[tex](x+7)^2-49=0\qquad\text{add 49 to both sides}\\\\(x+7)^2=49\iff x+7=\pm\sqrt{49}\\\\x+7=-7\ or\ x+7=7\qquad\text{subtract 7 from both sides}\\\\\boxed{x=-14\ or\ x=0}\\\\Answer:\\\\smaller\ x=-14\\larger\ x=0[/tex]
Answer:
x = -14 and x=0
Step-by-step explanation:
(x+7)^2-49=0
Add 49 to both sides
(x+7)^2-49+49=0+49
(x+7)^2 = 49
Take the square root of each side
sqrt((x+7)^2) = ±sqrt(49)
(x+7) = ±sqrt(49)
x+7 = ±7
Subtract 7 from each side to isolate x
x+7-7 = -7±7
x = -7±7
x = -7+7 and x = -7-7
x = 0 and x=-14
The value of y varies directly as x, and y is 10 when x is 5. What is the value of y when x is 4?
Answer:
8.
Step-by-step explanation:
As seen in the pattern y seems to be two times x so 4 x 2 = 8.
Hope that helps
is y = |x + 3| a linear function yes or noO
Answer:
Yes
Step-by-step explanation:
Because it passes vertical line test.
Yes, because y = x + 3 is a first degree function which is a linear function. Just ignore the absolute value.
Which expression is equivalent to (2x^4 y)^3 PLEASE HURRY!!!
Answer:
8x¹²y³
Step-by-step explanation:
(2x⁴y)³ Cube everything inside parentheses.
= 2² × (x⁴)³ × y³
= 8x¹²y³
give an example of linear equation that is parrell to the y-axis
Answer: x = 5
You can pick any number you want, as long as it's not zero. The equation x = 5 has all points on this line that have an x coordinate of 5. The y coordinate can be anything you want
Example points on this line are: (5,1) and (5,2)
Note: this is a vertical line with the slope undefined. There is no y intercept. This is not a function because it fails the vertical line test.
I need help with number 3, i’m stuck!
Gina can buy a 5-pound bag of apples that cost $4.50, or she can buy them by the pound for $0.85 or pound. Which of these best explains the least expensive way for Gino buy 5 pounds of apples?
A. Gina should buy the bag of apples for $4.50 because the unit price per pound is less than the by-the-pound price
B. Gina should buy the bag of apples for $4.50 because the unit price per pound is greater than the by-the-pound-price
C. Gina should buy apples by the pound because the unit price per pound for the bag of apples is less than the by-the-pound-price
D. Gina should buy apples by the pound because the unit price per pound for the bag of apples is greater than the by-the-pound price
the function y=3.28x converts length from x meters to y feet Im really stuck im not real sure what to do
Step-by-step explanation: So this one can be a little confusing, but I think I can help. You see if 'y'= number of feet and 'x'= number of meters then y=3.28x is a way for you to figure out how many feet are constant to every meter.
Look at it more like, Number of Feet= 3.28 times the number of meters.
If you want to figure out many feet are constant to let's say...2 meters, then you would replace the 'x' variable with 2 and multiply it by 3.28.
It would look something like this:
y=3.28(2)
y= 6.56
Thus, every 1 feet there are 6.56 meters, or 6.56 meters equals 1 foot.
Hope this helps a little, tell me if you need anymore help with this!
Find the greatest common factor of these three expressions. 5v2 , 14v4 , and 35
Question
Find the greatest common factor of these three expressions. 5v2 , 14v4 , and 35
Answer:
1Step-by-step explanation:
assuming that 5v2 is 5², and 14v4 is 14^4
5² = 25
14^4 = 38416
35 = 35
The factors of 25 are: 1, 5, 25
The factors of 35 are: 1, 5, 7, 35
The factors of 38416 are: 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 343, 392, 686, 784, 1372, 2401, 2744, 4802, 5488, 9604, 19208, 38416
--------------
the greatest common factor is 1
Given: m || n , <1 is congruent to <3
Prove: p || q
Answer:
A= Angle 1 congruent to angle 2
B= Transitive Property
C= Converse Corresponding angles theorem
Step-by-step explanation:
The basic measure of mass in the metric system is called
Answer:
Grams.
Step-by-step explanation:
Answer:
THE GRAM
Step-by-step explanation:
Question number 1: 5/8 (16b+24) -1/2b
Question number 2: 3/4 (16/64 + 12a) -9a
Answer:
Problem 1. (19/2)b + 15
Problem 2. 3/16
Step-by-step explanation:
Question number 1
5/8 (16b+24) -1/2b =
= (5/8) * (16/1) * b + (5/8) * 24 - (1/2)b
= 10b + 15 - (1/2)b
= (20/2)b - (1/2)b + 15
= (19/2)b + 15
Question number 2
3/4 (16/64 + 12a) -9a =
= (3/4) * (16/64) + (3/4) * 12a - 9a
= (3 * 16)(4 * 64) + (3/4) * (12/1) * a - 9a
= (3 * 1)(4 * 4) + (3 * 12)/(4 * 1) * a - 9a
= 3/16 + (3 * 3)/(1 * 1) * a - 9a
= 3/16 + 9a - 9a
= 3/16
Jason's grandparents gave him $500 for his 16 birthday. He put the money in the bark and decided to withdrow $35 each week. I need help with part b, how do I do the table??
Answer:
X Y
0 $500
1 $465
2 $430
3 $395
4 $360
5 $325
6 $290
Step-by-step explanation:
You subtract 35 from the first Y.
PLS HELP If g(n) varies inversely with n and g(n) = 6 when n = 2, find the value of n when g(n) = 1.5.
Answer:
g(2)=1.5. Which would be three.
Step-by-step explanation:
You would just plug in n=2 into the equation and then divide it out.
The value of n, when g(n) is 1.5, given that g(n), varies inversely with n and equals 6 when n is 2, we first find the constant of variation k = 12 and then divide k by 1.5 to get n = 8.
If g(n) varies inversely with n, the relationship between g(n) and n can be expressed as g(n) = k/n, where k is a constant. When g(n) = 6 and n = 2, we can find the constant k by multiplying 6 and 2 to get k = 12.
To find the value of n when g(n) = 1.5, we can set up the equation 1.5 = k/n. Using our previously found constant k (12), we substitute it into the equation to get 1.5 = 12/n. Solving for n, we multiply both sides of the equation by n and then divide both sides by 1.5 to get n = 12/1.5, which simplifies to n = 8.
Suppose a railroad rail is 2 kilometers and it expands on a hot day by 19 centimeters in length. Approximately how many meters would the center of the rail rise above the ground?
Answer:
rail rise approximately 0.19 m above the ground
Step-by-step explanation:
as we know that
1m=100cm
and 1cm=[tex]\frac{1}{100}[/tex] m
similarly
19cm=[tex]\frac{19}{100}[/tex]m
19cm=0.19m
rail rise approximately 0.19 m above the ground
The calculated sagitta is approximately 0 meters, considering the very small expansion compared to the original length of the rail.
Assuming the rail forms an arc of a circle with the expansion, the rail's ends remain on the ground, and only the center rises.
Consider the original length of the rail as the chord of the circle, and the expanded length as the arc of the circle. The rise of the rail's center is the sagitta (height) of the arc. The length of the chord (C) is 2000 meters, and the expansion (e) is 0.19 meters (19 centimeters). The length of the arc (A) is C + e, which equals 2000.19 meters.
The formula for the sagitta when the arc is very close to the chord in length is given by:
Sagitta (s) ≈ (e² / (8 * C)) + (C² / (8 * A))
Plugging in the values:
s ≈ (0.19² / (8 * 2000)) + (2000² / (8 * 2000.19))
After calculation:
s ≈ 2.25 × 10⁻³ m + 250 m
s ≈ 250.00225 m
Since we are dealing with a very small expansion relative to the size of the rail, the sagitta (height increase of the center of the rail) is very close to 0 meters.
ANSWER QUESTION 2 and 3 FOR 25 POINTS AND BRAINLIEST!!
Answer:
A and C
Step-by-step explanation:
It is certainly not D. She holds no hope for improvement, not really. She is sad that there has not been anything good happening and realistic enough to know that things are going from bad to worse.
C might be possible, but it doesn't really sound like she's blaming anyone, not in that passage.
B There's too much dispair in what she is saying to believe that a miracle will happen.
A would be my choice.
Three
Pinnacle means highest,not lowest. Answer C
The regular price of a newly released video game is $32. LeBron buys the video game when its on sale for 30% off the regular price. If sales tax is 10%, how much does LeBron pay for the video game.
Answer:
$24.64
Step-by-step explanation:
30% off is equal to multiplying by 0.7
(32*0.7)*1.1
Sales tax increases the price and so you multiply by 1.1 (equal to increasing 10%)
32*0.7*1.1=24.64
He will pay $24.64 for the game.
Determine the slope for the following:
-6x-2y=12
Answer:
New Slope is -3
Step-by-step explanation:
First we will need to simplify the equation to make it easier. so since all numbers are divisible by 2 so instead of -6x-2y=12 the new equation will be -3x-y=6. then you are gonna solve for y and the answer is -y=3x+6. so then you will divide by -1 to make y positive. then Your Final Equation is y=-3x-6
Your new slope is -3
A line passes through the points (-10,-5) and (20,10) what is the equation of the line A. y=5x B.Y=2x C.1/2 x Dy=1/5 x
Answer:
C. y = ½x
Step-by-step explanation:
Step 1. Find the slope of the line
The general equation for a straight line is
y = mx + b
The slope m is
m =(y₂ -y₁)/(x₂/x₁)
Your points are (-10, -5) and (20, 10).
m = [10 – (-5)]/[20 – (-10)] Remove inner parentheses
m = (10+5)/(20 + 10)
m = 15/30
m = ½
===============
Step 2. Find the equation of the line
Substitute the point (20, 10) into the general equation.
10 = ½×20 + b
10 = 10 + b
b = 0
The equation of the line is y = ½x.
The graph shows your line passing through your two points with a slope
m = ½ and a y-intercept at (0, 0).
ABC = PQR given ABC = PQR, m<B = 3v + 4, and m<Q = 8v vind m<B ans m<Qm
Answer:
v = 4/5 or 0.8
Step-by-step explanation:
Givens
These two corresponding parts are equal
<B = 3v + 4<Q = 8vEquation
3v + 4 = 8v Subtract 3v from both sides3v - 3v + 4 = 8v - 3v Combine4 = 5v Divide by 54/5 = 5v/5 DivideAnswer
v = 4/5 or v = 0.8
rhianna is planning to redecorator her bedroom with paint and new pillows.she has a buget of $200.the cans of paint she wants cost $32 each and thows pillows are $30 each.Which inquality can rhianna use to find out how many cans of paint,x,and pillow,y,she can afford?
Step-by-step explanation Eeė
Simplify: 1 ( x − 5 ) − 1 3 ( − 3 x + 12 )
So since 1 multiplied by a number or variable, the number always stays the same we can say that 1(x-5)=x-5. We then, can open the parenthesis for 13*-3x+13*12. The answer for that would be -39x+156. So we then know that x-5-39x+156. We can simplify this until -38x+151.
Hope this helps. <3
Lin Makes $18 per hour. He got a raise. Now Lin makes $22 per hour.What is the percent raise?
Answer:4% raise
Step-by-step explanation:
Jane moved from a house with 58 square feet of closet space to an apartment with 29.58 square feet of closet space. What is the percentage decrease of Jane's closet space? A. 96% B. 39% C. 49% D. 51%
Answer:
the answer is D 51 because if you do 29.58 divided by 58 you get .51 which is 51% decreased.
Step-by-step explanation:
Aldrin and Jan are standing at the edge of a huge field. At 2:00 p.m., Aldrin begins to walk along a straight path at a speed of 3 km/h. Two hours later, Jan takes a straight path at a 608 angle to Aldrin’s path, walking at 5 km/h. At what time the two friends be 13km apart?
Answer: After 2:29 hours both Aldrin and Jan will be 13 km apart from each other.
Time at that instant will be : 4:00 pm + 2.29 hours= 6:29 pm
Step-by-step explanation:
According to the figure:
Ab= c = 13 Km
AC = b = [tex]distance= speed\times time =5\times t[/tex]=5t Km
After two hours the distance covered by the Aldrin say till point D :
[tex]distance=speed\times time=3km/hr\times 2 hrs=6 Km[/tex]
Since, we are interested in determining the time at which Aldrin and Jan both 13 Km apart. For that Aldrin Additional distance covered by the Aldrin from point D to B is :
[tex]distance=speed\times time= 3km/hr\times t=3t Km [/tex]
CB= a = CD+DB= 6+3t
We will apply Laws of cosines:
[tex]C^2=A^2+B^2-2AB\times Cos\theta[/tex]
[tex](13)^2=(6+3t)^2+(5t)^2-2(5t)(6+3t)Cos 60^o[/tex]
[tex]19t^2+6t-133=0[/tex]
On solving the the above equation by quadratic formula we get two values of 't'
1) t = 2.49 hours , 2) t = -2.80 hours
Since,time cannot be in negative so we will ignore the negative value of t
t = 2.49 = 2:29 hours ,(0.49 hour=0.49 × 60 min=29.4 min)
After 2.49 hours after the walking of Jan. Both Aldrin and Jan will be 13 km apart from each other.
Time at that instant will be : 4:00 pm + 2:29 hours= 6:29 hour
What is the length of angle BC?
If you mean side BC (instead of angle BC), then the answer is 22 units.
To get this answer, set the sides AB and AC equal to each other and solve for x
AB = AC
2x - 24 = x - 2
2x-x = -2+24
x = 22
Since BC = x, and x = 22, this means BC is 22 units long.
We have m∠C = m∠B, therefore it's an isosceles triangle.
Therefore we have the equation:
2x - 24 = x - 2 add 24 to both sides
2x = x + 22 subtract x from both sides
x = 22
BC = x
Answer: |BC| = 22A steel rod that is 64 feet long must be cut into three pieces to fabricate the supports for a drill press. The longest piece is 3.09 times the shortest and the middle piece is 1.73 times the shortest. How long is each piece? Round nearest foot.
Answer:
let's x be the shortest piece
the middle piece is 1,73 *x
the longest piece is 3,09 x
then if we sum the 3 pieces we will get the steel rod that is 64 feet long
so x+1,73x+3,09x= 5,82x= 64 then x= 10,99 = 11
the shortest piece is 11 feet
the middle piece is 1,73*11=19,03 feet
The longest piece is: 3,09*11= 33,99= 34 feet
every month, omar buys pizzas to serve at a party for his friends. In may, he brought three more than twice the number of pizzas he bought in April. If Omar bought 15 pizzas in may, how many pizzas did he buy in April
Answer:
Step-by-step explanation:
Omar bought 15 pizzas in May.
In May, he bought 3 more than twice the number that he bought in April.
Since we don't know how many he bought in April, let X = the number of April pizzas.
Then, 15 = 2X + 3
Now you can subtract 3 from both sides, then divide both sides by 2 to leave X by itself and discover what it equals.
Final answer:
Omar bought 24 pizzas in April, calculated by setting up an equation based on the information that in May he bought three more than twice the pizzas he got in April.
Explanation:
The question is asking to find the number of pizzas Omar bought in April given that he bought three more than twice the number in May, and he bought 15 pizzas in May. To solve this, we can set up an equation: April Pizzas + 3 = 2 × (April Pizzas) + 2 × 3. Since we know that Omar bought 15 pizzas in May, we substitute 15 for the total number of Pizzas in May, which gives us: April Pizzas + 3 = 30. Subtracting 3 from both sides gives us April Pizzas = 27 - 3, so April Pizzas = 24. Therefore, Omar bought 24 pizzas in April.
Your model train is 18 inches long.
It is an exact model of a train that is 72 feet long.
A window on the train is how many times wider than a window on the model?
Answer:
48 times wider
Step-by-step explanation:
Convert length of train to inches:
[tex]72 * 12 = 864[/tex] inches
Divide the length of the train by the length of the model train to find the scale.
so, 864 ÷ 18 = 48
and since the model train is proportional to the train, the window on the train is 48 times wider than the window on the model.
Answer:
48
Step-by-step explanation:
Mary Jackson gets a student rate of $27.50 a month for health insurance. There is a $200 deductible. She recently received treatment for a covered condition. The bill was $2,350.00. Mary's insurance company provided payment of 80% of the bill less the deductible.
Answer:
the company's payment was $1720
Step-by-step explanation:
Mary's total cost (without the monthly premium) is $630
First fourth and tenth terms a(n) = 5 + (n + 1) 1/6
Answer:
a(4) = 5 5/6
a(10) = 6 5/6
Step-by-step explanation:
To find the 4th term, let n =4
a(n) = 5 + (n + 1) 1/6
a(4) = 5 + (4+1) 1/6
=5+5 * 1/6
= 5 + 5/6
= 5 5/6
To find the 10th term, let n =10
a(n) = 5 + (n + 1) 1/6
a(10) = 5 + (10+1) 1/6
=5+11 * 1/6
= 5 + 11/6
= 5 + 1 5/6
= 6 5/6