Answer:
x = - 3/7 or x = 1Step-by-step explanation:
7x² - 4x - 3 = 0
Rewrite - 4x as a difference
That's
7x² - 7x + 3x - 3 = 0
Factorize the expression
7x( x - 1) + 3 ( x - 1) = 0
(7x + 3)( x - 1 ) = 0
7x + 3 = 0 x - 1 = 0
7x = - 3 x = 1
x = -3/7
The solutions are
x = - 3/7 or x = 1
Hope this helps you
Solve 0 = 4x2+12x+9.
Select the equation that shows the correct
substitution of a, b, and c in the quadratic formula.
121 122 - 4(4309)
2(4)
X=
-12 + 122 +4(4)(9)
2(4)
o
-121 122 – 4(4)(9)
2(4)
Answer:
The correct substitution of a, b, and c in the quadratic formula is given by
[tex]$ x=\frac{-12\pm\sqrt{(12)^2-4(4)(9)}}{2(4)} $[/tex]
[tex]x = - \frac{ 3}{2} \: and \: x = -\frac{ 3}{2} \\\\[/tex]
The solutions of the given quadratic equation are real and equal.
Step-by-step explanation:
The given quadratic equation is
[tex]4x^2+12x+9 = 0[/tex]
The coefficients a, b and c are as follow:
[tex]a = 4 \\\\b = 12\\\\c = 9[/tex]
The quadratic formula is given by
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
The correct substitution of a, b, and c in the quadratic formula is given by
[tex]$ x=\frac{-12\pm\sqrt{(12)^2-4(4)(9)}}{2(4)} $[/tex]
Bonus:
The solution of this quadratic equation is given by
[tex]x=\frac{-12\pm\sqrt{(144 - 144)}}{8} \\\\x=\frac{-12\pm\sqrt{0}}{8} \\\\x=\frac{-12\pm 0}{8} \\\\x=\frac{-12 + 0}{8} \: and \: x=\frac{-12 - 0}{8}\\\\x= -\frac{ 3}{2} \: and \: x = -\frac{ 3}{2} \\\\[/tex]
Therefore, the solutions of the given quadratic equation are real and equal.
14) Marty weighs 64
pounds and Nathan weighs
4
76 pounds. How much more does Nathan weigh
2
than Marty?
Answer:
Nathan weighs 12 more pounds than Marty.
Step-by-step explanation:
If Marty weighs 64 pounds and Nathan weighs 76 pounds, we can subtract the weight of Marty from Nathan to get our answer.
[tex]76-64=12[/tex]
In case Nathan was actually 476 pounds, the answer would be 412.
Right triangle ABC is located in A(-1,-2), B(-1,1) and C(3,1) on a coordinate plane. what is the equation of a circle with radius AC?
A) (x+1)*2+(y+2)*2=9
B) (x+1)*2+(y+2)*2=25
C) (x-3)*2+(y-1)*2= 16
D) (x-3)*2+(y-1)*2=25
Answer:
Hey there!
First, we want to find the radius of the circle, which equals the length of line segment AC.
Length of line segment AC, which we can find with the distance formula: [tex]\sqrt{25\\[/tex], which is equal to 5.
The equation for a circle, is: [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h, k) is the center of the circle, and r is the radius.
Although I don't know the center of the circle, I can tell you that it is either choice B or D, because the radius, 5, squared, is 25.
Hope this helps :) (And let me know if you edit the question)
Answer: The equation of the circle is (x+1)²+(y+1)² = 25
Step-by-step explanation: Use the Pythagorean Theorem to calculate the length of the radius from the coordinates given for the triangle location: A(-1,-2), B(-1,1) and C(3,1) The sides of the triangle are AB=3, BC=4, AC=5.
Use the equation for a circle: ( x - h )² + ( y - k )² = r², where ( h, k ) is the center and r is the radius.
As the directions specify, the radius is AC, so it makes sense to use the coordinates of A (-1,-2) as the center. h is -1, k is -2 The radius 5, squared becomes 25.
Substituting those values, we have (x -[-1])² + (y -[-2])² = 25 .
When substituted for h, the -(-1) becomes +1 and the -(-2) for k becomes +2.
We end up with the equation for the circle as specified:
(x+1)²+(y+1)² = 25
A graph of the circle is attached. I still need to learn how to define line segments; the radius is only the segment of the line between the center (-1,-2) and (1,3)
What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 3.5?
Perimeter = 98 cm, area = 588 cm2
Perimeter = 42 cm, area = 109.25 cm2
Perimeter = 42 cm, area = 588 cm2
Perimeter = 98 cm, area = 109.25 cm2
Answer:
first option
Step-by-step explanation:
After it's enlarged, the new dimensions will be 6 * 3.5 = 21 and 8 * 3.5 = 28, therefore, the new perimeter will be 2(21 + 28) = 2 * 49 = 98 and the area will be 21 * 28 = 588.
write a function rule for the table be quick plzz
factor 16x to the 5th power subtract x to the third power
Answer:
X ^3 (4x+1) (4x-1)
Step-by-step explanation:
Factor x3 out of 16x5−x3
Rewrite 16x2 as (4x)2
Rewrite 1 as 1^2
Factor
x^3 (4x+1) (4x-1)
I hope I helped
Lauren owns a sign company. She borrows $75 000 to purchase a laser engraver. The
current interest rate is 7.2%/a compounded monthly. The term of Lauren's loan is 20
years. How much will Lauren pay per month?
Answer:
$1,313.3 per month
Step-by-step explanation:
A=p(1+r/n)^nt
P=principal=$75,000
r=interest rate=7.2%=0.072
t=20 years
n=12 months
A=p(1+r/n)^nt
=75,000(1+0.072/12)^12*20
=75,000(1+0.006)^240
=75,000(1.006)^240
=75,000(4.2026)
=315,195
A=$315,195
The term of Lauren's loan=20 years
20 years×12 months=240 months
Lauren's pay per month =$315,195/240
=$1,313.3125
Approximately $1,313.3 per month
How do you factor this expression: x^3 + 9x^2 + 27x + 27. Thanks! :)
Answer:
(x + 3)³
Step-by-step explanation:
Use rational root test to check for possible rational roots.
Factors of 27 are 1, 3, 9, and 27.
Factors of 1 are 1.
Possible rational roots are:
±1/1, ±3/1, ±9/1, ±27/1
Checking each one, we find that -3 is a root. So x + 3 is a factor.
Knowing that, we can use grouping to factor.
x³ + 9x² + 27x + 27
x³ + 9x² + 18x + 9x + 27
x (x² + 9x + 18) + 9 (x + 3)
x (x + 6) (x + 3) + 9 (x + 3)
(x + 3) (x (x + 6) + 9)
(x + 3) (x² + 6x + 9)
(x + 3) (x + 3)²
(x + 3)³
BRAINLIEST! ASAP! A boat travelling at top speed upstream moves at 15km/hr. When it travels downstream, again at top speed< it moves at 25km/hr. What is the boat's top speed in still water?
Answer:
20 km/hr
Step-by-step explanation:
The boat's still-water speed is the average of its speeds against and with the current:
(15 +25)/2 = 20 . . . km/hr
__
If you want to write equations, you can let b and c represent the speeds of the boat and current in km/hr.
b - c = 15 . . . . upstream speed
b + c = 25 . . . . downstream speed
Add these two equations, and you get ...
(b -c) +(b +c) = (15) +(25)
2b = 40
b = 20 . . . . divide by 2
The speed of the boat in still water is 20 km/hr.
Answer:
20 km/hr
Step-by-step explanation:
To solve this, you have to find the average speed it is going. To find this, you just add up all of the speeds mentioned and divide it by the number of speeds you added.
15 +25=40
40/2=20
20km/hr!!!
Good luck on what you are doing I hope you do well! Brainliest would be great :)
4(2n + 3) =44 pls someone help me with this??
Answer:
n = 4
Step-by-step explanation:
4(2n + 3) = 44
Expand the brackets.
4(2n) + 4(3) = 44
8n + 12 = 44
Subtract 12 on both sides.
8n + 12 - 12 = 44 - 12
8n = 32
Divide both sides by 8.
(8n)/8 = 32/8
n = 4
Solve the following question
The difference of two numbers is 12 and their sum is 20 find the numbers
Answer:
they are 16 and 4
Step-by-step explanation:
We can call the numbers x and y and we can write:
x - y = 12
x + y = 20
Adding these equations gives us 2x = 32 which means x = 16 and substituting this value into the first equation gives us y = 4.
Answer:
The numbers are 16 and 4
Step-by-step explanation:
Let the two numbers be x and y
x-y = 12
x+y = 20
Add the two equations together
x-y = 12
x+y = 20
-------------------
2x = 32
Divide by 2
2x/2 =32/2
x = 16
Now find y
x+y =20
16+y =20
Subtract 16
y = 20-16
y = 4
what is the frequency distribution table
Step-by-step explanation:
The frequency distribution table is a table that shows the particular values and corresponding frequencies. It consists of two tables first for clas interval and other for frequency.There are many types of frequency distribution such as Grouped frequency distribution, Cumulative frequency distribution., Relative cumulative frequency distribution etc.One way of organizing data is by constructing a frequency distribution table. A tally mark is used to record how often a particular score or number occurs. The number of times a score or number appears is called the frequency.
To construct a frequency distribution table:
a. list the scores or numbers from highest to lowest (or lowest to highest),
b. use tally marks to record how often each score or number appears, and
c. count the marks and record it in the frequency column.
Write the equations after translating the graph of y=|2x|−1: one unit to the left
Answer:
y = | 2(x + 1) - 1
Step-by-step explanation:
Given f(x) then f(x + c) represents a horizontal translation of f(x)
• If c > 0 then shift to the left of c units
• If c < 0 then shift to the right of c units
Here the shift is 1 unit to the left , thus
y = | 2(x + 1) ] - 1
plssssssss helppp 3x – 5 = 1
Answer:
x = 2
Step-by-step explanation:
Add 5 to both sides to get the 5 to the right side since we are trying to isolate the variable x:
3x – 5 + 5 = 1 + 5
Simplify: 3x=6
Divide each side by 3 to isolate and solve for x:
3x/3=6/3
Simplify: x=2
How do you solve -6(4d+5)+7d=-2d
Answer:
d = -2Step-by-step explanation:
-6(4d + 5) + 7d = -2d -24d - 30 + 7d = - 2d -17d - 30 = -2d+2d+30 +2d+30
-15d = 30÷(-15) ÷(-15)
d = -2my mistake it's actually d= -30/19 sometimes I forget you put them in fractions
List some typical benefits an employee might receive on top of their wage?
Answer:
paid vacation
paid medical
401k
If the area of the trapezoid below is 75 square units, what is the value of x? AB=17 DC=8
A. 1.5
B. 12
C. 6
D. 3
Diagram related to the question can be found in the attached picture below :
Answer: 6 units
Step-by-step explanation:
From the diagram attached to the question:
Length AB = 17
Length DC = 8
height (h) = x
Area of trapezium = 75sq units
The Area (A) of a trapezium is given by:
(1/2) × (a + b) × h
Where ;
a and b are the upper and base lengths of the trapezium
h = height of trapezium
A = (1/2) × (a + b) × h
75 = (1/2) * (17 + 8) * x
75 = 0.5*25*x
75 = 12.5x
x = 75 / 12.5
x = 6 units
For f(x) = 2x + 1 and g(x) = x2 – 7, find (f – g)(x).
Answer:
-x^2 +2x +8
Step-by-step explanation:
f(x) = 2x + 1
g(x) = x^2 – 7,
(f – g)(x) = 2x +1 - ( x^2 -7)
Distribute the minus sign
= 2x+1 - x^2 +7
Combine like terms
= -x^2 +2x +8
Answer:
its not true. Answer is (f + g)(x) = x2 + 2x - 6
Step-by-step explanation:
Trust me. Good luck.
The length of 7 (the minor arc) is 15 cm. What is the circumference of Z?
Answer:450 cm
Step-by-step explanation:
[tex]4^{3/4} * 2^{x} =16^{2/5}[/tex]
Answer:
[tex]\sf x=\frac{1}{10}[/tex]
Step-by-step explanation:
Rewrite expression with bases of 4.
[tex]\sf{4^{\frac{3}{4} }} \times \sf({4^\frac{1}{2} )^x =(4^2)^{\frac{2}{5} }[/tex]
Apply law of exponents, when bases are same for exponents in multiplication, add the exponents. When a base with an exponent has a whole exponent, then multiply the two exponents.
[tex]\sf{4^{\frac{3}{4} }} \times \sf{4^{\frac{1}{2} x}=4^{\frac{4}{5} }[/tex]
[tex]\sf{4^{\frac{3}{4} +\frac{1}{2} x}=4^{\frac{4}{5} }[/tex]
Cancel same bases.
[tex]\sf \frac{3}{4} +\frac{1}{2} x=\frac{4}{5}[/tex]
Subtract 3/4 from both sides.
[tex]\sf \frac{1}{2} x=\frac{1}{20}[/tex]
Multiply both sides by 2.
[tex]\sf x=\frac{1}{10}[/tex]
Step-by-step explanation:
2^{2*3/4} × 2^{x}=2^{4×2/5}
2^{3/2} × 2^{x}= 2^{8/5}
2^{3/2+x}=2^{8/5}
equate powers
{3+2x}/2= 2^2
5{3+2x}= 2{8}
15+10x=16
collect like terms
10x=16-15
10x=1
divide both sides by 10
x=1/10
x=0.1
A sample of college students was asked how they felt about their weight. Of the 143 women in the sample who responded, 38 women said that they felt overweight, 99 felt that their weight was about right, and 6 felt that they were underweight. Of the 78 men in the sample, 18 men felt that they were overweight, 35 felt that their weight was about right, and 25 felt that they were underweight (Data source: pennstate3 dataset on the companion website).
a. In the relationship between feelings about weight and sex, which variable is the explanatory variable and which is the response variable?
b. Summarize the observed counts by creating a table similar to Tables 2.2 and 2.3 (p. 21).
c. For the 143 women, find the percentage responding in each category for how they felt about their weight.
d. For the 78 men, find the percentage responding in each category for how they felt about their weight.
e. Using the percentages found in parts (c) and (d), summarize how the women and men differed in how they felt about their weight.
Answer:
a. Feelings about weight is the response (dependent) variable. Sex is the explanatory (independent) variable. The feelings about weight depend on the sex
b. Summary of observed counts
Women Men Total
Overweight 38 18 56
Right weight 99 35 134
Underweight 6 25 31
Number 143 78 221
c. Percentage of the 143 women responding in each category:
1. Overweight = 38/143 = 26.6%
2. Right weight = 99/143 = 69.2%
3. Underweight = 6/143 = 4.2%
d. Percentage of the 78 men responding in each category:
1. Overweight = 18/78 = 23.1%
2. Right weight = 35/78 = 44.9%
3. Underweight = 25/78 = 32%
e. Summary of feelings about weight:
Women Men
Overweight 26.6% 23.1%
Right weight 69.2% 44.9%
Underweight 4.2% 32%
Step-by-step explanation:
a) Data:
Sample size = 221
Women Men Total
Overweight 38 18 56
Right weight 99 35 134
Underweight 6 25 31
Number 143 78 221
b) To obtain the percentage of feelings about weight for each category, the number of those who feel overweight, right weight, or underweight is divided by the total number of women or men. The value obtained, which is in decimal form, is then converted to percentage by multiplying with 100.
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
C
Step-by-step explanation:
Line of symmetry
BRAINLIEST, THANKS, 5 STARS & 15 POINTS IF ANSWERED CORRECTLY.
What is the 52nd term of the sequence below?
-38, -35, -32, -29...
Answer:
115
Step-by-step explanation:
It adds 3 every time and starts with -38. Our equation is:
a52 = -38+3(52-1);
a52 = -38 + 153
a52 = 115
Answer:
115
Step-by-step explanation:
→ First we need to work out the nth term. First we find the difference between each term
-38, -35, -32, -29... ⇔ +3
→ We know the first bit is 3n now we have to find the other section. We need to write the 3 times tables on top of each corresponding term
3 , 6 , 9 , 12
-38, -35, -32, -29...
→ We can see the to get from 3 to -38 we minus 41. So the nth term is
3n - 41
→ Now we substitute in 52 for n
3 × 52 - 41
→ Simplify
115
Select all the expressions that represent the large rectangle's total area
Answer:
Area of a rectangle is w • L
w = 5 while L = (b + 3)
Area is
5 • (b + 3) = 5b + 15
So answer is 2. 3. and 4. which are all similar forms of the same expression.
Step-by-step explanation:
At what meter mark will Ario be when Miguel starts the race? Round to the nearest tenth. x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 A number line goes from 0 to 25. A line is drawn from 3 to 25. The point at 3 is labeled Start and the point at 25 is labeled End. Miguel and his brother Ario are both standing 3 meters from one side of a 25-meter pool when they decide to race. Miguel offers Ario a head start. Miguel says he will start when the ratio of Ario’s completed meters to Ario’s remaining meters is 1:4.
Answer: 7.4 meters
Step-by-step explanation:
Start Mark = 3m
End mark = 25m
Total length to race = 25 - 3 = 22m
Position of both Ario and miguel = 3 meter from one side of the pool; that is 3 meters behind the START MARK
Ario's completed to remain ratio = 1:4
Total ratio = 5
Ario's Completed meters = (22/5) * 1 = 4.4m
Therefore, when Miguel starts the race, Ario will be on (4.4meters + number of meters behind the start mark)
= 4.4 meters + 3 meters = 7.4meters
The distance of Ario from the start point when miguel starts is;
7.44 m
We are told that A line is drawn from 3 to 25.This means distance of line = 25 - 3 = 22 m
The start point is at the 3 m mark.Miguel and his brother Ario are standing 3 m from one side of the pool.
This means that they are both 3 meters behind the start point.
We are told that the ratio of Ario’s completed meters to Ario’s remaining meters is 1:4.Thus, ario's completed meters when Miguel will start is;
¹/₅ × 22 = 4.4 m
Since Miguel is 3 m from the start and Ario has just done 4.4 m, then it means that;Distance of miguel from Ario when miguel starts = 3 + 4.4 = 7.4 m
Read more about algebra at; https://brainly.com/question/11408596
Tammy has $20 to spend at the movie theater. She spends $9.50 on a movie ticket. If the snack counter sells bags of candy for $3.50 each, how many bags of candy can Tammy buy with the money she has left?
Answer:
She can buy 3 candy bags.
Step-by-step explanation:
Let the number of bags = x.
9.5 + 3.5x = 20
3.5x = 10.5
x = 3
Answer: She can buy 3 candy bags.
Answer:
3
Step-by-step explanation:
i need help quick i will mark brainilest
Answer:
x-y
Step-by-step explanation:
X is greater than y so we are subtracting the smaller number from the bigger number
That means we do not need the absolute value signs since x-y will be positive
|x-y| when x> y
x-y
Using numbers
| 5-2| 5>2
5-2
Mr. Kennedy raise beef cattle the stock tank near the windmill has a diameter of 3 m what it is for the water is 1.5 m deep how many cubic meters of water are in the stock tank when it is full use 3.14 for pi
Answer:
10.6
Step-by-step explanation:
radius = 1.5 height = 1.5 so it's 10.6
Answer:
10.6
Step-by-step explanation:
Trignometry Question Please help
Answer:
19.45°
Step-by-step explanation:
Suppose the post is 1 unit high. Then the distance from the post to another corner of the rectangle will satisfy the relation ...
distance/1 = tan(90° -angle of elevation)
So, for the near corner, the distance from the post is ...
distance = tan(90° -36°) = tan(54°) = 1.37638 . . . post lengths
For the other given corner, the distance from the post is ...
distance = tan(90° -22°) = tan(68°) = 2.47509 . . . post lengths
The Pythagorean theorem can be used to find the distance from the post to the diagonally opposite corner:
distance^2 = 1.37638^2 +2.47509^2 = 8.02048
distance = √8.02048 ≈ 2.83205
The relation of this to the angle of elevation is ...
tan(angle of elevation) = 1/2.83205
angle of elevation = arctan(1/2.83205) ≈ 19.45°
_____
In the attached diagram, we have used segments BP and CP as surrogates for the post, so we could determine distances PD and PE that are the sides of the rectangular courtyard. Then the courtyard diagonal is PF. Using PA as a surrogate for the post, we found the angle of elevation from F to A (the top of the post) to be 19.45°, as computed above.
Please answer quickly I am unsure what to do
Answer:
Investment B is £97 more than investment A
Step-by-step explanation:
For investment A
£160is saved for 2 years every month
Total amount at the end of the two years= 2*160*12= £3840
The the percentage interest added is
=2.5/100*3840
= £96
Total amount= 3840+96
Total amount=£ 3936
For investment B
£3800 is compounded every year for two years at 3%
Total amount= 3800(1+0.03/2)^(2*2)
Total amount= 3800(1+0.015)^4
Total amount= 3800(1.015)^4
Total amount= 3800(1.061363551)
Total amount= 4033.18
Total amount= £4033
The difference between the two investment= 4033-3936
= £97