The base of a triangle is 3 inches more than two times the height. If the area of the triangle is 7 in.² find the base and height.

The graph of the equation f(x) = 1/2x - 5 is the graph (b)

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

f(x) = 1/2x - 5

The above expression is a linear equation that implies that

Slope = 1/2

y-intercept = -5

Next, we determine the graph

The graph that has a slope of 1/2 and y-intercept of -5 is (b)

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Answer:

x = - 5 , x = 2

Step-by-step explanation:

f(x) = x² + 3x - 10

to find the zeros let f(x) = 0 , that is

x² + 3x - 10 = 0

consider the factors of the constant term (- 10) which sum to give the coefficient of the x- term (+ 3)

the factors are + 5 and - 2 , since

5 × - 2 = - 10 and 5 - 2 = + 3 , then

(x + 5)(x - 2) = 0 ← in factored form

equate each factor to zero and solve for x

x + 5 = 0 ( subtract 5 from both sides )

x = - 5

x - 2 = 0 ( add 2 to both sides )

x = 2

the zeros are x = - 5 , x = 2

Answer:

A acute angle is a angle that is less than 90*

The calculated length of the arc JK is 7π

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

Central angle = 140 degrees

Radius, IJ = 9 inches

Using the above as a guide, we have the following:

JK = Central angle/360 * 2 * π * Radius

Substitute the known values in the above equation, so, we have the following representation

JK = 140/360 * 2 * π * 9

Evaluate

JK = 7π

Hence, the length of the arc is 7π

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The triangles DEF and SRQ are not similar triangles

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

The triangles in this figure are

DEF and SRQ

These triangles are not similar

This is because:

The corresponding angles in the triangles are not equal

For DEF, the angles are

50, 90 and 40

For SRQ, the angles are

51, 90 and 39

This means that they are not similar by any similarity statement

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The nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

To determine the number of Lasix 20 mg tablets that should be administered to the patient, we need to calculate how many tablets are equivalent to the prescribed dose of 80 mg.

Given that each Lasix tablet contains 20 mg of the medication, we can divide the prescribed dose (80 mg) by the dosage strength of each tablet (20 mg) to find the number of tablets needed.

Number of tablets = Prescribed dose / Dosage strength per tablet

Number of tablets = 80 mg / 20 mg

Number of tablets = 4 tablets

Therefore, the nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

It is important to note that this calculation assumes that the Lasix tablets can be divided or split if necessary. However, it is crucial to follow the specific instructions provided by the prescribing physician or consult with a pharmacist if there are any concerns about the appropriate administration of the medication.

Additionally, it is important to consider any additional instructions, such as the frequency and timing of administration, as specified by the physician's order.

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Answer:

  4

Step-by-step explanation:

You want the sum of digits of the largest number that divides 1305, 4665, and 6905 with the same remainder.

We can look at 4665/1305 ≈ 3.57 and 6905/1305 ≈ 5.29 for a clue as to the divisor of interest. These quotients tell us that one possibility is the value that would give quotients of 4 and 6 after the remainder is subtracted from each of the numbers.

For 1305 and 4665, if r is the remainder, we require ...

  4(1305 -r) = 4665 -r

  5220 -4665 = 4r -r

  555/3 = r = 185

If 185 is the remainder in this scenario, then 1305 -185 = 1120 is the divisor. Checking the remainder with 6905, we find ...

  6905/1120 = 6 r 185

The sum of digits of this divisor is 1 + 1 + 2 + 0 = 4.

The sum of the digits in N is 4.

Answer:

a) r = .1880

b) a = .1186

c) r² = .0353

d) b = 3.6780

In general form, the equation 2x^2 - 4x + 6 = 1 can be represented as A = 2, B = -4, and C = 5.

To determine the values of A, B, and C in the general form of the quadratic equation 2x^2 - 4x + 6 = 1, we can compare the given equation with the standard form of a quadratic equation, which is ax^2 + bx + c = 0.

In the given equation, we have:

2x^2 - 4x + 6 = 1

To put it in the general form, we need to move all the terms to the left side of the equation, so the right side is equal to 0:

2x^2 - 4x + 6 - 1 = 0

2x^2 - 4x + 5 = 0

Now we can identify the coefficients A, B, and C in the general form:

A = 2 (coefficient of x^2)

B = -4 (coefficient of x)

C = 5 (constant term)

The values of A, B, and C in the general form of the equation 2x^2 - 4x + 6 = 1 are A = 2, B = -4, and C = 5.

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Answer:

(a) To find the average cost in 2011, substitute 11 for x in the function.

g(11) = -1,736.7 + 1,661.6 ln 11 = $2,247.64

The average cost in 2011 was $2,247.64.

(b) Using the graphing calculator, graph the function in the viewing window

[6, 15] by [1,000, 3,000].

The correct graph is B.

(c) A. The average cost increases at a slower rate as time goes on.

Answer:

would this not be a converse statement?

Step-by-step explanation:

triangle ABC is the hypothesis and it's conclusion is triangle DEF

Answer:

The number is 16

Step-by-step explanation:

This follows a multiplication rule,

4 times 1 = 4

4 times 2 = 8

4 times 3 = 12

4 times 4 = 16

So, the number is 16

Answer:  Choice C.   [tex]\displaystyle \boldsymbol{-\frac{\sqrt{5}}{3}}[/tex]

===================================================

Work Shown:

Part 1

[tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\\cos^2(\theta) = 1-\sin^2(\theta)\\\\\cos(\theta) = -\sqrt{1-\sin^2(\theta)} \ \ \text{ ..... cosine is negative in Q2}\\\\\cos(\theta) = -\sqrt{1-\left(\frac{2}{3}\right)^2}\\\\\\cos(\theta) = -\sqrt{1-\frac{4}{9}}\\\\[/tex]

Part 2

[tex]\cos(\theta) = -\sqrt{\frac{9}{9}-\frac{4}{9}}\\\\\cos(\theta) = -\sqrt{\frac{9-4}{9}}\\\\\cos(\theta) = -\sqrt{\frac{5}{9}}\\\\\cos(\theta) = -\frac{\sqrt{5}}{\sqrt{9}}\\\\\cos(\theta) = -\frac{\sqrt{5}}{3}\\\\[/tex]

The Peterson family used their sprinkler for 30 hours, while the Stewart family used theirs for 15 hours.

Let's assume that the Peterson family used their sprinkler for a certain number of hours, which we'll denote as x, and the Stewart family used their sprinkler for the remaining hours, which would be 45 - x.

The water output rate for the Peterson family's sprinkler is given as 35 L per hour. Therefore, the total water output for the Peterson family can be calculated by multiplying the water output rate (35 L/h) by the number of hours they used the sprinkler (x): 35x.

Similarly, for the Stewart family, with a water output rate of 40 L per hour, the total water output for their sprinkler is given by 40(45 - x).

According to the problem, the combined total water output for both families is 1,650 L. Therefore, we can write the equation:

35x + 40(45 - x) = 1,650.

Simplifying the equation, we get:

35x + 1,800 - 40x = 1,650,

-5x = 1,650 - 1,800,

-5x = -150.

Dividing both sides of the equation by -5, we find:

x = -150 / -5 = 30.

So, the Peterson family used their sprinkler for 30 hours, and the Stewart family used theirs for 45 - 30 = 15 hours.

Therefore, the Peterson family used their sprinkler for 30 hours, while the Stewart family used theirs for 15 hours.

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I agree with both Priya's and Han's equations.

To determine if either Priya or Han equation is correct, we can substitute the coordinates of the given point (1,2) into each equation and check if the equation holds true.

For Priya's equation, y - 2 = (1/3)(x - 1), substituting x = 1 and y = 2:

2 - 2 = (1/3)(1 - 1)

0 = 0

The equation holds true, so Priya's equation is correct.

For Han's equation, 3y - x = 5, substituting x = 1 and y = 2:

3(2) - 1 = 5

6 - 1 = 5

5 = 5

The equation also holds true, so Han's equation is correct.

Both Priya's and Han's equations are valid equations of the line with a slope of 1/3 passing through the point (1,2). The equations have different forms, but they are algebraically equivalent and represent the same line. Therefore, I agree with both Priya's and Han's equations.

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The parametric equation of the line passing through P1(2, 4, -3) and P(3, -1, 1) is:

x = 2 + t

y = 4 - 5t

z = -3 + 4t

To find the parametric equation of the line passing through points P1(2, 4, -3) and P(3, -1, 1), we can use the vector equation of a line.

Let's denote the direction vector of the line as d = (a, b, c). Since the line passes through P1 and P, the vector between these two points can be used as the direction vector.

d = P - P1 = (3, -1, 1) - (2, 4, -3) = (1, -5, 4)

Now, we can express the parametric equation of the line as follows:

x = x0 + at

y = y0 + bt

z = z0 + ct

where (x0, y0, z0) is a point on the line and (a, b, c) is the direction vector.

Let's choose P1(2, 4, -3) as the point on the line. Substituting the values, we get:

x = 2 + t

y = 4 - 5t

z = -3 + 4t

Therefore, the parametric equation of the line passing through P1(2, 4, -3) and P(3, -1, 1) is:

x = 2 + t

y = 4 - 5t

z = -3 + 4t

where t is a parameter that varies along the line.

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Answer:

Step Reason

∠NYR and ∠RYA form a linear pair

∠AXY and ∠AXZ form a linear pair Given

∠RYA≅∠AXY Given

∠NYR and ∠RYA are supplementary Definition of Linear Pair

If two angles form a linear pair, then they are supplementary angles Definition of Linear Pair

∠NYR and ∠AXY are supplementary Transitive Property of Equality

m∠NYR+m∠RYA=180

m∠AXY+m∠AXZ=180 Definition of Supplementary Angles

m∠NYR+m∠RYA=m∠AXY+m∠AXZ Substitution Property of Equality

m∠NYR+m∠RYA=m∠NYR+m∠AXZ Substitution Property of Equality

m∠RYA=m∠AXZ Subtraction Property of Equality

∠NYR and ∠AXY are supplementary Definition of Supplementary Angles

m∠NYR+m∠AXY=180

m∠NYR+m∠RYA=m∠NYR+m∠AXY Substitution Property of Equality

m∠RYA=m∠AXY Subtraction Property of Equality

∠NYR≅∠AXY Definition of Congruent Angles.

Answer: C

Step-by-step explanation:

The function exists at all points on the interval with no discontinuities (such as jump discontinuities).

Answer:

31

Step-by-step explanation:

you add the hats to get the total number of hats then divide the answer by

No, it is much too high. Then the correct option is B.

An equation is a statement of equality between two expressions consisting of variables and/or numbers.

Given the question above, we need to find if the hats is to high or low.

Calculating the total numbers of hats made, we have

[tex]21 + 29 + 12 = 62 \ \text{hats}[/tex]

If Edna wants to split 62 hats evenly between two hospital, then each hospital will get

[tex]\dfrac{62}{2} = 31 \ \text{hats}[/tex]

Therefore, if Edna works out that each hospital gets 62 hats, No it is too high, as that is the total of all the hat that is available

Hence, the correct option is B.

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Edna just joined a group that makes hats for babies in the hospital. Two weeks ago they made 21 hats. Last week they made 29 hats. This week they made 12 hats. All these hats will be split evenly between 2 nearby hospitals. Edna works out that's 62 hats for each hospital. Does that sound about right?

A. Yes

B. No, it is much too high

C. No, it is much too low

Hello!

Volume

= (18cm * 15cm * 6cm) + ((13cm - 6cm) * 15cm * 6cm)

= 1,620cm³ + 630cm³

= 2,250cm³

The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:

πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:

A = (πr^2)/2 + rh

To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:

r = (9 - 2h)/(π)

Now we can rewrite the area function in terms of h only:

A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)

Simplifying this equation, we get:

A = (1/2)(9h - h^2/π)

To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:

dA/dh = 9/2 - h/π = 0

Solving this equation, we find:h = 9π/2

Substituting this value of h back into the area function, we get:

A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4

Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

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Answer:

x ≈ 77.79 ft

Step-by-step explanation:

using the sine ratio in the right triangle

sin40° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{50}{x}[/tex] ( multiply both sides by x )

x × sin40° = 50 ( divide both sides by sin40° )

x = [tex]\frac{50}{sin40}[/tex] ≈ 77.79 ft ( to the nearest hundredth )

Answer:

∠ NPQ = 120°

Step-by-step explanation:

the central angle NPQ is twice the angle on the circle NRQ , subtended by the same arc NQ , then

∠ NPQ = 2 × 60° = 120°

Answer: 0.3464 (correct upto 4 decimal places )

Step-by-step explanation:

[tex]\sqrt{3/25}[/tex]= [tex]\sqrt{3} /\sqrt{25\\}[/tex]     (as the square root of 25 is 5)

=1.73205/5

=0.3464

Answer: The statement that correctly describes the data is:

The typical value is 17. Most values are close to 17, except 4, which is an extreme value.

This is because the value 17 appears most frequently in the data set, making it the mode or the typical value. The value 4 is an extreme value as it is the minimum value in the data set. The maximum value of 18 is not the typical value because it is not as representative of the overall distribution of ages in the data set as the mode, which is 17.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve these problems, we can use the Poisson probability formula:

P(x; λ) = (e^(-λ) * λ^x) / x!

Where:

P(x; λ) is the probability of x events occurring

e is the base of the natural logarithm (approximately 2.71828)

λ is the average rate of events occurring in the given time period

x is the number of events

(a) Probability of exactly 4 orders arriving in 30 minutes:

The average rate of orders is given as 5 orders per hour. To find the average rate of orders in 30 minutes, we divide it by 2 (since 30 minutes is half an hour):

λ = 5 orders/hour / 2 = 2.5 orders/30 minutes

Using the Poisson probability formula:

P(x = 4; λ = 2.5) = (e^(-2.5) * 2.5^4) / 4!

Calculating this:

P(x = 4; λ = 2.5) ≈ (0.082 * 39.0625) / 24

P(x = 4; λ = 2.5) ≈ 3.22265625 / 24

P(x = 4; λ = 2.5) ≈ 0.134

Therefore, the probability that exactly 4 orders will arrive in 30 minutes is approximately 0.134, or 13.4%.

(b) Probability of at least 2 orders arriving in an hour:

To find the probability of at least 2 orders, we need to calculate the probabilities of having 0 and 1 order and subtract it from 1 (since it's the complement).

Using the Poisson probability formula:

P(x = 0; λ = 5) = (e^(-5) * 5^0) / 0! = e^(-5) ≈ 0.0067

P(x = 1; λ = 5) = (e^(-5) * 5^1) / 1! ≈ 0.0337

P(at least 2 orders) = 1 - P(x = 0) - P(x = 1) ≈ 1 - 0.0067 - 0.0337 ≈ 0.9596

Therefore, the probability of at least 2 orders arriving in an hour is approximately 0.9596, or 95.96%.

Answer:

Step-by-step explanation:

39 !!!!!

0.612 can be rewritten as the simplified fraction 153/250.

Question: Rewrite as a simplified fraction. 0.612
To rewrite 0.612 as a simplified fraction, we need to convert the decimal into a fraction.
Step 1: Count the number of decimal places.
In this case, 0.612 has three decimal places.
Step 2: Write the decimal as a fraction with the decimal part as the numerator and the denominator as the place value of the rightmost digit.
Since there are three decimal places, the denominator will be 1000 (10 raised to the power of 3).
0.612 = 612/1000
Step 3: Simplify the fraction.
To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator. In this case, both the numerator and denominator are divisible by 4.
612/1000 = (612 ÷ 4) / (1000 ÷ 4) = 153/250

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Answer:

A) [tex]\displaystyle y=\left \{ {{x^3-4,\,x\leq 1} \atop {x^2-3,\,x > 1}} \right.[/tex]

Step-by-step explanation:

The first "piece" of the piecewise function, [tex]y=x^3-4[/tex], contains [tex]x=1[/tex] because of the closed dot there.

The second "piece" of the piecewise function, [tex]y=x^2-3[/tex], doesn't contain [tex]x=1[/tex] because of the open dot there.

What occurs between the two pieces is called a jump discontinuity.

Therefore, A is the correct answer.