The two equivalent expressions for the area of the cafeteria are:
a. x = 6² + 7² feet
b. 36 + 49 = x feet.
Given the length of the cafeteria is 7² ft and
the width of the cafeteria is 6² ft.
Area = length × width
let the area be 'x'.
x = 6² × 7²
According to the law of exponents.
x = 36 × 49
x = 1764 ft
hence we get the area as 1764 ft of the cafeteria.
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What is the solution set of the quadratic inequality 6x² + 1 ≤0?
O {X[XER}
O
{X1 X=-1}
Answer:
The empty set
Step-by-step explanation:
The square of a real number is non-negative, and thus the left hand side is always positive.
100⁰ - 2x 2x + 20° 5x -40°
solve for x
This could be wrong, but I think your answer is [tex]x=-2x^3+\frac{900^{\circ \:}x-360^{\circ \:}}{9}[/tex]
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Hope this helps!
Have a great day and God bless! :)
What is the sum of [4 -6 8] and [10 2 0]
Answer:
[14 -4 8]
Step-by-step explanation:
[4+10 -6+2 8+0]
[14 -4 8]
What must be added to 3x + y to get 2x + 3y?
Answer:
-x+2yStep-by-step explanation:
What must be added to 3x + y to get 2x + 3y?
3x + y + z = 2x + 3y
3x + z = 2x + 3y - y
3x + z = 2x + 2y
z = 2x-3x+2y
z = -x+2y
-------------------
check
3x + y + (-x) +2y =
2x + 3y
the answer is good
The following diagram depicts a construction of copying a line segment.
If AB is 6.7 cm, what would the length of line segment CD be?
The diagram depicting the construction of copying a line segment indicates that AB = CD = 6.7 cm.
How can the length of the constructed line segment, AB be found?A line segment, which can be expressed as a segment of a line, has definite length. It is a line drawn that has two endpoints.
A line segment can be named by the capital letters placed at the endpoints.
Copying a line segment, therefore gives a segment of equal length as the original line segment.
Given that the length of AB = 6.7 cm, and the line segment, CD, is obtained by copying segment AB, we have;
Length of CD = Length of AB = 6.7 cm
Therefore;
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at a gathering of50 people, there are 30 people who all know each other and 20 people who know no one. people who know each other hug, and people who do not know each other shake hands. how many handshakes occur within the group?
Total 790 number of handshakes occur within the group.
According to the given question.
Total number of people = 50
Number of people who know each other = 30
Number of people who know no one = 20
Since, 20 people doesn't knw each any one, so they will shake hands.
So, the total number of hand shakes by these 20 people
= 20(20 -1)/2
= 10(19)
= 190
Also, we have to consider that other 30 people will also shake hands with these 20 people.
So, the total number of hanshakes by these 30 and 20 people = 30 × 20 = 600
Therefore, the total number of handshakes occur within the group
= 600 + 190
= 790
Hence, total 790 number of handshakes occur within the group.
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What is the scale factor from polygon JKLM to polygon ABCD?
Answer:
for part c
JM=36
AD=12
36=3
JKLM is 3x bigger than polygon ABCD
an object moves along a parabolic path defined by the equation in such a way that the y-value is decreasing at a constant rate of 2 units per second. at what rate is the x-coordinate changing when x
So the change of rate of x is -1/3 .
The Derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
Given that object is decreasing at constant rate of 2 units per second so we have [tex]y = 2x^2 + 1[/tex]
[tex]\frac{dy}{dt} = 4x \frac{dx}{dt}[/tex]
given dy/dt = -2
when x = 3/2
-2 = 4(3/2) dx/dt
-2 = 6 dx/dt
dx/dt = -2/6
= -1/3
Hence the change of rate of x is -1/3 .
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Is the given point interior,exterior, or on the circle (x+2^)2+(y-3^)2=81? Q(3,0)
A
line passes through the point (-4, 3) and has a slope of 4
Write an equation in slope-intercept form for this line.
Step-by-step explanation:
the slope-intercept form :
y = ax + b
"a" being the slope, "b" being the y-intercept (the y value when x = 0).
but we have the slope and a point.
so, we can start with the point-slope form and then transform it :
y - y1 = a(x - x1)
"a" is again the slope, (x1, y1) is the given point.
so, we have
y - 3 = 4(x - -4) = 4(x + 4) = 4x + 16
y = 4x + 19
and that's it.
in simple linear regression the estimated slope from the regression of y on x is the same as the estimated slope in the regression of x on y.
In the given statement is:
In simple linear regression the estimated slope from the regression of y on x is the same as the estimated slope in the regression of x on y.
If Y depends on X then the regression line is Y on X.
Y is dependent variable and X is independent variable. If X depends on Y, then regression line is X on Y and X is dependent variable and Y is independent variable. The regression equation Y on X is Y = a + bx, is used to estimate value of Y when X is known.
What is Simple linear regression?
Simple linear regression is a regression model that estimates the relationship between one independent variable and one dependent variable using a straight line. Both variables should be quantitative.
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Trey bakes 70 cupcakes for the school Bake Sale. Worried they might run out, he bakes some extra and now has 112 cupcakes.
What is the Percent Change in the number of cupcakes?
The Percent Change in the number of cupcakes is 60%
How to determine the Percent Change in the number of cupcakes?The given parameters are:
Initial number of cupcakes = 70
Final number of cupcakes = 112
The Percent Change in the number of cupcakes:
Percent = (Final number of cupcakes - Initial number of cupcakes)/Initial number of cupcakes * 100%
This gives
Percent = (112 - 70)/70 * 100%
Evaluate the quotient
So, we have
Percent = 0.6 * 100%
Evaluate the product
So, we have
Percent = 60%
Hence, the Percent Change in the number of cupcakes is 60%
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Brianna picks tomatoes on a local farm. she receives 11 cents per crate. last week, her total piecework earnings was 500 dollars. express the number of crates she picked algebraically.
Answer:
4,545.45 crates
Step-by-step explanation:
.11x = 500
Divide both sides by .11
x = 4,545.45
The number of crates she picked algebraically is 4545.
Let us consider the variable "c" to represent the number of crates Brianna picked.
We know that she receives 11 cents per crate.
1 crate = $0.11 (11 cents)
Her total earnings from picking "c" crates can be expressed as:
Earnings = 0.11c
Now, we know her total piecework earnings for last week were $500. So, we can set up an equation:
Total Earnings = $500
0.11c = $500
To find the number of crates Brianna picked, we need to solve for "c":
c = $500 / 0.11
c = 4545.45...
c = 4545 crates
So, algebraically, Brianna picked approximately 4545 crates last week.
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Help please quite immediate am pro
i need help on this problem pls
Step-by-step explanation:
2 3 4 6...................
i need help with this question please
Answer:
5x-30
Step-by-step explanation:
x+15+4x-45
5x+14-45
5x-30
question 14(multiple choice worth 1 points) (01.05 lc) which calculation can be used to find the value of p in the equation p3
The response to this question is that p has a value of 8, or the cube root of 8. i.e. p=∛8.
Why do you use the term "Cube roots"?An integer y such that y³ = x is known as the cube root of a number x in mathematics. All nonzero complex numbers have three different complex cube roots, while all nonzero real numbers have exactly one real cube root and two complex conjugate cube roots. When we multiply a factor three times to obtain a number, we have obtained the cube root of that factor. Three cube root of, ending cubic root is the sign for the cube root. In contrast to cubing an integer, finding its cube root is a mathematical operation.
According to the equation, p³=8
We can clearly see that the power of p is 3.
Now by taking cube root on both the sides, we can see that the value of p is
∛p³=∛8
⇒p=∛8
The value of p in the equation cube root of 8.
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A carpenter has a wooden dowel that is 72 cm long. She wants to cut it into two pieces so that one piece is 7 times as long as the other. What is the length of the longer piece?
Answer: 39.5 cm long
Step-by-step explanation: The equation can also be written s 72=2x+7, (x= length of short piece) (x+7+length of long piece.):
72=2x+7
72-7=2x
65=2x
x=32.5
Then to find out the long piece:
x+7
32.5+7=39.5
Pleaseee help me I need this done rn.
Area of a right triangle ABC is 120 sq feet. If AABC goes through a dilation transformation with a scale
factor of 1.5, then what will be the area of the transformed triangle (in sq feet)?
Answer:
270
Step-by-step explanation:
The area is the same as the original area multiplied by the square of the scale factor.
What is the area of a rectangle with a length of 9 feet and a width of 7 grade
Answer:
63
Step-by-step explanation:
area=length×width so 9×7=63
a subset $b$ of the set of integers from 1 to 100, inclusive, has the property that no two elements of $b$ sum to 125. what is the maximum possible number of elements in $b$? (a) 50 (b) 51 (c) 62 (d) 65 (e) 68
We get the number of elements in the set B will be 62.
The universal set is A consists of the primary one hundred positive integers.
Set B is a subset of A.
One possibility is that B consists of the primary 62 positive integers.
Then only, the greatest quantity that may be shaped through the sum of any factors of set B is 123.
The number of elements in set B is equal to 62.
We also can selectively interchange one or more elements of B and and add them in complement of B
In most of these instances the number of elements in set B might be 62.
Therefore, we get the number of elements in the set B will be 62.
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question the benefit of using inferential statistics is that it allows a researcher to describe the data describe the data find the measures of central tendency find the measures of central tendency find the spread of the data find the spread of the data make generalizations about a population make generalizations about a population visualize the raw data
A researcher can make generalizations about a population by utilizing inferential statistics, which is a benefit.
What kind of statistics are inferential, for instance?Two purposes dominate the use of inferential statistics: estimating population numbers (for example, the mean SAT score of all 11th graders in the US). testing hypotheses to make population-level judgments (for example, the relationship between SAT scores and family income).
Inferential statistics that are helpful in the design of experimental and quasi-experimental studies or in the assessment of program outcomes.
When comparing the average performance of two groups on a single measure to check if there is a difference, one of the simplest inferential tests may be performed. You might be interested in learning whether math test results between eighth-grade boys and girls differ or if a program group differs from a control group in terms of the outcome measure.
The t-test for differences between groups should always be taken into consideration when comparing the average performance of two groups.
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17 cm/min=________m/h
Answer: .17 m/h
Step-by-step explanation: One centimeter is .01 meters/one hundredth of a meter, so you just need to move the decimal two digits to the right to convert.
A line intersects the points
(3, 2) and (5, 12).
m = 5
Write an equation in point-slope form
using the point (3, 2).
y - [?] = [](x-[ ])
The point slope of the the line using the point (3,2) and slope 5 is (y-2)=5(x-3).
Given that A line intersects the points (3, 2) and (5, 12) and asked to write an equation of line passing through (3,2) and having slope as 5.
Point slope form:
The point-slope form of a stright line is y-y1=m(x-x1)
Here (x1,y1) is the fixed point with which the line passes and m is the slope of the line
Here, (x1,y1) is given as (3,2) and m(slope)=5
The equation straight line in point-slope form is (y-2)=5(x-3).
Therefore,The point-slope form of the the line using the point (3,2) and slope 5 is (y-2)=5(x-3).
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you work as an assistant coach on the university swim team and earn $13 per hour. one day, you decide to skip the hour-long practice and go to the county fair instead, which has an admission fee of $10
23$ is the total cost .
What is cost and example?
The definition of cost is to be valued at something or to lose. A loaf of bread costing $3 is an example of a cost. Giving up your freedom in order to grant freedom to another person is an illustration of cost.Fixed and variable costs are the two main categories of expenses incurred by enterprises. Variable costs change with output, whereas fixed costs do not. Overhead costs are another name for fixed expenses. They must be paid whether a company produces 100 or 1,000 widgets.the total cost = 13$ + 10$= 23$ because he losses a hour in work .
13$ and additionally spending 10$ in carnival .
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The graph of y=f(x) is shown below. Find all values of xx where f(x)=3
Someone help with this, need it for hw,thanks!
Answer: B
Step-by-step explanation: you see how its by the 2 that means that its going to be where the 3 is
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Find the average rate of change of each function over the interval [0, 3]. Match each representation with its respective average rate of change.
The identify each representation's associated average rate of change. The average rate of change for the functions r, q, p is 5, 5, 7/3 over the range [0.3].
Given that,
We have to find over the range [0, 3], calculate each function's average rate of change. The identify each representation's associated average rate of change.
The equation for f(x) average's rate of change across [a,b] is
m=[tex]\frac{f(b)-f(a)}{b-a}[/tex]
The function provided is
r(x)=x²+2x-5
r(0)=(0)²+2(0)-5=-5
r(3)=(3)²+2(3)-5=9+6-5=15-5=10
Now,
m₁=[tex]\frac{r(3)-r(0)}{3-0}[/tex]
m₁=[tex]\frac{10+5}{3}[/tex]
m₁=15/3
m₁=5
It is clear from the graph that q(0)=2 and q(1)=3.
Now,
m₂=[tex]\frac{q(1)-q(0)}{1-0}[/tex]
m₂=[tex]\frac{3+2}{1}[/tex]
m₂=5/1
m₂=5
It is evident from the above table that s(0)=-2 and s(3)=5.
Now,
m₃=[tex]\frac{s(3)-s(0)}{3-0}[/tex]
m₃=[tex]\frac{5+2}{3}[/tex]
m₃=7/3
Therefore, The average rate of change for the functions r, q, p is 5, 5, 7/3.
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Six times a number w is at least -24
solve for the inequality
Answer:
w is -4
Step-by-step explanation:
W is -4 because a positive number times a negative number is always a negative that is why the answer is a negative and 6 times 4 is 24 but for the 24 to be a negative the 4 has to be a negative 4.
2-78.
Decide if each pair of triangles below is similar. If the triangles are similar,
justify your conclusion by stating the similarity condition you used. Also,
describe a possible sequence of transformations that would carry one onto
the other. If the triangles are not similar, explain how you know they are
not similar.
The pair of triangles is similar with the ASA similarity condition
How to decide if each pair of triangles is similar?The figure that completes the question is added as an attachment
From the figure, we have the following properties:
Two angles are congruent; This is indicated by the marks on one angle, and the corresponding right angleAlso, the hypotenuse of both triangles are similarThis means that the pair of triangles is similar with the ASA similarity condition.
Since the triangles share the same point
So, the transformation to carry the triangles onto one another is dilation
Hence, the pair of triangles is similar with the ASA similarity condition
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