Answer:
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Step-by-step explanation:
kindly solve these questions for me.
The perimeter of the rectangle based on the factors given is 46.
How to calculate the perimeter?The area of the rectangle is given as (x² + 13x - 90). This will be:
= (x² + 13x - 90)
= x² + 18x - 5x - 90
= x(x + 18) - 5(x + 18)
= (x - 5)(x + 18)
The sides of the rectangle are 5 and 18. The perimeter will be:
= 2(l + w)
= 2(5 + 18)
= 46
The area of the rectangle is given as (x² + 24x - 81.
= (x² + 24x - 81)
= x² + 27x - 3x - 81
= x(x + 27) - 3(x + 27)
= (x - 3)(x + 27)
The sides are 3 and 27. The perimeter will be:
= 2(l + w)
= 2(27 + 3)
= 60
= (x + 1)² + 3(x + 1) + 2
= (x + 1)(x + 1) + 3x + 3 + 2
= x² + x + x + 1 + 3x + 5
= x² + 5x + 6
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The estimated population of Los Angeles in 2019 was 3,979,576. Its area is 469 square miles. What is the population density of Los Angeles, in people per square mile?
Given that, the estimated population of Los Angeles in 2019 was 3,979,576 and its area is 469 square miles, the population density of Los Angeles is 8486 people per square miles.
What is the population density of Los Angeles, in people per square mile?Population density simply the measurement of population per unit area.
It is expressed as;
Population density = Number of people / Area
Given the data in question;
Number of people in Los Angeles N = 3,979,576 peopleArea of Los Angeles A = 469 square milesPopulation density = ?We substitute the given values into the above equation.
Population density = Number of people / Area
Population density = 3,979,576 people / 469 square miles
Population density = 8485.23667 ≈ 8486 people per square miles
Given that, the estimated population of Los Angeles in 2019 was 3,979,576 and its area is 469 square miles, the population density of Los Angeles is 8486 people per square miles.
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In a given year, residents of a country spent approximately $54.6 billion on their pets. Of this amount, $17.1 billion was for veterinarian bills. What percent of the total was spent on veterinary care
Percent of the total was spent on veterinary care is 31.3186% .
Applying simple percentage formula,
let x be the percentage
x=[tex]\frac{17.1}{54.6} \ 100[/tex]
x=31.3186 %
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Evan collected data about the amount of time each student in his math class spends studying. If the range of these data is 2, what does this reveal about the data?
All the students in his math class spend exactly 2 hours studying.
All the students in his math class spend an average of 2 hours studying.
The smallest and largest data values are 2 units away from each other.
The middle data value for time spent studying by all students in his class is 2 hours.
A range of 2 reveals that the smallest and largest data values are 2 units away from each other.
What does the range reveal?Range is the difference between the highest and lowest values of a set of observations. Range is a measure of variation.
Range = highest value - lowest value
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On a ΔABC, mΔA=80, mΔB=60
Find mΔC
The measure of angle C (m ∠C) is 40°
Calculating angles in a triangleFrom the question, we are to determine the measure of angle C (m ∠C)
In any given triangle, the sum of all the angles is 180°
Thus,
In ΔABC, the angles sum up to 180°
That is,
∠A + ∠B + ∠C = 180°
From the given information,
m ∠A = 80°, m ∠B = 60°
Thus,
80° + 60° + m ∠C = 180°
140° + m ∠C = 180°
m ∠C = 180° - 140°
m ∠C = 40°
Hence, the measure of angle C (m ∠C) is 40°
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Consider the equation 4x^4 - 38x^3 = 17x^2 + 30x. One of the real solutions to the equation is 10. What are the other solutions, both real and nonreal
Answer: Option (1)
Step-by-step explanation:
[tex]4x^4 -38x^3 -17x^2 -30x=0[/tex]
Dividing both sides by [tex]x-10[/tex] (10 is a root, so x-10 is a factor), yields
[tex]4x^3 +2x^2 +3x=0\\\\x(4x^2 +2x+3)=0\\\\x=0, 4x^2 +2x+3=0[/tex]
Solving the second case by the quadratic formula yields [tex]x=\frac{-1 \pm i\sqrt{11}}{4}[/tex].
So, the answer is Option (1).
Find the point on the line y = 5x + 2 that is closest to the origin.
Answer: [tex]\left(-\frac{5}{13}, \frac{1}{13}\right)[/tex]
Step-by-step explanation:
The shortest distance from a point to a line is the perpendicular distance. The origin is essentially a point with coordinates (0,0); hence, we have to find the equation of the line that's both perpendicular to [tex]y=5x+2[/tex] and crosses the origin.
We can do this by recognizing that slope of a perpendicular line is the opposite reciprocal of the slope of the original line.
Opposite Reciprocal of 5: [tex]-\frac{1}{5}[/tex]
Now that we have the slope and the point, we can use the point-slope form to get the equation of the perpendicular.
Point-Slope Form: [tex]y-y_1=m(x-x_1)[/tex] (m is slope, [tex]x_1[/tex] and [tex]y_1[/tex] are the point's coordinates)
[tex]y-0=-\frac{1}{5}(x-0)\\y=-\frac{1}{5}x[/tex]
Since we need to find a point on the original line that's closest to the origin, we need to find the intersection of the line and its perpendicular. We can do this by setting both lines equal to each other and solving for x and y.
[tex]5x+2=-\frac{1}{5}x\\25x+10=-x\\26x=-10\\x=-\frac{10}{26}\\x=-\frac{5}{13}[/tex]
Substituting x in any of the equations will give us y. Here, I will put it in the equation [tex]y=-\frac{1}{5}x[/tex]
[tex]y=-\frac{1}{5}*-\frac{5}{13}\\y=\frac{5}{65}\\y=\frac{1}{13}[/tex]
The closest point to the origin on the line [tex]y=5x+2[/tex] is [tex]\left(-\frac{5}{13}, \frac{1}{13}\right)[/tex]
The point on the line y = 5x + 2 that is closest to the origin is (-5/13, 1/13).
What is the point slope form?The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.
The given equation of a line is y=5x+2 ------(I)
The shortest distance from a point to a line is the perpendicular distance. The origin is essentially a point with coordinates (0,0); hence, we have to find the equation of the line that's both perpendicular to y=5x+2 and crosses the origin.
We can do this by recognizing that slope of a perpendicular line is the opposite reciprocal of the slope of the original line.
So, slope of perpendicular line is -1/5
The equation of the point slope form is: (y - y1) = m(x - x1)
Now, substitute m=-1/5 and (x, y)=(0, 0), we get
y-0=-1/5 (x-0)
y=-1/5 x -----(II)
Equate equation (I) and (II), we get
5x+2=-1/5 x
⇒ -x=25x+10
⇒ -26x=10
⇒ x= -5/13
So, y=-1/5 x =1/13
Therefore, the point on the line y = 5x + 2 that is closest to the origin is (-5/13, 1/13).
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3. A line with a slope of passes through the point (10,-5).
The equation of the line in slope intercept form
can be given by the formula y = mx + b
where m=
and b =
√x
The equation of the line is y = -3/2x + 10
How to determine the line equation?The given parameters are:
Slope, m = -3/2
Point, (x, y) = (10, -5)
The line equation is represented as
y = mx + b
Substitute the given parameters in the equation
-5 = -3/2 * 10 + b
This gives
-5 = -15 + b
Add 15 to both sides
b = 10
So, we have:
y = -3/2x + 10
Hence, the equation of the line is y = -3/2x + 10
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(-4, 7), (-6,-4)
find the slope of the line through each pair of points
Answer:
slope = 11/2
Step-by-step explanation:
If you are given two points, you can find the slope using the point-slope equation. The equation looks like this:
y₁ - y₂ = m(x₁ - x₂)
In this form, "m" represents the slope, "x₁" and "y₁" represent the values from one point, and "x₂" and "y₂" represent the values from the other point. You can plug the values from the points into the equation and simplify to find the slope.
Point 1: (-4, 7) Point 2: (-6, -4)
x₁ = -4 x₂ = -6
y₁ = 7 y₂ = -4
y₁ - y₂ = m(x₁ - x₂) <----- Point-slope form
7 - (-4) = m(-4 - (-6)) <----- Insert values
11 = m(2) <----- Simplify
11/2 = m <----- Divide both sides by 2
[tex]\huge\boxed{\frac{11}{2}}[/tex]
The slope is equivalent to vertical change divided by horizontal change, otherwise known as "rise over run".
Therefore, the slope can be represented with the following equation, where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are your points:
[tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values and simplify to find the answer.
[tex]\dfrac{(-4)-7}{(-6)-(-4)}[/tex]
[tex]\dfrac{-4-7}{-6+4}[/tex]
[tex]\dfrac{-11}{-2}[/tex]
[tex]\boxed{\frac{11}{2}}[/tex]
The prep club and honor society are joining forces
Given that the inequalities and that
x ⇒ pep club donations
y ⇒ represent donations raised by the honor society
The inequality is represented by x + y≥ 500
The solution for this is the shaded area above the solid line.
Given x ≥ 100, this is also indicated by the shaded region to the right
What does point (300, 100) represent? is it a viable Solution? why?The point (300,100) indicates that the contributions made for the pep club were $300 and the donations raised by the honor society were $100.
The point (300,100) is NOT a feasible solution since it does not conform to the gray area of the system of inequalities solution.
To proof the above,
Let x = 300; and y = 100
Plugin in both values in the inequalities we have:
300 + 100 [tex]\ngeq[/tex] 500
400 [tex]\ngeq[/tex] 500 ; Hence it is NOT true; also
300 [tex]\ngeq[/tex] 500.
What does (500, 200) represent? Is it a viable Solution? why?The point (500,200) indicates that the contributions raised for the pep club were $500 and the donations raised by the honor society were $200.
The point (500,200) IS A possible solution since it falls inside the darkened area of the system of inequalities solution.
To proof the above,
Let x = 500; and y = 200
Plugin in both values in the inequalities we have:
500 + 200 ≥ 500
700 ≥ 500; hence, this is true and it is safe to indicate that the ordered pair satisfies the inequality A.
Conclusion:
The point (500, 200) is a viable solution.
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Which is the graph of the function f(x)=√x?
The graph is shown in the attached image.
a local newspaper assigns a rating between 1 and 10 to every book and movie it reviews. Victor gathered data about five titles where the newspaper reviewed both the book and the movie version of the title. The ratings assigned by the newspaper are given in the table. Select the points that represent this data.
The points that represent this data are shown in the image attached below.
What is a scatter plot?A scatter plot is a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.
Based on the information provided in table above, the points that represent this data are shown in the image attached below.
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Answer:
please look at the picture
Which of the following choices will simplify 5-3•2?
here is a table of values for y= f(x)
mark the statements that are true.
Answer:
B. The domain for f(x) is the set {-2, -1, 0, 1, 2, 3, 4, 5, 6}
D. f(-1) = 6
Step-by-step explanation:
The question gives a table marking the different coordinate pairs for a function, where f(x) is y. The top row represents the x-values and the bottom row represents the y-values.
Domain
The domain of a function is the set of x-values that the graph covers. In this case, the x-values are all integers between -2 and 6. We can see this in the top row of the table. Answer choice B best represents this domain.
Solving for F(x)
F(x) represents a specific y-value, for example, f(-1) represents the y-value when x = -1. So, to test choice D, we need to find what y-value matches -1 on the table. The table shows that when x = -1, f(x) = 6. This means that answer choice D must be correct.
find each lettered angel measure
Answer:
a = 64°
b = 138.7°
Step-by-step explanation:
First, Let's find the measure a,
180° = 116° + a180 - 116 = aa = 64°______
Now,
90° + a + 82° + x + x + x = 360°90+ 64 + 82 + 3x = 360° 236 + 3x = 360 3x = 124/ 3x = 41.3°______
Now that we found out what x equals, let's find 'b'-
b + x = 180°b + 41.3 = 180b = 180 - 41.3b = 138.7°Sketch the graph of the equation y=2/3 x+2 and label three points on the graph.
Answer:
Step-by-step explanation:
(0,2)
Answer:
Step-by-step explanation
So, the graph goes through the points, (-3,0) and (2,0). 3 points on the graph can be (-3,0), (2,0), and (4,3)
Which point is the center of the Circle with the given equation.
(x + 5)2 + (y - 4)2 = 9
The center of the circle is (-5, 4)
How to determine the center of the circle?The circle equation is given as:
(x + 5)^2 + (y - 4)^2 = 9
A circle equation is represented as:
(x - a)^2 + (y - b)^2 = r^2
Where
Center = (a, b)
By comparing both equations, we have
(a, b) = (-5, 4)
Hence, the center of the circle is (-5, 4)
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What common base can be used to rewrite each side of the equation 2^x+3-3=5
The common base that can be used to rewrite each side of the equation is 2.
How to find the common base used to rewrite each equation?The common base that can be used to rewrite each side of the equation is as follows:
2ˣ⁺³ - 3 = 5
add 3 to both sides
2ˣ⁺³ - 3 + 3 = 5 + 3
2ˣ⁺³ = 8
Hence,
2ˣ⁺³ = 2³
Therefore, the common base that can be used to rewrite each side of the equation is 2.
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A sience teacher uses an overhead projector to display a diagram of a pulley sytem. the actual diagram is 6'' by 7.2''. The image projected onto the wall is 4' 2'' by 5'' what is the scale factor of the projection
Answer:
25/36, or .694444
Step-by-step explanation:
First, let's convert 6" to inches.
That gives us 72. After we convert 4'2" into inches, we get 50.
This means that the diagram goes from 72 inches wide to 50. Put this into a proportion to find the scale factor:
50/72 = 25/36 = .6944444
10. What is the product of 6% and 14%
use the sum to product formula to find exact values: if cos255 - cos195 = squrtroot a/ 2 then a=
By applying trigonometric expression and direct comparison, we conclude that a = 2 such cos 255° - cos 195° = √a / 2
How to analyze a trigonometric expression
In this question we need to simplify a trigonometric expression in order to find the value of a. In this case, we need to use the following formula:
[tex]\cos \theta - \cos \xi = - 2\cdot \sin \left(\frac{\theta + \xi}{2} \right)\cdot \sin \left(\frac{\theta - \xi}{2} \right)[/tex]
Then,
cos 255° - cos 195° = - 2 · sin 225° · sin 30°
cos 255° - cos 195° = - 2 · sin (- 135°) · sin 30°
cos 255° - cos 195° = 2 · sin 135° · sin 30°
cos 255° - cos 195° = 2 · (√2 / 2) · (1/2)
cos 255° - cos 195° = √2 / 2
Then, by direct comparison we find that a = 2.
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Find the area of the regular polygon. Round to the nearest tenth
Answer:
1/2×base×height
1/2×8×8
32cm²
Which person has a dept ratio that is higher the 18%
the person with the debt ratio that is higher than 18% can be found by dividing the person's debt by their income .
what is the debt ratio?the necessary information is not given so a general explanation will be given.
the debt ratio is found by the formula:
= monthly debt payment / monthly gross income
this figure allows creditors to see if a person can affort to incur more debt based on how much of their gross monthly income is being used to service debt.
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what’s 5x times 2-7 min
Answer:33
Step-by-step explanation: The expressions have equivalent values when x + 6
The expressions have equivalent values for any value of x.
When x=10 , both expressions have a value of 33.
Is this figure a polygon? Explain.
A cylinder has a olive of 200mm and a height of 17mm. The volume formula for a cylinder is
The radius of the given cylinder with a volume of 200 mm³ and a height of 17mm is: 1.93 mm.
How to find the Volume of a Cylinder?The formula for finding the volume of any cylinder is given as: πr²h, where r is the radius and h is the height of the cylinder.
Given the following:
Volume = 200 mm³
Height (h) = 17 mm
Radius (r) = ?
Plug the values into the formula for volume
πr²(17) = 200
r² = 200/17π
r² = 3.74
r = 1.93 mm
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According to the general equation for conditional probability, if P(AB) = and P(B) = 2, what is P(A/B)? 12 O A. 3/ О в. 4 O c. 2/ C. 5 O D. 9
Using conditional probability, it is found that:
[tex]P(A|B^\prime) = \frac{1}{3}[/tex]
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.For this problem, we are given that:
[tex]P(B^\prime) = 1 - P(B) = 1 - \frac{1}{3} = \frac{2}{3}[/tex].[tex]P(A \cap B^\prime) = \frac{2}{9}[/tex]Then:
[tex]P(A|B^\prime) = \frac{P(A \cap B^\prime)}{P(B^\prime)}[/tex]
[tex]P(A|B^\prime) = \frac{\frac{2}{9}}{\frac{2}{3}}[/tex]
[tex]P(A|B^\prime) = \frac{1}{3}[/tex]
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A rectangular lot has a perimeter of 80 meters and a length of 25 meters. Find the
width of the lot.
Fence->
25m
Meters
W
Answer:
15m
Step-by-step explanation:
Let w be the width, l the length and p the perimeter.
We know, by definition, that p = 2w + 2l. We also know that p = 80m and l = 25m.
So we can re-write the perimeter formula as:
80 = 2w + 50
2w = 30
w = 15m
So we now know that the width is 15m.
An employee worked for 8 hours on 2 days, 6 hours on 1 day, and 4 hours on 2 day
What is the average number of hours the employee worked per day?
A.) 6.0
B.) 6.5
C.) 7.0
D.) 7.5
E.) 8.0
Answer:
A) 6.0
Step-by-step explanation:
First, total amount of hours, since average is sum of the numbers by how many numbers there is.
Day 1=8x2 hr
Day 2=6x1 hr
Day 3=4x2 hr
which is, 16+6+8=30
then divide 30 by how many days there is, which is 5 days.
30/5=6
Which inequality in vertex form represents the region less than the quadratic function with vertex (-2, 2) and includes the point (-4, 14) on the boundary?
The inequalty that represents the statement must be y < - 6 · (x + 2)² + 2. (Right choice: None)
What is the inequality associated to a given statement
The standard form of the equation of the parabola is defined by the following expression:
y - k = C · (x - h)² (1)
Where:
h, k - VertexC - Vertex constantNow we proceed to find the vertex constant: (h, k) = (- 2, 2) and (x, y) = (- 4, 14)
14 - 2 = C · [- 4 - (- 2)]²
12 = C · (-2)
C = - 6
The equation of the parabola in vertex form is
y - 2 = - 6 · (x + 2)²
y = - 6 · (x + 2)² + 2
Then, the inequalty that represents the statement must be y < - 6 · (x + 2)² + 2. (Right choice: None)
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Answer:
y < 3(x + 2)2 + 2
Step-by-step explanation:
just do it