Primarily use the Distributive Property to solve this equation.
3(5 - x) - 2(5 + x) = 3(x + 1)
Distribute the outer terms.
3(5) + 3(-x) - 2(5) - 2(x) = 3(x) + 3(1)
15 - 3x - 10 - 2x = 3x + 3
-3x - 2x + 15 - 10 = 3x + 3
-5x + 5 = 3x + 3
Now, isolate all x terms.
-5x + 5x + 5 = 3x + 5x + 3
5 = 8x + 3
5 - 3 = 8x + 3 - 3
2 = 8x
2/8 = 8x/8
x = 1/4
with show work. trigonometry
Answer:
See below
Step-by-step explanation:
To find pole height
for a right triangle
sin 38 = opposite leg / hypotenuse = height /15 m
sin 38 = height / 15
15 sin 38 = height = 9.2 meters
To find rope DC
Use pythagorean theorem ( you have leg1 = height and leg 2 = 10.7)
DC ^2 = 9.2^2 + 10.7^2
DC = 14.1 m
If the breadth of a rectangle is reduced by 4cm it's are would be reduced by 240 cm². How long is the rectangle?
Answer:
Let the length be x. The breadth be y Area=xy. On reducing breadth by 4 new breadth will be (y-4). X(y-4)=xy-240. Xy-4x=xy-240. -4x=-240. X=60. Hence rectangle is 60cm long
Step-by-step explanation:
hope it will help
Jamal is constructing the bisector of angle ABC. He has a list of steps for the construction, but they are not in
order.
help me please!!!!!!!!
If [tex]$f(x)=4^x$[/tex] and [tex]$g(x)=4^{x+1}-3$[/tex] be the two functions then Horizontal translation 1 units right.
What is meant by functions?An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Let [tex]$f(x)=4^x$[/tex] and [tex]$g(x)=4^{x+1}-3$[/tex]
We can see that in place x , we have x + 1
so, f(x) exists shifted right side by 1 unit
and we can see that 2 exists added to y-value
so, it exists shifted upside by 2 units
horizontal translation 1 unit right
vertical translation 2 units up
Therefore, the correct answer is option e) Horizontal translation 1 units right.
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The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 14 units.
A solid oblique pyramid has an equilateral triangle base with a base edge length of 14 units. The base triangle is triangle A C D. The apex is point B. The angles formed with the lateral sides are 45 degrees.
What is BC, the height of the pyramid?
7 units
7StartRoot 2 EndRoot units
14 units
14StartRoot 2 EndRoot units
The height of the pyramid = BC = 14 units
What is a pyramid?It is a three-dimensional shape that has a polygonal base and flat triangular faces which joins at the apex at the top of the pyramid.
We have,
Base edge length = 14 units
From the figure below,
The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 14 units so,
We get,
AC = CD = AD = 14 units _____(1)
All sides in an equilateral triangle are equal.
In the right triangle ABC,
tan 45° = BC / AC
tan 45° = 1
1 = BC / AC _____(2)
From (1) and (2) we get,
1 = BC / 14
BC = 14 units
The height of the pyramid = BC = 14 units
Thus,
The height of the pyramid is 14 units.
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Answer: C 14 UNITS
Step-by-step explanation:
Round 2.629 to the nearest tenth.
Answer:
2.6
Step-by-step explanation:
cause it is 2.6299999999
2.629 to the nearest tenth is 2.6.
What is decimal?Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point.
Given:
A decimal number,
2.629.
Here, 2 is the whole number component and 0.629 is the fractional component part.
To round the number to the nearest tenth:
The number in tenth place is 6.
And the value right next to 6 is 2.
6 > 2.
So, the number will stay the same.
2.629 = 2.63
Then 2.63 = 2.6 to the nearest tenth.
Therefore, 2.6 is the required decimal.
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22. Which expression is equivalent to
0.71 × 2.8?
A
(B
(71 x 28) x (0.01 × 0.1)
(71 x 28) x (0.1 x 0.1)
(0.71 x 2.8) x (0.01 × 0.1)
D (71 x 28) x (100 × 10)
Answer: A
Step-by-step explanation:
A (71x28) x (0.01x0.1) = 0.71 x 2.8
B (71 x 28) x (0.1 x 0.1) = 7.1 x 2.8
C (0.71 x 2.8) x (0.01 × 0.1) = 0.0071 x 0.28
D (71 x 28) x (100 × 10) = 7100 x 280
the population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. after 3 hours it is observed that 400 bacteria are present. after 10 hours 2000 bacteria are present. what was the initial number of bacteria?
The initial number of bacteria in a culture is found as 200.
What is defined as the population growth?When demographers try to forecast changes in population size, they generally focus on four factors: fertility rates, high mortality (life expectancy), and the population's initial age profile.Using the model P = P₀e^(kt),
Where:
P(t) = the amount of bacteria at time t = 2000.
P₀ = initial amount at time t = 0
r = growth rate
t = time (number of periods)
k is the growth constant.
For t = 3 hours.
400 =P₀e^(k*3) ......eq 1
2000 = P₀e^(k*10) ......eq 2
Re writing eq 1.
400 = P₀e^(k*3)
as (400/P₀) = [e^k]^3,
Solve for e^k,
∛(400/P₀) = e^k
For eq 2.
2000 = P₀e^(k*10)
Rewrite it as;
(2000/P) = [e^k]^10.
Substituting ∛(400/P₀) for e^k, we obtain:
(2000/P₀) = (400/P₀ )^(10/3)
Solved for P.
Raise sides by the power of 3, we get:
(2000/P₀)^3 = (400/P₀)^10.
Therefore,
2000^3/ P₀^3 = 400^10/P₀^10
Solve,
2000^3/ 1 = 400^10/P₀^7
Taking reciprocal.
Solving
P₀^7 = 400^10/2000^3
P₀^7 = 1.31 x 10¹⁶
Take the 7th root of both sides;
P₀ = 200.67
Thus, the initial number of bacteria in a culture is found as 200.
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Skate world offers birthday parties for a fee of $130 plus $3 per person. If you can spend no more than $190 on your party. What is the maximum number of people who can attend?
Answer: 20
Step-by-step explanation:
130+60= 190
60 ÷ 3 = 20
At a dinner party, each guest is to receive a bag of small gifts. How many gifts should be placed in each bag if there are 8 guests and 32 gifts altogether?
Answer:
4Step-by-step explanation:
Total number of gifts = Sum of all gifts given to each guest
= (Number of guests) * (Number of gifts per guest)
By making the number of gifts per guest the subject of the formula:
Number of gifts per guest = Total number of gifts/Number of guest
But:
Total number of gifts = 32
Number of guests = 8
Number of gifts per guest = Total number of gifts/Number of guest
=32/8
=4Laura's Coffee Shop makes a blend that is mixture of two types of coffee. Type A coffee costs Laura $5.65 per pound, and type B coffee costs $4.35 per pound. This month, Laura made 158 pounds of the blend, for a total cost of $775.70. How many pounds of type A coffee did she use?
1) We can solve this problem by setting up a System of Linear Equations. So, based on this text, we can write out the following equations:
[tex]\begin{gathered} 5.65a+4.35b=775.70 \\ a+b=158 \end{gathered}[/tex]Note that the first equation relates itself to the total cost, and the second one to the amount of blend.
2) Now, we can solve this system of Linear Equations by the Elimination Method. Let's multiply the second equation by -5.65 so that we can add them both and eliminate "a"
[tex]\begin{gathered} 5.65a+4.35b=775.70 \\ -5.65a-5.65b=-892.7 \\ ---------------- \\ -1.3b=-117 \\ \frac{-1.3b}{-1.3}=\frac{-117}{-1.3} \\ b=90 \end{gathered}[/tex]Now, we can plug into the second equation b=90 and then solve it for a:
[tex]\begin{gathered} a+b=158 \\ a+90=158 \\ a+90-90=158-90 \\ a=68 \end{gathered}[/tex]Thus, the answer is:
[tex]a=68\: lbs,\: b=90\: lbs[/tex]Solve three fifths times v plus 3 equals two fifths times v minus 4. v = −35 v = 35 v equals negative seven fifths v equals seven fifths
The solution of the expression (3/5)v + 3 = (2/5)v - 4 would be v = - 35 which is the correct answer would be option (A).
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
We have to determine the solution of three-fifths times v plus 3 equals two-fifths times v minus 4.
Translate the phrase into an algebraic expression:
⇒ (3/5)v + 3 = (2/5)v - 4
Rearrange the likewise terms and apply arithmetic operations,
⇒ (3/5)v - (2/5)v = - 3 - 4
⇒ (1/5)v = - 7
⇒ v = - 7 × 5
⇒ v = - 35
Therefore, the solution of the expression (3/5)v + 3 = (2/5)v - 4 would be v = - 35.
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You have three $1 bills, four $5 bills, and two $10 bills in your wallet. You select a bill at random. Without replacing the bill, you choose a second bill at random. Find P($5 then $10)
1- 1/9
2- 1/12
3- 1/72
4- 2/27
Answer:
1- 1/9
Step-by-step explanation:
[tex]p(5 then 10) = \frac{4}{9} \times \frac{2}{8} [/tex]
[tex]p(5 then 10) = \frac{1}{9} [/tex]
Assuming without replacement
Need help finding the perimeter
13 + √85/3 is the perimeter of triangle .
Explain what a triangle is.
A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.The points P ( - 3 , -8 ) Q ( - 3, - 1) R ( -9,-8)
Distance between PQ = [tex]\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]
= [tex]\sqrt{( - 1 + 8)^{2} + ( -3 + 3)^{2} }[/tex]
= [tex]\sqrt{( -7 )^{2} +0 }[/tex]
= √49 ⇒ 7
Distance between QR = [tex]\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]
= [tex]\sqrt{( -9 + 3 )^{2} + ( -8 + 1)^{2} }[/tex]
= [tex]\sqrt{(- 6)^{2} + ( - 7)^{2} }[/tex]
= [tex]\sqrt{36 + 49}[/tex]
= √85
Distance between RP = [tex]\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]
= [tex]\sqrt{( - 3 + 9)^{2} + ( -8 + 8)^{2} }[/tex]
= [tex]\sqrt{(6)^{2} }[/tex]
= √36
= 6
perimeter = PQ + QR+RP/3
= 7 + √85 + 6/3
= 13 + √85/3
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The mass of two bodies are attracted with a force of 745N.if their distance of separation is 70.3m, find the mass of one the bodies, if the mass of the other is 2050kg (G=6.7by 10^-11Nm^2kg^2
The mass of two bodies are attracted with a force of 745N.if their distance of separation is 70.3m, then the mass of one the bodies is
[tex]m_{1} = 1.88(10)^{-7}[/tex]
What is mass ?The amount of matter that makes up every object or body is the greatest way to understand mass. Everything that we can see has mass. Examples of objects with mass include a table, a chair, your bed, a football, a glass, and even air. The mass of a thing determines whether it is light or heavy.
Given that : The mass of two bodies are attracted with a force of 745N.if their distance of separation is 70.3m
F=[tex]G\frac{m_{1} .m_{2} }{r^{2} }[/tex]
[tex]m_{1} =\frac{F.r^{2} }{Gm_{2} }\\ m_{1} =\frac{745.(70.3)^{2} }{6.7(10)^{-11}.2050 }\\\\[/tex]
[tex]m_{1} =\frac{26881.3(10^{7} )}{13735}[/tex]
[tex]m_{1} = 1.88(10)^{-7}[/tex]
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Help ASAP Giving 20 Points
Answer:
10.9 feet
Step-by-step explanation:
its Pythagoras but reversed. So instead of a squared plus b squared equals c squared its (c squared)-(a squared) equals (b squared)
so (12x12) - (5x5) = 119
square root of 119 is 10.9
sorry im replying on phone i cant do exponents and stuff
Solve for x and graph the solution on the number line below.
The solution is x ≤ -2 or x ≥ 10.
The inequalities are given in two parts which can be combined to form a single inequality as follows,
13 ≤ -5x + 3 or -47 ≥ -5x + 3
⇒ 13 ≤ -5x + 3 ≤ -47
Let's solve this.
First subtract 3 from all terms,
⇒ 10 ≤ -5x ≤ -50
Divide by 5 on all terms,
⇒ 2 ≤ -x ≤ -10
Multiply with (-1) on all terms, but then the inequality gets reversed as,
⇒ -2 ≥ x ≥ 10
We can now split the inequalities into two to make sense,
⇒ x ≤ -2 or x ≥ 10.
This solution can be graphed on a number line by darkening a line on the number line from 10, extended to the right of it. Then darken the line from -2, extend it to the left side.
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The figures below are congruent. Name the corresponding sides.
Answer:
AC=KM
AB=KL
BC=LM
Step-by-step explanation:
Answer:
AC=MK
AB=KL
BC=LM
This are corresponding sides
Anyone please help me this all and have solutions
Solutions are given below:
1. (14x^(5))/(5y^(2))=(2x^(4))/(10y) → x=y/14
2. ((x)/(y))((4y)/(3x))=((6y^(2))/(8x^(3))) → [tex]x=\frac{\sqrt[3]{36y^{2} } }{4}[/tex]
3. (5(y+6))/(2(xy-3))]=((y+6)/(4(xy-3))) → (-∞,∞)
4. ((x^(2)-4)/(x^(2)+5x+4))=((x+2)/(x+1)) → x=-2
What is a solution?
A designation of values to that same unknown variables that establishes the equality inside this equation is referred to as a solution.To put it another way, a solution is a figure or set of values one for every unknown) that, when used to replace the unknowns, cause the equation to equal itself.Equations or networks of equations can have just one unique solution when they are solved mathematically.Solutions are given below:
1. (14x^(5))/(5y^(2))=(2x^(4))/(10y) → x=y/14
2. ((x)/(y))((4y)/(3x))=((6y^(2))/(8x^(3))) → [tex]x=\frac{\sqrt[3]{36y^{2} } }{4}[/tex]
3. (5(y+6))/(2(xy-3))]=((y+6)/(4(xy-3))) → (-∞,∞)
4. ((x^(2)-4)/(x^(2)+5x+4))=((x+2)/(x+1)) → x=-2
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The area of a square is 150 square feet. What is the side length of the square?
Answer:37.5
Step-by-step explanation:
so basically a square has four sides so 150 divided by 4
PLEASE HELP
y= -2x^2+4x
Direction of opening
Equation of the axis of symmetry (x =___)
Coordinates of the vertex (x,y)
y-intercept (y=_)
Zeroes (if it has 2,1 or no zeroes)
maximum or minimum (y=_)
Answer:
see explanation
Step-by-step explanation:
given a quadratic in standard form
y = ax² + bx + c (a ≠ 0 )
• if a > o then curve opens up
• if a < 0 then curve opens down
for y = - 2x² + 4x ← in standard form with a = - 2, b = 4 and c = 0
here a = - 2 < 0 so curve opens down
-------------------------------------------------
the axis of symmetry is a vertical line passing through the vertex
the x- coordinate of the vertex, which is also the equation of the axis of symmetry is
x = - [tex]\frac{b}{2a}[/tex] = - [tex]\frac{4}{-4}[/tex] = 1
equation of axis of symmetry is x = 1
substitute x = 1 into the equation for y- coordinate of vertex
y = - 2(1)² + 4(1) = - 2 + 4 = 2
vertex = (1, 2 )
-----------------------------------------------------
to find the zeros let y = o , that is
- 2x² + 4x = 0 ← factor out - 2x from each term
- 2x(x - 2) = 0
equate each factor to zero and solve for x
- 2x = 0 ⇒ x = 0
x - 2 = 0 ⇒ x = 2
the zeros are x = 0 and x = 2
-----------------------------------------------------------
since the graph opens down then it has a maximum value
this is the y- coordinate of the vertex
thus maximum at y = 2
1. Write a matrix to represent the following system.
[tex]\left \{ {{-9x+4y =1} \atop {7x-9=5}} \right.[/tex]
Complete the matrix below.
[ _ _ | _ ]
[ _ _ | _ ]
[ _ _ | _ ]
2. Write a matrix to represent the following system.
[tex]\left \{ {{-5x+6y=1} \atop {5x-2y=9}} \right.[/tex]
Complete the matrix below.
[ _ _ | _ ]
[ _ _ | _ ]
[ _ _ | _ ]
The augmented matrices for each system are given as follows:
1.
[ -9 4 | 1 ]
[ 7 0 | 14]
2.
[ -5 6 | 1 ]
[ 5 -2 | 9]
How to build the augmented matrix of a system of equations?For a system of n variables, the first n columns of the matrix are composed by the coefficients of the variable of the system.
The two systems in this problem have variables x and y, hence:
The first column is composed by the coefficients of x.The second column is composed by the coefficients of y.Then the last column is composed by the values on the right side of the equations, that is, the results of the operations.
The second equation of the first system is:
7x - 9 = 5 -> 7x + 0y = 14 (this format is needed to build the augment matrix.
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Please help i havent been turning in my math work for days and im so close to getting detention
Answer: 1.one cup
2. 2 cups of each
Step-by-step explanation:
What is the equation of the parabola with the vertex of (1,-8) that passes through (2,-6)
Hello!
What is the standard form of the parabola:
[tex]\hookrightarrow y=(x-h)^2+k[/tex]
(h,k): vertex's coordinate=> h: x-coordinate of vertex
=> k: y-coordinate of vertex
Since our vertex is (1,-8)
[tex]\hookrightarrow \text{Our equation is }y=(x-1)^2}-8[/tex] <== Answer
Hope that helps!
i need help with this
∠1 and ∠8 are supplementary angles, ∠5 and ∠6 are Congruent, ∠6 and ∠8 are Congruent .
Supplementary angles are those angles that sum up to 180 degrees. Two or more angles that are identical to each other are referred to as Congruent angles.
We are provided with the figure shown in the question. We need to name the angles provided or need to tell the relation between two angles.
∠1 and ∠8 are supplementary angles as there sum is 180°.
∠1 + ∠8 = 180°
So, angle ∠1 and ∠8 are supplementary.
∠5 and ∠6 are Congruent as they are identical to each other.
∠5 = ∠6
∠6 and ∠8 are Congruent as they are identical to each other.
∠6 = ∠8
Thus, we can conclude that ∠1 and ∠8 are supplementary angles, ∠6 and ∠8 are Congruent , ∠5 and ∠6 are Congruent.
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Solve for y 10x -5y=30
Answer:
y=2(x−3)
Step-by-step explanation:
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
im lazzy thanks
Answer:
The answer is 18^4
Step-by-step explanation:
Its the answer
I like kinda need the answer to that : P
Answer:
its 16
Step-by-step explanation:
Answer:
FG = 16
Step-by-step explanation:
the angle between EF ( y- axis) and EH (x- axis) is right
thus the 4 angles in EFGH are right angles meaning the figure is a square.
the sides of a square are congruent , so
GH = FG , that is
3x + 1 = x + 11 ( subtract x from both sides )
2x + 1 = 11 ( subtract 1 from both sides )
2x = 10 ( divide both sides by 2 )
x = 5
Then
FG = x + 11 = 5 + 11 = 16
Evaluate. −8+(6+4)÷(−2)
Answer:
-1
Step-by-step explanation:
-8+10÷(-2)
2÷(-2)
-1
Bette used 3 jumbo cans of frosting to frost 105
cupcakes for the cupcake challenge at her school
and 5 jumbo cans of frosting to frost an
additional 175 cupcakes. How many jumbo cans
of frosting would she need to frost 280
cupcakes?
Bette needs 8 jumbo cans of frosting to frost 280 cupcakes.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
Bette used 3 jumbo cans of frosting to frost 105 cupcakes for the cupcake challenge at her school and 5 jumbo cans of frosting to frost an additional 175 cupcakes which are given in the question.
Let x jumbo cans of frosting would she need to frost 280 cupcakes
As per the given question, we can write the ratio as
3 jumbo cans of frosting : 105 cupcakes = x jumbo cans of frosting : 280 cupcakes
⇒ 3/105 = x/280
⇒ x = ( 280 × 3 )/ 105
⇒ x = 8
Therefore, she needs 8 jumbo cans of frosting to frost 280 cupcakes.
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