Answer:
y-4 =-1(x+1) point slope form
y-2 = -1(x-1)
y = -x +3 slope intercept form
Step-by-step explanation:
We have 2 points, we can find the slope
m = (y2-y1)/(x2-x1)
= (2-4)/(1--1)
(2-4)/(1+1)
-2/2
=-1
The slope is -1
Then we can use point slope form to find an equation
y-y1 =m(x-x1)
y-4 = -1(x--1)
y-4 =-1(x+1) point slope form
Using the other point
y-2 = -1(x-1)
Distribute the -1
y-2 = -1x +1
Add 2 to each side
y-2+2 = -x+1+2
y = -x +3 slope intercept form
Classify each diagram as either a perpendicular bisector or an angle bisector. You may have to zoom on this problem to see.
Answer:
look at explanation:
Step-by-step explanation:
1st picture: angle bisector
2nd picture: angle bisector
3rd picture: perpendicular bisector
4th picture: angle bisector
5th picture: perpendicular bisector
6th picture: perpendicular bisector
Please help meeeeeeeeeeeeeeeeeeeeeeee
Answer:
The second choice
Step-by-step explanation:
The histogram shows the following:
3 children are within the ages of 5-10
7 children are within the ages of 11-13
4 children are within the ages of 14-18
So all you need to do is find the set of data that shows that fit the intervals. So find the data that have three values within 5 to 10; seven values with the 11-13; and four values within 14 to 18.
what is the value of a?
Answer:
[tex]\large\boxed{5\dfrac{1}{3}\ units}[/tex]
Step-by-step explanation:
ΔZYW and ΔWYX are similar. Therefore corresponding sides are in proportion:
[tex]\dfrac{ZY}{YW}=\dfrac{YW}{YX}[/tex]
We have:
[tex]ZY=3,\ YW=4,\ YX = a[/tex]
Substitute:
[tex]\dfrac{3}{4}=\dfrac{4}{a}[/tex] cross multiply
[tex]3a=(4)(4)[/tex]
[tex]3a=16[/tex] divide both sides by 3
[tex]a=\dfrac{16}{3}\\\\a=5\dfrac{1}{3}[/tex]
Answer:
Hello guys im also here for that answer
Step-by-step explanation:
the roots of the equation 3x^2-4x+2=0
For this case we must find the roots of the following equation:
[tex]3x ^ 2-4x + 2 = 0[/tex]
We have that the roots will come from:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]
Where:
[tex]a = 3\\b = -4\\c = 2[/tex]
Substituting the values:
[tex]x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (3) (2)}} {2 (3)}\\x = \frac {4 \pm \sqrt {16-24}} {6}\\x = \frac {4 \pm \sqrt {-8}} {6}\\x = \frac {4 \pm \sqrt {-1 * 8}} {6}\\x = \frac {4 \pmi \sqrt {2 ^ 2 * 2}} {6}\\x = \frac {4 \pm2i \sqrt {2}} {6}\\x = \frac {2 \pmi \sqrt {2}} {3}[/tex]
We have two complex roots:
[tex]x_ {1} = \frac {2 + i \sqrt {2}} {3}\\x_ {2} = \frac {2-i \sqrt {2}} {3}[/tex]
Answer:
[tex]x_ {1} = \frac {2 + i \sqrt {2}} {3}\\x_ {2} = \frac {2-i \sqrt {2}} {3}[/tex]
what is the solution to y = x + 2 and y = 3x – 2 and how do you know? PLEASE HELPPPPP! THANK U!
Answer:
(2,4)
Step-by-step explanation:
We have the system:
y=x+2
y=3x-2.
This is already setup for substitution.
I'm going to replace my first y with what the second y equals.
That is, I'm going to write 3x-2=x+2.
Time to solve the following for x:
3x-2=x+2
Subtract x on both sides:
2x-2= 2
Add 2 on both sides:
2x. = 4
Divide both sides by 2:
x. = 2
Now that we know x=2 and we have an equation that relates x to y: either y=x+2 or y=3x-2, doesn't matter which we use, we can find y.
So we y=x+2 with x=2 which means y=2+2=4.
So the solution, the intersection, is (2,4).
Answer:
(2, 4 )
Step-by-step explanation:
Given the 2 equations
y = x + 2 → (1)
y = 3x - 2 → (2)
Substitute y = 3x - 2 into (1)
3x - 2 = x + 2 ( subtract x from both sides )
2x - 2 = 2 ( add 2 to both sides )
2x = 4 ( divide both sides by 2 )
x = 2
Substitute x = 2 into (1) for the corresponding value of y
y = x + 2 = 2 + 2 = 4
As a check
Substitute x = 2 into the 2 equations and check validity
(1) → y = 2 + 2 = 4 ← Correct
(2) → y = (3 × 2) - 2 = 6 - 2 = 4 ← Correct
Solution is (2, 4 )
Find the derivative of f(x)= -12x^2+9x
Answer:
- 24x + 9
Step-by-step explanation:
Differentiate each term using the power rule
[tex]\frac{d}{dx}[/tex] ( a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]
Given
f(x) = - 12x² + 9x, then
f'(x) = (2 × - 12)x + (9 × 1) [tex]x^{0}[/tex]= - 24x + 9
Rewrite without parenthesis
(3a^5b^6-7b^4(-6a^2b
Answer:
-18a⁷b⁷ + 42a²b⁵
Step-by-step explanation:
(3a⁵b⁶ - 7b⁴)(-6a²b)
= (3a⁵b⁶)(-6a²b) – (7b⁴)(-6a²b) Distributed the 6a²b term
= -18a⁷b⁷ - (-42a²b⁵) Multiplied and added exponents
= -18a⁷b⁷ + 42a²b⁵ Removed parentheses
Nine times the input minus seven is equal to the output. If the input is -1, what is the output
16
Answer: -16
Step-by-step explanation:
input is x
output is y
9x-7=y
9(-1)-7=y
-9-7=-16
Answer:
The answer is -16
Step-by-step explanation:
input is x
output is y
9x-7=y
9(-1)-7=y
-9-7=-16
Let f(x) = -4x - 2 and g(x) = 5x - 6. Find fxg and state its domain.
a. 8x^2 + 34x - 30; all real numbers except x = 1
b. -20x^2 + 14x + 12; all real numbers except x = 6
c.-20x^2 + 14x + 12; all real numbers
d.8x^2 + 34x - 30; all real numbers
Answer:
c) -20x^2+14x+12
all real numbers
Step-by-step explanation:
So (fg)(x)=f(x)g(x)=(-4x-2)(5x-6).
Need find the expression in standard form we need to use foil:
First: (-4x)(5x)=-20x^2
Outer: (-4x)(-6)=24x
Inner: (-2)(5x)=-10x
Last: (-2)(-6)=12
--------------------------Add like terms:
-20x^2+14x+12
Polynomials have domain all real numbers.
There are no restrictions on what x can be. For every number you plug in, you will get a number back.
Answer:
c.-20x^2 + 14x + 12; all real numbers
Step-by-step explanation:
f(x) = -4x - 2
g(x) = 5x - 6
Therefore, -20x^2 + 14x + 12; all real numbers.
A circle is inscribed a in a square. The side length of the square is X in. If the area of the shaded region is 20 pie, what is the radius of the circle?
Answer:
8.555 in.
Step-by-step explanation:
So the area of the square is x^2.
This makes that the area of the circle is x^2 - 20 pie.
The radius of the circle is half of the diameter, so it is 0,5x.
The formula for the circle area is:
Area = pie * r^2.
x^2 - 20 pie = pie * (0,5x)^2
x^2 - 20 pie = pie * 0,25x^2
x^2 - pie * 0,25x^2 = 20 pie
x^2 * (1 - 0,25 pie) = 20 pie
x^2 = 20pie / (1 - 0,25 pie)
x = square root (20pie / (1 - 0,25 pie)) = 17.11
So the radius is 0,5 * 17.11 = 8.555 in.
find the value of Q in the following system so that the solution to the system is (3,2) 4x-5y=2 and 6x+7y=Q
Answer:
Q = 32Step-by-step explanation:
We will check whether the given pair x = 3 and y = 2 is the solution of the first equation.
4(3) - 5(2) = 12 - 10 = 2 CORRECT
Put x = 3 and y = 2 to the equation 6x + 7y = Q:
Q = 6(3) + 7(2)
Q = 18 + 14
Q = 32
need some more help please!
For this case we have that by definition[tex]\pi[/tex] equals 180 degrees.
We must convert 135 degrees to radians, then:
[tex]135 * \frac {\pi} {180} =\\135 * \frac {3.14} {180} =\\\frac {423.9} {180} = 2.355[/tex]
Rounding off we have:
2.4 radians.
Answer:
2.4 radians
For the demand equation, express the total revenue R as a function of the price p per item
q = −6p + 60
P=
Answer:
R(p) = -6p^2 + 60p....
Step-by-step explanation:
Revenue, R = quantity sold * price
Price = p
Quantity sold = q = -6p + 60
R(p) = q*p
where q=-6p + 60
= (-6p + 60) * p = -6p^2 + 60p
Answer: R(p) = -6p^2 + 60p....
In the number 203500 the last two zeroes are called terminal zeroes. If the multiplication 30 x 40 x 50 x 60 x 70 is done, how many terminal zeroes will the product have
Answer:
6
Step-by-step explanation:
30 x 40 x 50 x 60 x 70 = 252,000,000
There are six zeros at the end. So there are 6 terminal zeros.
Which formula can be used to describe the sequence?
-2 2/3, -5 1/3, -10 2/3, -21 1/3, -42 2/3.
A: f(x + 1) = –2f(x)
B: f(x + 1) = -1/2 f(x)
C: f(x + 1) = 1/2 f(x)
D: f(x + 1) = 2f(x)
Answer:
the answer is A. f(x +1) = -2f(x)
Step-by-step explanation:
every new number in the sequence is multiplied by -2, making it -2f(x).
Answer:
(D) f(x+1)=2f(x)
Step-by-step explanation:
Which sequence is modeled by the graph below ?
Answer:
Geometric Sequence.
[tex]a_{n}=(2)^{n-1}[/tex]
Step-by-step explanation:
The x-coordinates represent the number of terms of the sequence while the y-coordinates represent the term of the sequence. So the series shown on the graph is:
1, 2, 4, 8
We can see that the ratio of two consecutive terms of the above sequence is constant. i.e.
2/1 = 2
4/2 = 2
8/4 = 2
Such a sequence in which the ratio of two consecutive terms is a constant is known as Geometric Sequence and this constant ratio is known as common ratio.
The general term of a geometric sequence is represented as:
[tex]a_{n}=a_{1}(r)^{n-1}[/tex]
Using the values for the given sequence we get:
[tex]a_{n}=1(2)^{n-1}[/tex]
[tex]a_{n}=(2)^{n-1}[/tex]
Where n represents the number of term.
Given the two sets which statement is true
Answer:a and b
Step-by-step explanation:
Answer:
[tex]A\subset B[/tex]
Step-by-step explanation:
Let A and B, be two non-empty sets, then set A is a subset of set B if all elements in set A can be found in set B.
The given sets are:
A={1,2} and B={1,2,3,4}
We can observe that, all the elements in set A are also in set B.
This means that set A is a subset of B.
We write this as:
[tex]A\subset B[/tex]
The correct answer is option D.
I need help I will help u with a wire if u help me
Answer:
See below.
Step-by-step explanation:
All the equations are one-step equations.
In each case, see what operation is being done to the variable, and do the opposite operation to both sides.
1.
t + 1.32 = 3.48
1.32 is being added to t.
Subtract 1.32 from both sides.
t + 1.32 - 1.32 = 3.48 - 1.32
t = 2.16
2.
b - 4.22 = 7.08
4.22 is being subtracted from b.
Add 4.22 to both sides.
b - 4.22 + 4.22 = 7.08 + 4.22
b = 11.3
4.
h + 4/9 = 7/9
4/9 is being added to h.
Subtract 4/9 from both sides.
h + 4/9 - 4/9 = 7/9 - 4/9
h = 3/9
h = 1/3
5.
-5/8 = x - 1/4
1/4 is being subtracted from x.
Add 1/4 to both sides.
-5/8 + 1/4 = x - 1/4 + 1/4
-5/8 + 2/8 = x
-3/8 = x
x = -3/8
7.
3.2c = 9.6
c is being multiplied by 3.2.
Divide both sides by 3.2.
3.2c/3.2 = 9.6/3.2
c = 3
8.
-5.04 = 1.26d
c is being multiplied by 1.26.
Divide both sides by 1.26.
-5.04/1.26 = 1.26d/1.26
-4 = d
d = -4
10.
-2/3 = 3/4t
t is being multiplied by 3/4.
Divide both sides by 3/4 which is the same as multiplying both sides by 4/3.
-2/3 * 4/3 = 3/4t * 4/3
-8/9 = t
t = -8/9
11.
w/2.5 = 4.2
w is being divided by 2.5.
Multiply both sides by 2.5.
w/2.5 * 2.5 = 4.2 * 2.5
w = 10.5
A pole is made to lean against a wall. The base of the pole is placed 7 feet
away from the wall. The top of the pole reaches 21 feet up the wall. How long is the pole?
Final answer:
To find the length of the pole, we can use the Pythagorean theorem.
Explanation:
To find the length of the pole, we can use the Pythagorean theorem. Since the base of the pole is 7 feet away from the wall and the top of the pole reaches 21 feet up the wall, we can envision a right triangle with the pole as the hypotenuse. Using the Pythagorean theorem, we can calculate:
c^2 = a^2 + b^2
Where c is the length of the pole, a is the base length (7 feet), and b is the height reached by the pole (21 feet).
Plugging in the values, we get:
c^2 = 7^2 + 21^2
Solving for c, we find that the length of the pole is √(7^2 + 21^2) feet.
The points (6, 2) and (0, 1) fall on a particular line. What is its equation in slope-intercept form?
Answer:
y=1/6x+1 because the formula is written as y=mx+b
Answer:
y=1/6x+1
Step-by-step explanation:
slope is the change in y over the change in . 2-1 is 1 and 6-0 is 6 so the slope will be 1/6. the y intercept is given by the second coordinate (0,1) which is why you add 1.
what is the y-intercept of y=8x+7
Answer:
(0,7)
Step-by-step explanation:
This equation you are given is in slope-intercept form, the form y=mx+b.
It is called slope-intercept from because it gives us the slope and the y-intercept.
The slope is m.
The y-intercept is b.
If we compare y=8x+7 to y=mx+b, we should make the conclusion that m=8 and b=7.
This tells the slope is 8 while the y-intercept is 7.
The y-intercept is 7 is sometimes required to be represented by a point. Since it is the y-intercept, the x is 0 so the point that represents the y-intercept is (0,7).
Answer:
0,7
Step-by-step explanation:
What is the slope of the line represented by the equation y = 4/5x-3?
y= mx+b ( equation for slope)
y= 4/5x-3
The slope (m)is 4/5
The y- intercept(b) is -3
Answer: slope is 4/5
Remember that the slope intercept formula is:
y = mx + b
m is the slope
b is the y-intercept
In this case:
m = 4/5
b = -3
This means that 4/5 is the slope of this line.
Hope this helped!
~Just a girl in love with Shawn Mendes
madison ran a total of 2 kilometers by running around the block 3 times. after running around the block 5 times how many kilometers will she have run ?
Step-by-step explanation:
Write a proportion. 3 laps is to 2 km as 5 laps is to x km.
3 / 2 = 5 / x
Cross multiply:
3x = 10
Divide:
x = 10/3
x = 3⅓
Madison will have run 3⅓ kilometers.
pamela wants to rent a car for 5 days, and she's interested in the loss damage waiver but not the collision damage waiver. If the daily rate is $39 and LDW is $52 what is her total rental cost?
A.$247
B.$249
C.$238
D.$228
Answer:
a.$247
Step-by-step explanation:
39×5=195
195+52=247
Answer:
The answer is $247 (Option A)
Step-by-step explanation:
Pamela will have the car for 5 days.
The cost per renting is variable, and it increases as the days do.
5*$39= $195
And the LDW (Loss Damage Waiver) is an only once cost of $52
You can get the total rental cost by adding both of them:
$195+$52= $247 (Option A)
Which value of b in an exponential function will result in the percent rate of change given? 23% decrease b = 8% increase b = 15% decrease b = 120% increase b =
Answer:
Given an exponential function of the form
y = a*(b)^x
The values of b that will result in the desired percentage values are:
Case 1
b = 23% decrease
1 - 0.23 = 0.77
y = a*(0.77)^x
Case 2
b = 8% increase
1 + 0.08 = 1.08
y = a*(1.08)^x
Case 3
b = 15% decrease
1 - 0.15= 0.85
y = a*(0.85)^x
Case 4
b = 120% increase
1 + 1.2 = 2.2
y = a*(2.2)^x
See attached picture for examples
The value of b in an exponential function is calculated as : For a 23% decrease = 0.77, For an 8% increase = 1.08, For a 15% decrease = 0.85, For a 120% increase = 2.20.
The student is trying to determine the corresponding exponential function base value (b) for a given percent rate of change.
In an exponential function y = abx, a positive b models exponential growth, while a value of b less than 1 models exponential decay.
We can convert the percent increase or decrease to a decimal and then add or subtract it from 1 to find the corresponding value of b.
For a 23% decrease, b = 1 - 0.23 = 0.77.
For an 8% increase, b = 1 + 0.08 = 1.08.
For a 15% decrease, b = 1 - 0.15 = 0.85.
For a 120% increase, b = 1 + 1.20 = 2.20.
How do I graph this?
Answer:
Draw a line across the points (6,0) and (0,3)
Step-by-step explanation:
This is the equation of a line, so it is enough to find two points (x,y), locate them and draw a straight line passing trough then,
Having said that, lets start.
The first easy point to find is the one that makes y=0, so we have the following equation: 0=-1/2 x +3, which gives that x=6, this point is (6,0)
The other easy point to find is the one that makes x=0, so we have the following equation y=-1/2 * 0 +3, which gives that y=3, this point is (0,3)
We have two points (6,0) and (0,3)
Line EF is tangent to circle G at point A.
If the measure of angle CAE is equal to 95 degrees, what is the measurement of line segment CBA??
Answer: 190°
Step-by-step explanation:
Angle CAE is 1/2 times the measure of arc CBA, therefore:
95° x 2=190°
The measure of arc CBA =190°
To understand the relationship between angle CAE and arc CBA, we need to delve into the properties of angles and arcs in circles. Here is a step-by-step explanation:
Step 1: Understanding Inscribed Angles
In a circle, an inscribed angle is an angle formed by two chords that intersect on the circle. The measure of an inscribed angle is always half the measure of the intercepted arc.
Step 2: Relationship between Angle CAE and Arc CBA
Given:
- Angle CAE is inscribed in the circle.
- Arc CBA is the intercepted arc for angle CAE.
According to the properties of inscribed angles:
[tex]\[ \text{Measure of Angle CAE} = \frac{1}{2} \times \text{Measure of Arc CBA} \][/tex]
Step 3: Using the Given Information
Let's denote:
[tex]- \( \angle CAE \)[/tex] as the measure of angle CAE.
[tex]- \( \text{Arc CBA} \)[/tex] as the measure of arc CBA.
From the given information, the measure of arc CBA is 95°. Using the inscribed angle property:
[tex]\[ \angle CAE = \frac{1}{2} \times \text{Arc CBA} \][/tex]
[tex]\[ \angle CAE = \frac{1}{2} \times 95^\circ \][/tex]
[tex]\[ \angle CAE = 47.5^\circ \][/tex]
However, if we are interpreting the problem differently and consider that angle CAE is given as 95°, and we need to find the measure of the arc intercepted by this angle when doubled, then we would calculate:
[tex]\[ \text{Arc CBA} = 2 \times \angle CAE \][/tex]
[tex]\[ \text{Arc CBA} = 2 \times 95^\circ \][/tex]
[tex]\[ \text{Arc CBA} = 190^\circ \][/tex]
Therefore, if angle CAE is half the measure of arc CBA, and given the angle CAE as 95°:
[tex]\[ \text{Arc CBA} = 2 \times 95^\circ = 190^\circ \][/tex]
This shows that the measure of arc CBA is 190°.
HELP me I need it lol !!
Answer:
A
Step-by-step explanation:
Given
x³ - 4x² - 3 divided by x + 1
Write the coefficients of the polynomial in descending order, including a zero for any terms not included in the polynomial.
In this case a 0 is required to denote the x- term
Division by ( x + h) is evaluated for x = - h, hence
division by x + 1 is evaluated for x = - 1, hence
- 1 | 1 - 4 0 - 3 ← is the required synthetic division → A
In zanders class,80% of the students are girls. There are 24 girls in the class. What is the total number of students in Zander's class?
A. 30
B.34
C.40
D.80
Answer:
A. 30
Step-by-step explanation:
30*.08=24
Find (f °g)(3)
f(-13) = 1 and g(3) = -13
Answer:
1
Step-by-step explanation:
(f °g)(3) = f(g(3)) = f(-13) = 1