Part I: Converting the terms into fraction form
Given equation:
3.4k + (0.63 - 0.81k) ÷ 0.9 = 5.7First, let's convert the terms (that are in decimals) into fractions.
3.4k = 34k/100.63 = 63/1000.81k = 81k/1000.9 = 9/105.7 = 57/10Replace the fraction forms in the equation:
3.4k + (0.63 - 0.81k) ÷ 0.9 = 5.734k/10 + (63/100 - 81k/100) ÷ 9/10 = 57/10Part II: Simplifying the division being performed
Since the expression in the parenthesis can't be simplified, we can open the parenthesis. Before we do that, we need to divide the expression by 9/10 (as division is third in BODMAS). This can be done by converting the divisor into it's reciprocal and changing the sign to a multiplication sign.
34k/10 + (63/100 - 81k/100) × 10/9 = 57/10Since there is no other division being performed, we can simplify the distributive property (as multiplication is fourth in BODMAS).
34k/10 + [63/100 × 10/9] - [81k/100 × 10/9] = 57/1034k/10 + [7/10] - [9k/10] = 57/1034k/10 + 7/10 - 9k/10 = 57/10Part III: Isolating "k" to determine it's value
Combine like terms as needed:
34k/10 + 7/10 - 9k/10 = 57/10k(34/10 - 9/10) + 7/10 = 57/1025k/10 + 7/10 = 57/10Subtract 7/10 both sides of the equation to isolate "x" and it's coefficient.
25k/10 + 7/10 - 7/10 = 57/10 - 7/1025k/10 = 50/10Cancel the denominators (as a/b = c/b ⇔ a = c)
25k/10 = 50/1025k = 50Divide both sides by 25 to isolate "k"
25k/25 = 50/25k = 2Are
Right triangles are a subcategory of triangle
Yes or no
Sonny is twice as old as Wale. Four years ago, he
was four times as old as Wale. When will the
sum of their ages be 66?
Let S be Sonny age now and W be Wale age now
[tex]S=2W[/tex]
[tex]S-4=4(W-4)[/tex]
[tex]S-4=4W-16[/tex]
[tex]S=4W-16+4=4W-12[/tex] but [tex]S=2W[/tex]
[tex]2W=4W-12[/tex]
[tex]2W-4W=-12[/tex]
[tex]-2W=-12[/tex]
[tex]W=12[/tex] ÷ [tex]2=6[/tex] years old age of Wale now[tex]S=2W=2(6)=12[/tex] years old age of Sonny nowWhen will the sum of their ages be 66? Let x be the number of years from now that the sum of their ages be 66, so Sonny will be [tex]12+x[/tex] and Wale will be [tex]6+x[/tex]:
[tex](12+x)+(6+x)=66[/tex][tex]18+2x=66[/tex][tex]2x=66-18=48[/tex][tex]x=48[/tex] ÷ [tex]2=24[/tex] years from nowTherefore, 24 years from now, Sonny will be [tex]12+24=36[/tex] years old and Wale will be [tex]6+24=30[/tex] years old and the sum of their ages will be [tex]36+30=66[/tex] years.
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Use the information to find and compare Δy and dy. (Round your answers to three decimal places. )
y = 0. 8x5 x = 1 Δx = dx = 0. 1
Δy = dy =
The computation shows that the values of Δy and dy will be 0.572 and 0.4 respectively.
How to compute the values?The value of Δy will be computed thus:
Δy = y(x + Δx) - y(x)
= y(1.1) - y(1)
= 0.5(1.1)⁸ - 0.5(1)⁸
= 0.572
The value of dy will be:
= y'(x)dx
= (0.5)⁸ × x⁷(0.1)
= 0.4 (1)⁷
= 0.4
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Which of the following is a composite number?
13
15
17
23
Answer:
15
Step-by-step explanation:
15= 3*5, so not prime
A rectangle measures 2
1
4
meters by 1
7
8
meters. What is its area?
Answer:
77/18 or 4 5/18
Step-by-step explanation:
Convert 2 1/3 and 1 5/6 into improper fractions then multiply:
7 11 77 5
-- x -- = -- = 4 --
3 6 18 18
Hopes this helps :)
Gary, the technology coordinator of a high school, is planning to
purchase one memory stick for each of the teachers. There are 86
teachers at the school. The English teachers requested memory sticks
that have a capacity of 32 gigabytes. Gary determines that $600 is the
maximum amount that can be spent for all of the memory sticks. Gary
finds the following prices for the purchases from Computer City.
Option
Memory Stick
Capacity
Cost Each
A
16 gigabyte
$5. 99
B
32 gigabyte
$9. 99
Free shipping for any order $35 or more.
1
If a represents the number of 16-gigabyte memory sticks
and b represents the number of 32-gigabyte memory sticks,
which equation represents the number of each kind of
memory stick that should be purchased for the teachers?
A a + b = 86
C 16a + 32b = 86
B a + b = 600
D 16a + 32b = 600
Answer:
D
Step-by-step explanation:
if school starts at 8:15 am and ends at 3:31 pm when how long is the school day
Answer:
7hours and 16 minutes
Step-by-step explanation:
8:15-9:15 is one hour. 9:15-10:15 is two hours. 10:15-11:15 is three hours.11:15-12:15 is four hours. 12:15-1:15 is five hours. 1:15-2:15 is six hours. 2:15-3:15 is seven hours. 3:15-3:31 is 16 minutes.
For a research study, 64 marmots were tagged and set free. Later, the researchers
returned to the site and found 36 tagged marmots out of the 900 marmots they counted. To
the nearest whole number, what is the best estimate for the marmot population?
Answer:
1067
Step-by-step explanation:
[tex] \frac{36}{64} = \frac{600}{ m} [/tex]
m=total amount of marmots
cross multiplication-
36×M = 64×600
[tex] \frac{64 \times 600}{36} [/tex]
=1066.666667
=1067 marmots
(2x+4)(x-1) express as a trinomial
Answer:
[tex]\\\\\hookrightarrow 2x^{2} +2x-4[/tex]
Step-by-step explanation:
[tex]\hookrightarrow (2x+4)(x-1) \\\\\hookrightarrow 2x(x-1)+4(x-1)\\\\\hookrightarrow 2x^{2} -2x+4x-4\\\\\hookrightarrow 2x^{2} +2x-4[/tex]
Answer:
[tex]\huge\boxed{\bf{(2x + 4)(x - 1) = 2x^2 + 8x - 4}} [/tex]
Step-by-step explanation:
[tex]\sf \to (2x + 4)(x - 1) [/tex]
[tex]\sf \to x(2x + 4) + 4(x - 1) [/tex]
[tex]\sf \to 2x^2 + 4x + 4x - 4 [/tex]
[tex]\sf \to 2x^2 + 8x - 4 [/tex]
[tex]\: [/tex]
[tex]\huge\colorbox{red}{BlackPain} [/tex]
The 2 in the hundreds place is _______ times greater than the value of the 2 in the tenths place.
Answer:
10 times
Step-by-step explanation:
20= tenths place
200=hundredths place
20 x 10= 200
helppppp please i need help
Step-by-step explanation:
to gat everything you have to find the Area.
to get the area you have to multiple the number 2 tims
Find each lettered angle measure A through H
(20 points)
The angles of the triangle can be found using angle on a straight line theorem, isosceles triangle theorem, sum of angles in a triangle, sum of angles in a quadrilateral, vertical angle theorem etc.
Angles in a triangleThe sum of angles in a triangle is equals to 180 degrees. Therefore, let's find the angles in the triangle
2a = 180 - 58(base angles of isosceles triangle)
a = 122 / 2
a = 61°
b = 180 - (180 - 90 - 40) = 130° (angle on a striaght line)
c = 130° (Known angles)
d = 180 - 33 - 88 = 59°(sum of angles in a triangle)
e = 180 - 69 = 111° (external triangle theroem)
f = 86° (vertically opposite angles)
g = 83° (vertically opposite angles)
h = 180 - 36 = 144° (sum of angles on a straight line)
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name the lengths of the sides of three rectangles with perimeters of 12 units
Answer:
Rectangle 1 4, 4, 2 and 2
Rectangle 2 5, 5, 1 and 1
Rectangle 3 3.5, 3.5, 2.5 and 2.5
Step-by-step explanation:
A company logo is made up of a square and two identical triangles, as shown in this image.
What is the area of the logo?
Enter your answer in the box.
cm2
Square with side length of 9 cm. The top and bottom sides of the square form the base of a triangle with a height of 6 cm.
The area of the company's logo is 135 square cm
Area of composite figureComposite figures are figures that are made up of two or more shapes
The area of the given logo = Area of square + Area of 2 triangles
A = l² + bh
A = 9² + (9)(6)
A = 81 + 54
A = 135 square cm
Hence the area of the company's logo is 135 square cm
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The clown at the birthday party made balloon animals for 8 children. Each animal used 4 balloons. The clown still has 24 balloons left. How many balloons did the clown start with?
Answer: 8
Step-by-step explanation:
4x8 gives you 32
Then you subtract:
32-24 =8
Given the conditional relative frequency table by column, what does the 0.14 represent? given that a student is a 10th grader, there is a 14% chance he or she has a job. given that a student has a job, there is a 14% chance he or she is a 10th grader. 14% of the students surveyed are 10th graders who have a job. 14% of the students are 10th graders.
The first option is correct because 0.14 represents that if a student is a 10th grader, there is a 14% chance he or she has a job.
What is a conditional relative frequency table?It is a special type of frequency table that shows relationships between two categories.
From the given table it is clear that 0.14 is the probability of getting a job if a student is a 10th grader,
Option B is incorrect, stating there is a 14% chance a student is a 10th grader if he/she has had a job because we do not know the number of students.
Option C is also incorrect stating that 14% of the students surveyed are 10th graders who have a job because we do not know the total number of students.
Option D is also incorrect because we do not know the number of students.
Therefore, First option is correct because 0.14 represents that if a student is a 10th grader, there is a 14% chance he or she has a job.
To get more about conditional relative frequency, refer to the link,
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Answer:
A. Given that a student is a 10th grader, there is a 14% chance he or she has a job.
Step-by-step explanation:
What are the coordinates of the image of P(3, −4) after a reflection in the x-axis? (3, 4) (−3, −4) (−3, 4) (3, −4)
Answer:
(3,4)
Step-by-step explanation:
If is reflected around the x-axis, then the x-coordinate stays the same. Since -4 is still 4 away from the x-axis, we can count 4 untis up to get (3,4).
3+ х = х2 + 3x
rewrite by completing the square
Answer:
Step-by-step explanation:
Completing square:
3 + x = x² + 3x
x² + 3x = x + 3
Step 1: Subtract 'x' from both sides
x² + 3x - x = 3
x² + 2x = 3
Step 2: Divide the coefficeint of x by 2 and square the result
2 ÷ 2 = 1
1² = 1
Step 3: Now add 1 to both the sides
x² + 2x + 1 = 3 + 1
x² + 2x + 1 = 4
The LHS of the equation is in the form a² + 2ab + b² = (a +b)²
(x + 1)² = 2²
Take square root,
x + 1 = ± 2
x + 1 = 2 ;x + 1 = -2
x = 2 - 1 ; x = - 2-1
x = 1 ; x = -3
Solution: x = 1,-3
Help please ASAP this is confusing first correct answer gets brainleist
8cm
First we need to look at the side opposite to the missing side
which it is 12cm
now we can see that on the missing side 4cm is right below it
so we do
12cm-4cm
this gives you
8cm
a) 12-4=8
b) 5+4+4+12+9=34
The perimeter is 34cm and the missing length is 8cm.
Or it could be 38 since this unknown length was determined.
What is the square root of 45?
Step-by-step explanation:
=3√5
thank me later....
5. Find the equation of the line that goes through the point (2.-3) and has a slope of -1.
y = -x-1
y = -x-3
y=2x-3
y=-x+2
6. Find the equation of the line that goes through the point (5.1) and has a slope of 0.
y = 5x + 1
y=5
y=1
x=5
Hope it helps.
Do comment if you have any query.
Answer:
A and C.
Step-by-step explanation:
what is 10x10,20x90,30x30,and 40x40
Answer:
100
1800
900
1600
Step-by-step explanation:
Easy way to solve :
remove the 0's eg
20*90 -> 2*9 = 18
then add the 0's back on
1800
Answer:
See below ↓↓↓↓
Step-by-step explanation:
10 x 10 = 10020 x 90 = 180030 x 30 = 90040 x 40 = 1600what is equivalent to x - 7 = 10
Answer:
17-7=10
Step-by-step explanation:
Answer:
17
Step-by-step explanation:
17-7=10
Find the domain and range of the graph below.
Answer:
8
Step-by-step explanation:
the answer is 8 because the answer is 8
In one particular suburb, there are 18 families that own a pug. If there are a total of 24 families that own a dog in general, then what percentage of dog owners have a pug? Round your answer to the nearest whole number if necessary.
Answer:
75% of people own a dog.
Step-by-step explanation:
We apply the percentage formula in this problem
Total People * X/100 = Groups of people
Fill in the values
24 * X/100 = 18
We now Simplify the equation.
After simplifying you should get X=75, meaning 75% of people own a dog.
how to find the axis of symmetry if the parabola doesn't cross the y axis
please i need help
Step-by-step explanation:
a parabolic graph is given by the equation ax^2 + bx + c
the axis of symmetry is equal to -b/(2a)
however it is worth noting that all parabolas have a y intercept since their domain is all real numbers.
make sure to inform me if you need further guidance.
Draw the image of \triangle ABC△ABCtriangle, A, B, C under a dilation whose center is PPP and scale factor is \dfrac{1}{3} 3 1 start fraction, 1, divided by, 3, end fraction.
Dilating the triangle ABC would create another triangle whose size is different from the triangle ABC
How to dilate the triangle?From the complete question, we have the following coordinates:
Point A = (-4,5)Point B = (7,-7)Point C = (-2,2)Point P = (1,-4)Scale factor, k = 1/3The dilation rule across the center P is:
(x, y) --> (1/3x – 1, 1/3y + 4)
So, the coordinates of the image of the triangle are:
A' = (-1/3 * 4 – 1, 1/3 * 5 + 4)
A' = (-7/3, 17/3)
B' = (1/3 * 7 – 1, -1/3 * 7 + 4)
B' = (4/3, 5/3)
C' = (-1/3 * 2 – 1, 1/3 * 2 + 4)
C' = (-5/3, 14/3)
From the above computation, the coordinates of the new triangle is:
A' = (-7/3, 17/3)
B' = (4/3, 5/3)
C' = (-5/3, 14/3)
See attachment for the image of triangle ABC
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Laura wants 3 scoops of ice cream. She can choose from vanilla, chocolate, mint, raspberry, blueberry, and coffee flavors. How many combinations of 3 scoops of ice cream can Laura choosefrom?
What is the absolute value of -7
Will mark brainlyest!!
Answer: 7
Step-by-step explanation:
The absolute value of -7 is 7 because to find the absolute value you take away the sign.
My geometry teacher doesn't really teach so I need help!
A.) g(x)=x^2 -3; find g(3)
How do I solve this? I think I'm mostly confused on what I'm supposed to do with the (x).
Answer:
g(3) = 6
Step-by-step explanation:
The right side of the equation is the part with all the information for the doing of the math.
x^2 - 3 means square the number and then subtract 3.
On the left side of the equation is the g(x). g(x) or f(x) or k(x) is literally just y. Someone could ask what is f(x)? It is y.
What is g(x)? It is y.
What is g? It is the name of the function. So instead of saying ..."the thing where you square a number and then subtract 3..." you can just say "g". Now the (x) beside g DOESNOT mean times, bc sometimes parenthesis means times. THIS IS NOT TIMES!
The (x) is like a billboard. Tells you who will be starring as x in the work on the right side of the equation.
If you see g(x)=x^2-3
then whatever is in the ( ) on the left, put that in the place of x on the right.
g() = ^2 - 3
g(12) = 12^2 - 3
g(-7) = (-7)^2 - 3
or like your question
g(3) = 3^2 - 3
do the calculation
g(3) = 9 - 3
g(3) = 6
done! Hope this helps!