The value of x is given as follows:
x = 1.5.
The measure of each segment is given as follows:
WX = 2.5.XY = 5.WY = 7.5.What is the segment addition postulate?The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.
For this problem, we have that segment WY is divided into two smaller segments, WX and XY.
This means that the equation to find the value of x is presented as follows:
WY = WX + XY
7x - 3 = 9x - 11 + 4x - 1
13x - 12 = 7x - 3
6x = 9
x = 1.5.
Hence the segment lengths are given as follows:
WX = 9x - 11 = 9(1.5) - 11 = 2.5.XY = 4x - 1 = 4(1.5) - 1 = 6 - 1 = 5.WY = 7x - 3 = 7(1.5) - 3 = 10.5 - 3 = 7.5.More can be learned about the segment addition postulate at https://brainly.com/question/2134445
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13) x=
14) x=
15) x=
16) x=
17) x=
18) x=
The angle measures of x are given as follows:
13) x = 50º.
14) x = 40º.
15) x = 112º.
16) x = 32º.
17) x = 22º.
18) x = 120º.
How to obtain the angle measures?For item 13, at the triangle at the right, we have that the sum of the measures of the internal angles of a triangle is of 180º, hence:
43 + 57 + y = 180
y = 80º.
Meaning that x is the base angle of an isosceles triangle, for which the top angle is of 80º, hence:
2x + 80 = 180
2x = 100
x = 50º.
For item 14, we have that the third angle in the triangle with angles 50º and 80º is the complement of x, hence:
50 + 80 + 90 - x = 180
x = 40º.
For item 15, the internal angles are given as follows:
2y + 44 = 180
2y = 136
y = 136/2
y = 68.
The external angle is supplementary with it's internal angle, hence:
x = 180 - 68 = 112º.
For item 16, the internal angles of the triangle are given as follows:
90º.x.180 - 122 = 58ºHence:
90 + x + 58 = 180
x = 32º.
For item 17, the internal angles are given as follows:
180 - (6x - 7).2x.103 - x.Hence the value of x is obtained as follows:
180 - (6x - 7) + 2x + 103 - x = 180
-6x + 7 + 2x + 103 - x = 0
5x = 110
x = 22º.
For item 18, we have an equilateral triangle, hence the internal angles are of 60º and the external angles, representing the value of x, are given as follows:
x = 180 - 60 = 120º.
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Tisha brought chocolate and vanilla cupcakes to school for her birthday. 50 students decided to take a cupcake, and 27 of them picked vanilla. What percentage of the students picked a vanilla cupcake?
Write your answer using a percent sign (%).
Answer:
48% of students picked a vanilla cupcake
Step-by-step explanation:
We can get 48% from this question by turning this data into a fraction
27 students picked vanilla out of a total amount of 50
= 27/50
= 48%
This equals a percentage of 48% of students picking a vanilla cupcake
Answer:
48%
Step-by-step explanation:
what is the value of x
Answer:
x = 2
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{EC}{BC}[/tex] = [tex]\frac{DE}{AB}[/tex] ( substitute values )
[tex]\frac{2x+3}{13x-1.5}[/tex] = [tex]\frac{6}{21}[/tex] ( cross- multiply )
6(13x - 1.5) = 21(2x + 3) ← distribute parenthesis on both sides
78x - 9 = 42x + 63 ( subtract 42x from both sides )
36x - 9 = 63 ( add 9 to both sides )
36x = 72 ( divide both sides by 36 )
x = 2
The water level in a tank measures 15 inches and is decreasing 0.5 inches every mintue. How many mintues, x, will it take for the water level to measure 9 inches deep?
It will take 12 minutes for the water level to measure 9 inches deep.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
The water level in a tank measures 15 inches and is decreasing 0.5 inches every minute.
In x minute, water will decrease (0.5x) inches deep.
To find the water level to measure 9 inches deep:
That means,
water level decreased
= 15 - 9
= 6 inches.
Now,
Division,
6/(0.5)
= 12 minutes.
Therefore, the required time is 12 minutes.
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What is the rate of change of the function y=6x-1
The linear function y = 6 · x - 1 has a rate of change equal to 6.
What is the rate of change of a linear function?
Linear functions are polynomials of the form y = m · x + b, where m is the slope of the line and b is the intercept of the line. The rate of change is the first derivative of the function, that is:
r = m
In other words, the rate of change of a linear function (r) is its slope (m).
First, write the linear function:
y = 6 · x - 1
Second, extract the slope of the function and determine the rate of change of the function:
m = 6
r = 6
According to the explanation given in this problem, the rate of change of the linear function y = 6 · x - 1 is equal to 6.
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Please can l have some assistance
Total no of people = 118
Women = 49 (d)
Men = 118- 49 = 69 (a)
Total no of people like tea = 63
Total no of people do not like tea = 118-63 = 55
No of Men do not like tea = 33(c)
No of Women do not like tea = 55- 33 = 22 (f)
No.of Women like tea = 49-22 = 27 (e)
No . of men like tea = 69 - 33 = 36(b)
47. The line of best fit for the scatterplot below passes through which pair of points?
A) P and Q
B) S and T
C) R and Q
D) S and Q
The line of best fit for the scatterplot below passes through D) S and Q pair of points.
What is scatterplot?A scatter plot is a type of plot or mathematical diagram that uses Cartesian coordinates to display values for typically two variables for a set of data. It is also known as a scatter graph, scatter chart, scattergram, or scatter diagram.
One more variable can be shown if the points are color-, shape-, or size-coded. The data are represented as a set of points, where each point's position on the horizontal axis is determined by the value of one variable, and its position on the vertical axis by the value of the other variable.
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I need help with this problem and a good explanation on using the formula to get deviations.
Check the picture below.
2.8 × 15.7 =
please show work
Answer:
Step-by-step explanation:
The answer is 43.96
First multiply 28x157, that equals 4,396
Since there are two decimal points we need to move the decimal. After moving the decimal two place values the answer becomes 43.96.
An experiment involves selecting a numbered chip, some black and some white, from a bag of chips. The probability of selecting a black chip with an even number is 1/2. The probability of selecting a black chip is 3/5.
What is the probability of selecting a chip with an even number given that the chip is black?
Enter your answer as a simplified fraction.
The probability of selecting a chip with an even number, given that the chip is black, is 1/10.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
Given:
An experiment involves selecting a numbered chip, some black and some white, from a bag of chips.
The probability of selecting a black chip with an even number is 1/2.
Let P(B and E) = 1/2
The probability of selecting a black chip is 3/5.
P(B) = 3/5
The probability of selecting a chip with an even number given that the chip is black
P(W) = 3/5 - 1/2
= 6-5/10
= 1/10
Therefore, the probability is 1/10.
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At a dog shelter, a 20 pound bag of dog food will feed 36 dogs a day. How many dogs would you expect to feed with a 15 pound bag of dog food?
15 pound of dog food will feed 27 dogs
How to calculate the number of dogs that will be fed with 15 pound of dog food?At the dog shelter, 36 dogs are fed in a day
These 36 dogs will be fed with 20 pound bag of dog food
Therefore the number of dogs that can be fed with 15 pound of dog food can be calculated as follows
= 36/20
= 1.8
The next step is to multiply 1.8 by 15
= 1.8 × 15
= 27
Hence 27 dogs will be fed with 15 pound of dog food
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Xavier is chopping 60 tomatoes for dinner. It took him 3 minutes to chop the first 15. What percent of the tomatoes has he chopped so far?
Answer:
25%
Step-by-step explanation:
15/60 x 100 = 25%
A rectangular poster that is 12 inches (in.)
by 9 inches is surrounded by a 1-inch
frame as shown in the diagram below.
1 in. -
12 in.
A 108
B 130
C 143
D 150
E 154
9 in.
1 in.
How many total square inches of space
on a wall will this framed poster cover?
The framed poster will cover 156 square inches of space on a wall. So the answer is D.
What is the Rectangle?
A rectangle is a four-sided geometric shape with four right angles. The opposite sides of a rectangle are of equal length, and the opposite sides are of equal width. It is defined by its length and width. The length is the longer side of the rectangle and the width is the shorter side. The area of a rectangle is found by multiplying the length by the width, and the perimeter is found by adding the lengths of all four sides.
The poster itself is 12 inches by 9 inches, so it covers a total area of 129 = 108 square inches.
However, we also need to include the area covered by the frame.
The frame is 1 inch wide on all four sides of the poster.
So, the total area covered by the frame is 41*12 = 48 square inches.
To find the total area covered by the poster and the frame, we add the area of the poster to the area of the frame:
108 + 48 = 156 square inches
Therefore, The framed poster will cover 156 square inches of space on a wall. So the answer is D.
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Write an equation of the line that passes through the given points.
(-3,7) and (4,-7)
The equation is _______. (Type your answer in slope-intercept form.)
Considering the expression of a line, the equation of the line that passes through the points (-3,7) and (4,-7) is y= -2x +1.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope can be calculated using:
m= (y₂ - y₁)÷ (x₂ - x₁)
Substituting the value of the slope m and one of the points in the expression of a line, the value of the ordinate to the origin can be obtained.
Equation in this caseIn this case, being (x₁, y₁)= (-3, 7) and (x₂, y₂)= (4, -7), the slope m can be calculated as:
m= (-7 - 7)÷ (4 - (-3))
m= (-7 - 7)÷ (4 +3)
m= (-14)÷ 7
m= -2
Considering point 1 and the slope m, you obtain:
7= (-2)× (-3) + b
7= 6+b
7 -6= b
1= b
Finally, the equation of the line is y= -2x +1.
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In construction, floor space must be planned for stair cases. If the vertical distance between the first and second floors it's 3.6 m and a contractor is using the standard step pattern of 28 cm wide for 18 cm high and how many steps are needed to get the first to the second floor and how much linear distance will be needed for the staircase? What is the length of the railing that would be attached to these stairs? Round to the nearest hundredth.
If in construction, floor space must be planned for stair cases. the length of the railing that would be attached to these stairs is: 6.657 meters.
How to find the length?First step is to convert the meter to centimeters and the find the number of step
3.6m =360cm
360cm/18cm = 20 steps
So,
20 steps × 28 cm = 560 cm long
x²= 3.6cm² + 5.6m²
x²= 12.96 + 31.36
x² = 44.32
x = √44.32
x = 6.657 meters
Therefore the length is 6.657 meters.
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If a^1/2=r then which of the following are true statements
For exponential equation a^1/n = r option D is true i.e. r^n=a.
What are exponential equations?
Exponents are used in exponential equations, as the name implies. We already know that the exponent of a number (base) specifies how many times the number (base) has been multiplied. But what happens if a number is variable? When the power is a variable in an equation, it is referred to as an exponential equation.
For example, 3^x = 81, 5^x - 3 = 625, 62^y - 7 = 121, etc are some examples of exponential equations.
Exponential equations are classified into three categories. These are :
Equations on both sides with the same base. (For instance, 4^x = 4^2)Equations that may be constructed to have the same base. (For example, 4^x = 16 can be represented as 4^x = 4^2.)Equations that cannot be constructed to have the same base. (For instance, 4^x = 15.As given,
a^1/n=r
Now we take 1/n from left side of exponential equation to right side i.e.
a=r^n (As a^1/2 = 4 ---> a=4^2)
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[3
A tent is formed of a cuboid with a pyramid on top, as
shown below. The top vertex of the pyramid is directly
above the centre of the base of the tent.
What is the height of the tent?
Give your answer in metres (m) to 1 d.p.
8m
?
6.5 m
5m
3 m
The total height of the tent formed using a cuboid and a pyramid is evaluated to be 9.0 m.
What is a cuboid and pyramid?
A polyhedron with six faces, eight vertices, and twelve edges is known as a cuboid. The cuboid's faces are parallel. However, a cuboid's faces do not all have the same size.
A pyramid is a structure that substantially resembles a pyramid in the geometric sense when its exterior surfaces are triangular and converge to a single step at the summit.
The height of the cuboid is a = 3m.
The base of the pyramid is b = 5m.
The slant height of the pyramid is c = 6.5 m.
To find the height of the pyramid, use the formula -
h = [tex]\sqrt{c^2-(\frac{b}{2})^2} }[/tex]
h = [tex]\sqrt{6.5^2-(\frac{5}{2})^2} }[/tex]
h = [tex]\sqrt{42.25-(2.5)^2}[/tex]
h = [tex]\sqrt{42.25-6.25}[/tex]
h = [tex]\sqrt{36}[/tex]
h = 6 m
The height of the pyramid is 6 m.
Now, the height of the tent = a + height of the pyramid (h).
Height of tent = 3 + 6
Height of tent = 9 m.
Therefore, the height value is obtained as 9.0 m.
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A pencil 10 cm long is kept inside a cylindrical glass as shown in figure. If the radius of the base of the glass is 3 cm, find its height.
The length of the cylinder for the condition is 11.66 cm
What is a cylinder?One of the fundamental three-dimensional shapes in geometry is the cylinder, which has two distant, parallel circular bases. At a predetermined distance from the centre, a curved surface connects the two circular bases. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases.
Given the height of the pencil = 10 cm
and kept diagonally in cylinder,
and radius of cylinder = 3 cm
the relation between height, radius and diagonal of cylinder is
d² = h² + (2r)²
h² = d² - (2r)²
where d is diagonal and r is radius
h² = 10² + (2 x 3)²
h² = 100 + 36
h² = 136
h = √136
h = 11.66 cm
Hence height of cylinder is 11.66 cm.
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the image of question is attached.
Answer:
Answer:height = √919.539cm
Step-by-step explanation:
we have to find height from slant height
we have to find height from slant heightso the formula is height= v(I²-r²)
we have to find height from slant heightso the formula is height= v(I²-r²)slant height I = 10 cm = 100 cm
we have to find height from slant heightso the formula is height= v(I²-r²)slant height I = 10 cm = 100 cmradius r = 3 cm = 9cm
we have to find height from slant heightso the formula is height= v(I²-r²)slant height I = 10 cm = 100 cmradius r = 3 cm = 9cmheight = √(100-9)
we have to find height from slant heightso the formula is height= v(I²-r²)slant height I = 10 cm = 100 cmradius r = 3 cm = 9cmheight = √(100-9)height = √91
we have to find height from slant heightso the formula is height= v(I²-r²)slant height I = 10 cm = 100 cmradius r = 3 cm = 9cmheight = √(100-9)height = √91height = 9.539 cm
Note
please make me brainalist and keep smiling dude I hope you will be satisfied with my answer :-)
A scalene triangle will have side lengths of 12, 8, and 6.
False
True
Answer:
FalseStep-by-step explanation:
FALSE
An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees
see the picture belowPlease answer this question ASAP.
The time that it will take the ink to diffuse a distance of 10⁻⁴ cm is; 10⁻³ seconds
How to solve the subject of the formula?The subject of a formula is defined as the variable that is being worked out. It can be recognized as the letter that is on its own on one side of the equals sign. For example, in the formula for the area of a rectangle;
A = base * height , the subject of the formula is A.
We are given t as the subject of a formula written as;
t = x²/2D
Where;
t is time in seconds that it takes molecules to diffuse a distance a centimeters.
D is the diffusion coefficient
We are given;
D = 10⁻⁵ cm²/s
Distance of diffusion; x = 10⁻⁴ cm
Thus;
t = (10⁻⁴ )²/10⁻⁵
t = 10⁻⁸/10⁻⁵
t = 10⁻⁸⁺⁵
t = 10⁻³ = 0.001 seconds
That is the time we conclude it will take the ink to diffuse.
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David, Tristan, and Jalen are running. David can run 2 miles in 27 minutes. Tristan can run 3 miles in 30 minutes. Jalen can run 6 miles in 66 minutes. Assume that they are running at a constant speed. Who is the fastest runner. How do you know?
Answer:
Tristan 0.1 miles/min
Step-by-step explanation:
Divide distance and time
David =0.074 miles/min
Jalen = 0.09 miles/min
Hope this helps
1/2 quart equals how many gallons?
Answer:
0.125 gallons
Step-by-step explanation:
1/2 quart is equal to 0.125 gallons.
Answer:
½ quart = 0.125 gallons
Step-by-step explanation:
We know that,
→ 1 quart = 0.25 gallons
Then 1/2 quarts will equals,
→ 1 quart = 0.25 gallons
→ 1 q = 0.25 gal
→ 1/2 q = (0.25/2) gal
→ 1/2 q = 0.125 gal
Hence, answer is 0.125 gal.
i rlly need help i don’t get it
The largest possible whole-number length for the third-side is 27 .
What is whole number ?
Whole numbers are made up of all the ordinal numbers and 0. Natural numbers are the names given to counting numbers in mathematics. Thus, the definition of a whole number is a grouping of all natural numbers plus 0. Along with zero, all positive integers are also considered whole numbers.
There are no fractions, decimals, or negative integers in whole numbers, which are actual numbers. There is no fraction or decimal equivalent to zero. It is neutral; neither good nor bad. The whole-number rule is observed by zero.
All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions. Whole numbers include counting numerals as well.
Consider a triangle with side lengths a , b ,c such that a < b < c
a = 18 and b = 10 are the two known sides
Let c be the missing side length
The missing side has the property that...
a - b < c < a + b
18 - 10 < c < 18 + 10
8 < c < 28
Meaning that if c is a whole number then it can take on any of these values { 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 }
So c = 27 is the largest possible third side, where only whole number sides are considered.
We can't have a third side of 28 because the two other sides add to a+b = 10 + 18 = 28 and a triangle wouldn't form (instead only a straight line would).
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A linear relationship is given in the table.
X-2 -10 1 2
y-12-7-2 3 8
What is the slope of the relationship?
5
-5
1/5
-1/5
The slope of the relationship is m = 5. Hence option A is the correct option.
What is the relationship?
A collection of ordered pairs having one item from each set makes up a relation between two sets. If the ordered pair (x,y) is present in the relationship and the objects x and y come from different sets, then the objects are said to be connected. One kind of relationship is a function.
Given linear relationship:
x y
-2 -12
-1 -7
0 -2
1 3
2 8
The slope of the linear relationship that passes through the points (x₁, y₁) and (x₂, y₂) is [(y₂ - y₁)/(x₂ - x₁)].
Here, x₁ = -2 , y₁ = -12, x₂ = -1, y₂ = -7
The slope is (-7 - (-12))/(-1 - (-2))
=(-7 + 12)/(-1 + 2)
= 5/1
= 5
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6) In the following rectangle ABCD, the sum of the lengths of AB, BC, and CD is 90 cm. The
sum of the lengths of BC, CD, and AD is 78 cm. What is the perimeter of rectangle ABCD?
The perimeter of rectangle ABCD will be 112 centimeters.
What is the perimeter of the rectangle?Let W be the rectangle's width and L its length.
The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be
Perimeter of the rectangle = 2(L + W) units
In the following rectangle ABCD, the sum of the lengths of AB, BC, and CD is 90 cm. The sum of the lengths of BC, CD, and AD is 78 cm.
We know that in a rectangle ABCD, AB = CD, and BC = AD. Then we have
AB + BC + CD = 90
2 AB + BC = 90 ...1
BC + CD + DA = 78
2 BC + AB = 78 ...2
From equations 1 and 2, we have
3AB + 3BC = 168
AB + BC = 56
2(AB + BC) = 112 cm
P = 112 cm
The perimeter of rectangle ABCD will be 112 centimeters.
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A dump truck normally carries 10 cubic yards of gravel. A cubic yard of gravel
weighs 1.35 tons. Road bans in the spring specify that the truck can only be
loaded to 85 percent of normal capacity.
How many tons of gravel can the truck carry when road bans are in effect?
The tons of gravel that the truck can carry with road ban in effect is 11.475 tons.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
Total load carried by truck is 10 cubic yards.
It can be converted into tons as,
10 cubic yards = 10 × 1.35
⇒ 13.5 tons.
The load carried by truck during ban is given as,
85% × Total load
⇒ 85/100 × 13.5 = 11.475 tons.
Hence, the amount of gravel to be carried by truck during ban is given as 11.475 tons.
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Please help me with this question
Answer:
The sum of any triangle's angles is always 180 degrees, so take the equations and add them together, equal to 180.
(2v- 20 + 2v - 15 + 31 = 180)
v = 46
Answer:
46°
Step-by-step explanation:
The sum of the interior angles of a triangle is 180°
fractions less than 1/2
show how you got the answer
The fractions from the given options that is less than 1/2 hence option A.
How can the fraction be determined?The concept that will be used is division of the numerator by the denominator. The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line.
The given fraction is 1/2, if we convert to decimal, by dividing the numerator by the denominator we have 0.5
Then we can conert the given options one after the other.
Option A ; 3/8 = 0.375
Option B = 5/8 = 0.625
Now from the result we can see that 0.375 < 0.5 < 0.625 , hence option A is correct.
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Find the sum and express it in simplest form.
(2y2 +9y + 4) + (-3y² - 3y)
Exponent (^)
Enter the correct answer.
Answer:
To find the sum of the two expressions, we can combine like terms. In this case, we have two terms with a coefficient of -3y² and two terms with a coefficient of -3y, so we can combine them to get:
(-3y² + -3y²) + (-3y + -3y) + (2y² + 9y + 4)
Simplifying the expression gives us:
-6y² - 6y + 2y² + 9y + 4
Combining the like terms again gives us:
-4y² + 15y + 4
Therefore, the sum of the two expressions is -4y² + 15y + 4. This is already in simplest form.
Construct a truth table for each of the following compound statements, where p, q, r. denote primitive statements.
a. ∼ ( p ⌄ ∼ q ) → ∼ p
b. p → ( q → r )
c. ( p → q ) → r
d. ( p → q ) → ( p ^ q)
Answer:
See below for solution
When I post this I lose the formatting but you should be able to figure it out
Step-by-step explanation:
Part a
p q ∼ ( p ∨ ∼ q ) → ∼ p
------------------------------------------------------------
True True True
True False True
False True True
False False True
Part b
p q r p → ( q → r )
-----------------------------------------------------------------
True True True True
True True False False
True False True True
True False False True
False True True True
False True False True
False False True True
False False False True
Part c
p q r ( p → q ) → r
-----------------------------------------------------------
True True True True
True True False False
True False True True
True False False True
False True True True
False True False False
False False True True
False False False False
Part d
p q (p → q)→(p ∧ q)
---------------------------------------------------
True True True
True False True
False True False
False False False
