Answer:
The answer is
[tex]x = \frac{ - 1 + \sqrt{21} }{2} \: \: \: or \: \: \: x = \frac{ - 1 - \sqrt{21} }{2} [/tex]Step-by-step explanation:
x² + x - 5 = 0
Using the quadratic formula
That's
[tex]x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]From the question
a = 1 , b = 1 , c = - 5
Substitute the values into the above formula and solve
We have
[tex]x = \frac{ - 1\pm \sqrt{ {1}^{2} - 4(1)( - 5) } }{2(1)} \\ x = \frac{ - 1\pm \sqrt{1 + 20 } }{2} \\ x = \frac{ - 1\pm \sqrt{21} }{2} [/tex]We have the final answer as
[tex]x = \frac{ - 1 + \sqrt{21} }{2} \: \: \: or \: \: \: x = \frac{ - 1 - \sqrt{21} }{2} [/tex]Hope this helps you
What vocabulary word describes a number that has a non-repeating/non-terminating decimal
Answer:
Irrational Numbers
Step-by-step explanation:Irrational numbers never end and never end/repeat.
what is the answer...
Answer:
64
Step-by-step explanation:
5x-16+6x=10x (combine like terms)
11x-16=10x (subtract 11x)
-16= -1x (divide by -1
16 = x
Now plug 16 into 5x-16.
5(16)-16 = 80-16 = 64
The gasoline gauge on a truck reads 1/8 full. after you add 30 gallons the gauge reads 3/4 full. what is the capacity of the tank?
Answer:
48 gallons
Step-by-step explanation:
[tex] \frac{3}{4} = \frac{6}{8} \\ \frac{6}{8} - \frac{1}{8} = \frac{5}{8} \\ 5 \div 30 = 6 \\ 6 \times 8 = 48[/tex]
Lawrence High prevailed in Saturday's track
meet with the help of 20 individual event
placers earning a combined 68 points. A
first place finish earns 5 points, a second-
place finish earns 3 points, and a third-place
finish earns 1 point. Lawrence had a strong
second-place showing, with as many second
place finishers as first and third-place
finishers combined.
Answer:
The answer is below
Step-by-step explanation:
Let x represent a first place finish, y represent a second place finish and z represent a third place finish.
Since there is a total of 20 individual events, hence:
x + y + z = 20 (1)
A first place finish is 5 point, a second place finish is 3 point and third place finish is 1 point. Therefore:
5x + 3y + z = 68 (2)
The second place finishers is as much as first and third-place finishers combined. Hence:
y = x + z (3)
Solving equation 1, 2 and 3 simultaneously gives:
x = 7, y = 10 and z = 3
This means the number of first place finishes was 7, second place finishes was 10 and third place finishes was 3
What is 3x=4+7 that. Is. My. Question
Answer:
I think the answer is 11/3
Carson needs 3 quarts of water to make fruit punch, but has only a 1-cup measuring cup. She knows there are 2 cups in 1 pint, and 2 pints in 1 quart. How can Carson find the number of cups of water she needs to make the punch.
FAST
Answer:
12
Step-by-step explanation:
3 quarts is 6 pints
6 pints is 12 cups
if there is 4 cups in a quart then 4x3=12
Three bags of jelly beans contain 26, 28, and 30 beans. The ratios of yellow beans to all beans in each of these bags are $50\%$, $25\%$, and $20\%$, respectively. All three bags of candy are dumped into one bowl. To the nearest percent, what is the percentage of yellow jelly beans in the bowl?
======================================================
Explanation:
The first bag has 26 beans total. Since 50% are yellow, this means 0.50*26 = 13 beans are yellow. Let A = 13.
The second bag has 28 beans, of which 25% are yellow, so 0.25*28 = 7 are yellow. Let B = 7.
The last bag has 30 means and 20% are yellow. So 0.20*30 = 6 are yellow. Let C = 6.
Add A,B,C to get A+B+C = 13+7+6 = 26 yellow from all three bags out of 26+28+30 = 84 beans total.
The percentage of yellow overall is 26/84 = 0.3095 = 30.95% approximately, which rounds to 31%
Plsss help me with this!!!!
The interior angles of a triangle add up to 180 degrees, meaning we can make an equation.
[tex]2x+36=180[/tex]
[tex]2x=144[/tex]
[tex]x=72[/tex]
Hope this helps.
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Teah was selling candy bars for a fundraiser. She spent $25 on a box of candy bars and sold each candy bar for $2.50. Her profit was $75. Teah wrote the equation 2.5c−25=75 for this situation, and she found c=40. Which statement is true about the solution c=40?
Answer:
The equation is not true. It is actually c=30
Step-by-step explanation:
First you have to divide amount of money she's selling the candy bars for which is $2.50.
If her profit was $75, you want to know how much bars she sold, you will have to divide the amount of money she's selling the candy bars for and the amount she's earning which is $75 divided by $2.50 which is 30.
So c= 30
I'm pretty sure I got something wrong in this assignment can someone see where it went down? Instructions included.
Answer:
The 12 4/9 in the bottom right corner is 13 7/9 and the 8 two squares to the left of it is 6 2/3.
Step-by-step explanation:
You actually did really well! It was only in the last two squares that you went wrong. The first wrong one was just the 12 4/9 in the last column and second to last row, which should be 13 7/9. Then with that the last square that is wrong is just the 8 in the 5th column and second to last row, which should be 6 2/3. Those are the only ones so you actually did really well, great job!
Hope this helped!
The Roberts family is taking a road trip. They plan to drive 1500 miles over two days, stopping for the night when they are halfway. How many hours will they drive for the first day if they average 50 mph over the course of the trip?
Explain:
Answer:
Answer:
The number of hours they would have to drive for the first day if they average 50 mph over the course of the is 15 hours
Step-by-step explanation:
The given parameters are;
The distance the Roberts family plan to drive = 1500 miles
The average speed at which they drove = 50 mph
We note that the formula for average speed = Total distance/(time)
Therefore, we have;
50 mph = 1500 miles/(time, t)
Time = 1500 miles/(50 mph) = 30 hours
Given that for the first day of the 2 days, they will cover half their total distance, which is 1500 m/2 = 750 m
The time taken = 750 miles/(50 mph) = 15 hours
The time take to cover half the distance = 15 hours
Therefore, the number of hours they would have to drive for the first day if they average 50 mph over the course of the is 15 hours.
(3y + 2)(7y) y= 1
How do I evaluate that. Please show work
Answer: 17
Step-by-step explanation:
y= 1
(3y + 2)(7y)
(3(1) + 2(7(1)) Replace y with given number
(3 + 2(7)) Multiply 1 to 3 and 7
(3 + 14) Multiply 2 and 7
(17) Add 3 and 14
Answer:
1. y = 1/7 = 0.143
2. y = 2/3 = 0.667
Step-by-step explanation:
STEP 1 :
Equation at the end of step 1
(3y - 2) • (7y - 1) = 0
STEP 2 :
Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
2.2 Solve : 3y-2 = 0
Add 2 to both sides of the equation :
3y = 2
Divide both sides of the equation by 3:
y = 2/3 = 0.667
Solving a Single Variable Equation:
2.3 Solve : 7y-1 = 0
Add 1 to both sides of the equation :
7y = 1
Divide both sides of the equation by 7:
y = 1/7 = 0.143
5-x<8;x=-3 value of the solution
Answer:
Step-by-step explanation:
5-x<8; x=-3
5-(-3)<8
5-3<8
^
8<8
i think that's how you do it ? sorry if this is wrong
What is 3x-8=4. Solve for x. Explain.
Answer:
4
Step-by-step explanation: 3 x 4 = 12.
12 - 8 = 4.
Plzzz hurry!!
Chris goes with Frederick to the beach to search for coins with his metal
detector. Chris has found both newer coins and antique coins. Chris found 76
newer coins and 19 antique coins. What percent of the coins that Chris found are
antique?
Answer:
20%
Step-by-step explanation:
Add 19 to 76 for the total, which is 95, then find the percent of 19 out of the 95
The percentage of the coins that Chris found are antique will be 20%
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Chris goes with Frederick to the beach to search for coins with his metal detector. Chris has found both newer coins and antique coins. Chris found 76 newer coins and 19 antique coins.
The total number of the coins = 76 + 19 = 95
The percentage will be calculated as,
Percentage = ( 19 / 95 ) x 100
Percentage = 0.2 x 100
Percentage = 20%
To know more about percentages follow
https://brainly.com/question/24304697
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What is the slope of the line that passes through the points (-4, 8) and (-14, 8) ?
Answer:
Step-by-step explanation:
(8-8)/(-14+4) = 0/-10 = 0 is the slope
4y – 2(1 – y) = –44?
Answer:
y= - 7
Step-by-step explanation:
4y-2+2y= -44
6y-2= -44
6y= -44+2
6y= -42
y= -7
Answer:
y=-7
Step-by-step explanation:
4y-2+2y=-44
6y-2=-44
6y=-44+2
6y=-42
7=-7
I have tried 3 times to solve this.
Step-by-step explanation:
Year 2006- y = 0.09 (6) + 0.04 = 0.58
Year 2008- y = 0.09 (8) + 0.04 = 0.76
Year 2010- y = 0.09 (10) + 0.04 = 0.94
Year 2012- y = 0.09 (12) + 0.04 = 1.12
Year 2014- y = 0.09 (14) + 0.04 = 1.3
"Let x = 6 which is corresponded to 2006", so 8 would correspond to 2008, 10 would correspond to 2010, 12 would correspond to 2012, and 14 would correspond to 14. Plug 6 for x into your equation and do them same for the others.
Hopefully this helps you! :)
From the top of a 224-ft lighthouse, the angle of depression to a ship in the ocean is 22°. How far is the ship from the base of the lighthouse? Give your answer to the nearest foot.
Answer:
x=554.41 m
Step-by-step explanation:
It is given that,
Height of the lighthouse, OA=224 ft
The angle of depression to a ship in the ocean is 22 degrees.
We need to find the distance between ship and the base of the lighthouse. The figure is attached. We can use trigonometry to find x.
[tex]\tan22=\dfrac{OA}{AB}\\\\\tan22=\dfrac{224}{x}\\\\x=\dfrac{224}{\tan22}\\\\x=554.41\ m[/tex]
So, there is a distance of 554.41 m between the ship and the lighthouse.
Find the shaded area of the shape
Answer:
340 mm²
Step-by-step explanation:
The shaded area seems to be a parallelogram. To find the area of a parallelogram, all we need to do is multiply the height and base together. In this case, the base is 20 and the height is 17 so the area is 20 * 17 = 340 mm².
Answer:
340 mm^2.
Step-by-step explanation:
The shaded area is a parallelogram whose area = base * altitude
= 20 * 17
= 340 mm^2.
choose the inequality that express the set:
Answer:
The third one
Step-by-step explanation:
Answer:
-1≤x≤-6
Step-by-step explanation:
-1≤x≤-6 since it is inclusive means that -1 and-6 included
Find the distance between the points (-8, -10) and (18, -10).
2014
16
12
8
4
4
-20
-16
--12
-8
-4
0
12
20
16
-4
-8
(18. -10
(-8, -10
--12
-16
-20
units
IN
Answer:
26 units
Step-by-step explanation:
(-8, -10) and (18, -10)
Since the y values are the same, we only need to worry about the x values
18 - -8
18+8
26
The distance is 26 units
Answer:
8
Step-by-step explanation:
A police car drives for 11/12 hours with a constant speed of 84 mph and then for another 2 hours 15 minutes with a constant speed of 72 mph. What distance did it go?
Answer:
1170 miles
Step-by-step explanation:
multiply 12 x 84 to get 1008 keep that 1008 for later. divide 72 by 60 you should get 1.2, times 1.2 and 15 and you should get 18 keep the 18. times 2 by 72 and get 144. add 144 and 18 to get 162. add 162 and 10008 to get 1170. the awnser is 1170 miles.
What are the coefficients of 12-8x+14y
Answer:
the 8 and 14 would be the coefficients
Step-by-step explanation:
coefficients are the numbers only next to the variables( like x or y) so since 8 and 14 are next to the variables they are the coefficients
my assignment is about multiplication and maybe division. The one of the multiplication problems are this one : Martin has 12 times as many baseball cards as Josie. Josie has 29 more cards then Kal. How many baseball cards does Martin have? write and solve equations. Matt has 14 times as many cards as Kal. How many cards does Matt have?
Answer:
well how many cards does kal have?? thats the main key to solving the question.
Un mecánico tiene un conjunto de 20 llaves. La medida de la llave más grande es 3/4 pulgada, mientras que la llave mas pequeña es 1/8 de pulgada. ¿Cual es la diferencia en números raciónales de estas medidas?
Answer:
La diferencia en los tamaños entre los siguientes tamaños de teclas es de 1/32 pulgadas
Step-by-step explanation:
El número de llaves que tiene el mecánico = 20 llaves
El tamaño de la llave más grande = 3/4 pulgadas
El tamaño de la llave más pequeña = 1/8 pulgadas
La diferencia de medida entre la tecla más grande y la más pequeña = 3/4 - 1/8 = 5/8 pulgadas
El aumento de la medición entre las teclas posteriores se puede dar de la siguiente manera;
D = 5 / (20 × 8) = 1/32 pulgadas
Los tamaños de las teclas son;
(Usando Excel y Word)
3/4 pulgadas, 5/7 pulgadas, 2/3 pulgadas, 2/3 pulgadas, 5/8 pulgadas, 3/5 pulgadas, 4/7 pulgadas, 1/2 pulgadas, 1/2 pulgadas, 1/2 pulgadas, 4/9 pulgadas, 2/5 pulgadas, 3/8 pulgadas, 1/3 pulgadas, 1/3 pulgadas, 2/7 pulgadas, 1/4 pulgadas, 2/9 pulgadas, 1/5 pulgadas, 1/6 pulgadas, 1/8 pulgadas
La diferencia en los tamaños entre los tamaños de clave posteriores = 1/32 pulgadas.
A box of popcorn weighs 15\16 pounds. The box contains 1/3 buttered popcorn and 2/3 cheesy popcorn. How much does the cheesy popcorn weigh?
Answer:
5/8 of a pound/10/16 of a pound
Step-by-step explanation:
15/6 x 2/3 = 5/8 of a pound simplified.
Combine like terms in the following expressions A. 10x − 4x. B. −15n + 3n. C. 7.5y + 1.6y − 2 D. m + 4 − 2m
Answer:
A. -6x
B. -12n
C. 9.1y
D. 3m
Explanation:
Add each expression to get the final answer.
Plz help it need to be done by to day anyone plz
The answer is 256 because 2304 divided by 9 equals 256.
Step-by-step explanation:
256. I showed work just in case you need to
sin 20.sin 10 as sum or difference
Answer:
see explanation
Step-by-step explanation:
The difference identity for the product is
sinxsiny = [tex]\frac{1}{2}[/tex] [ cos(x - y) - cos(x + y) ], thus
sin20sin10
= [tex]\frac{1}{2}[/tex] [ cos(20 - 10) - cos(20 + 10) ]
= [tex]\frac{1}{2}[/tex] ( cos10 - cos30 )