SOLUTION
The terms below make an A.P. Now we are told to find the sum of the AP.
Sum of an AP is given by
[tex]S\text{ = }\frac{n}{2}\lbrack2a\text{ + (n-1)d\rbrack}[/tex]Where S = sum of the AP, a = first term = 9, d = -5, n= ?
So we have to find n first before we can find the sum. The nth term which is the last term = -536. So we will use it to find the number of terms "n"
[tex]\begin{gathered} \text{From T}_{n\text{ }}=\text{ a +(n-1)d where T}_{n\text{ }}=\text{ -536} \\ -536\text{ = 9+(n-1)-5} \\ -536\text{ = 9-5n+5} \\ -536\text{ = 14-5n} \\ -5n\text{ = -536-14} \\ -5n\text{ = -550} \\ n\text{ = 110} \end{gathered}[/tex]Now let's find the sum
[tex]\begin{gathered} S\text{ = }\frac{n}{2}\lbrack2a\text{ + (n-1)d\rbrack} \\ S\text{ = }\frac{110}{2}\lbrack2\times9\text{ + (110-1)-5\rbrack} \\ S\text{ = 55\lbrack{}18+(119)-5\rbrack} \\ S\text{ = 55\lbrack{}18 - 595\rbrack} \\ S\text{ = 55}\times-577 \\ S\text{ = -31735} \end{gathered}[/tex]Therefore, the sum = -31735
Find the coordinates of each point under the given rotation about the origin (-5, 8); 180
As given by the question
There are given that the point, (-5, 8).
Now,
The given coordinate of point (-5, 8) which is lies on the second quadrant.
Then,
According to the question,
Rotate it through 180 degree about the origin
Then,
The given coordinate move from 2nd quadrant to 4th, where the value of x is positive and y is negative
Then,
The new coordinat will be, (5, -8).
Hence, the coordinate is (5, -8).
determine the area of the shaded regionA. 6 square unitsB. 19 square unitsC.20 square unitsD. 25 square units
area of the square:
[tex]\begin{gathered} a=l\times l \\ a=5\times5 \\ a=25 \end{gathered}[/tex]area of the rectangle
[tex]\begin{gathered} a=b\times h \\ a=3\times2 \\ a=6 \end{gathered}[/tex]area of the shaded region:
area of the square - area of the rectangle = area of the shaded region
[tex]25-6=19[/tex]answer: B 19 saquare units
The angle of elevation to the top of a Building in New York is found to be 7 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building.
_________ feet
The height of the building is 649.44 feet
Given,
The angle of elevation of the building from ground = 7°
The distance from base of the building to the angle = 1 mile
We have to find the height of the building:
As this information are noted, we will get a right angled triangle(image attached).
So, by trigonometry:
Tanθ = opposite side / adjacent side
here,
θ = 7 degree
opposite side = x
adjacent side = 1 mile
Then,
Tanθ = opposite side / adjacent side
tan(7°) = x / 1
x = tan(7°) × 1
x = 0.123 × 1
x = 0.123 miles
1 mile = 5280 feet
Then,
0.123 miles = 0.123 × 5280 = 649.44 feet
That is,
The height of the building is 649.44 feet.
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720÷5 WORK OUT NEEDED
144
Explanation:[tex]720\text{ }\div\text{ 5}[/tex]working the division:
The process:
7 ÷ 5 = 1 R 2
add the 2 to the next number: this gives 22
22 ÷ 5 = 4 R 2
add 2 to the next number: this gives 20
20 ÷ 5 = 4 R 0
The result of 720 ÷ 5 = 144
In the following expression, place a decimal point in the divisor and the dividend that is 4368÷6208 to create a new problem with the same answer as in question 11 that is 7 meters / 7
---------------------------------
436.8m -------------------> 62.08s
xm -------------------------->1s
Using cross multiplication:
[tex]\begin{gathered} \frac{436.8}{x}=\frac{62.08}{1} \\ \text{solve for x:} \\ x=\frac{436.8}{62.08} \\ x=7.036082474m \\ \end{gathered}[/tex]if two angles measure 90 and are complementary and congruent, the measure of each angle is
Leonardo, the answer is
45 degrees.
I need help with a word problem in algebra 2 please
We were given the following information:
Plan 1
Cost = $175
It has unlimited call & texts as well as 15gb
Plan 2
Cost = $50 per month
It has unlimited call & texts as well as 6gb
After 6gb, data is charged $5 per gb
From this we have the following equations:
[tex]undefined[/tex]Does anyone know the answer to this?
The most appropriate choice for equation of line in slope intercept form will be given by
x + 2y = -16 is the required equation of line
What is equation of line in slope intercept form?
Equation of line in slope intercept form is given by y = mx + c
Where, m is the slope of the line and c is the y intercept of the line
The distance from the origin to the point where the line cuts the x axis is called x intercept
The distance from the origin to the point where the line cuts the y axis is called y intercept
Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis
If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by
[tex]m=tan\theta[/tex]
If the line passes through ([tex]x_1, y_1[/tex]) and ([tex]x_2, y_2[/tex])
slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Here,
The line passes through (0, -8) and (-2, -7)
Slope =
[tex]\frac{-7 -(-8)}{-2-0}\\-\frac{1}{2}[/tex]
The line passes through (0, -8)
Equation of line
[tex]y - (-8) = -\frac{1}{2}(x - 0)\\\\y + 8 = -\frac{1}{2}x\\2y + 16 = -x\\x + 2y = -16[/tex]
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Solve the inequality: y-5-20Which of the following is the graph of the solution?
Given the inequality:
[tex]y-5>-20[/tex]Let's select the graph which represents the solution.
Let's solve the inequality.
Add 5 to both sides of the inequality:
[tex]\begin{gathered} y-5+5>-20+5 \\ \\ y>-15 \end{gathered}[/tex]Since y is greater than -15, the graph of the inequality will be a number line which has an open dot at the point -15, then shaded to the right of the number line.
Therefore, the graph of the solution is:
ANSWER:
A
8) What is the mass of the teddy bear if the toy car has a mass of 375 grams? 10 .S 0 4kg 3kg 1kg 2kg 000
The mass of the teddy is 1,225 grams
Here, we want to get the mass of the teddybear given the mass of the toy car
Since boith are on the scale, then it means they contribute to the mass on the scale
By reading the scale, we can see that the mass on the scale is 1.6 kg
As we know, 1000 g is 1 kg
It means 1.6 kg in g will be 1.6 * 1000 = 1,600 g
So, we can now subtract the mass of the toy car from this total to get the mass of the teddy
Mathematically, we have this as;
[tex]1600\text{ g - 375 g =1,225 g}[/tex]What is the prime factorization of 84.(A)2 x 3 x 7(B)2^2 X 3 X 7(C)2 X 21
Answer:
84=2^2 x 3 x 7
Explanation:
A prime number is any number that has only two factors: 1 and itself.
To find the prime factorization of 84, we are required to express it as a product of its prime factors.
[tex]\begin{gathered} 84=2\times42 \\ 84=2\times2\times21 \\ 84=2\times2\times3\times7 \\ =2^2\times3\times7 \end{gathered}[/tex]
Therefore, the prime factorization of 84 is:
84=2^2 x 3 x 7
Question 3 (9 points)Find Pred then green)What is the probability that you select a red marble, then a green marbleP (red) -P (then Green) - (Total of marbles will be 1 less)P (red then green) = *Hint: Multiply
Solution
Step 1
Write out an expression for the probability
[tex]\text{The probaility of an event occurring= }\frac{\text{Number of required events}}{\text{Total number of events}}[/tex]Step 2
Define terms
Total number of events = 8 marbles
Number of required events = red then marble
Number of red = 2 marbles2
Number of green = 2 marbles
Note: The question is without replacement.
Step 3
Get the required probabilities and the answer
[tex]\begin{gathered} Pr(\text{red marble) = }\frac{2}{8} \\ Pr(\text{green marble without replacement) =}\frac{2}{7} \end{gathered}[/tex]Hence the Pr(of red then green) is given as
[tex]\begin{gathered} =Pr(\text{red) }\times Pr(green\text{ without replacement)} \\ =\frac{2}{8}\times\frac{2}{7}=\frac{1}{14} \end{gathered}[/tex]Hence the probability of picking a red marble then a green marble = 1/14
HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
[tex]-1\frac{3}{4}[/tex] is located at a point 1 on the number line.
1.1125 is located at point 6 on the number line.
14 / 8 is located at point 8 on the number line.
-0.875 is located at point 3 on the number line.
What are the locations of the numbers?The numbers are made up of mixed fractions, improper fractions, decimals, positive numbers and negative numbers.
A mixed number is a number that has a whole number, a numerator and a denominator. The numerator that has a smaller value than the denominator. and a proper fraction. . An example of a mixed number is 1 1/4. An improper fraction is a fraction in which the numerator is bigger than the denominator. An example of an improper fraction is 14/8.
A negative number is a number that is smaller in value than 0. Negative numbers would be to the left of zero on number line. An example of a negative number is -1.4. A positive number is a number that is greater in value than 0. Positive numbers are located to the right of 0 on the number line. An example of a positive number is 4.2.
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[tex]-1\frac{3}{4}[/tex] is located at a point 1 on the number line.
1.1125 is located at point 6 on the number line.
14 / 8 is located at point 8 on the number line.
-0.875 is located at point 3 on the number line.
What are the locations of the numbers?The numbers are made up of mixed fractions, improper fractions, decimals, positive numbers and negative numbers.
A mixed number is a number that has a whole number, a numerator and a denominator. The numerator that has a smaller value than the denominator. and a proper fraction. . An example of a mixed number is 1 1/4. An improper fraction is a fraction in which the numerator is bigger than the denominator. An example of an improper fraction is 14/8.
A negative number is a number that is smaller in value than 0. Negative numbers would be to the left of zero on number line. An example of a negative number is -1.4. A positive number is a number that is greater in value than 0. Positive numbers are located to the right of 0 on the number line. An example of a positive number is 4.2.
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Which points are separated by a distance of 4 units?A. (3,6) (3,9)B. (2,7) (2,3)C. (1,5) (1,3)D. (4,2) (4,7)
let us take the point (2,7) and (2,3) the distance between these two is
[tex]\begin{gathered} d=\sqrt[]{(2-2)^2+(7-3)^2} \\ d=\sqrt[]{4^2} \\ d=4\text{ unit} \end{gathered}[/tex]Hence these two points are separated by 4 units.
So option B is correct.
A rectangular pool is 7 meters wide and 12 meters long. If you swim diagonally from one corner to the other, how many meters will you swim? Approximate the answer to the nearest tenth.
Answer: 15cm
Step-by-step explanation:
Your welcome
having trouble solving quadratic equations using factoring, examples are fine
Let's solve the quadratic equation using factorization:
x²-9x -22= 0
In order to solve using this method, we should beforehand factorize the polynomial:
The middle number is -9 and the last number is -22.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks? Let's think about two numbers that add up to -9 and multiply together to -22...
These numbers will be -11 and 2:
-11 +2= 9
-11*2= -22
So the factorization is:
(x+2)*(x-11) = 0
That means:
x + 2 =0
and
x - 11 = 0
Solving the equations:
x= -2
x= 11
S= {-2, 11}
simplify -5m²n³ × 15m⁴ n⁶
To simplify the given expression we will use the following property of exponents:
[tex]a^n\times a^m=a^{n+m}.[/tex]Using the above property we get:
[tex]-5m^2n^3\times15m^4n^6=(-5\times15)m^{2+4}n^{3+6}=-75m^6n^9.[/tex]Answer:
[tex]-5m^2n^3\times15m^4n^6=-75m^6n^9.[/tex]Divide 8 A) 3 B) 0) 7 16 D) 7. 32
Answer
3(1/2) or (7/2) or 3.5
Step-by-step Explanation
The question wants us to divide (7/8) by (1/4).
[tex]\frac{7}{8}\div\frac{1}{4}[/tex]The first step to solving division when it comes to fractions is to change the division sign to multiplication sign, which changes the fraction after the division sign to its inverse.
That is, in changing ÷ into ×, (1/4) changes to (4/1)
So,
[tex]\begin{gathered} \frac{7}{8}\div\frac{1}{4} \\ =\frac{7}{8}\times\frac{4}{1} \\ =\frac{28}{8} \\ =\frac{7}{2} \\ =3\frac{1}{2} \end{gathered}[/tex]Hope this Help!!!
what is 234,181 rounded to the nearest thousand
The figure 234,181 has the digit 4 in the thousands place.
Rounding to the nearest thouand would therefore be
234,000
This is because, the digit 1 that follows is not up to 5 and therefore is insignificant. So the digit 1 and the others after it are all rounded up to zeros.
what does -1 3/4+4.7=
-1 3/4 + 4.7 = -1.75 + 4.7 = 2.95
3/4 = 0.75, so -1 3/4 is -1.75
-1.75 + 4.7 = 2.95
Answer: 2.95
Please help nobody knows the answer to my question. Round to 2 decimal places.
To answer this question we will use the z-score.
Recall that the z-score is given as follows:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma}, \\ \text{where x is the observed value, }\mu\text{ is the mean, and }\sigma\text{ is the standard deviation.} \end{gathered}[/tex]The z-score of 54 is:
[tex]z=\frac{54-50}{5}=\frac{4}{5}=0.8.[/tex]The z-score of 56 is:
[tex]z=\frac{56-50}{4}=\frac{6}{5}=1.2.[/tex]Now, the probability of flipping 54, 55, or 56 heads is the same as the following probability:
[tex]P(0.8Now, recall, that:[tex]P(aNow, from the given table we get that:[tex]\begin{gathered} P(0.8)=0.7881, \\ P(1.2)=0.8849. \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} P(0.8Answer: 0.10.composition of functions, interval notation
Given the functions:
[tex]\begin{gathered} g(x)=\frac{1}{\sqrt[]{x}} \\ m(x)=x^2-4 \end{gathered}[/tex]I would like to find their domain as well and then complete the answers:
[tex]\begin{gathered} D_g=(0,\infty) \\ D_m=(-\infty,\infty) \end{gathered}[/tex]For the first question: g(x) / m(x)
[tex]\begin{gathered} \frac{g(x)}{m(x)}=\frac{\frac{1}{\sqrt[]{x}}}{x^2-4}=\frac{1}{\sqrt[]{x}\cdot(x^2-4)}=\frac{1}{x-4\sqrt[]{x}} \\ x-4\sqrt[]{x}\ne0 \\ x\ne4\sqrt[]{x} \\ x^2\ne4x \\ x\ne4 \end{gathered}[/tex]As we can see, the domain of this function cannot take negative values nor 4, 0. So, its domain is
[tex]D_{\frac{g}{m}}=(0,4)\cup(4,\infty)[/tex]For the second domain g(m(x)), let's find out what is the function:
[tex]\begin{gathered} g(m(x))=\frac{1}{\sqrt[]{x^2-4}} \\ \sqrt[]{x^2-4}>0 \\ x^2>4 \\ x>2 \\ x<-2 \end{gathered}[/tex]This means that x cannot be among the interval -2,2:
[tex]D_{g(m)}=(-\infty,-2)\cup(2,\infty)[/tex]For the last domain m(g(x)) we perfome the same procedure:
[tex]m(g(x))=(\frac{1}{\sqrt[]{x}})^2-4=\frac{1}{x}-4[/tex]For this domain it is obvious that x cannot take the zero value but anyone else.
[tex]D_{m(g)}=(-\infty,0)\cup(0,\infty)_{}[/tex]Ken wants to install a row of cerámic tiles on a wall that is 21 3/8 inches wide. Each tile is 4 1/2 inches wide. How many whole tiles does he need?
We have the following:
[tex]a\frac{b}{c}=\frac{a\cdot c+b}{c}[/tex]therefore:
[tex]\begin{gathered} 21\frac{3}{8}=\frac{21\cdot8+3}{8}=\frac{168+3}{8}=\frac{171}{8} \\ 4\frac{1}{2}=\frac{4\cdot2+1}{2}=\frac{8+1}{2}=\frac{9}{2} \end{gathered}[/tex]now, we divde to know the amount:
[tex]\frac{\frac{171}{8}}{\frac{9}{2}}=\frac{171\cdot2}{8\cdot9}=\frac{342}{72}=4.75\cong4[/tex]Therefore, the answer is 4 whole tiles
Which points are on the graph of y = cot x? (Select all that apply)A. (/3 , √3/2)B. (/2 , 0)C. (0 , )D. (/4 , 1)E. ( , 0)
Solution:
The graph function is given below as
[tex]y=cotx[/tex]The graph is given below as
Therefore,
The points on the graph are
[tex]\begin{gathered} \Rightarrow(\frac{\pi}{4},1) \\ \Rightarrow(\frac{\pi}{2},0) \end{gathered}[/tex]OPTION B AND option D are the right answers
p and q are roots of the equation 5x^2 - 7x +1. find to value of p^2 x q +q^2 x p and (p/q)+(q/p)
1) Let's find the roots of the equation: 5x² -7x +1
5x² -7x +1
2) Calling x_1 =p and x_2= q
Plugging them into the (p/q)+(q/p) expression, dividing the fractions. And then rationalizing it we'll have finally:
[tex]\frac{\frac{7+\sqrt[]{29}}{10}}{\frac{7-\sqrt[]{29}}{10}}+\frac{\frac{7-\sqrt[]{29}}{10}}{\frac{7+\sqrt[]{29}}{10}}=\frac{7+\sqrt[]{29}}{10}\cdot\frac{10}{7-\sqrt[]{29}}\text{ +}\frac{7-\sqrt[]{29}}{10}\cdot\frac{10}{7+\sqrt[]{29}}\text{ =}\frac{39}{5}[/tex]The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
50 X 5 X 3
answer divide
by 36
Darell made a scale drawing of a shopping center. The parking lot is 4 centimeters wide in the drawing. The actual parking lot is 40 meters wide. What scale did Darell use?
Answer:
1 cm to 10 m
Step-by-step explanation:
4 cm to 40 m = 1 cm to 10 m
Figure R = figure R". Describe a sequence of three transformations you canperform on figure R to show this. Show your work.
1) Rotate the figure 90º clockwise.
To rotate a figure 90º clockwise you have to perform the following transformation:
(x,y)→(y,-x)
So for each point of the figure you have to swich places between x and y.
And you have to multiply the x coordinate by -1.
R has 6 points:
(-4,-5)
(-7,-5)
(-7,-4)
(-5,-4)
(-6,-3)
(-2,-2)
First step: swich places between the coordinates of each point:
(x,y) → (y,x)
(-4,-5)→(-5,-4)
(-7,-5)→(-5,-7)
(-7,-4)→(-4,-7)
(-5,-4)→(-4,-5)
(-6,-3)→(-3,-6)
(-2,-2)→(-2,-2)
Second step, multiply the y-coordinate of the new set by -1
(y,x)→ (y,-x)
(-5,-4)→ (-5,4)
(-5,-7)→ (-5,7)
(-4,-7)→ (-4,7)
(-4,-5)→ (-4,5)
(-3,-6)→ (-3,6)
(-2,-2)→ (-2,2)
After the rotation, the figure moved from the 3rth quadrant to the 2nd quadrant.
In AOPQ, mZO = (6x – 14)°, mZP = (2x + 16)°, and mZQ = (2x + 8)°. Find mZQ.
Explanation
Step 1
the sum of the internal angles in a triangle equals 18o, so
[tex]\begin{gathered} (2x+16)+(6x-14)+(2x+8)=180 \\ 2x+16+6x-14+2x+8=180 \\ \text{add similar terms} \\ 10x+10=180 \\ \text{subtract 10 in both sides} \\ 10x+10-10=180-10 \\ 10x=170 \\ \text{divide both sides by 10} \\ \frac{10x}{10}=\frac{170}{10} \\ x=17 \end{gathered}[/tex]Step 2
now, replace the value of x in angle Q to find it
[tex]\begin{gathered} \measuredangle Q=(2x+8) \\ \measuredangle Q=(2\cdot17+8) \\ \measuredangle Q=(34+8) \\ \measuredangle Q=42 \end{gathered}[/tex]I hope this helps you
please help me understand how to find the average rate of change of the function over the given interval and please show me work.
To answer this, you'll need to recall a formula for finding the rate of change of one variable with respect to another. Given f(x)=x^2 + x +1, the rate of change of the variable with respect to x is given by:
[tex]\begin{gathered} \frac{\differentialD yy}{\square}y}{dx}=n(ax^{n-1}),\text{ where n is the power of variable term, and a is the coefficient.}y}{\square}yy}{dx}=\text{nax}^{n-1} \\ So\text{ when f(x)=x\textasciicircum 2+x+1 is differentiated, we will arrive at } \\ \\ \frac{dy}{dx}=2x+1\text{ The average rate of change of the function within the range (-3,-2) means, we have to use x as -3 and also x as -2 into the derivative function } \\ x=-3 \\ \frac{\differentialD yy}{\square}y}{dx}=2(-3)+1=-6+1=-5y}{\square}y}{dx}=2(-3)+1=-6+1=-5 \\ \text{Also, } \\ x=-2 \\ \frac{\differentialD yy}{\square}y}{dx}=2x+1\text{ becomes}y}{\square}yy}{dx} \\ \\ \end{gathered}[/tex]