Answer:
12 hours as a carpenter and 18 as a blacksmith.
Step-by-step explanation:
So she earns 20$ per hour as a carpenter. c can represent the amount of hours she worked as a carpenter, and the coefficient will be 20 (salary)
So she earns 25$ per hour as a blacksmith, b can represent the amount of hours she worked as a blacksmith, and 25 will be the coefficient (salary)
So we have the two equations:
c + b = 30
20c + 25b = 690
Now we can solve for c in terms of b and substitute that into the second equation:
Original equation:
c + b = 30
Subtract b from both sides
c = -b + 30
Original equation:
20c + 25b = 690
Substitute -b + 30 as c
20(-b + 30) + 25b = 690
Distribute the 20
-20b + 600 + 25b = 690
Simplify the equation
600 + 5b = 690
Subtract 600 from both sides
5b = 90
Divide both sides by 5
b = 18
Now plug this into either of the original equations to solve for c, but the first equation b + c = 30 is the easiest, so I'll use that equation
Original equation
b + c = 30
Substitute 18 as b
18 + c = 30
Subtract 18 from both sides
12 = c
Maria is going to purchase celery and onions for a new black bean soup recipe. The recipe calls for 1.5 times as many pounds of onions as celery. If she has $8.10, what is the most pounds of celery she can buy if celery costs $1.80 per pound and onions cost $1.50 per pound?
The maximum pounds of celery she can buy is 3.25 pounds.
What are the linear equations that represent the question?1.5c = o equation 1
1.50o + 1.80c = 8.10 equation 2
Where:
o = pounds of onions
c = pounds of celery
How many pounds of celery can she buy?
Substitute for o in equation 2 using equation 1
1.50(1.50) + 1.80c = 8.10
2.25 + 1.80c = 8.10
1.80 = 8.10 - 2.25
1.80c = 5.85
c = 5.85 / 1.80
c = 3.25 pounds
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Help me please im trying to do this but dont understand it at all.
The attached graph represents the graph of the function g(x)
How to determine the function g(x)?The function f(x) is an absolute value function.
An absolute value function is represented as:
y = a|x - h| + k
Where
Vertex = (h, k)
From the graph, we have:
(h, k) = (-3, -2)
So, we have:
y = a|x + 3| - 2
Also, we have:
(x, y) = (-1, 0)
So, we have:
0 = a|-1 + 3| - 2
This gives
0 = 2a - 2
Solve for a
a = 1
Substitute a = 1 in y = a|x + 3| - 2
y = |x + 3| - 2
This means that
f(x) = |x + 3| - 2
We have:
g(x) = 2f(x)
This means that:
g(x) = 2(|x + 3| - 2)
So, we have:
g(x) = 2|x + 3| - 4
See attachment for the graph of g(x)
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what is the surface area of the walls of a hall measuring length 14m,width9m and height 4m?
Answer:
184 m²
Step-by-step explanation:
lateral area of a prism = perimeter of base × height
A = 2(14 m + 9m) × 4 m
A = 184 m²
What is 10 1/2 divded by 2 1/4?
Answer:
4.66666666667
Step-by-step explanation:
Answer:
Step-by-step explanation:10 1/2÷ 2 1/4
solution:
=20/2 ÷ 8/4
= 10 ÷
=5
The mean on a Advanced Algebra test was 86 with a standard deviation of 4.5. If the test scores are normal distributed, find the interval about the mean that contains 68% of the scores. Use the empirical rule.
Using the Empirical Rule, the interval that contains 68% of the scores is [81.5, 90.5].
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.68% of the scores are within 1 standard deviation of the mean, hence the bounds of the interval are:
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Ten members of Balin’s soccer team ran warm ups for practice. Each member ran the same distance. Their combined distance was StartFraction 5 Over 6 EndFraction of a mile. To find the distance that each member ran, Balin wrote the expression below.
StartFraction 5 Over 6 EndFraction divided by 10
Which expression is equivalent to Balin’s expression?
The expression that is equivalent to Balin's expression is 5/6 x 1/10.
What is the equivalent expression?Division is the mathematical operation that is used to determine the quotient of a number.
In order to determine the distance ran by each member, divide the total distance ran by the total number of people.
5/6 ÷ 10
5/6 x 1/10
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The expression is equivalent to Balin’s expression is StartFraction 5 Over 6 EndFraction divided by 10
Division of fractionCombined distance = 5/6 mileNumber of Balin’s soccer team = 10Distance each member ran = Combined distance ÷ Number of Balin’s soccer team
= 5/6 ÷ 10
= 5/6 × 1/10
= 5/60
= 1/12 mile
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Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second. What does point I represent in this context?
CORRECT (SELECTED)
Chana's distance from the starting line at a time when she is behind Josiah.
Explanation: Point I is on line b, so it does represent Chana's distance at a certain time. Also, point I is below line a, so it represents a distance that is less than Josiah's distance.
The best representation for the point I is that Chana's distance from the starting line at a time when she is behind Josiah.
How to solve for the line BThe point I is the distance of Chana at a particular point in time. This distance is the line a.
At point a, the speed is more so below it, it shows a speed that is less than the distance which Josiah has covered.
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1. Given
G(n) = 4n-5
H(n) = 2n + 1
Find G(H(8))
Answer:
first H(8)= 2×8+1=16+1=17
and G(17)= 4×17-5=68-5=63
factor: 128 + 2d^3
cubes lol
The factorization if the given expression 128 + 2d³ is 2(64 + d³).
Factorization128 + 2d³
There are two parameters in the expression;
128 2d³The common factors between 128 and 2d³ is 2
So,
128 + 2d³
= 2(64 + d³)
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what term is defined by the formula b^2 = a^2 + c^2 - 2ac(cosB)
Answer:
It is cosine theorem
Step-by-step explanation:
It is cosine theorem.
Convert 3 tons, 569 pounds into pounds
Answer:
6,569 pounds
Step-by-step explanation:
Ton= 2,000 pounds each
Therefore, 3 x 2,000 (pounds) = 6,000(pounds). You can use a shortcut by multiplying 3 x 2 and adding the three zeros at the end. 6,000 pounds + 569 pounds will result in 6, 569 pounds.
What is an equation of the line that passes
through the point (5,
-2) and is parallel
to the line 2x
- 5y = 35?
Find the equation of the line through the points (3,-4) and (0,2) answer in slope intercept form
Answer:
y= -2x+2.
Step-by-step explanation:
1) according to the condition interception is '2' (point (0;2));
2) slope is: (2+4)/(0-3)= -2;
3) finally the required equation is: y=-2x+2.
P.S. the suggested option is not the only one.
On a coordinate plane, a line goes through points (negative 2, negative 2) and (4, 2).The graphed line can be expressed by which equation?
Answer:
y=⅔m-8 or 3y=2m-8
Step-by-step explanation:
put both equations in the form y=mx+c and solve simultaneously. when done, you will recive values for m and c. replace those values into y=mx+c
Which inequality does the shaded region correspond to?
Answer:
y < x + 1
Step-by-step explanation:
identify 2 points along the line (-1,0) and (0,1)
gradient = [tex]\frac{0-1}{-1-0} =1\\\\the \ y \ intercept = 1\\\\y=x+1\\\\[/tex]
let us choose point (0,0) which is within our origin and substitute
0 = 0 +1
0 = 1
but we know 0 < 1
so the region is well represented by : y < x + 1
Answer:
y > x + 1
Step-by-step explanation:
→ As the line is upward sloping we can eliminate the 2 negative equations options
y < x + 1 or y > x + 1
→ As the region shaded is above the line y = x + 1, it must be y > x + 1
Solve for x in the diagram below.
Answer:
35 degrees
Step-by-step explanation:
Given all 3 angles add up 180(Sum of angles in a straight line)
[tex]2x + 30 + 40 + 40 = 180 \\ 2x + 110 = 180 \\ 2x = 180 - 110 \\ 2x = 70 \\ x = 35deg[/tex]
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Solve for x in the diagram below.
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
Notice that all 3 of those angles together make a linear pair, or a [tex]\bf{180^\circ}[/tex] angle.
This is the key to solving this problem, because the sum of these angles is 180 degrees.
[tex]\bf{2x+30+40+40=180}[/tex] | arrange the like terms
[tex]\bf{2x+30=180-40-40}[/tex] | arrange the like terms
[tex]\bf{2x+30=100}[/tex] | subtract 30
[tex]\bf{2x=70}[/tex] | divide by 2
[tex]\bf{x=35}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=m\angle x=35^\circ}[/tex]
[tex]\LARGE\boxed{\bf{aesthetics \not1\theta l}}[/tex]
The linear function has the domain (-2, -1, 0, 1, 2). Find the range or output of. h(x) = 2x + 3
If the linear function has the domain (-2, -1, 0, 1, 2). Then the range of the function h(x) = 2x + 3 will be (-1, 1, 3, 5, 7).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The function is given as
h(x) = 2x + 3
The linear function has the domain (-2, -1, 0, 1, 2).
For x = -2
h(-2) = 2 (-2) + 3
h(-2) = -1
For x = -1
h(-1) = 2 (-1) + 3
h(-1) = 1
For x = 0
h(0) = 2 (0) + 3
h(0) = 3
For x = 1
h(1) = 2 (1) + 3
h(1) = 5
For x = 2
h(2) = 2 (2) + 3
h(2) = 7
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find the expression that represents the length of the hypotenuse of a right triangle whose legs measure 2x2-y2 and 2xy
The expression for hypotenuse is √4x^4 + y^4.
What is Pythagoras theorem?A theorem stating that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other sides.
Given:
one leg = 2x²- y²
another leg = 2xy
H² = (2x²- y²)² + (2xy)²
H² = 4x^4 + y^4 - 4x²y² + 4x²y²
H²= 4x^4 + y^4
H= √4x^4 + y^4
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Question Write an equation of the line that passes through (1, −2) and is parallel to the line y=7x+7. An equation of the parallel line is y= .
Answer:
Step-by-step explanation:
7 = (y+2)/(x-1)
Parallel lines have equal slopes.
You can "massage" the form into any form you need.
The terminal side of angle θ intersects the unit circle in the first quadrant at (16/19,y). What are the exact values of sinθ and cosθ?
The exact value of sin θ and cos θ is: sinθ =(√105)/19 and cosθ =16/19
The terminal side of an angle is the angle at the standard position. The terminal side of an angle θ drawn in angle standard position is the side which isn't the initial side.
Given that the point of intersection of the terminal side of θ an the unit circle is:
(16/19,y)
The exact value of sin θ and cos θ is: sinθ =(√105)/19 and cosθ =16/19
The given parameters is represented by:
(16/19,y)
This means that :
(cosθ ,sinθ )=(16/19,y)
Using the following trigonometric identity:
cos²θ +sinθ =1
We have:
(16/19)²+y²=1
Expand fraction:
(256/361)+y²=1
Collect like terms:
y²=1-(256/361)
Take LCM:
y²=(361-256)/361
y²=105/361
Take square roots
y=(√105)/19
Substitute value for y in
(cosθ ,sinθ )=(16/19,y)
By comparison:
cosθ =16/19
sinθ =(√105)/19
So the exact value of sin θ and cos θ is: sinθ =(√105)/19 and cosθ =16/19
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2 factored expressions equivalent to -20x-30
The two expression 2(10x +15) and -5x ( x+6) are equivalent to given expression
What are Expressions ?Expressions are the mathematical statement consisting of variables , constants and mathematical operators .
The expression given is
-20x -30
-2(10x +15)
-20x -30
-5x ( x+6)
Therefore these two expression 2(10x +15) and -5x ( x+6) are equivalent to given expression.
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Which of the following rational expressions has the domain restrictions x = -6 amd x = 1?
Answer:
The answer is A)
Step-by-step explanation:
There is a domain restriction meaning the denominator should not equal to zero. If you substitute 6 and -1 into x for A) :
(1-1)(-6+6)=0
The Denominator can't be zero
Hope it helps!
Last year, about 2,400 people participated in a local event. This year, about 3,200 people participated. What was the approximate percent increase in participation?
Answer:
33 %
Step-by-step explanation:
3200 - 2400 = 800
800 / 2400 x 100
1 /3 x 100
100/ 3
33 %
If it cost $6 to fill a gas tank in 1970, how much would it have cost to fill the same tank in 2010?
Step-by-step explanation:
Well since it cost 6$ and the price was 0.36 you can calculate how many gallons you needed to fill up your tank which is calculated by dividing the price to fill the gas tank by the price per gallon
6/0.36 = 16.667 gallons
Now multiply the amount of gallons you need to fill your gas tank by the price in 2010
16.667 * 2.84 = 47.36
You could also just look at the price as a percentage relative to 1970 prices and see that the price increased by 788.9% and the find what 788.9% is of 6$. Which can be done by dividing 788.9 by 100 to convert it into decimal form which gives you 7.889 and then multiply that by the original price of 6$ to fill your gallon to get 47.33 which is slightly different although this is likely due to rounding.
Please help!!! Select the quadratic equation that has no real solution.
Answer:
2x² + 6x + 20
Step-by-step explanation:
See the picture
For the pair of
functions, f and g, determine the domain of f + g.
f(x) = 4x + 19, g(x) = 12x + 14
Answer: (-∞,∞)
Step-by-step explanation:
f(x)=4x+19
g(x)=12x+14
f + g= 4x +19 + 12x + 14 = 16x + 33
Domain of 16x + 33 = (-∞,∞)
the results of a poll indicate that between 33% and 37% of the population of a town visit the library at least once a year. what is the polls margin of error?
The margin of error is ±2%
What is Margin error?A margin of error is a statistical measurement that accounts for the difference between actual and projected results in a random survey sample.
Let x be margin of error and y be the percentages of the population.
So,
y-x =33%
y +x = 37%
Solving above equations
2y= 70
y= 35%
and x= 2%
Hence, the margin of error is ±2%.
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Which table represents a linear function?
X
1
2
34
y
3 1/1/2
O
777772
X
1
2
3
4
O
11121314
X1234
y
X1234
7
6
13
21
y
0
6
16
30
Answer:
2
Step-by-step explanation:
The first table represents the linear function.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The first table represents a linear function because the slope remains constant through out the function
Hence, the first table represents the linear function.
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Most of Mauna Kea, a volcano on Hawaii, lies below sea level. If this volcano begins at 5998 meters below sea level and then rises 10,203 meters, find the height of the volcano above sea level.
Final answer:
Height of volcano above sea level is 4205m.
Step-by-step explanation:
Step 1
Height of volcano below sea level: 5998m
Step 2
Total height of volcano below and above sea level:
10203m
Step 3
Subtract height of volcano below sea level from total height of volcano to get height of volcano above sea level:
10203 - 5998
Step 4
Subtract the terms:
10203 - 5998 = 4205
In an olimpiad , each of the 25 questions is worth 3 marks. So every correct answer is awarded 3 marks. But for every incorrect answer 1 mark is subtracted. lesley scored 55 marks out of a possible 75. how many problems did leley get correct.
An equation is formed of two equal expressions. The number of questions that Lesley answered correctly is 20.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number of correct questions answered be x, while the number of questions incorrectly answered be y.
The total number of questions can be written as,
x + y = 25
Solving the equation for y,
y = 25 - x
The total marks can be written as,
3x - 1y = 55
Substitute the value of y,
3x - 25 + x = 55
4x = 80
x = 20
Hence, the number of questions that Lesley answered correctly is 20.
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