Answer:
9-x
Step-by-step explanation:
Find all points having an x-coordinate of 3 whose distance from the point (-1,-4) is 5
Answer: (3, -7) and (3, -1)
Step-by-step explanation:
Distance formula: a^2 + b^2 = c^2
c is the distance between different points which is 5 in this case
a=3-(-1)
a=3+1
a=4 ==> distance between x-coordinates
4^2+b^2=5^2
16+b^2=25
b^2=9
b=3
Distance from -4 and y-coordinate of a different point is equaled to 3.
How to express this in the form of an equation?
|-4-y|=3 ==> where y is the y-coordinate of a different point
-4-y=3
-4+4-y=3+4
-y=7
y=-7 ==> (3, -7)
-4-y=-3
-4+4-y=-3+4
-y=1
y=-1 ==> (3, -1)
(3, -7) and (3, -1)
Identify all the correct names for the given angle.
The correct names for the given angle is ∠PHV.
What is termed as the angle?An angle is formed in geometry when two rays have been merged at their endpoints. These rays are known as the angle's sides or arms.The arms as well as the vertex are the two main components of an angle.The Angle's Arms: The arms of the angle are the two rays that meet at a center element to form the angle.The angle's vertex: A vertex is a main endpoint shared by both rays.How to name the any angle?
For naming any angle, the common vertex must come in the middle of the name.
But it could start with any of the end point.
Thus, the angle given can be named either ∠PHV or ∠VHP.
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A cell phone tower covers a circular area with a radius of 15 miles.
(b) Will a person 11 miles west and 12 miles south of the tower have coverage? Explain.
A person 11 miles west and 12 miles south of the tower will not have coverage.
A circle is a closed curve that is drawn from a fixed point. This point is called the center. All points on the curve are equidistant from this center point.
The cell phone tower covers a circular area with radius 15 miles. This means that there will be coverage in all directions from center up to 15 miles.
The person is 11 miles west and 12 miles south of the tower.
Distance of person from center will be calculated using distance formula
[tex]d = \sqrt{(11^{2} + 12^{2} }[/tex]
∴ [tex]d = \sqrt{121 + 144}[/tex]
∴ [tex]d = 16.27[/tex] miles.
Since this distance is greater than the radius of circle (15 miles), the person will not have cell phone coverage.
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can someone help me im really stuck -57=y-2
Answer: y = -55
Step-by-step explanation:
-57 = y -2
-57 + 2 = y
-55 = y
A group of friends wants to go to the amusement park. They have $89.50 to spend on parking and admission. Parking is $7.75, and tickets cost $27.25 per person, including tax. Write and solve an equation which can be used to determine pp, the number of people who can go to the amusement park.
The number of people who can go to the amusement park is 3 people
EquationTotal amount with the group of friends = $89.50Cost of parking = $7.75Cost of tickets per person =$27.25Number of people who can go to the amusement park = p89.50 = 7.75 + 27.25p
subtract 7.75 from both sides89.50 - 7.75 = 27.25p
81.75 = 27.25p
divide both sides by 27.25p = 81.75 / 27.25
p = 3
Therefore, the number of people who can go to the amusement park is 3 people.
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HELP PLEASEEEE
Jerald is having drain issues at his home and decides to call a plumber. The plumber charges $45 to come to his house and $50 for every hour they work. If the plumber charges Jerald a total of $250, how many hours did the plumber work?
Write and solve an equation to determine the number of hours worked by the plumber.
45x + 50 = 250; x = 4.4 hours
45x − 50 = 250; x = 6.7 hours
50x + 45 = 250; x = 4.1 hours
50x − 45 = 250; x = 5.9 hours
Answer: The answer would be D. I hope this is helpful :))
Find each difference.
(5/2) - (13/4)
The difference is -3/4.
How to calculate the difference?Given,
(5/2) - (13/4)
Solution:
Taking L.C.M,
(5/2) - (13/4) = 10/4 - 13/4
= -3/4
The difference is -3/4.
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2. Open Response The table shows the amount
spent on tomatoes at three different stands
at a farmer's market. Which stand sold their
tomatoes at the least expensive price per
pound, and what is that price? Round to the
nearest cent, if necessary. (Lesson 1)
Stand Weight (lb) Cost ($)
A
2.00
B
C
100
NATA/W
3.45
14.85
Stand C sold their tomatoes at the least expensive price per pound that price is 2.70 per pound.
The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
We have to determine the price of sold tomatoes at the least expensive price per pound.
The price of sold tomatoes at stand A:
⇒ 2/(3/4) = 2/0.75 = 2.67 per pound.
The price of sold tomatoes at stand B:
⇒ 3.45/(5/4) = 3.45/1.25 = 2.76 per pound.
The price of sold tomatoes at stand C:
⇒ 14.85/(11/2) = 14.85/5.5= 2.70 per pound.
Here is the least expensive price per pound at stand C.
Hence, the stand C sold their tomatoes at the least expensive price per pound that price is 2.70 per pound.
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Consider the procedure used below to solve the given equation.
Given: 4(2x +5)-(3x-4)=15
Step 1: 8x+5-3x+4=24
Step 2: 5x + 9 = 24
Step 3: 5x = 24-9
Step 4: -5x = 15
Step 5:53= 15
Step 6: x=-3
Which statement about the solution of the given equation is true?
O The first mistake was made in Step 1.
O The first mistake was made in Step 2.
O The first mistake was made in Step 3.
O The answer is correct. Can you please show me the work please?
Answer:
A. The first mistake was made is Step 1
Step-by-step explanation:
The first mistake was in Step 1. Take a look below to see how Step 1 should've been.
4(2x +5)-(3x-4)=15
Use distributive property.
4(2x +5)-(3x-4)=15
8x+20-3x+4=15
Hope this helps!
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Have a great day! :)
Help please, I’m needing help with these questions
The equation of the line perpendicular to y = -²/₃x + 5 and passing through the point (6, -7) is; y = ³/₂x - 16
What is the equation of the line in slope intercept form?We want to find the equation of the line perpendicular to y = -²/₃x + 5 and passing through the point (6, -7).
Now, the slope that is perpendicular to that line is;
m = -1/(-²/₃) = 3/2
Thus;
Equation of the new line is;
y - (-7) = 3/2(x - 6)
y + 7 = 3x/2 - 9
y = ³/₂x - 16
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8.1 + u/7 = -3.1
Please help, Thanks!!
Felicia bought 4.5 bags of candy for her party baskets. Each bag has 146 pieces of candy. If she has 9 party baskets, how many pieces of candy will each party basket have?
Each party basket will have 73 pieces of candy
How to calculate the number of candies in each basket ?Felicia has 4.5 bags of candy for her party basket
Each bag has 146 pieces of candy
She has 9 party baskets, the number of candies in each party basket can be calculated by multiplying 4.5 by 146 and dividing the result by 9
4.5 × 146/9
= 657/9
= 73
Hence there are 73 pieces of candy in each basket
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If x2-x-2 > 0, which of the following is the solution set for x?
Ox>-1
Ox>2
O -1 < x < 2
Ox< -1 or x> 2
O No solutions are possible.
Solving the quadratic inequality, the solution set for x is given as follows:
x < -1 or x > 2.
When a function is positive and when it is negative?A function is positive when it is above the x-axis.A function is negative when it is below the x-axis.For this problem, the inequality is given by:
x² - x - 2 > 0.
To graph a quadratic inequality, first we have to find the roots of the quadratic function, hence:
x² - x - 2 = 0
(x - 2)(x + 1) = 0.
Hence the roots are:
x - 2 = 0 -> x = 2.x + 1 = 0 -> x = -1.As the graph given at the end of the answer shows, any concave up quadratic function is positive to the left and to the right of the roots, hence the solution set for the inequality is:
x < -1 or x > 2.
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Simplify 2¾+(3⅜-1½) please I need your help now, and I want you to explain it accordently ,am waiting
Answer:
1⁷/15
Step-by-step explanation:
2¾(3⅜-1½)
using the rule of BODMAS
change the fractions in the bracket into improper fraction
2¾(27/8-3/2)
find LCM of the fractions in the bracket
2¾(27-12)/8
2¾(15/8)
convert the other mixed fraction to an improper fraction
11/8(15/8)= 5.15625~ 5.2
Simplify:
PLEASE HELP
(3^2 x 3^3) 5
a
3^10
b
3^30
c
3^25
d
9^10
Answer:
1215
Step-by-step explanation:
Round the decimal to the nearest whole number, 14.2.
Answer:14.
Step-by-step explanation:
14.2 is closer to 14 than 15
Answer:
14
Step-by-step explanation:
The nearest whole number in 14.2 is 4.
Since 2 is less than 5, the 4 stays the same.
We get left with 14.
Austin runs a farm stand that sells raspberries and apples. Each pound of raspberries sells for $4 and each pound of apples sells for $1.50. Austin made $267.50 from selling a total of 95 pounds of raspberries and apples. Determine the number of pounds of raspberries sold and the number of pounds of apples sold.
Answer:
50 pounds of raspberries and 45 pounds of apples is sold
Solution:
Let "a" be the number of pounds of raspberries sold
Let "b" be the number of pounds of apples sold
Cost of each pound of raspberry = $ 4
Cost of each pound of apple = $ 1.50
Austin made $267.50 from selling a total of 95 pounds of raspberries and apples
Therefore,
a + b = 95
b = 95 - a ------ eqn 1
Austin made $267.50. Therefore,
number of pounds of raspberries sold x Cost of each pound of raspberry + number of pounds of apples sold x Cost of each pound of apple = 267.50
4a + 1.50b = 267.50 --------- eqn 2
Substitute eqn 2 in eqn 1
4a + 1.5(95 - a) = 267.50
4a + 142.5 - 1.5a = 267.50
2.5a = 125
a = 50
Substitute a = 50 in eqn 1
b = 95 - 50
b = 45
Thus 50 pounds of raspberries and 45 pounds of apples is sold
Step-by-step explanation:
hope it helps u
Use log₅ 2 ≈ 0.43 and log₅7 ≈ 1.21 and the properties of logarithms to approximate log₅ √14 without using a calculator.
[tex]log_{5} \sqrt{14}[/tex] ≈ 0.82
The property of logarithms log ab = log a + log b , log a/b = log a - log b
[tex]log_{5} 2[/tex] ≈ 0.43
[tex]log_{5} 7[/tex] ≈ 1.21
We need to find,
[tex]log_{5} \sqrt{14}[/tex]
= 1/2[tex]log_{5} 14[/tex]
= 1/2[tex]log_{5} 2*7[/tex] ( log ab = log a + log b)
= 1/2 ([tex]log_{5} 2[/tex] + [tex]log_{5} 7[/tex])
=1/2( 0.43 + 1.21)
= 1/2 × 1.64
= 0.82
Hence logarithms of [tex]log_{5} \sqrt{14}[/tex] = 0.82
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-9(1 - 10n) -2(3n + 9)
Answer:
[tex]84n-27[/tex]
Step-by-step explanation:
[tex]-9(1-10n) -2(3n+9)[/tex]
[tex]-9+90n-6n-18[/tex]
[tex]{84n-27}[/tex]
A year ago, a radio program was aired on r stations across the country. Today, the number of stations airing the radio program can be represented by the following expression: 0.82r Which set of statements is true?
A. The number of the stations airing the program increased by 18%. An equivalent expression that represents this situation is r+0.18r
B. The number of stations airing the program increased by 82%. An equivalent expression that represents this situation is r+0.82r
C. The number of stations airing the program decreased by 82%. An equivalent expression that represents this situation is r -0.82%
D. The number of stations airing the program decreased by 18%. An equivalent expression that represents this situation is r -0.18r.
The set of statements is true; B. The number of stations airing the program increased by 82%. the equivalent expression that represents this situation is r+0.82r.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
IT is given that year ago, a radio program was aired on r stations across the country.
Also Today, the number of stations airing the radio program can be represented by the following expression; 0.82r
Therefore, the equivalent expression that represents this situation is r+0.82r
Hence, The set of statements is true; B. The number of stations airing the program increased by 82%. the equivalent expression that represents this situation is r+0.82r.
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What is the equation of the slant asymptote of the rational function?
f(x)=10x3−15x2+x−15x2−2
Responses
y=x−3
y equals x minus 3
y=2x−115
y equals 2 x minus fraction 11 over 5
y=2x−3
y equals 2 x minus 3
y=x−115
The equation of the slant asymptote of the rational function is; y = 2x - 3
What is the equation of the slant asymptote of the rational function?We want to find the equation of the slant asymptote of the rational function given as;
f(x) = (10x³ - 15x² + x - 1)/(5x² - 2)
To solve this question, we will divide the numerator by the denominator. The result (not including the remainder) will be the equation of the slant asymptote.
We can tell the first term of the quotient will be 2x since 10x³/5x² = 2x. Thus, the answer from the given options will be either 2x − 3 or 2x − 11/5.
The easiest method to apply here is to simply multiply these options by the denominator to get;
(5x² − 2) (2x − 3) = 10x³ − 15x² − 4x + 6
(5x² − 2) (2x − 11/5) = 10x³ − 11x² − 4x + 22/5
So the answer must be 2x − 3
Thus, the equation of the slant asymptote of the rational function is; y = 2x - 3
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A number is divided by 6 and then the quotient is added to 12.The result is 4.Find the number
Answer:
So the number is -48
Step-by-step explanation:
Lets say that the number is x
(x /6)+12=4
x/6=-8
x=-48
Find the magnitude and direction of vector. →JK : J(-6,-4) and K(-10,-4)
The magnitude of vector →JK is 4
And the direction of vector →JK is given by an angle 360°
For given question,
Let J(-6, -4) = (x1, y1) and
K(-10,-4) = (x2, y2)
By distance formula, the magnitude of vector is,
[tex]|\vec{JK}|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\|\vec{JK}|=\sqrt{(-10+6)^2+(-4+4)^2}\\\\ |\vec{JK}|=\sqrt{(-4)^2}\\\\ |\vec{JK}|=4[/tex]
To find the direction of the vector JK:
[tex]tan\theta=\frac{y_2-y_1}{x_2-x_1} \\\\tan\theta=\frac{-4+4}{-10+6}\\\\ tan\theta=0\\\\\theta=0^{\circ}[/tex]
However, the angle is in the fourth quadrant, so we add 360° to obtain a positive angle.
Thus, 0° + 360° = 360°
Therefore, the magnitude of vector →JK is 4
And the direction of vector →JK is given by an angle 360°
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Find the geometric mean between each pair of numbers.
18 and 1.5
The geometric mean between the pair of numbers, 18 and 1.5, is 3√3.
Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.
To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.
The formula for the geometric mean is given by:
GM = n√x1 x2 . . . xn
Solving for the geometric mean between 18 and 1.5 using the formula:
GM = n√x1 x2 . . . xn
where n = 2, x1 = 18, and x2 = 1.5
GM = √(18)(1.5)
GM = √27
GM = 3√3
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I need help asap!!!!
the answer is negative 41
transposition of formulae
n=p+cr for r
Answer:
r = (n - p)/c
Step-by-step explanation:
n = p + cr
Subtract p from both sides
n - p = p + cr - p
n - p = cr
Divide both sides by c.
(n - p)/c = cr/c
r = (n - p)/c
Solve for x in the equation below.
Round your answer to the nearest hundredth.
Do not round any intermediate computations.
Answer:
Get natural log on both sides and subtract 8 to subject the unknown x.
Step-by-step explanation:
Since this seems to be a quiz-type question I cannot provide a direct answer.But I may help you to get it on your own with some effort from your side.You may follow these steps. I hope you have a calculator to simplify the terms.[tex]\begin{aligned}\\e^{x+8} &= 15\\\\ln(e^{x+8}) &=\small ln(15)\\\\(x+8) ln(e)&=\small ln(15)\\\\x+8&=\small ln(15) \cdots\cdots\cdots[ ln(e) = 1]\\\\x&=\small ln(15) -8\end{aligned}[/tex]
Let me know the answer.Answer:
x = -5.29
Step-by-step explanation:
e^(x+8) = 15
==> take log of both sides
log(e) * (x+8) = log(15)
==> divide both sides by log e (log(15)/log(e) = 2.70805)
x + 8 = 2.70805
==> subtract both sides by 8
x = -5.29 (rounded to the nearest tenth)
Which answer shows how to correctly multiply 2×4×(−6)?
Answer:
-48
Step-by-step explanation:
2 x 4 = 8
8 x -6 = -48
The scale on a map is 1 : 25 000
How many kilometres on the ground is represented by 9 cm on the map?
2.25 kilometers on the ground is represented by 9cm on the map
According to the question, the scale on the map is in the ratio 1 : 25000
That is the length on the map = length of the ground
1cm = 25000 cm
1 cm = 25000/100000 km
1 cm = 0.25 km
Now we have to find the length of the ground in kilometres which is represented by 9cm on the map
That is we have to find the ratio, 9cm : x km
As from above, we know that,
1cm = 0.25 km
9 cm = 0.25*9 km
= 2.25 km
Hence 2.25 km on the ground is represented by 9 cm on the map
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Answer any of the following if you know one but not the other!!
1. If the terminal side of angle θ, in standard position, passes through the point (4, -7), what is the numerical value of sinθ?
2. Given tanθ = 3/2 and angle θ is in quadrant III, find the exact value of sinθ in simplest radical form using a rational denominator.
3. Why is it true that sin(θ) = cos (90 - θ) and cos(θ) = sin (90 - θ)?
Step-by-step explanation:
1.
the length of the terminal side from (0, 0) to (4, -7) is the radius of the circle, while
x = 4 = cos(theta)×radius
y = -7 = sin(theta)×radius
so,
sin(theta) = -7/radius
radius² = (4 - 0)² + (-7 - 0)² = 4² + 7² = 16 + 49 = 65
radius = sqrt(65)
sin(theta) = -7/ sqrt(65) = -0.868243142...
FYI
theta = -60.2551187...°
or 299.7448813...°
2.
tan(theta) = 3/2
so,
sin(theta)/cos(theta) = 3/2
2×sin(theta) = 3×cos(theta)
square both sides
4×sin²(theta) = 9×cos²(theta)
completing the square
4×sin²(theta) + 9×sin²(theta) = 9×cos²(theta) + 9×sin²(theta)
13×sin²(theta) = 9×(cos²(theta) + sin²(theta)) = 9
sin²(theta) = 9/13
sin(theta) = 3/sqrt(13)
to make it a rational denominator we multiply by
sqrt(13)/ sqrt(13)
and we get
sin(theta) = 3×sqrt(13)/13
3.
because the sum of all angles in a triangle is 180°.
one angle is theta.
then we have the 90° angle at the origin (or center of the circle).
and that leaves 180 - 90 - theta = 90 - theta for the third angle.
this triangle can be flipped with putting 90 - theta in place of theta.
the flipped triangle is equivalent to the original triangle (all angles and side lengths are identical between the 2 triangles).
the baseline (radius) is the same length in both triangles.
in that flipped triangle the side formerly sin(theta) is now cos(90-theta) and cos(theta) is now sin(90-theta).
