The width of the doll house's front door is 2400 cm.
How to find area of Rectangle?The area of the rectangle is
(240 cm x 100 cm) / 2
= 2400 cm
Rectangle area in geometry refers to the area that a rectangle occupies on a two-dimensional plane. A quadrilateral, a form of two-dimensional object with four sides and four vertices, is what a rectangle is. The rectangle's four angles are all right angles or exactly 90 degrees. The rectangle's opposing sides are equal and parallel to one another. It should be noted that a parallelogram likewise has equal and parallel opposite sides, but the angles are not exactly 90 degrees. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth. whereas the perimeter of a rectangle is equal .To learn more about area of Rectangle refer to:
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The calls of Hazar was 2370 the last month. He received 1645 calls. The calls of Huzan was less than those of Hazar, but Huzan received more calls than Hazar. Write a system of linear inequalities to represent the situation, then solve it to determine the possible number of calls received by Huzan and the number of calls dialled by him.
The possible values of calls recieved by Huzan is more than 1645 and calls made is less than 2370.
What is Inequalities of equations ?
Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), larger than (or greater than or equal to), or not equal to signs are used in place of the equal sign.Inequality simply means that two things aren't equal. One of the items could be inferior to, superior to, greater than, or equivalent to the other things.
p ≠ q means that p is not equal to qp < q means that p is less than qp > q means that p is greater than qp ≤ q means that p is less than or equal to qp ≥ q means that p is greater than or equal to q
Different kinds of inequality exist. Important inequities include the following: the inequalities of polynomials
Inequalities in absolute values
Logic-based disparities
Calls made by Hazar = 2370
Calls recieved by Hazar = 1645Let the number of Calls by Huzan be x.
And the number of calls recieved by Huzan be y.
Then the inequalities arex< 2370 and y> 1645
The possible values of calls recieved by Huzan is more than 1645 and calls made is less than 2370.
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Which of thee i equal to co 47°?
Repone
A in 43°in 43°
B co 133°co 133°
C tan 43°tan 43°
D co 43°
Option (A) cos 47° is equal to sin 43°.
What is cos in trigonometry ?
The cos meaning in trigonometry defines the cosine of an angle. This angle is an acute angle in a right angled triangle, which is considered to find the ratios. Thus, cosine of an angle, in a right-triangle, is equal to the ratio of adjacent side of that angle and hypotenuse of the triangle.
What is sin in trigonometry ?
In trigonometry, the sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle. The sine function is used to find the unknown angle or sides of a right triangle.
Have given,
cos 47°,
We know that cos x = sin (90 - x),
Thus cos 47° = sin (90 - 47)
cos 47° = sin 43°
Therefore, cos 47° is equal to sin 43°.
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cos 47°,
We know that cos x = sin (90 - x),
Thus cos 47° = sin (90 - 47)
cos 47° = sin 43°
Therefore, cos 47° is equal to sin 43°.
What are the 7 whole numbers?
Answer:
There are an infinte amount of whole numbers
Step-by-step explanation:
7 examples are, 0, 3, 7 , 8 ,9 14, 39
graph the following features Y-intercept = 2 Slope = -5/4
The equation of the line in intercept form will be x / 1.6 + y / 2 = 1. Then the graph of the line is drawn below.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is negative 5/4 and the y-intercept of the line is 2. Then the equation of the line is given as,
y = -(5/4)x + 2
Convert the equations into intercept form. Then we have
y = -(5/4)x + 2
4y = -5x + 8
5x + 4y = 8
x / 1.6 + y / 2 = 1
The condition of the line in the capture structure will be x/1.6 + y/2 = 1. Then, at that point, the diagram of the line is drawn underneath.
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Solve pls brainliest
Answer:
In given right angled triangle,
h=30 cm,p=18 cm,b=?
By Pythagoras theorem,
h²=p²+b²
or,b²=h²-p²
or,b²=(30)²-(18)²
or,b²=900-324
or,b=√576
or,b=24 cm
hence, the length of missing side is 24 cm
Are all equilateral triangles congruent Why?
For a triangle to be equilateral all its angle should be same which is 60° but for them to be congruent their sides should also be same in measure.
Therefore two equilateral triangles are not always congruent with one another as because there can be difference in the measure of their sides.
The sum of angles of a triangle is 180 degree which is the sum of angles of the triangle's three angles.
There are three types of triangles based on different aspects .
Based on the lengths of their sides, triangles can be classified as
ScaleneIsoscelesEquilateralAs in an equilateral triangle all of the sides are of the same length. and all the angle measure will be 60 degrees. An equilateral triangle is also known as an equiangular triangle since its angles are all the same.
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What is a correct first step in solving the inequality 4 3 5x ≥ 6x 9 brainly?
The first step in solving the inequality is -12 + 20x ≥ -6x + 9
An inequality can be defined as a relationship that shows a non-equal comparison between two numbers or mathematical expressions.
Given the inequality
–4(3 – 5x)≥ –6x + 9
Solving the inequality
⇒-12 + 20x ≥ -6x + 9
Keeping all x on one side it can be written ,
⇒20x + 6x ≥ 12 + 9
Adding both sides,
⇒26 x ≥ 21
divide both sides by 26,
⇒x ≥ 0.80
So, the first step in solving the inequality is -12 + 20x ≥ -6x + 9
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The correct question is :
What is the correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?
Amelia has a summer job mowing the lawn and trimming hedges for a neighbor. The number of minutes that amelia spends mowing the lawn is 10 minutes longer than three times the number of minutes it takes to trim the hedges. It takes Amelia a total of 120 minutes to complete both tasks
Using system of linear equations, Amelia spent 92.5 minutes mowing the lawn and 27.5 minutes trimming the hedges
System of Linear EquationSystem of linear equations is the set of two or more linear equations involving the same variables. A linear equation can be defined as the equations of the first order, whereby the highest power of the variable in the equation is one.
To solve this problem, we have to write a system of linear equation;
Let;
x = number of minute spent mowing lawny = number of minute trimming the hedgesWe can represent the problem with two set of equations as;
x + y = 120 ...eq(i)
x = 3y + 10 ...eq(ii)
From equation 1
x + y = 120
x = 120 - y ..eq(iii)
Put eq(iii) into eq(ii)
120 - y = 3y + 10
collect like terms
120 - 10 = 3y + y
110 = 4y
y = 110 / 4
y = 27.5 minutes
Put y = 27.5 in equ(i)
x + 27.5 = 120
x = 120 - 27.5
x = 92.5 minutes
She spent 92.5 minutes mowing the lawn and 27.5 minutes trimming the hedges.
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A number, .f, rounded to 1 d.p. is 49.2
Another number, g,
rounded to 1 d.p. is 7.8
What are the lower and upper bounds of
f - g?
Answer:
3
Step-by-step explanation:
The lower bound of f-g is 41.31 .
The upper bound of f-g is 41.49 .
Given,
A number 'f' rounded to 1 decimal point is Number = 49.2
A number 'g' rounded to 1 decimal point is Number = 7.8
Now,
The range of f rounded to 1 decimal point is [49.15 , 49.24].
The range of g rounded to 1 decimal point is [7.75 , 7.84].
So,
Lower bound of f-g = 49.15 - 7.84
Lower bound of f-g = 41.31
Next,
Upper bound of f-g = 49.24 - 7.75
Upper bound of f-g = 41.49
Therefore the lower bound of f - g is 41.31 and upper bound of f - g is 41.49.
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I’LL MARK BRAINLIEST IF CORRECT!!
The display shows how much water is used in a household in a given day.
Which of the following describes this data set?
A) Categorical and bivariate
B) Categorical and univariate
C) Numerical and bivariate
D) Numerical and univariate
Find the slope from two points
Answer: 7/ -8
Step-by-step explanation:
The slope is rise/run
Our two points are (10,9) ( 2,16)
We see that y increased by 7, and the x decrease by 8
So the slope is 7/ -8
What is the median of the following set of scores 19 5/12 10 and 14?
The median of this set of scores 19,5/12,10 and 14 is 12.
To find the median of a set of scores, you first need to arrange the scores in numerical order. The median is the middle score in the set. If there is an odd number of scores, then the median is the middle score. If there is an even number of scores, then the median is the average of the two middle scores.
In this case, the scores are 5/12, 10, 14, and 19.
After arranging the scores in numerical order, we have 5/12, 10, 14, and 19.
There are four scores in this set, so the median is the average of the two middle scores, which are 10 and 14.
The median of the set is: (10 + 14) / 2 = 12.
The median of this set of scores is 12.
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What is the mean and standard deviation in which 7% of items are under 35 and 89% are under 63?
The mean and standard deviation are 50.292 and 10.362 respectively.
What is mean and standard deviation?The mean is the average of all available data value. And standard deviation is the measure of how far each data value apart from the mean value.
How to calculate mean and standard deviation of the given data value?We are given, 7% of item are under 35 and 89% of item are under 63.
Let, M refers to mean, and SD refers to standard deviation.
As per given data, P(x<35) = 35%
P(z<Z1) = 0.07
hence, Z-score= Z1 = -1.4758 [obtained from Z table]
we know that the z-score = (observed value - mean)/ standard deviation
Z1 = (x - M)/ SD
- 1.4758 = (35 - M)/ SD
-1.4758SD = 35 -M ......... equation 1
as per the 2nd condition in the given data
89% of items are under 63
so, X= 63, P(X<63)
hence, the z-score = 1.2265 [ obtained from Z table]
Z2= 1.2265= (X- mean)/ SD
1.2265SD = 63 - M.......equation 2
Solving equation 1 and 2, we get standard deviation = 10.362
Mean value = 50.292
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Find an equation of variation for the given situation.
y varies directly as x, and y = 0.1 when x = 0.5.
The equation of variation for the given situation is y = 5x.
Direct ProportionIn mathematics, a direct proportion is a comparison of two integers where the ratio of the two numbers equals a constant value. According to the concept of proportion, two ratios are in proportion when they are equal.
If a varies directly to b then the relation between them can represent as
=> a ∝ b
=> a = kb [ where 'k' is proportionality constant]
Here we have
y varies directly as x, this can be shown as
=> y ∝ x
=> y = kx ---- (1) [ Where 'k' is proportionality constant ]
Given that y = 0.1 and x = 0.5
Substitute the above values in (1)
=> 0.1 = k(0.5)
=> k = 0.5/ 0.1
=> k = 5
(1) => y = 5x
Therefore,
The equation of variation for the given situation is y = 5x.
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Do you think it is necessary to learn the concepts of measurement?
It offers a rich and meaningful environment for the application of spatial and mathematical concepts due to this it is necessary to learn the concepts of measurement.
what are concepts of measurement?Linking the various branches of mathematics together requires measurement. For instance, it offers a rich and meaningful framework for the application of math abilities and spatial concepts. Links between mathematics and other academic areas are also provided via measurement.
It makes comparison easier since we no longer need to locate several items to serve as the reference; instead, we may compare multiple objects by only comparing the numbers of a single established unit.
It offers a rich and meaningful environment for the application of spatial and mathematical concepts due to this it is necessary to learn the concepts of measurement.
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fred walks 20 miles toward the north. he turns left and walks 40 miles. he again turns left and walks 20 miles. finally, he walks 20 miles after turning to the left. how far is he from his starting point.
Using vector calculation and analyzing directions, The answer is 20 miles west from the starting point.
What is a vector?An item with both magnitude and direction is referred to be a vector. A vector can be visualized geometrically as a directed line segment, with an arrow pointing in the direction and a length equal to the magnitude of the vector. The vector points in a direction from its tail to its head.
What do you mean by vector addition?The process of adding two or more vectors together to create a vector sum is known as vector addition.
20 miles to north and 40 miles left .
Using triangle law of vector addition, Distance from point at the location = [tex]\sqrt{20^2 + 40^2}[/tex]
=[tex]20\sqrt 5[/tex] miles.
Now turns left walks 20miles , Using triangle law of vector addition,
distance from point at the location = [tex]\sqrt{(20\sqrt 5)^2 - 20^2}[/tex]
=40 miles from location.
This location is horizontally same from the start point.
So he turns left and walks 20miles again.
distance from point= 40-20
=20 miles west of start point.
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Problem Solving in Santa's Workshop
Clifford works in the gift-wrapping department of Santa's
workshop. His job is to finish all the packages with a bow.
He is running low on bows and only has 100 bows left. He
begins working at 5:00 a.m. During the first half-hour, he
uses 12 bows. In the second half-hour, he uses 9 bows.
During the third half-hour, he uses 14 bows and in the
fourth half-hour, he uses 11 bows. Clifford uses 16 bows
during the fifth half-hour. If the pattern continues, during
which half-hour will Clifford run out of bows?
Answer:
Eighth half-hour
Step-by-step explanation:
Given pattern:
1st half hour = 12 bows used2nd half hour = 9 bows used3rd half hour = 14 bows used4th half hour = 11 bows used5th half hour = 16 bows usedCalculate the differences between the number of bows used:
[tex]12\underbrace{}_{-3}9\underbrace{}_{+5}14\underbrace{}_{-3}11\underbrace{}_{+5}16[/tex]
Therefore, the pattern for the bows used is:
-3, +5, -3, +5, etc...If the pattern continues:
[tex]12\underbrace{}_{-3}9\underbrace{}_{+5}14\underbrace{}_{-3}11\underbrace{}_{+5}16\underbrace{}_{-3}13\underbrace{}_{+5}18\underbrace{}_{-3}15\underbrace{}_{+5}20[/tex]
6th half hour = 16 - 3 = 13 bows used7th half hour = 13 + 5 = 18 bows used8th half hour = 18 - 3 = 15 bows used9th half hour = 15 + 5 = 20 bows usedCreate a table with the given and found data, and add a cumulative total column:
[tex]\begin{array}{c|c|c}\vphantom{\dfrac12} \textsf{Half Hour} & \textsf{Bows used per half hour} & \sf Cumulative\; total\\\cline{1-3} \vphantom{\dfrac12} \sf 1st & 12 & 12\\\vphantom{\dfrac12} \sf 2nd &9 &21 \\\vphantom{\dfrac12} \sf 3rd & 14&35 \\\vphantom{\dfrac12} \sf 4th & 11& 46\\\vphantom{\dfrac12} \sf 5th & 16& 62\\\vphantom{\dfrac12} \sf 6th & 13& 75\\\vphantom{\dfrac12} \sf 7th &18 & 93\\\vphantom{\dfrac12} \sf 8th & 15& 108\\\vphantom{\dfrac12} \sf 9th & 20& 128\\\end{array}[/tex]
If Clifford has a total of 100 bows, he will run out of bows during the eighth half-hour.
Solve the system of equations
The required values are x = 12 and y = -3 solution to the given system of equations.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The system of equations is given as:
2x + 7y = 3 ....(i)
x = -4y ....(ii)
Substitute the value of x = -4y in the equation (i), and solve for y
2( -4y) + 7y = 3
-8y + 7y = 3-y = 3
y = -3
Substitute the value of y = -3 in equation (ii), and solve for x
x = -4(-3)
x = 12
Thus, the solutions are x = 12 and y = -3.
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Can the sides of a triangle have lengths 2, 18, and 20?
Answer: No triangle lengths have to add all three length together to equal 180 like 60 60 60 or 90 80 10
Step-by-step explanation:
The coordinate 3 has a weight of 2,
and the coordinate 9 has a weight of 1.
Find the weighted average.
PLEASEEE HELPPP
Answer:
1.5
Step-by-step explanation:
avj=total/n n=no of thingsavj=1+2/2avj=3/2 or 1.5Answer: Answer is
Step-by-step explanation:
I don't know how to explain it but I went over it with my teacher and it is
Finding an angle measure given a triangle and parallel lines
Answer:
[tex]x\textdegree = 120\textdegree[/tex]
Step-by-step explanation:
Because alternate exterior angles (of a transversal that intersects parallel lines) are congruent, the bottom left interior angle of the triangle is 55º.
Using this information, we can solve for the bottom right interior angle of the triangle (denoted θ) by setting the sum of the measures of the triangle's interior angles to 180º.
[tex]55\textdegree + 65\textdegree + \theta = 180\textdegree[/tex]
↓ subtract 55º and 65º from both sides
[tex]\theta = (180-55-65)\textdegree[/tex]
↓ simplify
[tex]\theta = 60\textdegree[/tex]
Now that we have the measure of the triangle's bottom right interior angle, we can solve for xº because an interior angle of a triangle and its corresponding exterior angle are supplementary (their angle measures add to 180º).
[tex]\theta + x\textdegree = 180\textdegree[/tex]
↓ plug in the solved value for θ
[tex]60\textdegree + x\textdegree = 180\textdegree[/tex]
↓ subtract 60º from both sides
[tex]x\textdegree = (180 - 60)\textdegree[/tex]
↓ simplify
[tex]x\textdegree = 120\textdegree[/tex]
5. Suppose you fill your truck's tank with fuel and begin driving down the highway for a
road trip. Assume that, as you drive, the number of minutes since you filled the tank and
the number of gallons remaining in the tank are related by a linear function. After 40
minutes, you have 28.4 gallons left. An hour after filling up, you have 26.25 gallons left.
Write this equation in SLOPE INTERCEPT FORM.
The equation that represent the situation in slope intercept form is y = -0.1075x + 32.7.
'
How to represent equation in slope intercept form?Equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptAs you drive, the number of minutes since you filled the tank and the number of gallons remaining in the tank are related by a linear function.
After 40 minutes, you have 28.4 gallons left. An hour after filling up, you have 26.25 gallons left.
Let's find the slope.
(40, 28.4)(60, 26.25)
m = 26.25 - 28.8 / 60 - 40
m = -2.15 / 20
m = - 0.1075
Hence, let's find the y-intercept using (40, 28.4)
y = - 0.1075x + b
where
x = number of minutesy = amount of fuel remainingTherefore,
28.4 = -0.1075(40) + b
28.4 + 4.3 = b
b = 32.7
Therefore, the equation of the line is y = -0.1075x + 32.7
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An equation for the line is
The linear equation of the given line on the graph is y = -1/2 + 5
What is a linear equation?A linear equation is an algebraic equation of the form y=mx+b.
where m is the slope and b is the y-intercept.
We have a graph.
We can see that the graph has two points:
(0, 5) = (a, b) and (4, 3) = (c, d)
The slope m is given by:
m = (d - b) / (c - a)
m = -2 / 4
m = -1/2 ,b = y-intercept
The y-intercept is at y = 5
b = 5
The linear equation is: y = mx + b
y = (-1/2) + 5
y = -1.2 + 5
Thus the linear equation of the given line on the graph is
y = -1/2 + 5
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8) Eugene and Kayla each improved their yards by planting daylilies and shrubs. They bought their
supplies from the same store. Eugene spent $87 on 10 daylilies and 9 shrubs. Kayla spent $60
on 5 daylilies and 10 shrubs. What is the cost of one daylily and the cost of one shrub?
A) daylily: $7, shrub: $1
C) daylily: $3, shrub: $6
12
B) daylily: S6, shrub: $3
D) daylily: $3, shrub: $1
i don't know girl i'm so sorry
What is the median of first 5 numbers?
The median of 1,2,3,4,5 is 3.
The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.
Here we have to find the median of 1,2,3,4,5.
Here we can see that there are 5 numbers given
so, n= 5 which is an odd number so we will use the formula for finding the median in the case of the odd number of data.
So, M = 5+1/2 = 3
Thus the median is the 3rd term which is 3.
Therefore, the median of 1,2,3,4,5 is 3.
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Can a 5 year old count to 100?
Yes, a 5 year old can typically count to 100.
What is counting?Counting is the process of determining the number of elements in a given set or group of objects. Counting is a basic numerical skill that is used in mathematics and other fields. It involves recognizing patterns and comparing numbers to identify how many items are in a given set. Counting is an important part of early childhood education, as it introduces children to the concepts of number and quantity.
Depending on the child's exposure to numbers, they may be able to count even higher. Counting to 100 is a fundamental skill that can be developed through practice and repetition. Teaching a 5 year old to count to 100 can be done through activities such as counting objects, counting steps, and playing counting games.
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I need help just on #6 please!
The two column proof is written as follows
Statement Reason
h || g given
j || g given
< 2 ≅ < 1 Alternate angle theorem
< 1 ≅ < 3 Corresponding angle theorem
< 1 ≅ < 3 Transitive property
What is transitive property?According to the transitive property, "all the quantities are equal to each other if two quantities are equal to the third quantity."
hence if < 2 ≅ < 1 and < 1 ≅ < 3, then < 1 ≅ < 3
What are alternate angles postulate?According to the alternate angle theorem, when a transversal cuts two parallel lines, the resulting alternate interior angles or alternate exterior angles are congruent. To demonstrate: If a transversal cuts two parallel lines, then the opposing interior angles are equal.
What are congruent angles?Two angles are said to be congruent when they are equal to each
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a normal distribution of scores has a standard deviation of 10. find the z-score corresponding to a score that is 30 points below the mean.
The z-score 30 points below the mean is -3
The normal distribution of scores has a standard deviation(σ) of 10
Below the mean is (X-μ)=-30
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
Z=(X-μ)/σ
Z=-30/10
Z=-3
Therefore, the z-score is -3.
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Solve the system of equations below by graphing both equations with a
pencil and paper. What is the solution?
Y = x-1
y = 1/2x+1
• A. (-2, 0)
O B. (-4, -3)
O C. (4, 3)
O D. (2, 1)
The solution to the system of equations is (4,3). Option C
What is a system of equations?Generally, To solve this system of equations by graphing, you can start by graphing each equation separately on the same set of axes.
For the first equation, Y = x - 1, you can start by plotting a few points to get a feel for the graph.
, if x = 0, then Y = -1.
If x = 1, then Y = 0.
If x = 2, then Y = 1.
You can continue plotting points like this to get a better idea of what the graph looks like.
For the second equation, y = 1/2x + 1, you can do the same thing. For example,
if x = 0,
then y = 1.
If x = 1,
then y = 1.5.
If x = 2,
then y = 2.
Again, you can plot a few more points to get a better sense of the graph.
Once you have graphed both equations, you can look for the point where the two graphs intersect.
This point will be the solution to the system of equations. In this case, the solution is (4,3), so the correct answer is C.
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Is the sum of 3 consecutive numbers a multiple of 3?
The sum of 3 consecutive numbers is always of the form 3(x+1) which is always a multiple of 3.
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.
Let us assume: 3 consecutive integers are x, x+1 , x+2.
on adding these three numbers we get,
x + x+1 + x+2 = 3x + 3
which can be further reduced to the form 3(x+1).
If you add any 3 consecutive numbers together it will always equal a multiple of 3, e.g.
1+2+3=6
2+3+4=9
3+4+5=12
4+5+6=15
5+6+7=18
Thus , the sum of 3 consecutive numbers is always of the form 3(x+1) which is always a multiple of 3.
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