1. The weight of the patient in kilograms is 27.216 kg. (60 lb * 0.4536 kg/lb = 27.216 kg)
2. The total dosage of medication required for the patient is 13.608 mg. [tex](0.5 mg/kg \times 27.216 kg = 13.608 mg)[/tex]
3. The patient should be administered 1.3608 mL of the stock medication. (13.608 mg / 10 mg/mL = 1.3608 mL)
To calculate the necessary values based on the given information, let's follow the steps below:
Determine the weight of the patient in kilograms:
Given that the patient weighs 60 lb, we can convert this to kilograms using the conversion factor of 1 lb = 0.4536 kg.
Weight (in kg)[tex]= 60 lb \times 0.4536 kg/lb = 27.216 kg.[/tex]
Calculate the total dosage of medication required for the patient:
The medication order is 0.5 mg/kg, and the patient weighs 27.216 kg.
Total dosage [tex]= 0.5 mg/kg \times 27.216 kg = 13.608 mg.[/tex]
Determine the amount of stock medication required in milliliters (mL):
The stock medication is available in a concentration of 10 mg/mL.
To find the volume required, we need to divide the total dosage by the concentration of the stock medication.
Volume (in mL) = Total dosage (in mg) / Concentration (in mg/mL) = 13.608 mg / 10 mg/mL = 1.3608 mL.
Therefore, based on the given information, the weight of the patient is 27.216 kilograms, the total dosage of medication required is 13.608 milligrams, and 1.3608 milliliters of the stock medication should be administered to the patient.
Please note that when administering medication, it is crucial to follow the guidance of a healthcare professional and consider other factors such as the specific medication instructions, patient's condition, and any allergies or contraindications.
For similar question on weight.
https://brainly.com/question/28795033
#SPJ11
Question: A patient weighs 60 lb, and the medication order is 0.5 mg/kg. The stock medication is available in a concentration of 10 mg/mL.
Based on this information, calculate the following
What is the weight of the patient in kilograms? (1 lb = 0.4536 kg)
What is the total dosage of medication required for the patient?
How many milliliters (mL) of the stock medication should be administered to the patient?
Please provide the necessary calculations and steps to find the answers based on the given information.
the radius of a sphere with a volume of 4.5π cubic centimeters.
hello
the answer to the question is:
volume of sphere = ⁴⁄₃πr³
4.5π = ⁴⁄₃πr³ ----> r³ = 3.375 ----> r = 1.5 cm
What is the intermediate step in the form (x+a)^2=b(x+a)
2
=b as a result of completing the square for the following equation?
x^2+22x=8x-53
By completing squares we will get the expression:
(x + 7)² = -4
How to complete squares in a quadratic equation?Here we have the quadratic equation:
x² + 22x = 8x - 53
First, move all the terms to the left side, then we will get:
x² + 22x - 8x + 53 = 0
x² + 14x + 53 =0
Now, remember the perfect square trinomial:
(a + b)² = a² + 2ab + b²
Then we can rewrite our expression as:
x² + 2*7*x + 53 =0
Now we can add and subtract 7², then we will get.
x² + 2*7*x + 7² - 7² + 53 =0
(x + 7)² - 7² + 53 = 0
(x + 7)² - 49 + 53 = 0
(x + 7)² + 4 = 0
(x + 7)² = -4
That is the expression we wanted.
Learn more about completing squares at:
https://brainly.com/question/10449635
#SPJ1
Matematicas III- Geometria analitica 1- Calcula el perimetro y área de las triángulos Cuyos vertices son a) A(2,2) B(7,-1) ((3,-8)
The perimeter of the triangle is √34 + √65 + √101, and the area is 2.5.
We have,
To calculate the perimeter and area of a triangle, we need to know the coordinates of its vertices.
Let's calculate the perimeter and area for the given triangles.
a) Triangle with vertices A(2,2), B(7,-1), C(3,-8)
To calculate the perimeter, we need to find the lengths of the three sides of the triangle and sum them up.
Side AB:
Length AB = √((x2 - x1)² + (y2 - y1)²)
= √((7 - 2)² + (-1 - 2)²)
= √(5² + (-3)²)
= √(25 + 9)
= √34
Side BC:
Length BC = √((x2 - x1)² + (y2 - y1)²)
= √((3 - 7)² + (-8 - (-1))²)
= √((-4)² + (-7)²)
= √(16 + 49)
= √65
Side AC:
Length AC = √((x2 - x1)² + (y2 - y1)²)
= √((3 - 2)² + (-8 - 2)²)
= √(1² + (-10)²)
= √(1 + 100)
= √101
Perimeter = AB + BC + AC
= √34 + √65 + √101
To calculate the area, we can use the formula for the area of a triangle:
Area = 1/2 x base x height
We can consider any side of the triangle as the base and find the height corresponding to that base.
Let's consider side AB as the base.
Height h = distance between point C and the line AB
Using the formula for the distance between a point (x0, y0) and a line Ax + By + C = 0:
h = |(Ax0 + By0 + C)| / √(A² + B²)
Equation of line AB:
(x2 - x1) (y - y1) - (y2 - y1)(x - x1) = 0
(7 - 2)(y - 2) - (-1 - 2)(x - 2) = 0
5(y - 2) + 3(x - 2) = 0
5y - 10 + 3x - 6 = 0
5y + 3x - 16 = 0
Plugging in the coordinates of point C (3, -8):
h = |(53 + 3(-8) - 16)| / √(5² + 3²)
= |-5| / √(25 + 9)
= 5 / √34
Area = 1/2 x AB x h
= 1/2 x √34 x (5 / √34)
= 1/2 x 5
= 2.5
Therefore,
The perimeter of the triangle is √34 + √65 + √101, and the area is 2.5.
Learn more about triangles here:
https://brainly.com/question/25950519
#SPJ1
The complete question.
Calculate the perimeter and area of the triangles whose vertices are a) A(2,2) B(7,-1) ((3,-8)
Una receta requiere 9/10 tazas de jugo de manzana. Pam está preparando 3/5 de la receta. ¿Cuántas tazas de jugo de manzana usará Pam?
Pam will use 27/50 cups of apple juice.
How many cups of apple juice will Pam use?An expression in math is a statement having minimum of two numbers, or variables, or both and an operator connecting them.
To get how many cups of apple juice Pam will use, we must calculate 3/5 of 9/10 cups.
The 3/5 of 9/10 is:
= (3/5) * (9/10)
= (3 * 9) / (5 * 10)
= 27/50
Therefore, Pam will use 27/50 cups of apple juice.
Translated question:
A recipe calls for 9/10 cups of apple juice. Pam is preparing 3/5 of the recipe. How many cups of apple juice will Pam use?
Read more about expression
brainly.com/question/1859113
#SPJ1
Use False-Position method to find a real root of f(x) = x3 - 2x - 5 = 0 correct to three decimal places. Please solution
The real roots of the function using false-position method are 1/2 and 5/8
What is the real root of the function?The real root of the function f(x) = x³ - 2x - 5 = 0 using the False-Position method can be calculated as;
1. Choose two initial guesses, a and b, such that f(a) and f(b) have opposite signs. In this case, we can choose a = 0 and b = 1.
[tex]c = \frac{(a * f(b) - b * f(a))}{(f(b) - f(a)}[/tex]
If f(c) = 0, then c is the root of the equation. Otherwise, replace a with b and b with c.
[tex]c = \frac{(0 * f(1) - 1 * f(0))}{(f(1) - f(0))} = \frac{1}{2}[/tex]
Since f(1/2) = -0.25, we can replace a with 1 and b with 1/2.
[tex]c = \frac{\frac{1}{2} * f(1) * f(\frac{1}{2}) }{(f(1) - f(\frac{1}{2}) } = \frac{5}{8}[/tex]
Since f(5/8) = 0.0625, we can stop here and say that the root of the equation is 5/8, which is approximately 0.625.
Where the roots of the equation are 1/2 and 5/8
Learn more on roots of equation here;
https://brainly.com/question/2833285
#SPJ1
PLEASE PLEASE I BEG YOU HELP MEEEE
1)
Surface area of rectangular prism:
SA = 2( hw + lw + lh )
h= height of prism .
w = width of prism .
l = length of prism .
Substitute the values,
h= 4m
w=1.2 m
l= 13.4 m
SA = 2(4*1.2 + 13.4*1.2 + 13.4*4)
SA = 148.96 m²
2)
Surface area of triangular prism:
SA = (S1 +S2 + S3)L + bh
h= height of prism .
b = base of prism .
S1 , S2 , S3 = sides of triangle .
Substitute the values,
SA = (3+ 4 + 0.5)4 + 0.5*3
SA = 31.5 in²
Learn more about prism,
https://brainly.com/question/21416050
#SPJ1
Omg can someone please help me with this
Answer:
6.98
Step-by-step explanation:
5.9454+1.03 =6.9754 which is rounded to 6.98
Find which case are appropriate with the given and look for the vertex, focus, opening of the graph, directrix, and latus rectum.
1. (x-3)^2 = 8(y-4)
2. y^2 = 4^2x
3. (y-2)^2 = 4(x-3)
The case are appropriate with the given:
(x-3)² = 8(y-4)
Vertex: (3, 4)Focus: (3, 6)Opening: UpwardDirectrix: y = 2Latus Rectum: 32 unitsy² = 4²x
Vertex: (0, 0)Focus: (1, 0)Opening: RightwardDirectrix: x = -1Latus Rectum: 16 units(y-2)² = 4(x-3)
Vertex: (3, 2)Focus: (4, 2)Opening: RightwardDirectrix: x = 2Latus Rectum: 16 unitsHow to determine appropriateness?Analyze each given equation to determine the appropriate case and find the vertex, focus, opening of the graph, directrix, and latus rectum.
1. (x-3)² = 8(y-4)
This equation represents a parabola with its vertex form given by (h, k) = (3, 4).
Case 1: The coefficient of (y - k) is positive, indicating an upward-opening parabola.
Vertex: The vertex is (3, 4).
Focus: The focus can be found using the formula (h, k + 1/4a), where a = coefficient of (y - k). In this case, the focus is (3, 4 + 1/4 × 8) = (3, 6).
Directrix: The directrix is a horizontal line located at y = k - 1/4a. In this case, the directrix is y = 4 - 1/4 × 8 = 2.
Latus Rectum: The latus rectum is the length of the chord passing through the focus and perpendicular to the axis of symmetry. In this case, it is equal to 4a = 4 × 8 = 32 units.
2. y² = 4²x
This equation represents a parabola with its vertex form given by (h, k) = (0, 0).
Case 2: The coefficient of x is positive, indicating a right-opening parabola.
Vertex: The vertex is (0, 0).
Focus: The focus can be found using the formula (h + 1/4a, k), where a = coefficient of x. In this case, the focus is (0 + 1/4 × 4, 0) = (1, 0).
Directrix: The directrix is a vertical line located at x = h - 1/4a. In this case, the directrix is x = 0 - 1/4 × 4 = -1.
Latus Rectum: The latus rectum is the length of the chord passing through the focus and perpendicular to the axis of symmetry. In this case, it is equal to 4a = 4 × 4 = 16 units.
3. (y-2)² = 4(x-3)
This equation represents a parabola with its vertex form given by (h, k) = (3, 2).
Case 3: The coefficient of (x - h) is positive, indicating a right-opening parabola.
Vertex: The vertex is (3, 2).
Focus: The focus can be found using the formula (h + 1/4a, k), where a = coefficient of (x - h). In this case, the focus is (3 + 1/4 × 4, 2) = (4, 2).
Directrix: The directrix is a vertical line located at x = h - 1/4a. In this case, the directrix is x = 3 - 1/4 × 4 = 2.
Latus Rectum: The latus rectum is the length of the chord passing through the focus and perpendicular to the axis of symmetry. In this case, it is equal to 4a = 4 × 4 = 16 units.
Find out more on latus rectum here: https://brainly.com/question/31664274
#SPJ1
write an equation of the line that passes through the points (0,-2),(3,13)
Answer: y = 5x-2
Step-by-step explanation:
2 In the diagram below: DC and DE are tangents to the circle at C and E respectively A is the centre of the circle B lies on the circle and BAE is a straight line L N 7.2.1 Prove that AABC|||ADEC 7.2.2 Hence, show that AE. EC = BC. DE (5) (3) [17] TOTAL: 10
DC and DE are tangents to the circle at C and E respectively A is the centre of the circle B lies on the circle and BAE is a straight line L N
7.2.1: AABC is parallel to ADEC (AABC|||ADEC).
7.2.2: This completes the proof of both statements:
AABC|||ADEC and AE · EC = BC · DE.
To prove that AABC is parallel to ADEC, we can make use of the properties of tangents and alternate angles.
Proof:
AABC|||ADEC
DC and DE are tangents to the circle at C and E, respectively.
BAE is a straight line.
To prove AABC|||ADEC, we need to show that the alternate interior angles are congruent.
First, let's consider angle AED and angle ABC.
These angles are alternate interior angles formed by transversal AE intersecting the lines DE and BC.
Since DE is a tangent to the circle at E, angle AED is a right angle (90 degrees).
We know that a tangent to a circle is perpendicular to the radius at the point of tangency.
angle AED = 90 degrees.
Let's consider angle ABC. Since DC is a tangent to the circle at C, angle ABC is also a right angle (90 degrees).
Again, this follows from the property that a tangent is perpendicular to the radius at the point of tangency.
Since both angle AED and angle ABC are right angles, they are congruent:
angle AED = angle ABC.
By the alternate interior angle if two lines are intersected by transversal and the alternate interior angles are congruent, then the lines are parallel.
AABC is parallel to ADEC (AABC|||ADEC).
7.2.2 Showing that AE · EC = BC · DE
To prove that AE · EC = BC · DE, we can use the fact that AABC is parallel to ADEC.
Since AABC is parallel to ADEC, we can apply the intercept theorem or the proportionality theorem.
According to the intercept two parallel lines intersect a set of parallel lines, then the segments formed on one transversal are proportional to the corresponding segments formed on any other transversal.
Using the intercept theorem, we can write the following proportion:
AE/BC = DE/EC
To find AE · EC, we can cross-multiply the proportion:
AE · EC = BC · DE
We have shown that AE · EC is equal to BC · DE.
For similar questions on circle
https://brainly.com/question/28162977
#SPJ11
How many pints are in 6 1/2 quarts?
Answer:
13 pints
Step-by-step explanation:
quarts times 2.
6.5•2=13
Answer:
13 pints.
Step-by-step explanation:
The conversion rate from pints to quarts is 1:2 meaning every 1 pints will result in 2 quarts. Therefore with this formula, (6 1/2)*2 brings the result to 13.
You're welcome!
What is the mode of the data represented in this line plot?
Enter your answer in the box.
A line plot. The number line ranges from 0 to 6. There are 2 xs above the 1. There are 5 xs above the 2. There are 3 xs above the 3. There are 4 xs above the 4. There are 2 xs above the 5.
Answer:
2
Step-by-step explanation:
You want to know the mode of a dot plot that could be represented as ...
1 | x x
2 | x x x x x
3 | x x x
4 | x x x x
5 | x x
ModeThe mode is the data element that appears most often in the data set.
The 5 xs above the 2 is the largest number of xs that appear anywhere, so 2 is the mode.
<95141404393>
Solve the inequality for x
5 3/2 x 2 1/3
Answer:
A
Step-by-step explanation:
5 - [tex]\frac{3}{2}[/tex] x ≥ [tex]\frac{1}{3}[/tex]
multiply through by 6 ( the LCM of 2 and 3 ) to clear the fractions
30 - 9x ≥ 2 ( subtract 30 from both sides )
- 9x ≥ - 28
divide both sides by - 9 , reversing the symbol as a result of dividing by a negative quantity.
x ≤ [tex]\frac{28}{9}[/tex]
Latasha split 36 cups of flour evenly into 39 cases. What decimal is
equivalent to the fraction of a cup of flour that was added to each
case?
Your answer may be exact or accurate to the nearest thousandth.
The decimal equivalent to the fraction of a cup of flour added to each case is approximately 0.923.
To find the decimal equivalent of the fraction of a cup of flour added to each case, we can divide the total amount of flour (36 cups) by the number of cases (39).
Decimal equivalent = Total amount of flour / Number of cases
Decimal equivalent = 36 cups / 39 cases
Calculating this division:
Decimal equivalent ≈ 0.923
Therefore, the decimal equivalent to the fraction of a cup of flour added to each case is approximately 0.923.
For such more questions on decimal equivalent
https://brainly.com/question/30452342
#SPJ11
Please help me I am stuck with this! please help! the triangular prism above undergoes a dilation whose scale factor is 2/3. what is the volume of the image? Round your answer to the nearest tenths place.
The volume of the triangular prism is determined as 2,520 yd².
What is the volume of the triangular prism?The volume of the triangular prism is calculated by applying the following formula as follows;
V = ¹/₂bhl
where;
b is the base of the triangular prismh is the height of the triangular prisml is the length of the triangular prismThe volume of the triangular prism is calculated as;
V = ¹/₂ x 12 yd x 14 yd x 30 yd
V = 2,520 yd²
Thus, the volume of the triangular prism is calculated by applying the following formula for volume of triangular prism.
Learn more about volume of triangular prism here: https://brainly.com/question/1284982
#SPJ1
Urgent help please!!!
The equation of the circle with a center at (-4, 6) and a point on the circumference at (-2, 9) is (x + 4)² + (y - 6)² = 13.
Given:
Center of the circle: (-4, 6)
Point on the circumference: (-2, 9)
The center of the circle (h, k) is given as (-4, 6), which means h = -4 and k = 6.
The formula for the distance between the center and the point on the circumference can be used to determine the radius (r).
The formula for distance is provided by:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
where (x₁, y₁) is the center (-4, 6), and (x₂, y₂) is the point on the circumference (-2, 9).
Putting in the values:
d = √((-2 - (-4))² + (9 - 6)²)
= √((2)² + (3)²)
= √(4 + 9)
= √13
So, the radius (r) is √13.
Now, we can substitute the values of h, k, and r into the general equation of the circle:
(x - h)² + (y - k)² = r²
(x - (-4))² + (y - 6)² = (√13)²
(x + 4)² + (y - 6)² = 13
Therefore, the equation of the circle is (x + 4)² + (y - 6)² = 13.
Learn more about equation of the circle click;
https://brainly.com/question/29104982
#SPJ1
0.045 × 2.05 /0.0025 leaving your answer in standard form
The value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.
To perform the calculation and express the answer in standard form, follow these steps:
Multiply 0.045 by 2.05:
0.045 × 2.05 = 0.09225
Divide the result by 0.0025:
0.09225 / 0.0025
= 36.9
Convert the answer to standard form by writing it as a decimal multiplied by a power of 10:
36.9 = 3.69 × 10
Therefore, the value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.
To learn more on Number system click:
https://brainly.com/question/22046046
#SPJ1
100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
Answer:
Step-by-step explanation:
Ok so, as given in the table, the cost of the 3rd tank is 800$, we can thus determine the cost of 1 cubic inch for a tank and use that to determine the cost of the other tanks.
[tex]volume =L\times W\times H\\=24\times 24\times 24\\=13824 in^3[/tex]
thus, to compute the cost of one cubic inch, we can divide the cost by the volume of the 3rd tank (in cubic inches)
[tex]\frac{800}{13824}=0.0579[/tex] [tex]usd/in^3[/tex]
now, we can determine the dimensions of the second tank that will make it cost 150$
[tex]0.0579\times 18\times W\times 24=150[/tex]
[tex]W=\frac{150}{0.0579\times 18\times 24} =6 in.[/tex]
Now to determine the cost of the first tank, we can multiply its volume by the cost per cubic inch:
[tex]cost=0.0579\times36\times 36\times 36=2700[/tex]$
As of question B, the cost will increase as the width increases.
For Question C, we can find the volume of the sphere by the formula:
[tex]volume=\frac{4}{3}\pi r^3 =\frac{4}{3}\pi \times 24^3=57905 in^3[/tex]
To find the cost of that tank, we just multiply its volume by the cost per unit volume:
[tex]cost=57905\times 0.0579=3352[/tex]$ (roughly)
Find the median of a list of consecutive integers from 31 to 65.
Answer: 48
Step-by-step explanation: median of list of consecutive integers is the mean of the endpoints. (31+65)/2
42. Using Chord-Chord theorem, what is the value of x?
5
10
2
The length of segment x in the two intersecting chords is determined as 4.
What is the value of x?The value of segment x is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
Also this theory states that the product of two segments of a chord is equal to the product of the two segments of second intersecting chord in a circle.
From the diagram, we can set up the following equations and solve for length x;
5 (x) = 10(2)
5x = 20
x = 20/5
x = 4
Learn more about chord length here: https://brainly.com/question/30804688
#SPJ1
Sorry if it's a bit blurry. The question is in the first attachment, the other two should help you figure out the question. Please show your work and explain it or else I won't get credit, thank you in advance
The actual area of logo 2 would be = 45ft²
The area of logo 2 would be = 2.5in²
How to determine the area of both the actual and model of logo 2?To determine the actual area of logo 2, the given dimensions are first converted to ft and the formula for the area of square is used. That is
Actual area of logo 2 = a²
a = 1/2 in (convert to ft)
But 1 in = 6 ft
1/2in = 3ft
Then divide the logo 2 in various squares to get 5 equal squares.
Area = 5(a²)
= 5×3×3
= 45ft²
The area of the logo 2 model = 5(0.5) = 2.5in²
Learn more about area here:
https://brainly.com/question/28470545
#SPJ1
PLEASEEE HELP IM BEGGING YOU
The area of sector in the given circle is 275π/6 square meters.
We have to find the area of sector which measures 165 degrees and radius of circle is 10m.
Area = (θ/360)πr²
where θ is the angle in degrees, π is the mathematical constant pi (approximately 3.14159), and r is the radius of the circle.
In this case, the angle is 165 degrees and the radius is 10 meters. Plugging these values into the formula, we get:
Area = (165/360)π(10)²
Area = (11/24) × π × 100
Area =1100/24π
=275π/6 square meters.
To learn more on Circles click:
https://brainly.com/question/11833983
#SPJ1
Find the average rate of change of g(x) = x over the interval
[-9, -2].
Write your answer as an integer, fraction, or decimal rounded to
nearest tenth. Simplify any fractions.
The average rate of change of [tex]\(g(x) = x\)[/tex] over the interval [tex]\([-9, -2]\) is 1.[/tex]
To find the average rate of change of a function over an interval, we calculate the difference in the function values at the endpoints of the interval and divide it by the difference in the corresponding x-values.
In this case, the function [tex]\(g(x) = x\)[/tex] and the interval is [tex]\([-9, -2]\)[/tex]. We can determine the average rate of change as follows:
[tex]\[ \text{Average rate of change} = \frac{g(-2) - g(-9)}{-2 - (-9)} \][/tex]
By substituting the function values, we get:
[tex]\[ \text{Average rate of change} = \frac{-2 - (-9)}{-2 - (-9)} \][/tex]
Simplifying the numerator and denominator, we have:
[tex]\[ \text{Average rate of change} = \frac{7}{7} = 1 \][/tex]
Therefore, the average rate of change of [tex]\(g(x) = x\)[/tex] over the interval [tex]\([-9, -2]\)[/tex] is [tex]1[/tex].
For more such questions on rate of change: https://brainly.com/question/29362528
#SPJ11
Start with the top figure. Which transformation was used to create the pattern?
translation
rotation
reflection
glide reflection
The transformation used to create the pattern in the top figure is reflection.
A reflection is a transformation that flips an object over a line, called the line of reflection. It produces a mirror image of the original object. In the case of the pattern in the top figure, we can observe that the pattern is symmetric about a specific line of reflection.
To determine if a reflection was used, we examine the pattern for mirror symmetry. Mirror symmetry means that one half of the pattern is a reflection of the other half. In the top figure, if we were to fold the pattern along a vertical line, the two halves would align perfectly, indicating mirror symmetry.
This mirror symmetry suggests that a reflection has been applied to create the pattern. Each shape in the pattern appears to have been reflected across the line of reflection to create its corresponding mirrored shape.
Other transformations such as translation, rotation, and glide reflection do not exhibit the same mirror symmetry as a reflection. A translation involves shifting an object without changing its orientation, a rotation involves rotating an object around a fixed point, and a glide reflection is a combination of a translation and a reflection.
In conclusion, based on the mirror symmetry observed in the top figure's pattern, the transformation used to create the pattern is a reflection.
For more such questions on pattern, click on:
https://brainly.com/question/28580633
#SPJ8
Solve for x. Round to the nearest tenth of a
degree, if necessary.
S
to
3.9
8.5
R
Q
Answer:
Set your calculator to degree mode.
[tex]x = {cos}^{ - 1} \frac{3.9}{8.5} = 62.7 \: degrees[/tex]
Angle x measures about 62.7°.
A triangle has vertices A(-4, 0),
B(4, 8), and C(8, - 12), and the following is true
Angle A " B" C " = D 3/2(D 1/2
(Angle ABC)
What is the perimeter of Angle
A" B"C"?
The perimeter of triangle A"B"C" is found as 43.78.
How do we calculate?
We first determine length of each side:
The distance formula has that :
AB = √[(4 - (-4))² + (8 - 0)²]
= √128
= 8√2
BC = √[(8 - 4)² + (-12 - 8)²]
= √320
= 8√5
CA = √[(-4 - 8)² + (0 - (-12))^²]
= √320
= 8√5
cos(ABC) = (AB² + BC² - CA²) / (2 * AB * BC)
cos(ABC) = (128 + 320 - 320) / (2 * 8√2 * 8√5)
cos(ABC) = 1 / (4√2)
ABC = [tex]cos^{-1}[/tex](1 / (4√2))
ABC = 78.46°
A"B" = AB = 8√2
B"C" = BC = 8√5
C"A" = CA = 8√5
We then find the perimeter of triangle A"B"C" is:
A"B" + B"C" + C"A"
= 8√2 + 8√5 + 8√5
= 8√2 + 16√5
= 43.78
Learn more about distance formula at:
https://brainly.com/question/1872885
#SPJ1
a number has the same digit in its hundreds place as its hundredths place.how many times greater is the value of the digit in the hundreds place than the value of the digit in the hundredths place
Based on the ratio of the digit in its hundred places compared to the same digit in its hundredth place, the number of times the value of the digit in the hundred places is greater than the value of the digit in the hundredth place is 10,000.
What is the ratio?The ratio is the relative size of one value, number, or quantity compared to another.
The ratio is computed as the quotient of one quantity divided by another.
We can express a ratio as a fraction, decimal, percentage, or in its standard form (:).
For instance, using the digit 4 in its hundred places will give 400. The same digit in its hundredth place gives 0.04.
The ratio of 400 to 0.04 = 10,000 (400 ÷ 0.04)
Thus, in this instance, we can conclude that 400 is 10,000 times greater than 0.04.
Learn more about ratios at https://brainly.com/question/12024093.
#SPJ1
Abigail jogged 10.6 miles in 2.5 hours. What's her jogging speed in miles per hour?
A) 4.24 miles/hour
B) 4.32 miles/hour
C) 4 miles/hour
D) 5.3 miles/hour
Answer:
A) 4.24 miles/hour
Step-by-step explanation:
To find Abigail’s jogging speed in miles per hour, we need to divide the distance she jogged by the time it took her to jog that distance.
Therefore, Abigail’s jogging speed is 10.6 miles / 2.5 hours = 4.24 miles/hour.
Answer: A) 4.24 miles/hour
Step-by-step explanation:
The jogging speed can be calculated by dividing the total distance by the total time. So, to find Abigail's speed in miles per hour, we would divide the total miles (10.6) by the total hours (2.5).
10.6 miles ÷ 2.5 hours = 4.24 miles/hour
Therefore, the answer is:
A) 4.24 miles/hour
A student spends 17/35 of his pocket money on transport. He spends 5/6 of the remainder on sweet, what fraction of his pocket money did he spend on sweet?
Answer:
Step-by-step explanation:
Let he have Rs . 1
spent on transport = 17/35
spent on sweet = 5/6 of 18/35
= 3/7
Find the value of the expression −a +b − −c if a =3, b = −6, and c=
−5
Answer:
-14
Step-by-step explanation:
You want to know the value of -a +b -(-c) when a=3, b=-6, c=-5.
Minus signsWe can simplify the given expression by recognizing that a double negative is a positive:
= -a +b +c
SubstitutionThe value is found by substituting the given numbers and doing the arithmetic:
= -(3) +(-6) +(-5)
= -3 -6 -5 = -(3 +6 +5) = -14
The value of the expression is -14.
__
Additional comment
Your calculator can help you find the value of a numeric expression.
<95141404393>
The value of the mathematical expression −a +b − −c with given values a =3, b = −6, and c= −5 is -4.
Explanation:The given mathematical expression is −a +b − −c. In this equation, we are given the values a =3, b = −6, and c= −5. We substitute these values into the equation to solve it. Thus, it becomes: -3 + (-6) - −(-5). When solved, -3 + (-6) +5 equals -4
https://brainly.com/question/34902364
#SPJ1