Answer:
x = 3/4
Step-by-step explanation:
5/2-3x-5+4x=-7/4
Combine like terms
-10/2 + 5/2 +x = -7/4
-5/2+ x = -7/4
Add 5/2 to each side
-5/2+5/2 +x = -7/4 + 5/2
x = -7/4+5/2
Get a common denominator
x = -7/4 + 10/4
x = 3/4
Tiles
4V3
332
233
375
Pairs
324
1
V48
1 1 1
354
745
Given:
The expressions are:
[tex]\sqrt[3]{24},\sqrt{48},\sqrt[3]{54},\sqrt{45}[/tex]
To find:
The simplified form of each expression.
Solution:
We have,
[tex]\sqrt[3]{24}[/tex]
It can be written as:
[tex]\sqrt[3]{24}=\sqrt[3]{2\times 2\times 2\times 3}[/tex]
[tex]\sqrt[3]{24}=2\sqrt[3]{3}[/tex]
Similarly,
[tex]\sqrt{48}=\sqrt{2\times 2\times 2\times 2\times 3}[/tex]
[tex]\sqrt{48}=(2\times 2)\sqrt{3}[/tex]
[tex]\sqrt{48}=4\sqrt{3}[/tex]
And,
[tex]\sqrt[3]{54}=\sqrt[3]{2\times 3\times 3\times 3}[/tex]
[tex]\sqrt[3]{54}=3\sqrt[3]{2}[/tex]
In the same way,
[tex]\sqrt{45}=\sqrt{3\times 3\times 5}[/tex]
[tex]\sqrt{45}=3\sqrt{5}[/tex]
Therefore, the required pairs are:
[tex]\sqrt[3]{24}\to 2\sqrt[3]{3}[/tex]
[tex]\sqrt{48}\to 4\sqrt{3}[/tex]
[tex]\sqrt[3]{54}\to 3\sqrt[3]{2}[/tex]
[tex]\sqrt{45}\to 3\sqrt{5}[/tex]
find the area of the following shapes. Show the formula used and all work. Round to 1 decimal place .
Answer:
[tex]\text{d. }106,250\:\mathrm{cm^2},\\\text{e. }38.5\:\mathrm{cm^2},\\\text{a. }85\:\mathrm{ft^2},\\\text{b. }7.89676\:\mathrm{m^2}[/tex]
Step-by-step explanation:
Part D:
The figure shows a parallelogram with base 425 cm and height 250 cm. Its area can be found by [tex]A=bh[/tex] and therefore the area of this shape is [tex]A=425\cdot 250=\boxed{106,250\:\mathrm{cm^2}}[/tex]
Part E:
The figure shows a trapezoid. The area of a trapezoid is equal to the average of its bases multiplied by the height. Since one base is 2 cm and the other base is 9 cm, the average of these bases is [tex]\frac{2+9}{2}=\frac{11}{2}=5.5\:\mathrm{cm}[/tex]. The height is given as 7 cm, therefore the area of the trapezoid is [tex]7\cdot 5.5=\boxed{38.5\:\mathrm{cm^2}}[/tex]
Part A:
The composite figure consists of two rectangles. The area of a rectangle with base [tex]b[/tex] and height [tex]h[/tex] is given by [tex]A=bh[/tex]. The total area of the figure is equal to the sum of the areas of these two rectangles.
Area of first rectangle (rectangle on bottom): [tex]5\cdot 13=65\:\mathrm{ft^2}[/tex]
Area of second rectangle (rectangle on top):
*Since we don't know the dimensions, we must find them. Start by converting 108 inches to feet:
[tex]108\:\mathrm{in}=9\:\mathrm{ft}[/tex]. Therefore, the dimensions of this rectangle are (10-5) ft by (13-9) ft [tex]\implies5\text{ by } 4[/tex] and this rectangle's area is [tex]5\cdot 4=20\:\mathrm{ft^2}[/tex]
Thus, the area of the figure is equal to [tex]65+20=\boxed{85\:\mathrm{ft^2}}[/tex]
Part B:
We've already found the area of the figure in the previous part in square feet. To find the area in square meters, use the conversion [tex]1\text{ square foot}=0.092903\text{ square meter}[/tex].
Therefore, the area of the figure, in square meters, is [tex]85\cdot 0.092903=\boxed{7.89676\:\mathrm{m^2}}[/tex]
A city has a 20% chance of having a flood in any given decade. The table shows the results of a simulation using random numbers to find the experimental probability that there will be a flood in the city in at least 1 of the next 5 decades. In the table below, 1 represents a decade with a flood. The numbers 2 to 5 represents a decade without a flood.
Answer:
4/10=40%
Step-by-step explanation:
Find the length of the diagonal for a square that is 6 cm. by 6 cm. Leave answer in simple radical form, if necessary.
please hurry I beg
Answer:
[tex]6\sqrt{2}[/tex]
Step-by-step explanation:
let the diagonal be d
using the pythagoras theorem,
[tex]6^{2} + 6^{2} = d^{2}[/tex]
[tex]d=\sqrt{72}[/tex]
which in radical form is
[tex]6\sqrt{2}[/tex]
Factor this trinomial completely.
2x2 + 10x + 8
A. 2(x+4)(x + 1)
B. 2(x + 4)(x - 1)
C. 2(x - 4)(x - 1)
D. 2(x 7,4)(x + 1)
Answer:
[tex]{ \tt{2 {x}^{2} + 10x + 8 }} \\ { \tt{ = (x + 1)(x + 4)}}[/tex]
Answer:
A. 2 ( x + 4 )( x + 1 )
Step-by-step explanation:
2x² + 10x + 8
factor out 2 from the equation
2 ( x² + 5 x + 4 )
write 5x as a sum and rewrite the expression
2 ( x² + 4x + x + 4 )
factor out x from the equation
2 ( x ( x + 4 ) + x + 4 )
factor out x + 4 from the equation
2 ( x + 4 ) ( x + 1 )
One of the byproducts of nuclear power generation is Uranium-233. Uranium is decaying at a constant 57% rate per
day. If 3,820 pounds are produced from a power plant, what will the amount be In 15 days?
Answer:
Approximately 0.0121 will be left after 15 days.
Step-by-step explanation:
We can write an exponential function to model the situation. The standard exponential function is given by:
[tex]y=a(b)^x[/tex]
Let x represent the amount of days. Since the initial amount is 3,820 pounds, a = 3820. It decays at a rate of 57% per day. So, after one day, it will only have 100% - 57% = 43% or 0.43 of its previous amount. So, b = 0.43.
Hence, our function is:
[tex]y=3820(0.43)^x[/tex]
After 15 days, x = 15. Substitute and evaluate:
[tex]y(15)=3820(0.43)^{15}\approx 0.0121\text{ pounds}[/tex]
answer choices
a.)36.94
b.)39.59
c.)18.41
d.)25.19
e.)19.74
f.)28.94
Answer:
x = 39.59
Step-by-step explanation:
take 43 degree as reference angle
using sin rule
sin 43 = opposite / hypotenuse
0.682 = 27 / x
x = 27 / 0.682
x = 39 . 589
x = 39. 59
Select a figure from the options which will replace the(?) as established by the problem figure
Answer:
a) is the correct answer.
What is the area? Bit confused on this one.
Answer:
A = 9x² + 12x
Step-by-step explanation:
The area (A) of the rectangle is calculated as
A = height × width
= 3(3x² + 4x) ← distribute parenthesis by 3
= 9x² + 12x
Answer:
For the blue one:
A1=length*breadth
=3*3x^2
=9x^2
For pink:
A2=length*breadth
=3*4x
=12x
So the total area is:
A=A1+A2
=9x^2+12x
Scott likes to run long distances. He can run 20 \text{ km}20 km20, start text, space, k, m, end text in 858585 minutes. He wants to know how many minutes (m)(m)left parenthesis, m, right parenthesis it will take him to run 52 \text{ km}52 km52, start text, space, k, m, end text at the same pace.
How long will it take Scott to run 52 \text{ km}52 km52, start text, space, k, m, end text?
Given:
Scott can run 20 km in 85 minutes.
To find:
How long will it take Scott to run 52 km?
Solution:
Let us consider x be the number of minutes it will take him to run 52 km.
We know that,
[tex]Speed=\dfrac{Distance}{Time}[/tex]
By using this formula, we get
[tex]Speed=\dfrac{20}{85}[/tex] ...(i)
[tex]Speed=\dfrac{52}{x}[/tex] ...(ii)
On equating (i) and (ii), we get
[tex]\dfrac{20}{85}=\dfrac{52}{x}[/tex]
[tex]20\times x=52\times 85[/tex]
[tex]20x=4420[/tex]
On dividing both sides by 20, we get
[tex]x=\dfrac{4420}{20}[/tex]
[tex]x=221[/tex]
Hence, it will take 221 minutes to run 52 km.
helpp
Plzzz
It’s
A
Question-
Steven earns extra money babysitting. He charges $29.00 for 4 hours and $50.75 for 7
hours.
Enter an equation to represent the relationship. Let x represent the number of hours
Steven babysits and y represent the amount he charges.
$50.00÷7hours=×$
$50.00÷7hours= 7.25
7.25 he charges per hour
GUYS HELP please!!!
Answer: Choice B
x+6y = 29 and x+3y = 24.5
==============================================
Explanation:
x is the cost of a throw blanket
On top of this cost is the cost to embroider letters on it
Your name has 6 letters so it costs you an extra 6y dollars. Overall, you pay x+6y dollars. It says that your cost is $29
So that's where x+6y = 29 comes from.
-------------
Similarly, your friend also pays x dollars for the blanket itself plus an extra 3y dollars for the 3 letters in their name. Overall, they pay x+3y dollars. We're told they spent $24.50 which is where the equation x+3y = 24.5 comes from.
Answer:
2nd one = x + 6y = 29 , x + 3y = 24.5
Step-by-step explanation:
Have a nice day!
1. Write the equation that models the height of the roller coaster. Start by writing the equation of the circle. (Recall that the general form of a circle with the center at the origin is x2 + y2 = r2. (10 points)
Answer:
[tex]y = \sqrt{900 - x^2[/tex]
Step-by-step explanation:
Given
From the complete question, we have:
[tex]r=30[/tex] --- radius
Required
Expression for the height of the roller coaster
We have:
[tex]x^2 + y^2 = r^2[/tex] --- equation of circle
Substitute 30 for r
[tex]x^2 + y^2 = 30^2[/tex]
[tex]x^2 + y^2 = 900[/tex]
Since the roller coaster is half of the circle, the height is defined by y.
So: make y the subject
[tex]y^2 = 900 - x^2[/tex]
Take square roots
[tex]y = \sqrt{900 - x^2[/tex]
Hence, the height is:
[tex]\sqrt{900 - x^2[/tex]
Find the slope of each side of this quadrilateral and use that information to explain why it is a rectangle
8
BI
Your answer might look like this (you can 'copy-paste' the sentences below and fill in the blanks)
The slope of the side BA is The slope of the side BC is_-
The slope of the side BA is__ The slope of the side AD is_
The slope of the side CD is
The slope of the side AD is_
The slope of the side CD is
The slope of the side BC is
Finding the slopes tell me that this quadrilateral is a rectangle because_
Step-by-step explanation:
the answer is in the above image
can someone please help for brainlest
Answer:
yes it is correct
Step-by-step explanation:
option 1
Answer:
Your answer is correct! 9:1
Step-by-step explanation:
Old Area = side x side
? = 2 x 2
4cm
New Area-
Step 1: Triple the sides
2 x 3 = ?
6cm
Step 2: Find the area
6 x 6 = ?
36cm
The ratio of the new area to the old area is:
36 : 4
But wait! You can simply it!
36 / 4 = 9
4 / 4 = 1
So the new ratio would be:
9 : 1
Hope this helps!
Good Luck!
:)
What is the approximate distance between the two points (2, 4) and (5,0)?
I am so lost on this question. I’ve never heard of a matrices so I have no clue where to even start to solve this problem.
Answer:
thas multiple matrix bro
Step-by-step explanation:
Are these lines parallel perpendicular or neither
Answer:
perpendicular
Step-by-step explanation:
start but putting each line into the standard line format
2x-y=-5
-y=-2x-5
y=2x+5
x+2y=-6
2y=-x-6
y=-(1/2)x-3
if lines are parallel the slopes would be the same. 2 is not equal to -1/2
if lines are perpendicular the slope of one would be the opposite inverse of the other.
negative inverse of 2 = - (1/2)
so the lines are perpendicular
A scientist is studying the growth of anew species of bacteria. Looking back on his meticulous records, the scientist sees that his starting population was 50 bacteria. Five hours later, he measured 550 bacteria. What is the population of the bacteria after 10 hours, after 20 hours?
Answer:
In 10 hours, the population is 6050 bacteria. In 20 hours, the population is 732050 bacteria.
Step-by-step explanation:
Bacterial populations can be assumed to grow exponentially. In 5 hours, since the population will have multiplied by 11, in 10 hours it will have multiplied by 121 (11^2) and by 14641 (11^4).
50 * 11 * 11 = 6050
50 * 11 * 11 * 11 * 11 = 732050
Answer:
Step-by-step explanation:
550 = 50 [tex]x^{5}[/tex]
11 = [tex]x^{5}[/tex]
ln(11) = 5 ln(x)
x = [tex]e^{ln(11)/5}[/tex]
x = 1.615
10 hours ....
A= 50 ([tex]1.615^{10}[/tex] )
A= 50 ([tex]1.615^{10}[/tex] )
A=6050
20 hours ....
A= 50 ([tex]1.615^{20}[/tex] )
A= 50 ([tex]1.615^{20}[/tex] )
A=732,050
square root of 129 is greater than, less than or equal to 95/8?
√129 is less than [tex] \frac{95}{8} [/tex].
[tex]\large\mathfrak{{\pmb{\underline{\purple{Step-by-step\:explanation}}{\purple{:}}}}}[/tex]
Let us first solve for √129.
➝[tex] \:\sqrt{129} [/tex]
➝[tex]\:11.3578[/tex]
Now,
➝[tex]\: \frac{95}{8} [/tex]
➝[tex]\:11.875[/tex]
Clearly,
➵[tex]\:11.3578 < 11.875[/tex]
➵[tex]\: \sqrt{129} < \frac{95}{8} [/tex]
Hence, √129 is less than [tex] \frac{95}{8}[/tex].
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35☂}}}}}[/tex]
the graph of y=-3x+4 is?
Answer:
B
Step-by-step explanation:
that is a linear equation, therefore it makes a line, eliminating choices C and D.
Lines can literally Any x or y. So it would be B, a set of all the solutions to the equations.
The list shows the number of points Emma scored in eight basketball games.
5, 11, 9, 9, 4, 5, 6, 7
Find the mean.
Answer:
Mean = 7
Step-by-step explanation:
Given the following data;
Number of games = 8
Scores = 5, 11, 9, 9, 4, 5, 6, 7
We would sum all the scores together to get a total score.
Total scores = 5 + 11 + 9 + 9 + 4 + 5 + 6 + 7 = 56
Now, to find the mean;
[tex] Mean = \frac {total \; scores}{number \; of \; games} [/tex]
Mean = 56/8
Mean = 7
Answer:
7 is the mean score.
Step-by-step explanation:
Now we have to,
→ find the required mean score.
The given scores are,
→ 5, 11, 9, 9, 4, 5, 6, 7
→ Numbers = 8
Then the mean score will be,
→ (5 + 11 + 9 + 9 + 4 + 5 + 6 + 7)/8
→ 56/8 = 7
Hence, the mean score is 7.
The sum of Aini’s age and Wani’s age is 62 years old. Three years later, Aini’s age is three times Wani’s age. How old is Aini now?
Answer:
48 years old
Step-by-step explanation:
a + w = 62
a+3 = 3(w+3) =>a+3=3w+9
=> a-3w = 6
a+ w = 62
a- 3w= 6
________-
4w = 56
w = 14
so, the Aini's age now is 62-14 = 48 years old
semoga membantu
A purse regularly priced at $70 is on sale for 20% off. What is the scale price of the purse?
2x + z = 46
3z= 18
2y + z= 40
Answer:
x=20, y=17, and z=6 or (20,17,6)
Step-by-step explanation:
Hi there!
We're given the system of equations:
2x+z=46
3z=18
2y+z=40
and we need to solve for x, y, and z
first, let's find the value of z, as we have z by itself (no other variables) in 3z=18
divide both sides by z
z=6
the value of z is found :)
now we can use z=6 to find the value of the other variables; for example, plug z as 6 into 2x+z=46 to solve for x
2x+6=46
subtract 6 from both sides
2x=40
divide by 2
x=20
Finally, let's find y
once again, we can substitute z as 6 in the equation 2y+z=40 to find y
2y+6=40
subtract 6 from both sides
2y=34
divide by 2
y=17
so the answer is: x=20, y=17, and z=6; if you need it in a point it's (20,17,6)
Hope this helps! :)
Find the area of the following composite figure please
Step-by-step explanation:
answer is in photo above
Solve
5x + 3 = x + 11
Step-by-step explanation:
5x + 3 = x + 11
4x=8
x=2
!!!!!
[tex]5x + 3 = x + 11 \\ 5x + 3 - x = 11 \\ 4x + 3 = 11 \\ 4x = 11 - 3 \\ 4x = 8 \\ x = \frac{8}{4} \\ x = 2[/tex]
HOPE IT HELPS!!!I NEED BRAINLIEST ✌️(4a+3b)(2a-5) expand
Answer:
6ab + 8a² - 15b - 20a
Step-by-step explanation:
Expand by using FOIL method
4(2a-5) + 3b(2a-5)
4a(2a) + 4a × -5 + 3b × -5
Simplify terms
8a² - 20a + 6ba -15b
6ab + 8a² - 15b - 20a
Jessica's teacher asks a class to find the largest number that is smaller than 4.5. Jessica's friend Jeevan gives the answer 4.4. a Why is Jeevan not correct?
Jeevan is not correct, the answer could be 4.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that Jessica's teacher asks a class to find the largest number that is smaller than 4.5.
Since Jessica's friend Jeevan gives the answer 4.4.
Therefore, we can see that 4.4 is not a whole number thus, it isn’t the largest number that is also less than 4.5.
The correct answer could be 4.
More about the Algebra link is given below.
brainly.com/question/953809
#SPJ2
Rami is solving the equation for x .
–6x – 1 = 5
–6x – 1 Empty square 1 = (5 Empty square 1)
–6x = 6
–6x Empty circle – 6 = 6 Empty circle –6
x = –1
Which operation symbols should Rami write in the Empty squareand the Empty circle?
Answer:
Empty square = +
Empty Circle = ÷
Step-by-step explanation:
In order to eliminate the extra numbers from the equation you have to do the opposite of the problem. So...
-6x-1=5
-6x -1+1 = 5+1 (eliminating the 1 from the -6x side and adding it to the other side)
-6x = 6
-6x ÷ -6 = 6 ÷ -6 ( eliminating the-6 so that one side just has x)
so... x= -1
Answer: Option B is your correct answer.