1.Distribute
-30=5(x+1). x
[tex]-30=5x^{2}+5x[/tex]
2. Move terms to the left side
[tex]-30=5x^{2} +5x[/tex]
[tex]-30-(5x^{2} +5x)=0[/tex]
3. Rearrange terms
[tex]-30-5x^{2} -5x=0[/tex]
[tex]-5x^{2} -5x-30=0[/tex]
Hope this helps! Sorry if I'm wrong
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{ORIGINAL EQUATION}\downarrow[/tex]
[tex]\large\textsf{ -30 = 5(x + 1)}[/tex]
[tex]\large\text{TURN the EQUATION}[/tex]
[tex]\large\textsf{5(x + 1) = -30}[/tex]
[tex]\large\text{DISTRIBUTE \textsf{5} WITHIN the PARENTHESES}[/tex]
[tex]\large\textsf{5(x) + 5(1) = -30}[/tex]
[tex]\large\textsf{5(x) = \bf 5x}\\\large\textsf{5(1) = 5}[/tex]
[tex]\rightarrow\large\textsf{5x + 5 = -30}[/tex]
[tex]\large\text{NEW EQUATION: \textsf{5x + 5 = -30}}[/tex]
[tex]\large\text{SUBTRACT \textsf{5} to BOTH SIDES}[/tex]
[tex]\large\textsf{5x + 5 - 5 = -30 - 5}[/tex]
[tex]\large\text{CANCEL out: \textsf{5 - 5} because that gives you \textsf{0}}[/tex]
[tex]\large\text{KEEP: \textsf{-30 - 5} because that helps you solve for your \textsf{x-value}}[/tex]
[tex]\large\textsf{-30 - 5 = \bf -35}[/tex]
[tex]\large\text{NEW EQUATION: \textsf{5x = -35}}[/tex]
[tex]\large\text{DIVIDE \textsf{5} to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{5x}{5}= \dfrac{-35}{5}}[/tex]
[tex]\large\text{CANCEL out: }\mathsf{\dfrac{5x}{5}}\large\text{ because that gives you the value of \textsf{1}}[/tex]
[tex]\large\text{KEEP: }\mathsf{\dfrac{-35}{5}}\large\text{ gives you the \textsf{x-value}}[/tex]
[tex]\large\textsf{x = }\mathsf{\dfrac{-35}{5}}[/tex]
[tex]\large\text{SIMPLIFY ABOVE \& YOU HAVE YOUR x-value}[/tex]
[tex]\boxed{\boxed{\large\textsf{ANSWER: \huge \bf x = -7}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Find the equation of a circle that is centered at the origin and is tangent to the circle (x−6)^2+(y−8)^2=25
Center: ( 6 , 8 )
Radius: 5
Answer:
[tex] x^2 +y^2 = 25 [/tex]
Step-by-step explanation:
Center of the required circle = (0, 0)
Center of the given circle = (6, 8)
Radius of the given circle = 5 units
Distance between the centers of both the circles
[tex] =\sqrt{(6-0)^2 +(8-0)^2} [/tex]
[tex] =\sqrt{(6)^2 +(8)^2} [/tex]
[tex] =\sqrt{36 +64} [/tex]
[tex] =\sqrt{100} [/tex]
[tex] =10\: units [/tex]
Since, required circle is tangent to the given circle with radius 5 units.
Therefore,
Radius of required circle = 10 - 5 = 5 units
Now, Equation of required circle can be obtained as:
[tex] (x - 0)^2 +(y - 0)^2 = 5^2 [/tex]
[tex] (x)^2 +(y)^2 = 25 [/tex]
[tex] x^2 +y^2 = 25 [/tex]
Simplify (5m - 4)2 using the square of a binomial formula.
A) 5m2 - 20m - 4
B) 25m2 – 40m + 16
C) 25m2 + 40m + 16
D) 5m2 – 40m + 4
Answer:
[tex]25m^{2} -40m+16[/tex]
Step-by-step explanation:
Rewrite (5m−4)^2 as (5m−4)(5m−4).
Expand (5m−4)(5m−4) using the FOIL Method.
[tex]25m^{2} -40m+16[/tex]
Find the measure of angle QZT.
========================================================
Explanation:
Minor arc QV is 80 degrees because it adds to minor arc VU = 100 to get 80+100 = 180. Note how angle QPU = 180, since it's a straight line and QU is a diameter of the circle.
Add up the minor arcs
TUUVVQto get: 44+100+80 = 224
This means arc TUQ is 224 degrees. Inscribed angle QZT subtends arc TUQ. Use the inscribed angle theorem to say that the inscribed angle is half of the arc it cuts off.
angle QZT = (arc TUQ)/2
angle QZT = 224/2
angle QZT = 112 degrees
Question 3 (4 marks)
A certain retail outlet found that 40% of all customers walking into their store will buy at least one item on
that occasion. Customers make a purchase independently from one another. Calculate the following
probabilities correct to 4 decimal places.
3.1. (2 marks) What is the probability that one or two out of the next four customers will make a purchase?
3.2. (2 marks) What is the probability that at least one out of the next four customers do not make a purchase?
Answer:
3.1 0.6912 = 69.12% probability that one or two out of the next four customers will make a purchase.
3.2 0.9744 = 97.44% probability that at least one out of the next four customers do not make a purchase
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they make a purchase, or they do not. The probability of a customer making a purchase is independent of any other customer. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
40% of all customers walking into their store will buy at least one item on that occasion.
This means that [tex]p = 0.4[/tex]
4 customers:
This means that [tex]n = 4[/tex]
3.1 What is the probability that one or two out of the next four customers will make a purchase?
This is:
[tex]P(1 \leq X \leq 2) = P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{4,1}.(0.4)^{1}.(0.6)^{3} = 0.3456[/tex]
[tex]P(X = 2) = C_{4,2}.(0.4)^{2}.(0.6)^{2} = 0.3456[/tex]
So
[tex]P(1 \leq X \leq 2) = P(X = 1) + P(X = 2) = 0.3456 + 0.3456 = 0.6912[/tex]
0.6912 = 69.12% probability that one or two out of the next four customers will make a purchase.
3.2. What is the probability that at least one out of the next four customers do not make a purchase?
This is:
[tex]P(X \leq 4) = 1 - P(X = 4)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{4,4}.(0.4)^{4}.(0.6)^{0} = 0.0256[/tex]
[tex]P(X \leq 4) = 1 - P(X = 4) = 1 - 0.0256 = 0.9744[/tex]
0.9744 = 97.44% probability that at least one out of the next four customers do not make a purchase
Name the three labeled segments that are parallel to EF
Answer:
Answer D
Step-by-step explanation:
The answer here is D since all of the other ones have at least one option that is perpendicular to segment EF.
What is 17% of 13.00
Answer:
The answer is 2.21
Step-by-step explanation:
Answer:
2.21
Step-by-step explanation:
13(.17)
The image of the point (-5, 1) under a translation is (-6,3). Find the
coordinates of the image of the point (2, -3) under the same translation.
Answer:
The coordinates are (1,-1).
Step-by-step explanation:
The image of the point (-5, 1) under a translation is (-6,3).
Point x was -5 and now is -6, and y was 1 and now is 3. Thus, the transaction rule is:
(x,y) -> (x - 1, y + 2)
Find the coordinates of the image of the point (2, -3) under the same translation.
(2,-3) -> (2-1, -3 + 2) = (1,-1)
The coordinates are (1,-1).
A bag contains 2 red marbles and 3 blue marbles. What is the probability of drawing a red marble, keeping it, and drawing another red marble?
Answer:
Step-by-step explanation:
the first marble has a probability of 2/5
the second marble has a probability of 1/4
P(r=2) = 2/5 * 1/4 = 2/20 = 1/10
Answer:
2/5, 1/4
Step-by-step explanation:
The total amount of marbles before drawing a marble is 2+3=5. There are 2 red marbles. Thus, the theoretical probability of drawing a red marble from the bag is 2/5.
If you keep the red marble, there are now 4 total marbles in the bag. There is also only 1 remaining red marble. Thus, the theoretical probability of drawing a red marble is now 1/4.
Please help me with this question!:))
Answer:
6
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
the two lines mean absolute value. The absolute value of a number is just the number positive. For example the absolute value of -5 is 5 and the absolute value of 5 is 5. So on C, when you plug in -6, you get the absolute value of -6 which is 6. 6 is not greater than 6
if that makes sense :)
QUESTIONS
A salt is packed in jars containing 32 grams. How many jars can be filled from 15kg of the salt? [
Answer:
Number of jars can be filled from 15kg of the salt = 468 or 469 jars (Approx.)
Step-by-step explanation:
Given:
Amount of salt containing in jar = 32 gram
Total amount of salt in jar = 15 kg
Find:
Number of jars can be filled from 15kg of the salt
Computation:
Total amount of salt in jar = 15 kg
Total amount of salt in jar (in grams) = 15 x 1000 g
Total amount of salt in jar (in grams) = 15,000 g
Number of jars can be filled from 15kg of the salt = Total amount of salt in jar (in grams) / Amount of salt containing in jar
Number of jars can be filled from 15kg of the salt = 15,000 / 32
Number of jars can be filled from 15kg of the salt = 468.75
Number of jars can be filled from 15kg of the salt = 468 or 469 jars (Approx.)
plz help 5th grade work
Answer:
I don't see where the question is...
Step-by-step explanation:
Which equation has a graph that lies entirely above the x-axis?
Answer: c
Step-by-step explanation:
y=(x-7)^2+7
There were 3 chihuahuas at the dog park last Saturday, along with 9 other dogs. Considering this data, how many of the next 20 dogs to arrive at the park next Saturday should you expect to be chihuahuas?
Answer:
5
Step-by-step explanation:
Since there are 3 chihuahuas out of 12 dogs IN TOTAL (which includes the 9 other dogs), the ratio is 1:4, or 1/4.
Assuming this ratio is consistent, (1/4)*20 is 5.
In conclusion, you can expect there to be 5 chihuahuas out of the next 20 dogs to arrive at the park.
Hope it helped, and have a beautiful day/night! <3
PLZ HELP ME , PLZ HELP AND PLEASE, PLZ HELP JUST PLZ HELP THANK YOU FOR YOUR TIME
Use the box plot to explain what you know about the spread of this data set.
Answer:
Step-by-step explanation:I found the answer only/3fcEdSx this web[tex]^{}[/tex]site. It seems correct! Link Below!
bit.[tex]^{}[/tex]
Answer:
The range of the data is 75 - 21 = 54 (the difference between the two "whiskers"
The median of the data is 50 (middle line inside the box)
The first quartile "Q1" is 34 (left edge of the box). This means that 25% of the values are < 34.
The third quartile "Q3" is 69 (right edge of the box). This means that 25% of the values are > 69.
The interquartile range is 69-34 = 35. (subtracting Q3 - Q1) 50% of the data falls in this range, from 34 -69. 50% of the data falls in the box.
Let me know if you have questions about this answer. I'm happy to help.
Which group of numbers could be the measures of the sides of a right
triangle?
Answer:
it's B. i individually solved all of them using the pythagorean theorem.
Step-by-step explanation:
"The Pythagorean theorem states that, in a right triangle, the square of the length of the hypotenuse (the side across from the right angle) is equal to the sum of the squares of the other two sides. So if the length of the hypotenuse is c and the lengths of the other two sides are a and b, then c^2 = a^2 + b^2"
sqrt61=6+5
square everything on both sides and ur left with
61=36+25
61=50+11
61=61
boom
100 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answer:
15
Step-by-step explanation:
To find the answer you multiply the length by the width.
5×3=15
Find the area of the figure
area: units2
Answer:
24 units²
Step-by-step explanation:
Top triangle: 1/2x2x4=4
Main rectangle: 2x4=8
Bottom trapezoid: 4+8=12. 12÷2=6. 6x2=12
4+8+12=24
Que sucede cuando dividimos un numero entre si mismo
Answer:
no pasa nada
Step-by-step explanation:
espero que eso te ayude:)
Answer:
Cualquier número dividido entre si mismo da como resultado 1
Rehan wants to add a fence along his triangular garden whose sides are 14m,16m and 20m. What will be the length of fencing material? Give your answer in cm.
Answer:
5000cm
Step-by-step explanation:
14 + 16 + 20 = 50m
50m x 100cm/m = 5000cm
Find the surface area of the rectangular prism
It takes 0.25 cup of sugar to make a batch of chocolate chip cookies. I have 5.50 cups of sugar. How many batches of cookies can I make?
Answer:
22
Step-by-step explanation:
5.50/0.25 = 22
Answer:
22
Step-by-step explanation:
5.50 cups of sugar divided by the .25 cups needed for each batch gives you 22 :)
la
You spend some time in the kitchen making sure the recipe is just right for
the cooking show. You spend 2 3/4 hours baking and half of an hour
cleaning up the kitchen. How much time were you in the kitchen?
solve this inequality 2(4x+1)<3(2x-3)
Answer:
x<-11/2
Step-by-step explanation:
but don't trust me too much bestie
The college bookstore tells prospective students that the average cost of its textbooks is $92 per book, with a standard deviation of $15. The engineering students think that the average cost of their books is higher than the average for all students. To test the bookstore’s claim against their alternative, the engineering students collect a random sample of size 45, and calculate x = $97.34.
Grade: 5 4 3 2 1
Communication strong ←− − − − − − −→ weak ×2
Required:
Conduct a hypothesis test with α = 0.05 to see if the students’ claim is supported. Use the classical approach.
Answer:
Following are the solution to the given question:
Step-by-step explanation:
Please find the attached file for the solution.
Please help me I would appreciate it a lot
Answer:
Juan can consume 2.22 calories per day
Step-by-step explanation:
[tex]68.820 \div 31 \: day \: month \: \\ \\ = 2.22[/tex]
football team scores 42 points in 3
games. Find the unit rate
Answer:
14
Step-by-step explanation: divide..
Answer:
14 points per game
Step-by-step explanation:
42/3 = 14
can someone help me find x
Answer:
x = 5
Step-by-step explanation:
Since this shape is a quadrilateral, the sum of the interior angles is 360.
Equation:
81 + 20x - 16 + 15x + 30 + 16x + 10 = 360
51x + 105 = 360
51x = 360 - 105
51x = 255
x = 5
What is the solution 5x-15=-25
Answer:
x= -2
Step-by-step explanation:
MARK AS BRAINLIEST!!
Answer: -2
Step-by-step explanation: -2 times 5 is -10. -10-15=-25
Need help with using the graph to find the numbers
Assignment is about evaluating composition of functions from graphs anything helps
Answer:
f(2) = -3
g(-3) = -5
Step-by-step explanation:
----------------------
A gallon of gas costs $3.05 per gallon. Joey's car gets 35 miles per gallon on the highway and 27 miles per gallon in the city. Using the
highway, Joey drives at an average speed of 54 miles per hour, and it takes him 0.5 hours to get to work. The highway has one $1.25 toll.
Using a city street route, Joey drives at an average speed of 36 miles per hour, and it takes him 1 hour to get to work.
Which quantities would be used to determine the total cost for Joey to drive to work using the highway? Choose all that apply. A. 0.5 hours B. 1 hour C. $1.25 per car D. $3.05 per gallon E. 27 miles per gallon F. 35 miles per gallon G. 36 miles per hour H. 54 miles per hour
Answer:
The quantities that would be used to determine the total cost for Joey to derive to work using the highway are:
A. 0.5 hours
C. $1.25 per car
D. $3.05 per gallon
F. 35 miles per gallon
H. 54 miles per hour
Step-by-step explanation:
Cost of a gallon of gas = $3.05
Distance travelled per gallon on the highway = 35 miles
Distance travelled per gallon in the city = 27 miles
Joey's average speed using the highway = 54 miles per hour
Number of hours to get to work using the highway = 0.5 hours
Toll on the highway = $1.25
Joey's average speed using the city street route = 36 miles per hour
Number of hours to get to work using the city street route = 1 hour
Relevant data for highway driving total costs:
Cost of a gallon of gas = $3.05
Distance travelled per gallon on the highway = 35 miles
Joey's average speed using the highway = 54 miles per hour
Number of hours to get to work using the highway = 0.5 hours
Toll on the highway = $1.25
Total costs for using the highway = $1.25 + ($3.05/35 * 54 * 0.5) = $3.60
Answer:
A, B, D, F, H
Step-by-step explanation: