If two algebraic expressions are equivalent, then they both have the same result when the same value of the variable is entered. 12x2 + x + 20 is the same as the given expression.
What other expression is the same as 3 5?6/10, 9/15, 12/20, etc. are fractions that are identical to 3/5. The value of equivalent fractions remains unchanged when lowered. Explanation: The numerator and denominator of equivalent fractions can be written by multiplying or dividing them both by the same value.
The given quadratic expression 12x^2+x-20
now, 12x^2 + 16x - 15x - 20
4x (3x+4) - 5(3x+4)
(4x-5) (3x+4)
the root of the equation is (4x-5) (3x+4)
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Activity 1: Keep Trying
Direction: Read, understand, analyze the given problem and solve it by applying the suggested
steps. Write your answer on the box provided.
1. Esther gave birth to a new-born baby weighing 5 kg at birth. Her friend told her that
the monthly average weight gained by a baby is 2 kg. If the rate of increase of the baby's
weight every month is constant, what is the weight of the baby after five months?
Perlom
Solution
Step 5
ernalia
Step 1
Step 2
Step 4
Step 3
nent anar
lia
The weight of the baby after five months is 15 Kg.
Step 1:
Given:
New-born baby weight = 5kg
Monthly average weight gained = 2kg
To find:
The weight of the baby after 5 months.
Average Weight of Baby:
Birth weight is the weight of the baby at birth. [1] The average birth weight of babies of European descent is 3.5 kilograms, with a normal range of 2.5 to 4.5 kilograms (5.5 to 9.9 pounds). On average, South Asian and Chinese babies weigh about 3.26 kg. The prevalence of low birth weight infants decreased slightly from 7.9% (1970) to 6.8% (1980), then increased slightly to 8.3% (2006) and is currently at 8.2% (2016).
Step 2:
Represent the unknown.
Let x-the number of months .
Let y-weight of the baby after 5 months.
Step 3:
Formulate the equation.
The mathematical equation is:
5+2x = y
Step 4:
Solve the equation.
5+2x = y
5+2(5) = y
5+10 = y
y = 15
Thus, the baby weight is 15kg after 5 months.
Step 5:
Using the equation 5+2x=y.
5+2x = y
5+2(5) = 15
5+10 = 15
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Write an equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5).
y =
The equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5) is 2x+y = -2.
The line between these locations' slopes must equal the negative reciprocal of the bisector's slope. It must go through the segment midway.
The slope of the line through the given points :
m = (y2 -y1)/(x2 -x1) = (5 -(-1))/(4 -(-8)) = 6/12 = 1/2
Then, The slope of the required bisector: m = -1/(1/2) = -2
The midpoint of the given segment:
((-8, -1) +(4, 5))/2 = (-8+4, -1+5)/2 = (-4, 4)/2 = (-2, 2)
Then the point-slope form of the equation of the bisector:
y -y1 = m(x -x1)
y -2 = -2(x -(-2))
y = -2x -4 +2
y = -2x -2 . . . . . . . slope-intercept form equation
2x +y = -2 . . . . . . .standard form equation
Thus, The equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5) is 2x+y = -2.
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What is the reflection of point 2/3 about y-axis?
When reflected in the y-axis, the image of the point (2/3) is (-2/3).
The sign of the x coordinate changes when a point is mirrored on the y-axis.
When a figure is built around a single point known as the point of reflection or the figure's centre, a reflection point results. There is an exact opposite point on the other side of each point in the figure. The shape and dimensions of the figure remain unchanged underneath the point of reflection.
The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).
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Can you help me with this
Answer:
slope = 2
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (1, 4) ← 2 points on the line
m = [tex]\frac{4-0}{1-(-1)}[/tex] = [tex]\frac{4}{1+1}[/tex] = [tex]\frac{4}{2}[/tex] = 2
Answer: The slope is 2.
Step-by-step explanation: To find the slope of a line, we first need to pick two points on a line. To solve this, I picked points (-2, -2) and (1, 4). The slope is rise over run, so you need to find the rise and run and divide.
We need to go 6 spaces up from (-2, -2) to get to (1, 4). This is our rise. Then, we go 3 spaces to the right. That is our run. 6 / 3 is 2, so that's your slope. Notice that if you cannot divide the rise and run into a whole number, keep it as a fraction instead.
Let me know if this is right! :)
Question 22 This question has two parts. First, answer Part A. Then, answer Part B. Part A STATE YOUR ASSUMPTION Liling is making a quilt. She starts with two small squares of material and cuts them along the diagonal. Then she arranges the four resulting triangles to make a large square quilt block. She wants the large quilt block to have an area of 36 square inches. A. What side lengths should Liling use for the two small squares of material? Explain. Round to the nearest tenth, if necessary. In. ; For the block to have an area of 36 square inches, each side must be V2 in. Or about inches. By the inches. This means the hypotenuse of each small right triangle is V2 inches 45°-45°-90° Triangle Theorem, the sides of these triangles measure Part B Do b. Explain any assumption that you make to answer part a. Next Question Check Answer Privacy and Cookies | Terms of Use | Minimum Requirements Platform Status 2021 McGraw-Hill Education. All Rights Reserved.
Blank space 1: 3
Blank space 2: 4.242
Blank space 3: 6
Blank space 4: 6
Blank space 5: 3
This can be solved using triangle theorem.
What is triangle theorem?The first theorem, a triangle's three inner angles can be added up to 180 degrees. According to this theorem, if ABC is a triangle, then ∠A + ∠B + ∠C = 180°.The second theorem states that an isosceles triangle's base angles are congruent or that its opposing sides' angles are also equal in size.The third theorem states that the total of the equivalent internal angles is equal to the size of the exterior angle of a triangle.Given that,
Liling is making a quilt. She starts with two small squares of material and cuts them along the diagonal.
The bigger square = 36 sq. in.
Then the side of the bigger square = √36 inch = 6 inch
Next, The side of the bigger square = Diagonal of the smaller square
Let the side of the smaller square = a (let)
Diagonal (smaller square): a√2 = 6 inch
so, a = 3√2 inch
Thus, a = 3 x 1.414 = 4.242
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The complete question is as follows:
What is the median? Help please
Answer:
-65
Step-by-step explanation:
Median = middle number
-76, -74, -67, -65, -63, -58, -48
out of the numbers I am shown, from the photo, I would say "-65" is the answer, but if there is another number I'm missing, add it to the row of numbers above and add the two numbers together and divide by 2
I hope this helps!
A linear function is shown on the graph.
A linear function beginning with open circle at negative 3 comma negative 5 and ending with an open circle at 3 comma 7.
What is the domain of the function?
{y | −5 ≤ y ≤ 7}
{y | −5 < y < 7}
{x | −3 ≤ x ≤ 3}
{x | −3 < x < 3}
Answer: D
Step-by-step explanation:
In this problem, we are asked to find the domain of the function. Domain is finding the interval of the function of the x value.
Since we are finding domain, we can eliminate A and B because those are looking at y interval, or range.
This leaves us with C and D. They are almost the same except for the ≤ in C and < in D. The difference between ≤ and < is the fact that ≤ includes and touches the point, and < doesn't.
The function has open circles at x=-3 and x=3. That means they don't touch and include x=-3 and x=3. The function only get's really close to those points, but not include them. This tells us that D is the answer.
The domain of the function is {x | −3 < x < 3}. Thus, Option D holds the truth.
The domain of a function refers to the interval of the x values of the function.
In this case, we are asked to find the domain of a linear function that is shown on a graph. The graph starts at an open circle at negative 3, negative 5 and ends at an open circle at 3, 7.
To find the domain, we need to look at the x interval of the function. Options A and B refer to the y interval or range and can be eliminated.
The remaining options, C and D, are similar, except for the fact that C includes and touches the point with "≤", while D doesn't with "<". The open circles at x=-3 and x=3 indicate that the function only gets close to these points, but does not include or touch them.
Thus, the correct answer is option D, {x | −3 < x < 3}.
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Olivia owns a pastry shop, and needs to fill an order for 700 cupcakes
She already has 15 cupcakes made, and she can make 137 cupcakes
hour. How many hours does Olivia need to fill the order?
Olivia needs
more hours.
Answer:
5 hours
Step-by-step explanation:
Olivia needs to make 700 - 15 = <<700-15=685>>685 cupcakes.
So she needs to work for 685 / 137 = <<685/137=5>>5 hours
The sum of two consecutive even numbers is 34. What numbers is it
Answer:
16 and 18
16 + 18 = 34 .......... .....
In our class there are 40 boys. 22 students are girls write a ratio comparing girls to boys
Answer:
Its 22:40
Step-by-step explanation:
Answer: 22:40
Pretty simple
Step-by-step explanation:
1. You may get up to 35 gallons of gas at a time at the gas station. What inequality is that?
The inequality is x ≤ 35, where x represents the amount of gas in gallons.
This question means by the statement that we have been given that the number of gallons cannot exceed 35 so it actually means that they are either 35 or less than 35. so will use < = sign to come up with this equation.
You can have up to 35 gallons of gas at a time at the gas station. The inequality x ≤ 35 represents the fact that x (the amount of gas in gallons) is less than or equal to 35.
This means that the equation will be x≤35
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Devin drove her truck. The fuel remaining in the truck's tank (in liters) as a function of distance (in kilometers) is graphed.
What is the approximate average fuel consumption rate, between the 100th kilometer and 400th kilometer?
Between the 100th and 400th kilometers, the average fuel consumption rate is 5/6 liters per kilometer.
What is the rate of change?A consequence of dividing the variation in a variable's function by the variation in the variable. For example The rate at which a distance changes in relation to time is known as velocity.
Given, Devin drove her truck. The fuel remaining in the truck's tank (in liters) as a function of distance (in kilometers) is graphed.
Since in the domain [100, 400] graph shows somewhat linear properties.
from the graph Fuel consumption at 100 = 375 liters
Fuel consumption at 400 = 125 liters
rate in a linear function between two points = (y₂ - y₁)/ (x₂ - x₁)
thus rate between [100, 400] = (375-125)/400-100
rate between [100, 400] = 250/300
rate between [100, 400] = 5/6litere per kilometer
therefore, the average fuel consumption rate, between the 100th kilometer and 400th kilometer is 5/6 liters per kilometer.
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Identify all of the necessary assumptions for a significance test for comparing dependent means.
>Categorical Data
>At least 15 successes and 15 failures in both groups
>Quantitative Data
>Random Samples or Random application of treatments
>n is greater than or equal to 30 OR Population of Differences could be Normally distributed.
>Both sample sizes are greater than 30 or Both population distributions could be Normally Distributed
The correct answer will be:
Quantitative data, both sample sizes are greater than 30 or Both population distributions could be Normally Distributed, Random Samples or Random application of treatments
There should be just one group for each subject. The observations in each category are unrelated to one another. There were no notable outliers in any category.
The following are the presumptions for a percentage significance test: Data come from a random sample [Sample is large enough, which is presumed to be true when. It should be noted that both quantitative and categorical data can be subjected to a significance test for a proportion.
Most parametric tests begin with the underlying presumption of population distribution. The ratio scale or interval scale measurements, easy random extraction, normal distribution of the data, a sufficient sample size, and homogeneity of variance are all prerequisites for performing the t-test.
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ine segment SU is dilated to create S'U' using point Q as the center of dilation. The scale factor of the dilation is
The scale factor of the dilation is 2. An expansion happens when the scaling factor's absolute value exceeds one.
What does a scale factor mean when defining dilation?The scale factor is defined as the proportion of the new image's size to that of the previous image. A fixed location in the plane serves as the center of dilatation. The scale factor and the center of dilation are used to determine the dilation transformation. The image stretches if the scaling factor is greater than 1.
As per the rule of scale factor
Q'U'/QU = SF
SF= Scale factor
= (5+5)/5= Scale factor
= 10/5= 2
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A triangle has sides with lengths of 12 feet, 16 feet, and 18 feet. Is it a right triangle?
Answer:
Step-by-step explanation: If the sides are a,b,c (in ascending order) and c squared = the sum of the squares of a and b, then it's a right triangle.
Answer:
No, it is not a right triangle.
Step-by-step explanation:
Right triangle fulfill the pythagorean theorem:
[tex]a^2+ b^2 = c^2[/tex]
Where, c is the hypothenuse or the longest side, and b and a are the remaining two sides.
[tex]12^{2} = 144\\16^2 = 256\\256 + 144 = 400\\\sqrt {400} = 20 \neq 18[/tex]
A particle moves along the x-axis so that at time
t
≥
0
t≥0 its position is given by
x
(
t
)
=
t
3
−
6
t
2
−
29.
x(t)=t
3
−6t
2
−29. Determine the total distance traveled by the particle from
0
≤
t
≤
7.
0≤t≤7.
The total distance traveled from 0 ≤ t ≤ 7, considering the position function x(t) = t³ - 6t² - 29, is given as follows:
288.75 units.
How to obtain the total distance traveled?The position function for this problem is defined as follows:
x(t) = t³ - 6t² - 29.
The total distance traveled over an interval [a,b] is given by the definite integral of the function x(t) over the interval from x = a to x = b.
The definite integral in this problem is calculated as follows:
I = 0.25t^4 - 2t³ - 29t, from t = 0 to t = 7.
Applying the Fundamental Theorem of Calculus, the total distance is calculated as follows:
I = 0.25(7)^4 - 2(7)³ - 29(7) - (0.25(0)^4 - 2(0)³ - 29(0))
I = 288.75 units.
(which is the absolute value of the result of the definite integral).
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which answer is this
A.43
B.38
C.61
D.81
HELP!!! Find the inverse of the matrix..
Answer:
The matrix does not have an inverse (D)
Step-by-step explanation:
The matrix is singular, therefore doesn't have an inverse
Write the equation of the line that passes through the points (6, 1) and
(6, -8). Put your answer in fully simplified point-slope form, unless it
is a vertical or horizontal line.
something noteworthy is that the x-coordinate is the same for each point, so Check the picture below.
Uncle Drew scored 28 points in 5 5/6 minutes during a game of basketball. How many points did he average per minute during that 5 5/6 minutes?
Answer:
He scored an average of 4.8 points per minute.
Tanner has $4.60 in nickels and quarters. If he has 14 more nickels than quarters, how many of each coin does he have?
quarters
nickels
The number of coins of nickels and quarters will be 27 and 13, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Tanner has $4.60 in nickels and quarters. If he has 14 more nickels than quarters.
Let 'x' be the number of nickels and 'y' be the number of quarters. Then the equations are given as,
x = y + 14 ....1
0.05x + 0.25y = 4.60 ....2
From equations 1 and 2, then we have
0.05(y + 14) + 0.25y = 1
0.05y + 0.70 + 0.25y = 4.60
0.30y = 3.9
y = 13
Then the value of 'x' is given as,
x = 13 + 14
x = 27
The number of coins of nickels and quarters will be 27 and 13, respectively.
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Hannah either walks or cycles to school. The probability that she walks to school is 0.75 If she walks, the probability that she is late is 0.6 If she cycles, the probability that she is late is 0.2 Work out the probability that on any one day Hannah will not be late for school.
If Hanna is walking there is a 0.4 chance of not being late. 0.75 x 0.4 = 0.3 probability of not being late.
If Hanna cycles there is a chance of 0.8 of not being late. 0.6 x 0.8 = 0.48.
0.48 + 0.3 = 0.78.
In other words, there is a 78% probability of her not being late.
Aisha bought 15 apples and oranges for $9.00. each orange costs $0.50, and each apple costs $0.65. let x represent the number of oranges and y represent the number of apples. which system can be used to find the number of apples and oranges aisha bought? x y = 15. 0.5 x 0.65 y = 9.00 x = y. 0.5 x 0.65 y = 9.00 x y = 9. 0.5 x 0.65 y = 15.00 x = y. 0.5 x 0.65 y = 15.00
Both (x + y = 15) and (0.5x + 0.65y = 9.00) make up the equation system.
What is an equation ?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
The statement is not an equation if there is no "equal to" sign in it
According to our question-
x is the quantity of oranges.
y is the quantity of apples.
Oranges plus apples equal 15, or x plus y equals 15, so Aisha purchased 15 pieces of fruit.
Apples cost $0.65 and oranges cost $0.50. The fruit cost Aisha $9.00.
0.5x (the total cost of the oranges) + 0.65y (the total cost of the apples) equals 9.00 (the total cost of the fruit).
x + y = 15
0.5x + 0.65y = 9.00
As a result, the system of equations is (0.5x + 0.65y = 9.00) and (x + y = 15).
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I NEED ANSWERS ASAP!!!!!!!!!!!
If WY is 4. 6, what is MZ? Round your
answer to the nearest tenth. Write NA if there
is not enough information given.
NA (There is not enough information given to determine the value of MZ)
In this question, we are given that WY is 4.6 for us to find the value of MZ We need more information to be in a position to answer this. More information includes maybe we know the value of M or at least having some relationship between WY and MZ for us to draw a conclusion and come up with the value of MZ. If at all we had a common value in WY and MZ say M then it could be easier to come to a conclusion and finally get the value of MZ.
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Study the example showing a function. Then solve
problems 1-6.
Example
The table and graph show the
relationship between the length
of the sides of a square, in feet, and
the perimeter of the square in feet.
Side Length (input) 1 2 3 4 S
Perimeter (output) 4
812 16 20
The relationship is a function because
there is only one output value for
each input value.
Perimeter (output)
20
18
16
14
12
10
8
6
4
2
Perimeters of Squares
0 1 2 3 4 5 6 7 8 9
Side Length (input)
1 Describe the relationship between the input and output
values in the example.
2 Can you represent the function in the example with an
equation? If so, what equation can you write? If not,
why not?
Vocabulary
function a rule that
The relationship between the input and output is that the perimeter of a square is always equal to four times the length of one of its sides.
What is the perimeter of square?The perimeter of a square is the total distance around the outside of the square. It is the sum of the lengths of all four sides. To find the perimeter of a square, you simply multiply the length of one side by four, since all sides of a square are equal in length. The formula is P=4S
1.The relationship established between (side length of the square) and output (perimeter of the square) represent that A square's perimeter is always equal to 4 times one of its sides.
2.Yes, the function can be represented with an equation. The equation would be:
Perimeter = 4 × Side Length.
Side Length (input) 1 2 3 4 5
Perimeter (output) 4 8 12 16 20
This equation states that the perimeter of a square is equal to four times the length of one of its sides.
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Find the volume of the cone either enter an exact anwer in term of pi or ue 3. 14. For pie. R= 5 l=6
The volume of the cone is 50π cubic units .
What is a cone ?A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex.
A cone has a circular base.
A cone has no edges, one face, and one vertex.
The length of the line segment from a cone's apex to any point around the circle of the cone's base is known as the slant height of the cone.
A right circular cone is a cone with its apex perpendicular to the base of the cone and directly above it.
An oblique cone is one that doesn't have its apex precisely over the base's circle.
Radius of the cone = 5
Height of the cone is 6
Volume of the cone = [tex]\frac{1}{3}\pi r^{2} h[/tex] = [tex]\frac{1}{3}\pi *5^{2}* 6 = 50\pi[/tex] cubic units.
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The diameter of a circle is 34 inches.What is the area of the circle in square inches?Use 3.14 as pi
Answer: 907.46 inches squared
Step-by-step explanation:
The formula for the area of the circle is:
[tex]A = \pi r^{2}[/tex]
In this question, pi is 3.14. The radius of a circle is half of its diameter. So:
[tex]\frac{34}{2} =17[/tex]
Plug these values into the equation:
[tex]A = (3.14)(17)^2[/tex]
Simplify:
[tex]A = 907.46[/tex]
The area of the circle is 907.46 inches squared.
Marissa is skateboarding on a straight stretch of sidewalk. In 3.0 minutes, she travels 486 meters. What is the magnitude of her velocity during this stretch?
Marissa velocity while skateboarding is 162 meters per minute
What is an equation?An equation is used to show the relationship between numbers and variables.
Velocity is the ratio of displacement to time taken. It is a vector quantity (has magnitude and direction) and it is given by:
Velocity = displacement / time
Marissa travels 486 meters in 3 minutes, hence:
Velocity = displacement / time
Velocity = 486 m / 3 min = 162 meters per minute
The velocity is 162 meters per minute
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Answer: The correct answer is 2.7m/s
Step-by-step explanation:
I took the test
How do you find mass using FG?
To find the mass of an object, one can use the formula (Force x Distance) / Gravitational Constant (FG). This formula involves multiplying the force applied to an object by the distance it moves, and then dividing the result by the gravitational constant (FG). The resulting number is the mass of the object in kilograms.
Mass can be found by using the formula (Force x Distance) / Gravitational Constant (FG).
For example, if a force of 10N is applied to an object that is moving 2 meters, the mass of the object can be calculated as follows:
Mass = (10 N x 2 m) / FG
Mass = 20 / 9.8
Mass = 2.04 kg
Finding mass using the force-distance formula (FG) is a simple process. To use it, one needs to know the force applied to an object, the distance it moves, and the gravitational constant (FG). The force and distance values can be measured or calculated depending on the situation. The gravitational constant is a fixed number and is equal to 9.8 m/s2. To calculate the mass, one needs to take the force multiplied by the distance and then divide it by the gravitational constant (FG). The resulting number is the mass of the object in kilograms. This formula is useful for calculating the mass of objects in a variety of situations. It is also useful for verifying the mass of an object that has already been measured.
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9. The expression (xn)(x5)3 is equivalent to x30. What is the value of n?
Answer: N= x24 over 3
Step-by-step explanation: