Answer:
-4, 4, 7i, -7i
Step-by-step explanation:
Basically any or each bracket must be equal to 0. If x^2+16 = 0, then x can be 4 and -4, and if x^2+49 is 0, then x =7i or -7i
calculate the distance between the point(5,6) and (7,8)
The base and height of a right triangle are 20 inches and 15 inches. Find the length of the hypotenuse.
Using the Pythagorean theorem:
Hypotenuse = sqrt( 20^2 + 15^2)
Hypotenuse = sqrt( 400 + 225)
Hypotenuse = sqrt(625)
Hypotenuse = 25
Answer: 25 inches
Answer:
25 inches
Step-by-step explanation:
We can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
20^2 + 15^2 = c^2
400 +225 = c^2
625=c^2
Taking the square root of each side
sqrt(625) = sqrt(c^2)
25 = c
At a certain point from a pole, the angle of the elevation to the top of the pole is 28 degrees if the pole is 6.3 feet tall, what is the distance from the pole
Answer:
11.85
Step-by-step explanation:
Tan 28 = opposite / adjacent
Answer:
the distance from the pole is 11.85 ft.
Step-by-step explanation:
Given;
the elevation to the top of the pole, θ = 28⁰
height of the pole, h = 6.3 ft
let the distance from the pole = x
If a sketch of a right triangle is made as follows, it will be observed that the base of the triangle forms the adjacent side of the triangle, which is equal to x.
↑
↑ h = 6.3 ft
↑
28⁰ ---------------
x
[tex]tan(28) = \frac{6.3}{x} \\\\x = \frac{6.3}{tan(28)} \\\\x = 11.85 \ ft[/tex]
Therefore, the distance from the pole is 11.85 ft.
Write an equation for a parabola with endpoints of the latus rectum at (-2, 3) and (-2, 15) and the directrix at x = 4.
Given:
The endpoints of the latus rectum at (-2, 3) and (-2, 15).
The directrix at x = 4.
To find:
The equation of the parabola.
Solution:
The equation of the parabola is:
[tex](y-k)^2=4p(x-h)[/tex] ...(1)
Where, [tex]x=h-p[/tex] is directrix and [tex](h+p,k\pm |2p|),p<0[/tex] are the end point of the latus rectum.
The directrix at x = 4. So,
[tex]h-p=4[/tex] ...(i)
The endpoints of the latus rectum at (-2, 3) and (-2, 15). So,
[tex](h+p,k-|2p|)=(-2,3)[/tex]
[tex](h+p,k+|2p|)=(-2,15)[/tex]
Now,
[tex]h+p=-2[/tex] ...(ii)
[tex]k-2p=3[/tex] ...(iii)
[tex]k+2p=15[/tex] ...(iv)
Adding (i) and (ii), we get
[tex]2h=2[/tex]
[tex]h=1[/tex]
Putting [tex]h=1[/tex] in (i), we get
[tex]1-p=4[/tex]
[tex]-p=4-1[/tex]
[tex]-p=3[/tex]
[tex]p=-3[/tex]
Putting [tex]p=-3[/tex] in (iii), we get
[tex]k-|2(-3)|=3[/tex]
[tex]k-6=3[/tex]
[tex]k=3+6[/tex]
[tex]k=9[/tex]
Putting [tex]h=1,p=-3,k=9[/tex] in (1), we get
[tex](y-(9))^2=4(-3)(x-1)[/tex]
[tex](y-9)^2=-12(x-1)[/tex]
Therefore, the required equation of the parabola is [tex](y-9)^2=-12(x-1)[/tex].
Four cans of cat food and 3 cans of dog food cost $1.99. Four cans of the same cat food and 1 can of the same dog food cost $1.33 hat is the cost of one can of cat food
Answer:
$0.25
Step-by-step explanation:
We can use System of Equations to find out how much a can of cat food costs.
Let's use variables to represent the cat food and dog food:
x = cost of 1 cat food can
y = cost of 1 dog food can
Here are our 2 equations based on the scenarios in the question:
4x + 3y = 1.99
4x + y = 1.33
Now let's set the second equation to y using basic algebra:
4x + y = 1.33
y = -4x+1.33
And we're going to plug that value of y, which is -4x+1.33 into the first equation and solve:
4x + 3y = 1.99
4x + 3(-4x+1.33) = 1.99
4x + -12x+3.99 = 1.99
-8x + 3.99 = 1.99
-8x = -2
x = 1/4
x = 0.25
1 can of cat food costs $0.25
Hope that helps (●'◡'●)
Answer:
.25
Step-by-step explanation:
set up equations
1)4c+3d=1.99
2)4c+d=1.33
Method of use:Elimination
4c+3d=1.99
- (4c+d)=-(1.33)
___________
=2d=.66
divide by two on both sides to get .33 for d.
plug in
4c+.33=1.33
subtract .33 on both sides
4c=1
divide by four on both sides to get c
c=1/4 or .25
Find the perimeter of the polygon.
Answer:
36 units
Step-by-step explanation:
this is a walk around problem
the sides of the triangle will be 10, 13, and 13
so the perimeter = 10 + 13 + 13
p = 36 units
Answer:
perimeter = 36
Step-by-step explanation:
Tangents drawn to a circle from an external point are congruent, then
perimeter = (5 + 5) + (8 + 8) + (5 + 5)
= 10 + 16 + 10
= 36
Multiply the polynomial vertically:
1/2x^2(12x^2 - 4x + 2)
Step-by-step explanation:
= 1/2x^2.12x^2 - 1/2x^2.4x + 1/2x^2.2
= 6x^4 - 2x^2 + x
find the mean of the following 2x-5y,5x+2y,8x+6y,x-y
Answer: 4x + 0.5y
Step-by-step explanation:
Concept:
Here, we need to understand the idea of the mean (average).
The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers.
If you are still confused, please refer to the attachment below for a graphical explanation.
Solve:
**Disclaimer** I assume the question is asking for the arithmetic mean instead of geometric. If it was, then you can refer to my answers. If it was not, then you can point it out and I will redo the question.
Terms: 2x-5y, 5x+2y, 8x+6y, x-y
Number of terms: 4
[(2x-5y) + (5x+2y) + (8x+6y) + (x-y)] / 4
=[2x + 5x + 8x + x + 2y - 5y + 6y - y] / 4
=[16x + 2y] / 4
=4x + 0.5y
Hope this helps!! :)
Please let me know if you have any questions
please! can somebody help me?
Step-by-step explanation:
The depth of the water is increasing by 2 feet each minute.
Two towns A and B are 220km apart. A bus left town A at 11.00 AM and travelled towards town B at 60km/hr. At the same time, a van left town B for town A and travelled at 80km/hr. The van stopped for a total of 45 minutes on the way before meeting the bus. Calculate the distance covered by the bus before meeting the van. Please show clear working and explanation to get a brainlist !!!
Answer:
Sa / Va = time traveled by bus a
Sb / Vb + 3/4 = time traveled by van b
Sa / Va = Sb / Vb + 3/4 times traveled are the same
= (220 - Sa) / Vb + 3/4
Sa ( 1 / Va + 1 / Vb) = 220 / 80 + 3/4
Sa (140 / 4800) = 3.5
Sa = 120 km
Check: 120 km / 60 km/hr = 2 hr = Ta
Sb = 1.25 * 80 = 100 km traveling for 1.25 hrs
A t-shirt cost 5 times as much as a singlet. For $800,a trader can buy 32 more singlet than t-shirts. How much does a t-shirt cost
Answer: [tex]\$100[/tex]
Step-by-step explanation:
Given
T-shirt cost 5 times as much as a singlet
Suppose the price of a singlet [tex]x[/tex]
Price of a T-shirt is [tex]5x[/tex]
According to the question, for $800, trader can buy 32 more singlet than T-shirt
[tex]\Rightarrow \dfrac{800}{x}=\dfrac{800}{5x}+32\\\\\Rightarrow \dfrac{800}{x}-\dfrac{160}{x}=32\\\\\Rightarrow 800-160=32x\\\\\Rightarrow x=20[/tex]
Thus, the price of a T-shirt is [tex]5x=\$100[/tex]
Find the equation of the line which is perpendicular to the line.
(a) with equcation y=5x-4 and passes through (0,7)
Answer:
[tex]y = - \frac{1}{5} x + 7[/tex]
Step-by-step explanation:
Slope -intercept form:
y= mx +c, where m is the slope and c is the y- intercept.
Since the given equation is already in the slope-intercept form, we can identify its slope by looking at the coefficient of x.
Slope of given line= 5
The product of the gradients of two perpendicular lines is -1.
m(5)= -1
[tex]m = - \frac{1}{5} [/tex]
Substitute the value of m into the equation:
[tex]y = - \frac{1}{5} x + c[/tex]
Substitute a pair of coordinates to find the value of c.
when x= 0, y= 7,
[tex]7 = - \frac{1}{5} (0) + c[/tex]
c= 7
Thus, the equation of the line is y= -⅕x +7.
help me with this math question
Answer:
points D and B. Answer choices D and E.
Step-by-step explanation:
The point, C, is at -1 1/4. Count over 2 points of either B or D, and you have your answer.
Given that a box has 3 blue marbles, 2 red marbles, and 4 yellow marbles, use the probability formulas to answer the following questions. Reduce all fractions. Use / as the fraction bar and do not use any spaces. What is the probability of... Drawing a blue marble?
P( Answer
)= Answer
Drawing a marble that is not red?
P( Answer
)= Answer
Drawing a red and yellow marble?
P( Answer
)= Answer
Drawing a red or blue marble.
P( Answer
)= Answer
Drawing a red marble, put it back, and then drawing a yellow marble?
P( Answer
)= Answer
Drawing a yellow marble, keeping it, and then drawing another yellow marble?
P( Answer
)= Answer
Drawing a yellow marble, given that a red marble was drawn on the first draw and not replaced?
P( Answer
)= Answer
Answer:
drawing a blue marble is a harder then the yellow but not as hard as the red.
Let 0 be an acute angle of a right triangle. Evaluate the other five trigonometric functions of 0.
Answer:
1. Cos θ = 6√2 / 11
2. Tan θ = 7 / 6√2
3. Cosec θ = 11 / 7
4. Sec θ = 11 / 6√2
5. Cot θ = 6√2 / 7
Step-by-step explanation:
From the question given above, the following data were obtained:
Sine θ = 7 / 11
Next, we shall determine the adjacent of the right triangle. This can be obtained as follow:
Sine θ = 7 / 11
Sine θ = Opposite / Hypothenus
Opp = 7
Hypo = 11
Adj =?
Hypo² = Opp² + Adj²
11² = 7² + Adj²
121 = 49 + Adj²
Collect like terms
Adj² = 121 – 49
Adj² = 72
Take the square root of both side
Adj = √72
Adjacent = 6√2
1. Determination of Cos θ
Adjacent = 6√2
Hypothenus = 11
Cos θ =?
Cos θ = Adjacent / Hypothenus
Cos θ = 6√2 / 11
2. Determination of Tan θ
Opposite = 7
Adjacent = 6√2
Tan θ =?
Tan θ = Opposite / Adjacent
Tan θ = 7 / 6√2
3. Determination of Cosec θ
Sine θ = 7 / 11
Cosec θ =?
Cosec θ = 1 ÷ Sine θ
Cosec θ = 1 ÷ 7 / 11
Cosec θ = 1 × 11/7
Cosec θ = 11/7
4. Determination of Sec θ
Cos θ = 6√2 / 11
Sec θ =?
Sec θ = 1 ÷ Cos θ
Sec θ = 1 ÷ 6√2 / 11
Sec θ = 1 × 11 / 6√2
Sec θ = 11 / 6√2
5. Determination of Cot θ
Tan θ = 7 / 6√2
Cot θ =?
Cot θ = 1 ÷ Tan θ
Cot θ = 1 ÷ 7 / 6√2
Cot θ = 1 × 6√2 / 7
Cot θ = 6√2 / 7
what is the value of a if va- vh is equals to 1
Answer:
[tex] \displaystyle a = \frac{1+vh}{v}[/tex]
Step-by-step explanation:
we want to figure out a value of a for the following condition
[tex] \displaystyle va - vh = 1[/tex]
to do so factor out v;
[tex] \displaystyle v (a - h )= 1[/tex]
divide both sides by v which yields:
[tex] \displaystyle \frac{(a-h) \cancel{(v)}}{ \cancel{v}}= \frac{1}{v} [/tex]
therefore,
[tex] \displaystyle a-h = { \frac{1}{v}}[/tex]
now,add h to both sides:
[tex] \displaystyle a = \frac{1}{v}+h[/tex]
further simplification if necessary:
[tex] \displaystyle a =\boxed{ \frac{1+vh}{v}}[/tex]
factor out of v
[tex]\sf{v(a-h)=1 }[/tex]Dividing both sides by (v)
[tex]\sf{\dfrac{v(a-h)}{(v)}=\dfrac{1}{(v)} }[/tex]cancel out (v)
[tex]\sf{\dfrac{\cancel{v}(a-h)}{\cancel{(v)}}=\dfrac{1}{(v)} }[/tex][tex]\sf{ a-h=\dfrac{1}{v} }[/tex]
add h in both sides
[tex]\sf{a-h+h=\dfrac{1}{v}+h }[/tex]cancelout h
[tex]\sf{a-\cancel{h}+\cancel{h}=\dfrac{1}{v}+h }[/tex] [tex]\sf{a=\dfrac{1}{v}+h }[/tex] [tex]\boxed{\sf{a=\dfrac{1+vh}{v} } }[/tex][tex]\sf{ }[/tex] [tex]\sf{ }[/tex]
Therefore:-the value of a if va- vh is equals to 1 is [tex]\bold{\dfrac{1+vh}{v} }[/tex]
Please help!!!!!!!!!!!!!!
Answer:
7^-22
Step-by-step explanation:
Exponent laws.
Solve for x. Round to the nearest tenth of a degree, if necessary. Please HELP!
Answer:
x = 29.5
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos x = adj side/ hypotenuse
cos x = 67/77
Taking the inverse cos of each side
cos^-1( cos x) = cos^-1 (67/77)
x = 29.52626525
To the nearest tenth
x = 29.5
Connor was given a box of assorted chocolates for his birthday. Each night. Connor
treated himself to some chocolates. There were originally 18 chocolates in the box
and after 3 nights, there were 9 chocolates remaining in the box. Write an equation
for C. in terms oft, representing the number of chocolates remaining in the boxt
days after Connor's birthday.
Submit RSE
acer
Answer:
c = 18 - 3d
Step-by-step explanation:
d = days after birthday
Answer:
C = 18 - 3t
Step-by-step explanation:
18 - 9 = 9
9 / 3 = 3
18 = chocolates at the beginning.
C = 18 - 3t
The answer is C = 18 - 3t.
The difference of a number and six is the same as five times the sum of a number and two what is the number
A random variable X has a Poisson distribution with a mean of 3. What is the probability that X P(1≤X≤3) ?.
Answer:
P(1≤X≤3) = 0.5974
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Mean of 3
This means that [tex]\mu = 3[/tex]
P(1≤X≤3) ?
[tex]P(1 \leq X \leq 3) = P(X = 1) + P(X = 2) + P(X = 3)[/tex]
So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]
[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]
[tex]P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240[/tex]
So
[tex]P(1 \leq X \leq 3) = P(X = 1) + P(X = 2) + P(X = 3) = 0.1494 + 0.2240 + 0.2240 = 0.5974[/tex]
Which of the answer choices could be the one missing data item for the following set, if the mode is 12?
7, 12, 9, 15, 12, 7, 9, 7, 12, 15
HELP I WILL GIVE BRAINLIEST
A. 15
B. 9
C. 7
D. 12
Answer:
D
Step-by-step explanation:
first of all, what is mode: it is the highest occuring number in a set of numbers.
now since 12 is supposed to be the mean and it occurs twice but 9 also occurs twice so for 12 to be the mode, we must add one more 12.
therefore the answer is 12
NEED THIS ASAP :)
What is the length of the y-component of the vector plotted below?
A. 3
B. 4
C. 1
D. 2
Answer:
4
Step-by-step explanation:
Length of the y component is how far the vector reaches vertically, so in this case it's 4
Jada worked at the bakery for 14 hours last week he spent $12 of his earnings on a cake for his father‘s birthday as he was last with $86 after buying the cake what is Gianna‘s hourly wage
Answer:
$7 is his Hourly Wage.
Step-by-step explanation:
We can start by finding out how much money Jada started with by adding the amount of money he had after buying the cake with how much he spent on the cake, 86 + 12 = 98.
We now know how much money he had before buying anything. Now we can just divide the total amount of money by how long he worked.
98 ÷ 14 = 7
Each participant in a certain study was assigned a sequence of 3 different letters from the set {A, B, C, D, E, F, G, H}. If no sequence was assigned to more than one participant and if 36 of the possible sequences were not assigned, what was the number of participants in the study? (Note, for example, that the sequence A, B, C is different from the sequence C, B, A.)
Answer: 300
Step-by-step explanation:
Based on the information given in the question, the number of participants in the study will be calculated thus:
The number if letters in the set are 8 from A - H. This means that there are 8 ways to choose 3 letter when the ordering matters.
This will be:
= 8!/(8 - 3)!
= 8 × 7 × 6
= 336
Since 36 sequences were not assigned, therefore the numbers that were assigned will be:
= 336-36
= 300.
There were 300 participants.
help me out please
(geometry)
Answer:
x = 17
Step-by-step explanation:
The angles are same side interior angles and they will add to 180 when the lines are parallel
6x+8 + 4x+2 = 180
10x+10 = 180
Subtract 10 from each side
10x+10-10 =180-10
10x = 170
Divide by 10
10x/10 = 170/10
x = 17
Answer:
x = 17
Step-by-step explanation:
Theorem:
If two lines are cut by a transversal such that same-side interior angles are supplementary, then the lines are parallel.
For the lines to be parallel, the sum of 6x + 8 and 4x + 2 must equal 180.
6x + 8 + 4x + 2 = 180
10x + 10 = 180
10x = 170
x = 17
HELPP! You will get 15 points!
AD is an angle bisector of
Answer:
<CAB
Step-by-step explanation:
Since CAD is equal to DAB
AD bisects CAB
En una situación en una institución educativa se realizó una encuesta a todos los estudiantes de cuarto grado de secundaria sobre las carreras desean seguir cuando termine sus estudios los resultados obtenidos se muestran en el siguiente cuadro gráfico
Answer:
La ingeniería es la opción más preferida y la contabilidad es la opción menos preferida entre los diferentes estudios.
Step-by-step explanation:
Los resultados obtenidos de la encuesta a estudiantes que siguen diferentes carreras luego de completar su 4 grado en la escuela secundaria. Cuando los estudiantes terminan sus estudios de secundaria, prefieren dedicarse más a la ingeniería. La escala salarial de los ingenieros es alta y también la demanda de ingenieros es alta en el país. La segunda mejor opción para los estudiantes serán los estudios comerciales, luego elegirán medicina, contabilidad y otros estudios. Las opciones están disponibles para que los estudiantes elijan su carrera preferida en la que identifiquen su interés.
What is the slope-intercept equation of the line below?
O A. y = 2 x + 1
O B. y --4x+1
O C. y - 4x +1
O D. y--3x+1
Answer:
A.) y = 3/4x + 1
Step-by-step explanation:
First let's find the slope using the slope formula, (y₂-y₁)/(x₂-x₁). The two points given are (0,1)₁ and (4,4)₂. We have to substitute those values.
y₂ = 4, y₁ = 1, x₂ = 4, x₁ = 0 --> (4 - 1)/(4 - 0) = 3/4
The slope is 3/4.
Now, we have to find the y-intercept, which is where the line meets the y-axis. It touches the y-axis at (0,1). The y-intercept is 1.
Finally, we build our equation in slope-intercept form.
y = mx + b
y = 3/4x + 1
In △MNP , point Q is between points M and N, and point R is between points N and P. Point H is the incenter of the triangle, HQ⊥MN, and HR ⊥NP. QN=36 and HN=39 . What is HR ? Enter your answer in the box.
Answer:
15
Step-by-step explanation:
The given parameters are represented by drawing the triangle with the details given using MS Visio
The point Q is located between points M and N in ΔMNP
The point R is located between points N and P in ΔMNP
The incenter of the triangle = H
Line HQ is perpendicular to side MN on ΔMNP
Line HR is perpendicular to side NP on ΔMNP
The length of the segment QN = 36
The length of the segment HN = 39
By Pythagoras' theorem, HQ = √((HN)² - (QN)²)
∴ HQ = √(39² - 36²) = 15
HQ = 15
Given that H is the incenter of ΔMNP, the lengths of the perpendicular from H to the sides of the triangle are equal to the radius of the inscribed circle of the triangle
Therefore, the radius lengths are HQ, and HR
∴ HR = HQ = 15
HR = 15.
