Answers
Final answer:
The trigonometric equation is solved using the sine difference identity, simplifying to sin(2x) = √2 sin(x). The solution involves finding values of x that satisfy the equation over the interval [0,2π). Trigonometric identities such as double angle formulas are essential in the process.
Explanation:
The student has presented a trigonometric equation involving sine and cosine functions to solve: sin(4x)cos(2x) - cos(4x)sin(2x) = √2 sin(x) over the interval [0,2π). This can be addressed by recognizing the left-hand side as the expansion of the sine difference identity: sin(A - B) = sin(A)cos(B) - cos(A)sin(B), where A = 4x and B = 2x. Therefore, the equation simplifies to sin(2x) = √2 sin(x). We solve this equation over the specified interval by looking for values of x that satisfy the condition.
However, none of the reference equations or principles provided directly align with solving the original question. Hence, we must rely solely on our knowledge of trigonometric identities, such as the double angle formulas which are relevant to this problem. The double angle identities state that sin(2θ) = 2sin(θ)cos(θ) and cos(2θ) = cos^2(θ) - sin^2(θ) or equivalently cos(2θ) = 2cos^2(θ) - 1 and cos(2θ) = 1 - 2sin^2(θ).
Related Questions
The parent function, f(x)=5^x has been vertically compressed by a factor of one-half shifted to the right three units and down two units.
Choose the correct function to represent the transformation
Answers
Function transformation involves changing the form of a function
The function that represents the transformation is: g(x) = 1/2(5^(x -3))
The parent function is given as:
f(x) = 5^x
When the function is vertically compressed by a factor of one-half, the function becomes
f'(x) = 1/2(5^x)
When the function is shifted 3 units right, it becomes
f"(x) = 1/2(5^(x -3))
Rewrite the function as:
g(x) = 1/2(5^(x -3))
Hence, the function that represents the transformation is: g(x) = 1/2(5^(x -3))
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The correct function representing the transformation is B) [tex]\( g(x) = \left(\frac{1}{2}\right)5^{x-2} - 2 \).[/tex]
Step 11. **Vertical Compression by a Factor of One-Half:**
To vertically compress the function by a factor of one-half, we multiply the function by [tex]\( \frac{1}{2} \)[/tex]. This affects the [tex]\( y \)[/tex]-coordinates of all points on the graph. So, the function becomes: [tex]\( \frac{1}{2} \cdot 5^x = \left(\frac{1}{2}\right)5^x \).[/tex]
2. **Shifted to the Left Three Units:**
To shift the function to the left three units, we add 3 to the [tex]\( x \)[/tex] -coordinate. This affects the input values. So, the function becomes: [tex]\( \left(\frac{1}{2}\right)5^{x+3} \).[/tex]
3. **Shifted Down Two Units:**
To shift the function down two units, we subtract 2 from the [tex]\( y \)-[/tex]coordinate. This affects the output values. So, the final transformed function becomes: [tex]\( \left(\frac{1}{2}\right)5^{x+3} - 2 \).[/tex]
Step 2 :Now, let's compare this transformation with the provided options:
A) [tex]\( g(x) = 5^{\left(\frac{n}{2}\right)+3} - 2 \)[/tex]
This option doesn't match the transformation. It introduces a variable [tex]\( n \)[/tex] and doesn't involve the original function [tex]\( 5^x \)[/tex].
B) [tex]\( g(x) = \left(\frac{1}{2}\right)5^{x-2} - 2 \)[/tex]
This option matches the transformation. It has the vertical compression by [tex]\( \frac{1}{2} \)[/tex], shifting to the left by three units, and shifting down by two units.
C) [tex]\( g(x) = \left(\frac{1}{2}\right)5^{x+5} - 2 \)[/tex]
This option doesn't match the transformation. It shifts the function to the right by five units instead of to the left.
D) [tex]\( g(x) = 5^{\left(\frac{1}{2}\right)^{x-3}} - 2 \)[/tex]
This option introduces a fractional exponent, which doesn't correspond to the given transformations. It also has an incorrect shift to the right by three units.
Therefore, the correct option representing the transformation is B) [tex]\( g(x) = \left(\frac{1}{2}\right)5^{x-2} - 2 \).[/tex]
Complete Question :
The parent function, f(x)=5^x has been vertically compressed by a factor of one-half shifted to the right three units and down two units.
Choose the correct function to represent the transformation
A) g(X)=5^(((n)/(2))+3)-2
B) g(x)=((1)/(2))5^(x-2)-2
C) g(x)=((1)/(2))5^(x+5)-2
D) g(x)=5^(((1)/(2))^(x-3))-2
The sum of 3 numbers is -4. The second number decreased by the third is equal to the first. The sum of the first and second numbers is -5. Write the system of equations and find the numbers.
Answers
b-c=a
a+b= -5
you can substitute a+b for -5.
-5+c= -4
c=1
you can also substitute a for b-c and c for 1
b-c+b+c= -4
2b= -4
b= -2
then substitute b for -2
a-2= -5
a= -3
A and B are vertical angles. If A = 4x - 10 and B = 6x - 30, find mA.
Answers
m<A = m<B
so
4x - 10 = 6x - 30
6x - 4x = -10 + 30
2x = 20
x = 10
m<A = 4x - 10
m<A = 4(10) - 10
m<A = 40 - 10
m<A = 30
can you please help me?
Answers
Subjects for the next presidential election poll are contacted using telephone numbers in which the last four digits are randomly selected (with replacement). find the probability that for one such phone number, the last four digits include at least one 0.
Answers
Answer:.344 if you have to round to the third decimal
Step-by-step explanation:
What is the probability of randomly drawing an odd number between 24 and 33?
Answers
How many numbers have we here? 10.
How many of these numbers are odd? {25, 27, 29, 31, 33}
Strictly speaking, "between 24 and 33" does not include {24, 33}.
Thus, the odd numbers between 24 and 33 are {25, 27, 29, 31}
The chances of drawing an odd number between 24 and 33 are then 4 / 10.
If, however, we omit the endpoints 24 and 33, then there are 8 numbers between 24 and 33: {25, 27, 29, 31}
and the odds of choosing an odd number from these eight numbers is 4/8, or 1/2, or 0.50.
Final answer:
The probability of drawing an odd number between 24 and 33 is 50%, as there are 5 odd numbers (25, 27, 29, 31, 33) within the 10 numbers in this range.
Explanation:
The probability of randomly drawing an odd number between 24 and 33 is calculated by identifying all the odd numbers in that range and dividing by the total number of possibilities.
The odd numbers between 24 and 33 are 25, 27, 29, 31, and 33. Since there are 10 total numbers (24 through 33), and 5 of these are odd, the probability is 5 out of 10, which simplifies to ½ or 50%.
Larry's bank charges a variable finance rate of 1.5 percent on purchases up to $100, and one percent for purchases over $100. If his unpaid balance is $246.07 this month, what is his finance charge?
A. $1.46
B. $2.46
C. $3.69
D. $2.96
Answers
Final answer:
To find the finance charge for an unpaid balance of $246.07, apply 1.5% on the first $100 and 1% on the remainder. The total charge is $2.9607, which rounds to $2.96, matching answer D.
Explanation:
To calculate Larry's finance charge for the unpaid balance of $246.07, we'll first divide the balance into the portions that are charged at different rates as per the bank's policy. So, the first $100 is charged at a higher rate of 1.5%, and the remaining balance ($146.07) is charged at a lower rate of 1%.
Calculate 1.5% on the first $100: $100 × 0.015 = $1.50
Calculate 1% on the remaining $146.07: $146.07 × 0.01 = $1.4607
Sum both charges to find the total finance charge: $1.50 + $1.4607 = $2.9607
After rounding to the nearest cent, Larry's total finance charge is $2.96, which corresponds to answer choice D.
what is 3w(p +18) equal?
Answers
3w(p +18) can be expanded to 3wp + 54w.
Kayla is knitting red sweaters to sell in her online store. The pattern requires 3 ounces of white yarn to trim each sweater. Kayla has 57 ounces of white yarn. How many sweaters can she trim with the yarn she has on hand?
Answers
Answer:
She can trim 19 sweaters.
Step-by-step explanation:
Kayla has a particular pattern in which she needs 3 ounces of white yarn.
That is in order to make a sweater of that particular pattern she requires white wool = 3 ounces
Kayla has total white wool = 57 ounces
one sweater requires = 3 ounces
number of sweater =[tex]\frac{total wool}{wool required for one sweater}[/tex]
=[tex]\frac{57}{3} = 19[/tex]
She can trim 19 sweaters with the Yarn she has on hand
Answer:
She can trim 19 sweaters.
Step-by-step explanation:
The perimeter of a rectangle is 400 yards. What are the dimensions of the rectangle if the length is 80 yards more than the width?
Answers
L=80+w
2(80+w)+2w=400
160+2w+2w=400
160+4w=400
4w=240
w=60
L=80+60
L=140
So, the length is 140 and the width is 60
The width is 60 yards and the length, being 80 yards more, is 140 yards.
To find the dimensions of the rectangle when the perimeter is 400 yards and the length is 80 yards more than the width, we can set up two equations based on the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
Let the width be w. Then the length is w + 80 yards.
Using the perimeter formula:
400 = 2(w + 80) + 2w
400 = 2w + 160 + 2w
400 = 4w + 160
Subtract 160 from both sides:
240 = 4w
Divide by 4:
w = 60 yards
Now, calculate the length:
l = w + 80 = 60 + 80
l = 140 yards
The width is 60 yards, and the length is 140 yards.
16,4,1,1/4,... Which exponential function describes the given sequence?
Answers
for example 4th term = 16(1/4)^3 = 1/4
Answer: Is D.
Step-by-step explanation:
A child types the letters q, w, e, r, t, y, randomly producing 1000 letters in all. what is the expected number of times that the sequence qqqq appears, counting overlaps
Answers
1000/1296 is less than 1.
Expected number of times qqqq (or any given 4-letter sequence) will appear in 1000 letters is 0.
The expected number of times the sequence 'qqqq' appears in 1000 random typings of 6 different letters is approximately 0.769 times.
Explanation:
This problem falls under the category of discrete probability in mathematics. The child randomly types one of 6 different letters.
Therefore, the probability of typing any one specific letter, such as 'q', is 1/6. The sequence 'qqqq' is a sequence of 4 specific letters. Thus, the probability of typing this sequence at any given point is (1/6)^4 or 1/1296. To find the expected number of times the sequence 'qqqq' will appear in 1000 typed letters, we multiply the probability of the event by the number of attempts. However, because 'qqqq' is a sequence of 4 letters, our attempts are based on 4-letter sequences and not individual letters. So, instead of 1000 letters, we have 1000 - 4 + 1 = 997 possible 4-letter sequences in 1000 letters.The expected number of times the sequence 'qqqq' will appear is then 997 * (1/1296) which is approximately 0.769. In simple words, we would expect the sequence 'qqqq' to occur around 0.769 times or less than once in 1000 random typings of the 6 different letters.Learn more about Expected Value here:https://brainly.com/question/35639289
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the product of two consecutive even positive integers is 10 more than seven times the larger . find the integers?
Answers
x(x + 2) = 7(x + 2) + 10
x^2 + 2x = 7x + 14 + 10
x^2 + 2x = 7x + 24
x^2 + 2x - 7x - 24 = 0
x^2 - 5x - 24 = 0
(x - 8)(x + 3) = 0
x - 8 = 0
x = 8
x + 3 = 0
x = -3...not this one because it is negative
x = 8
x + 2 = 8 + 2 = 10
so ur 2 consecutive even numbers are 8 and 10
of the 40 students who auditioned for the school play, 3/4 of them were called back for a second audition. How many students were called back for another audition.
Answers
40 * 3/4 = 30
30 people were called back for a second audition
Have an awesome day! :)
19,050,000 in scientific notation
Answers
1.905 * 10^7
Alex is constructing a square in which two of its vertices are points X and Y. He has already used his straightedge and compass to construct the lines and arcs shown.
What should Alex do for his next step?
A. Use a straightedge to draw a horizontal line that contains point Z.
B. Place the point of the compass on point X and draw any arc above it.
C. Use a straightedge to draw XZ¯¯¯¯¯ .
D. Place the point of the compass on point Y and draw an arc that intersects YZ¯¯¯¯¯ , using XY as the width of the opening of the compass.
Answers
Answer:
D. Place the point of the compass on point Y and draw an arc that intersects YZ¯¯¯¯¯ , using XY as the width of the opening of the compass.
Step-by-step explanation:
All sides of a square has to be equal.
Here it is given that X an Y are 2 of the vertices of the square. We can say that XY is the length of one side of the square.
So e should make sure that a length of the square on the YZ line is same as the XY line.
So,
Place the point of the compass on point Y and draw an arc that intersects YZ¯¯¯¯¯ , using XY as the width of the opening of the compass.
Answer:
D. Place the point of the compass on point Y and draw an arc that intersects YZ¯¯¯¯¯ , using XY as the width of the opening of the compass.
Step-by-step explanation:
Verified by test results
Hope this helps:)
Which expression below best shows how to estimate an answer for 5 3/4 divided by -3 3/8
6 divided by (-3)
6 divided by (-4)
5 divided by (-3)
5 divided by (-4)
Please answer ASAP!!
Answers
The best estimate for the division of 5 3/4 by -3 3/8 is 6 divided by -3 because rounding each number to the nearest whole provides the most accurate estimation.
To estimate an answer for 5 3/4 divided by -3 3/8, we should round each number to the nearest whole number. The number 5 3/4 rounds up to 6 because the fractional part (3/4) is more than half. The number -3 3/8 rounds to -3 because the fractional part (3/8) is less than half. Therefore, the closest estimation of the original division problem using whole numbers is 6 divided by (-3).
It is important to re-evaluate financial goals periodically. In which of the following situations would it be necessary to change an existing financial goal?
a. You fell sharply behind your expected schedule with regard to saving.
b. You recovered from an unexpected expense and are rattled that you did not see it coming.
c. You married, and your spouse has a similar financial goal.
d. You came across unexpected income.
Please select the best answer from the choices provided
A
B
C
D
Answers
You're financial goal and planning should be designed to fulfill a realistic expectation on your financial situation somewhere in the future.
When you're behind the schedule, you should either bring down the threshold for your financial goals to make it more realistic to achieve or find another source of income so your target could still be fulfilled even though you have to make additional sacrifice
Shane is trying to find the 5th term of a sequence where f(1)=4 and f(n)=2*f(n-1)+1 for each whole number greater than one. He reasons that he can find the 5th term by calculating (4*2*2*2*2)+1. Explain Shane's error
Note I am doing this for Shane not me
Answers
f(2) = 9
f(3) = 19
f(4) = 39
f(5) = 79
The Mistake made by Shane is shown below.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(1)=4 and f(n)=2f(n-1)+1
f(2)= 2f(1)+1
f(2) = 9
and, f(3)= 2f(2) + 1
f(3) = 19
and, f(4)= 2f(3)+1
f(4) = 37
so, for finding the 5th term of the function
f(5) = 2 f(4) + 1
So, we need f(4) and then value of f(4) is multiplied by 2.
As, f(5) = 2(37)+1 = 75
and, according to Shane f(5)= (4*2*2*2*2)+1 = 65
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Write the fact family for the numbers 32,8,and 4
Answers
32 8 4
16 2 4 2 2 2
4 4 2 2
2 2 2 2
there is less gravity on the planet trang than on earth. In fact, you could jump about 2 and 2/3 times as high on trang than on earth.if u can jump 4 and 1/4 feet on earth,how high could you jump on trang?
Answers
so if u can jump 4 1/4 ft on earth...then on trang u can jump :
2 2/3 * 4 1/4 =
8/3 * 17/4 = 136/12 = 11 1/3 ft <=== lol..they would have to have some really high basketball goals
The Frostburg-Truth bus travels on a straight road from Frostburg Mall to Sojourner Truth Park. The mall is 3 miles west and 4 miles south of the City Center. The park is 3 miles east and 5 miles north of the Center. How far is it from the mall to the park to the nearest tenth of a mile
Answers
Using the Pythagorean theorem: After applying the theorem, the hypotenuse, which represents the distance between the two points, is approximately 6.1 miles when rounded to the nearest tenth of a mile.
Explanation:To solve the problem of determining the distance from Frostburg Mall to Sojourner Truth Park, we can employ the Pythagorean theorem, which is used to find the length of the hypotenuse of a right-angled triangle.
Given that the mall is located 3 miles west and 4 miles south of the City Center, while the park is 3 miles east and 5 miles north, we can calculate the total east-west distance and the total north-south distance.
First, we add the east-west distances: 3 miles west of City Center to Mall plus 3 miles east from City Center to Park, which equals 6 miles in total.
Next, we calculate the north-south distance: 5 miles north from City Center to Park minus 4 miles south from City Center to Mall, resulting in 1 mile to the north.
We now have a right triangle where one leg is 6 miles and the other leg is 1 mile. Applying the Pythagorean theorem (a² + b² = c²), where 'a' and 'b' are the legs and 'c' is the hypotenuse:
c² = 6² + 1²
c² = 36 + 1
c² = 37
Finding the square root of 37, c ≈ 6.08 miles.
Therefore, the distance from the Frostburg Mall to the Sojourner Truth Park is approximately 6.1 miles to the nearest tenth.
Every 3 days Marco fills up his car with gas. Every 8 days he washed his car. On what day will Marco fill his car with gas and wash it
Answers
Ethel Meyer sells wheelchairs. SHE EARNS AN 11 PERCENT COMMISSION ON THEE FIRST $5,000 AN 14 PERCENT ON ALL SALES OVER $5000.HOW MUCH COMMISSION WILL SHE EARN ON $14,000 IN SALES?
Answers
and 14% on sales above 5,000 for 14,000 all of her commission would be 14% that means she would get $1,000 because 14% of 14,000 is 1,000
hope this helped.
**I really need help on this! Please answer!*
The table shows the scoring system for quarterbacks in Jeremy's fantasy football league. In one game, Jeremy's quarterback had 2 touchdowns passes, 16 complete passes, 7 incomplete passes, and 2 interceptions. How many total points did Jeremy's quarterback score?
**QUARTERBACK SCORING**
Touchdown pass - 6
Complete pass - 0.5
Incomplete pass - -0.5
Interception - -1.5
Answers
The total number of points = 13.5 points
What is the total amount of points gained?
We are given the scoring method as:
Touchdown pass: 6
Complete pass : 0.5
Incomplete pass : -0.5
Interception : -1.5
Now, we are told that Jeremy's quarterback had the following:
2 touchdowns passes,
16 complete passes,
7 incomplete passes,
2 interceptions.
Thus:
Total points = (2 * 6) + (0.5 * 16) + (-0.5 * 7) + (-1.5 * 2)
Total points = 13.5 points
i have 3 1/8 pounds of macaroni and want to make 10 equal serving of macaroni salad. how many pounds of macaroni do i have for each serving
Answers
= 5/16 or 0.3125 servings
Wilbur's widgets, a widget company, produces 100 widgets. its average fixed cost is $5 and its total variable cost is $300. what is the total cost of producing 100 widgets?
a. $300
b. $305
c. $500
d. $800
Answers
i hope this helps and have a wonderful day!!
The total cost of producing 100 widgets will be $800. Then the correct option is D.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Wilbur's widgets, a widget company, produce 100 widgets. its average fixed cost is $5 and its total variable cost is $300.
Then the equation is given as,
y = 5x + 300
Where 'x' is the number of widgets and 'y' is the total cost.
Then the total cost of producing 100 widgets will be given as,
y = 5 × 100 + 300
y = 500 + 300
y = $800
The total cost of producing 100 widgets will be $800. Then the correct option is D.
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This extreme value problem has a solution with both a maximum value and a minimum value. use lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, y, z) = 8x + 8y + 4z; 4x2 + 4y2 + 4z2 = 36
Answers
[tex]L_x=8+8\lambda x=0\implies 1+\lambda x=0[/tex]
[tex]L_y=8+8\lambda y=0\implies 1+\lambda y=0[/tex]
[tex]L_z=4+8\lambda z=0\implies 1+2\lambda z=0[/tex]
[tex]L_\lambda=4x^2+4y^2+4z^2-36=0\implies x^2+y^2+z^2=9[/tex]
[tex]yL_x=y+\lambda xy=0[/tex]
[tex]xL_y=x+\lambda xy=0[/tex]
[tex]\implies yL_x-xL_y=y-x=0\implies y=x[/tex]
[tex]2zL_x=2z+2\lambda xz=0[/tex]
[tex]xL_z=x+2\lambda xz=0[/tex]
[tex]\implies 2zL_x-xL_z=2z-x=0\implies x=2z[/tex]
[tex]2zL_y=2z+2\lambda yz=0[/tex]
[tex]yL_z=y+2\lambda yz=0[/tex]
[tex]\implies 2zL_y-yL_z=2z-y=0\implies y=2z[/tex]
[tex]x=y=2z\implies x^2+y^2+z^2=9\iff 4z^2+4z^2+z^2=9z^2=9\implies z=\pm1[/tex]
[tex]z=\pm1\implies y=x=\pm2[/tex]
So we have two critical points, (2, 2, 1) and (-2, -2, -1), which respectively give a max of 36 and a min of -36.
The extreme max value is "[tex]f(x,y,z) = 36[/tex]" and min value is "[tex]f(x,y,z) = -36[/tex]".
According to the question,
[tex]f(x, y, z) = 8x + 8y + 4z[/tex]let,
[tex]g(x,y,z) = 4x^2 + 4y^2 + 4z^2 - 36[/tex]By using Lagrange multipliers,
→ [tex]\bigtriangledown f= \lambda \bigtriangledown g[/tex]...(equation 1)
[tex]\bigtriangledown f = <8,8,4>[/tex][tex]\bigtriangledown g = <8x, 8y,8z>[/tex]∴ [tex]<8,8,4>=<8\lambda x, 8 \lambda y, 8 \lambda z >[/tex]
then,
[tex]8 \lambda x = 8[/tex]...(equation 2)[tex]8 \lambda y =8[/tex]...(equation 3)[tex]8 \lambda z = 4[/tex]...(equation 4)→ [tex](x = \frac{1}{\lambda}, y=\frac{1}{\lambda}, z =\frac{1}{2 \lambda} )[/tex]
As we know,
→ [tex]4x^2 +4y^2+4z^2=36[/tex]
By substituting the values, we get
→ [tex]4(\frac{1}{\lambda} )^2+ 4(\frac{1}{\lambda} )^2+4(\frac{1}{2\lambda} )^2 =36[/tex]
→ [tex]\frac{4}{\lambda^2} +\frac{4}{\lambda^2} +\frac{1}{\lambda^2} =36[/tex]
→ [tex]\frac{9}{\lambda^2}=36[/tex]
[tex]\frac{1}{\lambda}= \pm \frac{6}{3}[/tex]
[tex]\frac{1}{\lambda} = \pm 2[/tex]
∴ x = 2, y = 2, z = 1
then,
→ [tex]f(x,y,z) = 36[/tex] (Extreme max value)
and,
∴ x = -2, y = -2, z = -1
then,
→ [tex]f(x,y,z) = -36[/tex] (min value)
Thus the above answer is correct.
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!!!!!!!I NEED HELP WITH THESE PROBLEMS. THANK YOU!!!!!
1. Mike's salary is $6,500 per month. He saves 1/5 of his monthly salary and spends the rest.
How much money does Mike save every month?
$ ?
How much money does Mike spend every month?
$ ?
2. Fill in the missing values that makes the equation true.
−2/5×30= ?/2 x -4 = ?
3. Alex takes 1 hour and 30 minutes to get to the office.
How many hours does Alex spend getting to the office over 4 days?
? hours
4.Fill in the missing values that make the equation true.
−4/7×49= ?/6 x -14 = ?
5. Drag the equivalent expressions into the appropriate columns.
5(1/5+3c) 1/4(1/2 - 4c)
(5+15c), (1+15c), (1/8 - c), (1/8 - 4/4c), (-1/8 + -c), (5/5 + 15c)
6. Drag the equivalent expressions into the appropriate columns.
a(b + c) -x(m - n)
(ab - ac), (ab + ac), -(xm - xn), (-xm + -xn)
7. Part 1
18 × ? = 1
Part 2
Select all the statements that explain why the missing value you chose for Part A makes the equation true.
Answer Choices
A. The product of a rational number and its multiplicative inverse is always 1.
B. The sum of a rational number and its additive inverse is always 0.
C. The product of two positive rational numbers is always positive.
D. The product of any two rational numbers is always 1.
E. It is the multiplicative inverse of the multiplier.
F. It is the additive inverse of the multiplier.
8. This is an equation.
(-7)(-17)=1
Select all of the statements that explain why this equation is true.
Answer Choices
A. The fraction -17 is the multiplicative inverse of -71 .
B. The fraction -17 is the additive inverse of -71 .
C. The product of any two rational numbers is always 1.
D. The product of two negative rational numbers is always positive.
E. The product of a rational number and its multiplicative inverse is always 1.
F. The sum of a rational number and its additive inverse is always zero.
Answers
URGENT! PLEASE ANSWER!
Layla is using the model to solve a division problem. Which question would the model be most helpful in solving?
How many 1/6s are in 4?
How many 1/6s are in 2/3?
How many 2/3s are in 4?
How many 2/3s are in 1/6?
Answers
Answer:
the answer is B
Step-by-step explanation:
The model would be most helpful in solving the problem 'How many 1/6s are in 2/3?'. This is found by dividing 2/3 by 1/6 through fractional division, giving a result of 4.
Explanation:The model would be most helpful in solving the question 'How many 1/6s are in 2/3?'. Let me explain why:
To solve this, you simply need to divide 2/3 by 1/6. When we say 'how many 1/6s are in 2/3', it means how many times can 1/6 fit into 2/3. Division is the process of finding out how many times one number (the divisor) is contained within another (the dividend).
So we divide 2/3 by 1/6. But rather than directly divide, in fractional division we multiply the first fraction by the reciprocal of the second. The reciprocal of 1/6 is 6/1.
So, 2/3 * 6/1 = 4.
That means, there are 4 1/6s in 2/3.
Learn more about fractional division here:https://brainly.com/question/28635541
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