Gary has $4.40 in nickels and dimes he has 10 more nickels than dimes how many of each kind of coin does he have

The expression is simplified to 2

It is important to note that the table of exact values for trigonometric identity differ with the particular identity in study.

From the table of exact values, we have that;

sin 15 = 0. 25

sin 30 = 0. 5000

sin 45 = 0. 7071

sin 60 = 0. 8600

sin 75 = 0. 9659

sin 90 = 1

To determine the value of the expression, we have to substitute the value of sin 30 as 0. 5000

4 sin 30°

⇒ 4 × 0. 5000

multiply through

⇒ 2

The value determined is 2

Thus, the expression is simplified to 2

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Answer:

it would take 40 learners to finish the job in 3 hours.

Answer:

40

Step-by-step explanation:

This is a ratio that we can set up as follows and solve for x

\(\frac{3}{6}\) = \(\frac{20}{x}\)

Multiply both sides by x

\(\frac{x}{2}\) = 20

Multiply both sides by 2

x = 40

Answer:

2 13/16

Step-by-step explanation:

1 15

16

+

7

8

=  (1 + 0) + (

15

16

+

7

8

)

=  1 +

15

16

+

7 × 2

8 × 2

=  1 +

15

16

+

14

16

=  1 +

15 + 14

16

=  1 +

29

16

=  1 +

1 13

16

=  

2 13

16

The expression given is 3c + 5d and the expression when c = 24 and d =25 will be 197.

It should be noted that an expression is simply used to illustrate the relationship between the variables.

In this case, the expression given is 3c + 5d.

Therefore, the expression given is 3c + 5d and the expression when c = 24 and d =25 will be:

= 3c + 5d

= 3(24) + 5(25)

= 72 + 125

= 197

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Complete question:

The expression given is 3c + 5d. Evaluate the expression when c = 24 and d =25.

Answer:

constant is - 19

Step-by-step explanation:

the constant is the term in an expression with no variable attached to it.

12r + \(\frac{r}{2}\) - 19

the only term without the variable r attached to it is - 19

then the constant term is - 19

"The correct answer is option A." The missing coordinates of point Q are (a, c/2).We are given the coordinates of points P and N as (0, c) and (2a, 0), respectively. We are also given that point Q lies on the same line as points P, Q, and N. We need to find the missing coordinates of point Q.

Since point Q lies on the same line as P, Q, and N, its x-coordinate must be halfway between the x-coordinates of points P and N. That is, the x-coordinate of Q is:

x-coordinate of Q = (x-coordinate of P + x-coordinate of N) / 2

x-coordinate of Q = (0 + 2a) / 2 = a

So, we know that the x-coordinate of point Q is a.

To find the y-coordinate of point Q, we can use the fact that point Q lies on the same line as point P, which has coordinates (0, c). The equation of the line passing through P and N is:

y - c = (0 - c) / (2a - 0) * (x - 0)

Simplifying this equation gives:

y - c = -c/2a * xy = -c/2a * x + c

Substituting x = a in this equation gives:

y = -c/2a * a + cy = -c/2 + cy = c/2

So, we know that the y-coordinate of point Q is c/2.

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The equation of the line is y = x + 6

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following highlights

The graph intersect the y-axis at y = 6

This means that the intercept c is 6

Also, as x changes by 1, the y values changes by 1

This mean sthat the slope is 1

So, we have

y = mx + c

This gives

y = x + 6

Hence, the equation is y = x + 6

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The linear equation on the graph can be written as:

y = (3/2)*x + 6

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁), then the slope will be:

a = (y₂ - y₁)/(x₂ - x₁)

In this case we can see the points (0, 6)  (so the y-intercept is b = 6)  and (4, 10)

Then the slope will be:

a = (10 - 6)/(4 - 0) = 6/4 = 3/2

Then the linaer equation is:

y = (3/2)*x + 6

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Answer:

f(x) = x^2 -2x - 8

Step-by-step explanation:

A quadratic function in factored form (x-a)(x-b) has zeros at (a, 0) and (b, 0). We are given the zeros in the graph are (-2, 0) and (4, 0). Thus, insert that into the factored form equation:

(x - (-2))(x - 4)

(x + 2)(x - 4)

Next, plug in a point from the function into the equation to find if a dilation was applied. Since we currently don’t know what the dilation is, let’s set it to variable d. I’ll be using the point (2, -8)

-8 = d(2 + 2)(2 - 4)

-8 = 4*-2d

-8 = -8d

1 = d

The dilation is 1, so the remaining equation is just (x+2)(x-4). To convert it to standard form, just expand the equation:

x^2 -2x - 8

Answer:   whats the question

Step-by-step explanation:

its multiplcatuion tho

A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.

Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.

Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.

Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of

To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).

First, let's convert the fractions 1/5 and 2/3 to fifteenths:

\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)

\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)

Now we can rewrite the expression using the common denominator:

\(3 + \frac{3}{15}+\frac{10}{15}\)

Answer:

Step-by-step explanation:

  x + 6 I x³ + 2x²  - 10x + 84   I   x² - 4x + 14

              x³ + 6x²

            -     -      

                     -4x² - 10x

                    -4x²  - 24x

                    +       +    

                               14x + 84

                                14x + 84

                                -      -      

                                     0

P(x)  =(x +6)* ( x² - 4x + 14) + 0

Answer: I = $ 500.00

Step-by-step explanation:

Hello Microplays!

To solve this equation. First, convert R percent to r a decimal r = R/100 2.5%/100 = 0.025 per year, then, solving our equation

I = 5000 × 0.025 × 4

I = 5000 × 0.10

I = $ 500.00

The simple interest accumulated on a principal of $5,000.00 at a rate of 2.5% per year for 4 years is $500.00.

Hopefully this helps, and hope this is correct.

The total volume of the given figure is:

\(V = 311.65cm^3 + 246.97cm^3 = 558.62cm^3\)

Here we have two simple shapes.

Half a sphere, and a cone.

The volume of half a sphere of radius R is:

\(V = \frac{2}{3}*3.14*R^3\)

And here we know that R = 5.3cm, replacing that we get:

\(V = \frac{2}{3}*3.14*(5.3cm)^3 = 311.65cm^3\)

For a cone of radius R and height H, the volume is:

\(V = \frac{3.14*R^2*H}{3}\)

In this case, R = 5.3cm and H = 8.4cm

The volume of the cone is:

\(V = \frac{3.14*(5.4cm)^2*8.4cm}{3} = 246.97cm^3\)

Then the total volume is:

\(V = 311.65cm^3 + 246.97cm^3 = 558.62cm^3\)

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Answer:

False

Step-by-step explanation:

5 % pounds - (1 7/8 pounds + 1 1/2 pounds) = 2 5/8 pounds

The theory used in this question is algebra. Algebra is the branch of mathematics that studies the rules of operations and relations and the constructions and concepts arising from them.

In this question, algebra was used to solve for the number of pounds of plant food that Micah had left after using some for his tomato and pepper plants.

Step 1: Calculate the total amount of plant food that Micah bought: 5 % pounds

Step 2: Calculate the amount of plant food that Micah used for his tomato plants: 1 7/8 pounds

Step 3: Calculate the amount of plant food that Micah used for his pepper plants: 1 1/2 pounds

Step 4: Calculate the amount of plant food that Micah had left by subtracting the total amount of plant food used from the total amount of plant food bought: 5 % pounds - (1 7/8 pounds + 1 1/2 pounds) = 2 5/8 pounds

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Answer:

=−1±1 3√4

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

Move the constant to the left, 4x^2+2x-2-1=0

Calculate the difference, 4x^2+2x-3=0

then solve using quadratic equation (must too difficult to type out)

The proof demonstrates that given a well-ordered set W, an isomorphic ordinal can be found using the function F. The uniqueness of this ordinal is established using the Replacement Axioms. The set F(W) is shown to exist for each x in W, and if the least F(W) exists, it serves as an isomorphism of VV onto -y.

Lemma 2.7: This is a previously stated lemma that is referenced in the proof. Unfortunately, without the specific details of Lemma 2.7, it's difficult to provide further explanation for its role in the proof.

Well-ordered set W: A well-ordered set is a set where every non-empty subset has a least element. In this proof, W is assumed to be a well-ordered set.

Isomorphic ordinal: An ordinal is a mathematical concept that extends the notion of natural numbers to represent order and magnitude. An isomorphic ordinal refers to an ordinal that has a one-to-one correspondence or mapping with another ordinal, preserving their order and magnitude properties.

Function F: The function F is defined to assign an ordinal o to each element x in W. This means that for every x in W, there is a corresponding ordinal o.

Existence and uniqueness: The proof asserts that if there exists an ordinal o that is isomorphic to a specific initial segment of the ordinal VV (the set of all ordinals), then this ordinal o is unique. In other words, there is only one ordinal that can be mapped to the initial segment of VV given by x.

Replacement Axioms: The Replacement Axioms are principles in set theory that allow the construction of new sets based on existing ones. In this case, the Replacement Axioms are used to assert that the set F(W) exists, which is the collection of all ordinals that can be assigned to elements of W.

For each x in W: The proof states that for every x in W, there exists an ordinal o that can be assigned to it. If there is no such ordinal, the proof suggests considering the least x for which such an ordinal does not exist.

The least F(W): The proof introduces the concept of the least element in the set F(W), denoted as the least F(W). If this least element exists, it serves as an isomorphism (a one-to-one mapping) of the set of all ordinals VV onto the ordinal -y.

Overall, the proof outlines the existence and uniqueness of an isomorphic ordinal that can be obtained from a well-ordered set W using the function F, and it relies on the Replacement Axioms and the concept of least element to establish this result.

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GF preserves the identity and addition operations, and hence GF: V→U is an isomorphism.

First, we will show that GF is linear. Let u, v be vectors in V and c be a scalar in K. Then we have:

\(GF(cu + v) = G(F(cu + v)) = G(cF(u) + F(v)) = G(cF(u)) + G(F(v))= cG(F(u)) + G(F(v)) = c(GF(u)) + GF(v)\)

Thus, GF is linear.

Next, we will show that GF is bijective. Since F and G are isomorphisms, they are both invertible. Let\(F^-1\)and \(G^-1\) denote their respective inverses. Then for any u in U, we have:

\((GF)^-1(u) = F^-1(G^-1(u))\)

This shows that GF is invertible, and hence bijective.

Finally, we will show that GF preserves the identity and addition operations. Let v1, v2 be vectors in V. Then we have:

\(GF(v1 + v2) = G(F(v1 + v2)) = G(F(v1) + F(v2)) = G(F(v1)) + G(F(v2))= GF(v1) + GF(v2)\)

Also, since F and G are isomorphisms, they preserve the identity operations:

\(GF(0v) = G(F(0v)) = G(0w) = 0u\\GF(v) = G(F(v)) = G(0w) = 0u if v=0v\)

Thus, GF preserves the identity and addition operations, and hence GF: V→U is an isomorphism.

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Answer:

128 girls

Step-by-step explanation:

boys : girls = 5 : 8

Number of boys  = 5x

Number of girls = 8x

Total students  = 208

5x + 8x = 208

       13x = 208

           x = 208/13

x =  16

Number of girls = 8x = 8 * 16 = 16 * 8

                         = 128

Answer:

12

Step-by-step explanation:

Answer:

A.) 20h + 8

Step-by-step explanation:

The fence is shortest if the side facing the river is of 400m and the other two are 200 m.

Dimensions of rectangle

x = length of the side parallel to the river

y = length of each of the other two sides

If xy = 80,000, then y = 80,000/x

L = length of the fence

L = x + 2y

= x + 160,000/x, where x is greater than zero

L' = 1 - 160,000/x2 = (x2 - 160,000)/x2

When x = 400 or -400, L' equals 0.

As x cannot be negative, it must be 400.

When 0 x 400, L' is 0. As a result, L is diminishing.

L' > 0 for x > 400. As a result, L is growing.

As a result, with x = 400 m y = 80,000/x = 200 m, L has a relative and absolute minimum.

The fence is shortest if the side parallel to the river has length 400 m and the other 2 sides each have length 200 m.

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Part (a)

The cost is the initial cost plus the cost per slushie multiplied by the number of slushies sold.

\(C(x)=500+1.25x\)

Part (b)

The revenue is the number of slushies sold multiplied by the amount charged per slushie.

\(R(x)=3.50x\)

The value of d when h is 500m is approximately 1,813m

Give the heights above the ground (hm) after it has dropped expressed as:

h = 3/8(d-480),

If h = 500m, then;

500 = 3/8(d - 480)

Cross multiply

500*8 = 3(d - 480)

4000 = 3(d - 480)

Expand to have:

4000 = 3d - 1440

3d = 5440

d = 1,813.3m

Hence the value of d when h is 500m is approximately 1,813m

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Answer: The result can be shown in multiple forms.

Inequality Form:

x>−5

Interval Notation:

(−5,∞)

Step-by-step explanation:

Answer:because if we plug this in it will be -7 > -5, this is false because this is saying that -7 has a greater value that -5.

Step-by-step explanation:

hope the helps<3

Answer:

Step-by-step explanation:

You want points A(-4, 0), B(0, -1) and C(-3, -3) reflected across the y-axis and translated left 5 and up 2.

The reflection across the y-axis changes the sign of the x-coordinate:

  (x, y) ⇒ (-x, y)

The translation adds the translation vector to the reflected coordinates.

  (x, y) ⇒ (x -5, y +2) . . . . . . translation (by itself)

Then the result of both transformations is ...

  (x, y) ⇒ (-x -5, y +2)

For a number of points, this arithmetic is conveniently accomplished by a calculator. The result is ...

Answer:

x=21 y=17

Step-by-step explanation:

to find the opposite angle of (8y+2) you have to calculate 180-42

we know that in a parallelogram the opposite angles are equal

8y+2=138

8y=136

y=17

in a parallelogram the sum of the angles is 36

2(8y+2)+2*2x=360

2(8*17+2)+4x=360

2(136+2)+4x=360

272+4+4x=360

276+4x=360

4x=84

x=21

The exact values of the remaining trigonometric functions of θ are:

sin(θ) = √(1/64)

cos(θ) = -8

tan(θ) = -8√(1/64)

csc(θ) = 1

cot(θ) = -√(1/64) / 8

Given that sec(θ) = -8 and sin(θ) > 0, we can find the exact values of the remaining trigonometric functions using the Pythagorean identity:

sec^2(θ) = 1/sin^2(θ)

Substituting the value of sec(θ), we have:

(-8)^2 = 1/sin^2(θ)

64 = 1/sin^2(θ)

sin^2(θ) = 1/64

sin(θ) = ±√(1/64)

Since sin(θ) > 0, we take the positive square root:

sin(θ) = √(1/64)

Next, we use the reciprocal identity for cosecant:

csc(θ) = 1/sin(θ)

Substituting the value of sin(θ), we have:

csc(θ) = 1/√(1/64) = 8√(1/64) = 8/√(64) = 8/8 = 1

Next, we use the reciprocal identity for cotangent:

cot(θ) = 1/tan(θ)

We can find the value of tan(θ) using the definition:

tan(θ) = sin(θ) / cos(θ)

Substituting the values of sin(θ) and cos(θ), we have:

tan(θ) = √(1/64) / (-8) = -√(1/64) / 8

Finally, we use the reciprocal identity for a tangent:

tan(θ) = 1/cot(θ)

Substituting the value of cot(θ), we have:

tan(θ) = -8√(1/64)

Therefore, the exact values of the remaining trigonometric functions of θ are:

sin(θ) = √(1/64)

cos(θ) = -8

tan(θ) = -8√(1/64)

csc(θ) = 1

cot(θ) = -√(1/64) / 8

The complete question is:-

Find the exact value of each of the remaining trigonometric functions of

θ. Rationalize denominators when applicable.

secθ=−8, given that sinθ>0

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Answer:

A movie is $4.50 and a video game is $5

Step-by-step explanation:

Create a system of equations where m is the cost of each movie and v is the cost of each video game:

2m + 5v = 34

8m + 3v = 51

Solve by elimination by multiplying the top equation by -4:

-8m - 20v = -136

8m + 3v = 51

Add these together and solve for v:

-17v = -85

v = 5

So, a video game is $5. Plug in 5 as v into one of the equations, and solve for m:

2m + 5v = 34

2m + 5(5) = 34

2m + 25 = 34

2m = 9

m = 4.5

A movie is $4.50 and a video game is $5