7. The perimeter of a right triangle is 60 cm and its hypotenuse is 25 cm. Find the area of the triangle.
Answer:
150 cm²
Step-by-step explanation:
Given
Perimeter = 60 cmHypotenuse = 25 cmSolving
We need to find the lengths of the altitudesSince 25 cm is already covered there is (60 - 25) = 35 cm remainingThe lengths can be taken as x and 35 - xNow, since it's a right triangle, we can solve for x using the Pythagorean TheoremApplying the theorem
x² + (35 - x)² = 25²x² + 1225 - 70x + x² = 6252x² - 70x + 600 = 0x² - 35x + 300 = 0x = 35 ± √1225 - 4(1)(300) / 2x = 35 ± √25 / 2x = 35 ± 5 / 2x = 40/2 = 20 or x = 30/2 = 15Upon solving the lengths of the altitudes are 15 and 20Area of the triangle
1/2 x product of the altitudes1/2 x 15 x 2010 x 15150 cm²With decimal is equivalent to 76/9
Answer:
8.4
Step-by-step explanation:
76 ÷ 9 = 8.44444444
= 8.4 (rounded)
hope this helps!
Amanda and Molly are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of shiny wrapping paper. Amanda sold 3 rolls of plain wrapping paper and 3 rolls of shiny wrapping paper for a total of $60. Molly sold 1 roll of plain wrapping paper and 9 rolls of shiny wrapping paper for a total of $132. What is the cost each of one roll of plain wrapping paper and one roll of shiny wrapping paper? (no links please)
Answer:
Step-by-step explanation:
Solving system of symultaneous equation:
Let the cost of one roll of plain wrapping pair = x
Let the cost of one shiny wrapping paper = y
Amanda:
Cost of 3 rolls of plain paper + cost of 3 rolls of shiny paper = $ 60
3*x + 3*y = 60
3x + 3y = 60 ------------------(I)
Molly:
Cost of 1 roll of plain paper + cost of 9 rolls of shiny paper = $ 132
x + 9y = 132 ---------------------(II)
x = 132 - 9y ---------------(III)
Substitute x = 132 -9y in equation (I)
3*(132-9y) + 3y = 60
3*132 - 3*9y + 3y = 60
396 - 27y + 3y = 60
Combine like terms
396 - 24y = 60
Subtract 396 from both sides
-24y = 60 - 396
-24y = -336
Divide both sides by (-24)
y = -336/(-24)
[tex]\sf \boxed{y=14}[/tex]
Now, substitue y = 14 in equation (III)
x = 132 - 9*14
= 132 - 126
[tex]\sf \boxed{x = 6}[/tex]
cost of one roll of plain wrapping paper = $ 6
Cost of one roll of shiny wrapping paper = $ 14
Which value is equivalent to 1,250 - 352
a
7
250
b 35
352
40
In order to either condense or expand logarithms using their properties, what must be?
Group of answer choices
the need the same exponent
they need the same answer
the need to have the same base
Answer:
Answer C
Step-by-step explanation:
The rules of logarithmic functions require the two log functions to have the same base. If they do not have the same base, you cannot apply any of the rules.
Answer:
Last option
Step-by-step explanation:
They need same base inorder to apply any property
Like
log_a(bc)=log_a^b+log_a^clog_a(b/c)=log_a^b-log_a^cBecky says that when she simplifies the following expression, the value is 6 less than her age. What is Becky's age? (7+11) - 8÷2
20
14
26
11
Help me I need now plese
Answer:
Ex1. SAS, ASA, SSS, SAS
Ex2. There are 2 heights and equal length
Dtu =uts and ut common side du=us
Rq=sd and sq common side rs=qd
Does anyone know the answers to this, I had to do this yesterday but I didn´t know any of the questions.
Answer:
(A)
(1) NO
(2) YES
(B)
(3) YES
(4) NO
(5) YES
Step-by-step explanation:
According to the triangle sum theorem, the three interior angles of any triangle add up to 180 degrees. So, if we add up the three angles given, to be a triangle, they have to add up to 180 degrees.
38 + 42 + 110 = 190
So, ( (1) 38, 42, 110 ) is not a triangle becuase it adds up to more than 180 degrees (1).
20 + 40 + 120 = 180
So, ( (2) 38, 42, 110 ) is a triangle because it adds up to 180 degrees (2).
For the lengths for a triangle, the length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides. This is saying:
A-B < C
A+B > C
So to find if they can be, simply plug in the values.
(3)
4-3 < 3
True : 1 < 3
4+3 > 3
True : 7 > 3
(3) is a triangle.
(4)
3-2 < 5
True : 1 < 5
3+2 > 5
False : 5 > 5
(4) is not a triangle
(5)
5-2.5 < 4
True : 2.5 < 4
5+2.5 > 4
True : 7.5 > 4
(5) is a triangle
The data in the table represents the training times (in seconds) for Arnold and Jackson.
Arnold 102 86 87 99 92 100 94 89 84 97
Jackson 103 100 83 87 88 85 91 93 96 101
Question 1
Which person's training times had the greatest spread? Explain.
Select from the drop down menus to correctly complete each statement.
The range of Arnold's training times is
Choose...
. The range of Jackson's training times is
Choose...
. Thus,
Choose...
.
Question 2
The middle 50% of the training times of which person had the least spread? Explain.
The interquartile range of Arnold's training times is
Choose...
. The interquartile range of Jackson's training times is
Choose...
. Thus, the middle 50% of
Choose...
training times have the least spread.
Question 3
What do the range and interquartile range tell you about Arnold and Jackson's training times?
Select each correct answer.
Arnold's training times are more consistent than Jackson's.
Arnold and Jackson's training times have the same spread.
Jackson's training times are just as consistent as Arnold's.
Jackson's training times have the most spread.
Range for Arnold: 18; IQR: 12
Range for Jackson: 20; IQR: 13
Jackson's had the greatest spread.
Arnold's middle 50% had the least spread
What is the Range and Interquartile Range of a Data Set?Range = Maximum value - minimum value
Interquartile range (IQR) = Q3 - Q1
Range and IQR are both measures of variability. The larger the value, the more spread the data values in a data set are.
Range for Arnold's training times = 102 - 84 = 18
Range for Jackson's training times = 103 - 83 = 20
Therefore, Jackson's training times had the greatest spread.
Interquartile range for Arnold's training times = Q3 - Q1 = 99 - 87 = 12
Interquartile range for Jackson's training times = Q3 - Q1 = 100 - 87 = 13
Thus, Arnold's middle 50% of his training times had the least spread.
The range and interquartile range tells us that, Arnold's training times are more consistent than Jackson's.
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Which expression is equivalent to rootindex 4 startroot 144 a superscript 12 baseline b cubed endroot? assume a greater-than-or-equal-to 0 and b greater-than-or-equal-to 0.
An expression has numbers, variables, and mathematical operations. The expression that is equivalent to (144a¹²b³)⁰°⁷⁵ is 2a³(9b³)⁰°⁷⁵.
What is an expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The expression that is equivalent to [tex]\sqrt[4]{144a^{12}b^3}[/tex], this can be done in the following manner,
[tex]\sqrt[4]{144a^{12}b^3}\\\\= \sqrt[4]{2^4 \times 3^2 \times a^{12} \times b^3}\\\\= (2^4 \times 3^2 \times a^{12} \times b^3)^{\frac14}\\\\= 2^{(\frac14 \times 4)} \times 3^{(\frac14 \times 2)} \times a^{(\frac14 \times 12)} \times b^{(\frac14 \times 3)}\\\\= 2 \times 3^{(\frac12)} \times a^{3} \times b^{(\frac34)}\\\\[/tex]
[tex]= 2\times a^{3} \times 3^{(\frac12 \times \frac22)} \times b^{(\frac34)}\\\\= 2\times a^{3} \times 3^{(\frac24)} \times b^{(\frac34)}\\\\= 2\times a^{3} \times 9^{(\frac14)} \times b^{3(\frac14)}\\\\= 2\times a^{3} \times (9b^{3(\frac14)})\\\\=2a^3 \sqrt[4]{9b^3}[/tex]
Thus, The expression that is equivalent to (144a¹²b³)⁰°⁷⁵ is 2a³(9b³)⁰°⁷⁵.
Learn more about Expression:
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Answer:
its a
Step-by-step explanation:
on edge 2022
What is the solution to the equation 9r=4/7
Answer:
r=4/63
Step-by-step explanation:
Divide each term in 9r=47 by 9 and simplify.
Answer:
[tex]r=\frac{4}{63}[/tex]
Step-by-step explanation:
1) Divide both sides by the same factor
[tex]9r=\frac{4}{7}[/tex]
[tex]\frac{9r}{9} =\frac{\frac{4}{7} }{9}[/tex]
2) Simplify
Cancel terms that are in both the numerator and denominator[tex]\frac{9r}{9} =\frac{\frac{4}{7} }{9}[/tex]
[tex]r=\frac{\frac{4}{7} }{9}[/tex]
Divide the numbers[tex]r=\frac{\frac{4}{7} }{9}[/tex]
[tex]r=\frac{4}{63}[/tex]
Instructions: The following is the recorded earthquakes on South Carolina from August, 2016 to February, 2017. Use the data to find the residuals. Then draw a residual plot by hand. Use the residual plot to determine if the linear model is the best regression model for this data.
Magnitude Depth (km. )
[Table]
1. 7 2. 9
1. 1 0. 8
1. 4 1. 9
0. 7 3. 2
0. 8 4. 3
1. 9 4
1. 7 6. 3
1. 9 6. 9
1. 9 0. 9
1. 1 2
Source: USGS
x Residual (Round to nearest tenth)
1. 7 Answer
1. 1 Answer
1. 4 Answer
0. 7 Answer
0. 8 Answer
1. 9 Answer
1. 7 Answer
1. 9 Answer
1. 9 Answer
1. 1 Answer
Answer:
1.7 = -0.7
1.1 = -2.1
1.4 = -1.4
Unsure about 0.7
0.8 = 1.7
1.9 (unsure about both)
1.1 = -0.9
Step-by-step explanation:
Hope this helps :)))
The regression line is not a good model because the residuals are not randomly distributed.
What is the residual plot?For a residual plot to represent a good model, the points on the residual plot must be randomly distributed across the coordinates.
From a regression, the residual is the difference between the observed values and the predicted values.
Using the graph, we can see that the points that follow a pattern (or curve) regression line is not a good model because the residuals are not randomly distributed.
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1a. What formula would you use to find
the area of the rectangle below?
2 units
3 units
Answer:
Area = Width * Length
Step-by-step explanation:
This is the formula for a rectangle. If you plug in the values that were givin to you, the answer is 6 units^2.
This is Aleks! please help me with this! I have been stuck on this one for weeks!!
Answer:
1/12 + 3/12 = 4/12 (or 1/3)
Step-by-step explanation:
we want to express
1/12 + 1/4 as 1/12 + something / 12
1/12 + 1/4 = 1/12 + something/12
we already have the 1/12 part, so we're left with
1/4 = something / 12
first, we can calculate (denominator we want) / (denominator we have) = 12/4 = 3
then, we want to multiply our current value (1/4) by our result of the multiplication divided by itself.
3/3 = 1
1/4 = 1/4 * 1 = 1/4 * 3/3 = 3/12
thus, our second value is 3/12
we then have 1/12 + 3/12
if we have the same denominators, we can simply add the numerators up
1/12 + 3/12 = (1+3)/12 = 4/12
Need help with this fast
Answer:
it says 20% under the math part
Escribe una ecuación que represente la gráfica.
Margo used 78 square yards of fabric to make 52 dresses last year. She used the same amount of fabric to make each dress. How many square yards of fabric did Margo use to make each dress?
The amount of square yards of fabric that Margo used to make each dress is; 1.5 sq. yds
How to Solve Algebra word Problems?We are told that;
Last year, she used 78 yd² to make 52 dresses
We are told that she used the same amount of square yards for each dress.
Thus, to find the square yards of fabric that Margo used to make each dress, we just divide 52 by 78.
Square yards used for each fabric = 78/52 = 1.5 sq. yds
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Which statements about the figure must be true? select three options. angledbc is bisected by ray bd. angleabc is bisected by ray bd. bc = one-halfac line segment d b is-congruent-to line segment b c 2mangledbc = mangleabc
We can see that the statements that about the figure that must be true in the following:
∠ABC is bisected by ray BD.BC = One-half of AC2 ∠DBC = ∠ABC.What is angle?An angle actually refers to the figure that is formed when two rays share a common endpoint that is called vertex. Also, when two planes intersect, they also form angles.
Thus, we can see that the above options are the three options that makes the figure true.
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3x+4 = 4(2x+9)
Please Help I CANT DO THIS!!!
Answer:
x=(14+sqrt(88))/6=(7+sqrt(22))/3=3.897 can i get brainliest?
Vivian and her friend Maddie are each baking apple pies and tarts for a bake sale, using the same recipes. Vivian baked 10 apple pies and 10 apple tarts, using a total of 130 apples. Maddie made 10 apple pies and 5 apple tarts, which used 100 apples. How many apples does each dessert require?
Answer:
6.5
Step-by-step explanation:
Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
Answer:
area of triangle base ×height over 2= 10km×9.4 over 2
area rectangle l×w =10×10
Find the area of this triangle, round to the nearest tenth
Answer:
27.7 [tex]in^2[/tex]
Step-by-step explanation:
Find length of missing side:
11^2-6^2 = x^2
85=x^2
x = [tex]\sqrt{85}[/tex]
x = 9.22
9.22*6 / 2 = 27.66
Round to tenth:
27.7
the answer is 1575 but I need to show my work! (find the total volume)
I WILL GIVE BRAINLIEST!!!!!
Answer: 1575
Step-by-step explanation:
Volume of Pyramid: b*l*h/2 = 21*9*7/3 = 441
Volume of Rectangular prism = V= lwh = (21*12*9)/2 = 1134 (divide by two because it is half of a rectangular prism)
441 + 1134 = 1575
In
the number 22, how many times larger is the
value of the digit in the tens place than the value of
the digit in the ones place?
Answer: 10 times larger
Step-by-step explanation:
Melissa has a student dictionary on her desk. Her dictionary contains 99 pages. In this dictionary, more words start with the letter "S" than any other letter, occupying 11 full pages.
If she opens up the dictionary at random, what is the probability that the page contains words starting with "S"?
Answer:
I believe it is 1/9 or 11.1%
Step-by-step explanation:
11/99 /(divided by) 11 = 1/9
1/9 converted to a decimal is 0.1 (it's repeating- I am not sure how to do that on brainly w/ the fancy - over it, so it's 0.111111111...)
so as a percent, it makes it 11.1% (repeating) or 11 [tex]\frac{1}{9}[/tex]% (which is a more exact solution)
now if you need a ratio, it would be 1:9
hope this helps :)
Timmy drank 2 quarts of water yesterday. He drank twice as much water today as he drank yesterday.
How many cups of water did Timmy drink in the two days
Answer:
24 cups or 6 quarts
Step-by-step explanation:
2 x 2 = 4 4 + 2 = 6
6 x 4 = 24
Question is in image below.
Answer:
Step-by-step explanation:
Let's start with some conversions
-√113 = - 10.6301-120/11 = -10.90909-10.777... = -10.777...Remember that when you go to the negative side of the reals, the number that looks like it should be the largest, when negative is the smallest.
Answers
The smallest number of these three is -10.909
The second smallest is -10.777... repeat
The third smallest is -√113 which is -10.6301
The Largest one of the four is 10.7
Solve the system of equations y=-x+3 and 2x+2y=6
Answer:
y = -x + 3
Step-by-step explanation:
1. Substitute "y = -x + 3" in for y in the second expression:
2x + 2(-x + 3) = 6
2. Simplify:
2x + (-2x) + 6 = 6
0 + 6 = 6
6 = 6
Because the values are equal, the solution of y = -x + 3 is a valid input.
hope this helps!
Answer:
Answer to the first equasion is y=2: 2=-1+3
Step-by-step explanation:
y=-x+3 (x=1)
-3 y=-x
-3=2
2=-1+3
y=2
Hope this helps and makes sence
A diagram of a rectangular prism filled with unit cubes is shown below. Each unit cube has
side lengths measuring 1 foot.
What is the volume, in cubic feet, of the rectangular prism?
A. 12
B. 13
C. 54
D. 72
The volume of the rectangular prism filled with unit cubes each measuring the value of the length given is 72ft³.
Hence, Option D) 72ft³ is the correct answer.
Rectangular Prism and Cube
A rectangular prism is simply a three-dimensional solid shape with six faces which are rectangles.
The volume of a rectangular prism is expressed as;
V = l × w × h
Where l is length, w is width and h is height of the prism
A cube is a three-dimensional solid with six equal square-shaped sides.
Given the data in the question;
Length of the sides of the cube = 1 footLength of the rectangular prism l = 4 cubes × 1 foot = 4ftWidth of the rectangular prism w = 3 cubes × 1 foot = 3ftHeight of the rectangular prism l = 6 cubes × 1 foot = 6ftTo determine the volume of the rectangular prism, we substitute our given values into the expression above.
V = l × w × h
V = 4ft × 3ft × 6ft
V = 72ft³
Option D) 72ft³ is the correct answer.
Hence, the volume of the rectangular prism filled with unit cubes each measuring the value of the length given is 72ft³.
What is the mean absolute deviation of robin’s scores? m a d = startfraction 8 1 5 0 12 over 5 endfraction
The mean absolute deviation of the given scores of Robin as shown in the diagram atatched is: 5.2.
What is the Mean Absolute Deviation of a Data?The mean absolute deviation of a data set is determined by finding the average of the distance of each data point from the mean of the data set.
Given that the distance from the mean are: 8, 1, 5, 0, 12,
Mean absolute deviation = (8 + 1 + 5 + 0 + 12)/5
Mean absolute deviation = 26/5
Mean absolute deviation = 5.2.
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