Therefore , the solution of the given problem of equation comes out to be ratio of y to x is not constant in this situation, y does not directly change with x.
What is equation?The use of the same variable word in mathematical formulas frequently ensures agreement between two assertions. Mathematical equations, also referred to as assertions, are used to demonstrate expression the equality of many academic figures. Instead of dividing 12 into 2 parts in this instance, the normalise technique adds b + 6 to use the sample of y + 6 instead.
Here,
Checking whether there is a fixed ratio between y and x will help us determine whether y directly changes with x.
In general, straight variation is calculated as follows:
=> y = kx
where k is the variational constant.
Let's split both sides by x to check if the equation 3y = -7x - 18 can be expressed in this way:
=> 3y/x = -7 - 18/x
Now, 3y/x ought to equal some constant k if the relation between y and x is constant:
=> 3y/x = k
When we add this to the solution we previously determined, we get:
=> k = -7 - 18/x
Since the ratio of y to x is not constant in this situation, y does not directly change with x.
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How many cups of water will you need for 8
cups of flour?
Answer:
Step-by-step explanation:
2 cups of water.
PLEASE HELP ASAP!!! THANK YOU
Answer:
360 in^2
Step-by-step explanation:
Area of bottom rectangle : A = 7.5 x 17 = 127.5
Area of front rectangle: A = 6 x 17 = 102
Area of back rectangle: A = 4.5 x 17 = 76.5
Area of 2 triangles: 2(4.5 x 6) = 54
Total surface area = 127.5 + 102 + 76.5 + 54 = 360 in^2
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The measure of angle ABC is 40 degrees.
What is inscribed angle theorem ?
The inscribed angle theorem, also known as the central angle theorem, states that an angle inscribed in a circle is half the measure of the central angle that intercepts the same arc, or in other words, the angle that connects the endpoints of the arc.
In other words, if we draw a chord of a circle and an angle with its vertex on the circumference of the circle and its sides passing through the endpoints of the chord, then the measure of the inscribed angle is half the measure of the central angle that subtends the same arc as the inscribed angle.
According to the question:
By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the arc it intercepts.
Since chord AB is congruent to chord CB, we can conclude that angle A is congruent to angle C, because they both intercept the same arc AC. Thus, we have:
angle BAC + angle ABC + angle ACB = 180 degrees (by the angle sum property of triangles
Substituting the measure of arc AC, we get:
angle BAC + angle ABC + 70 degrees = 180 degrees
Simplifying, we get:
angle BAC + angle ABC = 110 degrees
Since angles A and C are congruent, we have:
2 x angle BAC + angle ABC = 180 degrees
Substituting angle BAC + angle ABC = 110 degrees, we get:
2 x 110 degrees - angle ABC = 180 degrees
Solving for angle ABC, we get:
angle ABC = 40 degrees
Therefore, the measure of angle ABC is 40 degrees.
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What is the outcome and sample space of getting a sum of 9 when three dice are rolled
The outcome of getting a sum of 9 when three dice are rolled is that the sum of the three numbers shown on the dice must add up to 9. The sample space for this scenario can be written as S = { (1,3,5), (2,3,4), (2,4,3), (3,2,4), (3,4,2), (4,2,3), (4,3,2), (5,1,3)}
What is outcome?Outcome refers to the result of an action or event. It is the end result of the process and can be positive, negative, or a mix of both. Outcome can also refer to the impact of an event, such as the effect it has on the environment, the people affected, or the economy.
The sample space for this scenario is the set of all possible combinations of three dice that add up to 9.
Each of the elements in this set represents a combination of numbers on the dice that will add up to 9 when rolled. For example, the first element of this set (1,3,5) means that if the three dice are rolled, the numbers shown on the dice will be 1, 3, and 5, and the sum of the numbers will be 9.
When determining the sample space for the outcome of rolling three dice, the order of the numbers does not matter. Therefore, the sets (2,3,4) and (4,2,3) are equivalent, since the sum of the numbers is still 9 regardless of the order.
In conclusion, the outcome of getting a sum of 9 when three dice are rolled is that the sum of the three numbers shown on the dice must add up to 9. The sample space for this scenario is the set of all possible combinations of three dice that add up to 9.
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16 sin 10° sin 30° sin 50° sin 70° sin 90°
Answer:
2 √3
Step-by-step explanation:
The value of sin 90° is 1, so we can simplify the expression as:
16 sin 10° sin 30° sin 50° sin 70° sin 90° = 16 sin 10° sin 30° sin 50° sin 70°
We can use the identity sin (90 - x) = cos x to rewrite sin 70° as cos 20°:
16 sin 10° sin 30° sin 50° sin 70° = 16 sin 10° sin 30° sin 50° cos 20°
We can use the identity sin (180 - x) = sin x to rewrite sin 170° as sin 10°:
16 sin 10° sin 30° sin 50° cos 20° = 8 sin 10° [2 cos 20° sin 30° sin 50°]
We can use the identity sin (2x) = 2 sin x cos x to simplify the expression inside the brackets:
8 sin 10° [2 cos 20° sin 30° sin 50°] = 8 sin 10° [sin 100° - sin 20°]
We can use the identity sin (180 - x) = sin x to rewrite sin 20° as sin 160°:
8 sin 10° [sin 100° - sin 20°] = 8 sin 10° [sin 100° - sin 160°]
We can use the identity sin (x + y) = sin x cos y + cos x sin y to rewrite sin 100° as sin (60° + 40°):
8 sin 10° [sin 100° - sin 160°] = 8 sin 10° [sin 60° cos 40° + cos 60° sin 40° - sin 160°]
We can use the identity sin (180 - x) = sin x to rewrite sin 160° as sin 20°:
8 sin 10° [sin 60° cos 40° + cos 60° sin 40° - sin 20°] = 8 sin 10° [sin 60° cos 40° + cos 60° sin 40° - sin 20°]
Now, we can use the values of sin 60°, cos 40°, and sin 20°, which are:
sin 60° = √3/2
cos 40° = √[(1+cos 80°)/2] = √[(1+sin 10°)/4]
sin 20° = sin (60° - 40°) = sin 60° cos 40° - cos 60° sin 40° = (√3/2)(√[(1+sin 10°)/4]) - (1/2)sin 10°
Substituting these values into the expression, we get:
8 sin 10° [sin 60° cos 40° + cos 60° sin 40° - sin 20°]
= 8 sin 10° [√3/2 × √[(1+sin 10°)/4] + 1/2 × sin 10° - (√3/2) × √[(1+sin 10°)/4]]
= 2 √3 sin 10° √[(1+sin 10°)/2]
Therefore, the value of the expression is:
16 sin 10° sin 30° sin 50° sin 70° sin 90° = 2 √3
Carmen's front porch is 7 feet wide and 12 feet long. Carmen wants to stain the wood on the porch next weekend. The stain costs $0.70 per square foot. How much will it cost to buy enough stain for the whole porch?
Answer: It will cost $58.80 to buy enough stain for the whole porch.
Step-by-step explanation: The area of Carmen's front porch is:
Area = length x width
Substituting the given values, we get:
Area = 12 ft x 7 ft
Area = 84 square feet
To find the cost of the stain, we need to multiply the area of the porch by the cost per square foot:
Cost of stain = Area x Cost per square foot
Cost of stain = 84 square feet x $0.70/square foot
Cost of stain = $58.80
Determine whether the argument is valid or invalid. You may compare the argument to a standard form or use a truth table.
Pq
q
..~P
Is the argument valid or invalid?
O Valid
< Question 9 of 11 >
Invalid
Using tautology, we can conclude that the argument here is invalid.
Define Tautology?A compound statement known as a tautology is one that is true regardless of whether the individual statements inside it are true or false.
The Greek term "tautology," which means "same" and "logy," is where the word "tautology" comes from.
We need to build a truth-table and examine the truth value in the last column in order to determine whether a particular statement is a tautology.
It is a tautology if all of the values are true.
In the given case:
p is TRUE
and
q is FALSE
In this case:
p→q : is FALSE (the assumption “TRUE implies FALSE” is FALSE)
So, here:
p → (p→q) is equal to as p → FALSE
But p is TRUE so in that case it’s TRUE→ FALSE, which is in fact FALSE.
Since there a case where the expression is not true, then it’s not valid.
It’s invalid.
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Nakia is an architect designing a house with a peaked roof. She is trying to decide what the limitations are on her design. If AB is 8 feet and triangle ABC will be isosceles, describe the possible lengths for AC.
The possible calculated length of the segment AC is a length of any value that exceeds around 7.15 feet.
How to use Pythagoras Theorem?If triangle ABC is an isosceles triangle, then the length of AC must be equal to the length of BC.
Let's denote the length of AC as "x".
To find the length of the diagonal line segment referred to as BD, which represents the height of the peaked roof, we can use the Pythagorean theorem:
BD² = AB² - (AC/2)²
BD² = 8² - (x/2)²
BD² = 64 - x²/4
In order for the roof to be peaked, BD must be less than x, otherwise the roof would be flat.
Therefore, we can set up the inequality:
x√(64 - x²/4) < x
64 - x²/4 < x²
Multiplying both sides by 4 gives:
256 - x² < 4x²
5x² > 256
Dividing both sides by 5 gives:
x² > 51.2
x > √(51.2)
x > 7.15 feet
As a result, any value greater than the square root of 51.2 (approximately 7.15 feet) is a possible length for AC.
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The possible lengths for AC are any values greater than 7.15 feet.
How to use Pythagoras theorem?We are given that the triangle ABC is an isosceles triangle. This means that the length of segment AC must be equal to the length of segment BC.
Let x denote the length of AC.
With the aid of the Pythagorean theorem, the length of the diagonal line segment BD which denotes the height of the peaked roof is:
BD² = AB² - (AC/2)²
BD² = 8² - (x/2)²
BD² = 64 - x²/4
If the roof is to be peaked, then the length of segment BD must be less than x. Thus, we generate the inequality:
BD < x
√(64 - (x²/4)) < x
Square both sides to get:
64 - x²/4 < x²
256 - x² < 4x²
5x² > 256
x² > 51.2
x > √(51.2)
x > 7.15 ft
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15. What is the name of an account managed by a third party who makes
payments according to a set of instructions, often used for insurance and tax
payments for a mortgage?
Which of these relations is a function?
➤
Video
Answer:
Step-by-step explanation:
Only the one on the bottom right is a function. It's the only one that does not have 2 of the same x value for a single y value.
I have enough money to buy 4 exercise books at 120 naira each. how many pencils costing 80 naira each can I buy for the same amount
Answer:
6 pencils
Step-by-step explanation:
120*4=480, 480/80=6
Which sets of numbers do 3/5 belong to
Answer:
Rational numbers, Real Numbers, Fractions, and Percentages.
What is the sum of 1h20, 2h40, 3h05?
Answer:
6h65
Step-by-step explanation:
Add up all the values:
1h+2h+3h= 6
20+40+05= 65
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As the Earth revolves around the sun, it travels at a speed of approximately 18 miles per second. Convert this speed to kilometers per second. At this speed, how many kilometers will the Earth travel in 10 seconds? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
Answer:
[tex]\frac{28.5km}{sec}[/tex]
In 10 seconds the earth will travel 288 km
Step-by-step explanation:
[tex]\frac{18miles}{sec}[/tex] x [tex]\frac{1.6km}{1 mile}[/tex] = [tex]\frac{28.8km}{sec}[/tex]
[tex]\frac{28.8km}{sec}[/tex] x [tex]\frac{10sec}{1}[/tex] = 288 km
Helping in the name of Jesus.
PLEASE PLEASE PLEASE HELP ASAP!! LOTS OF POINTS
The time taken, in hours, for the bacteria to double in size, found using the given function is 26.25 hours.
What is a function?
A relation between a set of inputs and a set of allowable outputs is called a function. It has the property that every input is associated with exactly one output. A function from one set X to another allocates precisely one element of the other set Y to each element of X. Both the set X and the set Y are referred to as the function's domain and codomain, respectively. The basic conception of functions was the relationship between fluctuating quantities and other variables.
The given function is:
[tex]y = y_0e^{(0.0264t)}[/tex]
We are asked to find the time taken for the bacteria to double.
y = a number of bacteria at present time t.
y₀ = initial number of bacteria
When y = 2y₀
The function becomes,
[tex]2y_0 = y_0e^{(0.0264t)}\\\\2 = e^{(0.0264t)}\\\\ln (2) = 0.0264t\\\\0.693 = 0.0264t\\\\t = 26.25[/tex]
Therefore the time taken, in hours, for the bacteria to double in size, found using the given function is 26.25 hours.
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5. Jennifer bought 14.75 gallons of gasoline for her car at a cost of $2.95 a gallon. Which is closest to the amount she paid for the gasoline? Responses
A. less than $35.00
B. between $35.00 and $40.00
C. between $40.00 and $45.00
D. more than $45.00
54000 rounded to the nearest ten
54,000 rounded to the nearest ten is 54,000 because the zeros after the 4 are insignificant
What is approximation?Rounding off in math is the process of approximating a number to a certain degree of accuracy. This involves changing the value of a number to one that is simpler or easier to work with, while still maintaining an acceptable level of accuracy.
For example, rounding off 3.75 to the nearest whole number would give you 4, while rounding off 3.75 to the nearest tenth would give you 3.8.
Rounding off 54000 to the nearest ten is still 54000 because the zeros after the 4 are insignificant
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Resuelva por medio de la función y = mx + b con los siguientes datos:
I. m =3 y b =7 ➔ f(x) = ¿?
Answer:
which of the following set of nos could not be the length of sides of aright angled triangles.
mrs. jo is purchasing food she is given two options for financing the $900 purchase option A is a 5 year term at a rate of 8% option B is a 2 year term at a rate of 10% which is the better option and how much will mrs. jo save by going with the better option
Using the simple interest formula it is seen that Mrs Jo saves an amount of $180 when she chooses option B over option A.
What is Simple Interest?
Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
To determine which option is better, we need to compare the total amount of interest paid for each option.
Option A -
The principal amount is $900 and the interest rate is 8%. The term is 5 years.
Using the formula for simple interest -
Interest = Principal × Rate × Time
Interest = $900 × 0.08 × 5
Interest = $360
Total amount paid = Principal + Interest
Total amount paid = $900 + $360
Total amount paid = $1260
Option B -
The principal amount is $900 and the interest rate is 10%. The term is 2 years.
Using the formula for simple interest -
Interest = Principal × Rate × Time
Interest = $900 × 0.10 × 2 = $180
Total amount paid = Principal + Interest
Total amount paid = $900 + $180
Total amount paid = $1080
Therefore, option B is the better option because it has a lower total amount paid by choosing option B.
Mrs. Jo will save -
$1260 - $1080 = $180
Therefore, Mrs. Jo will save $180 by choosing option B instead of option A.
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sk A pond in the shape of a right-angled triangle is shown below. Calculate the perimeter of the pond. Give your answer in metres to 1 d.p. 2.42 m.
The perimeter of the pond from the calculation is 5.42 meter
How to solve for the perimeter of the pondWe would first have to find the sides using the angle that we have here
b / 2.42 = sin 74
cross multiply
2.42 x sin 74 = 2.33 meters
h / 2.42 = cos 74
2.42 x cos 74 = 0.67 meters
Given that the sides of the triangle are 2.33 , 2.42 and 0.67 meters
The perimeter would be solved by 2.33 + 2.42 + 0.67
= 5.42 meters
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find (-21 ) + (13 ) + 20
Answer:
the correct answer is 12
Answer:
12
Step-by-step explanation:
50 hombres tienen provisiones para 20 días a razón de tres raciones diarias. Sí las
raciones se disminuyen en 1/3 y se aumentan 10 hombres ¿Cuántos días durarán
los víveres?
Answer:
Para resolver este problema, primero debemos encontrar la cantidad total de raciones que tienen los 50 hombres para 20 días a razón de tres raciones diarias:
50 hombres x 3 raciones por día x 20 días = 3000 raciones
Esto significa que tienen un total de 3000 raciones de alimentos para los 50 hombres durante 20 días.
Luego, podemos calcular la cantidad de raciones diarias después de la disminución en 1/3:
3 raciones diarias - (1/3)(3 raciones diarias) = 2 raciones diarias
Esto significa que cada hombre ahora recibe 2 raciones diarias en lugar de 3.
Después de aumentar el número de hombres en 10, tenemos un total de 60 hombres:
50 hombres + 10 hombres = 60 hombres
Podemos calcular la cantidad total de raciones diarias para los 60 hombres durante los días que durarán las provisiones:
60 hombres x 2 raciones por día = 120 raciones diarias
Finalmente, podemos calcular la cantidad de días que durarán los víveres:
3000 raciones totales / 120 raciones diarias = 25 días
Por lo tanto, los víveres durarán 25 días después de disminuir las raciones en 1/3 y aumentar el número de hombres en 10.
Step-by-step explanation:
Which system of equations can you use to find the roots of the equation? x3 – 10x = x2 – 6 y = x3 – x2 + 10x + 6 y = 0 y = x3 – x2 + 10x y = 6 y = x3 – 10x y = x2 – 6.
From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths. , ,
Answer:
429
Step-by-step explanation:
Help me! I need help with my homework! Ty! :)
Answer:763.02
Step-by-step explanation:
r=9
R=r+9=18
[tex]A=R^{2}\pi-r^{2}\pi = \pi (R^{2}-r^{2})=\pi =243\pi \\\pi =3.14\\243\pi=763.02[/tex]
Answer:
763.02
Step-by-step explanation:
Area of a circle is πr²
so the area of the whole circle is the sum of both radius
9+9 = 18
so Area = 3.14 × 18² = 1017.36
then we subtract the white part to leave the shaded part
area of the white circle = 3.14 × 9² = 254.34
then 1017.36 - 254.34 = 763.02
The graph of an exponential function is shown in the figure below.
The horizontal asymptote is shown as a dashed line.
Find the domain and the range.
Write your answers as inequalities, using x or y as appropriate.
Or, you may instead click on "Empty set" or "All reals" as the answer.
The range of this function is: (0, 2].
Which examples of exponential functions are there?f(x) = bx, where b is a positive integer between 0 and 1, denotes an exponential function. Like in every exponential expression, B and x are referred to as the base and exponent, respectively. An excellent illustration of an exponential function is bacterial proliferation. Some microorganisms reproduce every hour.
As all real numbers are the domain of an exponential function, the following is the domain of this function:
(-∞, ∞)
We must examine the function's behaviour as x gets closer to positive and negative infinity in order to determine the range. The function approaches the horizontal asymptote at y = 2 as x increases to positive infinity. The function gets close to 0, but never quite achieves it as x increases to negative infinity. The scope of this function is as follows:
(0, 2].
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Which of the following expressions can you multiply using the FOIL Method? Check all that apply
3x(2x^2+5x-4)
(x-1)(x^2+2x*5)
(6x-5)(x+4)
(x+g)(x-h)
Answer:
Option C
Step-by-step explanation:
3.5 cm
6 cm
3.5 cm that is my question I don’t understand it’s something. With pyramids
Based on the information provided, the volume of the pyramid would be 5308.33 cubic centimeters.
How to calculate the volume of a pyramid?The volume or the space occupied by the pyramid can be calculated using the following formula
V=(1/3)Ah
In this formula, A is the area of the base and h is the height.
Area of the base: 6.5 x 3.5 = 22.75 squared centimeters.
Now, let's calculate the volume:
V = (1/3)*22.75 x 700 cm = 5308.33 cm^3 (Cubic centimeters)
Here 1 meter = 100 cm, then 7 m = 700 cm
Note: This question is incomplete; here is the missing information:
The base of a pyramid is 6.5 cm by 3.5cm and its height is 7m. What is its volume?
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ey-intercept of the graph of the equation y = 4 (3^X) ?
Answer: 4
See the graph attached
Hope it helps
The expression (x−2)+x+(x+3) represents the combined hours a salesperson works on Monday, Wednesday, and Friday, respectively. Which statement is true? The salesperson works 2 hours less on Monday than Wednesday and works 3 hours less on Wednesday than Friday. The salesperson works 2 hours less on Monday than Wednesday and works 3 hours less on Wednesday than Friday. The salesperson works 2 hours less on Monday than Friday and works 3 hours less on Wednesday than Friday. The salesperson works 2 hours less on Monday than Friday and works 3 hours less on Wednesday than Friday. The salesperson works 3 hours more on Monday than Wednesday and works 2 hours less on Wednesday than Friday. The salesperson works 3 hours more on Monday than Wednesday and works 2 hours less on Wednesday than Friday. The salesperson works 3 hours more on Monday than Friday and works 2 hours less on Wednesday than Friday.
The salesperson works 2 hours less on Monday than Wednesday and works 3 hours less on Wednesday than Friday
Identifying the relationship between the daysGiven that
Combined hours = x - 2 + x + x - 3
When splitted, we have
Monday = x - 2
Wednesday = x
Friday = x + 3
To determine which statement is true, we need to compare the hours worked on Monday and Wednesday, and the hours worked on Wednesday and Friday.
By comparison, Option 1 is correct
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Write an equation in slope intercept form given m = 2 and the point (0,-5)
Answer:
y = 2x - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given m = 2 and point where line crosses y- axis (0, - 5 ) , then c = - 5
y = 2x - 5 ← equation of line