Step-by-step explanation:
-6y + y=-30
-5y = -30
y=6
x=-6 ×6= -36
A² + b² = 7b and b² + (2b-a)² = 7² find (a - b)².
Answer:
(a - b)^2 = 49 - 4b^2 +2ab
Step-by-step explanation:
Given: a^2 + b^2 = 7b (assuming A is really “a”)
b^2 + (2b - a)^2 = 7^2
Find; (a - b)^2
Plan: Use Algebraic Manipulation
Start with b^2 + (2b - a)^2 = 7^2 =>
b^2 + 4b^2 - 4ab + a^2 = 49 by expanding the binomial.
a^2 + b^2 + 4b^2 - 4ab = 49 rearranging terms
a^2 + b^2 -2ab - 2ab + 4b^2 = 49 =>
a^2 - 2ab + b^2 = 49 - 4b^2 +2ab rearranging and subtracting 4b^2 and adding 2ab to both sides of the equation and by factoring a^2 - 2ab + b^2
(a - b)^2 = 49 - 4b^2 +2ab
Double Check: recalculated ✅ ✅
(a - b)^2 = 49 - 4b^2 +2ab
Determina la masa molar y el volumen que ocupa la siguiente sustancia CO2, si su masa es de 28 gr. *
Answer:
Para el CO₂ sabemos que:
densidad = 0,001976 g/cm³
Sabemos que:
densidad = masa/volumen
Entonces, si tenemos una masa de 28 g, podemos escribir:
volumen = masa/densidad
volumen = (28g)/(0,001976 g/cm³) = 14,170 cm^3
Para obtener la masa molar (es decir, la masa de un mol de esta sustancia) simplemente sumamos la masa de un mol de cada componente.
Carbono: tiene una masa molar de 12 g/mol
Oxígeno: tiene una masa molar de 16 g/mol (y tenemos dos oxígenos)
entonces la masa molar va a ser:
masa molar = 12g/mol + 2*16g/mol = 44 g/mol
Es decir, un mol de CO₂, pesa 44 gramos.
10. What are the coordinates of point on the directed segment from A(2,-3) to B(8,-6) that
partitions the segment such that AC:CB is 4:2?
(1) (6,-5)
(3) (2,0)
(2) (-2, 2)
(4) (1, 1)
Answer:
(4, -4)
Step-by-step explanation:
Using the midpoint formula;
M(X,Y) = {(ax1+bx2)/a+b, (ay1+by2)/a+b}
X = (ax1+bx2)/a+b
Y = (ay1+by2)/a+b
Substitute
X = 4(2)+2(8)/4+2
X = 8+16/6
X = 24/6
X = 4
Also
Y = 4(-3)+2(-6)/6
Y = -12-12/6
Y = -24/6
Y = -4
Hence the required partition is (4, -4)
A car left the house traveling north at 10 A.M. Another car left the house traveling south two hours later. If the cars traveled at the same rate and were 550 miles apart at 4 P.M , what was the rate of each car.
Answer:
55 mph
Step-by-step explanation:
HURRY !!!!!! Which describes the correlation shown in the scatterplot?
Solve for y please and thank you
Answer:
c) y = 8[tex]\sqrt{3}[/tex]
Step-by-step explanation:
in a 30-60-90° Δ the ratio of the sides, respectively, is 1: [tex]\sqrt{3}[/tex] : 2
if the side opposite the 30°∡ is 8 then 'y' is 8[tex]\sqrt{3}[/tex] and 'x' is 16
The length of a spring varies directly with the mass of an object that is attached to it. When a 30-gram object is attached, the spring stretches 9 centimeters. Which equation relates the mass of the object, m, and the length of the spring, s?
s = StartFraction 3 Over 10 EndFraction m
s = StartFraction 10 Over 3 EndFraction m
m = StartFraction 3 Over 10 EndFraction s
m = StartFraction 1 Over 30 EndFraction s
Answer:
it is b
Step-by-step explanation:
Answer:
it is b
Step-by-step explanation:
the measures of the angles of a triangle are shown in the figure. solve for x
Answer:
solution,
x+41+59=180⁰ ( the sum of total angle of triangle is 180⁰)
or, x+ 100=180
or, X=180-100
so , X=80
Step-by-step explanation:
let us check
59+41+80=180
In a bowl of fruit, there are green grapes and black grapes in the ratio 3:4 If there are 24 green grapes, how many black grapes are there?
answer is 32
ask me more questions any time
Find the quadratic equation whose parabola has vertex (3,-2) and y-intercept (0, 16). Give your
answer in vertex form.
Answer:
y = 2*(x - 3)^2 - 2
Step-by-step explanation:
Remember that a quadratic equation of vertex (h, k) is written as:
y = a*(x - h)^2 + k
Where a is the leading coefficient.
So, if we know that the vertex is at (3, - 2)
we have:
y = a*(x - 3)^2 + (-2)
And we want the y-intercept to be (0, 16)
This means that, when we take x = 0, we must have y = 16
if we replace these in the above equation we get:
16 = a*(0 - 3)^2 - 2
now we can solve this for a
16 = a*(-3)^2 - 2
16 = a*9 - 2
16 + 2 = a*9
18 = a*9
18/9 = a
2 = a
Then the quadratic equation is:
y = 2*(x - 3)^2 - 2
use these functions a(x) =4x +9 and b(x) =3x -5 to complete the function operations listed below
Consider that we need to find [tex](a+b)(x), (a-b)(x), (ab)(x),\left(\dfrac{a}{b}\right)(x)[/tex].
Given:
The functions are:
[tex]a(x)=4x+9[/tex]
[tex]b(x)=3x-5[/tex]
To find:
The function operations [tex](a+b)(x), (a-b)(x), (ab)(x),\left(\dfrac{a}{b}\right)(x)[/tex].
Solution:
We have,
[tex]a(x)=4x+9[/tex]
[tex]b(x)=3x-5[/tex]
Now,
[tex](a+b)(x)=a(x)+b(x)[/tex]
[tex](a+b)(x)=4x+9+3x-5[/tex]
[tex](a+b)(x)=7x+4[/tex]
Similarly,
[tex](a-b)(x)=a(x)-b(x)[/tex]
[tex](a-b)(x)=4x+9-(3x-5)[/tex]
[tex](a-b)(x)=4x+9-3x+5[/tex]
[tex](a-b)(x)=x+14[/tex]
And,
[tex](ab)(x)=a(x)b(x)[/tex]
[tex](ab)(x)=(4x+9)(3x-5)[/tex]
[tex](ab)(x)=12x^2-20x+27x-45[/tex]
[tex](ab)(x)=12x^2+7x-45[/tex]
And,
[tex]\left(\dfrac{a}{b}\right)(x)=\dfrac{a(x)}{b(x)}[/tex]
[tex]\left(\dfrac{a}{b}\right)(x)=\dfrac{4x+9}{3x-5}[/tex]
Therefore, the required functions are [tex](a+b)(x)=7x+4[/tex], [tex](a-b)(x)=x+14[/tex], [tex](ab)(x)=12x^2+7x-45[/tex] and [tex]\left(\dfrac{a}{b}\right)(x)=\dfrac{4x+9}{3x-5}[/tex].
f(x) =-x²+16 and g(x) =x+4
f(x)/g(x) = (x2-16)/(x+4)
The domain is all real numbers except x = -4 (because the denominator is zero at x = -4 and division by zero is undefined.)
We can simplify by factoring the numerator:
(x2-16)/(x+4) = (x-4)(x+4)/(x+4) = (x-4)
The domain is the same as the original expression: all real numbers except x = -4
if f(x)=3x-1 and g(x)=x+2, find (f-g)(x)
Answer:
2x - 3
Step-by-step explanation:
3x-1 - (x+2)
3x-1 -x -2
2x - 3
On the last day of a Shakespeare class, an English teacher asked her students which play
they liked the best, and she recorded the results to date.
2 liked Hamlet
8 liked Twelfth Night
2 liked a Midsummer Night's Dream
What is the experimental probability that the next student to respond likes Hamlet best?
Write your answer as a fraction or whole number
Answer:
ok so if we add this up we get that there is 14 kids in the class who have been polled and 2/14 or 1/7 likes hamlet so the chance is 1 out of 7
The experimental probability that the next student to respond likes Hamlet best is [tex]\frac{1}{6}[/tex] .
Concept:Probability = [tex]\frac{Favourable \ Outcomes }{Total \ Outcomes}[/tex]To find total outcomes, we will add all the students.To find the favorable outcomes, we will count the number of students that likes hamlet.How to solve the given question?Probability = [tex]\frac{Favourable \ Outcomes }{Total \ Outcomes}[/tex]Total Outcomes = 2 + 8 + 2 = 12Favorable outcomes = 2∴ [tex]P(E) = \frac{Favourable \ Outcomes }{Total \ Outcomes} = \frac{2}{12} =\frac{1}{6}[/tex]Thus, the experimental probability that the next student to respond likes Hamlet best is [tex]\frac{1}{6}[/tex] .
Learn more about Probability here:
https://brainly.com/question/15161940
#SPJ2
Ryder used front end estimation to estimate the product of -24.98 - 1.29 what is the zestimate
Answer:
20
Step-by-step explanation:
The numbers whose product are to be obtained :
(–24.98)(–1.29)
To use front end approximation, numbers are rounded to the greatest place value :
For :
(-24.98) is rounded to - 20 (4 is rounded here to 0)
(-1.29) is rounder to - 1 (2 is rounded to 0)
Then, the product of the two numbers will be :
-20 * - 1 = 20
Learning Activities
Solve the following problems. Choose
the letter of the correct answer
(Show your complete solutions)
1.) The sum of all the sides of a STOP sign is 104 inches. A STOP sign is an
with all sides equal. How many inches does each side measure?
B. 11 in
C. 13 in
D. 16 in
2.) In A ABC, LA and Beach measure 70% How many degrees are there in 202
A. 400
B. 50°
C. 60
D700
3.) The measures of the three angles of a quadrilateral are 49. 58, and 127. What
is the measure of the fourth angle?
A. 116
B. 126
C. 54
D. 64
A. 8 in
4.) Solve for the value of x in DEFG.
E
D
(x + 40)
130
A 400
B. 70°
C. 500
D. 90°
F
(2x-10)
G
5.) if the length of the two sides of an isosceles triangle are 3 cm and 7 cm, then
what must be the length of the third side?
Step-by-step explanation:
answers I the above photo
some of the questions are not clear
Answer:
1. C(13inches)
2. A(40°)
3. B(126°)
4. C(50°)
5. 7cm
Step-by-step explanation:
According To the Question,
1. Given, The sum of all the sides of a STOP sign is 104 inches. A STOP sign is Octagon with all sides equal.
Thus, Octagon has 8 equal side
So, Each Side Measure = 104/8 ⇔ 13inches
2. Given, In Triangle ABC, ∠A & ∠B each measure 70°
And, We Know Sum of all angles of a triangle is 180°.
Thus, ∠C = 180° - (∠A + ∠B) ⇔ 180°-140° ⇒ 40°
3. Given, The measures of the three angles of a quadrilateral are ∠A=49° ,∠B=58° & ∠C=127° .
And, We know sum of all angles of quadrilateral is 360°.
Thus, ∠D=360° - (∠A+∠B+∠C) ⇔ 360°-234° ⇒ 126°
4. Given, The measure of all the Four angles of a quadrilateral are ∠A=(x+40)°, ∠B=130°, ∠C=x° & ∠D=(2x-10)° .
And, We know sum of all the angles of quadrilateral is 360°.
Thus, ∠A+∠B+∠C+∠D = 360°
Put all the Values, we get
x+40+130+x+2x-10 = 360
4x+160 = 360
4x = 200 ⇔ 200/4 ⇒ 50°
5. Given, the length of the two sides of an isosceles triangle are 3cm and 7cm .
Now, in order to form a triangle the sum of any two side of a triangle is always greater than the third side of a triangle.
So, We have an isosceles triangle in which two sides is always equal & we have given two sides of 3cm & 7cm .
Assume, if third side be 3cm (First Side+Third side > Second side)
3+3 ⇒6cm which is not greater than 7cm(thus, the Triangle not possible if we assume 3cm as triangle's third side)
Hence, The other Side of Triangle Surely be 7 cm.
13-?=7-2x
In the equation above what must ? be so that x has value of 2
Answer:
? = 10
Step-by-step explanation:
13 - (10) = 7-4 ....... 2×2 =4
3 = 3
a rectangle is twice as long as it is wide and its perimeter is 432cm
a) work out the dimensions of the rectangle.
b) work out the area of the rectangle.
Let
Width of rectangle=xLength of rectangle=2xPerimeter=432cmWe know that in a rectangle
☆ Perimeter=2(Length+Breadth)
[tex]\\ \sf\longmapsto 2(x+2x)=432[/tex]
[tex]\\ \sf\longmapsto 2x+4x=432[/tex]
[tex]\\ \sf\longmapsto 6x=432[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{432}{6}[/tex]
[tex]\\ \sf\longmapsto x=72[/tex]
[tex]\\ \sf\longmapsto 2x=2(72)=144[/tex]
Length=144cmBreadth=72cm☆Area=Length×Breadth
[tex]\\ \sf\longmapsto Area=144\times 72[/tex]
[tex]\\ \sf\longmapsto Area=10368cm^2[/tex]
What is the monthly net income?? Show work plz
Help find x and angle BEC
Answer:
x = 32 and BEC = 43
Step-by-step explanation:
3X + 41 = 137
3X = 96
X = 32
FOR BEC:
137 + 137 = 274
360-274=86 ( ANGLES AROUND A POINT ADD UP TO 360)
86/2 = 43
BEC/AED = 43 ( VERTICALLY OPPOSITE ANGLES ARE EQUAL)
hope this helps good luck!
the equation cos(x)( cos(x)-tan(x)sin(x)) simplifies to
10 normal six sided dice are thrown.Find the probability of obtaining at least 8 failuresif a success is 5 or 6.
Answer:
0.2992 = 29.92% probability of obtaining at least 8 failures.
Step-by-step explanation:
For each dice, there are only two possible outcomes. Either a failure is obtained, or a success is obtained. Trials are independent, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A success is 5 or 6.
A dice has 6 sides, numbered 1 to 6. Since a success is 5 or 6, the other 4 numbers are failures, and the probability of failure is:
[tex]p = \frac{4}{6} = 0.6667[/tex]
10 normal six sided dice are thrown.
This means that [tex]n = 10[/tex]
Find the probability of obtaining at least 8 failures.
This is:
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{10,8}.(0.6667)^{8}.(0.3333)^{2} = 0.1951[/tex]
[tex]P(X = 9) = C_{10,9}.(0.6667)^{9}.(0.3333)^{1} = 0.0867[/tex]
[tex]P(X = 10) = C_{10,10}.(0.6667)^{10}.(0.3333)^{0} = 0.0174[/tex]
Then
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1951 + 0.0867 + 0.0174 = 0.2992[/tex]
0.2992 = 29.92% probability of obtaining at least 8 failures.
solutia reala a ecuatiei 4x la a doua = 6 intregi si 1/4 (dau coroana)
Answer:
x = + 5/4 or x = - 5/4
Step-by-step explanation:
[tex]4 x^2 = 6\frac{1}{4}\\\\4 x^2 = \frac{25}{4}\\\\x^2 =\frac{25}{16}\\\\x = \pm \frac{5}{4}[/tex]
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 4 cos 5θ
Answer:
y-acis
Step-by-step explanation:
the function graph is symmetric about
- y-axis when it is an even function
-the origin ehen it is an even function
A symmetrical graph about the x-axis is not a function graph
f(×) is a even if and only if f(×) =f(×)
f(×) is a odd if and only f(×)=f(×)
We have the function r(0) = 4cos (50)
(only symmetry about the y-acis or about the origin)
Check r(-0)
r(-0) = 4cos (5-0) = 4cos (-50 = 4 cos (50)
Used cos (-× = cos ×
We have r(0). Therefore the graph of r(0) is symmectric about the y-axis.
Express as simply as possible with a rational denominator
7/√10
Answer:
7√10 / 10.
Step-by-step explanation:
7/√10
Multiply top and bottom by √10:
= 7√10 / 10
if 1/a+1/b+1/c=1/a+b+c then prove that 1/a^9+1/b^9+1/c^9=1/a^9+1/b^9+1/c^9
Answer:
The given relation is presented as follows;
[tex]\dfrac{1}{a} + \dfrac{1}{b} +\dfrac{1}{c} = \dfrac{1}{a + b + c}[/tex]
Where 'a', 'b', and 'c' are member of real numbers, we have;
a⁹, b⁹, and c⁹ are also member of real numbers
When a⁹ = x, b⁹ = y, and c⁹ = z
By the above relationship, we have;
[tex]\dfrac{1}{x} + \dfrac{1}{y} +\dfrac{1}{z} = \dfrac{1}{x + y + z}[/tex]
Substituting x = a⁹, y = b⁹, and z = c⁹, we get;
[tex]\dfrac{1}{a^9} + \dfrac{1}{b^9} +\dfrac{1}{c^9} = \dfrac{1}{a^9 + b^9 + c^9}[/tex]
Step-by-step explanation:
Find The Measure Of D
Answer:
138 Degrees
Step-by-step explanation:
Because it is adjacent to the 42 degrees, just subtract 42 from 180 to get 138 degrees.
Answer:
D+42*=180*
D=180-42
138
Step-by-step explanation:
mark as brainiest please
Help me solve these 4 plssss ASAP
Step-by-step explanation:
[tex]1) \\ - 2 \leqslant x \leqslant 1 \\ 2) \\ - 3 > x \geqslant 2 \\ 3) \\ x> 0[/tex]
[tex]4) \\ x \leqslant - 3 \\ 5) \\ - 4 \leqslant x \geqslant 1[/tex]
[tex]6) \\ - 2< x \leqslant 0[/tex]
Hey, can anyone help me with this pls
Answer:
it's B
Step-by-step explanation:
I'm quite sure it is. Hope it helps u
How many solutions exist for the system of equations in the graph?
Answer:
Two solutions
Step-by-step explanation:
The number of points of intersections represents the number of solutions to the system of equations. Since the parabola intersects the circle at two points, there are two solutions to the circle.
Furthermore, these two points of intersection are exactly the solutions to the system of equations. Finding the coordinates of the points of intersection will give you the solutions to the system of equations.