Answer:
A directly proportionality between x and y is written as:
y = k*x
where k is the constant of proportionality.
Then, if p is directly proportional to (q + p)^2
We can write this as:
p = k*(q + p)^2
Now we know that q = 1 when p = 1
Then we can replace these values in the above equation to find the value of k
1 = k*(1 + 1)^2
1 = k*2^2 = k*4
1/4 = k
Then the equation is:
p = (1/4)(p + q)^2
Now we want to find the value of q when p = 10
So we just replace p by 10, and solve the equation
10 = (1/4)*(q + 10)^2
10*4 = (q + 10)^2
40 = q^2 + 2*q*10 + 10^2
40 = q^2 + 20*q + 100
This is a quadratic equation for q, such that:
q^2 + 20*q + 100 - 40 = 0
q^2 +20*q + 60 = 0
This is the equation that gives the value of q when p = 10
To solve this, we can use Bhaskara's equation, which says that for a quadratic equation:
a*x^2 + b*x + c = 0
The solutions are given by:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]
In this case, the solutions for q are:
[tex]q = \frac{-20 \pm \sqrt{20^2 - 4*1*60} }{2*1} = \frac{-20 \pm 12.65}{2}[/tex]
Then we have two possible values for q:
q = (-20 + 12.65)/2 = -3.675
q = (-20 - 12.65)/2 = -16.325
Neil is buying steak for a cookout on Saturday. Steak is on sale for $9.62 per pound. If he buys 7.5 pounds of steak, how much money does he spend?
Answer:
$72.15
Step-by-step explanation:
x= pounds of steak
$[tex]9.62x[/tex] = money spent on steaks
If Neil buys 7.5 pounds of steak then x =7.5
$9.62(7.5) = $72.15
Answer:
$72.15
Step-by-step explanation:
1 pound = $9.62
7.5 pounds = $9.62 × 7.5
= $72.15
A rectangular room is 4 times as long as it is wide, and its perimeter is 50 meters. Find the dimension of the room
Answer:
Width=5m
Lenght= 20m
Step-by-step explanation:
L= Lenght
W= width
perimeter = (2L + 2W) ......eqn(1)
From the question, length of the rectangle is 4 times of it's width
Then
L = (4W)........eqn(2)
But perimeter = 50
Fromeqn(1)
(2L + 2W)= 50........eqn(3)
Sub eqn(1) in eqn(3)
2(4W) + 2W = 50
8W + 2W= 50
10W= 50
W=5
From (1)
L = (4W)
L= 4×5= 20
Lenght= 20
M is the midpoint of AD.
What single transformation is required to map one of
these congruent triangles onto the other?
o
B
O Reflection
O Rotation
27
27
O Translation
O Dilation
А
M
D
Answer:
Mapping congruent triangles
mis the midpoint of ad.
what single transformation is required to map one of
these congruent triangles onto the other?
reflection
o rotation
o translation
o dilation
27
) intro
✓ done
4 of 9
The single transformation required to map one congruent triangle onto the other is a translation. So, correct option is C.
The given information describes two congruent triangles, triangle ABM and triangle DCM, which share a common side, MC. The lengths of sides BM and MC are given as 27.
To determine the transformation required to map one congruent triangle onto the other, we need to consider the corresponding sides and angles of the triangles.
Since the corresponding sides AB and CD are congruent, and the corresponding side BM and MC are congruent, this suggests a translation transformation. A translation involves shifting the entire shape in a specific direction without any change in size or shape.
Therefore, the single transformation required to map one congruent triangle onto the other is a translation. It would involve moving triangle DCM along the direction of the congruent sides to align it with triangle ABM, while keeping the distances and angles unchanged.
No other transformation (reflection, rotation, or dilation) is needed because the triangles are already congruent, which means they have the same shape and size.
To learn more about transformation click on,
https://brainly.com/question/16356508
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Complete question is:
m is the midpoint of ad. triangles a b m and d c m are connected at point m. sides a b and c d are congruent. the lengths of sides b m and m c are 27. what single transformation is required to map one of these congruent triangles onto the other?
a. reflection
b. rotation
c. translation
d. dilation
What is the distance from the origin to point P graphed on the complex plane below?
Answer: (b)
Step-by-step explanation:
Given
Point P can be written as [tex]z=2-5i[/tex]
Distance of Point P can be given by [tex]\left | z \right |[/tex]
[tex]\Rightarrow \left | z\right |=\sqrt{2^2+(-5)^2}\\\Rightarrow \left | z\right |=\sqrt{4+25}\\\Rightarrow \left | z\right |=\sqrt{29}[/tex]
Thus, option (b) is correct.
Answer:
the answer is b
Step-by-step explanation:
Find the ratio of sin (A) please help
Answer:
8/17
Step-by-step explanation:
take angle A as reference angle
using sin rule
sin A = opposite / hypotenuse
sin A = 16/34
sin A = 16/34
sin A = 8/17
Answer this question pls? Its 20 pts
Answer:
B a = 180 -77-60
Step-by-step explanation:
The angles add to 180 degrees since they form a straight line
77+ 60+a = 180
a = 180 -77-60
The answer is B.
Step-by-step explanation:
We know that the sum of angles in a straight line = 180°
Therefore:
77° + 60° + a = 180°
a = 180° - 77° - 60°
Hence, option B is the answer.
Given that triangle GHJ = triangle XYZ What is m
If you get paid 30.00 per hour and you worked 8.5 hours how much do you get paid
Answer:
About 255
Step-by-step explanation:
$30 x 8.5= $225
Identify the coefficient in the term 7x^2 y^3. A. 7 B. 2 C. 3
Answer:
7
Step-by-step explanation:
it is because 7 is behind the variables
Which transformation performed on Triangle PQR will create an image Triangle P'Q'R' contained entirely in Quadrant II?
A
a counter-clockwise rotation of 90 degrees about the origin
B
a reflection over the x-axis
C
a reflection over the y-axis
D
a translation of 2 units to the left
-BRAINLIEST IF ANSWERED RIGHT-
Given the equation
5+x−12=x−7:
Part A. Solve the equation
5+x−12=x−7. In your final answer, be sure to state the solution and include all of your work.
Part B. Use the values
x=−4,0,5 to verify your solution to the equation
5+x−12=x−7.
In your final answer, include all of your calculations.
Answer:
Part A:
[tex]x\in \mathbb{R}[/tex] ([tex]x[/tex] is equal to all real numbers)
Part B:
[tex]5+(-4)-12=-4-7,\\-11=-11\:\checkmark,\\\\5+0-12=0-7,\\-7=-7\:\checkmark,\\\\5+5-12=5-7,\\-2=-2\:\checkmark[/tex]
Step-by-step explanation:
Part A:
Given [tex]5+x-12=x-7[/tex], combine like terms:
[tex]x-7=x-7[/tex]
Add 7 to both sides:
[tex]x=x[/tex]
Since this is merely a true statement for all real numbers (reflexive property), this equation is true for any real value of [tex]x[/tex].
Therefore,
[tex]x\in \mathbb{R}[/tex] ([tex]x[/tex] is equal to all real numbers).
Part B:
Using arbitrary values [tex]x=-4, x=0, x=5[/tex] as requested in part B, verify:
[tex]5+(-4)-12=-4-7,\\-11=-11\:\checkmark,\\\\5+0-12=0-7,\\-7=-7\:\checkmark,\\\\5+5-12=5-7,\\-2=-2\:\checkmark[/tex]
Translate the description as an algebraic expression:
the ratio of 3 and the product of 7 and r
I WILL GIVE YOU BRAINLIEST AS SOON AS I CAN, PLEASE HELP!
Answer:
1. The given equation is presented as follows;
[tex]3^{2 \cdot x - 1} = \dfrac{1}{9}[/tex]
The above equation can be rewritten as follows;
[tex]3^{2 \cdot x - 1} = 3^{-2}[/tex]...(1)
Therefore, taking logarithm to base 3 of both sides of the equation, the above equation can be rewritten without an exponent as follows;
[tex]log_3 \left (3^{2 \cdot x - 1} \right) =log_3\left(\dfrac{1}{9} \right) = log_3 \left( 3^{-2} \right)[/tex]...(2)
2. Inverse relationship of exponents is given as follows;
(1/a)ˣ = a⁻ˣ
Therefore, we have;
1/9 = 1/(3²) = (3²)⁻¹ = 3⁻²
Taking log of both sides of [tex]\left (3^{2 \cdot x - 1} = \dfrac{1}{9} = 3 ^{-2}\right)[/tex] gives;
[tex]log_3 \left (3^{2 \cdot x - 1} \right)= log_3 \left( 3^{-2} \right)[/tex]
From logarithm rules, we have;
From equation (2), we have;
[tex](2 \cdot x - 1) \cdot log_3 3 = -2 \cdot log_3 3[/tex]
Therefore, the equation can be simplified by dividing both sides by the common factor, [tex]log_3 3[/tex], as follows;
[tex]\dfrac{(2 \cdot x - 1) \cdot log_3 3 }{log_3 3} = \dfrac{-2 \cdot log_3 3}{log_3 3}[/tex]
Therefore, we get;
2·x - 1 = -2...(3)
3. Solving 2·x - 1 = -2, gives;
2·x - 1 = -2
2·x = -2 + 1 = -1
x = -1/2 = -0.5
x = -0.5
EQUATION 3
The given equation is presented as follows;
[tex]125^{x - 1} = 5^x[/tex]
1. By the property of exponents, we have;
[tex]\left(a^b \right)^x = a^{b \times x}[/tex]
125 = 5³
Therefore, we get;
[tex]125^{x - 1}= \left(5^3\right)^{x - 1} = 5^{3\times (x - 1)} = 5^{(3\times x - 3)}[/tex]
[tex]125^{x - 1}= 5^{(3\times x - 3)}[/tex]
2. Given that we can rewrite the given equation as follows;
[tex]125^{x - 1} = 5^{(3\times x - 3)} = 5^x[/tex]
Therefore;
[tex]5^{(3\times x - 3)} = 5^x[/tex]
Both sides of the equation are given in powers of 5, therefore, the appropriate base logarithm to use on both sides to rewrite the equation is logarithm to base 5
3. Using logarithm, by applying logarithm to both sides, we get;
[tex]log_5 \left (5^{(3\times x - 3)} \right) = log_5 \left(5^x \right)[/tex]
[tex](3\times x - 3) \cdot log_5 5 = x \cdot log_5 5[/tex]
Dividing both sides by log₅5 gives;
[tex]\dfrac{ (3\times x - 3) \cdot log_5 5}{log_5 5} = \dfrac{ x \cdot log_5 5}{log_5 5}[/tex]
∴ 3 × x - 3 = x
3 × x - x = 3
2·x = 3
x = 3/2 = 1.5
x = 1.5
Step-by-step explanation:
Each time one of you change the tires and 82 rows each row has an equal number of white and blue tile in town what is y ?
Answer:
5 blue tiles on each row
Step-by-step explanation:
Given
[tex]Tiles = 80[/tex]
[tex]Rows= 8[/tex]
[tex]Color = \{White, Blue\}[/tex]
[tex]White = Blue[/tex]
See comment for original question
Required
The number of blue in each row
First, we calculate the number of tiles in each row.
[tex]Unit = \frac{Tiles}{Rows}[/tex]
[tex]Unit = \frac{80}{8}[/tex]
[tex]Unit = 10[/tex]
The distribution of tiles on each row is:
[tex]White + Blue = Unit\ Tiles[/tex]
[tex]White + Blue = 10[/tex]
On each row, we have: [tex]White = Blue[/tex]
So, the equation becomes
[tex]Blue + Blue = 10[/tex]
[tex]2\ Blue = 10[/tex]
Divide both sides by 2
[tex]Blue = 5[/tex]
The coefficient of "x" in 7-15xz is
Answer:
-15
Step-by-step explanation:
7-15xz
The expression x^2 - 10x + 24 is equivalent to
Answer:
[tex](x−6)(x−4)[/tex]
Step-by-step explanation:
[tex]x^2 - 10x + 24[/tex]
[tex] {x}^{2} −6x−4x+24[/tex]
[tex]x(x−6)−4(x−6)[/tex]
[tex](x−6)(x−4)[/tex]
Hope it is helpful...Answer:
(x - 4 )(x - 6 )
Step-by-step explanation:
[tex]x^2 - 10x + 24 \\\\=x^2 - 6x - 4x +24 \\\\=x(x - 6) -4(x - 6) \\\\=(x - 4)(x-6) \\[/tex]
Which graph represents the function y - 3 = 3/2 (x-4)
Answer: Should be the graph with the slope of (3/2)
What is the approximate volume
Answer:
3053 in^3
Step-by-step explanation:
volume of a sphere is 4/3*pi*r^3
Diamaeter is 2*r
so r=9
7/3*(3.14)*9^3=3053.63 so answer is D or the bottom
THE AMOUNT RECIEVE BY JOY IF SHE WORKED m HOURS AT PHP300 PER HOUR?
Step-by-step explanation:
THE AMOUNT RECIEVE BY JOY IF SHE WORKED m HOURS AT PHP300 PER HOUR?
hi please mark me as brilliant
pls help me solve pls show how you got the answer
Answer:
$348
Step-by-step explanation:
Unit rate:
Sales clerk: $12/h
Assistant manager: 1/2 x 12= $6/h
Manager: 2 1/2 x 12= $30/h
Now for how long they will work (7.25 hours long):
Sales clerk: 12 x 7.25= $87
Assistant manager: 6 x 7.25= $43.5
Manager: 30 x 7.25= $217.5
In total: 87 + 43.5 + 217.5= $348 is paid in one day for each of the employees when they work 7.25 hours.
I hope this will help qwq
Which of the following sets is closed under subtraction?
none of the above
prime numbers
rational numbers
positive odd numbers
Find the area of the shape below 9cm 6cm 15 cm 11 cm
Answer:
8910cm^2
Step-by-step explanation:
Since there is no photo ill just multiply the 4 measurements
9x6x15x11
What's the shape? I'll be more than glad to help but I don't see the shape below. Comment underneath this and I'll try helping out.
Complete the angle addition postulate for the following angle
Answer:
measure of angle GEO.....
Choose the methods of solving quadratic equations
Completing the Square
Factoring
Square Root Method
Area Formula
Simplifying
Cross Multiplication
Guess and Check
Quadratic Formula
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Solve this quadratic equation using the quadratic formula.
x2 + 8x - 5 = 0
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Solve this quadratic equation using the quadratic formula.
2x2 - 2x = 1
Answer:
Factoring square root method quadratic formula completing the square method . x1=3+(check)3 and x2=3-(check)3 .
Step-by-step explanation:
Have an amazing day<3 thirty percent chance this is right 70 it’s wrong
I hate math, but math "love" me, keep on sticking to me.
For the given function, determine consecutive values of x between which each real zero is located. f(x)= -8x^4-3x^3-11x^2+8x+16
Answer:
Option C: there are zeros between x = 1 and x = 2, x = 0 and x = -1
Step-by-step explanation:
The function is given as;
f(x) = -8x⁴ - 3x³ - 11x² + 8x + 16
Since it's the real zero of the polynomial we are looking for, it means there is a possibility of getting an imaginary zero of the polynomial.
A zero is the value of x that will make the polynomial equal to zero.
Let's try;
x = -2;
f(-2) = -8(-2)⁴ - 3(-2)³ - 11(-2)² + 8(-2) + 16
f(-2) = -128 + 24 - 44 - 16 + 16
f(-2) = -148
Let's try x = -1;
f(-1) = -8(-1)⁴ - 3(-1)³ - 11(-1)² + 8(-1) + 16
f(-1) = -8 + 3 - 11 - 8 + 16
f(-1) = -8
Let's try x = 0;
f(0) = -8(0)⁴ - 3(0)³ - 11(0)² + 8(0) + 16
f(0) = 16
Lets try x = 1
f(1) = -8(1)⁴ - 3(1)³ - 11(1)² + 8(1) + 16
f(1) = -8 - 3 - 11 + 8 + 16
f(1) = 2
Let's try x = 2;
f(2) = -8(2)⁴ - 3(2)³ - 11(2)² + 8(2) + 16
f(2) = -128 - 24 - 44 + 16 + 16
f(2) = -164
From the values of f(x) gotten from x= -2 to x =2, we can see that the zeros will be closest to x = 0 and x = - 1 and also between x = 1 and x = 2 since that is the range that produced f(x) to be close to zero.
need help with this Q&A 5
Answer:
C
Step-by-step explanation:
anyone know the answer
Answer:
i have no clue
Step-by-step explanation:
BRAINIEST IF ANSWERED CORRECTLY
Create a single variable linear equation that has no solution. Solve the equation algebraically to prove that it does not have a solution. Create a single variable linear equation that has one solution. Solve the equation algebraically to prove that there is one distinct solution for the equation. Create a single variable linear equation that has infinitely many solutions. Solve the equation algebraically to prove that there is an infinite number of solutions for the equation
An example of something that doesn't have a solution is something like x+2 = x+3
If we subtract x from both sides, then we end up with 2 = 3, which is always false.
No matter what we plug in for x, the original equation will always be false. The right hand side is always 1 larger than the left side. So that's why we don't have any solutions here.
Side note: equations of this form are known as contradictions (or we could say the equation is inconsistent).
=====================================================
An example of something that has one solution is 3x+2 = 2x+7
Solving this equation leads us to...
3x+2 = 2x+7
3x-2x = 7-2
1x = 5
x = 5
To verify the solution, we plug it back into the original equation
3x+2 = 2x+7
3(5)+2 = 2(5)+7
15+2 = 10+7
17 = 17
We get the same thing on both sides, so we get a true statement. This confirms that x = 5 is the solution to 3x+2 = 2x+7.
=====================================================
An example of an equation with infinitely many solutions is 2x+4 = 2(x+2)
Notice how both sides are the same thing. The 2(x+2) distributes out to get 2x+4
Since we have the exact same identical expression on both sides, this ultimately means no matter what we plug in for x, we'll get a true statement. True statements (like the conclusion at the last section) are simply anything with the same number on both sides after simplifying everything.
Side note: equations of this form are known as identities
1. When 36 is subtracted from the square of a number, the result is five times the number. Create and solve an equation to find the possible values of this number.
Answer:
[tex]x^{2} -36 = 5x[/tex]
[tex]x^{2} -5x -36 =0[/tex]
(x-9)(x+4) = 0
x = 9 or x= -4
Step-by-step explanation: