F(x) = -3x + 3
replace x in the equation with -1:
F(-1) = -3(-1) + 3
Simplify:
f(-1) = 3+3
f(-1) = 6
Which set of ratios could be used to determine if one triangle is a dilation of the other
Final answer:
To determine if one triangle is a dilation of another, ratios of corresponding sides must be compared and set up as proportions to see if they are equivalent. When the proportions are equivalent, it indicates a consistent scale factor, confirming a dilation.
Explanation:
To determine if one triangle is a dilation of the other, we compare the ratios of corresponding sides from each triangle. A dilation occurs when all sides of one triangle are in proportion with the sides of a second triangle by the same scale factor. For example, if one triangle has sides of length 3, 4, and 5, and the second triangle has sides of length 6, 8, and 10, then the ratios of the corresponding sides (3/6, 4/8, 5/10) all simplify to 1/2, indicating that the second triangle is a dilation of the first.
To use ratios to determine if one triangle is a dilation of another, you need to set up proportions. For instance, we can express the ratios of corresponding lengths as fractions, and then set each of these ratios equal to the unit scale to form proportions. If the lengths of the triangles are given as 1 inch to 50 inches and 0.5 inches to 5 inches, we can set up the proportion 1/50 = 0.5/5 to show that they are equivalent.
In problems like this, proper notation and maintaining consistency across corresponding dimensions (e.g., width to width and length to length) is essential for accurate comparison.
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The net of a square pyramid is shown:
Answer:
The surface area of the pyramid is 0.6625 inches²
Step-by-step explanation:
* Lets explain how to find the surface area of the square pyramid
- The square pyramid has 5 faces
- A square base
- Four triangular faces
- Its surface area is the sum of the areas of the five faces
- Area of the square = L × L , where L is the length of its sides
- Area of the triangle = 1/2 × b × h , where b is the length of its base
and h is the length of its height
∵ The length of the side of the square is 0.25 inches
∴ Area of the base = 0.25 × 0.25 = 0.0625 inches²
∵ The length of the base of the triangle is 0.25 inches and the length
of its height is 1.2 inches
∴ The area of its triangular face = 1/2 × 0.25 × 1.2 = 0.15 inches²
∵ The surface area of the pyramid = the sum of the areas of the 5 faces
∵ The area of the four triangular faces are equal
∴ The surface area = 0.0625 + (4 × 0.15) = 0.0625 + 0.6
∴ The surface area = 0.6625 inches²
* The surface area of the pyramid is 0.6625 inches²
What are the solutions to the system of equations?
Answer:
A
Step-by-step explanation:
Given the 2 equations
y = x² - 4x + 8 → (1)
y = 2x + 3 → (2)
Since both express y in terms of x we can equate the left sides, that is
x² - 4x + 8 = 2x + 3 ( subtract 2x + 3 from both sides )
x² - 6x + 5 = 0 ← in standard form
(x - 1)(x - 5) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 5 = 0 ⇒ x = 5
Substitute these values into (2) for corresponding values of y
x = 1 : y = (2 × 1) + 3 = 2 + 3 = 5 ⇒ (1, 5)
x = 5 : y = (2 × 5) + 3 = 10 + 3 = 13 ⇒ (5, 13)
Solutions are (1, 5) and (5, 13)
Answer:
A. [tex](1,5)[/tex] and [tex](5,13)[/tex]
Step-by-step explanation:
We have been given a system of equations. We are asked to find the solution of our given system.
[tex]\left \{ {{y=x^2-4x+8}\atop {y=2x+3}} \right.[/tex]
Equate both equations:
[tex]x^2-4x+8=2x+3[/tex]
[tex]x^2-4x-2x+8-3=2x-2x+3-3[/tex]
[tex]x^2-6x+5=0[/tex]
Split the middle term:
[tex]x^2-5x-x+5=0[/tex]
[tex]x(x-5)-1(x-5)=0[/tex]
[tex](x-5)(x-1)=0[/tex]
Use zero product property:
[tex](x-5)=0\text{ (or) }(x-1)=0[/tex]
[tex]x=5\text{ (or) }x=1[/tex]
Now, we will substitute both values of x, in our given equation to solve for y.
[tex]y=2x+3[/tex]
[tex]y=2(1)+3[/tex]
[tex]y=2+3[/tex]
[tex]y=5[/tex]
One solution: [tex](1,5)[/tex]
[tex]y=2x+3[/tex]
[tex]y=2(5)+3[/tex]
[tex]y=10+3[/tex]
[tex]y=13[/tex]
2nd solution: [tex](5,13)[/tex]
Therefore, option A is the correct choice.
Rectangle ABCD is shown on the grid.
The area of rectangle ABCD in square units is_____ .
Anyone know how to do this math problem and if so could you please take your time to explain it in the comments below thank you!
Answer:
34 square units
Step-by-step explanation:
Step 1 : Write the formula for area of rectangle
Area of rectangle = length x breadth
From the graph:
AB = DC
AD = BC
Step 2 : Find the distance between AB and AD to find the length and breadth.
Coordinates : A (-1, 4), B (3, 3)
Distance between two points on AB
Formula : √(x2-x1)² + (y2-y1)²
= √(3-(-1))² + (3-4)²
= √17
Distance between two points on AD
Coordinates of A (-1, 4), D = (-3,-4)
Formula : √(x2-x1)² + (y2-y1)²
= √(-3-(-1))² + (-4-4)²
= √68
Area of rectangle = length x breadth
Area of rectangle = √17 x √68
Area of rectangle = 34
Therefore the area of rectangle = 34 square units
!!
Answer:
34
Step-by-step explanation:
Examine the quadratic equation: x^2+2x+1=0
A: What is the discriminant of the quadratic equation?
B: Based on the discriminant, which statement about the roots of the quadratic equation is correct?
Select one answer choice for question A, and select one answer choice for question B.
A: 3
A: 0
A: −3
B: There is one real root with a multiplicity of 2 .
B: There are two real roots.
B: There are two complex roots
Answer:
A: 0
B: There is one real root with a multiplicity of 2.
Step-by-step explanation:
[tex]\bf{x^2+2x+1=0}[/tex]
A:The discriminant of the quadratic equation can be found by using the formula: [tex]b^2-4ac[/tex].
In this quadratic equation,
a = 1b = 2c = 1I found these values by looking at the coefficient of [tex]x^2[/tex] and [tex]x[/tex]. Then I took the constant for the value of c.
Substitute the corresponding values into the formula for finding the discriminant.
[tex]b^2-4ac[/tex][tex](2)^2-4(1)(1)[/tex]Simplify this expression.
[tex](2)^2-4(1)(1)= \bf{0}[/tex]The answer for part A is [tex]\boxed{0}[/tex]
B:The discriminant tells us how many real solutions a quadratic equation has. If the discriminant is
Negative, there are no real solutions (two complex roots).Zero, there is one real solution.Positive, there are two real solutions.Since the discriminant is 0, there is one real root so that means that the first option is correct.
The answer for part B is [tex]\boxed {\text{There is one real root with a multiplicity of 2.}}[/tex]
Answer:
A: 0
B: There is one real root with a multiplicity of 2 .
Step-by-step explanation:
Given a quadratic equation:
[tex]ax^2+bx+c=0[/tex]
You can find the Discriminant with this formula:
[tex]D=b^2-4ac[/tex]
In this case you have the following quadratic equation:
[tex]x^2+2x+1=0 [/tex]
Where:
[tex]a=1\\b=2\\c=1[/tex]
Therefore, when you substitute these values into the formula, you get that the discriminant is this:
[tex]D=(2)^2-4(1)(1)\\\\D=0[/tex]
Since [tex]D=0[/tex], the quadratic equation has one real root with a multiplicity of 2 .
the values in the table represent a linear function. what is the common difference of the associated arithmetic sequence?
x: 1, 2, ,3 ,4 ,5
y: 6, 22, 38, 54, 70.
A) 1
B) 20
C) 16
D) 5
Answer:
c
Step-by-step explanation:
You can find that 22-6=38-22=54-38=70-54=16
so the answer is c 16
Answer: The correct opion is
(C) 16.
Step-by-step explanation: Given that the values in the following table represent a linear function.
x: 1, 2, 3, 4, 5
y: 6, 22, 38, 54, 70.
We are to find the common difference of the associated arithmetic sequence.
If y = f(x) is the given function, then we see that
f(1) = 6, f(2) = 22, f(3) = 38, f(4) = 54 and f(5) = 70.
So, the common difference of the associated arithmetic sequence is given by
[tex]f(2)-f(1)=22-6=16,\\\\f(3)-f(2)=38-22=16,\\\\f(4)-f(3)=54-38=16,\\\\f(5)-f(4)=70-54=16,~~~\cdots.[/tex]
Thus, the required common difference of the associated arithmetic sequence is 16.
Option (C) is CORRECT.
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Y intercept 3 and a slope of -6
Answer:
y=-6x+3
Step-by-step explanation:
Answer:
y=-6x+3
Step-by-step explanation:
because the slope will always have the X and in the middle you can put them together to get your answer
Find angle measures and use angles to classify triangles.
Answer:
1) 55 degrees
2) 90 degrees
3) 105 degrees
Step-by-step explanation:
All triangles equal to 180 degrees. So to find the missing angle measure you have to subtract the two given measures by 180.
First triangle:
180 - 50 - 75 = 55 degrees
Second triangle:
180 - 60 - 30 = 90 degrees
Third triangle:
180 - 45 - 30 = 105 degrees
NEED HELP with this word problem ASAP!
Answer:
[tex]t=280\ minutes[/tex]
Step-by-step explanation:
Let's call "v" the speed of the commercial airplane and call "t" at the travel time of the commercial plane
The distance in kilometers of the trip is: 1730 km
Then we know that:
[tex]vt=1730[/tex]
Then for the jet we have that the speed is:
[tex]2v[/tex]
The flight time for the jet is:
[tex]t-140[/tex]
Therefore:
[tex](2v)(t-140) = 1730[/tex]
Substituting the first equation in the second we have to:
[tex](2*\frac{1730}{t})(t-140) = 1730[/tex]
[tex](\frac{3460}{t})(t-140) = 1730[/tex]
[tex]3460-\frac{484400}{t} = 1730[/tex]
Now solve for t
[tex]\frac{484400}{t} = 3460 - 1730[/tex]
[tex]\frac{484400}{t} =1730[/tex]
[tex]\frac{t}{484400} =\frac{1}{1730}[/tex]
[tex]t=\frac{484400}{1730}[/tex]
[tex]t=280\ minutes[/tex]
You want to produce a scale drawing of your living room, which is 24 ft by 15 ft. If you use a scale of 4 in. = 6 ft, what will be the
dimensions of your scale drawing?
Answer:
The dimensions of the living room is the scale drawing are 16 in by 10 in
Step-by-step explanation:
we know that
The scale drawing is equal to
[tex]\frac{4}{6}\frac{in}{ft}[/tex]
That means ----> 4 inches in the drawing represent 6 feet in the real
so
Find the dimensions of the living room in the scale drawing
using proportion
For 24 ft
[tex]\frac{4}{6}\frac{in}{ft}=\frac{L}{24}\frac{in}{ft}\\ \\L=4*24/6\\ \\L=16\ in[/tex]
For 15 ft
[tex]\frac{4}{6}\frac{in}{ft}=\frac{W}{15}\frac{in}{ft}\\ \\L=4*15/6\\ \\W=10\ in[/tex]
therefore
The dimensions of the living room is the scale drawing are 16 in by 10 in
Factor 6(x − 4)2 − (x − 4) − 2 completely.
A (6x − 25)(x − 2)
B (3x − 14)(2x − 7)
C (3x − 2)(2x + 1)
D 2(x − 5)(3x − 11)
Answer:
B (3x − 14)(2x − 7)
Step-by-step explanation:
6(x − 4)^2 − (x − 4) − 2
Replace x-4 with m
6m^2 − m − 2
(3m -2 ) (2m+1)
Now replace m with x-4
(3 (x-4) -2) (2(x-4) +1)
Distribute
(3x-12 -2) (2x-8+1)
Combine like terms
(3x-14) (2x-7)
What type of number can be written as a fraction plq, where p and q are integers
and q is not equal to zero?
A. 7
B. All numbers can written in this way
C. A rational number is
D. An irrational number
Answer:
rational number
Step-by-step explanation:
written as a fraction p/q, where p and q are integers and q is not equal to zero, is called as rational numbers. Example - 4/5, 2, 100, 1/7 etc all are rational numbers.
define the radius of a circle
Answer: The radius is the distance between the center and the circumference of a circle and is half of the diameter of the circle .
Hopefully, this helps!
A line segment that joins the center of a circle to any point on the circle is called the radius of the circle. Whichever point on the circle we choose, the distance to the center of the circle will always be the same.
through: (1,-5), perpendicular to y=18x+26
Answer:
Step-by-step explanation:
If you're asking for the equation of a line that goes through (1,-5) and is perpendicular to y=18x+26 here's what you do.
1. find the slope of the new line by taking the negative reciprocal of the slope of the first line ([tex]-\frac{1}{18}[/tex])
2. plug in the point (1,-5) and the new slope into the point slope form equation
[tex]y_{2} -y_{1}=m(x_{2}-x_{1})[/tex]
3.Now that you have y-(-5)= -1/18(x-1) simplify
3.a y-(-5)= -1/18x + 1/18
3.b y=-1/18x - 89/18
4. final equation you get is y = -1/18 - 89/18
find the area of the parallelogram answer option 15 25 30 44
There is no picture of the parallelogram needed to answer this question.
What is the least common multiple of 4 and 6?
Answer:
12
Step-by-step explanation:
Consider the list of multiples
multiples of 4 are 4, 8, 12, 16, 20, ....
multiples of 6 are 6, 12, 18, 24, ....
The least common multiple is 12
1. Solve the equation m2 + 6m=-4 using the quadratic formula.
A. m = 5+3
O B. m = 3+V 5
c. m =-3+1 5
D.m=-5+13
Answer:
-3± √5
Step-by-step explanation:
It is given that,
m² + 6m = -4
Points to remember
Solution of a quadratic equation ax² + bx + c = 0
x = [-b ± v(b² - 4ac)]/2a
To find the solution of given equation
m² + 6m = -4
⇒ m² + 6m + 4 = 0
Here a = 1, b = 6 and c = 4
m = [-b ± v(b² - 4ac)]/2a
= [-6 ± √(6² - 4*1*4)]/2*1
= [-6 ± √(36 - 16)]/2
= [-6 ± √20]/2
= [-6 ± 2√5]/2
= -3± √5
Which rotation maps point K(8,-6) to K(-6, -8)?
Answer:
90 degree clockwise rotation about (0,0).
Step-by-step explanation:
That would be a clockwise rotation of 90 degrees about the origin (0,0).
The rotation that maps point K(8,-6) to K(-6,-8) is a counterclockwise rotation of 90 degrees about the point (0,0).
What is the transformation of geometry over the coordinate plane?Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.
Here,
To find the rotation that maps point K(8,-6) to K(-6,-8), we can use the following steps,
Plot the points K(8,-6) and K(-6,-8) on a coordinate plane.
Since point K(8,-6) is being mapped to point K(-6,-8), the rotation must be counterclockwise. As rotation about the origin with angle 90 gives the transformation equation,
(x, y) ⇒ (y, -x)
Therefore, the rotation that maps point K(8,-6) to K(-6,-8) is a counterclockwise rotation of 90 degrees about the point (0,0).
Learn more about transformation here:
brainly.com/question/18065245
#SPJ6
HELP me please !! I really need it
Answer:
D
Step-by-step explanation:
To find the critical values , that is the zeros
Solve the quadratic
x² - x - 20 = 0 ← in standard form
Consider the factors of the constant term (- 20) which sum to give the coefficient of the x- term (- 1)
The factors are - 5 and + 4, since
- 5 × 4 = - 20 and - 5 + 4 = - 1, hence
(x - 5)(x + 4) = 0
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 4 = 0 ⇒ x = - 4
Thus the critical values are - 4, 5 → D
Answer:
D. -4, 5
Step-by-step explanation:
x² - x - 20 factorised = (x - 5) (x + 4)
In order to get the answers, you have to make each bracket equal zero.
(x - 5) = x = 5
(x + 4) = x = -4
The crucial numbers are -4 and 5.
Hope this helps!
The base of a right circular cylinder has a diameter of 5.00 inches. Sally measured the circumference of the base cylinder and recorded it to be 15.5 inches. What is the percent of error in her measurement? Express your answer to the nearest tenth of a percent.
Please explain what you did to get your answer!
Answer:
The percent of error in her measurement is 1.3%
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=\pi D[/tex]
where
D is the diameter
we have
[tex]D=5\ in[/tex]
assume
[tex]\pi=3.14[/tex]
substitute
[tex]C=(3.14)(5)=15.7\ in[/tex] ----> This value represent the 100% (theoretical value)
Find the difference between the theoretical value and the measured value
[tex]15.7-15.5=0.2\ in[/tex]
Find the percentage by proportion
[tex]15.7/100=0.2/x\\ x=100*0.2/15.7\\ x=1.3\%[/tex]
Z varies directly with x and inversely with y. What happens to Z when both x and y are doubled? z stays the same. z is halved. z doubles. z is squared.
Answer:
z stays the same
Step-by-step explanation:
From the statements
z ∝ x and z ∝ 1/y
Combining both proportions
z ∝ x/y
z = k * (x/y)
The above equation defines the relationship between x,y and z
k is the proportionality constant.
Lets say that x and y are doubled
Then
z = k * (2x/2y)
2 in the numerator and denominator will be cancelled out
z = k * (x/y)
Therefore we can conclude that z will stay the same if x and y are doubled ..
Answer:
z stays the same
Step-by-step explanation:
We have been given that z varies directly with x and inversely with y.
Thus, we have the equation
[tex]z=\frac{kx}{y}...(i)[/tex]
Here k is constant of proportionality.
Now, x and y both are doubled, thus, the equation becomes
[tex]z=\frac{k(2x)}{2y}[/tex]
Cancel 2 from numerator and denominator
[tex]z=\frac{kx}{y}[/tex]
This is same as equation (i)
Hence, we can conclude that z remains same.
first option is correct.
5/6 n=10 what is n in this equation
Need to find A, B, and C!
Answer:
Mean: 4.44 add up every number and divide it by how many there is.
Median: 3 put from least to greatest and count till the middle.
Mode: 3 because it appears the most
Answer:
A. Mean = $41900
B. Median = $37000
C. Mode = $37000
Step-by-step explanation:
A. Mean
Here
n=40
Mean = Sum of values/n
[tex]Mean = \frac{(3)(18000)+(3)(22000)+(3)(25000)+(5)(34000)+(17)(37000)+(2)(45000)+52000+(5)(80000)+140000}{40}\\=\frac{54000+66000+75000+170000+629000+90000+52000+400000+140000}{40} \\=\frac{1676000}{40}\\=41900[/tex]
Mean = $41900
B. Median:
As the number of salaries is even,
the median will be mean of middle two terms
[tex]Median= \frac{1}{2}(\frac{n}{2}th\ term+ \frac{n+2}{2}th\ term)\\= \frac{1}{2}(\frac{40}{2}th\ term+ \frac{40+2}{2}th\ term)\\=\frac{1}{2} (20th + 21st)}\\[/tex]
The 20th and 21st term will be 37000
So their mean will be same
So,
Median = $37000
C. Mode
Mode is the value which occurs most of the time in data.
the occurrence of 37000 is highest in the given data.
So,
Mode = $37000 ..
Given f (x). find g(x) and h(x) such that f(x) = g(h(x)) and neither g(x) nor h(x) is solely x.
f(x)=
[tex] \sqrt{ - 2 {x}^{2} + 3 } - 5[/tex]
find g(x) and h(x)
[tex]g(x)=\sqrt x-5\\h(x)=-2x^2+3[/tex]
help with 1-10 , please!!!!!!
Step-by-step explanation:
hi I have answered ur question
Answers:
1. 75/w=5/6
5*w=75*6
5w=450
Divide by 5 for 5w and 450
5w/5=450/5
w=90
2. 1/5=11/p
1*p=5*11
p=55
3. 9/z=3/13
3z=13*9
3z=117
Divide by 3 for 3z and 117
3z/3=117/3
z=39
4. 210=15m
Divide by 15 for 210 and 15m
210/15=15/15m
m=14
5. 22n=11*19
22n=209
22/22n=209/22
n=9.5
6. 9p=180
9p/9=180/9
p=20
7. 100=5x
100/5=5x/5
x=20
8. 4*x=3*24
4x=72
x=18
9. 10*y=14*7
10y=68
10y/10=68/10
y= 68/10
10. 16x=8*15
16x=120
16x/16=120/16
x=7.5
How do you solve this?
Answer:
It's asking for you to calculate the volume of a cylinder and multiply it by 2/3. This is because the question is asking how much water is in a cylindrical vase with the height and radius.
The formula to calculate the volume of a cylinder is : 3.14 (r^2) (h)
R being the radius and H being the height.
Plug in the values then multiply it all by 2/3
Hoped this help you solve your problem.
[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=5\\ h=14 \end{cases}\implies V=\pi (5)^2(14)\implies V=350\pi \\\\\\ \stackrel{\pi =3.14}{V=1099}~\hfill \stackrel{\textit{how much is }\frac{2}{3}\textit{ of that?}}{1099\cdot \cfrac{2}{3}\implies \cfrac{2198}{3}}\implies \stackrel{\textit{rounded up}}{732.7}[/tex]
Consider the vectors u <-4,7> and v= <11,-6>
See picture for more information. Please help
Answer:
u + v = <7 , 1>
║u + v║ ≅ 7
Step-by-step explanation:
* Lets explain how to solve the problem
- We can add two vector by adding their parts
∵ The vector u is <-4 , 7>
∵ The vector v is <11, -6>
∴ The sum of u and v = <-4 , 7> + <11 , -6>
∴ u + v = <-4 + 11 , 7 + -6> = <7 , 1>
∴ The sum u and v is <7 , 1>
* u + v = <7 , 1>
- The magnitude of the resultant vector = √(x² + y²)
∵ x = 7 and y = 1
∵ ║u + v║ means the magnitude of the sum
∴ The magnitude of the resultant vector = √(7² + 1²)
∴ The magnitude of the resultant vector = √(49 + 1) = √50
∴ The magnitude of the resultant vector = √50 = 7.071
* ║u + v║ ≅ 7
Kayla rolls a die 84 times. How many times can she expect to roll a 3?
Answer:
14
Step-by-step explanation:
Assuming the die is 6 sided, there are only 6 possible rolls she can get. And assuming that this is a perfect world where probability is perfect, she will roll each number 14 times, because 84/6 is 14.
Final answer:
Kayla can expect to roll a number 3 approximately 14 times out of 84 rolls of a fair six-sided die, since each roll has a 1 in 6 chance of landing on any given number.
Explanation:
When Kayla rolls a die 84 times, she can expect to roll a 3 in a proportion equal to the probability of rolling a 3 on a single die. A fair six-sided die has a 1 in 6 chance of landing on any given number, including the number 3. Since each roll of the die is independent, we can calculate the expected frequency of rolling a 3 by multiplying the total number of rolls by the probability of rolling a 3.
The calculation is straightforward:
Probability of rolling a 3 = 1/6.Expected frequency of rolling a 3 = Total number of rolls × Probability of rolling a 3.Expected frequency of rolling a 3 = 84 × (1/6) = 14.Therefore, Kayla can expect to roll a 3 approximately 14 times in 84 rolls.