Ten bananas and ten pears will run you about £4.537.
Application of simultaneous equationSimultaneous equations are two equations with two unknown variables. From the given question;
If three bananas and two pears cost 95p and Five bananas and three pears cost £1.51, the equivalent equations will be:
3b + 2p = 0.95 * 3
5b + 3p = 1.51 * 2
Solve simultaneously;
6b + 6p = 2.85
10b + 6p = 3.02
Subtract
-4b = -0.17
b = 0.17/4
b = £0.0425
Since 3b + 2p = 0.95, hence
3(0.0425) + 2p = 0.95
0.1275 -0.95 = -2p
2p = 0.8225
p = 0.4112
The cost of ten bananas and ten pears will be:
Cost = 10(0.0425) + 10(0.4112)
Cost = 0.425 + 4.112
Cost = £4.537
Hence the cost of ten bananas and ten pears is approximately £4.537
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can you guys help me with this plsss
Answer:
30 inches
Step-by-step explanation:
The longest piece (15 in) is represented as 5 in the ratio, so we can find what one unit is. We can do 15÷5=3, so one unit is 3 inches. We could multiply each of them by 3 and add them up, but there's a simpler way. We can find the total of the ratio, 2+3+5=10. So, we can do 3x10=30 inches. Therefore, the length of the stick is 30 inches.
What is whole numbers class 8?
Whole Numbers are the numbers that include natural numbers and zero. Not a fraction or decimal. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …}.
Whole Numbers
Whole numbers are a set of numbers including all natural numbers and 0. They are a part of real numbers that do not include fractions, decimals, or negative numbers. Counting numbers are also considered as whole numbers.
Addition , Subtraction , Division and multiplication are also possible with the whole numbers as they are also numbers . Addition and Multiplication are closed which means the sum and multiplication of two numbers is also a whole number whereas Subtraction and Division are unclosed.
We know that natural numbers refer to a set of counting numbers starting from 1, 2, 3, 4 and so on. In simple words, whole numbers are a set of numbers without fractions, decimals, or even negative integers.
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What is the median of the following data sample 3 7 4 8 9 6 10 12 13 15?
The Median of the following sample 3 4 6 7 8 9 10 12 13 15 is 8.5.
One measure of central tendency is the median. The median of a set of numbers is its midway value. It splits a sample of given data into the upper and lower halves. A minimum of half of the observations are above the median and a minimum of half are below it.
When there are exactly even numbers of observations in a data collection, the median can be calculated as follows:
sort the data in ascending or descending order.
If there are an even number of observations (let's say n), identify the (n/2)nd and [(n/2) + 1] th observations.
The average of the top two observations is the same as the median of the data given (as determined in step 2).
Median = [tex]\frac{1}{2} [(\frac{n}{2} ) + (\frac{n}{2}+1 )][/tex].
Here n = 10, So [(10/2) + (10/2 + 1)]/2.
=> Median = 8.5.
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Why is 2 root 2 equal to root 2?
Therefore , the given expression of this problem of square root
2√2 not equal to √2.
What is square root?The value that results from multiplying the square root of an integer by itself is the number.
Example: Since 5* 5 = 25, 5 is the square root of 25. Observe that (5) (5) also equals 25, proving that (5) is a square root of 25.
Here,
In this case, the mathematical symbol for Root 2 is 2.
Root 2 then multiplied by Root 2.
√2 + √2 = 2√2
If we take the estimated value of 2 = 1.4142
Then
=> 2√2 = 1.4142 x 2
=> 2.8284 (approximately)
Please take note that 2 is an irrational number.
Alternatively, root2* root 2
√2 * √2 = 2
Because 2 is just the square root of 2,
Therefore,
what happens when root 2 + root 2 and root2 root 2 are different
2√2 - 2 = 2.8284 - 2 = 0.8284 (approx)
Therefore , the given expression of this problem of square root
2√2 not equal to √2.'
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The length of a
rectangle is 5 ft more than twice its width. The
area of the rectangle
is 33 ft^2. Find the dimensions of the rectangle.
The dimensions of the rectangle is length = 5ft and width = 3ft
Define System of equation
A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.
Let,
x = length of rectangle
y = width of rectangle
Next, set up system of equation
We have given, the length of a rectangle is 5 ft more than twice its width.
x = 2y + 5 --------(a)
Next, The area of the rectangle is 33 ft²
xy = 33 ----------(b)
x = 33/y
substitute the value of x in eq(a)
x = 2y + 5
33/y = 2y + 5
33 = 2y² + 5y
2y² + 5y - 33 = 0
Factor it,
2y² + 11y - 6y - 33 = 0
y( 2y + 11) - 3( 2y + 11) = 0
(y - 3) (2y + 11) = 0
Split the values,
y - 3 = 0 and 2y + 11 = 0
y = 3 and y = -11/2 (ignore this as width cannot be -ve)
Substitute y = 3 in eq(b)
x * 3 = 33
x = 11
So, we get
length = 11 ft and width = 3 ft
Hence, the dimensions of the rectangle is length = 5ft and width = 3ft
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How to solve x3 7x 6?
(x-1), (x-2) and (x+3) are the three factors of the above cubic polynomial. A degree three polynomial might be referred to as a cubic polynomial.
what is cubic polynomial ?A degree three polynomial might be referred to as a cubic polynomial. In other words, the number three will be the largest exponent of the variable in a cubic polynomial. A cubic polynomial would therefore have the generic form ax3+bx2+cx+d, where a ≠0.
here
Let p(x)=[tex]x^{3}[/tex]−7x+6
From figure, we have p(1)=0
Thus, (x−1) is a factor of p(x)
The other factor is [tex]x^{2}[/tex]+x−6
=(x+3)(x−2)
Therefore, [tex]x^{3}[/tex]−7x+6 =(x−1)(x+3)(x−2)
(x-1), (x-2) and (x+3) are the three factors of the above cubic polynomial.
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We can reduce the margin of error in an interval estimate of p by doing any of the following except ____. increasing the sample size. increasing the planning value p* to .5. increasing a reducing the confidence coefficient.
We can reduce the margin of error in an interval estimate of p by doing any of the following except using a planning value p* closer to 0.5.
The breadth of the confidence interval is affected by the following features:
Increase the sample size - Increasing the sample size is the most feasible strategy to reduce the margin of error.Reduce variability - You can estimate a population parameter more precisely the less variable your data are.Use a one-sided confidence interval - The margin of error is lower for a one-sided confidence interval than a two-sided confidence interval.Lower the confidence level - A narrower, more exact confidence interval is the benefit of a lower confidence level.Correct Question:
We can reduce the margin of error in an interval estimate of p by doing any of the following except ____.
increasing the sample size
using a planning value p* closer to 0.5
increasing the level of significance
reducing the confidence coefficient
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What is the coefficient of y² in the expression 3y²+ 4x?
The coefficient of y² in the expression 3y²+ 4x is 3.
A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6.
Firstly,
The given equation is 3y²+ 4x
To find : The coefficient of y²
The coefficient is nothing but the number beside the variable.
In the equation 3y²+ 4x, the number beside the variable y² is 3 and it is termed as coefficient of y² which is 3.
As we can see that the term that is in multiplication with y² is 3. Similarly, the term that is coefficient of x is 4.
Hence, the coefficient of y² in the equation is 3.
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How do you write more than 50?
More than 50 in mathematical expression is written as >50.
Any two integers can be compared using the greater than and less than symbols. Greater than and less than symbols are used to indicate whether one number is greater than or less than another. The greater than sign (>) is used when the first number exceeds the second number. The less than sign (<) is used when the first number is less than the second number.
The quantity on the left of the > sign is the greater quantity. It could be a variable or expression [like 3x - 2 > 50].
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A right triangle has side lengths of 15 in, 12 in, and 9 in. it is dilated by a scale factor and has new side lengths on 5 in, 4in, and 3 in. what was the scale factor?
Each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.
To find the scale factor of the dilation, we can divide the length of each side of the dilated triangle by the length of the corresponding side of the original triangle.
For example, for the side of length 5 inches in the dilated triangle, the scale factor is 5 inches / 15 inches = 1/3.
We can do the same for the other two sides and we will get the same scale factor for all three sides, since the dilation is uniform.
In this case, the scale factor is 1/3 for all three sides, so the scale factor for the dilation is 1/3.
This means that each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.
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The side of length 5 inches in the dilated triangle, the scale factor is 5 inches / 15 inches = 1/3.
We can do the same for the other two sides and we will get the same scale factor for all three sides, since the dilation is uniform.
In this case, the scale factor is 1/3 for all three sides, so the scale factor for the dilation is 1/3.
This means that each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.
stephanie knows that a correlation between the number of bars and the number of churches in her city does not, in itself, mean that more bars will lead to a higher number of churches. which of the following would not be a lurking variable in the above scenario? a.) the city's budget b.) stephanie's proximity to the center of the city c.) the day of the week that stephanie attends service d.) population density
The option that would not be a lurking variable in the above scenario is c.) the day of the week that stephanie attends service
What is a lurking variable?a variable that has a connection (e.g., may be correlated) with the response and the explanatory variable but is neither the explanatory variable nor the response variable. Although it is not taken into account in the study, it might affect how the variables are related.
When researching the relationship between two or more variables, we occasionally neglect the influences on the relationship that exist outside of these two variables. These are also known as lurking variables or extraneous variables. These significantly impact the relationship. Lurking variables are those that were not taken into consideration for the study but have an impact on the two studied variables.
The day of the week will not be a lurking variable since we are talking about the number of churches and bars. Hence, Option c is correct.
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Answer:
Step-by-step explanation:
a.) Correct.
A variable is a lurking variable if it can influence an explanatory/response relationship. So it must be related to both the explanatory and response variable. It is not likely street name length is related to the number of bars in a given area.
Solve angle ABC by using the measurements angle ABC = 90°, angle BAC = 35°, and a = 10. Round measures of sides to the nearest tenth and measures of angles to the nearest degree.
The measure of the sides 'b' and 'c' will be 5.7 units and 8.2 and angle C will be 55°.
What is the sine law?The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.
The sine law in the triangle ΔABC is given as,
AB / sin C = BC / sin A = CA / sin B
The measure of the third angle is given as,
∠A + ∠B + ∠C = 180°
35° + 90° + ∠C = 180°
∠C = 55°
Then the measure of the side c (AB) is calculated as,
AB / sin C = BC / sin A
c / sin 55° = 10 / sin 90°
c = 8.2
Then the measure of the side b (AB) is calculated as,
AC / sin B = BC / sin A
b / sin 35° = 10 / sin 90°
b = 5.7
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What are the qualifying conditions to avail the SSS sickness benefit?
The Side-Side-Side (SSS) criterion states that two triangles are similar if "sides of one triangle in two triangles are proportional to (i.e., in the same ratio of) the sides of the other triangle, then their corresponding angles are equal and so the two triangles are comparable."
Look at the triangles in the picture below. We can observe that the triangles' three sets of side pairs are all congruent. "SSS" or "side-side-side" are other names for this. Two triangles are congruent if they have three pairs of congruent sides, according to the SSS requirements for triangle congruence.
Congruence Rule Theorem for SSS
Two triangles are said to be congruent if the corresponding three sides of one triangle match the corresponding three sides of the other triangle exactly.
We shall now demonstrate the aforementioned theorem.
Given: [tex]\triangle A B C[/tex] and [tex]\triangle P Q R[/tex] such that AB=PQ, BC=QR and AC=PR.
To prove: [tex]\triangle A B C \cong \triangle PQR[/tex]
Construction: Let BC be the longest side of [tex]\triangle A B C[/tex] and so QR is the longest side of [tex]\triangle P Q R.[/tex]
Draw PS so that [tex]\angle R Q S=\angle C B A[/tex] and [tex]\angle Q R S=\angle B C A[/tex].
Join SQ and SR.
In [tex]\triangle ABC[/tex] and [tex]\triangle SQR[/tex],
BC=QR Given
[tex]\angle C B A=\angle R Q S[/tex] By construction
[tex]\angle B C A=\angle Q R S[/tex] By construction
[tex]\triangle A B C \cong \triangle SQR[/tex] By ASA congruence
[tex]\angle A=\angle S[/tex] By CPCTC
AB=SQ By CPCTC
AC=SR
Now, AB=PQ and AB=SQ => PQ=SQ
Similarly, AC=PR and AC=SR => PR=SR
Hence, [tex]\triangle ABC \cong \triangle PQR,[/tex]
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Help me rationalize the denominator
Answer:
[tex]\frac{2}{15} (3+\sqrt[3]{3})[/tex]
or
[tex]\frac{6+2\sqrt[3]{3} }{15}[/tex]
You can rationalize the denominator to simplify the answer so many different ways.
Step-by-step explanation:
Simplify the radicals.
What is the preimage in dilation?
A dilation is a type of transformation that enlarges or reduces a figure.It is also called pre image.To create new figure is called image.For this purpose we can use scale factor ,r how much bigger or smaller the dilation image will be compared to pre-image.
What is dilation?It is a transformation which is used to resize the image.It is used to make objects smaller or greater.But there is no difference in the size of the shape.The pre -image and image is not congruent.
How do you find the image figure is a dilation of the preimage?For this purposes we use scale factor.
When you dilates a image the scale factor find that how much image will be smaller or larger.
.If the scale factor is between o0 and 1 .Then image is smaller than preimage.Dilation with a scale factor between 0 and 1 i called transformation.
.if the scale factor is greater than 1.Then image will be larger than the preimage.
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Which formula can be used to find the missing number in an array of 1 100?
The formula can be used to find the missing number in an array of 1 100 is N * (N + 1) / 2.
How to find missing number in an array 1 100?The size of the array is N – 1. So the sum of n elements, that is the sum of numbers from 1 to N can be calculated by using the formula N * (N + 1) / 2. Now find the summation of all elements in the array and subtract it from the summation of first N natural numbers, the value obtained will be the value of the missing element.
The formula can be used to find the missing number in an array of 1 100 is N * (N + 1) / 2.
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What are the three consecutive numbers of 51?
The 3 consecutive odd numbers whose sum will be 51 are 16, 17, 18.
What are consecutive numbers ?
Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.
Since, we know that any odd number is always of the form (2k +1). We express an odd number in this form because we know that an odd number is not divisible by 2.
Let the numbers be x, x+1 and x+2.
Then the sum is : x + x+1+ x+2 = 3x + 3
3x + 3 = 51 (given)
3x = 51 – 3 = 48
x = 48 ÷ 3
x = 16
∴
Hence , the 3 consecutive odd numbers whose sum will be 51 are 16, 17, 18.
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what is simplify 4^-4
Answer:
1/256
Step-by-step explanation:
-4 times -4 times -4 times -4 = 256
A negative exponent means it's a fraction!
So, the answer is 1/256
answer :
1/256
steps:
negative exponent means it's a fraction
4^-4 =
1/4^4 :
4^4 =
4 * 4 * 4 * 4 =
256
again negative exponent means it's a fraction so
1/256
How would you describe the end behavior of the graph of a polynomial function based on its equation?
The end behavior of a polynomial function can be determined by examining the leading coefficient and degree of the polynomial. If the leading coefficient is positive, the graph will increase without bound as the x-values increase. If the leading coefficient is negative, the graph will decrease without bound as the x-values increase.
The end behavior of a polynomial function depends on the equation of the function. The degree of a polynomial is the highest power of the variable, and the leading coefficient is the coefficient of the term with the highest degree. If the leading coefficient is positive, the graph will increase without bound as the x-values increase. This is because the terms in the equation with positive coefficients will become increasingly larger than the terms with negative coefficients as the x-values increase. On the other hand, if the leading coefficient is negative, the graph will decrease without bound as the x-values increase. This is because the terms in the equation with negative coefficients will become increasingly larger than the terms with positive coefficients as the x-values increase. In addition, the degree of the polynomial can also affect the end behavior of the graph. If the degree is even, the graph will not have an extreme point. However, if the degree is odd, the graph will have an extreme point. The extreme point will be a maximum or a minimum depending on the sign of the leading coefficient.
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exercise 28 a sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.52 mpa and a sample standard deviation of 0.78 mpa. (a) calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (round your answer to two decimal places.)
95% confident that the true average proportional limit stress of all such joints is at least 8.19 mpa.
What is proportional limit?
The maximum stress at which stress and strain are directly proportional and the stress-strain graph is a straight line with a gradient equal to the elastic modulus of the material is known as the proportional limit.
To calculate the 95% lower confidence bound for the true average proportional limit stress of all such joints, we can use the following formula:
lower confidence bound = sample mean - (t-value * standard error)
The standard error of the mean is a measure of the variability of the sample mean, and is calculated as:
[tex]standard\ error = sample\ standard\ deviation / \sqrt{(sample \ size)}\\\\= 0.78 / \sqrt{(20)}\\\\= 0.19[/tex]
To find the t-value, we can consult a t-distribution table or use a t-distribution calculator. At a 95% confidence level with a sample size of 20, the t-value is approximately 1.725.
Substituting these values into the formula for the lower confidence bound, we get:
lower confidence bound = 8.52 - (1.725 * 0.19)
= 8.52 - 0.327
= 8.19
So the 95% lower confidence bound for the true average proportional limit stress of all such joints is approximately 8.19 mpa.
Hence, 95% confident that the true average proportional limit stress of all such joints is at least 8.19 mpa.
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Which example is continuous?
An example of continuous data is the temperature of a room over time. It can change gradually, or even rapidly, but the data is always changing.
Continuous data is data that can take on any value within a given range. It can be measured on an infinite scale and can have an infinite number of values. An example of continuous data is the temperature of a room over time. This data can change gradually or rapidly, but it is always changing. Continuous data can be measured directly, such as measuring the temperature of a room with a thermometer, or indirectly, such as measuring the temperature of a room through observation. Continuous data can also be used to describe physical or psychological phenomena, such as measuring a person’s heart rate over time or measuring the concentration of a chemical in a solution. Continuous data is often used in scientific research, as it allows researchers to observe trends and correlations over time.
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Hiro painted his room. After 3 33 hours of painting at a rate of 8 88 square meters per hour, he had 28 2828 square meters left to paint. Let y yy represent the area (in square meters) left to paint after x xx hours.
The function representing the area to paint as a function of time is A(t) = 52 - 8t, where A(t) represents the area left to paint after t hours.
The area to paint, A(t), can be represented as a linear function based on the given information. Initially, Hiro had the entire room to paint, which can be represented as A(0) = A₀, where A₀ is the total area of the room.
Given that Hiro painted at a rate of 8 square meters per hour, after t hours, he would have painted 8t square meters.
Therefore, the remaining area to paint after t hours can be expressed as A(t) = A₀ - 8t.
We are told that after 3 hours, Hiro had 28 square meters left to paint. Substituting t = 3 and A(t) = 28 into the equation, we can solve for A₀:
28 = A₀ - 8 x 3
28 = A₀ - 24
A₀ = 52
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The complete question:
Hiro painted his room at a rate of 8 square meters per hour. After 3 hours of painting, he had 28 square meters left to paint. Let A(t) denote the area to paint A (measured in square meters) as a function of time t (measured in hours). What is the Functions formula? A(t)=?
How many buses do you need for 500 people if each bus holds 40 people?
Answer:
13
Step-by-step explanation:
Divide 500 by 40 to find the amount of buses you need
500 ÷ 40 = 12.5
BUT, you cannot have .5 of a bus! So you need ONE extra bus to hold the remaining people
you'll need 13 buses
Answer:
13 buses
Step-by-step explanation:
12 buses but 20 people left so they need 12 buses, and the 13th bus will be half filed.
In which triangle all the sides are equal and all the angles are also equal *?
Equiangular triangle or Equilateral triangle have all the sides equal and all the angles are also equal.
A triangle that has equal-length sides is known as an equilateral triangle in geometry. The three angles that lie across the three equal sides are also equal in size since the three sides are also equal.
With each angle measuring 60 degrees, it is also known as an equiangular triangle.
An equilateral triangle has three interior angles that are all equivalent to one another and each measure 60 degrees in the basic Euclidean geometry. The term "regular triangle" is also used to describe this polygon because it is a regular polygon. The exceptional case of an isosceles triangle with three equal sides and angles is an equilateral triangle.
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How will you describe the relationship between the volume of a sphere and the volume of a cylinder?
The relationship between the volume of a sphere and the volume of a cylinder is said to be that the volume of any sphere is 2/3rd of the volume of any with equal radius and height which is equal to the diameter.
Assuming a cylinder with radius r, height h.
We are aware that the cylinder-volume formula is,
V₁ = π * r² * h
Consider a sphere with radius r₁.
We know that the formula for the volume of sphere is,
V₂ = 4/3 * π * r₁³
If the sphere and a cylinder have same radii and height of cylinder equal to the diameter then, r₁ = r and h = 2r
V₂ = 4/3 * π * r³
And V₁ = π * r² * (2r)
V₁ = 2 * π * r³
V₁ = 2 * 3/4 * V₂
V₁ = 3/2 * V₂
Volume of cylinder = (3 / 2) * Volume of sphere
Therefore, the Volume of a sphere = 2/3 * Volume of a cylinder
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How do you write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph of the given equation?
The equation of line in slope intercept form passing through (-5,-2) and parallel to y = -2x+1 is y = -2x -12 .
The Slope intercept form of the line is written as " y = mx + c " , where c is the y intercept and m is the slope of line .
the required line is parallel to the line with equation ⇒ y = -2x+1 ,
on comparing it with slope intercept form of line ,
we get the slope(m) as "-2" .
the required line is passing through (-5,-2).
substituting the values , we get ;
-2 = (-2)(-5) + c ,
-2 = 10 + c ,
c = -10 -2
c = -12 .
So , the equation is ⇒ y = -2x -12 .
Therefore , the slope intercept form of the required line is y = -2x -12 .
The given question is incomplete , the complete question is
How do you write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph of the given equation ? the point is (-5,-2); and is parallel to y = -2x + 1 .
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in the equation -2 - 6b = 32, the negative coefficient is ____??
Answer:
May be minus
Step-by-step explanation:
minus 2 and minus 6 means minus 8b than we have to find out the value of b so 8into 4 is equal to 32
Mary want to buy a bookcae to hold all of her 138 book. Bookcae A ha 4 helve and can hold 35 book on each helf. Bookcae B ha 5 helve and can hold 26 book on each helf. Which bookcae hould he buy?Bookcae A or bookcae B?
Answer:
Bookcase A
Step-by-step explanation:
Bookcase A
1 half = 35 book
4 half = 140 books
So, bookcase A can hold 140 books
Bookcase B
1 half = 26 books
5 half = 130 books
So, bookcase B can hold 130 books
So, Mary should buy bookcase A
Answer:
Bookcase A is the answer
Step-by-step explanation:
Mary has 138 books
Bookcase A = 4 shelves holds 35 books per shelf
= 4 * 35=140
Bookcase B = 5 shelves holds 26 books per shelf
= 5 * 26=130
He should buy Bookcase A, it has enough space for his books
suppose x is 5 and y is 7. choose the value of the following expression: (x != 7) && (x <= y)
The value of the following expression is true.
Expressions include operators and can consist of any set of variables and constants that can be evaluated to produce a result. Relational expressions are used in decision-making to compare operands and evaluate to 1 (true) or 0. (false).
If a logical expression is true when it is evaluated by C++, it returns an integer value of 1; if it is false, it returns an integer value of 0. Any value other than zero is treated as true in C++, while a value of zero is considered false.
Correct Question :
Suppose x is 5 and y is 7. Choose the value of the following expression: (x ! = 7) & & (x <= y)
a. false
b. true
c. 0
d. null
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