Answer:
The GCF is 2.
Step-by-step explanation:
In my opinion, one of the easier ways to find the greatest common factor of two numbers is to get the prime factors of both and multiply the common ones. The prime factorization of 8 is 2*2*2, and the prime factorization of 162 is 2*3*3 (you can make a factor tree for both of these numbers to verify this). The only common prime factor for both of these numbers is 2, which means the greatest common factor of 8 and 18 is 2.
The table below shows the x variable for a table. Choose a corresponding y table that will create a direct variation.
Answer:
table A
Step-by-step explanation:
A direct variation can be expressed as: [tex]\frac{y}{x}=k[/tex]. The y/x is equal to a constant value k. Multiply both sides by x you get: [tex]y=kx[/tex]. So as x increases by 1, y increases by some constant value. So to find which one will create a direct variation, see which of the tables has a constant y/x
Table A:
7/2 = 3.5
14/4 =3.5
17.5/5=3.5
21/6 = 3.5
this has a constant y/x so it is a direct variation
Table B:
7/2 = 3.5
14/4 = 3.5
21 / 5 = 4.2
this is not a direct variation, it doesn't have a constant y/x
table C:
7 / 2 = 3.5
14 / 4 = 3.5
15/5 = 3
This is not a direct variation, it doesn't have a constant y/x
table d:
7/2 = 3.5
14/4 =3.5
17/5=3.4
This is not a direction variation, it doesn't have a constant y/x
4(x + 4) + 6
Simplify algebraic expressions
Answer:
4x+22
Step-by-step explanation:
distribute 4(x+4)
it would become 4x+16+6
16+6 = 22
4x+22
Please help!! Which of the following graphs shows a parabola with a vertex of (1,-9) and solutions of (-2,0) and (4,0)?
The graphs show a parabola with a vertex that has Roots are -2 and 4.
We have given that,
vertex of (1,-9) and solutions of (-2,0) and (4,0).
What is the formula for the roots?
y=k*(x+2)(x-4)
Vertex = (1,-9) is a point of the parabola
-9=k*(1+2)(1-4) implies k=1
Equation of the parabola is y=(x+2)(x-4).
The graphs show a parabola with a vertex that has Roots are -2 and 4.
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(LOOK AT IMAGE)
Line CDE is a tangent to the circle below.
Work out the size of angle x and the size of angle y.
[tex]x=57^{\circ}[/tex] (alternate segment theorem)
[tex]y=67^{\circ}[/tex] (alternate segment theorem)
What is the pattern in the values as the exponents increase?
Powers of 2
Value
2 Superscript negative 5
StartFraction 1 Over 32 EndFraction
2 Superscript negative 4
StartFraction 1 Over 16 EndFraction
2 Superscript negative 3
StartFraction 1 Over 8 EndFraction
2 Superscript negative 2
One-fourth
2 Superscript negative 1
One-half
2 Superscript 0
1
add StartFraction 1 Over 16 EndFraction to the previous value
subtract StartFraction 1 Over 16 EndFraction from the previous value
divide the previous value by 2
multiply the previous value by 2
The pattern in the values as the exponents increase is multiply the previous value by 2.
What is exponents and powers?Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
Given:
Powers of 2 Values
[tex]2^{-5}[/tex] 1/32
[tex]2^{-4}[/tex] 1/16
[tex]2^{-3}[/tex] 1/8
[tex]2^{-2}[/tex] 1/4
[tex]2^{-1}[/tex] 1/2
As, from the given data we can see that negative powers of 2 reducing by 1.
as, 2^-5 * 2= 2^-4
Hence, multiply the previous value by 2 to obtain the next value.
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ASAP PLEASE (this is like five questions in one) GIVING 15 POINTS!!!
3. find x
4. find x
7. find y
6. find x
8. find y
Answer:
D
21√2/2
C
C
C
Step-by-step explanation:
For all problems, the ratios of the lengths of the sides are:
30-60-90 triangle 1 : √3 : 2
45-45-90 triangle 1 : √2 : √2
Problem 3:
30-60-90 triangle at left
Hypotenuse = 11
Short leg = 11/2
Long leg = 11/2 × √3
45-45-90 triangle at right
x = 11/2 × √3 × √2 = 11√6/2
Answer: D
Problem 4:
30-60-90 triangle at top
Hypotenuse = 7√3
Short leg = 7√3/2
Long leg = 7√3/2 × √3 = 7 × 3/2 = 21/2
45-45-90 triangle at right
x = 21/2 × √2 = 21√2/2
Answer: 21√2/2
Problem 7:
30-60-90 triangle
Long leg = 4√3
Short leg = y = 4√2/2 = 2√2
Answer: C.
Problem 6:
30-60-90 triangle at left
Hypotenuse = 12√6
Short leg = 12√6/2 = 6√6
Long leg = 6√6 × √3 = 6√2√3√3 = 18√2
45-45-90 triangle at right
x = 18√2/√2 = 18
Answer: C.
Problem 8:
45-45-90 triangle
Hypotenuse = 2
Leg = y = 2/√2 = 2√2/(√2√2) = √2
Answer: C.
What is the gradient of the graph shown?
Answer:
gradient = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
calculate the gradient m using the gradient formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 6, 0) and (x₂, y₂ ) = (0, 2) ← 2 points on the line
m = [tex]\frac{2-0}{0-(-6)}[/tex] = [tex]\frac{2}{0+6}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
Use the Law of Cosines to find the specified missing value. Approximate your answer to the nearest tenth.
C=60, a=120ft, b=66ft
Answer:
c=104.1 ft
Step-by-step explanation:
Law of Cosines
c^2 = 66^2 + 120^2 - 2 (66)(120)cos 60
c = 104.1 ft
Given quadrilateral ABCD and its image under a dilation centered at the origin, find the scale factor. (note: orange is original image)
The scale factor of the image under a dilation centered at the origin is 2.
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Translation is the movement of a point either up, down, left or right on the coordinate plane.
Let us assume that quadrilateral ABCD have vertices at A(2, 1) while its image has vertices at A'(4, 2), hence:
Scale factor = 4/2 = 2/1 = 2
The scale factor of the image under a dilation centered at the origin is 2.
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Alden is registering for classes next semester. he uses the quantitative reasoning process to decide between two teachers, dr. alvarez, and dr. bareno . he speaks to 17 friends that previously took the course from dr. alvarez and also speaks to 18 friends that took it from dr. bareno. eight of his friends said they highly recommend dr. alvarez. eleven of his friends highly recommend dr. bareno.
Based on quantitative reasoning, Alden should take the classes from Dr. Baeno in his next semester.
Quantitative Reasoning Behind Choosing Dr. Baeno
Alden talked to 17 friends that previously took course from Dr. Alvarez.
Eight out of 17 friends recommended Dr. Alvarez.
∴ The fraction of his friends in favor of Dr. Alvarez = 8/17
Also, Alden talked to 18 friends who took course from Dr. Baeno.
Eleven out of 18 friends recommended Dr. Baeno.
∴ The fraction of his friends in favor of Dr. Baeno = 11/18
Making Comparison
Now, since we know that,
11/18 > 8/17
The capacity for using knowledge and mathematics to address problems in the real world is known as quantitative reasoning.
Hence, applying quantitative reasoning, we can infer that it is more favorable for Alden to take classes from Dr. Baeno.
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Bethany wants to estimate the value of (4.296 times 10 Superscript 11) (1.8614 times 10 Superscript negative 14). Which statement about the estimate is true?
The value will be greater than 1 because 4.296 times 10 Superscript 11 is a very large number and multiplication always increases the size of a number.
The value will be greater than 1 because 4 times 2 = 8 and 8 is larger than 1.
The value will be less than 1 because (4.296 times 10 Superscript 11) (1.8614 times 10 Superscript negative 14) will be a negative number. All negative numbers are less than one.
The number will be less than 1 because when adding the exponents, 11 + (negative 14) = negative 3, and a number in scientific notation with a negative exponent is less than 1.
The statement that is true about the estimate is that the number will be less than 1 because when adding the exponents, 11 + (negative 14) = negative 3, and a number in scientific notation with a negative exponent is less than 1 (option D).
How to estimate an exponential function?According to this question, Bethany wants to estimate the value of (4.296 times 10 Superscript 11) (1.8614 times 10 Superscript negative 14).
This expression can be mathematically written as:
(4.296 × 10¹¹) (1.8614 × 10-¹⁴)
The result of this expression is 7.996 × 10-³, which is value less than 1.
Therefore, the number will be less than 1 because when adding the exponents, 11 + (negative 14) = negative 3, and a number in scientific notation with a negative exponent is less than 1.
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In the following diagrams calculate the
sides marked with letters x and y.
All dimensions are in cm.
Answer:
x=7.48 cm, y=6.94
Step-by-step explanation:
Start by finding the value of x.
Using the Pythagorean Theorem, [tex]13^{2}+x^{2} =15^{2}[/tex]
[tex]169+x^{2} =225\\x^2=56\\x=\sqrt{56}\\x=2\sqrt{14}[/tex]
Using this, we can again use the Pythagorean Theorem to find the value of y.
[tex]2.8^{2} +y^{2} =(2\sqrt{14} )^{2} \\7.84+y^{2} =56\\y^{2} =48.16\\y=\sqrt{48.16}[/tex]
(I rounded to two decimal places, not sure what is required here)
x=7.48 cm
y=6.94 cm
The endpoints of the
directed line segment AB
are A (1,7) and B(5, 15).
Find the coordinates of point
P along AB so that the ratio
of AP to PB is 3 to 1.
The coordinates of point P along AB so that the ratio of AP to PB is 3 to 1 is (4,13).
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
Given that the ratio of the two lines is 3:1, therefore, we can write,
m:n = 3:1
Also, the coordinate of the endpoints of the line are,
A = (x₁, y₁) = (1, 7)
B = (x₂, y₂) = (5, 15)
Now, Using the Section formula the coordinate of the point P can be written as,
[tex]P = (\dfrac{mx_2+nx_1}{m+n}\ , \dfrac{my_2+yx_1}{m+n})\\\\P = (\dfrac{3(5)+1(1)}{4}\ , \dfrac{3(15)+1(7)}{4})\\\\P = (4, 13)[/tex]
Hence, the coordinates of point P along AB so that the ratio of AP to PB is 3 to 1 is (4,13).
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Select
Select the correct answer from each drop-down menu.
Which system of Inequalities does the graph represent? Which test point satisfies both of the inequalities in that system?
The inequality equation of the lines are given as 4x – y ≤ 4 and 2x – 2y ≤ 3. Then the correct option is A.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The graph is given below.
From the graph, equation of the lines are given as
4x - y = 4 and 2x - 2y = 3
But for the inequality is shown in graph. Then the inequality equation of the lines are given as
4x – y ≤ 4 and 2x – 2y ≤ 3
Then the correct option is A.
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Try It #2
A city’s population has been growing linearly. In 2008, the population was 28,200. By 2012, the population was36,800. Assume this trend continues.
b. Identify the year in which the population will reach 54,000.
Answer:
The year in which population will be 54000, is 2020.
Step-by-step explanation:
In the question, it is given that the city's population is growing linearly. In 2008 , population was 28200 and in 2012 , it is 36800 .
It is required to identify the year in which population will be 54000 . equation.
Step 1 of 2
The population in 2008 was 28200 and in 2012 it was, 36800 .
The equation relating population and year is,
[tex]$$\begin{aligned}&y-28200=\left(\frac{36800-28200}{2012-2008}\right)(x-2008) \\&y-28200=\left(\frac{8600}{4}\right)(x-2008) \\&y-28200=2150(x-2008)\end{aligned}$$[/tex]
Step 2 of 2
The year in which population will be 54000 , can be determined by substituting 54000 for y,
[tex]54000-28200=2150(x-2008)$\\ $25800=2150(x-2008)$\\ $x-2008=12$\\ $x=2020$[/tex]
please answer algebra question. will mark brainliest
answers:
1. 9
2. 12
3. 18
4. 36 sq cm
Answer:
9 sq cm
Step-by-step explanation:
If you join the two triangles it will become a square of side 3cm.
3cm * 3cm = 9cm squared.
Hope you have a nice day :)
Any questions please comment.
PLEASE QUICKLY!!!
The length of a rectangular frame is represented by the expression 3x + 6, and the width of the rectangular frame is represented by the expression 3x + 4. Write an equation to solve for the width of a rectangular frame that has a total area of 120 square inches.
The width of the rectangle is 10 inches
How to determine the width?The given parameters are:
Length = 3x + 6
Width = 3x + 4
Area = 120
The area of a rectangle is
Area = Length * Width
So, we have:
(3x + 6) *(3x + 4) = 120
Expand
9x^2 + 12x + 18x + 24 = 120
Evaluate the like terms
9x^2 + 30x - 96 = 0
Using a graphing calculator, we have:
x = 2
Substitute x = 2 in Width = 3x + 4
Width = 3 * 2 + 4
Evaluate
Width = 10
Hence, the width of the rectangle is 10 inches
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Find side x, giving your answer to 1 decimal place.
7 cm
81°
X
40°
In the given diagram, the value of the side labelled x is 10.8 cm
Law of sinesFrom the question, we are to determine the value of side x
Using the law of sines
In any given triangle XYZ,
[tex]\frac{x}{sinX}=\frac{y}{sinY}=\frac{z}{sinZ}[/tex]
Thus,
In the given triangle,
[tex]\frac{x}{sin81^\circ} =\frac{7}{sin40^\circ}[/tex]
∴ [tex]x=\frac{7 \times sin81^\circ}{sin40^\circ}[/tex]
x = 10.75599
x ≈ 10.8 cm
Hence, the value of the side labelled x is 10.8 cm
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millimeters =equals 15centimeters 4millimeters
This shows that 154mm is equivalent to 15centimeters 4millimeters
Conversion of unitsUnits are measure of a quantity. From the given question, we are to convert 15cm4mm to millimeters
Since 10mm =1cm, hence;
15cm4mm = (15 * 10) + 4
15cm4mm = 150+ 4
15cm4mm = 154mm
This shows that 154mm is equivalent to1 5centimeters 4millimeters
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please help me asap thank you so so much u are so amazing!!
Answer:
7.76
Step-by-step explanation:
0.22×20=4.4
3.36(base amount ,average of the others)+4.4=7.76
What is the length of the circles radius?
Answer: D. 8 cm.
Step-by-step explanation:
[tex]l_{arc}=\frac{26}{9}\pi \ cm\ \ \ \ \Theta=65^0 \ \ \ \ \ r=?\\\boxed {l_{arc}=2\pi r*\frac{\Theta^0}{360^0} }\ \ \ \ \ \Rightarrow\\\boxed {r=\frac{{l_{arc}}*360^0}{2\pi *\Theta} }.\\r=\frac{\frac{26}{9}*\pi *360^0 }{2\pi *65^0} =\frac{13*360^0}{9*65^0} =\frac{40}{5}=8 \ (cm).[/tex]
x^(2)-5x+6=(x+h)^(2)+k solve for k
The value of k is [tex]-h^2 -2xh -5x + 6[/tex]
How to solve the expressionGiven;
x^(2)-5x+6=(x+h)^(2)+k
Expand the expression on the right side, we have
[tex]x^2 - 5x + 6 = (x+ h) (x+ h) + k[/tex]
[tex]x^2 -5x + 6 = x^2 +xh + xh + h^2 +k[/tex]
Collect like terms
[tex]x^2 -5x + 6 = x^2 + 2xh + h^2 + k[/tex]
[tex]x^2 -5x + 6 -x^2 - 2xh -h^2 = k[/tex]
We then have
[tex]-5x + 6 -2xh -h^2 = k[/tex]
[tex]k = -h^2 -2xh -5x + 6[/tex]
Thus, we have k as [tex]-h^2 -2xh -5x + 6[/tex]
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Jeanie is picking out clothing from her closet. She has 5 pairs of pants, 6 shirts, and 4 pairs of shoes to choose from. How many different ways can she arrange her outfit for the day?
Enter the total number of outcomes in the box, without units
A right triangle has side lengths AC = 7 inches, BC = 24
inches, and AB = 25 inches.
What are the measures of the angles in triangle ABC?
A) mZA= 46.2°, mZB=43.8°, mZC=90°
B) mZA= 73.0°, mZB= 17.0°, mZC = 90°
C) mZA 73.7°, mZB= 16.3°, mZC = 90°
D) mZA 74.4°, mZB= 15.6°, mZC = 90°
Therefore, the measures of the angles in triangle ABC is as follows:
m∠A 73.7°, m∠B = 16.3°, m∠C = 90°How to find angles of right triangle?The measure of the angles in the right triangle can be found as follows:
Using trigonometric ratios,
sin ∅ = opposite / hypotenuse
sin ∅ = 7 / 25
∅ = sin ⁻¹ 0.28
∅ = 16.2602047083
∅ = 16.3°
Hence,
m∠B = 16.3°
m∠C = 90°
m∠A = 180 - 90 - 16.3 = 73.7°
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PLEASE HURRY!!!!!!!
The manager of a local cable TV company wants to know which of its programs are most popular. Which population should the manager survey to best answer this question?
A. Employees of the cable company.
B. Subscribers to the cable company.
C. Adults listed in the town’s voter registration lists.
D. People who complete a survey on the company’s Web site.
Answer:
B
Step-by-step explanation:
cable subscribers
A counter in Lamar's kitchen is 1 yard wide and 2 yards long. Lamar wants to replace the counter with a granite countertop, which would cost $204.63 per square yard. How much would the granite countertop cost?
Answer:
Step-by-step explanation:
Comment
Find the number of square yards
Area = L * w
L = 2
w = 1
Area = 2 * 1
Area = 2
Now for the counter top
1 sq yard costs 204.63
2 sq yards cost 2 * 204.63
2 sq yards cost 409.26
Answer: 409.26
A simple random sample of size individuals who are currently employed is asked if they work at home at least once per week. Of the employed individuals surveyed, responded that they did work at home at least once per week. Construct a 99% confidence interval for the population proportion of employed individuals who work at home at least once per week.
The confidence interval of employes individuals from home
Construction of hypothesis:
0.10 - 0.047 < p < 0.10 + 0.047
A simple random sample size n = 250 . Of the 250 employed individuals surveyed,42 responded that they did work home a minimum of once per week.
Construct 99% confidence interval for population
For proportion : 42 / 250 = 1/10 = 0.16
Mean = 2.5 * sqrt [ 0.1 * 0.9 / 250]
= 2.5 * 0.01
= 0.47
Construction of hypothesis:
0.10 - 0.047 < p < 0.10 + 0.047
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is x + 3 a factor of f(x)=x^4+6x^3+5x^2-15x-2
x+3 is not a factor of f(x)=x^4+6x^3+5x^2-15x-2 because there is a remainder of 7 when we use the long division method to divide x+3 with the given function f(x).
What are the factors of a quadratic equation?The factors of a quadratic equation are the simplified form of the quadratic equation, that if multiplied together, results in the original quadratic equation.
Given that:
f(x)=x^4+6x^3+5x^2-15x-2[tex]\mathbf{=\dfrac{x^4+6x^3+5x^2-15x-2}{x+3} }[/tex]
[tex]\mathbf{=x^3+3x^2-4x-3+\dfrac{7}{x+3} }[/tex]
x+3 is not a factor of f(x)=x^4+6x^3+5x^2-15x-2 because there is a remainder of 7 when we use the long division method to divide x+3 with the given function f(x).
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Which equation has a graph that is a parabola with a vertex at (–2, 0)?
The equation of the parabola which has a vertex at (-2,0) is; y = x² +4x +4.
What is the equation of the parabola with vertex (-2,0)?From the task content, it follows that the vertex of the of the parabola described by the graph in discuss is given by the point; (-2,0).
Hence, the vertex form of the equation is;
y = (x-(-2))² +0
Hence, the equation is; y = x² +4x +4.
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Answer: B
Step-by-step explanation:
Edge 2023
A plane flying horizontally at an altitude of 1 mile and a speed of 570 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it has a total distance of 3 miles away from the station. (Round your answer to the nearest whole number.)
The rate at which the distance from the plane to the station increases is 537 miles/hour. Computed using Pythagoras Theorem and Differentiation.
We assume the station to be at point A.
The plane when directly over the station, takes point C.
As it is flying horizontally continuously at an altitude of 1 mile, AC = b = 1 mile.
The plane flies continuously, and when it is at a distance of 3 miles from the station, it is at point B.
The distance between the plane and the station of 3 miles can be shown as AB = c = 3 miles.
The movement of the plane from C to B can be shown as BC = a.
Now, from the given case, we get a right triangle ABC.
By Pythagoras' Theorem,
a² + b² = c² ... (i).
or, a² + 1² = 3²,
or, a² = 9 - 1 = 8,
or, a = 2√2 miles.
We are told that the plane is moving at a speed of 570 miles/hour.
This can be shown as, da/dt = 570 miles/hour.
As the plane is moving horizontally, the vertical distance between the plane and the station doesn't change, that is, db/dt = 0.
In the question, we are asked to find the rate at which the distance from the plane to the station is increasing, that is, we are asked to find dc/dt.
Differentiating (i), with respect to time t, we get:
2a(da/dt) + 2b(db/dt) = 2c(dc/dt).
Substituting values of a = 2√2 miles, b = 1 mile, c = 3 miles, da/dt = 570 miles/hour, and db/dt = 0, we get:
2(2√2)(570) + 2(1)(0) = 2(3)(dc/dt),
or, 2280√2 + 0 = 6(dc/dt),
or, dc/dt = 380√2 miles/hour = 537.40 miles/hour ≈ 537 miles/hour.
Thus, the rate at which the distance from the plane to the station increases is 537 miles/hour. Computed using Pythagoras Theorem and Differentiation.
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