An expression is defined as a set of numbers, variables, and mathematical operations. The value of x that will satisfy the given statement "the sum of a number x and 7 is 35" is 28.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given the statement that the sum of a number x and 7 is 35. Therefore, the given statement "the sum of a number x and 7 is 35" in the form of an expression can be written as,
x + 7 = 35
Subtract 7 from both the sides of the equation,
x +7 - 7 = 35 - 7
x = 28
Hence, the value of x that will satisfy the given statement "the sum of a number x and 7 is 35" is 28.
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When a prism and a pyramid have the same height and the same base the volume of the prism is greater than the pyramid?
Yes, the given statement is true the volume of the prism is greater than the volume of the pyramid when they have same base and same height.
As given in the question,
Formula required to calculate the volume of the pyramid and volume of the prism is given by :
Volume of a pyramid = (1/3) × (base area )× ( height )
Volume of a prism = (Base area) × (height)
When the base and height of the pyramid is same as that of the base and height of the prism then
Volume of the pyramid = ( 1/3) × ( Base area × height )
⇒Volume of the pyramid = ( 1/3) × ( Volume of the prism )
⇒Volume of the prism = 3 × ( Volume of the pyramid )
⇒Volume of the prism > Volume of the pyramid
Therefore, the volume of the prism is greater than the volume of pyramid is a true statement.
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What are the 4 types of roots math?
The types of roots in math are known as real roots , imaginary roots or repeated roots.
roots > 0 imaginary
roots < 0 real
roots = 0 repeated
When the roots are bigger than zero, they are referred to as real roots. When the value of the obtained roots is less than zero, the obtained roots are referred to be not real or imaginary roots.
When the sum of the obtained roots equals zero, we conclude that the roots are repeated.
In order to find the roots of a equation we can plot them on a graph and the solve them or we can factorize the given equation. We can also use the formula to calculate graph using determinant method.
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2.5x−20 when X = 15?
Answer:
17.5
Step-by-step explanation:
Since X is right next to 2.5 and x =15 2.5x15=37.5 and then you subtract 20
Answer:
x = 30/11 = 2 8/11 is approximate 2.727
Step-by-step explanation:
hope this helped:)
What is the value of k if 1 2 is a root of the equation x2 kx 5 4 0?
The value of k in the quadratic equation is k = 2
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
x² + kx - 5/4 = 0 be equation (1)
Now , on simplifying the equation , we get
If 1/2 is the root of given equation, then it will satisfy it.
So , when x = 1/2
( 1/2 )² + k ( 1/2 ) - 5/4 = 0
( 1/4 ) + k/2 - 5/4 = 0
k/2 - 1 = 0
Adding 1 on both sides of the equation , we get
k/2 = 1
Multiply by 2 on both sides of the equation , we get
k = 2
Therefore , the value of k is 2
Hence , the value of k in the equation is 2
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Evaluate the expression 2.5x−20 for x=15
Answer:
[tex]17.5[/tex]
Step-by-step explanation:
[tex]2.5x15-20[/tex]
[tex]37.5-20[/tex]
[tex]17.5[/tex]
Hope this helps you
I need helping finding the length and width of this shape the area is 183.65sqft ? Please help thank you.
Answer:
Below
Step-by-step explanation:
TOTAL AREA of circle with 15' radius = pi r^2 = 706.9 ft^2
this is a fraction of the total 360 degrees of the circle
x/360 = 183.65 /706.9
x = 93.5 ° or 1.63 Radians is the central arc angle
How do you find the discontinuity point of a function?
discontinuity point of a function is a point at which the function is not continuous. There are three types of discontinuities: removable, jump, and essential.
A removable discontinuity is a point at which the function is not defined, but the limit of the function as x approaches the discontinuity point from both sides is equal to a finite value.
A jump discontinuity is a point at which the function is defined, but the limit of the function as x approaches the discontinuity point from both sides is not equal.
An essential discontinuity is a point at which the function is not defined and the limit of the function as x approaches the discontinuity point from both sides is infinite or does not exist.
To find the discontinuity points of a function, you can:
Plot the function on a graph and look for any breaks or gaps in the graph.
Use the algebraic definition of continuity to determine whether the function is continuous at a given point.
Use the limit definition of continuity to determine whether the function is continuous at a given point.
Use a computer algebra system (CAS) to find the discontinuity points of a function.
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A point where the function is not defined and the limit of the function as x approaches the discontinuity point from both sides is infinite or does not exist is referred to as an important discontinuity.
A function's discontinuity points can be located by:
Plot the function on a graph and check the graph for any splits or gaps.
To ascertain whether the function is continuous at a specific point, use the algebraic notion of continuity.
Use the half-angle formulas to determine the exact values of the sine, cosine,
and tangent of the angle. 7π/8
The exact values for angles sine, cosine and tangent are
sin((7π/8)/2) = ±0.98078°
cos((7π/8)/2) = ±0.19509°
tan(7π/8) = ± 5.02733°
What is half angle identities?
In trigonometry, the half-angle formula is used to calculate the precise values of trigonometric ratios of angles like 15° (half of the standard angle 30°), 22.5° (half of the standard angle 45°), and so on. The half angle is represented by θ/2 if is an angle.
Let the given angle is θ = 7π/8.
We have to find the exact values of the sine, cosine and tangent angles using half angle formulas.
Consider, the half angle formula for sine,
sin(θ/2) = ± √((1 - cosθ) / 2)
sin((7π/8)/2) = ±√((1 - cos(7π/8)/2)
sin((7π/8)/2) = ±0.98078°
Now consider the half angle formula for cosine,
cos(θ/2) = ± √(1 + cosθ)/2
cos((7π/8)/2) = ± √(1 + cos(7π/8)/2)
cos((7π/8)/2) = ±0.19509°
Now consider the half angle formula for tangent,
tan(θ/2) = ± √((1 - cosθ)/(1 + cosθ))
tan(7π/8) = ± √((1 - cos(7π/8))/(1 + cos(7π/8)))
tan(7π/8) = ± 5.02733°
Hence, the exact values for angles sine, cosine and tangent are
sin((7π/8)/2) = ±0.98078°
cos((7π/8)/2) = ±0.19509°
tan(7π/8) = ± 5.02733°
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How do you translate coordinates?
To translate an entire triangle, find the coordinates of each of the triangle's vertices, add the horizontal translation then plot the three translated points.
Whenever an object is moved from one location to the next without changing its size, shape, or orientation, a translation takes place. If we know which way and how far the figure to be moved, we can draw the translation in the coordinate plane.
Use P′(x+a,y+b) to translate the point P(x,y), a unit to the right, and b unit up. Use P′(x−a,y−b) to translate the point P(x,y), a unit to the left and b unit to the lower.
There are some steps of translating the triangle:
Step 1: Find the coordinates of each of the triangle's vertices in step one.
Step 2: Add the horizontal translation value to each vertex's x-coordinate and the vertical translation value to each point's y-coordinate to translate each point. If the horizontal translation is to the left or the vertical translation is downward for these translations, add a negative number.
Step 3: Plot the three translated points and draw the triangle by drawing a straight line between each pair of points.
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Х
15
9
18
9
y
17
9
4
Is this relation a function?
yes
no
Determine the period.
X is 10
Y is 1
Answer:
9
Step-by-step explanation:
The top of the slope starts at 1, and it repeats at 9
Determine the x -intercepts of the quadratic y = x 2 + 2 x − 15 by factoring.
Answer:
x-intercepts: x=3, -5
Step-by-step explanation:
y = x^2 + 2x − 15
y = x^2 + 5x - 3x − 15 ==> 5*(-3)=-15 and 5+(-3) = 5-3=2
y = x^2 + 5x - 3x − 15
y = x(x+5) - 3(x+5)
y = (x-3)(x+5)
x-3=0 ==> x=3
x+5=0 ==> x=-5
x-intercepts: x=3, -5
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a = 5, c = 30 what is b square
Answer:
25 it's easy as 123 ABC 123 abc
How many terms are there in the expression x³ 4x² 7x − 2 *?
The provided phrase, x3+4x2+ 7x+ â' 2 has four terms.
What does the phrase mean?Expressions are made up of terms. A term might be either a constant, a variable, or a combination of both.
What kind of phrase would that be?A single letter, a single positive or negative integer, or a number of variables multiplied but never added or subtracted might be the only variable. A number is placed in front of some nouns that have variables. The number used before a sentence is called a coefficient. single-word illustrations: Three times in one phrase.
The mathematical operator + separates the four components in the equation x3+4x2+ 7x+â' 2.
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Determine the frequency of each class in the table shown. Number of Candles in a Glass Jar Class Frequency 1003 1062 1063 1122 1123 1182 1183 1242 1243 1302 1303 1362
The frequency of a class is the number of data points that fall within the class is 1.
To determine the frequency of each class in the table shown, we must first divide the data points into the respective classes. The classes are 1003, 1062, 1063, 1122, 1123, 1182, 1183, 1242, 1243, 1302, 1303, and 1362.
For the class 1003, the frequency is 1, since there is only one data point (1003) in this class.
For the class 1062, the frequency is also 1 since there is only one data point (1062) in this class.
For the class 1063, the frequency is also 1 since there is only one data point (1063) in this class.
For the class 1122, the frequency is 1 since there is only one data point (1122) in this class.
For the class 1123, the frequency is 1 since there is only one data point (1123) in this class.
For the class 1182, the frequency is 1 since there is only one data point (1182) in this class.
For the class 1183, the frequency is 1 since there is only one data point (1183) in this class.
For the class 1242, the frequency is 1 since there is only one data point (1242) in this class.
For the class 1243, the frequency is 1 since there is only one data point (1243) in this class.
For the class 1302, the frequency is 1 since there is only one data point (1302) in this class.
For the class 1303, the frequency is 1 since there is only one data point (1303) in this class.
For the class 1362, the frequency is 1 since there is only one data point (1362) in this class.
Therefore, the frequency of each class in the table shown is 1.
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Which of the following is an irrational number?
√70
√16
√1
√81
Answer:
70 it's a irrational number
Answer:
√70
Step-by-step explanation:
An irrational number is a number that cannot be expressed as a simple fraction and has an infinite, non-repeating decimal representation. Examples of irrational numbers include √2, π, and e.
Of the numbers you listed, √70 is an irrational number. The other numbers are not irrational because they can be expressed as simple fractions: √16 = 4, √1 = 1, and √81 = 9.
A 12-ounce bottle of shampoo lasts Erique 16 weeks. How long would you expect an 18-ounce bottle of the same brand to last him?
Answer: 24 weeks
Step-by-step explanation:
Take 12 divided by 16 = 0.75 ounce per week
Then take 18 divided by 0.75 = 24 weeks
What is the relationship between a function and its
inverse?
A function is a group of components or inputs that have a relationship and produce an outcome. A function's inverse is the function's opposite. When a function's inverse is applied, its domain changes to its range, and conversely.
What is a function?The core of calculus in math is the concept of functions. The unique types of connections are the ones with functions. Mathematical functions are represented as a rule that, for each input x, produces a distinct result.
As per the question, the relationship between a function and its inverse will be:
1. A group of elements or inputs that are related to one another and produce an output is referred to as a function.
2. A function's reverse is called a function's inverse.
3. When a function is inverse, the domain becomes the range, and vice versa.
4. The graphs of the two concepts—function and inverse—will resemble one another in reverse.
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They were so delighted with the song that they sang it right through five times in succession, and might have continued singing it all night if they had not been interrupted. Unfortunately, the uproar awoke mr. Jones, who sprang out of bed, making sure that there was a fox in the yard. He seized the gun which always stood in a corner of his bedroom, and let fly a charge of number 6 shot into the darkness. The pellets buried themselves in the wall of the barn and the meeting broke up hurriedly. Which historical event is this passage most reminiscent of?.
According to the passage, the historical event that is most reminiscent of this is Bloody Sunday. Thus, the correct option for this question is A.
Reminiscent experiences are ones that one should keep in mind from the past and are frequently recorded in books. It symbolizes the feeling of recollections of something similar coming back.
The song that they sang five times in a row creates a sensation of joy, according to the context of this inquiry. But regrettably, the commotion roused Mr. Jones, who sprang out of bed and checked to see whether there was a fox in the yard. The historical occurrence that most closely resembles this is Bloody Sunday.
Therefore, the historical event that is most reminiscent of this is Bloody Sunday.
Complete question:
They were so delighted with the song that they sang it right through five times in succession and might have continued singing it all night if they had not been interrupted, Unfortunately, the uproar awoke Mr. Jones, who sprang out of bed, making sure that there was a fox in the yard. He seized the gun which always stood in a corner of his bedroom, and let fly a charge of Number 6 shot into the darkness. The pellets buried themselves in the wall of the barn and the meeting broke up hurriedly.
Which historical event is this passage most reminiscent of?
A-Bloody Sunday
B-the Bolshevik Revolution
C- the rise of Lenin
D-collectivization
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The paragraph claims that Bloody Sunday is the historical occurrence that most closely resembles this one. As a result, choice A is the right response to this query.
Reminiscent experiences are ones from the past that one should remember and are usually written about in novels. It represents the sensation of memories of something similar returning.
According to the setting of this enquiry, the song that they sang five times in a row induces feelings of delight. Unfortunately, the noise woke up Mr. Jones, who quickly got out of bed to investigate if there was a fox in the yard. Bloody Sunday is the historical episode that most closely approaches this.
Bloody Sunday is the historical occurrence that most closely resembles this now.
Which historical event is this passage most reminiscent of?
A-Bloody Sunday
B-the Bolshevik Revolution
C- the rise of Lenin
D-collectivization
What are the solutions of x2 4x 7 0?
Answer: Solving x2 - 4x - 7 = 0 by completing the square, the solutions are x = ±√11 + 2.
Step-by-step explanation:
37. Rajiv gets pocket money from his farther everyday. Out of pocket money, he saves ₹ 2.75 on 1st day and on each
succeeding day he increases his saving by 25 paise
(i) On which day he saves 7.75?
(ii) Find the difference between the amount saved by Rajiv on 25th day and 14th day.
(iii) Find the sum of amount saved on first 10 days.
Step-by-step explanation:
first we come up with a formulae:
Amount of money saved = 2.25+0.25x,
where x is the number of days
Answer:
1. 7.75 = 2.25 + 0.25(x)
7.75 - 2.25/ 0.25 = x
x = 20
2. 2.25+0.25(25) - 2.25 +0.25(14)
= 9.75
3. 2.25 + 0.25(10)
= 4.75
I hope i explained it well...
( i ) 21st day he saves 7.75
(ii) the difference between the amount saved by Rajiv on the 25th day and the 14th day is 2.75 rupees.
(iii) the sum of the amount saved in the first 10 days is 5 rupees.
Solution: (i) given: on each succeeding day he increases his saving by 25 paise.
2.75 rupees he saves on the first day
so = 2.75 +(0.25×20)
= 2.75+5
= 7.75 rupees
(ii) amount saved by Rajiv on the 25th day is:
= 2.75+(0.25×24)
= 2.75 + 6
= 8.75
amount saved by Rajiv on the 14th day is :
=2.75+(0.25×13)
=2.75+3.25
=6
therefore the difference between Rajiv' saving on the 25th day and the 14th day is : = 8.75-6
= 2.75
(iii) the sum of the amount saved in the first 10 days is :
= 2.75+(0.25 ×9)
= 2.75+2.25
= 5
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Use the situation to answer the questions.
Latisha has a new job that pays her weekly. She has arranged for the same amount from
each paycheck to be deposited into her savings account. On week 9, her savings account
has a balance of $496, and on week 16, her savings account has a balance of $664.
6) What does the independent variable x represent in this problem?
7) What does the dependent variable y represent in this problem?
The independent variable x represents the initial amount of her savings account, and the dependent variable y represents the deposited amount into her savings account.
What is the independent and dependent variable?
In mathematical modeling, statistical modeling, and experimental sciences, dependent and independent variables are variables. Dependent variables are so named because their values are studied in an experiment under the assumption or demand that they are dependent, by some law or rule, on the values of other variables.
We have,
On week 9, her savings account has a balance of $496,
on week 16, her savings account has a balance of $664.
The equation which represents the situation is:
consider x for the initial amount in the account and y for the weekly deposited amount into her savings account.
so,
x + 9y = $496,
x + 16y = $664.
Hence, the independent variable x represents the initial amount of her savings account, and the dependent variable y represents the deposited amount into her savings account.
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Write the equation of the line in fully simplified slope-intercept form.
The required equation of the line is y = 3x + 2 in slope-intercept form.
To write the equation of a line in slope-intercept form, we need to know the slope of the line and the y-intercept. The slope of a line is defined as the change in y divided by the change in x for two points on the line.
According to the given graph, the required solution would be as:
For the given points (2, 2) and (4, 8),
So, the slope is : m = 8 - 2 / 4 - 2 = 6 / 2 = 3.
With the slope and y-intercept, we can write the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
For the point (2, 2), the y-coordinate is the y-intercept, so the y-intercept is 2.
So, the equation is y = 3x + 2
Therefore, the required equation of the line is y = 3x + 2 in slope-intercept form.
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For what value of A is x 4 a factor of 5x³ 7x² ax 28?
On solving the provided question, we can say that - equation [tex]5x^3 + 7x^2+ax = 28[/tex] at x= 4 that value of a is = - 101
What is factor?A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to discover factors. A number or other mathematical object is factorized or factored in mathematics by expressing it as the product of numerous factors, often smaller or simpler things of the same sort. One factorization of the polynomial x2 - 4 is 3 5, which is also a factorization of the number 15.
[tex]5x^3 + 7x^2+ax = 28\\5(4)^3 + 7(4)^2 + 4a = 28[/tex]
a= -404/4
a = -101
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What is the equivalent of 2 by 7?
Answer:
in ratio 4:14
Step-by-step explanation:
1. The product of 6, and a number increased by 2, is -24. What is the number?
Answer:
Step-by-step explanation: 6* (N + 6) = -24
6*n + 6*6=-24
6n+36=-24
-36 -24
6n=-60
n=-10
A band director is trying to decide what music to play for the halftime show. To get a sample, the director divides the band into groups based on their grade (freshmen, sophomores, juniors, and seniors). Then she randomly chooses a group and surveys every member of the chosen group. Which sampling method was used?
ANSWER: cluster sampling
The answer is random sampling in my thinking.
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How do you make a 4 quadrant line graph in Excel?
You can also manually convert a scatter plot to a four-quadrant graph
First, delete the trend line from your scatter diagram.
When does a graph represents a function?
A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y.
How do you make a 4 quadrant line graph in Excel?
You can also manually convert a scatter plot to a four-quadrant graph
First, delete the trend line from your scatter diagram.
Second, reformat your X-Axis. ...
Third, reformat your Y-Axis. ...
Once you have updated both the X and Y Axis Values, you should have a XY Scatter Diagram with Four Quadrants
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What is the median of 1 2 3 4?
The median number of 1 2 3 4 is 2.5
The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does. It reflects the midway of the data since it is the point above and below which half (50%) of the observed data falls.
The number given is 1 2 3 4
We have to determine the median of the above number.
If the number of words is even, we must add two middle terms and divide the result by two. The median is what we obtain as a mean.
Substitute the value in above equation we get,
=(2+3)/2
Adding the two number we get,
=5/2
Now dividing 5 by 2 we get,
2.5
Median=2.5
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what is the probability that an arrangement of a, b, c, e, f, g begins and ends with a vowel?
The probability that an arrangement of a, b, c, e, f, g begins and ends with a vowel is 1/ 5, that is 0.2.
Therefore, the answer is 0.2.
In an arrangement of a, b, c, e, f, g, the total number of alphabets is 6 and number of vowels is 2.
The probability that an arrangement of a, b, c, e, f, g begins with a vowel is
P1 = 2/ 6
P1 = 1/ 3
The probability that an arrangement of a, b, c, e, f, g ends with a vowel given it begin with a vowel( In this case the total number of alphabets left is 5 and number of vowels left is 1) is
P = 1/ 5
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