Answer:
A. (x – 3) and (x – 7)
Step-by-step explanation:
A. (x – 3) and (x – 7) = x^2 - 10x + 21
x*x = x^2
x*-7 = -7x
-3*x = -3x
-3*-7 = 21
x^2 - 7x + 3x + 21
x^2 - 10x + 21
Daina gives 2/3 of his money to Carol. Carol gives 6/7 of this money to Zak.
What fraction of Daina's money does Zak get?
NEED HELP ASAP EASY 10 POINTS
Answer:
2x+3
Step-by-step explanation:
factor into [tex](2x+3)^{2}[/tex]
then square root it [tex]\sqrt{(2x+3)^{2} }[/tex]
We know that,
[tex]{ \longrightarrow \bf \qquad \: {(a + b)}^{2} = {a}^{2} + 2.a.b + {b}^{2} }[/tex]
Solution :
[tex]{ \longrightarrow \sf \qquad \: {4x}^{2} + 12x + 9 }[/tex]
We can also write it as,
[tex]{ \longrightarrow \sf \qquad \: {4x}^{2} + 12x + {3}^{2} }[/tex]
Now, using the formula, we'll solve the expression.
[tex]{ \longrightarrow \sf \qquad \: {2x}^{2} + 2.2x.3 + {3}^{2} }[/tex]
[tex]{ \longrightarrow \sf \qquad \: (2x + 3)^{2} }[/tex]
Since,
Area = (side)²Therefore,
The Length of one side is (2x + 3) .The houses in a row are numbered consecutively from 1 to 49. Show that there exists a value of x such that the sum of numbers of houses preceding the house numbered x is equal to sum of the number of houses following x.
Don't Spam
Answer:
Number of the houses as x =35
Step-by-step explanation:
The number of houses is 1, 2, 3, ..., 49
By observation, the numbers of houses are in an A.P.
Hence
First-term, a = 1
Common difference, d = 1
Let us assume that the number of xth house can be expressed as below:
We know that sum of n terms in an A.P. is given by the formula Sₙ = n/2 [2a + (n - 1) d]
Sum of number of houses preceding xth house = Sₓ ₋ ₁
Sₓ ₋ ₁ = (x - 1) / 2 [2a + ((x - 1) - 1)d]
= (x - 1) / 2 [2 × 1 + ( x - 2) × 1]
= (x - 1) / 2 [2 + x - 2]
= [x (x - 1)] / 2 ---------- (1)
By the given information we know that, sum of number of houses following xth house = S₄₉ - Sₓ
S₄₉ - Sₓ = 49 / 2 [2 × 1 + (49 - 1) × 1] - x / 2 [2 × 1 + (x - 1) × 1]
= 49 / 2 [2 + 48] - x / 2 (2 + x - 1)
= (49 / 2) × 50 - (x / 2) (x + 1)
= 1225 - [x (x + 1)] / 2 ---------- (2)
It is given that these sums are equal, that is equation (1) = equation(2)
x (x - 1) / 2 = 1225 - x (x + 1) / 2
x² / 2 - x / 2 = 1225 - x² / 2 - x / 2
On solving further we get,
x² = 1225
x = ± 35
As the number of houses cannot be a negative number, we consider the number of houses as x = 35
35 is the correct answer
Step-by-step explanation:
Given that the houses in a row are numbered consecutively from 1 to 49. We need to show that there exists a value of x such that the sum of numbers of houses preceding the house numbered x is equal to sum of the number of houses following x. Making it more simple for you; sum of (1, 2, 3, 4.... upto x - 1) is equal to sum of (x + 1), (x + 2), (x + 3).... upto 49.
→ Sum of (x - 1) terms = Sum of (49 - x) terms
"x" is the number of houses required. The sum of houses are in AP where the value of a is 1 and d is also 1; where 'a' is first term and 'd' is common difference. We know that sum of nth term of an AP is given by: T(n) = a + (n - 1)d and upto nth term by S(n) = n/2 (2a + (n - 1)d). And also by T(n) = S(n) - S(n - 1).
As per given problem:
→ (x - 1)/2 (Sum of first and last term) = (49 - x)/2 (Sum of first and last term)
→ (x - 1)(Sum of first and last term) = (49 - x) (Sum of first and last term)
Where first term and last term in LHS is 1 and (x - 1) & in RHS is (x + 1) and 49. Substitute them.
→ (x - 1) (1 + (x - 1)) = (49 - x) ((x + 1) + 49)
→ (x - 1) (1 + x - 1) = (49 - x) (x + 1 + 49)
→ (x - 1) (x) = (49 - x) (x + 50)
→ x² - x = 49x + 2450 - x² - 50x
On solving we get,
→ 2x² - 2450 = 0
→ 2x² = 2450
→ x² = 1225
→ x = ± 35
The number of houses is a positive integer. So negative value neglected. We left with x = 35. Therefore, the value of x is 35.
Find the measure of the missing angles .
Answer:
x = 29°, y = 61°
Step-by-step explanation:
x + 61 = 90
Because of the right angle symbol
x = 90 - 61
x = 29°
x + y = 90
Because vertically opposite angles are equal
29 + y = 90
y = 90 - 29
y = 61°
Factorisation of 3p^3 + 9p^2- 15pq
Answer:
STEP 1:Equation at the end of step 1 ((3 • (p3)) + 32p2) - 210p
STEP 2 :Equation at the end of step 2: (3p3 + 32p2) - 210p
STEP 3:STEP 4:
Pulling out like terms 4.1 Pull out like factors : 3p3 + 9p2 - 210p = 3p • (p2 + 3p - 70)
Trying to factor by splitting the middle term 4.2 Factoring p2 + 3p - 70 The first term is, p2 its coefficient is 1 .The middle term is, +3p its coefficient is 3 .The last term, "the constant", is -70 Step-1 : Multiply the coefficient of the first term by the constant 1 • -70 = -70 Step-2 : Find two factors of -70 whose sum equals the coefficient of the middle term,
which is 3 . -70 + 1 = -69 -35 + 2 = -33 -14 + 5 = -9 -10 + 7 = -3 -7 + 10 = 3 That's itStep-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and 10 p2 - 7p + 10p - 70
Step-4 : Add up the first 2 terms, pulling out like factors : p • (p-7) Add up the last 2 terms, pulling out common factors : 10 • (p-7)Step-5 : Add up the four terms of step 4 : (p+10) • (p-7) Which is the desired factorization
Final result : 3p • (p + 10) • (p - 7)
Step-by-step explanation:
mark me brainliest!!
Find the error in this and then solve it correctly
Answer: m<D = 30
Step-by-step explanation: In the third step of the problem, it says that E is next to itself and equals 90. However, this is not true. Angle BEA and angle CED are vertical angles and are both equal to 65°. This means that to find the measurement of angle D, subtract 65 and 85 from 180, which equals 30.
Please help me I need help
Will mark BRAINLIEST
Jack works at a party supply store. He sold 720 balloons in the last 16 days. What was his selling rate in balloons per day?
Answer:
he was selling balloons 45 / day
Step-by-step explanation:
sold 720 ballons in 16 days.
What was selling rate in balloons per day?-----------------------------------------
number of balloons ÷ number of days720 ÷ 1645 balloons/daywhat is the answer to 3 divided by 4/5
Answer:
3/ 4/5=3.75
Step-by-step explanation:
3/ 4/5
3/ 0.80
= 3.75
I TRIED TO MAKE IT AS EASY AS POSSIBLE!
PLS MARK AS BRAINLIEST!
At a shelter 15% of the dogs are puppies there are 60 dogs at the shelter. How many are puppies?
Explanation:
One method is to do the steps like this
15% of 60 = 0.15*60 = 9
Or you can solve like this
part/whole = percent/100
x/60 = 15/100
100x = 60*15
100x = 900
x = 900/100
x = 9
Bill is filling a box up with bottle caps. The box is 1 1/2 feet long, 15 inches wide, and 9 inches high. What is the volume of the box in cubic inches
11/2 so 15 inches high cubic box will get more high I guess
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer:
x=45
Step-by-step explanation:
The total length of a road trip was 13.2 hours. If highway signs are posted every 0.6 hours, including one at the end of the road trip, how many highway signs will there be on the road trip? HELP
Answer:
22
Step-by-step explanation:
Formula : total divide by every hour
13.2/0.6 = 22
Thus, There will be 22 highways sign on the road trip.
[RevyBreeze]
Brennan, a farmer, orders a large box of ladybugs to control pests in his greenhouse. To make sure that he was shipped as many ladybugs as he ordered, he decides to figure out approximately how many ladybugs there are in the box. He catches 30 ladybugs, marks them with special paint, and returns them to the box. Then a little while later, he catches 390 ladybugs and counts 13 marked ladybugs among them. To the nearest whole number, what is the best estimate for the ladybug population
Answer:
900
Step-by-step explanation:
1.analyze problem
2. 30/13*390
3.900
Mrs. Feiner gets 80% right on a quiz with 20 questions.
How many questions does she get right?
A. 15
B. 16
c. 18
D.19
16 answer correct
80×20
_______. =16
100
Brainliest
Brainy reward help me pls
Answer:
[tex]\sf \dfrac{2}{3} \ is \ the \ change \ per \ minute \ in \ the \ amount \ of \ water.[/tex]
explanation:
[tex]\sf unit \ rate : \dfrac{y_1-y}{x_1-x}[/tex]
[tex]\sf unit \ rate : \dfrac{7-5}{3-0}[/tex]
[tex]\sf unit \ rate : \dfrac{2}{3}[/tex]
Answer:
-2/3 gallons/min
Step-by-step explanation:
let x = time in minutes
let y = volume of water in gallons
when x = 0, y = 7
when x = 3, y = 5
[tex]\mathsf{rate \ of \ change \ = \dfrac{change \ in \ y}{change \ in \ x}=\dfrac{7-5}{0-3}=-\dfrac23 \ gallons/min}[/tex]
Decide which of the following is a reasonable answer for
Answer:
[tex]9 \frac{4}{5} [/tex]
Step-by-step explanation:
[tex] \frac{7}{5} \times 7 = \frac{7}{5} \times \frac{7}{1} [/tex]
[tex] \frac{7}{5} \times \frac{7}{1} = \frac{49}{5} = 9 \frac{4}{5} [/tex]
Elise paid 2/3 as much for a sweater as she did for a pair of shoes. How much did elise pay for the sweater if the shoes cost each given amount?Shoes Cost $60: Sweater cost $20,$40,$90
Work Shown:
(2/3)*60 = (2*60)/3 = 120/3 = 40
Notice how 40/60 = 2/3
What is the period of the function f(x) shown in the graph?
Enter your answer in the box.
period (T): the time it takes to travel one wave
= 2π - (-10π)
= 12π
The radius of a circle is 16 millimeters. What is the circle's area?
Use 3.14 for .
please answer windowesssssssssssssss
Answer:
803.84 millimeters²
Step-by-step explanation:
How do we find the area of a circle?
The area of a circle is πr², where r = radius. In this case, we have to approximate pi to 3.14.Solving
[tex]3.14 *16^2[/tex] [tex]3.14*256[/tex] [tex]803.84[/tex]Therefore, the area is 803.84 square millimeters.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
Solution:
We know that:
Radius = r = 16 mmArea of circle = (π)(r²)Finding the area of the circle:
Area of circle = (3.14)(16²)=> Area of circle = 3.14 x 16²=> Area of circle = 3.14 x 256=> Area of circle = 803.84 mm²y^2-4xy-7y+28x please send the answer asap
Answer:
= (y - 4x) (y - 7)
Step-by-step explanation:
y^2-4xy-7y+28x
--
factor out y from y^2 - 4x : y(y - 4x)
factor out 7 from 28x - 7y : 7(4x - y)
= y (y - 4x) + 7(4x - y)
7 (4x - y) + 7(y - 4x)
= y (y - 4x) - 7(y - 4x)
= (y - 4x) (y - 7)
The shaded part of the circle below represents the portion of a garden where a landscaper planted rose bushes. What is the approximate area of the part of the garden used for rose bushes?
Answer:
942ft^2
Step-by-step explanation:
Use the equation (θ/360)*[tex]\pi[/tex][tex]r^{2}[/tex] to get the area of the shaded sector.
(120/360)*[tex]\pi[/tex]*[tex]30^{2}[/tex]
(1/3)*[tex]\pi[/tex]*900
≈942[tex]ft^{2}[/tex]
The area of the shaded region is 942 square ft if the radius of the circle is 30 ft option (G) is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
We have a circle shown in the picture.
The area of the shaded region:
[tex]\rm A = \dfrac{120}{360}\pi (30)^2[/tex]
A = 942.47 ≈ 942 square ft
Thus, the area of the shaded region is 942 square ft if the radius of the circle is 30 ft option (G) is correct.
Learn more about circle here:
brainly.com/question/11833983
#SPJ2
2. Given A=15°, b=8, and a=6, use the Law of Sines to solve the triangle (if possible)
for the value of c. If two solutions exist, find both. Round answer to two decimal places.
A) c=11.01
B) c=2.10 and 13.36
C) c=12.14
D= c=1.12 and 10.24
E) not possible
Answer:
B
Step-by-step explanation:
The Law of Sines states that
sinA/a = sinB/b = sinC/c
We know A, a, and b. Given this, we can solve for B, and given that, we can solve for C and then c.
First, we solve for B.
sinA/a = sinB/b
sin(15°)/6 = sinB/8
sin(15°)/6 * 8 = sinB
arcsin(sin(15°)/6 * 8) = B ≈ 20.187
Note that there can be a second B value. We can check if there is a second B value by first subtracting the B value we got from 180.
180 - 20.187 = 159.813
Next, we can add that to our existing angle, A = 15°. If that is less than 180, then we do have a second solution. 159.813 + 15 = 174.813 < 180 so there does exist a second solution where B = 159.813
Next, we can solve for C.
We know that the angles in a triangle add to 180°, so A + B + C = 180. Therefore, for the first solution:
15 + 20.187 + C = 180
C = 180 - 15 - 20.187 = 144.813°
and for the second:
15 + 159.813 + C = 180
C = 180 - 15 - 159.813 = 5.187
Finally,
sinA/a = sinC/c
multiply both sides by c to no longer have it as a denominator
sinA * c / a = sinC
divide both sides by (sinA/a) to isolate c
for the first solution:
c = sinC*a/sinA = 13.35868 ≈ 13.36
and for the second:
c = sinC*a/sinA ≈ 2.10
im back fellow humans..pls help
Answer:
-2, -10, and -3
Step-by-step explanation:
-2, -10, and -3 are all colder than -1.
Have an amazing day!!
PLEASE RATE AND MARK BRAINLIEST!!!
Answer:
a , d , e
Step-by-step explanation:
Tommy has 5 jars of marble. Each Jar is filled 2/3 with marbles. How many full Jars does tommy have? Make a model and shade in the model and complete the calculation.
Calculation: 5x 2/3= Blank/3 =______
5 / ( 2 / 3 ) = 7.5
7 full jars
the equation y = x + 8 represents the length, y, in inches of a sleeping bag for a person who is x inches tall. which ordered pair does not belong on the graph?
Answer:
i dont know can u help me
Step-by-step explanation:
An 8 inch by 12 inch sheet of cardboard has squares
cut out of the corners. What should the side length of
the squares be to maximize the volume?
Answer:
96
Step-by-step explanation:
100 POINTS!!!!! AND BRAINLIEST!!!!!!
Instructions: Find the equation of the line through point (1,5) and perpendicular to x+3y=6. Use a slash ("/") for fractions (e.g. 1/2 for 12). DO not include spaces in your answers.
Y=_______
1. Turn x+3y=6 into slope intercept form:
3y = 6 - x
y = 2 - 1/3x
2. The perpendicular slope is always the negative reciprocal.
-1/3 becomes 3/1
3. Find the intercept
5 = (3/1)1 +b
b = 2
Answer: y = 3x + 2, or y = 3/1x + 2
A jar contains 12 red marbles, 16 blue marbles, and 18 white marbles. Four marbles are chosen
without replacement. What is the probability that they are all white?
Answer:
10.6 all white marbles
Step-by-step explanation:
Submitted to you
William has scored a total of 235 points on the first three math tests taken in his mathematics class. If his mathematics test are always worth 100 points, how many points must he earn on his next test in order to have an average of 80%
Answer:
85 points
Step-by-step explanation:
His total points will be 235+x
Number of tests will be 4
(235+x)/4 = 80
multiply by 4
235+x= 4*80
235+x= 320
x=320-235
x= 85
He has to get 85 points to average 80