The points H(-8,-1),I (-6,-9), J (-2,-8) and K (-4,0) form a quadrilateral. Find the desired slopes and lengths, then fill in the words that best identifies the type of quadrilateral
Answers
Answer:
[tex]\text{Quadrilateral HJLK is a }Rec\tan gle[/tex]Explanation:
Here, we want to find the slopes and lengths of the sides of a quadrilateral
To find the slopes, we use the equation:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]To find the length, we use the equation:
[tex]L\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]We take the sides one after the other
a) HI
We have the slope as:
[tex]m\text{ = }\frac{-9+1}{-6+8}\text{ = }\frac{-8}{2}\text{ = -4}[/tex]We have the length as:
[tex]\begin{gathered} \sqrt[]{(-6+8)^2(-9+1)^2} \\ =\text{ }\sqrt[]{4+64} \\ =\text{ }\sqrt[]{68} \end{gathered}[/tex]b) IJ
We have the slope as:
[tex]m\text{ = }\frac{-8+9}{-2+6}\text{ = }\frac{1}{4}[/tex]We have the length as:
[tex]\begin{gathered} IJ\text{ = }\sqrt[]{(-6+2)^2+(-8+9)^2} \\ IJ\text{ = }\sqrt[]{17} \end{gathered}[/tex]c) JK
Slope:
[tex]m\text{ = }\frac{-8+0}{-2+4}\text{ = -4}[/tex]Length:
[tex]\begin{gathered} JK\text{ = }\sqrt[]{2^2+(-8)^2} \\ JK\text{ = }\sqrt[]{68} \end{gathered}[/tex]D) KH
Slope:
[tex]m\text{ = }\frac{0+1}{-4+8}\text{ = }\frac{1}{4}[/tex]Length:
[tex]\begin{gathered} KH\text{ = }\sqrt[]{(-4+8)^2+(0+1)^2} \\ KH\text{ = }\sqrt[]{17} \end{gathered}[/tex]From the answers obtained, the side lengths KH and IJ are the same, while the side lengths JK and KI are the same
Also, looking at the slopes, when the product of the slopes of two lines equal -1, the two lines are perpendicular
Since:
[tex]\frac{1}{4}\times\text{ (-4) = -1}[/tex]We can conclude that a set of two sides(KH, JK and HI, IJ) are perpendicular
Thus, we have it that the quadrilateral is a rectangle
Related Questions
i was absent for the day we reviewed the question and my teacher won't help me understand. the image given is my problem.
Answers
Step 1. Find the coordinates of point D.
In this problem, we have a segment called CD with two endpoints. We know one of the endpoints:
[tex](2,-1)[/tex]And we don't know the other endpoint, but we know the midpoint:
[tex](8,3)[/tex]We will label these known points as the first point (x1,y1) and the midpoint (xm, ym) as follows:
[tex]\begin{gathered} x_1=2 \\ y_1=-1 \\ x_m=8 \\ y_m=3 \end{gathered}[/tex]To find the second endpoint which we will call the second point (x2,y2) we use the midpoint formulas:
[tex]\begin{gathered} x_m=\frac{x_1+x_2}{2} \\ y_m=\frac{y_2+y_2}{2} \end{gathered}[/tex]Solving each equation respectively for x2 and y2:
[tex]\begin{gathered} x_2=2x_m-x_1 \\ y_2=2y_m-y_1 \end{gathered}[/tex]And substituting the known values for the first point and the midpoint:
[tex]\begin{gathered} x_2=2(8)-2=16-2=14 \\ y_2=2(3)-(-1)=6+1=7 \end{gathered}[/tex]We have found the second endpoint (x2,y2):
[tex](14,7)[/tex]Step 2. Once we know the two endpoints of the segment CD:
[tex]\begin{gathered} (2,-1) \\ \text{and} \\ (14,7) \end{gathered}[/tex]We make a graph for reference:
Note: the diagram is not to scale.
The length of the red line is what we are asked to find.
To find this length, draw a triangle between the points, shown here in green:
The triangle is a right triangle, this means we can use the Pythagorean theorem:
The Pythagorean theorem helps us find the hypotenuse ''x'' of the triangle when we know the legs a and b.
In this case, a and b are:
Substituting in the Pythagorean theorem:
[tex]\begin{gathered} x=\sqrt[\square]{a^2+b^2} \\ x=\sqrt[]{12^2+8^2} \end{gathered}[/tex]Solving the operations:
[tex]\begin{gathered} x=\sqrt[]{144-64} \\ x=\sqrt[]{80} \\ x=8.9 \end{gathered}[/tex]The solution is b. 8.9 units.
Answer: 8.9 units
Mia has $238.12 deducted from his monthly pay for group health insurance. His employer pays 85% of the cost. What is the annual premium?
Answers
$238.12
$238.12 -------------------------- 15%
x -------------------------100%
x = (100 x 238.12) / 15
x = 23812/15
x = $1587.5
Annual premium = 1587.5 x 12
= $19050
You are asked to create a graphic that would make it easy to quickly tell which locations require that ear protection be worn after 12 hours of exposure with the understanding that the sound level limit is 87. Would the proposed new graphic accomplish this purpose?
Answers
Answer:
Step-by-step explanation:
The answer would be "Yes, because ordering from lowest sound level to highest sound level makes it easy to use the exposure graph to see what time is permitted."
Hopes this helps.
find three comsecutive even integers whose sum is 162. enter your answers as a coma -seperated list.
Answers
To answer this question we will set and solve an equation.
Let x, x+2, and x+4 be three consecutive even integers whose sum is 162, then we can set the following equation:
[tex]x+x+2+x+4=162.[/tex]Adding like terms we get:
[tex]3x+6=162.[/tex]Subtracting 6 from the above equation we get:
[tex]\begin{gathered} 3x+6-6=162-6, \\ 3x=156. \end{gathered}[/tex]Dividing the above equation by 3 we get:
[tex]\begin{gathered} \frac{3x}{3}=\frac{156}{3}, \\ x=52. \end{gathered}[/tex]Therefore the three consecutive even integers whose sum is 162 are:
[tex]52,54,56.[/tex]Answer:
[tex]52,54,56.[/tex]
Use a table to find (x+3)(x+2).
Answers
We would set up the table as shown below
For each cell, we multiply the term for the row by the term for the column. By doing this, the first box is x * x = x^2. The second box is 3 * x = 3x
The third box is x * 2 = 2x
The fourth box is 3 * 2 = 6
By combining them, the equation would be
x^2 + 3x + 2x + 6
= x^2 + 5x + 6
3. Create a fraction with a denominator of 100 that is equivalent to to Your answer DELL
Answers
80/100
Explanation:We are to find an equivalent fraction to 8/10. But in this case the denominator needs to be 100
[tex]\begin{gathered} \text{Given denominator = 10} \\ \text{new denominator = 100} \\ \frac{\text{new denominator }}{\text{given denominator }}=\frac{100}{10}=\text{ 10} \end{gathered}[/tex]This means the multiplying number to the given denominator is 10.
For equivalent fraction, we multiply the numerator and the denominator by the same number
So we would multiply the given numerator too by the multiplying number 10
[tex]\begin{gathered} \text{Given numerator = 8} \\ \text{New numerator = 8}\times10\text{ = 80} \end{gathered}[/tex]The equivalent fraction to 8/10 becomes:
[tex]\begin{gathered} Thefraction=\frac{\text{new numerator}}{\text{new denominator}} \\ Thefraction=\frac{80}{100} \end{gathered}[/tex]the results for a survey of 120 students were selected randomly are listed below
Answers
The percentage of students that have a cell phone plan with company Y is:
36 / 120 (total of the surveyed students) *100 = 30%
Then, we use that percentage with the total of the students (380)
30 % of 380
30/100*380
114 (Multiplying)
The answer is the option A.
Rodney thinks that sqaure to the third power of 64 is greater than 17/4. Sam thinks that 17/4 is greater. Who is right and why?
Answers
The result of a square to the third power is a number that mutiplied 3 times by itself results in the number inside the square.
For example
[tex]\sqrt[3]{8}=2[/tex]because 2*2*2=8.
In this case:
[tex]\sqrt[3]{64}=4[/tex]That is because 4*4*4=64.
Now, we compare this with 17/4:
[tex]\frac{17}{4}=4.25[/tex]Thus, since 4 is less than 17/4. The one who is right is Sam, because 17/4 is greater than 4
Focus (1,4)Directrix=x-7,What is the vertex (h,k)?what is p?what is the equation?
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Let's begin by listing out the information given to us:
[tex]undefined[/tex]#7 iDecide whether there is enough information to prove that alb. If so, state the theroem you would usebHNo, there is not enough informationYes. Alternate Interior Angles ConverseYes. Alternate Exterior Angles ConverseYes Consecutive Interior Angles ConverseYes Corresponding Ang
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Given:
A figure is given with the corresponding angles.
Required:
Choose the correct statement that proves that the lines a and are parallel.
Explanation:
The given angles in the figure are corresponding angles. They are located within the two parallel lines and the transversal line intersecting them.
The corresponding angles are congruent thus lines a and b will be parallel.
Final Answer:
The last option is the correct answer.
What is the equation of the lime that is perpendicular to y=1/3x+12 that contains the point (-6,-1)
Answers
In order to find the equation of the perpendicular line. Take into account that the realtion between the slopes of two perpendicular lines is given by:
[tex]m_1=-\frac{1}{m_2}[/tex]where m1 and m2 are the slopes of the lines.
The general form of the equation of a line is:
y = mx + b
where m is the slope and b the y-intercept. By comparing the previous equation with the given equation y = 1/3x + 12, you can notice that m=1/3.
If you take this slope as m2, then the slope of the perpendicular line is:
[tex]m_1=-\frac{1}{\frac{1}{3}}=-3[/tex]Next, consider that the equation of a line can be also written as follow:
y - yo = m(x - xo)
where (xo,yo) is a point of the line. In this case the point is (-6,-1).
Replace the values of xo, yo and m=m2, into the previous equation and solve for y:
y - (-1) = (-3)(x - (-6))
y + 1 = -3x - 18
y = -3x -19
Hence, the equation of the perpendicular line is y = -3x - 19
Choose the answer that best completes the visual analogy.62Х**is to.oOХo*asis to?
Answers
The question wants us to choose the answer that best completes the visual analogy.
Before we will choose, let's first of all know what visual analogy is is.
Visual analogies are use to determine graphical patterns.
Theses are the ways you can determine a complete image.
When the corresponding shapes are the same , then the transformed shape is a square.
When the corresponding shapes are not the same, the shape at the top top takes precedence over the shape st the bottom.
So, from the above illustrations, the answer that completes the analogy would be the Third image.
On the grid below triangle MNP is plotted with vertices at M(-10,-2), N(-6,-9) and P(1,-5). The line y=-2/3x is also drawn.(a) Draw the image of triangle MNP after a reflection in y=-2/3x. Give the coordinates of the transformed vertices below.(b) Explain why triangle M'N'P' must have the same area as triangle MNP.
Answers
We have the following:
The reflection is:
[tex]\begin{gathered} M(-10,-2)\rightarrow M^{\prime}(2,10) \\ N(-6,-9)\rightarrow N^{\prime}(9,6) \\ P(1,-5)\rightarrow P^{\prime}(5,-1) \end{gathered}[/tex]a) The graph is:
b)
Since the sides are still the same length, for this reason keep the same area
Suppose you were given $600 from your uncle. You deposited that money in a bank and added $50 per month.
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The 1-variable equation that we need to solve to find how many months it would take to save $10,000 is given when we equal s(x)=10,000.
Hence, the answer is:
[tex]50m+600=10,000[/tex]Now, to find how many months it would take to save 10,000, we need to solve for m the previous equation. Therefore:
[tex]50m+600=10,000[/tex]Subtract both sides 600
[tex]50m+600-600=10,000-600[/tex][tex]50m=9400[/tex]Then, divide both sides by 50:
[tex]\frac{50m}{50}=\frac{9400}{50}[/tex][tex]m=188[/tex]Hence, it would take 188 months to save $10,000
7. Georgina balances her budget by using this plan. For every $100 she earns, she budgets $10 for charity, $20 for savings, $20 for books, and $50 for other expenses. What amount does she give to charity each week if her income is $500 per week? A. $500 B. $5 C. $250 D. $50
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to solve this question, we can find the percentage she gives to charity o every dollar she earns
if she earns $100, she gives $10 to charity. let's find the percentage on this.
[tex]\frac{10}{100}\times100=0.1\times100=10\text{ \%}[/tex]from the calculation, she gives 10% of are earnings to charity.
now we can find 10% of $500 to solve this question.
[tex]\begin{gathered} 10\text{ \% of \$500} \\ \frac{x}{500}=\frac{10}{100} \\ \frac{x}{500}=0.1 \\ x=0.1\times500 \\ x=50 \end{gathered}[/tex]from the calculations above, she gives out $50 on charity weekly from her $500 income.
Items 8-10. triangle DEF is shown below.8. What is measure DEF9.Select all the descriptions for segment GE.10. Select all the points that segment GE contains.
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8.
ΔDEF is an isosceles triangle, therefore:
[tex]\begin{gathered} m\angle DEF=m\angle DEG+m\angle FEG \\ \text{where:} \\ m\angle DEG=3y+4 \\ m\angle FEG=5y-10 \\ m\angle DEG=m\angle FEG \\ 3y+4=5y-10 \\ \text{solving for y:} \\ 2y=14 \\ y=7 \\ m\angle DEG=m\angle FEG=3(7)+4=25 \\ m\angle DEF=25+25 \\ m\angle DEF=50 \end{gathered}[/tex]9.
C. Perpendicular bisector
A. Angle bisector
D. Altitude ( If your teacher mean height)
B. Median
10.
A. Circumcenter
B. Incenter
C. Orthocenter
D. Centroid
QuestionFind the volume of a rectangular solid with the given dimensions: length 8 feet, width 9 feet, and height 11 feet. Give youranswer without units.
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We can use the next formula in order to find the volume
[tex]V=l\times w\times h[/tex]l is the length
w is the width
h is the height
in our case
l=8ft
w=9ft
h=11ft
we substitute the values
[tex]V=8\times9\times11=792ft^3[/tex]Find the number of complex roots and the number of possible real roots for the equation: 2x^4-3x^3+x^2-7x+3=0
Answers
You have the following polynomial:
2x⁴ - 3x³ + x² + 7x + 3 = 0
Based on the grade of the previous polynomial, you can conclude that there are 4 roots.
The complex roots are always present in pairs. Then, it's possible the given polynomial has 4 complex roots. In case there are 2 real roots, then, there are two comlpex roots.
Otherwise, there are 4 real roots.
Then, you can conclude for the possible roots of the polynomial:
- 4 real roots
- 4 complex roots
- 2 real roots and 2 complex roots
identify the class in their frequency choose the correct answer below
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Given the following question:
Identify the classes and their frequencies
Using the histogram we can find....
60-69 is 2
It wouldn't be option A because you can see the length of the bar is 60 - 70, - 80 - 90 etc...
The answer would be the third option where it gives a accurate descprition of the 7th graders IQ scores where it's rounded to the nearest whole number.
I need help with a graph in question (To graph the point (5,2))
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To graph a point in the cartesian plane you can use rectangular coordinates. These coordinates (in a 2D plane) are given by values of x and y:
So if you want to graph a point, let's say (a,b). You must move "a" steps to the right and "b" steps upwards.
In your exercise, you have to graph the point (5,2), therefore you have to move "5" steps to right and "2" steps upwards:
the graph of each function is shown. write the function in factored format. do not include complex numbers
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Notice that the graph passes through the point (-3,0), this means that the function f(x) has a root on x = -3. Then, we can use sintetic division to find the quotient of x+3 with f(x):
notice that on the last row, the last digit is 0, this means that the remainder is 0 and we can write f(x) in the following factored form:
[tex]\begin{gathered} f(x)=x^3+5x^2+12x+18= \\ (x+3)(x^2+2x+6)_{} \end{gathered}[/tex]Find the value of x and y if DEFG is congruent to SPQR
Answers
ANSWER
• x = 8
,• y = 10
EXPLANATION
If DEFG is congruent to SPQR, then side QR is congruent to side FG,
[tex]2x-4=12[/tex]Add 4 to both sides of the equation,
[tex]\begin{gathered} 2x-4+4=12+4 \\ 2x=16 \end{gathered}[/tex]And divide both sides by 2,
[tex]\begin{gathered} \frac{2x}{2}=\frac{16}{2} \\ x=8 \end{gathered}[/tex]For the same reason, angles F and Q are congruent,
[tex]6y+x=68[/tex]Replace x by the value we found before,
[tex]6y+8=68[/tex]Subtract 8 from both sides of the equation,
[tex]\begin{gathered} 6y+8-8=68-8 \\ 6y=60 \end{gathered}[/tex]And divide both sides by 6,
[tex]\begin{gathered} \frac{6y}{6}=\frac{60}{6} \\ y=10 \end{gathered}[/tex]Hence, the answers are x = 8 and y = 10.
Question 8 of 10, Step 1 of 15/10CorrectIn a park, the ratio of adults to children is 12 to 11. If there are 368 people in the park, how many children are there?AnswerекеKeyboard ShochildrenSubmit Answer
Answers
STEP - BY - STEP EXPLANATION
What to find?
Number of children in the park.
Given:
• Ratio of adult to children =12: 11
,• Total ratio =23
,• Number of people in the park =368
To solve the given problem, we will follow the steps below:
Step 1
Use the formula below to solve the given problem:
[tex]Number\text{ }of\text{ }children=\frac{ratio\text{ of children}}{total\text{ ratio}}\times number\text{ of people}[/tex]Step 2
Substitute the values into the formula.
[tex]Number\text{ }of\text{ }children=\frac{11}{23}\times368[/tex][tex]=\frac{4048}{23}[/tex][tex]=176[/tex]Therefore, there are 176 children in the park.
What is the perimeter of a rectangle with coordinates A (1, 7), B (8, 7), C (8, -3), and D (1, -3)?
A. 35 units
B. 68 units
C. 370 units
D. 34 units
PLEASE HELP ILL GIVE BRANLIEST
Answers
The perimeter of the rectangle ABCD will be 34 units. Then the correct option is D.
What is the perimeter of the rectangle?The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be
Perimeter of the rectangle = 2(L + W) units
The coordinates of the rectangle are A(1, 7), B(8, 7), C(8, -3), and D(1, -3).
The distance between AB will be given as,
AB² = (8 - 1)² + (7 - 7)²
AB² = 49
AB = 7 units
The distance between BC will be given as,
BC² = (8 - 8)² + (-3 - 7)²
BC² = 100
BC = 10 units
Then the perimeter of the rectangle will be given as,
P = 2(AB + BC)
P = 2(7 + 10)
P = 2 x 17
P = 34 units
The perimeter of the rectangle ABCD will be 34 units. Then the correct option is D.
More about the perimeter of the rectangle link is given below.
https://brainly.com/question/15287805
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A researcher is studying the relationship between sugar consumption and weight gain. Twelve volunteers were randomly assigned to one of two groups. The first group had five participants which were put on a diet low in sugar and the other group with the remaining seven participants received 10% of their calories from sugar. After 8 weeks, weight gain was recorded from each participant.Which of the following principles was not used in this study?A.Repeated measures B. Blinding C. Randomization D. Control
Answers
Principles in Statitstic Studies
A. Repeated measures design is a research design that involves multiple measures of the same variable taken on the same or matched subjects either under different conditions or over two or more time periods.
This is performed in the described study since the same subjects are measured in different periods and in different conditions of weight.
B. Blinding in Statistics. Blinding, or double-blinding, is when a patient does not know what treatment they are receiving so it does not influence the final outcomes. This principle is used here, because none of the participants knew what was given to them.
C. Randomization refers to the practice of using chance methods (random number tables, flipping a coin, etc.) to assign subjects to treatments. We are not sure how the participants were assigned to the specific diet. They were randomly selected. This could refer to randomization.
D. Control refers to directly influency over the conditions of the subject of the study to ensure they all go through the exact same proccesses during the study. We know the groups received different diets in sugar contents, but the rest of their living variables were not controlled, thus this last principle was not used in this study
Write each of the numbers one, four, nine, 16 and 25 as a base raise to the second power. Explain why these numbers sometimes are called “perfect squares”.BUT ONLY NUMER 5
Answers
In all the following cases you obtain the first number as result of the multiplication of the base of the base of the cond number by itself.
1 = 1²
4 = 2²
9 = 3²
16 = 4²
25 = 5²
Graph the following inequalitys.4x + y ≥ 0
Answers
SOLUTION
We want to graph the inequality
[tex]4x+y\ge0[/tex]This becomes
The shaded region is known as the required region and contains the solution set for the inequality
Coordinates we can see from the shaded region are
[tex]\begin{gathered} (2,2) \\ (4,4) \\ (4,6) \\ (6,2) \\ (6,4) \end{gathered}[/tex]To make the line, pick two points at
[tex](-1,4)\text{ and }(1,-4)[/tex]Then join the points with a straight-line and shade the area above the line.
the following ordered pairs give the entrance exam scores x and the grade-point averages y after 1 year of college for 10 students.find the equation of a line that models entrance exam scores and GPA.
Answers
If this is a linear function between x and y, the slope will be constant.
We can pick any two ordered pairs, like (75, 2.3) and (82, 3) and calculate the slope as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-2.3}{82-75}=\frac{0.7}{7}=0.1[/tex]We can write the point-slope form of the equation and rearrange to find the value of the y-intercept and the slope-intercept form of the equation:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-3=0.1(x-82) \\ y=0.1x-0.1\cdot82+3 \\ y=0.1x-8.2+3 \\ y=0.1x-5.2 \end{gathered}[/tex]We can test if the equation is correct with another point, like (65,2):
[tex]\begin{gathered} y=0.1x-5.2 \\ y(65)=0.1(65)-5.2 \\ y(65)=6.5-5.2 \\ y(65)=1.3 \end{gathered}[/tex]This is not a exact line, so we have to apply a regression model to find the approximate line that best represent this relationship:
Answer: the linear regression model that best represents the relation between x and y is y=0.0736x-3.0166.
The distance between two cities on a map is 25 inches. The actual distance between the two cities is 500 miles. How many miles would 35 inches be on the map?
1.75 miles
20 miles
510 miles
700 miles
Answers
35 inches on the map will translate to an actual distance of 700 miles (fourth option).
What is the distance in miles?The first step is to determine the scale of the map. In order to determine the scale, divide the actual distance between the two cities by the distance on the map.
Scale = distance between the two cities / distance on the map
Scale = 500 / 25 = 20
Now, multiply the distance on the map by the scale.
Distance in miles = 20 x 35 = 700 miles
To learn more about scale drawings, please check: https://brainly.com/question/26388230
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Answer:
35 inches on the map will translate to an actual distance of 700 miles (fourth option).What is the distance in miles?The first step is to determine the scale of the map. In order to determine the scale, divide the actual distance between the two cities by the distance on the map. Scale = distance between the two cities / distance on the map Scale = 500 / 25 = 20 Now, multiply the distance on the map by the scale. Distance in miles = 20 x 35 = 700 milesTo learn more about scale drawings, please check: brainly.com/question/26388230#SPJ1
Step-by-step explanation:
Please help and show me how you got it as best as possible step by step im struggling and need to show my work
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the formula for area of a rectangle
[tex]Area=length\times width[/tex]STEP 2: Write the given measure of the sides
[tex]\begin{gathered} length=3x+2 \\ width=2x-1 \end{gathered}[/tex]STEP 3: Calculate the area
By substitution,
[tex]\begin{gathered} Area=(3x+2)(2x-1) \\ \mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd \\ \left(3x+2\right)\left(2x-1\right)=3x\cdot \:2x+3x\left(-1\right)+2\cdot \:2x+2\left(-1\right) \\ =3x\cdot \:2x+3x\left(-1\right)+2\cdot \:2x+2\left(-1\right) \\ =6x^2+x-2 \end{gathered}[/tex]Hence, the area of the rectangle is
[tex]6x^2+x-2[/tex]