Step-by-step explanation:
Move expression to the left side and change its sign
5
y
−
3
+
10
y
2
−
y
−
6
−
y
y
+
2
=
0
Write
−
y
as a sum or difference
5
y
−
3
+
10
y
2
+
2
y
−
3
y
−
6
−
y
y
+
2
=
0
Factor out
y
and
−
3
from the expression
5
y
−
3
+
10
y
(
y
+
2
)
−
3
(
y
+
2
)
−
y
y
+
2
=
0
Factor out
y
+
2
from the expression
5
y
−
3
+
10
(
y
+
2
)
(
y
−
3
)
−
y
y
+
2
=
0
Write all numerators above the least common denominator
5
(
y
+
2
)
+
10
−
y
(
y
−
3
)
(
y
+
2
)
(
y
−
3
)
=
0
Distribute
5
and
−
y
through the parenthesis
5
y
+
10
+
10
−
y
2
+
3
y
(
y
+
2
)
(
y
−
3
)
=
0
Collect the like terms
8
y
+
20
−
y
2
(
y
+
2
)
(
y
−
3
)
=
0
Use the commutative property to reorder the terms
−
y
2
+
8
y
+
20
(
y
+
2
)
(
y
−
3
)
=
0
Write
8
y
as a sum or difference
−
y
2
+
10
y
−
2
y
+
20
(
y
+
2
)
(
y
−
3
)
=
0
Factor out
−
y
and
−
2
from the expression
−
y
(
y
−
10
)
−
2
(
y
−
10
)
(
y
+
2
)
(
y
−
3
)
=
0
Factor out
−
(
y
−
10
)
from the expression
−
(
y
−
10
)
(
y
+
2
)
(
y
+
2
)
(
y
−
3
)
=
0
Reduce the fraction with
y
+
2
−
y
−
10
y
−
3
=
0
Determine the sign of the fraction
−
y
−
10
y
−
3
=
0
Simplify
10
−
y
y
−
3
=
0
When the quotient of expressions equals
0
, the numerator has to be
0
10
−
y
=
0
Move the constant,
10
, to the right side and change its sign
−
y
=
−
10
Change the signs on both sides of the equation
y
=
10
Check if the solution is in the defined range
y
=
10
,
y
≠
3
,
y
≠
−
2
∴
y
=
10
Answer:
I think "Product" is the answer. Not really sure.
What is the value of x in the equation 4(2x + 14) = 0?
A. 9
B. 7
C. -7
D. -9
Answer:
-7
Step-by-step explanation:
2(2x+14)=0
2x+14=0
2x=-14
x=-14/2
x=-7
Answered by GAUTHMATH
PLEASE HELP ASAP
Solve the triangle. Round your answers to the nearest tenth.
Answer Options:
A. m∠A=41, b=11, c=29
B. m∠A=41, b=13, c=29
C. m∠A=41, b=10, c=29
D. m∠A=41, b=13, c=25.9
Answer:
Optiom B
Step-by-step explanation:
If you use sine rule here, you'll find the other two sides
for the angle, do 180-24-115 = 41
Answered by GAUTHMATH
-1 1/4 × -4/5+1/4÷3
5/9×1/11+5/9×4/11-5/9×14/11
Answer:/11-5/9×14/11
Step-by-step explanation:
-4/5+1/4÷3
Find the missing length.
Answer:
[tex]\frac{12}{16} =\frac{16-x}{12}[/tex] → [tex]144=256-16x[/tex]
[tex]16x=256-144[/tex]
[tex]16x=112[/tex] → [tex]x=7[/tex]
OAmalOHopeO
find the slope intercept form and the point slope (HELP)
- the line perpendicular to 4x-7y=2 going through (-6,1)
Answer:
1) slope intercept y= (-7/4)*x-19/2 2) point slope y-1= -7/4*(x+6)
Step-by-step explanation:
4x-7y=2
7y= 4x-2
y=(4/7)*x-2/7
To find the m2 (the number near x, it is called slope) for searched the slope intercept
use the formula for perpendicular lines
m1*m2=-1
m1= 4/7
m2= -1/ (4/7)= -7/4.
The slope intercept must look like y=m2*x+b
Use the coordinates of given point of the searched line (-6,1) and m2= -7/4.
1= (-7/4) *(-6) +b
b= -19/2
So slope intercept is y= (-7/4)*x-19/2
Point slope formula is y-y1= m2(x-x1) m2=-7/4. x1=-6 y1=1
y-1= -7/4(x+6)
If g(x) = 2(x − 4), find the value of x if g(x) = 20
Answer:
x=14
Step-by-step explanation:
g(x) = 2(x − 4)
Let g(x) = 20
20 = 2(x − 4)
Divide each side by 2
20/2 = 2(x-4)/2
10 = x-4
Add 4 to each side
10+4 = x-4+4
14 =x
Find the square roots of these numbers by division method.
a-6090
A bag contains 15 cups of sugar if 3/4 of a cup is needed for each batch of cookies what's the greatest number of batches of cookies that can be made with the bag of sugar
Answer:
20 batches
Step-by-step explanation:
Cups of sugar in a bag = 15
Cups of sugar per batch of cookie = 3/4 cup
Cups of sugar per batch of cookie : batch of cookies = 3/4 : 1
what's the greatest number of batches of cookies that can be made with the bag of sugar
Let
x = batches of cookies made with a bag of sugar
Cups of sugar per batch of cookie : batch of cookies = 15 : x
Equate the ratios
3/4 : 1 = 15 : x
3/4 ÷ 1 = 15/x
3/4 × 1/1 = 15/x
3/4 = 15/x
Cross product
3 * x = 4 * 15
3x = 60
x = 60/3
x = 20
x = batches of cookies made with a bag of sugar = 20 batches
Which represents the solution(s) of the system of equations, y = x2 – 2x – 15 and y = 8x – 40? Determine the solution set algebraically.
Answer:
Therefore, the value of x is 5.
Step-by-step explanation:
We can match each equation to find the solutions.
[tex]8x-40=x^{2}-2x-15[/tex]
[tex]0=x^{2}-2x-8x-15+40[/tex]
[tex]x^{2}-10x+25=0[/tex]
Now, we need solve this quadratic equation.
[tex](x-5)^{2}=0[/tex]
Therefore, the value of x is 5.
I hope it helps you!
A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side a. Find the area of the signal board, using Heron’s formula.If its perimeter is 180 cm, what will be the area of the signal board?
Answer:
[tex]900\sqrt{3}\:\mathrm{cm^2}\text{ or }\approx 1,558.85\:\mathrm{cm^2}[/tex]
Step-by-step explanation:
Heron's formula can be used to find the area of any triangle and is given by:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex], where [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are three sides of the triangle and [tex]s[/tex] is the semi-perimeter ([tex]s=\frac{a+b+c}{2}[/tex]).
By definition, all three sides and angles of an equilateral triangle are equal. Therefore, if the total perimeter is 180 cm, each side must have a length of [tex]180\div 3=60\text{ cm}[/tex].
The semi-perimeter is therefore:
[tex]s=\frac{60+60+60}{2}=90\text{ cm}[/tex]
Substitute values into Heron's formula to get:
[tex]A=\sqrt{90(90-60)(90-60)(90-60)},\\A=\sqrt{90\cdot 30\cdot30\cdot 30},\\A=\sqrt{2,430,000},\\A=\boxed{900\sqrt{3} \:\mathrm{cm^2}}\approx \boxed{1,558.85\:\mathrm{cm^2}}[/tex]
How high up the wall can a 12-foot ladder reach if its base is 4 feet from the wall? Round your answer to the nearest tenth of a foot if necessary.
Answer:
11.3 feet
Step-by-step explanation:
let x= answer
x²+4²=12²
x²=128
x=11.3137085
which rounds to
11.3
Answer:
≈ 11.3 ft.
Step-by-step explanation:
In order to solve this, we must use some trigonometry, in this case, SOH-CAH-TOA. If you don't know what it is, here's a quick explanation:
- SOH: Sin(θ) = Opposite / Hypotenuse
- CAH: Cos(θ) = Adjacent / Hypotenuse
- TOA: Tan(θ) = Opposite / Adjacent
(Remember, SOH-CAH-TOA can ONLY be used for right triangles. If the problem does not clearly show a right triangle, meaning that there's no box in the corner, you cannot use it)
When using SOH-CAH-TOA, we first must choose an angle, either the top one or the bottom one. We can't use the right angle as, well, you just can't :). First, we have to find the bottom angle, so circle it. Literally, just circle the angle, you'll thank me later. I'll explain why we don't solve the top angle later on.
After that, we just do some labeling on the sides of the triangle. First, label the shortest side that forms the circled angle, which is the floor (4 ft), as the Adjacent side. Then label the longest side of the triangle, which is the ladder (12 ft), as the Hypotenuse. Finally, label the side that doesn't form the circled angle as the Opposite side. This is why the circling comes in handy :)
Then, out of SOH, CAH, and TOA, we choose the one that has the sides that forms the circled angle. In this case, it's CAH, or cosine, as the adjacent and hypotenuse form the circled angle.
Next, we write out the formula and solve:
Cos(m∠Circled Angle) = Adjacent/Hypotenuse
Cos(m∠Circled Angle) = 4/12
Cos(m∠Circled Angle) x Cos^-1 = 1/3 x Cos^-1
m∠Circled Angle ≈ 70.5288 (Rounding to the nearest ten-thousandth)
Note: Pay attention to the 3rd line. 'Cos^-1' is basically the equivalent of '÷ Cos'.
The reason why we did the bottom angle first is because you cannot have two unknown variables when solving for one of them. That would've been the case if we did choose the top angle as we wouldn't know the measure of the wall nor the angle. Now that we have solved the bottom angle, we can move onto solving the length of the wall.
Looking at SOH-CAH-TOA, we can either use sine or tangent as we have the measures for both the adjacent and hypotenuse. I'll use sine cause why not? Anyways, let's move on!
Just like last time, we write out the formula and solve:
Sin(m∠Circled Angle) = Opposite/Hypotenuse
Sin(70.5288) = Opposite/12
0.9428 = Opposite/12
0.9428 x 12 = Opposite/12 x 12
11.3137 ≈ Opposite (Wall)
Wall ≈ 11.3 ft. (Rounding to the nearest tenth, as asked to do so by the problem)
Note: Be careful with SOH-CAH-TOA because I've messed up multiple times with my calculator while typing out my explanation, so just make sure you go over it several times before submitting your answer when solving trig problems :). But I'm confident with my answer, so just submit it without hesitation as I've already double-checked my work.
Given g(x) = x2 - 4x + 7 , find g (3)
a) 4
b) 9
c) 12
d) 1
Answer:
The correct answer would be A. 4
By using the given functions, you can simplify g(3) and you'd get your answer.
Is the domain of an arithmetic sequence discrete or continuous? Is the range of an arithmetic sequence discrete or continuous?
Answer:
continuous, continuous
Step-by-step explanation:
The discrete domain are set of input variables that have numbers in an interval. A continuous domain has all numbers in an interval. The point representing the solution of an equation are distinct. The range of sequence is the merely a set of defines the sequence and is represented as X1, X2, X3, or N = 1, 2, 3.Suppose we have a stick of length 1.a) We randomly uniformly choose a point and break the stick into two pieces.Find the expected length of the smaller piece.b) We randomly uniformly choose two points (independently) and break thestick into three pieces. Find the probability that the three resulting piecescan be arranged to form a triangle (i.e. all triangle inequalities are satisfied;i.e no piece is longer than the sum of the other two).
Answer:
Step-by-step explanation:
1) The smaller sticks will range in length from almost 0 unit up to a maximum of 0.5 unit, with each length equally possible.
Therefore, the average length will be about (0 + 0.5)/2 = 0.25 unit
2)If you assume that each break in the stick is uniformly distributed along the length of the stick and is independent of the location of the other break, then the odds are 25% that you will be able to form a triangle with the 3 pieces.
We'll call the length of the stick 1, so each break can occur at a position in the interval [0,1]. Let x and y represent the two breaks. Then we can look at the area of the region in the square bounded x=0, x=1, y=0, y=1, which represents combinations of x and y, for which we can form a triangle. Since the area of the whole square is 1, the area of the region inside is our probability.
If y>x, then the lengths of the pieces are x, y-x, and 1-y.
The triangle inequality must hold for each combination of edges.
for y>x ...
x+y−x≥1−y
x+1−y≥y−x
y−x+1−y≥x
these simplify to...
for y>x ...
y≥1/2
x+1/2≥y
x≤1/2
If we cut our 1x1 square into two triangles along the line x=y,
then the region in the upper triangle which satisfies the inequalities above forms a smaller triangle which connects the midpoints of the upper triangle.
The lower triangle (x>y), is just a reflection about x=y of the upper triangle, so together, the entire region looks like a bow-tie at a 45 degree angle.
This region takes up 25% of the square, so the probability that you can form a triangle is 25%
Which is the graph of y = RootIndex 3 StartRoot x EndRoot?
Given:
The equation is:
[tex]y=\sqrt[3]{x}[/tex]
To find:
The graph of the given equation.
Solution:
We have,
[tex]y=\sqrt[3]{x}[/tex]
The table of values is:
x y
-8 -2
-1 -1
0 0
1 1
8 8
Plot these points on a coordinate plane and connect them by a free hand curve as shown in the below graph.
Answer:
D
Step-by-step explanation:
edge 2020
Determine the x-intercept and the y-intercept for the graph of this equation:
2x - 3y + 36 = 0
QUESTION:- DETERMINE THE X-INTERCEPT AND THE Y-INTERCEPT FOR THE GRAPH OF THE EQUATION.
EQUATION:- 2x - 3y + 36 = 0
STANDARD EQUATION:- y=mx+c
where
m-> slope.c-> Y-INTERCEPTx&y are the coordinates.SO GIVEN EQUATION:- 2x - 3y + 36 = 0
WE CAN SOLVE THIS TO CHANGE IN FORMAT OF STANDARD EQUATION
[tex]2x - 3y + 36 = 0 \\ 2x + 36 =3y \\ y = \frac{2}{3} x + \frac{36}{3} \\ y = \frac{2}{3} x + \frac{ \cancel{36}^{ \: \: 12} }{ \cancel3} \\ y = \frac{2}{3} x + 12 \\ [/tex]
SO :-
[tex]m = \frac{2}{3} \\ y - intercept = 12 \: ans[/tex]
[tex]slope = \frac{y2 - y1}{x2 - x1} \\ \frac{2}{3} = \frac{0 - 12}{x - 0} \\ 2x = ( - 12) \times 3 \\ x = \frac{ - \cancel{12}^{ \: \: 6} \times 3 }{ \cancel{2}} \\ x = - 18 \: \: ans[/tex]
Solve the equation.
3х - 6 = 6x - 9
Answer:
x=1
Step-by-step explanation:
3х - 6 = 6x - 9
Subtract 3x from each side
3х-3x - 6 = 6x-3x - 9
-6 = 3x-9
Add 9 to each side
-6+9 = 3x-9+9
3 =3x
Divide by 3
3/3 = 3x/3
1 =x
Answer:
3x-6=6x-9
3x-6x=-9+6
-3x=-3
-3x÷-3=-3÷-3
x=1
Solve for u. 42 = –7(u + 41)
Help please!
Find the inverse equation of this function
f(x) = (x + 6)^2 + 1
Thank you!!
Step-by-step explanation:
you're just going to switch x and y and then solve for y
Answer:
Hello,
Step-by-step explanation:
The problem is that the inverse function is not a function but
an union of 2 functions.
[tex]y=(x+6)^2+1\ is\ the\ orignal\ function\ f(x).\\\\Inverting\ x\ and\ y\ gives: \ x=(y+6)^2+1\\\\(y+6)^2=x-1 \ nota\ bene\ x-1\geq 0 \\(y+6)^2-(x-1)=0\\\\((y+6)-\sqrt{x-1} ) * ((y+6)+\sqrt{x-1}) =0\\\\y=-6+\sqrt{x-1}-6\ or\ y=-6-\sqrt{x-1}\\[/tex]
For the fun
,[tex]f_1(x)= (x+6)^2+1=0\ if\ x<6\\f_1^{-1}(x)=-6-\sqrt{x-1} =0\ if\ x<6\\\\f_2(x)=(x+6)^2+1=0\ if\ x \geq 6\\\\f_2^{-1}(x)=-6+\sqrt{x-1} =0\ if\ x\geq 6\\[/tex]
Na
C
9
Which rule describes the transformation?
Parallelogram ABCD is rotated to create image
A'B'C'D'.
SEE
0 (x, y) - (y, -x)
O (x, y) + (-y, x)
O (x, y) + (-X, -y)
(x, y) - (x,-y)
5
VX
4
R
D
2
1
C
-5.-5.4.-3.-2.-
23
4
SIB
Х
2
D
A
C
B
no
Answer:
(x, y) → (y, -x)
Step-by-step explanation:
The coordinates of the vertices of parallelogram ABCD are; A(2, 5), B(5, 4), C(5, 2), and D(2, 3)
The coordinates of the vertices of parallelogram A'B'C'D' are; A'(5, -2), B'(4, -5), C'(2, -5), and D'(3, -2)
The rule that escribes the transformation of the rotation of parallelogram ABCD to create the image A'B'C'D' is presented, by observation, is therefore;
(x, y) → (y, -x)
The resulting transformation used will be (x, y) -> (y, -x)
Transformation of coordinatesTransformation are rules applied to an object to change its orientation
For the given parallelogram, in order to know the rule used, we need the coordinate of the image and preimage
The coordinate of A is (2, 5) while that of A' is (5, -2).
From both coordinates, you can see that the coordinate was switched and the resulting y coordinate negated.
Hence the resulting transformation used will be (x, y) -> (y, -x)
Learn more on transformation here: https://brainly.com/question/17311824
identify the area of a regular decagon with side length 2 m rounded to the nearest tenth
Answer:
Area = 14.8
Step-by-step explanation:
Area = 5/2 + a^2*sqrt(5 + 2 sqrt(5) )
This formula given the side length, calculates the area.
a = 2
Area = 2.5 + 2^2 * sqrt(5 + 2*sqrt(5) )
Area = 2.5 + 4 * sqrt(5 + 2*2.236)
Area = 2.5 + 4* sqrt(5+ 4.4721)
Area = 2.5 + 4*sqrt(9.4721)
Area = 2.5 + 4*3.0776
Area = 2.5 + 12.3107
Area = 14.8107
Answer:
A ≈ 30.8 m2
Step-by-step explanation:
simplified expression of 3(7/5x+4)-2(3/2-5/4x)
Answer:
6,7 x+9
Step-by-step explanation:
[tex]3( \frac{7}{5} x + 4) - 2( \frac{3}{2} - \frac{5}{4} x) \\ 4.2x + 12 - 3 + 2.5x \\ 6.7x + 9[/tex]
Is the rate of change of the function 5? help pls :')
Answer: B
No, because y does not change by 5 every time x changes by 1
Step-by-step explanation:
rate of change is basically slope
if the rate of change of the function of 5, then the slope will be 5/1
The x changes by 1 every time y changes by 4
so the slope of the function is 4
Un alambre de longitud x s3. E dobla en forma de cuadrado exprese su área en términos de la ingitud x
Respuesta:
A = 1/16 × x²
Explicación paso a paso:
Un alambre de longitud x se dobla en forma de cuadrado. Como un cuadrado tiene 4 lados iguales la longitud de cada lado (l) será:
l = 1/4 × x
Para calcular el área de un cuadrado (A) usaremos la siguiente fórmula.
A = l²
A = (1/4 × x)²
A = 1/16 × x²
helpppppppppppppppppppppppppppppppppppp
Answer:
5
Step-by-step explanation:
Given: i = 5¹
5¹ = 5
Therefore, the correct option is 5
Land surveyors outlined a park as shown. What is the area of the park?
Answer:
70.875
Step-by-step explanation:
Area of park=Area of rectangle+Area of triangle
Area of park=13.5*4.8+(0.5)*(13.5)*0.9=70.875
10.(a) Nadira has some T-shirts that are either white or blue or green.
The numbers of T-shirts are in the ratio white : blue : green= 5:4:1.
48 of the T-shirts are blue.
Work out the total number of T-shirts.
Answer:
120
Step-by-step explanation:
white : blue : green
5 :4 :1
48 are blue
48/4 = 12
Multiply each by 12
white : blue : green
5*12 4*12 1*12
60 48 12
Add the numbers together to get the total
60+48+12
120
Make x the subject of the formula
I need help on this one too
E=7x+8f
Thank you so much if you answer!
Answer:
Step-by-step explanation:
To make x the subject, isolate x
7x + 8f = E
Subtract 8f from both sides
7x = E - 8f
Divide both sides by 7
[tex]x =\frac{E-8f}{7}[/tex]
Answer:
x = [tex]\frac{E-8f}{7}[/tex]
Step-by-step explanation:
Given
E = 7x + 8f ( subtract 8f from both sides )
E - 8f = 7x ( isolate x by dividing both sides by 7 )
[tex]\frac{E-8f}{7}[/tex] = x
MY LAST QUESTION PLEASE HELP
Given the special right triangle below, what is the value of the hypotenuse?
30°
60°
6
A
6
B
673
С
123
D
12
Answer:
12
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hyp
cos 60 = 6/hyp
hyp = 6 / cos 60
hyp = 6 / (1/2)
htp = 12
3. How many right angles and parallelogram has
Answer:
parallelogram has 4 right angle.
Answer:
It has 4 angles
Step-by-step explanation:
