On solving the the provided question we can say that - in the equation we have 12a - 3b = 84 - 30 = 54
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
here, we have
a = 7 and b = 10
so, 12a - 3b
84 - 30 = 54
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Determine the maximum deflection of the simply supported beam. E= 200 GPa and.i = 39,9 (10^6) M^4
The maximum deflection of the simply supported beam, given the applied load P, the length of the beam L, the Young's Modulus E of the beam material, and the moment of inertia I, is equal to (5*P*L^3)/1536.3*10^15 m.
The maximum deflection of the simply supported beam is given by:
Maximum deflection = (5PL^3)/(384EI)
where P is the load applied to the beam, L is the length of the beam, E is the Young's Modulus of the beam material, and I is the moment of inertia of the beam.
Substituting the given values into the equation, we get:
Maximum deflection = (5*P*L^3)/(384*200*10^9*39.9*10^6)
= (5*P*L^3)/(1536.3*10^15)
= (5*P*L^3)/1536.3*10^15 m
The maximum deflection of the simply supported beam, given the applied load P, the length of the beam L, the Young's Modulus E of the beam material, and the moment of inertia I, is equal to (5*P*L^3)/1536.3*10^15 m.
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12. The histogram shows student's scores from last month's math test how many students scored in the 80-89 range?
13. how total students took the math test
14. Eight new students took a make-up test today and received the following scores. 72,75,76,84,88,97,98,99
Using your pencil, add these scores to the histogram to the right by extending the height of the bars as necessary.
help me please thx v: ✌
Answer:
12. 12 students scored in the 80-89 range
13. 31 students took the maths test
In the diagram, ABCD is a square. Point E is the midpoint of AD. Points F and G lie on CE, and H and J lie on AB and BC, respectively, so that FGHJ is a square. Points K and L lie on GH, and M and N lie on AD and AB, respectively, so that KLMN is a square. The area of KLMN is 99. Find the area of FGHJ.
Answer:
Step-by-step explanation:
Pull FG together, and assume FG is 11. HJ, must be the same as FG, so it is 11. Our answer is 121.
How do you write 1 2 on a graph?
To write the point (1, 2) on a graph, you would first locate the point on the x-axis where x = 1, and then go up 2 units on the y-axis.
The point (1, 2) is on the Cartesian plane and it represents the coordinates of a point in the 2-D space. This point is located 1 unit to the right of the y-axis and 2 units above the x-axis.
It can be represented graphically as a point on a coordinate plane where the x-coordinate is 1 and the y-coordinate is 2.
On the graph, you can plot the point by first drawing the x and y axes and their respective scales, then place a dot on the point (1,2) which represents the coordinates of the point.
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The following spreadsheet can be used to compute total weekly pay, given the hours, hourly rate, and overtime rate.
The formula to compute the total weekly in cell H2 is H2=D2+G2
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
(a).By using formula we get;
Regular gross pay= Regular Hours x Hourly Rate
D2=B2*C2
(b) By using the formula we get;
Overtime Hours = Hours Worked -Regular Hours
E2=A2-B2
(c) By using the formula we get;
Time-and-a-half overtime
hourly rate = Hourly rate 1.5
F2=C2x1.5
(d) By using the formula we get;
Total overtime pay
=Overtime Hours x Overtime rate
G2=E2 x F2
(e) By using the formula we get;
Total weekly pay = Regular pay + Overtime pay
H2=D2+G2
Therefore, the unitary answer will be H2=D2+G2
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Help me solve this triangle cuz im at 99
Answer:
Given: QR = QS (by given)
We are to prove: LS = ZR
Proof:
Since QR = QS, by the SAS (Side-Angle-Side) congruence postulate, we know that triangle QRS is congruent to triangle QSZ (both have two equal sides and included angle).
By the AAS (Angle-Angle-Side) congruence postulate, we know that if two angles of one triangle are congruent to two angles of another triangle, and the included side is congruent, then the two triangles are congruent.
Therefore, by using AAS congruence, we can say that triangle QRS is congruent to triangle QSZ.
By the CPCTC (Corresponding parts of congruent triangles are congruent), we know that if two triangles are congruent, then their corresponding sides are congruent.
Therefore, LS is congruent to ZR.
Therefore, we have proved LS = ZR
Note: The above proof uses the properties of congruence of triangles, if the student is not familiar with this, it might be challenging for them.
The graph shows the total cost for a lawn mowing service to mow a lawn. Find the rate of change. I need help its due tomorrow. I can't find a single answer for it at all.
By analyzing the given graph, we can see that the rate of change of the linear equation is 8.
How to find the rate of change?A general linear equation can be written as:
y = a*x + b
Where a is the slope (also known as the rate of change, this is what we are looking for here) and b is the y-intercept.
If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope can be written as:
a = (y₂ - y₁)/(x₂ - x₁)
Here we can see the points:
(1, 28) and (2, 36) and we can use these two to find the slope.
a = (36 - 28)/(2 - 1)
a = 8
So the slope (thus, the rate of change) is 8.
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what is the surface area of a box with a height of 8 inches, a length of 12 inches, and a width of 6 inches?
The surface area of the box with a height of 8 inches, a length of 12 inches, and a width of 6 inches is 432 square inches.
The surface area of a box with a height of 8 inches, a length of 12 inches, and a width of 6 inches can be calculated using the formula SA = 2lw + 2lh + 2wh. In this case, SA stands for surface area, l stands for length, w stands for width and h stands for height.
To calculate the surface area of the box, substitute the given values for l, w and h into the formula and solve:
SA = 2(12)(6) + 2(12)(8) + 2(6)(8)
SA = 144 + 192 + 96
SA = 432 square inches
Therefore, the surface area of the box with a height of 8 inches, a length of 12 inches, and a width of 6 inches is 432 square inches.
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What is the equation
of the line that passes through the point (-6, 3) and has
slope of -4/3
y + 3 = (-4/3)(x - 6) is the equation of the line that passes through the point (-6, 3) and has slope of -4/3.
Define line?A line is an endlessly long object without breadth, depth, or curvature in geometry.Thus, despite the fact that they can exist in two, three, or higher dimensional environments, lines are one-dimensional things. The term "line" can also refer to a line segment that has two locations that serve as its ends in daily life.Straight lines have very little depth or width. You will learn about a variety of lines, including perpendicular lines, intersecting lines, transversal lines, etc. A figure in which two rays leave from the same point is called an angle. Alternative and related perspectives could possibly be found in this area.To learn more about line refer to:
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Have a conversation with your guardian regarding monthly expenses/budget in different sectors and represent the information in pie chart and frequency curve
Therefore , the solution of the given problem of pie chart comes out to be the amount he spent on living expenditures was $1634.5.
Define pie chart.A pie chart, also known as a circle chart, is a visual representation of the various values of a given variable or a way to summarize a set of nominal data (e.g. percentage distribution). This kind of chart consists of a circle with numerous segments. Each segment stands for a specific category.
Here,
living expenses are 35% of the monthly budgeted income of $4670.
Next, we must utilize the rule of four:
4670 $ => 100%
x=> 35%
Clearing x:
=> x=(35/100)*(4670)
=> x=1634.5$
The amount he spent on living expenditures was $1634.5.
Therefore , the solution of the given problem of pie chart comes out to be the amount he spent on living expenditures was $1634.5.
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According to state census information, the population of lavergne, tennessee in 2012 was 3.3777 * 104. the population of murfreesboro, tennessee in 2012 was 1.14038 * 105. what was the combined population of both cities?
(a) The Population of LaVergne, Tennessee in Standard Form is 33,777.
(b) The combined population of both cities is 147,815
In the given question, according to state census information, the population of LaVergne, Tennessee in 2012 was 33.777 x [tex]10^3[/tex].
The population of Murfreesboro, Tennessee in 2012 was 1.14038 x [tex]10^5[/tex].
(a) We have to write the Population of LaVergne, Tennessee in Standard Form.
The population of LaVergne, Tennessee in 2012 = 33.777 x [tex]10^3[/tex]
The population of LaVergne, Tennessee in 2012 = 33.777 x 1000
Now multiplying
The population of LaVergne, Tennessee in 2012 = 33,777
(b) We have to find the combined population of both cities.
The population of LaVergne, Tennessee in 2012 = 33,777
The population of Murfreesboro, Tennessee in 2012 = 1.14038 x 100,000
The population of Murfreesboro, Tennessee in 2012 = 114038
The combined population of both cities = The population of LaVergne, Tennessee + The population of Murfreesboro, Tennessee
The combined population of both cities = 33,777 + 114038
The combined population of both cities = 147,815
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you find a wood fragment during a village excavation in tibet. your analysis shows that c-14 has been reduced to 25% of the amount the tree had when it was alive. how old is the wood fragment?
The wood fragment is 11,460 years old by C-14 dating if only 25% of the amount the tree had when it was alive is left.
The process of carbon-14 dating can be used to determine the age of an organic material such as wood. Carbon-14 is a radioactive isotope of carbon that is present in all living organisms. When an organism dies, the carbon-14 begins to decay at a known rate, and the amount of carbon-14 in the material decreases over time. By measuring the amount of carbon-14 remaining in a sample, it is possible to determine how long ago the organism died.
If the analysis shows that the C-14 has been reduced to 25% of the amount the tree had when it was alive, it means that 75% of C-14 has decayed, and the material is therefore 75% of its way through its radioactive decay.
Carbon-14 has a half-life of 5,730 years, which means that after 5,730 years, half of the carbon-14 in a sample will have decayed. To find the age of the wood fragment, you would need to multiply the sample's decay percentage (75%) by the material's half-life (5730 years) to get the number of years that have passed.
[tex]t = \frac{5730\ ln(0.25)}{-ln2}[/tex]
Where t is the number of years to decay to 25%.
t = 5730 × ( ln(4)/ ln(2))
t = 5730 × 2
t = 11,460
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find the point on the line y=2x+3 that is closest to the origin
From the given line equation, the closet point to the origin is (-6/5, 3/5).
Here we have given that the point on the line y=2x+3 that is closest to the origin.
As we all know that the closest point from origin will be the perpendicular distance from origin to the line.
Here we need to find an equation of the perpendicular from (0,0) on y = 2x + 3.
As we all know that the standard form of the equation is in slope-intercept form is written as,
=> y = mx + c
While we comparing this with the given equation, then we get the value of the Slope that is m = 2 and the Slope of the perpendicular is calculated as,
=> - (1/m) = -1/2
Now, we have to write the equation of the perpendicular is found by using the formula,
=> (y - y1) = m (x - x1)
Apply the value on the equation, then we get,
=> y - 0 = (-1/2) (x - 0)
=> y = (-1/2)x
therefore, the resulting perpendicular equation is written as,
=> 2y + x = 0 ----------------(2)
When we solving (1) and (2), then we get,
=> 5y = 3
Therefore, y = 3/5
And the value of x is calculated as
=> x + 2(3/5) = 0
=> x = -6/5
So the point on the line is (-6/5, 3/5).
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2.) a swim contest of 10 people has three winners. a.) in how many ways can those three winners be chosen?
Answer:
720 Should be the answer I think.
devaunte goes to barnes and noble to buy a book that is originally $14.50. devaunte was trying to save money, so he made sure to bring a coupon that gives him 20% off of his book
which expression(s) could you use to solve this problem? select all that apply answers asap i will give brainlyist
b) p is directly proportional to the square of q. p is 3825 when q is 15. Work out p when q is 20.
Answer:
Step-by-step explanation:
a radio station plays 12 songs each hour. they never stop for commercials, news, weather, or traffic reports. write an expression to describe how many songs are played by the radio station every h hours.
The expression describing how many songs are played by the radio station in H hours is 12H
The phrase used to describe how many songs the radio station plays in H hours is Number of songs = 12 xH
288 songs are played in a 24-hour period.
60 nonstop songs are played over the course of 5 hours.
Given
Every hour, a radio station plays 12 songs.
Compose an expression that indicates how many songs the radio station plays in H hours.
There are 12 songs performed throughout an hour.
Then,
Number of songs= songs played in one-hour x songs played in H hour
Number of songs=12H
The expression describing how many songs are played by the radio station in H hours is 12H
The phrase used to describe how many songs the radio station plays in H hours is 12H
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Relationship between scale factor,area and volume of enlarged figures
Therefore , area and capacity of volume values equal f2 f 2 and f3 f 3, respectively, if the curve is f, f, and also the rim step size is f, f.
How do you increase volume by increasing the scale factor?When we enlarge a shape by a scale factor, we multiply the area of the shape by the square of the scale factor. When we enlarge a shape by a scale factor, we multiply the volume of the shape by the cube of the scale factor. The scale factor is the proportional relationship that exists between the sides of similar figures.
Here,
Similar geometric shapes' edges, areas, and volumes are also connected to the scale factor.
The peripheral scale factor is f, f if the curve is f, f, and the surface and volume ratios are f2 f 2 but also
f3, f 3, respectively, if the correction factor is f, f.
Therefore , area and capacity values equal f2 f 2 and f3 f 3, respectively, if the curve is f, f, and also the rim step size is f, f.
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write an explicit rule for the sequence {-7,-1,5,11,17}. what is the position number for the term 47?
The position number for term 47 is 269.
This is an arithmetic sequence since each term has a common difference. Let us test it.
The difference between 1st and 2nd terms is
-7 + d = -1
d = -1 + 7
= 6
Now we check the difference for term
The difference between 3rd and 4th terms is
5 + d = 11
d = 11 – 5
= 6
So the difference is the same so we can apply a common equation for arithmetic sequence
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + d ( n - 1 )
Where :
[tex]a_{n}[/tex] = number at term n
[tex]a_{1}[/tex] = first number of sequence
d = difference for each number sequence
n = term
From the question, we need to find the number at position term 47
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + d ( n - 1 )
[tex]a_{47}[/tex] = -7 + 6 ( 47 - 1 )
= -7 + 6 ( 46 )
= -7 + 276
= 269
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72 in. = ? cm? i cant solve it please helppppp
Answer: 72 in = 182.88cm
Step-by-step explanation:
3. Find the distance between (-4, 6) and (0, 6). Round to the nearest tenth if needed.
A. 4
B. -3
C. -4
D. 3
Answer: A. [tex]4[/tex]
Step-by-step explanation:
Since the points have the same [tex]y[/tex]-coordinate, take the absolute value of the difference of the [tex]x[/tex]-coordinates. Doing so yields [tex]|-4-0|=4[/tex].
Some please help me with this: 2y - z + z^2
2y - z + z^2 is an algebraic expression. It represents a mathematical operation that includes three different terms: 2y, -z and z^2. It can be simplified depending on the context and the values of y and z.
In the given expression, 2y is the coefficient of y, which is multiplied by y. -z is subtracted from 2y and z^2 is added to the result.
In order to simplify this equation, you could combine like terms, which means combining the same variable or powers of the same variable with each other.
This expression does not have any like terms, so it can't be simplified anymore.
It can be evaluated by replacing y and z with specific values and then performing the mathematical operations in the given order.
What is the total displacement of the car after 5 h? question 8 options: 0 km 15 km 20 km 40 km.
The total displacement of the car after 5hrs is 0km.
Displacement is a vector quantity that refers to the object's overall change in position.changing in final position from its initial positioncalculating the distance between an object's initial position and its final position.In physics terms, displacement is referred to as the variables. The displacement formula is as follows:s =sf– si
where, s = displacement.
In the given graph, there is the change in distance covered with the time that is:
after two hours car reaches 15 km away from the initial pointafter 4 hours it reaches 20 km away from the initial pointAfter 5 hours car returns back to the initial point.Thus, the displacement will be 0 km as the final point and initial point are the same.
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Mi-cha and her friends are going to a bounce music festival in new orleans. they decide to buy hoodies at the festival. a table showing the relationship between the number of hoodies and the total cost of the hoodies shown. how does the total cost of the hoodies is shown.
Answer:d
Step-by-step explanation:
if g(x)=x-2 and h(x)=x^2-1 , what is ( g•h)(x)
The composition of two functions, g(x) and h(x), is written as (g•h)(x).
What is function?Function in math is a relationship between two variables where one variable determines the behavior of the other. It is a mathematical expression that assigns each element in a set to a specific output. Functions can be used to represent things like motion, growth, and decay. They are used to create models that can be used to make predictions and analyze data. Functions are used throughout mathematics and science and can be used to solve real-world problems.
This means that the output of function g(x) is used as the input of function h(x). In this case, (g•h)(x) is equal to h(g(x)). So, (g•h)(x) = h(x-2) = (x-2)^2 - 1.
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For every one litre of water used to make medicine,199ml of sucrose and 271ml of saline solution are used. express the amount of water,sucrose and saline solution needed as a ratio in its simplest form.
The ratio of water, sucrose, and saline solution needed is 1000:199:271 in its simplest form.
The amount of water, sucrose, and the saline solution used can be expressed as a ratio in its simplest form by finding the greatest common divisor (GCD) of the three quantities and dividing each by it.
1l of water = 1000 ml of water.
Let's find the GCD of the three quantities:
GCD(199,271,1000) = 1
So we can express the amount of water, sucrose, and saline solution needed as a ratio in its simplest form by dividing each of the three quantities by 1
Water : Sucrose : Saline solution = 1000 : 199/1 : 271/1 = 1000:199:271
Hence, the ratio of water, sucrose, and saline solution needed is 1000:199:271 in its simplest form.
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pleaaase help i’ll give brainliest to whoever provides an explanation for their answer
The measure of the angle subtended at the center of this circle is 78°.
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
We know the angle subtended at the center of a circle is twice the measure of any angle subtended at any point of the circumference of the circle.
Given, The measure of the angle subtended at the circumference of this circle is 39°.
Therefore, The measure of the angle subtended at the center is,
= (2×39)°.
= 78°.
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Help I will give 88 points to who ever answers I have an exam on this so please explain!!!!
Pythagorean Theorem: Sylvie is making book ends for her shelf. She needs to make 2 identical book ends and she wants to cover the edges in felt so they don’t scratch. Sylvie knows the vase will be 8 inches long and the height will be 12 inches. How much felt does she need to cover all 3 sides of both book ends?
The length that needs to cover all 3 sides of both book ends will be √208 inches.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
Sylvie realizes the container will be 8 inches long and the level will be 12 inches.
Then the length is given as,
H² = 12² + 8²
H² = 144 + 64
H² = 208
H = √208 inches
Then the length that needs to cover all 3 sides of both book ends will be √208 inches.
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band-aids are packaged in 100 per box. you had four full boxes when you started work yesterday. at the end of the day, you had two full boxes left. what percentage of them were used yesterday?
Out of 400 band-aids, 200 were used yesterday. Therefore, the percentage of band-aids used yesterday is 50%.
You started with 4 boxes × 100 band-aids per box
= 400 band-aids.
You ended with 2 boxes × 100 band-aids per box
= 200 band-aids
So you used
400 band-aids - 200 band-aids = 200 band-aids yesterday.
To find the percentage of band-aids used, you can divide the number of band-aids used by the total number of band-aids you started with and multiply by 100:
= (200 band-aids / 400 band-aids) × 100
= (1/ 2) × 100
= 50%
Therefore, 50% of the band-aids were used yesterday.
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