The remainder is 44
Explanations:The given polynomial is:
[tex]4x^4-3x^3+2x^2-5x\text{ + 6}[/tex]The function is to be divided by x - 2
The remainder of the division will be calculated using the remainder theorem
The remainder theorem states that " If a function g(x) is divided by x - a, the remainder of the division will be g(a)"
[tex]\text{Let g(x) = 4x}^4-3x^3+2x^2-5x+6[/tex]The remainder when g(x) is divided by x -2 is g(2)
[tex]\begin{gathered} g(2)=4(2)^4-3(2)^3+2(2)^2-\text{ 5(2) + 6} \\ g(2)\text{ = 4(16) - 3(8) + 2(4) -5(2) + 6} \\ g(2)\text{ = 64 - 24 + 8 - 10 + 6} \\ g(2)\text{ = 44} \end{gathered}[/tex]Evaluate each expression.5. -36.97. 13 +-28. -12-8
7) 13 + -2 = 13 + (-2) = 13 - 2 = 11
8) -12 - 8 = - (12 + 8) = - (20) = -20
please I need helpppppppppppp
The value of angle a will be = 50 degrees
Since the given figure has 4 sides hence it is a quadrilateral, we know that the sum of all 4 sides should be equal to 360 degrees so,
Sum of all 4 sides = 360 degrees
The sum of the given 3 sides = 100+100+110 = 310 degrees
Angle a = Sum of all 4 sides - the sum of the given 3 sides
Angle a = 360 - 310
Angle a = 50 degrees
Hence the value of the remaining angle a = 50 degrees
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I kind of understand but what I'm having trouble with is when u simply it 6/5 ×5/6=6/5×40 how are they getting 48 i get 33.3
37 = -3 + 5(x + 6)
Distributing:
37 = -3 + 5(x) + 5(6)
37 = -3 + 5x + 30
Commuting:
37 = -3 + 30 + 5x
37 = 27 + 5x
27 is adding on the right, then it will subtract on the left.
37 - 27 = 5x
10 = 5x
5 is multiplying on the right, then it will divide on the left
10/5 = x
2 = x
Tell me how I can eliminate the y-terms in this system! ASAP!
4x-8y=20
3x+4y=5
Multiply by what number on both sides
Answer:
2?
Step-by-step explanation:
I couldn't find an answer but 2 was the most appropriate so try that, and sorry I wasn't much of a help
Answer:
2
Step-by-step explanation:
10. Wesley willed his estate to Margaret, Betty Jo, and Johnny. He gave Margaret $20,000. Betty Jo got 22 times as much as Margaret. Johnny got 32 times as much as Margaret. What was the total value of the estate? (1) $26,000 (2) $50,000 (3) $70,000 (4) $120,000 (5) $1,140,000
We were told that Wesley willed his estate to Margaret, Betty Jo, and Johnny.
Given that he gave Margaret $20,000. Betty Jo got 22 times as much as Margaret, it means that the amount the at Betty Jo got is 22 * 20000 = 440000
Given that Johnny got 32 times as much as Margaret, it means that the amount that Johnny got is
20000 * 32 = 640000
Therefore, the total value of the estate is
20000 + 440000 + 640000 = 1100000
The total value of the estate is $1,100000
What is the answer for this equation 3X+y=5
The equation
[tex]3x+y=5[/tex]has two variables: x and y.
And since we have only one equation, the variables have infinite possible values, which are related to that equation.
Another way of seeing that is by calling x the independent variable, and then y will be the dependent variable (its value depends on the value of x).
So, we can isolate y on the left side of the equation, to obtain:
[tex]\begin{gathered} 3x+y=5 \\ \\ 3x+y-3x=5-3x \\ \\ y=-3x+5 \end{gathered}[/tex]Now, we see that the above equation represents a line (an infinite set of points), that has a slope -3 and a y-intercept 5.
Therefore, all the points on that line are solutions to the given equation.
If we graph that set of solutions on a xy-plane, we obtain the line below:
Which condition would prove AJKL - AXYZ?
J
O A. JK
XY
OB.
O C. KL
=
JL
X 2/2 = 1/2
XZ
118
O D. JL
118
= 8
YZ
3=8
XZ
K
56
L
N
7
Y
X
ΔJKL and ΔXYZ are similar triangles with condition KL / YZ = 8
Two triangles are said to be Similar triangles if they have same shape but not necessarily the same size , ratio of all the corresponding sides are same and corresponding angles are equal to each other
In ΔJKL and ΔXYZ ,
1 . The shape of both triangles are same
2 . ∠KLJ = ∠YZX
3 . Ratio of corresponding sides KL / YZ = 56 / 7
= KL / YZ = 8
so , KL / YZ = 8 is condition to prove ΔJKL and ΔXYZ are similar triangles.
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Answer:
KL/YZ=8 have a nice day:)
Please help right now!
An artist is making a scale model of a statue. On the model 2 inches represents 1 foot on the actual statue. Which graph best represents this relationship?
The graph best represents this relationship of the scale model of a statue is B.
What is meant as the scale factor?A scale factor is described as the ratio of the scale of a provided original object to the scale of a new object that is its depiction but of a various sizes (bigger or smaller). It is necessary to specify how much the shape has already been enlarged when describing enlargement. Scale factor 3 signifies that the new shape is three times the size of the original shape.The shape will be smaller if the scale factor is a fraction. This is known as reduction.For the given question;
On the model 2 inches represents 1 foot on the actual statue.
Thus, model 4 inches represents 2 foot on the actual statue.
This is given by graph B.
Thus, the graph best represents this relationship of the scale model of a statue is B.
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The x-coordinates of the points of intersection of the given function graphs are;
1) x = 0 and x = 2
2) x = -1
3) x = 0
What is the point of intersection of the graph?The point of intersection of a graph is in simple terms explained as the point or coordinates where two lines or even curves intersect.
1) The first question gives us the functions as;
f(x) = -³/₄x² + 3x + 1
g(x) = 2ˣ
Therefore;
From the first graph, At f(x) = g(x), the coordinates of intersection is at (2,4 and (0, 1)
2) In the second question, we are given the functions as;
f(x) = x² + 4x + 2
g(x) = (¹/₂)ˣ + 1
Therefore;
From the first graph, At f(x) = g(x) the coordinates of intersection is at (-1. 3)
C) In the third question, we are given the functions as;
f(x) = -⁷/₃x - 3
g(x) = 2ˣ - 4
Thus;
From the graph, At f(x) = g(x), the coordinates of the point of intersection is at (0, -3)
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combine like terms: 3(x - 6) + 4x
7x - 18
Explanations:The given expression is:
3 (x - 6) + 4x
Open the brackets by expanding the expression
3x - 18 + 4x
Combine like terms
3x + 4x - 18
7x - 18
In one country, approximately 193,200 of 920,000 residences are rentals. Determine the percentage of residences in the country that are rentals.The percentage of residences in the country that are rentals is %.
To find the percentage of the residences in the country that are rentals is calculated with this formula:
[tex]\begin{gathered} =\frac{\text{population of rental residence}}{total\text{ country population}}\times100\text{ \%} \\ \text{Given:} \\ \text{Population of rental reseidence = 193,200} \\ \text{Total country population = 920,000} \end{gathered}[/tex]Now substituting the given information, into the above percentage expression, we will have:
[tex]\begin{gathered} =\frac{193,200}{920,000}\times100\text{ \%} \\ =0.21\times100\text{ \%} \\ =21\text{ \%} \end{gathered}[/tex]The percentage of residences in the country that are rentals is 21 %.
Maria used a number line to find 12 ÷ 4.
Explain how she can use the number line to model the division.
Maria can draw a number line connecting the points 0 and 12, then divide the distance between them into four equal parts. The division operation produces the location of the point closest to zero.
What is number line ?A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in elementary mathematics. Every point on a number line is assumed to be a real number, and every real number is assumed to be a point.
Integers are frequently represented as specially marked points evenly spaced on a line. Despite the fact that the image only shows the integers from -3 to 3, the line includes all real numbers, which continue indefinitely in each direction, as well as numbers that are between the integers. It is frequently used to help teach simple addition and subtraction, particularly with negative numbers.
The number line is also known as a real line or real number line in advanced mathematics. It is formally defined as the set R of all real numbers viewed as a geometric space, namely the Euclidean space of dimension one. It's also known as a vector space, metric space, topological space, measure space, or linear continuum.
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Given two circles on a coordinate plane, use transformations to prove that both circles are similar
The two circles are said to be similar because they undergo a rigid transformation that does not change its shape.
How to prove similarity using transformation?A similarity transformation is defined as one or more rigid transformations (reflection, rotation, translation) followed by a dilation. Now, when a figure is transformed using a similarity transformation, an image is created that is similar to the original figure. This means that, two figures are similar if a similarity transformation will map the first figure to the second figure.
By definition of similarity transformation, looking at the given diagram, both shapes are circles and as such it is obvious that one circle has been dilated by a scale factor to get the other circle.
Thus, they have the same shape and are similar circles.
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A small television cost $120, the sales tax is 6.5%. What is the total cost of the television? * Your answer
∵ The cost of the television = 120 dollars
∵ The sale tax = 6.5%
→ Find at first the value of tax by multiplying 6.5% by 120
∵ 6.5% = 6.5/100 = 0.065
∴ The tax = 0.065 x 120 = 7.8 dollars
→ Add the tax to the cost to find the total cost
∵ The tota
What is the unit rate in price per ounce for choice A? Round your answer to the nearest hundredth.
Choice A: 25 ounces of potato chips for $3.49
Choice B: 45 ounces of potato chips for $4.79
a
$7.16 per ounce
b
$0.14 per ounce
c
$9.39 per ounce
d
$0.11 per ounce {jackpot points} {if you dont know DON'T ANSWER}
The unit rate in price per ounce for choice A is $0.1396, using arithmetic operation.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
The given question, 25 ounces of potato chips cost $3.49
So for 1 ounce the price will be 3.49/25 = $0.1396
Hence, the unit rate in price per ounce for choice A is $0.1396
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An architect makes a model of a new house. The model shows a tile patio in the backyard. In the model, each tile has length 2/3 in. and width 1/2. The actual tiles have length 1/2 ft and width 3/8 ft. What is the ratio of the length of a tile in the model to the length of an actual tile? What is the ratio of the area of a tile in the model to the area of an actual tile? Use pencil and paper. Describe two ways to find each ratio. The ratio of the length of a tile in the model to the length of an actual tile is?
The ratio of the length of an actual tile is 4/3, and the ratio of area is 16/9.
What is ratio?
A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.
Given,
the length of tile is 2/3 and width = 1/2
The length of actual tile is 1/2 and width = 3/8
Therefore, the ratio of the actual length of tile = 2/3 ÷ 1/2
=2/3×2/1
=4/3
The area of the tile in the model to the area of tile in actual tile = 2/3×1/2÷(1/2×3/8)
=1/3÷3/16
=1/3×16/3
=16/9
And another method is property of dilation,
The ratio of the areas = (4/3)^2
=16/9
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Find the equation of a straight line passing through the points (1, 1) and (2, -1)
The equation of a line with slope a and y-intercept b can be expressed in the for y = ax + b.
For a line passing through the points (1,1) and (2,-1), its slope is given by:
[tex]a=\frac{(-1)-1}{2-1}=-2[/tex]To find the intercept, we can just replace x and y by one of the given pairs of coordinates:
[tex]\begin{gathered} y=-2x+b \\ 1=(-2)\cdot1+b \\ b=1+2 \\ b=3 \end{gathered}[/tex]Therefore, the equation of the line is y = -2x + 3
2.5x+6 find value of x
Answer:
I only got 8.5 but I could be wrong
Step-by-step explanation:
A heptagon has angles measure of 105°, 141°, 132°, 109°, 143° and 131°. What is the measure of the seventh angle?
HELP plsss i dont know how to do this problem
b) -2
Step-by-step explanation:Hey! Let's help you with out with this question!
Alright! So! We're trying to figure out the slope of the table. And how do we do that? Well, there is actually a formula that can help us here! And that is using the slope between two points.
What is the formula for the slope between two points?The formula is as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
It allows us to figure out the slope by taking two coordinate points and sub them into the formula to find m, which in this case is the slope!
Let's use this equation twice, we do this to make sure that the slope is consistent throughout the table.
Using the formula for the first two points:The first two points are:
(3, 36)(6, 30)Now, we apply the formula as such:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{30-36}{6-3}[/tex]
[tex]m=\frac{-6}{3}[/tex]
[tex]m=-2[/tex]
Alright, so we have a slope [tex]m=-2[/tex] for the first two points! Let's check if the last two points have the exact same slope as well!
Using the formula for the last two points:The last two points are:
(9, 24)(12, 18)We apply the formula again!
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{18-24}{12-9}[/tex]
[tex]m=\frac{-6}{3}[/tex]
[tex]m=-2[/tex]
Conclusion:Well, what do you know? Given our application of the slope between two points, we get a common answer [tex]m=-2[/tex]. So, therefore, it would be b) [tex]m=-2[/tex]
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11 1/2
+ 3 5/8
Write your answer as a mixed number with the fractional part in lowest terms
Answer:
Step-by-step explanation:
11 [tex]\frac{1}{2}[/tex] + [tex]\frac{5}{8}[/tex]
make all the fractions an improper fraction
(11×2)+1/2 = 23/2
(3x5)+5/8 = 29/8
you need to make sure both fractions have a common denominator
to make 23/2 common with 5/8 you multiply 23/2 by 4/4
wich will make 92/8
continiue with the question
92/8 + 29/8= 121/8
simplify by dividing by 8 to get a mixed number
15 1/8
four students write algebraic math expressions and equations on their whiteboard. Which of the following students wrote expressions?
The students who write expressions when the students write algebraic math expressions and equations on their whiteboard is student 1 and 4.
What is an expression?In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions. An expression or mathematical expression in mathematics is a finite combination of symbols that is well-formed according to context-dependent rules.
An algebraic expression is one that is composed of integer constants, variables, and algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). 3x² 2xy + c, for example, is an algebraic expression.
In this case, student 1 wrote 1/2x + 6 and student 4 wrote 5 - x. It should be noted these are algebraic expressions as they don't have equal signs.
The diagram is attached.
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The curve above is the graph of a sinusoidal function. It goes through the points (- 4, 0) and (2, 0) Find a sinusoidal function that matches the given graph If needed, you can enter pi = 3.1416 as in your answer, otherwise use at least 3 decimal digits
A sinusoidal function that matches the given graph is y=cosπx/3+2.
From the given question, the curve is the graph of a sinusoidal function.
It goes through the points (- 4, 0) and (2, 0).
We have to find the sinusoidal function that matches the given graph.
For this problem, we can use either of these general equations :
y = Asin(Bx + C) + D or y = Acos(Bx + C) + D.
A = amplitude = distance on Y-axis from centre of graph to highest or lowest point.
So from the given graph
A = 1
T = period = distance on X-axis over one complete cycle
So from the given graph
T = 6.
So B=2π/6 =π/3
D = distance that graph has been moved up or down on the Y-axis
D = 0
C= horizontal shift (left side if positive)
From the given Graph
C = 2
So, equtaion is
y = Acos(Bx + C) + D
Putting the each variable value
Using π =3.1416.
y = 1*cos(π/3 x + 2) + 0
y = cosπx/3 + 2
Hence, a sinusoidal function that matches the given graph is y=cosπx/3+2.
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Describe how the graph of g (x) is related to the graph of the parent function
g(x) = -x-2
vertical translation:
horizontal translation
dilation:
reflection:
The graph of the function is reflected across the y-axis and vertically translation by 2 units downwards.
The parent function of the graph is f(x) = x
Now the first is the reflection along the y-axis.
Hence the graph of the function h(x) becomes h(x) = -x
Now there is a translation by 2 units downwards. or a vertical translation of 2 units downwards.
Hence the graph of f becomes g(x) = -x -2
In mathematics, a shape can be translated by moving up, down, left, or right. Since they seem to have the same proportions as the original shapes, the translated shapes are consistent with one another. Just a few more adjustments have been made to the instructions.
As we just saw, before translations are carried out, a shape is referred to as a "preimage," and when translations are complete, a shape is referred to as an "image."
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evaluate the expression (7-4)/(8÷2)
Start simplifying both numerator and denominator,
[tex]\begin{gathered} 7-4=3 \\ 8\div2=4 \end{gathered}[/tex]rewrite the expression
[tex]\frac{(7-4)}{8\div2}=\frac{3}{4}[/tex]An item is regularly priced at $29. Jane bought it at a discount of 55% off the regular price.  how much did Jane pay?
Answer:
Jane payed $15.95 for the item.
Step-by-step explanation:
55% as a decimal is 0.55
You can multiply 0.55, or get 55%, of 29.
0.55x29 = 15.95
Now you have your answer!
As inflation increases, the value of the dollar decreases at the same rate. The value of the dollar after t months of inflation can be found by raising the difference of 1 and the rate of inflation, r, to the power of t. If the current rate of inflation is 10%, what will the value of the dollar, d, be after 7 months? Round to the nearest cent.
Answer: 1.428571428571429
Step-by-step explanation:
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Find the area of the triangle whose vertices are (−6,3), (5,3) and (8,7).
Answer:
Area of the triangle is 22 units²------------------------------
GivenTriangle with vertices (−6,3), (5,3) and (8,7)Two of the vertices are on horizontal line with same y-coordinate of 3.
These two vertices form the base of the triangle which is:
b = 5 - (-6) = 11 units longThe height is the difference of the y-coordinates of the third vertex with the first two:
h = 7 - 3 = 4Find the areaA = bh/2A = 11*4/2 = 22 units²If a box holds 540 balls, and each layer holds 18 balls. How many layers does the box have?
Does it have 30 layers because 540 divided
by 18=30
Answer:
You are absolutely correct!
Step-by-step explanation:
To find the area of a cube, we do length (l), times width (w), times height (h).
Let's say that the length is 6, while the width is 3. That would make the first layer 18, like in your problem.
18 × 10 = 180
18 × 20 = 360
18 × 30 = 540
So, yes! You are correct!
As each layer can hold 18 balls 540 balls can be placed in 30 layers.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, A box holds 540 balls, and each layer holds 18 balls.
∴ To determine no. of layers we have to divide the total no. of balls by no. of balls in one layers,
= (540/18) layers.
= 30 layers.
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