To find the integer c that satisfies the given congruences, we can use the properties of modular arithmetic. For each congruence, we substitute the given values of a and b and simplify the congruences to solve for c. The possible values of c are then determined using the Chinese Remainder Theorem when appropriate.
Explanation:To find the integer c that satisfies the given congruences, we can use the properties of modular arithmetic:
a) To find c such that a.c ≡ 13a (mod 19), we divide both sides of the congruence by a. This gives us c ≡ 13 (mod 19).
b) To find c such that b.c ≡ 8b (mod 19), we divide both sides of the congruence by b. This gives us c ≡ 8 (mod 19).
c) To find c such that c.c ≡ a - b (mod 19), we square both sides of the congruence. This gives us c^2 ≡ (a - b)^2 (mod 19). Since we know a ≡ 11 (mod 19) and b ≡ 3 (mod 19), we substitute these values and simplify the congruence to c^2 ≡ 8 (mod 19). To solve this quadratic congruence, we can use the Chinese Remainder Theorem to find the two square roots of 8 modulo 19, which are 7 and 12. Therefore, c ≡ 7 (mod 19) or c ≡ 12 (mod 19).
d) To find c such that c.c ≡ 7a + 3b (mod 19), we substitute the given congruences for a and b into the congruence and simplify to obtain c^2 ≡ 7(11) + 3(3) ≡ 4 (mod 19). Similar to part (c), we use the Chinese Remainder Theorem to find the square roots of 4 modulo 19, which are 2 and 17. Therefore, c ≡ 2 (mod 19) or c ≡ 17 (mod 19).
e) To find c such that c.c ≡ 2a^2 + 3b^2 (mod 19), we substitute the given congruences for a and b into the congruence and simplify to obtain c^2 ≡ 2(11^2) + 3(3^2) ≡ 2(121) + 3(9) ≡ 149 ≡ 2 (mod 19). Therefore, c ≡ ±4 (mod 19).
f) To find c such that c ≡ a^3 + 4b^3 (mod 19), we substitute the given congruences for a and b into the congruence and simplify to obtain c ≡ 11^3 + 4(3^3) ≡ 11^3 + 4(27) ≡ 11^3 + 4(8) ≡ 11 + 32 ≡ 17 (mod 19). Therefore, c ≡ 17 (mod 19).
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Bob has 3 packs of model cars. He gave away 4. He has 11 left. How many were in a pack
Answer:15
Step-by-step explanation:he has 3 packs of model cars. 15 is in each pack if he gave away four he would have 11 left.
Help please!!!!!!!!!!!!
Answer:
[tex]\log_{9}{\dfrac{13}{x}}=\log_{9}{\boxed{13}}-\log_{9}{x}[/tex]
Step-by-step explanation:
The rule is ...
log(a/b) = log(a) -log(b) . . . . all logs to the same base
Then for a/b = 13/x, this becomes ...
log(13/x) = log(13) -log(x)
If the base of logarithms is 9, then this is ...
log9(13/x) = log9(13) -log9(x)
A set of numbers is shown below:
{0, 0.8, 1, 3, 6}
Which of the following shows all the numbers from the set that make the inequality 7x + 1 ≥ 8 true?
{1, 3, 6}
{3, 6}
{0, 0.8, 1}
{0, 0.8}
Answer:
I'm pretty sure it'd be set {3,6}
Answer:
A
Step-by-step explanation:
What is the point-slope form of a line with slope 6 that contains the same point (1,2)
The point-slope form of the line with slope 6 that contains the point (1, 2) is y - 2 = 6(x - 1).
The point-slope form of a line is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where m is the slope of the line and [tex]\( (x_1, y_1) \)[/tex] is a point on the line.
Given that the slope m = 6 and the point [tex]\( (x_1, y_1) = (1, 2) \)[/tex], we can substitute these values into the point-slope form:
y - 2 = 6(x - 1)
So, the point-slope form of the line with slope 6 that contains the point (1, 2) is y - 2 = 6(x - 1).
please help me out if you can!
Ok so we know that consecutive angles are supplementary and the diagonals bisect the angels so
2x-15+3x=90
5x=105
X=21
The two solids are similar and the ratio between the lengths of their edges is 2:7 what is the ratio of their surface areas?
Answer:
The ratio of their surface areas is [tex]\frac{4}{49}[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor
In this problem the scale factor is equal to the ratio [tex]\frac{2}{7}[/tex]
and
Remember that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
therefore
In this problem the ratio of their surface areas is [tex](\frac{2}{7})^{2}=\frac{4}{49}[/tex]
Final answer:
The ratio of the surface areas of two similar solids with a linear dimension ratio of 2:7 is 4:49.
Explanation:
The question deals with the concept of geometric similarity and the ratio of surface areas for similar solids. When two solids are similar, the ratio of their surface areas is the square of the ratio of their corresponding linear dimensions. Therefore, if the ratio between the lengths of their edges is 2:7, then the ratio of their surface areas would be the square of this ratio, which is (22):(72) or 4:49.
R is inversely proportional to A R = 12 when A = 1.5 a) Work out the value of R when A = 5 b) Work out the value of A when R = 9
Answer:
a) R = 3.6
b) A = 2
Step-by-step explanation:
To find the value, start by modeling the inverse proportionality by using the base equations with the original givens.
y = k/x
12 = k/1.5
18 = k
Now we use that to model the equation
R = 18/A
And we can now use that to solve parts a) and b)
a)
R = 18/A
R = 18/5
R = 3.6
b)
R = 18/A
9 = 18/A
2 = A
Regard y as the independent variable and x as the dependent variable and use implicit differentiation to find dx/dy. x5y2 − x4y + 2xy3 = 0
Answer:
dx/dy = (x^4 - 2x^5y - 6xy^2) / (5x^4y^2 - 4x^3y + 2y^3).
Step-by-step explanation:
x^5y^2 − x^4y + 2xy^3 = 0
Applying the Product and Chain Rules:
y^2*5x^4*dx/dy + 2y*x^5 - (y*4x^3*dx/dy + x^4) + (y^3* 2*dx/dy + 3y^2*2x) =0
Separating the terms with derivatives:
y^2*5x^4*dx/dy - y*4x^3*dx/dy + y^3* 2*dx/dy = x^4 - 2y*x^5 - 3y^2*2x
dx/dy = (x^4 - 2x^5y - 6xy^2) / (5x^4y^2 - 4x^3y + 2y^3)
Answer:
[tex]\frac{dx}{dy}=\frac{-2x^5y+x^4-6xy^2}{5x^4y^2-4x^3y+2y^3}[/tex]
Step-by-step explanation:
The given equation is
[tex]x^5y^2-x^4y+2xy^3=0[/tex]
Differentiate with respect to y.
[tex]\frac{d}{dy}(x^5y^2)-\frac{d}{dy}(x^4y)+\frac{d}{dy}(2xy^3)=0[/tex]
Using product rule we get
[tex]x^5\frac{d}{dy}(y^2)+y^2\frac{d}{dy}(x^5)-x^4\frac{d}{dy}(y)-y\frac{d}{dy}(x^4)+2x\frac{d}{dy}(y^3)+2y^3\frac{d}{dy}(x)=0[/tex] [tex](fg)'=fg'+gf'[/tex]
[tex]x^5(2y)+y^2(5x^4\frac{dx}{dy})-x^4(1)-y(4x^3\frac{dx}{dy})+2x(3y^2)+2y^3\frac{dx}{dy}=0[/tex]
[tex]2x^5y+5x^4y^2\frac{dx}{dy}-x^4-4x^3y\frac{dx}{dy}+6xy^2+2y^3\frac{dx}{dy}=0[/tex]
Isolate [tex]\frac{dx}{dy}[/tex] terms on left side.
[tex]5x^4y^2\frac{dx}{dy}-4x^3y\frac{dx}{dy}+2y^3\frac{dx}{dy}=-2x^5y+x^4-6xy^2[/tex]
[tex](5x^4y^2-4x^3y+2y^3)\frac{dx}{dy}=-2x^5y+x^4-6xy^2[/tex]
Isolate [tex]\frac{dx}{dy}[/tex] term.
[tex]\frac{dx}{dy}=\frac{-2x^5y+x^4-6xy^2}{5x^4y^2-4x^3y+2y^3}[/tex]
Therefore the value of [tex]\frac{dx}{dy}[/tex] is [tex]\frac{-2x^5y+x^4-6xy^2}{5x^4y^2-4x^3y+2y^3}[/tex].
What is the area of this triangle?
Round to the nearest hundredth.
Answer: 2.94 ft²
Step-by-step explanation:
Observe the figure attached:
The line LM divide the triangle into two right triangles.
Find the heigh "h" as following:
[tex]sin\alpha=\frac{opposite}{hypotenuse}\\\\sin(40\°)=\frac{h}{2.7}\\\\h=(2.7)(sin(40\°))\\h=1.73ft[/tex]
Apply the formula for calculte the area of a triangle:
[tex]A=\frac{Bh}{2}[/tex]
Where B (B=3.4 ft) is the base and h is the height (h=1.73ft)
Then:
[tex]A=\frac{(3.4ft)(1.73ft)}{2}=2.94ft^2[/tex]
How dose finding the square root of a number compare to finding the cube root of a number? Use the number 64 in your explanation.
30 points !!! Polygon ABCDE is reflected to produce polygon A?B?C?D?E?. What is the equation for the line of reflection? a. Y = 0 b. X = 0 c. X = 2 d. Y = 1
The equation for the line of reflection is x = 0 if the polygon ABCDE is reflected to produce polygon A'B'C'D'E'
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
We have a polygon ABCDE is reflected to produce polygon A'B'C'D'E' in the picture.
As we know, the reflection is the geometric transformation which create a mirror image of the object, but size or shape does not change.
The y-axis is the axis of reflection in this case.
The equation for the y-axis is x = 0
Thus, the equation for the line of reflection is x = 0 if the polygon ABCDE is reflected to produce polygon A'B'C'D'E'
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What is measure of angle A?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answer:
The measure of the angle A is [tex]53.13\°[/tex]
Step-by-step explanation:
we know that
In the right triangle ABC
The tangent of angle A is equal to the opposite side to the angle A divided by the adjacent side to angle A
so
[tex]tan(A)=\frac{BC}{AB}[/tex]
substitute
[tex]tan(A)=\frac{4}{3}[/tex]
[tex]<A=arctan(\frac{4}{3})=53.13\°[/tex]
An 8-pound boneless ham contains 36 servings of meat. How many servings would an 2 pound ham make? Show your work using equivalent ratios.
Answer:
9 servings of meat.
Step-by-step explanation:
The first ratio you are given is 8:36. You are trying to figure out what 2:__ is.
8/36 x 2/X
Multiply 2 x 36 and get 72. Now divide 72 by 8 to get 9.
Answer:
The answer really is 9 servings of meat.
Step-by-step explanation:
I had the same question and I got it right...but mine said: Write a proportion that could be used to solve this problem. Do not solve it.
Identify the domain and range of the following graph.
domain and range are both infinite
Camden lives 1 mile away from school. He has walked 2/3 of the way to school. How many feet does he have left to walk?
Answer:
Step-by-step explanation:
you take 5280( How many feet are in a mile) and dived it by 3. The equals 1760 and that is the answer because 1760 is 1/3 of 5280
Answer:1760
Given: Circle X with a Radius r and circle Y with radius s Prove: Circle x is similar to circle y
Answer:
Step-by-step explanation:
To prove that Circle X is similar to Circle Y, we need to show that their corresponding angles are equal and their corresponding sides are proportional. We can compare the ratios of the circumference to the diameter for both circles, which are equal, implying that the angles in the two circles are equal and Circle X is similar to Circle Y.
Explanation:To prove that Circle X is similar to Circle Y, we need to show that their corresponding angles are equal and their corresponding sides are proportional. Since the radii of the two circles are different (r for Circle X and s for Circle Y), we cannot directly compare their sides. However, we can compare their ratios. If we divide the circumference of Circle X by its diameter, we get the value of pi (π), which is approximately 3.14. Similarly, if we divide the circumference of Circle Y by its diameter, we would also get pi (π). This means that the ratios of the circumference to the diameter for both circles are equal, which implies that the angles in the two circles are equal and therefore, Circle X is similar to Circle Y.
Two sporting goods stores are having discount sales on basketballs. • At one store, a basketball is on sale for 20% off the regular price of $24.95. • At the other store, the same kind of basketball is on sale for 25% off the regular price of $25.80. What is the difference between the sale prices of the two stores?
Answer:
$0.61
Step-by-step explanation:
1. Find the sales price of each store by multiplying the regular price by the % off to find the discount - then subtract.
store A: 24.95*20% (or 0.20) = 4.99 (discount)
24.95 - 4.99 = 19.96 (sales price)
store B: 25.80 * 25% (or 0.25) = 6.45 (discount)
25.80 - 6.45 = 19.35
To find the difference of sales price, subtract 19.96 - 19.35 = 0.61
Answer:)
THE ANSWER IS A) $0.61
How many square feet will we need for this hole that has 4 feet 12 feet 3 feet 2 feet 1 feet 2 feet
I think you're answer is five hundred seventy six
PLZ help me
Select ALL the correct answers.
The graph below represents the number of dolphins in a dolphin sanctuary.
A.The graph is decreasing over the interval (0,∞ )
B.The graph has a y-intercept of 30
C.The graph is positive over the interval (0, ∞)
D.The graph is increasing over the interval (0, ∞)
E.The graph has a y-intercept of 185
F.As the number of years increases, the number of dolphins in the sanctuary increases
Answer:
B, C, D, and F
Step-by-step explanation:
The graph is an exponential curve rising upwards. By looking at the graph we can tell that the graph is only increasing, it touches the y-axis at 30 and it lies in the 1st quadrant.
So, option A is wrong, as the graph is increasing.
Option B is correct. The point where graph crosses/touches the y-axis is the y-intercept. So the y-intercept is 30.
Option C is correct. As the graph lies in 1st quadrant and is positive over the entire range of values.
Option D is also correct as the graph is increasing over entire range of values.
Option E is incorrect as y-intercept is 30.
Option F is correct. Since the graph is increasing, this means with every passing year the number of dolphins is increasing.
Therefore, the correct options are: B, C, D, and F
53.4*16.2 please please
Answer:
865.08
Step-by-step explanation:
✯Hello✯
↪ The answer is 865.08
↪ Times both of them by 10 so they are whole numbers
↪ Then it will be 534 x 162 = 86508
↪ Then divide by 100
❤Gianna❤
To multiply 53.4 and 16.2, calculate 534 * 162, then adjust the result by placing the decimal point two places from the right to get 865.08. This gives the final product of 865.08.
To find the product of 53.4 and 16.2, follow these steps:
First, ignore the decimal points and multiply the numbers as if they were whole numbers:534 * 162 = 86508Next, count the total number of decimal places in the original numbers.Here, 53.4 has one decimal place and 16.2 also has one decimal place, making a total of two decimal places.
Place the decimal point in the product, moving it two places from the right:86508 becomes 865.08Therefore, 53.4 * 16.2 equals 865.08.
Alma's math teacher said that there was 10 factorial (10!) possible different orders in which the problems on the next exam could be arranged. What does 10! mean?
A- 10^100
B- 10(9+8+7+6+5+4+3+2+1)
C- 10(9)(8)(7)(6)(5)(4)(3)(2)(1)
D- 10,000,000,000
Answer:
The 10! means 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 ⇒ answer C
Step-by-step explanation:
* Lets explain how to solve the problem
- Factorial number means a number which is multiply itself to its
decreasing numbers
- In mathematics, the factorial of a non-negative integer n, denoted by
n! is the product of all positive integers less than or equal to n
- That means n! = n × (n-1) × (n-2) × (n-3) × ...........× 1
- Ex: 5 ! = 5 × 4 × 3 × 2 × 1 = 120
* Lets solve the problem
- There was 10 factorial 10! possible different orders
- The meaning of 10! is the multiplication of all the numbers from
10 to 1
∴ 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
* The 10! means 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
The correct choice is C, 10(9)(8)(7)(6)(5)(4)(3)(2)(1). The expression 10! (ten factorial) means the product of all integers from 1 to 10, which is calculated as 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1.
Therefore, the correct choice is C. For example, 4! equals 4 × 3 × 2 × 1 = 24.
The expression 10!, read as 'ten factorial', represents the product of all integers from 1 to 10. It is calculated as follows:
10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
So, the correct choice for what 10! means is:
C- 10(9)(8)(7)(6)(5)(4)(3)(2)(1)
For example, the factorial of 4 is calculated as 4! which equals 4 × 3 × 2 × 1 = 24.
Similarly, for 10!, you multiply all integers from 10 down to 1.
patrick is going to paint the fence posts around the corral. the rectangular corral is 50 ft by 30 ft, with the fence posts spaced 5 feet apart. how many fence posts does patrick have to paint?
Answer:
32 posts
Step-by-step explanation:
In terms of fence-post spaces, the corral is 10 by 6, so its perimeter is ...
P = 2(10 +6) = 32 . . . . . fence post spaces.
Patrick intends to paint 32 fence posts.
Final answer:
Patrick needs to paint a total of 32 fence posts around the rectangular corral. This total counts the posts for both pairs of sides after considering that the four corner posts have been counted twice.
Explanation:
The question involves calculating the total number of fence posts needed to surround a rectangular corral. Since the corral is 50 ft by 30 ft, and fence posts are spaced 5 feet apart, we must calculate how many posts are needed on each side of the rectangle and then add them together.
To begin with, for each of the longer sides (50 ft), we would need 50 ft ÷ 5 ft/post = 10 posts per side. However, we need to add one more post to close the rectangle, so we have 10 + 1 = 11 posts on each of the longer sides. For the shorter sides (30 ft), it would be 30 ft ÷ 5 ft/post = 6 posts per side, plus the extra post to close the rectangle, resulting in 6 + 1 = 7 posts on each of the shorter sides.
To get the total number of posts, we add up the posts on all sides: (11 posts × 2) + (7 posts × 2) = 22 + 14 = 36 posts. However, we must consider that we have counted the corner posts twice, once for each side they join. Since there are four corners, we subtract four posts from our total, resulting in 36 - 4 = 32 posts that Patrick needs to paint.
In the figure, ΔGTS is similar to ΔFHS. What's the length of side GT?
A. 13.8
B. 12.8
C. 8.4
D. 2.7
[tex]GT=\frac{HF.TS}{SF}=\frac{4.8\times 21}{12}=8.4 [/tex]
What is the volume of this Hamsta' snacks box with a width of 1.5 inches,a length of 2.5 inches,and a height of 4 inches
Answer: 15 cubic inches.
Step-by-step explanation:
The volume of rectangular prism is given by :-
[tex]V=l\times w\times h[/tex], where l is length , w is width and h is height.
Given : Hamsta' snacks box has a width of 1.5 inches,a length of 2.5 inches,and a height of 4 inches.
Then, the volume of the box will be :-
[tex]V=2.5\times 1.5\times 4=15\text{ cubic inches}[/tex]
Hence, the volume of this Hamsta' snacks box is 15 cubic inches.
help fast, please
A. Expand the following and state the Law that is indicated.
1. log4(3x)
2. log3(27/x)
3. log4(x5)
ANSWER
1.
[tex]log_{4}(3x) = log_{4}(3) + log_{4}(x)[/tex]
2.
[tex]log_{3}( \frac{27}{x} ) = 3 - log_{3}(x)[/tex]
3.
[tex]log_{4}( {x}^{5} ) = 5 log_{4}(x) [/tex]
EXPLANATION
1. The given logarithmic expression is
[tex] log_{4}(3x) [/tex]
Use the product rule:
[tex] log_{a}(mn) = log_{a}(m) + log_{a}(n) [/tex]
We apply this rule to obtain:
[tex]log_{4}(3x) = log_{4}(3) + log_{4}(x)[/tex]
2. The given logarithmic expression is
[tex] log_{3}( \frac{27}{x} ) [/tex]
We apply the quotient rule:
[tex]log_{a}( \frac{m}{n} ) = log_{a}(m) - log_{a}(n) [/tex]
This implies that;
[tex]log_{3}( \frac{27}{x} ) = log_{3}(27) - log_{3}(x) [/tex]
We simplify to get;
[tex]log_{3}( \frac{27}{x} ) = log_{3}( {3}^{3} ) - log_{3}(x) [/tex]
Apply the power rule:
[tex] log_{a}( {m}^{n} ) = n log_{a}(m) [/tex]
[tex]log_{3}( \frac{27}{x} ) = 3 log_{3}( {3}) - log_{3}(x) [/tex]
simplify;
[tex]log_{3}( \frac{27}{x} ) = 3 (1) - log_{3}(x) [/tex]
[tex]log_{3}( \frac{27}{x} ) = 3 - log_{3}(x)[/tex]
3. The given logarithmic expression is;
[tex] log_{4}( {x}^{5} ) [/tex]
Apply the power rule of logarithms.
[tex]log_{a}( {m}^{n} ) = n log_{a}(m) [/tex]
This implies that,
[tex]log_{4}( {x}^{5} ) = 5 log_{4}(x) .[/tex]
Jenny has two congruent kleenex boxes. The first box has a volume of 72 in2, a length of 3 inches and a width of 4 inches. What is the height of the second box?
Answer:
The height of the second box is [tex]6\ in[/tex]
Step-by-step explanation:
we know that
If the two boxes are congruent
then
The volume of the first box is equal to the volume of the second box
The length of the first box is equal to the length of the second box
The width of the first box is equal to the width of the second box
The height of the first box is equal to the height of the second box
so
Find the height of the first box
Remember that
The volume of the box is equal to
[tex]V=LWH[/tex]
substitute the values and solve for H
[tex]72=(3)(4)H[/tex]
[tex]H=72/(12)=6\ in[/tex]
Help please ! (Photo attached)
Answer:
30.9 ft
Step-by-step explanation:
Simplify the expression (Picture provided)
Answer:
b. secx
Step-by-step explanation:
We have given a trigonometric expression.
csc(x)/cot(x)
We have to simplify it.
Since we know that
csc(x) is reciprocal to sin(x).
cscx = 1/sinx
cot(x) is ratio of cos(x) and sin(x).
cotx = cosx/sinx
Then, given expression becomes,
[tex]\frac{1/sinx}{cosx/sinx}[/tex]
[tex]\frac{1}{sinx}[/tex] × [tex]\frac{sinx}{cosx}[/tex]
[tex]\frac{1}{cosx}[/tex]
csc(x)/cot(x) = secx
PLEASE HELP ASAP
Which formula is used to calculate the standard deviation of sample data?
s=√\frac{n}{n-1} [tex]n∑(x₁-x⁻)^2
i=1
Lila ate 1/4of her sandwich.Alexis are 3/4 of her sandwich. How much more of the sandwich did Alexis eat than lila
Answer:
2/4
Step-by-step explanation:
1/4 = 0.25
3/4 = 0.75
0.75 - 25 = 0.50
0.50 is your answer