Answer:
10cos(5x)sin(10x) = 5[sin (15x) + sin (5x)]
Step-by-step explanation:
In this question, we are tasked with writing the product as a sum.
To do this, we shall be using the sum to product formula below;
cosαsinβ = 1/2[ sin(α + β) - sin(α - β)]
From the question, we can say α= 5x and β= 10x
Plugging these values into the equation, we have
10cos(5x)sin(10x) = (10) × 1/2[sin (5x + 10x) - sin(5x - 10x)]
= 5[sin (15x) - sin (-5x)]
We apply odd identity i.e sin(-x) = -sinx
Thus applying same to sin(-5x)
sin(-5x) = -sin(5x)
Thus;
5[sin (15x) - sin (-5x)] = 5[sin (15x) -(-sin(5x))]
= 5[sin (15x) + sin (5x)]
Hence, 10cos(5x)sin(10x) = 5[sin (15x) + sin (5x)]
If circle A has a radius of 4.7 cm, what is the diameter?
Answer:
7.4cm
Step-by-step explanation:
diameter =2radius
=2×4.7
=7.4cm
The diameter of circle A with a radius of 4.7 cm is 9.4 cm.
Explanation:To find the diameter of a circle, you can use the formula: diameter = 2 * radius. Given that circle A has a radius of 4.7 cm, the diameter would be 2 * 4.7 = 9.4 cm.
Learn more about diameter of a circle here:https://brainly.com/question/33058442
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What is the solution to the equality below? -2x + 6 > 3x - 4
Answer:
2 > x
Step-by-step explanation:
-2x + 6 > 3x - 4
Add 2x to each side
-2x+2x + 6 > 3x+2x - 4
6 > 5x-4
Add 4 to each side
6+4 > 5x-4+4
10 >5x
Divide each side by 5
10/5 > 5x/5
2 > x
Answer:
x < 2
Step-by-step explanation:
-2x + 6 > 3x - 4
6 + 4 > 3x + 2x
10 > 5x
2 > x
x < 2
When you go to the store, does tax increase or decrease the cost of your items?
yes because you have to pay more it's tricky
Complementary, Supplementary, Vertical, and Adjacent Angles
100 POINTS
Answer:
The first picture is A
The second picture is 21.8
The third picture is 20
The fourth picture is B
Step-by-step explanation:
4x + 8x = 180
12x = 180
x = 15
90 - 68.2 = 21.8
7x + 10 = 150
7x = 140
x = 20
Angle A = 63
180 - 63 = 117
Answer:
The first picture is A
The second picture is 21.8
The third picture is 20
The fourth picture is B
Step-by-step explanation:
hope this helps
Help me with the two again
Part A:
s = k + 4
Part B:
s = 13 + 4
s = 17
Therefore, Sylvia's age is 17 when Katie is 13.
Find the surface area of the prism. Write your answer as a decimal.
Answer:
1.5cm³
Step-by-step explanation:
Surface area of a prism = bh x 6
0.5 x 0.5 = 0.25 x 6 = 1.5
Answer:
1.5 cm
Step-by-step explanation:
a=6a^2
a=6(0.5)^2
a=6(0.25)
a=1.5 cm
If d represents how many days are left in school this year,which inequality states we have at most 95 days?
Answer:
d ≤ 95
Step-by-step explanation:
The inequality that states we have at most 95 days is d≤ 95.
What is an inequality?A connection between two expressions or values that is not equal to one another is referred to as "inequality" in mathematics.
The inequality can be resolved by adding the same amount to each side, subtracting the same amount from each side, multiplying or dividing each side by the same positive integer, and more. If you multiply or divide either side by a negative value, you must flip the inequality sign.
If d represents how many days are left in school this year.
And we have at most 95 days.
Then,
d can not be more than 95.
d ≤ 95
Therefore, the inequality is d ≤ 95.
To learn more about the inequality in mathematics;
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what is 32.5 cents as a decimal
Answer:
32.5
Step-by-step explanation:
its a trick question
Part of the graph of the function f(x) = (x – 1)(x + 7) is shown below. Which statements about the function are true? Select three options. The vertex of the function is at (–4,–15). The vertex of the function is at (–3,–16). The graph is increasing on the interval x > –3. The graph is positive only on the intervals where x < –7 and where x > 1. The graph is negative on the interval x < –4.
Answer:
The vertex of the function is at (–3,–16)
The graph is increasing on the interval x > –3
The graph is positive only on the intervals where x < –7 and where x > 1
Step-by-step explanation:
The roots of this function are the values that make f(x) = 0. As the equation is already factored, we can see that the roots are x1 = 1 and x2 = -7
The x-coordinate of the vertix can be calculated as:
x_v = (x1 + x2)/2 = -6/2 = -3
So the first statement: "The vertex of the function is at (–4,–15)" is wrong.
The y_coordinate of the vertex is:
f(x_v) = (x_v - 1)*(x_v + 7) = (-3 -1) * (-3 +7) = (-4) * (4) = -16
So the second statemente: "The vertex of the function is at (–3,–16)" is correct.
for values of x greater than x_v = -3, the graph increases, as the equation represents a parabola with concavity upwards. So the third statement is correct.
As the roots are 1 and -7 and the concavity is upwards, the parabola have positive values for x<-7 and x>1. So the fourth statement is correct.
For values of x< -4, the parabola can have both positive or negative values (it has positive values for x < -7) so the fifth statement is wrong.
Answer:
B. The vertex of the function is at (–3,–16).
C. The graph is increasing on the interval x > –3.
D. The graph is positive only on the intervals where x < –7 and where
x > 1.
A 10 meter flag pole casts a shadow 5 meters long. How long will the shadow be if the flag pole is 15 meters tall
Answer:
7.5 meters long
Step-by-step explanation:
10/2 = 5
15/2 = 7.5
The shadow is half as long as the pole.
hope this helps :)
Answer:
7.5 meters
Step-by-step explanation:
Actual : shadow
10 : 5
15 : X
10/5 = 15/X
X = 15 × 5/10
X = 7.5
f an investor puts $1500 dollars into an account at an annual rate of 4.8% interest compounded twice a month, how much will they have after two years?
Answer:
They will have $1651 after two years.
Step-by-step explanation:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.
$1500 dollars into an account at an annual rate of 4.8%
This means that [tex]P = 1500, r = 0.048[/tex]
Interest compounded twice a month.
A year has 12 months.
So 12*2 = 24 compundings, which means that [tex]n = 24[/tex]
How much will they have after two years?
This is A(2).
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(2) = 1500(1 + \frac{0.048}{24})^{24*2} = 1651[/tex]
They will have $1651 after two years.
The height of a right circular cylinder is 1.5 times the radius of the base. What is the ratio of the total surface area to the lateral (curved) surface area of the cylinder?
Answer:
The ratio of the total surface area to the lateral (curved) surface area of the cylinder is 5:3
Step-by-step explanation:
The height of a right circular cylinder is 1.5 times the radius of the base.
Let the radius of base be x
So, Height of a right circular cylinder = 1.5x
Total surface area of cylinder =[tex]2 \pi r h + 2 \pi r^2 = 2 \pi r(h+r)=2 \pi \times x(x+1.5x)=2 \pi \times x \times 2.5x[/tex]
Curved surface area of cylinder = [tex]2 \pi rh = 2 \pi \times x \times 1.5 x[/tex]
So, Ratio of the total surface area to the lateral (curved) surface area of the cylinder = [tex]\frac{2 \pi \times x \times 2.5x}{2 \pi \times x \times 1.5 x}=\frac{2.5}{1.5}=\frac{25}{15}=\frac{5}{3}[/tex]
Hence the ratio of the total surface area to the lateral (curved) surface area of the cylinder is 5:3
A computer is sold for a certain price and then its value changes exponentially over time.
The graph describes the computer's value (in dollars) over time (in years).
value (dollars)
500
400+
300+
5
200+
100+
time
(years)
0.5
1
1.5
2
2.5
3
3.5
How does the computer's value change over time?
Answer: the computer loses 50% of its value each year
Step-by-step explanation:
The Smiths spend 10% of their budget on entertainment. Their total budget this year is $3,000 more than last year, and this year they plan to spend $5,000 on entertainment. What was their total budget last year?
Answer:
$47,000
Step-by-step explanation:
Let u represent the unknown amount of budget
10/100× u = $5000
10u/100=$5000
Cross multiply both sides
10u= $500000
Divide both sides by the coefficient of u
10u/10=$500000/10
u= $50000
Therefore, this year's budget is $50000
Since Smith's budget this year is $3000 greater than last year's budget, to find last year's budget we simply subtract the difference from this year's budget.
$50000- $3000
= $47000
Thus, Smith's total budget for last year was $47000.
Answer: $47,000
Step-by-step explanation:
Hi, to answer this question we have to write an equation:
Their total budget this year is $3,000 more than last year, so we have to add 3000 to their total budged of last year (x). x+3000
Since they spend 10% of their budget on entertainment, we have to multiply the previous expression by the percentage in decimal form (divided by 100).
(x +3000) 10/100 = (x+3000) 0.1
Finally, that expression must be equal to the amount that they will spend in entertainment this year (5000).
(x + 3000) 0.1 =5000
Solving for x:
x+3000 = 5000/0.1
x +3000= 50,000
x = 50,000-3,000
x = $47,000
Feel free to ask for more if needed or if you did not understand something.
Which angle is congruent to angle AGC
Find the measure of y.
A.85
B.102
C.122
D.138
Answer:
102
Step-by-step explanation:
A college president says, "More than two-thirds of the alumni support my firing of Coach Boggs." The president's statement is based on 200 emails he has received from alumni in the past three months. The college's athletic director wants to perform a test of H0: p = ⅔ versus Ha: p > ⅔, where p = the true proportion of the college's alumni who favor firing the coach. Check if the conditions for performing the significance test are met. Random? No, volunteer response sample
A. Random? No, volunteer response sample Large Counts? Yes
B. Random? Yes Large Counts? fails
C. Both fails
D. Random? Random sample of 100 students Large Counts? np0 = 100(0.13) = 13 ≥ 10 and n(1-p0) = 100(0.87) = 87 ≥ 10
What is the amplitude of the function below?
1
2
(pi)
2(pi)
Answer:
B. 2
Step-by-step explanation:
on Edg2020
Answer:
B. 2 got it right
Step-by-step explanation:
Polynomials - Guided Notes 11.2
Part 1: Find the degree of the polynomial.
1. 3x + 2
2. 4x3 + 17x - 5
3. 13x" + 5xn-2
4. 0.55x2 + 0.7x
5. 7x3 + 10x + 15
Answer:
1. 3x + 2 - First degree
2. 4x3 + 17x - 5 - Third degree
3. 13x" + 5xn-2 - Second degree
4. 0.55x2 + 0.7x - Second degree
5. 7x3 + 10x + 15 - Third degree
Step-by-step explanation:
The degree of a polynomial is given by the highest power of the given variable (x in this case) in the polynomial. All the elements are considered in selecting the highest power of x in the polynomials.
Considering all; the highest degree of x in the polynomials given is 3 while the lowest is 1 hence we have polynomials ranging from the first to third degrees.
Need this answered today, will give brainliest: The Steelers are on the Cowboys’ fifteen-yard line. Use your place value mat or number line to calculate how
much farther the Steelers need to travel to score a touchdown.
Answer: 15 yards
Step-by-step explanation:
From the question, we have been informed that the Steelers are on the Cowboys' fifteen-yard line. Using the place value mat to calculate how much farther Steelers need to travel to score a touchdown goes thus:
Since the play is 15 yards from the Cowboys end-zone, therefore Steelers need to travel 15 yards for them score a touchdown.
Final answer:
The Steelers are 85 yards away from the end zone.
Explanation:
To calculate how much farther the Steelers need to travel to score a touchdown, we need to know the distance from the Cowboys' fifteen-yard line to the end zone. The distance between each yard line on a football field is 10 yards. Since the Steelers are on the fifteen-yard line, they are 85 yards away from the end zone (100 yards - 15 yards = 85 yards).
The distance from the center of a circulartrashcan to the edge of the trashcan is 15 inches.What is the area of the top of the trashcan?
Answer:
706.95in²
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, a cylinder
Step one
The trash can has a cylindrical shape
The distance from the center to the edge is the radius r= 15in
Step two
Area of top (circular ) = πr²
A= 3.142*15²
A= 3.142*225
A= 706.95in²
X/3 - 2 + 6 what is the answer
Answer:
[tex]\frac{x}{3}[/tex]+4
Step-by-step explanation:
I don't think it can be simplified more than that
Answer:
x= -12
Step-by-step explanation:
x/3 -2+6 =0
x/3 +4 =0
x/3 = -4
x/3 (3) = -4 (3)
x = -12
Simplify -12.5 - (-4.8)
Answer: -17.5
Step-by-step explanation:Use this rule:
1. -a-b=-(a+b)−a−b=−(a+b).
-(12.5+4.8)−(12.5+4.8)
2.Use the algorithm method.
1
1 2 . 5
+ 4 . 8
1 7 . 3
3.After simplification, we have:
-(12.5+4.8)=-17.3−(12.5+4.8)=−17.3
4. Therefore, -12.5-4.8=-17.3−12.5−4.8=−17.3.
-17.3−17.3
Which correctly compares 4.06 and 4.6?
A) 4.6 < 4.06
B) 4.6 = 4.06
C) 4.06 > 4.6
D) 4.06 < 4.6
Answer:
B is your answer
Step-by-step explanation:
Final answer:
The correct comparison is that 4.06 is less than 4.6 because when looking at the decimal parts, '0.6' (4.6) is greater than '0.06' (4.06).
Explanation:
To compare the numbers 4.06 and 4.6, we need to look at the decimal parts, since the whole number part (4) is the same for both. In the number 4.06, the decimal part is '06', which is actually '0.06' when read as a fraction of the whole number. On the other hand, 4.6 has a decimal part of '6', which is '0.6' as a fraction of the whole number. When comparing '0.6' and '0.06', it is clear that '0.6' is larger because '6' tenths is greater than '6' hundredths.
Therefore, the correct comparison between 4.06 and 4.6 is 4.06 < 4.6, which corresponds to option D in the question.
Help...i dont know how to solve this
X^2- 64
Answer:
x = ±8
Step-by-step explanation:
X^2- 64
Set this equal to 0
x^2 -64 =0
Add 64 to each side
x^2-64+64 = 64+64
x^2 = 64
Take the square root on each side
x = ±sqrt(64)
x = ±8
Answer:
Step-by-step explanation:
a²-b²=(a+b)(a-b)
x²-64=x²-8²
=(x+8)(x-8)
If f(x) = − 5, what is f(8.6)? 3 4 8 9
Answer:
B or 4
Step-by-step explanation:
Maya scored 32 out of 40 for a Math's test and 41 out of 55 for a science's test. For which test did she score a lower percentage.
Answer:
He score lower on the 41 out of 55
Step-by-step explanation:
32/40 = .80 or 80%
41/55 = 0.75 or 75%
Answer:
Lower score in Science
Step-by-step explanation:
32/40 × 100 = 80%
41/55 × 100 = 74 6/12 %
PLEASE HELP ME!!! I ONLY HAVE 2 HOURS!!!
I am completing a color sheet for my math class. I have a set of markers with 2 purples, 1 black, 3 reds, 2 yellows, and 2 blues. What is the probability that I will randomly select a red marker, keep it, and then randomly select a yellow marker?
A. 47/90
B. 3/10
C. 1/15
D. 2/9
First, we have to add them all together to get the total amount of markers.
2 + 1 + 3 + 2 + 2 = 10
Red: 3/10
Yellow: 2/9
3/10 x 2/9 = 6/90
Simplify: 6/90 = 1/15
C. 1/15 would be your answer.
Hope this helps! Have a great day!
What is the y-intercept when f(0)=6^0
Answer:
(0,1)
Step-by-step explanation:
Any real number to the power of 0, including 6, is equal to 1. Therefore, f(0) is 1, and the y intercept is (0,1). Hope this helps!
I need help solving this and could you give me the answer this time thx 7(4p + 2q + 3r) =?
Answer:
Step-by-step explanation:
7(4p +2q +3r)= 7*4p + 7*2q + 7*3r
= 28p + 14q + 21r
Answer:
28p + 14q + 21r
Step-by-step explanation:
There you go hope that helps