Answer: (C) r² = (x+5)²+(y-4)²
Solution:-
The given endpoints are (-7,1) and (-3,7)
so the center will be at the mid point of the line connecting these two points.
hence, center ={ (-7+-3)/2, (1+7)/2 }
hence, C= (-5,4)
so, the equation of the circle is:-
⇒ (x-(-5))²+(y-4)²=r²
or, (x+5)²+(y-4)²=r²
Hi, so I know the answer to this problem (now that I got it wrong) but I'm not quite sure why I was wrong, help?
2x² + 2x + ? = x
⇒ ? = x - 2x² - 2x
⇒ ? = -2x² - x
Your answer is incorrect because 2x² - x² would mean x² is part of the answer, which is clearly incorrect.
If [tex]\rm \: x = log_{a}(bc)[/tex], [tex]\rm \: y = log_{b}(ca)[/tex], [tex]\rm \: z = log_{c}(ab)[/tex] , the xyz is equal to :
(a) x + y + z
(b) x + y + z + 1
(c) x + y + z + 2
(d) x + y + z + 3
Use the change-of-basis identity,
[tex]\log_x(y) = \dfrac{\ln(y)}{\ln(x)}[/tex]
to write
[tex]xyz = \log_a(bc) \log_b(ac) \log_c(ab) = \dfrac{\ln(bc) \ln(ac) \ln(ab)}{\ln(a) \ln(b) \ln(c)}[/tex]
Use the product-to-sum identity,
[tex]\log_x(yz) = \log_x(y) + \log_x(z)[/tex]
to write
[tex]xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}[/tex]
Redistribute the factors on the left side as
[tex]xyz = \dfrac{\ln(b) + \ln(c)}{\ln(b)} \times \dfrac{\ln(a) + \ln(c)}{\ln(c)} \times \dfrac{\ln(a) + \ln(b)}{\ln(a)}[/tex]
and simplify to
[tex]xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)[/tex]
Now expand the right side:
[tex]xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}[/tex]
Simplify and rewrite using the logarithm properties mentioned earlier.
[tex]xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1[/tex]
[tex]xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}[/tex]
[tex]xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}[/tex]
[tex]xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)[/tex]
[tex]\implies \boxed{xyz = x + y + z + 2}[/tex]
(C)
a and b are positive integers and 7a+5b=49. Find the values of a and b.
a and b are positive integers and 23a+17b=320. Find the values of a and b.
please hel you can get 30 points
Solving a system of equations, it is found that the value of a is of -191.75 and the value of b is of 278.25.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the equations are:
7a + 5b = 49.23a + 17b = 320.Multiplying the first equations by 17 and the second by -5, we have that the system is:
119a + 85b = 833.-115a - 85b = -1600.Then, adding them:
4a = -767
a = -767/4
a = -191.75
Then:
[tex]b = \frac{49 - 7a}{5} = \frac{49 - 7(-191.75)}{5} = 278.25[/tex]
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Given a=b+c2d solve for c
Step-by-step explanation:
rewrite the equation as follows
c2d = a - b
divide both sides by 2d
c = (a - b)/2d
its math can you help out
Answer:
81
Step-by-step explanation:
27 people will tell 3 people each. 3x27=81
Answer:
81
Step-by-step explanation:
Approximate the area under the curve y = x^2 from x = 0 to x = 3 using a Right Endpoint approximation with 6 subdivisions.
Will mark brainliest
Subdivide the interval [0, 3] into 6 subintervals of equal length, ∆x = (3 - 0)/6 = 1/2. Then the partition is
[tex]\left[0,\dfrac12\right] \cup \left[\dfrac12,1\right] \cup \left[1,\dfrac32\right] \cup \cdots \cup \left[\dfrac52,3\right][/tex]
The right endpoint of the [tex]i[/tex]-th subinterval is
[tex]r_i = \dfrac12 + (i-1)\times\dfrac12 = \dfrac i2[/tex]
with [tex]i\in\{1,2,3,\ldots,6\}[/tex].
Then the area under the [tex]y=x^2[/tex] on the interval [0, 3] is approximately
[tex]\displaystyle \int_0^3 x^2 \, dx \approx \sum_{i=1}^6 (r_i)^2 \Delta x = \frac18 \sum_{i=1}^6 i^2[/tex]
Recall that
[tex]\displaystyle \sum_{n=1}^N n^2 = \frac{N(N+1)(2N+1)}6[/tex]
Then the approximate value of the area is
[tex]\displaystyle \int_0^3 x^2 \, dx \approx \frac{6\times7\times13}{48} = \boxed{\frac{91}8}[/tex]
The actual value of the area is 9, so this approximation is an overestimation, as is always the case when using a right endpoint sum for an increasing function.
x + 4 is prime x2 – 9 can be factored using the formula.
Answer:
difference-of-squares
Step-by-step explanation:
If the proportion of the total disposable income spent on consumer goods and services is 93 percent and if
consumers spend 85 percent of each additional dollar, what is
a. the apc?
b. the aps?
c. the mpc?
d. the mps?
Answer:
what?????????????????
Choose all of the following angles that cannot
be an interior angle in a regular polygon.
24° 72°
72°
135°
135° 164° 179⁰
In a regular polygon, all interior angles have equal measures because the polygon has congruent sides and angles. The sum of all interior angles in a polygon can be found using the formula:
(n-2) * 180°,
where n represents the number of sides of the polygon.
Based on this, we can determine which angles cannot be interior angles in a regular polygon.
24°: This angle can be an interior angle in a regular polygon because it is smaller than the interior angles of any polygon with more than 6 sides.
72°: This angle can be an interior angle in a regular pentagon (5 sides) or any polygon with more sides, as it satisfies the requirement for interior angles.
135°: This angle cannot be an interior angle in a regular polygon because it is larger than the interior angles of any polygon with less than 8 sides.
164°: This angle cannot be an interior angle in a regular polygon because it is larger than the interior angles of any polygon with less than 9 sides.
179°: This angle cannot be an interior angle in any regular polygon because it is larger than the maximum measure of interior angles in any polygon.
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It takes 405 bricks to build 1 wall of a room. If there are 5 rooms (with 4 walls each), how many bricks will be needed to build all the walls?
Answer:
Bricks for 1 wall= 405
If there are 5 rooms with 4 walls,
Walls= 5 x 4= 20
Bricks= 405 x 20
= 8100
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Mariana runs a farm stand that sells bananas and grapes. Each pound of bananas sells for $1 and each pound of grapes sells for $2.25. Mariana made $72 from selling a total of 52 pounds of bananas and grapes. Graphically solve a system of equations in order to determine the number of pounds of bananas sold, x, and the number of pounds of grapes sold, y.
Answer:
jackson sold 27 pounds of bananas and 12 pounds of grapes :D
Step-by-step explanation:
Taking into account the definition of a system of linear equations, the number of pounds of bananas and grapes sold are 36 and 16 respectively.
System of linear equationsA set of two or more first-degree equations with two or more connected unknowns is referred to as a system of linear equations.
Finding the value of each unknown in order to satisfy all of the system's equations constitutes the process of solving an system of equations. To put it another way, it is necessary to find the values of the unknowns, as they must be replaced with values that, when used to solve the equations, is the process of solving a system of equations
This caseIn this case, a system of linear equations must be proposed taking into account that:
"x" is the number of pounds of bananas sold."y" is the number of pounds of grapes sold.You know:
Each pound of bananas sells for $1 and each pound of grapes sells for $2.25. Mariana made $72 from selling a total of 52 pounds of bananas and grapes.The system of equations to be solved is
x +y= 52
x + 2.25y= 72
There are several methods to solve a system of equations, it is decided to solve it using the graphical method. The system's equations are graphically represented by graphs in the graphical method. The solution of the system is the point of intersection between the graphs, since the coordinates of said point satisfy both equations.
Graphically, it can be seen that the intersection point is (36; 16). That is, the value of x is 36 and the value of y is 16.
Finally, the number of pounds of bananas sold are 36 and the number of pounds of grapes sold are 16.
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HELP THIS IS URGENT I NEED IT SOON! PLEASE
If f(x) = x2 − 6x − 4 and g(x) = 5x + 3, what is (f + g)(−3)?
41
35
11
−35
Answer:
11
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= x² - 6x - 4 +5x + 3 ← collect like terms
= x² - x - 1
then
(f + g)(- 3) = (- 3)² - (- 3) - 1 = 9 + 3 - 1 = 11
Answer:
11
Step-by-step explanation:
F(–3)=(–3)²–6(–3)–4===> 9+18–4=23
g(–3)=5(–3)+3=‐15+3=–12
23–12=11
Ella has a collection of vintage action figures that is worth $430. If the collection
appreciates at a rate of 4% per year, which equation represents the value of the
collection after 7 years?
The equation representing the value of the collection after 7 years is value of collection = 430 + (0.04 * 430 )* 7 or value of collection = $550.4
What is an Equation ?An equation is a mathematical statement , where the algebraic expression is equated to another algebraic expression.
It is given that
Ella has a collection of vintage action figures that is worth $430.
collection
appreciates at a rate of 4% per year
equation representing the value of the collection after 7 years is
value of collection = 430 + (0.04 * 430 )* t
value of collection = 430 + (0.04 * 430 )* 7
= $550.4
Therefore the equation representing the value of the collection after 7 years is value of collection = 430 + (0.04 * 430 )* 7 or value of collection = $550.4
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The distance between points (x₁, y₁) and (4, 8) is the square root of
(x₁ - 8)² + (₁-4)².
True or False?
The statement is given as the distance between points (x₁, y₁) and (4, 8) is the square root of (x₁ - 8)² + (₁-4)². Hence, the given statement is false, it is √[(x₁-4)² + (y₁-8)²].
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
D = √[(x-p)² + (y-q)²]
WE have been given two points.
So,
The distance between points (x₁, y₁) and (4, 8)
D = √[(x-p)² + (y-q)²]
D = √[(x₁-4)² + (y₁-8)²]
But the statement is given as the distance between points (x₁, y₁) and (4, 8) is the square root of (x₁ - 8)² + (₁-4)².
Hence, the given statement is false, it is √[(x₁-4)² + (y₁-8)²].
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Figure B is a scaled copy of figure A.
What is the scale factor from figure A to figure B
Answer:
1/3
Step-by-step explanation:
We multiply 33(Figure A side) by 1 /3 to get 11(Figure B side).
John bought 8 watches for $56 and his friend victor bought 7 watches for $63. whose watch is expensive ?
A flag pole is casting a 20ft. shadow. The flag pole measures 16 ft. Find the Angle of elevation of the sun.
Let's see
tanØ=16/20tanØ=4/5tanØ=0.8Ø=53°Answer:
53 the correct answer off your question.
Let g be the piecewise defined function shown.
g(x)=
x + 4, −5 ≤ x ≤ −1
2 − x, −1 < x ≤ 5
Evaluate g at different values in its domain.
g(−4) =
g(−2) =
g(0) =
g(3) =
g(4) =
Answer:
g(4)= -2
g(-2)= 2
g(0)= 2
g(3)= -1
g(-4)= 0
Step-by-step explanation: See attachment, and don’t forget to check just in case ;)
Answer:
g(−4) = 0
g(−2) = 2
g(0) = 2
g(3) = -1
g(4) = -2
Step-by-step explanation:
Please Thank!
dentify the method that will be used in solving for x.
5 + x = three-fourths
distributive property
multiplication property of equality
division property of equality
subtraction property of equality
Answer:
I believe you're trying to say 5+x= 3/4
The sum of a number 8 and twice the number X is 28
ANSWERS ARE AT THE BOTTOM
To solve this question, we need to write the questions algebraically. Let's look at the problem first: The sum of a number 8, and twice the number x is equal to 28.
Algebraic form:
8 + 2x = 28
Lets solve this!
8 + 2x = 28 (Algebraic Form)
2x = 28 - 8 (Subtract 8 from both sides)
2x = 20 (Divide by 2)
x = 10 (Answer)
ANSWER:
x = 10
If+you+invest+$100+at+an+interest+rate+of+15%,+how+much+will+you+have+at+the+end+of+eight+years?
Answer:
$305.9022863 or $305.90 (rounded to 2 decimal places)
Step-by-step explanation:
It is a compound interest, meaning an interest accumulates on an initial amount every period. The formula
A= P(1+R)^n
A= the total amount P=Initial amount R= rate n=time period
P=$100 R=15% or 0.15(decimal) n=8 (years)
A= 100 (1.15)^8
A= 100(3.059022863)
A=305.9022863
The amount you will have after 8 years is $220
Calculating simple interestThe formula for calculating simple interest is expressed as:
SI =PRT
P is the principal = $100
T is the time = 8 years
R is the rate. = 15%
SI = 100 * 8 * 0.15
SI = $120
Amount after 8years = $100 + $120
Amount after 8years = $220
Hence the amount you will have after 8 years is $220
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y = 7x (6/7,-1/4) ….
Answer:
This point is not on the line, NOT TRUE
Step-by-step explanation:
The equation of the line is written in the slope-intercept form,
y = mx + b
where m represents the slope
b represents the y-intercept
where the format of a point is (x, y)
Given: y = 7x (6/7, -1/4)
we can plug in the point (6/7, -1/4)
-1/4 = 7(6/7)
-1/4 = 6
-1/4 does not equal 6 so this point is not on the line
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In the diagram below, a sequence of rigid motions maps ABCD onto JKLM.
If m/ A = 76, m/ B = 110°, and m / L = 116, the m/ M ?
In the diagram, the value of the last angle will be 158°.
How to calculate the angle?It should be noted that the total angle is a quadrilateral is 360°.
In this case, the value of the last angle will be:
= 360° - (76° + 110° + 116°)
= 360° - 302°
= 158°
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Find the range of the given function y = 3x + 2 for the domain 4 and -4.
Answer:
Range: (-10 , 14)
Step-by-step explanation:
Given information:
Equation: y = 3x +2Domain: (-4 , 4)Range: (x , y)?
Plug in domain of x = -4 and x = 4 into equation to find range.
f(-4) = 3 * -4 + 2 = -10
f(4) = 12 + 2 = 14
Range: (-10 , 14)
Just a question about the problem, dont need the answer if you dont want to solve it, but would 15 be negative? Thats all, Thanks!
[tex]f(x)=x^{2} +15x+3[/tex]
Answer:
[tex]x = -\frac{15}{2}[/tex]
Step-by-step explanation:
Hello!
The formula for the AOS is given to you, and you simply have to plug in the information given by the equation.
Equation of a Parabola (Standard): [tex]y = ax^2 + bx + c[/tex]
Comparing it to our equation:
a = 1b = 15c = 3Plug it in to the AOS formula:
[tex]x = \frac{-b}{2a}[/tex][tex]x = \frac{-15}{2(1)}[/tex][tex]x = -\frac{15}{2}[/tex]You only have to input 15 in to the correct box since the negative sign is already placed for you.
Please help!!!!! ASAP, If you can, i would love the steps on how to do it!! Thanks
Answer:
(5,18) & (-5 , 38)
Step-by-step explanation:
Solutions of linear and quadratic system of equations:A linear equation represented by a line in a graph intersect the quadratic equation represented by a parabola zero, one or two times.
f(x) = x² - 2x + 3 -------------------(I)
f(x) = -2x + 28 ---------------------(II)
x² - 2x + 3 = -2x + 28
x² - 2x + 2x + 3 - 28 = 0
x² - 25 = 0
x² = 25
x = √25 = √5*5
x = ± 5
Plugin x = 5 in equation (II),
f(5) = -2*5 + 28
= -10 + 28
= 18
(5 , 18)
Plugin x = -5 in equation (II),
f(-5) = -2*(-5) + 28
= 10 + 28
= 38
(-5, 38)
Answer:
(5, 18) and (-5, 38)
Step-by-step explanation:
Given system of equations:
1) f(x) = x² - 2x + 3 ⇒ y = x² - 2x + 3
2) f(x) = -2x + 28 ⇒ y = -2x + 28
Solve using the Substitution Method:
Step 1: Substitute the the first equation into the second equation.
⇒ x² - 2x + 3 = -2x + 28
Step 2: Solve for x.
x² - 2x + 3 = -2x + 28 [ Add 2x to both sides. ]
x² - 2x + 2x + 3 = -2x + 2x + 28
⇒ x² + 3 = 28 [ Subtract 28 from both sides. ]
x² + 3 - 28 = 28 - 28
⇒ x² - 25 = 0 [ Factor using the following rule: a² - b² = (a - b)(a + b). ]
(x - 5)(x + 5) = 0
⇒ x - 5 = 0, x + 5 = 0 [ Solve for the values of x. ]
x - 5 + 5 = 0 + 5, x + 5 - 5 = 0 - 5
⇒ x = 5, x = -5
Step 3: Solve for y.
Substitute the found x-values into one of the given equations.
y = x² - 2x + 3 ⇒ y = (5)² - 2(5) + 3 ⇒ y = 25 - 10 + 3 ⇒ y = 18
y = x² - 2x + 3 ⇒ y = (-5)² - 2(-5) + 3 ⇒ y = 25 + 10 + 3 ⇒ y = 38
The solutions to the system of equations are:
⟹ x₁ = 5, y₁ = 18 ⇒ (5, 18)
⟹ x₂ = -5, y₂ = 38 ⇒ (-5, 38)
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Find the equation of the line through point (4,−7) and parallel to =−2/3+3/2 Use a forward slash (i.e. "/") for fractions (e.g. 1/2
Answer:
y=-2/3x-13/3
Step-by-step explanation:
parralel line have the same gradient
y=mx+c is the general straight line equation
m represents the gradient
if the equation is y=-2/3x+3/2
m=-2/3
the coordinates (4,-7)
x=4
y=-7
substitute into equation
-7=-2/3×4+c
-7=-8/3+c
c=-7+8/3
c=-13/3
so the equation is :
y=-2/3x-13/3
please solve and tell me all that apply
Answer:
-x+4, 4+-x
Step-by-step explanation:
Obtain these answers by moving the X and 4 around and multiplying the equation by -1
What is the degree of polynomial: 2x- root 5
Answer: 1
Step-by-step explanation:
[tex]2x-\sqrt{5}=2x^{1}-\sqrt{5}[/tex], and thus the highest exponent of x is 1
!!!! PLEASE HELP !!!!
The senior classes at High School A and High School B planned separate trips to
New York City. The senior class at High School A rented and filled 4 vans and 3
buses with 133 students. High School B rented and filled 9 vans and 1 bus with 167
students. Each van and each bus carried the same number of students. How
many students can a van carry? How many students can a bus carry
A) Van: 23, Bus: 16
C) Van: 6, Bus: 34
B) Van: 25, Bus: 36
D) Van: 16, Bus: 23
