Answer:
[tex]x^{4}[/tex] - 256
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor, that is
x²(x² - 16) + 16(x² - 16) ← distribute both parenthesis
= [tex]x^{4}[/tex] - 16x² + 16x² - 256 ← collect like terms
= [tex]x^{4}[/tex] - 256
Answer:
Step-by-step explanation:
(x²+16)(x²-16) = (x²)² - 16² = x^4 - 256 use identity a²-b² = (a-b)(a+b)
For the ordered pair, give three other ordered pairs with θ between −360° and 360° that name the same point.
(−3, 330°)
Three other ordered pairs with θ between −360° and 360° that name the same point as (−3, 330°) are (−3, 30°), (−3, 690°), and (−3, -30°).
Explanation:Given the ordered pair (−3, 330°), we can find three other ordered pairs that name the same point by adding or subtracting 360° from the given angle:
(−3, 30°)(−3, 690°)(−3, -30°)These three ordered pairs have angles between −360° and 360° and represent the same point as the given ordered pair.
the product of a 3x3 and a 6x6 matrix would be
54 54 54
54 54 54
54 54 54
Find the product of 7 and 28. Use place value and the distributive property to rewrite the product. 7(28) = 7(20 + 8)
To find the product of 7 and 28 using place value and the distributive property, rewrite the product as 7(20 + 8). Distribute the 7 to both terms inside the parentheses and then add the resulting products.
Explanation:To find the product of 7 and 28 using place value and the distributive property, we can rewrite the product as 7(20 + 8). This is because 28 can be decomposed into 20 + 8.
Using the distributive property, we can distribute the 7 to both terms inside the parentheses: 7(20) + 7(8).
The product of 7 and 20 is 140 and the product of 7 and 8 is 56. Therefore, the final product is 140 + 56 = 196.
Ms. Hartman’s class is going on a field trip to planetarium. There are 25 students in the class, and each students need to purchase a day pass to the planetarium and a lunch ticket. The day pass costs $10 and the lunch ticket costs t dollars
Pick all the expressions that represent the total costs for the field trip
250+10t
t(25+10)
250+25t
25(10+t)
the sum of two numbers is 32. the sum of 3 times the larger and 7 times the smaller is 128
Answer:
Smaller number = 8 (x)
Larger number = 24 (y)
Step-by-step explanation:
x+y=32
7x+3y=128
Solving by Elimination
-3x-3y= -96
7x+3y=128
4x=32
4x/4=32/4
x=8
-7x-7y= -224
7x+3y=128
-4y= -96
-4y/-4= -96/-4
y=24
Check answer
x+y=32
8+24=32
7x+3y=128
7(8)=3(24)=138
56+72=128
128=128
Two hundred thousand twenty five
confused as to what you want but if you want to see the number then its 200,025
Answer:
200,025
Step-by-step explanation:
200 1000s so 200,0000 and add 25
What is the equation in point slope form of the line that passes through the point (1, −2) and has a slope of 3?
(A) y+2=3(x−1)
(B) y+1=3(x−2)
(C) y−2=3(x+1)
(D) y−1=3(x+2)
Answer:
(A) y+2=3(x-1)
Step-by-step explanation:
y-y1=m(x-x1)
y-(-2)=3(x-1)
y+2=3(x-1)
How are the graphs of the functions f(x) = 16and g(x) = 3/64"related?
Answer:
The graphs of the functions are both straight lines and parallel to x-axis
Step-by-step explanation:
The graph of f(x) is the line y = 16 which is parallel to x-axis.
This is because for every value of x the function f(x) only takes the value 16
Similarly the graph of g(x) is also a straight line but is characterized by y = 3/64. This line is also parallel to the x-axis.
For every value of x the function g(x) only takes the value 3/64
What is the slope of the line?
Answer:
[tex]\displaystyle 2[/tex]
Step-by-step explanation:
Starting from the y-intercept of [tex]\displaystyle [1, 1],[/tex]you do [tex]\displaystyle \frac{rise}{run}[/tex]by either moving two blocks south over one block west or two blocks north over one block east [west and south are negatives]. Doing this will give you the equation below:
[tex]\displaystyle y = 2x + 1[/tex]
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Need help asap !!!!!
Answer:
The answer is x = 5.
Step-by-step explanation:
Given:
Δ ABC is an Isosceles triangle with AB = CA
m∠ ABC = ( 6x + 4 )°
m∠ BAC = 73°
m∠ BCA = ( 8y - 7 )°
To Find:
x = ?
Solution:
Properties of an Isosceles Triangle.
Base angles or two angles are equal.Any two sides are equal.Here , Δ ABC is an Isosceles triangle with AB = CA
∴ m∠ BAC = m∠ BCA
[tex]73= 8y-7\\8y=73+7\\8y=80\\y=\frac{80}{10} \\y=10[/tex]
∴ m∠ BCA = ( 8y - 7 )°
= 8 × 10 - 7
m∠ BCA = 73 Which is same as ∠ CAB
Property of a Triangle is Sum of the measures of the angle of a triangle is 180°.
[tex]\angle ACB + \angle CAB + \angle CBA = 180[/tex]
Substituting the values we get,
[tex]73 + 73 + (6x+4) = 180\\6x+4=180-146\\6x=34-4\\6x=30\\x=\frac{30}{6} \\x=5\\[/tex]
The answer is x = 5.
need help asap thank you..
Answer:
r = 0.93
Step-by-step explanation:
The correlation coefficient gives us the "strongness" of two variables associated.
This is the value "r".
It is positive if there is strong relationship (one goes up, another goes up and vice versa)
It is negative, if one goes up and another goes down (inverse relationship)
First of all, from the scatter points, we see that as x increases, y also tend to increase. And if we were to draw a line of best fit that goes through max points, we would see the line slopes UPWARD (means as x increases, y also increase).
Thus, the value of "r" will be positive. So we can eliminate first and second choice. Now remains the other two choices
0.64
0.93
The closer the value to 1, the more that line is slopier, and less that value from 1, the line will be less "slopy".
A perfect one would be a line with slope 1, as 1 unit increase in x, the y increases 1 unit as well.
So, if we were to draw a line, we would see that it will be very close to a value of 1. The value of 0.64 can be eliminated because the points are not much "relaxed" as it should be for 0.64.
So, the correct choice is the 4th choice, r = 0.93
Which graph best represents the function f(x) = (x - 1)(x + 3)(x-3)?
Answer:
C) –|x| + 3
I got the answer correct!!!
the child weighs 55 lbs. Calculate the child’s weight in pounds to kilograms
I don’t know where to start with this problem
Answer:
√(4/5)
Step-by-step explanation:
First, let's use reflection property to find tan θ.
tan(-θ) = 1/2
-tan θ = 1/2
tan θ = -1/2
Since tan θ < 0 and sec θ > 0, θ must be in the fourth quadrant.
Now let's look at the problem we need to solve:
sin(5π/2 + θ)
Use angle sum formula:
sin(5π/2) cos θ + sin θ cos(5π/2)
Sine and cosine have periods of 2π, so:
sin(π/2) cos θ + sin θ cos(π/2)
Evaluate:
(1) cos θ + sin θ (0)
cos θ
We need to write this in terms of tan θ. We can use Pythagorean identity:
1 + tan² θ = sec² θ
1 + tan² θ = (1 / cos θ)²
±√(1 + tan² θ) = 1 / cos θ
cos θ = ±1 / √(1 + tan² θ)
Plugging in:
cos θ = ±1 / √(1 + (-1/2)²)
cos θ = ±1 / √(1 + 1/4)
cos θ = ±1 / √(5/4)
cos θ = ±√(4/5)
Since θ is in the fourth quadrant, cos θ > 0. So:
cos θ = √(4/5)
Or, written in proper form:
cos θ = (2√5) / 5
HELP ASAP!!! A circle has a radius of 6 meters. What is the circumference of the circle?
A.12 Pi
B. 9 Pi
C.6 Pi
D.3 Pi
Answer:
12Pi
Step-by-step explanation:
circumference of a circle can be worked out as Pi x diameter
Diameter = 2 x radius, therefore here d = 12 and circumference = 12 Pi
The circumference of the circle is C = 12π meters
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the radius of the circle be r = 6 meters
Now , circumference of circle = 2πr
On simplifying , we get
C = 2π ( 6 )
C = 12π meters
Hence , the circumference is 12π meters
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How would I solve this?
Answer:
The valid value of x is x=-2
Step-by-step explanation:
we know that
The sum of the interior angles of any quadrilateral must be equal to 360 degrees
so
[tex](7x^{2}-24x)+100+(24-46x)+(3x^{2}+56)=360[/tex]
solve for x
Combine like terms
[tex]10x^{2}-70x+180=360[/tex]
[tex]10x^{2}-70x-180=0[/tex]
Divide by 10 both sides
[tex]x^{2}-7x-18=0[/tex]
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2}-7x-18=0[/tex]
so
[tex]a=1\\b=-7\\c=-18[/tex]
substitute in the formula
[tex]x=\frac{-(-7)(+/-)\sqrt{-7^{2}-4(1)(-18)}} {2(1)}[/tex]
[tex]x=\frac{7(+/-)\sqrt{121}} {2}[/tex]
[tex]x=\frac{7(+/-)11} {2}[/tex]
[tex]x=\frac{7(+)11} {2}=9[/tex]
[tex]x=\frac{7(-)11} {2}=-2[/tex]
Remember that
The measure of the interior angle cannot be a negative number
For x=9
we have that the measure of one interior angle of quadrilateral is
[tex]24-46x[/tex]
substitute the value of x
[tex]24-46(9)=-390\°[/tex]
therefore
The value of x=9 cannot be a solution
For x=-2
The measure of the interior angles are
[tex](7(-2)^{2}-24(-2))=76\°\\100\°\\(3(-2)^{2}+56)=68\°\\24-46(-2)=116\°[/tex]
therefore
The valid value of x is x=-2
lets say you start with the equation 12b=24. what step should you take to find the quantity that equals 4b
Answer:
4b = 8
Step-by-step explanation:
Given 12b = 24
This is written as (4 X 3)b = 24
⇒ 4b X 3 = 24
Dividing by 3 throughout, we have
4b = [tex]$ \frac{24}{3} $[/tex] = 8.
Therefore, the value of 4b is 8.
Given the function y = 1/2x - 1
Find and plot the points for x = -4, X = 2, and x = 6
please show me the graph
Answer:
Step-by-step explanation:
if y = 1/2x - 1 is the function
y = 1/2(-4) - 1
y = -2 - 1
y = -3
(-4, -3)
y = 1/2(2) -1
y = 1 - 1
y = 0
(2, 0)
y = 1/2(6) - 1
y = 3 - 1
y = 2
(6, 2)
the pictures should be in order
Answer:
[tex]\displaystyle 2 = f(6), 0 = f(2), -3 = f(-4)[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{1}{2}[6] - 1 = 3 - 1 = 2 \\ \\ \frac{1}{2}[2] = 1 - 1 = 0 \\ \\ \frac{1}{2}[-4] - 1 = -2 - 1 = -3[/tex]
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Mr. Milligan bought a puppy for $287 and
sold him for $324. Find his gross profit.
How much money did he have
Answer:
His profit would be $37 of the money he got back.
Step-by-step explanation:
Solve x2 + 2x = 4 for x by completing the square. x equals plus or minus square root of 5 plus 1 x equals plus or minus square root of 5 minus 1 x = 1 x = 3
Answer:
x equals plus or minus square root of 5 minus 1
Step-by-step explanation:
we have
[tex]x^{2} +2x=4[/tex]
Divide by 2 the coefficient of the x-term
[tex]2/2=1[/tex]
squared the number
[tex]1^2=1[/tex]
Adds both sides
[tex]x^{2} +2x+1=4+1[/tex]
[tex]x^{2} +2x+1=5[/tex]
Rewrite as perfect squares
[tex](x+1)^{2}=5[/tex]
take the square root both sides
[tex]x+1=(+/-)\sqrt{5}[/tex]
[tex]x=(+/-)\sqrt{5}-1[/tex]
therefore
x equals plus or minus square root of 5 minus 1
Answer - B. x = ± [tex]\sqrt{5[/tex] - 1
984÷x=3 remainder:84
The value of x in 984 ÷ x = 3 remainder: 84 is 300
Step-by-step explanation:
In the division problem A ÷ B = Q [tex]\frac{R}{B}[/tex], where
A is the dividendB is the divisorQ is the quotientR is the remainderIf A is divisible by B, then R = 0
Examples:
23 ÷ 5 = 4 [tex]\frac{3}{5}[/tex] , The dividend is 23, the divisor is 5, the quotient is 4, and the remainder is 354 ÷ 6 = 9, 54 is divisible by 6 , then the remainder = 0The rule of the dividend is ⇒dividend = (divisor × quotient) + reminder
Let us use this rule to find x
984 ÷ x = 4, remainder 84
∵ Dividend = 984
∵ Divisor = x
∵ Quotient is 3
∵ Remainder = 84
- Substitute these values in the rule of dividend above
∵ 984 = (x × 3) + 84
∴ 984 = 3x + 84
- Subtract 84 from both sides
∴ 900 = 3x
- Divide both sides by 3
∴ 300 = x
∴ The value of x = 300
The value of x in 984 ÷ x = 3 remainder: 84 is 300
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A school receives a shipment of books. There are 60 cartons, and each carton weighs 42 pounds. The school’s elevator can hold 2200 pounds. What is the greatest number of cartons that can be carried on the elevator at one time if no people ride with them? Show all of your work. Then, explain your solution.
Answer:
52
Step-by-step explanation:
2200 / 42 = 52.381
You cannot bring a section of a carton, and 53 cartons is too much
53 * 42 = 2226. This goes over the weight limit.
52 * 42 = 2184. 2184 is less than 2200, so 52 is the greatest number you can bring
By dividing the elevator's weight capacity of 2200 pounds by the weight of one 42-pound carton, we find it can carry a maximum of 52 whole cartons simultaneously without exceeding the weight limit.
Explanation:To solve this problem, we can use simple mathematical analysis. We need to calculate how many 42-pound cartons can fit into an elevator that has a maximum capacity of 2200 pounds without exceeding this limit.
We start with the equation:
Divide the maximum weight the elevator can hold by the weight of one carton. 2200 pounds ÷ 42 pounds/carton = 52.38 cartons.Since you can't have a fraction of a carton, you need to round down to the nearest whole number. The greatest number of whole cartons is 52.Therefore, the elevator can safely carry 52 cartons at once, without any people in it.
Darren has a piece of wood that is 7 in by 8 in. Explain how he could divide this large rectangle into smaller rectangles
The rectangle can be divided into 6 ways as, 1 × 56 or 56 × 1, 2 × 28 or 28 × 2, and 4 × 14 or 14 × 4.
What is rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.
Given:
Darren has a piece of wood that is 7 in by 8 in
The area of the rectangle can be given by,
[tex]Area = Length\times width[/tex]
Area = 7 × 8
Area = 56
You can now divide the length and width as shown below,
Rectangle = 1 × 56 or 56 × 1
Rectangle = 2 × 28 or 28 × 2
Rectangle = 4 × 14 or 14 × 4
Therefore, the rectangle can be divided into 6 ways as 1 × 56 or 56 × 1, 2 × 28 or 28 × 2, and 4 × 14 or 14 × 4.
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A function is shown f(x)=2/3x+3 what is the value of f(12)
Answer:
55/18
Step-by-step explanation:
f(x) = 2/3*12 +3
= 1/18 +3
=55/18
The value of f (12) will be;
⇒ f (12) = 11
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The function is,
⇒ f (x) = 2/3x + 3
Now,
Since, The function is,
⇒ f (x) = 2/3x + 3
Substitute x = 12 in above equation, we get;
⇒ f (x) = 2/3x + 3
⇒ f (12) = 2/3 × 12 + 3
⇒ f (12) = 2 × 4 + 3
⇒ f (12) = 11
Thus, The value of f (12) will be;
⇒ f (12) = 11
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What is 62 divided by 5,841
Answer:
5,841 divided by 62 is 94.2
Which expressions are equivalent to 6^-10 6^-8
Answer:
The equivalents are 1/6¹⁰ and 1/6⁸
Step-by-step explanation:
1. Let's recall the rule about the negative exponents to find the equivalents to the expressions provided:
The rule says that any number different than zero, raised to a negative power equals its reciprocal raised to the opposite positive power.
Thus, x ⁻ⁿ = 1/x ⁿ
2. Now, let's find the equivalents after following the rule:
6 ⁻ ¹⁰ = 1 ÷ 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 = 1/6 ¹⁰
6 ⁻ ⁸ = 1 ÷ 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 = 1/6 ⁸
solve quadratic equation using factoring
z^2-5z+4=0
Answer:
[tex]z^2-5z+4=(z-4)(z-1)[/tex]
Step-by-step explanation:
To factorize a cuadratic equation, one must use the well known formula to find the roots of the equation: [tex]\frac{-b(+-)\sqrt{b^2-4ac} }{2a}[/tex], where a (a=1) is the coefficient that accompanies the cuadratic term, b is the coefficient that accompanies the linear term (b=-5) and c is the constant (c=4).Then, applied to this specific case, the previous formula results: [tex]\frac{5(+-)\sqrt{(-5)^2-4\times{1}\times{4}} }{2\times1}[/tex]. Then, the two roots of the equation come from [tex]\frac{25(+-)\sqrt{9} }{2}[/tex].Consecuently, [tex]z_1=\frac{5+\sqrt{9}}{2} =4[/tex], and [tex]z_2=\frac{5-\sqrt{9}}{2} =1[/tex].Finally, the cuadratic function can be expressed like this: [tex](z-4)(z-1)[/tex] (which comes from the fact that any polynomial can be expressed as the product of [tex](x-x_i)[/tex], where i are the roots of the polynomial). To corroborate that the procedure is correct, you can resolve this product, and you will obtain the inicial expression.Identify the vertex, the axis of syn
y = x2 + 8x + 16
The vertex is
. (Type an ordere
What is the min and max porabala
Good evening ,
Answer:
Vertex (-4 , 0)
axis x = -4
It’s a parabola.
Min = 0
Step-by-step explanation:
x2 + 8x + 16 = (x + 4)².
Please answer this correctly
Answer:
120 50 pound bags
Step-by-step explanation:
first you see how much 50 pounds is to one ton which one 50 pound bag is equal to .025 tons
then you multiply .025 by 120 to get 3 (tons)
that shows that the answer is correct
What is the difference between an equation with a variable and an inequality with a variable?
Answer:
An equation is a statement that maintains the equal value of two mathematical expressions. If the statement is true for all variable values, it is called an identity. ... An equation shows the equality of two variables while an inequality shows the inequality of two variables
An equation with a variable expresses a precise equality between expressions, while an inequality with a variable represents a range of possible values expressing that one value is greater or less than another. Equations typically have a definitive set of solutions, whereas inequalities signify a continuum of solutions that satisfy the relational condition.
Explanation:The difference between an equation with a variable and an inequality with a variable lies in the relationship they describe between the variables. An equation states that two expressions are equal by means of the equal sign (=), implying a specific value or set of values for the variables involved. For example, in the equation of a line y = mx + b, where x and y are the variables on the horizontal and vertical axis respectively, and b and m represent the y-intercept and the slope, we can see a direct relationship between x and y that determines the position of a point on a Cartesian plane. Conversely, an inequality such as x > y or x < 10 indicates a range of possible values rather than a single specific value, expressing a relationship where one value is either greater than or less than another value, but not equal to it.
In the context of a graph, the independent variable typically plotted on the x-axis is assumed to be the cause or input which then determines the value of the dependent variable, depicted on the y-axis. The dependent variable changes in response to the independent variable, thereby showing their relationship. This is often represented by inequalities when a range of outcomes is possible, extending beyond the linear relationship that might be depicted with an equation.