Answer:
Step-by-step explanation:
Graph a line given a point and a slope
Plot the given point.
Use the slope formula to identify the rise and the run.
Starting at the given point, count out the rise and run to mark the second point.
Connect the points with a line.
What is the sum of the complex numbers -9 - i and -5 - i?
1. -14 - 2i
2. 14 - 2i
3. 14 + 2i
4. -14 + 2i
. If a, b, c are real numbers such that ac # 0
then show that at least one of the equations
ax + bx+ c=0 and -ax + bx+ c=0 has real
roots.
Answer:
if one equation has no real roots, the other must have real roots. Hence, at least one equation has real roots.
Step-by-step explanation:
The discriminant of the first equation is ...
d1 = b^2 -4ac
The discriminant of the second equation is ...
d2 = b^2 +4ac
__
Suppose the first equation has no real roots. Then ...
d1 < 0
b^2 -4ac < 0
b^2 < 4ac
We know that b^2 is non-negative, so this means 4ac is positive. For that case,
d2 = b^2 +4ac
is the sum of a positive number and a non-negative number so will be positive. When the discriminant is positive, there are two real roots.
When the first equation has no real roots, the second one must have two real roots.
__
Suppose the second equation has no real roots. Then ...
d2 < 0
b^2 +4ac < 0
b^2 < -4ac
Again, b^2 is non-negative, so -4ac must be positive. For this case, the sum ...
d1 = b^2 -4ac
is the sum of a non-negative and a positive number, so will be positive. The positive discriminant means there are two real roots.
When the second equation has no real roots, the first one must have two real roots.
One of these equations will have real roots, or not. If not, the other must have (distinct) real roots.
The park shown is in the shape of a square. Is the perimeter rational or irrational? Area = 24,200 yd 2
Answer:
Perimeter is irrational
Step-by-step explanation:
The attachment is missing but the question is still answerable
Given
[tex]Area = 24200 yd^2[/tex]
Required
Determine if the Perimeter is rational or not
First, we need to determine the sides of the square;
[tex]Area = Length * Length[/tex]
Substitute [tex]Area = 24200 yd^2[/tex]
[tex]24200 = Length * Length[/tex]
[tex]24200 = Length^2[/tex]
Take Square root of both sides
[tex]\sqrt{24200} = Length[/tex]
[tex]Length = 155.563492[/tex]
The perimeter of a square is calculated as:
[tex]Perimeter = 4 * Length[/tex]
[tex]Perimeter = 4 * 155.563492[/tex]
[tex]Perimeter = 622.253968[/tex]
Because the value of perimeter can't be gotten by dividing two integers, then perimeter is irrational
What is the equation of the line perpendicular to the line y = 3x + 2 and passing through the point (3, -4)?
Answer:
Step-by-step explanation:
perp. -1/3
y + 4 = -1/3(x - 3)
y + 4 = -1/3x + 1
y = -1/3x - 3
2. What is an expression for the distance between the origin and a point P(x, y)?
Step-by-step explanation:
Using distance formula: { origin is (0,0)}
√(x - 0)² + (y - 0)²
√x² + y²
The distance between the origin and the point P(x,y) is √(x² + y²).
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The distance between the origin (0,0) and the point P(x,y) is calculated as below:-
Distance = √(x - 0)² + (y - 0)²
Distance = √(x² + y²)
Therefore, the distance between the origin and the point P(x,y) is √(x² + y²).
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ACTIVIDAD 1: En el Parque Nacional Selva de Florencia Un explorador
se pierde dentro de un inmenso terreno circular de diámetro 27 km.
La información que se tiene es que si camina 10 km hacia el Occidente
o 5 km hacia el Oriente, llegará al borde de la circunferencia.
Responde:
a) El punto del borde más cercano a la posición del explorador a
cuantos Km se encuentra?
b) ¿Cuánto mide el perímetro y área de este terreno sabiendo
que tiene un diámetro de 27 Km?
Answer:
a) La distancia desde el punto del borde más cercano a la posición del escáner es 5 · √5 km
b) El perímetro del área = 84,823 km
El área de la tierra = 572.555 km²
Step-by-step explanation:
a) La distancia desde el punto del borde más cercano a la posición del escáner viene dada por la fórmula de Pitágoras;
r = √a² + b²
Por lo tanto, la distancia = √ (10² + 5²) = √125 = 5 · √5 km
La distancia desde el punto del borde más cercano a la posición del escáner es 5 · √5 km
b) El perímetro está dado por la fórmula para el perímetro de un círculo que es, perímetro, s = π × D
Dónde;
D = El diámetro de la tierra = 27 km.
El perímetro = π × 27 = 84.823 km
El perímetro del área = 84.823 km
El área está dada por la fórmula del área de un círculo = π × D² / 4
El área = π × 27² / 4 = 572.555 km²
El área de la tierra = 572,555 km².
a theater has 675 seats. there are three times as many seats in a row as their are rows
Answer: 15 rows with 45 seats each
Step-by-step explanation:
Let x = the number of rows, then 3x= the number of seats in a row.
seats × row= total
3x × x=675
3x²=675
x²=225
x=15
Answer:
Step-by-step explanation:
let the number of rows=x
seats in each row=3x
so number of seats=x(3x)=3x²
3x²=675
x²=225
x=15
number of rows=15
and seats in each row=15×3=45
The diameter of a car wheel is 60 cm, if the car travels at an average speed of 13.2m/s, find the number of revolutions made by the car per hour , hiving the awnser correct to nearest whole number. (take pie to be 3.142 )
The wheel has diameter 60 cm = 0.60 m, and thus circumference π(0.60 m) ≈ 5.923 m.
In one complete revolution, a point on the edge of the wheel covers this distance, so that the wheel has an angular speed of
(13.2 m/s) * (1/5.923 rev/m) ≈ 2.229 rev/s
There are 60 seconds to each minute, and 60 minutes to each hour, so converting to rev/h gives
(2.229 rev/s) * (60 s/min) * (60 min/h) ≈ 8024 rev/h
When constructing the bisector of a line segment, you are also constructing the perpendicular bisector of a line segment. true or false Explain your reasoning.
Answer:
True
Step-by-step explanation:
A perpendicular bisector may be defined as the line segment that intersects some other given line perpendicularly and it also divides it into two congruent or equal parts. Now, two lines are said to be cut at right angles or perpendicular to each other if they intersect in a way that they form ninety degrees to each other.
Constructing a line bisector.
1. Take any line segment of any length.
2. Take your compass and adjust its length to more than the half of the length of the line segment.
3. Placing the compass pointer on one edge at a time cut arcs above and below the line segment.
4. Now mark the points where both opposite arcs meet and join the point to cut the given line segment in two equal parts.
Thus the bisector will divide the line into two equal line segments and it will be at right angles to the given line segment.
Thus it is true that constructing a line bisector is also constructing a perpendicular bisector of the line segment.
Six friends each use a $2-off coupon to buy themselves a movie ticket. They spend a total of $42. What is the price of one movie ticket without the coupon?
Answer:
$9
Step-by-step explanation:
1.) First, divide 42 by 6 since there are six people and the total is $42.
42/6 = 7
2.) Now, add $2 to 7 since 7 was the price of the movie ticket AFTER the $2 were taken off of it
x = 7+2x=9
4.) So, one movie ticket (x) = $9
7/3+3(2/3−1/3)*2 I need an answer to this question really quick, and by the way the two in the end is a second power
Answer:
[tex]\frac{8}{3}[/tex]
Step-by-step explanation:
Given
[tex]\frac{7}{3}[/tex] + 3([tex]\frac{2}{3}[/tex] - [tex]\frac{1}{3}[/tex] )²
= [tex]\frac{7}{3}[/tex] + 3 ([tex]\frac{1}{3}[/tex] )²
= [tex]\frac{7}{3}[/tex] + 3 × [tex]\frac{1}{9}[/tex]
= [tex]\frac{7}{3}[/tex] + [tex]\frac{1}{3}[/tex]
= [tex]\frac{8}{3}[/tex]
Answer:
8/3
Step-by-step explanation:
7/3+3(2/3-1/3)^2
=7/3+3(1/3)^2
=7/3+3(1/9)
=7/3+3/9
=7/3+1/3
=8/3
1 point
Two benefits of having a checking account are safety and convenience.
Which of the following statements is FALSE?
a. If you have a checking account, you won't need to carry as much cash with you
b. With a checking account, you have several options for how to pay bills
c. You can cash checks for free when you cash your paycheck at your bank
d. In order to shop online, you must use a debit card
the answer is A right
Un tanque de almacenamiento de agua instalado en una comunidad tiene forma de prisma rectangular y una capacidad de 8 000 litros, su base mide 2.5 m por 2 m. ¿Qué altura tiene este tanque? ¿Qué cantidad de agua contendría si sólo llegara el agua a una altura de 75 cm?
Answer:
a) la altura es de 1.6 metros
b) contendría 3750 litros
Step-by-step explanation:
1000 litros = 1m³
8000 litros = 8000/1000 = 8m³
La formula del volumen de un prisma rectangular es:
v = área de la base * altura
el área de la base es:
ab = 2.5m * 2m = 5m²
entonces:
v = 5 * altura
v = 8m³
así que:
8m³ = 5m²* altura
altura = 8m³/5m²
altura = 1.6 metros
Si la altura fuese de 75cm1 metro = 100 centímetros
75 cms = 75/100 = 0.75 metros
entonces:
volumen = 5m² * 0.75m
volumen = 3.75m³
3.75m³ = 3.75*1000 = 3750 litros
El agua que contendría sería de:
3750 litros
The surface area S of the sphere varies directly as square of radius r and = 16 when = 2. Find when = 36 ........ with proper steps and explanation.
Answer:
r = 3
Step-by-step explanation:
Here in this question, we are told that the surface area of the sphere varies directly as square of radius;
The first thing to do here is to assign variables;
let s be the surface area and r be the radius;
Now;
Since it is a direct proportional relationship;
s = k•r^2
where k represents the constant of proportionality.
now, let’s get k at first.
From the first part of the question, s = 16 and r = 2; Substituting this, we have
16 = k•2^2
4k = 16
k = 16/4
k = 4
Now from the second part of the question, we want to find r when s = 36
Let’s rewrite our equation;
s = k•r^2
where in this case, r = ? and s = 36
36 = 4 * r^2
4r^2 = 36
r^2 = 36/4
r^2 = 9
r = √9
r = 3
Kindly note we do not pick the negative square root value as radius cannot be negative
The surface area of the sphere when the radius is 5 inches is [tex]100\pi[/tex] and this can be determined by using the given data.
Given :
The surface area of a sphere varies directly as the square of the radius. The surface area is 36 when the radius is 3 inches.The following steps can be used in order to determine the surface area S of the sphere:
Step 1 - According to the given data, the surface area S of the sphere varies directly as the square of the radius.
Step 2 - The mathematical expression of the above statement is:
[tex]\rm S= k\times r^2[/tex] --- (1)
where k is the proportionality constant.
Step 3 - Now, substitute the value of r and S in the above expression.
[tex]\rm 36\pi=k \times 3^2[/tex]
[tex]\rm k = 4\pi[/tex]
Step 4 - Now, substitute the value of [tex]\rm k = 4\pi[/tex] and r = 5 in the expression (1).
[tex]\rm S = 4\pi \times 5^2[/tex]
[tex]\rm S = 100\pi[/tex]
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William's car used 2 gallons to travel 68 miles. How far can he travel on 9 gallons?
Answer:
306 miles
Step-by-step explanation:
68 divided by 2 is 34
34 times 9 equals
Answer:
306 miles
Step-by-step explanation:
68 divided by 2 = 34
a.k.a. 34 miles a gallon
34 times 9 miles = 306 miles
William's car can travel 306 miles with 9 gallons in its tank.
convert y=2x-5 to slope intercept form
Answer:
y = 2x - 5
Step-by-step explanation:
y = 2x - 5 is in the form
y = mx + b
which is the slope-intercept form.
Answer: Answer below :)
The graph of y= |x| is reflected across the x axis and then scaled vertically by a factor of 7 what is the equation of the new graph
Answer:
Option (B)
Step-by-step explanation:
Given equation of the absolute function is,
y = |x|
When this function is reflected across the x-axis, new equation of the graph will be
y = -|x|
Now the image of the given function has been scaled vertically by a factor of 7,
Therefore, equation of the new graph will be,
y = -7|x|
Option (B) is the correct option.
Using the frequency table given, find the mean, median, and mode.
You must show all of your work to receive credit.
Answer:
[tex]Mean = 69[/tex]
[tex]Mode = 66[/tex]
[tex]Median = 69[/tex]
Step-by-step explanation:
Given
The frequency table
Required
Determine the mean, median and mode
Calculating Mean
[tex]Mean = \frac{\sum fx}{\sum f}[/tex]
Where
fx = product of frequency and inches
f = frequency
So;
[tex]Mean = \frac{63 * 2 + 65 * 1 + 66 * 4 + 67 * 3 + 68 * 1 + 69 * 2 + 70 * 2 + 71 * 1 + 72 * 3 + 74 * 2 + 75 * 2}{2 + 1 + 4 + 3 + 1 + 2 + 2 + 1 + 3 + 2 + 2}[/tex]
[tex]Mean = \frac{1587}{23}[/tex]
[tex]Mean = 69[/tex]
Calculating Mode
[tex]Mode = 66[/tex]
Because it highest frequency of 4
Calculating Median
[tex]Median = \frac{\sum f}{2}th\ position[/tex]
[tex]Median = \frac{2 + 1 + 4 + 3 + 1 + 2 + 2 + 1 + 3 + 2 + 2}{2}th\ position[/tex]
[tex]Median = \frac{23}{2}th\ position[/tex]
[tex]Median = 11.5th\ position[/tex]
Approximate
[tex]Median = 12th\ position[/tex]
At this point we, need to get the cumulative frequency (CF)
Inches ---- Frequency ---- CF
63 -------------2------------------2
65 -------------1------------------3
66 -------------4------------------7
67 -------------3------------------10
68 -------------1------------------11
69 -------------2------------------13
70 -------------2------------------15
71 -------------1------------------16
72 -------------3------------------19
74 -------------2------------------21
75 -------------2------------------23
From the above table
Since the median fall in the 12th position, then we consider the following data
69 -------------2------------------13
because it has a CF greater than 12
Hence;
[tex]Median = 69[/tex]
Sally begins hiking at an elevation of 224 ft then she descends 131 ft and climbs 67 feet higher than her current position she then descends 163 ft write an addition sentence to describe the situation then determine and interpret the sum
Answer:
Sally ends at 3 feet below zero point.
Step-by-step explanation:
Let be [tex]h[/tex] the height with respect to zero point, which is represented by the following sum:
[tex]h = \Sigma_{i=1}^{n} h_{i}[/tex]
Where:
[tex]h_{i}[/tex] - i-th travelled height, measured in feet.
In addition, positive sign means ascension, whereas negative sign means descent.
The statement can be translated into the following mathematical identity:
[tex]h = h_{1}+h_{2}+h_{3}+h_{4}[/tex]
[tex]h = 224\,ft+(-131\,ft)+67\,ft -163\,ft[/tex]
[tex]h = -3\,ft[/tex]
Sally ends at 3 feet below zero point.
Given the formula: d=m/V , which answer choice correctly rearranges the variables to solve for V?
Answer:
V = m/dStep-by-step explanation:
[tex]d = \frac{m}{V} \\Cross\:Multiply\\\\dV = m\\\\Divide\:both \:sides \:of\:the\:equation\:by\:d\\\\\frac{dV}{d} = \frac{m}{d} \\\\\\V = \frac{m}{d}[/tex]
Grace and Bill bought a vacation home for $182,000. A serious medical crisis forced them to sell at $110,000. What was their percentage of loss?
a) 30%
b) 40%
c) 50%
d) 55%
Answer:
Loss percentage = 40% (Approx)
Step-by-step explanation:
Given:
Cost price of home = $182,000
Sales price = $110,000
Find:
Loss percentage
Computation:
Loss = Cost price - Sales price
Loss = $182,000 - $110,000
Loss = $72,000
Loss percentage = [Loss / Cost price]100
Loss percentage = [72,000 / 182,000]100
Loss percentage = 39.5604
Loss percentage = 40% (Approx)
Solve for the two possible values of X:
( 5x – 17)(7x + 12) = 0
what is it ?
(i really need this answer asap)
EXAMPLE 11 Show that the points (1,-1),(5,2) and (9,5) are collinear
Answer:
see explanation
Step-by-step explanation:
They are collinear if the have the same slope
(2 - -1)/(5 - 1) = 3/4
(5 - 2)/(9 - 5) = 3/4
(5 - -1)/(9 - 1) = 6/8 = 3/4
Step-by-step explanation:
Hey, there!!!
Your question is about showing the points A(1,-1), B(5,2) and C(9,5) as a collinear point.
We generally slope to find weather the points are collinear or not.
So, let's find slope for AB.
[tex]slope(m) = \frac{y2 - y1}{x2 - x1} [/tex]
[tex] slope = \frac{2 + 1}{5 - 1} [/tex]
Therefore, slope of AB = 3/4.
Now, slope of BC.
[tex]slope(m) = \frac{y2 - y1}{x2 - x1} [/tex]
[tex]slope \: (m) = \frac{5 - 2}{9 - 5} [/tex]
Therefore, the slope is 3/4.
now, lastly slope of AC.
[tex]slope(m) = \frac{y2 - y1}{x2 - x1} [/tex]
[tex]slope(m) = \frac{5 + 1}{9 - 1} [/tex]
Therefore, the slope of AC is 3/4.
As all point have same slope. They are collinear point.
Hope it helps...
Does anybody know what -3/4 = -1/8x is? And can you please show work. Thank uuu.
Answer:
x = 6
Step-by-step explanation:
3 1
- ---- = - ---- x
4 8
3 1
- ---- = - ---- x
4 2³
3 x
- ---- = - ----
4 2³
x = 6
f(x)=1-3x and g(x)=x+4 calculate f(-2)
Answer:
7Step-by-step explanation:
[tex]f(x)=1-3x\\f(-2) = 1-3(-2)\\= 1+6\\=7[/tex]
A sequence starts, 1/2,1/4,1/8... Give a rule that the sequence could follow.
Answer:
A rule that the sequence could follow is that the number so for example 1/8 will have to be multiplied by 1/2 so your answer would be 1/16.
Step-by-step explanation:
10. A bird flies at a speed of 4 m/s. It flies for 2160 seconds from its nest to the field. How much
distance did the bird cover?
Answer:
8640 m, or 8.64 km, assuming it flew in a straight line
Step-by-step explanation:
Distance = rate (or speed) * time (d = rt)
The rate is 4 m/s and the time is 2160 s.
d = rt
d = 4 * 2160
d = 8640 m, or 8.64 km, assuming it flew in a straight line
Dan is a software salesman Y represent his total pay in dollars let X represent the number of copies English is fun he sells suppose that X and y are related by the equation 80x+2400=y
Answer:
1. 80
2. 2400
Step-by-step explanation:
1. what is the change in Dan's total pay for each copy of math is fun he sells?
2. what is Dan's total pay if he doesn't sell any copies of math is fun?
Given
y=80x + 2400
When x=0
y=80(0)+2400
=0+2400
=2400
When x=1
y=80x + 2400
=80(1) + 2400
=80+2400
=2480
change in Dan's total pay for each copy of math is fun he sells is
= 2480 - 2400
=80
2. Dan's total pay if he doesn't sell any copies of math is fun?
y=80x+2400
When x=0
y=80(0)+2400
=0+2400
=2400
A candy store makes a 12-lb mixture of gummy bears, jelly beans, and Runts. The cost of gummy bears is $1.50 per pound, jelly beans cost $1.00 per pound, and Runts cost $1.00 per pound. The mixture calls for three times as many gummy bears as jelly beans. The total cost of the mixture is $15.00. How much of each ingredient did the store use?
Answer:
g= 6
j = 2
r= 4
Step-by-step explanation:
Gummy bears = $1.50 per pound
Jelly beans = $1.00 per pound
Runt = $1.00 per pound
Total cost of the mixture = $15.00
Let
g = quantity of gummy bears
j = quantity of jelly beans
r = quantity of runts
g + j + r=12 (1)
1.5g + 1.0j + 1.0r = 15 (2)
three times as many gummy bears as jelly beans.
g=3j
Substitute g=3j into 1
g + j + r = 12
3j + j + r =12
4j + r =12 (3)
Substitute g=3j into 2
1.5g + 1.0j + 1.0r = 15
1.5(3j) + 1.0j + 1.0r =15
4.5j + 1.0j + 1.0r = 15
5.5j + 1.0r =15 (4)
4j + r =12 (3)
5.5j + 1.0r =15 (4)
Subtract (3) from (4)
5.5j - 4j = 15-12
1.5j = 3
Divide both sides by 1.5
j = 3/1.5
= 2
j = 2
Substitute j = 2 into (3)
4j + r =12
4(2) + r =12
8 + r = 12
r= 12-8
r= 4
Substitute j=2 and r= 4 into (1)
g + j + r=12
g + 2 + 4 = 12
g + 6 = 12
g = 12-6
=6
g=6
g= 6
j = 2
r= 4
i will give brainliest for anyone that can correctly answer my question, its in a photo
Answer:
x = 122
Step-by-step explanation:
Step 1: State what is known
In the picture we can see they marked ∠ABC with a box meaning it is a 90° angle, given that information we can now solve
Step 2: Solve
∠ABC = x - 32
90 = x - 32
90 + 32 = x
122 = x
Therefore 'x' is equal to 122