Since the denominator of 2/9 is 9, 2/9 is equal to a repeating decimal.
[tex]\frac{2}{9}=0.222222\ldots=0.\bar{2}[/tex]Answer: repeating decimal
solve for the value of s
110°
(8s-2)°
The value of s for equation 110=8s-2 will be 14 by solving the linear equation.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7. a formula that expresses the connection between two expressions on each side of a sign. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
Here,
110=8s-2
8s=112
s=14
By resolving the linear equation, we obtain the value of s for equation 110=8s-2 as 14.
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9. A coin is tossed and a number cube is rolled. What is the probability of getting tails and rolling a two?
Okay, here we have this:
Considering the provided information, we are going to calculate the requested probability, so we obtain the following:
Probability of getting tails and rolling a two=Probability of getting tails * Probability of getting a two
And basing ourselves on the fact that when tossing a coin there are two possible events and in this case a favorable one, and when tossing the die there are 6 possible events and one favorable for this case, we have:
Probability of getting tails and rolling a two=1/2*1/6
Probability of getting tails and rolling a two=1/12
Finally we obtain that the probability of getting tails and rolling a two is 1/12.
please explain steps to get correct answer in pic below
Let's use the properties of the sum:
[tex]\begin{gathered} \sum ^{11}_{i\mathop=1}(3i^2+17)=\sum ^{11}_{i\mathop{=}1}3i^2+\sum ^{11}_{i\mathop{=}1}17 \\ =3\sum ^{11}_{i\mathop{=}1}i^2+17\cdot11 \end{gathered}[/tex]Therefore the answer is the last option.
To simplify this we use the properties listed below:
[tex]\sum ^n_{i\mathop{=}1}na_i=n\sum ^n_{i\mathop{=}1}a_i[/tex][tex]\sum ^n_{i\mathop{=}1}(a_i+b_i)=\sum ^n_{i\mathop{=}1}a_i+\sum ^n_{i\mathop{=}1}b_i[/tex][tex]\sum ^n_{i\mathop{=}1}c=cn[/tex]which of the following does not show the commutative property of addition 9+x=x+9a+b=b+aab=ba3x+4y=4y+3x
The commutative property of addition is such that two or more values or numbers when added up ould alays have the same result no matter how the numbers are rearranged.
Options 1, 2 and 4 shows the commutative property of addition, but OPTION 3 DOES NOT.
The correct answer here is option 3, hich is
ab = ba
find each measure 113° 23°x=?
We have that a vertex outside a circle is just the half of the difference of the angles:
Then, in this case:
[tex]x=\frac{113-23}{2}=\frac{90}{2}=45[/tex]Answer: x = 45º
A 20% tip on a $26.00 dinner bill ishow much money?
Mela, this is the solution:
Dinner bill = $ 26
Tip = 20% or 0.2
Tip = 26 * 0.2
Tip = $ 5.20
The fancy restaurant Mackenzie atel at was having asale so her dinner was 80% of the original cost. Theoriginal cost of her dinner was $20.00. What is the saleprice?
Given data:
The original cost of dinner C=$20.00.
The sale price is 80% of the original cost.
[tex]\begin{gathered} S=\frac{80}{100}(20)_{} \\ =0.8(20) \\ =16 \end{gathered}[/tex]Thus, the final sale price is $16.00.
Find AB. A =20B = 10C = 54 D = 12
Answer:
C. 54
Explanation:
The triangles ABD and ACD are congruent by SAS (Side - angle - side) becuase
AD is congruent to itself
∠ADB = ∠ADC
BD is congruent to CD
So, the length of AB is equal to the length of AC and we can write the following equation
AB = AC
4x + 6 = 5x - 6
Solving for x, we get:
4x + 6 + 6 = 5x - 6 + 6
4x + 12 = 5x
4x + 12 - 4x = 5x - 4x
12 = x
Then, the length of AB is
AB = 4x + 6
AB = 4(12) + 6
AB = 48 + 6
AB = 54
Therefore, the answer is
C. 54
Find the equation of the line in standard form that passes through the following points simplify your answer
Given: Two points
[tex]\begin{gathered} Point1:(10,11) \\ Point2:(10,7) \end{gathered}[/tex][tex]\begin{gathered} Point1:(10,11) \\ Point2:(10,7) \end{gathered}[/tex]To Determine: The equation of the line in standard form that passes through the given points
Solution
The equation of a line passing through two different points is given as
[tex]\begin{gathered} Point1:(x_1,y_1) \\ Point2:(x_2,y_2) \\ \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Substitte the given coordinates of the points given into the formula
[tex]\begin{gathered} \frac{y-11}{x-10}=\frac{7-11}{10-10} \\ \frac{y-11}{x-10}=\frac{-4}{0} \\ cross-multiply \\ Since\text{ the slope is undefine} \\ The\text{ equation of the line is } \\ x=10 \end{gathered}[/tex]The standard form of a line is given as
[tex]Ax+By=C[/tex]But since the x-coordinates of the points are equal, then the formula for slope is not applicable (the denominator equals 0).
In this case, we say that the slope is undefined (the line is vertical).
This means that the equation of the line doesn't contain y.
Thus, the equation of the line is x=10.
Answer: the slope is undefined.
The equation of the line is x = 10.
dividing 5 by 10 + 1
Please see the picture for the question and my answer is wrong
Given sentence:
Five more than half the input is the output
y is the output, x is the input
To interpret the sentence, we should break it into parts:
-half the input: we half the input
- 5 more than we add 5 to the new input
- the sum of these is the output
The equation that represents the given sentence:
[tex]y\text{ = 5 + }\frac{1}{2}x[/tex]Answer:
[tex]y\text{ = 5 + }\frac{1}{2}x[/tex]Solve the equation. |k + 6| = 3
Question 7 options:
{–3, 9}
{–3, 3}
{–9, –3}
{all real numbers greater than or equal to –9 and less than or equal to –3}
Step-by-step explanation:
k= {-3,-9}
Because || always gets positive numbers.
For example |-5|=5, and |5|=5.
so |-9+6|=|-3| which is |-3|=3
and |-3+6|=|3| which is equal to 3.
Answer:
c) k = {-9,-3}
Step-by-step explanation:
Given equation,
→ |k + 6| = 3
Now the value of k will be,
→ |k + 6| = 3
→ k + 6 = 3 || → -(k + 6) = 3
→ k = 3 - 6 || → -k = 3 + 6
→ [ k = -3 ] || → [ k = -9 ]
Hence, value of k is -3 & -9.
an object is thrown upward from the top of a 160 foots building with an initial velocity of 48 feet per second .solve the equation -16^2 + 48t + 160=0 find the time(t) in seconds at which the object hits the ground.
The given equation represents the distance travelled by the object at time t.
The given equation is expressed as
-16t^2 + 48t + 160
At the point where it hits the ground, the distance woule be 0. Thus, we would so;ve the equation,
-16t^2 + 48t + 160=0
We would divide through by - 16. We have
t^2 - 3t - 10 = 0
We would find two terms such that their sum or difference is - 3t and their product is - 10t^2. They are 2t and - 5t. We have
t^2 + 2t - 5t - 10 = 0
By factorising, we have
t(t + 2) - 5(t + 2) = 0
(t + 2)(t - 5) = 0
t + 2 = 0 or t - 5 = 0
t = - 2 or t = 5
Since the time cannot be negative, the correct answer is
time = 5 seconds
5/3×(-3/4) what's the answer
using the definition of multiplication between two fractions
[tex]\frac{a}{b}\times\frac{c}{d}=\frac{a\cdot c}{b\cdot d}[/tex]we obtain,
[tex]\frac{5}{3}\times-\frac{3}{4}=-\frac{5\cdot3}{3\cdot4}=-\frac{5}{4}[/tex]Which equation is true when the value of x is -12
We are told to check for the correct equation that satisfies when the value of x = -12.
Let us resolve that by picking one of the options and testing it to confirm if it satisfies the value of x = -12.
Starting with OPTION B
[tex]15-\frac{1}{2}x=21[/tex]Solve for x
Subtract 12 from both sides
[tex]\begin{gathered} 15-15-\frac{1}{2}x=21-15 \\ -\frac{1}{2}x=6 \end{gathered}[/tex]Multiply both sides by 2
[tex]\begin{gathered} 2\times-\frac{1}{2}x=2\times6 \\ -1x=12 \end{gathered}[/tex]Divide both sides by -1
[tex]\begin{gathered} \frac{-1x}{-1}=\frac{12}{-1} \\ x=-12 \end{gathered}[/tex]From the solution, we can conclude that the above equation is true when the value of x = -12.
The correct option is Option B.
Simplify 5(3p - 2) + 2(p +4)
Here, we want to simplify the expression
To do this, we shall use the term outside the bracket to multiply the terms inside the brackets before we proceed to add them together
We have this as follows;
[tex]\begin{gathered} (5\times3p)-(5\times2)\text{ + (2}\times p_{})\text{ + (2}\times4) \\ =\text{ 15p - 10 + 2p + 8} \\ =\text{ 15p}+2p-10+8 \\ =\text{ 17p -2} \end{gathered}[/tex]Mary is 4 years older than Sue. If the sum of their ages is 16. How would you set up the equations?
Answer:
A. x=y-4, x+y=16
C. x=y-4, x+y=16
Explanation:
• Let Sue's age = x
Mary is 4 years older than Sue, therefore:
• Mary's age, y = x+4
[tex]\begin{gathered} y=x+4 \\ \implies x=y-4 \end{gathered}[/tex]Next, the sum of their ages is 16. This gives:
[tex]x+y=16[/tex]Therefore, the equation is:
[tex]\begin{gathered} x=y-4 \\ x+y=16 \end{gathered}[/tex]The correct choices are A and C.
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. A flashlight is projecting a triangle onto a wall, as shown below. A The original triangle and its projection are similar. What is the missing length n on the projection? O 35 0224 10 40
We can see that the scale factor from the smaller triangle to the projected triangle is 2.
Multiply each length of the original triangle by the scale factor, to obtain the side lengths of the second triangle:
15 x 2 = 30
15x 2 = 30
20 x 2 = 40
answer : 40
which line is steeper y=+2 or y= -7/3x -5
The inclination of the lines in the coordinate system is given by their slopes, so to determine which line is steeper you have to compare the absolute values of both slopes.
The first equation y=2 has no slope, if you draw it you will see that for any value of x, y doesn't change, it is always 2.
You can also say that the slope of this equation is equal to zero.
For the second equation y=-7/3x-5, the slope is equal to -7/3.
The second equation is steeper than the first one since the absolute value of its slope is greater.
Which equation represents the graphed function?1. y=4x-22. y=-4x-23. y=1/4x-24. y=-1/4x-3
The general equation of a line is:
[tex]y=m\cdot x+b[/tex]Where m is the slope of the line and b its the value of the y-intercept of the line.
Q) The question asks about the equation of a graphed line.
A) In order to find the equation of the line, we note that it passes through the points:
[tex]\begin{gathered} (x_1,y_1)=(0,-2) \\ (x_2,y_2)=(4,-1) \end{gathered}[/tex]The first point give us the value of the y-intercept of the line (b), so the y-intercept is y = -2, and we have:
[tex]b=-2[/tex]Now we must calculate the slope (m) of the line. In general the slope of a line is given by the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1,y1) and (x2,y2) are the coordinates of two points of the line. Using the points of above and the last formula we find that:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-(-2)}{4-0}=\frac{2-1}{4}=\frac{1}{4}[/tex]Answer
Using the values of m and b, and the general equation, we find that the equation of the line is:
[tex]y=m\cdot x+b=\frac{1}{4}x-2[/tex]Or: y = 1/4 x - 2
So the correct option is option number 3.
Which of the following sa rational number? [tex] \sqrt{5} [/tex][tex] - \frac {3}{4} [/tex]Pi[tex] - \sqrt{7} [/tex]
First of all, we need to remember what is a rational number.
In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.
Now, from your options we can deduce that:
[tex]\frac{3}{4}[/tex]is the rational number.
How much money will he raise based on the two donations?
The neighbor will donate $0.25 for every 40ft run.
The aunt will donate $18 for every mile run.
To determine how much he will raise if he runs 5miles, you have to calculate the amount per donor and then add them:
Neighbor
1 mile is equal to 5280 feet
To determine how many feet correspond to 5 miles, multiply the distance by 5280
[tex]5\cdot5280=26400ft[/tex]Next, calculate how much we will make:
40ft → $0.25
26400ft → $x
[tex]\begin{gathered} \frac{0.25}{40}=\frac{x}{26400} \\ 26400\cdot\frac{0.25}{40}=26400\cdot\frac{x}{26400} \\ 165=x \end{gathered}[/tex]For running 5miles, Dustin will raise $165 from the neighbor.
Aunt
The aunt will donate $18 per mile run, to determine how much she will donate, multiply $18 by 5
[tex]18\cdot5=90[/tex]For running 5 miles, Dustin will raise $90 from the neighbor.
Next, add both amounts:
[tex]165+90=255[/tex]Dustin will raise $255 for running 5 miles.
Find -7/8 - 2 1/6. Write your answer as a mixed number in simplest form.
Answer:
3 1/24
Step-by-step explanation:
How would you solve this question or similar questions? It is solving for x.
Given the initial expression
[tex]\sqrt[]{2x+3}=\sqrt[]{2x}+3[/tex]Then,
[tex]\begin{gathered} \sqrt[]{2x+3}=\sqrt[]{2x}+3 \\ \Rightarrow(\sqrt[]{2x+3})^2=(\sqrt[]{2x}+3)^2 \\ \Rightarrow2x+3=2x+6\sqrt[]{2x}+9 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \Rightarrow3=6\sqrt[]{2x}+9 \\ \Rightarrow-6=6\sqrt[]{2x} \\ \Rightarrow\sqrt[]{2x}=-\frac{6}{6}=-1 \\ \Rightarrow\sqrt[]{2x}=-1 \\ \Rightarrow\sqrt[]{2}\sqrt[]{x}=-1 \\ \Rightarrow\sqrt[]{x}=-\frac{1}{\sqrt[]{2}} \end{gathered}[/tex]And sqrt(x)>=0 for any real number.
Therefore, there is no real solution to the equation.
The total annual sales for Herman's Hardware Store was $1,246,135 and the total accounts receivable was $41,728. What was the average collection period to the nearestwhole day?12 days14 days18 days24 daysNone of these choices are correct.
The average collection Period formula is
[tex]\text{Average collection period=}\frac{Account\text{ receivable}}{\frac{Annual\text{ sales}}{365}}[/tex][tex]\begin{gathered} \text{Annual sales=\$1,246,135} \\ \text{Account receivable =\$41,728} \end{gathered}[/tex]Substitute the values above in the average collection period
[tex]\begin{gathered} \text{Average collection period =}\frac{41728}{\frac{1246135}{365}} \\ =\frac{41728}{3414.06} \\ =12.222 \\ \approx12days \end{gathered}[/tex]Hence the average collection period to the nearest whole day is 12 days
I need help with this work question 10Find the area of each regularpolygon. Leave your answer insimplest form.
Given:
Number of sides in octagon = 8
Length of apothem = 14.1
Side length = 11.7
Required: Area
Explanation:
The area of a regular polygon is one-half the product of its apothem and its perimeter.
Here, the area of the regular octagon is
[tex]\begin{gathered} A=\frac{1}{2}ap \\ =\frac{1}{2}\times14.1\times8\times11.7 \\ =659.88 \end{gathered}[/tex]Final Answer: Area of the regular octagon is 659.88 square units.
84 is 75% of what number
Answer:
112
Explanation:
We need to find a number that represents 100% when 84 represents 75%, so we will use the following
[tex]100\text{ \% }\times\frac{84}{75\text{ \%}}=\frac{100\times84}{75}=\frac{8400}{75}=112[/tex]Therefore, 84 is 75% of 112.
Answer:112
Step-by-step explanation: - 84 is 75% of 112. 100% of 112 is 112, hope this helps
Solve the y system of inequalities by choosing the correct graph.y> 3y< |x-2|
The solution graph of the system of inequalities : y> 3 and y< |x-2| is attached below.
The given inequalities are:
y>3 and y< |x-2|
Now we will solve y< |x-2|
applying absolute value we get
x - 2 < -y or x - 2 > y
Now we will solve the two equations graphically.
Using the graph we can clearly see that the red part represents the inequality y< | x - 2 | while the blue part denotes the inequality y > 3
Hence the solution of the two inequalities will be the region shaded by both the graphs.
Any monotonically increasing function can, by definition , be applied both for sides of just an inequality without distorting their relationship as long as both expressions fall inside the scope of the function. If a monotonically falling function are applied to both sides of an inequality, the inequality relation might be reversed.
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How many ways can the 4 flowers be chosen?Jeanine Baker makes floral arrangements. She has 16 different cut flowers and plans touse 4 of them. How many different selections of the 4 flowers are possible?vaTO#.voMore(1,1)Clear AllHelp Me Solve ThisView an ExampleGet More Help
Given:
Jeanine Baker makes floral arrangements. She has 16 different cut flowers and plans to use 4 of them
We will find a number of ways to select of the 4 flowers
As the arrangement is not necessary
We will use the combinations
So, the number of ways =
[tex]16C4=\frac{16!}{(16-4)!\cdot4!}=1820[/tex]So, the answer will be 1820 possible ways to select 4 flowers
Write the inequality shown by the shaded region in the graph with the boundary line y = 1/3x+1
From the graph, the suitable inequality is
[tex]y\leq\frac{1}{3}x+1[/tex]