Consider the statement: “In a triangle, the measure of an
exterior angle is always greater than the measure of the
adjacent interior angle."
Which of the following would serve as a counterexample?
Answer:
See the example given in the picture attached.
Step-by-step explanation:
No options are given, so I made my own example. In the picture attached, we can see that the measure of the exterior angle A is less than the measure of the adjacent interior angle B.
On the coordinate plane shown, each grid unit represents 10 feet. Polygon QRST has vertices Q(20, 30), R(−10, 30), S(−10, −20), and T(20, −20), and represents the floor plan of a room. Find the perimeter and area of the room.
The coordinate plane is missing, so i have attached it.
Answer:
Perimeter of room = 140 ft
Area of room = 1200 sq.ft
Step-by-step explanation:
From the cordinate plane attached, we can see the polygon QRST which represents the floor plan of the roo.
Thus;
The length of the sides of the room are;
ST = RQ = 30
QT = RS = 40
Perimeter of a rectangle is the sum of all sides of the rectangle.
Thus, perimeter of the room = (30 × 2) + (40 × 2) = 140 ft
Now, area of a rectangle is the product of two perpendicular sides.
Thus area of room = 40 x 30 = 1200 sq.ft
which points are separated by distance of 6 units?
A. (5,6) (4,6)
B. (1,3) (6,3)
C. (8,1) (1,1)
D. (7,2) (1,2)
Option (D) points (7,2) (1,2) are separated by distance of 6 units.
What is distance between two points?It is the length of the straight line connecting these points in the coordinate plane. This distance can never be negative, therefore we take the absolute value while finding the distance between two given points. The distance formula is an application of the Pythagorean theorem.
For the given situation,
The distance between the two points must be 6 units.
Let the points be (x1,y1) and (x2,y2)
The distance formula is
[tex]d=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2} }[/tex]
We need to check all the options.
Option A: (x1,y1) = (5,6), (x2,y2) = (4,6)
⇒ [tex]d=\sqrt{(4-5)^{2} +(6-6)^{2} }[/tex]
⇒ [tex]d=\sqrt{(-1)^{2} +(0)^{2} }[/tex]
⇒ [tex]d=\sqrt{1}[/tex]
⇒ [tex]d=1[/tex]
Distance ≠ 6. So option A is incorrect.
Option B: (x1,y1) = (1,3), (x2,y2) = (6,3)
⇒ [tex]d=\sqrt{(6-1)^{2} +(3-3)^{2} }[/tex]
⇒ [tex]d=\sqrt{(5)^{2} +(0)^{2} }[/tex]
⇒ [tex]d=\sqrt{25}[/tex]
⇒ [tex]d=5[/tex]
Distance ≠ 6. So option B is incorrect.
Option C: (x1,y1) = (8,1) , (x2,y2) = (1,1)
⇒ [tex]d=\sqrt{(1-8)^{2} +(1-1)^{2} }[/tex]
⇒ [tex]d=\sqrt{(-7)^{2} +(0)^{2} }[/tex]
⇒ [tex]d=\sqrt{49}[/tex]
⇒ [tex]d=7[/tex]
Distance ≠ 6. So option C is incorrect.
Option D: (x1,y1) = (7,2) , (x2,y2) = (1,2)
⇒ [tex]d=\sqrt{(1-7)^{2} +(2-2)^{2} }[/tex]
⇒ [tex]d=\sqrt{(-6)^{2} +(0)^{2} }[/tex]
⇒ [tex]d=\sqrt{36}[/tex]
⇒ [tex]d=6[/tex]
Distance = 6. So option D is correct.
Hence we can conclude that option (D) points (7,2) (1,2) are separated by distance of 6 units.
Learn more about distance between points here
https://brainly.com/question/14645718
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3. A telephone pole is supported by two wires on opposite sides. At the top of the pole, the wires
form an angle of 55º. On the ground, the ends of the wires are 11.0 m apart. One wire makes a
(4) 41° angle with the ground.
a) How long is each wire? (round to the nearest tenth)
b) How tall is the pole? (round to the nearest tenth)
I understand A, but please help with B ASAP!!!!
Answer: a) length of the wires are 8.1m and 13.4m
b) length of pole is 8.8m
Step-by-step explanation:
The diagram representing the scenario is shown in the attached photo. Triangle ABC is formed. Since the sum of the angles in a triangle is 180°, it means that angle B would be
180 - (41 + 55) = 84°
a) AC and BC are the lengths of each wire.
CD is the height of the pole
To determine AC, we would apply sine rule which is expressed as
a/SinA = b/SinB = c/SinC
Therefore,
11/Sin55 = BC/Sin 41 = AC/Sin84
1) 11//Sin 55 = BC/Sin 41
Cross multiplying, it becomes
11Sin41 = BCSin55
11 × 0.6561 = BC × 0.8192
BC = 7.2171/0.8192 = 8.8m
2) 11/Sin55 = BC/Sin 41 = AC/Sin84
1) 11//Sin 55 = AC/Sin 84
Cross multiplying, it becomes
11Sin84 = ACSin55
11 × 0.9945 = AC × 0.8192
AC = 10.9395/0.8192
AC = 13.4m
b) triangles ACD and BCD are right angle triangles. To determine CD, we would apply the sine trigonometric ratio.
Sin # = opposite side/adjacent side
Considering triangle ACD,
Sin 41 = CD/13.4
CD = 13.4Sin41 = 13.35 × 0.6561
CD = 8.8m
A cake has circumference of 25 1/7inches. what is the area of the cake? use 227 to approximate π. round to the nearest hundredth. enter your answer in the box.
Answer:
Step-by-step explanation:
Hello,
The circumference of the cake is 25(1/7), but we don't know the area of the cake.
Assuming the cake has a shape of a circle,
Circumference of a circle = 2πr
Where r = radius of the circle.
Area of a circle = πr²
But π = 22 / 7
We have to first find the value of r.
2πr = 25(1/7)
2×(22/7)×r = 25(1/7)
(44/7)r = 176 / 7
(44 × 7)r = 176 × 7
44r = 176
r = 176 / 44
r = 4 inches
Area of the circle = πr²
A = (22 / 7) × 4²
A = 22 / 7 × 16
A = 352 / 16
A = 22 (inches)²
The area of the cake is 22in²
The whole is 1,000,000. 50,000 is what percent of that
Answer:
500000000
Step-by-step explanation:
50,000 percent is or 1,000,000 is 500000000. I hope this is correct. I did the answer by multiplying them together.
Solve for y.
–1(y–10)–11≤–19
Answer:
y≥18
Step-by-step explanation:
Answer:
y≥18
Step-by-step explanation:
Step 1 : Equation at the end of step 1 : ((0 - (y - 10)) - 11) - -19 ≤ 0
Step 2 : Equation at the end of step 2 : 18 - y ≤ 0
Step 3 : 3.1 Multiply both sides by (-1) Flip the inequality sign since you are multiplying by a negative number
Solve Basic Inequality
Inequality Plot
Answer: y ≥ 18
Hope this helps.
3 intersecting lines are shown. A line contains points E, D, A, and B. Another line intersects the line at point A and contains points F, A, C. A line connects points D and F.
Given Line segment E D is-congruent-to Line segment D B , which statements about the figure are true? Check all that apply.
Line segment E B is bisected by Line segment D F .
A is the midpoint of Line segment F C .
Line segment F C bisects Line segment D B.
Line segment E B is a segment bisector.
FA = One-halfFC.
Line segment D A is congruent to Line segment A B .
Answer:
The one with arrows are the answers
->Line segment E B is bisected by Line segment D F .
->A is the midpoint of Line segment F C .
Line segment F C bisects Line segment D B.
->Line segment E B is a segment bisector.
->FA = One-halfFC.
Line segment D A is congruent to Line segment A B .
Step-by-step explanation:
I did it on edge and got it right
Answer:
1. Line segment E B is bisected by Line segment D F .
2. A is the midpoint of Line segment F C .
4.Line segment E B is a segment bisector.
5. FA = One-halfFC.
1 72 miles in 24 hour
Unit rate please!!!!!
Answer:
7.1
Step-by-step explanation:
What is the solution to the system of equations 2x + 3y = 40 and y = x +
10?
oy - y - 12
Answer:
hope this is correct
On a coordinate plane, triangle L M N has points (2, 1), (1, 1), (1, 3). Triangle L prime M prime N prime has points (negative 4, negative 4), (negative 3, negative 4), (negative 3, negative 2). Which sequence of transformations produces TriangleL'M'N' from TriangleLMN? a translation 5 units down and 2 units to the right followed by a reflection across the y-axis a reflection across the y-axis followed by a translation 5 units down and 2 units right a translation 5 units down and 2 units to the left followed by a reflection across the y-axis no sequence of transformations
Answer:
(A)a translation 5 units down and 2 units to the right followed by a reflection across the y-axis
Step-by-step explanation:
If a point is reflected across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite.
Triangle LMN has points (2, 1), (1, 1), (1, 3).
Triangle L'M'N' has points (-4,-4), (-3,-4), (-3,-2).
From the given options:
Option A: A translation 5 units down and 2 units to the right followed by a reflection across the y-axis
Given the points: (2, 1), (1, 1), (1, 3) of Triangle LMN
A translation 5 units down(x,y-5): (2,-4), (1,-4), (1,-2)2 units to the right(x+2, y-5): (4, -4), (3, -4), (3, -2)Reflection across the y-axis: (-4,-4), (-3,-4), (-3,-2)Therefore, the sequence of transformation in Option A produces Triangle L'M'N'.
Answer:Which sequence of transformations produces
TriangleL'M'N' from TriangleLMN?
a reflection across the y-axis followed by a translation 5 units down and 2 units right
a translation 5 units down and 2 units to the left followed by a reflection across the y-axis
no sequence of transformations
the answer is ''A'' a translation 5 units down and 2 units to the right followed by a reflection across the y-axis.
Step-by-step explanation:
i took the quiz today.
On a shopping trip, Rachel spent $3 on a bus ticket, $10 on a book, and $4 for a smoothie . She had $21 left after the trip. How much money did she start with?
i have no idea how to do word problems and they’re a little harder
Answer: Answer choice 1, 3, 5
Step-by-step explanation:
This is more of analyzing a graph rather than a word problem.
We are told that 4 pm is at 16 hrs after midnight. You can see that the graph increases up to 4 pm. We can say 1 is correct.
After 6 pm at 18 hrs, we can see that the graph decreases. We can say 3 is correct.
Looking at the slope of the graph, 12 to 16 has a steeper slope than 8 to 12. We can say the temperature increases faster at 12 to 16 than 8 to 12.
Choose the correct product of (8x − 4)(8x + 4). (1 point) 64x2 − 16 64x2 + 16 64x2 − 64x + 16 64x2 + 64x + 16
Answer:
The correct answer is "[tex]64*x^2 - 16[/tex]".
Step-by-step explanation:
The product [tex](8*x - 4)*(8*x + 4)[/tex] is a notable product, which happens when we have the product of the sum of two values with the subtraction of these same two values. In cases like this the answer will always be the first term squared minus the second term squared, therefore we have:
[tex](8*x - 4)*(8*x + 4) = 64*x^2 - 16[/tex]
The correct answer is "[tex]64*x^2 - 16[/tex]".
Answer:
64x^2 -16
took the test
identify the graph of the equation and find (h k). x^2-2x-y^2-2y-36=0
Answer:
c. hyperbola, (1,-1)
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
In 1626, the Dutch bought Manhattan Island, now part of New York City, for $24.75 worth of merchandise. Suppose that, instead, $24.75 had been invested in an account that paid 3.75% interest each year. Find the balance in 2020
Answer:
The balance in 2020 is $47,810,662.65576
Step-by-step explanation:
In order to find the balance in 2020, first we would have to calculate the number of year as follows:
number of years, t=2020-1626
number of years, t=394
Therefore, to calculate the balance in 2020, we would have to use the following formula:
f(t)= 24(1.0375)∧394
f(t)=24*1,992,110.94399
f(t)=$47,810,662.65576
The balance in 2020 is $47,810,662.65576
Solve this inequality; 4.2x+5.6<7.2 - 8.3x isolate the constant term on the left side odf the inequality by.................... Both sides of the inequaity
Answer:
x < 0.128
Step-by-step explanation:
The inequality given is:
4.2x + 5.6 < 7.2 - 8.3x
Let us collect like terms:
4.2x + 8.3x < 7.2 - 5.6
12.5x < 1.6
=> x < 1.6/12.5
x < 0.128
Is triangle PTC congruent to triangle LAF?
Answer:
Yes; LA (D)
Step-by-step explanation:
one of the legs are congruent. LA and PT are congruent. This makes up the "L" part of "LA"
Also, angle PCT and angle LFA are congruent base on the diagram. This makes up the "A" part of "LA"
2 people are trying different phones to see which one has the better talk time. ChatLong has an average of 18 hours with a standard deviation of 2 hours and Talk-a-Lot has an average of 20 hours with a standard deviation of 3. The two people who tested their phones both got 20 hours of use on their phones. For the z-scores I got 1 for the ChatLong company and 0 for Talk-a-lot. What is the percentile for each z-score?
Answer:
Step-by-step explanation:
The percentile for the z scores are gotten from the normal distribution table. The z cores are already known.
1) For the ChatLong company, the z score is 0. The area corresponding to the z score from the normal distribution table is 0.5. Therefore, the percentile is
0.5 × 100 = 50%
2) For the Talk-a-lot company, the z score is 1. The area corresponding to the z score from the normal distribution table is 0.84. Therefore, the percentile is
0.84 × 100 = 84%
In the distribution, the first quartile,median and mean are 30.8,48.5 and 42.0 respectively. If the co efficient skewness is -0.38, find the third quartile?
Answer:
The third quartile is 56.45
Step-by-step explanation:
The given parameters are;
The first quartile, Q₁ = 30.8
The median or second quartile, Q₂ = 48.5
The mean, [tex]\bar x[/tex] = 42.0
Coefficient of skewness = -0.38
The Bowley's coefficient of skewness (SK) is given as follows;
[tex]SK = \dfrac{Q_3 + Q_1 - 2 \times Q_2}{Q_3 - Q_1}[/tex]
Plugging in the values, we have;
[tex]-0.38 = \dfrac{Q_3 + 30.8 - 2 \times 48.5}{Q_3 - 30.8}[/tex]
Which gives;
-0.38×(Q₃ - 30.8) = Q₃ + 30.8 - 2 × 48.5
11.704 - 0.38·Q₃ = Q₃ - 66.2
1.38·Q₃ = 11.704 + 66.2 = 77.904
Q₃ = 56.45
The third quartile = 56.45.
The slope between (1, 6) (-5, -7)
Answer:
Step-by-step explanation:
So the right answer is 13/6
please see attached picture for full solution
hope it helps
Good luck on your assignment
3/7 of 8th graders play sports. is 3/5 of the 8th graders that play sports are boys, what fraction of the 8th graders are boys
Answer:
[tex]\dfrac{9}{35}[/tex] is the fraction of 8th graders who are boys.
Step-by-step explanation:
Let total number of 8th graders = [tex]x[/tex]
Given that, [tex]\frac{3}{7}[/tex] of 8th graders play sports
[tex]\Rightarrow[/tex] 8th graders who play sports = [tex]\frac{3}{7} \times x[/tex]
Also, Given that, [tex]\frac{3}{5}[/tex] of 8th graders that play sports are boys
Number of 8th graders that play sports, and are boys = [tex]\frac{3}{5} \times \text{Number of 8th graders who play sports}[/tex]
[tex]\Rightarrow \dfrac{3}{5} \times \dfrac{3}{7} \times x\\\Rightarrow \dfrac{9}{35} \times x[/tex]
Hence, the answer is:
[tex]\dfrac{9}{35}[/tex] is the fraction of 8th graders who are boys.
Bety compró 16 pares de calcetas, entre blancas y negras, y pagó $339. Los pares de calcetas blancas cuestan $24 y las negras $19. Plantea el sistema de ecuaciones y resuelve por el método que creas conveniente. Después toma foto y súbela en donde se indica.
Answer:
Sistema de ecuaciones:
x+y= 16
24x+19y=339
Respuesta:
x=7, y=9
Step-by-step explanation:
Con la información del enunciado puedes plantear las siguientes ecuaciones:
x= cantidad de calcetas blancas
y= cantidad de calcetas negras
x+y= 16 (1)
24x+19y=339 (2)
Para resolver las ecuaciones, debes iniciar despejando x en 1:
y=16-x (3)
Después, debes reemplazar (3) en (2) y despejar x para encontrar su valor:
24x+19(16-x)=339
24x+304-19x=339
5x=339-304
x=35/5
x=7
Luego, puedes reemplazar el valor de x en (3) para encontrar y:
y=16-x
y=16-7
y=9
De acuerdo a esto, x= 7, y=9.
Please help me with this quick!!!!
Solve the following:
A) 4x-1/2=x+7
B) 3x+2=2x+13/3
C) 2x-7/4=x+3/3
Answer:
A) 2.5
B) 7/3
C) 11/4
Step-by-step explanation:
A)
4x-1/2=x+7
3x-1/2=7
3x=7.5
x=2.5
B)
3x+2=2x+13/3
x+2=13/3
x=7/3
C)
2x-7/4=x+3/3
x=11/4
Hope this helps!
What is the solution to the equation Negative (5 minus (a + 1)) = 9 minus (5 minus (2a minus 3))?
[tex]\text{Solve:}\\\\-(5-(a+1))=9-(5-(2a-3))\\\\-(5-a-1))=9-(5-2a+3))\\\\-(4-a)=9-(8-2a)\\\\-4+a=9-8+2a\\\\-4+a=1+2a\\\\\text{Subtract a from both sides}\\\\-4=1+a\\\\\text{Subtract 1 from both sides}\\\\\boxed{-5=a}[/tex]
Answer:
The answer is A: a=-5
Step-by-step explanation:
took the test
Please help me now plz
Answer:
B
Step-by-step explanation:
The equation of the circle is (x + 1)² + (y + 3)² = 6². When we plug in (-6, -6) we get (-6 + 1)² + (-6 + 3)² = 6², which is a true statement so that means that the point is on the circle.
please help image attached i have everything before question 11 it’s due this morning
Answer:
11. 7x+28
Step-by-step explanation:
Answer:
Step-by-step explanation:
10) 4x+12
11) 7x+28
12)2x+16
13)9x+54
14)3x+33
15) 5x+35
16) 6x+24
17)8x+72
18) 4x+20
AFGH is a right triangle.
Answer:
A. TRUE
Step-by-step explanation:
7²+√51²= 10²
49+51=100
Answer is TRUE
A woman is 27 years older than her daughter, if the daughter is Y years old, what is the sum of their age
find the center and radius of the circle: (x+9)^2+(y-6)^2=25
Answer:
The center is (-9,6) and the radius is 5
Step-by-step explanation:
We can write the equation of a circle as
(x-h)^2+(y-k)^2=r^2
where (h,k) is the center and r is the radius
(x - -9)^2+(y-6)^2=5^2
The center is (-9,6) and the radius is 5
Circle equation: (x - h)^2 + (y - k)^2 = r^2
(h, k) is the center.
r is the radius.
(h, k) in the given equation is (-9, 6). This is the center.
We need to take the square root of 25 since the formula has r^2.
√25 = 5
So, the radius is 5.
Best of Luck!