remember the pythagorean theorem:
a² + b² = c²
where c is the hypotenuse.
so:
[tex] {a}^{2} + {b}^{2} = { ( \sqrt{26)}}^{2} [/tex]
the square and the square root cancel each other out, so...
a² + b² = 26
we know that a and b are of equal length given the angles.
so it's
[tex] { \sqrt{13} }^{2} + { \sqrt{13} }^{2} = 26[/tex]
here the squares and square roots also cancel, but to keep the equation from the formula true we need to write them. that makes the difference between optional and B
Option A is correct,
[tex] \sqrt{13} inches[/tex]
5 times a number is 110 less than 7 times that number
Answer:
55
Step-by-step explanation:
let the number=x
5x=7x-110
7x-5x=110
2x=110
x=110/2=55
Write the sum of three odd consecutive integers if the last one is m-2
Answer:
the sum is 3m-12
Step-by-step explanation:
The nunbers are:
[tex]m-2\\m-4\\m-6\\the~sum~is:\\sum=(m-2)+(m-4)+(m-6)\\sum=m-2+m-4+m-6=m+m+m-2-4-6\\sum=3m-12[/tex]
The sum of three odd consecutive integers is 3m - 12
What are odd integers?"These are the integers which are not divisible by 2."
For given question,
We need to find the sum of three consecutive odd integers.
Let x, x + 2, x + 4 be three consecutive odd integers.
We have been given the last one is m - 2
This means x + 4 = m - 2
So, the second odd integer would be,
x + 2 = m - 4
and the first odd integer would be,
x = m - 6
, we find the sum of the three odd consecutive integers.
⇒ (m - 6) + (m - 4) + (m - 2)
= m + m + m - 6 - 4 - 2
= 3m - (6 + 4 + 2)
= 3m - 12
Therefore, the sum of three odd consecutive integers is 3m - 12
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Use the theoretical method to determine the probability of the outcome or event given below.
The next president of the United States was born on Monday
Answer:
[tex]\frac{1}{7}[/tex] probability that the next president of the United States was born on Monday
Step-by-step explanation:
A theoretical probability is given by the number of desired outcomes divided by the number of total outcomes.
The next president of the United States was born on Monday
Any person, including the next president of the United States, can be born on 7 possible days: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday or Saturday, one of which is Monday.
So
[tex]\frac{1}{7}[/tex] probability that the next president of the United States was born on Monday
The area of a rectangle is 110 square units. Its length measures 11 units. Find the
length of its diagonal. Round to the nearest tenth of a unit.
Answer:
A
=
w
l
d
=
w
2
+
l
2
Solving for
d
d
=
l
2
+
(
A
l
)
2
=
11
2
+
(
110
11
)
2
≈
14.86607
The length of the diagonal of the rectangle is 14.9 units.
What is a diagonal?A diagonal is the longest line that divides a plane shape into two halves.
To calculate the diagonal of the rectangle, we use Pythagoras theorem.
Formula:
A = lw.............. Equation 1Where:
A = Area of the rectanglel = Length of the rectanglew = width of the rectangle.make w the subject of the equation
w = A/l.............. Equation 2From the question,
Given:
A = 110 square unitsl = 11 unitsSubstitute these values into equation 2
w = 110/11w = 10 units.Finally, to calculate the diagonal of the rectangle, we use the formula below
d² = l²+w²............. Equation 3Given:
w = 10 unitsl = 11 units.Substitute these values into equation 3
d² = 10²+11²d² = 100+121d² = 221d = √221d = 14.9 units.Hence, the length of the diagonal of the rectangle is 14.9 units.
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Jerry leaves home driving at 50 miles per hour. Ten minutes later, Jenny drives after him at the speed 65 miles per hour. When will she overtake him?
Hi there!
[tex]\large\boxed{\approx 43.33 min}}[/tex]
Recall:
d = st, where:
d = distance
s = speed
t = time
We can set up an expression where the extra ten minutes is taken into account:
50x = 65(x - 10) <--- because J left 10 minutes after, we must subtract from the time variable, or "x".
Solve for x:
50x = 65x - 650
Subtract 65x from both sides:
-15x = -650
Divide both sides by -15:
x ≈ 130/3 or 43.33 min
A researcher designs an experiment by manipulating the following variables: temperature (low or high), illumination level (low or high), and time of testing (day or night). For a repeated measures design, how many participants would the researcher require in order to have 10 participants per condition?
Answer:
10
Step-by-step explanation:
As it could be inferred from the name, repeated measure design may be explained as experimental measures involving multiple (more than one) measures of a variable on the same observation, subject or participants which are taken at either various times or periodic intervals, different levels, different conditions. Hence, a repeated measurement taken with the same sample but under different treatment conditions. Therefore, since the measurement will be performed on a the same subjects(paired) , then the number of subjects needed will be 10. As it is this same samples that will be used for the other levels or conditions.
Anyone know this question?
Answer:
[tex](f + g)(4) = 191[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 5x^2 - 5x + 15[/tex]
[tex]g(x) = 6x^2 + 7x - 8[/tex]
Required
[tex](f + g)(4)[/tex]
First, calculate [tex](f + g)(x)[/tex]
This is calculated as:
[tex](f + g)(x) = f(x) + g(x)[/tex]
So, we have:
[tex](f + g)(x) = 5x^2 - 5x + 15+6x^2 + 7x - 8[/tex]
Collect like terms
[tex](f + g)(x) = 5x^2 +6x^2 - 5x+ 7x + 15 - 8[/tex]
[tex](f + g)(x) = 11x^2 + 2x + 7[/tex]
Substitute 4 for x
[tex](f + g)(4) = 11*4^2 + 2*4 + 7[/tex]
[tex](f + g)(4) = 191[/tex]
express the ratio 60cm to 20m in the form 1:n
Answer:
1:1/3
Step-by-step explanation:
60:20
6:2
1:1/3
n=1/3
Brainliest please~
The value of n=100/3
As per given the value of 1m 100cm
then the ratio of value be 60/2000 is equal to the 1/(2000/60) 1/(100/3) on compare with 1:n then the Value be
n=100/3
What does it mean to express it as a ratio?
In mathematics, a ratio indicates how often one number contains another. For example, if you have 8 oranges and 6 lemons in a fruit bowl, the ratio of oranges to lemons will be 8: 6 (that is, 8: 6, or 4: 3).
For example, if you have one boy and three girls, you can write the ratio as follows: 1: 3 (every boy has 3 girls) 1/4 is a boy and 3/4 is a girl. 0.25 is a boy (by dividing 1 by 4)
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Stuck on this question
Answer:
the answer of this question is b
You are charged $9.33 total for a meal, assume the 7% sales tax, how much was the menu price of this item?
I have already tried
$8.68
$8.71
$8.67
all were wrong
Answer:
$8.71.
Step-by-step explanation:
Given that you are charged $ 9.33 total for a meal, assuming the 7% sales tax, to determine how much was the menu price of this item, the following calculation must be performed:
100 + 7 = 107
107 = 9.33
100 = X
100 x 9.33 / 107 = X
933/107 = X
8.71 = X
Therefore, the menu price of this item was $ 8.71.
Will give brainliest if correct
Which congruence theorem can be used to prove △BDA ≅ △BDC?
Triangles B D A and B D C share side B D. Sides B C and B A are congruent. Sides A D and D C are congruent.
HL
SSA
AAS
SSS
Answer:
SSS or D on edge
Step-by-step explanation:
.
The three sides of triangle ΔBDA are equal to the three sides of triangle ΔBDC.
The congruency theorem that can be used to prove ΔBDA ≅ ΔBDC is; SSSReasons:
The given parameters are;
The common side to ΔBDA and ΔBD = BD
BC ≅ BA
AD ≅ DC
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reasons
BC ≅ BA [tex]{}[/tex] Given
AD ≅ DC [tex]{}[/tex] Given
BD ≅ BD [tex]{}[/tex] By reflexive property
Therefore, we have;
ΔBDA ≅ ΔBDC [tex]{}[/tex] By Side-Side-Side SSS, congruency ruleThe congruency theorem that can be used to prove ΔBDA ≅ ΔBDC is therefore;
SSSThe Side-Side-Side congruency rule states that if three sides of on triangle are congruent to three sides of another triangle, then the two triangles are congruent.
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Is 237405 divisible by 11
Hello!
237405 | 11 ?
237405 : 11 = 21582,(27)
Answer: false
Good luck! :)
Hello,
Is 237405 divisible by 11?
a=sum of digits in rank odd : 5+4+3 = 12
b=sum of digits in rank even: 0+7+2=9
Calculate the difference: d=a-b=12-9 =3
d is not a multiple of 11 so, then number 237405 is not divisible by 11.
Ali is hiking on the hill, whose height is given by f(u,v)=n^2 e^((u+n)/(v+n)). Currently, he is positioned at point (3, 5). Find the direction at which he moves down the hills quickly. Take n =12
Answer:
[tex]<-144e^{0.88},7.47e^{0.88}>[/tex]
Step-by-step explanation:
We are given that
[tex]f(u,v)=n^2e^{\frac{u+n}{v+n}}[/tex]
Point=(3,5)
n=12
We have to find the direction at which he moves down the hills quickly.
[tex]f(u,v)=144e^{\frac{u+12}{v+12}}[/tex]
[tex]f_u(u,v)=144e^{\frac{u+12}{v+12}}[/tex]
[tex]f_u(3,5)=144e^{\frac{3+12}{5+12}}[/tex]
[tex]f_u(3,5)=144e^{\frac{15}{17}}=144e^{0.88}[/tex]
[tex]f_v(u,v)=144e^{\frac{u+12}{v+12}}\times (-\frac{u+12}{(v+12)^2})[/tex]
[tex]f_v(3,5)=144e^{\frac{15}{17}}(-\frac{15}{(17)^2}[/tex]
[tex]f_v(3,5)=-\frac{2160}{289}e^{\frac{15}{17}}=-7.47e^{0.88}[/tex]
[tex]\Delta f(3,5)=<f_u(3,5),f_v(3,5)>[/tex]
[tex]\Delta f(3,5)=<144e^{0.88},-7.47e^{0.88}>[/tex]
The direction at which he moves down the hills quickly=-[tex]\Delta f(3,5)[/tex]
The direction at which he moves down the hills quickly=[tex]<-144e^{0.88},7.47e^{0.88}>[/tex]
Lost-time accidents occur in a company at a mean rate of 0.4 per day. What is the probability that the number of lost-time accidents occurring over a period of 9 days will be no more than 5
Answer:
0.8441
Step-by-step explanation:
This question can be solved by using the microsoft excel command.
we start off by solvingfor the mean rate for 9 days
mean rate = 0.4
for 9 days = 0.4*9 = 3.6
using the excel command,
POISSON (5, 3.6, TRUE)
p(x≤ 5) = 0.8441
so in conclusion 0.8441 is the probability that lost time accidents over 9 days would not be greater than 5.
the attachment is an excel sheet showing the input and the result.
Solve for x. Round your answer to the nearest tenth if necessary. Please look at the picture above
Answer:
veoba
Step-by-step explanation:
the mean of 5 numbers is 198. the numbers are in ratio 1:2:3:4:5 find the smallest number
Answer: 13.2
In fraction form, this is 66/5
=============================================================
Explanation:
The five values are in the ratio 1:2:3:4:5 which scales up to 1x:2x:3x:4x:5x for some positive number x.
Add up the pieces of the second ratio and set that sum equal to 198. Then solve for x.
1x+2x+3x+4x+5x = 198
15x = 198
x = 198/15
x = 66/5
x = 13.2 is the smallest number since 1x = 1*13.2 = 13.2 was the smallest value of the ratio 1x:2x:3x:4x:5x.
Roger has found a home to be purchase for $120,372 and has agreed to pay 28% down. Find the amount of Roger's down payment. Find the amount of money that Roger would need to borrow through a mortgage in order to purchase the home.
If Roger found a 30 year mortgage with a 5.9% APR. Find Roger's monthly payment. Using the monthly payment how much did Roger pay over the life of the mortgage?
Round your answer to the nearest cent.
Answer:
He needs to borrow: 86667.84
His monthly payment would be: 514.06
He would pay a total of: 185061.6 over the life of the loan
Step-by-step explanation:
roger would need to borrow .72*120372= 86667.84
2.)
calculate the effective rate .059/12= .004916667
[tex]86667.84=x\frac{1-(1+.004916667)^{-30*12}}{.004916667}\\x=514.0585984[/tex]
which we round to 514.06
3.) he is going to pay a total of 514.06*30*12= 185061.6 over the life of the loan
Will give brainliest.
Answer: Assuming there isnt a fourth answer, the answer is the second choice.
Step-by-step explanation: Point A is located in the first quadrant, Point B is located at 3, -1/2 and Point C is reflected off the y axis, in the second choice.
in the diagram below, BD is parallel to XY. what is the value of y?
a. 70
b. 130
c. 110
d. 20
I can't see the diagram sorry.
Step-by-step explanation:
Is there supposed to be a picture attached?
What is the HCF of 1280 and 630
Given:
The two numbers are 1280 and 630.
To find:
The HCF of the given numbers.
Solution:
First write the given numbers in prime factorization form.
[tex]1280=2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 5[/tex]
[tex]630=2\cdot 3\cdot 3\cdot 5\cdot 7[/tex]
Now the product of all the common prime factors is known as the HCF of 1280 and 630.
[tex]HCF=2\cdot 5[/tex]
[tex]HCF=10[/tex]
Therefore, the HCF of 1280 and 630 is 10.
rank the three fractions from smallest to largest? and why
2/7, 4/14, 8/11
Answer:
2/7 = 4/14 so from smallest to largest the fractions are:
2/7 4/14 and 8/11
Step-by-step explanation:
the old building at the back of the school is badly in need of repair. the company Hsa and the executive are planning to renovate the building to accommodate a new music room. There are 15 rooms in the building and the dimension of the rooms to be redone with tiles are 6m long and 4 m wide. ted the tile man has 500 one meter square tiles.
Explain how you would estimate whether Ted has enough tiles to cover all the kitchen floors in the entire apartment building?
How many tiles, each measuring 1 square meter, are needed to cover one room floor?
How many tiles are needed to cover all the floors in the entire building? Show your work?
Answer:
a. If the area of the tiles is greater than or equal to the area of all the rooms.
b. 24
c. 360
Step-by-step explanation:
a. Explain how you would estimate whether Ted has enough tiles to cover all the kitchen floors in the entire apartment building?
Ted would have enough tiles if the area of the tiles is greater than or equal to the area of all the rooms. Since we have 500 one meter square tiles, we have 500 m² of tiles.
Since the rooms are 6 m long and 4 m wide, the area of each room is 6 m × 4 m = 24 m². Since there are 15 rooms, the area of all the rooms is 15 × 24 m² = 360 m².
Since the area of the tiles = 500 m² is greater than the area of the rooms = 360 m², Ted would have enough tiles to cover all kitchen floors in the entire apartment building.
b. How many tiles, each measuring 1 square meter, are needed to cover one room floor?
Since the area of each room floor is 24 m² and the area of each tile is 1 m², so the number of 1 square meter tiles needed to cover each floor is n = area of floor/area of tile = 24 m²/1 m² = 24.
c. How many tiles are needed to cover all the floors in the entire building?
Since 24 tiles are needed to cover each floor and there are 15 rooms in the building, we would require 24 tiles/room × 15 rooms/building = 360 tiles.
So we require 360 tiles.
Find m∠GHIm∠GHI if m∠GHI=14x+6m∠GHI=14x+6, m∠QHI=130∘m∠QHI=130∘, and m∠GHQ=3x−3m∠GHQ=3x−3.
Answer:
m∠GHI = 160
Step-by-step explanation:
From the question given above, the following data were obtained:
m∠GHI = 14x + 6
m∠QHI = 130°
m∠GHQ = 3x – 3
m∠GHI =?
Next, we shall determine the value of x. This can be obtained as follow:
m∠GHI = m∠QHI + m∠GHQ
14x + 6 = 130 + (3x – 3)
14x + 6 = 130 + 3x – 3
Collect like terms
14x – 3x = 130 – 3 – 6
11x = 121
Divide both side by 11
x = 121 / 11
x = 11
Finally, we shall determine the value m∠GHI. This can be obtained as follow:
m∠GHI = 14x + 6
x = 11
m∠GHI = 14(11) + 6
m∠GHI = 154 + 6
m∠GHI = 160
The equivalent equation is found by distributing the
1
to get
4.
The question is incomplete, complete version is written in the comment section below :
Answer:
Kindly check explanation
Step-by-step explanation:
1 / 4 (16 + 12x) = 28
Opening the bracket :
1/4 * 16 + 1/4 * 12x = 28
4 + 3x = 28
Subtract 4 from both sides :
4 + 3x - 4 = 28 - 4
3x = 24
Divide both sides by 3
3x / 3 = 24 / 3
x = 8
what is the value of -2x²y³ when ×=2 and y=4?
Answer:
1024
Step-by-step explanation:
Given :-
x = 2 y = 4Value of -2x²y³
2x³ y³2 * (2)³ * (4)³2 * 8 * 64 1024Answer:
254
Step-by-step explanation:
^ <- this is the square sign
-2x^y^3
x=2
y=4
put x values in to x place and y value in to y place.
-2(2)^2(4)^3
Find the squares and - it with 2
-2(4)(64)
2-256=254
:. the value of -2x^2y^3 =254
That the answer.
Hope this is what you asked.
The sum of the angles of a triangle is 180. Find the three angles if one angle is twice the smallest angle and the third angle is 36 degrees greater than the smallest angle. Place them in order from least to greatest.
Answer:
36°, 72°, 72°Step-by-step explanation:
The angles are x, y and z:
x = 2y, z = y + 36Their sum is:
x + y + z = 1802y + y + y + 36 = 1804y = 144y = 36Then find the other angles:
x = 2*36 = 72z = 36 + 36 = 72Now we have to,
find the three angles if one angle is twice smallest angle and third angle is 36° greater than smallest angle.
Then take the values as,
→ smallest angle = x
→ y = 2x
→ z = x + 36°
Let we find the angles,
→ x + y + z = 180°
→ x + 2x + x + 36° = 180°
→ 4x = 180 - 36
→ 4x = 144
→ x = 144/4
→ [x = 36°]
Now the value of y is,
→ y = 2x
→ y = 2 × 36°
→ [y = 72°]
Then the value of z is,
→ z = x + 36°
→ z = 36° + 36°
→ [z = 72°]
Placing values from least to greatest,
→ 36°, 72°, 72°
Hence, the order is 36°, 72°, 72°.
Hannah ran 12 laps for 8 days. How many laps did she run in total if she take a break of 1 complete day and 1 half day.
Answer:
The correct answer would be - 9.75 laps (if runs 12 laps in 8 days) or 78 laps (if 12 laps each day for 8 days)
Step-by-step explanation:
Given:
a) Laps covered in 8 days = 12
interval = 1 and half day
total laps = ?
Solution:
To know the total laps with intervals we need to calculate the laps run each day :
= 12/8 laps per day
= 3/2 laps per day
Now multiply the daily run with days
= (3/2)*6.5 (due to 8 - 1.5 = 6,5 days)
= 9.75 laps
B) Given:
Laps covered in 8 days = 12*8 =96
interval = 1 and half day
total laps = ?
Solution:
To know the total laps with intervals we need to calculate the laps run each day :
= 96/8 laps per day
= 12laps per day
Now multiply the daily run with days
= 12*6.5 (due to 8 - 1.5 = 6,5 days)
= 78 laps
If you spin two times, what is the probability of landing on
green both times? (leave answer in fraction form in lowest
terms)
Red
Green
Yellow
Red
1/9
1/30
1/6
1/360
Hannah would like to make an investment that will turn 8000 dollars into 33000 dollars in 7 years. What quarterly rate of interest, compounded four times per year, must she receive to reach her goal?
Answer:
20.76%
Step-by-step explanation:
[tex]33000=8000(1+\frac{i}{4})^{4*7}\\4.125=(1+\frac{i}{4})^{28}\\\sqrt[28]{4.125}=1+\frac{i}{4} \\i= .207648169[/tex]
which rounds to 20.76%
Answer:
About 0.2076 or 20.76%.
Step-by-step explanation:
Recall that compound interest is given by the formula:
[tex]\displaystyle A=P\left(1+\frac{r}{n}\right)^{nt}[/tex]
Where A is the final amount, P is the principal, r is the interest rate, n is the number of times the interest is applied per year, and t is the number of years.
Since Hannah wants to turn an $8,000 investment into $33,000 in seven years compounded quarterly, we want to solve for r given that P = 8000, A = 33000, n = 4, and t = 7. Substitute:
[tex]\displaystyle \left(33000\right)=\left(8000\right)\left(1+\frac{r}{4}\right)^{(4)(7)}[/tex]
Simplify and divide both sides by 8000:
[tex]\displaystyle \frac{33}{8}=\left(1+\frac{r}{4}\right)^{28}[/tex]
Raise both sides to the 1/28th power:
[tex]\displaystyle \left(\frac{33}{8}\right)^{{}^{1}\! / \! {}_{28}}= 1+\frac{r}{4}[/tex]
Solve for r. Hence:
[tex]\displaystyle r= 4\left(\left(\frac{33}{8}\right)^{{}^{1}\! / \! {}_{28}}-1\right)[/tex]
Use a calculator. Hence:
[tex]r=0.2076...\approx 0.2076[/tex]
So, the quarterly rate of interest must be 0.2076, or about 20.76%.
I WILL GIVE BRAINLIEST FAST
TRUE OR FALSE?
The triangles shown below must be congruent
B is the answer.
The triangles doesnt creates a SSS,SAS,SAA, scenario.
This triangle isn't ASA because the triangles share the same side but it have different angles that include the side.