[tex] \frac{9}{8} [/tex]
Step-by-step explanation:
you would want to get rid of the -1/2 so you have to add one half to the other side of the equation and since 1/2 equals 4/8 the equation would be
4/8 plus 5/8 which equals 9/8
(9x - 3) - (2x2 + 3x + 7)
Answer:
8 - 6x
Step-by-step explanation:
just trust me the other guy's wrong
1. Find the length of side "a" in the figure below. Also identify the type of triangle and
explain how you arrived at the answer.
Answer:
It's a right triangle. a = 5.Step-by-step explanation:
Look at the picture.
We have the triangle 30° - 60° - 90°. The sides are in ratio 1 : √3 : 2.
We have:
[tex]a\sqrt3=5\sqrt3[/tex] divide both sides by √3
[tex]a=5[/tex]
It's a right triangle.
Solve for x.
12 = x + 3 X=_____
For this case we must find the value of the variable "x" of the following equation:
[tex]12 = x + 3[/tex]
So, we follow the steps:
Subtracting 3 from both sides of the equation we have:
[tex]12-3=x+3-3[/tex]
Different signs are subtracted and the sign of the major is placed:
[tex]9 = x\\x = 9[/tex]
Thus, the value of x is 9.
Answer:
[tex]x = 9[/tex]
A sphere has a radius of 3m. Calculate its surface area and round to the nearest hundredth for your final answer.
a. 125.63 sq. m
b. 113.04 sq. m
c. 120.3 sq.m
d. 123.8 sq.m
Answer:
B
Step-by-step explanation:
formula s =4*pi*r^2
s=4(3.14)(3^2)
s = 12.56(9)s= 113.04
Solve the inequality 171>-6x and graph the solution what does the graph look like
To solve the inequality, you need to isolate/get x by itself:
171 > -6x Divide -6 on both sides [dividing/multiplying a negative number on
-28.5 < x [dividing/multiplying a negative number in an inequality causes the sign (<, >, ≤, ≥) to flip]
-28.5 < x [x is a number greater than -28.5]
So your graph should have an open circle at -28.5 (the first small line next to -28), and the arrow pointing to the right since x is greater than -28.5 (increasing) The 1st option is your answer
[use the o---> and put it at -28.5]
Multiply
(3x – 7)(3x – 5)
Question 5 options:
9x2 – 36x + 35
9x2 + 36x + 35
9x2+ 6x + 35
9x2 – 36x – 35
Answer:
[tex]\large\boxed{(3x-7)(3x-5)=9x^2-36x+35}[/tex]
Step-by-step explanation:
[tex]\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(3x-7)(3x-5)\\\\=(3x)(3x)+(3x)(-5)+(-7)(3x)+(-7)(-5)\\\\=9x^2-15x-21x+35\qquad\text{combine like terms}\\\\=9x^2+(-15x-21x)+35\\\\=9x^2-36x+35[/tex]
Write an equation of the line passing through the point (4, –3) that is perpendicular to the line y−3=−9 (x+4).
Answer:
see explanation
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y - 3 = - 9(x + 4) ← is in point- slope form
with slope m = - 9
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-9}[/tex] = [tex]\frac{1}{9}[/tex]
The point (a, b) = (4, - 3), hence
y + 3 = [tex]\frac{1}{9}[/tex] (x - 4) ← equation of perpendicular line
What is the x-value of the solution to the system of equations?
5x + 4y = 8
2x – 3y = 17
oooo
Answer:
x = 4
Step-by-step explanation:
Simplify the equation 5x + 4y = 8 to get y = 2 - [tex]\frac{5}{4}[/tex] x
then substitute the y into 2x - 3y = 17 to get the answer. sorry im not good at explaining but it should be right.
To find the x-value of the solution to the system of equations, we can use the method of substitution. Solve one equation for x, substitute it into the other equation, and solve for y. Finally, substitute the value of y back into the expression for x to find the x-value.
Explanation:To find the value of x in the system of equations, we can use the method of substitution. Firstly, solve one of the equations for x or y. Let's solve the second equation for x:
2x - 3y = 17 → 2x = 17 + 3y → x = (17 + 3y)/2
Now substitute this value for x into the first equation and solve for y:
5((17 + 3y)/2) + 4y = 8 → 17 + 3y + 4y = 8 → 17 + 7y = 8 → 7y = -9 → y = -9/7
Finally, substitute the value of y back into the expression we found for x:
x = (17 + 3(-9/7))/2 → x = (17 - 27/7)/2 → x = (119/7 - 27/7)/2 → x = 92/7/2 → x = 92/14 → x = 46/7
Therefore, the x-value of the solution to the system of equations is 46/7.
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Which of the following coordinates exits on the line y=3x+2
It is B
-2 =3(-1) + 1
Let me know the answer plz
Answer:
The correct answer option is A. [tex]\frac{1}{16}[/tex].
Step-by-step explanation:
We are given the following geometric sequence and we are to find its 8th term:
[tex]1024, 256,64,...[/tex]
Here [tex]a_1=1024[/tex] and common ratio [tex](r) = \frac{64}{256} =0.25[/tex].
The formula we will use to find the 8th term is:
nth term = [tex]a_1 \times r^{(n-1)}[/tex]
Substituting the values in the formula to get:
8th term = [tex]1024 \times 0.25^{(8-1)}[/tex]
8th term = [tex] \frac { 1 } { 1 6 } [/tex]
There are 4 grams of fiber in 1/2 cup of oats. How many grams of fiber are in 3 1/2 cups of oats?
Answer:
28 grams
Step-by-step explanation:
1 cup is 8 grams of fiber, since a half a cup is 4 you times it by 2
then 8x3 because you're multiplying the fiber of one cup by 3. which equals 24, but you still have a half of cup of oats left. and since 4 grams equal a half a cup you just simply add 4 onto 24 which equals 28
Answer:
28 grams
Step-by-step explanation:
because i a mulpitplyed the numbers to get my answer
Federico owns a care with a 18.4 gallon fuel tank. How many gallons are there in half
tank of gas?
Answer:
9.2 gallons
Step-by-step explanation:
18.4/2 = 9.2 gallons
find the real zeros x4-11x2+18=0
Answer:
x=√2, x=-√2, x= 3 and x=-3
Step-by-step explanation:
We need to solve the equation x^4 - 11x^2+18=0
We can replace x^4 = u^2 and x^2 = u
So, the equation will become
u^2 -11u+18 = 0
Factorizing the above equation:
u^2 -9u-2u+18 =0
u(u-9)-2(u-9)=0
(u-2)(u-9)=0
u=2, u=9
As, u = x^2, Putting back the value:
x^2 =2 , x^2 =9
taking square roots:
√x^2 =√2 ,√x^2=√9
x=±√2 , x = ±3
so, x=√2, x=-√2, x= 3 and x=-3
Final answer:
The real zeros of the polynomial equation x^4 - 11x^2 + 18 = 0 are found by factoring the equation as a quadratic in x^2, which yields the real zeros x = 3, x = -3, x = √2, and x = -√2.
Explanation:
To find the real zeros of the polynomial equation x4 - 11x2 + 18 = 0, we can attempt to factor it. Notice that the equation resembles a quadratic in form, with x2 taking the place of x. If we let y = x2, our equation becomes y2 - 11y + 18 = 0, which is a quadratic equation.
Factoring the quadratic equation gives us (y - 9)(y - 2) = 0. Thus, the solutions for y are y = 9 and y = 2. Since y = x2, we now solve for x by finding the square roots of these solutions.
For y = 9, the values of x are x = 3 and x = -3. For y = 2, the values of x are x = √2 and x = -√2. Therefore, the real zeros of the original polynomial equation are x = 3, x = -3, x = √2, and x = -√2.
the center of a circle is A(-3, 3) and B(1, 6) is on the circle. Find the area in terms of pi.
Answer:
[tex]\large\boxed{A=25\pi}[/tex]
Step-by-step explanation:
The formula of an area of a circle:
[tex]A=\pi r^2[/tex]
r - radius
We have the center A(-3, 3) and the point on the circle B(1, 6).
The radius is equal to the distance between the center and the any point on the circle.
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute:
[tex]r=\sqrt{(1-(-3))^2+(6-3)^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5[/tex]
[tex]A=\pi(5^2)=25\pi[/tex]
The area of the circle centered at A(-3, 3) and passing through B(1, 6) is 25π square units.
Explanation:The subject of this problem is geometry, specifically about the area of a circle.To find the area of a circle, we need to know the radius. Since B is on the circle, AB is the radius. The area (A) of a circle is found using the formula A = πr², where r represents the radius of the circle. Here, the radius of the circle can be determined by finding the distance between the center A(-3, 3) and a point on the circle B(1, 6).
The formula for distance between two points in a plane is √[(x₂ - x₁)² + (y₂ - y₁)²]. Substituting values, we get r = √[(1 - -3)² + (6 - 3)²] = √[(4)² + (3)²] = √[16 + 9] = √25 = 5. Therefore, the radius is 5.
Substitute r = 5 in the area formula: A = π * (5)² = 25π square units.
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What is the general form of the equation for the given circle centered at O(0, 0)?
let's notice that the center of the circle is at the orgin, and that the distance from the center to an endpoint B is its radius.
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ O(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}[/tex]
[tex]\bf \stackrel{radius}{r}=\sqrt{(4-0)^2+(5-0)^2}\implies r=\sqrt{4^2+5^2} \\\\\\ r=\sqrt{16+25}\implies r=\sqrt{41} \\\\[-0.35em] ~\dotfill\\\\ \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{0}{ h},\stackrel{0}{ k})\qquad \qquad radius=\stackrel{\sqrt{41}}{ r} \\\\\\ (x-0)^2+(y-0)^2=(\sqrt{41})^2\implies x^2+y^2=41[/tex]
Answer:
The correct answer is option B
Step-by-step explanation:
B. x2 + y2 − 41 = 0
X+2y is greater than or equal to 10. Which of the following ordered pairs are solutions to the system
Answer:
(4,4), (2,8) (4,8) and all points in the shaded region as attached below
Step-by-step explanation:
This question is on solutions for inequalities equations
Give the equation as;
x+2y ≥ 10.......................................rewrite the equation for graphing purposes
x+ 2y = 10.............................................compose a table for values of x with corresponding values of y
x -2 0 2
y 6 5 4
Plot and shade the wanted region as show in the attached graph
For example point (4,4) or point (2,6) will satisfy the inequality x+2y ≥ 10 as;
(4,4)........ x+2y ≥ 10------4+2(4) ≥ 10
20 ≥ 10 ,,,,,,,,,,,,,,,,,,which is okay
A rectangular prism with a volume of
5 cubic units is filled with cubes with side lengths of
1/3 unit. How many 1/3 unit cubes does it take to fill the prism?
Answer:I believe the answer is 12 because it takes 4, 1/4 unit cube to make 1 cubic unit so to make 3 cubic units you need 12, 1/4 unit cubes if that makes any sense. :) Please make Brainliest if this helped.
Anderson car co. Has determined that the relationship between the number of cars sold and their net profit can be determined by a polynomial function F(x) in which x represents the number of cars sold and F(x) represents their net profits (in dollars) what would be an appropriate domain for this function? A. All nonnegative integers B. x>0 C. All real numbers D. x<0
Answer:
a
Step-by-step explanation:
Option: A is the correct answer.
The appropriate domain for the function is:
A. All non-negative integers
Step-by-step explanation:We know that a domain of a function is the set of all the value of the independent variable at which the function is defined.
Here x represents the number of cars sold and F(x) represents their net profits (in dollars)
As we know that the profit will be zero when none of the car will be sold and also the car will be sold as a whole.Also, the profit is calculated when some cars are sold.
Hence, the x-value will be the set of all the positive integers.
Hence, the correct answer is:
Option: A
The isosceles trapezoid is part of an isosceles triangle with a 42 degree vertex
What is the measure of an obtuse base angle of the trapezoid? The diagram is not drawn to scale
PLEASE HELP ME SOLVE Questions 5. And 6. !!! Please
Answer:
the measure of the obtuse base angle of the trepezoid is 111.
Step-by-step explanation:
An isosceles triangle has one vertex angle and two congruent base angles. Also, we know that the sum of all angles in a triangle must equal 180 degrees. So we can say that:
Vertex Angle + Base Angle + Base Angle = 180.
Vertex Angle + 2 x (Base Angle) = 180.
2 x (Base Angle) = 180 - Vertex Angle
2 x (Base Angle) = 180 - 42
2 x (Base Angle) = 138
Base Angle = 69
Also, we know that angles on one side of a straight line always add to 180 degrees.
So we can say that:
Base Angle + ? = 180
? = 180 - Base Angle
? = 180 - 69
? = 111
So, the measure of the obtuse base angle of the trepezoid is 111.
A person began running due east and covered 15 kilometers in 2.0 hours. What is the average velocity of the person? Show all your work!
15/2.0=7.5. The average velocity of the person is 7.5.
Which expression is equivalent to 60x^20y^24/30x^10y^12 ?
Answer:
2x^(10)y^(12)
Hope This Helps! Have A Nice Day!!
Answer:
The correct answer is 2X¹⁰Y¹²
Step-by-step explanation:
Points to remember
identities
Xᵃ * Xᵇ = X⁽ᵃ⁺ᵇ⁾
Xᵃ/Xᵇ = X⁽ᵃ⁻ᵇ⁾
To find the equivalent to given expression
It is given that,
60X²⁰Y²⁴/30X¹⁰Y¹²
Using identities we can write,
60X²⁰Y²⁴/30X¹⁰Y¹² = (60/30) * (X²⁰/X¹⁰) * (Y²⁴/y¹²)
= 2 * X⁽²⁰ ⁻ ¹⁰⁾ * Y⁽²⁴ ⁻ ¹²⁾
= 2 * X¹⁰ * Y¹²
= 2X¹⁰Y¹²
The correct answer is 2X¹⁰Y¹²
Consider that ΔLMN is similar to ΔPQR and the measure of ∠P is 80°. What is the measure of ∠L?
A) 20°
B) 70°
C) 80°
D) 90°
Answer:
C
Step-by-step explanation:
Given ΔLMN and ΔPQR are similar, then
∠L, ∠P and ∠M, ∠Q and ∠N, ∠R are congruent
Hence ∠L = ∠P = 80° → C
Answer:
The Answer is C, 80 degrees
Step-by-step explanation:
What is the equation of the line with an x-intercept of -2 and a y-intercept of 1
Answer:
y = 2x + 1
Step-by-step explanation:
This line goes through the points (-2, 0) (the x-intercept) and (0, 1) (the y-intercept).
As we move from -2 to 0, x increases by 2, and at the same time y increases from 0 to 1, that is, by 1. Thus, the slope of this line is m = rise / run = 2/1 = 2.
Starting with the slope-intercept formula for a straight line:
y = mx + b becomes y = 2x + 1. (We had already found b.)
The equation of line is x - 2y + 2 = 0.
What is Equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Here, x-intercept = -2
y- intercept = 1
Now, equation of line
x/a + y/b = 1
x/-2 + y/1 = 1
(x - 2y)/-2 = 1
x - 2y = -2
x - 2y + 2 = 0
Thus, the equation of line is x - 2y + 2 = 0.
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Simplify the expression –2(p + 4)2 – 3 + 5p. What is the simplified expression in standard form?
Answer:
-2p² − 11p − 35
Step-by-step explanation:
Simplifying:
-2(p + 4)² − 3 + 5p
-2(p² + 8p + 16) − 3 + 5p
-2p² − 16p − 32 − 3 + 5p
-2p² − 11p − 35
This is also the standard form.
Answer:
-2p^2 - 11 p - 35
Step-by-step explanation:
Please, use " ^ " to indicate exponentiation. Thus:
–2(p + 4)^2 – 3 + 5p
Now perform the exponentiation first, obtaining:
-2(p^2 + 8p + 16) - 3 + 5p, or
-2p^2 - 16 p - 32 - 3 + 5p
Now rearrange these terms in descending order by powers of p:
-2p^2 - 11 p - 32 - 3, or
-2p^2 - 11 p - 35
What is the axis of symmetry for the graph of y =2x^2-8x+2? x=
You can use this equation to find the axis of symmetry or the vertex of the quadratic equation as long as it is in standard form
X= (-b/2a)
The answer is x=2
Answer:
The answer will be x = 2.
Step-by-step explanation:
x + 3y = 7
x - 3y = 1
Solve the system of equations.
Answer:
y = 1
x = 4
{x,y} = {4,1}
Step-by-step explanation:
[2]
x - 3y = 1
+ 3y +3y
x = 3y + 1
[1]
x + 3y = 7
(3y + 1) + 3y = 7
- 1 - 1
(3y) + 3y = 6
6y = 6
6 6
y = 1
--------------------------------
x = 3y + 1
y = 1
x = 3(1) + 1
x = 4
y = 1
x = 4
{x,y} = {4,1}
Numbers to the power of a fraction help pls
Answer:
see explanation
Step-by-step explanation:
Using the rules of exponents
• [tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]
• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]
(a)
[tex]27^{\frac{1}{3} }[/tex] = [tex]\sqrt[3]{27}[/tex] = 3
(b)
[tex]25^{-\frac{1}{2} }[/tex]
= [tex]\frac{1}{25^{\frac{1}{2} } }[/tex] = [tex]\frac{1}{\sqrt{25} }[/tex] = [tex]\frac{1}{5}[/tex]
A group of 4 adults and 5 children is visiting an amusement park.
Admission is $15 per adult and $9 per child. Find the total cost of
admission for the group.
Answer:
105
Step-by-step explanation:
15 x 4 = 60
9 x 5 = 45
45 + 60 = 105
Answer:
105
Step-by-step explanation:
4x15=60
5x9=45
45=60=105
2 Points
The statement "If A, then B" can best be described as
O
A. If Ais false, then B must be false
O
B. If A is true, then B might be true.
O
C. If Ais false, then B might be false
D. If A is true, then B must be true.
Answer:
D
Step-by-step explanation:
This is called "implication". So if A (is true), then B MUST be true. If B is false, the implication is false. In all other cases, the implication is true. Suppose A is false, then it doesn't matter what B is, the implication is true, since we don't care what B is.
It's a bit confusing I suppose. Below is a truth table using P and Q in stead of A and B.
Final answer:
The correct answer is D: If A is true, then B must be true. This represents a logical conditional where the statement is true unless the antecedent A is true and the consequent B is false.
Explanation:
The statement "If A, then B" is a logical conditional, which can be represented as A
ightarrow B in logical notation. This statement best matches option D: If A is true, then B must be true. In logic, the only time a conditional statement is false is when the first part (the antecedent A) is true and the second part (the consequent B) is false. Otherwise, the statement is considered true, regardless of the individual truth values of A or B. This includes when A is false; the truth value of B does not affect the truth value of the conditional in this case. Therefore, if A is true, the conditional obliges B to also be true for the statement to remain true.
Which number is a rational number?
Answer: Sqrt(36/16)
sqrt(36/16)=6/4=3/2 rational