Answer:
smaller x: -4
larger x: 1
Step-by-step explanation:
We need to factor this. In order to do so, we need to find factor pairs of the coefficient of x^2 (which is 1 in this case) and of the constant (-4 in this case) such that they add up to 3.
Here, the factors of 1 are obviously just 1 and 1. The factors of -4 are (1, -4), (-1, 4), and (2, -2). Notice that 1 * 4 + 1 * (-1) = 3, so we know that our factor pair from 1 is (1, 1) and our factor pair from -4 is (-1, 4).
Then, we factor this quadratic into: (x - 1)(x + 4) = 0. Now, solve for x by setting each of these two factors equal to 0:
x - 1 = 0 ⇒ x = 1
AND
x + 4 = 0 ⇒ x = -4
So, the solutions are x = -4 and x = 1.
Hope this helps!
Answer:
smaller x= -4
larger x= 1
Step-by-step explanation:
x² + 3x - 4 = 0
x² + 4x - x - 4 = 0
x(x + 4) - (x + 4) = 0
(x - 1)(x + 4) = 0
x = -4, 1
How are the graphs of the functions f(x) = V16 and g(x) = 3/64 related?
The functions f(x) and g(x) are equivalent.
The function g(x) increases at a faster rate.
The function g(x) has a greater initial value.
The function g(x) decreases at a faster rate.
Answer:
Step-by-step explanation:
hello :
* 64 = 4^3 so : g(x) = (∛4^3)^x = 4^x
* 16=4² so : f(x) = (√4²)^x = 4^x
the functions f(x) and g(x) are equivalent
Select all solutions for the equation (3x + 5)(2x + 8) = 0
Answer:
x=-1.67 or x=-4
Step-by-step explanation:
3x+5=0 and 2x+8=0
3x=0-5 2x=-8,,,divide both sides by 2, the two's cancel then x=-4
3x=5 Divide by 3 to hve x on one side,,, thus the answer is -5÷3=1.666...
Answer:
-5/3 and -4
Step-by-step explanation:
I got it correct.
work out the following questions
Answer:
work out the following questions
Step-by-step explanation:
a.
[tex] \frac{3}{4} \times \frac{1}{2} [/tex]
[tex] \frac{3}{8} [/tex]
Now
b.
[tex] \frac{4}{7} \times \frac{21}{40} [/tex]
Now here we can see 21 is 3 times of 7 and 40 is 10 times of 4 so
[tex] \frac{3}{10} [/tex]
Hope this helps.
I need to find the surface area
Answer:
389.846
Step-by-step explanation
Sorry if its wrong
I need help with #1 and #2 how do I do this?
Answer:
2
Step-by-step explanation:
2
Answer:
The answer to your question is below
Step-by-step explanation:
Data
1) AB = 6 BC = 4 AE = 9 ED = ?
Use proportions to solve this problem
AB / AE = 6/9 (AB + BC) / (AE + ED) = (6 + 4) / (9 + ED)
-Equal both proportions
6/9 = 10 / (9 + ED)
-Solve for ED
9 + ED = 10(9)/ 6
-Simplification
9 + ED = 90/6
9 + ED = 15
ED = 15 - 9
-Result
ED = 6
2.- AB = 12 AC = 16 ED = 5 AE = ?
Use proportions to solve this problem
AE / AB = AE / 12 AD/AC = (AE + 5) / 16
-Equal both proportions
AE/12 = (AE + 5 ) / 16
-Solve for AE
16AE = 12(AE + 5)
16AE = 12AE + 60
16AE -12AE = 60
4AE = 60
AE = 60/4
-Result
AE = 15
Calculate the portion of skiing in degrees Soccer - 5 hours Jogging - 20 Hours Walking - 10 hours Skiing - 5 hours Football - 10 hours Total - 50 hours
Answer: The portion of skiing is 36 degrees (36°)
Step-by-step explanation: In order to calculate the value of any of the given variables in degrees, we must calculate it as a fraction of the total and then convert it to a degree measure in relation to a total of 360 degrees. (Please note that a pie chart has a total of 360 degrees measurement for all the variables given)
The variables are;
Soccer - 5
Jogging - 20
Walking - 10
Skiing - 5
Football - 10
Total - 50
Therefore, the fraction that represents skiing is given as
Skiing = 5/50
Skiing = 1/10
Calculating this portion in degrees becomes,
Skiing = 1/10 x 360
Skiing = 36 degrees (36°)
Answer:
x = 36° represents the proportion of hours spent on skiing.
Step-by-step explanation:
Solution:-
- The time taken for various activities is to be represented using a pie chart.
- The individual times for various activities are given:
Soccer : 5 hours
Jogging : 20 hours
Walking : 10 hours
Skiing : 5 hours
Football : 10 hours
=========================
Total time : 50 hours
=========================
- An entire pie chart is represented by a circle. Where the angle representation of a complete circle is 360° - mapping the total number of hours taken for all activities.
- So, 360° ............. Total Time = 50 hours
- So we will use direct proportions to evaluate the angle representation for the number of hours spent on skiing for a pie chart:
x ................. Skiing time = 5 hours
======================================
50*x = 5*360
x = 36°
what is the probablility of flipping a coin tails all three times and all three time you get tails?
Answer:
If the coin is fair, then the odds of getting heads or tails should be equal, 12. Then 3 tosses of tails will have a chance of 12⋅12⋅12=18. Tossing of the coin is an independent event. The probablility of each event is 12.
What is the volume of this rectangular prism? 6/5cm 8/3cm 15/4cm
Explanation of how to calculate the volume of a rectangular prism with given dimensions.
Explanation:The volume of a rectangular prism is calculated by multiplying its length, width, and height.
Given dimensions: length = 6/5 cm, width = 8/3 cm, height = 15/4 cm
Volume = (6/5) cm x (8/3) cm x (15/4) cm = 24 cm³
Hannah is at an arcade where each game requires her to use 2 tokens. She buys 40 tokens to begin. Let n be the number of games Hannah has played. Find the number of games Hannah has played if she has 16 tokens left.
Answer:
n = 12, she has played 12 games
Step-by-step explanation:
40 = 16 + 2n
24 = 2n
24/2 = n
n = 12
The division is one of the four fundamental arithmetic operations. The number of games that Hannah has played is 12.
What is Division?Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that Hannah is at an arcade where each game requires her to use 2 tokens. Also, the total number of tokens Hannah has is 40.
Therefore, the number of tokens that Hannah has used is,
Number of tokens Hanna used
= Total number of toke - Number of tokens left
= 40 - 16
= 24
Now, the number of games that Hannah has played is,
Number of games Hannah has played = Number of tokens used / Number of token per game
n = 24 / 2
n = 12 game
Hence, the number of games that Hannah has played is 12.
Learn more about Division here:
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. Classify ABC if the vertices are A(-12,5), B(12,5), and C(10, 17).
A-right scalene'
B-obtuse scalene
C- acute scalene
D-none of these
Answer:
acute scalene
Step-by-step explanation:
Caitlyn finds that experimental probability of her making a three-point shot is 30%. Out of 500 three-point shots, about how many could she predict she would make?
Answer: 150 shots.
Step-by-step explanation: Since her three-point shot probably is 30%, we can assume that for any total of three-point shots, only 30% of them will be "correctly shot."
Here are two methods of how to find the answer, depending on how your teacher is teaching you to calculate percentages.
Method A. Proportions
Therefore, let's make a proportion. Out of 500 shots, only 30% will be made.
[tex]\frac{30}{100} =\frac{x}{500}[/tex]
Solve for x, which in a proportion, is done by cross-multiplying and then dividing.
[tex](30 * 500) / 100[/tex]
[tex]= 150[/tex]
Out of all the 500 shots, only 150 can be made by her prediction.
Method B. Simple multiplication
30% is equal to 0.3
Therefore, you multiply [tex]0.3 * 500[/tex], which you get [tex]150[/tex].
Lu is making a quilt that is 20 squares wide and has 18 rows the border of the quilt is made by using each toy design equally as often there are a total of 6 toy designs each square can hold 1 design how many of each design does she use for the border?
Answer:
The correct answer is two designs are used 12 times each and other four designs are used for 13 times each.
Step-by-step explanation:
Width of the quilt Lu is making is 18 rows of 20 squares each.
Thus the perimeter of the quilt is 20 + 20 + 18 + 18 = 76.
We can also say there are 76 square as the boundary which are to be bordered with toy designs.
Each square can hold 1 design of toy and there are 6 different designs of toys.
Thus number of times each design is used [tex]\frac{76}{6}[/tex] = 12 [tex]\frac{4}{6}[/tex].
Thus there are two designs used 12 times each and other four designs are used for 13 times each.
If 5^3b-1 = 5^b-3 what is the value of b?
Answer:
b = -1
Step-by-step explanation:
Your equation is ...
(5^3)b -1 = 5^b -3
This is a mix of exponential and linear terms, and cannot be solved algebraically.
___
We suspect you might mean ...
5^(3b -1) = 5^(b -3)
We can equate the exponents to find a value for b:
3b -1 = b -3
2b = -2 . . . . add 1-b to both sides
b = -1 . . . . . . divide by 2
Mikes milk shakes had a total of 9 gallons of ice cream they used 3 3/9 gallons this week and 1 1/3 gallons last week how many gallons of ice cream do they have left
Answer:
Step-by-step explanation:
[tex]3 \frac{3}{9}=\frac{3 \times 9+3}{9}=\frac{30}{9}=\frac{10}{3}\\1\frac{1}{3}=\frac{1\times 3+1}{3}=\frac{4}{3}\\Total~used=\frac{10}{3}+\frac{4}{3}=\frac{14}{3}\\Left~over=9-\frac{14}{3}=\frac{9 \times 3-14}{3}=\frac{13}{3}=4 \frac{1}{3}~gallons[/tex]
Answer: 4
Step-by-step explanation:
[tex]9-(3\frac{3}{9} + 1\frac{1}{3} )\\9-(\frac{30}{9} + \frac{4}{3})\\ 9-(\frac{10}{3}+ \frac{4}{3})\\ 9-(\frac{14}{3} )\\= \frac{(9)(3)-14}{3} \\= \frac{27-14}{3} \\=\frac{13}{3}\\ \\or\\\\4 gallons[/tex]
or
= [tex]4\frac{1}{3}[/tex]
approximately
Write 1.7.7.7.7.7 using an exponent
Answer:
1^7 is the answer you are looking for
Step-by-step explanation:
If x represents the amount Rita earns each week, which expression represents the amount she earns in a year?
x+52
52-
Which expressions represent the area of the entire shaded
region, including the light and dark shading? Select three
options.
12a cm2
2b cm
(6a - b) cm
(12a + 2b) cm
(6a + b) cm
Answer:
12a cm2
2b cm2
(6a + b) cm2
Step-by-step explanation:
The complete question is
The figure consists of 12 congruent equilateral triangles. The area of one equilateral triangle is a cm2. The area of the hexagon, shaded slightly darker, is b cm2.
Which expressions represent the area of the entire shaded region, including the light and dark shading? Check all that apply.
12a cm2
2b cm2
(6a - b) cm2
(12a + 2b) cm2
(6a + b) cm2
The picture of the question in the attached figure
we know that
The area of the entire shaded region is equal to the area of the the light and dark shading
so
step 1
Find the area of the light shading
The area is equal to the area of six congruent equilateral triangles
[tex]A_1=6a\ cm^2[/tex]
step 2
Find the area of the dark shading
The area is equal to the area of the regular hexagon
[tex]A_2=b\ cm^2[/tex]
step 3
1) Find the total area
[tex]A=A_1+A_2=(6a+b)\ cm^2[/tex]
2) Remember that the figure consists of 12 congruent equilateral triangles
so
[tex]A=12a\ cm^2[/tex]
3) The area of the light shading is the same that the area of the dark shading
so
6a=b
therefore
[tex]A=2b\ cm^2[/tex]
Answer: 1 2 5
Step-by-step explanation:
PLSSSSSSSSSS HELLLPPPPPP!!! ASAP!!!! 6th GRADE MATH!!!!!!!!!! ITS FOR MY COUSIN!!!!!!FIRST TO ANSWER BOTH GETS MARKED BRAINLIEST!!!!
Answer:
I believe its 15
Step-by-step explanation:
Answer for 12+7+(-4)= 15
Answer for -1.75+(-6.25)+6= -2
I hope this helps
okay so The top of the slide is 12 feet from the ground and has an angle of depression of 53 degree . What is the length of the slide? Round your answer to the nearest whole number. please help!!!
To find the length of the slide, you can use trigonometry and the angle of depression. The length can be found using the tangent function, and rounding to the nearest whole number gives an answer of approximately 9 feet.
Explanation:To find the length of the slide, we can use trigonometry and the angle of depression. We can use the tangent function, which is opposite over adjacent, to find the length of the slide. In this case, the opposite side is the height of the slide (12 feet) and the adjacent side is the length of the slide. So we have:
tan(53 degrees) = opposite/adjacent
tan(53 degrees) = 12/adjacent
To solve for the length of the slide, we can rearrange the equation:
adjacent = 12/tan(53 degrees)
Using a calculator, we can find that the length of the slide is approximately 9 feet when rounded to the nearest whole number.
What is the mean for this data. Plz explain
Answer:
18
Step-by-step explanation:
Mean is the average of the data.
There is one 7.
Three 9's.
Two 10's
7+9+9+9+10+10=54
There are only 3 numbers with actual data so 6 and 8 don't matter.
54÷3=18
Eight less than twice a number is fourteen.
Answer:
x = 11
Step-by-step explanation:
2x - 8 = 14
2x = 22
x = 11
Tell me if I am wrong.
Can I get brainliest
Answer:
Let that number be 'x'
Now first part of the question tells us that 8 less than twice a number which is"x".
so twice a number would be 2x
then 8 less than would 2x-8
and the given result of the equation is 14
so the equation iis 2x-8=14
2x=14+8
2x=22
x=22/2
x=11 So the number is 11
Hope you find it helpful
Trent began his math work at 5:29 p.m. He finished at 6:04 p.m. How many minutes did Trent spend on his math homework?
Answer: I am pretty sure it is 35 min
Step-by-step explanation:
Answer
Trent spent 35 minutes on his work.
Step-by-step explanation:
Part A
in the table describe the shape of the cross section formed when a particular plane passes through the cone
Answer:
plane parallel to the circular base, not passing through the tip of the cone: circle
plane parallel to the circular base, passing through the tip of the cone: A point
plane not parallel to the base, not passing through the base, and making an angle with the horizontal that is less than that made by the slant height of the cone: an oval that becomes more elongated as the angle with the horizontal increases
plane making an angle with the horizontal that is greater than that made by the slant height, passing through the tip of the cone : an isosceles triangle
Step-by-step explanation:
What is the cross section of a shape?A cross-section is a plane section that is a section of a three-dimensional object that is parallel to one of its planes of symmetry or perpendicular to one of its lines of symmetry. Describe shapes formed by cross-sections (square, rectangle, triangle, etc.)
Learn more about Cross Section here:
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For two days in a row, Windstone rescued tadpoles from a puddle. He rescued 54 on Friday. This is 17 less Then the number he rescued on Saturday. Write and solve a subtraction equation to find how many tadpoles he rescued on Saturday.
Answer:
71 tadpoles
Step-by-step explanation:
Windstone rescued 54 on Friday.
Let the number rescued on Saturday =x
The number rescued on Friday is 17 less than the number he rescued on Saturday.
This is written as:
54=x-17To solve for x, we add 17 to both sides of the equation
54+17=x-17+1771=xx=71Windstone Rescued 71 tadpoles on Saturday
Answer:
71 tadpoles
Step-by-step explanation:
let 't' represent the number of tadpoles he rescued on Saturday.
According to the problem,
Windstone rescued 54 on Friday.
If the number rescued on Friday is 17 less than the number he rescued on Saturday.
The equation to find the number of tadpoles he rescued on Saturday will be:
t-17 = 54
Further solving for 't'
t= 54+17
t= 71
Therefore, Windstone Rescued 71 tadpoles on Saturday
A home decor store donated a percent of every sale to charity .The total sales were $7,400 so the store donated $148.What percent of $7,400 was donated to charity
The correct answer is 2%. The store donated 2% of $7,400 to charity.
To find out what percent of $7,400 was donated to charity, we need to divide the amount donated by the total sales and then multiply by 100 to convert it into a percentage.
Let's denote the percent donated as P. The amount donated is given as $148, and the total sales are $7,400. The relationship between the percent donated, the total sales, and the amount donated can be expressed as:
[tex]\[ P \times 7,400 = 148 \][/tex]
To find P, we divide both sides of the equation by 7,400:
[tex]\[ P = \frac{148}{7,400} \][/tex]
Now, we calculate the value of P:
[tex]\[ P = \frac{148}{7,400} = \frac{2}{100} \] \[ P = 0.02 \][/tex]
To express P as a percentage, we multiply by 100:
[tex]\[ P = 0.02 \times 100 \] \[ P = 2\% \][/tex]
Is 24, 45, and 51 a right triangle?
Answer: The dimensions are that of a right triangle.
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
you can solve by checking with the Pythagorean theorem (a^2 + b^2= c^2)
24 and 45 are the legs because the hypotenuse is the largest side so they will be substituted for a and b. if c is equal to 51 then it would be a right triangle
24^2 + 45^2= c^2
576 + 2025 = c^2
2601 = c^2
51 = c
because c = 51 and 51 was the hypotenuse on the triangle previously mentioned 24 45 51 is a right triangle
The distance traveled can be calculated using the formula D
= S. t where s is the speed and t is the total time. Which of
the situations below represent a total distance of 120 km?
Select all that apply.
A) 40 km/hr for 3 hours
B) 60 km/hr for 2 hours
C) 30 km/hr for 4 hours
D) 25 km/hr for 5 hours
Final answer:
Situations A (40 km/hr for 3 hours), B (60 km/hr for 2 hours), and C (30 km/hr for 4 hours) represent a total distance of 120 km when applying the formula D = S * t. Situation D (25 km/hr for 5 hours) does not represent the required distance of 120 km.
Explanation:
The distance traveled can be calculated using the formula D = S * t where S is the speed and t is the total time. To find out which situations represent a total distance of 120 km, we will apply this formula to each of the given situations.
A) 40 km/hr for 3 hours: D = 40 km/hr * 3 hr = 120 kmB) 60 km/hr for 2 hours: D = 60 km/hr * 2 hr = 120 kmC) 30 km/hr for 4 hours: D = 30 km/hr * 4 hr = 120 kmD) 25 km/hr for 5 hours: D = 25 km/hr * 5 hr = 125 kmAfter calculating each situation, we can see that situations A, B, and C each yield a total distance of 120 km, while situation D yields a total distance of 125 km, which is not the distance we are looking for.
PLZZZZZ HELP!!!!! WILL MARK BRAINLIEST. solve for t
–4(t − 12) + 12 = –4
t =
Answer:
t = 16
Step-by-step explanation:
–4(t − 12) + 12 = –4
-12 -12
-4(t - 12) = -16
/-4 /-4
t - 12 = 4
+12 +12
t = 16
or
–4(t − 12) + 12 = –4
distribute the -4
-4t + 48 + 12 = -4
simplify
-4t + 60 = -4
-60 -60
-4t = -64
/-4 /-4
t = 16
Answer:
64/3
Step-by-step explanation:
A manufactured lot of buggy whips has 20 items, of which 5 are defective. A random sample of 5 items is chosen to be inspected. Find the probability that the sample contains exactly one defective item (a) if the sampling is done with replacement. (b) if the sampling is done without replacement.
Answer:
a. 39.55%
b. 44.02%
Step-by-step explanation:
We have the following data:
n = 5
x = 1
p = 5/20 = 0.25
to. If the sampling is done with replacement.
We apply the binomial distribution formula, which is as follows:
P = nCx * (p ^ x) * ((1-p) ^ (n-x))
Where nCx, is a combination, and is equal to:
nCx = n! / x! * (n-x)!
replacing we have:
5C1 = 5! / 1! * 4! = 5
replacing in the main formula:
P = 5 * (0.25 ^ 1) * ((1- 0.25) ^ (5-1))
P = 0.3955
that is, without replacing the probability is 39.55%
b. if the sampling is done without replacement.
Here it is a little different from the previous one, but what you should do is calculate three cases,
the first was the one at point a, when n = 5 and x = 1
5C1 = 5! / 1! * 4! = 5
the second is when n = 20 and x = 5, this is all possible scenarios.
20C5 = 20! / 5! * 15! = 15504
and the third is when n = 15 (20-5) and x = 4 (5-1), which corresponds to the cases when none were damaged
15C4 = 15! / 4! * 11! = 1365
In the end, it would be:
P = (5C1 * 15C4) / 20C5
Replacing:
P = 5 * 1365/15504
P = 0.4402
Which means that without replacing the probability is 44.02%
Andy promises opie that he will give him 5000 upon his graduation from college at mayberry u. How much must andy invest today to make good on his promise, if opie is expected to graduate in 12 years and andy can earn 5% on his money?
Answer: Andy should invest RS. 2784.19 for 12 years .
Step-by-step explanation:
Since we have given that
Amount = Rs. 5000
Time = 12 years
Rate of interest = 5%
So, We need to find the sum:
Using "Compound interest" , we get :
[tex]A=P(1+r)^t\\\\5000=P(1+0.05)^{12}\\\\5000=P(1.05)^{12}\\\\\dfrac{5000}{1.05^{12}}=P\\\\2784.19=P[/tex]
Hence, Andy should invest RS. 2784.19 for 12 years .
Final answer:
To find out how much Andy needs to invest today to fulfill his promise to Opie in 12 years with a 5% interest rate, we use the present value formula. Andy needs to invest approximately $2475.64 today to ensure he can fulfill his promise to Opie.
Explanation:
To calculate how much Andy must invest today to fulfill his promise to Opie, we can use the concept of present value.
First, we need to find the present value of $5000 that Opie will receive in 12 years with a 5% interest rate.Using the present value formula: P = F / (1 + r)^n, where P is the present value, F is the future value, r is the interest rate, and n is the number of years, we can plug in the values and calculate the amount Andy must invest today.By calculating the present value, Andy needs to invest approximately $2475.64 today to ensure he can fulfill his promise to Opie.