Answer:
The coordinates of vertex A" is (3 , 1)
Step-by-step explanation:
* Lets revise The translation of a point
- If the point (x , y) translated horizontally to the right by h units
then the new point = (x + h , y)
- If the point (x , y) translated horizontally to the left by h units
then the new point = (x - h , y)
- If the point (x , y) translated vertically up by k units
then the new point = (x , y + k)
- If the point (x , y) translated vertically down by k units
then the new point = (x , y - k)
* Now lets solve the problem
∵ Δ ABC has a vertex A = (-4 , 2)
∵ The Δ ABC is translated 2 units right and 5 units down to form
triangle A′B′C′
- From the rule above the x coordinate id added by 2 and the
y-coordinate is subtracted by 5
∴ A' = (-4 + 2 , 2 - 5) = (-2 , -3)
∴ The image of vertex A is A' = (-2 , -3)
∵ Δ A'B'C' is then translated 5 units right and 4 units up to form
triangle A″B″C″
- From the rule above the x coordinate is added by 5 and the
y-coordinate is add by 4
∴ A" = (-2 + 5 , -3 + 4) = (3 , 1)
* The coordinates of vertex A" is (3 , 1)
Answer:
it is a
Step-by-step explanation:
the value of cosec35°- sec55° will be
Answer:
0
Step-by-step explanation:
1/cosecx = sin(x)
cosec(x) = 1/sin(x)
1/sec(x) = cos(x)
sec(x) = 1/cos(x)
1/sin(35) - 1/cos(55)
1.74344 - 1.7344 isn't that something?
0
Which is equivalent
For this case we must find an expression equivalent to:
[tex](x ^ {\frac {4} {3}} * x ^ {\frac {2} {3}}) ^ {\frac {1} {3}}[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
So, rewriting the expression we have:
[tex]x ^ {\frac {4} {3 * 3}} * x ^ {\frac {2} {3 * 3}} =[/tex]
[tex]x ^ {\frac {4} {9}} * x ^ {\frac {2} {9}} =[/tex]
By definition of multiplication of powers of the same base, we put the same base and add the exponents:
[tex]x ^ {\frac {4} {9} + \frac {2} {9}} =\\x ^ {\frac {4 + 2} {9}} =\\x ^ {\frac {6} {9}} =\\x ^ {\frac {2} {3}}[/tex]
Answer:
Option B
Answer:
[tex]x^{2/3}[/tex]
Step-by-step explanation:
The question is on rules of rational exponents
Here we apply the formulae for product rule where;
[tex]= a^{n} *a^{t} = a^{n+t} \\\\\\\\=(x^{4/3} *x^{2/3} ) = x^{4/3 + 2/3} = x^{6/3} = x^{2} \\\\\\=(x^2)^{1/3} \\\\\\=\sqrt[3]{x^2}[/tex]
[tex]=x^{2/3}[/tex]
find the measurement of the indicated angle to the nearest degree
Answer:
54°
Step-by-step explanation:
Since the triangle is right use the cosine ratio to solve for angle
cos? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{26}{44}[/tex], hence
? = [tex]cos^{-1}[/tex] ( [tex]\frac{26}{44}[/tex] ) ≈ 54° ( nearest degree )
Find the slope and the y-intercept of the line whose equation is 5x+y = −5.
Answer:
slope is -5
y-intercept is -5
Step-by-step explanation:
Solve for y to write in y=mx+b
m is slope
b is y-intercept
5x+y=-5
Subtract 5x on both sides
y=-5x-5
slope is -5
y-intercept is -5
(if f(x)=4x^2 and g(x)=x+1, find (f o g)(x)
Answer:
f(g(x)) = x² + 2x +1
Step-by-step explanation:
The given functions are:
f(x) = 4x²
g(x) = x+1
f(x) = 4x²
(fog)(x) = f(g(x))
f(g(x)) = 4(x+1)² [f(x) = x² ]
we know that (a+b)² = a² + b² + 2ab
f(g(x)) = 4(x²+1²+2(x)(1))
f(g(x)) = 4(x² + 1 + 2x )
f(g(x)) = 4x² + 8x +4
Arianne is taking a geometry course and is working with the area of triangles. She knows the area and the height but needs to find the base. Rearrange the following equation for b, where A is the area, b is the base, and h is the height of the triangle.
A = one half b times h
A.b = 2A − h
B.b equals two times A over h
C.b = 2A + h
D.b = 2Ah
Answer:
B
Step-by-step explanation:
Area of a triangle is given by the formula:
[tex]A=\frac{1}{2}bh[/tex]
Now, we need to solve for b. We multiply the right side, cross multiply, and follow rules of algebra to isolate b. Shown below:
[tex]A=\frac{1}{2}bh\\A=\frac{bh}{2}\\2A=bh\\b=\frac{2A}{h}[/tex]
Thus, b is 2 times A over h, the answer choice B is right.
Answer:
The Answer is B. b equals two times A over h
Hope This Helps!
Graph ARST with vertices R(6, 6), S(3, -6), and T(0, 3) and its image after a
reflection over the y-axis.
Answer:
The answer is the second figure and the vertices of Δ R'S'T' are:
R' = (-6 , 6) , S' = (-3 , -6) , T' = (0 , 3)
Step-by-step explanation:
* Lets revise some transformation
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
- If point (x , y) reflected across the line y = x
∴ Its image is (y , x)
- If point (x , y) reflected across the line y = -x
∴ Its image is (-y , -x)
- Now we can solve the problem
∵ R = (6 , 6) , S = (3 , -6) , T = (0 , 3), they are the vertices of ΔRST
- The triangle RST is reflected over the y-axis
- According to the rule above the signs of x-coordinates will change
∵ R = (6 , 6)
∴ Its image is (-6 , 6)
∵ S = (3 , -6)
∴ Its image is (-3 , -6)
∵ T = (0 , 3)
∴ Its image is (0 , 3)
* Now lets look to the figure to find the correct answers
- The image of Δ RST is ΔR'S'T'
∵ The vertices of the image of ΔRST are:
R' = (-6 , 6) , S' = (-3 , -6) , T' = (0 , 3)
* The answer is the second figure
. If f(x) and g(x) are inverses, what will be the values of f(g(x)) and g(f(x))?
Answer:
f(g(x)) = g(f(x)) = x
Step-by-step explanation:
Lemma;
If f(x) and g(x) are inverses, then the compositions f(g(x)) = g(f(x)) = x
What is the name of the relationship between ∠1 and ∠8
Answer: alternate exterior angles
Step-by-step explanation:
In Mexico people use pesos for money. There are about 12.8 pesos in 1 dollar. About how much is 1 peso worth in dollars? Show your work, and give your answer to the nearest hundredth of a dollar and a nursing.
Answer:
$0.08 (rounded to nearest hundredth, 2 decimals)
Step-by-step explanation:
This is very easy if we setup a unitary method ratio.
" If 12.8 pesos equal 1 dollar, 1 peso is HOW MANY (let it be x) dollars?"
We translate the above sentence in ratio and solve for x:
[tex]\frac{Peso}{Dollar}=\frac{12.8}{1}=\frac{1}{x}\\12.8x=1\\x=\frac{1}{12.8}\\x=0.08[/tex]
Thus, it is worth about $0.08
The expression shown below describes a sequence of numbers HELP ME
Answer:
B
Step-by-step explanation:
Given the expression
2n + 3
To determine the terms in the sequence generated by this expression
Substitute n = 1, 2, 3, 4, ... into it
a₁ = (2 × 1) + 3 = 2 + 3 = 5
a₂ = (2 × 2) + 3 = 4 + 3 = 7
a₃ = (2 × 3) + 3 = 6 + 3 = 9
a₄ = (2 × 4) + 3 = 8 + 3 = 11
a₅ = (2 × 5) + 3 = 10 + 3 = 13
The first 5 terms of the sequence are 5, 7, 9, 11, 13
If f(–5) = 0, what are all the factors of the function ? Use the Remainder Theorem.
a. (x – 2)(x + 5)(x – 3)
b. (x + 2)(x – 5)(x + 3)
c. (x – 2)(x + 5)
d. (x + 2)(x – 5)
Answer:
Without any other information the answers could be a and c because they contain the factor x+5
Step-by-step explanation:
f(-5)=0 means that x=-5 is a zero which means x+5 is a factor
Without any other information f can be any of the expressions that have the factor (x+5)
Answer:
A. (x-2)(x+5)(x-3) is the correct answer to this question
Hope it helps!
Which Equation represents a function
A.X=13
B. X-12-34
C. 2y-12
D. 2x-4X=7
E. X/2=15
C is the correct answer.
What is the product of 6 and n
Answer:
6n
Step-by-step explanation:
Lesson: ⇒ Algebric Expression
Product: ⇒ multiply
6n is the correct answer.
I hope this helps you, and have a wonderful day!
[tex] \sqrt{28 } + \sqrt{343} \div 2 \sqrt{63 } [/tex]
Answer:
Step-by-step explanation:
sqrt(28): sqrt(4*7)
sqrt(4) = 2;
sqrt28)=2*sqrt(7)
sqrt(343): sqrt(7 * 7 * 7) = 7 * sqrt(7)
Note: the rule is if you have 3 equal primes under the root sign, you leave one, you throw one away, and you put one outside the root sign.
2 sqrt(63) = 2 sqrt(3*3*7) The above rule gets modified to throw 1 three away and take the other one outside the root sign.
2sqrt(63) = 2*3 sqrt(7)
Numerator: 2*sqrt(7) + 7sqrt(7) = 9sqrt(7)
9sqrt(7)
======
6 sqrt(7)
3/2
Note without brackets I cannot be certain that I have interpreted this correctly. The division only apply to sqrt(343) / 2 sqrt(63). If this is so please leave a note.
Which Of the following Rational Functions is graphed below ?
Answer:
Option A.
Step-by-step explanation:
If you look closely at the graph, we can notice that the function is not defined at two different points.
If you look at functions B and C, you will notice that both functions are not defined at just one point. The function B is not defined at x= -5/2 and function C is not defined at x=-5. Both options are discarded, given that our function should not be defined at two fiferent points.
Now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.
By analyzing the vertical asymptotes, we will see that the correct option is A.
How to determine the rational function?
We know that the vertical asymptotes in the graph of a rational function are at the values of x that make the denominator equal to zero.
Here, we can see that we have the asymptotes at x = -2 and at x = 5, so we can assume that the denominator is of the form:
d(x) = (x + 2)*(x - 5)
Now if you look at the options, there is only one that has this denominator, which is A:
[tex]f(x) = \frac{1}{(x + 2)*(x - 5)}[/tex]
If you want to learn more about rational functions, you can read:
https://brainly.com/question/1851758
What is the slope-intercept form of the equation of the line that passes through the points (2,7) and (4, - 1)?
Answer:
y = -4x + 15
Step-by-step explanation:
Slope-intercept form is y = mx + b
m = slope ([tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex])
b = y-intercept (where the line crosses the y-axis)
It doesn't matter which coordinate pair you use for (x₁,y₁).
(x₁,y₁) = (2,7)
(x₂,y₂) = (4,-1)
[tex]\frac{-1 - 7}{4 - 2}[/tex] Simplify
[tex]\frac{-8}{2}[/tex] Simplify
-4 = your slope (m)
To get this information into slope-intercept form, you have to plug it into point-slope form, y - y₁ = m(x - x₁). It doesn't matter which coordinate pair you use for (x₁,y₁).
y - y₁ = m(x - x₁) Let's use (2,7) since it doesn't have negatives.
y - 7 = -4 (x - 2) Distribute
y - 7 = -4x + 8 Add 7 to both sides
y = -4x + 15
Check your answer by plugging both coordinate pairs in.
y = -4x + 15
7 = -4(2) + 15
7 = -8 + 15
7 = 7
and
-1 = -4(4) + 15
-1 = -16 + 15
-1 = -1
Answer:
y = -4x + 15
Step-by-step explanation:
m = -y₁ + y₂\-x₁ + x₂
Find the Rate of change [Slope] using the above formula:
-7 - 1\-2 + 4 = -4
Next, we use the Point-Slope Formula [y - y₁ = m(x - x₁)] to convert to Slope-Intercept Formula [y = mx + b]:
y + 1 = -4[x - 4]
y + 1 = -4x + 16
- 1 - 1
________________
[tex]y = - 4x + 15[/tex]
I am joyous to assist you anytime.
find the multiplicative inverse, or reciprocal, of 5/9?
The multiplicative inverse (or reciprocal) is the number by which you multiply another to get a product of 1. For any fraction, simply switch the numerator and the denominator. For any whole number, place it under 1.
The reciprocal of 5/9 is 9/5.
Hope this helps!!
Hello There!
To find the reciprocal of a number, just flip the numerator and the denominator so if the numerator is 5 and the denominator is 9, the new numerator would be 9 and the new denominator would be 5.
Our multiplicative inverse of 5/9 is
[tex]\frac{9}{5}[/tex]
The number of possible solutions of a polynomial can be found by looking at...
Answer:
Number of different operations
Step-by-step explanation:
Find the slope of (-2,-5) and (8,-5) And find the slope of the line passing through the points (4,9) and (4,-7)
Answer:
Part 1) [tex]m=0[/tex]
Part 2) The slope is undefined
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Part 1
we have
[tex]A(-2,-5)\ B(8,-5)[/tex]
Substitute the values
[tex]m=\frac{-5+5}{8+2}[/tex]
[tex]m=\frac{0}{10}[/tex]
[tex]m=0[/tex] ----> is a horizontal line (parallel to x-axis)
Part 2
we have
[tex]A(4,9)\ B(4,-7)[/tex]
Substitute the values
[tex]m=\frac{-7-9}{4-4}[/tex]
[tex]m=\frac{-16}{0}[/tex] ----> is a vertical line (parallel to y-axis)
The slope is undefined
im very confused on finding y
Answer:
In this case, you can use the concept of cosine to calculate y, and things are even easier when you have one of the special angles which is a 45° angle.
So we know that: cos45° = √2/2
This fact will always be true. In our case, we have:
cos45° = 7/y
Therefore, we have the equation:
7/y = √2/2
⇔ 14 = y√2
⇔ y = 14/√2
⇔ y = √196/√2 = √(196/2) = √98 = 7√2
So y is equal to 7√2
Answer:
7√2
Step-by-step explanation:
By observation, we can determine that because this is a right angle triangle with one of the internal angles = 45°, that the remaining unknown angle is also 45°, which makes this an isosceles triangle.
This means that x = 7
we can find y by using the Pythagorean equation:
y² = x² + 7²
y² = 7² + 7²
y² = 98
y = √98 = 7√2
does 1/3 have a greater unit rate than 2/3
Answer: No, because 1/3 is smaller than 2/3
Hope this helps :)
Step-by-step explanation:
Paul, Colin and Brian are waiters.
One night the restaurant earns tips totalling £77.40.
They share the tips in the ratio 1:3:5.
How much more does Brian get over Paul?
whenever we have an amount to be divided in ratios, we simply divide the total amount by the sum of those ratios and then distribute accordingly. In this case, let's divide 77.40 by (1+3+5) and then distribute accordingly to each chap.
[tex]\bf \stackrel{Paul}{1}~~:~~\stackrel{Colin}{3}~~:~~\stackrel{Brian}{5}~\hfill \cfrac{77.40}{1+3+5}\implies 8.6 \\\\\\ \stackrel{Paul}{1\cdot 8.6}~~:~~\stackrel{Colin}{3\cdot 8.6}~~:~~\stackrel{Brian}{5\cdot 8.6}\qquad \implies \qquad \stackrel{Paul}{8.6}~~:~~\stackrel{Colin}{25.8}~~:~~\stackrel{Brian}{43} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{Brian get this much more than Paul}}{43-8.6\implies 34.4}~\hfill[/tex]
Answer:
£34.40
Step-by-step explanation:
Paul, Colin and Brian are waiters.
One night the restaurant earns tips totalling £77.40
They share the tips in the ratio 1:3:5
Paul gets [tex]\frac{1}{9}[/tex] × £77.40 = £8.60
Brian gets [tex]\frac{5}{9}[/tex] × £77.40 = £43.00
Brian gets £43.00 - £8.60 = £34.40 more than Paul.
| 16+(-4)-7-
[tex]16 + ( - 4) - 7 = [/tex]
Answer:
Step-by-step explanation:
16+(-4)-7=16 -(4+7)=16-28 = -12
The slope of a graphed line is -9 and the y-intercept is (0, -2). What is the
slope-intercept equation of the line?
Answer:
y = -9x - 2Step-by-step explanation:
The slope-intercept form of an equation of a line:
y = mx + b
m - slope
b - y-intercept (0, b)
We have the slope m = -9 and the y-intercept (0, -2) → b = -2.
Substitute:
y = -9x + (-2) = -9x - 2
The slope-intercept equation of a line with a slope of -9 and a y-intercept of (0, -2) is y = -9x - 2.
The slope-intercept equation of a line is in the form y = mx + b, where m is the slope and b is the y-intercept.
Given a slope of -9 and a y-intercept of (0, -2), the slope-intercept equation is y = -9x - 2.
Therefore, the slope-intercept equation of the line is y = -9x - 2.
If y is 2.5 when x ls 5 and y varies directly with x, find y when x is 10
Answer:
y = 5
Step-by-step explanation:
Given y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 2.5 when x = 5
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{2.5}{5}[/tex] = 0.5
y = 0.5x ← equation of variation
When x = 10, then
y = 0.5 × 10 = 5
Alex has three times as much money as Jennifer. Jennifer has $12 less than Shannon. Together they have $91. How much money does Alex have?
Answer:
The amount of money that Alex has is $47.4
Step-by-step explanation:
Let
x----> amount of money that Alex has
y----> amount of money that Jennifer has
z----> amount of money that Jennifer Shannon has
we know that
x+y+z=91 ----> equation A
x=3y -----> equation B
y=z-12 -----> z=y+12 -----> equation C
substitute equation B and equation C in equation A and solve for y
(3y)+y+(y+12)=91
5y=91-12
y=79/5
y=$15.8
Find the value of x
x=3y ----> x=3(15.8)=$47.4
If f(x)=x^2 and g(x)=1÷2x+3 find g(f(-1))
ANSWER
[tex]g(f( - 1)) = \frac{1}{5 }[/tex]
EXPLANATION
The given function is:
[tex]f(x) = {x}^{2} [/tex]
and
[tex]g(x) = \frac{1}{2x + 3} [/tex]
[tex]g(f(x)) = g( {x}^{2} )[/tex]
[tex]g(f(x)) = \frac{1}{2{x}^{2} + 3 } [/tex]
To find g(f(-1)), we substitute x=-1, to obtain;
[tex]g(f( - 1)) = \frac{1}{2{( - 1)}^{2} + 3 } [/tex]
We simplify the square in the denominator to get,
[tex]g(f( - 1)) = \frac{1}{2+ 3 } [/tex]
We now add the denominator to obtain;
[tex]g(f( - 1)) = \frac{1}{5 } [/tex]
20m to 21m what is the percentage change
Answer: The correct answer is: " 5% increase " .
_________________________________________
Step-by-step explanation:
_________________________________________
Note: The particular "percentage change" is a "percent increase" ; since we are going from "20" to "21" which is an "increased value of "1" .
_________________________________________
Note the formula for "percent increase" ; as follows:
_________________________________________
Percent increase = [(new value - original value)/original value] * 100 ;
_________________________________________
So; let us "plug in" our known values; to solve for the "percentage change"
→ [i.e. "percent increase" (in this case)] :
_________________________________________
Percent increase = [(21 - 20)/20] * 100 ;
= [1/20] * 100 ;
= [100/20] ;
= 5.
_________________________________________
The correct answer is: " 5 % increase" .
_________________________________________
Hope this helps!
Best wishes to you!
_________________________________________
Tom is riding his bike to the store. After 2
minutes he has traveled 3 blocks, after 6
minutes, he has traveled 9 blocks. Find his
average speed in blocks per minute.
O 1.5 blocks per minute
O 2/3 blocks per minute
O 3.2 blocks per minute
06 blocks per minute
The answer is:
The correct option is the first option, the average speed in blocks per minute is 1.5 blocks per minute.
[tex]AverageSpeed=1.5\frac{Block}{minute}[/tex]
Why?To calculate the average speed we need to calculate the total distance traveled and the total time taken to cover that distance.
From the statement we know that:
[tex]Distance_{1}=3blocks\\Distance_{2}=9blocks-3blocks=6blocks\\time_{1}=2minutes\\time_{2}=6minutes[/tex]
So, we need to use the following formula in order to calculate the average speed:
[tex]AverageSpeed=\frac{distance_{1}+distance_{2}}{t_{1}+t_{2}}[/tex]
Then, substituting we have:
[tex]AverageSpeed=\frac{3blocks+9blocks}{2minutes+6minutes}[/tex]
[tex]AverageSpeed=\frac{12blocks}{8minutes}=1.5\frac{blocks}{minutes}[/tex]
Hence, we have that the correct option is the first option, the average speed in blocks per minute is 1.5 blocks per minute.
[tex]AverageSpeed=1.5\frac{Block}{minute}[/tex]
Have a nice day!