"The value of [tex]\angle1 +\angle3[/tex] lies between [tex]90^{\circ} < \angle1+\angle3< 180^{\circ}[/tex].
Given,[tex]\angle 1,\angle2, \angle3[/tex] have the following relationships.
[tex]\angle 1[/tex] and[tex]\angle2[/tex] are acute vertical angles. [tex]\angle 3[/tex] is an obtuse angle adjacent to both [tex]\angle 1[/tex] and [tex]\angle 2[/tex].We have to find the sum of measure of [tex]\angle1[/tex] and the measure of [tex]\angle3[/tex].
Angle sum property:We know that the angle sum property of triangle states that the sum of all angles of a triangle is equal to [tex]180 ^{\circ}[/tex].
[tex]\angle 1+\angle 2+\angle3= 180^ {\circ}[/tex]
[tex]\angle1+\angle3= 180-\angle2[/tex]
So, the value [tex]\angle1 and \angle3[/tex] is always greater than [tex]90{^\circ}[/tex] because [tex]\angle 3[/tex] is the obtuse angle and it is being added to [tex]\angle1[/tex],
so it is always greater than right angle and less than [tex]180^{\circ}[/tex].
Hence the value of [tex]\angle1 +\angle3[/tex] lies between [tex]90^{\circ} < \angle1+\angle3< 180^{\circ}[/tex].
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What is the approximate solution of this system of equations?
y = x2 + 3x + 3
y = x2 + x + 2
(-0.5, 0.2)
(-0.5, 1.7)
(-0.1, 1.2)
(0.2, 1.5)
The value of a boat is $23,400. It loses 8% of its value every year. Find the approximate monthly percent decrease in value. Round your answer to the nearest hundredth of a percent.
(NOT 67%)
Final answer:
The approximate monthly percent decrease in value is 0.67%.
Explanation:
To find the approximate monthly percent decrease in value, we need to first calculate the annual percent decrease. We know that the boat loses 8% of its value every year. So, the annual percent decrease is 8%.
To find the monthly percent decrease, we need to divide the annual percent decrease by 12 (since there are 12 months in a year).
Therefore, the approximate monthly percent decrease in value is 0.67%.
Final answer:
The approximate monthly percent decrease in value of the boat that depreciates at 8% annually is 0.65% when rounded to the nearest hundredth of a percent.
Explanation:
To find the monthly percent decrease in value of a boat that costs $23,400 and depreciates 8% annually, we need to calculate the equivalent monthly rate. The formula for monthly depreciation is (1 - (1 - annual depreciation rate)^(1/12)). In this case, the annual depreciation rate is 0.08 for 8%. Applying the formula, we get:
Monthly depreciation = 1 - (1 - 0.08)^(1/12) = 1 - (0.92)^(1/12)
= 1 - (0.92)^(0.08333...)
= 1 - 0.99347... (value calculated using a calculator)
= 0.00653... or 0.653% (after converting to a percentage).
To round to the nearest hundredth of a percent, we get approximately 0.65% monthly depreciation. This is the approximate monthly percent decrease in the boat's value.
Broderick had $420 in his checking account. He made 6 deposits of $35.50 each. He needs to write 4 checks for $310.75 each.How much money does Boderick need to add to his account to cover his checks ? Show your work.
Broderick initially has $420, adds $213 from deposits, and needs $1,243 for checks, resulting in him needing to add $610 to cover his checks.
Explanation:To calculate how much money Broderick needs to add to his account to cover his checks, we must first figure out his total deposits and then subtract the total amount he needs for the checks.
Broderick starts with $420 in his account and makes 6 deposits of $35.50 each. To find the total amount deposited, we multiply the number of deposits by the amount of each deposit:
6 deposits × $35.50/deposit = $213Adding this total to his initial amount gives us:
$420 + $213 = $633Next, Broderick needs to write 4 checks for $310.75 each. The total amount for the checks is:
4 checks × $310.75/check = $1,243To determine how much additional money is needed, we subtract Broderick's available money from the total amount needed for the checks:
$1,243 (total for checks) - $633 (total available in account) = $610Therefore, Broderick needs to add $610 to his account to cover the checks.
Solve the system of equations.
4x-9y - 2=0
12x-5y+38=0
x equals?
y equals?
Answer:(-4,-2)
Step-by-step explanation:
Marcus saves $13 each week.in how many weeks will he saved at least $100
Line JM intersects line GK at point N. Which statements are true about the figure? Check all that apply.
GNJ is complementary to JNK.
MNL is complementary to KNL.
MNG is complementary to GNJ.
KNJ is supplementary to MNL.
GNM is supplementary to JNK.
Answer:
its 2 and 5
Step-by-step explanation:
Elena always puts 5/12 of the money she makes at work in her savings account. If she made $192 at work, how much money did she put in her savings account?
If she made $192 at work. Then the amount of money she puts in her savings account will be $80.
What is division?Division means the separation of something into different parts, sharing of something among different people, places, etc.
Elena always puts 5/12 of the money she makes at work in her savings account. If she made $192 at work.
Then the amount of money she puts in her savings account will be
→ 5/12 x 192
→ 80
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Your cookie recipe calls for 34 cup of flour. You want to make 3 batches of cookies. Which diagram shows how much flour you need? ...
Please help me i need help please please
Answer:
√(100² + 60²) = √(10,000 + 3,600) = √13,600 = 20√34 = about 116.6 m
116.6 goes into the box.
An architect has a scale drawing of an addition that is to be added to a house with a scale of 1 inch : 2 feet. If the drawing is 6 inches by 10 inches, how big is the addition to the house going to be?
a man deposited$800 in his account at a bank which offers 6% simple interest per annum. how much interest would he receive on the $800 after 9 months?? how long would it take for the $800 to increase to $992
It would take 1.8 years to to get $992 with a 6% simple interest annually.
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time peroid.
Simple Interest = (Principal × Rate × Time) / 100
Given that man deposited $800 in his account at a bank which offers 6% simple interest per annum.
Principal = $800
Rate = 6%
Time = 9
Simple Interest = (Principal × Rate × Time) / 100
Simple Interest = (800× 6× 9) / 100
Simple Interest = 432 dollar
Also, Simple Interest = (Principal × Rate × Time) / 100
$992 = (800 × 6× Time) / 100
992 = 48× Time
Time= 20.6
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write 0.21 as a fraction in simplest form
0.21 as a fraction in simplest form is 21/100.
What is a fraction?In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
In this exercise and scenario, we would convert the given decimal number 0.21 into a fraction by converting it into a percentage as follows;
0.21 = 21/100
Fraction: 21/100 = 0.21.
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Which sample is representative of the population being studied?
A.To learn the in-flight seat preferences of passengers, an airline polls all its business travelers.
B.To learn how many Americans like action movies, a group of students survey people at a downtown movie theater.
C.To learn which of two writers, Charles Dickens or Leo Tolstoy, is more popular among students of literature, Dean surveyed students in one college library.
D.To learn how many students at her school spend more than $10 on books in a month, Mia speaks to every sixth student she meets in the school hallway.
Answer:
D
Step-by-step explanation:
if you take one 10 minute shower a day, how many gallons of water are used
If you take a 10-minute shower each day, you would use approximately 25 gallons of water.
Explanation:The average person in the U.S. uses approximately 100 gallons of water per day, which includes daily activities such as cooking, washing dishes and clothes, flushing the toilet, and bathing. If you take a 10-minute shower each day, you would use a certain amount of water.
To calculate the amount of water used during a 10-minute shower, you would need to know the flow rate of your showerhead. On average, a showerhead has a flow rate of 2.5 gallons per minute. So, multiplying the flow rate by the duration of the shower gives us:
2.5 gallons/minute * 10 minutes = 25 gallons
Therefore, if you take one 10-minute shower a day, you would use approximately 25 gallons of water.
Jonah finished a race in 11.62 seconds. Marco finished the same race in 9.8 seconds. How many seconds faster did Marco finish the race than Jonah?
A. 1.82 seconds
B. 2.22 seconds
C. 10.64 seconds
D. 11.36 seconds
50 points 3/8 x 54
Plz help!I don’t understand
Three different two digit numbers total is 286.what is the smallest of the three numbers
The smallest number is 90.63
We have three different two digit numbers total is 286.
We have to determine the smallest of the three numbers.
A two-digit number and a three-digit number sum up to give a value [tex]x[/tex] which is greater than 1000. Which number is the smallest ?The two digit numbers can be in only in range of 1 to 99.
While a three digit number can be in range from 100 to 1000.
Hence, the two-digit number is smallest.
According to the question -
Let's assume that the three numbers are - x, y and z.
Now -
x + y + z = 286
If we assume three equal two digit numbers will together make 286, than each two digit number will be = [tex]\frac{286}{3}[/tex] = 95.33.
In this case - x = 95.33 y = 95.33 z = 95.33
Now, subtract 95.33 from 100 = 100 - 95.33 = 4.7
Assume, that we take 4.7 out from x, then x will be equal to -
x = 95.33 - 4.70 = 90.63
And divide 4.7 equally to both y and z -
y = z = 97.6
However, you can divide the 4.7 in any ratio among the numbers y and z for getting different numbers. Since we are focused on finding the smallest number of three we will not do it here.
Hence, the smallest number is x = 90.63
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I’m rohmbus ABCD, AB= 14 and AC= 26. Find the area of the rhombus to the nearest tenth.
From the pythagoras theorem AB² = AX² + BX²
14² = 13² + BX²
196 = 169 + BX²
27 = BX²----- > BX=√27
BX = 5.20
The four triangles formed by construction of the diagonals are all congruent since the diagonals are perpendicular bisectors.
Total area of the rhombus is 4 times of ABX triangle
please help! what is the value of K
A recycling bin is in the shape of a right rectangular prism. The bin is 12 meters long, 5 1/2 meters wide, and 6 1/2 meters tall.
What is the volume of the recycling bin?
The volume of the recycling bin will be 429 m³.
What is mean by Rectangle?
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The bin is 12 meters long, 5 1/2 meters wide, and 6 1/2 meters tall.
Now,
Since, We know that;
The volume of right rectangular = Length x Width x Height
Hence, The volume of right rectangular prism = 12 x 5 1/2 x 6 1/2
= 12 x 11/2 x 13/2
= 3 x 11 x 13
= 429 m³
Thus, The volume of the recycling bin will be 429 m³.
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Solve the equation V - E + F = 2 for E
The given equation can be solved in terms of E as E = V + F - 2.
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
The given equation is V - E + F = 2.
It can be solved as,
⇒ V - E + F = 2
⇒ V + F = 2 + E
⇒ E = V + F - 2
Hence, the solution for E can be obtained as E = V + F - 2.
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Final answer:
The equation V - E + F = 2 is solved for E by simple algebraic manipulation, resulting in the solved equation E = V + F - 2.
Explanation:
To solve the equation V - E + F = 2 for E, we need to isolate E on one side of the equation. This can be done through simple algebraic manipulation as follows:
Start with the original equation: V - E + F = 2.Add E to both sides: V + F = E + 2.Now, subtract 2 from both sides to solve for E: E = V + F - 2.The solved equation for E is thus E = V + F - 2.
This equation shows the relationship between the vertices (V), edges (E), and faces (F) in a polyhedron, known as Euler's formula in the context of geometry.
A vet weighs two puppies. The small puppy weighs 4 2/3 pounds. The large puppy weighs 4 2/3 times as much as the small puppy. How much does the large puppy weigh?
Answer:
21
Step-by-step explanation:
Jessica opened an appeal shop five years ago.
there are 5280 feet in a mile. how many feet are in 7/11 of a mile
To find the number of feet in 7/11 of a mile, you multiply 5280 (the number of feet in a mile) by 7/11. The answer is 3360 feet.
Explanation:To calculate how many feet are in 7/11 of a mile, you first have to understand that there are 5280 feet in one mile. If you need to find out the feet in a fraction of a mile, you can multiply this number of feet in one mile by that fraction. In this case, the fraction is 7/11. So, the calculation would go as follows:
5280 feet/mile * 7/11 mile = 3360 feet.
Therefore, 7/11 of a mile is equivalent to 3360 feet.
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Solver the equation 5= w + 1.5.
What is 24% of w plus 50% of y?
Answer:
0.24w+0.5y
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The number of visitors to a certain Web site triples every month. The number of visitors is modeled by the expression 300 •3m, where m is the number of months after the number of visitors was measured. Evaluate the expression for m=minus−1. What does the value of the expression represent in the situation?
The value of expression at m=-1 is 100, so there were 100 visitors 1 months before the number of visitors was measured
A survey asked 10 boys and 10 girls how many hours they spent playing video games the previous week. The number of hours are given in the line plots.
Two line plots one above the other, both are labeled from two to twenty by twos. The top line plot is labeled Boys and it has three Xs above ten, two Xs above fifteen and one X above eight, twelve, thirteen, fourteen and twenty. The bottom line plot is labeled Girls and it has three Xs above four, two Xs above ten and one X above three, six, seven, eight and fifteen.
Select from the drop-down menus to complete each statement.
The range of boys and girls is 12 hours.
The median for boys is 12.5 hours
The median for girls is 6.5 hours.
What is a range in a set of data?The range is the difference between the highest value and the lowest value of a given set of data.
We have,
From the line plot,
Boys:
Hours Number of boys
1
2
3
4
5
6
7
8 x
9
10 x x x
11
12 x
13 x
14 x
15 xx
16
17
18
19
20 x
Girls:
Hours Number of girls
1
2
3 x
4 xxx
5
6 x
7 x
8 x
9
10 xx
11
12
13
14
15 x
Now,
Range:
Boys:
= Longest time - Shortest time
= 20 - 8
= 12 hours
Girls:
= 15 - 3
= 12 hours
Median:
Boys:
= 8, 10, 10, 10, 12, 13, 14, 15, 15, 20
= 12.5
Girls:
= 3, 4, 4, 4, 6, 7, 8, 10, 10, 15
= 6.5
Thus,
The range is the same for both boys and girls.
The median for boys is 12.5.
The median for girls is 6.5.
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The complete question:
Find the range and median for both boys and girls.
Ben and Angela were riding their bicycles one afternoon. They kept track of their own cycling rates, as shown in the graphs below.
The student's question pertains to the mathematical analysis of motion, specifically through the interpretation of velocity versus time and position versus time graphs related to cycling activities and races.
Explanation:The question involves interpreting graphs that represent the velocity versus time and position versus time of two individuals riding bicycles and a race between friends. Students in middle school are often introduced to concepts of speed, velocity, and displacement and are tasked with analyzing graphs to understand these concepts in a practical scenario. The problem sets mentioned, including the velocity-time graphs, position-time graphs, and measurements of motion through various activities such as biking or collision events, are all connected to the mathematical analysis of motion in physics. By understanding how to read these graphs, students can determine factors such as constant velocity, average speeds, displacement, and the outcomes of simple collisions. These skills are essential in developing an understanding of kinematics, which is a branch of classical mechanics that describes the motion of points, objects, and systems of bodies without considering the causes of motion.