Answer:
measure of each base angle = 80 each angle
measure of vertex angle = 20
Step-by-step explanation:
x=base angle
2x+ x/4= 180
Multiply everything by 4 to eliminate the fraction
8x+x = 720
9x=720
x=80
80/4=12
Final answer:
In an isosceles triangle where the vertex angle is one-fourth the measure of a base angle, using the properties of a triangle and the Triangle Angle Sum Theorem, we find each base angle measures 80 degrees and the vertex angle measures 20 degrees.
Explanation:
Given an isosceles triangle, where the vertex angle is one-fourth the measure of a base angle, we can find the measures of the angles using the properties of a triangle. From the Triangle Angle Sum Theorem, we know that the sum of the angles in any triangle is 180 degrees.
Let's denote the measure of the base angle as 'b'. Since the triangle is isosceles, both base angles are equal, so we have 2b for the sum of the base angles. The vertex angle, being one-fourth of a single base angle, is ¼×b = b/4. According to the Triangle Angle Sum Theorem, we can write:
2b + (b/4) = 180
Multiplying through by 4 to clear the fraction gives us:
8b + b = 720
Combining like terms:
9b = 720
Dividing both sides by 9 gives us:
b = 80
Now that we have the measure of the base angle, we can find the measure of the vertex angle:
measure of vertex angle = b/4
Substitute b = 80 into the equation:
measure of vertex angle = 80/4
measure of vertex angle = 20
So, the measure of each base angle is 80 degrees, and the measure of the vertex angle is 20 degrees.
Convert 118.6% to an improper fraction in lowest terms
Answer: 593/500
Step-by-step explanation: To write a percent as a fraction in lowest terms, first remember that a percent is a ratio that compares a number to 100.
So here, 118.6% can be written as the ratio 118.6 to 100 or 118.6/100.
To write 118.6/100 in lowest terms, we first will need to multiply the numerator and the denominator by 10 to remove the decimal point. When we do this, we get the equivalent fraction 1186/1000.
Now, we can divide the numerator and the denominator by the greatest common factor of 1186 and 100 which is 2 and we get the equivalent fraction 593/500.
Therefore, 118.6% can be written as the improper fraction 593/500.
Austin has two Marvel posters he wants to hang on the wall in his bedroom. The wall
is 16.5 feet wide and each poster is 5 3/4 feet wide. Austin wants to place the
posters on the wall so that the distance from the edge of each poster to the nearest
edge of the wall is the same as the distance between the posters, as shown in the
diagram below. Which choice below represents that distance?
Answer:
Answer is 1 2/3 pretty sure thats it bc i just took the same quiz and got that question right.
Step-by-step explanation:
Which of the following expressions are equivalent to 4^-3/4^-8?
Answer:
A. [tex]\frac{4^{8} }{4^3}[/tex]
D. [tex]4^{5}[/tex]
Step-by-step explanation:
We have to calculate to find the result -
The expression is = 4^(-3)/4^(-8)
According to the indices rule, the power will be deducted if it is a division.
Therefore, [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{m-n}[/tex]
Using that formula,
= [tex]4^{-3-(-8)}[/tex]
= [tex]4^{-3+8}[/tex]
= [tex]4^{5}[/tex]
Therefore, the answer choice D is the option, and the answer is 4^5.
Option A is also correct. Because we can find 4^5 with the help of that option.
[tex]\frac{4^8}{4^3}[/tex]
= [tex]4^{5}[/tex]
Alternative way,
4^(-3)/4^(-8)
= 4^(-3+8)
= 4^(8-3)
= 4^8/4^3
In the is way, we can also find option A is correct.
Answer:
A&D
1 & 4
[tex]\frac{4^8}{4^3}[/tex] and [tex]4^{5}[/tex]
Step-by-step explanation:
edge 2021
albert needs 30 meters of wood to build a large wooden frame> He bought three different lengths of wood measuring 12.5, 11.43 and 7.244 metere. After he builds the frame, how many meters will albert have left?
Answer:
After Albert builds the frame, 1.174 meters of wood will be left.
Step-by-step explanation:
Here, the total length of wood required to build wooden frame = 30 meters
The length of the wooden pieces collected are:
First piece = 12.5 m
Second Piece = 11.43 m
and Third Piece = 7.244 m
Now, the total length of wood all pieces combined
= Length of (First + second + third ) Piece
= 12.5 m + 11.43 m + 7.244 m = 31.174 m
So, the combined length of all wooden pieces = 31.174 m
Now, the left over length = Total wood collected - The length required
= 31.174 m = 30 m = 1. 174 m
Hence, after he builds the frame, 1.174 meters wood will be left.
Given the domain {-4, 0, 5}, what is the range for the relation 12x + 6y = 24?A.{12, 4, -6}B.{-4, 4, 14}C.{2, 4, 9}D.{-12, -4, 6}
Answer:
{12, 4, -6}
Step-by-step explanation:
The relation is given by the equation as 12x + 6y = 24 ........... (1)
Now, the domain of this function is {-4, 0, 5}
We have to find the range of this function corresponding to the given domain.
Now, for x = - 4,
12(-4) + 6y = 24 {From equation (1)}
⇒ 6y = 72
⇒ y = 12
Now, for x = 0,
12(0) + 6y = 24 {From equation (1)}
⇒ 6y = 24
⇒ y = 4
Now, for x = 5,
12(5) + 6y = 24 {From equation (1)}
⇒ 6y = -36
⇒ y = -6
Hence, the range for the relation is {12, 4, -6} (Answer)
If there was 10 pine trees & 2 ash trees how many more pine trees were there? Answer is 8 but need to know how to show the work??
Answer:
The number of pine tress more than the number of ash trees is 8 .
Step-by-step explanation:
Given as
The number of pine trees = 10
The number of ash trees = 2
Let The number of pine tree more than that of ash tress = x
So, The number of ash trees + x = 10
Or, 2 + x = 10
I.e x = 10 - 2
∴ x = 8
So, The pine trees is 8 more than the ash trees
Hence The number of pine tress more than the number of ash trees is 8 . Answer
If I graduated highschool in 2017 what year was I in 5th grade
Answer:
the year 2010
Step-by-step explanation:
since the end of high school is 12th grade, you have to numbers. 12, and 5.
subtract 5 from 12 and you get seven. subtract seven from 2017, and you get 2010
You were in 5th grade in the year 2010.
Explanation:To determine what year you were in 5th grade, you can subtract 7 from the year you graduated high school. In this case, if you graduated in 2017, you subtract 7to get 2010. Therefore, you were in 5th grade in the year 2010.
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57 first-year teachers and 19 experienced teachers attended a school staff meeting meeting. What percentage of the teachers in the meeting were first-year teachers?
Write your answer using a percent sign (%).
75% of the teachers were first-year teachers
Step-by-step explanation:
the formula for percentage will be used for the problem
The percentage is given by:
[tex]Percentage=\frac{Quantity}{Total}*100\\[/tex]
Here
Total teachers = 57+19 = 76
First-year teachers = 57
So,
[tex]Percentage\ of\ first\ year\ teacher = \frac{57}{76}*100\\=0.75*100\\=75\%[/tex]
Hence, 75% of the teachers were first-year teachers
Keywords: Percentage, Percent
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Is 2 yd greater than 200 cm
Answer:
no
Step-by-step explanation:
1 foot is 30.48 cm
So 1 yard is 3(30.48 cm) = 91.44 cm (less than 100 cm = 1 meter)
So 2 yards is about 183 cm, less than 200 cm
12.8 rounded to the nearest whole number
Answer:
13
Step-by-step explanation:
you're kidding, how do you not know this but I mean I'm here to help even if you're not the brightest
Answer:
the answer is 13. because you round up
Betech Inc. has $50,000 in its bank account and $3,000 worth of goods in its warehouse. What is this amount ($53,000) known as in accounting
terms?
A slow variable
B. flow variable
C. stock variable
D. flock variable
Answer:
(C) Stock Variable
Step-by-step explanation:
With the $50,000 in the bank, it is assumed the value is earnings from stock. $3,000 worth of goods in the warehouse also make up the stocks hence the $50000 plus $3000 to make up $53,000 stock variable
Aquarius is an underwater ocean laboratory located in the Florida keys national marine sanctuary. Solve the equation 31/25x = -62 to find the value of x.
Answer:
x=-50
Step-by-step explanation:
31/25x=-62
x=-62/(31/25)
x=(-62/1)(25/31)
x=--1550/31
x=-50
Answer:
X = 50
Step-by-step explanation:
31/25 x = 62
25 times 31/25 x = 62 times 25
31x = 1550
31/31 = 1550/31
x = 50
Nathaniel is saving money to buy a new graphics card for his computer that
costs $260.
If he is saving $18 a month and already has $134, in how many
more months will he have enough money for the graphics card?
Answer:
7 months
Step-by-step explanation:
260=134+18m
126=18m
7=m
Answer: 7 months.
$18 × 7 months = $126
$134 + $126 = $260
If y varies directly as x, and y is 400 when x is r and y is r when x is 4 what is the numeric constant of vanation in this relation
Answer:
y = 10*x
Step-by-step explanation:
y = kr --> 400
r = 4k
400 = k (4k) = 4k^2
k^2 = 400/4 = 100
k = sqrt(100) = 10
k = 10
Order these numbers from least to greatest 3% 1/50 0.046 1/50
Answer:
1/50 then 3% then 0.046
Step-by-step explanation:
For a scientific Experiment, A physicist must make sure that the temperature of a metal at 0°C gets to no colder than -80°C. the physicist changes the metals temperature at a steady rate of -4°C per hour. Let t represent the temperature in degrees Celsius. Write an inequality. use the fact that the rate of change in temperature times the number of hours equals the final temperature.
Answer:
- 4 h ≥ - 80
Step-by-step explanation:
The temperature of the metal is 0°C and the gets to no colder than - 80°C.
If the temperature is decreasing at the rate of - 4°C per hour, then the temperature after h hours will be t = 0 + (- 4) h which will not be less than - 80°C.
So the inequality that models the situation is 0 + (- 4) h ≥ - 80
⇒ - 4 h ≥ - 80 (Answer)
Final answer:
The inequality to ensure that the temperature of the metal does not fall below -80°C as it drops steadily at -4°C/hour is 0 - 4h ">= -80. This represents the highest number of hours (h) the physicist can allow before the temperature reaches the limit.
Explanation:
The student has asked to write an inequality based on a physicist's experiment where a metal's temperature decreases at a steady rate of -4°C per hour and should not get colder than -80°C. Starting at 0°C, the relationship between time (in hours) and temperature can be represented mathematically.
To express this as an inequality, we can set up a relationship where the temperature (t) after a certain number of hours (h) is no less than -80°C. Since the temperature is decreasing at -4°C per hour, we can write the inequality as:
t ≥ -80
Where t = 0 + (-4 × h), and h represents the number of hours passed.
Substituting the expression for t into the inequality:
0 - 4h ≥ -80
This inequality tells us that regardless of how many hours go by at this rate, the temperature of the metal should remain higher than -80°C.
Fiona wants to know the average weight of the animals in her town’s zoo. She finds the weight of one random animal from each pen or aquarium. The mean of her data is 145.4 pounds, and the median of her data is 106 pounds. Which prediction matches this data?
Answer:
A. About half of the animals at the zoo weigh less than 106 pounds
B. The average weight of al animals at the zoo is about 145.50
Step-by-step explanation:
The median weight is 106 pounds and the average weight of the animals at the zoo are 145.40
a letter is chosen from the word line and another is chosen from the word ride find the probability that the two letters chosen are the same
Answer:
2/16 or 1/8 or 12.5%
Step-by-step explanation:
2 of the outcomes are the same and it's out 16 total outcomes, so you would do 2 divided by 16 which is 12.5% or as a a fraction 2/16 or as a simplified fraction 1/8.
What is the value - 3/2 ( 24 - 5 1/4 ) ?
A) - 44
B) - 41 1/3
C) - 28
D) 30 2/3
Answer:
-225/8
Step-by-step explanation:
-3/2(24-5 1/4)
5 1/4=21/4
-3/2(24-21/4)
-3/2(96/4-21/4)
-3/2(75/4)
-225/8
Alexandra has 127 flowers. She puts
the same number of flowers in each
of her vases. How many flowers will
be left over?
How many vases are there?
The number of flowers in each vase is 31 and the number of flowers left over is 3.
Given that, Alexandra has 127 flowers and 4 vases.
What is the division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Here,
The same number of flowers in each of her vases =Total number of flower/Number of vases
= 127/4
Now, 4|127|31
124
_______
3
Number of flowers left over =3
Therefore, the number of flowers in each vase is 31 and the number of flowers left over is 3.
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"Your question is incomplete, probably the complete question/missing part is:"
Alexandra has 127 flowers and 4 vases. She puts the same number of flowers in each of her vases. How many flowers will be left over?
An construction company poured a cylindrical shaped concrete column 15 feet long with a radius of 3 feet. How much concrete did it take to make the column, in terms of π?
Answer:
[tex]135\pi\ ft^3[/tex]
Step-by-step explanation:
we know that
The volume of a cylinder (concrete column) is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]r=3\ ft\\h=15\ ft[/tex]
substitute
[tex]V=\pi (3)^{2}(15)[/tex]
[tex]V=135\pi\ ft^3[/tex]
Please answer asap ok its only 15 points but please
Answer: 66.5
Step-by-step explanation:
divide the figure into a triangle (the top part) and a rectangle (the lower part)
To find the area of the rectangle use the formula:
length times width = area
(LW=A)
8 times 7 is 56 so the area of the rectangle is 56.
the formula for area of a triangle is base times height halfed
(BH)1/2
the height is 3 because the height of the entire figure is 11 so subtract the height of the rectangle from that (8) to get 3.
the base is 7 so
7(3)(1/2) is 10.5
add up the two areas together (10.5+56) to get 66.5 cm squared.
answer: 66.5
declan ran 509 meters in 5 minutes . calculate the unit rate
Answer:
101.8 meters in 1 minute
Step-by-step explanation:
509/5=101.8
If x varies directly as y, and x=4 when y=15, find x when y=36.
Answer:
x = 9.6
Step-by-step explanation:
Given that x varies directly as y then the equation relating them is
x = ky ← k is the constant of variation
To find k use the condition x = 4 when y = 15
k = [tex]\frac{x}{y}[/tex] = [tex]\frac{4}{15}[/tex]
x = [tex]\frac{4}{15}[/tex] y ← equation of variation
When y = 36, then
x = [tex]\frac{4}{15}[/tex] × 36 = [tex]\frac{144}{15}[/tex] = 9.6
The problem is related to direct variation and can be solved using the formula x=ky which expresses the direct proportionality of x and y. The constant of variation k is found using the values of x and y given and is applied to find the new x value when y=36.
Explanation:The problem discussed here is related to the concept of direct variation or direct proportionality. When we say that 'x varies directly as y', it means that x is proportionally related to y, and that relationship can be expressed by the equation x = ky, where k is the constant of variation.
In this case, you are given that x = 4 when y = 15. So, you can find the constant of variation 'k' by dividing x by y. Hence, k = x/y = 4/15.
Now, you are asked to find the value of x when y = 36. Given that x = ky, simply substitute k = 4/15 and y=36 into this equation. Therefore, x = (4/15)*36 which will yield the value of x.
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Jenna bought 5 reams of paper at the store for a total of $21 . The tax on her purchase was $1 . Write a equation and solve to find the price of each ream of paper
Answer:
The equation needed is [tex]\textrm{Cost of 1 ream of paper} = \frac{20}{5} [/tex]
The cost per ream of paper = $4
Step-by-step explanation:
Here, the cost of 5 reams of paper = $ 21
The tax on her purchase = $1
So, the actual cost of 5 reams of paper = Total Cost paid - Tax amount
= $ 21 - $ 1 = $20
So, the actual cost of 5 reams of the paper is $20.
Now, to find out the cost of 1 ream of paper:
[tex]\textrm{Cost of 1 ream of paper} = \frac{\textrm{Total amount paid for 5 reams}}{\textrm{ 5}} \\= \frac{20}{5} = 4[/tex]
= $4
Hence, the cost of each ream of paper = $ 4.
Please answer for brainiest
Which of the following is the probability against drawing a 7 from a standard deck of 52 cards on the first try?
97%
89%
92%
77%
Answer:
92%
Step-by-step explanation:
there are 4 cards of "7"
52-4=48
48÷52×100=92.307...%
Solving Problems with Unit Rates - Item 1097
Question
A car travels at a constant speed.
What is the car's speed between checkpoints, expressed as a unit rate?
Use the information given in the picture.
Checkpoint A
Checkpoint B
Time: 1:00p.m.
Time: 3:00 pm
Total Miles Driven: 120
Total Miles Driven: 208
CHECK
miles per hour
Answer:
44 miles per hour
Answer:
44 miles per hour
Step-by-step explanation:
For the last five months, Vivian borrowed ($35 from her brother to pay for her gym
membership. Vivian just received a raise and wants to repay the money she borrowed from
her brother. Vivian can only afford to repay $25 each month to her brother. How many
months will it take Vivian to repay her brother the money she borrowed?
Answer:7 months
Step-by-step explanation:
$35 x 5 months = $175
175 / 25 = 7
Answer:
7 months
Step-by-step explanation:
Write y+7=4(x+2) in standard form.
Answer:
[tex]1 = 4x -y[/tex]
Step-by-step explanation:
Distribute the 4
[tex] y + 7 = 4x + 8[/tex]
Subtract the 7
[tex]y = 4x - 1[/tex]
Subtract y and add 1
Answer:
y = 4x - 1
Step-by-step explanation:
Distribute the 4
y + 7 = 4x + 8
Subtract the 7
y = 4x - 1
how do you factor
- 8x2 + 28x +60
Answer:
4 • (x - 5) • (2x + 3)
Step-by-step explanation:
Step-1 : Multiply the coefficient of the first term by the constant 2 • -15 = -30
Step-2 : Find two factors of -30 whose sum equals the coefficient of the middle term, which is -7 .
-30 + 1 = -29
-15 + 2 = -13
-10 + 3 = -7 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and 3
2x2 - 10x + 3x - 15
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (x-5)
Add up the last 2 terms, pulling out common factors :
3 • (x-5)
Step-5 : Add up the four terms of step 4 :
(2x+3) • (x-5)
Which is the desired factorization