Answer:
I would say the third one ( 15x + 10 = 10 )
Step-by-step explanation:
I say this because, if we take 10 from both sides, 15x = 0. Even if you tried to divide by 15, x = 0. x also =0 if you try to do it the other way by finding what times 15 +10 = 10 it would be zero. The third one is your Answerr
Since the only solution to the equation is 0, hence 15x + 10 = 10 is the only equation With a solution.
Equation of functions With only one solution
Equations With just one solution are knoWn to have a leading degree of one and Without a modulus sign
Fro the linear function 15x + 10 = 10
Check:
Subtract 10 from both sides
15x + 10 - 10 = 10 - 10
15x = 10 - 10
15x = 0
Dividde both sides by 15 to have:
15x/15 = 0/15
x = 0
Since the only solution to the equation is 0, hence 15x + 10 = 10 is the only equation With a solution.
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if f(x)=3x + 10 and g(x)= 2x - 4 find (f-g)( x)
[tex](f-g)(x)=3x+10-(2x-4)=3x+10-2x+4=x+14[/tex]
Which expression is equivalent to..? Assume
Answer:
The equivalent ratio of (3m⁻²n)⁻³/6mn⁻² = m⁵/2n
Step-by-step explanation:
Points to remember
Identities
xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾
xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾
(xᵃ)ᵇ = xᵃᵇ
x⁻ᵃ = 1/xᵃ
To find the equivalent ratio of (3m⁻²n)⁻³/6mn⁻²
By using identities,
(3m⁻²n)⁻³ = 3m⁶n⁻³
(3m⁻²n)⁻³/6mn⁻² = 3m⁶n⁻³/6mn⁻²
= 3m⁽⁶⁻¹⁾n⁽⁻³ ⁻ ⁻²⁾/6
= m⁵n⁻¹/2
= m⁵/2n
Therefore the equivalent ratio of (3m⁻²n)⁻³/6mn⁻² = m⁵/2n
The chart shows how the Lewis family spends their money. Make a circle graph to display the data.
Lewis Family spending:
Housing $10,500
Food $ 7,500
Clothing $3,000
Investments $3,000
Miscellaneous $6,000
Witch represents the inverse of the function f(x)=1/4x-12
Answer:
y=4x+48
Step-by-step explanation:
2. y = -x + 3
x+y = -1
how many solutions
Answer:
Step-by-step explanation:
y=-x+3
x+y=-1
y=-x+3
y=-x-1
-x+3=-x-1
add x to both sides
3=-1
no solutions
Calculate the sale price on a pair of blue jeans if the original price is $45.50 and the markdown is 15%.
Answer:
38.68
Step-by-step explanation:
First we need to find the markdown
markdown = original price * markdown rate
= 45.50 * 15%
= 45.50 * .15
= 6.825
Then we need to find the sale price
sale price = original price- markdown
= 45.50 - 6.825
=38.675
Rounding to the nearest cent
= 38.68
The sale price is 38.68
A system of equations has no solution. If y=8x +7 is one of the equations,which could be the other equation
Answer:
Step-by-step explanation:
Two lines that are parallel have the same slope but different y intercepts.
So you could have any equation that satisfies y = 8x + b. The only value that b cannot have is 7. All other values including 0 are fine.
So here are a couple of examples.
y = 8x b = 0
y = 8x + 92
y = 8x + 1/2
y = 8x + pi
y = 8x - 13
7 = 8x - pi
A. 15 degrees
B. 45 degrees
C. 30 degrees
D. 60 degrees
Answer: C. 30 degrees
Step-by-step explanation:
By definition, an hexagon is a polygon with six sides.
The sum of the interior angles of an hexagon is 720 degrees.
Based on this, the measure of eac interior angle is:
[tex]interior\ angle=\frac{720\°}{6}=120\°[/tex]
Therefore, the measure of ∠1 is:
[tex]\angle 1=\frac{120\°}{2}\\\\ \angle 1=60\°[/tex]
So, to find the angle ∠2, you can divide ∠1 by 2:
[tex]\angle 2=\frac{60\°}{2}\\\\ \angle 2=30\°[/tex]
8. Suppose the curve y = x4 + ax3 + bx2 + cx + d has a tangent line when
x = 0 with equation y = 2x + 1, and a tangent line when x = 1 with equation
y= 2 – 3x. Find the values of a, b, c and d.
Answer:
a=1, b=-6, c=2, d=1
Step-by-step explanation:
You are given the function
[tex]y=x^4+ax^3+bx^2+cx+d[/tex]
Find the derivative:
[tex]y'=4x^3+3ax^2+2bx+c[/tex]
The curve has a tangent line when x = 0 with equation y = 2x + 1, so
[tex]y'(0)=2\\ \\y(0)=1[/tex]
Hence,
[tex]y'(0)=4\cdot 0^3+3a\cdot 0^2+2b\cdot 0+c=2\Rightarrow c=2\\ \\y(0)=0^4+a\cdot 0^3+b\cdot 0^2+2\cdot 0+d=1\Rightarrow d=1[/tex]
The curve has a tangent line when x = 1 with equation y = -3x + 2, so
[tex]y'(1)=-3\\ \\y(1)=-3+2=-1[/tex]
So,
[tex]y'(1)=4\cdot 1^3+3a\cdot 1^2+2b\cdot 1+c=4+3a+2b+2=-3\Rightarrow 3a+2b=-9\\ \\y(1)=1^4+a\cdot 1^3+b\cdot 1^2+2\cdot 1+d=1+a+b+2+1=-1\Rightarrow a+b=-5[/tex]
From the second equation, a=-5-b, substitute it into the first one:
[tex]3(-5-b)+2b=-9\\ \\-15-3b+2b=-9\\ \\-b=-9+15\\ \\-b=6\\ \\b=-6\\ \\a=-5-b=-5-(-6)=-5+6=1[/tex]
What is the general form of the equation of a circle with center at (a, b) and radius of length m?
Answer:
bru thats not the answer^
Step-by-step explanation:
selct the function that represents a geometric sequence
Answer:
A.Step-by-step explanation:
[tex]\text{If}\ A(n)\ \text{represents a geometric sequence, then}\ \dfrac{A(n)}{A(n-1)}=\bold{constant}.\\\\A.\\\\A(n)=P(1+i)^{n-1}\\\\A(n-1)=P(1+i)^{n-1-1}=P(1+i)^{n-2}\\\\\dfrac{A(n)}{A(n-1)}=\dfrac{P(1+i)^{n-1}}{P(1+i)^{n-2}}\\\\=(1+i)^{(n-1)-(n-2)}=(1+i)^{n-1-n+2}=(1+i)^1=1+i=\bold{constant}[/tex]
[tex]B.\\\\A(n)=(n-1)(P+i)^n\\\\A(n-1)=(n-1-1)(P+i)^{n-1}=(n-2)(P+i)^{n-1}\\\\\dfrac{A(n)}{A(n-1)}=\dfrac{(n-1)(P+i)^n}{(n-2)(P+i)^{n-1}}=\left(\dfrac{n-1}{n-2}\right)(P+i)^{n-(n-1)}\\\\=\left(\dfrac{n-1}{n-2}\right)(P+i)^{n-n+1}=\left(\dfrac{n-1}{n-2}\right)(P+i)^1\neq\bold{constant}[/tex]
others the same
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant. This is different from a quadratic function which does not represent a geometric sequence.
Explanation:In mathematics, a function represents a geometric sequence when each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. The general form of a geometric sequence can be written as a, ar, ar^2, ar^3, ... where 'a' is the first term, and 'r' is the common ratio.
The important factor in a geometric sequence is the multiplication by a constant. For example, let's say we have a sequence 2, 4, 8, 16. This is a geometric sequence because each term is multiplied by 2 to get the next term.
In contrast, a quadratic function, for instance, does not represent a geometric sequence as it's formed by the equation ax^2 + bx + c where a, b, and c are constants.
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What is the perimeter of a rectangle if the length is 5 and the width is x?
Answer:
The perimeter of the rectangle is 10 + 2x.
Step-by-step explanation:
The formula for the perimeter of a rectangle is 2(l + w) where l = length and w = width because you add up the length of all the sides.
So we can plug in our givens into the formula and simplify:
2(5 + x)
So the perimeter is: 10 + 2x
Notice that we cannot simplify the expression further because there is an unknown (the length).
Answer:
2x + 10
Step-by-step explanation:
A rectangle has opposite sides equal
2(5 + x)
2x + 10
what is the value of x?
14
15
16
17
Answer:
X = 14
Step-by-step explanation:
The given figure is a quadrilateral .In a Quadrilateral sum of angles is 360 degrees.
The given four angles in the quadrilateral are 70°,110°,110° and 5x °.
Applying angle sum property of quadrilateral:
70+110+110+5x=360°
Adding ,
290+5x=360
Subtracting both sides by 290 so that x term can be isolated,
290-290+5x=360-290.
5x=70
Dividing both sides by 5
x=14.
Value of x is 1
Answer:
x=14
Step-by-step explanation:
what is the domain of the graphed function
ANSWER
Option C is correct.
EXPLANATION
The given function is
[tex]y = \sqrt[3]{x - 1} + 3[/tex]
The base function is
[tex]y = \sqrt[3]{x} [/tex]
The given function has the same domain as its base function which is all real numbers.
Any real number you plug into this function is defined.
Since the function has no restriction, the domain is all real numbers.
[tex]x | x \: is \: real \: number[/tex]
Last week , Donnell practiced the piano 3 hours longer than Marcus . Together, Marcus and Donnell practiced the piano 11 hours . For how many hours did each young man practiced the piano
Answer:
Marcus practiced for 4 hours and Donnell practiced for 7 hours
Step-by-step explanation:
We can set up this problem as a system of linear functions
We'll use d to represent Donnell and m to represent Marcus
Since Donnell practiced 3 hours more than Marcus, we can represent this as an equation:
d=m+3
And since they both practiced for a combined total of 11 hours, we can represent this an an equation:
d+m=11
We can substitute d=m+3 into d+m=11 and we get:
m+3+m=11
2m+3=11
2m=8
m=4
Now we can substitute m=4 into d+m=11
d+4=11
d=7
Therefore, Donnell practiced for 7 hours and Marcus practiced for 4 hours
Solve the system of equations below. Enter your answer in the boxes.
8a + 12b = 92
6a – 4b = 4
The solution of the system of equations is a = 4 and b = 5.
What is the system of equations?A system of equations is a set of two or more equations that you deal with at one time.
The given system of equations are;
8a + 12b = 92
6a – 4b = 4
From equation 1
[tex]\rm 8a + 12b = 92\\\\ 8a=92-12b\\\\a=\dfrac{92-12b}{8}[/tex]
Substitute the value of a in the equation 2
[tex]\rm 6a-4b=4\\\\6\times \dfrac{92-12b}{8}-4b=4\\\\3\times \dfrac{92-12b}{4}-4b=4\\\\ 276-36b-16b=16\\\\-52b=16-276\\\\-52b=-260\\\\b=\dfrac{-260}{-52}\\\\b=5[/tex]
Substitute the value of b in the equation 2
[tex]\rm 6a – 4b = 4\\\\6a-4\times 5=4\\\\6a-20=4\\\\6a=4+20\\\\6a=24\\\\a=\dfrac{24}{6}\\\\a=4[/tex]
Hence, the solution of the system of equations is a = 4 and b = 5.
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Which of the following describe an angle with a vertex at E?
Check all that apply.
Answer: The correct options are
(A) DEF.
(C) FED.
Choices:
A. DEF B. DFE C. FED D. EFD
Answer:
FED and DEF
Step-by-step explanation:
vertex is the middle letter
Earth revolves on its axis once every 24 hours. Which statements are true? Check all that apply.
The angular velocity of Earth is π/12 radians per hour.
The angular velocity of Earth is π/12 radians per day.
The angular velocity of Earth is 2π radians per hour.
The angular velocity of Earth is 2π radians per day.
The angular velocity of Earth is 12π radians per day.
Answer:
The angular velocity of Earth is π/12 radians per hour.
The angular velocity of Earth is 2π radians per day.
Step-by-step explanation:
A full circumference of a circle (as the Equator line on Earth) is 2π radians.
Since the planet does a full revolution in 24 hours... that means it makes a full turn in a day.
So, we can see that in a day, the planet rotates 360 degrees... or 2π radians per day!
Now, if you want to find the angular velocity per HOUR... you divide that by 24... so 2π/24 = π/12 radians
So, we can also say it does π/12 radians per hour.
Answer:
a and d on ed
Step-by-step explanation:
At a competition with 5 runners, medals are awarded for first, second, and
third places. Each of the 3 medals is different. How many ways are there to
award the medals?
Decide if this is a permutation or a combination, and find the number of ways
to award the medals.
Answer:
a
Step-by-step explanation:
thanks
Answer:
B: Permutation; Number of ways are 60
Step-by-step explanation:
At a competition with 5 runners, medals are awarded for first, second, and third places.
Each of the 3 medals is different.
This is a case of Permutation and the Number of ways are 60.
We have to award 3 medals among 5 runners.
This can be done in 5P3 ways.
= [tex]\frac{5!}{(5-3)!}[/tex]
= [tex]\frac{5\times4\times3\times2\times1}{2\times1}[/tex]
= [tex]5\times4\times3=60[/tex]
Therefore, the answer is option A.
Angela rode his bike around a bike trail that was 1/4 of a mile long he rode his bike around the trail eight times Angelo says he wrote a total of 8/4 miles Teresa says he is wrong and that he actually rode 2 miles who is correct use words and drawings to explain how you know
Similiar triangles can have congruent angles and sides
Answer:
The statement is true.
Step-by-step explanation:
The statement is true.
This is true. Since they could be considered similar even when they are congruent, since in similar triangles, the measurements are proportional. In congruent triangles, this proportion is just one. or 1/1
Hope this helps!
please help ASAP! i will mark brainliest
Use two pints on the graph to find the slope:
(0,0) and (5,1)
Slope = Change in Y over the change in x.
Slope = (1-0) / (5-0) = 1/5 = 0.20
The slope of the given equation is 0.25 which is greater than 0.20.
The unit rate is greater in the equation.
Simplify 8x + 9x completely.
Answer:
[tex]17x[/tex]
Step-by-step explanation:
[tex]8x + 9x = 17x[/tex]
To simplify the expression 8x + 9x, you combine the like terms by adding the coefficients. The result is 17x.
Explanation:The process involved in simplifying an equation like this is known as combining like terms. In this example, the terms are 8x and 9x. Because they both contain the same variable, x, you can combine them.
To perform this operation, you add the coefficients (the numbers in front of the variable). In this case, the coefficients are 8 and 9. So, 8x + 9x simplifies to 17x.
Therefore, the simplified form of the equation 8x + 9x is 17x.
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The sum of four numbers is 1,320. The sum of three of the numbers is 40% more than the other number, x. What is the value of x ?
Since the numbers are not consecutive natural numbers, how about if I let the 4 numbers be a, b, c, and d?
The sum is given to be 1320.
a + b + c + d =1320...I will call this the first equation.
Can I then say that the second equation is b + c + d = 0.4a + a? Yes, I can do this.
Simplifying my second equation,
I get b + c + d = 1.4a.
Plugging this into my first equation, I get
a +1.4a =1320
2.4a =1320
So, a =1320/(2.4) =550.
Answer: 550
Answer:
550
Step-by-step explanation:
We aren't given that they are consecutive so lets just pretend the numbers are x, y, z , and r.
We are given x+y+z+r=1320
We are also given that y+z+r=.4x+x
Simplifying my second equation gives us y+z+r=1.4x. I'm going to plug this into first equation giving me
x+1.4x=1320
2.4x=1320
So x=1320/2.4=550
6) A cereal box has the following dimensions:
height of 12 inches and width of 2 inches. If
the volume of the box is 192 cubic inches.
find the length of the box.
Hint: V = lwh
Answer:
8 inches
Step-by-step explanation:
The problem gives us a basic formula, the volume formula for a rectangular prism. All we have to do is use this formula, plug in all the values that are given, and solve for the unknown value.
[tex]V = lwh[/tex]
[tex]192 = l(12)(2)[/tex]
[tex]192 = 24l[/tex]
From here, all we need to do is divide 24 from both sides of the equation, since what you do to one side of the equation you must do to the other!
[tex]8 = l[/tex]
The length of the box will thus be 8 inches.
it is going to be 8 inches Hope it helps !!!!!
What is the name of an interior angle of a triangle that is not adjacent to a given exterior angle of the triangle?
exterior angle
adjacent interior angle
remote interior angle
alternate interior angle
Answer:
Remote Interior Angle
Step-by-step explanation:
The name of an interior angle of a triangle that is not adjacent to a given exterior angle of the triangle is Remote Interior Angle.
If you take a look at the picture attached, you will find three angles: ∠A, ∠C and ∠D. In this case, we have that ∠A comes to be the exterior angle while ∠C and ∠D are the remote interior angle given that they are not adjacent to ∠A
Find the value of x for which the lines are parallel.
Answer: 64 °
64-1=63.
The parallel lines make the angles equal so they have the same measurement.
Writing Linear Equations
Instruction Active
Writing an Equation Given Two Points on the Line
Write the equation of the line that passes through the points (7,-4) and (-1,3), first in point-slope form, and then in
slope-intercept form.
The slope of the line is
When the point (7.-4) is used, the point-slope form of the line is
The slope-intercept form of the line is
Answer:
[tex]\text{The slope:}\ m=-\dfrac{7}{8}\\\\\text{The point-slope form:}\ y+4=-\dfrac{7}{8}(x-7)\\\\\text{The slope-intercept form:}\ y=-\dfrac{7}{8}x+\dfrac{17}{8}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have two points (7, -4) amd (-1, 3).
Calculate the slope:
[tex]m=\dfrac{3-(-4)}{-1-7}=\dfrac{7}{-8}=-\dfrac{7}{8}[/tex]
The point-slope form of an equation of a line:
[tex]y-(-4)=-\dfrac{7}{8}(x-7)\\\\y+4=-\dfrac{7}{8}(x-7)[/tex]
Convert to the slope-intercept form:
[tex]y+4=-\dfrac{7}{8}(x-7)[/tex] use the distributive property
[tex]y+4=-\dfrac{7}{8}x+\dfrac{49}{8}[/tex] subtract 4 = 32/8 from both sides
[tex]y=-\dfrac{7}{8}x+\dfrac{17}{8}[/tex]
The equation of the line passing through (7,-4) and (-1,3) has a slope of -7/8, the point-slope form is y + 4 = -7/8(x - 7), and the slope-intercept form is y = -7/8x + 17/8.
To write the equation of the line that passes through the points (7,-4) and (-1,3), we first need to calculate the slope of the line using the formula m = (y2 - y1) / (x2 - x1).
Applying this to our points, we get m = (3 - (-4)) / (-1 - 7), which simplifies to m = 7 / -8 = -7/8. Now, using the point-slope form y - y1 = m(x - x1), and the point (7, -4), we can write the equation as y - (-4) = -7/8(x - 7).
Next, to convert this to slope-intercept form, we simplify the point-slope equation to solve for y: y + 4 = -7/8x + 49/8, and then subtract 4 (or 32/8) from both sides to get y = -7/8x + 17/8. This is our slope-intercept form, where -7/8 is the slope, and 17/8 is the y-intercept.
what is the scale factor of two similar pyramids with volumes of 64 cubic feet and 8 cubic feet
Answer: 2:1
Step-by-step explanation:
Volume of a pyramid (V) = [tex]\dfrac{1}{3}\times l\times w\times h\bigg[/tex]
For simplicity, let's assume that l = w = h, then [tex]V = \dfrac{1}{3}s^3[/tex]
Pyramid 1 has a volume of 64:
[tex]64=\dfrac{1}{3}s^3\\\\3\times 64=s^3\\\\\sqrt[3]{3\times 64}=\sqrt[3]{s^3} \\\\4\sqrt[3]{3} =s[/tex]
Pyramid 2 has a volume of 8:
[tex]8=\dfrac{1}{3}s^3\\\\3\times 8=s^3\\\\\sqrt[3]{3\times 8}=\sqrt[3]{s^3} \\\\2\sqrt[3]{3} =s[/tex]
Comparing the sides of Pyramid 1 to the sides of Pyramid 2:
[tex]\dfrac{4\sqrt[3]{3}}{2\sqrt[3]{3}}=\dfrac{2}{1}\implies \text{scale factor of }2:1[/tex]
The scale factor of two similar pyramids with volumes of 64 cubic feet and 8 cubic feet is 2.
Understanding the Scale Factor of Similar Pyramids
To find the scale factor between two similar pyramids, we need to understand the relationship between their volumes and their corresponding dimensions. The volumes of the two pyramids given are 64 cubic feet and 8 cubic feet.
The formula for the volume of similar shapes indicates that the volume varies as the cube of the scale factor. This can be mathematically expressed as:
If V1 and V2 are the volumes of two similar figures with a scale factor of k, then: V1 / V2 = k3
For this problem:
64 ÷ 8 = k3
Simplifying:
8 = k3
Taking the cube root of both sides:
k = 2
So, the scale factor of the two similar pyramids is 2.
Find the circumference of a circle with a radius of 6. Leave your answer in terms of 3 6 12 36
Answer:
C≈37.7 or 36
Step-by-step explanation:
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Answer:
2x3.14x6=36
Step-by-step explanation: