Answer:
x = -1
y = 3
Step-by-step explanation:
2x + y = 1
3x - y = -6
Let's find x first by adding both equations
5x = -5
x = -1
Now put -1 in the spot of the variable x
2(-1) + y = 1
-2 + y = 1
y = 3
Corey i making a wall-mounted bookhelf. It ha 2 helve, with a third piece of wood interecting them. To upport the helve, Corey order ome L-bracket to put between the helve and the cropiece. He meaure angle 6. How many bracket hould he order to have one for every angle that i congruent to angle 6? Explain. Two parallel line interected by a tranveral. The angle formed along the top line, tarting at the top left and moving clockwie, are 1, 2, 4, and 3. The correponding angle formed along the bottom line, tarting at the top left and moving clockwie, are 5, 6, 8, and 7. A. 2; ∠7 i congruent to ∠6. B. 2; ∠3 i congruent to ∠6. C. 3; ∠7, ∠3 are both congruent to ∠6. D. 4; ∠7, ∠2, ∠3 are all congruent to ∠6
Corey would be needing six L-brackets to have one for every angle that is congruent to angle 6 in order to meet the requirement .
As we know that in order to support the shelves, Corey needs to buy six L-brackets. This is to be done in such a way that the two shelves, combined with the connecting piece, will form a shape with six congruent angles.
This is so because the connecting piece, the two shelves, and the form they make have six congruent angles. Corey will therefore require six brackets to hold up all the angles.
Corey will require one bracket for each angle in order to support it. To make sure he orders the proper size bracket for each angle, the length of the angle should be measured correctly.
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Which function is increasing on the interval (-∞, ∞)?
O A. g(x) = -4(2^x)
O B. f(x) = -3x + 7
O c. h(x) = 2^x - 1
O D. j(x) = x² + 8x + 1
Which function is growing on the (-, ) interval? O A. g(x) = "-4(2^x)" O B. f(x)= "-3x"+7 O C. h(x)= 2x—1 O D. j(x)= x2 + 8x+1
Try searching for Which function is rising on the range (-, ) instead. O A. g(x) = -4(2^x) O B. f(x) = -3x + 7, O c. h(x) = 2x - 1, and O D. j(x) = x2 + 8x + 1.
Which function is increasing on the interval (- ∞ ∞?
Image result for Which function is increasing on the interval (-∞, ∞)? O A. g(x) = -4(2^x) O B. f(x) = -3x + 7 O c. h(x) = 2^x - 1 O D. j(x) = x² + 8x + 1
Since, x and y are arbitrary values, therefore, f (x) < f (y) whenever x < y. Therefore, the interval (-∞, ∞) is a strictly increasing interval for f(x) = 3x + 5
The interval is increasing if the value of the function f(x) increases with an increase in the value of x and it is decreasing if f(x) decreases with a decrease in x.
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Type the correct answer in the box.
Find the length of SU in the isosceles trapezoid.
SW = 1.7
VW = 3
SV = 1.5
TU= 1.5
SU=
W
T
U
The value of SU is 4.7 units
What is an isosceles trapezoid?An isosceles trapezoid can be defined as a trapezoid in which non-parallel sides and base angles are of the same measure.
Given is an isosceles trapezoid,
In an isosceles trapezoid, the triangles Δ SWV and Δ TWU must be congruent. Then, the corresponding sides are congruent too:
TW ≅ SW
UW ≅ VW
From the given information,
UW = 3
SU = SW+UW
Finally, using the values of SW and UW:
SU = 1.7+3 = 4.7
Hence, the value of SU is 4.7 units.
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Answer:
4.7
Step-by-step explanation:
each time you put a dollar in a vending machine you get a snack. your response (putting money in the machine) is reinforced according to which of the following schedules? a. fixed ratio b. variable interval c. fixed interval d. variable ratio
A fixed ratio schedule is a type of reinforcement schedule in which a response is reinforced after a specific number of responses. In this case, the response of putting money in the machine is reinforced after every 1 response.
If each time you put a dollar in a vending machine you get a snack, then your response is reinforced according to a fixed ratio schedule.
Variable interval, fixed interval, and variable ratio schedules are all different types of reinforcement schedules that are based on different criteria. A variable interval schedule is a type of reinforcement schedule in which a response is reinforced after a random interval of time. A fixed interval schedule is a type of reinforcement schedule in which a response is reinforced after a fixed interval of time. A variable ratio schedule is a type of reinforcement schedule in which a response is reinforced after a random number of responses.
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Multiply the binomial (8p-2)(6p+2)
Answer:
48p²+4p-4
Step-by-step explanation:
(8p-2)(6p+2)
=48p²+16p-12p-4
=48p²+4p-4
to obtain a smaller margin of error choose a larger confidence level. choose a smaller confidence level.om/input?i
To obtain a smaller margin of error, choose a smaller confidence level.
Margin of error is defined as the degree of the sampling errors in statistics. It can be calculated using the formula below.
MOE = z x (SD / √n)
where MOE = margin of error
z = found by using a z-score table
SD = sample standard deviation
n = sample size
Based on the formula, to reduce the margin of error, the z-score, z, must be small. In order to have a smaller value of z, the probability, p, should also be small. And to obtain a small probability, choose a smaller confidence level.
Hence, to reduce the margin of error, use a lower confidence level.
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Andrea knows that she can regroup and rewrite the number sentence so that she won't have to multiply by 12. To do this, she needs to find the total for each kind of oatmeal separately. Let's help her. First we need to find the number of boxes of plain oatmeal
The number sentence needed to find the number of boxes of plain oatmeal is given as follows:
6 x 7 = 42.
How to obtain the number of boxes of plain oatmeal?From the image given at the end of the answer, we have that:
Andrea has 6 rows of boxes of plain oatmeal.Each row contains 7 boxes of plain oatmeal.Then the expression that gives the total number of boxes of plain oatmeal can be given by the addition of six terms seven, as follows:
7 + 7 + 7 + 7 + 7 + 7.
Consecutive additions are nothing more than multiplication expressions, hence the number sentence needed to find the number of boxes of plain oatmeal is given as follows:
6 x 7 = 42.
(this is because the product of 6 and 7 has a result of 42, that is, 7 + 7 + 7 + 7 + 7 + 7 = 42).
Missing InformationThe problem is given by the image shown at the end of the answer.
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The diameter of a penny is 19 mm. How far from your eye must it be held so that it has the same apparent size as the moon?
For a penny of diameter 19mm to be of the same apparent size as the moon it should be held at a distance of about 2.1m away from the eye.
Therefore, the answer is 2.1m.
Distance of moon from earth is 384,400km, that is 384,400,000m. Also 3,474.8km that is 3,474,800m.
For penny to have same apparent size as the moon, it should subtend equal angle as moon to the viewer. See the attached figure for reference. Thus ΔABC is similar to ΔEDB by AA criterion as ∠A is common and ∠BAC = ∠DEB as they are corresponding angles.
Let distance between penny and observer be x. Then
x/ ED = 384,400,000m/ AB
x/ 19mm = 384,400,000m/ 3,474,800m
x/ 19mm = 961000/ 8687
x = 961000/ 8687 × 19
x ≈ 2101.88mm
x = 2.1m
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In the triangles below, Angle AOI is congruent to Angle IEA. Find each missing measure.
The values of the variables and the measures of the angles, found using the congruency of ΔAOI and ΔIEA are;
w = 2 [tex]{}[/tex] ∠EAI = 45°
x = 4 [tex]{}[/tex] ∠AOI = 128°
y = 7 [tex]{}[/tex] ∠OIA = 45°
z = 20 [tex]{}[/tex] ∠IEA = 128°
What are congruent triangles?Two triangles are congruent if two angles and a non included side of one triangle are congruent to two angles and a non included side of another triangle.
The relationship between the triangles ΔAOI and ΔIEA is ΔAOI ≅ ΔIEA
Therefore; ∠IEA is congruent to ∠AOI, by Corresponding Parts of Congruent Triangles are Congruent, CPCTC
∠IEA ≅ ∠AOI
Therefore; ∠IEA = ∠AOI by the definition of congruency
(6·z + 8)° = (7·z - 12)°
7·z - 6·z = (8 + 12)° = 20°
z = 20°
∠AOI = (7·z - 12)°
Therefore;
∠AOI = (7 × 20 - 12)° = 128°
∠IEA = 128°
Similarly; AO ≅ EI by CPCTC
AO = EI definition of congruency
5·w - 6 = 2·w
5·w - 2·w = 6
3·w = 6
w = 6 ÷ 3 = 2
w = 2
∠OIA ≅ ∠EAI by CPCTC
Therefore; ∠OIA = ∠EAI definition of congruency
(7·x + 17)° = 3·(4·x - 1)° substitution property
(7·x + 17)° = 3·(4·x - 1)° = (12·x - 3)°
12·x - 7·x = 17° + 3° = 20°
5·x = 20°
x = 20° ÷ 5 = 4°
x = 4°
∠EAI = 3·(4·x - 1)°
∠OIA = (7·x + 17)°
Therefore;
∠EAI = 3·(4×4 - 1)° = 45°
∠OIA = (7×4 + 17)° = 45°
y° + (7·z - 12)° + 3·(4·x - 1)° = 180° (angle sum property of a triangle)
∠AOI = (7·z - 12)° = 128°
∠EAI = 3·(4·x - 1)° = 45°
Therefore;
y° + 128° + 45° = 180°
y° = 180° - (128° + 45°) = 7°
y° = 7°
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3. Jennie and Ada are playing a card game where they score points. After one round the ratio of Jennie's points
to Ada's points is 4 to 7. If Ada has 15 more points than Jennie, how many points does Jennie have?
Jennie has 20 points.
Explanation:
to Ada's points is 4 to 7. If Ada has 15 more points than Jennie, how many points does Jennie have?
To solve this problem, we can use proportions. We know that the ratio of Jennie's points to Ada's points is 4 to 7, so we can set up the following proportion:
4/7 = Jennie's points / Ada's points
We also know that Ada has 15 more points than Jennie, so we can add 15 to both sides of the proportion to represent this:
4/7 = Jennie's points / (Jennie's points + 15)
Next, we can cross-multiply to solve for Jennie's points:
4 * (Jennie's points + 15) = 7 * Jennie's points
4 * Jennie's points + 60 = 7 * Jennie's points
We can then subtract 4 * Jennie's points from both sides to isolate the variable:
60 = 3 * Jennie's points
Finally, we can divide both sides by 3 to find the value of Jennie's points:
Jennie's points = 60/3 = 20
Thus, Jennie has 20 points.
Is (22, 11) a solution to the following
system of equations: y 5 2x 2 5,
y 5 4x 2 3? Explain.
Answer:
Step-by-step explanation:
11 = 5 * 2 * 22 + 2 * 5
11 = 110 + 10
11 = 120
Since 11 does indeed equal 120, the first equation is satisfied. Similarly, for the second equation, we get:11 = 5 * 4 * 22 + 2 * 3
11 = 440 + 6
11 = 446
Please let me know if you have any questions.
please help me solve this algebraic expression
Answer: 0
Solution Steps:
m=25 n=5
25/5-5
What is the exact value of sin(x/2), cos(x/2) and tan(x/2) if cos(x/6)=3/5
+explaination
Step-by-step explanation:
x/2 = 3×x/6
sin(x/2) = sin(3x/6)
cos(x/2) = cos(3x/6)
tan(x/2) = tan(3x/6) = sin(3x/6)/cos(3x/6)
looking up triple angle identities for trigonometric functions we find :
cos(3x) = 4cos³(x) - 3cos(x)
so,
cos(x/2) =
cos(3x/6) = 4cos³(x/6) - 3cos(x/6) = 4(3/5)³ - 3×3/5 =
= 4×27/125 - 9/5 = 108/125 - 9×25/125 =
= 108/125 - 225/125 = -117/125 =
= -0.936
sin(3x) = 3×sin(x) - 4×sin³(x)
so,
sin(x/2) =
sin(3×x/6) = 3×sin(x/6) - 4×sin³(x/6)
also remember,
sin²(x) + cos²(x) = 1
therefore,
sin²(x/6) + cos²(x/6) = 1
sin(x/6) = sqrt(1 - cos²(x/6)) = sqrt(1 - (3/5)²) =
= sqrt(1 - 9/25) = sqrt(25/25 - 9/25) =
= sqrt(16/25) = 4/5 = 0.8
so, again
sin(x/2) =
sin(3×x/6) = 3×sin(x/6) - 4×sin³(x/6) =
= 3×4/5 - 4×(4/5)³ =
= 12/5 - 4×64/125 = 12×25/125 - 256/125 =
= 300/125 - 256/125 = 44/125 =
= 3×0.8 - 4×0.8³ = 0.352
tan(x/2) = sin(x/2)/cos(x/2) =
= 44/125 / -117/125 = -44/117 =
= 0.352 / -0.936 =
= -0.376068376...
Write an equation for the relationship between x and y. Simplify any fractions. (IXL K.5 Seventh Grade Math)
The equation of the line that represents the graph will be y = x.
What is a linear equation?
A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
From the graph, the two points are (0, 0) and (1, 1).
The line is passing through the origin that is (0, 0), then we have
0 = m (0) + c
c = 0
Then the equation is given as,
y = mx
The equation also passes through (1, 1), then we have
1 = m (1)
m = 1
Then the equation is written as,
y = x
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Select the graph of the solution. Click until the correct graph appears.
|x| + 3 > 7
Answer:
graph B
Step-by-step explanation:
if x ≥ 0
x + 3 > 7
x > 7 - 3
x >4
if x < 0
-x + 3 > 7
-x > 7-3
-x > 4
x < -4
final solution
x < -4 ∨ x > 4
Please Help!! 25 points!!!
Find the value of X
Answer: x = 0.1396263404
Step-by-step explanation:
The expression x+16 = 4x-15
(3 x (-1)) * degrees =-0.0523598776
6 x degrees) + (5 x degrees) =0.191986218
For #1
Line u passes through points (7, 2) and (10, 10). Line v passes through points (10, 8) and
(2, 11). Are line u and line v parallel or perpendicular?
Line u and line v are perpendicular lines by the relation of their slopes.
What is Slope?Slope of a line is the ratio of the difference of the y coordinates of two points to the x coordinates of those points. Slope is commonly denoted by the letter 'm'.
If a line passes through the points (x₁, y₁) and (x₂, y₂), then slope of the line,
m = (y₂ - y₁) / (x₂ - x₁)
Slopes of two lines, m₁ and m₂, are equal if they are parallel ⇒ m₁ = m₂.
Slopes of two lines, if the lines are perpendicular have the relation,
m₁ × m₂ = -1.
First let's find the slopes of the given lines.
Let m₁ be the slope of line u and m₂ be the slope of line v.
Line u passes through (7, 2) and (10, 10).
m₁ = (10 - 2) / (10 - 7) = 8/3
Line v passes through (10, 8) and (2, 11).
m₂ = (11 - 8) / (2 - 10) = 3/(-8)
Slopes are not equal, so they are not parallel.
m₁ × m₂ = [tex]\frac{8}{3}[/tex] × [tex]\frac{3}{-8}[/tex] = -1.
So the lines are perpendicular.
Hence the given lines u and v are perpendicular.
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Find the length of AC
The length of side AC of the triangle ABC using cosine rule is; 10.252 cm
How to use cosine rule?The cosine formula to find the side lengths of the triangle is given by:
b = √[a² + c² – 2ac cos B]
Where a, b and c are the sides of the triangle.
The Cosine Rule is useful in any triangle that we are trying to relate all three sides to one angle. Thus, when we want to find the length of a side, we need to know the other two sides and the opposite angle.
Considering triangle ABC, we have;
a = 8cm
c = 11 cm
B = 63°
Thus;
b = √[8² + 11² – 2(8 * 11) cos 63]
b = √(185 - 79.9)
b = 10.252 cm
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Solve for x. Round to the nearest tenth if necessary.
20
X
25
X type your answer.
The value of the side x for the given similar triangle will be 12 units.
What is a triangle?The three-sided shape known as a triangle is sometimes used to allude to it. Every triangle has three sides and three angles, some of which might be the same.
The area of a triangle is defined as (1/2) base height, and the sum of all three angles within a triangle will be 180°.
As per the given both triangle,
The one angle of both triangles is 90° and one angle is the common angle.
Since the two angles are the same thus the third angle will be the same thus by the AAA postulate both triangles will be similar.
By a similar triangle rule,
20/x = 25/(√(25² - 20²))
x = 20/25 (15)
x = 12
Hence "The value of side x will be 12 units by AAA postulate".
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3^4 + 18 ÷ 3 +2 pls what is the =
The value of the given expression, 3^4 + 18 ÷ 3 +2, is 89
Evaluating an expressionFrom the question, we are to determine the value of the given expression
The given expression is
3^4 + 18 ÷ 3 +2
First, we will write the expression properly
The given expression written properly is
3⁴ + 18 ÷ 3 +2
Using PEMDAS
P - Parentheses
E - Exponent
M - Multiplication
D - Division
A - Addition
S - Subtraction
Then,
3⁴ + 18 ÷ 3 +2
81 + 18 ÷ 3 + 2
81 + 6 + 2
= 89
Hence, the value is 89
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use implicit differentiation to find ∂z/∂x and ∂z/∂y. e7z = xyz
The implicit differentiation of [tex]\dfrac {dz}{dx}[/tex] is [tex]\dfrac {yz}{7e^{7z}-xy}[/tex] and for [tex]\dfrac {dz}{dy}[/tex] it is [tex]\dfrac {xz}{7e^{7z}-xy}[/tex].
In implicit differentiation, we differentiate every aspect of an equation with variables (commonly x and y) through treating one of the variables as a feature of the other.
It is given that,
[tex]e^{7z}=xyz[/tex]
Differentiate both sides with respect to x,
Only treat y as constant and z and x as variables.
[tex]\frac{{e^{7z}}{dx} }{\frac{dz}{dx}} =\frac{yd(xz)}{dx}[/tex]
use chain rule in left hand side
[tex]\frac {e^{7z}}{dx} \times \frac{dz}{dx} =\frac{yd(xz)}{dx}[/tex]
use product rule in RHS
[tex]7e^{7z} \times\frac{dz}{dx}=yx \times\frac{dz}{dx+z} \\\\7e^{7z} \times\frac{dz}{dx}=xy \times\frac{dz}{dx} +yz\\\\\frac{dz}{dx}=\frac{yz}{7e^{7z-xy}}[/tex]
It is given that,
[tex]e^{7z}=xyz[/tex]
Differentiate both sides with respect to y,
Only treat x as constant and z and y as variables.
[tex]\dfrac {d (e^7z)}{dy}= \dfrac {d(xyz)}{dy}[/tex]
use chain rule in left hand side
[tex]\dfrac {d (e^7z)}{dy} \times \dfrac{dy}{dx}=\dfrac {yd(xz)}{dy}[/tex]
use product rule in RHS
[tex]7 (e^{7z}) \times \dfrac{dz}{dy}=xy \dfrac{dz}{dy+z}\\\\(7e^{7z})\times \dfrac{dz}{dy}=xz\\\\\dfrac{dz}{dy}=\dfrac {xz}{7e^{7z}-xy}[/tex]
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your friend claims that it is possible to draw an quilateral triangle for which the circumecenter, incenter, centroid, and orthocenter are not all the same point. do you agree?
No, it is not possible to draw an quilateral triangle for which the circumecenter, incenter, centroid, and orthocenter are not all the same point.
Explain the term equilateral triangle?An equilateral triangle, which is frequently referred to as a "regular" triangle, is a triangle with three equal-length sides.
For the stated question-
The three out-of-the-way sections were not formed of a situation and were not sketched precisely.The Ortho Center is the point of convergence of the medians, and the in center is the point of convergence of the angle by sectors.All four of these would go to the exact same point in an equilateral triangle.Thus, the statement given by the friend is incorrect.
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Type the correct answer in the box. use numerals instead of words. enter the number of the topic sentence.Consider this expression. underroot x4-y2When r = 3 and y = -6, the value of the expression is____.
When the variables r = 3 and y = -6, the value of the expression is -27.
What is an expression?In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables, parameters, and numerical quantities (number).
Based on the information provided, the mathematical expression is given by;
Mathematical expression = √x⁴ - y²
Substituting the given parameters into the mathematical expression, we have;
Mathematical expression = √(3)⁴ - (-6)²
Mathematical expression = √81 - 36
Mathematical expression = 9 - 36
Mathematical expression = -27.
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Complete Question:
Type the correct answer in the box. use numerals instead of words. Enter the number of the topic sentence.
Consider this expression. √x⁴ - y². When r = 3 and y = -6, the value of the expression is____.
The area of a square is square units. What is the side length of one side of the square? units units units units.
The side length of the square is (b) 8n¹⁸ units
How to determine the side length of the squareSee below for the complete question
From the question, we have the following parameters that can be used in our computation:
Area = 64n36 square units
Express the exponents as superscripts
So, we have the following representation
Area = 64n³⁶ square units
Take the square roots of both sides
So, we have the following representation
√Area = √64n³⁶ square units
Evaluate the exponents
Length = √64n³⁶ units
So, we have
Length = 8n¹⁸ units
Hence, the side length is (b) 8n¹⁸ units
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Complete question
The area of a square is 64n36 square units. What is the side length of one side of the square?
8n6 units
8n18 units
64n6 units
64,18 units
Work out how many triangles can be drawn between the labelled points in the diagram below
The triangles that are congruent to (a) ΔCDE, and (b) ΔCDF include ΔBFG, ΔADG, ΔBDE, and ΔABH, ΔBHCΔ, ΔGHE respectively
How to find congruent triangles?We should know that when two or more objects in geometry have the same shape and size, or if one has the same shape and size as the mirror image of the other, they are congruent.
From the object drawn the congruent triangles to ΔCDE include the following
ΔBDF
ΔABG
ΔBDE
ΔABI
ΔACH
ΔBCJ
ΔIHJ
All the triangle has side, side, right angle
The triangles that are congruent to ΔCDF include the following
ΔABG
ΔBHC
HGE
These triangles have SIDE, SIDE, SIDE (SSS)
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Ryan invested \$4,800$4,800 in an account in the year 1990, and the value has been growing exponentially at a constant rate. The value of the account reached \$6,300$6,300 in the year 1998. Determine the value of the account, to the nearest dollar, in the year 2007.
well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8[/tex]
[tex]\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r[/tex]
now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02[/tex]
To solve 3÷1/5, Jordan thinks about giving monkeys 1/5 of a banana each and how many monkeys he could give a banana piece to if he had 3 whole bananas. What is the quotient of 3 and 1/5?
The quotient of 3 and 1/5 is 15.
How to find the quotient?A quotient is a quantity produced by the division of two numbers in arithmetic. The quotient is widely used in mathematics and is also known as the integer part of a division, a fraction, or a ratio.
The quotient is the result of performing division operations on two numbers. It is essentially the result of the division method. In arithmetic division, four main terms are used: divisor, dividend, quotient, and remainder
In this case, we want to divide 3 and 1/5. This will be:
= 3 ÷ 1/5
= 3 × 5
= 15.
The quotient is 15.
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Jen Butler has been pricing Speed-Pass train fares for a group trip to New York Three adults and four children must pay $120. Two adults and three children must pay $85. Find the price of the adult's
ticket and the price of a child's ticket.
The adult's ticket will cost $20 while the children's ticket will cost $15.
To find the cost of the ticketsFrom the question, we have that;
Three adults and four children must pay $120
Representing this in an equation
Let adults = a
Let children = c
3a + 4c = 120 -----1
Also;
Two adults and three children must pay $85.
Representing this in an equation
2a + 3c = 85 -----2
From equation 1
a = [tex]\frac{120 - 4c}{3}[/tex] ----- 3
Substituting a in equation 2
[tex]2 (\frac{120 - 4c}{3} ) + 3c = 85[/tex]
[tex]\frac{240 - 8c}{3} + 3c = 85[/tex]
Multiplying through by 3
240 - 8c + 9c = 255
c = 15
To find a when c = 15
Substitute c = 15 in equation 3
[tex]a = \frac{120 - 4(15)}{3}[/tex]
[tex]a = \frac{120 - 60}{3}[/tex]
a = 20
Therefore, the Adult's ticket is $20 and the children's ticket is $15.
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Let R be the region in the first and second quadrants bounded above by the graph of y=201+x2and below by the horizontal line y=2, how do you find the area?
37.96 sq units is the area enclosed by the graph [tex]y=\frac{20}{1+x^2}[/tex] and y=2
To calculate the area enclosed by 2 graphs we have to firstly find the intersection point of both graph
to find the intersection point we will equate given equation
=> [tex]\frac{20}{1+x^2}[/tex] = 2
=> [tex]1+x^2[/tex] = 10
=> [tex]x^2[/tex] = 9
=> x= 3,-3
so we have to find area of graph from x=-3 and x=3
so the formula for equation is given by:
[tex]\int\limits^b_a {\frac{20}{1+x^2} -2} \, dx[/tex]
where a=-3 and b=3
=>[tex]\int\limits^a_b {\frac{20}{1+x^2} } \, dx - \int\limits^a_b {2} \, dx[/tex]
[tex]\int\limits {\frac{1}{1+x^2} } \, dx = tan^-^1x[/tex] +c
=> 20 [tex]\left \{ {{x=3} \atop {x=-3}} \right.[/tex] [tex]tan^-^1x[/tex] - [tex]\left \{ {{x=3} \atop {x=-3}} \right.[/tex] 2x
=> 20 ( [tex]tan^-^1 3 - tan^-^1 (-3)[/tex] - 2*(3+3)
=>40 * 1.249 -12
=> 49.96 -12
=> 37.96
so the area enclosed by the given graphs is 37.96 sq. units
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What is the value of K if the expression (- 5x3 + 4x2 – 3x + K) is divided by (x-1), and obtains a remainder of 10?
Answer:
14
Step-by-step explanation:
To find the value of K, we need to use the remainder theorem. The remainder theorem states that if a polynomial is divided by (x - a), where a is a number, the remainder of the division will be equal to the value of the polynomial when x is equal to a. In this case, the remainder of the division is 10, so we need to find the value of the polynomial when x is equal to 1.
To find this value, we need to plug 1 into the original polynomial and evaluate it. This gives us (- 5 * 1^3 + 4 * 1^2 – 3 * 1 + K) = (- 5 + 4 – 3 + K) = (- 4 + K). Since the remainder of the division is 10, we know that (- 4 + K) = 10. This means that K = 14.
Therefore, the value of K in the original polynomial is 14.
The value of K is 14.
What is Remainder Theorem?If a polynomial function f(x) is divided by (x - c), the remainder R is given by: R = f(c)
According to the remainder theorem, if a polynomial f(x) is divided by (x - c), where c is a constant, the remainder is equal to f(c).
In this case, we know that the remainder is 10 when the expression is divided by (x - 1). So, we can substitute x = 1 into the expression and set it equal to 10 to find the value of K.
Substituting x = 1 into the expression, we get:
(-5 (1)³ + 4(1)² - 3(1) + k)= 0
-5 + 4 -3 + k = 0
k -4 = 0
k = 4
Therefore, the value of K is 14.
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