The solution for the equations are :
She subtracts 12 from w , divides by 3 , then multiplies by 6 = 2w - 24
She subtracts 12 from w , multiplies by 3 , then divides by 6 = w/2 - 6
She multiplies w by 3 , subtracts 12 , then divides by 6 = w/2 - 2
She divides w by 3 , subtracts 12 , then multiplies by 6 = 2w - 72
She multiplies w by 6 , subtracts 12 , then divides by 3 = 2w - 4
She divides w by 6 , subtracts 12 , then multiplies by 3 = w/2 - 36
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Winnie is thinking of a number = w
Now ,
a)
She subtracts 12 from w , divides by 3 , then multiplies by 6
So , the equation will be
A = ( (w - 12 ) / 3 ) x 6
A = ( w - 12 ) x 2
A = 2w - 24
Therefore , the equation is 2w - 24
b)
She subtracts 12 from w , multiplies by 3 , then divides by 6
So , the equation will be
A = ( ( w - 12 ) x 3 ) / 6
A = ( w - 12 ) / 2
A = w/2 - 6
Therefore , the equation is w/2 - 6
c)
She multiplies w by 3 , subtracts 12 , then divides by 6
So , the equation will be
A = ( 3w - 12 ) / 6
A = w/2 - 2
Therefore , the equation is w/2 - 2
d)
She divides w by 3 , subtracts 12 , then multiplies by 6
So , the equation will be
A = ( ( w/3 - 12 ) ) x 6
A = ( w/3 ) x 6 - 12 x 6
A = 2w - 72
Therefore , the equation is 2w - 72
e)
She multiplies w by 6 , subtracts 12 , then divides by 3
So , the equation will be
A = ( 6w - 12 ) / 3
A = ( 6w ) / 3 - 12/3
A = 2w - 4
Therefore , the equation is 2w - 4
f)
She divides w by 6 , subtracts 12 , then multiplies by 3
So , the equation will be
A = ( w/6 - 12 ) x 3
A = ( w/6 ) x 3 - 12 x 3
A = w/2 - 36
Therefore , the equation is w/2 - 36
Hence , the equations are evaluated and solved
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Trevor asked his mother how old a tree is in my yard his mother says the sum of 10 and 2/3 of the trees age is in years is equal to (10+2/3)a =50, where A is the tree age in years. his equation is not correct. what error did he makea.the variable a should be mulitplied by 10 only and then added to 2/3b.the variable A should be multiplied by 2/3 only and then added to 10c.The variable A should be multiplied by 50, not by sum of 10 and 2/3d.c.The variable A should be multiplied by 2/3 and 50 and set equal to 10
Dhamby, this is the solution:
When solving the following system of equations, which variable would be the easiest to solve for? {x+6y=25{2x+2y=9 A) the x in the first equationB)the y in the second equationC) the y in the first equationD) the x in the second equation
SOLUTION
From the first equation, we have
[tex]\begin{gathered} x+6y=25 \\ we\text{ can easily solve for x by subtracting 6y from both sides, we have } \\ x+6y-6y=25-6y \\ x=25-6y \end{gathered}[/tex]So we can easily solve for x in the first equation.
Hence the answer is option A
4. Find the value of x.*60°,150°3x°Ox= 20O х = 30Ox= 60
The sum of the angles of a quadilateral is 360 degree. So the equation for the sum of angles is,
[tex]\begin{gathered} 90^{\circ}+60^{\circ}+150^{\circ}+3x=360^{\circ} \\ 300^{\circ}+3x=360^{\circ} \\ 3x=360^{\circ}-300^{\circ} \\ x=\frac{60^{\circ}}{3} \\ =20^{\circ} \end{gathered}[/tex]So the value of x is 20.
Use the drop-down menus to complete each statement to show why 65–√ is between 12 and 18.
it is proven that 6√5 between 12 and 18, Irrational numbers
What are Irrational numbers?
The group of real numbers known as irrational numbers are those that cannot be written as a fraction of the form p/q, where p and q are integers. Additionally, the decimal expansion of an irrational integer is neither terminating nor recurring.
Irrational numbers are real numbers that cannot be expressed as a straightforward fraction. These cannot be stated as ratios, such as p/q, where p and q are integers, q0. It is a contradiction of rational numbers.
It has been given in question 4 < 5 < 9 and we have to show 6√5 is between 12 and 18.
For box number 1.
4 < 5 < 9 ⇒ √4 < √5 < √9
For the box number 2.
√4 < √5 < √9 ⇒ 2 < √5 < 3
For the box number 3.
we multiply the inequality by 6.
6×(2 < √5 < 3)
⇒ 6×2 < 6×√5 < 6×3
So the 6×2 < 6×√5 < 6×3
⇒ 12 < 6√5 < 18
Hence it is proven that 6√5 between 12 and 18.
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Ethan delivers newspapers during the week. The graph shows the number of newspapers he delivers. Choose any two points and draw a slope triangle. Dilate the slope triangle along the graph to determine whether or not the slope is constant. Explain what the slope means in this situation.
Answer:
400/5 =40 after dilation is the same 200/5=40
This means the slope of the line are the same before and after dilation. The value of the sácale factor does not affect the slopes in the graph.
The slope of the graph is constant and it represents rate of change of papers delivered with rate respect to rate of change of days.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
By observing the graph we conclude that when days = 5,
papers delivered = 200 and when days = 10, paper delivered = 400.
Now, 400/10 = 40 and 200/5 = 40 so the slope of the graph is constant.
Slope in this situation represents rate of change of papers delivered with rate respect to rate of change of days.
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( 1 - v ) (5v +9 ) = 0Find v
We know that if XY = 0 then there are two options: X = 0 or Y = 0
Then, in this case:
If ( 1 - v ) (5v +9 ) = 0 then
( 1 - v ) = 0 or (5v +9) = 0
We find v for both cases:
1 - v₁ = 0
1 = v₁
5v₂ + 9 = 0
5v₂ = -9
v₂ = -9/5
Answer: v₁ = 1, v₂ = -9/5a company has 14 employees with a salary of $20,800, 10 employees with a salary of $23,600, 16 employees with a salary of $25,300 , 3 employees with a salary of $30,700, 6 employees with a salary of $38,700 and 1 employee with a salary of $149,300 find the mean salary for the employees
We have the following:
In this case, what we must do is calculate the weighted average, as follows:
[tex]\begin{gathered} m=\frac{14\cdot20800+10\cdot23600+16\cdot25300+3\cdot30700+6\cdot38700+1\cdot149300}{14+10+16+3+6+1} \\ m=\frac{1405600}{50} \\ m=28112 \end{gathered}[/tex]The mean salary is $28112
Solve log^6 (x + 1) + log^6 (x – 1) = 2.
suppose that g(x) = f(x) -7 which statement best compares the graph of g(x) with the graph of f(x)
It implies that when F(x) shifts 7 units to the left, we get the value equal to G. (x). As a result, the graph of G(x) is the graph of F(x) with 7 units added to the left.
How is the graph of G related to the graph of f?The graph of g is the reflection of the graph of f. If g(x) = f(-x), then the graph of g is obtained from the graph of f by reflecting about the y-axis.
For instance, the result of multiplying f(x) and g(x) is h(x) = fg (x), or h(x)=f(x)g (x). if f is the function denoted by f(x) = x2 and g is the function denoted by g(x) = x + 3.
Therefore,
The Correct answer is : The two functions G(x) and F are provided to us (x).
We must determine which assertion most accurately contrasts the graphs of G(x) and F(x).
Suppose
F(x) = x [/ tex]
G(x) = x-7
When x = 1 is substituted
So, F(x) = 1
G(x) = 1-7 = -6
It implies that we obtain the value equal to the value of G when F(x) shifts 7 units to the left (x).
The graph of G(x) is therefore the graph of F(x) with 7 units added to the left.
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A bag of marbles comes with 3 blue marbles, 2 red marbles, and 5 yellow marbles.
What is the ratio of RED MARBLES to ALL THE MARBLES?
2 to 5
2 to 10
2 to 8
2 to 3
Answer:
B
Step-by-step explanation:
There are 2 red marbles so the ratio will start with 2, there are also 3 (blue marbles) + 5 (yellow marbles) = 8 marbles. But it says ALL the marbles so also add the red ones, 8 + 2 = 10. The answer is 2 to 10.
Principal = AED 900; rate = 3.1%; time = 6 years What is the simple interest?
helpppppp!!!!!
The simple interest is AED 167.4
Given,
principle=AED 900
rate=3.1%
time=6 years
To calculate simple interest use formula,
[tex]I=\frac{Ptr}{100}[/tex]
Where,
p=principle
t=time period(years)
r= interest rate
[tex]I=\frac{900*6*3.1}{100}\\\\I=\frac{16740}{100} \\\\I=167.4[/tex]
Thus, the simple interest is AED 167.4
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Solve the division problem. Round answer to the nearest hundredth.9.2/52.063
In order to divide these numbers, first let's start with a 0 in the unit place, since 9.2 is smaller than 52.063.
Then, we multiply 9.2 by 10, this way we will calculate the tenths place.
Now, dividing 92 by 52.063, we have 1 as the result.
The remainder will be 92 - 52.063 = 39.937.
Again, let's multiply the remainder by 10, so now we will calculate the hundredths of the result.
Dividing 399.37 by 52.063 we have 7.
The remainder is 399.37 - 7*52.063 = 34.929.
Multiplying by 10, we have 349.29, and now we calculate the thousandths.
Dividing 349.29 by 52.063 we have 6.
Until now, the result of the division is 0.176.
Rounding to the nearest hundredth, we have 0.18 as the result of the division.
The price of a necklace was increased by 10% to £121.
What was the price before the increase?
Answer:
the anwser is 110
Step-by-step explanation:
The price before was £108.9 because 10% of £121 is £12.1 so if you subtract that you would get £108.9
Serena Wilson paid a tax of 288 on a house assessed at $48,000 using the same tax rate find the tax on a house assessed at $59,000
EXPLANATION
Let's see the facts:
Cost = $48,000
Tax= $288
The proportionality for a $59,000 is as follows:
[tex]\text{tax}_{59,000}=\frac{288}{48,000}\cdot59,000[/tex]Simplifying the fractions:
[tex]\text{tax}_{59,000}=0.006\cdot59,000=354[/tex]Answer: the tax for a $59,000 dollars house is of $354.
Triangle UVW, with vertices U(-6,2), V(-4,6), and W(-8,5), is drawn inside arectangle, as shown below.What is the area, in square units, of triangle UVW?
Okay, here we have this:
Considering the provided vertices, we are going to calculate the requested area, so we obtain the following:
Then we will first calculate the measure of each side and later with Heron's formula we will find the area, then we have:
[tex]\begin{gathered} u=\sqrt{((-4-(-8))^2+(6-5)^2)} \\ u=\sqrt{4^2+1^2} \\ u=\sqrt{17} \end{gathered}[/tex][tex]\begin{gathered} w=\sqrt{(-6-(-4))^2+(2-6)^2} \\ w=\sqrt{2^2+(-4)^2} \\ w=\sqrt{20} \end{gathered}[/tex][tex]\begin{gathered} v=\sqrt{(-6-(-8))^2+(2-5)^2} \\ v=\sqrt{2^2+(-3)^2} \\ v=\sqrt{13} \end{gathered}[/tex]Then, the area is:
[tex]\begin{gathered} A=\sqrt{\frac{(\sqrt{13}+\sqrt{17}+\sqrt{20})}{2}(\frac{\sqrt{13}+\sqrt{17}+\sqrt{20}}{2}\sqrt{13})(\frac{\sqrt{13}+\sqrt{17}+\sqrt{20}}{2}\sqrt{17})(\frac{\sqrt{13}+\sqrt{17}+\sqrt{20}}{2}\sqrt{20})} \\ =\sqrt{49} \\ =7 \end{gathered}[/tex]Finally we obtain that the triangle's area is equal to 7 square units.
y varies directly with x. if y =75 when x =25, find x when y=25
Answer:
x = 8.33
Explanation:
y varies directly with x if y can be calculated as a constant k times x. So:
y = k*x
If y is equal to 75 and x is equal to 25, we can calculate the value of k as:
[tex]\begin{gathered} 75=k\cdot25 \\ \frac{75}{25}=\frac{k\cdot25}{25} \\ 3=k \end{gathered}[/tex]Therefore, y = 3*x
So, to find x when y = 25, we need to replace y by 25 and solve for x as follows:
[tex]\begin{gathered} 25=3\cdot x \\ \frac{25}{3}=\frac{3\cdot x}{3} \\ 8.33=x \end{gathered}[/tex]Therefore, x is equal to 8.33
Find the value of a machine at the end of 4 years if the original cost was $1038 and r=0.28. Round to two decimal places.
We have a value function of a machine at the end of the year t that is:
[tex]V=C(1-r)^t[/tex]We know that C = 1038 and r = 0.28.
We have to calcula the value of the machine after 4 years (t = 4).
Then, we replace the parameters with their values and calculate V as:
[tex]\begin{gathered} V(t)=C(1-r)^t \\ V(4)=1038\cdot(1-0.28)^4 \\ V(4)=1038\cdot0.72^4 \\ V(4)=1038\cdot0.26873856 \\ V(4)\approx278.95 \end{gathered}[/tex]Answer: the value is $278.95.
help me determine the length of segments of this triangle
GE = 3.35, AG = 6.7, AE = 10.05
DG = 3.145, GC = 6.29, DC = 9.435
BG = 2.982, GF = 1.491, BF = 4.473
Explanation:Given: distance of the centriod to the vertex is twice the distance from centroid to the midpoint on the opposite side:
centroid: (14/3, 4/3)
[tex]\begin{gathered} AG\text{ = 2GE} \\ BG\text{ = 2GF} \\ GC\text{ = 2DG} \end{gathered}[/tex][tex]\begin{gathered} \text{Centriod = G = (14/3, 4/3) } \\ E\text{ = midpoint of BC} \\ B\text{ (}2,\text{ 0) and C (8, -4)} \\ \text{Midpoint = }\frac{1}{2}(x_1+x_2),\text{ }\frac{1}{2}(y_1+y_2) \\ \text{midpoint = }\frac{1}{2}\text{(2 + 8), }\frac{1}{2}(0-4) \\ \text{midpoint = 5, -2} \\ \\ GE\text{ = distance from G to E} \\ dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ =\text{ }\sqrt[]{(5-\frac{14}{3})^2+(-2-\frac{4}{3})^2}\text{ = }\sqrt[]{0.1111+11.1111} \\ GE=\text{ }3.35 \\ AG\text{ = 2GE = 2(3.35)} \\ \text{AG = }6.7 \\ AE\text{ = GE + AG} \\ AE\text{ = 3.35 + 6.7 } \\ AE\text{ = 10.05} \end{gathered}[/tex][tex]\begin{gathered} D\text{ = midpoint of AB} \\ A(4,\text{ 8), B(2, 0)} \\ \text{midpoint = }\frac{1}{2}(4\text{ + 2), }\frac{1}{2}(8+0) \\ \text{midpoint = 3, 4} \\ DG\text{ = distance from D to G} \\ dis\tan ce\text{ = }\sqrt[]{(3-\frac{14}{3})^2+(4-\frac{4}{3})^2} \\ \text{distance = }\sqrt[]{2.7778+7.1111}\text{ = }3.145 \\ \text{DG = 3}.145 \\ \\ GC\text{ = 2DG = 2(3.145)} \\ GC\text{ = }6.29 \\ DC\text{ = DG + GC} \\ DC\text{ = 3.145 + 6}.29 \\ DC\text{ = }9.435 \end{gathered}[/tex][tex]\begin{gathered} F\text{ is the midpoint of AC:} \\ A(4,\text{ 8) , C(8, -4)} \\ \text{midpoint = }\frac{1}{2}(4+8),\text{ }\frac{1}{2}(8+(-4)) \\ \text{midpoint = 6, 2} \\ \text{Distance GF from G}(\frac{14}{3},\text{ }\frac{\text{4}}{3}\text{) to F(6, 2)} \\ \text{Distance = }\sqrt[]{(2-\frac{4}{3})^2+(6-\frac{14}{3})^2} \\ \text{Distance = }\sqrt[]{\text{0.4445+1.7777}}\text{ = 1.491} \\ G\text{F = 1.491} \\ \\ BG\text{ = 2GF = 2(1.491)} \\ BG\text{ = 2.982} \\ BF\text{ = BG + GF} \\ BF\text{ = 2.982 + 1.491} \\ BF\text{ = 4.473} \end{gathered}[/tex]A state offers specialty license plates that contain 5 numbers followed by 2 letters. License plates are assigned randomly. All license plates are equally likely. Findthe number of possible license plates that can be issued using this system.O1.188,137,600 possible license platesO 12,500 possible license platesO 67,600,000 possible license plates039,917,124 possible license plates
Given:
There are 5 numbers followed by 2 letters.
Solution:
To find the answer, we will have a plate number that consists of 5 numbers followed by 2 letters. In that 5 numbers, each place has 10 choices-from 0 to 9. It will be: 10 * 10 * 10 * 10 * 10 = 100,000 .
Now, for the letters, there are 26 letters in the alphabet. We have two places for the letters and each place have 26 choices-from A to Z that will give us: 26 * 26 = 676
We will now multiply the acquired data for both the numbers and letters to arrive at the correct answer.
100,000 * 676 = 67,600,000
ANSWER: 67,600,000 possible license plates
Please please help I need to do it for tomorrow
Answer:
657000
Step-by-step explanation:
first you solve the 10^5 and 10^4. Then you solve the multiplication. Last, you solve the addition:
(6.31 * 10^5 ) + (2.6 * 10^4) =
(6.31 * 100000 ) + (2.6 * 10000) =
631000 + 26000 =
657000
Find the sum of an infinite geometric series where a1 = 180, and the common ratio is r = 3∕4 ?A) 240B) 720C) 135D) 360
Answer:
The sum to infinity of the geometric series is;
[tex]S_{\infty}=720[/tex]Explanation:
Given an infinite geometric series where;
[tex]\begin{gathered} a_1=180 \\ r=\frac{3}{4} \end{gathered}[/tex]Recall that the sum to infinity of a geometric series can be calculated using the formula;
[tex]S_{\infty}=\frac{a_1}{1-r}[/tex]substituting the given values;
[tex]\begin{gathered} S_{\infty}=\frac{a_1}{1-r}=\frac{180}{1-\frac{3}{4}}=\frac{180}{\frac{1}{4}}=180\times4 \\ S_{\infty}=720 \end{gathered}[/tex]Therefore, the sum to infinity of the geometric series is;
[tex]S_{\infty}=720[/tex]1
Which graph represents the linear function below?
The graph that represents the given linear function is attached below.
We are given a function. A function connects an input with an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input. The equation is linear in nature. It represents a straight line. The equation is given below.
(y - 4) = (4/3)(x - 2)
A line's general equation in slope-intercept form is y = mx + c. We will convert the given equation into this form.
y - 4 = (4/3)x - 8/3
y = (4/3)x - 8/3 + 4
y = (4/3)x + 4/3
The slope of the given equation is 4/3. The y-intercept for the given equation is 4/3.
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Explain IN WORDS how to determine the equation of a line when you are given two points...
SOLUTION:
Step 1:
In this question, we are given the following:
Explain IN WORDS how to determine the equation of a line when you are given two points.
Step 2:
The answers are as follows:
How to Find the Equation of a Line from Two Points:
1. Find the slope using the slope formula.
[tex]\begin{gathered} \text{ m = }\frac{y_2-y_1}{x_2-x_1}, \\ \\ \text{where ( x}_1,y_1) \\ and \\ \text{( x}_2,y_2)\text{ are the two pairs of points} \end{gathered}[/tex]2. Use the slope and one of the points to solve for the y-intercept (b).
3. Once you know the value for gradient, m, and the value for b, you can plug these into the slope-intercept form of a line:
[tex]\text{y = mx + b}[/tex]to get the equation for the line.
Pls Help and show work please
The values of x and y in the intersecting lines are as follows;
x = 12.7y = 6How to find angles in intersecting lines?When parallel lines are cut by a transversal line angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.
Therefore, the angle relationships can be used to find the value of x and y in the intersecting lines.
6y + 14 = 11y - 16 (vertically opposite angles)
Vertically opposite angles are congruent.
6y - 11y = - 16 - 14
-5y = -30
y = -30 / -5
y = 6
Therefore,
13x - 25 + 11y - 26 = 180 (sum of angles on a straight line)
13x - 25 + 66 - 26 = 180
13x = 180 + 25 - 66 + 26
13x = 165
x = 165 / 13
x = 12.6923076923
x = 12.7
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find the sector area for the angle of 7pi/6 on a circle with a radius of 6cm
In order to calculate the sector area, we can use the following rule of three, knowing that an angle of 2pi (complete circle) has an area of pi*r² (area of the circle).
So we have:
[tex]\begin{gathered} \text{angle}\to\text{sector area} \\ 2\pi\to\pi r^2 \\ \frac{7\pi}{6}\to x \end{gathered}[/tex]Now, we can write the following proportion and solve the equation for x:
[tex]\begin{gathered} \frac{2\pi}{\frac{7\pi}{6}}=\frac{\pi r^2^{}}{x}^{} \\ x\cdot2\pi=\frac{7\pi}{6}\cdot\pi r^2 \\ x=\frac{\frac{7\pi}{6}\cdot\pi r^2}{2\pi} \\ x=\frac{7}{12}\pi r^2 \\ x=\frac{7}{12}\pi\cdot6^2 \\ x=\frac{7}{12}\pi\cdot36 \\ x=21\pi\text{ cm}^2 \end{gathered}[/tex]Therefore the sector area is 21pi cm².
For 1960, the national debt was…….% of GDPIn the same year, the national debt was $0.3 trillion use this information to determine the GDP for 1960 $ trillion
From the graph, the national debt in 1960 was 46%.
It was given that the national debt in 1960 is $0.3 trillion.
Let the GDP be represented by G. This means that 46% of this value is:
[tex]\Rightarrow\frac{46}{100}\times G[/tex]Equating this to the debt amount, we have:
[tex]0.3=\frac{46}{100}\times G[/tex]Solving for G, we have:
[tex]\begin{gathered} 46G=0.3\times100 \\ 46G=30 \\ G=\frac{30}{46} \\ G=0.65 \end{gathered}[/tex]Therefore, the GDP in 1960 was $0.65 trillion.
Customer account "numbers" for a certain company consist of 4 letters followed by 4 numbers. How many different account numbers are possible if repetitions of letters and digits are allowed?
45697600 different account numbers are possible if repetitions of letters and digits are allowed.
Calculation:-
The 4 letters can be chosen in 26 ways each and the two numbers in 10 ways each
Number of account numbers possible = 26^4 * 10^2 = 45697600
What is problem-solving?
Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
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heyyyyyyyyyyyyyyyyyyy
Let the length of tape required be x centimeter
15centimeters to rap 5 present
x centimeters will rap 6 present
[tex]\begin{gathered} 15\operatorname{cm}=5 \\ x\text{ cm=6} \\ \text{hence} \\ 5x=15\times6 \\ 5x=90 \\ \text{divide both side by 5, we have} \\ x=\frac{90}{5} \\ x=18\operatorname{cm} \end{gathered}[/tex]H
help me pls 2mins left
Answer:
(5,1)
Step-by-step explanation:
A function is a set of ordered pairs in which no two different ordered pairs have the same x -coordinate. An equation that produces such a set of ordered pairs defines a function.
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A rectangle has a diagonal of 12 feet and length of 9 feet. What is ghye width of the rectangle, in simplified form? (No decimal Answers (
The width of the rectangle is;
[tex]3\sqrt[]{7}\text{ ft}[/tex]Here, we want to get the width of the rectangle
To do this, we need a pictorial representation
We have this as;
As we can see, the rectangle is divided into two equal right-triangles
We have represented the width by w
We can use Pythagoras' theorem to get the width
The square of the diagonal (the hypotenuse) is equal the sum of the squares of the two other sides
Thus, we have;
[tex]\begin{gathered} 12^2=9^2+w^2 \\ 144=81+w^2 \\ w^2\text{ = 144-81} \\ w^2\text{ = 63} \\ w\text{ = }\sqrt[]{63} \\ w\text{ = 3}\sqrt[]{7}\text{ ft} \end{gathered}[/tex]