Answer:
5
Step-by-step explanation:
when it has the two bars think of the exact opposite of that certain number and thats what it is (its called absolute value).
What is an equation of the line that passes through the point (6,−4) and is perpendicular to the line 2x−y=5?
Answer:
An equation of the line that passes through the point (6,−4) and is perpendicular to the line will be:
[tex]y=-\frac{1}{2}x-1[/tex]Step-by-step explanation:
We know that the slope-intercept form of the line equation
y = mx+b
where m is the slope and b is the y-intercept
Given the line
[tex]2x-y=5[/tex]
converting the line into slope-intercept form
y = 2x-5
comparing with the slope-intercept form of the line equation
The slope of the line = m = 2
We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:
slope = m = 2
Thus, the equation of new line = – 1/m = -1/2 = -1/2
using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values of the slope = -1/2 and the point (6,−4)
[tex]y-\left(-4\right)=-\frac{1}{2}\left(x-6\right)[/tex]
[tex]y+4=-\frac{1}{2}\left(x-6\right)[/tex]
Subtract 4 from both sides
[tex]y+4-4=-\frac{1}{2}\left(x-6\right)-4[/tex]
[tex]y=-\frac{1}{2}x-1[/tex]
Therefore, an equation of the line that passes through the point (6,−4) and is perpendicular to the line will be:
[tex]y=-\frac{1}{2}x-1[/tex]An equation of the line that passes through the point (6,−4) and is perpendicular to the line 2x−y=5 is [tex]y=-\frac{1}{2}x-1[/tex]
Given:
An equation of the line that passes through the point (6,−4) and is perpendicular to the line 2x−y=5
First we find the slope of given equation 2x-y=5
y=mx+b is the equation of the line . where 'm' is the slope
[tex]2x-y=5\\2x-5=y\\y=2x-5[/tex]
Slope m=2.
Slope of perpendicular lines are negative reciprocal of one another
Slope of perpendicular line is [tex]-\frac{1}{2}[/tex]
The line passes through the point (6,-4)
Use the point and slope to get the equation of the perpendicular line
slope m = [tex]-\frac{1}{2}[/tex]
Point slope form of line is
[tex]y-y_1=m(x-x_1)\\y+4=-\frac{1}{2}(x-6)\\y+4=-\frac{1}{2}x+3\\y=-\frac{1}{2}x-1[/tex]
An equation of the line that passes through the point (6,−4) and is perpendicular to the line 2x−y=5 is [tex]y=-\frac{1}{2}x-1[/tex]
Learn more : brainly.com/question/19864665
-4(2m + 2n) + 2(3m-2n)
Answer:
-2m -12n
Step-by-step explanation:
-8m -8n +6m-4n
Step-by-step explanation:
= -8m-8n+6m-4n
= -8m+6m-8n-4n
= -2m-12n
hope it helps.
Help me solve this (pls show working)
Answer:
The area of the polygon is 92.75 cm^2
Step-by-step explanation:
To find the area of the polygon, we simply add up the areas of the constituent triangles
At any point in time;
Area of a triangle = 1/2 * base * height
So we proceed as follows;
(1/2 * 12 * 4.5) + (1/2 * 12 * 5)
= 27 + 30 = 57 cm^2
There is a last triangle with 12 cm and 5 cm as the sides and we need the length of the hypotenuse
The length of the hypotenuse for that triangle will be 13 cm. This is because 5,12 and 13 are Pythagorean triple and they form the sides of a right-angled triangle
So for the last triangle, the area will be;
1/2 * 13 * 5.5 = 35.75 cm^2
So the total area is;
35.75 + 57 = 92.75 cm^2
Can someone help me please
Answer:
125
Step-by-step explanation:
100% Meiling and Jackie are playing a game of chance with a six-sided number cube. The sides of the cube are numbered 1 to 6. Meiling scores a point each time she rolls a number greater than 4.
Answer:
I'm not completely sure but I beileve Jackie less than 4
Step-by-step explanation:
good luck tho
Answer:
D
(i scored 100 on the quiz)
What is the only prime number HURRY
HELPPPP...When you have a division problem like the one listed below... What do you do with the exponents?
P^12-2t^7-7r^2-1
p^10r
you just substracting
Sue has 20 biscuits in a tin.
There are: 12 plain biscuits
5 chocolate biscuits
3 currant biscuits
Sue takes at random two biscuits from the tin.
Work out the probability that the two biscuits were not the same type.
Answer:
[tex]\frac{111}{190}[/tex]
Step-by-step explanation:
Probability is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
The probability that the two biscuits were not the same type is 111/190.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Number of total biscuits = 20
Number of plain biscuits = 12
Number of chocolate biscuits = 5
Number of current biscuits = 3
The probability that two randomly chosen biscuits were not the same type.
= [tex]^{12}C_1 \times ^5C_1[/tex] / [tex]^{20}C_2[/tex] + [tex]^{12}C_1 \times ^3C_1[/tex] / [tex]^{20}C_2[/tex] + [tex]^5C_1 \times ^3C_1[/tex] / [tex]^{20}C_2[/tex]
= 12 x 5 / 190 + 12 x 3 / 190 + 5 x 3 / 190
= (60 + 36 + 15) / 190
= 111 / 190
Thus,
The probability that the two biscuits were not the same type is 111/190.
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ2
Please help the last question of the day! For brainliest
Answer:
2\10
Step-by-step explanation:
1\2 = 5\10
7\10 - 2\10 = 5\10
Math problem :Belvedere swam 35 laps in 1 2 / 3 hours. Find his swimming rate in laps
per hour.
Answer:
21 laps per hour
Step-by-step explanation:
2/3 = 20/30
20/30 × 2 = 40/60
1 and 2/3 = 1 hour 40 mins
60 + 40 = 100 mins
35 (laps) = 100 (mins)
÷10
3.5 = 10
×6
21 = 60
21 laps in 1 hour
so 21 laps per hour
Please help! I have 35 minutes left! You can get 100 points!
Which expression is equivalent to 8 - (6r + 2)?
-6r + 6
2r +2
6r + 10
-6r + 10
Answer:
The expression equivalent to 8 - (6r + 2) is -6r + 6 ⇒ A
Step-by-step explanation:
Let us solve the question
∵ The expression is 8 - (6r + 2)
→ Multiply the bracket by (-)
∵ (-) × (+) = (-)
∴ 8 - (6r + 2) = 8 - 6r - 2
→ Add the like terms
∵ 8 - (6r + 2) = (8 - 2) - 6r
∴ 8 - (6r + 2) = 6 - 6r
→ Switch the terms
∴ 8 - (6r + 2) = -6r + 6
∴ The expression equivalent to 8 - (6r + 2) is -6r + 6
Circle the polygon(s) which are similar to the shaded one:
Answer:
circle the second and forth one
Answer
Out of the 5 triangles, including the shaded one, the similar ones are the second (right next to the shaded) and 4th (to the left of the last one)
Step-by-step explanation:
In the given diagram ⃤ ABC and ⃤ CDE are equilateral triangles. If ∠EBD = 62° then find the measure of 1/2 of ∠AEB.
Answer:
Given
△ABC and △CDE are equilateral.
AE
= 25
To find perimeters of the two triangles,
Let us consider the lengths of
AC
and
CE
to be
′
x
′
and
′
y respectively.
As △ABC is equilateral,
AC
=
AB
=
BC
= x
As △CDE is equilateral,
CE
=
CD
=
DE
= y
From the figure,
AE
=
AC
+
CE
25 = x + y
x + y = 25
Perimeter of the triangle is the sum of all sides of the triangle.
For △ABC,
Perimeter of △ABC =
AC
+
AB
+
BC
= x + x + x
= 3x
For △CDE,
Perimeter of △CDE =
CE
+
CD
+
DE
= y + y + y
= 3y
Now,
Perimeter of two triangles = Perimeter of △ABC + Perimeter of △CDE
= 3x + 3y
= 3 × (x + y)
= 3 × 25 (from above)
= 75
Therefore, Perimeter of the two triangles is'75′units.
Step-by-step explanation:
Hope it is helpful...
Seventh graders collected some gold sand on a class field trip.
Class 7A collected 40 oz of gold sand that contains 12% gold.
Class 7B collected 55 oz of gold sand that contains 11% gold.
How much pure gold did 7A collect?
Answer:
Class 7A collected 4.8 ounces of pure gold.
Step-by-step explanation:
Key skills required are: Percentages, Multiplication
We only need the information about Class 7A. They collected 40 oz that contains 12% gold. In other words, this means that 12% of that 40 oz gold sand is pure gold.Here we have to do 12% x 40 to find the number of oz of pure gold. We first have to convert 12% into a decimal. Divide it by a 100 (or move the decimal point 2 places to the left) and you will get 0.12.
Do 0.12 x 40 and you will get 4.8
Therefore, there are 4.8 oz of pure gold in Class 7A's gold sand
Help please!!
If y varies directly with x, and x = 7 when y= 28, find y when x = 13.
1. y= 4
2. y=17
3. y= 42
4. y = 52
Each morning a gardener uses 25 gallons of water from a barrel. Each afternoon, she adds 15 gallons of water to the barrel. By how much has the volume of water in the barrel changed after 5 days?
Given :
Each morning a gardener uses 25 gallons of water from a barrel.
Each afternoon, she adds 15 gallons of water to the barrel.
To Find :
By how much has the volume of water in the barrel changed after 5 days.
Solution :
Amount of of water used from the barrel per day is :
A = 25 - 15 gallons
A = 10 gallons
Now, volume of water in the barrel changed after 5 days is :
V = A × 5 gallons
V = 10 × 5 gallons
V = 50 gallons
Therefore, volume of water in barrel is changed by 50 gallons.
Evaluate the following expression:
3y2 - 4x + 2xy, when x = 2 and y = 5
Answer:
87Step-by-step explanation:
3×(5)^2 - 4×2 + 2×2×5
3×(5)^2 - 4×2 + 2×2×53×25 - 8 + 20
3×(5)^2 - 4×2 + 2×2×53×25 - 8 + 2075 + 20 - 8
3×(5)^2 - 4×2 + 2×2×53×25 - 8 + 2075 + 20 - 8 95-8
3×(5)^2 - 4×2 + 2×2×53×25 - 8 + 2075 + 20 - 8 95-887
Find the solution mentally.
-12 • c = 12
On a game show, one contestant correctly answered 43% of the questions. What fraction of the questions did she answer correctly
7
Two different schools, school A and school B, attended a conference.
12% of the attendees were teachers, the rest were students,
47% of the attendees were from school A.
48% of the attendees were students from school B.
One of the attendees is selected at random.
Find the probability that they are a teacher from school A
Answer as a %*
Answer:
is the any options?
Step-by-step explanation:
Someone please help me, I’m stuck!
Answer:
.....................................
Step-by-step explanation:
y = 30 & x = 3
A model rocket is launched from ground level. Its height, h meters above the ground, is a function of time t seconds after launch and is given by the equation . What would be the maximum height, to the nearest meter, attained by the model? (First find the axis of symmetry x= (-b/2a), then plug this value into the equation)
Answer:
The maximum height attained by the rocket is 240.1 m.
Step-by-step explanation:
The height above the ground is a function of time t is given by :
[tex]h= -4.9t^2 + 68.6t[/tex] ...(1)
We need to find the maximum height of the model. First we find the time of max height using axis of symmetry of the equation as follows :
[tex]x=\dfrac{-b}{2a}[/tex]
We have, a = -4.9 and b = 68.6
So,
[tex]t=\dfrac{-(68.6)}{2\times -4.9}\\\\=7\ s[/tex]
Put t = 7 in equation (1)
[tex]h= -4.9(7)^2 + 68.6(7)\\\\=240.1\ m[/tex]
So, the maximum height attained by the rocket is 240.1 m.
[tex]\frac{a-3b}{a+2b} = \frac{4}{3}[/tex]
what is the value of a:b??
Given:
[tex]\sf \dfrac{a\ -\ 3b}{a\ +\ 2b}\ =\ \dfrac{4}{3}[/tex]
To find: The value of a:b.
Answer:
[tex]\sf \dfrac{a\ -\ 3b}{a\ +\ 2b}\ =\ \dfrac{4}{3}[/tex]
Cross-multilpying,
[tex]\sf 3\ \times\ (a\ -\ 3b)\ =\ 4\ \times\ (a\ +\ 2b)\\\\3a\ -\ 9b\ =\ 4a\ +\ 8b[/tex]
Bringing the like terms together,
[tex]\sf 3a\ -\ 4a\ =\ 8b\ +\ 9b\\\\\\-a\ =\ 17b\\\\\\\dfrac{-a}{b}\ =\ 17\\\\\\\dfrac{a}{b}\ =\ -17[/tex]
Therefore, a:b = -17.
Which statement is true about the polynomial 3j4k−2jk3+jk3−2j4k+jk3 after it has been fully simplified? It has 2 terms and a degree of 4. It has 2 terms and a degree of 5. It has 1 term and a degree of 4. It has 1 term and a degree of 5.
Answer:
Hence the simplified form has has 1 term and a degree of 4
Step-by-step explanation:
Given the expression
3j⁴k - 2jk³+jk³-2j⁴k+jk³
Collect like terms
= 3j⁴k-2j⁴k- 2jk³+jk³+jk³
= j⁴k- 2jk³+jk³+2jk³
= -j⁴k-2jk³+2jk³
= - jk⁴
Hence the simplified form has has 1 term and a degree of 4
Answer:
It has 1 term and a degree of 5.
Step-by-step explanation:
can someone help me to find the answer?
Questions:
Factorise completely 4-(x-1)²
please help me how to get the answer?:/
Step-by-step explanation:
Given
4 - (x -1 ) ²
= 2² - ( x - 1) ² [ putting it into the formula a² - b² = (a+b) (a - b) ]
= ( 2 + x - 1) ( 2 - x + 1)
= ( x + 1 ) ( 3 - x)
Hope it will help :)❤
15х +6y = 21
7х + бу = -3
What is the solution for each of these
Answer:
15x +6y = 21. is equal to 07x +6y = -3. is equal to 0Step-by-step explanation:
15x +6y = 2 is equal to 0 because when we move the constant to the left and divide both sides of the equation by 3 we get:
5x + 2y - 7 = 0Same with 7x +6y = -3, when we move the constant to the left and sum the two opposites equal to 0 it give us:
7x + 6y + 3 = 01. The daily wages of 50 workers in a factory are given below:
Daily wages
in )
340-380 380-420 420-460 460-500 500-540 540-580
16
Number of
workers
9
12
2.
7
4
Construct a histogram to represent the above frequency distribution.
6
Using the equation S = (n − 2) 180, find the measure for one Interior angle of a decagon (10-sides). Round to one decimal place if necessary.
Answer:
1140
Step-by-step explanation:
A decagon has 10 sides so substitute it like this:
(n-2) x 180
(10-2) x 180
8 x 180= 1140
<
y=-5%
3 2
4
21
2
2
✓-
zero slope
positive slope
undefined slope
negative slope
(9x + 5) - (4x + 3)
Please show work
Answer:
Step-by-step explanation:
Simplifying
(9x + 5) + -1(4x + 3) = 0
Reorder the terms:
(5 + 9x) + -1(4x + 3) = 0
Remove parenthesis around (5 + 9x)
5 + 9x + -1(4x + 3) = 0
Reorder the terms:
5 + 9x + -1(3 + 4x) = 0
5 + 9x + (3 * -1 + 4x * -1) = 0
5 + 9x + (-3 + -4x) = 0
Reorder the terms:
5 + -3 + 9x + -4x = 0
Combine like terms: 5 + -3 = 2
2 + 9x + -4x = 0
Combine like terms: 9x + -4x = 5x
2 + 5x = 0
Solving
2 + 5x = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-2' to each side of the equation.
2 + -2 + 5x = 0 + -2
Combine like terms: 2 + -2 = 0
0 + 5x = 0 + -2
5x = 0 + -2
Combine like terms: 0 + -2 = -2
5x = -2
Divide each side by '5'.
x = -0.4
Simplifying
x = -0.4
easy boy