Answer:
f(x) = x³ - 4x² - 25x + 28
Step-by-step explanation:
Given the zeros x = 1, x = 7 and x = - 4 , then the corresponding factors are
(x - 1), (x - 7), (x + 4)
The polynomial is then the product of the factors, that is
f(x) = a(x - 1)(x - 7)(x + 4) , a is a multiplier
let a = 1 and expand the first pair of factors using FOIL
f(x) = (x² - 8x + 7)(x + 4) ← distribute
= x³ - 8x² + 7x + 4x² - 32x + 28 ← collect like terms
= x³ - 4x² - 25x + 28
The number of kilometers traveled by a bus is represented by x. If a train traveled 200 kilometers farther than the bus, represent the number of kilometers traveled by the train.
Answer:
The train travelled x + 200 km
Answer:
The number of kilometres traveled by the bus is x kilometres. The train travels 200 kilometres farther than the bus, meaning that the train traveled x kilometres, and an additional 200 kilometres.
So, the number of kilometres traveled by the train would be the x km traveled by bus, plus 200 km; or x + 200 km.
Hope this helps!
Jessica can paint 12 rocks in 8 minutes. How many rocks can she paint in 48 minutes
Answer:
72 rocks.
Step-by-step explanation:
A "easier" way to find out the answer, is to find how much rocks Jessica paints in 1 minute.
Divide 12 with 8:
12/8 = 1.5
Next, multiply the number you got (1.5) with 48:
48 x 1.5 = 72
Jessica can paint 72 rocks in 48 minutes.
~
Answer:
72 rocks
Step-by-step explanation:
So let’s create the following ratio 12:8
The 12 is the amount of rocks and the 8 is the time in minutes.
So we have to find how many rocks she can paint in 48 minutes.
So we make the following ratio x:48.
So we need to find x the amount of rocks she can paint in 48 minutes.
So to find x we have to divide 48 by 8 = 6.
So if the ratio is x6 we can just do 12 * 6 which is 72.
So she can paint 72 rocks in48 minutes.
can someone help i have less than an hour !!
Answer:
[tex]x \geqslant 4[/tex]Option D is the correct option.
Explanation:
Since, there is a solid circle(blue) at X=4 which implies the value '4' is included in the inequality solution.
Hope this helps...
Good luck on your assignment...
7 x (-3) x (-12)^2=? A. -84 B. -48 C. 84 D. 48
━━━━━━━☆☆━━━━━━━
▹ Answer
B. -48
▹ Step-by-Step Explanation
Distribute each number to factor so you can solve
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
-3024
Step-by-step explanation:
7 x (-3) x (-12)^2=
PEMDAS says exponents first
7 x (-3) x (144)=
Then multiply from left to right
-21 x (144)=
-3024
Jayden measured a community college and made a scale drawing. He used the scale 22 millimeters : 9 meters. The actual length of a building at the college is 99 meters. How long is the building in the drawing?
Hey there! :)
Answer:
x = 242 mm.
Step-by-step explanation:
Begin by setting up a proportion between the actual college building and the drawing.
[tex]\frac{22mm}{9m} = \frac{x}{99m}[/tex]
Cross multiply:
99 × 22 = 9 × x
2178 = 9x
Divide both sides by 9:
2178/9 = 9x/9
x = 242 mm.
Claire is designing a banner that will hang in her classroom. The length of one diagonal of the banner is 48 inches, and the sides are 25 inches long. Is the banner a square?
Answer: No the banner is not square.
Step-by-step explanation:
If it were square, the diagonal would be about 35.36 inches.
Pythagorean Theorem: a² + b² + = c²
?25² + 25² = 48² ?
625 + 625 ?=? 2304
1250 ≠ 2304
√1250 ≈ 35.3553
Answer:
The second option
Step-by-step explanation:
Source: trust me bro
An observer (O) spots a plane flying at a 55° angle to his horizontal line of sight. If the plane is flying at an altitude of 21,000 ft., what is the distance (x) from the plane (P) to the observer (O)? (4 points)
If the plane is flying at an altitude of 21,000 feet, it is perpendicular to the observer's horizontal line of sight. Thus, I concluded that the given information be assigned to the attachment below.
Given -
( Observer at point O, plane flying at point P
( Plane at 55° angle to horizontal line of sight, altitude of 21,000 feet
The distance ( x ), is represented by the line segment OP, with which we have to determine the length of. Therefore we can conclude the following -
[tex]Sin( 55 ) = Altitude / Distance,\\Sin( 55 ) = 21,000 / x,\\----------------\\x = \frac{21,000}{Sin( 55 )},\\x = 21,000 / 0.81915204428\\\\x = ( About ) 25636 feet\\[/tex]
As you can see, the distance from the plane to the observer is about 25,636 ft!
Answer:
25,636 feet
Step-by-step explanation:
I took the test on FLVS and got 100%
Bridget and Caroline win some money and share it in the ratio 7:3. Bridget gets £40 more than Caroline. How much did they get all together?
Answer:
£100
Step-by-step explanation:
if the ratio is 7:3, the difference between them is 7-3 . = 4.
So,
4x = £40
Now, calculate x
x = £10
Now,
we are able to calculate:
7x (Bridget's share) = £70
3x (Caroline's share) = £30
Sum = £100
Hope this helps.
Good Luck
Plz help!! Brainleist answer will be given if explanation is performed
Answer:
x = 76 roses
Step-by-step explanation:
Step 1: Define variables
x = # of roses
y = # of tulips
Step 2: Write systems of equations
x = 4y + 8
5x + 2y = 414
Step 3: Use Substitution
5(4y + 8) + 2y = 414
20y + 40 + 2y = 414
22y = 374
y = 17
Step 4: Plug in y to find x
x = 4(17) + 8
x = 68 + 8
x = 76
Answer:
x = 76
Step-by-step explanation:
x = Roses
y = Tulips
x = 4y + 8
5x + 2y = 414
5(4y + 8) + 2y = 414
20y + 40 + 2y = 414
22y = 374
y = 17
x = 4(17) + 8
x = 68 + 8
x = 76
dentify the type of observational study (cross-sectional, retrospective, or prospective) described below. A research company uses a device to record the viewing habits of about 50005000 households, and the data collected todaytoday will be used to determinenbsp the proportion of households tuned to a particular sportssports program.. Which type of observational study is described in the problem statement?
Answer:
- A cross-sectional study.
Step-by-step explanation:
A Cross-sectional study is demonstrated as the type of observational study in which the data or a representative subset of a population collected at a particular point in time is analyzed.
As per the given details, the observational study conducted by the research company would exemplify 'a cross-sectional study' as it aims to evaluate the data('viewing habits of about 50005000 households) collected at a specific point in time i.e. 'today' in order to 'determine the proportion of households tuning to a particular sports program.'
The price of a ring was increased by 9% to £1800. What was the price before the increase? Give your answer to the nearest penny.
Answer:
see steps
Step-by-step explanation:
New price was increase from 100% to 109% at £1800.
By proportionality,
old price / 100% = 1800 / 109%
Cross multiply to get
old price = $1800 * 100% / 109% = £1651.38
Help plzzzzzzzz do these two questions and I’ll mark Brainlynest
Answer:
Step-by-step explanation:
Q1: <B = 150 °
If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
8x-10 = 3x+90
5x=100 (subtract 3 from both sides)
x=20 (divide both sides by 5)
x = 20
<B= 3x +90
<B = 3 (20) +90
<B = 60 + 90
<B = 150
Q2: 62
An angles complement (not compliment, haha) is what the number that added to the angle equals 90°.
An angle is 34 more than its complement.
Let x represent the angle.
Let y represent its complement.
x= 34 +(90-x)
y= (90-x)
x + y = 90
34 + (90-x) + (90-x) =90
x= 62
Check the answer.
x= 34 more than complement.
62-34=28
62+28=90
Checked!
Words of encouragement:
Good luck!
What is the next number in the pattern below?
3, 5, 9, 15, 23, ___
A.
31
B.
33
C.
35
D.
37
Answer:
the answer you are looking for is the letter B. 33
Find the area of this triangle..
Answer:
Step-by-step explanation:
Use the Pythagorean theorem to find the altitude.
h^2 = 9^2 - 6.4^2
h^2 = 40.04
h = 6.328
area = base * height/2
area = (2 * 6.4) * 6.328/2
area = 40.5 square units
please help me solve
Answer:
$110
Step-by-step explanation:
we know
selling price = cost price + profit.
given
selling price of TV = $121
profit = 10%of cost
selling price of TV = cost of TV + 10%cost of TV
121 = cost of TV + 10/100 cost of TV
=> 121 = (100 cost of TV + 10 cost of TV)/100
=> 121*100 = 110 cost of TV
=> cost of TV = 121*100/110 = 110
Thus, cost price of TV is $110(option A)
Can someone attempt part A) for me, or at least explain it.
Step-by-step explanation:
if AB and CD are parallel then
90 -x +83 +46 = 180 --> x= 39
Answer:
x = 39
Step-by-step explanation:
Using the properties of parallel lines, then
x + 44 = 83 ( subtract 44 from both sides )
x = 39
Here are the dates of three pivotal female mathematicians: Sophie Germain (French) 1776-1831, Sonja Kowalevsky (Russian) 1850-91, Emmy Noether (German) 1882-1935. Arrange them in order with the shortest-lived first.
There are 125 people in a sport centre. 59 people use the gym. 70 people use the swimming pool. 55 people use the track. 25 people use the gym and the pool. 30 people use the pool and the track. 17 people use the gym and the track. 6 people use all three facilities. A person is selected at random. What is the probability that the person uses exactly one of the facilities? There are 125 people in a sport centre. 59 people use the gym. 70 people use the swimming pool. 55 people use the track. 25 people use the gym and the pool. 30 people use the pool and the track. 17 people use the gym and the track. 6 people use all three facilities. A person is selected at random. What is the probability that the person uses exactly one of the facilities?
Answer:
Step-by-step explanation:
No of people using both gym and pool that is N( gup ) = 25
No of people using both track and pool that is N( tup ) = 30
No of people using both track and gym that is N( tug ) = 17
No of people using all that is N( gutup) = 6
No of people using two or three facilities
= 25+30+17- 2 x 6
= 60
Total no of people = 125
No of people using only one facility
= 125 - 60
= 65 .
Ratio of people using only one facility
= 65 / 125
.52
Required probability
= .52 .
probability that the person uses exactly one of the facilities
= .52
A rectangular octagon is shown in the ceiling of a cathedral. The radius is 10.5 feet and the perimeter is 64 feet. The regular octagon in the ceiling of this cathedral has a radius of 10.5 feet and a perimeter of 64 feet. What is the length of the apothem of the octagon? Round your answer to the nearest tenth of a foot. feet Using your answer for the length of the apothem, what is the area of the regular octagon? Round your answer to the nearest tenth of a square foot. square feet
Answer:
9.7 , 310.4
Step-by-step explanation:
length of each side = 64/8=8
using theorem Pythagoras
A²=10.5² – (8/2)²
A=9.7 ft
area of triangle
1/2×8×9.7=38.8
area of octagon
38.8×8=310.4
The Length of the octagon is 9.7 and the area of octagon is 310.4.
Length and area of octagonLength of octagon
Length of each side = 64/8
Length of each side =8
Pythagoras theorems
A²=√10.5² – (8/2)²
A²=√110.25 – 16
A²=√94.25
A=9.7 ft
Area of octagon
Area of triangle=1/2×8×9.7
Area of triangle=38.8
Area of octagon=38.8×8
Area of octagon=310.4
Therefore the Length of the octagon is 9.7 and the area of octagon is 310.4.
Learn more about Length and area of octagon here:https://brainly.com/question/358118
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Please answer it now in two minutes
Answer:
47
Step-by-step explanation:
It's just aligning each number / line to each matching one.
Answer:
47 degrees
Step-by-step explanation:
The angle that matches the angle U is angle C
The measure of angle U is 47 degrees
given the vertex (2,9) and the foci (5,9), what is the equation of the directrix
Answer:
x = -1
Step-by-step explanation:
The vertex is halfway between the focus and the directrix.
So here the directrix is a vertical line to the left of the vertex and passing through the point (2-3, 9) = (-1, 9)
It is x = -1.
describe fully the single transformation that takes shape A to shape B
Answer:
Divide by 2 or -2
Step-by-step explanation:
The edges lengths have decreased:
4/2=2
2/2=1
6/2=3
Transformation involves changing the position and size of a shape.
The single transformation from shape A to B is: dilate A by 1/2, then rotate by 180 degrees
From the figure, we have:
The side lengths of shape A are twice as large as the side lengths of shape BShape A can be rotated 180 degrees to map onto shape B, after dilation.So, the scale of dilation from shape A to B is:
[tex]\mathbf{Scale = \frac{1}{2}}[/tex]
Hence, the single transformation from shape A to B is: dilate A by 1/2, then rotate by 180 degrees
Read more about transformations at:
https://brainly.com/question/11707700
Nick has fraction 1 over 2 cup of syrup. He uses fraction 1 over 6 cup of syrup to make a bowl of granola. How many bowls of granola can Nick make with fraction 1 over 2 cup of syrup?
Answer:
3
Step-by-step explanation:
1/2 is 3 times 1/6, because 3/1 [tex]\frac{3}{1} * \frac{1}{6} = \frac{3}{6}[/tex] and 3/6 is the same as 1/2. Thus, he can make 3 bowls of granola.
could someone please answer 1 and 7:)
Answer:
1- %50
0.2008
Step-by-step explanation:
0.0008 1/5
(0.0008*5)+1=0.004+1=1.004/5
0.2008
→Answer:
1) 50%
7) 5.02
→Step-by-step explanation:
1)
Even if a coin is tossed many times and its still heads there is still 50% it is tails. It doesn't change.
7)
.0008 1/5 as a fraction.
So first we need to put .0008 into 1/5.
To do that we do .0008*5 which is .004.
So the fraction is now 1.004/5
To make that a decimal we do 1.004 divided by 5 which is 5.02
Someone..... I beg you!!! I will definitely mark you as a brainliest if you give me the correct answer!
Answer :
[tex]x = - 6 \\ x = 1[/tex]
Solve the triangle. Round your answers to the nearest tenth.
Answer:
m∠A ≈ 43°
m∠B ≈ 55°
mBC ≈ 20
Step-by-step explanation:
Law of Sines: [tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
Step 1: Find m∠B
[tex]\frac{29}{sin82} =\frac{24}{sinB}[/tex]
Step 2: Solve for ∠B
29sinB = 24sin82°
sinB = 24sin82°/29
B = sin⁻¹(24sin82°/29)
B = 55.038°
Step 3: Find m∠A
180 - (55.038 + 82)
180 - 137.038
m∠A = 42.962°
Step 4: Find BC
[tex]\frac{29}{sin82} =\frac{BC}{sin42.962}[/tex]
Step 5: Solve for BC
29sin42.962° = BCsin82°
BC = 29sin42.962°/sin82°
BC = 19.9581
Which arrow would most likely represent the phase change that involves the same amount of energy as arrow 1?
2
3
4
5
Answer:
arrow 4
Step-by-step explanation:
The amount of energy needed in the transformation from liquid to gas is equal to the gas to liquid transition.
Boiling is the mechanism by which a substance passes from the liquid phase to the gaseous form.
Like water diagram in phase:
Evaporisation is a method of phase shift in which the water transitions from a liquid to a gas (water vapour).
Condensation is the process of phase shift in which water transitions from a gas to a liquid, and the vapour becomes a cloud.
Answer:
4
Step-by-step explanation:
ya boy did the test
what is the slope and y-intercept (−6,5),(-3,-3)
Answer:
Step-by-step explanation:
The values of the slope and y-intercept are
m =- 8/3
and b = − 11
What is the difference of the fractions below 5/2 - 3/5
Answer:
19/10 or 1 9/10
Step-by-step explanation:
you first put them into common denominators
so the least common denominator is 10
so 5/2= 25/10
and 3/5= 6/10
so 25/10 minus 6/10= 19/10
hope this helps
Answer:
1 9/10
Step-by-step explanation:
5/2 - 3/5
Get a common denominator of 10
5/2 *5/5 - 3/5 *2/2
25/10 - 6/10
19/10
10/10 + 9/10
1 9/10
Urgent pls. The diagram shows a parallelogram. Work out the area of the parallelogram. Give your answer to 2 significant figures.
Answer:
54.88 square cm
Step-by-step explanation:
If d1 and d2 are the diagonal of parallelogram and [tex]\alpha[/tex] is the angle between then
then its area is given by
area = d1*d2 sin [tex]\alpha[/tex]
given
in the problem
for one diagonal one part is 7cm
we know that diagonal intersects each other to divide each part of same diagonal equally.
hence if one part is of length 7 then other part is also of 7cm length
hence full length of this diagonal is 7+7 = 14cm
similarly full length of other diagonal is 4+4 = 8cm
now area of this parallelogram
area = d1*d2 sin [tex]\alpha[/tex] = 14*4 sin100
we know sin100 = 0.98
area = 56*0.98
area = 54.88
Thus, area of given parallelogram is 54.88 square cm.