Answer:
x=3.91
Step-by-step explanation:
29.46=13.82+4x
13.82+4x=29.46
subtract 13.82 from both sides
4x=15.64
divide by 4
x=3.91
If the sales tax rate is 5%, how much tax will you pay on a $35 sweatshirt? * 5 points
$36.75
$1.75
$35.75
$2.25
Answer:
$36.75
Step-by-step explanation:
You do 5% of 35 which equals 1.75 that’s your sales tax.
then add 1.75+35.00= 36.75
find the mean median and mode of the data set :15,11,14,10,12,15,15
Answer:
Mean = 13.14, Median = 14, Mode = 15
Step-by-step explanation:
The mean is the numbers added together divided by the number of numbers
15 + 11 + 14 + 10 + 12 + 15 + 15 = 92
92 / 7 = About 13.14
The median is the middle of the numbers ordered from least to greatest
10 11 12 14 15 15 15
14 is in the middle so that is the median.
The mode is the number showing up the most.
15 shows up 3 times so it is the mode.
how do you find the perpendicular distance between a line segment and a point? (photo attached) i’m stuck
Answer:
Exact Distance = [tex]\frac{4\sqrt{10}}{5}[/tex]
Approximate Distance = 2.529822
============================================
Explanation:
This process is quite involved if you don't know the shortcut formula. I'll go over the long method first, and then show the shortcut in the next section.
First we'll need the equation of the line through points O and M. Use of the slope formula will show line OM has slope -1/3, which you are correct in stating.
Then use point slope form to determine the equation of line OM is y = (-1/3)x+11/3. This converts to the standard form x+3y = 11.
For anything in the form Ax+By = C, the equation perpendicular to this is of the form Bx-Ay = D. The A,B coefficients swap, and one item is negated. This helps form the negative reciprocal slope needed for the perpendicular line.
Compare x+3y = 11 to Ax+By = C. We see that A = 1 and B = 3.
So Bx-Ay = D turns into 3x-y = D. Then plug in the coordinates of H(-3,2) and compute to get
3x-y = 3(-3)-2 = -9-2 = -11. So D = -11
The equation 3x-y = D turns into 3x-y = -11 which is the equation of the line through point H and this line is perpendicular to line OM.
At this point, we have this system of equations
x+3y = 11
3x-y = -11
Solve that system however you wish. Substitution may be the best choice. Doing so leads to the intersection point (-2.2, 4.4)
The last step is to apply the distance formula between the points H(-3,2) and the intersection point (-2.2, 4.4)
The distance you should get is [tex]\frac{4\sqrt{10}}{5} \approx 2.529822[/tex]
I'm skipping steps because listing everything out would take up way too much space in my opinion.
--------------------------------------------------------
The first section goes over a fairly lengthy process of finding the perpendicular distance. Luckily, there's a shortcut.
Consider an equation of the form Ax+By=C, aka standard form. Now consider a point P located at (m,n) that is not on the line Ax+By = C. We can find the distance from P to the line using this formula below
[tex]d = \frac{|Am+Bn-C|}{\sqrt{A^2+B^2}}[/tex]
In this case, A = 1, B = 3 and C = 11 found back in the previous section. So you'll still need to calculate the equation of line OM.
Also, we'll use (m,n) = (-3,2) which are the coordinates of point H
From here it's a fairly straightforward computation
[tex]d = \frac{|Am+Bn-C|}{\sqrt{A^2+B^2}}\\\\d = \frac{|1*(-3)+3*2-11|}{\sqrt{(1)^2+(3)^2}}\\\\d = \frac{|-8|}{\sqrt{1+9}}\\\\d = \frac{8}{\sqrt{10}}\\\\[/tex]
Optionally we can rationalize the denominator like so
[tex]d = \frac{8}{\sqrt{10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{10}\sqrt{10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{10*10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{100}}\\\\d = \frac{8\sqrt{10}}{10}\\\\d = \frac{2*4\sqrt{10}}{2*5}\\\\d = \frac{4\sqrt{10}}{5}\\\\d \approx 2.529822\\\\[/tex]
There are different ways to write down the answer, but they all represent the same number.
Which expression represents each mathematical phrase?
Drag the answer into the box to match each phrase.
(1) the product of 7 and a number
(2) the sum of 7 and a number
(3) 7 less than a number
(4) 7 more than twice a number
(a) 2+x+7
(b) 7+x
(c) 2x+7
(d) x-7
(e) 7x
(f) 7-x
Answer:
(1) = (e) 7x. (2) = (b) 7+x. (3) = (d) x-7. (4) = (c) 2x+7
In your sock drawer you have 4 blue socks, 5 grey socks, and 3 black socks. Half asleep one morning, you grab 2 socks at random and put them on. Find the probability that you end up wearing exactly 1 black sock.
3 out of 12
1 out of 4
yea hopefully correct
Tickets for a family of 6 to go skiing cost $48. whats the unit price ?
Find the average rate of change of the function f(x)=(3/-3x-5), on the interval x ∈ [0,3]
Answer:
The average rate of change on the given interval is 9/70
Step-by-step explanation:
Here, we are to find the average rate of change of the function on the given interval
We proceed as follows;
on an interval [a,b] , we can find the average rate of change using the formula;
f(b) - f(a)/b-a
From the question;
a = 0
b = 3
f(0) = -3/5
f(3) = -3/14
Substituting the values, we have;
-3/14-(-3/5)/3-0
= 3/5-3/14/3
= (42-15)/70/3
= 27/70/3
= 27/70 * 1/3 = 9/70
a) An agent sold some carpets at the rate of Rs 4500 each and received Rs 9000 as commission
at 10%. Find the number of carpets he sold.
Answer:
A
Step-by-step explanation:
not sure gusto ko lang tumulong
rationalise the denoninator of 1 ÷ 5 - square root of 2
Answer:
Square root2 /3
Step-by-step explanation:
1. Multiply both numerator and denominator by square root of 2.
2. Square root 2 times itself is just 2 that so denominator is 5-2
3. 1 times Square root 2 is just Square root 2. So numerator is Square root 2
4. 5-2=3 so final answer is Square root 2 over 3
Here's a graph of a linear function.
Write the
equation that describes that function.
Express it in slope-intercept form.
Answer:
y = 1/2x + 3Step-by-step explanation:
As per graph, using the points (-6, 0) and (0, 3) we determine that:
the y-intercept is 3 and the slope is m = (3-0)/(0 - (-6)) = /3/6 = 1/2So the equation is:
y = mx + by = 1/2x + 3The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets.
Part A: Write a system of equations to represent the given scenario. Use the variables "s" for senior citizen tickets and "c" for child.
Part B: Solve the system of equations from Part A algebraically. Show your work.
Part C: Explain what the solution to the system of equations represents in context of the problem. Hint: You will need to put words here, not an equation.
Answer:
The school took in $52 on there second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen
Step-by-step explanation:
When loaded with bricks, a lorry has a mass of 11600kg. If the mass of the bricks is three times that the mass of the empty lorry, find the mass of the bricks.
Answer:
8700kg
Step-by-step explanation:
lorry + bricks = 11600kg
bricks = 3(mass of empty lorry)
lorry mass is x
there for bricks = 3x
x+3x = 11600
4x =11600
x= 2900kg
mass of bricks = 3(2900)
=8700kg
Write and solve an equation for seven less than fou
times a number is 29.
Find the value of x.
Answer:
x=102
Step-by-step explanation:
On Wednesday mornings, admission to the park swimming pool is $3.00 per adult and $2.00 per child. Which expression can be used to find the cost of admission to the pool for a group of adults (a) and children (c)?
A. 3ac
B.5+ac
C. 3a+2c
D. 2(3)+ac
WILL GIVE BRAINLIEST I NEED THIS FAST
Answer:
C.) 3a + 2c
Step-by-step explanation:
$3 per adult (a)
$3(a)
+
$2 per child (c)
$2(c)
Answer:
C. 3a+2c
Step-by-step explanation:
It is 3 $ for a adult hence the 3a and 2$ for a child hence 2c
Review: Angle Bisectors
A
Directions: Label the diagram with the
proper congruence markings and known
measurements.
Answer:
m∠AOC = 15°m∠BOC = 15°Step-by-step explanation:
Given the angle ∠AOB
It is stated that CO is the angle bisector of ∠AOB.
Given that ∠AOB = 30°
As we know that the angle bisector bisects the angle into two equal angles.
Thus, the angle bisector CO bisects the angle ∠AOB into two equal angles, which are:
m∠AOCm∠BOCas
∠AOB = 30°
Thus, the two formed angles i.e m∠AOC and m∠BOC by the angle bisector would be half of the angle bisector as the angle bisector bisects the angle ∠AOB into two equal angles.
Therefore,
m∠AOC = 15°m∠BOC = 15°Three different coins are tossed. What is P(tail, head or tail, head, or tail)
Answers:
Probability of landing all three coins on head: [tex]\frac{1}{8}[/tex]
Probability of landing all three coins on tail: [tex]\frac{1}{8}[/tex]
Probability of landing two coins on head and one on tail: [tex]\frac{3}{8}[/tex]
Probability of landing two coins on tails and one on head: [tex]\frac{3}{8}[/tex]
Step-by-step explanation (Read Carefully):
-How to calculate this is that there are three possible outcomes when tossing the three coins. So, if you group all the possible outcomes of heads and tails when tossing the three coins in one event, you’ll get eight events. Let’s take a look at it:
-A way to organize this is to have:
H = heads
T = tails
-Total of eight events, where each event is the probability of the three coins being tossed (possible events with equal probability, and order matters):
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
Now, let’s apply some questions:
⇒ Probability of landing all three coins on heads: [tex]\frac{1}{8}[/tex]
Explanation: Look at the events above. How many times (out of the eight events) that all three coins land on heads? Well, you can see that there is only one possible event that has HHH. So, the probability of landing all three coins on heads (out of the eight events) is [tex]\frac{1}{8}[/tex].
⇒ Probability of landing all three coins on tails: [tex]\frac{1}{8}[/tex]
Explanation: Look at the events above. How many times (out of the eight events) that all three coins land on tails? Well, you can see that there is only one possible event that has TTT. So, the probability of landing all three coins on tails (out of the eight events) is [tex]\frac{1}{8}[/tex].
⇒ Probability of landing two coins on heads and one on tails: [tex]\frac{3}{8}[/tex]
Explanation: Look at the events above. How many times (out of the eight events) where two coins land on heads and one on tails? Well, you can see that there are three possible events that include HHT, HTH, THH. So, the probability of landing two coins on heads and one on tails (out of the eight events) is [tex]\frac{3}{8}[/tex].
⇒ Probability of landing two coins on tails and one on heads: [tex]\frac{3}{8}[/tex]
Explanation: Look at the events above. How many times (out of the eight events) where two coins land on tails the one on heads? Well, you can see that there are three possible events that include HTT, THT, TTH. So, the probability of landing two coins on tails and one on heads (out of the eight events) is [tex]\frac{3}{8}[/tex].
I hope you understand and that this helps with your question! :)
8x – 12y = 48
Find the x-intercept and y-intercept
Answer:
my answer came out to x = 6 + 1.5y
Step-by-step explanation:
may someone plz answer this
Answer:
At least 2 weeks
Step-by-step explanation: You divide until you reach 200
Diana worked on her science project for 513 hours. Gabe worked on his science project 114 times as long as Diana. Paula worked on her science project 34 as long as Diana. How long did Gabe and Paula work on their projects?
Answer:
Gabe worked for 6 2/3 hours and Paula worked for 4 hours.
Step-by-step explanation:
It is given that,
Diana worked on her science project for 5 1/3 hours.
Gabe worked on his science project 1 1/4 times as long as Diana.
Paula worked on her science project 3/4 as long as Diana.
Solution,
ATQ,
Gabe worked for :
[tex]5\dfrac{1}{3}\times 1\dfrac{1}{4}\\\\=\dfrac{16}{3}\times \dfrac{5}{4}\\\\=\dfrac{20}{3}\ h\\\\=6\dfrac{2}{3}\ h[/tex]
Pauls worked for :
[tex]\dfrac{3}{4}\times 5\dfrac{1}{3}\\\\=\dfrac{3}{4}\times \dfrac{16}{3}\\\\=4\ h[/tex]
Hence, Gabe worked for 6 2/3 hours and Paula worked for 4 hours.
I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!!!
Choose one of the following.
Parallel lines have ____________________.
A. one solution
B. 10 solutions
C. infinitely many solutions
D. no solution
D. no solution
Because they never found each other, the point they cross on is the solution.
Answer: D
Step-by-step explanation: it just is
what is the x-coordinate of R' ?
Answer:
3
Step-by-step explanation:
Answer:
12
The x-axis is the horizontal one. The full coordinate is (12, 0), which the x-coordinate (or x-intercept) is 12.
solve each system of equation by elimination
{y=-x+1
{y= 4x-14
Answer:
(3, -2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = -x + 1
y = 4x - 14
Step 2: Rewrite Systems
y = 4x - 14
Multiply everything by -1: -y = -4x + 14Step 3: Redefine Systems
y = -x + 1
-y = -4x + 14
Step 4: Solve for x
Elimination
Combine equations: 0 = -5x + 15Isolate x term: -15 = -5xIsolate x: 3 = xRewrite: x = 3Step 5: Check
Define equation: y = -x + 1Substitute in x: y = -3 + 1Add: y = -2Sue wakes up at 7:45 A.M. and jogs for 40 minutes. She then spends 45 minutes dressing for school before she catches the bus. At what time does Sue get on the bus?
Answer:
9:00
Step-by-step explanation:
Mr. Mills is 5 feet and 11 inches tall. How many inches tall is he?
Answer:
71
Step-by-step explanation:
There are 12 inches in a foot:
12 inches x 5 feet = 60
60 + 11 inches = 71 inches total
Answer:
71 inches
Step-by-step explanation:
12 inches in a foot
12*5
60+11
71 inches
Hope this hopes. Have a great day. May it be filled with joy and happiness.
(Geometry)
Find the value of X
Show work
Is (-8,7), (0,1), (2,-6), (2,3), (7,9) a function?
What’s the domain and range?
Can someone pls answer these if someone gives me a step by step answer gets brainliest and 100pts
Quadrilateral ABCD has been dilated by a scale factor of -5/3, Quadrilateral A'B'C'D' is an enlargement of the pre-image.
Question 17 options:
True
False
Question 18 (5 points)
Quadrilateral MNPQ has been dilated by a scale factor of 1/2, Quadrilateral M'N'P'Q' is an enlargement of the pre-image.
Question 18 options:
True
False
9514 1404 393
Answer:
17. True
18. False
Step-by-step explanation:
A dilation will be an enlargement when the magnitude of the scale factor is greater than 1.
__
17. The magnitude of the scale factor is 1 2/3, a value greater than 1. The dilation is an enlargement (True).
__
18. The magnitude of the scale factor is 1/2, a value less than 1. The dilation is not an enlargement. The statement is False.
drummer and a guitarist each wrote songs for their band. The guitarist wrote 8 fewer than
wice the number of songs that the drummer wrote. They wrote a total of 46 songs.
Vhich system of equations models this situation if the drummer wrote d songs and the
guitarist wrote g songs?
Answer:
g = 2d - 8
g + d = 46
i need this question answered by 2:30 its for 20 points pls help
Answer:
46800
Step-by-step explanation:
10x15x24x13=46800