For all x,
sin²(x) + cos²(x) = 1
so we have
(1 - cos²A) csc²A = sin²A csc²A
and since csc(x) = 1 / sin(x), so the expression reduces to 1.
You are ordering shirts for the math club at your school. Short-sleeved shirts cost $10 each. Long-sleeved shirts cost $12 each. You have a budget of $300 for the shirts. The equation $10x+12y=300$ models the total cost, where $x$ is the number of short-sleeved shirts and $y$ is the number of long-sleeved shirts. a. Graph the equation. Interpret the intercepts
Answer:
a. i) Please see the included graph of the equation $10·x + $12·y = $300
ii) The intercepts give the maximum number of either short-sleeve (x-intercept) long-sleeved (y-intercept) that can be ordered
Step-by-step explanation:
The given information are;
The cost of each short-sleeved shirt = $10
The cost of each long-sleeved shirt = $12
The amount available in the budget = $300
The equation for the total cost = $10·x + $12·y = $300
Where;
x = The number of short-sleeved shirts
y = The number of long-sleeved shirts
Rewriting the equation given in slope and intercept form, we have;
$10·x + $12·y = $300
$12·y = $300 - $10·x
y = $300/$12 - $10·x/$12
y = 25 - 5/6·x
Please find attached, the graph of the equation made with Microsoft Excel
The values of the data that can calculated to plot the graph are;
x, y
(0, 25 )
(5, 20.83 )
(10, 16.67)
(15, 12.5 )
(20, 8.33)
(25, 4.17)
(30, 0 )
The x-intercept gives the number of short-sleeve shirts that can be purchased with the $300 available budget, while the y-intercept gives the number of short-sleeve shirts that can be purchased with the $300 available budget.
The graph of the equation is shown below.
The x-intercept is at point (30,0), which means the number of short-sleeved shirts is 30 when the number of long-sleeved shirts is 0.
The y-intercept is at point (0,25), which means the number of long-sleeved shirts is 25 when the number of short-sleeved shirts is 0.
Given:
Short-sleeved shirts cost $10 each.
Long-sleeved shirts cost $12 each.
The total budget is $300.
The given equation is:
[tex]10x+12y=300[/tex]
where [tex]x[/tex] is the number of short-sleeved shirts and [tex]y[/tex] is the number of long-sleeved shirts.
To find:
The graph of the given equation and the interpretation for the intercepts.
Explanation:
We have,
[tex]10x+12y=300[/tex]
Substitute [tex]x=0[/tex].
[tex]10(0)+12y=300[/tex]
[tex]12y=300[/tex]
[tex]y=\dfrac{300}{12}[/tex]
[tex]y=25[/tex]
So, the y-intercept is at point (0,25).
Substitute [tex]y=0[/tex].
[tex]10x+12(0)=300[/tex]
[tex]10x=300[/tex]
[tex]x=\dfrac{300}{10}[/tex]
[tex]x=30[/tex]
So, the x-intercept is at point (30,0).
Plot the points (30,0) and (0,25) on a coordinate plane and connect them by a straight line.
The x-intercept is at point (30,0), which means the number of short-sleeved shirts is 30 when the number of long-sleeved shirts is 0.
The y-intercept is at point (0,25), which means the number of long-sleeved shirts is 25 when the number of short-sleeved shirts is 0.
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estimate 728 x 12 please help
Answer:
8736
Step-by-step explanation:
Answer:
8,736
Step-by-step explanation:
728 x 12 = 8,736
8(k - 6) +58 = 2(4k + 5)
one solution
no solutions
infinite solutions
Answer:
infinite solutions
Step-by-step explanation:
Given
8(k - 6) + 58 = 2(4k + 5) ← distribute parenthesis on both sides
8k - 48 + 58 = 8k + 10 , that is
8k + 10 = 8k + 10
Since both sides are equal then any value of x will make the equation true.
There are an infinite number of solutions
Select the correct answer.
You reflect triangle PQR, with vertices P(-2, -4), Q(-3, -1), and R(-4, -4), across the y-axis to get triangle P′Q′R′. What are the coordinates of triangle P′Q′R′?
A.
P′(-2, 4), Q′(-3, 1), R′(-4, 4)
B.
P′(2, -4), Q′(3, -1), R′(4, 4)
C.
P′(-2, 4), Q′(-3, 1), R′(4, -4)
D.
P′(2, -4), Q′(3, -1), R′(4, -4)
Reset Next
Answer:
C
Step-by-step explanation:
what is the answer to 9/11 - 4/11
Answer:
the answer is approximately 0.4545
Step-by-step explanation:
I just searched it on google. i got you my guy
Answer: 5/11
The denominator (bottom number) stays the same when adding or subtracting fractions. In this case, you simply subtract 4 from 9 and get 5, which is your numerator (top number).
So: 9/11 - 4/11 = 5/11
Jessica completed 20 haircuts in 8 hours. On average how many haircuts per hour did Jessica do?
Answer:
two and a half
Step-by-step explanation:
If f(x) = x2 – 3, find f (5)
Answer:
5*2 - 3
10-3
7
Step-by-step explanation:
mark me as the brainliest
Will do a brainly! 4/7=18/31.5
Answer:
True
Step-by-step explanation:
4 ÷ 7 = 0.571418 ÷ 31.5 = 0.5714Because they are the same result, the two fractions are equal. Therefore, the equation is true.I hope this helps!
Ax + 4y = 2, (3, -1) : Find A
Answer:
Step-by-step explanation:
we can subsitiute 3 and -1 for x and y respectively to get 3A - 4 = 2. After this you add 4 to both sides and get 3A = 6. divide by 3 and you get a = 2
After a bad break up, you decide to burn all the things a former boyfriend/girlfriend has given to you and any keepsakes. You have 50 items to put into the "pit" to burn. There are 85% of the items remaining at the end of 5 minutes. When will all your memories be gone?
Answer:
5.9 minutes
Step-by-step explanation:
85% of 50 items is gone in 5 minutes
42.5 items = 5 minutes
50 items = x minutes
42.5 items × x minutes = 50 items × 5 minutes
x = 50 items × 5 minutes/42.5 items
x = 5.8823529412 minutes
x ≈Approximately to 1 decimal place 5.9 minutes
All your memories be gone in 5.9 minutes
HELP ITS MATH AND I SUCK AT MATH WILL GIVE BRAINLIEST :)))))
Answer:
i believe it's A. f(x) slope is greater than g(x) slope
Step-by-step explanation:
the slope of f(x) is -2, while g(x) is -6. you may think "why isn't -6? 6 is bigger, isn't it?" In this case, they're both negative so the number closer to zero is the greater one
Answer:
A
Step-by-step explanation:
the school will repave the play yard at a cost of $23.00 per yard squard yard. the yard measures 108 ft by 135 ft. what is the total square footage of the play yard how much will the paving cost
Answer:
$5589
Step-by-step explanation:
I added 108+135
then got 243 then i multiplyed 23.00 times 243
got 5589
how many solutions does this equation have? -2(3h-1)=5(2h-3) have
the answer is a decimal
Step-by-step explanation:
-2(3h-1) = 5(2h-3)
clear brackets
-6h+2 = 10h-15
collect like terms
-6h-10h = -15-2
-16h = -17
divide the coefficient of h
h = -17 \ -16
h = 1.0625
A factory uses 30 yards of leather to make belts. Each belt is 2/3 yard long. How many belts can the factory make?
Answer:
your answer is 45
Step-by-step explanation: it is 45 because 30 divided by 2/3 is 45
Mathematical Connections Jake's solution to
the equation - 4(2x - 3) = 36 is shown.
-4(2x - 3) = 36
-8x + 12 - 36
- 8x + 12 - 12 = 36 - 12
-8x = 24
8x24
-8
X=-3
How is the solution to -4(2x - 3) > 36 similar to
and different from the solution shown?
The solution x > -3 represents all values of x that are greater than -3. On the other hand, the solution x = -3 represents a single value of x that is equal to -3.
Given that,
An equation is,
- 4(2x - 3) = 36
Here, Jake's solution to the equation - 4(2x - 3) = 36 is,
-4(2x - 3) = 36
Apply distributive property,
-8x + 12 - 36
- 8x + 12 - 12 = 36 - 12
Subtract 12 on both sides,
-8x = 24
x = - 24/8
x = - 3
So, the solution x = -3 represents a single value of x that is equal to -3.
Therefore, x > -3 represents a range of values greater than -3, while x = -3 represents a single value that is equal to -3.
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this one is tricky for me
I love theseeee
Answer:
the constant of proportionality is 10
Step-by-step explanation:
to find the constant you have to get the first number or x to be 1 so 3÷3 equals one and whatever you do to one side do to the other so 30÷3=10
hope this helps and makes sense
Part C: Create a graph that represents the solutions to the equation from Part A
Answer: Dear friend google
Step-by-step explanation: search it up
HELP PLZ WILL MARK U BRAINLIEST
9x2 - 4x + 2
2x2 + 9x - 3
For each pair of mathematical expressions, determine if the expressions have equal values. Select each pair of expressions that came out to be equal.
Please note, not all pairs will come out to the same value. We want you to determine if the expressions in each answer option have the have the same value.
Question options:
36÷3+3 and 22+2
36
÷
3
+
3
a
n
d
2
2
+
2
−(23)2and 49
-
(
2
3
)
a
n
d
4
9
8(−9) and −12−60
8
(
-
9
)
a
n
d
-
12
-
60
1+24 and 1−14
7x + 3 = 4x - 5x + 12
Answer:
x=1.125
Step-by-step explanation:
Answer:
1.125
Step-by-step explanation:
7x + 3 = 4x - 5x + 12
7x + 3 = -x + 12
+x +x
8x + 3 = 12
-3 -3
8x = 9
x = 1.125
How would you graph x > 0 on a number line?
А
Draw an open circle over 0, and shade the arrow to the right.
B
Draw a closed circle over 0, and shade the arrow to the right.
С
Draw an open circle over 0, and shade the arrow to the left.
D
Draw a closed circle over 0, and an open circle over 10.
Answer:
A
Step-by-step explanation:
The correct way to graph x > 0 on a number line is option B) Draw a closed circle over 0 and shade the arrow to the right.
In this case, the inequality x > 0 represents all values of x that are greater than zero. By placing a closed circle on zero, we include the value of zero in the solution set. The shading of the arrow to the right indicates that all values greater than zero are included in the solution.
Since the inequality is strict (x > 0), we use a closed circle to represent zero, indicating that zero is part of the solution set. An open circle would be used if the inequality was non-strict (x ≥ 0), excluding zero from the solution set. However, in this case, zero is included, so a closed circle is used.
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Rewrite in simplest terms: -3(-4g-6g-2)-8g
Answer:
22g+6
Step-by-step explanation:
-3(-4g-6g-2)-8g To simplify this, we have to distribute first.
12g+18g+6-8g Now, we can combine like terms. (I underlined the parts with the variable to make it easier to see which parts were considered like terms.)
22g+6 This is your simplified answer!!
Hope this helps...have a wonderful day c:
On what date did Thomas jefferson submit the Declaration of Independence to peers for editing?
A. April 19, 1775
B. June 7, 1776
C. June 28, 1776
July 4, 1776
Answer:
C. June 28, 1776
Step-by-step explanation:
Submitting the Declaration of Independence to the Continental Congress, June 28, 1776. This image is considered one of the most realistic renditions of this historical event.
Select all the true statements. Triangle A B C where the measure of angle A is 2 x plus 1 degree, angle B is x degrees, and angle C is x plus 15 degrees. Group of answer choices From smallest to largest: ∠B, ∠C, ∠A x = 49 m∠C = 56 m∠A = 99 (4x + 16) = 180
Answer:
m∠C = 56 and (4x + 16) = 180
Step-by-step explanation:
The sum of angle in a triangle is 180, hence:
<A+<B+<C = 180
Given
<A = 2x+1
<B = x
<C = x+15
Substitute
2x+1+x+x+15 = 180
collect like terms:
2x+x+x+1+15 = 180
4x+16 = 180
4x = 180-16
4x = 164
Divide both sides by 4
4x/4 = 164/4
x = 41°
Since <A = 2x+1
<A = 2(41)+1
<A = 82+1
<A = 83
<B = x = 41
<C = x+15
<C = 41+15
<C = 56
Based on the calculation above, the true statements are:
m∠C = 56 and (4x + 16) = 180
Calculate the slope given the two points on a line: (7,8) and (10,17)
Answer:
gvvvvvbb
Step-by-step explanation:
gghhhhbbhhjhhhhh
First person to answer gets brainly!!
please help! i will give brainliest!
Answer:
B represents 9. The opposite would be -9
Step-by-step explanation:
HELP ASAPPPP
(8x - 14)*
(2x + 4)*
Answer:
X is 17
Step-by-step explanation:
HELP WILL MARK AS BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Sandy bought a car for $17,500. Her monthly car payment is $346. The first month the amount applied to the principal is $283 and the interest amount is $63 Assume that each month the amount applied to the principal increases by $1 and the interest amount decrease by $1 Which spreadsheet shows the amount of interest she paid in the six months?
Answer:
I'm not quite sure how to point to which graph exactly, but I will tell you that it is the one that principal increases by one for six months, and interest decreases. It has "Month, Principal, Interest, and Total" written across the top in bold. Down the left-hand side, it has numbers 1-6. On the bottom, the first total is $363, and the second is $2076.
Step-by-step explanation:
There is very limited math involved in this question. The first step is to find a graph where each month, the principal number increases by one dollar and the interest decreases by one dollar. This should go on for six months. We can now eliminate two graphs. For a third, you must remember that the interest starts in the sixty, and the principal payment is in the two hundred eighties. By now, we have our graph. The final step to double-check this is to add up the total interest and principal (which should be on the side). All totals should be $346 as we're basically just trading one number for another (-1+1). You should also go to the bottom and fill in the blank in the principal column. In this box, you should put the total of all principals together.
Hope this helps!
The graph shows the relationship between inches, x,
and miles, y, on a map. Which equation represents the
proportional relationship?
O y = x + 5
O
х
O y = 5x
O y = 10x
Answer:
B
Step-by-step explanation:
Since one inch on a map must represent a few miles in reality, B is the only logical answer to this question