Answer:
41/20
Step-by-step explanation:
or 2 1/20
solve fox x 8 = 3a - 4
!!!!????????!!!!!??????
Answer:
h = 19 mm
Step-by-step explanation:
the volume (V) of the prism is calculated as
V = Ah ( A is the area of the base and h the height )
the base is a regular pentagon whose area (A) is calculated as
A = [tex]\frac{1}{2}[/tex] pa ( p is the perimeter and a the apothem )
p = 5 × 12 = 60 mm and a = 5 mm , then
A = [tex]\frac{1}{2}[/tex] × 60 × 5 = 30 × 5 = 150 mm²
given V = 2850 , then
150h = 2850 ( divide both sides by 150 )
h = 19 mm
- Select the equivalent expressions. 71-9y and (7x - y) (9) 5 (3t - 6) and 15 - 30 4 (6a +86) and 10a + 126 16 + 72n and (2 + 9n) (8)
Answer:
D. 16 + 72n and (2 + 9n) (8)
Step-by-step explanation:
Select the equivalent expressions.
71 - 9y and (7x - y) (9) 5(3t - 6) and 15 - 30 4(6a +86) and 10a + 126 16 + 72n and (2 + 9n) (8)Distribute to find the equivalent expressions:
A.
71 - 9y and (7x - y) (9)
71 - 9y = 9(7x) + 9(-y)
71 - 9y = 63x - 9y
Not equivalent
B.
5(3t - 6) and 15 - 30
5(3t) + 5(-6) = 15 - 30
15t - 30
Not equivalent (it's missing the variable - t)
C.
4(6a + 86) and 10a + 126
4(6a) + 4(86) = 10a + 126
24a + 344 = 10a + 126
Not equivalent
D.
16 + 72n and (2 + 9n) (8)
16 + 72n = 8(2) + 8(9n)
16 + 32n = 16 + 72n
Equivalent
Therefore the correct answer is D
Hope this helps!
One side of a rectangle is 7 inches longer than another side. If the longer side of this rectangle decreases by 3 inches, and the shorter side increases by 2 inches, the area of the new rectangle equals the area of the original rectangle. Find the dimensions of the original rectangle.
Answer:
Length = 8+7 = 15
Width = 8
Step-by-step explanation:
New
Length = x+7 , x+4
Width = x ,x+2
(x+7) x = (x+4)( x+2)
expand and simplify x =8
The length of the shorter side length of original rectangle is 8 inches and of original rectangle longer side length is 15 inches.
Area of rectangleLet l is the length and b is the breadth of the rectangle.
then the area of the rectangle is ab.
How to find the dimensions of the original rectangle?Given One side of a rectangle is 7 inches longer than another side.
then shorter side length is x and the large side length is 7+x.
then the area of the original rectangle is x(x+7)
Now calculate the sides of the new rectangle.
longer side of this rectangle decreases by 3 then new side is 7+x -3= 4+x
The shorter side increases by 2 inches then x+2.
So new rectangle area is (x+4)(x+2)
Both rectangle area is equal then
(x+4)(x+2) = x(x+7)
x² +2x+4x+8 = x²+7x
x²+6x+8 = x²+7x
x²-x²+7x-6x = 8
x = 8
Since a shorter side length is 8 inches and a longer side length is 8+7 =15 inches.
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simplify (-3x)^2
please I need to know this answer
Answer:
9x²
Step-by-step explanation:
(- 3x)²
= - 3x × - 3x
= - 3 × - 3 × x × x
= 9 × x²
= 9x²
Write an equation in slope-intercept form that is perpendicular to 4x - 5y = 1 and passes through (-3, 4).
Answer:
y=[tex]\frac{-5}{4}[/tex]x + [tex]\frac{-1}{ 4}[/tex]
Step-by-step explanation:
4x-1=5y
4/5 is the original slope and negative [tex]\frac{5}{4}[/tex] is the perpendicular slope.
Using that to put (-3,4) and the slope into point-slope form:
y-4=[tex]\frac{-5}{4}[/tex](x+3)
distribute and isolate y
y=[tex]\frac{-5}{4}[/tex]x + [tex]\frac{-1}{4}[/tex]
Answer:
y = -5/4x + 1/4
Step-by-step explanation:
*Pependicular line have negative reciprocal slopes*
Rewrite your equation to slope-intercept form: y = mx + b
y = mx + b
m = slopeb = y-intercept (when x = 0)4x - 5y = 1 <== subtract 4x from both sides
-4x -4x
-5y = -4x + 1 <== divide both sides by -5
/-5 /-5
y = 4/5x - 1/5
Find the Negative reciprocal of the line:
Steps:
1. Take your original slope (4/5)
2. Flip it (5/4)
3. Change the sign (-5/4)
The slope of the perpendicular line would be: -5/4 (y = -5/4x + b)
We need to find the y-intercept (b) for the perpendicular line using (-3, 4):
y = -5/4x + b <== substitue -3 for x and 4 for y
4 = -5/4(-3) + b
4 = 15/4 + b <== multiplify both sides by 4
4(4 = 15/4 + b)
16 = 15 + 4b <== subtract 15 from both sides
-15 -15
1 = 4b <== divide both sides by 4
/4 /4
1/4 = b
y = -5/4x + b changes to y = -5/4x + 1/4
Hope this helps!
Solve the equation and show your work.
A . 17x + 12 = 54 - 4x
B . 5x - 10 + 2x = 6(x + 1) - x
Answer:
A. x= 2
B. x= 8
Step-by-step explanation:
Solving an equation refers to finding the value of the variable in the equation.
A. 17x +12= 54 -4x
Bring all x terms to one side, constant to the other:
17x +4x= 54 -12
21x= 42
x= 42 ÷21
x= 2
B. 5x -10 +2x= 6(x +1) -x
7x -10= 6x +6 -x
7x -10= 5x +6
Bring all x terms to one side, constant to the other:
7x -5x= 10 +6
2x= 16
Divide both sides by 2:
x= 16 ÷2
x= 8
Hey ! there
Answer:
Value of x in equation A is 2 .Value of x in equation B is 8 .Step-by-step explanation:
In this question we are provided with two equations that are 17x + 12 = 54 - 4x and 5x - 10 + 2x = 6(x + 1) - x . And we are asked to solve the equation that means we have to find the value of x for both the equations .
Solution : -
A)[tex] \longmapsto \qquad \: 17x + 12 = 54 - 4x[/tex]
Step 1 : Subtracting 12 on both sides :
[tex] \longmapsto \qquad \: 17x + \cancel{ 12} - \cancel{12} = \bold{54} - 4x - \bold{ 12}[/tex]
Simplifying it ,
[tex] \longmapsto \qquad \: 17x = 42 - 4x[/tex]
Step 2 : Adding 4x on both sides :
[tex] \longmapsto \qquad \: 17x + 4x = 42 - \cancel{4x} + \cancel{4x}[/tex]
On further calculations, we get :
[tex] \longmapsto \qquad \: 21x = 42[/tex]
Step 3 : Dividing with 21 on both sides :
[tex] \longmapsto \qquad \: \dfrac{ \cancel{21}x}{ \cancel{21} } = \cancel{ \dfrac{42}{21} }[/tex]
We get :
[tex] \longmapsto \qquad \: \red{\underline{\boxed{ \frak{x = 2}}}} \quad \bigstar[/tex]
Henceforth , value of x is 2 .Verifying : -
Now , we are verifying our answer by substituting value of x as 2 in the given equation . So ,
17x + 12 = 54 - 4x 17 ( 2 ) + 12 = 54 - 4 ( 2 )34 + 12 = 54 - 846 = 46L.H.S = R.HSHence , Verified .Therefore , our solution is correct .
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
B)[tex] \longmapsto \qquad \: 5x - 10 + 2x = 6(x + 1) - x[/tex]
Step 1 : Adding like terms on left side :
[tex] \longmapsto \qquad \: 7x - 10 = 6(x + 1) - x[/tex]
Step 2 : Solving parenthesis on right side by using distributive property . ( Multiplying 6 with x and 1 both ) :
[tex] \longmapsto \qquad \: 7x - 10 = \bold{6x} + 6 - \bold{x}[/tex]
Step 3 : Solving like terms on right side :
[tex] \longmapsto \qquad \: 7x - 10 = 5x + 6[/tex]
Step 4 : Adding 10 on both sides :
[tex] \longmapsto \qquad \: 7x - \cancel{10} + \cancel{ 10} = 5x + 6 + 10[/tex]
Simplifying it ,
[tex] \longmapsto \qquad \: 7x = 5x + 16[/tex]
Step 5 : Subtracting 5x on both sides :
[tex] \longmapsto \qquad \: 7x - 5x = \cancel{5x }+ 16 - \cancel{5x}[/tex]
On further calculations , we get :
[tex] \longmapsto \qquad \: 2x = 16[/tex]
Step 6 : Dividing with 2 on both sides :
[tex] \longmapsto \qquad \: \dfrac{ \cancel{2}x}{ \cancel{2}} = \cancel{\dfrac{16}{2} }[/tex]
We get :
[tex] \longmapsto \qquad \: \red{\underline{\boxed{ \frak{x = 8}}} } \quad \bigstar[/tex]
Henceforth , value of x is 8 .Verifying : -
Now , we are verifying our answer by substituting value of x as 8 in the given equation . So ,
5x - 10 + 2x = 6(x + 1) - x5 ( 8 ) - 10 + 2( 8 ) = 6 ( 8 + 1 ) - 840 ( - 10 ) + 16 = 6 ( 9 ) - 856 - 10 = 54 - 846 = 46L.H.S = R.H.SHence , Verified .Therefore , our solution is correct.
#Keep LearningFactor 15x ^2 −42xy+24y^2
Eliminate the parameter.
x = 5t, y = t + 8 (2 points)
Answer: y = [tex]\frac{1}{5}[/tex]x + 8
Step-by-step explanation:
This is asking us to remove the parameter. In other words, we want an equation with only the relation between x and y, so we need to remove the t. There are a few ways to do this, but I am going to set one equation equal to t and then plug it into the next one.
Given:
x = 5t
Divide both sides of the equation by 5:
t = [tex]\frac{1}{5}[/tex]x
-
Given:
y = t + 8
Plug in:
y = ([tex]\frac{1}{5}[/tex]x) + 8
Answer:
y = [tex]\frac{1}{5}[/tex]x + 8
Find the missing side of the right triangle.
options:
6.5 ft
7 ft
5.5 ft
6 ft
Answer:
6ft, the missing side is the base(b), 10ft is the hypotenuse(h) and 8ft is the perpendicular(p). The formula for base is root over h²-p² and root over 10²-8² equals 6.
Consider these scenarios.
1. An elephant weighs 1.5 × 104 units.
2. A mouse weighs 2.13 × 10-5 units.
3. A puppy weighs 1.2 × 102 units.
Determine the unit of measurement that best represents each scenario.
1.
2.
3.
1. Pounds
2. Tons
3. Ounces
You guys have a good day :)
Answer:
1.pounds
2.tons
3.ounces
Step-by-step explanation:
just got it right on edge
What is the greatest common denominator of 24 and 25
Answer:
1
Step-by-step explanation:
The only number 24 and 25 can both have is 1
23). figure b is a scale image of figure a enter the scale factor applied.
24). to figure A to produce fiber B
Answer:
9
Step-by-step explanation:
The scale factor is the ratio of a Figure B dimension to the corresponding Figure A dimension.
__
The ratio of left-side dimensions is ...
scale factor = fig B/fig A = 81/9 = 9
The scale factor is 9.
Answer:9
Step-by-step explanation:
A train museum has a toy train that goes around the entire museum. the train goes around 10 times in 2 hours.
A student calculated the amount of times it takes for the train to go around 1 time. the work is shown.
2 hours ÷ 10 = 0.2 hour
0.2 is the same as 0.20, so it takes 20 minutes for the train to go around 1 time
the student's work is incorrect.
explain any error in the student's work
explain how to correct the student's work and find the amount of time it took for the train to go around the museum 1 time
Answer:
See below
Step-by-step explanation:
.2 of an hour is .2 * 60 min = 12 min
120 min / 10 times = 12 min per trip
The train takes 12 minutes to go around the museum once.
What is multiplication?A mathematical arithmetic operation is multiplication. Moreover, it is the practice of repeatedly adding the same expression kinds.
Example: 2 x 3 means that 2 is multiplied by 3 or that 3 is multiplied by 2 times.
A toy train that travels the length of a train museum is present. In two hours, the train travels roughly ten times.
The error in the student's work is converting 0.2 hours to 20 minutes. 0.2 hours is equal to 12 minutes, not 20 minutes.
To correct the student's work, we can multiply 0.2 by 60 to convert it to minutes:
0.2 hours × 60 minutes/hour = 12 minutes
Therefore, it takes 12 minutes for the train to go around the museum 1 time.
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The hypotenuse of a right triangle ensures 17cm and one of its legs measures 13cm
Answer:
sqrt (120)
Step-by-step explanation:
Use pythag theorem
Leg1 ^2 + Leg2^2 = Hypot ^2
13^2 + Leg2^2 = 17^2
Leg2^2 = 17^2 - 13^2
Leg2 = sqrt (120)
help me find m and n please
Answer:
n is 68 and m is 44
Step-by-step explanation:
Opposite of 3 less than 10
Answer:
-13
Step-by-step explanation:
Answer:
-13
Step-by-step explanation:
Becuase 13's opposite is -13.
(If you still dont understand you can search up negative and positive number lines up to 20!)
Please help me I’m really bad at geometry
Answer:
x+15=180(being co-interior angle)
x=180-15
x=165
chris took a spelling quiz last week.she got 12 out of 16 problems correct.what percentage did chris get correct
Answer:
Chris got 75% correct.
Step-by-step explanation:
[tex]\frac{12}{16}[/tex] x 100 = 75
So, the percentage chris got correct is 75%
Answer:
He got 75% correct
Step-by-step explanation:
you can do it like this:
[tex]\frac{12}{16}[/tex] × 100 = 3× 25= 75%
Hope you understood and it helped!!
What expression can be used to subtract 2/3 - 4/9
Answer:
[tex]\frac{2}{9}[/tex]
Step-by-step explanation:
1. [tex]\frac{2}{3} -\frac{4}{9}[/tex]
2. Multiply [tex]\frac{2}{3}[/tex] by [tex]\frac{3}{3}[/tex] to get a denominator equal to [tex]\frac{4}{9}[/tex]
3. [tex]\frac{2}{3} *\frac{3}{3} =\frac{6}{9}[/tex]
4. [tex]\frac{6}{9}-\frac{4}{9} =\frac{2}{9}[/tex]
The expression is: [tex]\frac{2}{3}*\frac{3}{3} -\frac{4}{9}[/tex]
Answer:
6/9-4/9
Step-by-step explanation:
ez pls mark branliest
Select the correct answer from each drop-down menu. the four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4. the four angles of the quadrilateral are °, °, °, and °.
The four angles of a quadrilateral are 30°, 60°, 150°, and 120° if the four vertices of an inscribed quadrilateral divide a circle in the ratio 1:2:5:4.
What is quadrilateral?It is defined as the four-sided polygon in geometry having four edges and four corners.
We have the four vertices of an inscribed quadrilateral divide a circle in the ratio:
1:2:5:4
Let the sides of the quadrilateral be x, 2x, 5x, 4x.
We know the sum of all angles of quadrilateral = 360°
x+2x+5x+4x=360
12x = 360
First angle, x = 30°
Seconds angle, 2x = 2×30 ⇒ 60°
Third angle, 5x = 5×30 ⇒ 150°
Fourth angle, 4x = 4×30 ⇒ 120°
Thus, the four angles of a quadrilateral are 30°, 60°, 150°, and 120°
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The four angles of a quadrilateral are 30°, 60°, 150°, and 120°
Step-by-step explanation:
What is the fourth term of the geometric sequence whose first term is 7 and has a common ratio of -2
Answer:
-56
Step-by-step explanation:
It is often easiest to find terms of a sequence by simply writing each one based on the previous one. Here, the common ratio of -2 tells you that each term is -2 times the previous term.
The first four terms are ...
7, -14, 28, -56
The fourth term is -56.
what is an equation of the line that passes through the points (6,3) and (-6,1)
Answer: y = [tex]\frac{1}{6}[/tex]x + 2
Step-by-step explanation:
[1] First, we will graph the points given. See the attachment with [1] in the corner.
[2] Next, we will find the slope.
(2a) Using rise over run. See the attachment with [2] in the corner.
(2b) Use the slope equation:
[tex]\displaystyle \frac{1-3}{-6-6}= \frac{-2}{-12} =\frac{1}{6}[/tex]
[3] Find the y-intercept. Look to the graph. See the attachment with [3] in the corner.
This gives us a final answer of y = [tex]\frac{1}{6}[/tex]x + 2
Helppppp pls
I don’t understand I’ll give brainliest
Answer:
m∠5 = 75°
Step-by-step explanation:
Angle 2 and Angle 4 are the same as they are alternate interior angles.
Since m∠2 = 45°
We then have m∠4 = 45°
We are given m∠3 = 60°
Now, we just have to find 7∠5.
The sum of the angle of a triangle adds up to 180°.
So, m∠3 + m∠4 + m∠5 = 180°.
60° + 45° + m∠5 = 180°.
Solving for ∠5
m∠5 = 180° - (60° + 45°)
m∠5 = 180° - (105°)
m∠5 = 75°
Which one is it
(1, 100)
(3, 49)
(4, 50)
(2, 74)
Answer:
(1, 100) » First one
(3, 49) » Third one
(4, 50) » Forth one
(2, 74) » Second one
Step-by-step explanation:
[tex]{}[/tex]
What is the perimeter of the figure?
Answer:
68.7
Step-by-step explanation:
Lets say this triangle is represented as ABC.
AB = BC
So:
23+23+22.7 = p
p = 68.7
hi guys I need this ASAP please answer ty
Answer:
6. 30% 7. -30%
Step-by-step explanation:
6. The total comment after the song released =5000
Then, the next day comment add up by 1500
Thus, (1500/5000) × 100
=30% of increase
7. 15.5-10.75 =4.75
(4.75/15.5 )×100= 30%
So, the decrease is -30%( If its about increase then its a positive number, but if its decrease just add a '-')
Answer:
See below ↓↓
Step-by-step explanation:
6.
% increase = Total - Original / Original5000 + 1500 - 5000 / 50001500 / 50000.330% increase8.
% decrease = | New - Original | / Original10.75 - 15.50 / 10.754.25 / 10.750.39539.5% decrease32,000 is what fraction of 106,000
Step-by-step explanation:
I hope this helps, you can ask any questions for clarification
A glass jug can hold (p + 6) quarts less water than a plastic container, 2 glass jugs and
2 plastic containers contain 6p quarts of water in all
how much water can the plastic container hold? give your answer is terms of p.
Answer:
12
Step-by-step explanation:
collect the like terms and divide
(p+6)2×2=64p+24=6p1) Water in a plastic container, p'= 10 - 3 p
2) Water in a glass container = 27 quarts
Water in a plastic container = 1 quarts
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A glass jug can hold (p + 6) quarts less water than a plastic container, 2 glass jugs and 2 plastic containers contain 6p quarts of water in all.
Now,
Let j represents water in one glass jag while p' represents the water in one plastic container,
Hence, According to the question,
⇒ j - p' = 6p+8 --------(1)
And, 2j+2p'=56p --------(2)
2 × equation (1)
⇒ 2 j - 2 p' = 12p + 16 ---------(3)
Equation (2) + equation (3)
We get, 4 j = 12 p + 72
⇒ j = 3 p + 18
Putting this value in equation (1),
We get, 3p+18-p'=6p+8
p' = -3p + 10 = 10 - 3p
Thus, water in a plastic container, p'= 10 - 3 p
b) If p=3
Water in a glass container = 3 × 3 + 18 = 27 quarts
Water in a plastic container = 10 - 3 × 3 = 1 quarts
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HELPPPP PLEASEEE!!!!!!!!!!!!!!!!!!!!
Answer:
I can't see the full question but as far as I can tell
by the picture
x=100