Answer:
hypotenuse is not a rational number
Step-by-step explanation:
In a Right angled triangle , if a, b are the sides and h be the hypotenuse then relationship between them is given by
[tex]h^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex]
Here,
a= 4 in. [Given]
b = 6 in. [Given]
Thus ,
[tex]h^{2}[/tex] = [tex]4^{2}[/tex] + [tex]6^{2}[/tex]
[tex]h^{2}[/tex] = 16 + 36
[tex]h^{2}[/tex] = 52.
h = [tex]\sqrt{52}[/tex] = 7.21110255......
Clearly, h is not a rational number
can someone please help me???
What is the result of subtracting the second equation from the first?
2
x
+
7
y
=
−
8
2
x
−
5
y
=
−
1
2x
See in the explanation:
Explanation:Here we have the following system of linear equations in two variables:
[tex](1) \ 2x+7y=-8 \\ \\ (2) \ 2x-5y=-1[/tex]
So if you graph these two equations you will get two lines with different slopes. The question is:
What is the result of subtracting the second equation from the first?
So this can be written mathematically as:
[tex]2x+7y-(2x-5y)=-8-(-1) \\ \\ Breaking \ parentheses: \\ \\ 2x+7y-2x+5y=-8+1 \\ \\ \\ Combining 'like 'terms: \\ \\ 2x-2x+7y+5y=-7 \\ \\ 12y=-7 \\ \\ y=-\frac{7}{12}[/tex]
So the result of subtracting the second equation from the first is:
[tex]12y=-7[/tex]
and from this we can calculate y.
Learn more:Methods for solving System of Linear Equations:
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the ratio of red ribbons to green ribbons is 4 to 6 if there a total of 32 red ribbons then how many green ribbons are there?
There are 48 green ribbons
Solution:Given that the ratio of red ribbons to green ribbons is 4 to 6
Which can be written in following way:-
[tex]\frac{\text {Red} r i b b o n}{\text {Green ribbon}}=\frac{4}{6}[/tex]
There are total number of 32 red ribbons
We have to determine the number of green ribbon
Let the number of green ribbon be ‘6a’
And number of red ribbons be "4a"
Given number of red ribbons = 32
4a = 32
a = 8
number of green ribbon = 6a = 6(8) = 48
Therefore number of green ribbons is 48
Final answer:
To find the number of green ribbons, the ratio of red to green is scaled to match the actual count of red ribbons. With 32 red ribbons and a ratio of 4:6, there are 48 green ribbons.
Explanation:
To solve the problem, we need to find out how many green ribbons there are when we know that the ratio of red ribbons to green ribbons is 4 to 6 and there are 32 red ribbons in total.
First, let's use the given ratio. Ratios can be scaled up by the same factor on both sides to represent actual quantities. So, if we have 4x red ribbons and 6x green ribbons, and we know 4x = 32, we can solve for x: x = 32 / 4 = 8. This means for every 8 red ribbons, there are 12 green ribbons since 6x = 6 × 8 = 48.
Therefore, if there are 32 red ribbons, there are (32 / 8) × 12 = 4 × 12 = 48 green ribbons.
1092 flowers are arranged into 26 vases with the same number of flowers in each vase. How many flowers would be needed to fill 130 such vases?
Answer:
5460
Step-by-step explanation:
Leslie has $80 in a savings account. the interest rate is 5% per year and is not compounded.how much will she have in 1 year?n
Answer:
[tex]\$84[/tex]
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=1\ years\\ P=\$80\\ A=\$?\\r=5\%=5/100=0.05[/tex]
substitute in the formula
[tex]A=80(1+0.05*1)[/tex]
[tex]A=80(1.05)[/tex]
[tex]A=\$84[/tex]
What is BC ? Enter your answer in the box.
Units An isosceles triangle A B C. Side B C is the base. Sides A B and A C are equal. Sides A B and A C are labeled with single tick marks. Side A B is labeled as 4 x plus 1, side A C is labeled as 2 x plus 23, and side B C is labeled as 3 x minus 8.
Answer:
BC=25
Step-by-step explanation:
The provided data in the figure is different from the written text. We'll use the set of conditions in the figure
We know the triangle is isosceles, so the sides AC and AB are equal, i.e.
4x+4=6x-14
Operating
4+14=6x-4x
x=18/2=9
Knowing that x=9, then
BC=2x+7=18+7=25
Note: If we used the data provided in the text, the answers would be
x=11, BC=25
Answer:25
Step-by-step explanation:
i did the test lol
A rectangle has a length of 34 inches less than 5 times it’s width. If the area of the rectangle is 867 square inches, find the length of the rectangle.
Length of the rectangle is 51 inches
Solution:
Given that
Length of the rectangle in 34 miles less than 5 times its width
Area of rectangle = 867 square inches
Need to determine length of the rectangle.
Let assume width of the rectangle be represented by variable x.
So 5 times width of the rectangle =5x
34 inches less than 5 times width of the rectangle = 5x – 34
As Length of the rectangle in 34 miles less than 5 times its width
=> Length of the rectangle = 5x – 34
The formula for rectangle is given as:
[tex]\text { area of rectangle }=length \times width[/tex]
As given that Area of rectangle = 867 square inches
[tex]\begin{array}{l}{=>867=(5 x-34) \times(x)} \\\\ {=>5 x^{2}-34 x-867=0}\end{array}[/tex]
On solving quadratic equation by using quadratic formula
[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
In our case a = 5, b = -34 and c = -867
On substituting value of a, b and c in quadratic formula we get
[tex]\begin{array}{l}{x=\frac{-(-34) \pm \sqrt{(-34)^{2}-4 \times 5 \times(-867)}}{2 \times 5}} \\\\ {=>x=\frac{34 \pm \sqrt{18496}}{10}=\frac{34+136}{10}} \\\\ {=>x=\frac{34+136}{10}=17 \text { or } x=\frac{34-136}{10}=-10.2}\end{array}[/tex]
Since x represents width, it cannot be negative, so x = 17
Length of the rectangle = 5x – 34 = 5(17) – 34 = 51
Hence length of the rectangle is 51 inches
16 points will mark brainiest
Answer:
E=5
Step-by-step explanation:
Given,
[tex]32= 2^E[/tex]
We know [tex]32[/tex] can be written as [tex]2^5[/tex]
Substituting [tex]2^5[/tex] in place of [tex]32[/tex]
We get,
[tex]2^5 = 2^E[/tex]
Since the base is equal, now comparing the exponent.
Therefore [tex]E=5[/tex] is the missing exponent.
Answer:
E = 5 and [tex]32 = 2^5[/tex]
Step-by-step explanation:
Given:
[tex]32 = 2^E[/tex]
Now we know that E is denoted as an exponent term,
Exponent term indicates the value which can be to the power of a number.
Now 32 can be written as,
[tex]32 = 2\times 2\times2\times 2\times2[/tex]
Hence from above we can say that 2 can be multiplied 5 times to get the value as 32.
hence we can say that,
[tex]32 = 2^5[/tex]
Hence E=5
What is the domain of the composite function W(x) = f(g(x)) when f(x) =5/(x-1) and g(x) =4/(3x-2) ?
A set of scales is used to show that two lemons and seven tomatoes are required
to balance one cabbage. If two lemons balance one tomato, how many tomatoes will balance one cabbage?
Answer:
8 tomatoes are required to balance 1 cabbage
Step-by-step explanation:
Given :
Two lemons and seven tomatoes are required to balance one cabbage:
2 Lemons + 7 tomatoes = 1 cabbage (equation 1)
two lemons balance one tomato
2 lemons = 1 tomato
put in equation 1:
1 tomato + 7 tomatoes = 1 cabbage
8 tomatoes = 1 cabbage
8 tomatoes required to balance one cabbage
14. Solve: 3x² + 5x – 12 = 0
B. 4-3
C. 8, - 18
Answer:
b
Step-by-step explanation:
The equation:
3
x
2
−
5
x
−
12
=
0
is in the form:
a
x
2
+
b
x
+
c
=
0
with
a
=
3
,
b
=
−
5
,
c
=
−
12
The roots are given by the quadratic formula:
x
=
−
b
±
√
b
2
−
4
a
c
2
a
x
=
5
±
√
(
−
5
)
2
−
4
(
3
)
(
−
12
)
2
(
3
)
x
=
5
±
√
25
+
144
6
x
=
5
±
√
169
6
x
=
5
±
13
6
That is:
x
=
5
+
13
6
=
18
6
=
3
or
x
=
5
−
13
6
=
−
8
6
=
−
4
3
Melvin spends 6 1/4% of his monthly salary on transportation. if his salary is 1,600 a month how much does he spend on transportation
Answer:
$100
Step-by-step explanation:
6 1/4=25/4
25/4%=0.0625
0.0625*1600=100
---------------------------
Annual sales for a restaurant were $575,000 in 2006. Since then, the sales increased at a rate of 3% per year. Write and use an exponential model to find the sales in 2018.
Answer:
The correct answer is that the annual sales for 2018 is US$ 819,813 (Rounding to the whole nearest dollar)
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Annual sales for a restaurant in 2006 = US$ 575,000
Duration of the sales analysis = 12 years
Annual sales increase rate = 3%
2. Let's find the annual sales turnover after 12 years in 2018, using the following formula:
Sales 2018 = Sales 2006 * (1 + r) ⁿ
Sales 2006 = US$ 575,000
number of periods (n) = 12
rate (r) = 3% = 0.03
Replacing with the real values, we have:
Sales 2018 = 575,000 * (1 + 0.03) ¹²
Sales 2018 = 575,000 * 1.42576089
Sales 2018 = US$ 819,813 (Rounding to the whole nearest dollar)
Answer:
$819,812.50
Step-by-step explanation:
Shouldn't round in this case because they're asking for the numerical value of money which the .50 in cents is vital to the problem.
The value of the expression 4 square root of 81^3 is ______.
Choices:
9
27
350
1.4
2.3
Answer:27
Step-by-step explanation:
Suppose a,b,and c are all negative numbers how do you find the distance between points (a,b) and (a,c)?
Answer:
Distance = |b - c|
Step-by-step explanation:
Suppose a, b, and c are all negative numbers.
We have to describe the way to find the distance between points (a,b) and (a.c).
Since the x-coordinates of the two points are the same and are a, therefore, the distance between the y-coordinates of the two points will give the distance between the two points.
Mathematically the distance d will be given by d = |b - c|, where |x| is the absolute value function of x. (Answer)
How many different four-letter secret codes can be formed if the first letters must be an S or a T
The number of different four-letter secret codes can be formed if the first letters must be an S or a T is; 35,152
How to solve permutation and combination?
If the first letters of a four-letter secret code must be an S or a T, there are 26 possible choices for the remaining two letters. This is because there are 26 letters in the alphabet, and each letter can be one of the remaining 26 letters after the first two are used.
To calculate the total number of possible combinations, you can use the following formula:
26×26×26×2.
This formula represents the number of possible combinations for each of the remaining letters. Multiplying these values together gives you the total number of possible four-letter secret codes:
26×26×26×2=35,152
So, there are 35,152 different four-letter secret codes that can be formed if the first letters must be an S or a T
Order from least to greatest
Look at picture.
WILL MARK AS BRAINIEST IF RIGHT!
Answer:
7.5% < 7.49 < [tex]7\frac{49}{50}[/tex]
Step-by-step explanation:
To make this easier to look at, first you change them into the same form. Let us make them all into fractions and compare:
7.49 as a fraction is [tex]7\dfrac{49}{100}[/tex]
[tex]7\dfrac{49}{50}[/tex] is already a fraction so let's leave it first.
7.5% in fraction form is [tex]\dfrac{75}{1000}[/tex]
Now knowing this, we can already say that 7.5% is already the least comparing it to the others.
Now we compare the two:
[tex]7\dfrac{49}{100} < 7\dfrac{49}{50}[/tex]
If we make them into similar fractions:
[tex]7\dfrac{49}{50} = 7\dfrac{98}{100}\\\\Then\\\\7\dfrac{49}{100}<7\dfrac{98}{100}[/tex]
At a high school with 300 students, 32 play soccer, 18 play basketball, and 10 play both sports. If a student is selected at random, find the probability that a student plays soccer or basketball.
Answer:
P(student plays both soccer or basketball)= 40/300
Simplify : 2/15
In a group of 300 students, 18 students play basketball, 11 students play football. 10 students play both sports.
Now, A student is chosen randomly from this group.
What is the probability that the student plays both soccer or basketball?
Probability of any event=no. of favorable outcomes/total no. of outcomes
Here, no. of favorable outcomes
=no. of students who plays both soccer or basketball
= 32+18-10
= 40
and, total no. of outcomes= 300
If a student is selected at random, the probability that a student plays soccer or basketball is [tex]\frac{2}{15}[/tex]
To start, we list the variables given
32 ----- Soccer
18 ---- Basketball
10 ----- Basketball + Soccer
If you look at the question, it was stated that 10 people plays basketball and soccer. The keyword being "and". While we are asked to find the probability that a student plays basketball or soccer. This then means that we add the number of people playing basketball together with those playing soccer.
32 + 18 = 40.
Probability of a student playing soccer or basketball is then 40/300 = 2/15
learn more about probability here https://brainly.com/question/23044118
A grocery store clerk put only packages of flour tortillas and packages of corn tortillas on the shelf. The ratio of the number of packages of corn tortillas to the total number of packages on the shelf was 7 to 16.
Which number could be the number of packages of flour tortillas the clerk put on the shelf?
The number of flour tortilla packages could be 9 or any number that results from subtracting 7 (corn tortilla packages) from a multiple of 16 (total packages). It's necessary to keep the ratio between corn tortillas and total packages at 7:16.
Explanation:The subject of this question refers to the mathematical concept of ratios. Given the ratio of corn tortillas to the total number of packages is 7:16, this means that out of every 16 packages, 7 are corn tortillas. Therefore, the remaining packages must be flour tortillas.
To figure out the possible number of packages of flour tortillas, you would subtract the number of corn tortilla packages (7) from the total (16). So, there could be 9 packages of flour tortillas on the shelf.
Please note that this ratio can apply to any multiple of 16. As long as the number of packages is divisible by 16, you can use the ratio to find the number of flour tortilla packets. For example, if the total number of packages was 32, you could have 18 packages of flour tortillas (since 32-14=18) and so on.
Learn more about Ratios here:https://brainly.com/question/32531170
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Laws of sine and cosine
Law of Sines
[tex]\displaystyle \frac{sin∠C}{c} = \frac{sin∠B}{b} = \frac{sin∠A}{a} \\ \\ \frac{sin\:40°}{5} = \frac{sin∠C}{7} → \frac{7sin\:40°}{5} = sin∠C → 0,8999026535... = sin∠C → 64,14527443...° = sin^{-1}\:0,8999026535... \\ \\ 64° ≈ m∠C[/tex]
As you can see, the inverse function had to be used towards the end, or the answer would have been thrown off.
I am joyous to assist you at any time.
the mean temperature for the first 7 days in January was 3c
the temperature the 8 day was 5c
what is the mean temperaturefot first 8 days in January?
Answer:
Mean = 3.25°C
Step-by-step explanation:
The mean (or average) is given by the formula:
Mean = Sum/Number of Numbers
For first 7 days, the mean was 3, so we can say:
Mean = Sum/Number of Numbers
3 = Sum/7
Sum = 3 * 7 = 21
Then on 8th day, the temperature was 5, so the new sum would be (for 8 numbers):
New Sum = 21 + 5 = 26
Now we calculate the mean for 8 numbers:
Mean = 26/8
Mean = 3.25°C
if 2 is the square root of four what is the squre root of 81
What is the symmetry in modern echinoderms called? 10 part symmetry
5 part symmetry
lateral symmetry
bilateral symmetry
Answer:
5 part symmetry
Step-by-step explanation:
I did the test
Answer:
5 part symmetry.
Step-by-step explanation:
I took the test and got it right.
The diagram below shows the construction of a line through point T perpendicular to line 1
This construction demonstrates that the set of points equidistant from the endpoints of a line segment
is the perpendicular
of the segment.
Which of the following words is the most appropriate to fill in the blank?
A. Bisector
B. Line
C. Slope
D. Transversal
Answer:
A
Step-by-step explanation:
When we read your example. we can see that we have not diagram, but we have text and we can conclude what is that tell.
This construction demonstrates that the set of points equidistant from the endpoints of a line segment
is the perpendicular
of the segment.- this text tells us that it is bisector
Answer:
a
Step-by-step explanation:
Find A U B. please help much needed!
Answer:
A u B = {3,5,6,7,8,11,12}
Step-by-step explanation:
A = {3,6,7,11}
B = {3,5,7,8,12}
A u B = {3,5,6,7,8,11,12}
please solve with working much appreciated
Answer:
5 cm
Step-by-step explanation:
What you have there is an equilateral triangle. An equilateral triangle is a triangle that has sides with equal lengths and interior angles are equal as well. So if all angles are equal in a triangle, then that means that this is an equilateral triangle. So we can say that if one side of this triangle is 5cm
then the n would also be equal to 5cm.
Study the steps used to solve the equation. Given: c/2-5=7 Step 1: c/2-5+5=7+5 Step 2: c/2+0=12 Step 3: c/2=12 Step 4: 2 (c/2)=12(2) Step 5: c=24 Choose the property that justifies each step of the solution.
Answer:
step 1: addition property of equality
step 2: additive inverses
step 3: additive identity
step 4: multiplication property of equality
Step-by-step explanation:
edg 2020
Answer:
step 1: addition property of equality
step 2: additive inverses
step 3: additive identity
step 4: multiplication property of equality
Step-by-step explanation:
Matt has answered 20/25 questions on a test. What percentage of the test has he completed?
Answer:
80%
Step-by-step explanation:
=20/25 x 100
= 4/5 x 100
=4 x 20
= 80%
Jessie estimated the weight of his cat to be 12 pounds. The actual weight of the cat is 15 pounds.
What is the percent error?
Round your answer to the nearest whole percent.
Answer:
20%
Step-by-step explanation:
% of error is given by the following formula:
% Error = [tex]\frac{|\textrm {Approx Value - Exact Value}|}{\textrm {Exact Value}} \times 100[/tex]
Now, Jessie estimated the weight of his cat to be 12 pounds i.e. Approximate value is 12 pounds.
Again, The actual weight of the cat is 15 pounds i.e. the exact value is 15 pounds.
Therefore, the % error = [tex]\frac{|12 - 15|}{15} \times 100 = \frac{3}{15} \times 100 = 20[/tex]% (Answer)
Answer:
20%
Step-by-step explanation:
Jessie thinks to greatly of his cat
and I took the test
Edurado started a business selling sporting goods.He spent $ 7500 to obtain hos merchandise , and it cost him $300 per week for general expenses.He earns $850 per week in sales. What is the minimum number of weeks Edurado will take to make a profit?
Answer:
C) It will take 14 weeks for Edurado to make a profit.
Step-by-step explanation:
The money spent on obtaining the merchandise = $ 7500
The general expense per week = $300
Let us assume Eduardo has to work for N weeks to break Even.
So, the general expense in N weeks = N x( Expense per week)
= N x ( $300) = 300 N
So, the total expense in N weeks = Money spent on merchandise + general expense
or, the TOTAL EXPENSE = $ 7500 + 300 N .... (1)
Now, the earning per week = $850
So, the total earning in N weeks = N x ( Earning in 1 week) = N x ( $850)
or, the TOTAL EARNING = 850 N .... (2)
Now, for N weeks ,
TOTAL EXPENSE = TOTAL EARNING
⇒ $7500 + 300 N = 850 N
or, 7500 = 850 N - 300 N = 550 N
⇒ N = 7500/550 = 13.63
So, number of weeks should at least be 13.63
Among the given options, N = 14 weeks is the most feasible answer.
Hence, it will take 14 weeks for Edurado to make a profit.