Hello!
Answer:
[tex]\huge\boxed{x = 4.5}[/tex]
Starting with:
5x + 4(-x - 2) = -5x + 2(x - 1) + 12
Distribute terms outside of the parenthesis:
5x + 4(-x) + 4(-2) = -5x + 2(x) + 2(-1) + 12
5x - 4x - 8 = -5x + 2x - 2 + 12
Combine like terms:
x - 8 = -3x + 10
Isolate for the "x" variable by adding 3x for both sides:
4x - 8 = 10
Add 8 to both sides:
4x = 18
Divide both sides by 4:
x = 18/4
x = 4.5
Hope this helped! :)
Answer:
[tex] \boxed{x = 4.5}[/tex]
Step-by-step explanation:
[tex] \mathrm{5x + 4( - x - 2) = - 5x + 2(x - 1) + 12}[/tex]
Distribute 4 through the parentheses
Similarly, Distribute 2 through the parentheses
[tex] \mathsf{ 5x - 4x - 8 = - 5x + 2x - 2 + 12}[/tex]
Collect like terms
[tex] \mathsf{ x - 8 = - 3x - 2 + 12}[/tex]
Calculate the sum
[tex] \mathsf{x - 8 = - 3x + 10}[/tex]
Move variable to L.H.S and change its sign
Similarly, Move constant to R.H.S and change its sign
[tex] \mathsf{ x + 3x = 10 + 8}[/tex]
Collect like terms
[tex] \mathsf{4x = 10 + 8}[/tex]
Calculate the sum
[tex] \mathsf{4x = 18}[/tex]
Divide both sides of the equation by 4
[tex] \mathsf{ \frac{4x}{4} = \frac{18}{4}} [/tex]
Calculate
[tex] \mathsf{x = 4.5}[/tex]
Hope I helped!
Best regards!
Mia’s average driving speed is 6 kilometers per hour faster than Kirk’s. In the same length of time it takes Mia to drive 558 kilometers, Kirk drives only 522 kilometers. What is Mia’s average speed?
Answer:
93km/hr
Step-by-step explanation:
Using the formula Speed = Distance/Time. From the formula we can substitute for time as shown;
Time = Distance/Speed
Let the distance and speed travelled by Mia be Dm ans Ds respectively
Distance travelled by Kirk be Km and and Ks respective.
Time taken be Mia to travel Tm = Dm/Sm
Time taken be Kirk to travel Tk = Dk/Sk
Since it takes the same length of time for both of them to travel, then Tm = Tk. Hence Dm/Sm = Dk/Sk
Given parameters
Dm = 558 kilometers
Dk = 522 kilometres
If Mia’s average driving speed is 6 kilometers per hour faster than Kirk’s, then Mia's driving speed Sm = 6 + Sk
Required
Mia’s average speed (Sm)
Since Dm/Sm = Dk/Sk
Substituting the given values to get Sk first we have;
558/6+Sk = 522/Sk
Cross multiply
558Sk = 522(6+Sk)
open the parenthesis
558Sk = 3132 + 522SK
558Sk-522Sk = 3312
36Sk =3132
Sk = 3132/36
Sk =87km/hr
SInce Sm = 6+Sk
Sm = 6+87
Sm = 93km/hr
Hence Mia's average speed is 93km/hr
El siguiente diagrama A, B, C, D, E, F denotan islas, y las líneas de unión son puentes. El hombre empieza en A y camina de isla en isla. El hombre no puede cruzar el mismo puente dos veces. Hallar el número de maneras que puede hacer su recorrido antes de almorzar.
A-B-C-D
E-F
A esta conectado a B, B a C y C a D. B está conectado a E, C esta conectado a F y hay una linea que conecta E y C
Answer:
hey good
Step-by-step explanation:
Complete the point-slope equation of the line through (8,−8) (9,8) Use exact numbers. y-8=
Answer:
y-8=16(x-9)
Step-by-step explanation:
slope m=y2-y1/x2-x1
m=8+8/9-8 ⇒ m=16
y-8=m(x-x1)
y-8=16(x-9)
The equation of the line that is passing through (8, −8) and (9, 8) will be y = 16x − 120.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).
Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
The points are given below.
(8, −8) and (9, 8)
The equation of the line that is passing through (8, −8) and (9, 8) will be given as,
(y + 8) = [(8 + 8) / (9 − 8)](x − 8)
Simplify the equation, then we have
(y + 8) = [(8 + 8) / (9 − 8)](x − 8)
(y + 8) = 16(x − 8)
y + 8 = 16x − 128
y = 16x − 120
The equation of the line that is passing through (8, −8) and (9, 8) will be y = 16x − 120.
More about the line passing through two points link is given below.
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Complex numbers
[ = square root symbol
-[-64
How would I find this?
[tex]-\sqrt{-64}=-\sqrt{8^2\cdot (-1)}-8\sqrt{-1}=-8i[/tex]
A square of side 40 cm and a rectangle of length 50 cm has the same perimeter. Which has greater area? Please write the answer with steps.
Answer:
[tex]\huge\boxed{The\ area\ of\ square\ is\ greater.}[/tex]
Step-by-step explanation:
Perimeter of Square:
P = 4(Length)
P = 4(40)
P = 160 cm
This means that the rectangle also has a perimeter of 160 cm
So, Finding the width of rectangle by Perimeter formula:
2L + 2W = Perimeter
2(50) + 2W = 160
100 + 2W = 160
Subtracting 100 to both sides
2W = 60
Dividing both sides by 2
W = 30
Now, Area of Square:
Area = Length * Length
Area = 40 * 40
Area = 1600 cm²
Area of Rectangle:
Area = Length * Width
Area = 50 * 30
Area = 1500 cm²
When we compare both of the area of the figure, we come to know that the area of square is greater.
A circle is circumscribed around a square and another circle is inscribed in the square. If the area of the square is 9 in2, what is the ratio of the circumference of the circumscribed circle to the one of the inscribed?
Answer:
√2:1
Step-by-step explanation:
First we need to know that the length of the side of the square is equal to the diameter of the inscribed circle i.e
L = di
Given the area of the square to be 9in², we can get the length of the square.
Area of a square = L²
L is the length of the square.
9 = L²
L = √9
L = 3in
Hence the length of one side of the square is 3in
This means that the diameter of the inscribed circle di is also 3in.
Circumference of a circle = π×diameter of the circle(di)
Circumference of inscribed circle = π×3
= 3π in
For the circumscribed circumscribed circle, diameter of the outer circle will be equivalent to the diagonal of the square.
To get the diagonal d0, we will apply the Pythagoras theorem.
d0² = L²+L²
d0² = 3²+3²
d0² = 9+9
d0² = 18
d0 = √18
d0 = √9×√2
d0 = 3√2 in
Hence the diameter of the circumscribed circle (d0) is 3√2 in
Circumference of the circumscribed circle = πd0
= π(3√2)
= 3√2 π in
Hence, ratio of the circumference of the circumscribed circle to the one of the inscribed will be 3√2 π/3π = √2:1
a shopkeeper allows 10% discount on his goods to make 20% profit, if he sold a watch for Rs.10170 with 13% vat, by what percent is the discount to be increased to make only 12% profit
Answer:
16% of MP
Step-by-step explanation:
Key concepts to learn :
Discount is always applied on marked price.
Profit = SP - CP
VAT is applied on Selling Price
SP = 10170/113 x 100 = 9000
If profit is 20% then :
CP = 9000/120 x 100 = 7500
MP = 9000/90 x 100 = 10000
For 12% profit, SP = 7500 x 112/100 = 8400
=> SP = 8400/10000 x 100 = 84% of MP
=> Discount = 16% of MP
Mia’s house and her aunt’s house are 15.4 inches apart on the map. If every 4 inches on the map represents 10 miles, what is the actual distance from Mia’s house to her aunt’s house, to the nearest tenth of a mile? 2.6 6.2 38.5 61.6
Answer:
38.5 miles
Step-by-step explanation:
We know that the distance between Mia's house and her aunt's house is 15.4 inches apart.
We also know that every 4 inches on the map represent 10 miles.
4 inches = 10 miles
Divide :
1 inch = 2.5 miles
Multiply the shown distance in the question by the amount of miles per inch
15.4 * 2.5
= 38.5 miles in total.
Answer:
C.)38.5
Step-by-step explanation:
It took the exam:P
Michael is drawing a card from a standard 52-card deck, which includes 4 aces: the ace of clubs, the ace of diamonds, the ace of hearts, and the ace of spades. For each trial, he drews a card, records which cards he drew, and returns it to the deck. He draws an ace 240 times
Michael is drawing a card from a standard 52-card deck, which includes 4 aces: the ace of clubs, the ace of diamonds, the ace of hearts, and the ace of spades. For each trial, he draws a card, records which cards he drew, and returns it to the deck. He draws an ace 240 times
Of the times he draws an ace, which of the following would be a good estimate for the number of times the ace drawn is the ace of hearts?
Answer:
Step-by-step explanation:
From the information:
Let consider the following variables,
assume p to be the number of times an ace was drawn,
also, q should be the number of aces and r to be the number of outcomes.
Thus ;
[tex]\mathtt{r = \dfrac{p}{q}}[/tex]
where;
p = 240
q = 4
[tex]\mathtt{r = \dfrac{240}{4}}[/tex]
r = 60
It is literally unlikely that exactly 25% of the drawings are going to be the ace of hearts, therefore, the best answer will be 60 or the value closest to 60
Rearrange the equation so x is the independent variable. y+6=5(x-4)
Answer:
x = (y + 26)/5
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out equation
y + 6 = 5(x - 4)
Step 2: Distribute
y + 6 = 5x - 20
Step 3: Isolate x
y + 26 = 5x
Step 4: Isolate variable x
(y + 26)/5 = x
Step 5: Rewrite
x = (y + 26)/5
Answer:
y = 5x - 26
Step-by-step explanation:
Since x is the independent variable, you have to solve for y.
y + 6 = 5(x-4)
Now distribute:
y + 6 = 5x - 20
subtract the 6 from both sides
y + 6 - 6 = 5x - 20 - 6
y = 5x - 26
A boy is twice as tall as his little sister and he is 30 cm shorter than his father. The
combined height of these three family members is 3.8m.Write an appropriate
equation, using h' as the sister's height and use this to find the boy's height in cm.
Boy = x
His Sister = y
Father = z
x = 2*y
y = x/2
x = z-30 or z = x+30
3.8 m = 380 cm
x+y+z = 380
x + x/2 + x+30 = 380
multiply by 2
2x +x + 2x +60 = 760
5x = 700
x = 140 cm
y = x/2
= 140 /2 = 70 cm
z = x+30
= 140 + 30 = 170 cm
There
x (Boy) = 140 cm
y (His Sister) = 70 cm
z (Father) = 170 cm
Using an appropriate equation, the boy's height is 140 cm.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Let Boy = x and His Sister = y
Father = z
So, x = 2*y
y = x/2
x = z-30 or z = x+30
Now, substitute
3.8 m = 380 cm
Equation form;
x+y+z = 380
x + x/2 + x+30 = 380
then multiply by 2
2x +x + 2x +60 = 760
5x = 700
x = 140 cm
Thus,
y = x/2 = 140 /2 = 70 cm
z = x+30 = 140 + 30 = 170 cm
There are x (Boy) = 140 cm
y (His Sister) = 70 cm
z (Father) = 170 cm
Hence, Using an appropriate equation, the boy's height is 140 cm.
Learn more about equations here;
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please help me.. thanks if you do
Answer:
B
Step-by-step explanation:
We can graph the line using the y and x-intercepts. To find the y-intercept, we substitute x = 0 into y = -2x - 2 so the y-intercept is (0, -2). To find the x-intercept, we substitute y = 0 into y = -2x - 2 so the x-intercept is (-1, 0). The line that goes through both of these points is line B.
Answer:
B.
Step-by-step explanation:
Here's a picture of me graphing it:
Sorry for dark mode :/
Newly planted seedlings approximately double their weight every week. If a seedling weighing 5 grams is planted at time t=0 weeks, which equation best describes its weight, W, during the first few weeks of its life?
Answer:
[tex]W(t)=5(2^t)[/tex]
Step-by-step explanation:
Given that the Newly planted seedlings approximately double their weight every week and a seedling weighing 5 grams is planted at time t = 0 weeks. This represent an exponential function with an equation in the form:
[tex]W(t)=ab^t[/tex].
W(t) is the weight in t weeks, t is the weeks and a is the weight when t = 0. At t = 0, W = 5 g:
[tex]W(t)=ab^t\\W(0)=ab^0\\5=ab^0\\a=5[/tex]
Since the weight double every week, b = 2. The exponential function is given as:
[tex]W(t)=ab^t\\\\W(t)=5(2^t)[/tex]
The city soccer club has thirteen new members and fifty-two returning members. If they break up into teams of eleven players, how many complete teams would there be?
Answer:
5
Step-by-step explanation:
The easiest way to do this is to add the new members to the old and then divide by 11. Ignore the remainder.
13 + 52 = 65
65 / 11 = 5 with 10 left over. Ignore the 10. That's not a complete team.
The answer is 5
Please I need your help. Answer the questions following the grammar rules.
1. How much money do you spend a month on shopping?
2. Who do you normally go shopping with?
3. Do you enjoy shopping? Why? Why not?
4. Do you buy things on the internet? Why? Why not?
Answer:
Question 1: $100
Question 2: Myself
Question 3: Yes, because you get to buy things you might have been wanting, or saving up for.
Question 4: Yes, because its an easier way of shopping, and gets sent straight to your home.
Step-by-step explanation:
Hope this helps.
HELP PLSSSSSSSS ( needed 20 characters)
Answer:
A
Step-by-step explanation:
It have the same sides!
on a map, the distance between jacksonville FL and tallahasse FL is about 5 inches. According to the scale, 1 inch represents 25 miles. About how far apart are these two cities?
Will has 2 quarters, 6 dimes, some nickels, and 4 pennies. If the ratio of pennies to the total number of coins he has is 1:5, how many nickels are there?
Answer:
8 nickels
Step-by-step explanation:
Let n be the number of nickels.
4: (2+ 6 + 4 + n) = 1:5
4÷(12 + n) = 1÷5
4 x 5 = 1 x (12 + n)
20 = 12 + n
n = 8
Use the drop-down menus to label the graph according to its type. On a coordinate plane, a graph has two straight lines that connect at (0, 0). One line has a positive slope from (0, 0) going through (3, 2) and the other has a negative slope from (0,0) going through (4, negative 3). The graph above:
The point of intersection of the graph of y = (2/3)x and y = (-3/4)x is at point (0, 0).
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The straight line passing through (0, 0) and (3, 2) have an equation of y = (2/3)x while the straight line passing through (0, 0) and (4, -3) have an equation of y = (-3/4)x
The point of intersection of the graph of y = (2/3)x and y = (-3/4)x is at point (0, 0).
Find out more on equation at: https://brainly.com/question/2972832
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Answer:
Relation (But not a function) Your welcome.
Step-by-step explanation:
NEED HELP..... Select the polynomial that is a perfect square trinomial. 36x^2 − 4x + 16 16x^2 − 8x + 36 25x^2 + 9x + 4 4x^2 + 20x + 25
===============================================
Explanation:
Perfect square trinomials are in the form (a+b)^2 = a^2+2ab+b^2
So the first and last terms must be perfect squares. The middle term is twice that of the square roots of each first and last term.
Choice D fits the description because 4x^2 = (2x)^2 is the first term, so a = 2x and 25 = 5^2 is the last term meaning b = 5. Note how 2ab = 2*2x*5 = 20x is the middle term.
-------------
(a+b)^2 = a^2+2ab+b^2
(2x+5)^2 = (2x)^2+2*2x*5+5^2
(2x+5)^2 = 4x^2 + 20x + 25
Answer:
(2x+5)² or (2x+5)(2x+5)
Step-by-step explanation:
4x²+ 20x + 25
(2x ) (2x ) first step 2x*2x=4x²
(2x + 5 )(2x + 5 ) the constant sign is plus so it can be ( minus × minus=plus OR plus×plus=plus) look at the middle value it is positive so the two signs are positive or plus sign.
(2x+5)²
-8+4x-12=-4(2x-8) help me plz
Answer:
x = 13/3Step-by-step explanation:
[tex]-8+4x-12=-4\left(2x-8\right)\\\\\mathrm{Group\:like\:terms}\\\\\mathrm{Subtract\:the\:numbers:}\:-8-12=-20\\\\4x-20=-4\left(2x-8\right)\\\\\mathrm{Expand\:}-4\left(2x-8\right):\quad -8x+32\\4x-20=-8x+32\\\\\mathrm{Add\:}20\mathrm{\:to\:both\:sides}\\4x-20+20=-8x+32+20\\\\Simplify\\\\4x=-8x+52\\\\\mathrm{Add\:}8x\mathrm{\:to\:both\:sides}\\\\4x+8x=-8x+52+8x\\\\\mathrm{Simplify}\\\\12x=52\\\\\mathrm{Divide\:both\:sides\:by\:}12\\\\\frac{12x}{12}=\frac{52}{12}\\\\x=\frac{13}{3}[/tex]
Answer:
Step-by-step explanation:
-8+4x-12 =-8x+32
4x+8x=32+8+12
12x=52
x=52\12
x=41.3
Last month, Seth made money by selling stocks. His investment income was $401. This month, Seth's investment income is - $261. what does this mean
Answer:
This means that because of this month Seth's investment income has decreased by 261, and now is $140.
401-261=140
Answer:Seth lost money
Step-by-step explanation:
Since the investment income was $401
And now is -261 meaning that Seth lost money last month
Katherine's class is selling raffle tickets for $3 to raise money for charity. Katherine's class raised $504. Which equation would you use to find the number of tickets sold?
Answer:
3T=504
Step-by-step explanation:
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
What is the value of m that makes the equation true? 18m- 2+ 7m- 8= -60
Answer:
m = -2
Step-by-step explanation:
First, let's move all variables to one side of the equation. (Don't forget to change the signs when you move the numbers to the other side.)
18m + 7m = -60 + 2 + 8
Now we simplify to get this:
25m = -50
Now we divide -50 by 25 which gets us -2.
Therefore, m = -2
Hope this helps!
20 POINTS AND BRAINLIEST!! Which of the following statements can be supported by the evidence shown in the graph?
A. The line best fit shows a positive correlation between month number and minutes
B. The line of best fits shows a negative correlation between the number of months and the number of minutes
C. The line of best fits shows no correlation between the month number and the number of minutes
Answer:
B. The line of best fits shows a negative correlation between the number of months and the number of minutes
Step-by-step explanation:
In a scatter plot, when the data points are clustered along the line of best fit, it shows a trend, and it implies there's a correlation between the x-variable and the y-varisble.
Also, when the line of best fit slopes upward, from your left to your far right, it shows a positive correlation between the variables on the x-axis and y-axis.
On the other hand, if the line of best fit slopes downwards, from your left down to your right, this shows a negative correlation.
Thus, considering the line of best fit in the question, the line of best fit shows a negative correlation between the number of months and the number of minutes. The line of best fit slopes downwards, from your left to your right.
This shows that, as month number increases, number of minutes decreases.
PLEASE ANSWER QUICKLY ASAP
Answer:
67°
Step-by-step explanation:
● cos<PQR = adjacent/hypotenus
● cos<PQR = 5/13
● cos< PQR = 0.384
Using a calculator:
● cos^-1(0.384) = 67°
● <PQR = 67°
Father's age is 3 times the sum of ages of his two children. After 5 years his age will be twice the sum of ages of two children. Find the age of father.
Answer:
45 is the father's age
Step-by-step explanation:
what is the expression of 28 19/100
Answer:
the mixed form is 28 [tex]19/100[/tex]
the improper form is ( 28 x 100) = 19 / 100
2819 / 00
| Find the quadratic polynomial whose
Sum and products of zeros are 21/8 and 5/16
Answer:
[tex]16x^{2} -42x+5[/tex]
Step-by-step explanation:
Sum of its zeroes=[tex]\alpha +\beta =\frac{21}{8} \\[/tex]
Product of its zeroes=[tex]\alpha \beta[/tex]=[tex]\frac{5}{16}[/tex]
Formula to form a quadratic polynomial:
[tex]p(x)=k[x^{2} -(\alpha +\beta )x+\alpha \beta ][/tex]
p(x)=[tex]k[x^{2} -(\frac{21}{8} )x+\frac{5}{16}][/tex]
p(x)=[tex]16[x^{2} -(\frac{21}{8} )x+\frac{5}{16}][/tex]
p(x)=[tex][16x^{2} -42x+5][/tex]
The quadratic polyniomial is [tex]16x^{2}-42x+5[/tex]
Simplify 6.920
A.-1
B.0
C.1
D.6.92
I'm pretty sure the answer is 6.92 cause when you simplify it you'll get that exact answer
Answer:
D 6.92
Step-by-step explanation:
6.920 and 6.92 are equal
