Answer:
y = -5 (x+2)
Step-by-step explanation:
We can use the point slope form of a line
y-y1 = m(x-x1) where (x1,y1) is the point and m is the slope
y-0 = -5(x--2)
y = -5 (x+2)
which of the following steps were applied to ABCD to obtain A’B’C’D’?
a- shifted 2 units right and 3units up.
b- shifted 2 units right and 4 units up.
c- shifted 3 units right and 4 units up.
d- shifted 3units right and 2 units up.
Answer:
c- shifted 3 units right and 4 units up
Step-by-step explanation:
In this problem, we have a quadrilateral named as ABCD. Recall that a quadrilateral is a two-dimensional shape having four sides. So, we need to identify what transformation has been performed to get A'B'C'D', which is the same quadrilateral shifted certain units right and up. So take one point, say, B, so how do we need to do to obtain point B'? well, we need to move that point 3 units right and 4 units up, but how can we know this? just count the number of squares you need to move from B to B' horizontally and vertically, which is in fact 3 units right and 4 units up.
Answer: The correct option is
(c) shifted 3 units right and 4 units up
Step-by-step explanation: We are given to select the correct steps that were applied o ABCD to obtain A'B'C'D' as shown in the figure.
From the graph, we note that
the co-ordinates of the vertices of quadrilateral ABCD are A(2, 3), B(4, 8), C(6, 8) and D(8, 3).
And, the co-ordinates of the vertices of quadrilateral A'B'C'D' are A'(5, 7), B'(7, 12), C'(9, 12) and D'(11, 7).
So, the transformations from the vertices of ABCD to the vertices of A'B'C'D' are as follows :
A(2, 3) ⇒ A'(5, 7) = (2+3, 3+4),
B(4, 8) ⇒ B'(7, 12) = (4+3, 8+4),
C(6, 8) ⇒ C'(9, 12) = (6+3, 8+4),
D(8, 3) ⇒ D'(11, 7) = (8+3, 3+4).
Therefore, the required rule of translation from ABCD to A'B'C'D' is
(x, y) ⇒ (x+3, y+4). That is, 3 units right and 4 units up.
Thus, the required steps applied to ABCD to obtain A'B'C'D' are
Shifted 3 units right and 4 units up.
Option (c) is CORRECT.
I don’t understand questions 1 and 2.
Answer:
Step-by-step explanation:
One
2/3 = 0.6666
4/5 = 0.8
5/6 = 0.8333
On a number line, the last 2 would be close to 1 and 4/5 would be closer to the center than 5/6.
2/3 is over half so it would be closest to the 1/2 point and the furthest left of the the points.
_____________________________|____________|___|_______
O 2/3 4/5 5/6
Two
What primes make up the number given
38: 2 * 19
18: 3 *3 * 2
24:2*2 * 2 * 3
81: 3 * 3 * 3 * 3
Use the figure above to identify a pair of similar triangles, then find the scale factor. The image is not drawn to scale.
A. HEF ~EGH with a scale factor of root 3.2.
B. HEG-GEF with a scale factor of 2:1.
C. HEF -EGF with a scale factor of root 3.1.
D. HEF -GEF with a scale factor of 3.1.
Answer:
Option C.
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem triangles HEF and EGE are similar
because
[tex]EF/GF=HF/EF[/tex]
substitute the values
[tex]\frac{\sqrt{3}}{1}=\frac{3}{\sqrt{3}}\\ \\3=3[/tex]
Is true
The sides are proportional
and
∠HFE=∠GFE
∠EHF=∠GEF
∠HEF=∠EGF
The angles are congruent
The scale factor is equal to
[tex]EF/GF[/tex]
[tex]\frac{\sqrt{3}}{1}[/tex]
Answer:
Option C
Step-by-step explanation:
Two triangles are similar if they have at least 2 equal angles
Note that the HEF triangle has angles of 90 °, 60 ° and 30 °
Note that the EGF triangle has angles of 90 ° and 30 ° so the third angle must be 60 °
Then HEF and EGF are similar triangles.
By definition for similar triangles it is satisfied that if they have sides of length a, b, c and a ', b' c' then
[tex]\frac{a}{a'}=\frac{b}{b'}=\frac{c}{c'}=k[/tex]
Where the constant k is known as "scale factor"
In this case
[tex]\frac{HF}{EF}=\frac{HE}{EG}=\frac{FE}{GF}=k[/tex]
[tex]k=\frac{3}{\sqrt{3}}=\frac{2\sqrt{3}}{2}=\frac{\sqrt{3}}{1}=\sqrt{3}[/tex]
[tex]\frac{FE}{GF}=\frac{\sqrt{3}}{1}[/tex]
or
[tex]\sqrt{3}:1[/tex]
The answer is Option C
cos x = sin 34°
What is the value of x?
Enter your answer in the box.
[tex]\bf \textit{Cofunction Identities} \\\\ sin\left(90^o-\theta\right)=cos(\theta) \qquad cos\left(90^o-\theta\right)=sin(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ cos(x)=\stackrel{90-56}{sin(\stackrel{\downarrow }{34^o})}\implies cos(\stackrel{\downarrow }{x})=sin(90^o-\stackrel{\downarrow }{56^o})\implies cos(56^o)[/tex]
There are 2 way to find value of x
cos x = sin 34°
First
Co-function identities
sin(90° -∅ ) =cos(∅) cos(90 -∅) =sin(∅)
90-56 ↓
cos(x)=sin(34°)⇒ cos (x) =sin(90°-56)⇒ cos(56°)
∴ value of x = 56°⇒ 0.5592
Second way to find value x
x = cos-1(0.5592)
This is much simpler,
cos (90 - x)= sin x
So,
90 - 34 = 56
∴ x = 56
cos(56) = 0.5592
sin(34) = 0.5592.
What is Trigonometry ?A branch of mathematics that studies relationships between side lengths and angles of triangles.
What is the exact value of sin 34?Sin 34 degrees is the value of the sine trigonometric function for an angle equal to 34 degrees. The value of sin 34° is 0.5592
The value of cos 34
= 0.829
The value of cos 34° is equal to the x-coordinate (0.829).
∴ cos 34° = 0.829.
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ughh , anyone know how to do this or what the answer is
Answer:
1730
Step-by-step explanation:
The exponential function is of the form
y = a × [tex]b^{n}[/tex]
where y is the insect population and n the number of weeks
a and b have to be found by using values from the table.
Using (0, 20), then
20 = a × [tex]b^{0}[/tex] ⇒ a = 20
Using (1, 30), then
30 = 20 × [tex]b^{1}[/tex] ⇒ b = [tex]\frac{30}{20}[/tex] = 1.5
Hence
y = 20 × [tex]1.5^{n}[/tex] ← exponential function
When n = 11
y = 20 × [tex]1.5^{11}[/tex] ≈ 1730 ( nearest whole number )
what is the most basic function in a family of the functions?
Answer:
A family of functions is a group of functions that can all be derived from transforming a single function called the parent function. The parent function is the most basic function in the family of functions, the function from which all the other functions in the family can be derived.A family of functions is a group of functions that can all be derived from transforming a single function called the parent function. The parent function is the most basic function in the family of functions, the function from which all the other functions in the family can be derived.
Step-by-step explanation:
All of the functions within a family of functions can be derived from the parent function by taking the parent function's graph through various transformations.
These transformations include horizontal shifts, stretching or compressing vertically or horizontally, reflecting over the x or y axis, and vertical shifts.
Answer:
The parent function is the most basic.
A cube has a volume of 800 cubic inches. What
is the length of an edge of the cube, in inches?
A. 23/100
B. 43/50
C. 83/100
D. 1003/2
E. 1003/8
Answer:
Step-by-step explanation:
Not sure
Can someone please help me out with this question??
For this case we have that the variable "s" represents the quantity of slices for each pizza.
In total, 9 pizzas were purchased and 72 slices were obtained. Then we can raise the following equation:
[tex]9s = 72[/tex]
To know the amount of slices of each pizza we clear "s":
[tex]s = \frac {72} {9} = 8[/tex]
Answer:
[tex]9s = 72\\s = 8[/tex]
Write this trinomial in factored form. 3b^2+b-14
Answer:
(b - 2)(3b + 7)
Step-by-step explanation:
Consider the factors of the product of the coefficient of the b² term and the constant term which sum to give the coefficient of the b- term
product = 3 × - 14 = - 42 and sum = + 1
The factors are - 6 and + 7
Use these factors to split the b- term
3b² - 6b + 7b - 14 ( factor the first/second and third/fourth terms )
= 3b(b - 2) + 7(b - 2) ← factor out (b - 2) from each term
= (b - 2)(3b + 7) ← in factored form
What is the slope of the line through (–4, 3) and (5, 3)?
Question 16 options:
a)
0
b)
undefined
c)
1
d)
9
Answer:
slope = 0
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 4, 3) and (x₂, y₂ ) = (5, 3)
m = [tex]\frac{3-3}{5+4}[/tex] = [tex]\frac{0}{9}[/tex] = 0
What is the sum of the geometric sequence 1, −6, 36, … if there are 6 terms?
Answer:
The sum of the geometric sequence is: -6665
Step-by-step explanation:
By looking at the geometric sequence, we can note that each term is multiplied by -6.
So, the fourth term is going to be: -216
The fifth term is going to be: 1296
The sixth term is going to be: -7776
The sum of the geometric sequence is: 1 - 6 + 36 - 216 + 1296 - 7776 = -6665
Pablo wants to save $800 to buy a TV. He saves $19 each week. The amount, A (in dollars), that he still needs after
weeks is given by the following function.
A(w) = 800-19 w
Answer the following questions.
(a) How much money does Pablo still need after 6 weeks?
si )3
(b) If Pablo still needs $477, how many weeks has he been saving?
I weeks
Answer:
a) $686
b) 17 weeks
Step-by-step explanation:
a) Set [tex]w=6[/tex], as Pablo has already saved for 6 weeks. Plug in the value and solve for [tex]A(6)[/tex].
[tex]A(w)=800-19w[/tex]
[tex]A(6)=800-19(6)[/tex]
[tex]A(6)=800-114[/tex]
[tex]A(6)=686[/tex]
Pablo still needs $686.
b) Set [tex]A(w)=477[/tex], as it is the "final amount" for that week. Solve for [tex]w[/tex].
[tex]A(w)=800-19w[/tex]
[tex]477=800-19w[/tex]
[tex]-323=-19w[/tex]
[tex]w=17[/tex]
Pablo has been saving for 17 weeks if he still needs $477.
Answer:
Pablo wants to save $800 to buy a TV.
He saves $19 each week.
The amount, A (in dollars), that he still needs after weeks is given by the following function.
[tex]A(w)= 800-19w[/tex]
(a) How much money does Pablo still need after 6 weeks?
Putting w = 6 in the equation;
[tex]A(6)= 800-19(6)[/tex]
= $686
(b) If Pablo still needs $477, how many weeks has he been saving?
This means Pablo has already saved [tex]800-477=323[/tex] dollars
Means he has saved for [tex]\frac{323}{19}=17[/tex] weeks.
He has been saving for 17 weeks now.
What is the common ratio of the sequence?
-2, 6, -18, 54,...
−3
−2
3
8
Answer:
-3
Step-by-step explanation:
Consider the geometric sequence:
[tex]b_1=-2\\ \\b_2=6\\ \\b_3=-18\\ \\b_4=54\\ \\....[/tex]
Note that
[tex]b_2=b_1\cdot q\\ \\b_3=b_2\cdot q\\ \\b_4=b_3\cdot q\\ \\...[/tex]
So,
[tex]6=-2q\\ \\-18=6q\\ \\54=-18q\\ \\...[/tex]
From all of these equalities we can state that
[tex]q=-3[/tex]
Answer:
r = - 3
Step-by-step explanation:
The sequence is geometric if a common ratio r exists between consecutive terms.
6 ÷ - 2 = - 3
- 18 ÷ 6 = - 3
54 ÷ - 18 = -3
The sequence is geometric with common ratio r = - 3
From the side view, a gymnastics mat forms a right
triangle with other angles measuring 60° and 30°. The
gymnastics mat extends 5 feet across the floor. How
high is the mat off the ground?
Answer:
its b
Step-by-step explanation:
The height of the mat off the ground is 5√3 / 3 feet.
What is a right triangle?
A triangle is a three-sided polygon with three edges and three vertices. A right triangle is a triangle in which one of its angles measures 90 degrees.
What is the height of the mat?In order to determine he height of the mat, tan would be used.
Tan = opposite / adjacent
Tan 30 = opposite / 5
1 / √3 = opposite / 5 = 5
Opposite = 5√3 / 3 feet
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Help please!
Find x
Answer:
6√2
Step-by-step explanation:
A 45 45 90 right triangle, so ratio of leg : leg: hypotenuse = a: a : a√2 (a = value of leg)
Given: leg = 6
So the ratio of leg : leg: hypotenuse = 6 : 6 : 6 √2
Answer:
x = 6√2
Answer:
B
Step-by-step explanation:
Since the triangle is right use the sine ratio to solve for x
and the exact value for sin45° = [tex]\frac{1}{\sqrt{2} }[/tex], then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{6}{x}[/tex]
Multiply both sides by x
x × sin45° = 6 ( divide both sides by sin45° )
x = [tex]\frac{6}{sin45}[/tex] = [tex]\frac{6}{\frac{1}{\sqrt{2} } }[/tex] = 6[tex]\sqrt{2}[/tex]
Solve the following system of equations graphically. Complete your work in the space provided or upload a file that can
display math symbols if your work requires it. Be sure to include the solution graphically and numerically.
x + y=0
x- y+ 2 = 0
PLEASE HELP :(
Answer:
So value of x = -1 and value of y = 1
Solution Set (-1,1)
Step-by-step explanation:
x+y =0
x-y +2 =0
We need to solve these equations to find value of x and y
x+y =0 eq(1)
Add -2 on both sides
x-y = -2 eq(2)
Add equation 1 and 2
x+y = 0
x-y =-2
______
2x = -2
x = -2/2
x = -1
Now, put value of x = -1 in equation 1
x+y = 0
-1 +y =0
Adding +1 on both sides
-1+1+y = 0+1
y = 1
So value of x = -1 and value of y = 1
Solution Set (-1,1)
We would plot the values of x= -1 and y = 1 on the graph.
Graph is attached in the figure below.
What is the surface area of the right cone below? Thanks!!
[tex]A=\pi r(r+l)\\r=4\\l=13\\\\A=\pi \cdot 4(4+13)=4\pi \cdot 17=68\pi[/tex]
The question appears to be about finding the surface area of a cone, but the provided information discusses a concave mirror instead, which is not relevant for the surface area calculation of a cone.
Explanation:The question asks for the surface area of a right cone. However, the information provided pertains to the cross-sectional area of a concave mirror that is a quarter-section of a cylinder and not a cone. To find the surface area of a cone, one would use the formula A = πrs + πr^2 where r is the radius of the base and s is the slant height of the cone. In the given text, the radius of the mirror is mentioned to be 80.0 cm, and the insolation is 900 W/m². This data seems to be mistakenly provided instead of the cone's dimensions and is irrelevant for calculating the surface area of a cone.
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If I purchase this product for 79.99 and two accessories for 9.99 and 7.00 how much would I owe after the 8.75 tax is applied
77.99+7.00+9.99=96.98
96.98 times 8.75% or 0.0875=8.48575 or 8.49 8.49+96.98=$105.47
What is the value of (-7 + 31) – (2 - 6/)?
The arithmetic expression (-7 + 31) minus (2) equals 22 when you apply the order of operations, which requires us to calculate expressions within parentheses first.
Explanation:To solve this arithmetic problem, let's break down the expression into two parts, working within the parentheses first. The term inside the first set of parentheses is -7 + 31 which equals 24. The term inside the second set of parentheses appears to have missing or incorrect data.
If we ignore that, we have just (2). Now we subtract the second term (2) from the first term (24). Thus, the value of (-7 + 31) – (2) is 22.
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What are the domain and range of the function f(x)=-square root x+3-2?
For this case we have the following function:
[tex]f (x) = - \sqrt {x + 3} -2[/tex]
By definition, the domain is given by all the values for which the function is defined.
The given function is no longer defined if the argument of the root is negative. So:
[tex]x + 3 \geq0\\x \geq-3[/tex]
Thus, the domain of the function is given by all the values of x greater than or equal to -3.
Domain: [-3, ∞)
Substituting the values of the domain, we find the range.
[tex]f (-3) = - \sqrt {-3 + 3} -2 = -2[/tex]
The function evaluated in ∞ gives -∞. So the range is given by:
(-∞, 2]
Answer:
Domain: [-3, ∞)
Range: (-∞, 2]
The answer for this equation is C.
Chau is saving money to buy a game. The game cost $20, and so far he has saved four-fifths of this cost. How much money has Chau saved?
Answer:
16
Step-by-step explanation:
You need to multiply 4/5 * $20 = $16
What is the answer to 3/2x-5=5/6x-3
Answer:
x=3
Step-by-step explanation:
3/2x-5=5/6x-3
3/2x-5-5/6=5/6x-3-5/6x
2/3x-5=-3
2/3x-5+5=-3+5
2/3x=2
(3/2)*(2/3x)=(2)*(3/2)
x=3
Hope this helps a bit,
Flips
Henry recorded the number of miles he biked each day for a week. His miles were 25, 40, 35, 25, 40, 60, and 75. Enter the data into the statistics calculator.
what is the standard deviation of the miles Henry biked to the nearest tenth?
Answer:
17.1
Step-by-step explanation:
1. Find the Mean
(25+40+35+25+40+60+75)/7 = 42.9
2.For each number, subtract the Mean and square the result.
(25-42.86)^2=319
(40-42.86)^2=8.2
(35-42.86)^2=61.8
(25-42.86)^2=319
(40-42.86)^2=8.2
(60-42.86)^2=293.8
(75-42.86)^2=1033
3. Find the Mean of those squared differences.
(319+8.2+61.8+319+8.2+293.8+1033)/7=291.9
4.Take the square root of that and this is what you want.
square root of 291.9 = 17.1
The standard deviation of the given data is 17.1
What is standard deviation?Standard deviation meaning in statistics is a measure of how much the data points vary from the mean or average. It is calculated as the square root of the variance, which is the average of the squared deviations of each data point from the mean.
Given is a data set, we need to find the standard deviation of the data set,
S = 25, 40, 35, 25, 40, 60, 75
Finding the mean =
(25+40+35+25+40+60+75)/7 = 42.86
Finding the variance =
(25-42.86)² = 319
(40-42.86)² = 8.2
(35-42.86)² = 61.8
(25-42.86)² = 319
(40-42.86)² = 8.2
(60-42.86)² = 293.8
(75-42.86)² = 1033
(319+8.2+61.8+319+8.2+293.8+1033)/7=291.9
Therefore, the standard deviation =
√291.9 = 17.1
Hence, the standard deviation of the given data is 17.1
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Use the function below to find f(3).
f(x) =1/3* 4*
Answer:
f(3) = 64/3
Step-by-step explanation:
f(x)=1/3•4^x
Let x = 3
f(3) = 1/3* 4^3
= 1/3 * 64
= 64/3
Answer:
64/3 (APEX)
Step-by-step explanation:
Write an equation of the line that is parallel to y=1/2x+3 and passes through the point (10,-5)
Answer:
13
Step-by-step explanation:
x y
y=1/2x+3 and passes through the point (10,-5) 10 = x and -5 =y 1/2(10) - this mean times
-5 = 1/2(10) +3
1/2(10/1) = 1 x 10 and 2 x 1 = 10/2 = 5
-5 = 5 + 3 = 7
-5 = 7 + 5 + 7
+5 +5
= 13
(I wish You'll understand)
How much is the sales tax on $29.50 worth of goods if the tax rate is 7%?
$0.21
$0.42
$2.07
$4.21
Answer:
Third Option: $2.07
Step-by-step explanation:
Sales tax is the tax that is applied on the sales of goods by the government paid by the public. Here,
Given
Amount = $29.50
And
Sales tax rate = 7%
The formula for calculation of tax is:
Sales tax = Amount * tax rate
= 29.50 * 7/100
= 29.50*0.07
= 2.065
Rounding off will give
$2.07
So third option is correct ..
Answer:
$2.07
Step-by-step explanation:
Solve the inequality.
x – 1 ≤ – 9
Answer:
[tex]X\leq -8[/tex]
This solution provides a step-by-step explanation to solve the inequality x – 1 ≤ -9, which results in the solution x ≤ -8. This solution indicates that all numbers x that are less than or equal to -8 will satisfy this inequality.
Explanation:To solve the given inequality x – 1 ≤ – 9, you should first isolate the variable on one side of the inequality:
Add 1 to both sides. This will cancel out the -1 on the left side of the inequality, and therefore, the inequality becomes: x ≤ -9 + 1.Then, simplify the right side by combining the constants, which results in: x ≤ -8.So, the solution to the inequality is x ≤ -8, which means all numbers x that are less than or equal to -8 will satisfy this inequality.
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Solve 4/x-4=x/x-4-4/3 for x and determine if the solution is extraneous or not
Answer:
x = 4 (extraneous solution)
Step-by-step explanation:
[tex] \frac { 4 } { x - 4 } = \frac { x } { x - 4 } - \frac { 4 } { 3 } \\ \frac { 4 } { x - 4 } - \frac { x } { x - 4 } = - \frac { 4 } { 3 } \\ \frac { 4 - x } { x - 4 } = - \frac { 4 } { 3 } \\ 3 ( 4 - x ) = - 4 ( x - 4 ) \\ 1 2 - 3 x = - 4 x + 1 6 \\ 4 x - 3 x = 1 6 - 1 2 \\ x = 4 \\[/tex]
This solution is extraneous. Reason being that even if it can be solved algebraically, it is still not a valid solution because if we substitute back [tex]x=4[/tex], we will get two fractions with zero denominator which would be undefined.
Can someone please help me out with this question ??
Answer:
A = 28 units ^2
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh
The base is 14 and the height is 4
A = 1/2 (4) * 14
A = 28 units ^2
a quadrilateral has 2 right angles. the measure of the third angle is 73, what is the measure of the forth angle?
Answer: 107 degrees.
Step-by-step explanation:
A quadrilateral is defined as a 2-dimensional closed shape which has four sides and four vertices.
By definition the interior angles of a quadrilateral add up 360 degrees.
We know that this quadrilateral has 2 right angles (which are angles that measure 90 degrees) and we know that the measure of the third angle is 73 degrees.
Let be "x" the measure of the fourth angle.
Then you can write this expression:
[tex]360\°=90\°+90\°+73\°+x[/tex]
And finally solve for "x":
[tex]360\°=253\°+x[/tex]
[tex]360\°-253\°=x[/tex]
[tex]x=107\°[/tex]