Answer:
[tex]\large\boxed{y-3=3(x+2)}\qquad\text{point-slope form}\\\boxed{y=3x+9}\qquad\text{slope-intercept form}\\\boxed{3x-y=-9}\qquad\text{standard form}\\\boxed{3x-y+9=0}\qquad\text{general form}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
We have the slope m = 3 and the point (-2, 3). Substitute:
[tex]y-3=3(x-(-2))\\\\y-3=3(x+2)[/tex]
the point-slope form
[tex]y-3=3(x+2)[/tex] use the distributive property
[tex]y-3=3x+6[/tex] add 3 to both sides
[tex]y=3x+9[/tex]
the slope-intercept form
[tex]y=3x+9[/tex] subtract 3x from both sides
[tex]-3x+y=9[/tex] change the signs
[tex]3x-y=-9[/tex]
the standard form
[tex]3x-y=-9[/tex] add 9 to both sides
[tex]3x-y+9=0[/tex]
the general form
Simplify each of the following powers of i. i^32
Answer:
the answer is 1. the trick here is to divide the exponent to 4.
Step-by-step explanation:
i^32 32÷4=8
i
-1
-i
1
Answer: The required value of the given power of i is 1.
Step-by-step explanation: We are given to simplify the following power of i :
[tex]P=i^{32}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the value of the imaginary number i(iota) is given by
[tex]i=\sqrt{-1}~~~~~\Rightarrow i^2=-1.[/tex]
From expression (i), we get
[tex]P\\\\=i^{32}\\\\=(i^2)^{16}\\\\=(-1)^{16}\\\\=(1)^8\\\\=1.[/tex]
Thus, the required value of the given power of i is 1.
What is the median of this data set?
24, 28, 51, 54, 67, 70
Answer:
I'm guessing you need this now, So I'm just going to give the answer without the explanation
Step-by-step explanation:
52.5
Prove ABC~EDC ?
AA similarity theorem
ASA similarity theorem
AAS similarity theorem
SAS similarity theorem
Answer:
AA similarity theorem
Step-by-step explanation:
we know that
AA (Angle-Angle) Similarity states that In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar
In this problem we have that
∠BCA=∠ECD ----> by vertical angles
∠BAC=∠DEC ---> because AB is parallel to ED (alternate interior angles)
therefore
Triangles ABC and EDC are similar by AA similarity theorem
Central Park in New York City is rectangular in shape, 4km in length and 0.8 km wide. How far would a run in central be?
Answer:
basically you have to calculate the perimeter-
Step-by-step explanation:
4+4+0.8+0.8=8+1.6=9.6
First you need to find the parameter
P= (L x 2)+(W x 2)
P=(4km x 2)+(0.8km x 2)
P=8km+1.6km
P=9.6km
What is the value of (63 + 9) ÷ 3(2) ? A 8 B 12 C 48 D 576
For this case we have the following expression:
(63 + 9) ÷ 3 (2)
To find the value of the expression we must first solve the terms associated with parentheses, that is:
[tex](63 + 9) = 72\\3 (2) = 6[/tex]
So:
72 ÷ 6 =
12
So, the correct option is 12.
Answer:
(63 + 9) ÷ 3 (2) = 12
Option B
First add the numbers inside the parentheses, then divide the result by 3, and finally multiply that result by 2. The final answer is 48, matching option C.
First, we add the numbers inside the parentheses: 63 + 9 = 72.Next, we must carry out the division and then the multiplication in the order they appear, keeping in mind that multiplication and division are on the same level of the order of operations (PEMDAS/BODMAS rules). So, we first divide 72 by 3, which gives us 24.Finally, we multiply the result by 2. Thus, 24 * 2 = 48.Therefore, the answer to (63 + 9) ÷ 3(2) is 48, which corresponds to option C.
Let f (x) = 1/x
and g(x) = x² – 3x. What
two numbers are not in the domain of fºg?
For this case we have the following equations:
[tex]f (x) = \frac {1} {x}\\g (x) = x ^ 2-3x[/tex]
We must find [tex](f_ {o} g) (x):[/tex]
By definition of composition of functions we have to:
[tex](f_ {o} g) (x) = f (g (x))[/tex]
So:
[tex](f_ {o} g) (x) = \frac {1} {x ^ 2-3x}[/tex]
We must find the domain of f (g (x)). The domain will be given by the values for which the function is defined, that is, when the denominator is nonzero.
[tex]x ^ 2-3x = 0\\x (x-3) = 0[/tex]
So, the roots are:
[tex]x_ {1} = 0\\x_ {2} = 3[/tex]
The domain is given by all real numbers except 0 and 3.
Answer:
x other than 0 and 3
ANSWER
0 and 3
EXPLANATION
The given functions are
[tex]f(x) = \frac{1}{x} [/tex]
and
[tex]g(x) = {x}^{2} - 3x[/tex]
[tex]( f \circ g)(x) = f(g(x))[/tex]
[tex]( f \circ g)(x) = f( {x}^{2} -x )[/tex]
[tex]( f \circ g)(x) = \frac{1}{ {x}^{2} - 3x} [/tex]
Factor the numerator:
[tex]( f \circ g)(x) = \frac{1}{ x(x - 3)} [/tex]
The function will be undefined if the denominator is zero.
[tex]x(x - 3) \ne0[/tex]
[tex]x \ne0 \: and \: x \ne3[/tex]
Therefore 0 and not in the domain of the composed function.
24. Solve for x and y.
Answer:
x = 10√3 and y = 10Step-by-step explanation:
We have the triangle 30° - 60° - 90°. The sides are in ratio 1 : √3 : 2.
(look at the picture).
We have 2a = 20. Therefore a = y = 20 : 2 = 10 and a√3 = x = 10√3
Which is the same function as -3x + 7 = y?
a)f(x) = -3x + 7
b)f(-3x) = 7
c)f(7) = -3x
d)f(x) = -3 + 7
Answer:
A) f(x) = -3x+7
Step-by-step explanation:
f(x) is interchangeable with y when writing a function, so the functions are the same.
The function that corresponds to the equation -3x + 7 = y is f(x) = -3x + 7, which maintains the same relationship between x and y as the given equation.
Explanation:The equation -3x + 7 = y can be rewritten in function notation, which typically uses the format f(x) = some expression involving x. The correct corresponding function is one that maintains the relationship between x and y as displayed in the original equation. Therefore, among the options provided:
a) f(x) = -3x + 7 is the correct answer because it is exactly the original equation -3x + 7 = y written in function notation.b) f(-3x) = 7 incorrectly suggests that -3x is the variable and not just x.c) f(7) = -3x suggests that 7 is the variable, which is incorrect.d) f(x) = -3 + 7 is simply the sum of two numbers and does not involve the variable x in a way that matches the original equation.The correct answer indicates that the function of x (f(x)) is given by the linear equation -3x + 7.
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To find the slope, Jackie makes right triangle P by using the graph of the line as the hypotenuse of the triangle as shown in the figure. To check her work, she repeats the process and makes a right triangle Q as shown. Which statement explains why the slope of the line should be the same when calculated with either triangle?
A
The two triangles are similar.
B
The two triangles are congruent.
C
One triangle is a translation of the other triangle.
D
The lengths of the hypotenuse of each triangle are equal.
Answer:
A
Step-by-step explanation:
Answer: A
Step-by-step explanation:
I need help with this question
Answer: First option.
Step-by-step explanation:
Given the function f(x):
[tex]f(x)=2x-7[/tex]
And the function g(x):
[tex]g(x)=-6x-3[/tex]
You need to add them to get [tex]f(x)+g(x)[/tex]. Then:
[tex]f(x)+g(x)=(2x-7)+(-6x-3)[/tex]
Therefore, when you add the like terms you get that [tex]f(x)+g(x)[/tex] is:
[tex]f(x)+g(x)=2x-7-6x-3[/tex]
[tex]f(x)+g(x)=-4x-10[/tex]
Since it is a linear function, the Domain is: All real numbers.
You can observe that the result obtained matches witht the first option.
What is the scale factor?
AFGH - AMNO
G
9
The scale factor [tex]\( k \)[/tex] is [tex]\( \frac{x}{6} = \frac{10}{6} = \frac{5}{3} \)[/tex].
The scale factor between two similar triangles is the ratio of the corresponding side lengths. In this case, we can find the scale factor by comparing the corresponding sides of triangles FGH and MNO.
Let's denote the scale factor as [tex]\( k \)[/tex]:
[tex]\[ k = \frac{MN}{FG} \][/tex]
Given that NO = 15 units and FG = 6 units, and MN is denoted as [tex]\( x \)[/tex], we can substitute these values into the formula and solve for [tex]\( x \)[/tex]:
[tex]\[ k = \frac{x}{6} \][/tex]
Since [tex]\( k = \frac{NO}{FG} \)[/tex] we can set up the equation:
[tex]\[ \frac{x}{6} = \frac{15}{9} \][/tex]
Now, solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{15}{9} \times 6 \][/tex]
[tex]\[ x = 10 \][/tex]
So, the scale factor [tex]\( k \)[/tex] is [tex]\( \frac{x}{6} = \frac{10}{6} = \frac{5}{3} \)[/tex].
The scale factor of the given figures is 5 : 3.
The value of x is 10
What is the scale factor?
Scale factor is calculated by finding the ratio of the dimensions of the new shape to the dimensions of the original shape.
15 : 9 = x : 6
15/9 = x/6
Cross product
15 × 6 = 9 × x
90 = 9x
Divide both sides by 9
x = 90/9
x = 10
Therefore, the scale factor 15 : 9
= 15/9
= 5/3
= 5 : 3
Find the missing angle of a triangle if the first two values are 91* and 87 degrees
Answer:
The missing angle has a measure of 2 degrees.
Step-by-step explanation:
Every triangle's inner angles can be added and will always equal 180. Therefore, use subtraction to find any missing angle. In this case,
180 - 91 = 89
89 - 87 = 2
So, your answer is 2.
If the two angles of the triangle are 91° and 87°. Then the measure of the third angle of the triangle will be 2°.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The two angles of the triangle are 91° and 87°.
Then the measure of the third angle of the triangle will be
Let x be the third angle. Then we have
91° + 87° + x = 180
x = 180° - 87° - 91°
x = 2°
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Instead of using the values {1,2,3,4,5,6}
on dice, suppose a pair of dice have the
following: {1,2,2,3,3,4} on one die and
{1,3,4,5,6,8} on the other. Find the
probability of rolling a sum of 9 with
hy these dice. Be sure to reduce.
Answer:
1/9
Step-by-step explanation:
Of the 36 possible sums, 4 of them are 9. The probability is 4/36 = 1/9.
_____
Comment on these dice
Interestingly, the probability of any given sum is the same as it is with "normal" dice.
put the steps for rewriting the equation of a circle below in standard form completing the square in order
Answer:
a) 1.
f)6.
d)5.
c)7.
g)3.
e)4.
b)2.
Step-by-step explanation:
putting the steps for rewriting the equation of a circle below in standard form completing the square in order:
Step 1)
a. where 36 is added on both sides of the equation
as it is square of half of 12.
x^2 +12x+36 +y^2 +30y=24+36 ..........(1)
Step 2)
f. where 225 is added on both sides of equation as it is square of half of 30
x^2 +12x+36 +y^2 +30y+225=24+36+225 ............(6)
Step3)
d. adding numbers on r.h.s
x^2 +12x+36 +y^2 +30y+225=285 ............(5)
Step4)
c) Factoring the x values into binomial factors
(x+6)(x+6) +36 +y^2 +30y+225=285 .............(7)
Step5)
g) re-writing x factors as squares
(x+6)^2 +36 +y^2 +30y+225=285 ...............(3)
Step6)
e)Factoring the y values into binomial factors
(x+6)^2 +36 +(y+15)(y+15)=285 ...............(4)
Step7)
b)re-writing x factors as squares
(x+6)^2 +36 +(y+15)^2=285 ...........(2)!
Find the value of x.
pls help! tysm
Answer:
x = 30.
Step-by-step explanation:
The angle next to the 60 degree angle = 180 - 60 = 120 degrees (adjacent angles are supplementary).
Let the angle just above 3x be y. The sum of 3x and y = 120 degrees (as opposite angles of a parallelogram are equal).
We have the following equations.
3x + y = 120............(1)
2x + 90 + y = 180
2x + y = 90.............(2)
Subtracting, (1) - (2):
x = 30.
Write the equation for an exponential function, in the form y=a•b^x, whose graph passes through the coordinate points (1,7.5) and (3,16.875)
[tex]\bf (\stackrel{x}{1}~~,~~\stackrel{y}{7.5})\implies 7.5=ab^1\implies \boxed{7.5=ab} \\\\\\ (\stackrel{x}{3}~~,~~\stackrel{y}{16.875})\implies 16.875=ab^3\implies 16.875=ab^{1+2}\implies 16.875=abb^2 \\\\\\ 16.875=\boxed{7.5}b^2\implies \cfrac{16.875}{7.5}=b^2\implies 2.25=b^2 \\\\\\ \sqrt{2.25}=b\implies \blacktriangleright 1.5=b \blacktriangleleft \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf 7.5=ab\implies \cfrac{7.5}{b}=a\implies \cfrac{7.5}{1.5}=a\implies \blacktriangleright 5=a \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=5(1.5)^x~\hfill[/tex]
A moving truck rental company charges $35.95 to rent a truck, plus $0.98 per mile. Suppose the function C(d) gives the total cost of renting the truck for one day if you drive 24 miles.
Give the total rental cost if you drive the truck 24 miles. Give the function notation in the first box, the answer in the second box, and choose the correct units from the third box.
Answer:
0.98x24=23.52+35.95=59.47 hope im right
Step-by-step explanation:
The total cost of renting the truck for one day if you drive 24 miles is $58.47.
Explanation:The function notation for the total cost of renting the truck for one day if you drive 24 miles is C(24). The total rental cost can be calculated by multiplying the cost per mile ($0.98) by the number of miles driven (24) and adding the base cost ($35.95). So, the total rental cost would be $35.95 + ($0.98 x 24) = $58.47.
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Kalon has $175 and needs to save at least $700 for a new computer. If he can save $35 per week, what is the minimum number of weeks Kalon will need to save to reach his goal?
700-175=525. 525/35=15
A mason is building a rectangular foundation wall that is to be 75 feet by 40 feet.what is the total distance around the wall?
Answer: 230ft
Step-by-step explanation:
The perimeter is just all 4 sides added together, so,
75+75+40+40=230
The total distance around the wall is 230ft.
Vicky's checking account charges a $12.25 monthly service fee and a $0.26
per-check fee. If Vicky writes 16 checks per month, should she switch to a checking account that charges a $16.50 monthly service fee and no per-check fee?
Answer:
No
Step-by-step explanation:
0.26*16 + 12.25 = 16.41
16.41 < 16.50
Answer:
No, Vicky should not switch.
Step-by-step explanation:
Vicky's checking account charges a monthly service fee = $12.25
Account also charges per-check fee = $0.26
Vicky writes checks per month = 16
His total monthly charges = 12.25+( 16 ×0.26 )
= 12.25 + 4.16
= $16.41
Another account that charges a $16.50 monthly service fee and no per-check fee.
Comparison between account = 16.50 > 16.41
So Vicky should not switch to another account because it charges more than her current account.
find the magnitude and direction angle for the vector v = 5 cos 144°j
Answer:
5, 144°
Step-by-step explanation:
A vector with magnitude v and angle θ can be split into x and y components as:
vx = v cos θ
vy = v sin θ
Here, we're given the components and asked to find the magnitude and direction. By matching, we can see the magnitude is 5 and the angle is 144°.
So the answer is 5, 144°.
A restaurant offers a "Create Your Own Pizza" menu option. There are 33 types of meat, 66 types of vegetables, and 33 kinds of cheese. Customers may choose one meat, one vegetable, and one cheese. Enter values to answer the questions below.
Enter values to answer the questions below.
1) How many different possible pizzas can be made by choosing one meat, one vegetable, and one cheese? (WHOLE NUMBER)
2) You decide to have the chef choose the toppings randomly. What is the probability that the chef will make a pizza with chicken, banana peppers, and ricotta cheese? (FRACTION)
Process would be helpful!
Answer:
54
Step-by-step explanation:
You have to do the number of options in each category by itsself
21. In your day-to-day routines, you likely use measurement to cook or do home renovations, such as adding new tile flooring. How do you imagine that you will use measurement in your healthcare career?
Answer:
Depending of the exact career but measurements are plentiful in the healthcare business.
First, you'll most likely deal with weight and height... since that's part of most health care consultations.
Then, if you deal with medication, you'll use grams, milligrams, milliliters, liters all the time. depending if the medication is in solid or liquid form.
Even as a nutritionist, you'll deal with grams and such for portion sizes.
There are countless of ways you'll use maths and measurements in the healthcare sector.
Answer:
Measurement can be used in healthcare career also. Like - the doctors and nurses are well trained to give medicines accurately as per measurement of milligrams or nano-gram. High doses can prove fatal with some medicines, so the correct measurement is very necessary.
Similarly, measurement is used in syrups. Like a child can be given upto 5 mg of syrup twice daily.
Ryder shot a model rocket over an area that consists of two grassy areas, shown in green, and an area with no grass, shown in white. What is the probability that the rocket has landed in the grassy area, 0.2 0.3 0.4 0.6
Answer:
its 0.4
Step-by-step explanation:
Answer:
The answer is C) 0.4
Each of the 12 cards shown has a number and a color or pattern. Each card is equally likely to be drawn. Find each probability.
Please check linked image ^^
Answer:
A) P(stars) = 1/3
B) P(odd)= 4/7
C)P(solid grays or stars or striped)= 1
D)P(1,4 or 7)= 3/7
E)P(not striped)= 2/3
Step-by-step explanation:
Given:
sample set contains 1-7 solid gray, 1-7 stars and 1-7 striped cards
Let solid gray be x
stars be y
striped be z
then sample set be
1x,2x,3x,4x,5x,6x,7x,
1y,2y,3y,4y,5y,6y,7y,
1z,2z,3z,4z,5z,6z,7z
total number of cards in sample set =21
Now
a)Finding probability of stars
Number of star cards in above sample set = 7
P(stars)= 7/21
P(y)=1/3
b)Finding probability of odd
Number of odd cards in above sample set = 12
P(odd)= 12/21
=4/7
c)Finding probability of solid grays or stars or striped
P(solid grays or stars or striped) = P(x or y or z)
=P(x U y U z)
As the events are mutually exclusive
P(x U y U z)= P(x)+P(y)+P(z)
now P(x)= 1/3
P(y)=1/3
P(z)=1/3
P(x U y U z) = 1/3 + 1/3 + 1/3
= 3/3
=1
d)Finding probability of 1,4 or 7
Number of 1,4 or 7 cards in above sample set = 9
P(1,4 or 7) = P(1 U 4 U 7)
As the events are mutually exclusive
P(1,4 or 7) = P(1) + P(4) + P(7)
P(1)= 3/21
=1/7
P(4)= 3/21
=1/7
P(7)= 3/21
=1/7
P(1,4 or 7)= 1/7 + 1/7 + 1/7
=3/7
e)Finding probability of not striped
Number of not striped cards in above sample set = 14
P(not striped)= 14/21
= 2/3 !
Write two and thirty-one hundredths as a decimal number.
A) 0.231
B) 2.031
C) 2.31
D) 231.00
Answer:
c
Step-by-step explanation:
The table below shows the number of tickets sold, t, at a high school basketball game, and the amount of money collected, m.
Tickets Sold (t) Money Collected (m)
25 $62.50
35 $87.50
40 $100
Which equation will calculate the amount of money collected after t tickets are sold?
Answer:
t x 2.5 =m
Step-by-step explanation:
select the correct statement about the function represented by the table.
The correct statement about the function represented by the table is:
D. It is a linear function because the y-value increase by an equal difference over equal intervals of x-values.
Step-by-step explanation:The table of values are given as follows:
x y
1 26
2 44
3 62
4 80
5 98
We know that the function is said to be linear if the rate of change is constant.Here with the x-value is increasing by each 1.
Hence, we will check whether the difference in y-value is equal or not.
( Since, the rate of change is the ratio of the change in y-value to the change in x-value)
Hence,
44-26=18
62-44=18
80-62=18
and 98-80=18
Hence, we get that the change in y-value is equal .
Hence, we get that the slope or rate of change of the function is constant.
Hence, the function is linear.
HELP ME PLEASE! I really need help on this question
Answer:
given
Step-by-step explanation:
The vertically opposite angles, ∠4 and ∠2 are equals.
What is vertically opposite angles?Vertical angles are angles opposite each other where two lines cross.
What is linear pair?A linear pair can be defined as two adjacent angles that add up to 180° or two angles which when combined together form a line or a straight angle.
According to the given question.
On line m, we have
∠4 + ∠1 = 180 degrees ...(i) (by linear pair)
On line n, we have
∠1 + ∠2 = 180 degrees ...(ii) (by linear pair)
from equation (i) and (ii)
∠4 + ∠1 = ∠1 + ∠2
⇒ ∠4 = ∠2
Hence, we proved that the vertically opposite angles ∠4 and ∠2 are equals.
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Find a segment length indicated. Assume that lines which appear to be tangent are tangent.
Answer:
17.872, 8
Step-by-step explanation:
Chords that pass through the center are the diameter, and lines that are tangent to the circle are perpendicular to the diameter at that point.
Therefore, what we are looking at are right triangles, and we can find the distance using Pythagorean theorem.
c² = a² + b²
(19.5)² = (7.8)² + b²
b ≈ 17.872
c² = a² + b²
(10)² = (6)² + b²
b = 8