Answers
Answer:
[tex]\sin\theta=\dfrac{15}{17}[/tex]
[tex]?=15[/tex]
Step-by-step explanation:
Use the trigonometry formula
[tex]\cos^2\theta+\sin^2\theta=1[/tex]
You are given that
[tex]\cos \theta=\dfrac{8}{17}[/tex]
Substitute into the first formula
[tex]\left(\dfrac{8}{17}\right)^2+\sin^2\theta=1\\ \\\dfrac{64}{289}+\sin^2\theta=1\\ \\\sin^2\theta=1-\dfrac{64}{289}=\dfrac{289-64}{289}=\dfrac{225}{289}\\ \\\sin \theta=\pm \dfrac{15}{17}[/tex]
Angle [tex]\theta[/tex] is acute angle, then the sine of this angle is positive and
[tex]\sin\theta=\dfrac{15}{17}[/tex]
Related Questions
is √10 rational or irrational
Answers
√10 is irrational because a rational number is a number that is a/b where a and b are integers and b is a nonzero number.√10 does not follow this.
If you need a better explanation just as in the comments.
Happy to help! Please mark as BRAINLIEST! Thanks
Rational numbers are numbers that can be expressed as a ratio (or divided by one)
In a class of 20 students, 17 of the students
passed a prerequisite skills quiz What percent of
the students passed the quiz?
Answers
Answer = 85%
The correct answer is [tex]\(\frac{17}{20} \times 100\%\)[/tex].
To find the percentage of students who passed the quiz, we need to divide the number of students who passed by the total number of students, and then multiply by 100 to convert the fraction to a percentage.
Given that 17 students passed out of 20, the calculation is as follows:
[tex]\[ \text{Percentage of students who passed} = \left( \frac{\text{Number of students who passed}}{\text{Total number of students}} \right) \times 100\% \][/tex]
[tex]\[ \text{Percentage of students who passed} = \left( \frac{17}{20} \right) \times 100\% \][/tex]
This fraction can be simplified to a decimal or a mixed number if necessary, but it is most accurate and precise in its fractional form as given above. To convert it to a decimal, one would divide 17 by 20 and then multiply by 100, which would yield 85%. Thus, 85% of the students passed the quiz.
Two parallel lines are intersected by a third line so that angles 1 and 5 are congruent. 2 parallel horizontal lines are intersected by a third line. On the first horizontal line where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 1, 2, 4, 3. On the second horizontal line, where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 5, 6, blank, blank. Which statement is true about angles 3 and 5? They are acute. They are congruent. They are complementary. They are supplementary.
Answers
Answer:
"They are supplementary" ⇒ last answer
Step-by-step explanation:
* Look to the attached figure
- Two parallel horizontal lines are intersected by a third line
- The angles formed form intersection are labeled on the figure
- From the two parallel lines and
∠5 ≅ ∠1 ⇒ corresponding angles
m∠5 = m∠1
- A linear pair is two angles that are adjacent and form a line and
they are supplementary
∠1 and ∠3 form a line
∠1 and ∠3 are linear pair
* lets prove that ∠3 and ∠5 are supplementary
∵ m∠1 = m∠5 ⇒ corresponding angles
∵ ∠1 and ∠3 form a linear pair
∵ Linear pair are supplementary
∴ m∠1 + m∠3 = 180°
- By substitute ∠1 by ∠5
∴ m∠5 + m∠3 = 180
∴ ∠5 and ∠3 are supplementary
* The true statement is "They are supplementary"
Angles 3 and 5 are congruent because they are alternate interior angles formed by a transversal intersecting two parallel lines. This is supported by the Alternate Interior Angles Theorem.
To determine the relationship between angles 3 and 5 when two parallel lines are intersected by a transversal, we can use the properties of alternate interior angles.
Given that angles 1 and 5 are congruent, we identify that they are alternate interior angles formed by the transversal intersecting two parallel lines. By the Alternate Interior Angles Theorem, since the lines are parallel, angles 1 and 5 are congruent.Angles 3 and 5 in this setup are also alternate interior angles, and by the same theorem, they are congruent.
This leads us to the conclusion that:
Angles 3 and 5 are congruent.
Enter the terms and coeffidents -80+8p-2z
Answers
Step-by-step explanation:
Look at the picture
-80 + 8p - 2z
Terms: -80, 8p, -2z
Coefficients: -80, 8, -2
write a linear equation in slope -intercept form that passes through the points (-8,4) (1,-5)
Answers
[tex]\bf (\stackrel{x_1}{-8}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-8)}}}\implies \cfrac{-9}{1+8}\implies \cfrac{-9}{9}\implies -1[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-1}[x-\stackrel{x_1}{(-8)}]\implies y-4=-(x+8) \\\\\\ y-4=-x-8\implies y=-x-4[/tex]
solve this problem y=(x-3)^2 when x=9
Answers
it basically says y=(9-3)^2
which is y=6^2
which is then y=36
The price of an item has been reduced by 60%. The original price was $55. What is the price of the item now?
Answers
55x.60=33 is the correct answer
Answer:
Step-by-step explanation:
55*.60=$33
SO, 55-33=22THE ITEM IS $22 NOW
What is the solution to the equation 3/7(x+3)+5=3x+2?
Answers
Answer:
5/3
Step-by-step explanation:
i added a picture that will help you solve it.
The solution to the equation[tex]\dfrac{3}{7}(x+3)+5=3x+2[/tex] when "x" is an unknown variable is [tex]\dfrac{5}{3} .[/tex]
Two algebraic expressions separated by an equal symbol between them and with the same value are called equations.
Example = 2x +4 = 12
here, 4 and 12 are constants and x is variable.
To solve the equation[tex]\dfrac{3}{7}(x+3)+5=3x+2[/tex] we can follow these steps:
Multiply \dfrac{3}{7} into the brackets or inside the parentheses
[tex][\dfrac{3}{7}x + \dfrac{3}{7}\times3] + 5 = 3x + 2[/tex]
[tex]\dfrac{3}{7}x +\dfrac {9}{7} + 5 = 3x + 2[/tex]
On solving we get,
[tex]\dfrac{3x+9}{7} = 3x +2-5[/tex]
[tex]\dfrac{3x+9}{7} = 3x -3[/tex]
On cross multiplication we get,
[tex]{3x+9} = 7(3x -3)[/tex]
Opening the parenthesis we get
[tex]{3x+9} = (21x -21)[/tex]
Taking the variables to one side and constants on the right side we get,
[tex]{9+21} = (21x -3x)[/tex]
On further solving we get,
30 = 18 x
Simplify and solve for x:
Divide both sides by 18, and we get
[tex]\dfrac{30}{18} = x[/tex]
Now, in standard form
[tex]\dfrac{5}{3} = x[/tex]
In decimals, we get 1.66666.
Therefore, the solution to the equation [tex]\dfrac{3}{7}(x+3)+5=3x+2[/tex] is [tex]\dfrac{5}{3}[/tex].
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A rectangle is
7 times as long as it is wide. The perimeter is
48 feet. Find the dimensions.
Answers
Answer:
21 by 3
Step-by-step explanation:
3x7=21
21+21=42
3+3=6
42+6=48
The sides of a triangle are a + 3 ¼, 2a, and 7 ½ - a. If a = 4 1/8, what is the length of each of the three sides? Also, find the perimeter of the triangle showing steps for your work.
Answers
Answer: Side one is 7 3/8
Side two is 8 2/8
Side three is 3 3/8
Perimeter is 19
Step-by-step explanation:
The first side is a+3 1/4
the second side is 2a
The third side is 7 1/2-a
Plug 4 1/8 in for a
First side 4 1/8+3 1/4
Find the common denomnator which is 8
4 1/8+3 2/8
7 3/8
First side is 7 3/8
Second side 2(4 1/8)=4 1/8 +4 1/8= 8 2/8
Third side is 7 1/2-4 1/8
Find the common denominator which is 8
7 4/8-4 1/8= 3 3/8
Third side is 3 3/8
The perimeter is adding all the three sides together
7 3/8+8 2/8+ 3 3/8=18 8/8
Reduce 18 8/8=18 +1=19
Answer:
Perimeter = 19 units
Step-by-step explanation:
Given a = 4 1/8
[tex]Side1 = a + 3\frac{1}{4}\\Side2 = 2a\\Side3 = 7\frac{1}{2}-a[/tex]
The next step is substituting the a value in the expressions:
[tex]Side1 = 4\frac{1}{8}+ 3\frac{1}{4}\\Side2 = 2*(4\frac{1}{8})\\Side3 = 7\frac{1}{2}-4\frac{1}{8}[/tex]
Then, fractions with different denominators must be converted to the same denominator. Also, the multiplication of a whole number by a mixed number can be done by using distributive law:
[tex]Side1 = 4\frac{1}{8}+ 3\frac{2}{8}\\Side2 = 8\frac{2}{8}\\Side3 = 7\frac{4}{8}-4\frac{1}{8}[/tex]
[tex]Side1 = 7\frac{3}{8}\\Side2 = 8\frac{1}{4}\\Side3 = 3\frac{3}{8}[/tex]
Now, the perimeter is the sum of all the sides. Therefore, the perimeter is:
[tex]Perimeter = 7\frac{3}{8} + 8\frac{1}{4} + 3\frac{3}{8}[/tex]
Which is 19 units.
Write 10 x 10 x 10 x 10 x 10 x 10 with an exponent. Explain how you decided what exponent to write
Answers
10x10x10x10x10x10=1000000
[tex] {10}^{6} [/tex]
means 10x10x10x10x10x10
as it's basically saying 10 is multiplied by itself 6 times which gives you 1000000
The expression 10 × 10 × 10 × 10 × 10 × 10 can be written with an exponent as [tex]10^{6}[/tex]
What is an exponent?In Mathematics and Geometry, an exponent can be represented or modeled by this mathematical expression;
[tex]b^n[/tex]
Where:
the variables b and n are numbers (numerical values), letters, or an algebraic expression.n is known as a superscript or power.Based on the information provided above, we can logically deduce the following expression;
10 × 10 × 10 × 10 × 10 × 10
[tex]10^{1+1+1+1+1+1}=10^{6}[/tex]
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what is the value of x?
AC= 32
Answers
8x + 8 = 32
8x = 32 - 8
8x = 24
x = 24 ÷ 8
x = 3
hope this was helpful!
Your welcome:)
1.) Michelle works at Bloomingdale's and earns a 20% commission for her daily sales. Yesterday, Michelle
sold $2,235 worth of merchandise. What was her commission?
Answers
Answer:
$447
Step-by-step explanation:
2,235 multiplied by .20
2235(1.25)=2682
2682-2235=447
Answer Michelle’s commission was $447
15 - 2(3 - 2x) = 46
Answers
Answer:
x=33
Step-by-step
subtract 15 and 2 you get 13
13 times 3 =39
subtract 39 with 39 and 46 with 39
at the end you will get -26x=7
reverse negative into positive and then add -26 with 26 and you will be left with x and then you add 7 with 26 and your answer is
x=33
-2 (3-2x) = 31
3-2 = -31/2
-2x = -31/2 - 3
-2x = -37/2
X = 37/2/2
X = 37/2 x 2
X= 37/4
Represent the geometric series using the explicit formula.
12, −36, 108, −324, …
f(n) = f(n − 1) ⋅ (−3)
f(n) = f(n − 1) ⋅ (3)
f(n) = 12 ⋅ (−3)(n−1)
f(n) = 12 ⋅ (3)(n−1)
Answers
The explicit formula for the geometric sequence 12, -36, 108, -324, ... is f(n) = 12 * (-3)^(n-1), where 'n' is the term number.
Explanation:The series provided is a geometric series. In a geometric series, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio, denoted by 'r'. In our given series 12, -36, 108, -324, ..., you can determine that the common ratio (r) is -3. Now, using the formula for a geometric sequence given by f(n) = a * r^(n-1), where 'a' is the first term (12 in this case) and 'n' is the term number, we can write the explicit formula as
f(n) = 12 * (-3)^(n-1).
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The geometric series is represented by the explicit formula f(n) = 12 * (-3)^(n-1)
Explanation:The given sequence is an example of a geometric progression where each term is found by multiplying the previous term by a constant ratio. In this case, the common ratio is -3.
The explicit formula for a geometric series is given by f(n) = a * r^(n-1), where 'a' is the first term and 'r' is the common ratio. In this sequence, the first term (a) is 12 and the common ratio (r) is -3.
Plugging in the values into the formula, we can write the explicit formula for this geometric series as f(n) = 12 * (-3)^(n-1).
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Simplify: 7 exponent9 7 exponent3
Answers
Answer:
7^9= 40,353,607
7*7*7*7*7*7*7*7*7=40,353,607
7^3 =343
7*7*7=343
positive whole numbers less than 9
Answers
0 is a negitave number
4 can be one too because its less than 9 and its a whole number
Hope it helps :)
the graph of y= -4×+7 is
Answers
Answer:
Step-by-step explanation:
The graph of y= -4×+7 is a straight line with slope -4 and y-intercept 7. Please do not use × to represent the independent variable; use x instead. × represents multiplication.
To graph this function, first plot the y-intercept, b, which is (0, 7).
Next, starting with your pencil point at (0, 7), move the point 1 unit to the right and plot another point (which will be (1, 7) ). Now move your pencil point 4 units down and plot your third point, which will be (1, 3).
Finally, draw a straight line thru the first and third points, that is, thru (0, 7) and (1, 3). Notice how this line has the slope -4 and the y-intercept (0, 7).
How do I get from this guy 3/2/(15/4) to 2/5?
Answers
[tex]\bf \cfrac{~~\frac{3}{2}~~}{\frac{15}{4}}\implies \cfrac{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix}2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{\underset{5}{~~\begin{matrix} 15 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \cfrac{2}{5}[/tex]
To simplify the expression 3/2/(15/4), first convert the division of fractions to multiplication by the reciprocal, giving (3/2) * (4/15). Multiply the numerators and denominators and then reduce the fraction by dividing both by their greatest common divisor. The simplified result is 2/5.
To simplify the expression 3/2/(15/4), you would follow these steps:
Understand that dividing by a fraction is the same as multiplying by its reciprocal. In this case, 15/4 is the divisor, so we take its reciprocal which is 4/15.Multiply the original fraction 3/2 by the reciprocal of 15/4 which is 4/15.Perform the multiplication: (3/2) * (4/15).First, simplify by multiplying the numerators together and the denominators together: 3 * 4 = 12 and 2 * 15 = 30.So, you have 12/30, which can be reduced. Divide both the numerator and denominator by their greatest common divisor (GCD), which is 6.12 / 6 = 2 and 30 / 6 = 5, therefore the fraction simplifies to 2/5.Following these steps results in the original expression 3/2/(15/4) simplifying to 2/5.
- 7(2-1) = 28
The solution is?
Answers
Answer:
Is there a x somewhere or is that litteraly how the equation is?
If so, -7 multiplied by 2 is -14,
-1 times -7 is 7,
add it together and you get
-7=28,
you could add 7 to both sides or subtract 28 from both sides and you'll get either 0=35 or -35=0
which would make the solution false since both sides are not the same
What is the slope of the line passing through the points
(-1,7) and (4,-1)
Answers
Answer:
(5 , -18)
Hope this helps.
From your vro Que
Answer: [tex]\dfrac{-8}{5}[/tex]
Step-by-step explanation:
The slope of a line passing through points (a,b) and (m,n) is given by :-
[tex]\text{Slope}=\dfrac{n-b}{m-a}[/tex]
Given points : (-1,7) and (4,-1)
Then, the slope of the line passing through the points (-1,7) and (4,-1) will be :-
[tex]\text{Slope}=\dfrac{-1-7}{4-(-1)}\\\\=\dfrac{-8}{4+1}\\\\=\dfrac{-8}{5}[/tex]
Hence, the required slope = [tex]\dfrac{-8}{5}[/tex]
4. Thirty divided by seven times a number
A. 30 + 7n
B. in
30
30(7n)
None of the above
30:7.
Answers
Answer:
30/7n
Step-by-step explanation:
let n be the no.
seven times a no. is 7n
so ans is 30/7n
which inequality symbols do i use for a-d if can help please comment picture of how number line will look
Answers
Answer:
a. <
b. >
c. >
d.<
Step-by-step explanation:
6 1/4 is less than 6 2/3
-3 is greater than -4
-5 is greater than -5.2
-5 is lesson that -4.8
Determine the slope and the y intercept. Y= -2. Then use the slope and the y- intercept to graph the equation
Answers
Answer:
y-intercept: [0, -2]; 0 = m
Step-by-step explanation:
Anything set to equal y is what is known as a zero rate of change [slope] because it is a horizontal line.
I am joyous to assist you anytime.
Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes. x+y=6
Answers
Answer:
x-intercept = 6 → (6, 0)y-intercept = 6 → (0, 6)Step-by-step explanation:
x + y = 6
x-intercept is for y = 0. Substitute:
x + 0 = 6
x = 6
y-intercept is for x = 0. Substitute:
0 + y = 6
y = 6
Your bank offers the Bradys a 30-year mortgage with a rate of 5%. At that rate, the monthly payments for principal and interest on the loan will be $5.37 for every $1,000 financed.
Answers
Answer:
Your answer would be 30a - year
Hope this helped. Please mark brainliest if this helped.
Monthly payment is the principal and interest payment for each year for $1000 financed. he payment of the mortgage is $4639.75
Given information-The period for which the mortgage offered is 30 years.
The rate for which the mortgage offered is 5 percent.
The interest on the loan is $5.37 for every $1000 financed.
Monthly paymentMonthly payment is the principal and interest payment for each year for $1000 financed.
He has to pay for 30 years. As there is 12 month in one year. Therefore the total months in 30 years,
[tex]n=30\times12\\ n=360[/tex]
Thus the value of n is 360.
The formula for the principal amount can be given as,
[tex]P=a\times\dfrac{r}{n} [/tex]
Put the values
[tex]5.37=a\times \dfrac{0.41667}{360} \\ [/tex]
Solving it for the a
[tex]a=4639.75[/tex]
Thus the payment of the mortgage is $4639.75.
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solve each compound inequality (show your work!)
[tex] - 6 < 2x - 4 < 12[/tex]
[tex]4x \leqslant 12 \: and - 7x \leqslant 21[/tex]
[tex]15x > 30 \: or \: 18x < - 36[/tex]
Answers
Answer: -1 < x < 8
x = 3
x ≠ 2
Step-by-step explanation:
Isolate x in the middle. Perform operations to all 3 sides.
-6 < 2x - 4 < 12
+4 +4 +4
-2 < 2x < 16
÷2 ÷2 ÷2
-1 < x < 8
**************************************************************************
Isolate x. Solve each inequality separately. Remember to flip the sign when dividing by a negative.
4x ≤ 12 and -7x ≤ 21
÷4 ÷4 ÷-7 ÷-7
x ≤ 3 and x ≥ 3
Since it is an "and" statement, x is the intersection of both inequalities.
When is x ≤ 3 and ≥ 3? when x = 3
****************************************************************************
Isolate x. Solve each inequality separately.
15x > 30 or 18x < -36
÷15 ÷15 ÷18 ÷18
x > 2 or x < 2
Since it is an "or" statement, x is the union of both inequalities.
When we combine the inequalities, x is every value except 2.
x ≠ 2
Find x please!!!!!!!!!
Answers
Solve 6+2x^2-3x=8x^2
Answers
Answer: 6x^2+3x-6
Step-by-step explanation:
6+2x^2-3x=8x^2
-2x^2. -2x^2
6-3x=6x^2
= 6x^2+3x-6
Answer:
Step-by-step explanation:
Given the function f(x)=x2+2x+1, find:
f( 2a−3/5 )
Answers
Answer:
[tex]f(2a-\frac{3}{5})=4a^2+\frac{8a}{5}+\frac{4}{25}[/tex]
Step-by-step explanation:
we have
[tex]f(x)=x^{2} +2x+1[/tex]
Find [tex]f(2a-\frac{3}{5})[/tex]
That means -----> substitute the value of [tex]x=(2a-\frac{3}{5})[/tex] in the function and evaluate
[tex]f(2a-\frac{3}{5})=(2a-\frac{3}{5})^{2} +2(2a-\frac{3}{5})+1[/tex]
[tex]f(2a-\frac{3}{5})=(4a^2-\frac{12a}{5}+\frac{9}{25})+(4a-\frac{6}{5})+1[/tex]
[tex]f(2a-\frac{3}{5})=4a^2+\frac{8a}{5}-\frac{21}{25}+1[/tex]
[tex]f(2a-\frac{3}{5})=4a^2+\frac{8a}{5}+\frac{4}{25}[/tex]