Answer:
[tex]y=2x+1[/tex]
Step-by-step explanation:
Let the linear equation be [tex]y=mx +b[/tex].
The slope of a linear equation is the same as the rate of change of that linear linear equation.
The rate of change of y with respect to x is given in the question as 2.
[tex]\implies m=2[/tex]
We substitute this slope to obtain the partial equation;
[tex]y=2x+b[/tex]
If the coordinate (0,1) is a solution, then it must satisfy this equation.
[tex]\implies 1=2(0)+b[/tex]
[tex]\implies 1=b[/tex]
The required equation is:
[tex]y=2x+1[/tex]
the equation of the line is y = 2x + 1.
The student asked for the equation of a linear function where the rate of change of y with respect to x is two, and the coordinate (0,1) is a solution. This means the slope (m) of the line is 2, and it passes through the point (0,1). The general form of a linear equation is y = mx + b, where m is the slope, and b is the y-intercept.
Since we know the slope is 2 and it passes through (0,1), we can substitute these values into the equation to find b:
1 = 2(0) + b.
So, b = 1. Therefore, the equation of the line is y = 2x + 1.
A system of equations is given below. y = 2x + 1/4 and 2x - 1/4
Which of the following statements best describes the two lines?
They have the same slope but different y-intercepts, so they have no solution.
They have the same slope but different y-intercepts, so they have one solution. They have different slopes but the same y-intercept, so they have no solution.
They have different slopes but the same y-intercept, so they have one solution.
Answer:
They have the same slope but different y-intercepts, so they have no solution.
Step-by-step explanation:
As the slopes are the same (2) but the y-intercepts are different, it means that the straights are parallel. Parallel equations have no solution as the straights don't intercept each other.
Answer: They have the same slope but different y-intercepts, so they have no solution.
The given equations are [tex]y=2x+\frac{1}{4}[/tex] and [tex]y=2x-\frac{1}{4}[/tex].
We compare them with y = mx + b.
So the slope of both of them is m=2.
y-intercept for the first one is = b = 1/4
y-intercept for the second one is = b = -1/4
Hence, the lines are parallel and will never meet and will have no solution.
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What is the slope-intercept equation for the line below?
(0, 2)
Answer:
Step-by-step explanation:
There is no given equation, so it is impossible to figure this out. I apologize.
2(x + 2) – 4x = 12
Solve for x in the equation below.
Answer:
x = -4
Step-by-step explanation:
Distribute 2 inside the parentheses
[tex]2\times x = 2x\\ 2\times2=4\\ 2x+4 - 4[/tex]
Combine like terms
[tex]-4x + 2x = -2x + 4 = 12[/tex]
Subtract 4 from both sides
-2x = 8
x = -4
The solution of the linear equation 2(x + 2) – 4x = 12 will be negative 4.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given below.
2(x + 2) - 4x = 12
Solve for x in the equation 2(x + 2) - 4x = 12. Then we have
2(x + 2) - 4x = 12
2x + 4 - 4x = 12
-2x = 12 - 4
-2x = 8
x = -8/2
x = -4
The solution of the linear equation 2(x + 2) – 4x = 12 will be negative 4.
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Find the product. Simplify your answer. a/a^2-16 × a+4/a^2
Answer:
[tex]\frac{1}{a(a-4)}[/tex]
Step-by-step explanation:
Factor the denominator of the first fraction
a² - 16 ← is a difference of squares and factors as
a² - 16 = (a - 4)(a + 4), thus fraction becomes
[tex]\frac{a}{(a-4)(a+4)}[/tex] × [tex]\frac{a+4}{a^2}[/tex]
Cancel the factor (a + 4) on numerator/denominator and the a and a², leaving
[tex]\frac{1}{a(a-4)}[/tex]
What is tan 11(3.14)/6
Answer:
A) -sqrt(3)/3
Step-by-step explanation:
If you know your unit circle (attached), 11pi/6 has the value of (sqrt(3)/2,-1/2), where the coords are (cosine, sine).
Tangent is sine/cosine:
(-1/2)/(sqrt(3)/2)
We can convert this to multiplication by miltiplying the reciprocal of sqrt(3)/2:
(-1/2)*(2/sqrt(3))
Multiplied out to:
-2/(2sqrt(3))
We have to rationalize this by multiplying the numerator and denominator by sqrt(3):
-2(sqrt(3))/2sqrt(3)(sqrt(3)
two of the same square roots multiplied together equals the number without the sqrt:
-2(sqrt(3))/2*3
we can factor out 2 from the numerator and denominator:
-sqrt(3)/3
Therefore, the answer is A
????????????????????
Answer:
ASA
Step-by-step explanation:
In the 2 triangles
∠J = ∠L
side OJ = side IL
∠O = ∠I
The triangles are congruent by the angle/side/angle (ASA ) postulate
can you find angle a
Check the picture below.
Solve 15 ≥ -3x or 2/5 x ≥ -2.
Answer:
x ≥ -5
Step-by-step explanation:
15≥-3x
switch sides
-3x≤15
Multiply both sides by -1 (reverse the inequality)
(-3x)(-1)≥15(-1)
Simplify
3x≥-15
Divide both sides by 3
3x/3≥ -15/3
Simplify
x≥ -5
Answer:
{x | x ≥ -5}
Step-by-step explanation:
Trying to help everyone!
The graph of y = ax2 + bx + c is a parabola that opens up and has a vertex at (0, 5). What is the solution set of the related equation 0 = ax2 + bx + c?
Answer:
The equation 0 = ax2 + bx + c has no real roots or no solution.
Step-by-step explanation:
We are told that the graph of y = ax2 + bx + c is a parabola that opens up and has a vertex at (0, 5). Since the parabola opens up, the vertex (0, 5) will be the lowest point on the graph of the function. This implies that the parabola does not intersect the x-axis; the line y = 0. Therefore, the equation;
0 = ax2 + bx + c will have no real roots or no solution. Find the attached.
use the distributive property to rewrite the expression without parentheses
(t+11)(-3)
Answer:
-3t - 33
Step-by-step explanation:
Distribute -3 to all terms within the other parenthesis:
(-3)(t + 11) = (-3)(t) + (-3)(11)
Simplify by multiplying:
(-3)(t) + (-3)(11)
-3t + (-33)
-3t - 33 is your answer.
~
a fair die is cast four times. Calculate the probability of obtaining exactly two 6's round to the nearest tenth of a percent
[tex]|\Omega|=6^4=1296\\|A|=1\cdot1\cdot5\cdot5\cdot\dfrac{4!}{2!2!}=25\cdot6=150\\\\P(A)=\dfrac{150}{1296}\approx11.6\%[/tex]
What is the equation of the line which includes points (1, 3) and (2, 8)?
The equation will be like this: y=ax+c. a is the slope and c is where the line crosses the (vertical) y axis - AKA the y-intercept.
As for the slope, it can be found like [(8-3)/(2-1)]. That gives 5. Another way to see it is to notice that between (1,3) and (2,8), the line moved up 5 points and went to the right only 1.
And for the y-intercept, make the equation y = 5x + c. Solve for c by filling x and y with information from any of the two points. Let's choose (1,3). Plugging in gives the equation 3=5(1)+c. C equals -2.
So, the final equation is:
y = 5x - 2
Answer:
y - 3 = 5(x - 1)
Step-by-step explanation:
Slope: as we move from (1, 3) to (2, 8), x increases by 1 and y increases by 5. Hence, the slope of this line is m = rise / run = 5/1, or just m = 5.
In point-slope form, the pertinent equation is
y - 3 = 5(x - 1)
a line, segment, or ray which divides the interior angels of a triangle into two equal parts what is it?
Answer:
A ray
Step-by-step explanation:
Answer:
ray
Step-by-step explanation:
I really need help on question 22, can anyone help me?!
Answer:
First, we need to find the missing side which is BC ( using pythagorean theorem)
AB² + BC² = AC²
=> 16² + BC² = 20²
=> BC² = 20² - 16² = 144
=> BC = √144 = 12
Now apply the formulars:
Just to make things easier, let's point out exactly what will the hypotenuse, opposite side and adjacent side.
So in this case:
The hypotenuse will be AC
The opposite side (of angle A) is BC
The adjacent side (of angle A) is AB
Therefore:
sin A = opposite/hypotenuse = BC/AC = 12/20 = 3/5
cos A = adjacent/hypotenuse = AB/AC = 16/20 = 4/5
tan A = opposite/adjacent = BC/AB = 12/16 = 3/4
4/x-3+5=2
What is the solution
Answer:
[tex]x=\frac{5}{3}[/tex]
Step-by-step explanation:
Let do algebra and figure out the value of x:
[tex]\frac{4}{x-3}+5=2\\\frac{4}{x-3}=2-5\\\frac{4}{x-3}=-3\\4=-3(x-3)\\4=-3x+9\\3x=9-4\\3x=5\\x=\frac{5}{3}[/tex]
Note: assuming that the problem is [tex]\frac{4}{x-3}+5=2[/tex]
Answer:
The answer is 5/3
Step-by-step explanation:
It costs $14.50 to rent a canoe and $6 to use the canoe for an hour. You have $32.50. Write an equation that represents the number h of hours you can rent the canoe.
Answer:
The maximum number of hours that can rent the canoe is 2 hours
Step-by-step explanation:
Let
h ----> the number of hours you can rent the canoe
we know that
The inequality that represent this situation is
[tex]14.5+6h\leq 32[/tex]
Solve for h
Subtract 14.5 both sides
[tex]6h\leq 32-14.5[/tex]
[tex]6h\leq 17.5[/tex]
Divide by 6 both sides
[tex]h\leq 17.5/6[/tex]
[tex]h\leq 2.9\ hours[/tex]
The maximum number of hours that can rent the canoe is 2 hours
The equation that represents the number of hours you can rent the canoe is h = ($32.50-$14.50)/$6.
Explanation:The subject of this question is Mathematics and it appears suitable for a Middle School level. Given the scenario you presented, we will need to create a linear equation to determine the number of hours of canoe rental. In this case, the $14.50 is a fixed cost, like the $31.50 in one of your examples. Additionally, the $6 per hour to use the canoe is a variable cost. To create an equation that represents the amount of hours you can rent the canoe, we first deduct the fixed cost from your total budget. This gives you $32.50 - $14.50 = $18 left to work with. Each hour of canoe use costs $6, so we divide the remaining amount by 6 to find how many hours (h) you can rent the canoe. This gives us the equation, h = ($32.50-$14.50)/$6.
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Can someone pls help me with 15 and 16
How many vertices are in the polyhedron?
Answer:
There are 20 vertices in the polyhedron.
The number of vertices in a polyhedron can be determined using Euler's formula or the specific properties of certain polyhedra such as platonic solids. The number of vertices varies depending on the type and structure of the polyhedron.
The number of vertices in a given polyhedron depends on the specific characteristics of the shape. According to the Euler's formula, represented as V - E + F = 2 (where V is the number of vertices, E the number of edges, and F the number of faces), we can determine the number of vertices if the other values are known.
For instance, a tetrahedron has 4 vertices, an octahedron has 6, a icosahedron has 12, a cube (also known as a regular hexahedron) has 8, and a dodecahedron has 20 vertices.
Cate purchases $1600 worth of stock and her broker estimates it will increase in value by 4.2% each year. After about how many years will the value of Cate’s stock be about $2000?
Answer:
Since the money appreciates 4.2% each year, then:
2000=1600x(1.042)^n, where n is the number of years
Then:
1.25=1.042^n
ln 1.25=ln 1.042^n=n ln 1.042
n=5.424 years
Cate's $1600 stock investment, growing at 4.2% annually, will take approximately 5.21 years to reach a value of about $2000.
Explanation:Given that Cate purchases $1600 worth of stock with an estimated increase in value by 4.2% each year, we are looking to find out after how many years the value will be about $2000. To determine this, we can use the formula for exponential growth, P = P_0 (1 + r)^t, where P is the future value, P_0 is the initial value, r is the rate of increase, and t is the time in years.
Cate's initial investment is $1600 (P_0), and we aim for a future value of $2000 (P). The annual growth rate r is 4.2%, or 0.042 when expressed as a decimal. Plugging these values into the formula and solving for t gives us:
2000 = 1600 (1 + 0.042)^t1.25 = (1.042)^tt = ln(1.25) / ln(1.042)t ≈ 5.21So, it will take approximately 5.21 years for Cate's investment to reach a value of about $2000, assuming a steady 4.2% growth rate.
Find the value of x.
log 2 x = 3
A. 5
B. 6
C. 8
D. 9
Answer: Option C
[tex]x =8[/tex]
Step-by-step explanation:
To solve this problem use the properties of the logarithms.
We know that the inverse function of [tex]y = log_2 (x)[/tex] is [tex]y = 2 ^ x[/tex].
So when composing the function with its inverse function we have to:
[tex]2 ^ {log_2 (x)} = x[/tex].
Now apply this property on both sides of the equation
[tex]log_2(x) = 3\\\\2^{log_2(x)}=2^3\\\\x = 2^3\\\\x = 8[/tex]
the answer is the option C
Evaluate 3(a + b + c)2 for a = 2, b = 3, and c = 4
Answer: 243
Step-by-step explanation:
We have the expression
[tex]3(a + b + c)^2[/tex]
Note that the expression depends on 3 variables
a, b and c
in this case we want to evaluate the expression for
[tex]a = 2\\b = 3\\c = 4[/tex]
Then change the variable a by the number 2, the variable b by the number 3 and the variable c by the number 4
So we have
[tex]3(2 + 3 + 4)^2[/tex]
Now simplify the expression
[tex]3(9)^2[/tex]
[tex]3*81=243[/tex]
The answer is 243
ANSWER
[tex]243[/tex]
EXPLANATION
The given expression is
[tex]3 {(a + b + c)}^{2} [/tex]
We want to evaluate this expression for:
a = 2, b = 3, and c = 4.
We substitute the given values into the expression to get:
[tex]3(2 + 3 + 4)^{2} [/tex]
Let us perform the addition inside the parenthesis to get:
[tex]3(9)^{2} [/tex]
[tex]3(81) =24 3[/tex]
Therefore the given expression evaluates to:
[tex]243[/tex]
S=_ft ?? Please also tell me how to do it
Answer:
[tex]70ft^2[/tex]
Step-by-step explanation:
Surface area is the sum of all sides of the area. Since it is a rectangular prism, each surface area will be multiplied by two to account for the opposite side (ex. top and bottom are the same area).
The front/back area is [tex]1*11[/tex] or 11. So the sum of the areas is 22.
The right/left area is [tex]2*1[/tex] or 2. So the sum of the areas is 4.
The top/bottom area is [tex]2*11[/tex] or 22. So the sum of the areas if 44.
We add these together to find the surface area.
[tex]22+4+44=70[/tex]
The surface area is [tex]70ft^2[/tex]
If f(x) = 2x - 6 and g(x) = 3x + 9, find (f - g)(x).
A. (f-g)(x) = x + 15
O
O
B. (f- g)(x) = -x - 15
O c. (f- g)(x) = 5x + 3
O D. (f- g)(x) = -x+3
SUBMIT
Answer:
[tex]\large\boxed{B.\ (f-g)(x)=-x-15}[/tex]
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=2x-6,\ g(x)=3x+9\\\\\text{Substitute:}\\\\(f-g)(x)=(2x-6)-(3x+9)\\\\=2x-6-3x-9\qquad\text{combine like terms}\\\\=(2x-3x)+(-6-9)\\\\=-x-15[/tex]
which expression means three minus the product of two times a and five?
Answer:
[tex]3-(2a)(5)[/tex]
Step-by-step explanation:
we know that
The algebraic expression of the phrase "three minus the product of two times a and five" is equal to
[tex]3-(2a)(5)[/tex]
[tex]3-10a[/tex]
Find the area of a trapezoid with bases 14 cm and 18 cm and height 10 cm.
A: 126 cm2
B: 160 cm2
C: 140 cm2
D: 180 cm2
Answer:
The answer is C) 57.46cm2
Step-by-step explanation:
To find the area of a trapezoid you add together the parallel lines and times the answer by the height. Then you divide it by 2.
Answer:
The answer is B, 160 cm2
Step-by-step explanation:
To find the area of a trapezoid we have to use the following equation:
A= 0.5*(b1*b2)*h
a= area
b1: base 1
b2: base 2
h: height
Then,
A= 0.5*(14cm+18cm)*10cm = 160 cm2.
A school spent $150 on advertising for a breakfast fundraiser. Each plate of food was sold for $8.00 but cost the school $2.00 to prepare. After all expenses were paid, the school raised $2,400 at the fundraiser. Which equation can be used to find x, the number of plates that were sold?
6x – 150 = 2,400
6x + 150 = 2,400
10x – 150 = 2,400
10x + 150 = 2,400
Answer:
A. 6x-150=2400
X=425
Step-by-step explanation:
Solve.
6x-150=2400
First, you add 150 from both sides of equation.
6x-150+150=2400+150
Then, simplify.
2400+150=2550
6x=2550
Divide by 6 from both sides of equation.
6x/6=2550/6x
Simplify to find the answer.
2550/6=425
X=425 is the correct answer.
A. 6x-150=2400 is the correct answer.
Answer:
6x – 150 = 2400
Step-by-step explanation:
Each plate of food was sold for $8, but cost the school $2 to prepare:
-2x + 8x = 6x
A school spent $150 on advertising for a breakfast fundraiser:
-150
After all expenses were paid, the school raised $2400 at the fundraiser:
6x – 150 = 2400
In case you want to solve it:
6x – 150 = 2400
+ 150 + 150
_________________
6x = 2550
___ _____
6 6
x = 425
So, four hundred twenty-five plates were sold.
I am joyous to assist you anytime.
Find the slope of the line that goes through (-4, 5) and (3,-1)
Answer:
y = (-6/7)x + 11/7
Step-by-step explanation:
Going from (-4, 5) to (3,-1), x increases by 7 and y decreases by 6. Hence, the slope, m, of this line is m = rise / run = -6/7.
Making use of the slope-intercept form of the equation of a str. line, we have:
y = mx + b → 5 = (-6/7)(-4) + b, or
5 = 24/7 + b. Thus, b = 11/7, and
y = (-6/7)x + 11/7
The formula to find slope when you know two points is
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
In this case...
[tex]y_{2} =-1\\y_{1} =5\\x_{2} =3\\x_{1} =-4[/tex]
^^^Plug these numbers into the formula for slope...
[tex]\frac{-1 - 5}{3 - (-4)}[/tex]
[tex]\frac{-6}{7}[/tex]
^^^This is your slope
Hope this helped!
~Just a girl in love with Shawn Mendes
One diagonal of a rhombus has endpoints (-11, -9) and (-5, -3).
What are the endpoints of the other diagonal?
(-10, -4) and (-6, -8)
(-8, -3) and (-5, -6)
(-8, -4) and (-8, -8)
(-10, -8) and (-6, -4)
Answer:
(-10, -8) and (-6, -4)
Step-by-step explanation:
we know that
The diagonals of a rhombus are perpendicular
If two lines are perpendicular, then the product of their slopes is equal to -1
m1*m2=-1
step 1
Find the slope of the given diagonal
we have
(-11, -9) and (-5, -3)
m=(-3+9)/(-5+11)
m=-6/6=-1
Find the slope of the other diagonal
we have
m1=-1
Find m2
m1*m2=-1
(-1)*m2=-1
m2=1
step 2
Verify the slope of each of the endpoints of the other diagonal
The slope of the other diagonal must be equal to 1
so
case a) (-10, -4) and (-6, -8)
m=(-8+4)/(-6+10)
m=-4/4=-1
therefore
The points of case a) cannot be the end-points of the other diagonal
case b) (-8, -3) and (-5, -6)
m=(-6+3)/(-5+8)
m=-3/3=-1
therefore
The points of case b) cannot be the end-points of the other diagonal
case c) (-8, -4) and (-8, -8)
m=(-8+4)/(-8+8)
m=-4/0 -----> undefined
therefore
The points of case c) cannot be the end-points of the other diagonal
case d) (-10, -8) and (-6, -4)
m=(-4+8)/(-6+10)
m=4/4=1
therefore
The points of case d) can be the end-points of the other diagonal
What are the coordinates of the center of the ellipse shown below? (x+2)^2+(y-4)^2/9+36=1
Answer: -2,4
Step-by-step explanation:
Center = (-2,4) are the coordinates of the center of the ellipse .
What is the centre of ellipse?The major and minor axes' midpoints meet at the center of an ellipse. At their intersection, the axes are perpendicular. The foci are always on the major axis, and the constant sum of the distances between the foci is greater than the sum of the distances from the foci to any point on the ellipse.
The equation of an ellipse is [tex]\frac{\left(x - h\right)^{2}}{a^{2}} + \frac{\left(y - k\right)^{2}}{b^{2}} = 1[/tex]
where (h,k) is the center, b and a are the lengths of the semi-major and the semi-minor axes.
Our ellipse in this form is [tex]\frac{\left(x - \left(-2\right)\right)^{2}}{9} + \frac{\left(y - 4\right)^{2}}{36} = 1[/tex]
Thus, h = -2, k = 4
Center = (-2,4).
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Can someone please help me understand why the coefficient of 'a' in a over 2 is 1/2 instead of 1?
Answer:
What you need to consider is what multiplied by 2 results in a/2. This number is the coefficient of a.
We can easily see that a/2 = 1/2 * a and therefore the coefficient is 1/2.
Answer:
Step-by-step explanation:
a/2 (a over 2) is rewritten as a×1/2 (a multiplied by half ) so now you can easily see that the coefficient of "a" is 1/2