[tex] \Large{\boxed{\sf 7 \times \dfrac{4}{21} = \dfrac{4}{3}}} [/tex]
[tex] \\ [/tex]
Explanation:[tex] \blue{\begin{gathered}\begin{gathered} \\ \boxed { \begin{array}{c c} \\ \blue{ \sf{\boxed{ \sf Multiplication \: of \: fractions \text{:}}}} \\ \\ \sf \dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{a \times c}{b \times d} \\ \\ \end{array}}\\\end{gathered} \end{gathered}} [/tex]
[tex] \\ [/tex]
[tex] \sf 7 \times \dfrac{4}{21} [/tex]
[tex] \\ [/tex]
First, write 7 as a fraction:
[tex] \\ [/tex]
[tex] \sf 7 \times \dfrac{4}{21} = \dfrac{7}{1} \times \dfrac{4}{21} [/tex]
[tex] \\ [/tex]
Then, identify the value of a, b, c, and d:
a = 7b = 1c = 4d = 21[tex] \\ [/tex]
We can finally find our answer:
[tex] \\ [/tex]
[tex] \sf \dfrac{7}{1} \times \dfrac{4}{21} = \dfrac{7 \times 4}{1 \times 21} = \dfrac{28}{21} [/tex]
[tex] \\ [/tex]
Let's simplify our answer:
[tex] \\ [/tex]
[tex] \sf \dfrac{28}{21} = \dfrac{4 \times 7}{4 \times 7} = \boxed{\boxed{\sf \dfrac{4}{3}}} [/tex]
[tex] \\ \\ [/tex]
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The base of a triangle is 13 cm rounded to the nearest integer.
The perpendicular height of the triangle is 4.7 cm rounded to 1 dp.
Write the error interval for the area, a, of the triangle in the form m ≤ a < n.
Answer:
30.55 <_ a < 30.55
Step-by-step explanation:
a = 1/2 × b × h
a = 1/2 × 13 × 4.7
a = 30.55 cm^2
30.55 <_ a < 30.55
covert 104% into a decimal
Answer:
104 divided by a 100
1.04
Step-by-step explanation:
it is the same as moving the decimal two places to the left
15 POINTS! NEED ANSWER RIGHT AWAY!!!
Select from the drop-down menus to correctly complete the statements about the expression 5k + m/3.
The expression 5k + m/3 is a Choose… [sum or difference]. The term 5k is an addend, but it is also a Choose…[product or difference]. The term m/3
is an addend, but it is also a Choose…[sum or quotient].
Answer:
911
Step-by-step explanation:
The expression 5k+m3 is a sum. The term 5k is an addend, but it is also a product. The term m3 is an addend, but it is also a quotient.
Solve the equation by completing the
square. Enter the smallest solution first
and round to the nearest tenth.
s? - 8s - 4 = 0
-
s = [?]
Answer:
s ≈ - 0.5 , s ≈ 8.5
Step-by-step explanation:
s² - 8s - 4 = 0 ( add 4 to both sides )
s² - 8s = 4
To complete the square
add ( half the coefficient of the s- term )² to both sides
s² + 2(- 4)s + 16 = 4 + 16
(s - 4)² = 20 ( take square root of both sides )
s - 4 = ± [tex]\sqrt{20}[/tex] ( add 4 to both sides )
s = 4 ± [tex]\sqrt{20}[/tex]
Then
s = 4 - [tex]\sqrt{20}[/tex] ≈ - 0.5 ( to the nearest tenth ) ← smaller solution
s = 4 + [tex]\sqrt{20}[/tex] ≈ 8.5 ( to the nearest tenth ) ← larger solution
Rewrite 1/3 book for 5/6 an hour as a unit rate.
A.2/5 book/an hour
B. 1/5 book/hour
C. 2 1/2 books/hour
D. 5 books/hour
Answer:
A
Step-by-step explanation:
Write a proportion relating the side lengths of the triangle to any other triangle that has the line as a hypotenuse, a horizontal length of x units, and a vertical length of y units.
Answer:
y/x = 2 or y = 2xStep-by-step explanation:
The given triangle has:
Vertical segment = 2 unitsHorizontal segment = 1 unitThe ratio (slope) is:
2/1 = 2For any triangle using same line the proportion is:
y/x = 2 ory = 2xA wire bent in the form of a semi circle encloses an area of 7700cm2. If the same wire is bent into a square, calculate the area enclosed by the square
please hurry and answer fast..thank uuu so much
Answer: 8100 cm2
Step-by-step explanation:
First find radius
Area of semi circle = Pi*r2 / 2
7700 = 22/7 * r2/2
r2 = 7700 * 7 * 2 / 22
r2 = 700 * 7
r = square root of 7*7*10*10 ( I converted 700 into simpler numbers)
r = 7 x 10
r = 70 cm
Perimeter = r(Pi + 2)
= 70 ( 22/7 + 14/7)
= 70 * 36/7
= 360 cm
Let us take side of square as “x”
4x = 360
x = 360 / 4
x = 90
Area of square = side * side
= 90 * 90
= 8100 cm2
A semicircle is simply the half of a complete circle, and it can be gotten by dividing the circle through its center into equal halves.
The area of the enclosed square wire is 3025 square meters
The given parameters are:
[tex]\mathbf{Area= 7700cm^2}[/tex]
The area of a semicircle is
[tex]\mathbf{Area= \frac{\pi r^2}{2}}[/tex]
Substitute 7700 for Area
[tex]\mathbf{\frac{\pi r^2}{2} = 7700}[/tex]
Express pi as 22/7
[tex]\mathbf{\frac{22 \times r^2}{7 \times 2} = 7700}[/tex]
Divide through by 22
[tex]\mathbf{\frac{r^2}{7 \times 2} = 350}[/tex]
Multiply both sides by 14
[tex]\mathbf{r^2 = 4900}[/tex]
Take square roots of both sides
[tex]\mathbf{r = 70}[/tex]
Next, calculate the circumference of the semicircle
[tex]\mathbf{C = \pi r}[/tex]
So, we have:
[tex]\mathbf{C = \frac{22}{7} \times 70}[/tex]
[tex]\mathbf{C = 220}[/tex]
This means that the length of the wire is 220 meters.
This also represents the perimeter of the square.
The perimeter of the square is calculated using:
[tex]\mathbf{P = 4L}[/tex]
Where L represents the side length
So, we have:
[tex]\mathbf{4L = 220}[/tex]
Divide both sides by 4
[tex]\mathbf{L = 55}[/tex]
The area of the enclosed square is then calculated using:
[tex]\mathbf{Area = L^2}[/tex]
So, we have:
[tex]\mathbf{Area = 55^2}[/tex]
Evaluate the square
[tex]\mathbf{Area = 3025}[/tex]
Hence, the area of the enclosed square wire is 3025 square meters
Read more about areas at:
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WILL GIVE 25 PONITS! ANSWER CORRECTLY! (in attachments)
Answer:
you got to do it
Step-by-step explanation:
A line goes through the points (8,11) and (-2,7). What is the slope of the line? Show your work. Write the equation of the line in point-slope form. Show your work. Write the equation of the line in slope-intercept form. Show your work.
Answer:
Step-by-step explanation:
( 1 - 7n) times 5
What are the steps to solving it?
Answer:
5 - 35n.
Step-by-step explanation:
5(1 - 7n)
Using the Distributive Law:
= 5*1 + 5 *-7n
= 5 - 35n.
To solve two-step equations, it is useful to use reverse ________________ as a guide to isolate the variable efficiently. *
Answer:
operations
Step-by-step explanation:
to solve two-step equations, it is useful to use reverse operations as a guide to isolate the variable efficiently.
Which statement best explains why the sum of the areas of the two white squares in Figure two is the same as the area of the white square in figure one
Answer:
Statement 1 best explains why the sum of the areas of the two white squares in fig 2 is the same as the area of the white square in fig 1.
Step-by-step explanation:
Statement 1:
In each figure the total area is equal and the area of 4 triangles is equal, so the remaining white area must also be equal.
Explanation:
Total area of each square = ab*ab
Fig 1 has 4 triangle each with area = ab/2
Total area of non-white part in fig 1 = 4*(ab/2) = 2*ab
Fig 2 has 2 non-white rectangles each with area = a*b
Total area of non-white rectangles in fig 2 = 2*ab
As non-white area of fig 1 = non-white area of fig 2
The remaining white area must also be equal.
Find x.
8x-4=4x+12
Thank you!!
Answer:
4
Step-by-step explanation:
8x - 4 = 4x + 12
Add 4 to both sides:
8x = 4x + 16
Subtract 4x from both sides:
4x = 16
Divide by 4 from both sides"
x = 4
Convert into an exponential expression
Answer:
Step-by-step explanation:
The product of two consecutive positive odd numbers is 195.By constructing a quadratic equation and solving it, find the two numbers
Please help
Step-by-step explanation:
x = one odd number
the second odd number is (x+2), as both are consecutive.
so,
x × (x + 2) = 195
x² + 2x = 195
x² + 2x - 195 = 0
the formula to solve this is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 2
c = -195
x = (-2 ± sqrt(4 - 4×1×-195))/(2×1) =
= (-2 ± sqrt(4 + 4×195))/2 = (-2 ± sqrt(784))/2 =
= (-2 ± 28)/2 = -1 ± 14
x1 = -1 + 14 = 13
x2 = -1 - 14 = -15 which is invalid as the numbers are positive.
so, the two numbers are 13 and 15.
A packet of Hobnobs claims to be 24% bigger!!
It now contains 31 biscuits. How many did it have before?
Answer:
25
Step-by-step explanation:
124% = 31
1% = 0.25
100% = 25 biscuits
...YUMMY!
Answer:
24
Step-by-step explanation:
The graph shows the number of possible passengers for a given
number of roller coaster cars that leave the platform. Complete parts a
and b.
Answer:
a. Use two sets of coordinates to write an equation to describe the relationship.
m = [tex]\frac{24-16}{3-2} = \frac{8}{1}[/tex]
y = 8x
b. Interpret the equation in words.
Each roller coaster car holds 8 passengers.
What is the slope of the line ( part 2 )
Answer:
[tex]m=-\frac{1}{2}[/tex]
Step-by-step explanation:
Same as last time, take any 2 points you want:
(0, 3) and (4, 1)
Use the slope formula to calculate the slope:
[tex]m=\frac{1-3}{4-0}\\m=\frac{-2}{4}\\m=-\frac{1}{2}[/tex]
On small problems like these, you don't really even need to calculate it like that. You can just look at the graph, see that it goes down 1 and over 2 from one point to the next, and have your slope that way. Again, rise over run. It "rises" by -1, and runs by 2. -1 over 2, there's your slope.
Please help ill mark brainlyst please
Answer:
x = 8°
y = 21°
Step-by-step explanation:
27 + 3y = 90
3y = 63
y = 21°
x + 8x + 18 = 90
9x = 72
x = 8°
I'll also give brainliest to the first to answer
1+1=x
A) x=1
B) x=2
C) x=3
D) x=4
Answer:
B) x = 2
Step-by-step explanation:
1 + 1 = x
2 = x
1 + 1 = 2
What is the quotient of 9198 and 14?
Answer:
656.36
Step-by-step explanation:
you just divide then have to round the decimal point to 36
Solve the system of equations 5x - y = -9 and 3x + 4y = 13 by combining the
equations.
Answer:
2+2 =22. ♀️ ................
Boris buys a car for $23,000. The value of this car reduces by 8% each year. Find the number of complete years it takes for the value of the car to fall below $11,500.
Answer:
2 years
Step-by-step explanation:
casue if you multilpy 2 x 11,500 you get 23,000
In the year 2000, the population of Florida was 16 million people. Since then, the population has grown at least 2% each year. How many years will it be before the state's population is at least 30 million people? Round to the nearest tenth of a year.
Using an exponential function, it is found that it will take 31.7 years for the state's population to be of at least 30 million people.
An increasing exponential function is given by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem:
The initial population is of 16 million people, hence [tex]A(0) = 16[/tex].The growth rate is of 2%, hence [tex]r = 0.02[/tex]Then:
[tex]A(t) = A(0)(1 + r)^t[/tex]
[tex]A(t) = 16(1 + 0.02)^t[/tex]
[tex]A(t) = 16(1.02)^t[/tex]
It will be 30 million after t years, for which A(t) = 30, hence:
[tex]A(t) = 16(1.02)^t[/tex]
[tex]30 = 16(1.02)^t[/tex]
[tex](1.02)^t = \frac{30}{16}[/tex]
[tex](1.02)^t = 1.875[/tex]
[tex]\log{(1.02)^t} = \log{1.875}[/tex]
[tex]t\log{1.02} = \log{1.875}[/tex]
[tex]t = \frac{\log{1.875}}{\log{1.02}}[/tex]
[tex]t = 31.7[/tex]
It will take 31.7 years for the state's population to be of at least 30 million people.
A similar problem is given at https://brainly.com/question/14773454
A line has a slope of -4. The line passes through the point (-2,1). What is the point- slope form of the line?
A. y - 1 = -4 (x + 2)
B. y - 4 = -2 (x - 1)
C. y - 1 = 4 (x - 2)
D. y - 2 = -4 (x - 1)
Answer:
A y - 1 = -4(x + 2)
Step-by-step explanation:
point-slope form: [tex]y - y_{1} = m(x -x_{1} )[/tex]
y - 1 = -4(x -(-2) )
y - 1 = -4(x + 2)
A 66-inch candle burns down in 12 hours. After how many hours will it have burned 5 3/4 inches?
Answer:
9.5 hours
Step-by-step explanation:
Which relation is not a function?
A. {(2, 4), (1, 2), (0,0), (-1,2), (-2,4)}
B. {(2,4), (1, 1), (0,0), (-1, 1), (-2,4)}
C. {(2, 2), (1, 1), (0,0), (-1,1), (-2, 2)}
D. {(2, 2), (1, 1), (0,0), (1,-1), (2,-2)}
Answer: Choice D
Explanation:
We have the two points (2,2) and (2,-2) which have a repeated x coordinate. This is not allowed if we wanted a function. A function must have any x input lead to exactly one and only one output (assuming the input is in the domain).
Answer:
the correct is C. because they are lines going to 2.
Choose all of the proportional relationships that have a greater unit rate than the unit rate of this graph.
10
9
8
7
6
5
4
3
2
1
5
7
B
00
9 TD
X
y
2
5
10
15
low
y
3
6
9
6
12
18
6
y = 2x
y = 0.25%
y
2
4
y
3
6
9
8
16
24
8
12
The proportional relationships that have a unit rate that is greater than that of the one of the graph are: the first and third tables, and y = 2x.
How to Determine the Unit Rate of a Proportional Relationship?The unit rate can be calculated as, m = y/x. In an equation that represents a proportional relationship, y = mx, the value of m is the unit rate.
Using a point on the graph, (5, 2):
Unit rate of the graph = y/x = 2/5
Unit rate = 0.4.
Unit rate for the first table = 3/5 = 0.6 [greater than 0.4]
Unit rate for the second table = 2/6 = 0.3 [less than 0.4]
Unit rate for y = 2x, is 2 [greater than 0.4].
Unit rate for y = 0.25x, is 0.25 [less than 0.4].
Unit rate for the third table = 2/4 = 0.5 [greater than 0.4]
Unit rate for the second table = 3/8 = 0.375 [less than 0.4]
Those that have a unit rate that is greater than the one of the graph are: the first and third tables, and y = 2x.
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x÷12;x=2/3 Help ASAP please.
Answer:
I think this is it 2/36=1/18
Step-by-step explanation:
if x = 2/3 then you will multiply by the reciprocal of 12 which is 1/12.
2/3x1/12= 2/36
simplified 1/18
What is the symbol for a square root
Answer:
The symbol for a square root is [tex]\sqrt{}[/tex].
:)
Answer:
√
Step-by-step explanation:
Math=Explanitory