The height of the frame is 1 m and the width is 1.5 meters.
The height and width are the two dimensions that are used to measure the perimeter of a rectangular frame.
The perimeter is defined as the sum of all sides of a polygon. For a rectangle it is equal to twice the sum of height and width.
Perimeter(p)=2×[height(h)+width(w)]
The given dimensions of the frame is that the height is [tex]\frac{2}{3}[/tex] the width.
Let us consider the width be x.
Hence height=[tex]\frac{2}{3} x[/tex]
Now perimeter =
[tex]2\times(x+\frac{2}{3}x) \\=\frac{10}{3} x[/tex]
But the given perimeter is 5 meter.
Therefore:
[tex]\frac{10}{3} x=5\\or,x=5\times 3\div 10\\or,x=1.5[/tex]
Therefore the width is 1.5 meters.
Height=[tex]\frac{2}{3} \times 1.5\\[/tex]=1 meter.
So we can conclude that the width is 1.5 meters and the height is 1 meter.
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What is an equation of the line that passes through the point (-4,-6) and is parallel to the line 2x-y=6
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]2x-y=6\implies -y=-2x+6\implies y=\stackrel{\stackrel{m}{\downarrow }}{2} x-6\leftarrow \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is 2 and it passes through (-4 , -6)
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-4)}) \implies y +6= 2 (x +4) \\\\\\ y+6=2x+8\implies y=2x+2[/tex]
Pls help 15 points going out
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Which of the following options are examples of how you can name the angle?
Answer:
3rd and 4th
Step-by-step explanation:
Answer:
∠C and ∠DCB and ∠BCD
Step-by-step explanation:
We can name an angle either using one letter that represents it or use all three letters together.
When we use a single letter to represent or point an angle we must choose the center letter, C in this case.
And when we use all three letter to point an angle we must place the center letter, again C in this case, in the middle
Therefore the angle can be named as
∠C or ∠DCB or ∠BCD
Which of the following options are examples of how you can name the angle? Select all that apply.
Answer:
∠A
∠EAU
∠UAE
Step-by-step explanation:
You can name an angle by their middle vertex letter which, in this case, is A.
You can also name an angle using the three letters provided: E, A, U.
However, the vertex letter should always be in the middle. So, it could be ∠EAU and ∠UAE.
Let me know if you don't understand or need more explanation.
A cubical die is 3 m long. Find its volume. How much space does it occupy?
Answer:
27 m³
Step-by-step explanation:
Formula we use,
→ V = a³
Let's solve the problem,
→ V = a³
→ V = 3³
→ [ V = 27 m³ ]
Hence, it occupies 27 m³.
if i walked 4 miles for 180 days how much miles would i have walked
Answer:
720
Step-by-step explanation:
4x180=720 u have to multiply because 4 miled in 180 days is the same as 4x180
Find constants and in the function ()= such that (12)=1 and the function has a local maximum at =12
When the function changes from increasing to decreasing, a local maximum occurs. The value of a = 5e.
What is meant by local maximum?A local maximum point on a function is a point (x, y) on the function's graph whose y coordinate is greater than all other y coordinates on the graph at "close to" points (x, y).
When the function changes from increasing to decreasing, a local maximum occurs. This means that the function's derivative will shift from positive to negative.
Let the function be [tex]&F(x)=a x e^{b x} \\[/tex]
[tex]&F '(x)=d / d x\left(a x e^{b x} ) \\[/tex]
[tex]&=a(d / d x)\left(x e^{b x}) \\[/tex]
simplifying the above equation, we get
[tex]&=a\left[\left(d / d x* x\right) e^{b x} +\left(x* d / d x* e^{b x} )\right] \\[/tex]
[tex]&=a\left[e^{b x} +b x e^{b x} \right] \\[/tex]
[tex]$&=a[1+b x] e^{b x}[/tex]
For critical points, set [tex]$f^{\prime}(x)=0$[/tex] and solve for x
[tex]&a[1+b x] e^{b x} =0 \\[/tex]
simplifying the above equation, we get
1 + bx = 0
bx = -1
x = -1/b
The value of x = -1/b
Given that f(x) has local max at 1/5, critical point x = 1/5 then
-1/5 = -1/b
Therefore, b = -5
[tex]&F(x)=a x e^{-5x}\\[/tex]
[tex]&F(1 / 5)=a / 5 e^{-1}\\[/tex]
1 = a/5e
Therefore, the value of a = 5e.
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which of the following ordered pairs make this question true y=2x-4?
Answer:
There is not a single ordered pair which is a solution to y=2x−4 .
-23/20 in a decimal form long division
(-23/20) in a decimal form long division will be equal to (-1.15)
As per the question statement, we are provided with a fraction: (-23/20).
We are required to calculate the simplest form of the fraction in decimals using to the long division method.
The long division method works with 4 component: dividend, divisor, quotient and remainder. And the steps to perform the long division method are as follows:
Step 1: To take the first digit of the dividend from the left and check if this digit is greater than or equal to the divisor.
Step 2: Then, to divide it by the divisor and write the answer on top as the quotient.
Step 3: To subtract the result from the digit and write the difference below.
Step 4: To bring down the next digit of the dividend (if present).
Step 5: To Repeat the same process.
Hence, converting the fraction (-23/20) to decimal values using the process of long division method mentioned above, we get (-1.15).
Long Division method: In Mathematics, long division is a standard division algorithm suitable for dividing multi-digit Hindu-Arabic numerals that is simple enough to perform by hand, by breaking down a division problem into a series of easier steps, as mentioned above.To learn more about Long Division method, click on the link below.
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answer this question
The equation of the function g(x) is g(x) = -2|x - 2| + 5
How to determine the equation of the function g(x)?The function f(x) is given as
f(x) = 2|x - 2| - 5
The rule of the transformation is a reflection across the x-axis
This is represented as
g(x) = -f(x)
So, we have
-f(x) = -2|x - 2| + 5
Substitute g(x) = -f(x) in -f(x) = -2|x - 2| + 5
g(x) = -2|x - 2| + 5
Hence, the equation of the function g(x) is g(x) = -2|x - 2| + 5
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2.2 question 7) Which lines are perpendicular? The_____ lines are perpendicular (blue and green) How do you know? The product of their slopes is....
what is 1+1?
And hows ur day???
Answer:
The answer is 2, and thanks for asking my day's good :D
How's your day?
Step-by-step explanation:
R, S, and T are collinear. S is between R and T. RS =2w + 1, ST = w - 1, and RT = 18. Use the Segment Addition Postulate to slove for w. Then determine the lenght of RS.
R, S, and T are collinear . Then 13 is the length of RS.
What do collinear points mean?
Collinear points are those that are situated along a single or shared straight line. In Euclidean geometry, two or more points are said to be collinear if they are located on a line either near or far from one another.The question to know
RS + ST = RT
RS = w + 1 , ST = w - 1
RT = 18
2w + 1 + w - 1 = 18
3w = 18
w = 18/3
w = 6
RS = 2 * 6 + 1 = 13
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[tex]y \geq \frac{1}{3}x+4\\[/tex]
In linear equation, y ≥ x + 12/3 is simple version .
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.y ≥ 1/3 x + 4
y ≥ x/3 + 4
y ≥ x + 12/3
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Two families visited an amusement park. The first family bought 2 hot dogs and 3 bottles of waters, which totaled $18. The second family bought 4 hot dogs and 2 bottles of waters, which totaled $28. How much did one hot dog cost?
$2
$4
$5
$6
The answer is 6.
6x4=24
and that leaves the water to =2 per bottle.
so, 24+4=28
Answer:
$6.00
Step-by-step explanation:
To solve this problem, we have to construct two separate equations for each family, and then use any of the methods for solving simultaneous equations.
Let's consider h to represent the cost of 1 hot dog, and w to mean the cost of 1 water bottle.
• For the first family:
[tex]2h + 3w = 18[/tex]
We can rearrange the equation to make w the subject:
⇒ [tex]3w = 18 - 2h[/tex]
⇒ [tex]w = \frac{18 - 2h}{3}[/tex]
• For the second family:
[tex]4h + 2w = 28[/tex]
Since we have previously obtained an expression for w in terms of h, we can substitute that expression for w in the above equation, and then solve for h:
⇒ [tex]4h + 2(\frac{18 - 2h}{3}) = 28[/tex]
⇒ [tex]4h + \frac{36 - 4h}{3} = 28[/tex]
⇒ [tex]12h + 36 - 4h = 84[/tex] [Multiplying both sides of the equation by 3]
⇒ [tex]8h + 36 = 84[/tex]
⇒ [tex]8h = 48[/tex]
⇒ [tex]h = \bf 6[/tex]
∴ The price of one hot dog is $6.00.
The cost of one hot dog at an amusement park is $6.
What are linear and non-linear functions?A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x - 2 depicts a linear function because it is a straight line in the coordinate plane.
Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.
An example of a non-linear function is a quadratic function.
Let, the cost of hot dogs is 'x' and the cost of bottles of water be 'y'.
From the given information the two linear equations can be formed as,
2x + 3y = 18...(i) and 4x + 2y = 28...(ii)
Multiplying equation (i) by 2 and subtracting form (ii) we have,
4x + 2y = 28.
(-) 4x + 6y = 36
_____________
- 4y = - 8.
y = 2.
And hence x is equal to, 4x + 4 = 28 ⇒ 4x = 24 ⇒ x = 6.
So, The cost of one hog dog is $6.
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Which equation represents a linear function? Iready- Understand functions, Level H.
Answer:
y = 4x + 5
Step-by-step explanation:
y = 4x + 5 is the only one that graphs a straight line
MAPS Leila is walking from the park at point P to a restaurant at point R. She wants to stop for a break when the distance she has traveled and the distance she has left to travel has a ratio of 3:5. At which point should Leila stop for her break?
The point at which Leila should stop to take break is (6.25 , 3.75)
Given P(10 , 3) and R (0 , 4)
The ratio is 3:5
Let the break point be point B.
The formula is : (n(x₁) ₊ m(x₂)/ m₊n , n(y₁) ₊ m(y₂)/ m₊n)
P(10,3) = (x₁ , y₁)
R(0,4) = (x₂ , y₂)
m:n = 3:5
B = (5(10) ₊ 3(0)/3₊5 , 5(3) ₊ 3(4)/3₊5)
B = (50₊0/8 , 15₊12/8)
B = (50/8 , 27/8)
B = (6.25 , 3.75)
Hence Leila should stop at point (6.25 , 3.75) for her break.
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PLEASE I ONLY HAVE 15 MINS LEFT, HELP! Find the inverse of the following matrix:
Answer:
The inverse is [-4/3 -5/3 1]
[-4/3 -8/3 1]
[1/3 2/3 0]
Sorry, I didn't know how to type it well.
Under her cell phone plan, Caroline pays a flat cost of $54.50 per month and $5 per gigabyte. She wants to keep her bill at $74 per month. Write and solve an equation which can be used to determine gg, the number of gigabytes of data Caroline can use while staying within her budget.
To stay within budget, she must use 3.9 gigabytes.
Giving the following information:
Under her cell phone plan, Sofia pays a flat cost of $54.50 per month and $5 per gigabyte. She wants to keep her bill at $ 74 per month.
First, we need to establish the total cost formula:
Total cost= 54.5 + 5*x
x= number of gigabytes
Now, we isolate x:
74= 54.5 + 5x
19.5/5= x
3.9= x
To stay within budget, she must use 3.9 gigabytes
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Which equation can be used to find the answer to 30 divided by 5
Answer:
[tex]30 \div 5[/tex]
Way A
• 5 divided by 0 is 0.
• 5 divided by 3 is 0.6, flip the number, and you get 6.
Way B
• Divide 30 by 5 to get 6.
The ratio of a to b is constant, and
a = 9 when b = 6. What is the value of
b when a = 2?
Answer:
Step-by-step explanation:
a : b
9 : 6
2 : x
Cross multiply
6*2 = 9x
12 = 9x
12/9 = x
4/3 = x
I need help finding the m with m
The value of x in the angles is 17
How to determine the value of x?The angles are given as
3x + 10 and 2x - 5
These angles are complementary angles
So, we have
3x + 10 + 2x - 5 = 90
Collect the like terms
So, we have
3x + 2x + 10 - 5 = 90
Evaluate the like terms
So, we have
5x = 85
Divide both sides by 5
x = 17
Hence, the value of x in the angles is 17
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Enrollment at a golf academy has grown exponentially since the academy opened. A graph depicting this growth is shown. Determine the percentage rate of growth.
1.5%
5%
50%
0.5%
GRAPH IS BELOW
Answer:
We can see that after 2 years, enrollment becomes 35 instead of 15.
35/15=2.333...)
Since it's exponential, take sqrt(2.333...)=about 1.5
So the growth is 50%
Each leg of an isosceles triangle is twice as long as its base. Express the perimeter in terms of the length of the base.
The perimeter of the triangle in discuss expressed in terms of the length of the base as required in the task content is; Perimeter= 5x.
What is the perimeter of the isosceles triangle in terms of the length of the base?According to the task content, it follows that the perimeter of the triangle in terms of the length of the base is to be determined.
Let x = length of the base
Therefore, length of each leg = 2x.
Therefore, since the perimeter of the triangle is the sum of all sides; it follows that we have;
Perimeter = x + 2x +2x
Perimeter = 5x.
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How do you write 0.00603 in scientific notation?
Answer: .[tex]306^{-3}[/tex]
Step-by-step explanation:
Answer: +6.03E-3
Step-by-step explanation:
[tex]0.00603=6.03*10^{-3}[/tex]
6.03*10⁻³=+6.03E-3
Please, help me. I have no idea.
which of the following situations best descrbies a student engaged in active learing 1. A student uses only one of the resources provided by the teacher 2. A student skips parts of lessons that she find difficult 3. A student records questions to ask the teacher about a concept 4. A student does not discuss math outside of lessons.
Answer:1.c 2.b 3.a
Step-by-step explanation:
a phrase that describes a set of real numbers is given. express the phrase as an inequality involving an absolute value. all real numbers x more than 2 units from 0
All real numbers x more than 2 units from 0 will be |x - 2| ≤ 0.
What does "real number" mean?
In mathematics, a real number is a quantity that may be represented by an endless number of decimal expansions. In contrast to the natural numbers 1, 2, 3,... that result from counting, real numbers are utilized in measurements of continuously altering quantities such as size and time.All real numbers x at most 2 units from 0
This means if x is centered at 2 then it can move at the max 2 units on either side (i.e. 4 units after 2 and 0 units before 2)
This will be |x - 2| ≤ 0
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4. Liness and t are parallel. Find the value of x.
Answer: The value of X = 50°
Step-by-step explanation:
from diagram:
40° = 40°(vertically opposite angles)
40° + 90° + opposite side of X = 180 °(exterior angle property)
130° + opposite side of X = 180°(linear pair property)
opposite side of X = 180° - 130°
= 50°
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Ms. Jordan bought a box of 32 granola bars. Every day each of her three children ate one granola bar for lunch. Now there are only 11 bars left. Which equation can be used to find the number of days, n, that the children ate the bars for lunch? 32 =-11 32 = 3n - 11 ○ 32 = 3 +11 32 = 3n+ 11
The equation that can be used to find the number of days is 32 - 3n = 11
How to determine the equation that can be used to find the number of days?The given parameters are
Initial amount = 32
Rate = 3 i.e. 3 children
Amount left = 11
Let the number of days be n
So, we have:
Initial amount - number of days * rate = amount left
This gives
32 - 3n = 11
Hence, the equation that can be used to find the number of days is 32 - 3n = 11
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