What is 1 and 3 5ths divided by 2 and one half
Answers
1 3/5 converts to 8/5
2 1/2 converts to 5/2
8 x 2 = 16
5 x 5 = 25
final answer: 16/25
hope this helps
Related Questions
What is the length of 3rd side of each triangle?
Answers
The sum of squares of two sides is equal to the square of the third side.
Finding the Third Side of a Triangle with Two Sides
Let's assume that the triangle is right-angled, as the third side of a right-angled triangle can only be found when the other two sides are known.
According to Pythagoras' Theorem, the sum of squares of two sides is equal to the square of the third side.If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root: a = √(c² - b²)If leg b is unknown, then: b = √(c² - a²)For hypotenuse c missing, the formula is: c = √(a² + b²)A right-angle triangle is what?
This particular sort of triangle adheres to the Pythagoras theorem and may be calculated using the trigonometry tool.
We are aware that the right-angled triangle follows Pythagoras' Theorem.
According to the Pythagorean Theorem, the third side's square equals the sum of the first two sides' squares.
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The complete question should be:
What is the length of 3rd side of a triangle?
In triangle EFG, m∠E = 95.2° and m∠F = 43.7°. Determine the measure of the exterior angle to ∠G.
138.9°
84.8°
51.5°
41.1°
Answers
95.2 + 43.7 = 138.9
Answer: 138.9
The measure of the exterior angle to ∠G is 138.9°.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
Given, In triangle EFG, m∠E = 95.2° and m∠F = 43.7°.
We know the sum of all the interior angles in a triangle is 180°.
We also know that the measure of an exterior angle in a triangle is the sum of the two opposite interior angles.
∴ The measure of the exterior angle to m∠G is = m∠E + m∠F.
= 95.2° + 43.7°.
= 138.9°.
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the fractiions 3/k,4/k ,dand 5/k are in lowest terms. what could be the value of k if the numbers are 48,49,50,51,52?
Answers
The value of k could be 48, 49, 50, 51, or 52, as these all result in the fractions being in lowest terms.
What could be the value of k if the numbers are 48,49,50,51,52?To further explain, let's look at each of the possible values of k and see how they result in the fractions being in lowest terms:
If k = 48, then the fractions are 3/48, 4/48, and 5/48. These can all be simplified to 1/16, 1/12, and 1/9.6, respectively, which are in lowest terms.If k = 49, then the fractions are 3/49, 4/49, and 5/49. These cannot be simplified further, so they are already in lowest terms.If k = 50, then the fractions are 3/50, 4/50, and 5/50. These can all be simplified to 1/16.666..., 1/12.5, and 1/10, respectively, which are in lowest terms.If k = 51, then the fractions are 3/51, 4/51, and 5/51. These can all be simplified to 1/17, 1/12.75, and 1/10.2, respectively, which are in lowest terms.If k = 52, then the fractions are 3/52, 4/52, and 5/52. These can all be simplified to 1/17.333..., 1/13, and 1/10.4, respectively, which are in lowest terms.More information about Lowest terms here: https://brainly.com/question/8933457
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23x² + 6x + 7 please help
Answers
Answer:
the expression can be factored into (x+4)(23x + 7) and it is a product of two binomials.
Step-by-step explanation:
The expression 23x² + 6x + 7 is in the form of a quadratic equation. A quadratic equation is an equation in the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. In this case, the coefficients of the x², x, and the constant term are a = 23, b = 6, c = 7.
One way to factor a quadratic equation is by using the factoring by grouping method, where we group the terms in pairs and factor out the greatest common factor (GCF) from each group.
Here is one way to factor this equation:
23x² + 6x + 7 = (23x² + 6x) + 7
= (23x² + 6x) + 7
= (23x² + 6x + 6x) + 7
= (23x² + 12x) + 7
= (23x(x) + 3x(4)) + 7
= (23x(x+4) + 7)
= (x+4)(23x + 7)
So the expression can be factored into (x+4)(23x + 7) and it is a product of two binomials.
It's important to note that the above expression factors into a product of two binomials and not two factors of 23x² + 6x + 7
You can also use Quadratic formula to solve the above expression if this method seems confusing.
A game has a deck of cards with 10 red cards and 4 blue cards. You randomly choose one card and without replacing it choose another card. What is the probability of choosing a red card and then a blue card?
Answers
Answer:
21.97%
Step-by-step explanation:
In 1895, the first U.S. Open Goif Championship was held. The winner's prize money was $150, In 2016 , the winner's check was $2.3 million. What was the percentage increase per year in the winner's check over this period? foo not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e,9. 32.16.)
Answers
Rounded to two decimal places, the percentage increase per year in the winner's check over this period is approximately 15,332.33%.
To calculate the percentage increase per year in the winner's check over the period from 1895 to 2016, we can use the following formula:
Percentage increase = [(Final value - Initial value) / Initial value] * 100
Initial value: $150
Final value: $2,300,000
Number of years: 2016 - 1895 = 121 years
Percentage increase = [(2,300,000 - 150) / 150] * 100
= (2,299,850 / 150) * 100
= 15,332.33%
Rounded to two decimal places, the percentage increase per year in the winner's check over this period is approximately 15,332.33%.
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7/16 times 2 PLEASE ANSWER SIMPLIFY AND ANSWER HAS TO BE A SIMPLIFIED FRACTION PLS PLS PLS MAKE IT A MIXED NUMBER
Answers
Answer:
\(\frac{14}{16}\) simplified to \(\frac{7}{8\\}\)
Step-by-step explanation:
\(\frac{7}{16} times \frac{2}{1} you get \frac{14}{16} \\this \\simplifies \\to \frac{7}{8}\)
I have a math question could I send you a picture of that to solve that for me
Answers
2) In these problems, let's make use of the Law of Cosines since in each triangle we have their legs and just want to know the measure of one angle.
a) Let's begin with that, bearing in mind the following formula:
\(\begin{gathered} a^2=b^2+c^2-2bc\cdot\cos (A) \\ r^2=s^2+t^2-2st\cdot cos(R) \end{gathered}\)Note that the leg "r" is opposite to the angle (R):
\(r^2=s^2+t^2-2st\cdot cos(R)\)But note that we have a right triangle and we don't know the side "t". So, let's use the Pythagorean Theorem to find the missing side "t":
\(\begin{gathered} a^2=b^2+c^2 \\ 10^2=8^2+c^2 \\ 100-64=c^2 \\ c=\sqrt[]{36} \\ c=6 \end{gathered}\)So now, let's get back to the Cosines Law:
\(\begin{gathered} r^2=s^2+t^2-2st\cdot cos(R) \\ 8^2=10^2+6^2-2(10)(6)\cdot\cos (R) \\ 64=100+36-120\cos (R) \\ 64=136-120\cos (R) \\ 120\cos (R)=136-64 \\ \frac{120\cos (R)}{120}=\frac{72}{120} \\ R=\cos ^{-1}(\frac{72}{100}) \\ R=43.94\approx44^{\circ} \end{gathered}\)b) In this one, we can see the angle 38º and the missing angle "A". We can use the Law of the Sines to find that angle.
\(\begin{gathered} \frac{c}{\sin(C)}=\frac{b}{\sin (B)} \\ \frac{55}{\sin(38)}=\frac{85}{\sin (B)} \\ 55\sin (B)=85\cdot\sin (38) \\ \frac{55\sin (B)}{55}=\frac{85\cdot\sin (38)}{55} \\ \sin (B)=0.95147 \\ B=\sin ^{-1}(0.95147) \\ B=72.5865\approx73^{\circ} \end{gathered}\)Now, that we know angle B, we can write out this equation since the sum of the interior angles is 180º
\(\begin{gathered} \angle A+\angle B+\angle C=180^{\circ} \\ \angle A+73+38=180 \\ \angle A=180-(73+38) \\ \angle A=69^{\circ} \end{gathered}\)c) Finally, we can apply the Cosines Law for this triangle:
\(\begin{gathered} p^2=q^2+r^2-2qr\cdot\cos (P)_{} \\ 2.5^2=1.7^2+2.2^2-2(1.7)(2.2)\cos (P) \\ 6.25=2.89+4.84-7.48\cos (P) \\ 6.25=7.73-7.48\cos (P) \\ 6.25-7.73=-7.48\cos (P) \\ -1.48=-7.48\cos (P) \\ P=\cos ^{-1}(\frac{1.48}{7.48}) \\ P=78.58^{\circ}\approx79^{\circ} \end{gathered}\)2) Thus the answer is:
\(\angle R=44^{\circ},\angle A=69^{\circ},\angle P=79^{\circ}\)
When Angela was born, her grandparents deposited $2,500 into a college savings account paying 3% interest compounded CONTINUOUSLY. Using the formula, A=Pert, how many years until the account is worth $20,000. Round to the nearest year.
Answers
Answer:
akhavkreugvakrehfgv
Step-by-step explanation:
consider an undirected random graph of eight vertices. the probability that there is an edge between a pair of vertices is 1/2. what is the expected number of unordered cycles of length three?
Answers
In this random graph, we expect to find approximately 14 unordered cycles of length three.
In an undirected random graph of eight vertices, where the probability of an edge existing between any pair of vertices is 1/2, we can calculate the expected number of unordered cycles of length three.
To determine the expected number, we need to analyze the probability of forming a cycle of length three through any three vertices.
To form a cycle of length three, we must select three distinct vertices. The probability of selecting a particular vertex is 1, and the probability of not selecting it is (1 - 1/2) = 1/2. Hence, the probability of selecting three distinct vertices is (1)(1/2)(1/2) = 1/4.
Since we have eight vertices, the number of ways to choose three distinct vertices is given by the combination formula C(8, 3) = 8! / (3! * (8 - 3)!) = 56.
Therefore, the expected number of unordered cycles of length three is the product of the probability and the number of ways to choose the vertices: (1/4) * 56 = 14.
Therefore, in this random graph, we expect to find approximately 14 unordered cycles of length three.
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(5 MARKS) Prove by CVI that every natural number n > 2 is a product of prime numbers. NOTE. A prime number p is defined to satisfy (a) p > 1 and (b) the only divisors of p are 1 and p.
Answers
Every natural number n > 2 is a product of prime numbers.
To prove that every natural number n > 2 is a product of prime numbers, we will use the principle of complete induction (CVI).
First, let's establish the base case. For n = 3, we know that 3 is a prime number, and therefore it is a product of prime numbers. This satisfies the base case.
Now, let's assume that for some natural number k > 2, every natural number between 3 and k (inclusive) is a product of prime numbers. We want to prove that this implies that the next natural number, k+1, is also a product of prime numbers.
There are two possibilities for k+1: either it is a prime number itself, or it is composite (i.e. not prime). Let's consider each case separately.
Case 1: k+1 is a prime number.
If k+1 is a prime number, then it is obviously a product of prime numbers (since it is itself prime). Therefore, our assumption that every natural number between 3 and k is a product of prime numbers implies that k+1 is also a product of prime numbers.
Case 2: k+1 is composite.
If k+1 is composite, then it can be written as the product of two natural numbers a and b, where a and b are both greater than 1. Since a and b are both less than k+1, we know that they are both products of prime numbers (by our assumption). Therefore, k+1 can be written as the product of prime numbers (namely, the prime factors of a and b).
Since we have established the base case and shown that our assumption implies the next natural number is a product of prime numbers, we can conclude by CVI that every natural number n > 2 is a product of prime numbers.
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The circumference of a circle with diameter is 28 is
Answers
Answer:
the answer is 87.96
Step-by-step explanation:
Answer:
87.92 units
Step-by-step explanation:
circumference = D x Pi = 28(3.14) = 87.92
Find an equation of the line in the form ax +by=c, where a, b, and care integers with no factor common to all three and a 20. The line with y-intercept 2 and perpendicular to x + 4y = 19Te equation of the line is
Answers
The equation of the line with value of a = 20 in the standard form ax + by =c is equal to 20x - 5y = -10.
An equation of the line is,
ax + by = c
Equation is,
x + 4y = 19
Equation can be rearranged into the standard form,
⇒ x + 4y = 19
⇒4y = -x + 19
⇒y = (-1/4)x + (19/4)
Line is perpendicular to this line,
⇒ Slope is the negative reciprocal of (-1/4).
m = -1/m₁
= -1/(-1/4)
= 4
Since the line has y-intercept 2,
Use the point-slope form of the equation of a line
Then the equation of the line is,
y - y₁= m(x - x₁)
Substitute the values we have,
⇒ y - 2 = 4(x - 0)
⇒y - 2 = 4x
Rearranging this equation into the desired form ax + by = c, we get,
-4x + y =2
Multiplying both sides by -5 to ensure that a = 20
And there are no common factors between a, b, and c,
20x - 5y = -10
Therefore, the equation of the line in the desired form is 20x - 5y = -10.
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Which of the following is a univariate display of quantitative data? histogram mosaic plot bar chart scatterplot
Answers
A histogram is a univariate display of quantitative data that organizes data into bins and shows the frequency of observations within each bin.
A histogram is a graphical representation that displays the distribution of quantitative data. It consists of a series of contiguous bars, where each bar represents a specific range or bin of values, and the height of the bar corresponds to the frequency or count of observations falling within that range.
Histograms are commonly used to visualize the shape, central tendency, and spread of a dataset. By examining the heights of the bars, one can determine the frequency of values within each bin and identify patterns such as peaks or clusters. This makes histograms an effective tool for exploring the distribution and characteristics of a single variable in a dataset.
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is 4,8,10 pithogoreon triplet
Answers
Answer:
no
Step-by-step explanation:
Since 4² + 8² = 10² is a false statement, 4, 8, 10 is not a Pythagorean Triple.
Una fábrica produce 12 480 borradores cada semana. Estos artículos se venden empacados en cajas de una docena. ¿Cuántas cajas de borradores saldrán a la venta cada semana?
Answers
Antibody identification interpretations would be considered correct 95% of the time or have a P value of 0.05 (5% probability that the result is due to chance) if you have:
Answers
Antibody identification interpretations would be considered correct 95% of the time or have a p-value of 0.05 (5% probability that the result is due to chance) if certain steps are followed in the analysis.
To achieve a correct interpretation rate of 95% or a p-value of 0.05 in antibody identification, the following steps are typically followed:
Sample Collection: Obtain a sample from the individual being tested, typically blood serum or plasma.
Testing Method: Use a reliable and validated testing method for antibody identification, such as enzyme-linked immunosorbent assay (ELISA) or immunoblotting.
Control Samples: Include appropriate control samples in the testing process to ensure accuracy and reliability.
Statistical Analysis: Conduct statistical analysis to evaluate the results and calculate the p-value. The p-value represents the probability that the observed result is due to chance.
Interpretation: Based on the statistical analysis and comparison with control samples, interpret the results of the antibody identification test.
By following these steps and ensuring the use of validated methods and appropriate statistical analysis, antibody identification interpretations can achieve a correct rate of 95% or have a p-value of 0.05, indicating a low probability of chance findings.
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can someone help find the circumference and area of this???
Answers
Answer:
Step-by-step explanation:
area formula is
π\(r^{2}\)
plug in values:
9π
which equals
28.2743339
or you can write 9π im not sure what your teacher prefers
circumference formula is
2πr
which equals
6π
or
18.8495559
if a is a skew symmetric n xn matrix such that n is an odd number, evaluate det(a).
Answers
The determinant of a skew-symmetric matrix of odd dimension is always 0. A skew-symmetric matrix is a square matrix where the elements below the main diagonal are the negatives of the corresponding elements.
Above the main diagonal. In other words, for a skew-symmetric matrix A, it satisfies the property \(A^T = -A\), where \(A^T\) is the transpose of A.
For any odd-dimensional skew-symmetric matrix, when we take the transpose of the matrix, we end up with the negative of the original matrix. Since the determinant of a matrix is unchanged when taking its transpose, we have \(det(A) = det(A^T) = det(-A)\).
Since -A is a matrix with all the elements negated, each term in the expansion of the determinant will have a corresponding term with the opposite sign. When we sum up these terms, they will cancel each other out, resulting in a determinant of 0.
Therefore, for a skew-symmetric matrix A of odd dimension, the determinant det(A) = 0.
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Which expression is equivalent to (-4x-3y-5)2? Select all that apply.
Answers
Answer: -8x-6y-10
Step-by-step explanation:
The expression (-4x-3y-5)2 is equivalent to the expression - 8x - 6y - 10 none of the options are correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
The expression is:
= (-4x-3y-5)2
After using the distributive property:
= - 8x - 6y - 10
Thus, the expression (-4x-3y-5)2 is equivalent to the expression - 8x - 6y - 10 none of the options are correct.
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Find the areas of the trapezoids.
Answers
Answer:
12 square units
Step-by-step explanation:
A = 1/2·h(sum of bases)
A = 1/2(4)(2+4)
A = 2(6) which is 12 square units
Scarlett bought a pair of shoes online for $36. She used a coupon code to get a 30%
discount. The website also applied a 10% processing fee to the price after the
discount. How much did Scarlett pay, in the end? Round to the nearest cent.
Answers
Scarlett paid $27.72 in the end. Rounded to the nearest cent, this is $27.71.
What is percentage ?
Percentage can be defined as product of ratio of given value, total value and hundred.
Given,
Scarlett bought a pair of shoes online for $36. She used a coupon code to get a 30%discount.
The website also applied a 10% processing fee to the price after the discount.
The initial price of the shoes was $36. With a 30% discount, Scarlett would pay only 70% of the initial price, which is:
0.7 x $36 = $25.20
Next, the website applied a 10% processing fee to this discounted price. To calculate the processing fee, we multiply the discounted price by 10% (or 0.1):
0.1 x $25.20 = $2.52
So the total cost for Scarlett, including the processing fee, is:
$25.20 + $2.52 = $27.72
Therefore, Scarlett paid $27.72 in the end. Rounded to the nearest cent, this is $27.71.
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Answer:
Scarlett pays $27.72 in the end.
Step-by-step explanation:
First, let's calculate the amount of the discount. The discount is 30% of the original price, which can be calculated as:
0.3 × $36 = $10.80So Scarlett gets a discount of $10.80.
--------------------------------------------------------
The new price after the discount is:
$36 - $10.80 = $25.20--------------------------------------------------------
Next, we need to apply the 10% processing fee to the new price. The processing fee is 10% of $25.20, which can be calculated as:
0.1 × $25.20 = $2.52So the processing fee is $2.52.
--------------------------------------------------------
The final price Scarlett pays is the new price after the discount plus the processing fee:
$25.20 + $2.52 = $27.72Therefore, Scarlett pays $27.72 in the end. Since, "27.72" is already rounded to 2 decimal places (nearest cent), we do not need to round it, even if we do, we will get the same result (27.72).
________________________________________________________
Which calculation shows the best method for estimating the result of 384 divided by three-sixteenths?
Answers
Answer:
the answer to this is 2048
Step-by-step explanation:
Answer: B
Step-by-step explanation: Just round
The work of a student to solve the equation 3(2x − 4) = 8 + 2x + 6 is shown below: Step 1: 3(2x − 4) = 8 + 2x + 6 Step 2: 5x − 7 = 14 + 2x Step 3: 5x − 2x = 14 + 7 Step 4: 3x = 21 Step 5: x = 7 In which step did the student first make an error and what is the correct step? (5 points) Group of answer choices Step 3; 5x + 2x = 14 + 7 Step 3; 5x − 2x = 14 − 7 Step 2; 6x − 12 = 14 + 2x Step 2; 6x − 7 = 2(6 + x + 4)
Answers
Suppose the height of a ball in feet is given by the quadratic equation below, where T is in seconds. What expression will give the time when the ball reaches its maximum height? h=-16t^2+50t+8. Please look at the image for the available answers. Thank you.
Answers
Answer:
t = -50/(2 * (-16))
Step-by-step explanation:
For quadratics of the form
y = ax^2 + bx + c
the x coordinate of the vertex is
x = -b / 2a
----------------------
h = -16t^2 +50t + 8
a = -16
b = 50
t at Vertex
t = -50/(2 * (-16))
Do the points P (-1, 6), Q (3, 7) and R (3, -5) form a right triangle?
( show your work )
Answers
Step-by-step explanation:
best I could, hopefully this helps
show work and answer the question!! will mark brainliest
Answers
X=1 Y=0
Y-12X+15+3X^2-16X+13-Y=3X^2
-12X+15-16X+13=0
-28X+28=0
X=1
Y=3-16+13=0
Is it possible to prove that the triangles are congruent by using the AAS congruence theorem?
Answers
Yes, it is possible to prove that two triangles are congruent by using the AAS congruence theorem.
The AAS congruence theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. This theorem can be used to prove that two triangles are congruent if two of the angles in the triangle and the side between them are congruent to two angles and the side between them of the other triangle. To prove congruence using the AAS congruence theorem, it is important to use the right angle and side measurements to ensure that the two triangles are congruent. If the measurements are correct, then the two triangles will be congruent.
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Yes, it is possible to prove that two triangles are congruent by using the AAS congruence theorem.
The AAS congruence theorem
it states that if two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.
This theorem can be used to prove that two triangles are congruent if two of the angles in the triangle and the side between them are congruent to two angles and the side between them of the other triangle.
To prove congruence using the AAS congruence theorem, it is important to use the right angle and side measurements to ensure that the two triangles are congruent. If the measurements are correct, then the two triangles will be congruent.
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What is the slope from (−4, 6) to (2, 2/3)
Answers
The slope from of (−4, 6) to (2, 2/3) can be written as -17/18
How can the slope be written?The slope of line can be represented as =slope whereby (x1, y1) = serves as the coordinates of first point in the line (x2, y2)serve as as the coordinates of second point in the line
From the question, x1 = -4, y1 = 6 , x2 = 2, y2 =2/3 then we can set up into the formula as
(y2 - y1) / (x2 - x1)
(y2 - y1) =(2/3 - 6) =-17/3
(x2 - x1) = (2 - (-4))= 6
Hence slope = -17/18
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let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b) find sin (θ+y)
Answers
In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement
\(\sin (\theta)=\frac{3}{5}\)Describes the following triangle
To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation
\(x^2+3^2=5^2\)Solving for x, we have
\(\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}\)The missing length of the first triangle is equal to 4.
For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression
\(\tan (y)=\frac{12}{5}\)Describes the following triangle
Using the Pythagorean Theorem again, we have
\(5^2+12^2=h^2\)Solving for h, we have
\(\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}\)The missing side measure is equal to 13.
Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.
The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles
\(\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}\)To calculate the sine and cosine of the sum
\(\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}\)We can use the following identities
\(\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}\)Using those identities in our problem, we're going to have
\(\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}\)
