Answer:
x² + 4x - 7 = (x + 2)² - 11
Step-by-step explanation:
Let us solve the question
∵ The expression is x² + 4x - 7
∵ The form is (x + a)² - b
→ To express the equation in the given form quate them
∴ x² + 4x - 7 = (x + a)² - b
→ Simplify the right side then equate the like terms to find a and b
∵ (x + a)² = (x + a)(x + a)
∴ (x + a)² = (x)(x) + (x)(a) + (a)(x) + (a)(a)
∴ (x + a)² = x² + ax + ax + a²
→ Add the like terms
∵ (x + a)² = x² + (ax + ax) + a²
∴ (x + a)² = x² + 2ax + a²
→ Substitute (x + a)² in the right side by x² + 2ax + a²
∵ x² + 4x - 7 = x² + 2ax + a² - b
→ Equate the coefficients of the like terms
∵ 4x and 2ax are like terms
∴ 4 = 2a
→ Divide both sides by 2
∴ 2 = a
∵ -7 and a² - b are like terms ⇒ constant terms
∴ -7 = a² - b
∵ a = 2
∴ -7 = (2)² - b
∴ -7 = 4 - b
→ Subtract 4 from both sides
∵ -7 - 4 = 4 - 4 - b
∴ -11 = -b
→ Divide both sides by -1
∴ 11 = b
→ Substitute the values of a and b in the given form
∴ (x + a)² - b = (x + 2)² - 11
∴ x² + 4x - 7 = (x + 2)² - 11
gustavo ronaldo says, if you subtract 11 from my number and multiply the difference by -3, the result is -51 . what is s number?
Answer:
28
Step-by-step explanation:
-3 * (x-11) = -51
x-11 = 17
x = 28
a
100 cm²
b
9 cm²
c
225 cm²
d
28.26 cm²
Answer:
28.26 cm^2
Step-by-step explanation:
A = (pi)r^2
A = 3.14 * (3 cm)^2
A = 3.14 * 9 cm^2
A = 28.26 cm^2
calculate the maximum of ( 68 x 42) / 120 to the nearest whole number
(write your answer correct to 2 d.p)
Answer:
23.8 will be it's answer
who was Queen Elizabeth 1
Easy Question>>?????????????help
Answer:
thanswer to this is...................
Step-by-step explanation:
unknown
or 148 degrees
Answer:
148 degrees... if it's so easy then why u couldn't u answer it
please help me asap
Answer:
6
Step-by-step explanation:
s=9, t=12
2s-t = 2*9 -12 = 18 -12 = 6
Answer:
the answer is 6
Step-by-step explanation:
Because you do 2 times 9 = 18 then 18 - 12 = 6
What is the unit rate of 15 laps in 3 days
Answer:
the answer to that is 5 laps per day
Step-by-step explanation:
15 laps ÷ 3
3 days ÷3
5 laps
=
1 day
5 laps=days
The time period, T, of a simple pendulum is directly proportional to the square root of the length, d, of the pendulum.
When d=6, T=5
Find the value of T when d=3
Input note: give your answer correct to 2 decimal place.
Step-by-step explanation:
T = k * sqrt(d), where k is a real constant.
When d = 6, T = 5.
k = T / sqrt(d) = 5 / sqrt6.
Therefore when d = 3, T = (5 / sqrt6) * sqrt3 = 3.53.
what number should be placed in the Box to complete the division calculation
Answer:
Umm !! it's 260
Step-by-step explanation:
Hope I'm right ?!!!!?!??
In right triangle ABC, ZCis a right angle and sin A= sin B. What is mZA
Answer:
∠A = 45°
Step-by-step explanation:
It is given that,
sin A = sin B
∠C is a right angle.
If sin A = sin B, it means
sin 45 = sin 45 = [tex]\dfrac{1}{\sqrt2}[/tex]
It means that angle A and angle B is 45 degrees.
which of the following circles have their centers on the y-axis check all that apply
Write an equation of the line that passes through a pair of points: (-4, -3), (-3, 1)
a. y = 4x -13)
b. y = -4× 13)
c. y = 4x +13)
d. y = 4x -1/13
Answer:
C. y=4x+13
Step-by-step explanation:
To solve this equation first find the slope. Do this by using the slope formula, m=[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], so plug in the points[tex]\frac{1+3}{-3+4}[/tex] which equals 4/1 or 4. Since now we know the slope is 4 we can put the equation into slope-point form, I will be using (-4,-3) for this equation. y+3=4(x+4), then solve for y. After solving you get y=4x+13.
please help thx so much
Answer:
I think c is the answer....
George has 28 tomato seedlings. He wants to put them into 7 equal groups to sell. Which number sentence could be used to find the number of seedlings in each group
Answer:
4
Step-by-step explanation:
7+7+7+7 or 28/7 =4
Please help will give brainliest
Answer:
I'm not completely sure but i'm going to guess on D the domain is 1 < f < 7, the range is 24 < c(f) < 168
Step-by-step explanation:
because 1 cup is < to a cup of Flour (f), and the expression says 7 cups in total so i f is less than or equal to the total number of cups 7. then the range says c(f)=24(f), meaning you get 24 cookies for the input amount "f" of cups of flour. So the range would be 24 is grater of equal to the c(f)which in total (7 x 24) is equal to 168
Just tell me if these soccer balls show a reflection. Its for a math assignment i just need to know if this shows a reflection
Answer: Yes
Step-by-step explanation:
Answer:
yesh it does :>
Step-by-step explanation:
The price of a technology stock has dropped to $9.71 today. Yesterday's price was $9.80. Find the percentage decrease.
Answer:
The percentage decrease = 0.9%
Step-by-step explanation:
Initial value = $9.80Final value = $9.71Using the formula
Percentage Decrease = [ (Initial Value - Final Value) / |Initial Value| ] × 100
= [(9.80 - 9.71 ) / (9.80)] × 100
= [0.09 / 9.80] × 100
= 0.009 × 100
= 0.9%
Therefore, the percentage decrease = 0.9%
Complementary angles are 2 angles with a sum of 90.
Answer:
Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.
Which polynomial function has a leading coefficient of3 and roots -4, i, and 2, all with multiplicity 1?
Answer:
Step-by-step explanation:
f(x) = 3(x + 4)(x – i)(x + i)(x – 2)
What input is NOT allowed for f(x) = 3/ x-5
Answer:
x ≠ 5
Step-by-step explanation:
x ≠ 5
The reason for this is because if we use the input 5, this will be the result:
f(x) = 3/(5) - 5
f(x) = 3/0 = Undefined
an art collector bought 20 paintings at an art fair, and wants to know the average price of the paintings ahe purchased at the fair. She adds the prices of all the paintingsand dividesthis number by 20 to find an average price of $3550. Is this price a sample mean or a population mean, and which symbol would be used to donate it?
Answer:
The calculated mean price is a sample mean and it is denoted by x.
Step-by-step explanation:
Given that
Mean price of paintings = $3550
Number of paintings = 20
In order to decide whether it is a population mean or a sample mean we have to understand the terms first.
Population:
Population is the overall collection from which a sample or observations are taken.
Sample:
The small or less number of observations that we take from a large population to perform data analysis is called sample.
In the given scenario, all the paintings at the art fair are population while the number of paintings that the art collector bought is a sample.
Hence,
The calculated mean price is a sample mean and it is denoted by x.
Jen has 81 beads. Ana has 44 red beads and 29 blue beads.
How many more beads does Ana need to have 81 beads also?
Ana needs
more beads to have 81 beads.
(8th grade. 4.4 Practice A.)PLEASE HELP!! what's the answer to all the CIRCLED questions. 85 points!!!
Answer:
1. is Line C
2. is line A
(slope, y-intercept)
4. (1, 4)
6. (-5/7, -2)
8. (6, 2)
9. (1/2, -7)
10.
a) you've already done this
b)-4200
c)21000
d) 5
11.
draw a line between the intercepts and add arrows to each end to graph the line easily
y- intercept is -6 ( at 0, -6)
x intercept is 2 ( at 2, 0)
Simplify. Express the answers using positive exponents
Answer:
C
Step-by-step explanation:
The simplified expression of the given expression -5[tex]w^2y^{-2[/tex] / -15[tex]w^{-6}y^2[/tex] is [tex]w^{16[/tex].
The expression -5[tex]w^2y^{-2[/tex] / -15[tex]w^{-6}y^2[/tex] can be simplified as follows:
= -5 * [tex]w^{2 - (-6)[/tex] * [tex]y^{-2 - 2[/tex] / -15 * [tex]w^{-6 - 2[/tex] * [tex]y^{2 - (-2)[/tex]
= -5 * [tex]w^8[/tex] * [tex]y^{-4[/tex] / -15 * [tex]w^{-8[/tex] * [tex]y^4[/tex]
= (-5 / -15) * ([tex]w^8[/tex] / [tex]w^{-8[/tex]) * ([tex]y^{-4[/tex] / [tex]y^4[/tex])
= 1 * [tex]w^{16[/tex] * [tex]y^0[/tex]
= [tex]w^{16[/tex]
Therefore, the simplified expression is w^16.
Here is a breakdown of the steps involved in the simplification:
The powers of w and y are combined using the distributive property of exponents.
The negative exponents are changed to positive exponents by dividing by the same base raised to the power of the negative exponent.
The factors of 5 and 15 are simplified.
The common factors of w and y are simplified.
To learn more about expression here:
https://brainly.com/question/12909556
#SPJ2
Question 5 6 pts Alanis goes to work with her father. He gives out the paychecks to the employees at his company. Alanis notices that one man worked 31.25 hours for the week, and he was paid $9.20 per hour. How much was the man's paycheck? O A. $270.00 O B. $287.50 c. $1 150.00 O D. $1,437.50 Question 6 6 pts
HELPPPPPPPPPPP PLEASEEEEEEE!!!!!!!!
A population of insects increases at the rate of 200 10t 13t2 what is the change in the population of insects between day 0 and day 3
Answer:
762 days
Step-by-step explanation:
Given
[tex]Rate = 200 + 10t + 13t^2[/tex]
Let the rate be R.
So the rate change with time is represented as:
[tex]\frac{dR}{dt} = 200 +10t + 13t^2[/tex]
So:
[tex]dR = (200 + 10t + 13t^2)\ dt[/tex]
To get the number of insects between day 0 and day 3, we need to integrate dR and set the bounds to 0 and 3
i.e.
[tex]dR = (200 + 10t + 13t^2)\ dt[/tex] becomes
[tex]\int\limits^3_0 {dR} \, =\int\limits^3_0 (200 + 10t + 13t^2)\ dt[/tex]
[tex]R =\int\limits^3_0 (200 + 10t + 13t^2)\ dt[/tex]
Integrate
[tex]R = 200t + \frac{10t^2}{2} + \frac{13t^3}{3} [3,0][/tex]
Solve for R by substituting 0 and 3 for t
[tex]R = (200*3 + \frac{10*3^2}{2} + \frac{13*3^3}{3}) - ( 200*0 + \frac{10*0^2}{2} + \frac{13*0^3}{3})[/tex]
[tex]R = (200*3 + \frac{10*9}{2} + \frac{13*27}{3}) - (0 + \frac{10}{2} + \frac{0}{3})[/tex]
[tex]R = (200*3 + 5*9 + 13*9) - (0)[/tex]
[tex]R = 600 + 45 + 117 - 0[/tex]
[tex]R =762[/tex]
The population of insect between the required interval is 762
The required change in the population of insects between day 0 and day 3 is 762.
Given that,
A population of insects increases at the rate of 200++ 10t + 13t2.
We have to determine,
What is the change in the population of insects between day 0 and day 3.
According to the question,
The rate change with time is represented as:
[tex]\frac{dr}{dt} = 200+10t+13t^{2}[/tex]
To determine the change in the population of insects between day 0 and day 3,
Integrating the given function with respect to time with limit 0 days to 3 days.
[tex]\int\limits^3_0 dr = \int\limits^3_0 (200+10t+13t^{2} ). dt\\\\\int\limits^3_0dr =\int\limits^3_0 \, 200dt + \int\limits^3_0 10tdt +\int\limits^3_0{13t^{2} dt\\\\\\\\R = [200t]^3_0 + [5t^{2} ]^3_0 + [\frac{13t^{3} }{3} ]^3_0\\\\R = 200[(3) - (0)] + 5 (3^{2} - 0^{2} ) + \frac{13}{3} [ 3^{3} - 0^{3} ]\\\\R = 200(3) + 5 (9) + \frac{13}{3}(27)\\\\R = 600+45+117\\\\R = 762[/tex]
Hence, The required change in the population of insects between day 0 and day 3 is 762.
To know more about Rate change click the link given below.
https://brainly.com/question/24540629
which statement is true when parallel lines are cut by transversal?
Answer:
If two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent . When two lines are cut by a transversal, the pairs of angles on either side of the transversal and outside the two lines are called the alternate exterior angles .
Step-by-step explanation:
Three sisters purchased treats at a bake sale. The oldest sister spent $2.70 on brownies. The middle sister spent four times as much on cookies as the older sister spent on brownies. The youngest sister spent $3.68 less on a cake than the middle sister spent on cookies. How much did each sister spend?
Answer:
the oldest sister spent 2.70$ (given)
the middle sister spent 10.80$
and the youngest sister spent 7.12$
Step-by-step explanation:
One quarter has a mass of 5.67 grams. Which is the mass of two rolls of quarters each containing 40 quarters?
9514 1404 393
Answer:
453.6 g
Step-by-step explanation:
The mass of 80 quarters will be 80 times the mass of 1 quarter:
80 × 5.67 g = 453.6 g
The mass of two rolls of quarters is 453.6 grams.
_____
Additional comment
That's about 1.0000 pounds.