The measure of the smallest angle of the quadrilateral is 60° .
In the question ,
it is given that ,
the angle measure of the quadrilateral are in the ratio 4 : 5 : 6 : 9 .
So , the measure of the largest angle is = 9x
and the measure of the smallest angle is = 4x .
we know that the sum of the measure of all the angles of the quadrilateral is 360° .
that means ,
4x + 5x + 6x + 9x = 360°
24x = 360
dividing both sides by 24 ,
x = 360/24
x = 15 .
the smallest angle is = 4(15) = 60°
Therefore , The measure of the smallest angle of the quadrilateral is 60° .
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The scale factor of a model of a hot air balloon to the actual hot air balloon is 1 to 5. The volume of the actual balloon is 5000m³.
What is the volume of the model?
The volume of the model of the air balloon is 1000m³.
What is volume?Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units. Volume and the notion of length are connected.The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim.So, the volume of the model:
The ratio of the volume of, the model: actual balloon = 1:5The volume of an actual air balloon is 5000m³.So, calculate the volume of the model as follows:
1/x = 5/50005000 = 5x5x = 5000x = 1000m³Therefore, the volume of the model of the air balloon is 1000m³.
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The trim loss percent for rutabagas is 19%. If you purchase rutabaga for $0.79 per pound, how much would 3 pounds 9 ounces cost?
3 pounds 9 ounces of rutabagas would cost $2.28
How to determine the cost of rutabagasThe question is a percentage problem
The trim loss percent for rutabagas is 19%
= 19 percent
= 19 / 100
= 0.19
trim loss factor = 1 - 0.19 = 0.81
selling price of rutabagas = $0.79 * 0.81 = 0.6399
converting all the unit in pounds
3 pounds 9 ounces: if 1 pound is 16 ounces then 9 ounces will be
3 pounds 9 ounces: 9/16 ounces = 0.5625
therefore we have 3.5625 pounds of rutabagas
3.5625 pounds of rutabagas will cost
= 3.5625 * 0.6399
= $2.28
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During a rainstorm, a pail collects 1 3 of an inch of water in 5 6 of a minute. At what rate is the pail collecting water?.
The rate at which the pail is collecting the water is [tex]\frac{2}{5}[/tex] of an inch per minute.
What is rate in mathematics?
A rate is the ratio of two related quantities expressed in different units. the numerator of the ratio expresses the corresponding rate of change in the other (dependent) variable. One unit of one of these quantities is used to represent the ratio's denominator, and if it can be altered consistently, then the ratio can be stated as follows: (i.e., is an independent variable).
The rate can be configured as.
Rate = [tex]\frac{1/3}{5/6}[/tex]
Rate = [tex]\frac{2}{5}[/tex]
Hence, the rate at which the pail is collecting the water is [tex]\frac{2}{5}[/tex] of an inch per minute.
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You have 14 pens and markers. You have six more markers than pens. How many of each item do you have?
Answer: 13 markers and one pen
Step-by-step explanation:
14/2 = 7
7+6=13 markers
Which means there is only one pen left
From the obtained equation, there are 4 pens and 10 markers.
Given that, there are 14 pens and markers.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of pens be p.
Then, the number of markers will be p+6
Now, the equation is p+p+6=14
⇒ 2p+6=14
⇒ 2p=8
⇒ p=4
Thus, p+6=10
Therefore, from the obtained equation, there are 4 pens and 10 markers.
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Compare the scenarios to determine which represents a greater speed. Explain your choice including a written description of each scenario. Be sure to include the rates in your explanation.
The scenario that represents a greater speed is scenario 1, which is 60 miles per hour.
What is Speed?Speed can be defined as the time it takes a moving object or body to cover a specific distance. In order words, it is calculated as:
Speed = distance/time.
In scenario 1, using one point on the graph, (1, 60), we can find the unit rate which is the speed in miles per hour:
Speed = y/x = distance/time = 60/1
Speed for scenario 1 = 60 miles per hour.
In scenario 2, we are given the equation, y = 55x:
55 is the unit rate which is the speed.
Speed for scenario 2 = 55 miles per hour.
The greater speed is 60 miles per hour.
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-18t=-3(t+5) distributive property I only have 10 points.
Answer: t=1
Step-by-step explanation:
1. Distribute the -3
-18t=-3t-15
2. Move the -3t to the other side
-15t=-15
3. Divide by -15 to solve for t
t=1
the height and arm span of a sample of 50 teenagers identify the explanatory variable and the response variable for this relationship, if possible. either variable, height or arm span, could be the explanatory variable, because each could be used to predict or explain the other. the explanatory variable, arm span of teenagers, helps explain the response variable, height of teenagers. the explanatory variable, height of teenagers, helps explain the response variable, armspan of teenagers. the explanatory variable, teenagers, helps explain the response variable, armspan of teenagers. the explanatory variable, teenagers, helps explain the response variable, height of teenagers.
For the height and arm span of a sample of 50 teenagers explanatory variable and the response variable for this relationship is the explanatory variable, height of teenagers, helps explain the response variable, arm span of teenagers. (Option C)
An explanatory variable refers to the variable that can be manipulated in experiment by the researcher and is the independent variable whereas a response variable refers to the variable that is modified as a result and is the dependent variable. In the given case, the height is the explanatory variable while the arm span is the response variable as a teenager's arms spread is influenced by their height.
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Select the correct answer from each drop-down menu.
For the diagram shown, complete a true statement.
A
B
G
DE is the ray with endpoint
D
E
GA and DF
intersect.
The DE is the ray with end point E and the ray GA and ray DF will not intersect
From the given diagram
Consider the ray DE,
The starting point of the ray DE = D
Then the end point of the ray DE = E
The D is the starting point and E is the end point of the ray DE
Therefore DE is the ray with end point E
Consider the ray GA and DF, those rays are not in contact and going opposite direction, therefore it will not intersect
The GA and DF will not intersect
Hence, the DE is the ray with end point E and the ray GA and ray DF will not intersect
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Part H is not showing including H too, can someone please help me
The scale factor k=5
corresponding parts are:
AL--> TD
TK---> AH
DK---> LH
angle A-----> angle T
angle D-----> angle L
angle H-----> angle K
What is scale factor?
The difference in scale between an original object's scale and that of a new, smaller representation is known as a scale factor (bigger or smaller). By multiplying each side by a certain number, say 2, we can increase the size of a rectangle with sides of 2 cm and 4 cm.
The letter H lies on the line TK
Scale factor k
=( side length of new image)/ ( corresponding side length of new image)
=TD/AL=15/3=5
k=5
From the figure, corresponding parts are as below:
AL--> TD
TK---> AH
DK---> LH
angle A-----> angle T
angle D-----> angle L
angle H-----> angle K
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A lighthouse is 160 feet tall. A scale model of the lighthouse has a scale of 1 in: 8 ft. How tall is the model of the lighthouse in inches?.
The height of the model of the lighthouse in inches is 20 inches
The real height of the lighthouse = 160 feet
The scale model of the light house has scale of
1 inch : 8 feet
Consider the height of the model of the lighthouse is x
Then the proportion of the scale model of the lighthouse and the actual height will be
1 inch / 8 feet = x inches / 160 feet
Cross multiply the terms
1 × 160 = 8x
Multiply the terms
8x = 160
Divide both side of the equation by 8
8x / 8 = 160 / 8
x = 20 inches
Hence, the height of the model of the lighthouse in inches is 20 inches
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A container releases fuel at a rate of 5 gallons per second. If y represents the amount of fuel remaining in the container and represents the number of seconds that have passed since the fuel started
dispensing, then x and y satisfy a linear relationship.
If the tank begins with 103 gallons, how many gallons will remain after 2 seconds?
If the tank begins with 103 gallons, then 93 gallon will remain after 2 seconds
The quantity of fuel releases from the container = 5 gallon per second
Consider the fuel remaining in the container = y
Consider the number of seconds that have passed since the fuel started dispensing = x
Then x and y satisfy a linear relationship
The quantity of fuel in the tank at the beginning = 103 gallon
Time taken = 2 seconds
Then the equation will be
y = 103 - 5x
Time taken is x = 2
y = 103 - 5× 2
y = 103 - 10
y = 93 gallon
Hence, if the tank begins with 103 gallons, then 93 gallon will remain after 2 seconds
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How many millimeters(mm)are there in 3.5 meters(m)
Answer:
3,500 Millimeters
Step-by-step explanation:
1 Meter = 1,000 Millimeters so,
3.5 meters = 3,500 Millimeters
Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
18, 14, 10, .
Answer: The sequence has a common difference between consecutive terms
14 - 18 = 10 - 14 = - 4
This indicates it is an arithmetic sequence with a common difference - 4
Step-by-step explanation:
What is Desmos in math?
Answer:
Desmos is a free graphing and teaching tool for math available on the web as well as on iOS and Android. In addition to plotting equations, classroom activities are available to help students learn about a variety of math concepts.
A definition of Desmos has been given below
What is Desmos?
Desmos can be applied in a variety of contexts. Students can avoid spending $100 on a graphing calculator by using it for free. It can be used by teachers to create stunning images for tests and presentations. But Desmos really shines in the classroom exercises. Teachers can use Desmos to assist students in making the connection between mathematical concepts and actual, concrete shapes and images. It's simple to begin an activity with your students: Just instruct the children to enter the website's activity code. Try the student preview of an activity before assigning it. In the teacher moves section at the bottom of each activity, you can find specific ways to guide your children while they work. The teacher dashboard allows for the tracking of progress.
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can you substitute y=2x+4 y=2
Answer: x = -1
Step-by-step explanation:
Since, you know y = 2, substitute that y-value into the other function:
[tex]2=2x+4\\\\2x=2-4=-2\\\\x=\frac{-2}{2} =-1[/tex]
Solve the simultaneous equations
Answer:
(x = -0.90, y = 2.31) and (x = 1.40, y = 9.19)
Step-by-step explanation:
See the attached image
1. Stanley's cat weighs 5 pounds. Stanley's dog weighs 3 3/5 times as much as his cat.
How much does Stanley's dog weigh?
Answer:
18
Step-by-step explanation:
Answer:
18 pounds
Step-by-step explanation:
5x 3 3/5= 18
Please I need help please
Answer:
m∠T = 60°
m∠U = 60°
TS = 13 cm
SU = 13 cm
Step-by-step explanation:
The diagram shows that 2 sides, UT and TS, are equal, so it is an isosceles triangle. Since it is an isosceles triangle, the two angles opposite the equal sides are also congruent to each other, so m∠S = m∠U = 60°.
Now we know the measure of 2 angles, we can find the measure of the third angle, by subtracting the 2 known angles from 180°.
m∠T = 180° - m∠S - m∠U
m∠T = 180° - 60° - 60°
m∠T = 60°
Since all 3 angles are congruent, it is an equilateral triangle, therefore all the sides must be congruent too. So UT = TS = SU = 13 cm.
Mr. Ready went to Walmart for some groceries. A large bag of chips is $4 and each
pound of meat is $2. Create an equation that represents the number of bags of chips
and the pounds of meat he bought if he spent $38.
Answer:
[tex]38=4c+2m[/tex]
Step-by-step explanation:
I will use the letter c to represent bags of chips, and the letter m to represent pounds of meat.
The total cost of c bags of chips is 4 times c. The total cost of m pounds of meat is 2 times m. The total amount that he spends is $38. Therefore, this equation can be written.
[tex]38=4c+2m[/tex]
What is the equation of the line shown in this graph?
Answer:
Step-by-step explanation:
formula of a linear line - y=mx+c
so y=
m= gradient x =x coodinate c=y-intercept
c= -3
m = 0
which is y=-3
pls give me brainliest
pls:(
Answer:
y = - 3Step-by-step explanation:
Points given:
(- 2, - 3) and (3, - 3)This is a horizontal line with constant y - value of - 3.
So it equation is y = - 3.
Does anyone know the answer to the last part of this question ?? I already got the rest, I just need the last one.
PLEASE HELP !!
DONT ANSWER IF YOU DONT KNOW IT !! i will report you if you answer with anything else.
Only answer if you know!!
Answer: 62.5
Step-by-step explanation:
To break even, profit equals zero.
[tex]1.60n-100=0\\\\1.60n=100\\\\n=62.5[/tex]
What’s the IQR for jacobs data set
The IQR for Jacob's data set is determined as: 2 seconds.
What is the Interquartile Range of a Data Set?To find the interquartile range (IQR) of a Data set, find the third quartile value and the first quartile value. Their difference is the Interquartile Range (IQR) of the data.
Interquartile Range (IQR) = third quartile - first quartile.
In the box plot given, we can deduce that:
Third quartile = 15.5
First quartile = 13.5
Interquartile Range (IQR) = 15.5 - 13.5
Interquartile Range (IQR) = 2 seconds
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Answer: 2 seconds
Step-by-step explanation:
What is the slope of a line parallel to the line whose equation is x + y = 6
Answer:
-1
Step-by-step explanation:
put this equation in slope intercept form : y=mx+b
x+y=6
-x. -x
y=-1x+6
The slope of this line is -1 and for it to be parallel they both have to have the same slope
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A construction crew is lengthening a road. The road started with a length of 54 mlles, and the crew is adding 4 mlles to the road each day.
Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D. Then use this equation to find the total length of the road after the crew has worked 37 days.
Equation:
Total length of the road after 37 days:___miles
The equation that relating the total length of the road L and the number of days D is L = 54 + 4d, the length of the road after 37 days is 202 miles
The length of the road at starting = 54 miles
The rate of lengthening the road per day = 4 miles per day
Where L is the total length of the road in miles
D is the number of days the crew has worked
Then the equation will be
L = 54 + 4D
The number of days = 37 days
Substitute the value of D
L = 54 + 4×37
L = 54 + 148
L = 202 miles
Hence, the equation that relating the total length of the road L and the number of days D is L = 54 + 4d, the length of the road after 37 days is 202 miles
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I drove to my summer home at 75 mph. The next day I drove back, it took me a hour longer because of traffic, and I drove at 50 mph. How long was the drive on the first day?
Answer:
2 hours
Step-by-step explanation:
time it took on the first day = x
speed = d/t
time it took on second day = x + 1
75 = d/x
50 = d/x + 1
75x = d
50 = 75x/(x + 1)
50(x + 1) = 75x
50x + 50 = 75x
50 = 25x
x = 50/25
x = 2
enter a quadratic polynomial which has zeros at -7 and 7
The required quadratic polynomial whose roots are -7 and 7 is
[tex]x^{2} - 49[/tex]
As the zeroes are given, i.e., 7 and -7.
∴ Sum of roots = 7+(−7) = 7− 7 = 0
Product of roots = 7×(−7) = −49
As we know, a quadratic polynomial whose zeroes are given can be represented as-
[tex]x^{2}[/tex] - (Sum of roots)x + (product of roots) = 0
[tex]x^{2} -0*x +(-49) = 0\\\\x^{2} - 49 = 0[/tex]
Hence, the required quadratic polynomial whose roots are -7 and 7 is
[tex]x^{2} - 49[/tex]
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19x=y
in standerds form
Answer:
19x − y = 0
__
The length of a rectangle i 12m and the length of it diagonal i 15m.Find
the width of the rectangle.
Answer:
width = 9 m
Step-by-step explanation:
the diagonal divides the rectangle into 2 right triangles.
using Pythagoras' identity on one of the triangles
with legs 12 and width (w) and hypotenuse (diagonal) 15 , then
w² + 12² = 15²
w² + 144 = 225 ( subtract 144 from both sides )
w² = 81 ( take square root of both sides )
w = [tex]\sqrt{81}[/tex] = 9
that is the width of the rectangle is 9 m
Find the circumference of a circular swimming pool with a diameter of 22 feet. Use 3.14 as an approximation for pie. Round your answer to the nearest whole foot. Enter only the number.
Answer:
380 ft²
Step-by-step explanation:
diameter = 22 ft
radius = diameter/2 = 22 ft/2 = 11 ft
area = πr²
area = 3.14 × (11 ft)²
area = 379.94 ft²
Answer: 380 ft²
(b) Bill removed 70 fish from his pond over a period of 7 days. He removed the same number of
fish each day. What was the change in the number of fish in the pond each day?
-70 fish
Answer:
ROC=10/1
Step-by-step explanation:
ROC=change in y-change in x
We can first write out a few more points.
(7,70), (14,140), (21,210)
210-140=70
140-70=70
21-14=7
14-7=7
So the ROC is 70/7 or 10/1