The camera melissa wanted for her birthday is on sale at 27%off the usual price. theamount of the discount is $99.90.what was the original price of the camera?$nothing
divide the discount by the percentage off
so:
99.90/0.27 = 370
the original price was 370 dollars
Write the equation in standard form for the parabola with vertex (0,0) and directrix y=-6
To find the equation of a parabola with a vertex at (0,0) and a directrix of y=-6, we determine the focus is at (0,6), leading to the standard form equation of the parabola as y = 1/4x^2.
Explanation:The question asks for the equation of a parabola in standard form given its vertex at (0,0) and directrix as y=-6. In parabolic equations, the standard form is usually y = ax^2 + bx + c for horizontal parabolas, or x = ay^2 + by + c for vertical parabolas. Given the vertex is at the origin (0,0) and the directrix is y = -6, this means the focus is at (0,6) because the distance from the vertex to the focus is equal to the distance from the vertex to the directrix but in the opposite direction.
For a parabola that opens upwards or downwards, the standard form is y = ax^2 (since the vertex is at the origin, b and c are 0). Given that the distance from the vertex to the focus (which is also the distance from the vertex to the directrix) is 6, the parabola opens upwards, and its focal distance (p) is 6. Hence, the value of 4p = 24, which leads us to conclude that a = 1/4. Therefore, the equation of the parabola is y = 1/4x^2.
a triangle has two sides of lengths 7 and 9.what value could the length of the third side be?
Answer:
13, 10, 8, 5
Step-by-step explanation:
2+7=9 9=9 the requirment is it has to be greater than the third length not equal to
You are taking a multiple-choice test that has 10 questions. each of the questions has four answer choices, with one correct answer per question. if you select one of these four choices for each question and leave nothing blank, in how many ways can you answer the questions?
Show that the equation is not an identity by finding a value of x for which both sides are defined but not equal. cos x - cos x sinx = cos3 x
Answer:
The answer is pi/4
Step-by-step explanation:
You substitute each x for "pi/4", you will see that the equation is incorrect, the two values are no longer equal.
The equation is not an identity. Value of x = nπ, where n∈I , I → set of integers, for which both sides are defined but not equal.
What are the trigonometric identities?Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.
We have the equation,
cos x - (cos x) (sin x) = cos³x
Simplifying,
cos x [ 1 - (sin x) ] = cos²x (cos x)
1 - sinx = cos²x
1 - sinx = 1 - sin²x
1 - sinx = 1² - sin²x
1 - sinx = (1 - sinx)(1 +sinx)
1 = 1 + sinx
sinx = 0
x = nπ, where n∈I , I → set of integers.
It is not an identity equation.
cos x - (cos x) (sin x) ≠ cos³x
Therefore, both sides are defined but not equal.
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If θ is in Quadrant III and cosθ -2/3, then sinθ = _____.
Answer:
[tex]\sin\theta=-\dfrac{\sqrt{5}}{3}[/tex]
Step-by-step explanation:
If θ is in Quadrant III
[tex]\cos\theta=-\dfrac{2}{3}[/tex]
As we know in III quadrant cosine and sine both are negative.
using trigonometry identity
[tex]\sin\theta=-\sqrt{1-\cos^2\theta}[/tex]
[tex]\sin\theta=-\sqrt{1-(\frac{2}{3})^2}[/tex]
[tex]\sin\theta=-\sqrt{1-\frac{4}{9}}[/tex]
[tex]\sin\theta=-\dfrac{\sqrt{5}}{3}[/tex]
Hence, The value of [tex]\sin\theta=-\dfrac{\sqrt{5}}{3}[/tex]
2x^3y + 18xy - 10x^2y - 90y Part A: Rewrite the expression so that the GCF is factored completely. (3 points)
To factor 2x^3y + 18xy - 10x^2y - 90y, find the GCF of the terms, rewrite the expression, factor out the GCF from the terms inside the parentheses, and simplify the expression.
Explanation:To factor the expression 2x^3y + 18xy - 10x^2y - 90y, we can begin by finding the greatest common factor (GCF) of the terms. The GCF of the coefficients is 2, and the GCF of the variables is y.
So, we can rewrite the expression as 2y(x^3 + 9x - 5x^2 - 45).
Next, we can factor out the GCF from the terms inside the parentheses. The GCF of x^3, 9x, -5x^2, and -45 is x. Factoring out x, we get x(x^2 + 9 - 5x - 45).
Finally, we simplify the expression inside the parentheses. Rearranging the terms, we have x(x^2 - 5x + 9 - 45). Combining like terms, we get x(x^2 - 5x - 36).
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Jacob and Isaiah are brothers. Their combined ages are 63. Jacob is 7 years older than Isaiah. How old are each of the boys?
Final answer:
To solve this problem, set up a system of equations and solve for the variables. Isaiah is 28 years old and Jacob is 35 years old.
Explanation:
To solve this problem, we can set up a system of equations.
Let's say Isaiah's age is represented by x. Jacob's age is then represented by x + 7, since he is 7 years older than Isaiah.
We know that the sum of their ages is 63, so we can set up the equation: x + (x + 7) = 63.
Simplifying the equation gives us: 2x + 7 = 63.
Subtracting 7 from both sides of the equation gives us: 2x = 56.
Dividing both sides of the equation by 2 gives us: x = 28.
So, Isaiah is 28 years old, and Jacob is 28 + 7 = 35 years old.
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If tan y = 3 over y and cos x = y over z what is the value of sin x??
A. sin x = 3/z
B. sin x = 3y
C. sin x = z/3
D. sin x = 3z
Answer: (A) sin x° = 3/z
Step-by-step explanation: i couldnt find it anywhere else but i figured it out and dont worry i got it right on the quiz
Someone help me please !
AE x BE = DE x CE
6x5 = 30
6 x DE = 30
DE = 30/6 =5
DC = DE +CE = 5+6 =11
Answer is C) 11
Guys help me out with this one plizz
Getting two 6's in four rolls can happen in 6 ways. 4C2 = 6
The probability of getting two 6's is 1/36. Therefore,
6 times 1/36 = 1/6 or 0.16666666...
Converting to a percent to the nearest tenth is 16.7%
The sum of three consecutive odd integers is 207. What are the integers?
Why is 8.8 classified as a rational number?
Jess observed that 60% of the people at a mall on a particular day shopped for clothes. If 2500 people at the mall did not shop for clothes that day, the number of people who shopped for clothes that day was ______.
Answer:
3750
Step-by-step explanation:
3750
Find the slope of the line on the graph. Write your answer as a fraction or a whole number, not a mixed number or decimal.
Answer: -3
Step-by-step explanation:
The points (1,1) (2,-2) plugged into slope formula m = y2 - y2/x2 - x1
-2 is y2
1 is y1
2 is x2
1 is x1
Subtract and simplify
8y - 1 = x 3x = 2y Solve the system of equations by substitution.
the question is............
a hot air balloon holds 3,249 cubic meters kf helium. the density of the helium is 0.1785 kilograms per cubic meter. how many kilograms of helium does the balloon contain, round to the nearest tenth of a kilogram?
What is the measure of an exterior angle of a regular 11-sided polygon?
The measure of an exterior angle of a regular 11-sided polygon is 32.73°.
The measure of an exterior angle of a regular 11-sided polygon can be calculated using the formula:
60° divided by the number of sides.
In this case, for an 11-sided polygon, each exterior angle would measure 360° / 11 = 32.73°.
If a cone and a sphere have the same radius and the same height what is the relationship among the volumes of the two shapes
Answer:
the volume of the sphere will be 4 times the volume of the cone;
Step-by-step explanation:
The question is on volume comparison
Volume of a sphere=4/3 ×r³
Volume of a cone= /3×r²h
where r is the radius and h is the height
Apply the condition
If r=h=1 unit
Then volume of sphere will be= 4/3 × ×1³ = 4/3
And volume of the cone will be= /3 ×1²×1 =/3
We can see the volume of the sphere will be 4 times the volume of the cone;
4/3 = 4×/3
John's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs John $4.70 per pound, and type B coffee costs $5.90 per pound. This month, John made 181 pounds of the blend, for a total cost of $967.10 . How many pounds of type A coffee did he use?
A +B = 181
A=181-B
4.70A+5.90B= 967.10
4.70(181-B) +5.90B =967.10
850.70-4.70B+5.90B=967.10
850.70+1.2B =967.10
1.2B=116.40
B =116.40/1.2 = 97
A=181-97 = 84 pounds of type A coffee
Which expression is equivalent to (2x^2 + 4x – 7)(x – 3)?
A. x(2x^2 + 4x – 7) + 3(2x^2 + 4x – 7)
B. x(2x^2 + 4x – 7) – 3
C. –3x(2x^2 + 4x – 7)
D. (2x^2 + 4x – 7)(x) + (2x^2 + 4x – 7)(–3)
The expression (2x² + 4x – 7)(x – 3) is equivalent to the expression (2x² + 4x – 7)(x) + (2x² + 4x – 7)(–3) option (D) is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
= (2x² + 4x – 7)(x – 3)
After using the distributive property:
= (2x² + 4x – 7)(x) + (2x² + 4x – 7)(–3)
Distributed the whole term (2x² + 4x – 7) with (x - 3)
Thus, the expression (2x² + 4x – 7)(x – 3) is equivalent to the expression (2x² + 4x – 7)(x) + (2x² + 4x – 7)(–3) option (D) is correct.
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A parent rewards a child with 50 cents for each correctly solved mathematics problem and fines the child 30 cents for each incorrectly solved problem. if the child nets $22.00 after 100 problems. how many problems were solved correctly?
x = correct answer
y = incorrect answer
0.50x-0.30(100-x)=22.00
0.50x-30.00+0.30x=22.00
0.80x=22.00+30.00
0.80x=52.00
x=52.00/0.80
x= 65
y=100-65 = 35
0.5x65 = 32.50
35*0.30=10.5
32.5-10.5 = 22
there were 65 correct answers
Answer:
65 problems were solved correctly, 35 incorrecly.
Step-by-step explanation:
1. Data:
Total answers= 100
50 cent = $0.50 for each correct answer
-30 cent = -$0.30 for each incorrect answer
Net reward= $22.00
2. Define Variables:
x= Correct answers
y= Incorrect answers
3. Formulate the Equations
Total number of answers (Eq 1)
[tex]x+y=100\\y=100-x[/tex]
Net reward (Eq 2)
[tex]0.50*x-0.30*y=22.00[/tex]
4. Solve by replaccing the Eq 1 in Eq 2 as follows:
[tex]0.50*x-0.30*y=22.00\\0.50*x-0.30*(100-x)=22.00[/tex]
5. Apply distrivutive property and operate:
[tex]0.50x-(0.30*100)+(0.30*x)=22.00\\0.50x-30.00+0.30x=22.00[/tex]
6. Separate numbers and variables on each side of the equation and solve
[tex]0.50x+0.30x=22.00+30.00\\0.80x=52.00[/tex]
7. Solve x
[tex]x=\frac{52.00}{0.8} \\x=65[/tex]
Now you know that correct answers are equal to 65
8. Find Incorrect Answers with Eq 1.
[tex]y=100-x\\y=100-65\\y=35[/tex]
Now you know that incorrect answers are equal to 35
9. Answer
65 problems were solved correctly, 35 incorrecly.
A worker produced a total of 198 mousetraps during a 6 hour run with no rejects and no downtime. A report states that this worker produced at a rate of 2 mousetraps per minute. Based on the actual production, is the rate of 2 mousetraps per minute accurate?Exit Test
Based on the actual production, the rate of 2 mousetraps per minute is not accurate.
What is Rate?Rate of a quantity is the amount of that quantity with respect to some amount of another quantity.
If the quantity with respect to which the rate is measured is taken as single unit or one unit, then the rate is called unit rate.
Production of mousetraps by the worker in 6 hours = 198
Production of mousetraps by the worker in 1 hour = 198/6 = 33
That is, production of mousetraps by the worker in 60 minutes = 33
Production of mousetraps by the worker in 1 minute = 33/60 = 0.55
The worker produced mousetraps at a rate of 0.55 mousetraps per minute.
But the report states that this worker produced at a rate of 2 mousetraps per minute, which is not correct.
Hence the statement of report that the worker produced at a rate of 2 mousetraps per minute is not accurate, because he is only producing 0.55 mousetraps per minute.
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Jamie has invested $1500 in a savings account. Each month the account pays an interest of 3.8%. How much money will she have in her account 4 years later if she does not make any deposits or withdrawals (round to the nearest dollar)?
A) $1,257
B) $1,557
C) $1,559
D) $2,341
Answer:
$4236.
Step-by-step explanation:
We have been given that Jamie has invested $1500 in a savings account. Each month the account pays an interest of 3.8%. We are asked to find the total amount Jamie will have in her account after 4 years.
We will use simple interest formula to solve our given problem.
[tex]A=P(1+rt)[/tex], where,
A = Final amount after t years,
P = Principal amount,
r = Interest rate in decimal form,
t = Number of years.
Let us convert our given rate in decimal form.
[tex]3.8\%=\frac{3.8}{100}=0.038[/tex]
Since the we have been given monthly interest rate, so we will convert the given rate to annual interest rate by multiplying 0.038 by 12.
Upon substituting our given values in above formula we will get,
[tex]A=\$1500(1+0.038*12*4)[/tex]
[tex]A=\$1500(1+1.824)[/tex]
[tex]A=\$1500(2.824)[/tex]
[tex]A=\$4236[/tex]
Therefore, Jamie will have $4236 in her account after 4 years.
Stan and hilda can mow the lawn in 30 min if they work together. if hilda works twice as fast as stan, how long does it take stan to mow the lawn alone?
Find the area of the square.
Which of the following is a key property of the linear parent function
A it is in quadratic ll and lV
B is has a slope of 1
C it is a curved line
D it does not go through the origin
Answer:
The correct option is B.
Step-by-step explanation:
The equation of linear parent function is
[tex]y=x[/tex]
Key property of the linear parent function are:
1. It is in quadratic l and lII.
2. It has a slope of 1.
3. It is a straight line.
4. It passes through the origin.
The graph of parent function is shown below.
In the given options only the statement " It has a slope of 1" is true.
Therefore the correct option is B.
.........simplify 3^2*3^5