Laine reads 200 pages in 240 minutes.
If Laine reads 25 pages at the same rate, how long will it take her?

The correct statements that are true of the function shown in the graph is,

A. The function is increasing over the interval 0 < x < 3.

E. The function is decreasing over the interval 0 < x < 1.

Since, A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Since, We have to given that;

Graph of the Function are shown in figure.

Now, By graph we can see that,

The function is decreasing over the interval 0 < x < 1 as it goes down.

And, The function is increasing over the interval 0 < x < 3 as it goes upwards direction.

Thus, The correct statements that are true of the function shown in the graph is,

A. The function is increasing over the interval 0 < x < 3.

E. The function is decreasing over the interval 0 < x < 1.

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Hello!

We have all angles of the triangle:

We will use the law of cosines. This relation is valid for all sides of any t

We have:

angle A = 12°

côté a = 10

angle B = 150°

This is therefore the first case of application of the sine law.

So:

\(\sf \dfrac{b}{sin~B} = \dfrac{a}{sin~A}\)

\(\sf b =\dfrac{sin~B~*~a}{sin~A} = \dfrac{sin~150~*~10cm}{sin~12} = \dfrac{arcsin~0.5~*~10cm}{arcsin~0.2079116908} = \dfrac{30~*~10cm}{12} = \dfrac{300cm}{12} = \boxed{\sf25cm}\)

Answer:

1/2x equal to or greater than 17

Cindy has 34 flowers in her garden

Step-by-step explanation:

To solve the pair of equations graphically: A. find the point of intersection of the two lines, y = -3x + 5 has a slope of -3, and y-intercept of 5, and y = x + 2 has a slope of 1, and y-intercept of 2.

To solve for the pair of equations graphically, you have to plot each of the line of each equation on a coordinate plane, then find the coordinates of the point where both lines intersect each other.

The point of intersection is the solution to the system of equations that both lines represent.

Given the equations:

y = -3x + 5 --> eqn. 1

y = x + 2 --> eqn. 2

The slope of the line of y = -3x + 5 is -3, while the y-intercept is 5.

The slope of the line of y = x + 2 is 1, while the y-intercept is 2.

Thus, the red line in the image is the graph of y = -3x + 5, while the blue is for y = x + 2.

The point of intersection, which is the solution is: (075, 2.75).

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Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$. Therefore $x=y=12\sqrt{3}$, which is our answer

In a 30-60-90 triangle, the sides have the ratio of $1: \sqrt{3}: 2$. Let's apply this to solve for the variables in the given problem.

Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x=y=Let's first find the ratio of the sides in a 30-60-90 triangle.

Since the hypotenuse is always twice as long as the shorter leg, we can let $x$ be the shorter leg and $2x$ be the hypotenuse.

Thus, we have: Shorter leg: $x$Opposite the $60^{\circ}$ angle: $x\sqrt{3}$ Hypotenuse: $2x$

Now, let's apply this ratio to solve for the variables in the given problem. We know that $x = y$ since they are equal in the problem.

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$

Therefore, $x=y=12\sqrt{3}$, which is our answer.

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Answer:

45 feet.

Step-by-step explanation:

The Lighthouse is half of the Base.

Answer:

c light energy

Step-by-step explanation:

I did this quiz in school easy I think

In the given triangles RTS and PTQ

Angle RTS = Angle PTQ (Common Angle)

Agle SRT = Angle QPT (Corresponding angle)

Thus, from Angle Angle similarity, triangle RTS and PTQ are similar

From the properties of similar triangle, The ratio of corresponding sides of the similar triangle always equal:

In the given figure :

RT = RP + PT

RT = 2 + 18

RT = 20

Substitute each value and simplify :

As TS = TQ + QS

30 = 27 + SQ

SQ = 30 - 27

SQ = 3

Answer : C) 3 cm

Answer:

43.6 has 3 significant figures.

9514 1404 393

Answer:

  7(1/4) = 7/4 = 1 3/4

Step-by-step explanation:

Multiplication is used to simplify repeated addition. The multiplier represents the number of times the sum includes the repeated value.

Here, the term 1/4 appears in the sum 7 times. That means we can write the equivalent expression ...

  7 × 1/4 . . . . written as a multiplication expression

The product is found by multiplying the numerator of the fraction by the integer factor.

  7 × 1/4 = 7/4

This improper fraction can be written as a mixed number.

  7/4 = 1 3/4 . . . . the value of the sum

Answer:

1/4 + 1/4+1/4+1/4+1/4+1/4+1/4

(1/4) x 7

Step-by-step explanation:

Answer:

v=m/d

Step-by-step explanation:

D=m/v

D*v=m

d*v/d=m/d

v=m/d

The required solution for v is v = m/D.

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign =.

The given equation is,

D = m/v

To solve for v we need to isolate v to one side and other variables to another side.

Therefore multilpying the equation both the side by we get,

Dv = v*m/v

Solving we obtain,

Dv = m

Now divide the equation both side by D we obtain,

Dv/D = m/D

Solving we obtain,

v = m/D

which is the required solution for v.

Thus, the required solution for v is v = m/D.

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The sum of expected marks is given as follows:

9375.

Each question has four choices, hence the probability of choosing the correct choice is given as follows:

p = 1/4 = 0.25.

Then the expected number of correct answers is given as follows:

E(X) = 0.25 x 150

E(X) = 37.5.

Then the expected grade for a single student is given as follows:

37.5 - 0.25(150 - 37.5) = 9.375.

The expected sum for the 1000 students is then given as follows:

1000 x 9.375 = 9375.

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Check if the equation is exact, which happens for ODEs of the form

\(M(x,y)\,\mathrm dx+N(x,y)\,\mathrm dy=0\)

if \(\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}\).

We have

\(M(x,y)=x^2+y^2+x\implies\dfrac{\partial M}{\partial y}=2y\)

\(N(x,y)=xy\implies\dfrac{\partial N}{\partial x}=y\)

so the ODE is not quite exact, but we can find an integrating factor \(\mu(x,y)\) so that

\(\mu(x,y)M(x,y)\,\mathrm dx+\mu(x,y)N(x,y)\,\mathrm dy=0\)

is exact, which would require

\(\dfrac{\partial(\mu M)}{\partial y}=\dfrac{\partial(\mu N)}{\partial x}\implies \dfrac{\partial\mu}{\partial y}M+\mu\dfrac{\partial M}{\partial y}=\dfrac{\partial\mu}{\partial x}N+\mu\dfrac{\partial N}{\partial x}\)

\(\implies\mu\left(\dfrac{\partial N}{\partial x}-\dfrac{\partial M}{\partial y}\right)=M\dfrac{\partial\mu}{\partial y}-N\dfrac{\partial\mu}{\partial x}\)

Notice that

\(\dfrac{\partial N}{\partial x}-\dfrac{\partial M}{\partial y}=y-2y=-y\)

is independent of x, and dividing this by \(N(x,y)=xy\) gives an expression independent of y. If we assume \(\mu=\mu(x)\) is a function of x alone, then \(\frac{\partial\mu}{\partial y}=0\), and the partial differential equation above gives

\(-\mu y=-xy\dfrac{\mathrm d\mu}{\mathrm dx}\)

which is separable and we can solve for \(\mu\) easily.

\(-\mu=-x\dfrac{\mathrm d\mu}{\mathrm dx}\)

\(\dfrac{\mathrm d\mu}\mu=\dfrac{\mathrm dx}x\)

\(\ln|\mu|=\ln|x|\)

\(\implies \mu=x\)

So, multiply the original ODE by x on both sides:

\((x^3+xy^2+x^2)\,\mathrm dx+x^2y\,\mathrm dy=0\)

Now

\(\dfrac{\partial(x^3+xy^2+x^2)}{\partial y}=2xy\)

\(\dfrac{\partial(x^2y)}{\partial x}=2xy\)

so the modified ODE is exact.

Now we look for a solution of the form \(F(x,y)=C\), with differential

\(\mathrm dF=\dfrac{\partial F}{\partial x}\,\mathrm dx+\dfrac{\partial F}{\partial y}\,\mathrm dy=0\)

The solution F satisfies

\(\dfrac{\partial F}{\partial x}=x^3+xy^2+x^2\)

\(\dfrac{\partial F}{\partial y}=x^2y\)

Integrating both sides of the first equation with respect to x gives

\(F(x,y)=\dfrac{x^4}4+\dfrac{x^2y^2}2+\dfrac{x^3}3+f(y)\)

Differentiating both sides with respect to y gives

\(\dfrac{\partial F}{\partial y}=x^2y+\dfrac{\mathrm df}{\mathrm dy}=x^2y\)

\(\implies\dfrac{\mathrm df}{\mathrm dy}=0\implies f(y)=C\)

So the solution to the ODE is

\(F(x,y)=C\iff \dfrac{x^4}4+\dfrac{x^2y^2}2+\dfrac{x^3}3+C=C\)

\(\implies\boxed{\dfrac{x^4}4+\dfrac{x^2y^2}2+\dfrac{x^3}3=C}\)

To solve the expression 1 - (1 + 0.04/12)^(-12x10), you can follow these steps: Step 1: Simplify the exponent. In this case, -12x10 simplifies to -120.

Step 2: Evaluate the term within the parentheses first. 0.04/12 simplifies to 0.0033333 (approximately).

Step 3: Add 1 to 0.0033333 to get 1.0033333.

Step 4: Raise 1.0033333 to the power of -120.

Step 5: Calculate the value inside the parentheses using a calculator or software. The result is approximately 0.742657.

Step 6: Subtract the value obtained in Step 5 from 1.

1 - 0.742657 = 0.257343 (approximately).

Hence, the value of the expression 1 - (1 + 0.04/12)^(-12x10) is approximately 0.257343.

It's important to follow the order of operations (PEMDAS/BODMAS) when solving mathematical expressions. In this case, the exponent is evaluated first, followed by addition and subtraction. Utilizing a calculator or software that supports exponentiation and parentheses can help simplify complex expressions and obtain accurate results efficiently.

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The simplified expression is 28 - 4 using distributive property.

To simplify the expression (4 + )(7 – ), we can use the distributive property of multiplication over addition.

First, we have to multiply the 4 by both the terms inside parentheses:

(4 + )(7 – ) = (47) + (4- )

Next, we distribute negative sign to second term inside parentheses:

(47) + (4- ) = 28 - 4

The simplified expression = 28 - 4.

In other words, the phrase is the outcome of adding 4 to an unknown quantity, taking it out of 7 after that, and then taking the outcome of that subtraction out of 28. The operation's outcome is simplified to 24, which can be used in additional calculations or problem-solving.

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Answer:

Let's denote:

- The number of orders Diane served as `D`

- The number of orders Sam served as `S`

- The number of orders Boris served as `B`

From the problem, we know:

1. `D + S + B = 54` (the total number of orders they served)

2. `D = S - 6` (Diane served 6 fewer orders than Sam)

3. `B = 2S` (Boris served 2 times as many orders as Sam)

We can substitute equations 2 and 3 into equation 1 to solve for the variables:

Substitute `D` and `B` in equation 1:

`(S - 6) + S + 2S = 54`

Combine like terms:

`4S - 6 = 54`

Add 6 to both sides:

`4S = 60`

Divide by 4:

`S = 15`

Now that we know `S = 15`, we can find `D` and `B` by substituting `S` into equations 2 and 3:

`D = S - 6 = 15 - 6 = 9`

`B = 2S = 2 * 15 = 30`

So, Diane served 9 orders, Sam served 15 orders, and Boris served 30 orders.

Answer:

yes

Step-by-step explanation:

y = 4x + 4

24 = 4(5) + 4

24 = 20 + 4

24 = 24

This equation has infinitely many solutions.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Here, we have

Given: 3x+4y = -10...(1),

y = -3/4x - 5/2....(2)

We solve this linear equation and we get

We multiply equation (2) by 4 and we get

4y + 3x = -5(2)

4y + 3x = -10

Hence, this equation has infinitely many solutions.

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Answer:

This is the website for the answer it's the fourth question.

https://mathsheetz.weebly.com/uploads/1/0/9/1/109181607/03-07-18_key_notes___hw_geometric_sequences.pdf

Step-by-step explanation:

Hope this helped! :)

The angle m∠J  in the right angle triangle is 58.1 degrees.

One of the angle of a right tangle triangle is 90 degrees. The sum of

angles in a triangle is 180 degrees.

Therefore, the side length LK can be found using Pythagoras's theorem and the angle can be found using trigonometric ratios.

Hence,

tan ∠J = opposite / adjacent

tan ∠J = 15.1 / 9.4

∠J = tan⁻¹ 1.60638297872

∠J = 58.0909229196

Therefore,

m∠J = 58.1 degrees

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The circumference of the given circle is 41 cm

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

The circumference of a circle is the boundary length of the circle, it is basically the perimeter of the circle, in degree measure it can not exceed by 360°

Given that, a circle, with diameter, 13 cm, we need to find it circumference.

We know that, the circumference of a circle is given by,

Circumference of the circle = π × diameter

= 3.14 × 13

= 40.82

≈ 41 cm

Hence, the circumference of the given circle is 41 cm

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Answer: A: 3/5

Step-by-step explanation:

He made 9 shots

He attempted 15

The ratio will be 9/15, which can be simplified to 3/5

Have a nice day :)

Answer:

A) 3/5

Step-by-step explanation:

No.of baskets attempted = 15

No.of baskets made = 9

Given, To find the ratio of no.of baskets made to no.of baskets attempted

9:15 (or) 9/15

If we simplify 9/15, we get 3/5

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Solving a quadratic equation, we will see that the object will hit the ground after 5.9 seconds.

The equation for the vertical movement of an object will be:

H(t) = -16*t^2 + v0*t + h0

Where v0 is the initial velicity, in this case 85ft/s, and h0 is the initial height,  55ft.

Then the height equation is:

H(t) = -16*t^2 + 85*t + 55

The object will hit the ground when the height is equal to zero, then we need to solve:

-16*t^2 + 85*t + 55 = 0

Using the quadratic formula we will get:

\(t = \frac{-85 \pm \sqrt{(85)^2 - 4*(-16)*55} }{2*-16} \\\\t = \frac{-85 \pm 103.7 }{-32}\)

We only care for the positive solution, which is:

t = (-85 - 103.7)/-32 = 5.9

So it will take 5.9 seconds for the object to hit the ground.

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Answer:

The biggest decrease in time from the 1st leg and the 2nd leg is:

1st leg: 55.037 seconds

2nd leg: 40.38 seconds

Step-by-step explanation:

where's the graph? ( ಠ_ಠ)

The equation of the circle with radius 9 and center ( -1,-8 ) is( x + 1 )² + ( y + 8  )² = 81.

The standard form equation of a circle with center (h, k) and radius r is:

( x - h )² + ( y - k )² = r²

Given that the circle has a center of (-1, -8) and the radius is 9.

Hence; from the standard form of the equation of the circle:

Center ( h , k ) = ( -1, -8 )

h = -1

k = -8

And radius r = 9

Plug these values into the above formula and simplify.

( x - h )² + ( y - k )² = r²

( x - ( -1 ) )² + ( y - ( -8 ) )² = 9²

Simplify

( x + 1 )² + ( y + 8  )² = 81

Therefore, the equation of the circle is ( x + 1 )² + ( y + 8  )² = 81.

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Answer:

She needs 32 quarters.

Step-by-step explanation:

d = dime   q = quarters

d + q = 28   so    d = 28-q

0.1d + 0.25q = 5.50

0.10 * (28-q) + 0.25q = 5.50

2.80 - 0.10q + 0.25q = 5.50

0.15q = 5.50 - 2.80

0.15q = 2.70

q = 2.70 / 0.15

q = 18 quarters (she has)

50-18= 32 quarters (she needs)

Answer:

$246

Step-by-step explanation: