Solve for a.
ab + c = d

Answer:

\(12(x - 4)\)

Step-by-step explanation:

The question says, "twelve times the difference of a number and four"

Let's start with the first number, which is twelve = 12. Moving on, we have times = ×, then the difference which is minus(-). A number is unknown, any aphabet can be used to represent the number, so, we represent with 'x', and then four = 4.

Arranging them, we have:

\(12 \times x - 4\)

in algebraic equations, times is always represented by bracket. Therefore, our final answer is:

\(12(x - 4)\)

I hope this helps.

Then 1 - 3/5 = 2/5. This means that 2/5 of the frogs in that particular part of the rainforest are not poisonous. This fraction can also be expressed as 40/100 or 0.4 in decimal form.

In the given scenario, we know that 3/5 of the frogs in a particular part of the rainforest are poisonous. This means that the remaining fraction of the frogs are not poisonous.

To find this fraction, we need to subtract 3/5 from 1 (since the sum of the fractions of poisonous and non-poisonous frogs is equal to 1).

It's important to note that just because a frog is not poisonous, it doesn't mean it's safe to touch or handle them. It's always best to admire these beautiful creatures from a safe distance and leave them alone in their natural habitat.

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Answer:

y = 63

Step-by-step explanation:

Reverse the equation and do (8+1) x 7 = y.

8 + 1 = 9.

9 x 7 = 63.

Answer:

#1

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

did it on ed

Answer:

x=9

Step-by-step explanation:

2x+10=3x+1

10=x+1

9=x

Answer:

x = 3; y = -6

Step-by-step explanation:

 x - 2y =  15

2x + 4y = -18​

Multiply both sides of the first equation by 2. Write the second equation below it, and add the two equations.

     2x - 4y = 30

(+)  2x + 4y = -18

---------------------------

     4x         = 12

4x/4 = 12/4

x = 3

Now we substitute 3 for x in the first equation and solve for y.

x - 2y = 15

3 - 2y = 15

-2y = 12

y = -6

Answer: x = 3; y = -6

Answer:

A. Using the lens equation, 1/p + 1/q = 1/f, and substituting f = 5 cm and q = 7 cm, we can solve for p:

1/p + 1/7 = 1/5

Multiplying both sides by 35p, we get:

35 + 5p = 7p

Simplifying and rearranging, we get:

2p = 35

Therefore, the distance from the lens to the object, p, is:

p = 35/2 cm

B. Solving the lens equation, 1/p + 1/q = 1/f, for q, we get:

1/q = 1/f - 1/p

Substituting f = 5 cm, we get:

1/q = 1/5 - 1/p

Multiplying both sides by 5qp, we get:

5p = qp - 5q

Simplifying and rearranging, we get:

q = 5p / (p - 5)

Therefore, the expression that gives q as a function of p is:

q = 5p / (p - 5)

C. Here is a sketch of the graph of q(p):

The graph is a hyperbola with vertical asymptote at p = 5 and horizontal asymptote at q = 5. The image distance q is positive for object distances p greater than 5, which corresponds to a real image. The image distance q is negative for object distances p less than 5, which corresponds to a virtual image.

D. Taking the limit of q as p approaches infinity, we get:

lim q(p) = 5

This represents the horizontal asymptote of the graph. As the object distance becomes very large, the image distance approaches the focal length of the lens, which is 5 cm.

Taking the limit of q as p approaches 5 from the positive side, we get:

lim q(p) = -infinity

This represents the vertical asymptote of the graph. As the object distance approaches the focal length of the lens, the image distance becomes infinitely large, indicating that the lens is no longer able to form a real image.

In order for the lens to form a real image, the object distance p must be greater than the focal length f. When the object distance is less than the focal length, the lens forms a virtual image.

Answer:

1. scalene

Step-by-step explanation:

1. scalene - none of the sides are equal

We can't find volume through given information.

Lets find the area

\(\\ \sf\longmapsto Area=LB\)

\(\\ \sf\longmapsto Area=\dfrac{7}{2}\times \dfrac{9}{4}\)

\(\\ \sf\longmapsto Area=\dfrac{63}{6}\)

Answer:

1800 dollars

Step-by-step explanation:

We can set up an equation here to represent the exponential growth in Terry's bank account.

\(y = 1600(1.04)^x\)

We can plug in 3 for x since x is the # of years the account is receiving compound interest on.

\(y = 1600(1.04)^3\)

\(1.04^3 = 1.124864\\1.124864*1600= 1800\)

Using the information in the given diagram, the value of the missing angle is: m∠1 = 75°

The transverse line theorem states that If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.

Now, when we draw a horizontal line parallel to lines a and b and directly cutting across the vertex of angle 1, we can see that angle 1 will be composed of two angles.

Now, for the transverse line theorem we can say that:

Angle 1 will be composed of two angles namely:

48 degrees and (180 - 153) degrees.

Thus:

m∠1 = 48° + 27°

m∠1 = 75°

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Carson's work is correct for solving the equations.

Given that;

Carson wants to solve this system of equations.

y = x² + 5x − 6

y = x − 1

Now, We can solve first equation as;

y = x² + 5x - 6

y = x² + 5x - 6 = 0

⇒ x = - 5 ± √5² - 4×1×- 6 / 2

⇒ x = - 5 ± √25 + 24 / 2

⇒ x = - 5 ± √49 / 2

⇒ x = - 5 ± 7/2

⇒ x = - 5 + 7 / 2

⇒ x = 2/2

⇒ x = 1

⇒ x = - 5 - 7 / 2

⇒ x = - 12 / 2

⇒ x = - 6

Hence, From (ii);

⇒ y = x - 1

At x = 1;

y = 1 - 1

y = 0

At x = - 6;

y = - 6 - 1

y = - 7

Hence, Carson's work is correct.

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Parallelogram have two pairs of opposite sides that are parallel and congruent.

In a parallelogram, two pairs of opposite sides are parallel and congruent. A parallelogram is a quadrilateral with opposite sides that are parallel and congruent. Therefore, any pair of opposite sides in a parallelogram satisfies the criteria of being both parallel and congruent.

For example, let's consider a parallelogram ABCD:

These two pairs of opposite sides, AB and CD, and AD and BC, are parallel (they never intersect) and congruent (they have the same length).

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Answer: I think that the answer is 3/4 miles

Step-by-step explanation:

Answer:

Your answer is 11.8

Step-by-step explanation:

-1.8 degrees is 11.8 degrees warmer than -13.6. Hope this helps you!

The value of angle B and C are 63° and 61° respectively.

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

Therefore;

32/sin56 = 34/sinC

32sinC = 34sin56

32sinC = 28.187

divide both sides by 32

sinC = 28.187/32

sinC = 0.88

C = sin^-1(0.88)

C = 61°( nearest degree)

The sum of angle in a triangle is 180°

therefore, B = 180-(61+56)

B = 180-(117)

B = 63°

therefore the value of angle B and C are 63° and 61°.

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Answer:

(-11/2; -4)

Step-by-step explanation:

The point that lies on the line is symmetry is the middle point of the segment

M(x) = (-8-3)/2 = -11/2

M(y) = -4

Answer:

(-11/2; -4)

Step-by-step explanation: The point that lies on the line is symmetry is the middle point of the segment

M(x) = (-8-3)/2 = -11/2

M(y) = -4

Answer:

x = 8

Step-by-step explanation:

4(8) + 6(5) = 62

32 + 30 = 62

62 = 62

Answer:

x = 8

Step-by-step explanation:

y = 5 and 4x + 6y = 62

4x + 30 = 62

Subtract 30 from each side:

4x + 30 - 30 = 62 - 30

4x = 32

Divide each side by 4:

4x ÷ 4 = 32 ÷ 4

x = 8

Based on the information given, there are a total of 118 solutions.

This is a problem of solving a Diophantine equation subject to some conditions. Let's introduce a new variable y4 = 20 - (x1 + x2 + x3 + x4). Then the problem can be restated as finding the number of solutions to:

x1 + x2 + x3 + y4 = 20

Subject to the following conditions:

0 ≤ x1 < 3

0 ≤ x2 < 4

0 ≤ x3 < 5

0 ≤ y4 < 6

We can solve this problem using the technique of generating functions. The generating function for each variable is:

(1 + x + x^2) for x1

(1 + x + x^2 + x^3) for x2

(1 + x + x^2 + x^3 + x^4) for x3

(1 + x + x^2 + x^3 + x^4 + x^5) for y4

The generating function for the equation is the product of the generating functions for each variable:

(1 + x + x^2)^3 (1 + x + x^2 + x^3 + x^4 + x^5)

We need to find the coefficient of x^20 in this generating function. We can use a computer algebra system or a spreadsheet program to expand the product and extract the coefficient. The result is: 1118

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Answer: This problem involves finding the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints. We can use the stars and bars method to solve this problem.

Suppose we have 20 stars representing the sum x₁ + x₂ + x3 + x₁. To separate these stars into four groups corresponding to x₁, x₂, x₃, and x₄, we need to place three bars. For example, if we have 20 stars and 3 bars arranged as follows:

**|**||

then the corresponding values of x₁, x₂, x₃, and x₄ are 2, 4, 6, and 8, respectively. Notice that the position of the bars determines the values of x₁, x₂, x₃, and x₄.

In general, the number of ways to place k identical objects (stars) into n distinct groups (corresponding to x₁, x₂, ..., xₙ-₁) using n-1 separators (bars) is given by the binomial coefficient (k+n-1) choose (n-1), which is denoted by C(k+n-1, n-1).

Thus, the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints is:

C(20+4-1, 4-1) = C(23, 3) = 1771

However, this count includes solutions that violate the upper bounds on x₁, x₂, x₃, and x₄. To eliminate these solutions, we need to use the principle of inclusion-exclusion.

Let Aᵢ be the set of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints, where xᵢ ≥ mᵢ for some integer mᵢ. Then, we want to find the cardinality of the set:

A = A₀ ∩ A₁ ∩ A₂ ∩ A₃

where A₀ is the set of all non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20, and Aᵢ is the set of solutions that violate the upper bound on xᵢ.

To find the cardinality of A₀, we use the formula above and obtain:

C(20+4-1, 4-1) = 1771

To find the cardinality of Aᵢ, we subtract the number of solutions that violate the upper bound on xᵢ from the total count. For example, to find the cardinality of A₁, we subtract the number of solutions where x₂ ≥ 4 from the total count. To count the number of solutions where x₂ ≥ 4, we fix x₂ = 4 and then count the number of solutions to the equation x₁ + 4 + x₃ + x₄ = 20 subject to the constraints 0 ≤ x₁ < 3, 0 ≤ x₃ < 5, and 0 ≤ x₄ < 6. This count is given by:

C(20-4+3-1, 3-1) = C(18, 2) = 153

Similarly, we can find the cardinalities of A₂ and A₃ by fixing x₃ = 5 and x₄ = 6, respectively. Using the principle of inclusion-exclusion, we obtain:

|A| = |A₀| - |A

Step-by-step explanation:

Answer:

Rose: 6/5 or 1.2

Hank: 6/10 ÷ 6 = 0.1

Step-by-step explanation:

89% out of 100 that this is correct

Answer:

k = 2

Step-by-step explanation:

in such a case we look immediately at the cases y = 0 and/or x = 0

only if that does not lead us to an answer, do we need to look further.

y = 0, that means according to the graph that x = -2.

so, we have

0 = |x + k| = |-2 + k|

that can only be the case, if k = 2

and we are done.

Answer:

It would be a lot of bavgeria

Answer:

450000

Step-by-step explanation:

125×(60×60)

=125×3600

=450000

x and y have the values 7 and 7√2, respectively.

The sides of a right triangle with 45-degree acute angles have a unique ratio of 1:1:2.

We can use this information to determine the values of x and y because the base is specified as being 7.

Let's give the perpendicular side the value of x, and the hypotenuse the value of y.

The perpendicular side (x) and the base (7) have the same length because the acute angles are both 45 degrees.

Consequently, x = 7.

We can determine that x:y:2x using the ratio of 1:1:2.

When we enter the value of x, we may calculate y:

7:y:√2(7)

Simplifying even more

7:y:7√2

Given that the hypotenuse (y) equals 72, we can write:

y = 7√2

Thus, x and y have the values 7 and 7√2, respectively.

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The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer:

Step-by-step explanation:

1/2x - 2/3 × 15 = 30

1/2x - 10 = 30

1/2x = 30 + 10

1/2x = 40

x = 40 × 2

x = 80

hope this helps

plz mark it bas brainliest!!!!!!!!!

Answer:

24

Step-by-step explanation:

Answer:

the remainder is 81

Step-by-step explanation:

so , equate x +3 to 0 , as in x + 3 = 0 then x = -3

so now we know the value of x so just replace it in the expression to get the remainder

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