Answer:
Step 1: Add 3y to both sides.
2x−3y+3y=−8+3y
2x=3y−8
Step 2: Divide both sides by 2.
2x
2
=
3y−8
2
x=
3
2
y−4
Answer:
x= 3/2 y -4
x+3y=14
x+3y=14
Step 1: Add -3y to both sides.
x+3y+−3y=14+−3y
x=−3y+14
Answer:
x=−3y+14
Step-by-step explanation:
Answer:
X=2, y=4
Step-by-step explanation:
Elimination method:
2x-3y=-8 equation 1
x+3y=14 equation 2
3x+0=6 add above 2 equations
3x=6
x=2
solve for y by substituting x in either equation
x+3y=14
2+3y=14
3y=12
y=4
Substitution method:
2x-3y=-8 equation 1
x+3y=14 equation 2
x=14-3y isolate x in equation 2
2(14-3y)-3y=-8 substitute value of x from equation 2 into equation 1
28-6y-3y=-8
-9y=-36
y=4
solve for x by substituting value of y into either equation
2x-3y=-8
2x-3(4)=-8
2x-12=-8
2x=4
x=2
A. Dilate triangle ABC using center p and scale factor 3/2.
B. What do properties of dilations tell you about B'? (please answer B)
Part A
See the diagram below. We end up with a triangle where the sides are 3/2 = 1.5 times longer compared to the original diagram. Because segment AC is going through P (center of dilation), this means that segment A'C' will also go through P. Furthermore, it means AC and A'C' overlap. However, as mentioned earlier, A'C' is 1.5 times longer than AC.
Another thing to note: line BC is parallel to line B'C', and line AB is parallel to A'B'.
==========================================================
Part B
Dilations may change the size of an object, but the shape will remain intact. This means all angles will remain the same no matter what the scale factor is.
Here's a real world example:
Cut out a triangle from a piece of paper. It can be any triangle whether right, acute, or obtuse. Then mark one of the angles (say 90 degrees). Next, hold up the triangle in front of you at arms length. Move it closer to your eye and you'll notice the triangle's size is increasing, but the marked angle of 90 degrees is not changing at all. Here the dilation is being applied with some scale factor larger than 1. When you move the triangle further away from you, the sides will shrink but the angles stay the same here as well.
So again, dilations preserve angle measures. The angles will not change.
This means angle B' is the same measure as angle B.
The triangle ΔA'B'C' formed following the dilation of ΔABC is a similar
triangle to ΔABC.
The correct responses are;
5. a. Please find attached the drawing of the dilated triangle ΔA'B'C', created with MS Excelb. The properties of dilations indicate that ∠B = ∠B'Reasons:
5. a. With the assumption that the vertices of the triangle are;
A(0, -3), C(0, 5), and B(6, 3)
Let point P = (0, 0)
We have;
[tex]\displaystyle A' = \frac{3}{2} \times (0, -3) = \left(0, \ -\frac{9}{2} \right) = \mathbf{ (0, \, -4.5)}[/tex]
[tex]\displaystyle C' = \frac{3}{2} \times (0, \ 5) = \left(0, \ \frac{15}{2} \right) = \mathbf{(0, \, 7.5)}[/tex]
[tex]\displaystyle B' = \frac{3}{2} \times (6, \, 3) = \left(9, \ \frac{9}{2} \right) = \mathbf{ (9, \, 4.5)}[/tex]
b. From the attached diagram, and from the properties of dilation, given
that the image of ΔABC is larger than the image of ΔA'B'C' by a scale
factor of 1.5, we have that the ratio of the corresponding sides of ΔABC
and ΔA'B'C' are equal and therefore the angle formed by segment BC and
BA which is ∠B and the angle formed by segment B'C' and B'A' which is
∠B'. are equal.
[tex]\displaystyle \frac{AC}{AB} = \mathbf{\frac{A'C'}{A'B'}}[/tex]
[tex]\displaystyle \frac{AC}{sin(B)} = \frac{AB}{sin(C)}[/tex]
[tex]\displaystyle \frac{AC}{AB} = \mathbf{\frac{sin(B)}{sin(C)}}[/tex]
Similarly, we have;
[tex]\displaystyle \frac{A'C'}{A'B'} = \frac{sin(B')}{sin(C')}[/tex]
Therefore;
[tex]\displaystyle \frac{sin(B)}{sin(C)} = \mathbf{\frac{sin(B')}{sin(C')}}[/tex]
According to the properties of dilation, ∠B = ∠B'
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Panchito needs to make 80 ml of a 39% alcohol solution. He is going to make it by mixing a 50% alcohol solution with a 6% alcohol solution. How much if each should he use?
Answer:
60ml of the 50% alcohol solution and 20ml of the 6% alcohol solution
Step-by-step explanation:
We can build a system of equation for solve this problem
x = first solution
y = second solution
x + y = 80
0.5x + 0.06y = 80 * 0.39
x + y = 80
0.5x + 0.06y = 31.2
x = 80 -y
0.5(80-y) + 0.06y = 31.2
40 - 0.5y + 0.06y = 31.2
-0.44y = -8.8
y = 20
x = 80 - 20 = 60
Find the measure of COA. Then, classify the angle.
Answer:
The Angle COA=110°
An Obtuse Angle
6 There were 35 children and 10 adults at a cookout. What is the ratio of children to total people at the cookout?
find the selling price of a camera it's original price is $180, discount is 30%
Answer:
Step-by-step explanation:
30 percent off 180.00 is 126.00.
the difference is $54
HELLO CAN SOMEONE HELP ME WITH THIS! MATH IM FAILING NO FAKE ANSWERS PLZ!
Answer:
45 square ft^2
Step-by-step explanation: The formula of the area of the trapezoid is A=(a+b)/2 x h. A represents the top while b represents the bottom. 15+3=18 and 18/2=9. If multiply the result by 5, you get 45 as the answer.
25. The sides of the base of the square prism drawn below have been doubled, but its height has not been changed. Determine the ratio of the prism's new volume to its original volume.
A.8:1
B.2:1
C.4:1
D.16:1
Answer:4:1
Step-by-step explanation:
is x=2a solution 10 3x+4=12 show work don't just say yes or no
9514 1404 393
Answer:
x = 2 2/3 is the solution; x = 2 is not a solution.
Step-by-step explanation:
The solution is ...
3x +4 = 12 . . . . . . given
3x = 8 . . . . . . . . . .subtract 4
x = 8/3 = 2 2/3 . . . divide by 3
x = 2 is not a solution. The correct solution is x = 2 2/3.
two bicycle riders start from the same point and ride in opposite directions. one rider is moving twice as the other. in 3 hours, they are 72 miles apart. find the rate of each rider.24
Let the speed of one rider = x
The speed of the second rider would e 2x ( twice as fast)
The total speed of the two riders would be x + 2x = 3x
Speed = Distance / time
Using the numbers:
3x = 72/3
Simplify:
3x = 24
Divide both sides by 3:
x = 8
The speed of one rider is 8 miles per hour
The speed of the second rider is 2(8) = 16 miles per hour.
In a certain city, the average 20- to 29-year old man is 69.6 inches tall, with a standard deviation of 3.1 inches, while the average 20- to 29-year old woman is 64.1 inches tall, with a standard deviation of 3.9 inches. Who is relatively taller, a 75-inch man or a 70-inch woman?
Answer:
the 20-29 year old man are relatively taller.
Step-by-step explanation:
for the old man we have next z- score=75-69.6/3.1=1.74
for the old women we have next z-score=70-64.1/3.9=1.51
Solve the system of equations using substitution or graphing.
y= -x2 + 4x + 5
y= x + 1
OA) (-1,0) and (6,7)
OB) (-1,0) and (4,5)
C) (1, 2) and (4,5)
D) (1, 2) and (6,7)
5^2 - 3(3 -1) =
SHOW YOUR WORK STEP BY STEP PLS
Answer:
x = 19
Step-by-step explanation:
Let's start solving:
5² - 3(3-1) = x
Multiply 5 and 5 and also multiply 3(3-1)
25 - (9-3) = x
Subtract 6 from 25
25 - 6 = x
Simplify
x = 19
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
A collection of books is set up into 34 rows. The first row has 96 books, and each row after that one
has 2 less books than the preceding row. (a) How many total books are there in the structure and (b)
how many books are in the 17th row?
Answer:
Part A: 3197
Part B: 62
Step-by-step explanation:
Part A: To make this easier just multiply 96 books by 34 rows which is 3264 books, but then since you are taking away 2 books for every row, multiply 2 by the 34 rows which is 68 but since the first row starts at 96 we will take away 1 row from the 68 which is 67. Then subtract 67 from the 3264 books and get 3197 books.
Part B: To make this easier just multiply 17 by 2 since we know for every row, 2 books are taken away and that equals 34 so subtract 34 from 96 and get 62.
Answer:
a(17) = 64
Step-by-step explanation:
you can create an arithmetic sequence formula as follows:
a(n) = a(1) + d(n-1) where a(1) is the first value and d is the common difference
a(17) = 96 -2(17-1)
a(17) = 96 - 32
a(17) = 64
HELPPP
PLLS
DUE RN
WILL
GIVE BRAINLIST
X
X
X
X
Answer:
33% of the people preferred onions
can i get brainliest now lol
Write the equation in either slope-intercept or point-slope form for the
line that goes through (1,1) and (3,-5). *
Answer:
y = mx + b
m = (-5-1)/(3-1)
m = -3
1=(-3)1 + b
b= 4
y= -3x + 4
PLEASE ANSWER CORRECTLY WILL GIVE BRAINLIEST
Answer:
r = [tex]\sqrt{x} A/4\pi[/tex] , or the third option :)
Step-by-step explanation:
Answer:c
Step-by-step explanation:
Points A,B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of ABC is 180 degrees
Answer:
Step-by-step explanation:
Statements Reasons
1). Points A, B and C form the triangle 1). Given
2). Let DE be a line passing through 2). Definition of parallel lines
B and parallel to AC
3). ∠3 ≅ ∠5 and ∠1 ≅ ∠4 3). Theorem of Alternate
interior angles
4). m∠1 = m∠4 and m∠3 = m∠5 4). Definition of alternate angles
5). m∠4 + m∠2+ m∠5 = 180° 5). Angle addition and definition
of straight lines
6). m∠1 + m∠2+ m∠3 = 180° 6). Substitution
PLEASE HELPPP!!
Sam and Ava compared the weights of their puppies each month during the first half of 2015. The graphs generated from this data are shown below.
Which claim is best supported by the graph?
A. At the start of 2015, the weight of Sam's puppy was two times the weight of Ava's puppy.
B. At the start of 2015, the weight of Ava's puppy was two times the weight of Sam's puppy.
C. During the first half of 2015, the weight of Sam's puppy increased two times as fast as the weight of Ava's puppy.
D. During the first half of 2015, the weight of Ava's puppy increased two times as fast
Answer:
i think B correct me if wrong pls
Step-by-step explanation:
Option (D) During the first half of 2015, the weight of Ava's puppy increased two times as fast is the correct answer.
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. A graph is a diagram that represents the variation of a variable in comparison with that of one or more other variables.
For the given situation,
Sam and Ava compared the weights of their puppies each month during the first half of 2015.
The graph shows the comparison between Sam's and Ava's puppies.
From the graph,
At the beginning of the month both the puppies have same weight. After a month, Ava's puppies weight increased rapidly than Sam's puppy.
Hence we can conclude that option (D) During the first half of 2015, the weight of Ava's puppy increased two times as fast is the correct answer.
Learn more about graphs here
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Solve for y
3 times 10 ^ 2y = 3600
Answer:
y≈1.778 (or y=log(3600)/2 or y=log(6)+1)
Step-by-step explanation:
10^2y=3600
log(10^2y)=log(3600)
2y=log(36)+log(100)
2y=log(6²)+2
2y=2log(6)+2
2y-2=2log(6)
y-1=log(6)
y=log(6)+1
y≈1.778
18. If an apprentice can do a piece of work in 24 days, and the apprentice and
instructor together can do it in 6 days, how long would it take the instructor to do
the work alone?
18. If an apprentice can do a piece of work in 24 days, and the apprentice and
instructor together can do it in 6 days, how long would it take the instructor to do
the work alone?
Answer:
the number of days when instructor do the work alone is 8 days
Step-by-step explanation:
Given that
The apprentice can do the work in 24 days
And, the apprentice and instructor together can do it in 6 days
We need to find out the number of days when instructor do the work alone
So,
[tex]= \frac{1}{6} - \frac{1}{24} \\\\= \frac{4 - 1}{24} \\\\= \frac{3}{24} \\\\= \frac{1}{8} \\\\= 8[/tex]
hence, the number of days when instructor do the work alone is 8 days
Read the sentence.
The young soldier had been stationed overseas for two years. When it was time to come home, he decided to surprise his mom. It was a poignant moment when the soldier reunited with his mom.
What is the meaning of poignant?
A) touching
B) pitiful
C) relaxing
D) lonely
Answer: A
Step-by-step explanation:
The meaning of poignant is "touching", option A is correct.
What is Poignant?The meaning of poignant is touching or emotionally moving.
The word "poignant" is used to describe something that is deeply touching or emotionally moving.
It is often used to describe situations or experiences that evoke strong feelings of sadness, nostalgia, or sentimentality.
In the given sentence, the word "poignant" is used to convey the emotional impact of the soldier reuniting with his mother after two years of being stationed overseas.
The word suggests that the moment was very emotional and deeply touching for both the soldier and his mother, likely evoking feelings of happiness, relief, and nostalgia.
Hence, the meaning of poignant is "touching", option A is correct.
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You are wrapping a birthday gift that is packaged in a specially made pyramid-shaped box. The base of the box measures 10 inches by 9 inches and the slant height is 6 inches. How much paper do you need to wrap the box
Answer:
2826 inches^2
Step-by-step explanation:
The general formula for the total surface area of a regular pyramid is
T.S.A.=12pl+B
Where p represents the perimeter of the base, l the slant height and B the area of the base.
The perimeter of the base is.
p=2L+2W
P=2*10+2*9
P=20+18
P= 38 inches
The area of the base is.
B=10*9
B=90in^2
T.S.A.=12(38)(6)+90
T.S.A=2736+90
T.S.A=2826 inches^2
Hence the paper needed is 2826 inches^2
PLEASE PLEASE PLEASE HELP!
use the distributive property to express the sum 24 + 30 with a common factor multiplied by a sum of two whole numbers with no common factor
Answer:
6(4+5)
Step-by-step explanation:
PLZ HELP PLZ PLZ this is my last final plz
A restaurant sells soups and salads. Soup costs $5.50, and a salad costs $8. On a particular day, the restaurant sells 58 items and makes $371.50.
Which system of equations can be used to find the amount of soup, x, and salad, y, the restaurant sold?
OA
5.50x = 58
8y = 371.50
OB.
5.50x = Sy
58x = 371.50y
x + y = 58
Oc.
5.50x + 8y = 371.50
x+y = 371.50
OD.
5.50x + 8y = 58
Answer:
b
Step-by-step explanation:
What is 713,753 rounded to the nearest hundred thousand?
Answer:
700,000
Step-by-step explanation:
Answer:
700,000
Step-by-step explanation:
It's closer to 700,000 than 800,000. Hope this helps! Have a nice day :)
Please help! need to know how to solve this Urgent!
Step-by-step explanation:
I dont know if this helps but that what I came up with
= [tex] log_{ 3}({x}^{2} - 4) - log_{3}(x - 2) + log_{3}(x) [/tex]
= [tex] log_{ 3}(\dfrac{{x}^{2} - 4}{x - 2}) + 2 × 1[/tex]
= [tex] log_{ 3}(\dfrac{(x-2)(x+2)}{x - 2}) + 2 × 1[/tex]
= [tex] log_{ 3}(x+2) + 2 × 1[/tex]
A point with a positive x-coordinate and a negative y-coordinate is reflected over the y-axis.
Which sentence describes the coordinates of the new point?
Find an equation of the line that passes through the point (2, 4) and is perpendicular to the line 4x + 9y - 2 = 0 (let x be the independent variable and y be the dependent variable.
Answer:
y = 9/4x -1/2
Step-by-step explanation:
4x + 9y -2=0
solve for y: 4x-2=-9y
(4x-2)/-9 =
y =4/-9x-2/9
perpendicular means reciprocal of slope. So 4/-9 changesz to 9/4
For the point plug in y and x:
9/4*2+b=4
b = -0.5
I attached graph as proof
Solve x2 + 4x − 12 = 0. (1 point) x = 2, x = −6 x = −2, x = −6 x = 3, x = −4 x = −3, x = 4
Find the distance between points F and H.