lesson 6 unit 7 triangles sample work for geometry (I just need answers to the highlighted ones) 15pts
Answers
Answer:
2. Circumcenter is (-2, 1)
4. Orthocenter is (5, 0)
6. II ∠DOS and ∠CAT are vertical and III ∠DOS and ∠CAT are adjacent
8. m∠PBC = 30°
10. KV, VM, KM
12. DC is greater
14. x = 12
Step-by-step explanation:
2. Equation of the perpendicular bisector of AB is x = -2 and the equation of the perpendicular bisector of BC is y = 1.
Circumcenter is the point of intersection of the perpendicular bisectors of the sides of the triangle.
Hence, circumcentre is (-2, 1).
4. Orthocenter is the point of intersection of the altitudes. Here, AB and BC are two altitudes and B is their point of intersection.
Hence, the orthocenter is (5, 0).
6. Adjacent angles are angles separated by a line and vertical angles are angles vertically opposite to each other.
Hence, statements II and III contradict to each other.
8. If P is equidistant from all the three sides, then P is the center of the in-circle and hence it is the incenter of the triangle.
If P is the incentre, then PB is the internal bisector.
Therefore, ∠PBC = [tex]\frac{1}{2}[/tex] ∠ABC = 30°
10. From the triangle sum property, ∠ M = 180 - (110 + 40) = 30.
Since, the side opposite to the smallest is the shortest, the correct order is:
KV, VM, KM
12. Clearly, ∠ ABD is acute. Therefore, ∠ DBC > ∠ ABD.
Since, side opposite to larger angle is greater, DC is greater.
14. Let the sides of the top triangle be p and q. So, two sides of whole triangle are 2p and 2q.
Now, if we compare the top small triangle and the whole triangle, they are similar by SAS similarity since,
the top angle is common and [tex]\frac{p}{2p}=\frac{q}{2q}=\frac{1}{2}[/tex].
Since, corresponding parts of similar triangles are proportionate,
[tex]\frac{3x}{5x+12} =\frac{1}{2}[/tex]
6x = 5x + 12
6x - 5x = 12
x = 12
Answer:
2. Circumcenter is (-2, 1)
4. Orthocenter is (5, 0)
6. II ∠DOS and ∠CAT are vertical and III ∠DOS and ∠CAT are adjacent
8. m∠PBC = 30°
10. KV, VM, KM
12. DC is greater
14. x = 12
Step-by-step explanation:
Related Questions
what is the sum of 121/4+5 5/6 reduced to lowest terms thanks
Answers
Answer:18 1/12
Step-by-step explanation:i first added the whole numbers 12 and 5 to get 17; i then addled 1/4 and 5/6; i did this by finding a common denominator of both fractions and converted them into 6/24 and 20/24; i added them to get 26/24 which simplifies to 1 and 2/24, which equals 1 1/12; i added 1 to 17 and got 18, then added 1/12 to get 18 1/12
The sum of 121/4 and 5 5/6 is found by converting the mixed number to an improper fraction, finding a common denominator, adding the fractions, and simplifying if possible. The final answer is 433/12, which is already in its lowest terms.
The question asks for the sum of the numbers 121/4 and 5 5/6 reduced to the lowest terms. To answer this, we must first convert the mixed number to an improper fraction and then add it to the other fraction. Here's how to do it step by step:
Convert 5 5/6 to an improper fraction: 35/6.
Add 121/4 to 35/6. To do this, find a common denominator, which would be 12 in this case.
Convert both fractions to have the common denominator: 121/4 becomes 363/12, and 35/6 becomes 70/12.
Add the two fractions: 363/12 + 70/12 equals 433/12.
Reduce the fraction if possible. In this case, 433/12 is already in its lowest terms.
Therefore, the sum of 121/4 and 5 5/6 reduced to lowest terms is 433/12.
A car rental agency advertised renting a car for $ 26.95$26.95 per day and $ 0.28$0.28 per mile. If GregGreg rents this car for 22 days, how many whole miles can he drive on a $ 250$250 budget?
Answers
Answer:
892.85 miles for 22 days
Step-by-step explanation:
which order pairs are solutions of the inequality -7y +2x ≤ 3
A (0,0)
B (1,1)
C (-3,5)
Answers
Answer: A & B
Step-by-step explanation:
-7y + 2x ≤ 3
(0, 0): -7(0) + 2(0) ≤ 3
0 + 0 ≤ 3
0 < 3 TRUE
(1, 1): -7(1) + 2(1) ≤ 3
-7 + 2 ≤ 3
-5 < 3 TRUE
(-3, 5): -7(-3) + 2(5) ≤ 3
21 + 10 ≤ 3
31 < 3 FALSE
if f(x)=x^2-x and g(x)=x+1, determine f (g(x)) in simplest from
Answers
Answer:
f(g(x)) = x^2 +x
Step-by-step explanation:
To find f(g)(x) , we substitute g(x) in for x in the function f(x)
f(x) = x^2 -x
f(g(x)) = g(x)^2 -g(x)
= (x+1)^2 - (x+1)
= (x+1)*(x+1) - (x+1)
FOIL the square
(x+1) (x+1)
First x*x = x^2
outer x*1 = x
inner 1*x = x
last 1*1 =1
Add them together
x^2 + x+x+1 = x^2+2x+1
f(g(x)) = (x+1)*(x+1) - (x+1)
= x^2+2x+1 -(x+1)
Distribute the -1
= x^2 +2x+1 -x-1
= x^2 +x
f(g(x)) is basically replacing the x with g(x).
So, f(x)=(g(x))^2 - g(x)
g(x), in turn, equals x+1
Replace g(x) with x+1
(x+1)^2 - (x+1)
Expand: x^2+x+x+1 - x - 1
Cancel out x and 1
f(g(x))=x^2+x
If you require factoring it's
f(g(x))=x(x+1)
Construct a regular hexagon with vertex A inscribed in the given circle
Answers
Im not sure if this is right but.
Make the diameter by putting the line on points A and C. Then put the middle of the tool on point A and make the width to point C and draw a circle. Do the same for point B (other side of point A) without changing the width. Then plot the lines where the circles intersect and you have a hexagon :)
Answer:
there is one photo without the hexagon drawn out, and one with it drawn, so you can see it all. there's one small hexagon and one long one.
guys I need help.....
Answers
Answer:
.224 / 7 = .032
Step-by-step explanation:
.224 / 7
7 goes into 2 0 times with 2 left over
7 goes into 22 3 times with 1 left over
7 goes into 14 2 times with 0 left over
.224 / 7 = .032
Answer:
.032
Step-by-step explanation:
You are the new warehouse manager and you have a facility that has 25 storage racks that are 25 feet long, 12 feet high and 3 feet wide. The boxes that you need to store are 15x8x10 inches and there are 5000 of the boxes. Do you have enough storage space?
Answers
Answer is shown in the attached image, in RED.
Use synthetic division to solve (4x3-3x2+5x+6)/(x+6). What is the quotient?
Answers
Answer:
[tex]\text{The quotient is }4x^2 -27x +167[/tex]
Remainder is -996
Step-by-step explanation:
[tex]\text{Given the polynomial }4x^3-3x^2+5x+6\text{ which is to be divided by }x+6[/tex]
we have to find the quotient using synthetic division
x+6 =0 , so x=-6
We divide by -6.
The steps for synthetic division are
Step 1: Set up the synthetic division.
Step 2: Put down the leading coefficient to bottom row.
Step 3: Multiply divisor which is on left by the value just written on the bottom row.
Step 4: Add the column created in above step.
Step 5: continue until we reached last column.
The synthetic division is shown in attachment.
[tex]\text{The quotient is }4x^2 -27x +167[/tex]
Remainder is -996
When you divide 4x³- 3x² + 5x + 6 by (x+6) using synthetic division, the quotient is 4x²- 27x + 162
To divide ([tex]4x^3-3x^2+5x+6[/tex]) by (x+6) using synthetic division, follow the steps provided.
Arrange the terms of the dividend in descending order of degree, filling in any missing terms with a coefficient of 0.
Set up the synthetic division table with the divisor (x+6) as the divisor and the coefficients of the dividend (4, -3, 5, 6) as the dividend.
Perform the synthetic division:
Bring down the first coefficient, 4.
Multiply the divisor (x+6) by the value in the bottom row of the divisible column (which is 4).
The result is written in the next row.
Add the value in the next row to the coefficient in the next column and write the sum in the next row.
Repeat this process until all rows are completed.
The numbers in the bottom row of the table represent the coefficients of the quotient.
The quotient for this division is [tex]4x^2 - 27x + 167.[/tex]
Therefore, the quotient of ([tex]4x^3-3x^2+5x+6[/tex])/(x+6) is [tex]4x^2 - 27x + 167.[/tex]
Learn more about Synthetic division here:
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y^-9*y^-8*y^10= (its algebra 2 and i cant figure it out it please help)
Answers
[tex]Use:\\\\a^n\cdot a^m=a^{n+m}\\\\y^{-9}\cdot y^{-8}\cdot y^{10}=y^{-9+(-8)+10}=y^{-7}[/tex]
Stephen Had $1200. He spent 40% of it. How much money did he spend?
Answers
[tex]p\%=\dfrac{p}{100}\\\\40\%=\dfrac{40}{100}=\dfrac{4}{10}=0.4\\\\40\%\ of\ \$1200\ is\ 0.4\cdot\$1200=\$480\\\\Answer:\ \text{He spend}\ \$480.[/tex]
Final answer:
To determine the amount Stephen spent from his $1200 at 40%, the percentage is converted to a decimal (0.40) and multiplied by $1200, resulting in $480 spent.
Explanation:
Stephen had $1200. To calculate the amount of money he spent after using 40% of his money, we need to find 40% of $1200. We can write this as 0.40 × $1200.
Step 1: Convert the percentage into a decimal: 40% = 0.40
Step 2: Multiply the decimal by the total amount of money Stephen had: 0.40 × $1200 = $480.
Hence, Stephen spent $480 out of his $1200.
Determine the type of triangle that has angle measurements of 45°, 45°, 90°.
Answers
Answer:
I might be wrong but i think it is 90 Degree Angle
Step-by-step explanation:
Answer:
right triangle
Step-by-step explanation:
90 degrees is a right angle so it will be a right triangle
The graph shows the number of people infected with a virus as a function of time.
The graph shows exponential ___
A- decay
B- growth
As the amount of people infected with the virus decreases, time ___
A- increases
B- decreases
Answers
The graph shows exponential B
exponential decay is when the graph is decreasing/going down
exponential growth is when the graph is increasing/going up
The graph is shown to be increasing, so it is exponential growth
As the amount of people infected with the virus decreases, time B
If you look at the graph, as time increases, the number of infected people also increases. So when the # of infected ppl decreases, so does time
Answer:
1. Growth
2. Decreases
Step-by-step explanation:
The graph shows the number of people infected with a virus as a function of time.
1.
The graph shows exponential growth because the graph is increasing above. It is going upwards, as the time is increasing.
2.
As the amount of people infected with the virus decreases, time decreases.
As it is a growth graph, if we study this in the opposite direction, that is from upwards to downwards, we can see that as the graph is going down, the values on the y axis are also decreasing.
In a regular deck of cards calculate the probability that a face card is drawn given that it is a heart
nevermind it the answer is D=0.23 or 23%
Answers
Answer:
Option 4) Probability = 30%
Step-by-step explanation:
We are given the following information:
We have a deck of cards.
We have to find the probability of drawing a face card given that is a heart.
Formula:
[tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex]
Conditional probability:
The probability of happening of event A given event B:
[tex]P(A|B) = \displaystyle\frac{P(A \cap B)}{P(B)}[/tex]
[tex]P(\text{Face card}|\text{Hearts}) = \displaystyle\frac{P(\text{Face card} \cap \text{Hearts})}{P(\text{Hearts)}}\\P(\text{Hearts}) = \displaystyle\frac{13}{52}\\\\P(\text{Face card} \cap \text{Hearts}) = \frac{4}{52}\\\\P(\text{Face card}|\text{Hearts}) = \frac{4/52}{13/52} = \frac{4}{13}\\\\=\frac{4}{13}\times 100\% = 30.77\%[/tex]
Line segment AB has endpoints A(1,4) and B(6,2). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 2:3
Answers
Answer:
[tex](3,3\frac{1}{5})[/tex]
Step-by-step explanation:
We use the formula;
[tex](\frac{mx_2+nx_1}{2},\frac{my_2+ny_1}{2})[/tex]
where m:n=2:3 and [tex]x_1=1,x_2=6,y_1=4,y_2=2[/tex]
We substitute these values to get;
[tex](\frac{2(6)+3(1)}{2+3},\frac{2(2)+3(4)}{2+3})[/tex]
We simplify to get:
[tex](\frac{15}{5},\frac{16}{5})[/tex]
[tex](3,3\frac{1}{5})[/tex]
Answer:
(3,16/5)
Step-by-step explanation:
(2)(6)+(3)(1)/(2+3),(2)(2)+(3)(4)/(2+3)=3,16/5
Find the unit rate to the nearest cent per ounce.
A 24-ounce box of cornflakes costs $4.59
Answers
Answer:
0.19125
Step-by-step explanation:
You divided 4.59 by the amount 24-oz
(Or about 19 cents)
Hope this helps!
what is 3a2(ab2+b2) =
Answers
Answer: 3a^3 b^2+3a^2 b^2
Step-by-step explanation:
3a^2(ab^2+b^2)
=(3a^2)(ab^2+b^2)
=(3a^2)(ab^2)+(3a^2)(b^2)
=3a^3 b^2+3a^2 b^2
hope this helps
please mark brainliest answer
Answer:
3a3b2 + 2a2b2
Step-by-step explanation:
3a2(ab2 + b2) =
= 3a2*ab2 + 3a2*b2
= 3a3b2 + 2a2b2
Determine whether the rational root theorem provides a complete list of all roots for the following polynomial functions. f(x) = 4x2 − 25 g(x) = 4x2 + 25 h(x) = 3x2 − 25
Answers
Rational root theorem is used to determine the possible root of a function.
Rational root theorem provides a complete list of all roots of [tex]\mathbf{(a)\ f(x)= 4x^2 - 25}[/tex]Rational root theorem does not provide a complete list of all roots of [tex]\mathbf{(b)\ g(x)= 4x^2 + 25}[/tex]Rational root theorem does not provide a complete list of all roots of [tex]\mathbf{(c)\ h(x)= 3x^2 - 25}[/tex][tex]\mathbf{(a)\ f(x)= 4x^2 - 25}[/tex]
Set to 0
[tex]\mathbf{4x^2 - 25 = 0}[/tex]
Add 25 to both sides
[tex]\mathbf{4x^2 = 25}[/tex]
Divide both sides by 4
[tex]\mathbf{x^2 = \frac{25}{4}}[/tex]
Take square roots
[tex]\mathbf{x = \pm\frac{5}{2}}[/tex]
The function has rational roots.
This means that: rational root theorem provides a complete list of all roots
[tex]\mathbf{(b)\ g(x)= 4x^2 + 25}[/tex]
Set to 0
[tex]\mathbf{4x^2 + 25 = 0}[/tex]
Add -25 to both sides
[tex]\mathbf{4x^2 = -25}[/tex]
Divide both sides by 4
[tex]\mathbf{x^2 = -\frac{25}{4}}[/tex]
Take square roots
[tex]\mathbf{x = \pm \sqrt{-\frac{25}{4}}}[/tex]
The function has complex roots.
This means that: rational root theorem does not provide a complete list of all roots
[tex]\mathbf{(c)\ h(x)= 3x^2 - 25}[/tex]
Set to 0
[tex]\mathbf{3x^2 - 25 = 0}[/tex]
Add -25 to both sides
[tex]\mathbf{3x^2 = 25}[/tex]
Divide both sides by 4
[tex]\mathbf{x^2 = 8.333}[/tex]
Take square roots
[tex]\mathbf{x = \pm 2.89}[/tex]
The function has irrational roots.
This means that: rational root theorem does not provide a complete list of all roots
Read more about rational roots at:
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Explanation of the Rational Root Theorem and its application to polynomial functions f(x), g(x), and h(x).
The Rational Root Theorem provides a list of possible rational roots for a polynomial function. However, it does not guarantee that all roots will be rational. Let's examine the given polynomial functions:
For f(x) = 4x² - 25: The rational root theorem suggests possible rational roots, but the roots could also be irrational.For g(x) = 4x² + 25: As this polynomial has no real roots (due to the presence of complex numbers under the square root), the rational root theorem won't provide all roots.For h(x) = 3x² - 25: Again, the rational root theorem gives possible rational roots, but not the complete list of roots.What division problem does this model represent
Answers
The five fifth grade teachers ans six fourth grade teachers ordered 2 large pizzas all together. Each pizza costs $13.75. If they are going to spilt the cost evenly, how much will each person need to pay?
Answers
Answer:
80 Cents
Step-by-step explanation:
Answer: Each person will need to pay $1.25
Step-by-step explanation: $13.75 divided by the 11 people = $2.25
Perhaps brainliest?
solve
4x+6<-6
I could really use the help
Answers
Answer:
x < -3
Step-by-step explanation:
First subtract 6 from both sides of the inequality.
[tex]4x+6-6<-6-6[/tex]
[tex]4x<-12[/tex]
Divide 4 on both sides.
[tex]\frac{4x}{4} < \frac{-12}{4}[/tex]
[tex]x<-3[/tex]
A new car is purchased for 22300 dollars. The value of the car depreciates at 10.25% per year. What will the value of the car be, to the nearest cent, after 6 years?
Answers
Answer : The value of car will be, $11654.98
Step-by-step explanation:
Given,
Principle = $22300
Time = 6 years
Rate of depreciation = 10.25 %
Formula used :
[tex]A=P(1-\frac{R}{100})^t[/tex]
where,
A = amount
P = principle
R = rate of depreciation
T = time
Now put all the given values in the above formula, we get:
[tex]A=P(1-\frac{R}{100})^t[/tex]
[tex]A=\$ 22300(1-\frac{10.25}{100})^{6}[/tex]
[tex]A=\$ 11654.98[/tex]
Therefore, the value of car will be, $11654.98
how do u solve 1736÷56 step by step
Answers
Answer:
31
Step-by-step explanation:
use a step by step calculator.
This is the graph of f(x). What is the value of f(2)?
Answers
Look at the picture.
f(2) = 8 or f(2) = 9Answer: f(2) = 9From the graph, the value of the function at x = 2 will be 9. Then the correct option is B.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
The graph of the function is shown.
From the graph, the value of the function at x = 2 will be 9.
Then the correct option is B.
More about the function link is given below.
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the formula for the volume of a cylinder is V=3.14r^2h. The volume of a cylinder is 3 times the volume of a cone with the same radius and height. If the volume of a cone with the same height as a cylinder equals the volume of the cylinder, the equation for the radius of cone R in terms of the radius of a cylinder is?
Answers
Answer:
The equation for the radius of cone R in terms of the radius of cylinder (r) is,
R = r√3
Step-by-step explanation:
Volume of the cone = πR²H/3 (where Height is H and Radius is R)
Volume of the Cylinder = πr²h (where Height is h and Radius is r)
Now, both are same in height, so H = h and Their volume are same. So,
πR²H/3=πr²h
or, R²/3=r²
or, R²=r²×3
or, R = √(r²×3)
or, R = r√3
Answered by GAUTHMATH
Final answer:
The relationship between the volume of a cylinder and a cone with the same radius and height leads to the equation for the radius of the cone in terms of the cylinder's radius. By equating the volumes and simplifying, we find that the cone's radius R is equal to the square root of 3 times the cylinder's radius r, or R = √3 * r.
Explanation:
We start with the formula for the volume of a cylinder V = πr²h and the volume for a cone, which is a third of the cylinder's volume, V = ⅓πr²h. Since we are given that the volume of a cone equals the volume of a cylinder with the same radius and height, we can set up an equation to find the radius of the cone R in terms of the cylinder's radius r.
We know that the volume of the cone is one third the volume of the cylinder, so when they are equal, the cone must be larger to compensate for this ratio. Therefore, the volume equation becomes V = πR²h, where R is the radius of the cone and h is the height. To find R in terms of r, we equate the two volume formulas: πR²h = 3πr²h. Simplifying, we get R² = 3r² and hence, R = √3 * r.
What is the largest fraction 3/4 7/8 8/10 7/9?
Answers
Answer:
7/8 ths
Step-by-step explanation:
3 divided by 4 is .75
* 7 divided by 8 is .875
8 divided by 10 is .80
7 divided by 9 is .77
If you divide the fractions you can compare the values and the highest value is your largest fraction.
The fraction with largest value of numerator is largest fraction in the two or more fraction number with same denominator. The fraction 7/9 has the largest fraction.
Given information-
The set of the fraction given in the problem is,
[tex]\dfrac{3}{4}, \dfrac{7}{8}, \dfrac{8}{10}, \dfrac{7}{9}[/tex]
What is the order of fraction?The order of the fraction is arranging the fraction number from the smallest to the largest number.
The fraction with largest value of numerator is largest fraction in the two or more fraction number with same denominator.
To compare the fraction, make the denominator with same.
[tex]\dfrac{3}{4}, \dfrac{7}{8}, \dfrac{8}{10}, \dfrac{7}{9}[/tex]
To make the denominator same find out the least common factor of denominators which are 4,8,10 and 9 which is 360.
Multiply and divide with 360 in the given fractions to bring the 360 in denominator,
[tex]\dfrac{3\times360}{4\times360}, \dfrac{7\times360}{8\times360}, \dfrac{8\times360}{10\times360}, \dfrac{7\times360}{9\times360}[/tex]
[tex]\dfrac{270}{360}, \dfrac{315}{360}, \dfrac{288}{360}, \dfrac{315}{360}[/tex]
As the numerator 315 is the highest among all. Hence the fraction 7/9 has the largest fraction.
Learn more about the largest fraction here;
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The coordinates of point P are (-3, 5). Point R is a reflection of point P across the x-axis. Point S is a reflection of point P across the y-axis.
Point R is located in quadrant . Point S is located in quadrant .
Answers
Answer:
R is in the third quadrant and S is in the first quadrant
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y )
P(- 3, 5 ) → R(- 3, - 5 ) ← third quadrant
Under a reflection in the y-axis
a point (x, y ) → (- x , y )
P(- 3, 5 ) → S(3, 5 ) ← first quadrant
In a reflection across the x-axis, the y-coordinate is negated, and in a reflection across the y-axis, the x-coordinate is negated. Thus, Point R (-3, -5) from point P (-3, 5) is in the fourth quadrant and Point S (3, 5) is in the first quadrant.
Explanation:The given point P has the coordinates (-3, 5). When a point is reflected across the x-axis, the y-coordinate changes its sign. So, the reflection of point P across the x-axis (Point R) would be at (-3, -5). This places Point R in the fourth quadrant.
Similarly, when a point is reflected across the y-axis, the x-coordinate changes its sign. Therefore, the reflection of point P across the y-axis (Point S) would be at (3, 5). This places Point S in the first quadrant.
In summary, Point R is located in the fourth quadrant and Point S is located in the first quadrant.
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whats is the ratio of 3 dogs to 4 cats
Answers
Answer:
3 to 4
or
3:4
Step-by-step explanation:
Alexandria wants to go hiking on Saturday. She will choose from several parks considering these conditions:
• She wants to hike for 2 hours.
• She wants to spend no more than 6 hours away from home.
• She can average 65 miles per hour to and from the park.
Choose and solve the inequality that represents the possible distances from Alexandria’s home to a park that satisfies the conditions above.
Answers
Answer:
The correct answer for this problem is 200 miles.
What is the awnser for 1/2 x + 8 equals 16
Answers
Answer:
What do mean by equals 16?
Step-by-step explanation:
1/2x+8=16
1/2x=16-8
1/2x=8
x=8:1/2
x=8*2
x=16
Hope this helps! <3
Is this a true proportion ? 3/4,8/12
Answers
now look this answer,
3:4:8:12
Question
Is this a true proportion ? 3/4,8/12
Answer:
FalseStep-by-step explanation:
3/4 = 8/12
semplify
3/4 = 2/3
or you can solve in this way
3/4 = 8/12
0.75 = 0.66≈