Answer:
(x - 9)(x + 2)
x = 9 or -2
Step-by-step explanation:
First, we need to find factors of 18 that add up to -7
Factors of 18:
1 and 18
2 and 9
3 and 6
Add/Subtract them to have a total sum of -7
18 - 1 = 17 ...... 1 - 18 = -17 (not -7)
9 - 2 = 7 ........ 2 - 9 = -7 (sum of -7)
6 - 3 = 3 ......... 3 - 6 = -3 . (not -7)
Hence the numbers that would go in the brackets would be -9 and 2
(x - 9)(x + 2)
x² - 7x - 18
Answer:
(x-9)(x+2)
Step-by-step explanation:
The first term is the product of two x's being multiplied together. the second term (-7x) is the sum of the two numbers. -18 (the third term) is the product of those numbers.
Think: what two numbers will add up to -7 and multiply to -18
Those numbers are -9 and 2
Now, this is a quadratic trinomial, and you factor these kinds of equations like this: (x+a)(x+b) (a and b as placeholders for actual numbers)
Now, plug -9 and 2 in
(x-9)(x+2)
Hope this helps!
Consider x >5 and 2.x > 2.5. Identify a solution to the first
inequality. Show that this solution also makes the second
inequality true.
answer=
step by step:
2 x 6 =12
6 > 5
Henry and Irene working together can wash all the windows of their house in 1 h 40 min. Working alone, it takes Henry 2 1 2 h more than Irene to do the job. How long does it take each person working alone to wash all the windows?
Answer:
Step-by-step explanation:
Henry and Irene working together can wash all the windows of their house in 1 h 40 min. Working alone, it takes Henry 2 1 /2 h more than Irene to do the job. How long does it take each person working alone to wash all the windows?
Let us represent
The number of hours Irene takes to do the job alone =x
1/x=Irene's work rate
The number of hours Henry takes to do the job alone = x + 2.5
1/(x+2.5)=Henry's work rate
1 hr and 40 min
Converting the 40 minutes to hour
60 mins = 1 hour
40 mins = x
x = 40/60
x = 0.6666666667 hour
1 hour 40 minutes = 1.67hours
Irene and Henry working together to do the job
Their work rate working together
sum of individual work rates=work rate when working together
1/x+1/(x+2.5)=1/1.67
LCD:(x)(x+2.5)(1.67)
(x+2.5)(1.67)+(1.67)(x)=(x)(x+2.5)
1.67x+ 4.175 +1.67x=x^2+2.5x
x^2+ 2.5x - 3.38x - 4.175
x^2- 0.84x - 4.175
Using Almighty formula
x = 42 minutes
x + 2.5 +
0.42 + 2.5 = 2.92 hours
A real estate agent sold a house for $315,000 last week. If her commission is 3.25% of the selling price of the home, find the amount of her commission?
Answer:
Total commission= $10,237.5
Step-by-step explanation:
Giving the following information:
A real estate agent sold a house for $315,000 last week.
Commission= 3.25%
To calculate the value of the commission, we need to use the following formula:
Total commission= house value*commission percentage
Total commission= 315,000*0.0325
Total commission= $10,237.5
Every 8th person at a concert receives a free t-shirt. Every 10th person receives a free keychain. If there are 160 people who attended the concert how many people will receive both a t-shirt and a keychain?
Answer:
4 people will receive both a t-shirt and a keychain.
Step-by-step explanation:
To determine how many people will receive both a t-shirt and a keychain,
First we will determine those that will receive a t-shirt and as well determine those that will receive a keychain.
For those that will a receive a t-shirt
Since every 8th person receives a t-shirt, then
The 8th, 16th, 24th, 32nd, 40th, 48th, 56th, 64th, 72nd, 80th, 88th, 96th, 104th, 112th. 120th, 128th, 136th, 144th, 152nd, and 160th persons will receive a t-shirt.
For those that will receive a keychain
Since every 10th person receives a keychain, then
The 10th, 20th, 30th, 40th, 50th, 60th, 70th, 80th, 90th, 100th, 110th, 120th, 130th, 140th, 150th, and 160th persons will receive a keychain.
From above, those that will receive both a t-shirt and a keychain are the 40th, 80th, 120th, and 160th persons.
Hence, 4 people will receive both a t-shirt and a keychain.
Obtener las coordenadas del punto medio del segmento determinado de los puntos P(5,-2) Q(6,7)
Answer:
could you provide an image and translation please?
Step-by-step explanation:
solve the system by Substitution 4x+4y=-4 y=-7x-7
Answer: {-1, 0}
Explanation: Since y = -7x - 7, we can replace the y in our first equation with
a -7x - 7 and our first equation now reads 4x + 4(-7x - 7) = -4.
To solve this equation, first distribute the 4 through the parenthses.
So we have 4x - 28x - 28 = -4.
Now simplify the left side to get -24x - 28 = -4.
Adding 28 to both sides, we have -24x = 24.
Dividing both sides by -24, we find that x = -1.
To find y, plug a -1 back into either equation.
So we have y = -7(-1) - 7 or y = 0.
Our final answer is {-1, 0}.
Answer:
x= -1,
y=0
Step-by-step explanation:
[tex]\begin{bmatrix}4x+4y=-4\\ y=-7x-7\end{bmatrix}\\\\\mathrm{Subsititute\:}y=-7x-7\\\\\begin{bmatrix}4x+4\left(-7x-7\right)=-4\end{bmatrix}\\\\Simplify\\\\\begin{bmatrix}-24x-28=-4\end{bmatrix}\\\\Isolate\:x \:for \:-24x-28=-4\:\::x =-1\\\\\mathrm{For\:}y=-7x-7\\\\\mathrm{Subsititute\:}x=-1\\\\y=-7\left(-1\right)-7\\\\-7\left(-1\right)-7 =0\\\\y=0\\\\\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}\\x=-1,\:y=0[/tex]
Determine whether each quadrilateral is a parallelogram. Justify your answer. a Yes; opposite angles are congruent. b Yes, opposite sides are parallel and congruent. c Yes; consecutive angles are supplementary. d No; none of the tests for parallelograms are fulfilled..
A parallelogram is a quadrilateral with congruent and parallel opposite sides. Thus, to justify that the given quadrilateral is a parallelogram, option C is correct.
i.e C. Yes; consecutive angles are supplementary.
Quadrilaterals are shape with four straight sides. Examples are; square, rectangle, parallelogram, trapezium etc.
A parallelogram is a type of quadrilateral that has opposite sides to be equal and parallel. It has some distinguishing properties which can be used to differentiate it from other quadrilaterals. Some of the are:
opposite sides are equalopposite sides are parallelconsecutive angles are supplementary opposite angles are congruentThus, in the given question the required option is C. consecutive angles are supplementary.
For more on properties parallelogram, check: https://brainly.com/question/3100335
For the triangle ABC determine if the following statement is true or false
Answer:
i think the answer is true.
Step-by-step explanation:
Answer:
Its true
Step-by-step explanation:
please help. are they Parallel, perpendicular or neither?
Answer:
The are Parallel
Step-by-step explanation:
As you can see the points, they are going straight which mean they will not intersect (Parallel)
Answer:
parallel
Step-by-step explanation:
yeah i think so
This is due at 11:20
Simplify 10^6/10^-3 (1 point)
1/10^3
1/10^18
10^3
10^9
Answer:10^9
Step-by-step explanation: they both equal 1000000000
Xavier Cantor works on an 8 hour day. He is paid $13.69 an hour for regular-time work and time-and-a-half for any hours over 8 hours a day. Xavier worked these hours last week: Monday 9 3/4, Tuesday 8, Wednesday 6, Thursday 8 1/2, Friday 8. Complete all five stages to find Xavier's gross wages for last week. *
Answer:
Step-by-step explanation:
Xavier is paid $13.69 for 8 hours and 1.5times this amount on the hours above 8 which will be $20.475
Monday Tuesday Wednesday Thursday Friday
[tex]8hr[/tex] +[tex]1\frac{3}{4} hr[/tex] [tex]8hr[/tex] [tex]6hr[/tex] [tex]8hr + 1/2hr[/tex] [tex]8hr[/tex]
$145.35 $109.52 $82.14 $119.76 $109.52
total= $566.29
A road rises 1 m for every 15 m measured along the road. a) What is the angle of inclination of the road to the nearest degree? b) How far does the car travel horizontally when it travels 15 m along the road ? Give the answer to the nearest tenth of a metre.
Answer:
The answer is below
Step-by-step explanation:
The road increases by a height of 1 m for every 15 m distance. The slope of a line is the ratio of its rise to run. The slope (m) is the tangent of the inclination. Hence:
Slope = rise / run = tanθ
Where θ is the angle of inclination.
a) Given rise = 1 m, run = 15 m
Slope of road (m) = rise / run
m = 1 m/ 15 m
m = 0.0667
slope = tanθ
tanθ = 0.0667
θ = tan⁻¹(0.0667)
θ = 3.81
θ ≈ 4°
b) cosθ = horizontal distance / 15 m
horizontal distance = 15 m × cos 4
Horizontal distance = 14.96
Horizontal distance = 15 m to nearest tenth
Can anyone help? I'll mark you the brainliest
Answer:
angles 7,17 and 19
Step-by-step explanation:
If a and b are parallel then their angles will correspond.
The ratio of the radii of two circles is 2:3. The diameter of the smaller circle is 15 mm. What is the length of the diameter of the larger circle? 10.00 mm 11.25 mm 22.50 mm 30.00 mm
Answer:
The diameter of the larger circle is 22.50 mm
Step-by-step explanation:
Given;
ratio of radii of two circles = 2:3
diameter of the smaller circle, d = 15 mm
let the diameter of the larger circle = D
The ratio of the radii of the two circles is given by;
[tex]\frac{2r}{2R}= \frac{d}{D}= \frac{2}{3}\\\\ D= \frac{3d}{2}\\\\ D = \frac{3*15}{2} \\\\D = 22.50 \ mm[/tex]
Therefore, the diameter of the larger circle is 22.50 mm
Answer:
The diameter of the larger circle is 22.50 mm
Step-by-step explanation:
Given;
ratio of radii of two circles = 2:3
diameter of the smaller circle, d = 15 mm
let the diameter of the larger circle = D
The ratio of the radii of the two circles is given by;
Therefore, the diameter of the larger circle is 22.50 mm
Step-by-step explanation:
5(-3.4k - 7) + (3k + 21)
Interest: Zoe has $3000 to put into a savings account. The account earns an annual interest rate of 3%. Fill in the following table: Number of years in account Amount in account ($) 0 3000 1 2 3 4 How much will Zoe have in the account after 7 years? How long will it take for the money to grow to $4000?
Step-by-step explanation:
$3000.00 +3%= $3,090
annual is once a year So $90.00 in interest per year
$90×7=$630 for 7 years of interest
What is the area of the triangle?
Answer:
14cm^2
Step-by-step explanation:
use A=1/2(b)(h)
A=1/2(7)(4)
A=1/2(28)
A=14cm^2
Answer/Step-by-step explanation:
7 x 4 = 28 divided by 2 = 14.
Make sure to find the square root of the answer or it will be a square and not a triangle.
If y is directly proportional to x, and y = 56 when x = 6, what is
the value of x when y = 84?
A)6
B)9
C)13
D)15
Answer:
B) 9
Step-by-step explanation:
According to the statement, we have the following relationship:
[tex]y \propto x[/tex]
[tex]y = k\cdot x[/tex] (Eq. 1)
Where:
[tex]k[/tex] - Proportionality constant, dimensionless.
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
Such constant is eliminated by constructing this relationship:
[tex]\frac{y_{2}}{y_{1}} = \frac{x_{2}}{x_{1}}[/tex]
[tex]x_{2} = \left(\frac{y_{2}}{y_{1}} \right)\cdot x_{1}[/tex] (Eq. 2)
If we know that [tex]y_{1} = 56[/tex], [tex]x_{1} = 6[/tex] and [tex]y_{2} = 84[/tex], then the value of [tex]x_{2}[/tex] is:
[tex]x_{2} = \left(\frac{84}{56} \right)\cdot (6)[/tex]
[tex]x_{2} = 9[/tex]
Hence, the correct answer is B.
i need help please!!!!!!!
Answer:
28°
Step-by-step explanation:
Complementary angles sum to 90° , thus
∠ DEF + ∠ LMN = 90°, that is
62° + ∠ LMN = 90° ( subtract 62° from both sides )
∠ LMN = 28°
Bailey went to the beach. After 1 day of collecting shells, he had 19. He had 26 shells on day 2, and 33 shells on day 3. Which expression can be used to find the nth term of the sequence created by this scenario?
Answer:
12 + 7s = NumOfShells
75 Shells on day 9
Step-by-step explanation:
You are able to find the number of shells on the ninth or nth day of the sequence of days by finding the differences and calculating them
April took out a $600 loan from the bank. At the end of 5 years, she pays back the principal, plus $60 simple interest. What was the interest rate? Enter your answer in the box.
Answer:
2%
Step-by-step explanation:
Is the relationship linear?
If yes, what is the rate of
change?
Answer
Linear, [tex]\frac{4}{-3}[/tex] is the slope
Step-by-step explanation:
Its linear because the rate of change doesn't change throughout our points.
Lets use our coordinate points for the bottom and middle one, making 1 our rate of our graph.
The bottom one that's closest to the x-axis would be (8,2). Move 8, the x, to the right, and up 2, the y The middle one of the points would be (5,6). Move 5, the x, to the right, and up 6, the y.
We have our points, now we find the rate of change, also known as slope.
So the equation for slope is m = [tex]\frac{db}{ca}[/tex] and our points together is (8,2)(5,6). Line up the variables with our points. So for example, 8 would be A, 2 would be B, 5 would be C and so on.
Then we have [tex]\frac{6-2}{5-8}[/tex]. Solve it, and we get [tex]\frac{4}{-3}[/tex].
yea hoped that help
(-5x²)³
Thanks for answering when you do answer
The following table shows how far a bus has gone in t hours. Which of the following equations represents this information?
Hours (t) Distance in Miles (d)
2 122
5 305
6 366
10 610
Answer:
T=61d
Step-by-step explanation:
Hope this helps!
Answer:
t = 61d
Step-by-step explanation:
The girls’ soccer team scored 60 points in 10 games. If this trend were to continue, what would be the points scored in 15 games?
Answer:
90 points
Step-by-step explanation
You and a group of friends participate in a game where you must use clues to escape from a room. You have a limited amount of time to escape and are allowed 3 free clues. Additional clues may be requested, but each removes 5 minutes from your remaining time. What integer represents the total change in the time when you use 5 clues?
Answer:
The integer that represent the total change in time when 5 clues are used is 10
Step-by-step explanation:
The given parameters are;
The number of free clues available = 3
The number of minutes removed for an additional clue = 5 minutes
Therefore, the total change in time when 5 clues are used is given as follows;
The number of free clues available 3
The number of clues for which 5 minutes is removed from the remaining time when 5 clues are selected = 5 - 3 = 2 clues
Therefore, the total change in time = The number additional clues × 5 minutes/clue
The total change in time = 2 clues × 5 minutes/clue = 10 minutes
The total change in time = 10 minutes
Therefore, the integer that represent the total change in time (in minutes) when 5 clues are used = 10.
Answer:
-10
Step-by-step explanation:
Multiply (-4r^3)(-5r^3) =
Answer:
20r^6
Step-by-step explanation:
I'm not sure
Answer:
20 r ^6
Step-by-step explanation:
-4*-5=20
3+3=6
The product of powers rule states that when multiplying two powers with the same base, just add the exponents.
If we know that 6 cups of flour is used to make 24 biscuits how many biscuits can be made with 18 cups of flour? I don’t get it can someone help me plz??
Select the correct answer.
Find the value of f(-142) for the function below.
f(x) = -0.2(x + 223)
A.
81
B.
-186.6
C.
-16.2
D.
251.4
Answer:
c
Step-by-step explanation: