Answer:
x = -3
Step-by-step explanation:
If the equation is correctly written as 15·x = -27 + 6·x
Then we have;
15·x = -27 + 6·x
We subtract 6·x from both sides to have all the variables (x) on one side as follows;
15·x - 6·x= -27 + 6·x - 6·x
Which gives;
x·(15 - 6) = -27 + x·(6 - 6)
We note that 6 - 6 = 0, therefore, we have;
x × 9 = -27 + x × 0
We not that x × 0 = 0, therefore;
x × 9 = -27
We now divide both sides with the 9 to get the value of x alone as follows;
x×9/9 = -27/9
Which gives;
x = -27/9 = -3
x = -3
Simplify the following expression. (10-4i)(4-5i)+(-15+20i)
Answer:
5-46i
Step-by-step explanation:
1. Multiply (10-4i) and (4-5i), I recomnd using foil:
40-50i-16+20i^2 + (-15+20i)
2. Remove the parenthesis around -15+20i
*we can do this since there is a "+":
40-50i-16+20i^2 + (-15)+20
3. Simplify i^2
* i^2 is -1 by textbook defination:
40-50i-16+20(-1) + (-15)+20
4. Simplify
40-50i-16-20 + (-15)+20
6. Combine like terms:
-5-50i-16i+20i
5-46i
And the problem is done
Nathan, a tutor, buys 5 calculators for $7.50 each at a store, planning to provide one to each of his clients. However, the next day, he discovers that the same calculators has gone on sale for $5.00 and also discovers that he will only have three tutoring clients instead of five. He returns the five calculators and purchases three calculators at the new sale price. He uses the following expression to determine the amount he should receive back from the store. (5 x $7.50) - (3 x $5.00) Which of the following expressions could Nathan have used. 5 ($7.50 - $5.00). $7.50 - $5.00. (5 x $7.50) - $5.00. (5 x $7.50) - $5.00. 3 ($7.50 - $5.00) +2 x $7.50
Answer: 5 (7.50-3 )
Step-by-step explanation:
Given: Previous price of calculator = $7.50
Number of client =5
Total price = (Number of calculators) x (Price for each calculator)
Total price of 5 calculators = (5 x $7.50)
New price of calculator = $5.00
Number of client =3
Total price of 3 calculators = (3 x $5)
Price will receive = (Total price of 5 calculators) -(Total price of 3 calculators )
= (5 x $7.50) - (3 x $5)
= 5 (7.50-3 )
Required expression: 5 (7.50-3 )
solve 3(11)× =3,993 for x
Hi there! :)
Answer:
[tex]\huge\boxed{x = 3}[/tex]
Given the equation:
[tex]3(11)^{x} = 3993[/tex]
Divide both sides by 3:
[tex](11)^{x} = 1331[/tex]
Rewrite both sides of the equation with a base of 11.
[tex]1331 = 11^{3}[/tex], therefore:
[tex](11)^{x} = 11^{3}[/tex]
x = 3.
Answer:
121
Step-by-step explanation:
121 x 33 = 3993
kind of urgent!! Please describe a real-world scenario in which it would be important to know how to apply scale factors.
One example is that you're given blueprints and you want to find out how large the object is in real life, rather than just on paper. The scale factor will help find those real life measurements. Let's say a house on paper is 2 inches long, and also let's say the scale factor is labeled "1 inch = 20 feet". This means the real life house is 2*20 = 40 feet long.
You could think of it as 1 inch = 20 feet, so 2 inches = 40 feet (multiply both sides by 2).
Scale factors are also used in maps. Look at the bottom corner of any map and it will show you how each distance on paper corresponds to a real life distance (in miles or kilometers maybe). Usually it shows a checkered "ruler" of sorts.
Answer:
everyday living
Step-by-step explanation:
Scale factors are involved in virtually every aspect of the logistics of everyday life. Scale factors of number of units, price per unit, and tax rate are applied to every shopping experience. Scale factors of miles per gallon, or daily rate, or number of travelers are applied to most travel experiences. Scale factors of number of people and/or serving size are applied to food planning--even when ordering pizza.
Scale factors are involved in virtually every aspect of engineering, from specifying or estimating a job, to scheduling, material choice, purchase, and application. Sometimes, these are "rules of thumb", and sometimes they are based on careful calculation.
Much of modern technology is based on the observation that computing power doubles every 2 years or so--a scale factor consistently seen for more than 50 years. This has informed systems planning in many different industries.
How would I solve this? (y-z) ÷ z y=-2 and z=4/5
Answer:
-3.5
Step-by-step explanation:
The problem you have stated is (y-z)/z where y=-2 and z = 4/5. To solve, substitute the values of y and z into the problem. Then, you have (-2-4/5)/4/5. (-2-4/5) simplifies to -14/5 so then you have (-14/5)/4/5. To divide, multiply -14/5 by 5/4 {multiplying by the reciprocal}. That equals -70/20 which is equal to -3.5
Answer:
[tex]\large\boxed{-3.5}[/tex]
Step-by-step explanation:
(y - z) ÷ z y = -2 and z = 4/5
Substitute in the given values for y and z into the equation
(y - z) ÷ z
(-2 - 4/5) ÷ 4/5
Subtract inside the parenthesis (-2 - 4/5)
-2.8 ÷ 4/5
Convert 4/5 into a decimal (in this case that can be done by multiplying both the numerator and denominator by 20)
4/5 = (4 * 20) / (5 * 20) = 80 / 100
80 / 100
Divide numerator and denominator by 10
8/10 = 0.8
Substitute into previous equation
-2.8 ÷ 4/5 = -2.8 ÷ 0.8
Divide
[tex]\large\boxed{-3.5}[/tex]
Hope this helps :)
Consider 6x2 + 6x + 1. Which term immediately tells you that this expression is NOT a perfect square trinomial? Justify your answer.
Answer:
Step-by-step explanation:
The 6x^2 because 6 is not a perfect square.
Answer:
6x^2
Step-by-step explanation:
6 isn't a perfect square
Evaluate the following expression.
28 – 10 – 15 = 3 =
and this is the order of operations
Answer:
28 - 10 - 15 - 3
=> 18 - 15 - 3
=> 3 - 3
=> 0
Another way:
=> 28 - 10 - 15 - 3
=> 28 - 25 - 3
=> 28 - 28
=> 0
The slope of the line whose equation is x + y = 6 is: -1 1 6
Answer:
the slope of the line x+y = 6 is -1.
Step-by-step explanation:
slope = - coefficient of x
----------------------
coefficient of y
slope = -1 /1
slope = -1
Answer:
A: -1
Step-by-step explanation:
Simplify -1-7 +41. N
Answer:
-3
Step-by-step explanation:
-7+4=-3
The absolute value of -3 is 3
The negative sign in front of the absolute value bracket makes it -3
For the mathematics projects, a teacher divides 27 students into 2 groups. One group has more students than twice the number of students in the other group by 3. Find the number of students in both groups.
Write as a equation.
Answer:
8, 19
Step-by-step explanation:
let group 1 have x students and group 2 have y students
x + y = 27
but group 2 has 2x + 3 students
the sum of students from both groups is 27
x + 2x + 3 = 27
3x + 3 = 27
3x = 24
x = 8
y = 2x + 3
y = 19
Please answer this question now
Answer:
200 cm³ is the volume of the pyramid
Answer:
200 cubic centimeters
Step-by-step explanation:
l = length = 10 cm
w = width = 10 cm
h = height = 6cm
V = lwh / 3
= 10 * 10 * 6 / 3
= 100 * 6 / 3
= 600 /3
= 200 cubic cm
Hope this helps! Tell me if I am incorrect!
SOMEBODY PLEASE HELP ME ON THIS ; DUE TODAY, i’ll mark u the brainliest
Answer: Angle Addition Postulate
Step-by-step explanation:
According to the angle addition postulate, the measure of an angle formed by two angles side by side is the sum of the measures of the two angles. It is used to evaluate the measure of an angle formed by two or more angles .In the given picture, we have ∠MRO and ∠MRS on line SRO.
So, ∠SRO = ∠MRO +∠MRS [By angle addition postulate]
So the postulate that justify the statement " ∠SRO = ∠MRO +∠MRS" is Angle Addition Postulate.
this is progression
i need to know C plsssss
thankssssssssssßsssssss
Answer:
[tex]l = 28[/tex]
Step-by-step explanation:
Given
[tex]S = \sum (2k - 3); k = 4\ to\ l[/tex]
Required
What is l when S = 725
This can be solved using Sum of n terms of an AP;
[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]
Where
[tex]S_n = 725[/tex]
[tex]T_1 = first\ term[/tex]
To get T1; we substitute 4 for k in 2k - 3
[tex]T_1 = 2 * 4 - 3[/tex]
[tex]T_1 = 8 - 3[/tex]
[tex]T_1 = 5[/tex]
[tex]T_n = last\ term[/tex]
To get Tn; we substitute l for k in 2k - 3
[tex]T_n = 2 * l - 3[/tex]
[tex]T_n = 2l - 3[/tex]
n = the number of terms;
Since k = 4 to l, then
[tex]n = l - 4 +1[/tex]
[tex]n = l - 3[/tex]
Substitute these values in [tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]
[tex]725 = \frac{l-3}{2}(5 + 2l - 3)[/tex]
Collect Like Terms
[tex]725 = \frac{l-3}{2}(2l + 5- 3)[/tex]
[tex]725 = \frac{l-3}{2}(2l + 2)[/tex]
Open the bracket
[tex]725 = \frac{l-3}{2} * 2l + \frac{l-3}{2} * 2[/tex]
[tex]725 = (l-3) * l + (l-3)[/tex]
[tex]725 = l^2-3l + l-3[/tex]
[tex]725 = l^2-2l -3[/tex]
Subtract 725 from both sides
[tex]725 - 725 = l^2-2l -3 - 725[/tex]
[tex]l^2-2l -3 - 725 = 0[/tex]
[tex]l^2-2l - 728 = 0[/tex]
[tex]l^2 + 26l - 28l - 728 = 0[/tex]
[tex]l(l + 26) - 28(l + 26) = 0[/tex]
[tex](l - 28)(l + 26) = 0[/tex]
[tex]l - 28 = 0[/tex] or [tex]l + 26 = 0[/tex]
[tex]l = 28[/tex] or [tex]l = -26[/tex]
But l must be positive;
Hence, [tex]l = 28[/tex]
x/t+m=b need to make x the subject
Answer:
x=(t+m)/b is the answer
Step-by-step explanation:
Hope it will help :)
Answer:
x = t(b-m)
Step-by-step explanation:
x/t + m =b
subtract m from each side
x/t +m-m = b-m
x/t =b-m
Multiply each side by t
x/t *t = t(b-m)
x = t(b-m)
Suppose triangle TIP and triangle TOP are isosceles triangles. Also suppose that TI=5, PI=7, and PO=11. What are all the possible lengths TO? Enter the possible values, separated by commas.
===========================================
Explanation:
Refer to the diagram below.
In order for triangle TOP to be isosceles, the missing side x must be either 5 or 7. This way we have exactly two sides that are the same length.
--------
If TP = 5, then the value of y could be either 5 or 11 to ensure that triangle TIP has exactly two sides the same length.
If TP = 7, then y = 7 or y = 11 for similar reasons.
--------
Therefore, the possible lengths for segment TO are 5, 7, and 11.
Answer:
7, 11
Step-by-step explanation:
its right- trust me-
On Tuesday, Dec. 3, I began drinking a glass of cola every day except Saturday and Sunday. I drank my 22nd glass of cold on A) Dec. 24 B) Dec. 25 C) Dec. 31 D) Jan. 1
Answer:
The correct option is;
D) Jan. 1
Step-by-step explanation:
The given information are;
The date at which drinking a glass of cola a day of cola began = Dec 3
The days in which to drink cols = Every day of the week except Saturday and Sunday
The number of glasses of drinking cola = 22
In the fires week, number of days in which to drink cola = Tuesday, Wednesday, Thursday, and Friday which is 4 days
On the week commencing Dec 9, 5 glasses drank
On the week commencing Dec 16, 5 glasses drank
On the week commencing Dec 23, 5 glasses drank
On the week commencing Dec 30, 3 glasses drank
Therefore on the week commencing Dec 30, cola was drank on the 30th, 31st and the 22nd glass was drank on Jan. 1
The correct option is Jan. 1.
Find the vertex of the parabola.
f (x) = x squared minus 6 x + 13
a.
( 4, 0)
c.
( 3, 4)
b.
(0, 3)
d.
( 4, 3)
Answer:
The vertex is (3,4)
Step-by-step explanation:
f (x) = x^2 - 6 x + 13
Completing the square
-6/2 = -3 and squaring it = 9
= x^2 -6x +9 +4
= ( x-3) ^2 +4
The equation is now in vertex form
a( x-h) ^2 +k
where the vertex is ( h,k)
The vertex is (3,4)
Answer:
C on edge
Step-by-step explanation:
Simplify cos^2theta(1+ tan^2theta)
Answer:
1
Step-by-step explanation:
We will use x instead of theta
● cos^2 x *(1+tan^2x)
We khow that: 1+ tan^2 x = 1/cos^2 x
Replace 1+tan^2 x by the new expression
● cos^2 x (1/cos^2 x)
● cos^2x/ cos^2 x
● 1
I REALLY need help with these 3 questions plz!!!!
Answer:
6. No. See explanation below.
7. 18 months
8. 16
Step-by-step explanation:
6. To rewrite a sum of two numbers using the distributive property, the two numbers must have a common factor greater than 1.
Let's find the GCF of 85 and 99:
85 = 5 * 17
99 = 3^2 + 11
5, 3, 11, and 17 are prime numbers. 85 and 99 have no prime factors in common. The GCF of 85 and 99 is 1, so the distributive property cannot be used on the sum 85 + 99.
Answer: No because the GCF of 85 and 99 is 1.
7.
We can solve this problem with the lest common multiple. We need to find a number of a month that is a multiple of both 6 and 9.
6 = 2 * 3
9 = 3^2
LCM = 2 * 3^2 = 2 * 9 = 18
Answer: 18 months
We can also answer this problem with a chart. We write the month number and whether they are home or on a trip. Then we look for the first month in which both are on a trip.
Month Charlie Dasha
1 home home
2 home home
3 home home
4 home home
5 home home
6 trip home
7 home home
8 home home
9 home trip
10 home home
11 home home
12 trip home
13 home home
14 home home
15 home home
16 home home
17 home home
18 trip trip
Answer: 18 months
8.
First, we find the prime factorizations of 96 an 80.
96 = 2^5 * 3
80 = 2^4 *5
GCF = 2^4 = 16
Answer: 16
4x- 3y = -13 -x + 6y = -44
Answer:
3x and 9y and -31 is the correct answer if you are bloviating.
Step-by-step explanation:
bloviate the factors of x and y.
4 (hx - 1) -3 (x +h) ≡ 5 (x + k)
Work out the value of h and k
H and k are integer constants
Answer:
4hx - 8x - 3h - 4
k = ------------------------
5
8x + 5k + 4
h = ------------------------
4x - 3
Step-by-step explanation:
4 (hx - 1) - 3 (x + h) = 5 (x + k)
4hx - 4 - 3 (x + h) = 5 (x + k)
4hx - 4 - 3x - 3h = 5 (x + k)
4hx - 4 - 3x - 3h = 5x + 5k add 3h both sides
4hx - 4 - 3x - 3h + 3h = 5x + 5k + 3h simplify
4hx - 4 - 3x = 5x + 5k + 3h add 4 both sides
4hx - 4 - 3x + 4 = 5x + 5k + 3h + 4 simplify
4hx - 3x = 5x + 5k + 3h + 4 subtract 5x from both sides
4hx - 3x - 5x = 5x + 5k + 3h + 4 - 5x simplify
4hx - 8x = 5k + 3h + 4
4hx - 8x - 3h - 4 = 5k
4hx - 8x - 3h - 4
k = ------------------------
5
solving for h;
4hx - 3h = 8x + 5k + 4
h(4x - 3) = 8x + 5k + 4
8x + 5k + 4
h = ------------------------
4x - 3
The value of h and k are h = (8x + 5k + 4) / (4x - 3) and k = (4hx - 8x - 3h - 4) / 5 respectively
Given:
4 (hx - 1) -3 (x +h) ≡ 5 (x + k)
open parenthesis
4hx - 4 - 3x - 3h = 5x + 5k
4hx - 4 - 3x - 3h - 5x - 5k = 0
4hx - 8x - 3h - 5k - 4 = 0
For k
4hx - 8x - 3h - 4 = 5k
[tex]k = (4hx - 8x - 3h - 4) / 5[/tex]
For h
4hx - 8x - 3h - 5k - 4 = 0
4hx - 3h = 8x + 5k + 4
h(4x - 3) = 8x + 5k + 4
[tex]h = (8x + 5k + 4) / (4x - 3)[/tex]
Therefore, the value of h and k are h = (8x + 5k + 4) / (4x - 3) and k = (4hx - 8x - 3h - 4) / 5 respectively
Read more:
https://brainly.com/question/21406377
A ship travels a distance of 700 km. On the return trip it averages 10km/hr faster and 8 hours less, tp travel the 700km back. Determine how long the original part of the trip took in hours
Answer:
The total duration of the trip is 48 hours.
Step-by-step explanation:
Let suppose that ship travels at constant speed during its travel. Each stage is represented by the following kinematic equation:
[tex]v =\frac{\Delta s}{\Delta t}[/tex]
Where:
[tex]\Delta s[/tex] - Travelled distance, measured in kilometers.
[tex]\Delta t[/tex] - Time, measured in hours.
[tex]v[/tex] - Speed, measured in kilometers per hour.
Now, each stage is represented by the following expressions:
Outbound trip
[tex]v = \frac{700\,km}{\Delta t}[/tex]
Return trip
[tex]v + 10\,\frac{km}{h} = \frac{700\,kh}{\Delta t - 8\,h}[/tex]
By eliminating [tex]v[/tex] and simplifying the resulting expression algebraically:
[tex]\frac{700\,km}{\Delta t} + 10\,\frac{km}{h} = \frac{700\,km}{\Delta t -8\,h}[/tex]
[tex](700\,km)\cdot \left(\frac{1}{\Delta t - 8\,h}-\frac{1}{\Delta t} \right) = 10\,\frac{km}{h}[/tex]
[tex]\frac{1}{\Delta t - 8\,h}-\frac{1}{\Delta t} = \frac{1}{70}\,\frac{1}{h}[/tex]
[tex]\frac{8\,h}{\Delta t \cdot (\Delta t-8\,h)} = \frac{1}{70}\,\frac{1}{h}[/tex]
[tex]560\,h^{2} = \Delta t\cdot (\Delta t - 8\,h)[/tex]
[tex](\Delta t )^{2}-8\cdot \Delta t - 560 = 0[/tex]
This equation can be solved by means of the Quadratic Formula, whose roots are presented below:
[tex]\Delta t_{1} = 28\,h[/tex] and [tex]\Delta t_{2} = -20\,h[/tex]
Only the first roots offers a physically resonable solution. Then, total duration of the trip is:
[tex]t_{T} = 28\,h +20\,h[/tex]
[tex]t_{T} = 48\,h[/tex]
The total duration of the trip is 48 hours.
The parent council is in charge of making lemonade for field day.They purchased 19 bags of lemon.each bag has 24 lemons.The recipe says that a gallon of lemonade will require 8 lemons.they will be able to pour 12 cups of lemonade from each gallon that they make.How many cups of lemonade will the parent council be able to serve?
Answer:
684
Step-by-step explanation:
19 x 24 = 456
456 divided by 8 = 57
57 x 12 = 684
Help me with 1 please
Answer:
[tex]\huge\boxed{Mass = 11600\ kg}[/tex]
Step-by-step explanation:
Given:
Density = ρ = 2900 kg/m³
Volume = V = 4 m³
Required:
Mass = m = ?
Formula:
Mass = Density × Volume
Solution:
Mass = 2900 * 4
Mass = 11600 kg
Olivia has 4 2/3 yards of fabric to make scarves. She needs 3/4 yards for one scarf. How many
scarves can she make?
Answer:
6 scarves
Step-by-step explanation:
So we know that 3/4 yd. = 1 (scarf)
We have 4 2/3 material to make the scarves
=> convert to an improper fraction 4 2/3 = 14/3
=> Divide material by needed amt.
=> 14/3 / 3/4 = 14/3 x 4/3=> 14/3 x 4/3 = 56/9
56/9 = 6 2/9
But 6 2/9 is not our answer. Since we need a full amt. of scraves, we round down to our final answer of 6 scarves.
Hope this helps!
PLEASE HELP MEEE How can a company use a scatter plot to make future sale decisions
Answer:
by tracking data of how much money was made on one product in a certain amount of time
Step-by-step explanation:
Please help me solve this. With Reasoning
6 2/5 - 4 2/3
Answer:
1 and 11/15.
Step-by-step explanation:
To solve, we can separate the integers from the fractions.
(6 - 4) + (2/5 - 2/3)
= 2 + (6/15 - 10/15)
= 2 + (-4/15)
= 1 + 15/15 - 4/15
= 1 + 11/15
= 1 and 11/15
Hope this helps!
Make up an expression of your own that satisfies the following:
Must have at least: 4 terms, 1 constant, 2 variables with coefficients and appropriate
operation signs.
There are infinitely many ways to answer this as there is no one single answer to pick from.
Here is one possible answer: x^3 + 5x^2 + 7x + 12The four terms are x^3, 5x^2, 7x and 12. They are separated by the plus signs.
The constant is 12. It does not have any variable attached to it.
Terms 5x^2 and 7x have coefficients of 5 and 7 respectively.
The leading term x^3 has a coefficient of 1, but 1*x^3 = x^3, meaning it's convention to leave the 1 out. So technically x^3 does not have a coefficient directly written/shown. Instead, its more implied.
A man drove 16 mi directly east from his home, made a left turn at an intersection, and then traveled 2 mi north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?
Answer:
16. 1 miles
Step-by-step explanation:
Using Pythagorean Theorem,
a^2 + b^2 = c^2
Since the road that goes from his home to work directly is c^2...
Plug in the rest of the numbers
16^2 + 2^2 = c^2
256 + 4 = c^2
260 = c^2
The reverse square of 260 is
16. 1 miles
What is the formula for finding mean or average?
Answer:
LOOK BELOW
Step-by-step explanation:
I would not call the explanation a formula
All you have to do to solve mean or average is add all of the numbers up and divide by the total amount of numbers
so for example
0,2,4,0,2,3,2,8,6 <-------- lets find the mean/average
0+2+4+2+3+2+8+6= 27/amount of numbers
amount of numbers=9
(count the zeros too!)
27/9=3
3 is the mean or average!!!
