I'm confused with this question please help.
Answer:
70
Step-by-step explanation:
Ill give it to you if you really need it its gonna take a while to explain
:)
What is the domain of the function y = 2x²? To answer the question, ask yourself if there
are any restrictions on the values you may substitute for x.
Answer:
Step-by-step explanation:
Any value of x may be substituted into this function. So the domain is:
[tex]D=(-\infty , \infty)[/tex] or D=all real [tex]x[/tex]
I am not sure the format how you have been taught to write the answer.
Patricia has a savings account with $89 in it that earns 4.7% simple interest per year. How much money, to the nearest penny, will Patricia have in 5 years?
Answer:simpler interest is 109.92. Annual compounded interest is 111.98
Step-by-step explanation:
Answer: $209.2
Step-by-step explanation:
hey! i'm gonna try to make this as simple as possible;
with simple interest, the formula to this is I = PRT (Interest = Principle x Rate x Time).
we're going to take the $89 , 4.7% simple interest and the 5 years together into the same sentence like the formula.
89 (Principle, the money) x 4.7% (Interest rate) x 5 (Time). we'll narrow down the decimal by moving the decimal forward once so we get a decimal of .47 / 0.47.
back to the equation, it is now 89 x .47 x 5. multiply all those and you'll get a sum of 209.15! by the end of the five years, patricia will have $209.15. to the nearest penny, she will have $209.2. (5 or more, it goes to the next number. 4 or less, it stays in the same place.)
hope this helped :)
Write a statement to match this number sentence. |-5| = |5|
Statement to match the given number sentence is The absolute value of -5 is equal to the absolute value of 5.
What is absolute value?It is the distance of a number from zero on a number line, and is always positive.
The absolute value of -5 is 5 because -5 is 5 units away from zero on the number line.
Similarly, the absolute value of 5 is 5 because 5 is also 5 units away from zero on the number line.
Therefore, the absolute value of -5 is equal to the absolute value of 5, and the statement for this number sentence is "The absolute value of -5 is equal to the absolute value of 5."
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please help with solving find the value of k and the two roots of x
The approximate value of K of the given quadratic equation is: 16.842
How to solve Quadratic equations?The general expression of a quadratic function is:
ax² + bx + c = 0
The quadratic formula to find the roots is expressed as:
x = [-b ± √(b² - 4ac)]/2a
The product of the 2 roots of the quadratic equation is equal to the constant term.
Let a and b be used to denote the roots of a given quadratic equation.
But according to given condition, one root is equal to the square of the other root. Thus: b = a²
Thus:
a + a² = k
a * a² = 48
a³ = 48
a = 2∛6
Thus:
2∛6 + (2∛6)² = k
k = 16.842
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stion 6 of 10
A circular fence is being used to surround a goldfish pond as shown.
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7.25 m
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I'm sorry, but I don't see a question or any context for your statement. Could you please provide more information or clarify your request?
The table represents some points on the graph of an exponential function
Which function represents the same relationship?
The function [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex] represents the same relationship.
Here given a function f(x)
When x= 0,1,2,3,4 the value of f(x) will be 648,216,72,24,8 respectively.
The function that represents the same relationship as the table is [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex]
We can see that each successive value of f(x) is one-third of the previous value. So, we know that the function is of the form [tex]f(x) = a { (\frac{1}{3} )}^{x} [/tex] for some constant a.
To find the value of a, we can use the fact that f(0) = 648.
Substituting x = 0 into the equation gives f(0) = a(1/3)⁰ = a = 648
So, the function is [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex]
Therefore, the correct answer is [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex]
So, option D is the correct option.
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a) Complete the number machine so that z = 5w-3 Input
Output z obtained as: multiply w with 5 and then subtract 3 from the result: w --> *5 ---> -3 ---> z.
Explain about the linear equations?There are only one or two variables in a linear equation.
No variable can be multiplied by a number larger than one or can be utilized as the denominator of either a fraction in a linear equation.All of the points fall on the same line when you identify the values that together constitute a linear equation true as well as plot those values on a coordinate grid. A linear equation has a straight line as its graph.The relationship involving distance and time in this equation will be linear for any provided steady rate. However, as distance is commonly defined as a positive number, the first quadrant of this relationship's graphs will typically include the only points.The given expression is:
z = 5w-3
Here:
Input value : 5w-3
Output value : z
So,
Output z obtained as:
multiply w with 5 and then subtract 3 from the result:
w --> *5 ---> -3 ---> z
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Ruby wants to make 45 cupcakes.
Use your answer to b) to work out fi she has enough sugar left.
Since Ruby has 3 cups of sugar left, she has enough sugar to make the 45 cupcakes she wants
How to solveIf Ruby needs 2 cups of sugar to make 45 cupcakes, then we can calculate how much sugar she needs for one cupcake by dividing 2 cups of sugar by 45 cupcakes:
2 cups of sugar / 45 cupcakes = 0.0444 cups of sugar per cupcake (rounded to 4 decimal places)
To make 45 cupcakes, Ruby would need:
45 cupcakes x 0.0444 cups of sugar per cupcake = 1.998 cups of sugar (rounded to 3 decimal places)
Since Ruby has 3 cups of sugar left, she has enough sugar to make the 45 cupcakes she wants (3 cups of sugar > 1.998 cups of sugar needed for 45 cupcakes).
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Ruby wants to make 45 cupcakes.
Use your answer to b) to work out fi she has enough sugar left.
Ruby needs 2 cups of sugar to make 45 cupcakes, and she has 3 cups of sugar left.
(X+3)(X-8) = -30 solve using the quadratic formula
Answer:
X = 3,2
Step-by-step explanation:
1)Expand.
[tex]x^{2}[/tex] - 8X+3X - 24 = -30
2)Simplify [tex]x^{2}[/tex]-8X+3X-24 to [tex]x^{2}[/tex]-5X - 24.
[tex]x^{2}[/tex] – 5X – 24 = –30
3)Move all terms to one side.
[tex]x^{2}[/tex] - 5X - 24+ 30 = 0
4)Simplify [tex]x^{2}[/tex]–5X-24+30 to [tex]x^{2}[/tex] - 5X + 6.
[tex]x^{2}[/tex] - 5X + 6 = 0
5)Factor [tex]x^{2}[/tex]–5X+6.
(X-3)(X-2) = 0
6)Solve for X.
X = 3,2
The sum of interior angles of a regular polygon is
1800⁰. Calculate the size of one exterior angle of
the polygon.
Answer:
36
Step-by-step explanation:
i need help with work attached
The equation of the polynomial using finite difference is y = 18x^3 - 126x^2 + 269x - 163 and other solutions are shown below
Finding the equation of the polynomialTo find the equation of the polynomial table using finite difference, we need to calculate the differences.
The differences are obtained by subtracting each value of y from the next value of y and this is repeated for the differences
So, we have
x 1 2 3 4 5
y -2 15 -4 49 282
1st 17 -19 53 233
2nd -36 72 180
3rd 108 108
Since the third differences are all the same, this indicates that the original data can be represented by a cubic polynomial.
We can use the formula for a cubic polynomial:
y = ax^3 + bx^2 + cx + d
Using the table of values, we have:
a + b + c + d = -2
8a + 4b + 2c + d = 15
27a + 9b + 3c + d = -4
64a + 16b + 4c + d = 49
Using a graphing calculator, we have
a = 18, b = -126, c = 269 and d = -163
So, we have
y = 18x^3 - 126x^2 + 269x - 163
Equations of the cubic polynomialWe can use the formula for a cubic polynomial:
y = a(x - x1)(x - x2)(x - x3)
Using the ordered pairs, we have:
y = a(x + 3)(x + 1)(x - 2)
At (0, -12), we have
a(0 + 3)(0 + 1)(0 - 2) = -12
a = 2
So, we have
y = 2(x + 3)(x + 1)(x - 2)
Expand
y = 2x^3 + 4x^2 - 10x - 12
Equations of the cubic polynomialWe can use the formula for a cubic polynomial:
y = a(x - x1)(x - x2)(x - x3)
Using the ordered pairs, we have:
y = a(x + 10)(x + 5)(x - 4)
At (-8, -2), we have
a(-8 + 10)(-8 + 5)(-8 - 4) = -2
a = -1/36
So, we have
y = -1/36(x + 10)(x + 5)(x - 4)
Expand
[tex]y = -\frac{x^3}{36}-\frac{11x^2}{36}+\frac{10x}{36}+\frac{200}{36}[/tex]
The number of solutions in g(x)We have
g(x) = -9x^5 + 3x^4 + x^2 - 7
g(x) is a polynomial function of odd degree (5), so it will have at least one real root.
Also, the leading coefficient is negative;
So, g(x) has at least one root in the interval (-∞, ∞).
Since g(0) = -7 < 0 and g(1) = -12 < 0, and g(x) is continuous, there exists a root of g(x) in the interval (0, 1).
Similarly, since g(-1) = 6 > 0 and g(-2) = 333 > 0, there exists a root of g(x) in the interval (-2, -1).
Since g(x) is a polynomial of odd degree, it cannot have an even number of real roots.
Therefore, g(x) has exactly one real root.
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Anyone know how to do this?
The value of length of side of triangle AD using the angle bisector theorem is obtained as: AD = 4.68.
Explain about the angle bisector theorem?Angles are measurements created by joining two lines, also known as the vertex. Geometric forms such as triangles but also rectangles contain internal angles produced by their sides.
The sum of the internal angles of each geometric figure gives it a general size. We can do operations like bisecting an angle geometrically.Every angle that is bisected is split into two equal-sized angles. Starting at the vertex that makes up the primary angle, the bisector is drawn.Using the angle bisector theorem in the given triangles:
The ratios of the sides will be equal.
AB / BC = AD / DC
AB = 9 ; BC = 11.7 AD = 3.6
Put the values.
9/11.7 = 3.6 / AD
AD = 3.6*11.7 / 9
AD = 4.68
Thus, the value of length of side of triangle AD using the angle bisector theorem is obtained as: AD = 4.68.
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Write the expression as a single power of 6 6^8/6^4
To simplify this expression, we can use the rule of exponents that states when dividing two powers with the same base, we can subtract their exponents. Therefore:
6^8/6^4 = 6^(8-4) = 6^4
So the expression 6^8/6^4 can be simplified as a single power of 6, which is 6^4.
Show that if AB = AC and A is nonsingular, then the cancellation law holds; is, B = C.
When AB = AC and A is nonsingular, then the cancellation law holds; is, B = C. The statement is true.
In matrix algebra, the cancellation law is a crucial property to know. It states that if AB = AC, then B = C when A is a nonsingular matrix.
The given statement is true, which means that if AB = AC and A are nonsingular, then B = C. The cancellation law in matrix algebra is a property that helps in solving linear equations involving matrices. It states that if AB = AC and A is a nonsingular matrix, then B = C.
Therefore, we can say that if AB = AC and A is nonsingular, then B = C is true.
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distribute and simplify the following: (v+8)•(v+9)
Answer:
(v+8) x (v+9)
We can multiply v into the other two terms in the second bracket, then we can do the same with 8.
(v*v + v*9) + (8*v + 8*9)
v² + 9v + 8v + 72
v² + 17v + 72.
can you please answer this for me
Answer:
x = 8
Step-by-step explanation:
the angle between the tangent and the radius at the point of contact A is 90°
then Δ ABP is right at A
using Pythagoras' identity in the right triangle
BP² = AP² + AB² , that is
(x + 9)² = x² + 15² ← expand parenthesis on left side using FOIL
x² + 18x + 81 = x² + 225 ( subtract x² from both sides )
18x + 81 = 225 ( subtract 81 from both sides )
18x = 144 ( divide both sides by 18 )
x = 8
Find the area of a sector with a central angle of 180° and a diameter of 5. 6 cm. Round to the nearest tenth
The area of the sector with a central angle of 180° and a diameter of 5.6 cm is approximately 11.8 [tex]cm^2[/tex].
To find the area of a sector, we need to know the central angle and the radius or diameter of the circle that the sector is a part of. In this case, we are given a central angle of 180° and a diameter of 5.6 cm.
Find the radius of the circle is the first step. We can do this by dividing the diameter by 2:
radius = diameter/2 = 5.6/2 = 2.8 cm
Next, we can use the formula for the area of a sector:
Area of sector = (central angle/360°) x π x [tex]radius^2[/tex]
Plugging in the given values, we get:
Area of sector = [tex](180/360) * \pi * (2.8)^2[/tex]
= [tex](1/2) * 3.14 * 2.8^2[/tex]
= [tex]11.77 cm^2[/tex]
Rounding to the nearest tenth, we get:
Area of sector ≈ 11.8 [tex]cm^2[/tex]
Therefore, the area of the sector is approximately 11.8 [tex]cm^2[/tex].
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sami planned to spend the weekend camping, so on friday night he drove from his house to the nearest campsite at a speed of 60 miles per hour. after the weekend was over, he went the same way home, but he drove at a speed of 40 miles per hour because of the bad weather. if altogether he spent a total of 7 hours driving, how many hours did the trip to the campsite take?
The trip to the campsite took 2 hours for Sami.
The total time taken by Sami on his journey = 7 hours
Let the time taken by Sami while going from his house to the campsite be 'x' hours
And, the time taken by Sami while coming back from the campsite to his house be 'y' hours
Speed while going from house to campsite = 60 miles per hour
Speed while coming back from campsite to house = 40 miles per hour
Distance from house to campsite and back will be equal as Sami will take the same route.
Let the distance be 'd'.
So, according to the question,
Distance = Speed × Time
We know that,
Time taken while going from house to campsite + Time taken while coming back from campsite = 7 hours
x + y = 7 ...(1)
Distance while going from house to campsite = Distance while coming back from campsited = 2d ...(2)
Distance = Speed × Timex = d/60 ...(3)
y = d/40 ...(4)
Substituting (2), (3) and (4) in (1), we get,
d/60 + d/40 = 7
Solving the equation, we get d = 120
Therefore, Time taken while going from house to campsite, x = d/60 = 2 hours
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The measures of the angles of a triangle are shown in the figure below. Solve for x. (2x+10) 36
Maya is cutting strips of fabric to use when she makes a basket. She cuts a strip of fabric that is 9 1/3 yards long into pieces that are 2/3 yards long.
How many 2/3-yard long pieces can she cut from the strip of fabric?
A. 9 2/3
B. 9 1/3
C. 14
D. 6 2/9
Answer:
Step-by-step explanation:
the hypotenuse of a right triangle is 3 times as long as its shorter leg. the longer leg is 12 centimeters long. to the nearest tenth of a centimeter, what is the length of the triangle's shorter leg?
Choose ALL answers that describe the polygon ABCD if measure A is congruent to measure B, and measure C is congruent to measure D.
and segment Ab is parallel to segment CD
Parallelogram
Quadrilateral
Rectangle
Rhombus
Square
Trapezoid
The answers that describe the polygon ABCD if measure A is congruent to measure B, and measure C is congruent to measure D, and segment AB is parallel to segment CD are;
A. Parallelogram
B. Quadrilateral
C. Rectangle
D. Rhombus
E. Square
What is a parallelogram?In Mathematics, a parallelogram simply refers to a four-sided geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that is composed of two (2) equal and parallel opposite sides.
What is a rhombus?In Mathematics and Geometry, a rhombus is a type of quadrilateral that is composed of four (4) equal sides and opposite interior angles that are congruent (equal).
In conclusion, a square, parallelogram, rectangle, rhombus, and quadrilateral satisfies the given conditions.
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Determine whether the quadratic function y=x^2+6x+10 has a maximum or minimum value.
Pls helpppp and explain if you canI’ll mark you brainlist
Answer:
B) a 180° rotation about the origin
Step-by-step explanation:
question in picture below
The inequality shown by the graph is 4y+3x≤8x+2y+16 (option C).
Describe Inequality?In mathematics, an inequality is a statement that compares two values, expressing that one value is greater than, less than, or equal to the other. It is represented by symbols such as <, >, ≤, ≥, and ≠. For example, 5 > 3 is an inequality that means "5 is greater than 3", while 2x + 3 ≤ 7x - 2 is an inequality that means "the sum of 2 times x and 3 is less than or equal to 7 times x minus 2". Inequalities are commonly used in algebra, geometry, and real analysis to express relationships between quantities and to find solutions to equations and systems of equations.
To determine the inequality shown by the graph with coordinates (0,8) and (0, 3.25), we need to find the slope-intercept form of the equation for the line passing through these points.
The slope of the line is:
(y2 - y1) / (x2 - x1) = (3.25 - 8) / (0 - 0) = -4.75 / 0 (which is undefined)
Since the line is vertical, its equation is x = 0.
Substituting this into the inequality options, we can see that only option C results in a true statement:
A) 4y+3x≤8x+6y+16 -> 4(8) + 3(0) ≤ 8(0) + 6(8) + 16 -> 32 ≤ 64 (not true)
C) 4y+3x≤8x+2y+16 -> 4(8) + 3(0) ≤ 8(0) + 2(8) + 16 -> 32 ≤ 32 (true)
B) 4y-3x≤5x+2y+16 -> 4(8) - 3(0) ≤ 5(0) + 2(8) + 16 -> 32 ≤ 32 (true)
D) 4y-3x≤8x+2y+16 -> 4(8) - 3(0) ≤ 8(0) + 2(8) + 16 -> 32 ≤ 32 (true)
Therefore, the inequality shown by the graph is 4y+3x≤8x+2y+16 (option C).
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What is the measure of angle ABC?
I measured it with a protractor and it is around 135 degrees.
I honestly don't know if this is correct but I hope this helps. Feel free to remove my answer if you think this is wrong.
a square with side length is inscribed in a right triangle with sides of length , , and so that one vertex of the square coincides with the right-angle vertex of the triangle. a square with side length is inscribed in another right triangle with sides of length , , and so that one side of the square lies on the hypotenuse of the triangle. what is ?
The value of x/y is 35/37. The correct answer is option B).
Let's start by the first right triangle and the inscribed square. We know that the square has side length x and is inscribed in the right triangle with sides 3, 4, and 5, where 5 is the hypotenuse. Since one vertex of the square coincides with the right-angle vertex of the triangle, we have that the side length x of the square is also the length of the altitude from the right angle to the hypotenuse of the triangle. Therefore, we can write:
x = [tex](3*4)/5 = 12/5[/tex]
Now the second right triangle and the inscribed square:
We know that the square has side length y and is inscribed in the right triangle with sides 3, 4, and 5, where 5 is the hypotenuse. Since one side of the square lies on the hypotenuse of the triangle, we have that the sum of the areas of the two smaller squares is equal to the area of the larger square. Therefore, we can write:
[tex]x^{2} + y^{2} = 5^{2} = 25[/tex]
Substituting[tex]$x = {12}/{5}[/tex] gives
[tex](12/5)^{2} + y^{2} = 25[/tex]
Simplifying this equation gives
[tex]y^{2} = 25 - (144/25) = (25^{2} - 144)/25 = 481/25[/tex]
Taking the square root of both sides gives
y = [tex]\sqrt{481}/5[/tex]
Finally, we compute x/y:
x/y = [tex]12*\sqrt{481}/ \sqrt{481}*5[/tex]
x/y = 35/37
The correct option is B)
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--The given question is incomplete, the complete question is
"A square with side length x is inscribed in a right triangle with sides of length 3, 4, and 5 so that one vertex of the square coincides with the right-angle vertex of the triangle. A square with side length y is inscribed in another right triangle with sides of length 3, 4, and 5 so that one side of the square lies on the hypotenuse of the triangle. What is x/y?
(A) 12/13
(B) 35/37
(C) 1
(D) 37/35
(E) 13/12"
a random digit dialing sample of 2092 adults found that 1318 used the internet. of the users, 1041 said that they expect businesses to have web sites that give product information. in your business economics class at school, your teacher said that 80% of all internet users believe this. what is the appropriate z-value to use in this situation?
The appropriate z-value to use in the situation given in the question is 1.28.
Given,Total number of adults in the sample = 2092
Number of adults using the internet = 1318
Number of internet users who expect businesses to have websites that give product information = 1041
Probability of internet users who expect businesses to have websites that give product information as per the teacher's statement = 80% = 0.8
To find the appropriate z-value to use in this situation, we need to calculate the standard error of proportion, which is given by:
SEp = √[p(1-p)/n]
where p is the proportion of internet users who expect businesses to have websites that give product information and n is the sample size.
Substituting the given values in the formula,
SEp = √[(1041/1318)(1-1041/1318)/1318]SEp = 0.019
z-value is given by:
z = (p - P)/SEp
where P is the proportion of internet users who expect businesses to have websites that give product information as per the teacher's statement.
Substituting the given values in the formula,
z = (0.8 - 1041/1318)/0.019
z = - 1.28
The appropriate z-value to use in this situation is -1.28.
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?
What is 2+2 x 2+y equaled to
Answer:
6 + y
Step-by-step explanation:
By BODMAS rule,
1st : Multiply
Then add,
2 + 2 x 2 + y
2 + (2 x 2) + y
= 2 + 4 + y
= 6 + y