Answer:
[tex]x=k\frac\pi2; k\in \mathbb{Z}[/tex]
Step-by-step explanation:
Let's use the formulas that change a sum of two sines into a product:
[tex]sin\ p + sin\ q =2 sin{\frac{p+q}2}cos{\frac{p-q}2}[/tex]
[tex]sin 3x+sinx =2sin \frac{3x+x}2 cos \frac{3x-x}2 = 2(sin2x)(cosx)=0[/tex]
At this point it's either [tex]sin 2x =0 \implies 2x= k\pi \rightarrow x = k\frac{\pi}2[/tex]
or [tex]cosx=0 \rightarrow x=\frac\pi2+ k\pi = (2k+1)\frac\pi2[/tex]
with the usual condition of [tex]k\in \mathbb{Z}[/tex].
Now if you look at both sets of solutions, first one considers all multiples of [tex]\frac\pi2[/tex], while the second only the odd multiples. it means that the first includes the second.
If ABCD is a parallelogram, m
Answer:
ABCD are the first 4 letters ina alphabet sooooo brooo wheres the parallelogram??
Step-by-step explanation:
A triangle has sides measuring 7 centimeters and 13 centimeters that form an angle measuring 44°. Which of these is CLOSEST to the length of the third side of the triangle? A) 8.1 centimeters B) 8.7 centimeters C) 9.3 centimeters D) 9.9 centimeters
Answer:
9.3 centimeters
Step-by-step explanation:
Help help math math
Answer:
1
Step-by-step explanation:
We can use the slope formula to find the slope
m = ( y2-y1)/(x2-x1)
= ( -15 - -14) / ( -11 - (-10))
= (-15+14) /(-11 + 10)
= -1 / -1
= 1
Answer:
The answer is 1
Step-by-step explanation:
The manager of a store increases the price of a popular product by 9%. Let t be the original price of the product. The new price is t+0.09t. Write an equivalent expression by combining like terms. If the original price was $15.99, estimate the new price by first rounding the original price to the nearest dollar.
Answer:
new equation : 1.09t = new price
Step-by-step explanation:
1.09(15.99) = 17.4291
it's about $17
volume of
a
cone
are
The
and a cylinder
in 9
the ratio 1:9 respectively. The height and diameter
of
16cm and 14cm. The diameter of
the
28cm. Find the height of the cylinkes.
the
cone
are
15
cylinder
The given ratio of the volumes indicates that the volume of the cylinder is 9 times the volume of the cone.
The height of the cylinder is 12 cmReasons:
The given parameter are;
Ratio of the volume of the cone to the cylinder to the 1 : 9
The height and diameter of the cone are; 16 cm and 14 cm
The diameter of the cylinder = 28 cm
Required:
To find the height of the cone:
Solution:
[tex]\displaystyle The \ volume \ of \ a\ cone = \frac{1}{3} \cdot \pi \cdot r^2 \cdot h[/tex]
[tex]\displaystyle The \ volume \ of \ the \ cone = \frac{1}{3} \times \pi \times \left(\frac{14}{2} \right)^2 \times 16 = \mathbf{ \frac{784}{3} \cdot \pi}[/tex]
Volume of a cylinder, V = π·r²·h
[tex]\displaystyle Radius \ of \ the \ cylinder = \frac{28 \, cm}{2} = 14 \, cm[/tex]
Volume of the cylinder, V = π × 14² × h = 2,352·π
The volume of the cylinder = 9 × The volume of the cone
Therefore;
[tex]\displaystyle Volume \ of \ the \ cylinder =9 \times \frac{784}{3} \cdot \pi = \mathbf{2,352 \cdot \pi}[/tex]
[tex]\displaystyle Height \ of \ the \ cylinder, \, h = \mathbf{\frac{2,352 \cdot \pi}{14^2 \cdot \pi}} = 12[/tex]
The height of the cylinder, h = 12 cm
Learn more about ratios here:
https://brainly.com/question/4713715
Write an equation in slope-Intercept form for the line with slope 2 and y-Intercept - 1. Then graph the line.
Answer:
Solution given in the photo
PLEASE HELP ME IN THIS QUESTION THE ASSIGNMENT IS DUE IN 2 MINUTES
Dog food is sold in 7 pound bags. Sketch
a graph to show the weight of dog food
purchased by a customer who buys 0, 1, 2, 3, or 4 bags. Tell whether the graph is continuous or discrete.
Answer:
Continuous
Step-by-step explanation:
The radioactive compound 14CO2 may be used as a tracer to study metabolism in plants. Suppose that a compound isolated from a plant exhibited 28, 32, 27, 39 and 40 counts of radioactive decays per minute. A blank sample used to measure the background counts of the radiation counter gave 28,21, 28 and 20 counts per minute. It appears that the isolated compound gives more counts than those from background. Can we be 95% confident that the compound is indeed radioactive?
Using the t-distribution, it is found that since the test statistic is more than the critical value for the right-tailed test, it can be conclude that the isolated compound gives more counts than those from background, and hence, we can be 95% confident that the compound is indeed radioactive.
At the null hypothesis, it is tested if isolated compounds do not give more counts than those from background, that is:
[tex]H_0: \mu_1 - \mu_2 \leq 0[/tex]
At the alternative hypothesis, it is tested if the give more counts, that is:
[tex]H_1: \mu_1 - \mu_2 > 0[/tex]
Using a calculator, the mean and the standard deviation for each sample are given by:
[tex]\mu_1 = 33.2, s_1 = 6.058[/tex]
[tex]\mu_2 = 24.25, s_2 = 4.35[/tex]
Considering the sample sizes of 5 and 4, respectively, the standard errors are given by:
[tex]s_1 = \frac{6.058}{\sqrt{5}} = 2.71[/tex]
[tex]s_2 = \frac{4.35}{\sqrt{4}} = 2.175[/tex]
For the distribution of differences, the mean and standard error are given by:
[tex]\overline{x} = \mu_1 - \mu_2 = 33.2 - 24.25 = 8.95[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{2.71^2 + 2.175^2} = 3.4749[/tex]
The standard error was found from the standard deviation for each sample, hence, the t-distribution is used.
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis, hence:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{8.95 - 0}{3.4749}[/tex]
[tex]t = 2.58[/tex]
The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with 5 + 4 - 2 = 7 df and a 0.05 significance level is of [tex]t^{\ast} = 1.895[/tex]
Since the test statistic is more than the critical value for the right-tailed test, it can be conclude that the isolated compound gives more counts than those from background, and hence, we can be 95% confident that the compound is indeed radioactive.
A similar problem is given at brainly.com/question/24826023
(x^2−x−6x^2−8x+16)/(x2−x−12)
What number cannot be the value of x in the expression above? Why?
Question 12 options:
-3 and 4 cannot be the values of x in the given expression
The expression is given as:
[tex]\frac{(x^2-x-6x^2-8x+16)}{(x^2-x-12)}[/tex]
Start by equating the denominator to 0
[tex]x^2 - x - 12 = 0[/tex]
Expand the above equation
[tex]x^2 - 4x + 3x - 12 = 0[/tex]
Factorize the equation
[tex]x(x - 4) + 3(x - 4) = 0[/tex]
Factor out x - 4
[tex](x + 3) (x - 4) = 0[/tex]
Split
[tex](x + 3)= 0\ or\ (x - 4) = 0[/tex]
Remove brackets
[tex]x + 3= 0\ or\ x - 4 = 0[/tex]
Solve for x
[tex]x =- 3\ or\ x = 4[/tex]
Hence, -3 and 4 cannot be the value of x in the given expression
Read more about expressions at:
https://brainly.com/question/2972832
Given the formula A= P(1+r/n)nt you are investing $2,150 in savings account with an
interest rate of 3.315% compounded monthly. How much will you investment be worth after 15 years?
Answer:
3532.59341
Step-by-step explanation:
P= 2150
r= 3.315%
n= 12
t= 15
Simple interest ending balance $41,900 at 4% for 2 years?
The simple interest is $3352.
Step-by-step explanation:Using PRT/100, we can find the interest.
=> 41,900 x 4 x 2/100 => 419 x 4 x 2=> $3352Conclusion:Therefore, the simple interest is $3352.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
if 5a+b=14 then a = what
explain how you got it pls
Answer:
[tex]a = \frac{14 - b}{5}[/tex]
Step-by-step explanation:
The rule to know and follow is:
You can add, subtract, multiply or divide by anything so long as the same thing is done to both sides of the equals sign;
5a + b = 14
If we want to get: "a = ...", then we use the rule to isolate the variable a on one side of the equation;
Firstly, we subtract b from both sides:
5a + b - b = 14 - b
5a = 14 - b
Then, divide both sides by 5:
[tex]\frac{5a}{5} = \frac{14 - b}{5} \\\\ a = \frac{14 - b}{5}[/tex]
Could somebody please explain this to me?
Answer: call 911
Step-by-step explanation: call 911
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Draw a dilation of the figure using the given scale factor )
Answer:
A (2,2) B (4, -2) C (-4,0)
Step-by-step explanation:
K = 2
K is the scale factor so the y and x distance between the points will double
just take to coordinates and multiply them by 2
A 1,1 new 2,2
B 2, -1 new 4,-2
C -2,0 new -4,0
2 3/7 + (-1 3/4) i need help please
Answer:
1/28
Step-by-step explanation:
Which pair of expressions are equivalent?
A
3x+2+2x and 7x
B
8(x−3) a
nd 8x−24
C
4(x+1) and 4x+1
D
3(5x) and 8x
How many yards is 24 feet
Answer:
8 yards
Step-by-step explanation:
1 yard is equal to 3 feet, so we just do 24/3 = 8 yards
Answer:
8
Step-by-step explanation:
1 feet is 3 yards so 24 yards is 8
The amount of milk in a carton is modeled by the equation y = 64 - 4x. The number of ounces of milk left
is represented by y. The number of servings of milk poured from the carton is represented by x.
4.) How many ounces of milk are in an unopened carton?
5.) How many ounces of milk are in each serving?
Answer:
-Below.
Step-by-step explanation:
4) When the carton is unopened the number of servings x = 0.
So there are 64-4(0) = 64 ounces in an unopened carton.
5) When all the milk has been poured out no. ounces left (y) = 0 so
64 - 4x = 0
4x = 64
x = 16
So each serving contains 16 ounces of milk.
Pls help fast i will mark brainlyest
Answer:
x = 20
Hope you could get an idea from here.
Doubt clarification - use comment section
How do you multiply a fraction and a whole number? Please explain step by step to get marked as brainliest!
Answer: 1 1/2 x 4 4/7
= 3/2 x 32/7
= 96/14
Step-by-step explanation:
1. Write the whole number as a fraction with a denominator of 1.
2. Multiply the numerators.
3. Multiply the denominators
4. Simplify. If needed, if your answer is greater than 1, you may want to write your answer as a mixed number.
Factor the following expression. Type x^2 for 22 as needed. If it is not factorable, type unfactorable.
22-8x+16
Answer:
63
Step-by-step explanation:
you divide and add then subtract
Select the correct answer.
Simplify the following expression.
Answer:
B. 1/3
Step-by-step explanation:
This question is designed to show if you know the exponent rules. Exponent Rules are short cuts. If you are multiplying two terms and they both have the same base (the big bottom number), then you could ADD the exponents (the small font raised numbers) Here the base is 3 in both terms. We keep that base. Then add 2/5 and -7/5 to get -5/5. This is just -1.
Another Exponent Rule is how to use negative exponents. So far we have 3^-1 (that means three to the negative one power)
In order to make that negative exponent positive, you just move it across the fraction bar. So we would lower it below the fraction bar to make it a positive one exponent. So you end up with 1/3
M is the midpoint of the segment. Find the length of XM.
Answer:
Step-by-step explanation:
4x+3=3x+5
x+3=5
x=2
Subsitute: 4x+3=11
XM=11
An ice cream stand uses the expression to determine the cost (in dollars) of an ice cream cone that has scoops of ice cream.2 + 0.5x2+0. 5x2, plus, 0, dot, 5, xxxx
How much does an ice cream cone with scoops cost?55
Answer:
answer: 0
Step-by-step explanation:
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
(x+4)•(x-1)
——————————— • 2 = 0 • 2
2
Now, on the left hand side, the 2 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
(x+4) • (x-1) = 0
7.2 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
simple form
x = 1
x = -4
5. How much would d dollars earn in one year at thē rate of p percent compounded annually?
Answer:
a
Step-by-step explanation:
a
Please solve the question on the file.
Answer:
Step-by-step explanation:
they arent similar because the ratio of 8 to 14 and 10 to 18 arent the same.
answer pls having problem in this
[tex]\dfrac{\sqrt[3]{343}}{\sqrt[3]{-343}}=\dfrac{\sqrt[3]{343}}{-\sqrt[3]{343}}=-1[/tex]
Find the Values of X and Y
X=
Y=
Answer:
14 and 12
Step-by-step explanation:
What is 10% of 75? Use the double number line below to label your work and answer.
Answer: the answer is 7.5
Step-by-step explanation: