Step-by-step explanation:
5 × -8a = -40a
5 × -9 = -45
-40a - 45 = 5(-8a - 9)
5 × -8a = -40a
5 × -9 = -45
-40a - 45 = 5(-8a - 9)
Here are graphs of functions f and g. For each, determine the value of k so that g(x) = k(x).
The graph of the function f(x) = x² - 10x. and the graph of the function
g(x) = x² - 30x.
What are some rules for function transformations?
Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over the y-axis, (-x, y).
-f(x) = Reflection over the x-axis, (x, -y).
The graph of the first function is a quadratic function.
f(x) = (x - 0)(x - 10).
f(x) = x² - 10x.
Now, g(x) = (x - 0)(x - 30).
g(x) = x² - 30x.
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What ratios are equivalent to 6/9
Answer: 2:3
Step-by-step explanation:
from there you can multiply by 2 and find the other ratios
Reduce the fraction!
Answer:
(y-3)/4
Step-by-step explanation:
(y-3)(y+3)/(4(y+3))
What is the value of x in the equation 3/5(x + 2) = x−4
Answer:
x = 13
good luck
In the Summer Olympics in Sydney in 2000, the United States won gold silver, and bronze medals. The ratio of gold to silver medals was 5/3. The ratio of silver medals to bronze medals was 8/11. What were the total numbers of gold, silver, and bronze medals won by the United States?
Answer:
97
Step-by-step explanation:
Gold:silver
=5:3
=40:24
silver:bronze
=8:11
=24:33
total number=40+24+33=97
What is the answer? i need help
The surface area of the cube will be 181.50 square cm.
What is a surface area of a cube?Suppose that: The side length of the considered cube is L units. Then, we get:
Surface area of that cube = 6L² square units.
From the diagraph, the edge length of the rectangular prism is 5.5 cm long, 5.5 cm wide, and 5.5 cm tall. Then the rectangular prism is a cube. Then the surface area of the cube is given as,
Surface area of that cube = 6 × (5.5)² square cm
Surface area of that cube = 6 × 30.25 square cm
Surface area of that cube = 181.50 square cm
The surface area of the cube will be 181.50 square cm.
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1) Which math component are taught in the curriculum, problem solving, procedural fluency, missed mathematical concepts, etc.?
2) What are some specific types of mathematical instruction that are promoted?
3) Are there any specific procedures used to teach basic mathematical instruction?
1) Note that Math curriculum typically covers concepts such as number and operations, algebra, geometry, and statistics/probability. Problem-solving and procedural fluency are emphasized, as well as addressing missed concepts.
2) Instruction in math often includes hands-on activities, real-world problem-solving, visual models, and abstract reasoning. Emphasis on concept development and connecting math to real life.
3) Common instructional methods in basic math include direct instruction, teacher-led practice, and independent work with a gradual release of responsibility. Emphasis on understanding concepts through concrete examples.
What is procedural Fluency?Procedural fluency refers to the ability to efficiently and accurately perform mathematical procedures, such as computations and formulaic processes.
It's important because it enables students to tackle complex problem-solving with ease and confidence.
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murder rates. the data represent the murder rate per 100,000 individuals in a sample of selected cities in the united states. find the sample variance.
To calculate the sample variance for the homicide rate per 100,000 individuals in a sample of selected cities in the United States, you need to use the following formula:
Sample Variance = (∑ (x - X) 2) / (n - 1)
Where x is each homicide rate value in the sample, X is the mean of the homicide rate values, and n is the number of values in the sample.
For example, if the sample contains the following homicide rate values:
100, 200, 300, 400
The mean (X) would be 250, and the sample variance would be:
Sample Variance = ( ∑ ( x - 250 ) 2) / (4 – 1)
= (100,000 + 50,000 + 10,000 + 0) / 3
= 160,000 / 3
= 53,333.3
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Captain Tiffany has a ship, the H. M. S. Khan. The ship is two furlongs from the dread pirate Omar and his merciless band of thieves. The Captain has probability \dfrac{1}{2} 2 1 start fraction, 1, divided by, 2, end fraction of hitting the pirate ship. The pirate only has one good eye, so he hits the Captain's ship with probability \dfrac{2}{7} 7 2 start fraction, 2, divided by, 7, end fraction. If both fire their cannons at the same time, what is the probability that both the pirate and the Captain hit each other's ships?
Step 1: Calculate the probability that the Captain will hit the pirate ship. Since the Captain has a probability of \dfrac{1}{2} 2 1 start fraction, 1, divided by, 2, end fraction of hitting the pirate ship, the probability that the Captain will hit the pirate ship is 0.5.
Step 2:Calculate the probability that the pirate will hit the Captain's ship. Since the pirate only has one good eye, he hits the Captain's ship with probability \dfrac{2}{7} 7 2 start fraction, 2, divided by, 7, end fraction, the probability that the pirate will hit the Captain's ship is 0.286.
Step 3: Calculate the probability that both ships will hit each other. To calculate the probability that both ships will hit each other, multiply the probability that the Captain will hit the pirate ship (0.5) by the probability that the pirate will hit the Captain's ship (0.286). This gives us a total probability of 0.143.
Therefore, the probability that both ships will hit each other is 0.143.
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4 Type the correct answer in the box. Use numerals instead of words. A car enters a traffic circle at point R. and moves counterclockwise 296 feet before exiting the traffic circle at point P. To the nearest degree, what is the measure of the central angle, ZPQR? 150 ft Q m. All rights reserved. The measure of ZPQR is approximately ?
The measure of ZPQR is approximately 113°
What is Geometry?One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects. A geometer is a mathematician who specializes in geometry.
Therefore, to find the measure of ZPQR, we would follow the following steps:
Let x= measure of <PQR
Hence, the measure of <PQR
296 = x/360 x 3.14 x 2 x 150
Hence, x = 113.12 °
Approximately, the measure of ZPQR is 113 °
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Answer: the person above is right
Step-by-step explanation: have a good day:)
Express 2x² — 12x + 23 in the form a (x + b)² + c.
-
Answer:
Below
Step-by-step explanation:
This is changing the form of the parabola from quadrtatic form to vertex form using the 'complete the square method'
2x^2 - 12x + 23 first, to complete the square the x^2 coefficient must be =1
so factor out 2 form the x components
2 (x^2 -6x) + 23 now....take 1/2 of the 'x' coefficient ( this would be -3)
square it and add this value in the parentheses and subtract it on the outside of the parentheses ( it will be multiplied by the '2' when you need to subtract it....making it -18) )
2 (x^2 - 6x +9 ) - 18 + 23 now reduce the underlined portion
2(x-3)^2 +5 Done .
Compare the key features (slope and y-intercept)
of each linear function g with those of the graph
of f(x) 2x+3. Describe how the value of k
affects the key features. SEE EXAMPLES 1, 2, AND 3
23. g(x)= 3(2x + 3)
25. g(x) = (2x + 3)
24. g(x)= 2(0.5x) + 3
26. g(x) = 2(1)x+ 3
Answer:
Step-by-step explanation:
The definition of k is not given. Is k the slope?
See the attached graph of all the equations. The referenced equation, f(x) = 2x+3 is the top equation and the line is shown in black. This line has a slope of 2 and a y-intercept of +3.
The g(x) functions are also graphed, and noted. Two of the g(x) equations are the same as the reference equation: 25 and 26. Both have a slope of 2 and a y-intercept of +3.
#23 has a slope of 6 and a y-intercept of 9. This has the steepest rise of all the lines (higher slope).
#24 has a slope of 1 and a y-intercept of +1. This has the slowest rise, but it is still a positive sdlope (going up)
Solve the proportion x+10/x+7=x+2/2x-1
Answer:
x = - 12 , x = 2
Step-by-step explanation:
[tex]\frac{x+10}{x+7}[/tex] = [tex]\frac{x+2}{2x-1}[/tex] ( cross- multiply )
(2x - 1)(x + 10) = (x + 2)(x + 7) ← expand both sides using FOIL
2x² + 19x - 10 = x² + 9x + 14 ← subtract x² + 9x + 14 from both sides
x² + 10x - 24 = 0 ← in standard form
(x + 12)(x - 2) = 0 ← in factored form
equate each factor to zero and solve for x
x + 12 = 0 ⇒ x = - 12
x - 2 = 0 ⇒ x = 2
-2 - Complete the identities Find values that make the equations below identities. - 6(x-4) + 2(x+5) = ax + b − 3(x + c) − 4(x + d) Complete these identities. 3x - 24 = +X = X 5(x + 5) = = (x a) (x b) = (a + b) + c = c + ( |(x - - 7x - 15 X + x² - ( 1) x + ab [2] [1] [2] [1] [4] a = C = b = d = [2] [2]
1. Complete the identities
a = -4
b = 34
c = 1
d = 3
2. Complete the identities
3x - 24 = 3(x - 8)
0 + x = x
5(x + 5) = 5x + 25
(a + b) + c = c + (a + b)
(x - a)(x - b) = x² - (a + b)x + ab
Before solving the above equation, we need to know the algebraic formula. The algebraic formula is
a(x + b) = ax + ab
1.
- 6(x - 4) + 2(x + 5) = ax + b
⇒ -6x + 24 + 2x + 10 = ax + b
-6x + 2x + 24 + 10 = ax + b
-4x + 34 = ax + b
So we get the values a and b.
-4x = ax ⇔ a = -4
b = 34
− 3(x + c) − 4(x + d) = - 7x - 15
-3x - 3c - 4x - 4d = -7x - 15
-3x - 4x - 3c - 4d = -7x - 15
-7x - (3c + 4d) = -7x - 15
-7x + 7x - (3c + 4d) = - 15
- (3c + 4d) = - 15
3c + 4d = 15
Let c = 1
3c + 4d = 15
3(1) + 4d = 15
3 + 4d = 15
4d = 15 - 3
4d = 12
d = 3
2.
3x - 24
= 3 × x - 3 × 8
= 3(x - 8)
.... + x = x
-x + x = 0
5(x + 5) = 5 × x + 5 × 5
= 5x + 25
(a + b) + c = c + (a + b)
Let (x + a)(x + b)
(x + a)(x + b) = x² + ax + bx + ab
= x² + (a + b)x + ab (not eligible)
Let (x + a)(x - b)
(x + a)(x - b) = x² + ax - bx - ab
= x² + (a - b)x - ab (not eligible)
Let (x - a)(x + b)
(x - a)(x + b) = x² - ax + bx - ab
= x² - (a - b)x - ab (not eligible)
Let (x - a)(x - b)
(x - a)(x - b) = x² - ax - bx + ab
= x² - (a + b)x + ab (eligible)
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Joe is thinking of a number. Eleven more than one third of the number is -1. What is the number?
The number Joe is thinking of is -36.
To find the number Joe is thinking of, use algebraic expression and equation.
Let x be the number Joe is thinking of
According to the problem, "Eleven more than one third of the number is -1". We can translate this into an algebraic expression such as:
x/3 + 11 = -1
To find the value of x, we'll isolate it on one side of the equation:
x/3 = -12
Next, we'll multiply both sides of the equation by 3 to cancel out the fraction:
x = -36
Therefore, the number Joe is thinking of is -36.
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Drew is experimenting on a circuit. He wants to know if the size of the wire used affects battery life. Identify the variables in drew's experiment
independent variable
dependent variable
controlled variables
PLEASE HELP ASAP THANK YOUU SO MUCH
The size of the wire is the dependent variable and the battery life is the independent variable.
What are dependent and independent variables?In any equation, the variables that represent the input and output are referred to as independent and dependent variables, respectively.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Drew is experimenting on a circuit. He wants to know if the size of the wire used affects battery life.
Here, the battery life is the independent variable, while the size of the wire is the dependent variable.
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In proof testing of circuit boards, the probability that anyparticular diode will fail is 0.01.Suppose a circuit board contains 200 diodes. How manydiodes would you expect to fail, and what is the standarddeviation of the number that are expected to fail? What is the (approximate) probability that atleast four diodes will fail on a randomly selected board?If five boards are shipped to a particularcustomer, how likely is it that at least four of them willwork properly? (A board works properly only if all its diodes work)
The standard deviation is 1.482 when the probability of any particular diode is 0.01, and the circuit board is 200 diodes.
A Bernoulli trial is defined as a random experiment with exactly two possible outcomes, that are "success" and "failure", in which the probability of success is the same every time the experiment is conducted.
The probability for the Binomial distribution is given as:
[tex]P(X)=(^{n} C_x)P^x(1-P)^n^-^x[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]^nC_x=\frac{x!}{(n-x)!x!}[/tex]
For this case, we assume that the random variable of interest X= number of circuits that are expected to fail in a sample of 200 selected and we know that:
X simBino (n=200,p=0.01)
The expected value is given by:
E(x)=n*p=200*0.01=2
The variance is given by:
Var(x)np(1-P)=200*0.01*(1-0.01)=1.98
And the deviation is given by:
sd(X)=√1.98-1.407
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What is a general solution of a differential solution?
Answer: A general solution of a differential equation is a solution that contains all possible solutions of the equation, including all arbitrary constants. It provides a general form of the solution that can be customized to fit the specific conditions of the problem.
For example, the general solution of a second-order linear homogeneous differential equation of the form
y'' + p(x)y' + q(x)y = 0
is a combination of two linearly independent functions, often represented by y = c1y1(x) + c2y2(x), where c1 and c2 are arbitrary constants and y1(x) and y2(x) are two linearly independent solutions of the differential equation.
The general solution represents the most general form of the solution that takes into account all possible solutions, including all arbitrary constants. To find a specific solution, one must apply initial or boundary conditions to determine the values of the arbitrary constants.
Step-by-step explanation:
Mention FOUR study methods that matrics/Grade 12s could use to study their work more
effectively.
Active reading, mnemonics, practice testing, and spaced repetition are just a few examples of study methods that matrics/Grade 12s can use to study their work more effectively.
What is the study method?Study methods are strategies or techniques that students use to learn and retain information more effectively. Here are four study methods that matrics/Grade 12s could use to study their work more effectively:
1. Active Reading: Active reading is a technique where students actively engage with the text while reading it. This helps students to focus on the most important concepts and better understand the material.
2. Mnemonics: Mnemonics are memory aids that help students remember information by creating an association between new information and something that is already familiar to them.
3. Practice Testing: Practice testing involves creating practice quizzes or tests to help students test their knowledge and identify areas where they need to focus their studying. This technique has been shown to be highly effective in improving memory retention and recall.
4. Spaced Repetition: Spaced repetition involves spacing out study sessions over a longer period of time rather than cramming all the studying into one session. This technique helps students retain information for longer periods of time and can help reduce stress and anxiety associated with last-minute cramming.
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Find the volume of the solid generated by rotating the region bounded by y = sin(x), y = 0, x = 0, and x = π/2, about the x-axis.
Step-by-step explanation:
To find the volume of this solid, we will use the method of cylindrical shells. We will integrate the cross-sectional area of a cylinder, given by πr^2, over the height of the solid. The height of the solid is given by the difference between the upper and lower bounds of the region, which are y = sin(x) and y = 0, respectively. The radius of each cylindrical shell is given by the height y = sin(x).
So, the volume of the solid is given by the integral:
V = ∫[0, π/2] π * [sin(x)]^2 dx
Using the antiderivative of π * sin^2(x), which is -π * cos(x), we can find the definite integral:
V = -π * [cos(x)] from 0 to π/2
Evaluating the definite integral and simplifying, we get:
V = (2π - 2) units^3
So, the volume of the solid is (2π - 2) units^3.
Answer:
Step-by-step explanation:
V = (2π - 2) units^3
So, the volume of the solid is (2π - 2) units^3.
Given x varies inversely with y and xy = 2, what is the value of x when y = 1?
-1
One-half
1
2
The value of x when y = 1 is 2.
Option D is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 7 is an equation.
We have,
x varies inversely with y.
This means,
x ∝ 1/y
x = k/y
And,
xy = 2
This means,
k = 2
Now,
For y = 1,
xy = 2
x = 2/y
x = 2/1
x = 2
Thus,
x is 2 when y = 1
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Express each of the following in km/hour.
(a) 8.4km/min
(b) 315m/second
(c) 242m/min
(d) 125cm/s
a) We convert per minute to per hour so we multiply it by 60 to get:
=> 504km/h
b) We convert per second to per hour so we multiply it by 3600 to get:
=> 1134000m/h
=> We then convert meters into km to get:
=> 1134km/h
c) We convert per minute to per hour so we multiply it by 60 to get:
=> 14520m/h
=> Now we convert meters into km once again so we get:
=> 14.52km/h
d) We convert per second to per hour so we multiply it by 3600 to get:
=> 450000cm/h
=> We now convert cm into km which means we divide it by 100,000
=> 4.5km/h
5p(2p-3)(p+7)=0
Please show work!
p=___ so the equation = 0
Answer:
brainliest plss
Step-by-step explanation:
5p(2p-3)(p+7)=0
p=0
(2p-3)=0
(p+7)=0
p=0
p=3/2
p=-7
Answer:
p = 0, p = ³/₂, p = -7
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{Zero Product Property}\\\\If\; $a \cdot b = 0$ \;then either \;$a = 0$ \;or\; $b = 0$ (or both).\\\end{minipage}}[/tex]
Given equation:
[tex]5p(2p-3)(p+7)=0[/tex]
Using the Zero Product Property, set each factor equal to zero and solve for p.
Factor 1
[tex]\begin{aligned}5p&=0\\5p \div 5&=0 \div 5\\p&=0\end{aligned}[/tex]
Factor 2
[tex]\begin{aligned}2p-3&=0\\2p-3+3&=0+3\\2p&=3\\2p \div 2&=3 \div 2\\p&=\dfrac{3}{2}\end{aligned}[/tex]
Factor 3
[tex]\begin{aligned}p+7&=0\\p+7-7&=0-7\\p&=-7\end{aligned}[/tex]
Therefore, p = 0, p = ³/₂, p = -7.
what is 4k^1/2 radical form
Answer:
Below
Step-by-step explanation:
4 [tex]\sqrt[2]{k}[/tex] or just 4 [tex]\sqrt{k}[/tex]
The 1/2 power exponent means square root
if it had been 1/5 then the answer would be 4 [tex]\sqrt[5]{k}[/tex]
El peso de un objeto en le polo norte es 0.53% mayor que en el ecuador.cuanto pesa en el polo norte un objeto de 50 libras en el ecuador?
Answer:
Step-by-step explanation:
el awnser es 0.265 libras mas
jaya is taking two books along on her holiday vacation. with probability 0.5 she will like the first book; with probability 0.4 she will like the second book; with probability 0.3 she will like both books. what is the probability she will like neither book? give your answer using 2 decimal places.
The probability that Jaya likes neither book is 1 - 0.6 = 0.4, or 40%. To two decimal places, the answer is 0.40.
The probability that Jaya will like neither book can be found by subtracting the probability that she likes at least one book from 1.
The probability that Jaya likes at least one book is the sum of the probabilities that she likes the first book, the second book, or both books:
P(likes at least one book) = P(likes first book) + P(likes second book) - P(likes both books)
P(likes at least one book) = 0.5 + 0.4 - 0.3 = 0.6
So, the probability that Jaya likes neither book is 1 - 0.6 = 0.4, or 40%. To two decimal places, the answer is 0.40.
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Kwame reads that the mass of an average
elephant's brain is 3 4/10 kilograms greater
than an average man's brain. How many
kilograms is an average elephant's brain?
In linear equation, 4.9 kilograms is an average elephant's brain .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
An average human's brain is 1.5 kilograms.
= 1.5 + 3 4/10
= 1.5 + 3.4
= 4.9
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A swimming pool is shaped like a right rectangular prism with length 20 feet, height 8 feet, and width 15 feet. If the pool's water line is one foot below the top of the pool, find the volume of water in the pool.
The volume of the swimming pool will be 2400 cubic feet.
What is the volume?The capacity of an object is measured by its volume. For instance, a cup's volume is said to be 100 ml if it can hold 100 ml of water in its brim. The amount of space occupied by a three-dimensional object can also be used to define volume.
Given that a swimming pool is shaped like a right rectangular prism with a length of 20 feet, a height of 8 feet, and a width of 15 feet.
The volume of the swimming pool will be calculated as:-
Volume = L x W x H
Volume = 15 x 20 x 8
Volume = 2400 cubic feet
Therefore, the volume of the pool will be 2400 cubic feet.
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HELP ASAP!!!!The Singh family ordered a large pizza with a diameter of 20 inches for dinner. If one of the members of the family ate one eighth of the pizza, how many square inches of pizza are remaining? Use 3.14 for π.
274.75 square inches
39.25 square inches
314 square inches
157 square inches
Answer:
274.75 in²
Step-by-step explanation:
Area of a circle = πr² = (3.14)(20/2)² = 314 in²
(314 in²)(1/8) = 39.25 in²
Pizza remaining = 314 - 39.25 = 274.75 in²
Answer: 274.75
Step-by-step explanation:
Diameter=20
r= 20/2=10
A= π[tex]r^{2}[/tex]
= 3.14*10*10
= 314 square inches
1/8 of 314 = 39.25
So, are of remaining pizza = 314-39.25
= 274.75 square inches
does 2 less than the product of 8 and e = 8e - 2
Answer:
Yes
8e - 2 in words is 2 less than the product of 8 and e
Step-by-step explanation:
product of 8 and e ==> 8e
two less than the product of 8 and e ==> 8e - 2