The correct answer is (5x + 1) / (x+7).
What error did the student make?
The student made an error in adding the rational expressions. They attempted to add the numerators directly without finding a common denominator.
To add rational expressions, we must first find a common denominator, which is the Least Common Multiple (LCM) of the two denominators. Then, we can add the numerators.
Here is the correct solution:
Problem:
(5x) / (x+7) + 1 / (x+7)
First, note that both rational expressions have the same denominator (x+7). In this case, the LCM is simply (x+7). We can now add the numerators:
Work:
(5x) / (x+7) + 1 / (x+7) = (5x + 1) / (x+7)
Solution:
(5x + 1) / (x+7)
The correct answer is (5x + 1) / (x+7).
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If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, where will B' be?
Reflection over the y-axis, rotation 90° clockwise, and translation (x + 2, y - 1)
The coordinates of B' after the sequence of transformations are given as follows:
B'(3,-4).
How to obtain the coordinates of B'?The coordinates of B are given as follows:
B(-3,1).
After a reflection over the y-axis, the x-coordinate of B is exchanged, hence:
B'(3, 1).
The rule for a 90º clockwise rotation is that (x,y) becomes (y,-x), hence the coordinates of B' after the 90º clockwise rotation are given as follows:
B'(1, -3).
The translation (x + 2, y - 1) means that 2 is added to the x-coordinate while 1 is subtracted from the y-coordinate, hence the final coordinates of B' are given as follows:
B'(3,-4).
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If triangle ABC has points A(2, -4), B(-3, 1), and C(-2, -6) and you perform the following transformations, B' would be at B' (3, -4).
What is a rotation?In Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).
By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:
Coordinate B = (-3, 1) → Coordinate B' = (-(-3), 1) = (-3, 1).
Next, we would apply a rotation of 90° clockwise as follows;
(x, y) → (y, -x)
Coordinate B' = (-3, 1) → Coordinate B' = (1, (-3)) = (1, 3)
Finally, we would apply a translation (x + 2, y - 1) as follows:
Coordinate B' = (1, 3) → (1 + 2, 3 - 1) = B' (3, 2).
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John can mow a lawn in 90 minutes. Bullwinkle can mow the same lawn in 60 minutes. How long does it take for both John and Bullwinkle to mow the lawn if they are working together? Express your answer as a reduced fraction.
Answer:
32
Step-by-step explanation:
Find the surface area obtained by rotating the curve [tex]y=4e^2^x[/tex] on the interval x=0 to x=2 about the x-axis
Which of the following sets of numbers could not represent the three sides of
a triangle?
{14, 24, 37}
{15, 30, 43}
{9, 21, 32}
{10, 19, 26}
The triangle that would not represent the three sides of a triangles is: {9, 21, 32}
How do determine this triangleWe can determine this through the use of the triangle rule. The rule tells us that the sum of the two sides of the triangle have to be greater than that of the other side.
With this in mind, we have that for each of this
14 + 24 > 37
15 + 30 > 43
9 + 21 < 32
10 + 19 > 26
Hence the third option does not fulfill the rule
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SEE ATTACHED IMAGE
1) 12x^3+8x
2) 18a^2+2a
3) 25b^4+30b^3
1. Factor each term and mark the common factors.
2. Multiply the common factors to find the GCF.
3. Rewrite each term as the product of the GCF and other factors.
4. Rewrite the expression using the factors from the previous step.
5. Use the distributive property: ab ac + = a b( ) +c .
Step-by-step explanation:
remember the GCF (greatest common factor) ?
every number or term is the product of certain prime numbers (prime factors).
the product of factors that the discussed numbers or terms have in common is the GCF.
1)
12x³ + 8x
12x³ :
12 / 2 = 6
6 / 2 = 3
3 / 2 no
3 / 3 = 1 finished
12 = 2×2×3
x³ = x×x×x
so,
12x³ = 2×2×3×x×x×x
8x :
8 / 2 = 4
4 / 2 = 2
2 / 2 = 1 finished
8 = 2×2×2
x = x
so,
8x = 2×2×2×x
what factors do they have in common ?
2×2×x = 4x
so, the GCF = 4x
that means
12x³ + 8x = 4x×3x² + 4x×2 = 4x(3x² + 2)
2)
18a² + 2a
18a² :
18 / 2 = 9
9 / 2 no
9 / 3 = 3
3 / 3 = 1 finished
18a² = 2×3×3×a×a
2a :
2 / 2 = 1 finished
2a = 2×a
so, they have 2×a = 2a in common.
the GCF = 2a.
that means
18a² + 2a = 2a×9a + 2a×1 = 2a(9a + 1)
3)
25b⁴ + 30b³
25b⁴ :
25 / 2 no
25 / 3 no
25 / 5 = 5
5 / 5 = 1 finished
25b⁴ = 5×5×b×b×b×b
30b³ :
30 / 2 = 15
15 / 2 no
15 / 3 = 5
5 / 3 no
5 / 5 = 1 finished
30b³ = 2×3×5×b×b×b
so, they have 5×b×b×b = 5b³ in common.
the GCF = 5b³
that means
25b⁴ + 30b³ = 5b³×5b + 5b³×6 = 5b³(5b + 6)
I’m so confused please help me
We can claim that after answering the above question, the As a result, angles the regular polygon has ten sides.
what are angles?An angle is a shape in Euclidean geometry that is made up of two rays, known as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays may combine to generate an angle in the plane in which they are located. An angle is formed when two planes collide. They are known as dihedral angles. In plane geometry, an angle is a potential configuration of two rays or lines that share a termination. The English term "angle" derives from the Latin word "angulus," which means "horn." The vertex is the point at where the two rays, also known as the angle's sides, converge.
The interior angle of a regular polygon with n sides is calculated as follows:
(n-2) * 180° / n = interior angle
The internal angle of the polygon is presented to us as 144°. When we plug this into the formula, we get:
144° = (n - 2) * 180° / n
144° * n = (n - 2) * 180°
144° * n = 180° * n - 360°
144° * n + 360° = 180° * n
360° = 36° * n
n = 10
As a result, the regular polygon has ten sides.
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Evaluate the following expressions.
Accοrding the given expressiοns this is the right answer (1/2)⁵ = 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/32
(1/5)³= 1/5 × 1/5 × 1/5 = 1/125
What is an expressiοn?In mathematics, an expressiοn is a cοmbinatiοn οf numbers, variables, and οperatοrs that represents a mathematical relatiοnship οr fοrmula. It can include numbers, variables, and mathematical οperatοrs such as additiοn, subtractiοn, multiplicatiοn, divisiοn, expοnents, and rοοts. Fοr example, 2x + 3y is an expressiοn that includes the variables x and y, and the οperatοrs additiοn and multiplicatiοn. Expressiοns can be simplified, evaluated, οr used tο represent mathematical relatiοnships.
a) (1/2)⁵ = 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/32
b) (1/5)³ = 1/5 × 1/5 × 1/5 = 1/125
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please help! the question is in the picture ! PLEEAASSEE
If the circle is dilated by a factor of 2, the equation of the circle is: C. (x + 3)² + (y - 2)² = 18.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.By critically observing the graph of this circle, we have the following parameters:
Radius, r = 3 units.Center, (h, k) = (-3, 2).By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - (-3))² + (y - 2)² = 3²
(x + 3)² + (y - 2)² = 9.
By dilating with a scale factor of 2, we have:
(x + 3)² + (y - 2)² = (9 × 2)
(x + 3)² + (y - 2)² = 18
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You deposit $1000 each year into an account earning 8% compounded annually.How much will you have in the account in 10 years?
Answer:
If you deposit $1000 each year into an account earning 8% compounded annually, you will have $13,366.37 in the account in 10 years. Using the compound interest formula A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years, we can calculate the amount. Plugging in the values, we get A = 1000(1 + 0.08/1)^(1*10) = $2,159.15. Therefore, the total amount after 10 years will be $13,366.37, which is the sum of the principal and the interest earned.
Given,
Annual deposit = $1000
Rate = 8% compounded annually
Time(n) = 10 year
Amount = ?
As we know the formula ,
Amount = P(1+r/100)ⁿ
Amount = 1000(1+8/100)¹⁰
Amount = 1000(1+0.08)¹⁰
Amount =1000(1.08)¹⁰
Amount = 1000 × 2.15892
Amount = $2158.92
Hence, amount in 10year will be $2158.92
maria scored points 92 in 4 games how many points will it be in 17 games
Answer:
The answer to this question is 391 points will be scored in 17 games. to find this answer you divide 94 by 4 to find the total points per single game, then multiply that by 17. in this case is is 92 divided by 4 = 23 then 23 X 17 = 391
Cuántos meses son 44 semanas
Answer:
Step-by-step explanation:
Para convertir 44 semanas a meses, debemos saber cuántas semanas hay en un mes. El número de semanas en un mes no es exacto, pero generalmente se considera que hay alrededor de 4.33 semanas en un mes (ya que el año tiene aproximadamente 52 semanas y 12 meses).
Entonces, para calcular cuántos meses hay en 44 semanas, podemos dividir 44 por 4.33:
44 semanas / 4.33 semanas por mes = 10.16 meses (aproximadamente)
Por lo tanto, 44 semanas equivalen aproximadamente a 10.16 meses.
In this unit, you learn about linear functions and graphing lines in the coordinate plane. Linear functions are used in businesses, construction, and planning cities. The slope of a line determines its steepness. Why do you think a horizontal line (flat) has zero slopes, but a vertical line (straight up and down) is considered to have no slope. What's the difference between zero slope and no slope?
Answer:
Step-by-step explanation:
In math, slope is used to describe the steepness and direction of lines. ... You can determine the slope of a line from its graph
what are the different types of graphs; i know there’s constant speed, things like that. looking for a quick answer!!
A graph is made up of vertices, or points, and edges, or lines connecting those vertices.
Explain about the graphs and its types?Graphs come in a wide variety of forms in discrete mathematics.
These are a few of them:
A graph with no edges connecting all of its vertices is referred to as a null graph, sometimes known as an empty graph.A graph that has assigned weights, essentially numerical values, to each of its edges is referred to as a weighted graph.A disconnected graph is one in which not every vertex is always connected by the path of the edges.Simple graph: Any undirected graph where there is just one edge, or an edge from one vertex to itself, among each pair of vertices and there are no loops.Know more about the graph
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The correct question is-
what are the different types of graph.
ABCD Is a rectangle that represents a park.
The lines show all the paths in the park.
The circular path is in the centre of the rectangle and has a diameter of 15m.
Calculate the shortest distance from A to C across the park,using only the lines shown.
The circumference's shortest distance between points A and C is 102.91m.
What is a rectangle?A rectangle is a quadrilateral with four right angles in the Euclidean plane.
It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal.
A square is a rectangle with four equally long sides.
As a result, a square is a particular form of rectangle since it has rectangles with equal-length sides.
So, we know that:
AC = 80 m
CD = 50 m
Apply the Pythagorean theorem to the right triangle using ADC.
AC = √AD² + CD²
AC = √80² + 50²
AC = 94.34m
The shortest path through the park from point A to point C must only follow the lines depicted in the diagram.
Hence, we must deduct AC by 15 meters in diameter.
94.34m - 15m = 79.34m
The shortest distance is 79.34 miles plus one-half a circle's circumference.
As the circle's diameter is 15 meters, the radius is 15/2 = 7.5m.
The circumference would be:
2*π*r = 47.14m
The half circumference would be:
47.14/2 = 23.57m
Then,
79.34m + 23.57m = 102.91m
Therefore, the circumference's shortest distance between points A and C is 102.91m.
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Help please! For 2 and 3
1. Answer (a) Positive. The leading coefficient of the polynomial on the right is positive.
Answer (b) 3, the highest power of the variable is 3, so the minimum degree of the polynomial is 3.
2. Answer (a) 2, Answer (b) 1
3. Answer (a) 3, Answer (b) 1 and 5
What is polynomial?A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Polynomials can have constants and variables, and they usually have multiple terms that are separated by addition or subtraction.
1. The leading coefficient of a polynomial is the coefficient of the highest degree term. In the graph, the highest degree term is x3, and it is positive. Therefore, the leading coefficient of the polynomial on the right is positive.
The degree of a polynomial is the highest power of the variable in the equation. In the graph, the highest power of the variable is 3, so the minimum degree of the polynomial is 3.
2. The number of real zeros of a polynomial is the number of times the polynomial crosses the x-axis. In the graph, the polynomial crosses the x-axis twice, so it has 2 real zeros.
The number of imaginary zeros of a polynomial is the number of times the polynomial bounces off the x-axis. In the graph, the polynomial bounces off the x-axis once, so it has 1 imaginary zero.
3. The polynomial p(x) bounces off the x-axis at x=3 because the polynomial changes direction at this point.
The polynomial p(x) crosses the x-axis at x=1 and x=5 because the polynomial intersects the x-axis at these points.
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You move up 7 units and down 4 units. You end at (-2, -2). Where did you start?
Answer:-2,-5
Step-by-step explanation:
7-4=3
You move 3 units up
You land on -2, -2
the higher units you move up, the higher the number gets to.
Which ones would equal to less than 300 square centimeters
The circles having an area less than 300 square centimeters are;
Option A: A circle with a radius of 9. 5 centimeters
Option D: A circle with a diameter of 15 centimeters
How to determine the circlesIt is important to note the formula for calculating the area of a circle is expressed as;
A = πr²
Such that the parameters are;
A is the area of the circle.π takes the constant value of 3.14 or 22/7r is the radius of the circleFrom the information given, we have that;
radius = 9.5 centimeters
Substitute the value
Area = 3.14 × (9. 5)²
Area = 283. 4 cm²
For diameter of 15 centimeters
Radius = 7.5 centimeters
Substitute the values
Area = 3.14 × (7.5)²
Area = 176. 6 cm²
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A local doctor wants to test the effects of a new diet she decided to lower triglycerides on 10 randomly selected patients. The triglyceride level of each patient is checked twice, once before they start the diet, and again at three weeks after that time. The results are in the table below, (the photo). All data is in milligrams per deciliter (mg/dL).
The Null and alternative hypothesis for the study are (in the photo)
! Thank you , 100 points!!
A) test statistic T equals -1.952; P value, 0.0414. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
B) test statistic, T equals 0.3619. P value, 0.6392. There is insufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
C) test statistic, T = -1.952; p value, 0.0509. There is sufficient evidence to reject the no hypothesis of no difference between a triglyceride test levels.
D) test statistic T equals 0.3651. P value, 0.6425. There is insufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
The correct answer is A) test statistic T equals -1.952; P value, 0.0414.
How would you define hypothesis?An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true. In the scientific process, the hypothesis is developed before any pertinent research—aside from a basic background review—has been conducted.
The null hypothesis that there is no difference between the triglyceride test levels is sufficiently refuted by the available data.
With 9 degrees of freedom and a significance threshold of 0.05, this can be ascertained by comparing the derived test statistic (T) with the critical value of t from the t-distribution table. We reject the null hypothesis if the estimated T value is in the rejection zone (i.e., T value is smaller than the critical value of t).
The computed T value in this instance is -1.952, which is in the rejection region (i.e., less than the critical value of t of -1.833). Hence, we get to the conclusion that there is enough data to imply that the new diet has an effect on lowering triglyceride levels and reject the null hypothesis that there is no difference between the triglyceride test levels.
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Farrah borrowed $155 from her brother. She has already paid back $15. She plans to pay back $35 each month until the debt is paid off. Which describes the number of months it will take to pay off the debt? Select three options. x + 15 + 35 = 155 35 x + 15 = 155 35 x = 155 minus 15 It will take 8 months to pay off the debt. It will take 4 months to pay off the debt.
Answer: 3. 35x + 15 = 155
Step-by-step explanation:
35 x 4 = 140
140 + 15 = 155
Rose has made this scale drawing of her house. If her house actually 56 feet wide, then scale of her drawing is
If her hοuse actually 56 feet wide, then scale οf her drawing is scale = 56 feet / (drawing width)
What is the slοpe?The slοpe is a mathematical cοncept that refers tο the steepness οf a line. It is cοmmοnly denοted by the letter "m" and can be calculated using the fοrmula:
slοpe (m) = (change in y) / (change in x)
Withοut having the actual measurements οf the drawing, we cannοt determine the scale.
Tο find the scale οf a drawing, yοu need tο knοw the actual measurements οf the οbject being drawn as well as the cοrrespοnding measurements in the drawing. Fοr example, if yοu knοw that the actual width οf Rοse's hοuse is 56 feet and the width οf the hοuse in the drawing is 8 inches, yοu can determine the scale by using the fοllοwing fοrmula:
scale = actual width/drawing width
Using this fοrmula with the given infοrmatiοn, we get:
scale = 56 feet / (drawing width)
Therefοre, we dο nοt have the drawing width, we cannοt calculate the scale.
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what is a number halfway between 8.34 and 8.35
Answer:
8.345
Step-by-step explanation:
(8.34+8.35)/2 = 16.69/2
= 8.345
The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A and B, which are 48 miles apart. When the satellite is on one side of the two stations, the angle of elevation at A Is 87° and the angle of elevation at B Is 84°.
How far is the satellite from station A?
How High is the satellite above the ground?
Round all answers to 3 decimal places.
The distance of the satellite from station A is approximately 47 miles
The satellite is approximately 911 miles above ground
How to find the distanceLet the distance from station A to the satellite be a and the distance from the station B to the satellite be a + 48
Using trigonometry
tan 87 degrees = height of the satellite above the ground, h / a
tan 87 degrees = h / a
h = a * tan 87
while
tan 84 degrees = h / a + 48
h = (a + 48) tan 84
substituting for h
a * tan 87 = (a + 48) tan 84
a (tan 87 - tan 84) = 48 tan 84
a (9.567) = 48 tan 84
a = 48 tan 84 / 9.567
a = 47.436
The distance of the satellite from station A is approximately 47 miles
The height above ground
h = a * tan 87
h = 47.436 * tan 87
h = 910.857 miles
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2. Solve based on the diagram below.
What is the value of angle x? How do you know (what type of angle pairs are they)?
Answer: 160
Step-by-step explanation: The straight line or line X is 180 degrees. So subtracted 20. This is because X is intersected by another line which makes the upper notch 20 degrees.
A container contains 145.2 ounces of lemonade. If the lemonade is poured equally into 15 cups, how many ounces will be poured into each cup?
A. 8.78
B. 9.12
C. 9.64
D. 9.68
Show answer.
Answer: D. 9.68
Step-by-step explanation:
145.2 oz/ 15 cups = 9.68 oz per cup
Christy is training for a race in the summer. Every day she jogs the same number of miles. She also rides her bicycle 7.5 miles each day. During a 5-day training period, she jogs and rides a total of 53 miles. How many miles does Christy jog each day during training? Explain how you solved the problem.
5 miles each day so 5×7=35 miles a week
Steps for solving t|u prove mt=mu
We may conclude after answering the presented question that As a equation result, we have demonstrated that mt = mu when t | u.
How to solve the problem?Make a note of the definition of t | u. It denotes the existence of an integer k such that u = tk.
To get mt = m, substitute u = tk into mt = mu (tk).
Rewrite m(tk) as (mt)k using the associative property of multiplication.
To get mt = (mt)k, substitute (mt)k for m(tk) in the equation mt = mu.
Multiply both sides by mt. If mt is greater than zero, we obtain 1 = k. If mt is zero, we must also have mu = 0, hence the equation holds.
Since 1 Equals k, we get u = tk = t(1) = t.
We get mt = mt by substituting u = t into the original equation mt = mu.
As a result, we have demonstrated that mt = mu when t | u.
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1 is subtracted from the square of a number.
Represent the following sentence as an algebraic expression. Where “ a number” is the letter X. You don’t need to simplify. Please help.
The sentence represented as an algebraic expression is x² - 1
What are algebraic expression?Algebraic expressions can be defined as a mathematical expression that consists of terms, variables, constants, coefficients and fractions.
Also, these algebraic expressions are identified with arithmetic or mathematical operations. These operations are;
AdditionMultiplicationSubtractionBracketParenthesesDivisionFrom the information given, we have that;
Let the number be x
If 1 is then subtracted from the square of a number.
Fiirst, the square of the number is x²
This is represented as;
x² - 1
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find the area of this shape (4.5 ft 3 ft 3ft)
Answer:assuming its a rectangle its 13.5
Step-by-step explanation: L x H = Area
On bonfire night at sleepaway camp, Lily's counselor puts marshmallows, graham crackers, and several chocolate bars on the snack table. Lily uses
3/4
of a chocolate bar to make herself a s'more. Now 3 1/4
chocolate bars remain on the table.
Which equation can you use to find the number of chocolate bars b the counselor puts on the table?
3/4b = 3 1/4
b - 3/4 = 3 1/4
b + 3 1/4 = 3/4
b + 3/4 = 3 1/4
Answer:
The correct equation is:
b - 3/4 = 3 1/4
Explanation:
Lily used 3/4 of a chocolate bar, so the remaining chocolate bars can be found by subtracting 3/4 from the total number of chocolate bars b:
b - 3/4 = remaining chocolate bars
The problem tells us that there are 3 1/4 remaining chocolate bars, so we can substitute this value in the equation and solve for b:
b - 3/4 = 3 1/4
b = 3 1/4 + 3/4
b = 4
Therefore, the counselor put 4 chocolate bars on the table.
Find the equation of the line.
Use exact numbers.