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PROBLEM
Inequalities
Method
When solving linear inequalities, change or switch the sign of the inequality when you divide or multiple with negative.
[tex]\begin{gathered} - \\ -5b\text{ }\ge\text{ 20} \\ \text{Divide through by -5} \\ \frac{-5b}{-5}\text{ }\leq\text{ }\frac{20}{-5} \\ b\text{ }\leq\text{ -4} \end{gathered}[/tex]Related Questions
i don’t kno how to do this paper i need help with the answers
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Solution:
Given:
The three interior angles of a triangle are;
[tex]6x+1,9x+4,6x-14[/tex]To find the value of x, we use the theorem for the sum of interior angles in a triangle.
The sum of interior angles in a triangle is 180 degrees.
Hence,
[tex]\begin{gathered} (6x+1)+(9x+4)+(6x-14)=180^0 \\ \text{Collecting the like terms,} \\ 6x+9x+6x+1+4-14=180 \\ 21x-9=180 \\ 21x=180+9 \\ 21x=189 \\ \text{Dividing both sides by 21 to get the value of x,} \\ x=\frac{189}{21} \\ x=9 \end{gathered}[/tex]Therefore, the value of x is 9.
la has a swimming pool in her backyard that is rectangular with a length of 26 feet and a width of 16 feet.wants to install a concrete walkway of width c around the pool. Surrounding the walkway, she wants to> a wood deck that extends w feet on all sides. Find an expression for the perimeter of the wood deck.0 74+ 86 + 8wO 416 + 6c + 2wO 42 + 4c + 4w0 84 + 80 + 8w
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Given that the length of the pool is 26 feet and the width is 18 feet.
The width of the walk way=c feet.
The width of the wood deck =w feet.
The wood deck is in a rectangle shape.
The length of the wood deck = the length of the pool + 2 times of the width of the walkway+ 2 times of the width of the wood deck.
The length of the wood deck l =26+2w+2c.
The width of the wood deck = the width of the pool + 2 times of the width of the walkway+2 times of the width of the wood deck.
The width of the wood deck w = 16+2w+2c.
The perimeter of the wood deck is
[tex]P=2(l+w)[/tex]Substitute l=26+2w+2c and w=16+2w+2c, we get
[tex]P=2(26+2w+2c+16+2w+2c)[/tex][tex]P=2(42+4w+4c)[/tex][tex]P=2\times42+2\times4w+2\times4c[/tex][tex]P=84+8w+8c[/tex]Hence the perimeter of the wood deck is 84+8c+8w
The fourth option is correct.
f(x)=3x+2;g(x)=x+2 ; find f(g(x))
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We have the functions:
[tex]f(x)=3x+2[/tex]and
[tex]g(x)=x+2[/tex]and we need to find the composite function f(g(x)), to do this we plug the function g(x) instead of x in the function f(x), that is:
[tex]\begin{gathered} f(g(x))=f(x+2) \\ =3(x+2)+2 \\ =3x+6+2 \\ =3x+8 \end{gathered}[/tex]Therefore:
[tex]f(g(x))=3x+8[/tex]78.93 × 32.4 this requires standard algorithm take the long way
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For this operation, let's start
After all the single multiplications we must add them in rows, and count the dots after
After each multiplication, let's tab or start writing each row one digit to the left, from top to bottom. adding zeros (in red) .
So the product of 78.93 x 32.4 = 2557.332
2 cups of blue paint was mixed with 10 cups of yellow paint to make aparticular shade of green. How much thue paint will be needed to make the sameshade of green, using 600 cups of yellow paint?
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Step 1 : To make a particular shade of green, we use 2 cups of blue paint and 10 cups of yellow paint, this ratio is expressed below
[tex]\begin{gathered} 2\text{ blue cups : 10 yellow cups}\Rightarrow\text{ green} \\ 2\colon10\Rightarrow1\colon5 \end{gathered}[/tex]Step 2: To obtain the number of cup of blue paint to mix with 600 cups of yellow paint to have the same shade of green, let the number of cups be x, then we will have
[tex]\begin{gathered} x\text{ blue cups : 600 yellow cups}\Rightarrow\text{ Green} \\ x\colon600 \end{gathered}[/tex]Step 3: Since we will have the same shade of green with the second mixture, then;
[tex]\begin{gathered} 1\rightarrow5 \\ x\rightarrow600 \end{gathered}[/tex]By cross multiplying
[tex]\begin{gathered} 5(x)=1(600)^{} \\ 5x=600 \end{gathered}[/tex]Divide both side by 5 to find x
[tex]\begin{gathered} \frac{5x}{5}=\frac{600}{5} \\ x=120 \\ \end{gathered}[/tex]Hence, it will take 120 cups of blue paint to be mixed with 600 cups of yellow paint to have the same shade of green
The answer is 120 cups of blue paint
What is the surface area of a cylinder with a radius of 8 yd and a height of 6 yd.
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We need to find the surface area of a cylinder with a radius of 8 yd and a height of 6 yd. This cylinder and its lateral surface are shown below:
Notice that its lateral surface corresponds to a rectangle with a width equal to the height of the cylinder, and a length equal to the perimeter of the cylinder's base.
Thus, the lateral surface area is given by:
[tex]6\text{ yd}\cdot2\pi8\text{ yd }=96\pi\text{ yd}^2[/tex]And the area of each base is the area of a circle with a radius of 8 yd:
[tex]\pi(8\text{ yd})^2=64\pi\text{ yd}^2[/tex]Since it has a top and a bottom base, we need to multiply the last result by two and then add it to the lateral surface area to find the total surface area. We obtain:
[tex]2\cdot64\pi\text{ yd}^2+96\pi\text{ yd}^2=224\pi\text{ yd}^2[/tex]If we approximate the answer to one decimal place, we obtain:
[tex]703.7\text{ yd}^2[/tex]Answer: Approximately 703.7 yd²
As the number of years decreases from 3 to 2 in the following graph, does the population increase, decrease, or remain the same?
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Statement Problem: As the number of years decreases from 3 to 2 in the following graph, does the population increase, decrease or remain the same?
Solution:
From the graph provided;
As the time (number of years) reduces from 3 to 2, the population increases
if using the method of completing the square to solve te quadratic equation x squared+4x+3=0, which number would have to be added to complete the square
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The quadratic equation is given as,
[tex]x^2+4x+3=0[/tex]Apply the Method of Completing Squares as follows,
[tex]\begin{gathered} (x)^2+2(x)(2)+(2)^2-(2)^2+3=0 \\ (x+2)^2=4-3 \\ (x+2)^2=1 \\ x+2=1\text{ or x+2=-1} \\ x=1-2\text{ or }x=-1-2 \\ x=-1\text{ or }x=-3 \end{gathered}[/tex]Thus, the roots of the given equation are -1 and -3.
fx D Triangle ABC with vertices A(2,-2) B(2,-7) C(8,-7) Translate 2 units right and 3 units up then Rotate 180 degrees. What are the coordinates of the final image?
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So the answer is: the coordinates are H(4, -4), I(-2, -4) and G(4, -9).
Find the selling price of a $65 item after a 40% markup.
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the selling price is $ 91
Explanation
to solve this we can use a rule of three
let x represents the selling price
hence
if
[tex]\begin{gathered} 100\text{ \%}\Rightarrow\text{ \$ 65} \\ \text{then} \\ 140\text{ \%}\Rightarrow\text{ x} \end{gathered}[/tex]hence
the proportion is
[tex]\frac{100}{65}=\frac{140}{x}[/tex]solve for x
[tex]\begin{gathered} \frac{100}{65}=\frac{140}{x} \\ 100x=140\cdot65 \\ x=\frac{140\cdot65}{100} \\ x=91 \end{gathered}[/tex]therefore, the selling price is $ 91
Given B(17, 5), C(11, -3), D(-1, 2), and E(x, -6), find the value of x so that BC is parallel to DE
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First we need to find the equation of the line BC
B (17,5)=(x1,y1)
C(11,-3)=(x2,y2)
First we need to find the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m=\frac{-3-5}{11-17}=\frac{-8}{-6}=\frac{4}{3}[/tex]Because DE is parallel to BC they have the same slope
D(-1,2)=(x1,y1)
E(x,-6)=(x2,y2)
[tex]m=\frac{4}{3}=\frac{-6-2}{x+1}=\frac{-8}{x+1}[/tex][tex]\frac{4}{3}=\frac{-8}{x+1}[/tex][tex]\frac{(x+1)4}{3}=-8[/tex][tex]\frac{4x+4}{3}=-8[/tex][tex]4x+4=-8(3)[/tex][tex]4x+4=-24[/tex][tex]4x=-24-4[/tex][tex]4x=-28[/tex][tex]x=\frac{-28}{4}=-7[/tex]x=-7
If the incandescent 100 - watt light bulb is left on for 168 hours ( a whole week),and it costs $0.12 per kwh ,how much does it cost for this lightbulb?A: $20.20B: $2.02 C:20.16D: $0.16
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Suppose that the light bulb consumes 100W per hour, in other words, 0.1kWh. Therefore, in 168 hours, the total energy consumption is
[tex]0.1\text{kWh}\cdot168\text{hrs}=16.8kW=16.8\cdot1000W=16800W[/tex]Thus, the total cost is
[tex]0.12\cdot16.8=2.016\approx2.02[/tex]The answer is, approximately $2.02, option B.
If two lines are perpendicular,then the slope of one is thenegative reciprocal of the slopeof the other. What is the slopeof the line that is perpendicularto the line 5x - 2y = 7?
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First, convert the given equation into slope-intercept form by solving in terms of y
[tex]\begin{gathered} 5x-2y=7 \\ -2y=-5x+7 \\ \frac{-2y}{-2}=\frac{-5x+7}{-2} \\ y=\frac{5x}{2}-\frac{7}{2} \\ \\ \text{The slope of the line therefore is }m=\frac{5}{2}. \end{gathered}[/tex]Get the negative reciprocal of the slope and we get
[tex]\begin{gathered} \frac{5}{2}\Longrightarrow-\frac{2}{5} \\ \\ \text{Therefore, the slope of the line that is perpendicular to the line} \\ 5x-2y=7\text{ is }-\frac{2}{5} \end{gathered}[/tex]What type of number is -47?Choose all answers that apply:AWhole numberBIntegerсRationalIrrational
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The whole numbers are all positive numbers without decimal or fraction
Integers are all numbers (positive, negative, and zero) without fraction or decimal
Rational numbers are all numbers that can be written in the form of a fraction
Irrational numbers are the numbers that have approximated values like the roots of the number, not a square number
Since -47 is a negative number and has no decimal or fraction part, then it is
Integer
Rational
The answers are B and C
-5x+7=52how would i answer this
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Answer:
x = - 9
Explanation:
The given equation is
- 5x + 7 = 52
We want to solve for x
Subtracting 7 from both sides, it becomes
- 5x + 7 - 7 = 52 - 7
- 5x = 45
Dividing both sides of the equation by - 5, we have
- 5x/- 5 = 45/- 5
x = - 9
find the coordinates of dilation of (3,-4) by scale factor of 3
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find the coordinates of dilation of (3,-4) by scale factor of 3
the rule of teh dilation is
(x,y) -------> (ax,ay)
where a is the scale factor
In this problem
a=3
so
(3,-4) --------> (9,-12)
answer is (9,-12)Which algebraic expression represents "the product of a number and five"?5+пОООО
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EXPLANATION
The algebraic expression that represents "the product of a number and five" is 5n
Graph y intercept (0,5) and axis of symmetry is x=3
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Given:
[tex]\begin{gathered} y-\text{ntercept}=(0,5) \\ \text{axis of symmetry, x = 3} \end{gathered}[/tex]The above is what the given can produce
Determine whether the equation below has one solutions, no solutions, or an infinite number of solutions . Afterwards, determine two values of x that support your conclusion.x = x + 2
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x = x + 2
For this kind of equation, the general rule applies which is, collect like terms. That is, bring the unknown variables to one side of the equation and bring the known (or constants) to the other side.
We move the x on the right to the left and we now have this;
x - x = 2
**Note that when a positive value crosses from one side of the equation to the other, it becomes negative (and vice versa). Hence x has now become a negative as soon as it crossed to the left.**
x - x = 2
0 = 2
Now we know that this is not possible, that is 0 does not equal to 2.
At this point its safe to say that the equation has NO SOLUTION.
This is because upon close observation, the equation ideally should read;
x = x
However, the moment the constant 2 comes into the equation, then the value of x on the left must change by a factor of "+ 2"
In conclusion, there is no value of x that can satisfy this equation. Because if you attempt to input "x = 0 on one side of the equation, you MUST do the same on the other side of the equation.
PLEASE HELP!!To the nearest square unit, what is the area of the regular heptagon shown below? A.2772 square unitsB.1572 square unitsC.792 square unitsD.5545 square units
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We are given an heptagon. NOte that we can divide the heptagon in triangles as follows
(The picture is an approximation).
This triangles are all the same , so to calculate the area of heptagon, we simply calculate the area of one of the triangles and then multiply it by 7.
We have the following triangle
REcall that the area of a triangle of base b and height h is given by the formula
[tex]\frac{b\cdot h}{2}[/tex]By taking b=20.8 and h = 21.6, we get
[tex]\frac{20.8\cdot21.6}{2}=224.64[/tex]So, the whole area would be
[tex]7\cdot224.64\text{ =1572.48}[/tex]which rounded to the nearest square unit is 1572
Put these points into an equation IN STANDARD FORM!!!!
(6,0) and (0,4)
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The equation of the line in standard form is 2x + 3y = 12
How to determine the line equation?From the question, the points are given as
(6, 0) and (0, 4)
To start with, we must calculate the slope of the line
This is calculated using
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (6, 0) and (0, 4)
Substitute the known parameters in Slope = (y₂ - y₁)/(x₂ - x₁)
So, we have
Slope = (4 - 0)/(0 - 6)
Evaluate
Slope = -2/3
The equation of the line can be calculated using as
y - y₁ = m(x + x₁)
Where
(x₁, y₁) = (0, 4) and m = slope = -2/3
Substitute the known values in the above equation
So, we have the following equation
y - 4 = -2/3(x - 0)
This gives
y - 4 = -2/3x
Rewrite as
2/3x + y = 4
Multiply by 3
2x + 3y = 12
Hence, the line has an equation of 2x + 3y = 12
Read more about linear equations at
brainly.com/question/4074386
#SPJ1
can you please help me find the answer to the question?
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To determine the distance between the forest ranger and the fire, simply use the trig. ratio
Let the distance between the forest ranger and the fire
we have: angle theta = 18 degree
adjacent=350 and opposite = x
The best trig. ratio to use is:
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex][tex]undefined[/tex]For the following problem, the answers is given. Show the calculations that are needed to get to the answer.ProblemSolutionSolve this system of equations:X = 10a) - 4x - 3y = -22y = -6b) 4x - 14y = 124Show your work here:
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Solution:
Given the system of equations;
[tex]\begin{gathered} -4x-3y=-22\ldots\ldots\ldots\text{.equation}1 \\ 4x-14y=124\ldots.\ldots\text{.}\mathrm{}\text{equation}2 \end{gathered}[/tex]We would show calculation that lead to the answer by elimination method.
STEP 1: Add equation 1 to equation 2;
[tex]\begin{gathered} -4x+4x-3y+(-14y)=-22+124 \\ -17y=102 \end{gathered}[/tex]STEP 2: Divide both sides by -17;
[tex]\begin{gathered} -\frac{17y}{-17}=\frac{102}{-17} \\ y=-6 \end{gathered}[/tex]STEP 3: Substitute the value of y in equation 1;
[tex]\begin{gathered} -4x-3y=-22 \\ -4x-3(-6)=-22 \\ -4x+18=-22 \\ \end{gathered}[/tex]STEP 4: Subtract 18 from both sides;
[tex]\begin{gathered} -4x+18-18=-22-18 \\ -4x=-40 \end{gathered}[/tex]STEP 5: Divide both sides by -4;
[tex]\begin{gathered} -\frac{4x}{-4}=-\frac{40}{-4} \\ x=10 \end{gathered}[/tex]Thus, the solution of the system of equation is;
[tex]x=10,y=-6[/tex]if 75 equals 17 multiplied by 2 divided by 84628277 and you find the square root what is the answer in fraction form
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In triangle ABC, A is a right angle and mB = 45. Find BC. If your answer is not an integer, leave it in simplest radical form. Not drawn to scale O 20 ft 10 ft 20 2 ft 10 2 ft
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as we have a right triangle, we can use a trigonometric function to find the hypotenuse
so
Step 1
a)Let
[tex]\begin{gathered} angle=m\measuredangle B=45 \\ opposite\text{ side=10 ft} \\ hypotenuse=BC \end{gathered}[/tex]so, we need a function that relates those values, it is
[tex]sin\theta=\frac{opposite\text{ side}}{hypotenuse}[/tex]b) now, replace and solve for hypotenuse
[tex]\begin{gathered} sin\theta=\frac{opposite\text{ side}}{hypotenuse} \\ sin\text{ 45=}\frac{10}{BC} \\ isolate\text{ BC} \\ BC=\frac{10}{sin\text{ 45}} \\ BC=\frac{10}{\frac{\sqrt{2}}{2}}=\frac{20}{\sqrt{2}} \\ BC=\frac{20}{\sqrt{2}} \\ Multiply\text{ by }\frac{\sqrt{2}}{\sqrt{2}} \\ BC=\frac{20}{\sqrt{2}*}\frac{\sqrt{2}}{\sqrt{2}} \\ BC=\frac{20\sqrt{2}}{2}=10\sqrt{2} \\ BC=10\sqrt{2} \end{gathered}[/tex]so, the answer is
[tex]10\sqrt{2}\text{ ft}[/tex]I hope this helps you
In the equation y=4x+5,if the 4 was changed to 6, how would the graph of the line be affected?
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If we change the value of the slope of the equation by 6, the line will be steeper, that is, it will have a larger angle regarding the x-axis.
We can see this because the value of 4 is actually the value for the slope. With a slope of 6, the value of the slope increases. We can see this graphically:
This is sketched in the graph. The red line is the equation y = 4x + 5, and the blue line is the equation y = 6x +5. The line in blue has a greater angle with respect to the x-axis. It is steeper.
Then the option is STEEPER.
If A denotes the area of the sector of a circle of radius r formed by the central angle 0, find the missing quantity. Ifnecessary, round the answer to two decimal places.6) r = 8 inches, 0 = 5 radians, A = ?F) 40 in2G) 160 in2H) 20 in2J) 320 in2
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In order to find the area A of the sector of the given circle, use the following formula:
A = 1/2·r²θ
where θ is in radians.
In this case, you have r = 8 in and θ = 5 radians. Replace these values into the formula for A:
A = 1/2·(8 in)²(5 rad)
A = 160 in²
Hence, the area of the sector is 160 in²
6. Solve for x and y. I H EH = FH = HG
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In the figure shown, triangle EHF is an isosceles triangle. Lines EH equals FH (as shown by the strokes on the line segments). Therefore;
[tex]\begin{gathered} EH=FH \\ 9x-2=7x+4 \\ \text{Collect like terms and you'll have;} \\ 9x-7x=4+2 \\ 2x=6 \\ \text{Divide both sides by 2} \\ x=3 \\ \text{Also, triangle EGH is isosceles, therefore;} \\ EH=HG \\ 9x-2=5y \\ 9(3)-2=5y \\ 27-2=5y \\ 25=5y \\ \text{Divide both sides by 5} \\ 5=y \end{gathered}[/tex]Therefore x = 3
y = 5
which two expressions are equivalent F. 2× +24 and 2(×+4 G. 9+3× and 3(3+× H. 4(×-1) and 4×-14 J 5(2x-1) and 5x-5
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The expressions we have are:
[tex]\begin{gathered} 2x+24\text{ and }2(x+4) \\ 9+3x\text{ and }3(3+x) \\ 4(x-1)\text{ and }4x-14 \\ 5(2x-1)\text{ and }5x-5 \end{gathered}[/tex]To find the correct answer, we have to use the distributive property on the options and check if the expressions are the same.
Let's analyze the options:
In option F we have:
[tex]2x+24\text{ and }2(x+4)[/tex]We need to use distributive property on the second expression and check if we get the same as in the first of the expressions.
[tex]2(x+4)[/tex]Distributive property tells us to multiply the outside number by both of the terms inside the parenthesis:
[tex]2\cdot x+2\cdot4[/tex]Solving the multiplications:
[tex]2x+8[/tex]This is different from 2x+24, so the expressions are not equivalent.
In Option G we have:
[tex]9+3x\text{ and }3(3+x)[/tex]Using distributive property on the second expression:
[tex]3(3+x)=3\cdot3+3\cdot x=9+3x[/tex]As we can see, the second expression is 9+3x, which is also the first expression, this means that the expressions are EQUIVALENT.
Answer: G
[tex]9+3x\text{ and }3(3+x)[/tex]
Describe what it means to bisect an arc.
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Answer
To bisect any segment of a line, arc or a figure simply means dividing that segment into two.
And to bisect an arc, the image below for bisecting an arc AB will help the explanation.
The first step to bisecting an arc is to place the pin end of the compass on each of the ends of the arc, that is, first at point A and then point B,
Then, an arbitrary arc is then drawn for these two cases.
The points where the two arcs drawn meet are then connected to each other using a straight line.
This straight line then bisects the arc AB.
Hope this Helps!!!