Answer:
the possible answers are 80 and 140
Step-by-step explanation:
since one angle has a measure of 20 in isosceles triangle let this be vertex angle and other two as base angles then
in isosceles triangle base angles must be equal to each other so
x+x+20 = 180
2x+20 = 180
2x = 160
x=80
so the base angles are equal to 80
now if you suppose 20 as base angle then other base angle should also be 20 since it is an isosceles triangle and the vertex angle can be calculated as
20+20 + x = 180
x = 140
Write a linear equation in y=mx+b form to represent the scenario.Todd has $450 in his savings. He withdraws $10 per week.
The linear equation in y=mx+b form that represents this scenario is:
y = -10x + 450.
What is a linear equation?
A linear equation is a mathematical equation in which the highest power of the variable(s) is one.
ax + b = 0
or
y = mx + b
where a, b, and m are constants and x and y are variables. In the first form, x is a variable and a and b are constants. In the second form, x and y are variables, m is the slope of the line, and b is the y-intercept.
Let x be the number of weeks that have passed since Todd started withdrawing money from his savings account. Initially, Todd had $450 in his savings, so the amount of money he has left after x weeks is:
450 - 10x
The rate of change of the amount of money Todd has with respect to time is -10, since he is withdrawing $10 per week. Therefore, the slope of the line that represents this situation is -10.
The y-intercept represents the initial amount of money Todd had in his savings, which is $450. Therefore, the linear equation in y=mx+b form that represents this scenario is:
y = -10x + 450
where y is the amount of money Todd has in his savings after x weeks.
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What is the area of the real object that the scale drawing models? Scale factor. 1:5 Area = 10 square cm Scale drawing Real object
Answer:
D. 50 square centimeters
Y=3x^2-4x-1 what is the sign of leading coefficient
Answer:The leading term in a polynomial is the term with the highest degree.
Step-by-step explanation:
Step-by-step explanation:
y = 3 x^2 - 4 x - 1
leading coefficient is 3 and its sign is ' + ' or positive
THINK
12. SOLVE
EXPLAIN
SHORT RESPONSE During a vacation,
Alice went fly-fishing. She rented a
driftboat.
Rick's Rental
fishing rod
driftboat
$12
$8/hour
If she spent a total of $96, write and
solve an equation to find how many
hours she rented the boat.
Answer:
The equation to represent the situation is 96 = 12 + 8x and the number of hours she rent the boat is 10.5 hours.
How to find the number of hours she rented the boat?During a vacation, Alice went fly-fishing. She rented a drift boat. Rick's Rental fishing rod drift boat cost $12 plus $8/hour.
She spent a total of 96 dollars. The equation to solve the situation can be calculated as follows:
Hence,
y = 12 + 8x
where
y = total costx = number of hours spentTherefore,
96 = 12 + 8x
8x = 96 - 12
8x = 84
divide both sides by 8
x = 84 / 8
x = 10.5 hours
Therefore,
hours she rented the boat = 10.5 hours
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Investing $1,000 at a 5% annual interest rate for 6 years, compounded every two months,
yields $1,348.18. Without doing any calculations, rank these four possible changes in order
of the increase in the interest they would yield from the greatest increase to the least
increase:
• Increase the starting amount by $100.
• Increase the interest rate by 1%.
• Let the account increase for one more year.
• Compound the interest every month instead of every two months.
Once you have made your predictions, calculate the value of each option to see if your
ranking was correct.
Answer:
Step-by-step explanation:
Ranking:
Compound the interest every month instead of every two months.
Increase the interest rate by 1%.
Let the account increase for one more year.
Increase the starting amount by $100.
Calculations:
If the interest is compounded monthly instead of every two months, the final value would be $1,357.36, which is an increase of $9.18 compared to the original value.
If the interest rate is increased to 6%, the final value would be $1,411.58, which is an increase of $63.40 compared to the original value.
If the account increases for one more year at the same interest rate, the final value would be $1,435.09, which is an increase of $86.91 compared to the original value.
If the starting amount is increased by $100, the final value would be $1,421.61, which is an increase of $73.43 compared to the original value.
Read the story. A group of sixth-grade students volunteered to pick up garbage at Elver Park for Earth Day. To make it more fun, they set up a contest to see whether girls or boys could pick up the most garbage. The girls won, picking up 8 pieces of garbage for every 5 pieces the boys picked up. Pick the diagram that models the ratio in the story.
We may conclude after answering the presented question that This ratio indicates that the guys picked up 5 pieces of rubbish for every 8 pieces of rubbish picked up by the girls.
what is ratio?In mathematics, ratios demonstrate how frequently one number is contained in another. For example, if there are 8 oranges and 6 lemons in a fruit plate, the ratio of oranges to lemons is 8 to 6. In a similar vein, the orange-to-whole-fruit ratio is 8, whereas the lemon-to-orange ratio is 6:8. A ratio is an ordered pair of integers a and b represented as a / b, where b is not zero. A ratio is an equation that equates two ratios. For example, if there is one male and three girls (for every boy she has three daughters), 3/4 are girls and 1/4 are boys.
The ratio in the narrative is represented by the following diagram:
Girls : Boys=8:5
This indicates that the guys picked up 5 pieces of rubbish for every 8 pieces of rubbish picked up by the girls.
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each classroom has 6 rows of 5 desks. how many desks are thre in 45 classrooms?
There are 1,350 desks in 45 classrooms that each have 6 rows of 5 desks.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Each classroom has 6 rows of 5 desks.
So the total number of desks in one classroom.
= 6 rows x 5 desks per row
= 30 desks
To find the total number of desks in 45 classrooms, we can multiply the number of desks in one classroom by the number of classrooms.
= 30 desks per classroom x 45 classrooms
= 1,350 desks
Therefore,
There are 1,350 desks in 45 classrooms that each have 6 rows of 5 desks.
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Given sin(a) = 7/9 and a is in quadrant I, find the exact value of sin(a/2).
Note: You are not allowed to use decimals in your answer.
Answer:
We can use the half-angle formula for sine to find the exact value of sin(a/2) in terms of sin(a):
sin(a/2) = ±√[(1 - cos(a))/2]
where the ± sign depends on the quadrant of a/2.
To use this formula, we first need to find cos(a). We can do this using the identity:
sin^2(a) + cos^2(a) = 1
Substituting sin(a) = 7/9, we get:
(7/9)^2 + cos^2(a) = 1
Simplifying and solving for cos(a), we get:
cos(a) = ±4/9
Since a is in quadrant I, we take the positive value of cos(a):
cos(a) = 4/9
Now we can use the half-angle formula for sine to find sin(a/2):
sin(a/2) = ±√[(1 - cos(a))/2]
Substituting cos(a) = 4/9, we get:
sin(a/2) = ±√[(1 - 4/9)/2]
Simplifying, we get:
sin(a/2) = ±√(5/18)
Since a is in quadrant I, a/2 is also in quadrant I, so we take the positive value of sin(a/2):
sin(a/2) = √(5/18)
Therefore, the exact value of sin(a/2) is √(5/18)
Please help me w my trig
Answer:
Assuming that the expression is asking for the tangent of 1 radian, we can use the tangent half-angle formula to find an exact value:
tan(1) = 2tan(1/2) / (1 - tan^2(1/2))
To find tan(1/2), we can use the half-angle formula for tangent:
tan(1/2) = sin(1) / (1 + cos(1))
We cannot simplify this expression any further without a calculator. Therefore, the exact value of tan(1) is:
tan(1) = 2sin(1) / (cos(1) - cos^2(1) + 1)
Again, we cannot simplify this expression any further without a calculator.
For the second expression, we are asked to find the value of:
tan(arctan(6/4))
By definition, tan(arctan(x)) = x for all x, so we have:
tan(arctan(6/4)) = 6/4 = 3/2
Therefore, the exact value of the expression tan(6/4) is 3/2.
change 3 5 to a decimal fraction
Answer:
7/20
its the answer to your question
PLEASE PLEASE HELP ME!!!!!!!!
The trapezoid A’B’C’D is a dilation of the trapezoid ABCD. What is the scale factor of the dilation?
Simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.
PLEASE LOOK AT PICTURE!!!!!!
All four ratios are equal to 1/3, the scale factor of the dilation is 1/3
Describe Scale factor?In mathematics, a scale factor is a ratio that describes how much larger or smaller an object or shape is in comparison to its original size. In particular, a scale factor is often used to describe the effect of dilation on an object.
Dilation is a transformation in which an object is enlarged or reduced uniformly in all directions from a fixed point known as the center of dilation. The scale factor for dilation is the ratio of the length of the image to the length of the pre-image.
For example, if a square has a side length of 4 units and is dilated by a factor of 2, the resulting image will have a side length of 8 units. In this case, the scale factor for dilation is 2.
More generally, if an object is dilated by a factor of k, then the length of any given segment in the image will be k times the length of the corresponding segment in the pre-image. Thus, the scale factor for dilation is simply k.
To find the scale factor of the dilation, we need to find the ratio of the corresponding side lengths of the trapezoid A'B'C'D' to the side lengths of trapezoid ABCD.
We can start by finding the length of each side of trapezoid ABCD:
AB = √[(9-(-3))² + (3-0)²] = √(144+9) = √153
BC = √[(9-9)² + (9-3)²] = 6
CD = √[(-3-9)² + (3-9)²] = √(144+36) = √180
DA = √[(-3-(-3))² + (3-0)²] = 3
Next, we can find the length of each corresponding side of trapezoid A'B'C'D':
A'B' = √[(3-(-1))² + (1-0)²] = √(16+1) = √17
B'C' = √[(3-3)² + (3-1)²] = 2
C'D' = √[(-1-3)² + (1-3)²] = √(16+4) = √20
D'A' = √[(-1-(-3))² + (1-0)²] = √4 = 2
Finally, we can find the ratio of the corresponding side lengths of the trapezoid A'B'C'D' to the side lengths of trapezoid ABCD by dividing the lengths of the corresponding sides:
[tex]\frac{A'B'}{AB} =\frac{\sqrt{17} }{153} \\\frac{B'C'}{BC} =\frac{2}{6}=\frac{1}{3} \\\frac{C'D'}{CD} =\frac{\sqrt{20} }{80} =\frac{\sqrt{45} }{445} =\frac{\sqrt{5} }{3\sqrt{5} } =\frac{1}{3} \sqrt{5} \\\frac{D'A'}{DA} =\frac{2}{3}[/tex]
Since all four ratios are equal to 1/3, the scale factor of the dilation is 1/3.
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Leslie is making these two recipes. Which takes
longer to make, the strawberry bread or the
spaghetti sauce? How many minutes longer
Based on the information in the image, we can infer that the recipe that takes the longest is the one for spaghetti sauce.
How to identify the recipe that takes the longest?To find the recipe that takes the longest we must take into account the information of each of the recipes. In this case, we have preparation time and cooking time. To know the total time we must add these two values.
Additionally, we must establish a magnitude to be able to relate all the values, in this case the most appropriate would be the number of minutes.
So, the preparation of the spaghetti sauce takes 10 minutes and its cooking takes an hour and a half, that is, 90 minutes. On the other hand, strawberry bread takes 20 minutes to prepare and 55 to cook:
10 + 90 = 100 minutes20 + 55 = 75 minutesAccording to the above, the spaghetti sauce takes longer because it takes 25 minutes longer than the strawberry bread.
Note: This question is incomplete. Here is the complete information:
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Which expression is NOT equivalent to the other 3 expressions?
A) 5z + z - 1
B) 5z - 1 - z
C) 7z - (1 + z)
D) (5z - 1) + z
11 points.
I need to know how to solve this problem and the answer of it.
Answer:
P = 8g⁵ - 15g + 14
Step-by-step explanation:
This question has expressions to represent the side lengths of a triangle.
The side lengths are:
-8g⁵ - 7g
10g⁵ - 8g
6g⁵ + 14
They ask for a simplified expression for the perimeter. The purpose of this question is to combine like terms.
P = s₁ + s₂ + s₃ where s is a side length of the triangle.
P = (-8g⁵ - 7g) + (10g⁵ - 8g) + (6g⁵ + 14)
P = 8g⁵ - 15g + 14
HELPPPPP PLEASEEEEEE
18. A business invests $10,000 in an
account that earns 3.2% interest
that is compounded quarterly.
What type of function best
represents the growth of the
investment?
◻ linear
◻ quadratic
◻ exponential
19. What is the value of the account
described in Item 18 after 5 years?
Round to the nearest cent.
Answer: Exponential & $11,709.83
Step-by-step explanation:
The growth of the investment can be represented by an exponential function because the interest is being compounded quarterly, which means that the interest is being added to the account balance and the account balance is growing exponentially over time.
The formula for the future value of an investment with continuous compounding is:
A = P e^(rt)
Where A is the future value, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate expressed as a decimal, and t is the time in years.
In this case, the principal investment is $10,000, the annual interest rate is 3.2%, and the interest is compounded quarterly, so the quarterly interest rate is 3.2%/4 = 0.8%. The time period is 5 years, so t = 5.
The formula for the future value of an investment with quarterly compounding is: A = P (1 + r/n)^(nt)
Where n is the number of compounding periods per year, which is 4 in this case.
Substituting the values, we get:A = $10,000 (1 + 0.032/4)^(4*5) = $11,709.83
Therefore, the value of the account after 5 years is $11,709.83 rounded to the nearest cent.
48805 rounded to the nearest thousand
Answer: 49,000
48805 is greater than 48500, so it rounds to 49,000
If sin a = -1/4 and π < a <3pi/2 and cos b= 5/9 and 0 < b < pi/2, find the exact value of the following. Show all your work and simplify your answers.
sin(a + B) =
Answer:
Step-by-step explanation:
evaluate [(- 5/4) ^ - 2] ^ 3
Answer:
4096/15625 or
0.262144 or
(4/5)^6
HELP ASAP WILL GIVE 100 PTS AND BRAINLYEST FOR CORRECT ANSWER
the answers and questions are all in the attachment box
Answer:
Picture number 1: y=1/2x+2
Picture number 2: y=3x-5
Picture number 3 : y=-x
Picture number 4: y=(x+3)^2-2
Any help please? i cant seem to understand it
The no of people take more than 19 mins are above 50%
1. Break it down: Divide the topic into smaller subtopics or concepts. This can make it easier to understand and digest each piece of information.
2. Research: Look up definitions, explanations, or examples related to the terms or concepts you're trying to understand. This can help clarify any confusion or uncertainty.
3. Take notes: Write down important information, key points, or definitions as you research. This can help you remember and better understand the material.
4. Ask questions: If you're still unsure about certain aspects, don't hesitate to ask for help or clarification from a teacher, tutor, or friend.
5. Practice: Apply what you've learned to related problems or questions. Practicing can help reinforce your understanding
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A cruise ship weighs 3.83×107 kilograms. A horse weighs 7.1×102 kilograms. Approximately how many horses weigh as much as one cruise ship?
Give your answer in scientific notation using only whole numbers.
5.394366197183099*10^4
Step-by-step explanation:1. Write the number as a decimal 53943.66197183099
2. Make it a new number between 1 and 10
Move the decimal point to make 53943.66197183099 a new number between 1 and 10. Because our number is greater than 10, we move the decimal point to the left. Drop any trailing zeros and place the decimal point after the first non-zero digit. Keep track of how many times we move the decimal point.
53943.66197183099 -> 5.394366197183099
Our new number is 5.394366197183099. We moved the decimal point 4 times.
Use a calculator and get the values from both equations, 3.83×10^7 and 7.1×10^2 then put the first value 38300000 into a calculator, then divide 38300000/710 and you will get the value 53,943.66197183099. Then run that through a scientific notion calculator to get 5.394366197183099*10^4.
There you go.
Approximately 54,000 horses weigh as much as one cruise ship.
Explanation:To find out how many horses weigh as much as one cruise ship, we need to divide the weight of the cruise ship by the weight of a horse. In scientific notation, the weight of the cruise ship is 3.83x107 kg and the weight of a horse is 7.1x102 kg.
Dividing the weight of the cruise ship by the weight of a horse, we get:
(3.83x107 kg) ÷ (7.1x102 kg) = 5.4x104
So approximately 54,000 horses weigh as much as one cruise ship.
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In 10-12, use the table.
10. Higher Order Thinking Complete the
table. Show some different ways that a
rectangular prism can have a volume of
12 cubic units.
11. Use Patterns and Structure Look across
each row of the table. What pattern do
you see?
12. Use the table to help. How many unit
cubes are needed to make a model of
a rectangular prism that is 4 units long,
10. The table is mentioned below 11. the product of the number of cubes long and the number of cubes wide is equal to 12. 12. The number of unit cubes needed to make this model is 24.
Describe Cubes?A cube is a three-dimensional geometric shape that has six square faces, 12 edges, and eight vertices (corners). All six faces of a cube are congruent squares, and all edges have the same length. The cube is a regular polyhedron, meaning that it has congruent faces and angles, and its symmetry group is the group of rotations and reflections that preserve the cube's structure. Cubes are widely used in geometry, mathematics, and physics because of their symmetry and regularity, and they also have practical applications in fields such as architecture and engineering.
10. Different ways a rectangular prism can have a volume of 12 cubic units:
Number of Cubes Long Number of Cubes Wide Number of Cubes Tall
1 1 12
2 2 1.5
2 3 1
3 2 2
4 3 1
6 2 1
11. The pattern we see is that for each row, the product of the number of cubes long and the number of cubes wide is equal to 12.
12. A rectangular prism that is 4 units long, 2 units wide, and 1 unit tall would have a volume of 8 cubic units. To make a rectangular prism with a volume of 12 cubic units, we can add another layer of 4 cubes to the top of this prism. Therefore, a rectangular prism that is 4 units long, 2 units wide, and 2 units tall would have a volume of 12 cubic units. The number of unit cubes needed to make this model is 24.
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State an equation you could use to find the value of X. Then solve for X
In the circle , the value οf x is 50°.
What is secant line in circle?A secant in geοmetry is a line that tοuches a curve at at least twο different pοints. The Latin wοrd secare, which means tο cut, is where the wοrd secant derives. A secant crοsses a circle at precisely twο pοints when it is a circle. A chοrd is the line segment that the twο pοints determine, i.e., the interval οn the secant whοse ends are the twο pοints.
Remember that a tangent line is οne that crοsses a circle at precisely οne pοint. The term "secant line" describes a line that passes thrοugh twο pοints οn a circle. Secant is a Latin wοrd that means "tο cut," and it is derived frοm secare. A chοrd is the line segment defined by the twο pοints where a secant tοuches a circle in a given space.
Here in the given circle using secant line fοrmula ,
=> 75° = [tex]\frac{1}{2}[/tex] (100°+x)
=> 2×75 = 100+x
=> 150 = 100+x
=> x= 150-100= 50°.
Hence the value of x is 50°.
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What is the GCF in simplify form
Answer: 9x^2y
the gcf of -63 , 9 and 90 is 9
And the gcf of the variables is x^2 and y
So, 9x^2y
Show your work.
Are the expressions (4c + 8) + 3c - 2 and 4c + 2(0.5c + 1) equivalent?
First, let's simplify the expression (4c + 8) + 3c - 2:
(4c + 8) + 3c - 2
= 4c + 3c + 8 - 2 (rearrange terms)
= 7c + 6 (combine like terms)
So the first expression simplifies to 7c + 6.
Next, let's simplify the expression 4c + 2(0.5c + 1):
4c + 2(0.5c + 1)
= 4c + 2(0.5c) + 2(1) (distribute the 2)
= 4c + c + 2 (simplify the parenthesis)
= 5c + 2 (combine like terms)
So the second expression simplifies to 5c + 2.
Now we can compare the two expressions:
7c + 6 vs. 5c + 2
These expressions are not equivalent because they do not have the same coefficients or constants.
Un cilindro cuya altura es de 1 pie tiene un volumen de 10 pies". ¿Cuál sería el volumen en pies cúbicos para un cilindro con la misma altura pero tres veces el diámetro?
The volume of the second cylinder is 90 square feet.
How to find the volume of the larger cylinder?Here we know that a cylinder whose height is 1 ft has a volume of 10 ft², remember that the volume for a cylinder of radius R and height H is:
V =pi*R²*H
Where p = 3.14
Then the radius here is:
10 = 3.14*R²*1
√(10/3.14) = R
If we triple the diameter we also triple the radius, then the volume of the other cylinder will be:
V = 3.14*(3*√(10/3.14))²*1
V = 90
The volume is 90 square feet.
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Please HELP DUE IN AN HOUR
Answer:
It is not true (equal sign with a slash in it) one side’s 23 and the other side is 20
What is the total surface area for the square pyramid below? Responses 144 in2 144 in, 2 288 in2 288 in, 2 352 in2 352 in, 2 208 in2 208 in, 2 (Image)
Answer:
To find the total surface area of the square pyramid, we need to find the area of each of its faces and add them up.
The pyramid has a square base with sides of 8 inches and each triangular face has an isosceles right triangle shape with two sides of 8 inches and a hypotenuse of 2 x 8 = 16 inches (using the Pythagorean theorem).
The total surface area is then:
Area of the square base: 8 x 8 = 64 square inches
Area of each triangular face: 1/2 x 8 x 8 = 32 square inches (since each triangle is isosceles with base and height of 8 inches)
Total surface area: 4 x 32 + 64 = 192 + 64 = 256 square inches
Therefore, the total surface area of the square pyramid is 256 in². So, the closest answer option is 256 in, 2.
Look At Screen Shot
Look At Screen ShotLook At Screen ShotLook At Screen ShotLook At Screen ShotLook At Screen Shot
Answer:
There is 5% of the juice left.
Step-by-step explanation:
We know that originally, the container had 80 oz of orange juice, this is 100% in our case.
Then we can write a relation:
80 oz = 100%
Now there are 4 ounces left, in the same way as before, we can write this as:
4 oz = X%
We want to find X%
First, let's write our equations:
4 oz = X%
80 oz = 100%
We can take the quotient between these two equations to get:
(4oz/80oz) = (X%/100%)
We need to solve this for X%, then we get:
(4oz/80oz)*100% = X% = 5%
This means that 4 oz is 5% of the initial volume of the juice container.
Then we can conclude that there is 5% of the juice left.
Make calculations for a 5-year loan of $20,000 with an annual interest rate of 6% compounded monthly. Calculate the balance owed if the loan had to be paid in full at the end of the 5-year period, and no monthly payments were required.
Answer: $28,383.68.
Step-by-step explanation:
The first step is to determine the number of monthly payments over the 5-year period, which is 5 years x 12 months/year = 60 months.
Next, we can use the formula for the future value of an annuity, which is:
FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)
where:
FV is the future value of the loan (the amount owed at the end of the 5-year period)
P is the initial principal amount ($20,000 in this case)
r is the annual interest rate (6%)
n is the number of compounding periods per year (12 for monthly compounding)
t is the total number of years (5)
Plugging in these values, we get:
FV = $20,000 * ((1 + 0.06/12)^(12*5) - 1) / (0.06/12)
FV = $28,383.68
Therefore, the balance owed at the end of the 5-year period would be $28,383.68.