Answer:
A) y = πStep-by-step explanation:
[tex]\text{The equation of a horizontal line:}\ y=a.\\\\\text{The equation of a vertical line:}\ x=a\\\\a-any\ real\ number\\\\\text{We have}\ x=-5.\ \text{It's a vertical line.}\ \text{The line that is perpendicular}\\\text{to the vertical line is a horizontal line.}\\\\\text{The line passes through the point}\ (1,\ \pi)\to x=1,\ y=\pi.\\\\\text{Therefore the equation is}\ y=\pi[/tex]
Question 101 points)
Which equation in slope-intercept form represents the line that passes through (5, 1) and
(-4,7)
Answer:
[tex]\large\boxed{y=-\dfrac{2}{3}x+\dfrac{13}{3}}[/tex]
Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\===============================[/tex]
[tex]\text{We have the point:}\\\\(5,\ 1)\ \text{and}\ (-4,\ 7).\ \text{Substitute:}\\\\m=\dfrac{7-1}{-4-5}=\dfrac{6}{-9}=-\dfrac{6:3}{9:3}=-\dfrac{2}{3}\\\\\text{We have the equation in form:}\\\\y=-\dfrac{2}{3}x+b\\\\\text{Put the coordinates of the point (5, 1) to the equation:}\\\\1=-\dfrac{2}{3}(5)+b\\\\1=-\dfrac{10}{3}+b\qquad\text{add}\ \dfrac{10}{3}\ \text{to the both sides}\\\\\dfrac{3}{3}+\dfrac{10}{3}=b\to b=\dfrac{13}{3}\\\\\text{Finally:}\\\\y=-\dfrac{2}{3}x+\dfrac{13}{3}[/tex]
(25 points) Can someone please solve this I just need to see how its solved to understand
x = total amount of students in 8th Grade.
we know only one-thrid of the class went, so (1/3)x or x/3 went.
we also know 5 coaches went too, and that the total amount of that is 41.
[tex]\bf \stackrel{\textit{one third of all students}}{\cfrac{1}{3}x}+\stackrel{\textit{coaches}}{5}=\stackrel{\textit{total}}{41}\implies \cfrac{x}{3}+5=41\implies \cfrac{x}{3}=41-5 \\\\\\ \cfrac{x}{3}=36\implies x=3(36)\implies x=108[/tex]
now, to verify, well, what do you get for (108/3) + 5?
again can someone help me please
Answer:
4,-2 and 1
Step-by-step explanation:
These are all quantities greater than -5
-5 < 4
-5 < -2
-5 < 1
So C, D and E
Factoring Trinomials (
Factor each completely.
1) 3p² – 2p - 5
Answer:
factors (3p - 5) and (p + 1)
Step-by-step explanation:
The quadratic formula always "works" when you're looking to factor a quadratic expression or equation. Here, the coefficients are a = 3, b = -2 and c = -5. The discriminant is thus b²-4ac, which here is (-2)²-4(3)(-5), or 4+60, or 64. Because this discriminant is positive, we know that the quadratic has two real, unequal roots. These roots are:
-(-2)±√64 2 ± 8
p = ------------------- = --------------- = 10/6 and -1, or 5/3 and -1.
2(3) 6
These roots correspond to the factors (3p - 5) and (p + 1).
Maggie has a container in the shape of a right prism. The formula for its surface area is SA = Ph + 2B. Solve for h.
A.h = SA minus two times B over P
B.h = SA plus two times B over P
C.h = SA plus P over two times B
D.h = SA minus P over two times B
Answer:
A. [tex]h=\frac{SA-2B}{P}[/tex]
Step-by-step explanation:
We have been given a formula for the surface area of a container in shape of right prism. We are asked to solve for h for our given formula.
[tex]SA=Ph+2B[/tex]
First of all, we will switch sides for our given equation as:
[tex]Ph+2B=SA[/tex]
Now, we will subtract 2B from both sides of our equation.
[tex]Ph+2B-2B=SA-2B[/tex]
[tex]Ph=SA-2B[/tex]
Now, we will divide both sides of our equation by P.
[tex]\frac{Ph}{P}=\frac{SA-2B}{P}[/tex]
[tex]h=\frac{SA-2B}{P}[/tex]
Therefore, option A is the correct choice.
Answer:
A
Step-by-step explanation:We have been given a formula for the surface area of a container in shape of right prism. We are asked to solve for h for our given formula
First of all, we will switch sides for our given equation as:
Now, we will subtract 2B from both sides of our equation.
Now, we will divide both sides of our equation by P.
therefore its option A
Yesterday, a factory used 2/3 of a tub of peanut butter. They use 1/6 of a tub of peanut butter for each batch of peanut butter cookies. How many batches of peanut butter cookies did the factory make yesterday?
The number of batches is 4.
What is the unitary method?When a problem arises if 4 is required for 2 of these things then how many things does 20 require?
We use the unitary method to solve the problem where we find how much is required for one thing and then multiply it by the required.
Solving the given problem.1/6 tub of peanut butter is used for one batch of cookies.
2/3 of it was used for the whole day.
So to find the total number of batches we divide the total tub used by the amount of tub used for one batch of cookies hence = 2/3/(1/6) = 4
Hence the answer to the given problem is 4.
Learn more about the Unitary method here
https://brainly.com/question/19423643
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find the quotient 16 2/3 ÷ 5 5/7
Answer:
2 11/12
Step-by-step explanation:
(50/3)/(40/7)
=50/3*7/40
=5/3*7/4
=35/12
=2 11/12
let's convert firstly, the mixed fractions to improper fractions and then divide.
[tex]\bf \stackrel{mixed}{16\frac{2}{3}}\implies \cfrac{16\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{50}{3}}~\hfill \stackrel{mixed}{5\frac{5}{7}}\implies \cfrac{5\cdot 7+5}{7}\implies \stackrel{improper}{\cfrac{40}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{50}{3}\div\cfrac{40}{7}\implies \cfrac{\stackrel{5}{\begin{matrix} 50 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}{3}\cdot \cfrac{7}{\underset{4}{\begin{matrix} 40 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}\implies \cfrac{35}{12}\implies 2\frac{11}{12}[/tex]
To the nearest hundredth of a centimeter, what is the length of the hypotenuse?
[1] cm
92.58 cm
Answer:
106.90 cm
Step-by-step explanation:
Given
Angle=30 degrees
Base=92.58 cm
So,
We will have to use the triangular ratios to find the hypotenuse.
The triangular ratio that will be used for this will be cosine because we know the value of angle and base since it involves both cosine will be used.
cosθ=Base/Hypotense
cos30=92.58/Hypotenuse
0.8660=92.58/Hypotenuse
Hypotenuse=92.58/0.8660
=106.90 cm ..
Answer:
Hypotenuse = 107.02
Step-by-step explanation:
Points to remember
If angles of a triangle are 30°, 60° and 90° then the sides are in the ratio
1 : √3 : 2
It is given a right angled triangle with angles 30°, 60°, 90°
and height = 95.58 cm
To find the hypotenuse
From the figure we can write,
Base : Height : Hypotenuse = 1 : √3 : 2 = Base : 92.58 : Hypotenuse
Therefore Hypotenuse = (92.58 * 2)/√3
= 107.02 cm
What is the other solution?
Answer:
-6
Step-by-step explanation:
m^2 - 36 = 0
Add 36 to each side
m^2 -36+36 = 0+36
m^2 = 36
Take the square root of each side
sqrt( m^2) = ± sqrt(36)
m = ±6
We know one root is 6
The other root is -6
If you apply the below transformations to the square root parent function,
F(x) = VX, what is the equation of the new function?
• Shift 12 units right.
• Shift seven units down.
Answer:
We have the following function: [tex]f(x) =\sqrt{x}[/tex]
We know that given a function f(x), the function g(x) = f(x+m) is exactly the same function f(x) but shifted m units to the left.
Therefore, to shift the function 12 units right we should:
[tex]f(x) =\sqrt{x}[/tex] ⇒ [tex]f(x-12) =\sqrt{x-12}[/tex]
We know that given a function f(x), the function g(x) = f(x)+m is exactly the same function f(x) but shifted m units up.
Therefore, to shift seven units down we should:
[tex]f(x) =\sqrt{x}[/tex] ⇒ [tex]f(x) =\sqrt{x}-7[/tex]
Find the missing factor.
4b2 + 17b + 15 = (b + 3)(
)
Answer:
(4b + 5)
Step-by-step explanation:
To get 4b^2 you already have b^2 if you put b inside the second set of brackets. But that would mean you don't have 4 anywhere to get 4b^2.
So the first step has to be
(b + 3)(4b
Now look at the 15 for a moment. It is plus 15. The only way you can get a plus 15 is if both signs are plus (after the b terms) or both terms are minus.
The middle term (17b) is plus so both terms after b are plus.
(b + 3)(4b +
Now we need something that multiplies to 15. 3*5 = 15. So the term you want is 5.
(b + 3)(4b + 5)
Does the middle term work?
5*b + 3*4b = 5b + 12b = 17b
Everything looks fine.
The second factor is 17b.
Let f(x)=x2+4x+12 . What is the vertex form of f(x)? What is the minimum value of f(x)?
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+12} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{4}{2(1)}~~,~~12-\cfrac{4^2}{4(1)} \right)\implies (-2~~,~~12-4)\implies (-2~,~8)[/tex]
well, the quadratic has a leading term with a positive coefficient, meaning is a parabola opening upwards, like a "bowl", comes from above down down down, reaches a U-turn, namely the vertex, and goes back up up up.
so the minimum value is at the vertex of course, and the minumum is well, just the y-coordinate of the vertex, 8.
Please explain how this function behaves when it approaches the given x values!
This is a piecewise function because it is defined by more than two functions. Basically, we want to take the limit here. Recall that if a function [tex]f(x)[/tex] approaches some value [tex]L[/tex] as [tex]x[/tex] approaches [tex]a[/tex] from both the right and the left, then the limit of [tex]f(x)[/tex] exists and equals [tex]L[/tex]. Here we won't calculate the limit, but apply some concepts of it. So:
a. [tex]as \ x \rightarrow +\infty, \ k(x) \rightarrow +\infty[/tex]
Move on the x-axis from the left to the right and you realize that as x increases y also increases without bound.
b. [tex]as \ x \rightarrow -\infty, \ k(x) \rightarrow 0[/tex]
Move on the x-axis from the right to the left and you realize that as x decreases to negative values y approaches zero.
c. [tex]as \ x \rightarrow 2, \ k(x) \rightarrow 0[/tex]
Since the function is continuous here, we can say that [tex]k(2)=0[/tex]
d. [tex]as \ x \rightarrow -2, \ k(x) \rightarrow 0[/tex]
The function is discontinuous here, but [tex]k(-2)[/tex] exists and equals 0 as the black hole indicates at [tex]x=-2[/tex].
e. [tex]as \ x \rightarrow -4, \ k(x) \rightarrow 2[/tex]
The function is also discontinuous here, but the black hole indicates that this exists at [tex]x=-4[/tex], so [tex]k(-4)=2[/tex]
f. [tex]as \ x \rightarrow 0, \ k(x) \rightarrow 4[/tex]
Since the function is continuous here, we can say that [tex]k(0)=4[/tex]
What is the answer to this question
For f(x) = 2x+1 and g(x)=x^2-7, find (f*g)(x).
Answer:
[tex](f*g) (x) =2x^3-13x^2-7 [/tex]
Step-by-step explanation:
We have the following functions
[tex]f (x) = 2x+1[/tex]
[tex]g (x) = x^2-7[/tex]
To find [tex](f*g)(x)[/tex] we must multiply the function f (x) with the function g (x)
Then we perform the following operation
[tex](f*g) (x) =(2x+1)(x^2-7)[/tex]
Apply the distributive property
[tex](f*g) (x) =2x^3-14x^2+x^2-7 [/tex]
[tex](f*g) (x) =2x^3-13x^2-7 [/tex]
Finally we have that:
[tex](f*g) (x) =2x^3-13x^2-7 [/tex]
Mrs. Culland is finding the center of a circle whose equation
is x2 + y2 + 6x + 4y - 3 = 0 by completing the square. Her
work is shown.
x2 + y2 + 6x + 4y – 3 = 0
x2 + 6x + y2 + 4y - 3 = 0
(x2 + 6x) + (y2 + 4y) = 3
(x2 + 6x + 9) + (x2 + 4y + 4) = 3 + 9 + 4
Answer:
The center of the circle is (-3,-2)
Step-by-step explanation:
we know that
The equation of a circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
(h,k) is the center
r is the radius
In this problem we have
[tex]x^{2} +y^{2}+6x+4y-3=0[/tex]
Completing the square
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](x^{2}+6x) +(y^{2}+4y)=3[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex](x^{2}+6x+9) +(y^{2}+4y+4)=3+9+4[/tex]
[tex](x^{2}+6x+9) +(y^{2}+4y+4)=16[/tex]
Rewrite as perfect squares
[tex](x+3)^{2} +(y+2)^{2}=16[/tex]
therefore
The center of the circle is (-3,-2)
Answer: ITS D !! ON EDGE
Step-by-step explanation:
Reflection Lines
A reflection line is equidistant from a pre-image point and its image.
Therefore, in segment AA’, point M is the
Answer:
Midpoint
Step-by-step explanation:
Equidistant from the pre = image AA would be the middle
Answer:
Mid Point, thats all there is, its the answer, just that
Step-by-step explanation:
The difference of 2 numbers is 21 and the quotient of the equation is 4 then what are the two numbers?
Answer:
The two numbers are 28 and 7.
Step-by-step explanation:
Let the first number be x
Let the second number be y
The difference of x and y is x-y=21
The quotient of two numbers is x/y = 4
x-y =21 (This is equation 1)
x/y=4 (This is equation 2)
By solving equation 2 we will get the value of x.
x/y=4
x=4y (Lets call it equation 3)
Now, put the value of x(equation 3) in (equation 1)
x-y=21
4y-y=21
3y=21
y=21/3
y=7
Now put the value of y in equation 3 to get the value of x
x=4y
x=4(7)
x=28
Solution Set {(x,y)(28,7)}
Answer:
28 and 7
Step-by-step explanation:
How can △WXY be mapped to △MNQ?
First, translate vertex w to vertex M. Next, reflect △WXY across the line containing
1) line segment WX
2) line segment WY
3) line segment XY
4) line segment MQ
Answer:
A: Line Segment WX
Step-by-step explanation:
100% on edge 2020
Answer:
WX is correct
Step-by-step explanation:
Got a 100 in edge quiz.
Find the arc length of the partial circle
Answer:
7pi/2
Step-by-step explanation:
If was a full, the circumference or the arc length would be 2pi*r where r in this case is 7 so it would be 14pi.
Now this only a quarter of that, so this arc length is actually 14pi/4.
This can be reduced 14pi/4 =7pi/2
Answer:
3.5pi
Step-by-step explanation:
KA
Paula Pruitt invested $4,334 in the stock market. The investment has declined 7% in value. Determine the worth of the investment now
Answer:
(4334/100)*93 = $ 4,030.62
Step-by-step explanation:
N/A
Please answer this question in the picture!
Ignore the writing over it and the answer! It’s probably wrong.
Answer:
c [tex]113\:m[/tex]
Step-by-step explanation:
[tex]113,391 = 4\frac{9}{10}[2\frac{1}{10}]^{2} + 135 \\ \\ 113 ≈ h[/tex]
I am joyous to assist you anytime.
Based on the graph below, how would you describe the curve?
A. The curve is a 'one-to-one' function
B. The curve is a linear function
c. The curve is not a function
D. The curve is a 'many-to-one" function
D. is the correct answer
Hopes this helps
Solve: 12x^2+5x-4=12^2x+6
okay so we need to solve for x.
--
FIRST STEP: 12x^2+5x-4=12^2x+6 would turn into x2 + 5x - 4 = 2x + 6 so it'd have equal bases.
SECOND STEP: move any number with "x" in it to the left side. it ends up as x2 + 3x - 4 = 6
THEN, we use the AC method to eliminate any unnecessary numbers.
you should end up with ( x - 2) (x + 5) = 0
SO, the answer is your third option. ( x = 2, x = -5)
Answer:
x=-5&x=2
Step-by-step explanation:
Since the bases on both sides of the equation are the same, they will cancel each other leaving the exponents
x²+5x-4 = 2x + 6
Collect like terms
x²+5x-2x-4-6=0
x²+3x-10=0
The highest power is 2 , so factorize
x²+5x-2x-10=0
x(x+5)-2(x+5)=0
(x+5)(x-2)=0
x = -5 or x = 2
Check
When x = -5
-5²+3*-5-10=0
25-15-10 =0
0=0
:.x=-5
When x=2
2²+3*2-10=0
4+6-10=0
0=0
Area of a square with half diagonal 12
Answer:
288 square units
Step-by-step explanation:
The formula for the area of a square when you know its diagonal is: [tex]\frac{1}{2} d^2[/tex]
So, since we know the half diagonal is 12, we need to multiply that by 2 to get the diagonal, which is 24.
Put 24 into the formula. [tex]\frac{1}{2} * 24^2[/tex]
Simplify the exponent. [tex]\frac{1}{2} * 576[/tex]
Finally, multiply. [tex]288[/tex]
what is the sum of 12x^2+3x+6 and -7x^2-4x-2
Answer: [tex]5x^2-x+4[/tex]
Step-by-step explanation:
In addition of polynomials, you only have to add the like terms.
Remember the multiplication of signs:
[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]
Then, given the polynomial [tex]12x^2+3x+6[/tex] and the polynomial [tex]-7x^2-4x-2[/tex], you can find the sum of them by adding the like terms.
Observe the procedure below:
[tex](12x^2+3x+6)+(-7x^2-4x-2)=12x^2+3x+6-7x^2-4x-2=5x^2-x+4[/tex]
Therefore, the sum is:
[tex]5x^2-x+4[/tex]
write the equation of the line that passes through the points (7,-4) and (-1,3), first in point slope form
The given line that passes through the points (7,-4) and (-1,3).
The slope is
[tex]m = \frac{3 - - 4}{ - 1 - 7} = - \frac{7}{8} [/tex]
The point-slope form is obtained using:
[tex]y-y_1= m (x-x_1) [/tex]
When (7,-4) is used the point-slope form is
[tex]y + 4= - \frac{7}{8} (x - 7) [/tex]
We expand now to get;
[tex]y = - \frac{7}{8}x + \frac{49}{8} - 4[/tex]
This implies that,
[tex]y = - \frac{7}{8}x + \frac{17}{8}[/tex]
45+45-6+122/5+92-35*9+12-10/2+19-25?
Answer:-568/5
Step-by-step explanation:
Answer:
-568/5 is the answer
The given graph represents the function f(x) = 2(5)
How will the appearance of the graph change if the a
value in the function is decreased, but rerrains greater
than 0?
The graph will increase at a slower rate.
The graph will show a decreasing, rather than
increasing, function.
The graph will show an initial value that is lower on
the y-axis
The graph will increase at a constant additive rate,
rather than a multiplicative rate.
What’s the awnser
Answer:
It's C on e2020
Step-by-step explanation:
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.
A(n) = -6 + (1 - 1)(1)
Answer:
-6
Step-by-step explanation:
A(n)=-6+(1-1)(1)
simplified, this equals:
A(n) = -6+(0)(1)
A(n)=-6+0
A(n) = -6, for any given n term.