Step 1: Write out the formula
The equation of a circle given by
[tex](x-a)^2+(y-b)^2=r^2[/tex][tex]\begin{gathered} \text{where} \\ (a,b)\text{ is the center of the circle} \\ r\text{ is the radius of the circle} \end{gathered}[/tex]Step 2: Write out the given equation and rewrite it in the form shown above
[tex]x^2+y^2+2x-6y+9=0[/tex][tex]\begin{gathered} x^2+2x+y^2-6y+9=0 \\ \text{ By completing the square, we have} \\ (x+1)^2-(+1)^2+(y-3)^2-(-3)^2+9=0 \\ \end{gathered}[/tex][tex]\begin{gathered} (x+1)^2+(y-3)^2-1-9+9=0 \\ (x+1)^2+(y-3)^2=1=1^2 \end{gathered}[/tex]By comparing the equation with the formula above, we have
[tex]a=-1,b=3,r=1[/tex]Therefore,
center (-1,3), radius = 1
Match the term on the left with its figure on the right.
Question:
Solution:
1. Equilateral triangle:
An equilateral triangle is a triangle in which all three sides have the same length.
This is the case of the following figure (D) :
2. A Scalene right triangle:
A scalene right triangle is a triangle in which all three sides are in different lengths and one of its angles is 90 degrees.
This is the case of the following figure (A):
3. Isosceles right triangle:
An isosceles right triangle has two equal sides and one angle of 90 degrees, as the following figure (C):
4. Isosceles obtuse triangle:
An isosceles obtuse triangle has two equal sides with any angle greater than 90 degrees, as in the following figure (B):
What is the equation to solve: if the sim of four consecutive integers is 26, what is the value of the first integer?
ANSWER:
5
STEP-BY-STEP EXPLANATION:
We set up the equation as follows:
Let x be the first integer
[tex]x+x+1+x+2+x+3=26[/tex]We solve for x:
[tex]\begin{gathered} 4x+6=26 \\ \\ 4x=26-6 \\ \\ x=\frac{20}{4} \\ \\ x=5 \end{gathered}[/tex]The value of the first integer is 5
the ratio of the cost price to selling price is 8:9 . If the cost price of the power generator is 8500 what is the selling price?
Find the value of x 6 : 9 = x : 72
To find x we write the proportion as a fraction:
[tex]\begin{gathered} \frac{6}{9}=\frac{x}{72} \\ x=\frac{72\cdot6}{9} \\ x=48 \end{gathered}[/tex]Therefore x=48
Can someone please help me solve the following?Please put numbers on graph
Given:
The equation of the hyperbola is given as,
[tex]\frac{y^2}{25}-\frac{x^2}{4}=1........(1)^{}[/tex]The objective is to graph the equation of the hyperbola.
Explanation:
The general equation of hyperbola open in the vertical axis of up and down is,
[tex]\frac{(y-h)^2}{a^2}-\frac{(x-k)^2}{b^2}=1\text{ . . . . . . . .(2)}[/tex]Here, (h,k) represents the center of the hyperbola.
The focal length can be calculated as,
[tex]c=\sqrt[]{a^2+b^2}\text{ . . . . (3)}[/tex]On plugging the values of a and b in equation (3),
[tex]\begin{gathered} c=\sqrt[]{5^2+2^2} \\ =\sqrt[]{25+4} \\ =\sqrt[]{29} \end{gathered}[/tex]The foci can be calculated as,
[tex]\begin{gathered} F(h,k\pm c)=F(0,0\pm\sqrt[]{29}) \\ =F(0,\pm\sqrt[]{29}) \end{gathered}[/tex]The vertices can be calculated as,
[tex]\begin{gathered} V(h,k\pm a)=V(0,0\pm5) \\ =V(0,\pm5) \end{gathered}[/tex]To obtain graph:
The graph of the given hyperbola can be obtained as,
Hence, the graph of the given hyperbola is obtained.
The price of hamburger increased from .50 cent to .60 cent. What is the percent increase
The hamburguer was .50 cent and increased to 0.60 cent. Let's calculate the percent increase:
The percent increase may be calculated using the formula:
percent increase = [(final value - initial value)/initial value]*100
So:
[tex]\begin{gathered} \frac{0.6-0.5}{0.5}\cdot100= \\ \frac{0.1}{0.5}\cdot100= \\ 0.2\cdot100=20 \end{gathered}[/tex]So, the percent increase was 20%
solving systems with subtraction y=7txy=3x+9
y = 7 + x
y = 3x + 9
To solve the simulataneous equation with subtraction,
Step 1: name the equations
y = 7 + x ---- equation 1
y = 3x + 9 ----- equation 2
Step 2: subtract equation 1 from 2
so that
y - y = (3 x -x ) + (9 - 7)
0 = 2x + 2
2x = - 2
divide oth sides by 2
x = -2/2
x = -1
To get y, substitute the value for x into equation 1
y = 7 + x
y = 7 + (-1)
y = 7-1 = 6
y = 6
hence the solution is (-1, 6)
Two angles in triangle PQR are congruent, ∠P and ∠Q; ∠R measures 36.25°. What is the measure of ∠Q?
143.75°
107.5°
71.875°
36.25°
Answer:
71.875
Step-by-step explanation:
p = q
180 - 36.25 = 143.75
p + q = 143.75
143.75 ÷ 2 = 71.875
RecommendationsSkill plansMathLE Language artsScienceSocial studiesDE TX StandaAlgebra 10.11 Solve a system of equations using elimination: word problems NHRYou have prizes to reveal! Go toWrite a system of equations to describe the situation below, solve using elimination, and fill inthe blanks.Students in a poetry class are writing poems for their portfolios. The teacher wants them towrite stanzas with certain numbers of lines each. Dan wrote 7 short stanzas and 6 longstanzas, for a total of 140 lines. Jim wrote 7 short stanzas and 2 long stanzas, for a total of84 lines. How many lines do the two sizes of stanzas contain?The short stanzas containlines and the long ones containlines.Submit
Answer:
Short stanzas contains 8 lines
Long stanzas contains 14 lines
Explanations:
Let the number of short stanzas be "x"
Let the number of long stanzas be "y"
If Dan wrote 7 short stanzas and 6 long stanzas, for a total of 140 lines, this is expressed mathematically as:
7x + 6y = 140 ............................ 1
Similarly, if Jim wrote 7 short stanzas and 2 long stanzas, for a total of
84 lines, this is expressed as:
7x + 2y = 84 ......................... 2
Solve both equations simultaneously using elimination method
7x + 6y = 140 ............................ 1
7x + 2y = 84 ......................... 2
Subtract both equations
6y - 2y = 140 - 84
4y = 56
y = 56/4
y = 14
Substitute y = 14 into equaton 1.
Recall that 7x + 6y = 140
7x + 6(14) = 140
7x + 84 = 140
7x = 140 - 84
7x = 56
x = 56/7
x = 8
This shows that the short stanzas contains 8 lines and the long ones contains 14 lines
Sketch the right triangle and find the length of the side not given if necessary approximate the light to the nearest thousandth
Let's take a look at our triangle:
Using the pythagorean theorem, we'll have that:
[tex]h^2=12^2+16^2[/tex]Solving for h,
[tex]\begin{gathered} h^2=12^2+16^2 \\ \rightarrow h=\sqrt[]{12^2+16^2} \\ \rightarrow h=\sqrt[]{400} \\ \\ \Rightarrow h=20 \end{gathered}[/tex]This way, we can conlcude that the missing side measures 20 units.
A Use the information given to answer the question. A student works at a job in order to save money to buy a desktop computer. • The student works 80 hours each month. • The desktop computer costs $850. Part B If the student has already saved $150 and plans to save an additional $100 each week, the function g(w) = 100w + 150 represents the total amount of money, in dollars, saved after w weeks. What is the value of g(5)?
The function given is:
[tex]g\mleft(w\mright)=100w+150[/tex]Where
w represents the week
g(w) represents the total money
We want to fing g(5).
This means, put "5" into the function g.
Put "5" in place of "w" in the function g.
Shown below:
[tex]\begin{gathered} g(w)=100w+150 \\ g(5)=100(5)+150 \\ g(5)=500+150 \\ g(5)=650 \end{gathered}[/tex]using trig to find a side
we have that
tan(16)=NO/OM -------> by opposite side divided by the hypotenuse
solve for NO
NO=OM*tan(16)
x=16*tan(16)
x=4.6 ftPls look at Question and answer pls If it’s a compound then you will need to choose if it’s conjunctional, disjunction, conditional, or biconditional
Three statements are given. It is required to determine if the statements are simple or compound, and if it's compound, it is required to choose which type.
Recall that a simple statement is a statement containing no connectives like 'or', 'and', and so on.
Recall also that a compound statement is a combination of two or more simple statements which are joined by connectives.
Compound statements joined by 'or' are called disjunctions, while those joined by 'and' are called conjunctions.
Compound statements with 'if-then' are called conditional, while the ones with 'if and only if' are called biconditional.
a) The first statement is: My cousins each have some sort of engineering degree.
Since the statement is not joined by any connectives, it is a simple statement.
b) The second statement is: My eyes are bad or this print is tiny.
Since it is a combination of two simple statements joined by the connective 'or', then, it is a compound statement, which is a disjunction.
c) The third statement is: The cat will come to you if and only if you set well.
Since it is a combination of two simple statements joined by the connective 'if and only if ', it follows that it is a compound statement and it is a biconditional.
Which equation represents a circle centered at (3.5) and passing through the point (-2.91?OA (+3)2 + (y + 5)² = 17OB. (-3)²+(y-5)² = 17OC. (x+3)²+(y+ 5)² = 41OD. (-3)2 + (y-5)² = 41ResetNext
ANSWER
[tex](x-3)^2+(y-5)^2=41[/tex]EXPLANATION
Given;
[tex]\begin{gathered} center=(3,5) \\ points=(-2,9) \end{gathered}[/tex][tex]\begin{gathered} (x-a)^2+(y-b)^2=(r)^2 \\ (x-3)^2+(y-5)^2=(\sqrt{41})^2 \\ \end{gathered}[/tex]You travel 5 hours and 50 minutes. If you drove at an average of 41 mph, how much distance you traveled?
First, let's convert those 50 minutes into hours:
This way,
[tex]x=\frac{50\cdot1}{60}\Rightarrow x=0.83[/tex]I would have driven for 5.83 hours.
Using this, and the average pace (46 miles in one hour),
We get that:
[tex]x=\frac{46\cdot5.83}{1}\Rightarrow x=268.18[/tex]I would have traveled 268.18 miles
When graphing an inequality in slope-intercept form, which of the folowing indicates that you have to shade ABOVE the boundary line? Select ALL that apply.
Explanation
When graphing an inequality in slope-intercept form, we are asked to find which of the folowing indicates that you have to shade ABOVE the boundary line. This can be seen below.
The symbols
[tex]>\text{ and }\ge[/tex]Indicates that one should shade above the boundary line, The only difference is that the boundary line is broken in the case of greater than and unbroken in the case of greater than or equal to.
Answer:
[tex]>\text{ and }\ge[/tex]
Determine the degree of the polynomial 2w with exponent of 2+ 2w:
The degree of the polynomial is 2, because the degree of a polynomial is defined as the same as the greater exponent on the polynomial.
In this case, w² is the greater, then the degree is 2.
if in 3 minutes you can do 45 sit-ups, how much can you do in 1 minutes?
First let's determine the number of squats per minute by finding the ratio of the number of squats per minute.
[tex]r=\frac{45\text{ sit ups}}{3\text{ min}}=15\text{ sit-up per minute }[/tex]This means that you can do 15 sit-ups in one minute.
Find an equation of the line that has a slope of -1 and a y intercept of 2. Write your answer in the formy = mx + b.
Based on the information the equation would be:
y = -1x + 2
m=slope
b= y-intercept
Please give me the correct answer.Please decide if these 4 statements is a function or not a function.
As according to given statement:
1). Each school has one principal so as there is a relation between school and principal so it is a function.
2). Each student has a unique student ID number: so as there are so many students and they allhave different unique student ID's so there is a function.
3). Shoe manufacturers make different type of shoes : so as there is relation but we can't describe a function between them.
4). Each month of the year has a total amount of rainfall measured in inches:
So it is a function between month and the rainfall measured in inches.
Name all the sets of numbers to which real number belongs: 6.5
Given the number 6.5
The number belongs to:
1) Rational Numbers because it can be written as a/b
(X^2+8x+12)/(x+2) que
Given:
[tex]\frac{x^2+8x+12}{x+2}[/tex]Let's divide the polynomials.
To divide, let's factorize the polynomial in the numerator.
Factorize using the AC method.
Find a pair of numbers whose product is 12 and whose sum is 8.
Thus, we have the numbers:
2 and 6
The factors of the polynomial in the numerator are:
(x+2) and (x+6)
We have:
[tex]\frac{(x+2)(x+6)}{x+2}[/tex]Now, cancel the common factors:
Therefore, the quotient after dividing the polynomials is = x + 6
ANSWER:
[tex]x+6[/tex]2 2. 8 friends are going on a camping trip. 5 friends own a sleeping bag. How many friends need a sleeping bag? + Il8-5=3
If 8 friends go camping and only 5 friends have sleeping bag
Then of the 8 friends, the number that need a sleeping bag would be
= 8 - 5
= 3
Hence 3 friends will be in need of a sleeping bag
How do you multiply 6x 1 1/3?
To multiply a mixed number, first, we have to convert it into a fraction as follows:
[tex]1\frac{1}{3}=\frac{1\cdot3+1}{3}=\frac{4}{3}[/tex]Now, we need to multiply 6 by 4/3, as follows:
[tex]6\cdot1\frac{1}{3}=6\cdot\frac{4}{3}=\frac{6\cdot4}{3}=\frac{24}{3}=8[/tex]The net of a rectangular prism is shown below. The surface area of each is labeled
Given:
Area of box I = 48 cm²
Area of box 2 = 24 cm²
Area of box 3 = 48 cm²
Area of box 4 = 24 cm²
Area of box 5 = 72 cm²
Area of box 6 = 72 cm²
• Let's find the values which represent the dimensions of the prism.
Let L represent the length.
Let w represent the width
Let h represent the height.
Now, to find the surface area of a rectangular prism apply the formula:
A = 2(wL + Lh + wh)
Now, given each rectangular face, we have:
Area of length and width, Lw = 72 cm²
Area of length and height, Lh = 48 cm²
Area of width and height, wh = 24 cm²
Now to find the dimensions, we have:
[tex]\begin{gathered} \frac{Lh}{wh}=\frac{48}{24} \\ \\ \frac{L}{w}=2 \\ \\ L=2w \end{gathered}[/tex]Now, substitute 2w for L in Lw:
[tex]\begin{gathered} Lw=72 \\ \\ 2w(w)=72 \\ \\ 2w^2=72 \\ \\ w^2=\frac{72}{2} \\ \\ w^2=36 \\ \\ \text{ take the square root of both sides:} \\ \sqrt{w^2}=\sqrt{36} \\ \\ w=6 \end{gathered}[/tex]Therefore, the width is 6 cm.
Now, substitute 6 for w in wh:
[tex]\begin{gathered} wh=24 \\ \\ 6*h=24 \\ \\ Divide\text{ both terms by:} \\ \frac{6*h}{6}=\frac{24}{6} \\ \\ h=4 \end{gathered}[/tex]Now, substitute 4 for h in Lh:
[tex]\begin{gathered} Lh=48 \\ \\ L*4=48 \\ \\ \text{ Divide both sides by 4:} \\ \frac{L*4}{4}=\frac{48}{4} \\ \\ L=12 \end{gathered}[/tex]Therefore, the values which represent the dimensions are:
4, 6, 12
ANSWER:
4, 6, 12
Find the first six terms of the sequence.a = 2n² - 2
We are given the nth term of a sequence:
[tex]a_n=2n^2\text{ - 2}[/tex]We are required to find the first six terms.
For each term, we substitute for n and evaluate.
First term (n =1)
[tex]\begin{gathered} a_1\text{ = 2 }\times(1)^2\text{ - 2} \\ =\text{ 2 -2 } \\ =\text{ 0} \end{gathered}[/tex]Second term (n = 2)
[tex]\begin{gathered} a_2\text{ =2 }\times(2)^2\text{ - 2} \\ =\text{ 2 }\times\text{ 4 -2} \\ =\text{ 8 - 2} \\ =\text{ 6} \end{gathered}[/tex]Third term (n = 3)
[tex]\begin{gathered} a_3\text{ = 2 }\times(3)^2\text{ - 2} \\ =\text{ 2 }\times\text{ 9 - 2} \\ =\text{ 18 - 2} \\ =\text{ 16} \end{gathered}[/tex]Fourth term (n =4)
[tex]\begin{gathered} a_4\text{ = 2}\times(4)^2\text{ - 2} \\ =\text{ 2 }\times\text{ 16 - 2} \\ =\text{ 32 - 2} \\ =\text{ 30} \end{gathered}[/tex]Fifth term ( n = 5)
[tex]\begin{gathered} a_5\text{ = 2 }\times(5)^2\text{ - 2} \\ =\text{ 2 }\times\text{ 25 - 2} \\ =\text{ 50 - 2} \\ =\text{ 48} \end{gathered}[/tex]Sixth term ( n = 6)
[tex]\begin{gathered} a_6\text{ = 2 }\times(6)^2\text{ - 2} \\ =\text{ 2 }\times\text{ 36 - 2} \\ =\text{ 72 - 2} \\ =\text{ 70} \end{gathered}[/tex]Hence, the first six terms of the sequence are : 0, 6, 16, 30, 48 and 70
Compare f(-4) and g(-4)f(-4) is >, <, or = to g(-4)
The answer is f(-4)
EXPLANATION
When we check the value of -4 for both functions on the graph
f(-4) gives 3
g(-4) gives a number slightly greater than 1
Therefore f(-4)>g(-4)
solve the equation1/4p-2/5=3/4p+7P=
Solve:
[tex]\frac{1}{4}p-\frac{2}{5}=\frac{3}{4}p+7[/tex]The LCM of the denominators is 4*5 = 20. So we multiply each term by 20 to eliminate denominators:
[tex]20\cdot\frac{1}{4}p-20\cdot\frac{2}{5}=20\cdot\frac{3}{4}p+20\cdot7[/tex]Operating:
[tex]5p-8=15p+140[/tex]Adding 8 and subtracting 15p:
[tex]5p-15p=8+140[/tex]Simplifying:
[tex]-10p=148[/tex]Dividing by -10:
[tex]p=\frac{148}{-10}[/tex]Simplifying:
[tex]p=-\frac{74}{5}[/tex]There were 55.5 million people enrolled in Medicare in 2015. In 2009, there were 46.6million enrolled. Which value best represents the unit rate of change (slope) in millions per year?a)-1.48b) 1.48c) 19.1%d) -0.674
Let the number of people enrolled in Medicare be represented by y
Let the year be represented by x
So that,
[tex]\begin{gathered} (x_1,y_1)=(2015,55.5\text{ million)} \\ (x_2,y_2)=(2009,46.6\text{ million)} \end{gathered}[/tex]The unit rate of change (slope) in millions per year can be calculated by:
[tex]\begin{gathered} slope=\frac{y_2-y_1}{x_2-x_1} \\ \text{Hence,} \\ slope=\frac{46.6million_{}-55.5million_{}}{2009_{}-2015_{}} \\ slope=\frac{-8.9}{-6} \\ slope=1.48 \\ \end{gathered}[/tex]Therefore, the unit rate of change in millions per year is 1.48 [Option B]
convert the following into a decimal you must include the decimal in your answer and round to the nearest thousands)3/8
3/8 = 0.375
Explanations:The given fraction is 3/8
Using the long division method to convert 3/8 to decimal
Therefore, 3/8 = 0.375