Answer:
[tex]d=\sqrt{101}[/tex]
Step-by-step explanation:
Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Simply plug in your 2 coordinates into the distance formula to find distance d:
[tex]d=\sqrt{(8-(-2))^2+(2-3)^2}[/tex]
[tex]d=\sqrt{(8+2)^2+(-1)^2}[/tex]
[tex]d=\sqrt{(10)^2+1}[/tex]
[tex]d=\sqrt{100+1}[/tex]
[tex]d=\sqrt{101}[/tex]
5) 3x2 - 16x + 20
Factor the Trinomial
Answer:
(3x -10)(x -2)
Step-by-step explanation:
You want to start by finding two factors of 3·20 = 60 that have a total of -16.
60 = (-1)(-60) = (-2)(-30) = (-3)(-20) = (-4)(-15) = (-5)(-12) = (-6)(-10)
The last of these factor pairs (-6, -10) have a total of -16, so these are what you need to rewrite the middle term:
3x² -6x -10x +20
Now, you can factor by pairs:
= 3x(x -2) -10(x -2)
= (3x -10)(x -2) . . . . your factored trinomial
Multiplication sentences that is equal to 2/7÷14/3
Two angles are complementary. The larger angle is 58 degrees larger than the smaller angle. Find the measure of both angles, and separate your answers with a comma.
Answer:
the bigger angle is 119
the smaller one is 61
a fish tank at an aquarium has a volume of 1568 cubic feet and a depth of 8 feet. if the base of the tank is square, what is the length of each side of the tank?
Answer:
14 feet.
Step-by-step explanation:
Volume=base area×height
1568=(L×L)×8
1568=8L²
Divide both sides by 8
L²=196
Then square root each side
L=14 feet
is 15 a factor or a multiple
Answer:
Factors of 15 include 3 and 5; multiples of 15 include 30, 45, 60, etc.
Step-by-step explanation:
Factors and multiples are different things. But they both involve multiplication. Factors are what we can multiply to get the number. Multiples are what we get after multiplying the number by an integer
I need help as soon as possible someone please help
Answer:
b
Step-by-step explanation:
Answer:
The answer is B
The area of a rectangular mirror is 8 15/16 square feet. The width of the mirror is 2 3/4 feet. If
there is a 4 foot tall space on the wall to hang the mirror, will it fit?
Answer:
yes
Step by-step explanation:
it will take up 8 12/16 space and the wall has 8 15/16
If AD is the altitude to BC , what is the slope of AD?
A. 1/3
B. 2/3
C. -1/3
D. 3
Answer:
D
Step-by-step explanation:
Slope of BC
= - 1/3
Altitude to BC
= 3
The required slope of the AD altitude to BC is given by option D. 3
AD is the altitude to BC
Altitude is defined as the perpendicular line to the line from the opposite vertex of the triangle.
for ΔABC, AD is the altitude to BC
Since, the slope of the perpendicular line is equal to the negative inverse of the slope of the line over which its is perpendicular.
so,
slope of AD= -1/slope of BC
slope of BC = -1-2/3+6
= -3/9
slope of BC = -1/3
Hence,
slope of AD = -1/-1/3
= 3
Thus, The required slope of the AD altitude to BC is given by 3.
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HELP PLEASE 9TH GRADE MATH
Answer:
B
Step-by-step explanation:
Perpendicular lines have a reciprocal slope with the opposite sign. The y-intercept does not matter
8n/9 = 6.4/0.45
Give me the answer TODAY and you will get 20 points!
Answer:
n = 16
Step-by-step explanation:
8n/9 = 6.4/0.45
Cross multiply.
0.45 * 8n = 9 * 6.4
3.6n = 57.6
n = 16
Answer:
n = 16Step-by-step explanation:
8n = 6.4
9 0.45
simplify:
8n = 14.222
9
cross multiply:
8n = 14.222 (9)
n = 128
8
n = 16
Find the equation of the line passing through the point (4,−1) that is parallel to the line 2x−3y=9
Answer:
[tex]y = \frac{2}{3} x - 3 \frac{2}{3} [/tex]
Step-by-step explanation:
Let's rewrite the given equation in the form of y= mx +c, where m is the gradient while c is the y-intercept.
2x -3y= 9
3y= 2x -9
Divide by 3 throughout:
[tex]y = \frac{2}{3} x - 3[/tex]
Thus, the gradient of given line is ⅔.
Parallel lines have the same gradient.
Therefore, gradient of line is ⅔.
Substitute m=⅔ into the equation:
[tex]y = \frac{2}{3} x + c[/tex]
To find the value of c, substitute a pair of coordinates.
When x=4, y= -1,
[tex] - 1= \frac{2}{3} (4) + c \\ - 1 = \frac{8}{3} + c \\ c = - 1 - \frac{8}{3} \\ c = - 3 \frac{2}{3} [/tex]
Substitute the value of c:
[tex]y = \frac{2}{ 3} x - 3 \frac{2}{3} [/tex]
This is for extra credit
Answer:
\
Step-by-step explanation:
its to blurry what does it say so i can help
Answer:
its too blurry
Step-by-step explanation:
Sam is planning to start a pool cleaning business from his home. He has developed the following cost analysis for the
set-up and operation for the first year of his business. He has $9,000 in savings and $23,000 in credit that he can use for
the business. Approximately what percent of the initial set-up and operation costs will Sam need to finance with a lender
or investor?
Item
Truck
Pool Cleaning Supplies
Payroll
Advertising
a. 19%
b. 23%
C.33%
d. 78%
Cost
$9,000
$6,000
$23,000
$1,500
Please select the best answer from the choices provided
Answer:
a. 19%
Step-by-step explanation:
The percent of the initial set-up and operation costs that Sam needs to finance with a lender or investor is A. 19%.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
to illustrate the percentage:
From the information given,
Sam is planning to start a pool cleaning business from his home.
he has developed a cost analysis for the set-up and operation for the first year of his business.
He has $9,000 in savings and $23,000 in credit that he can use for the business.
so, we get,
Here, the percent of the initial set-up and operation costs that Sam need to finance with a lender or investor is simply 19%.
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PLEASE HELP, BEST ANSWER GETS SHOUTOUT AND BRAINLIEST!!!!!!
Solve the problems. Write the complete proof in your paper homework and for online (only) respond to questions or statements (if any) that are parts of your proof or related to it.
1) Given: PQ = PR
m∠QPR = m∠SPK
m∠Q = m∠PRK
Prove: PS = PK
2) Segments AD and BC intersect at point O.
a) Prove that AC = BD
b) Prove that m∠ABC=m∠BAD
3) Solve the problems. Write the complete proof in your paper homework and for online (only) respond to questions or statements (if any) that are parts of your proof or related to it.
b
Given:
AB
∩
KL
= O
O midpoint of
AB
O midpoint of LK
Prove: ΔAOK ≅ ΔBOL
Answer:
△QPS≅△RPK by reason ASA, SAA
PS = PK , AC = BD , m∠ABC=m∠BAD, ΔAOK ≅ ΔBOL are proved.
What are congruent triangles?Congruent triangles are those of the same size and shape. This means that the corresponding sides are equal, as are the corresponding angles. We can determine whether two triangles are congruent without testing all of their sides and angles.
1) in ΔPQR we have ,
PQ = PR
IN, ∠PRQ = ∠PQR (Isosceles triangle)
180° - ∠PQR = 180° - ∠PQR
∠PQR = ∠PSQ
IN ΔPSQ = PRK
∠SPQ = ∠RPK
∠Q = ∠R IS GIVEN IN QUESTION SO,
∠SPQ = ∠RPQ
so, by ASA congruence we have ,
ΔPSQ ≅ ΔPRK
So, PS = PK
hence proved .
2) There are several ways two triangles can be congruent.
AC = BD congruent by SAS
ABC ≅ BAD congruent by the corresponding theorem
In ΔAOC and ΔBOD, we have the following observations
AO = DO ( O is the midpoint of line segment AD)
BO = CO ( Because O is the midpoint of line segment BC)
∠AOB = ∠COD (vertical angles are congruent)
∠AOC = ∠BOD ( vertical angles are congruent)
Using the SAS (side-angle-side) postulate, we have:
AC = BD
Using the corresponding theorem,
ΔABC ≅ ΔBAD
The above congruence equation is true because:
2 sides of both triangles are congruent
1 angle each of both triangles is equal
Corresponding angles are equal
Hence Proved.
3) There are several ways two triangles can be congruent.
ΔAOK ≅ ΔBOK
are congruent by SAS
In ΔAOL and ΔBOK, we have the following observations
AO = BO ( O is the midpoint of line segment AB)
∠AOL = ∠BOK ( vertical angles are congruent)
LO = KO ( O is the midpoint of line segment KL)
Using the SAS (side-angle-side) postulate, we have:
ΔAOK ≅ ΔBOK
The above congruence equation is true because:
2 sides of both triangles are congruent
1 angle each of both triangles is equal
Hence proved
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Tyson has 1/2of raisions
to divide into seven different bags what fraction of a pound will be in each bag
Answer:
Step-by-step explanation:
ZXVCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
Find the equation of the line perpendicular to y=−2 that passes through the point (4, −2).
(70 points please awnser quickly)
Answer: x = 4
Step-by-step explanation:
It will be a vertical line that passes through +4 and every y-value
Answer:
x=4
Step-by-step explanation:
This is because it will pass through the middle it should be a vertical line that passes through +4 and every y-value to get the right answer
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Josh has a total of 12.5 hours of baseball practice after school five days a week. How
many hours of practice will he have for 15 school days?
Answer:
37.5 hours
Step-by-step explanation:
12.5 for every 5 days
Question asks for 15 days
5 x 3 = 15
12.5 x 3 = 37.5 hours
Answer:
37.5 hours I think is the correct answer
1.588 times 10 to the negative 1sst power
Answer:
0.1588
Step-by-step explanation:
The maximum patent life for a new drug is 17 years. Subtracting the length of time required by the FDA for testing and approval of the drug provides the actual patent life for the drug—that is, the length of time that the company has to recover research and development costs and to make a profit. The distribution of the lengths of actual patent lives for new drugs is given below: Years, y 3 4 5 6 7 8 9 10 11 12 13 p(y) 0.03 0.05 0.07 0.10 0.14 0.20 0.18 0.12 0.07 0.03 0.01 • Find the mean patent life for a new drug. • Find the standard deviation of Y = the length of life of a randomly selected new drug. • What is the probability that the value of Y falls in the interval µ ± 2σ?
Answer:
a
[tex]\mu=E(y) = 7.9[/tex]
b
[tex]\sigma = 2.17[/tex]
c
[tex]P(4 < X < 12) = 0.96[/tex]
Step-by-step explanation:
From the question the data given is
y 3 4 5 6 7 8 9 10 11 12 13
p(y) 0.03 0.05 0.07 0.10 0.14 0.20 0.18 0.12 0.07 0.03 0.01
Generally the mean is mathematically represented as
[tex]\mu =E(y) = \sum_{n=3}^{13} x_i * P(x_i)[/tex]
=> [tex]\mu =E(y) = 3 * 0.03 + 4 * 0.05 + \cdots +13 * 0.01[/tex]
=> [tex]\mu=E(y) = 7.9[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{ [var(y)]}[/tex]
Here [tex][var(y)][/tex] is the variance which is mathematically represented as
[tex][var(y)] = [\sum_{n=3}^{13} x_i^2 * P(x_i)] -[ E(y)]^2[/tex]
=> [tex][var(y)] =[ (3^2 * 0.03 ) + (4^2 * 0.05)+ \cdots + (13^2 * 0.01)] -[ 7.9]^2[/tex]
=> [tex][var(y)] =67.14 - 62.41[/tex]
=> [tex][var(y)] =4.73[/tex]
Thus
[tex]\sigma = \sqrt{ 4.73}[/tex]
[tex]\sigma = 2.17[/tex]
Generally the interval given is µ ± 2σ i.e [ µ - 2σ , µ +2σ]
substituting values
[tex][7.9 - 2(2.17) ,7.9 - 2(2.17) ][/tex]
[tex][3.56 ,12.24 ][/tex]
Now approximating this interval to a whole number
[tex][4 ,12][/tex]
Hence the probability that the value of Y falls in the interval µ ± 2σ is mathematically represented as
[tex]P(4 < X < 12) = P(x__4} ) + \cdots + P(x__{12}})[/tex]
[tex]P(4 < X < 12) = 0.05 + \cdots +0.03[/tex]
[tex]P(4 < X < 12) = 0.96[/tex]
1 point
What is Nick required to do for an hour before soccer on Saturdays?
laundry
O read his dad's dictionary
practice his soccer skills
clean his room
Please help please lease ASAP
Brian made 72 widgets. If kelly and miranda together made three times as many widgets as brian, how many more widgets did they make?
Write the mathematical sentence and show the work .
72 x 3 = 216 ÷ 2 = 108
the difference between two negative umers is always negative
2 Ollie is at a gift shop where the total cost, y, of purchasing post cards can be
represented by y = 0.75x. If x is the number of post cards purchased, which of
the following represents the most reasonable domain?
a. All integers
b. All whole numbers
c. All real numbers
d. All positive real numbers
Answer:
it would be all positive #s (real #s)
Step-by-step explanation:
The domain can be All positive real numbers
What are real numbers?Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7).
Given:
y = 0.75x
where y is number of purchasing post cards and x is the number of post cards purchased.
as, x is number of postcard purchased.
So, number of postcard purchased cannot be negative, only positive real number are allowed.
Hence, the possible domain is All positive real numbers
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In the straight line figure below ,m
Answer:
7 t 24=31y
Step-by-step explanation:
Find distance between points : (2,6) and (7,18)
Answer:
the answer 18.0008
Step-by-step explanation:
Answer:
[tex]D=\sqrt{(2-7)^{2}(6-18)^{2} }D=\sqrt{(5)^{2}(12)^{2} } D=\sqrt{25+144} D=\sqrt{169} = 13[/tex]D = 13Step-by-step explanation:
1st step, we use the distance formula. After plugging in we simplify.
2-7 = 5 / 6-18 = 12.
Then we are left with 5^2 and 12^2
5x5 = 25 and 12x12 is 144
we added them up and get 169
The square root of 169 is the answer to the distance.
please help i need it asap
Answer:
[tex]sqrt{-64} =8i\\\\sqrt{-15} =isqrt{15} \\sqrt{-100} =10i\\sqrt{-25} =2i\sqrt{6}[/tex]
Step-by-step explanation:
I hope this helps
Mr. Hammond earns $13.75 per hours and worked 20.5 hours last week. How much did he earn last week?
Multiply total hours worked by pay rate:
20.5 x $13.75 = $281.88
Expanded form with fractions 74.052
Answer:
[tex]Digit = 7 * 10 +4 * 1 + \frac{0}{10} + \frac{5}{100} + \frac{2}{1000}[/tex]
Step-by-step explanation:
Given
[tex]Digit = 74.052[/tex]
Required
Expand
[tex]Digit = 74.052[/tex]
Split into individual digits
[tex]Digit = 7 * 10 +4 * 1 + 0 * 0.1 + 5 * 0.01 + 2 * 0.001[/tex]
Convert all decimals to fraction
[tex]Digit = 7 * 10 +4 * 1 + 0 * \frac{1}{10} + 5 * * \frac{1}{100} + 2 * * \frac{1}{1000}[/tex]
[tex]Digit = 7 * 10 +4 * 1 + \frac{0}{10} + \frac{5}{100} + \frac{2}{1000}[/tex]
The weight of an object rounds to 41.3 kilograms select the three posible weights that correctly round to 41.3 kilograms
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]Weight = 41.3kg[/tex]
Required
Determine the weights that approximates to 41.3kg
The options are not given but the question is still solvable
In approximation:
0 - 4 approximates to 0
This implies that:
41.30 to 41.34 approximates to 41.3
Also:
5 - 9 approximates to 1
This implies that:
41.25 to 41.29 approximates to 41.3
Bring the range together, we have:
[tex]Range = 41.25\ to\ 41.34[/tex]
Select any three numbers within this range, and you have your answer
Examples are: 41.25, 41.28, 41.34\
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