer in the box.
Answers
But first, we should solve for x
Opposite angles add up to 180 degrees.
So we'll use angles B and D
x + 10 + x + 24 = 180
combine like terms
2x + 34 = 180
subtract 34 from both sides
2x = 146
divide both sides by 2
x = 73
Now let's solve for the angles
Angle D: x + 24 = 97
Angle B: x + 10 = 83
Angle A: x + 15 = 88
Opposite angles add up to 180
we know that angle A is 88
C + 88 = 180
subtract 88 from both sides
C = 92
Hope this helps!
Answer:
92 is correct
Step-by-step explanation:
what is the difference of the rational expressions below? 13x/5 - 4x/5
a. 9x/5
b. 17x/5
c. 52x/5
d. 52x/25
Answers
a. 9x/5
What you must do in this case is a sum of fractions.
Step 1:
Common factor 5 in the denominator
Step 2:
Perform subtraction of numerator
Step 3:
Rewrite the expression.
See attached image.
Answer:
a. 9x/5
This week laptops are 25 percent off if a laptop cost $340 what is it's sale price
Answers
An airplane is flying at an altitude of 10,000 feet when it receives clearance to land at the airport. The angle of depression from the airplane to the airport is 4o. What is the horizontal (ground distance) from the airport to the airplane's position?
Answers
[tex]tan(40)= \frac{10000}{leg} [/tex]
[tex]leg= \frac{10000}{tan(40)} [/tex]
[tex]leg=11917.54[/tex]
We can conclude that the horizontal (ground distance) from the airport to the airplane's position is 11,917.54 feet.
The boys' basketball team at Washington High School has been doing really well so far this year. In the past six games, they've scored the following points.
84, 67, 74, 87, 67, 73
What is the mean of their scores, rounded to the nearest tenth?
Answers
.. (84 +67 +74 +87 +67 +73)/6 = 452/6 ≈ 75.3
Answer:
(84 +67 +74 +87 +67 +73)/6 = 452/6 = 75.3
Step-by-step explanation:
Exactly what you see :]
Container A can hold 9 cups of liquid. container B can hold 5 pints of liquid. Container c can hold 2 quarts of liquid. Whice container has the greatest capacity? Explain
Answers
1 cup = 0.5 pints
1 cup = 0.25 quarts
That means that 9 cups are equivalent to 4.5 pints and 2.25 quarts of liquid.
1 pint = 2 cups
1 pint = 0.5 quarts
That means that 5 pints are equivalent to 10 cups and 2.5 quarts of liquid.
1 quart = 4 cups
1 quart = 2 pints
That means that 2 quarts are equivalent to 8 cups and 4 pints of liquid.
FINAL ANSWER:
Judging by our calculations, Container B has the greatest capacity.
An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are β = 7° and θ = 10.5° (see figure). How far apart are the ships? (Round your answer to one decimal place.) ft
Answers
The ships are 21.5 feet apart.
We have,
Let's denote the distance between the observer and Ship 1 as x and the distance between the observer and Ship 2 as y.
Using the angles of depression, we can establish the following relationships:
tan(β) = x / 350
tan(θ) = y / 350
We need to find the distance between the ships, which is the difference between x and y.
To find x and y, we can rearrange the equations as follows:
x = 350 * tan(β)
y = 350 * tan(θ)
Now, we can calculate the distances x and y using the given angles of depression:
x = 350 * tan(7°)
x ≈ 42.9 feet
y = 350 * tan(10.5°)
y ≈ 64.4 feet
The distance between the ships is the difference between x and y:
Distance = y - x
Distance ≈ 64.4 - 42.9
Distance ≈ 21.5 feet
Therefore,
The ships are 21.5 feet apart.
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