Given the expression:
[tex]4(Q+2)[/tex]Let's multiply the expression.
To multiply apply the distributive property of multiplication.
Distribute 4 to the values in the parentheses:
[tex]\begin{gathered} 4(Q)+4(2) \\ \\ =4Q+8 \end{gathered}[/tex]ANSWER:
[tex]4Q+8[/tex]Determine the momentum of a system that consists of two objects. One object, m1, has a mass of 6 kg and a velocity of 13 m/s in the direction of the positive x-axis and a second object, m2, has a mass of 14 kg and a velocity 7 m/s in the direction of the negative x-axis.
Answer:
The solution to the question will be explained better using the image below
Concept:
The formula to calculate momentum is given below as
[tex]\begin{gathered} momentum=mass\times velocity \\ m=mv \end{gathered}[/tex]The first momentum will be
[tex]\begin{gathered} m_1=m_1v_1 \\ m_1=6\times13 \\ m_1=78kg\text{ m/s} \end{gathered}[/tex]The second momentum will be
[tex]\begin{gathered} m_2=m_2v_2 \\ m_2=14kg\times7 \\ m_2=98kg\text{ m/s} \end{gathered}[/tex]Since they are moving in different directions,
We will substract both momentums
[tex]\begin{gathered} momentum=m_1v_1-m_2v_2 \\ momentum=78-98 \\ momentum=-20kg\text{ m/s} \end{gathered}[/tex]Hence,
The momentum of a system that consists of two objects should be 20 kg m/s in the direction of the negative x-axis
b. The product (a - b)(a + b) is called the
when simplified, it is called
of two squares and, when simplified it is equivalent to
The product (a - b)(a + b) is called the special binomial product, when simplified it is called algebraic identity of two squares and, when simplified it is equivalent to a² - b²
What is simplification?An equivalent, simpler (typically shorter) mathematical expression is substituted for the original one through the process of simplification.
Computer algebra's simplification of algebraic expressionsLogic optimization involves simplification of boolean expressions.A more straightforward but typically non-equivalent formula results from simplification of conjunction elimination in inference in logic.simplification of fractionsIn propositional logic, simplification is a valid immediate inference, argument form, and inference rule that draws the conclusion that if the conjunction A + B is true, then A + B is true as well. By deriving one of the conjuncts of a conjunction on a line by itself, the rule enables the brevity of longer proofs.
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A hang glider dropped his cell phone from a height of 450 feet. How many seconds did it take for the cell phone to reach the ground? Use radical equations and round to the nearest tenth.
The cell phone will takes about 4.7 seconds to reach the ground.
What are equations of motion?There are three equation of motions that can be used when motion of the object is under constant acceleration and on a straight path.
They are listed below as:
[tex]v = u + at\\\\s = ut + \dfrac{1}{2} at^2\\\\v^2 = u^2 + 2as[/tex]
where u = initial velocity of the considered object
v = final velocity of the object
a = acceleration of the object
s = distance traveled by the object in 't' time.
Given that hang glider dropped his cell phone from a height of 450 feet:
Acceleration is rate of change of velocity.
[tex]s = ut + \dfrac{1}{2} at^2[/tex]
Height = h = 450 feet
Gravitational Acceleration = g = 9.8 feet/s²
Initial Velocity = u = 0 m/s
h = 1/2at²
h = √2h/g
h = √2 x 450/ 9.8
h = 9.58 s.
Therefore, the cell phone will take 9.58 seconds to reach the ground.
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1. no association 2. negative association 3. positive association 4. nonlinear association
From the graph it can be observed that line fits curve and line has positive slope as increase in hours cause increase in miles.
The line with postive slope represent the positive relation between the variables. So there is postive association between miles and time spent for running.
Answer: positive association
Which age group of this set of numbers has twice as many people as another age group?
A) 76-85
B) 15-25
C) 36-45
D) 46-55
Answer:I believe it is 15-25
Step-by-step explanation:
a stack of 20 identical boxes. The stack is 180cm tall, Julia then removes 3 boxes from the top. How tall is the stack now
A stack of 20 identical boxes are 180 cm tall, then after removing 3 boxes from the top it is 153 cm tall.
As given in the question,
Number of identical boxes in a stack=20
Stack of 20 identical boxes are 180 cm tall
Height of 1 box=180/20
=9cm
Julia removes 3 boxes from the top
Height of 3 identical boxes=9 × 3
=27 cm
Height of stack after removing 3 boxes from the top
=Original height - height of 3 boxes
=180 -27
=153cm
Therefore, a stack of 20 identical boxes are 180 cm tall, then after removing 3 boxes from the top it is 153 cm tall.
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B ВaAbСLet c=12, and a=4.020. What is tan(A) in radians? Round to 3 decimal places.
Answer
Tan (A) = 0.109 radians
Explanation:
The figure given is a right angles triangle
Given that AB = c is the hypotenus
AC = b = adjacent
BC = a = opposite
Tan A can be calculated using SOH CAH TOA
Tan A = opposite / adjacent
Tan A = BC / AC
BC = a = 4.020
We need to find b uisng pythagoras theorem
[tex]\begin{gathered} c^2=a^2+b^2 \\ 12^2=4.020^2+b^2 \\ 144=16.1604+b^2 \\ \text{Collect the like terms} \\ b^2\text{ = 144 - 16.1604} \\ b^2\text{ = 127.8396} \\ b\text{ = }\sqrt[]{127.8396} \\ b\text{ = 11.307} \end{gathered}[/tex]b = 11.307
Tan A = 4.020 / 11.307
Tan A = 0.3555
A = tan ^-1 (0.3555)
A = 19.570 degrees
Convert degrees to radian
since 1 pi = 180 degrees
x pi = 19.570
Cross multiply
19.570 * 1 = x * 180
x = 19.570 / 180
x = 0.109
Therefore, tan (A) is 0.109 radians
Represent the quadratic function
For the given table of ordered pairs, the quadratic function is represented in equation in standard form is equal to y = x² - 14x + 48 .
As given in the question,
From the table of ordered pairs, it is observed that the zeros of the quadratic function are at x = 6 and x = 8. The zeros are the points where the y value of the function becomes zero.
An equation of the function in the standard form is given by :
y = (x - 6)(x - 8)
⇒y = x (x - 8) - 6 (x - 8)
⇒ y = x² -8x -6x +48
⇒ y = x² -14x + 48
The quadratic function is represented as the product of the zeros of the graph when plotted on a Cartesian plane.
Therefore, for the given table of ordered pairs, the quadratic function is represented in equation in standard form is equal to y = x² - 14x + 48 .
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Solve ×^2-4×-5=?
Your Genius If You Answered This Correctly
Answer:
(x+1)(x-5)
Step-by-step explanation:
test score hours studying 2 3 4 test score 44 66 88 test score ratio hours studying 22 1 ? ?
The test score ratio for studying 2 : 2 : 1 hours is represented as
44 : 44 : 22
What is a ratio?The comparison of two similar quantities or the relationship between them is known as a ratio. Using ratio symbols or words, ratios can be expressed in three different ways while maintaining their meaning.
To put it another way, ratios can be expressed by putting a fraction bar, the word "to," or the ratio symbol ":" between the two values being compared.
If 2 hours of studying = 44 marks
If 3 hours of studying = 66 marks
If 4 hours of studying = 88 marks
Then total sum of hours of studying = 9 hours
9 hours of studying = Sum of all marks
= 44 + 66 + 88
= 198
1 hour of studying = 198/9
= 22 marks
So, the test score ratio for studying 2 : 2 : 1 hours is represented as
44 : 44 : 22
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The following are the temperatures in °C for the first 12 days of January: 4.5 , − 3 , − 2 , 2 , 2.5 , 3 , − 1 , 4 , − 2.5 , 7 , − 4 , 3.5 What is the median temperature for those 12 days? Give your answer as a decimal.
Answer:
First you will put the numbers in order least to greatest. So, it would be -4.5, -4, -3.5, -2, -1, 0, 1.5, 2, 2.5, 4, 6. 0 is the median because it in in the middle here’s how. You cross out -4.5 and 6 then 4 and -4 then -3.5 and 2.5 then 2 and -2 then -1 and 1.5 and you’re left with just the 0
Step-by-step explanation:
[tex]\rm\int_0^1 \frac{( {x}^ \varphi - 1 {)}^{2} }{ log {}^{2} (x) } dx\\[/tex]
I assume the natural logarithm, and not the base-10 log. Parameterize the integral as
[tex]\displaystyle I(a) = \int_0^1 \frac{(x^a - 1)^2}{\log^2(x)} \, dx[/tex]
Differentiate twice with respect to [tex]a[/tex].
[tex]\displaystyle I'(a) = 2 \int_0^1 \frac{x^{2a} -x^a}{\log(x)} \, dx[/tex]
[tex]\displaystyle I''(a) = 2 \int_0^1 (x^{2a} - x^a) \, dx[/tex]
Evaluate the last integral, then solve for [tex]I(a)[/tex] with the fundamental theorem of calculus, noting that [tex]I(0)=I'(0)=0[/tex].
[tex]\displaystyle I''(a) = 2\left(\frac1{2a+1} - \frac1{a+1}\right)[/tex]
[tex]\displaystyle I'(a) = 2 \int_0^a \left(\frac1{2t+1} - \frac1{t+1}\right) \, dt \\\\ ~~~~ = \log(2a+1) - 2 \log(a+1)[/tex]
[tex]\displaystyle I(a) = \int_0^a (\log(2t+1) - 2\log(t+1)) \, dt \\\\ ~~~~ = (2a+1) \log(2a+1) - 2(a+1) \log(a + 1)[/tex]
Let [tex]a=\phi[/tex] to recover the original integral.
[tex]\displaystyle I(a) = (2\phi+1) \log(2\phi+1) - 2(\phi+1) \log(\phi + 1)[/tex]
Using various properties of the golden ratio [tex]\phi[/tex], namely
[tex]\phi = 1 + \dfrac1\phi \implies \phi^2 = \phi + 1 \implies \phi^3 = \phi^2 + \phi[/tex]
[tex]2\phi+1 = \phi\left(2+\dfrac1\phi\right) = \phi(1 + \phi)[/tex]
[tex]\phi=\dfrac{1+\sqrt5}2 \implies \phi^3 = 2 + \sqrt5[/tex]
we can simplify the result to
[tex]\displaystyle I(\phi) = \int_0^1 \frac{(x^\phi-1)^2}{\log^2(x)} \, dx = \boxed{\sqrt5\,\log(\phi)}[/tex]
The mass of Earth is 5.97 × 10^24 kg.
The mass of Mercury is 3.29 × 10^23 kg.
The ratio of the mass of Earth to the mass
of Mercury can be written in the form
1: n.
Calculate the value of n.
Give your answer as an ordinary number
to 2 significant figures.
The value of n is 0.06.
What is the ratio between two quantities?A fraction that demonstrates how many times one quantity is of the other is the ratio of two quantities of the same kind and in the same units. The ratio is represented by the sign ":". The expression a/b, which stands for the ratio of two quantities a and b (b ≠0), is used.Given:
The mass of Earth is 5.97 × 10²⁴ kg.
The mass of Mercury is 3.29 × 10²³ kg.
The ratio of the mass of Earth to the mass of Mercury is represented as 1: n.
The ratio of the mass of Earth to the mass of Mercury can be calculated as,
= mass of Earth/mass of Mercury
⇒ [tex]\frac{5,97*10^{24} }{3.29*10^{23} } = \frac{1}{n}[/tex]
⇒ n = 0.0551
⇒ n ≅ 0.06 ( 2 significant figures)
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I have a problem what is 27 divided by 655
Answer:
0.04122137404 is the answer
Answer: 0.041221374
Step-by-step explanation: According to Bing, 0.041221374 is your answer.
The graph shows your distance from home while out on a walk. The next day, you jog the same route twice at a constant speed. The entire jog takes 1 hour. Compare your walk to your jog
Using proportions, it is found that your walk and jogging rates are given as follows:
Walking: 3.75 miles per hour.Jogging: 5 miles per hour.What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations.
One example of application, in the context of this problem, is for the relation between velocity, distance and time, as velocity is distance divided by time, that is:
v = d/t.
From the graph, the walk takes 40 minutes = 2/3 of an hour, and you walk 1.25 x 2 = 2.50 miles, as you walk 1.25 miles and then you come back home, hence the rate is given as follows:
v = 2.50/(2/3) = 3 x 2.50/2 = 3.75 miles per hour.
For the jog, you jog the same distance twice in one hour, hence you jog 5 miles in one hour, and the rate is given as follows:
v = 5/1 = 5 miles per hour.
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Find the lateral surface area and volume of the solid object in picture
Notice that s stands for the slant height of the pyramid, and this height is the height of each one of the lateral triangular faces.
We will need to use the next formulas
[tex]\begin{gathered} A_{\text{hex}}=\frac{3\sqrt[]{3}}{2}a^2\to\text{Area of a regular hexagon (a is one of its sides)} \\ A_{\text{tri}}=\frac{bh}{2}\to\text{Area of a triangle} \end{gathered}[/tex]Therefore, the surface area is
[tex]\begin{gathered} A_{\text{figure}}=A_{\text{hex}}+6\cdot A_{\text{tri}}=\frac{3\sqrt[]{3}(3)^2}{2}+6\cdot\frac{(3\cdot10.3)}{2} \\ =\frac{27\sqrt[]{3}}{2}+92.7 \\ \Rightarrow A_{\text{figure}}=\frac{27\sqrt[]{3}}{2}+92.7 \\ \Rightarrow A_{\text{figure}}\approx23.4+92.7=116.1 \\ \Rightarrow A_{\text{figure}}=116.1 \end{gathered}[/tex]Lateral Area=116.1 m^2
As for the volume, the volume of a regular pyramid is
[tex]V=\frac{A_{\text{base}}\cdot h}{3}[/tex]In our case,
[tex]V=\frac{3\sqrt[]{3}a^2}{2}\cdot\frac{h}{3}=\frac{\sqrt[]{3}}{2}a^2h[/tex]Therefore,
[tex]\Rightarrow V=\frac{\sqrt[]{3}}{2}(3)^2\cdot10=45\sqrt[]{3}[/tex]Volume= 77.9 m^3
The points H(3,-1), I(-6, -1), and J(3,-9) form a triangle. find the
perimeter of the triangle?
The perimeter of the given triangle having vertices H(3,-1); I(-6,-1) and J(3,-9) is 29.04.
The points which form a triangle are:
H(3,-1) ; I(-6,-1) and J(3,-9)
Perimeter of the given triangle with vertices H(3,-1); I(-6,-1) and J(3,-9) is required:
To find the length we have to find the distance between the points.
Using distance formula i.e.
[tex]\sqrt{ [ (x2 - x1)^2 + (y2 - y1)^2 ][/tex]
Let the length of the sides be A1, A2 , A3
On applying the distance formula to H(3,-1) and I(-6,-1) ;
We get,
A1 = [tex]\sqrt{[ (-6-3)^2 + (-1+1)^2 ][/tex]
= [tex]\sqrt{ [ (-9)^2 + (0)^2 ][/tex]
= [tex]\sqrt[ 81 + 0 ]}[/tex][tex]\sqrt{[ 81 + 0 ][/tex]
= [tex]\sqrt{81}[/tex]
= 9
On applying the distance formula to I(-6,-1) and J(3,-9);
We get,
A2 = [tex]\sqrt{ [ (3+6)^2 + (-9+1)^2 ][/tex]
= [tex]\sqrt{[ (9)^2 + (-8)^2 ][/tex]
= [tex]\sqrt{[ 81 + 64 ][/tex]
= [tex]\sqrt{145}[/tex]
= 12.04
On applying the distance formula to J(3,-9) and H(3,-1);
We get,
A3 = [tex]\sqrt{[ (3-3)^2 + (-9+1)^2 ][/tex]
= [tex]\sqrt{[ (0)^2 + (-8)^2 ][/tex]
= [tex]\sqrt{ [ 0 + 64 ][/tex]
=[tex]\sqrt{64}[/tex]
= 8
Hence,
The perimeter is 9 + 12.04 + 8 = 29.04
The perimeter of the triangle having vertices H(3,-1); I(-6,-1) and J(3,-9) is 29.04.
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The balance sheet for Tempest, Inc., is shown here in market value terms. There are 19,000 shares of stock outstanding.
Based on the number of shares outstanding and the market value, the price the stock is currently selling for is $31.40
How to find the selling price of the stock?To find the selling price of the stock the formula is:
= Equity value of stock / Number of stock outstanding
The number of stock outstanding is 19,000 shares. The equity value of the stock is $596,600.
The selling price of the stock today then is:
= Equity value of stock / Number of stock outstanding
= 569,600 / 19,000
= $31.40
Full question is:
What is the stock selling for today?
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For the rhombus below, solve for y
Notice that this set of angles is congruent
herefore,
[tex]y-60=56[/tex]Solving for y ,
[tex]\begin{gathered} y=56+60 \\ \rightarrow y=116 \end{gathered}[/tex]nswer: 116
Triangle MNP is dilated by a factor of 2 with a center of dilation at (0,0).
What are the new coordinates of point N?
A
(1, -1)
B
(-4, 4)
C
(4, 0)
D
(4, -4)
The new coordinates of the point N after the given dilation transformation is; (-2, 6)
What is the Dilation of the triangle?
From the attached image, we see the given triangle MNP. We see that it's coordinates are;
M(-1, -2)
N(0, 2)
O(2, -2)
Now, when we talk about dilation in transformation, we are simply referring to a transformation that produces an image that is the same shape as the original, but is a different size.
Thus, triangle MNP will be dilated according to the rule (x,y), where point P is the center of dilation.
Given the coordinate N = (0, 2)
The rule of dilation with scale factor k =2 and point P is the center of dilation is given by:
(x, y) = (2x - 2), (2x + 2)
Thus;
N = (0, 2) → N'(2(0) - 2), (2(2) + 2)
= N'(-2, 6)
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In order to make a specific shade of green paint, a painter mixes 1/2 of a gallon of blue paint with 4/5 of a gallon of yellow paint. How many gallons of yellow paint are needed to mix with 3 gallons of blue paint?
To make a specific shade of green paint, 4.8 gallons of yellow paint is needed to mix with 3 gallons of blue paint.
In the question ,
it is given that
to make a specific shade of green paint , the painter mixes 1/2 gallon of blue paint and 4/5 gallon of yellow paint .
so , the ratio of yellow paint to blue paint [tex]=\frac{\frac{4}{5} }{\frac{1}{2} }[/tex]
writing in the simplified form , we get
= 4/5 × 2/1
= 8/5
So, for the given specific shade of green , the ratio of yellow : blue paint will remain same ,
let the amount of yellow paint used to mix with 3 gallons of blue paint be x gallons .
[tex]\frac{8}{5} =\frac{x}{3}[/tex]
On simplifying
x = 24/5
x = 4.8
so yellow paint required is 4.8 gallons
Therefore , to make a specific shade of green paint , 4.8 gallons of yellow paint is needed to mix with 3 gallons of blue paint.
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Solve the formula for the small base b
Value of b is 2Ah - B.
What is area?The area that an object's shape designates as being within it. The amount of space occupied by a figure or any other two-dimensional geometric shape in a plane is known as its area. Area is the entire amount of space occupied by the shape of an object or a flat (2-D) surface.
On a piece of paper, draw a square with a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Numerous 2-D shapes, such as circles, triangles, squares, rectangles, parallelograms, and trapezoids, may be found all around us. On paper, you can trace each of these shapes. Since every shape is distinct and varied, its area is also determined in a different way.
Given Data
A= [tex]\frac{1}{2}[/tex]h ( B + b)
For the value of b
b + B = 2Ah
b = 2Ah - B
Value of b is 2Ah - B.
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Fats, sugars, and proteins are important food molecules. What do these types of molecules have in common?
The fact that Fats, sugars, and proteins molecules have in common is that all of these are macronutrients.
What are macronutrients?The many categories of macronutrients include proteins, lipids—also known as fats—carbohydrates, or sugars. These are the three primary nutrients that the body uses to function. This indicates that they are chemical substances that your cells use as a source of chemical energy and that you require in quite significant quantities. These nutrients also produce energy or calories. They are broken down into smaller components during digestion. Energy is derived from carbohydrates (glucose). After being broken down into fatty acids, fats are used for energy. Although it can be used as fuel, protein's primary function is in the synthesis of hormones, muscle, and other proteins.To know more about macronutrients visit:
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Answer:
They all have carbon atoms.
Step-by-step explanation:
7 lorries can carry 987 cartons of books. How many cartons of books can each lorry carry
Answer:
141 each
Step-by-step explanation:
Evaluate 1.5 X 3 - 0.5 ²
A. 2
B. 3.5
C. 4.25
D. 31.25
Answer:
c is the answer
Step-by-step explanation:
1.5 x 3 =4.5
4.5 - 0.25
= 4.25
Let g (x) be the reflection across the y-axis of the function f (x) = 5x + 8. Identify the rule for g (x). g(x) = 5x + 8g (x) = -5x+8g (x) = -5x -8g (x) = 5x - 8
Given a function f(x), we can write the function g(x), where g(x) is the reflection over teh y-axis of f(x) by:
[tex]g(x)=f(-x)[/tex]In this case, the function given is:
[tex]f(x)=5x+8[/tex]Thus the reflection over the y-axis is:
[tex]g(x)=f(-x)=5(-x)+8[/tex]Now simplify:
[tex]g(x)=-5x+8[/tex]hus the answer is:
g (x) = -5x+8 (second option)
please help! giving brainliest :)
2. Complete the table for the equation, and graph the equation. (4pts)
2x - y = - 3
Two buses are driving along parallel freeways that are 5mi apart, one heading east and the other heading west. Assuming that each bus drives a constant 55mph, find the rate at which the distance between the buses is changing when they are 13mi apart, heading toward each other.
The rate at which the distance between the buses is changing when they are 13mi apart, heading toward each other is 101.54 km per hour.
How to calculate the rate?Let l = distance further away at which they'll meet. This will be illustrated as:
l = ✓13² - ✓5²
= ✓169 - 25
= ✓144
= 13m
Assuming that each bus drives a constant 55mph. The passes towards each other will be:
= -(55 + 55)
= -110m/h
Therefore, h² + l² = b².
Differentiate
2hdh/dt + 2ldl/dt = 2bdb/dt
= 2 × 5 × 0+ 2 × 12 (-110)
= 3 × 13db/dt
= -101.54 m/h
The rate is 101.54 m/h.
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Solve the proportion. 7 42 = 1 w w=
When the given proportion is solved the value of w is calculated to be 6.
What is proportion?
A proportion can be commonly understood as two ratios that have been set equal to each other; a proportion is an equation that can be solved.
When it is said that proportion is two ratios that are equal to each other, it means in the sense of two fractions being equal to each other.
for example 5/10 = 1/2, 5:10 = 1: 2
7:42 = 1 : w
[tex]\frac{7}{42} = \frac{1}{w} \\[/tex]
[tex]\frac{1}6{} = \frac{1}{w}[/tex]w = 1 x 6
w = 6
When the given proportion is solved the value of w is calculated to be 6
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