x = (internal angle)
y,z = (externals)
Then
Angle x= < x= 180° - 50° -45° = 85°
Angle y= 180° - (180° - Angle z =
Then answers are
Angle x= 85°
Angle y= 137°
Angle z= 128°
Which of the following is equivalent to - sin ¹1?A. sin ¹111OB. - sin(-11)OC. sin(-11)D. sinReset Selection
The correct option is C.
Solve using elimination.–2x − 7y = 9x − 7y = –15
The question wants us to solve the following system of equations by elimination:
[tex]\begin{gathered} -2x-7=9 \\ x-7y=-15 \end{gathered}[/tex]Solution
[tex]\begin{gathered} -2x-7y=9\text{ (Equation 1)} \\ x-7y=-15\text{ (Equation 2)} \\ \\ \text{Subtract both equations} \\ -2x-7y-(x-7y)=9-(-15) \\ -2x-7y-x+7y=9+15 \\ -2x-x-7y+7y=24 \\ -3x=24 \\ \text{Divide both sides by -3} \\ -\frac{3x}{-3}=\frac{24}{-3} \\ \\ \therefore x=-8 \\ \\ \text{Substitute the value for x into Equation 1}.\text{ This will help us find y.} \\ -2x-7y=9 \\ -2(-8)-7y=9 \\ 16-7y=9 \\ \text{Subtract 16 from both sides} \\ -7y=9-16 \\ -7y=-7 \\ \text{Divide both sides by -7} \\ -\frac{7y}{-7}=-\frac{7}{-7} \\ \\ \therefore y=1 \end{gathered}[/tex]Answer
The answer to the system of equations is:
x = -8
y = 1
Fifty people in a room are wearing clothes either in red orwhite or a combination of the two colors. Thirty are wearingonly red and 16 are wearing a combination of both red andwhite. How many are wearing clothes that have white in them?
SOLUTION
We will solve the question using a Venn diagram
Let R represents people wearing clothes that have red
Let W represents people wearing clothes that have white
We have the Venn diagram as follow
So from the Venn diagram small letter w represent those wearing clothes that have only white. So we have that
[tex]\begin{gathered} 30+16+w=50 \\ 46+w=50 \\ w=50-46 \\ w=4 \end{gathered}[/tex]So those for "only" white is 4.
But those wearing clothes that have white in them will be only white plus those wearing combination of red and white. We have
[tex]16+4=20[/tex]Hence the answer is 20
The heights, in feet, of 12 trees in a park are shown below.8, 11, 14, 16, 17, 21, 21, 24, 27, 31, 43, 47Use the drop-down menus to explain the interquartile range of the data.
Given:
The heights, in feet, of 12 trees in a park are:
8,11,14,16,17,21,21,24,27,31,43,47.
Required:
To find the interquartile range of the given data.
Explanation:
We have given the heights of 12 trees in feet.
Therefore, the total number of quantitties (elements) in given data is even.
Thus, the median (M) of the data is,
[tex]\begin{gathered} M=\frac{21+21}{2} \\ \Rightarrow M=\frac{42}{2} \\ \Rightarrow M=21 \end{gathered}[/tex]The median (Q) of the first half of the data 8,11,14,16,17 is given by,
[tex]Q=14[/tex]since the number of quantities are odd.
The median (Q') of the second half of the data 24,27,31,43,47 is given by,
[tex]Q^{\prime}=31[/tex]since the number of quantities are odd.
Hence, the interqurtile range (R) is,
[tex]\begin{gathered} R=Q^{\prime}-Q \\ \Rightarrow R=31-14 \\ \Rightarrow R=17 \end{gathered}[/tex]Final Answer:
The interquartile range is,
[tex]R=17[/tex]The first option is spread.
The second option is range.
The third option is 17.
The fourth option is middle 50%.
The sum of two numbers is 122. The second number is 25 less than twice the first number. Find the number.
2. Simba pays $15 per month
for the phone he bought. His cell phone plan costs $49
per month and includes 15GB of
data. He also pays $5 for each additional 1GB
of data he uses over the 15GB limit. Using x to represent the GB of data
he uses over 15 GB, write an equation to represent Simba's monthly cell
phone bill and determine how much he will pay if one month he uses
23GB of data.
The equation can be given as B=64+5x
And the cost of phone bill if he uses 23GB will $104
What is an linear equation is one variable?
An linear equation is an equation of degree one. the highest exponent is 1 and one variable is number of variable is 1 in the equation
We are given that, Simba pays $15 per month for the phone he bought. His cell phone plan costs $49 per month.
He pay additional $5 for 1 gb data after 15gb data limit got over
Let the number of gb's used be x
Hence the total bill will be given by the equation
B= 15+49+5x
B= 64+5x
If he uses 23 gb of data the first 15 Gb are covered in his phone plan
And he has to pay $5 for each gb
The total cost is 8*5=$40
Hence the total phone bill is B=64+40
B=$104
Hence the equation can be given as B=64+5x
And the cost of phone bill if he uses 23GB will $104
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writing to explain in your own words tell what it meant by the absolute value of an integer
An absolute value of an integer is defined as a positive value/ digit of an integer regardless of the sign.
The symbol used is as shown below;
[tex]\parallel\text{ -3 }\parallel[/tex]or single lines as;
This means in absolute value of an integer , negative 2 is equal to positive 2.
Answer
In summary, an absolute value of an integer is a non-negative value , and the sign will only indicate direction, if well stated.
Kayla wants to have new doors installed in herhome. A door company charges a one-time fee of$125 plus $ per window installed. Write anexpression that represents the total cost to installnew windows in terms of the number of windows(w) installed.
Kayla wants to have new doors installed.
The door company charges $125 as a one time fee.
They also charge $50 per window installed.
If the number of new windows installed is w, then it means that to install w new windows, they will charge an additional:
w * 50 = $50w
This will be in addition to the one time fee.
Let T be the total cost of installation.
Therefore, the total cost for installing w new windows (in dollars) is:
T = 125 + 50w
8x +1312x + 7X == [?]Enter
The two angles given in the problem lie the opposite of each other with respect to the transversal line. This means that these two angles are supplementary angles. The sum of the two angles will be equal to 180 degrees, hence, we can set up an equation solving for x. We have
[tex]8x+13+12x+7=180[/tex]Solve for x, we have
[tex]\begin{gathered} 20x+20=180 \\ 20x=180-20 \\ \frac{20x}{20}=\frac{160}{20} \\ x=8 \end{gathered}[/tex]The value of x
Which of the following are maximum and minimum points of the function y = 2 cos x -1?
The graph of the function is shown below
From the options provided
Option A is correct because the maximum and minimum values are satisfied
Which of the following is equivalent to the expression below? (2+31) + (8-21) O A. 6+1 O B. 6+5; O C. 10+57 O D. 10 + 1
Given the expression:
[tex](2+3i)+(8-2i)[/tex]Let's find the equivalent expression from the choices given.
To find the equivalent expression, let simplify.
To simplify the expression, take the following steps:
• Remove the parentheses:
[tex]2+3i+8-2i[/tex]• Combine like terms:
[tex]\begin{gathered} 2+8+3i-2i \\ \\ 10+i \end{gathered}[/tex]Therefore, the equivalent expression is:
[tex]10+i[/tex]ANSWER: D
D. 10 + i
A cone has a height of 17 centimeters and a radius of 7 centimeters. What is its volume? Use = 3.14 and round your answer to the nearest hundredth. cubic centimeters
To find the volume of the cone, we will use the formula below:
[tex]V=\frac{1}{3}\pi r^2h[/tex]where r is the radius and h is the height
From the question,
π = 3.14
r =7
h=17
substitute the values into the formula
[tex]V=\frac{1}{3}\times3.14\times7^2\times17[/tex][tex]V\approx871.87\text{ cubic centimeters}[/tex]
in the diagram the figures are simular, what is x?triangle with 30cm and 13cmtriangle with 24cm and x
If the figures are similar, the proportion between the corresponding sides is the same.
The side of 30 cm corresponds to the side of 24 cm, and the side of 13 cm corresponds to the side of x cm.
So if the proportion is the same, we have that:
[tex]\begin{gathered} \frac{30}{24}=\frac{13}{x} \\ 30\cdot x=24\cdot13 \\ x=\frac{24\cdot13}{30}=\frac{4\cdot13}{5}=\frac{52}{5}=10.4 \end{gathered}[/tex]So the value of x is 10.4 cm, therefore the answer is b.
6 eggs weigh 3/4 of a pound. How much does each egg weigh? 1/4 pounds1/6 pounds1/8 pounds2/3 pounds
Find the exact value of sin,cos, and tan for the angle while simplifying all roots.
We can solve these values using the next triangle:
First, we need to label the sides using the angle of 30 degrees.
- The largest side is always the hypotenuse, h = 1.
- The opposite side is opposite to the angle, opp = 1/2.
- The adjacent side is between the angle of 30 degrees and the right angle,
adj = √3/2.
Now, we can solve the trigonometric expressions:
For sin:
sin θ = opposite side / hypotenuse
sin 30 = (1/2) / 1
sin 30 = 1/2
For cos:
cos θ = adjacent side / hypotenuse
cos 30 = (√3/2)/1
cos 30 =√3/2
For tan:
tan θ = opposite side / adjacent side
tan 30 =(1/2) / (√3/2)
Simplify the fractions:
tan 30 = 1/√3
Use the “complete the square” method to solve the following problemx^2 + 3x + 11 = 0
[tex]x^2+3x+11=0[/tex][tex](\frac{1}{2}\times3)^2=(+\frac{3}{2})^2[/tex][tex]\begin{gathered} x^2+3x=-11 \\ x^2+3x+(+\frac{3}{2})^2=-11+\frac{9}{4} \\ \\ (x+\frac{3}{2})^2=-\frac{35}{4} \\ \\ x+\frac{3}{2}=\sqrt{\frac{-35}{4}} \\ \\ x+\frac{3}{2}=\pm\frac{\sqrt{35}}{2}i \\ \\ x=\frac{-3}{2}\pm\frac{\sqrt{35}}{2}i \end{gathered}[/tex]
The answers are
[tex]x=\frac{-3}{2}+\frac{i\sqrt{35}}{2},\text{ }x=\frac{-3}{2}-\frac{i\sqrt{35}}{2}[/tex]what is the answer help pls
Answer:
1 ½ feet
Step-by-step explanation:
The shortest lizard is ½ a feet
The longest lizard is 2 feet
To find the difference in length:
2-½ = 1½ feet
A. Find the zeros in state the multiplicity of each zeroB. Write an equation expressed as the product of factors, of a polynomial function for the graph Using A leading coefficient of 1 or -1 and make the degree of F a small as possible.C. Use both the equation in part B and graph to find the Y intercept
Given the graph of a polynomial function:
We will find the following:
A. Find the zeros and state the multiplicity of each zero
The zeros of the function are the points of the intercept between the x-axis and the graph of the function
as shown, there are 3 points of intersection (3 zeros)
x = -1, multiplicity = 3
x = 1, multiplicity = 2
x = 2, multiplicity = 1
B. Write an equation expressed as the product of factors, of a polynomial function for the graph Using A leading coefficient of 1 or -1 and make the degree of F as small as possible.
Form A, the factors of the function will be:
(x+1), (x-1), and (x-2)
The equation of the function will be:
[tex]f(x)=(x+1)^3(x-1)^2(x-2)[/tex]C. Use both the equation in part B and graph to find the Y-intercept
The y-intercept is the value of (y) when (x = 0)
So, substitute with x = 0
So,
[tex]y=(0+1)^3\cdot(0-1)^2\cdot(0-2)=-2[/tex]So, the answer will be: y-intercept = -2
B.
The scale of figure A to figure B is 1 to 2. If the area of figure A is 7 ft2, what is the area of figure B?
OA. 3.5 ft²
OB. 35 ft²
OC. 14 ft²
OD. 28 ft²
JCPenney sells jeans for $49.50 that cost $38.00. What is the percent markup on cost? Check the cost.
The percent markup of the jeans is 30.2%
How to calculate the markup on cost ?
The selling price of the jeans is $49.50
The cost price is $38
Markup can be described as the difference between the selling price and the cost price of a product
The markup can be calculated by subtracting the cost price from the selling price
= 49.50 - 38
= 11.5
The percent markup can be calculated as follows
11.5/38 × 100
= 0.302 × 100
= 30.2%
Hence the percent markup is 30.2%
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Find f such that the given conditions are satisfied. f(x)=x2-3x + 12, f(0) = 9 O f(x) = 1x2 - 4x² + 12x +9 O O f(x) - x-x2 + 12x + 1 f(x) = 3x3-4x2 + 12x + 1 O f(x) = 3x - x? + 12x + 9
To find f(x) we will do an integration
[tex]\begin{gathered} f^{\prime}(x)=x^2-3x+12\text{ } \\ f(x)=\int (x^2-3x+12) \end{gathered}[/tex][tex]\int (x^2-3x+12)=\frac{x^3}{3}-\frac{3x^2}{2}+12x+c[/tex]To find c substitute x by 0 and y by 9 because f(0) = 9
[tex]\begin{gathered} f(x)=\frac{1}{3}x^3-\frac{3}{2}x^2+12x+c \\ f(0)=\frac{1}{3}(0)^3-\frac{3}{2}(0)^2+12(0)+c=9 \\ c=9 \end{gathered}[/tex]The function f(x) is
[tex]f(x)=\frac{1}{3}x^3-\frac{3}{2}x^2+12x+9[/tex]Answer D
Pyramid with the square base. Is this correct? Base=64in^2LA= 112in^2TA=176in^2
The given figures is of square pryamid with the square base
Area of square = side x side
In the given figure, the length of the base of the square = 8in
Area of base of square = 8 x 8
Area of base of square = 64 in²
The lateral area of a right pyramid can be calculated by
multiplying half of the perimeter of the base by the slant
height.
Lateral surface area = 1/2 x Perimeter of the base x slant height
Since, the base of the pryamid is square so, the perimeter for the base pf pryamid = 4side
Perimeter = 4 x side
Perimeter = 4 x 8
Perimeter of the base of pryamid is 32 in
Slant height is given as 7in
Lateral surface area = 1/2 x 7 x 32
LAteral surface area = 7 x 16
Lateral surface area = 112 in²
The total surface area can be calculated by adding base are to the lateral surface area
Total surface area = Lateral surface area + Base area
Total surface area = 112 + 64
Total surface area = 176 in²
Answer:
Area of base of square = 64 in²
Transforming the graph of a function by reflecting over an axis
ANSWER:
(a)
(b)
STEP-BY-STEP EXPLANATION:
(a)
We must do the following transformation:
[tex]y=f(x)\rightarrow y=f(-x)[/tex]In this case, reflects f(x) about the y-axis. The rule that follows the above, is like this:
[tex](x,y)\rightarrow(-x,y)[/tex]We apply the rule to the points of the function and it would be:
[tex]\begin{gathered} \mleft(-4.2\mright)\rightarrow(4,2) \\ (0,4)\rightarrow(0,4) \\ (4,6)\rightarrow(-4,6) \end{gathered}[/tex]We graph and we have:
(b)
We must do the following transformation:
[tex]y=g(x)\rightarrow y=-g(x)[/tex]In this case, reflects f(x) about the x-axis. The rule that follows the above, is like this:
[tex](x,y)\rightarrow(x,-y)[/tex]We apply the rule to the points of the function and it would be:
[tex]\begin{gathered} \mleft(-7,-2\mright)\rightarrow\mleft(-7,2\mright) \\ \mleft(-4,-5\mright?)\rightarrow\mleft(-4,5\mright) \\ \mleft(4,-1\mright)\rightarrow\mleft(4,1\mright) \end{gathered}[/tex]We graph and we have:
Help in solving for y. Need to know the slope and y-intercept in the equation
Given the following equation:
8x - 5y = 10
then, we can solve it for y as follows:
5y = 8x -10
y = (8/5)x - (10/5)
y = (8/5)x - 2
So, the slope is m = 8/5 and the y-intercept is yo = -2.
Simplify 3√12 +8✓12 - √6 how
In order to simplify this equation, we are going to start by simplifying the radicals.
[tex]\sqrt[]{12}=\sqrt[]{2^2\cdot3}=\text{2}\sqrt[]{3}[/tex]Now we have the radicals simplified and we are going to replace them on the equation that we already have.
[tex]\begin{gathered} 3\cdot(2\sqrt[]{3})+8\cdot(2\sqrt[]{3})-\sqrt[]{6} \\ 6\sqrt[]{3}+16\sqrt[]{3}-\sqrt[]{6} \\ 22\sqrt[]{3}-\sqrt[]{6} \end{gathered}[/tex]Todd forgot the first two numbers of his locker combination.The number can be any number 1 through 6. What is the probability that he will guess the first number correctly and the second number incorrectly
Todd forgot the first two numbers of his locker combination. The number can be any number 1 through 6. What is the probability that he will guess the first number correctly and the second number incorrectly?
______________________________________________
Please, give me some minutes to take over your question
________________________________________
The probability that he will guess the first number correctly and the second number incorrectly
1/6 (the first number correctly)
5/6 (the second number incorrectly)
1/6 * 5/6 = 5/36
_________________________________________
Answer
The probability that he will guess the first number correctly and the second number incorrectly is 5/36 = 0.1389 = 13. 89%.
find the explict formula for 15, 12, 9, 6
Given:
15, 12, 9, 6
To write the explicit formula, use the form:
[tex]a_n=a_1+d(n-1)[/tex]Where
a1 = first term = 15
d = common difference = 12 - 15 = -3
n = number of terms
Therefore, the explicit formula is:
[tex]\begin{gathered} a_n=15-3(n-1) \\ \\ a_n=15-3n+3 \\ \\ a_n=18-3n \end{gathered}[/tex]ANSWER:
[tex]a_n=18-3n[/tex]If an investment grew to $13,500 in 2 years and the interest amount earned was $1,150, calculate the nominal interest rate compounded quarterly.
The nominal interest rate compounded quarterly is 1.33%.
Given,
If an investment grew to $13,500 in 2 years.
and, the interest amount earned was $1,150.
To find the nominal interest rate compounded quarterly.
What is nominal interest rate?
The interest rate before inflation is referred to as the nominal interest rate.
Nominal can also refer to the advertised or stated interest rate on a loan, excluding any fees or interest compounding.
Now, According to the question:
Here given ,
P = $13500
i = ?
A = $1150
t = 2 yrs
n = 4 x 2 = 8
Formula of compound interest ,
A = P( 1 + I )ⁿ
$1150 = $13500 ( 1 + i ) ⁸
$1150 / $13500 = (1 + i)⁸
0.0851 = (1+ i) ⁸
1 +i = 8√.0851
1 + i = 2.33
i = 2.33 -1
i = 1.33 %
Hence, The nominal interest rate compounded quarterly is 1.33%.
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the variables x and y vary inversely. use x=-2 and y=3 to write and equation relating x and y. then find y when x=-1
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Define the variation that occurs in the Question.
Inverse Variation: Inverse variation is the relationship between two variables, such that if the value of one variable increases then the value of the other variable decreases.
STEP 2: Interpret the statements in the question tab
[tex]\begin{gathered} x\text{ varies inversely as y} \\ x\propto\frac{1}{y} \end{gathered}[/tex]STEP 3: Get the constant of variation
[tex]\begin{gathered} x\propto\frac{1}{y} \\ \text{Introducing the constant, we have;} \\ x=k\times\frac{1}{y},x=\frac{k}{y} \\ By\text{ cross multiplication,} \\ x=ky \\ \text{Divide both sides by y} \\ \frac{x}{y}=k \end{gathered}[/tex]STEP 4: Use the given values to get the equation relating x and y
[tex]\begin{gathered} \frac{x}{y}=k,x=-2,y=3 \\ By\text{ substitution,} \\ \frac{-2}{3}=k \\ k=\frac{-2}{3} \\ \\ \text{The equation relating x and y will be:} \\ x=-\frac{2}{3}y \\ x=\frac{-2y}{3} \end{gathered}[/tex]Hence, the equation relating x and y is:
[tex]x=\frac{-2y}{3}[/tex]STEP 5: Find y when x=-1
[tex]\begin{gathered} x=ky \\ \text{Divide both sides by k to get the value of y} \\ y=\frac{x}{k} \\ x=-1,k=-\frac{2}{3} \\ By\text{ substitution,} \\ y=\frac{-1}{\frac{-2}{3}} \\ y=-1\div-\frac{2}{3} \\ y=-1\times\frac{-3}{2}=\frac{-1\times-3}{2} \\ y=\frac{3}{2} \end{gathered}[/tex]Hence, the value of y when x=-1 is 3/2
Meg owes the bank more than $15. Use , or = to make the statement true. Meg's account value ? -$15 2 What is the value of point A? ? How far is point A from 0 (absolute value)? || HAR
Answer; Meg's account is < - $15
Meg is owing the bank more than -$15
This implies that, the amount she is owing is more that -$15
The amount she is owing the bank could be -$16, -$17
Therefore, her current back account is less than -$15
Meg's account value is < -$15