Answer:
p = 1.5 and q = 9
Step-by-step explanation:
Expand the right side then compare the coefficients of like terms on both sides, that is
4(x + p)² - q ← expand (x + p)² using FOIL
= 4(x² + 2px + p²) - q ← distribute parenthesis
= 4x² + 8px + 4p² - q
Comparing coefficients of like terms on both sides
8p = 12 ( coefficients of x- terms ) ← divide both sides by 8
p = 1.5
4p² - q = 0 ( constant terms ), that is
4(1.5)² - q = 0
9 - q = 0 ( subtract 9 from both sides )
- q = - 9 ( multiply both sides by - 1 )
q = 9
2. Solve 4(3c + 10) < 12c + 40.
use photo for Choices
Answer:
no solution
Step-by-step explanation:
4 (3c + 10) < 12c + 4012c +40 < 12c +4012c- 12c < 40 -40 0 < 0Left and right sides are equal so no solution
Answer:No solution
Step-by-step explanation: I got it right on the test :)
The force, F (Newtons), between two objects is inversely proportional to the square of the distance, d (metres), between them. The force is 0.052 Newtons when the distance between the objects is 1.6 metres. Work out d (rounded to 2 DP) when F = 0.74 Newtons.
Answer:
[tex]D = 0.42m[/tex]
Step-by-step explanation:
Given
Force = 0.052 N when Distance = 1.6 m
Required
Find Force; when distance = 0.74 N
The question says force is inversely proportional to square of distance;
Let F represent Force and D represent Distance;
Mathematically;
[tex]F\alpha \frac{1}{D^2}[/tex]
Convert proportion to equation
[tex]F = \frac{k}{D^2}[/tex]
Where k is the proportionality constant; This means that k is always constant
Make k the subject of formula
[tex]F * D^2 = \frac{k}{D^2} * D^2[/tex]
[tex]FD^2 = k[/tex]
When F = 0.052 and D = 1.6; the value of k is as follows
[tex]0.052 * 1.6^2 = k[/tex]
[tex]0.13312 = k[/tex]
[tex]k = 0.13312[/tex]
When F = 0.74;
Recall that k is always constant; so [tex]k = 0.13312[/tex]
To solve for D, we'll make use of [tex]F = \frac{k}{D^2}[/tex]
Substitute [tex]k = 0.13312[/tex] and F = 0.74;
[tex]0.74 = \frac{0.13312}{D^2}[/tex]
Multiply both sides by D²
[tex]0.74 * D^2 = \frac{0.13312}{D^2} *D^2[/tex]
[tex]0.74 * D^2 = 0.13312[/tex]
Divide both sides by 0.74
[tex]\frac{0.74 * D^2}{0.74} = \frac{0.13312}{0.74}[/tex]
[tex]D^2 = \frac{0.13312}{0.74}[/tex]
[tex]D^2 = 0.17989189189[/tex]
Take square roots of both sides
[tex]D = \sqrt{0.17989189189}[/tex]
[tex]D = 0.42413664294[/tex]
[tex]D = 0.42m[/tex] (Approximated)
For the diagram shown, which pairs of angles are vertical angles? Select all that apply. Angle1 and Angle3 Angle2 and Angle4 Angle2 and Angle3 Angle5 and Angle7 Angle5 and Angle8 Angle8 and Angle6
Answer:
2 & 4
1 & 3
5 & 7
8 & 6
Vertical angles are formed in a set of intersecting lines. They are two differrent angles that are opposite of eachother but have the same angle.
Angle pairs that are vertical angles in the diagram shown when a transversal intersects two parallel lines are:
<1 and <3
<2 and <4
<5 and <7; and
<8 and <6
Recall:
Angles that are regarded as pairs of vertical angles share the same vertex and are directly opposite each other at the point of intersection of two straight lines.
From the image given,<1 and <3 are directly opposite each other and share same vertex.
<1 and <3 are therefore are a pair of angles that are vertical angles.
In the same vein, the following pairs:<2 and <4; <5 and <7; and <8 and <6 are all directly opposite each other. They are vertical angles pair.
Therefore, angle pairs that are vertical angles in the diagram shown when a transversal intersects two parallel lines are:
<1 and <3
<2 and <4
<5 and <7; and
<8 and <6
Learn more here:
https://brainly.com/question/2889556
Use the graph to determine the input value for which f(x)=g(x) is true.
Answer:
x = 1.5
Step-by-step explanation:
We just have to find the x-coordinate of the point of intersection between the two functions. From the graph, they intersect at (1.5, 2) so the answer is 1.5.
What is the distance between (-6, 4)(−6,4)left parenthesis, minus, 6, comma, 4, right parenthesis and (-8, 6)(−8,6)left parenthesis, minus, 8, comma, 6, right parenthesis? Choose 1 answer: Choose 1 answer: (Choice A) A 222 (Choice B) B 333 (Choice C) C \sqrt{4} 4 square root of, 4, end square root (Choice D) D \sqrt{8} 8
Answer:
D. [tex]\sqrt{8}[/tex]
Step-by-step explanation:
We want to find the distance between (-6, 4) and (-8, 6).
First, we find the difference:
d = (-8 - (-6), 6 - 4)
d = (-8 + 6, 2)
d = (-2, 2)
We now find the magnitude:
[tex]|d| = \sqrt{x^2 + y^2}[/tex]
where x = x coordinate, y = y coordinate
[tex]|d| = \sqrt{(-2)^2 + (2)^2} \\\\|d| = \sqrt{4 + 4} = \sqrt{8}[/tex]
The answer is Choice D.
Answer:
D
Step-by-step explanation:
Khan said it was correct :)
I WILL MARK YOU AS BRAINLLEST
What is the parent function of the graph? y = |x| y = |x – 4| y = |x| – 4 y = |x| + 4
Answer:
y= | x |
Step-by-step explanation:
What is the parent function of the graph?
y = |x| y = |x – 4| y = |x| – 4 y = |x| + 4----------
a parent function is the simplest function of a family of functions that preserves the definition of the entire family.The parent function is:
y= | x | as it is the simplest one and all the others can be generated from thisi'm desperate at this point :( Please help.
Answer:
C. 0.377
Step-by-step explanation:
20 people drive to work in suburban areas out of 53.
20/53 = 0.377358
need help use screenshot(SAT Prep) In △ABC, AB = BC = 20 and DE ≈ 9.28. Approximate BD. bd equals?
Answer:
5.36
Step-by-step explanation:
Given that:
<BAD = <CAE, therefore, BD = EC
Let's take x to be the length of BD = EC
BD + DE + EC = BC
BC = 20,
BD = EC = x
DE ≈ 9.28
Thus,
x + 9.28 + x = 20
x + x + 9.28 = 20
2x + 9.28 = 20
Subtract 9.28 from both sides
2x + 9.28 - 9.28 = 20 - 9.28
2x = 10.72
Divided both sides by 2 to solve for x
[tex] \frac{2x}{2} = \frac{10.72}{2} [/tex]
[tex] x = \frac{10.72}{2} [/tex]
[tex] x = 5.36 [/tex]
BD ≈ 5.36
Find the product.
2x(x2-6x+3)
PLEASE HELP!!! ASAP!!!
Answer:
-8x^2+6x
Step-by-step explanation:
2x(2x−6x+3)
=(2x)(2x+−6x+3)
=(2x)(2x)+(2x)(−6x)+(2x)(3)
=4x2−12x2+6x
=−8x2+6x
Answer:
Your correct answer is 2(x2−6x+3)
Step-by-step explanation:
This is the simplified version.
Simple and easy question
please help
Answer:
Volume of a sphere = 4/3πr³
π = 3.14
r = radius which is 3in
Volume = 4/3 × 3.14 × 3²
= 37.68
= 38 cubic inches to the nearest hundredth
Hope this helps
Answer:
38 cubic inches
Step-by-step explanation:
The mean salary for the 20 workers in company A is $90 per week, whereas in company B the mean salary for its 30 workers is $85 per week. If the two companies merge, what is the mean salary for the 50 employees of the new company?
Answer:
The mean salary for the 50 employees of the new company = $87
Step-by-step explanation:
Mean for any n set of number is \
mean = sum of n terms/ n
_________________________________
For company A
The mean salary for the 20 workers in company A is $90 per week,
mean = $90
n = 20
using above formula
90 = sum of salary of 20 workers/20
sum of salary of 20 workers = 90*20 = $1800
__________________________________________________
For company B
The mean salary for the 30 workers in company A is $85 per week,
mean = $85
n = 30
using above formula
85 = sum of salary of 30 workers/30
sum of salary of 30 workers = 85*30 = $2,550
____________________________________________
If two companies merge
Total salary for all the 50 workers for both the company =
sum of salary of 20 workers in company A + sum of salary of 30 workers in company B = $1800 + $2550 = $4350
Mean salary of 50 workers will be
n= 50
mean = Total salary of 50 workers/50
mean salary of 50 workers = 4350/50 = 87
The mean salary for the 50 employees of the new company = $87
If x-14=y+196 and y is 14 times of x then x=WHAT??
Answer:
x is 226.154…
Step-by-step explanation:
1) x-14=y+196
x=y+196+14
x=y+210
2)x=14y
3) 14y=y+210 collect like terms together
14y-y=210
13y=210 divide both sides by 13
y=16.154
4)x=y+210 meaning:
x=16.154+210
=226.154
Find Y. Round to the nearest tenth
Answer:
32.7 degress
Step-by-step explanation:
In this question we are to find the value of the angle
The best way to do with the information given is the cosine rule
Mathematically that would be;
y^2 = x^2 + z^2 -2xzCosY
where x = 90 ft , y = 55ft and z = 50 ft
Plugging the values we have;
55^2 = 90^2 + 50^2-2(90)(50)CosY
-7575 = -9000cosY
cosY = 7575/9000
cosY = 0.841666666667
Y = cos^-1 0.841666666667
Y = 32.68 degrees which is 32.7 to the nearest tenth
Answer:
32.7
Step-by-step explanation:
Volume of this prism
Answer:
840 cm³
Step-by-step explanation:
To find it's volume , let's just divide the whole prism into two rectangular prisms.
Rectangular Prism 1:
Volume = [tex]Length * Width * Height[/tex]
Volume = 8 * 15 * 6
Volume = 720 cm³
Rectangular Prism 2:
Volume = [tex]Length * Width * Height[/tex]
Volume = 5 * 4 * 6
Volume = 120 cm³
Whole Prism:
Volume = 720+120
=> 840 cm³
Answer:
840 cm^3
Hope this helps :)
A company rounds its losses to the nearest dollar. The error on each loss is independently and uniformly distributed on [–0.5, 0.5]. If the company rounds 2000 such claims, find the 95th percentile for the sum of the rounding errors.
Answer:
the 95th percentile for the sum of the rounding errors is 21.236
Step-by-step explanation:
Let consider X to be the rounding errors
Then; [tex]X \sim U (a,b)[/tex]
where;
a = -0.5 and b = 0.5
Also;
Since The error on each loss is independently and uniformly distributed
Then;
[tex]\sum X _1 \sim N ( n \mu , n \sigma^2)[/tex]
where;
n = 2000
Mean [tex]\mu = \dfrac{a+b}{2}[/tex]
[tex]\mu = \dfrac{-0.5+0.5}{2}[/tex]
[tex]\mu =0[/tex]
[tex]\sigma^2 = \dfrac{(b-a)^2}{12}[/tex]
[tex]\sigma^2 = \dfrac{(0.5-(-0.5))^2}{12}[/tex]
[tex]\sigma^2 = \dfrac{(0.5+0.5)^2}{12}[/tex]
[tex]\sigma^2 = \dfrac{(1.0)^2}{12}[/tex]
[tex]\sigma^2 = \dfrac{1}{12}[/tex]
Recall:
[tex]\sum X _1 \sim N ( n \mu , n \sigma^2)[/tex]
[tex]n\mu = 2000 \times 0 = 0[/tex]
[tex]n \sigma^2 = 2000 \times \dfrac{1}{12} = \dfrac{2000}{12}[/tex]
For 95th percentile or below
[tex]P(\overline X < 95}) = P(\dfrac{\overline X - \mu }{\sqrt{{n \sigma^2}}}< \dfrac{P_{95}- 0 } {\sqrt{\dfrac{2000}{12}}}) =0.95[/tex]
[tex]P(Z< \dfrac{P_{95} } {\sqrt{\dfrac{2000}{12}}}) = 0.95[/tex]
[tex]P(Z< \dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}}) = 0.95[/tex]
[tex]\dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}} =1- 0.95[/tex]
[tex]\dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}} = 0.05[/tex]
From Normal table; Z > 1.645 = 0.05
[tex]\dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}} =1.645[/tex]
[tex]{P_{95}\sqrt{12} } = 1.645 \times {\sqrt{{2000}}}[/tex]
[tex]{P_{95} = \dfrac{1.645 \times {\sqrt{{2000}}} }{\sqrt{12} } }[/tex]
[tex]\mathbf{P_{95} = 21.236}[/tex]
the 95th percentile for the sum of the rounding errors is 21.236
The tape diagram represents an equation. Write an equation to represent the image.
Answer:
5n = 1.75
Step-by-step explanation:
The 2 bars are equal thus lower equals upper, that is
5n = 1.75
This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation can be used to find the side lengths.
If one of the longer sides is 6.3 centimeters, what is the length of the base?
cm
Answer:
b=3.1 cm
Step-by-step explanation:
Both of the longer sides will be equal so you can set up the equation (6.3+6.3)+b=15.7. Simplified you get 12.6+b=15.7, subtracting 12.6 from both sides you get that b=3.1 cm. This can be checked because it is also shorter than 6.3 and works correctly in the perimeter.
Verify the property a x (b+c) =(a x b)+(a x c) by taking: a = -7, b = (2/5), c = (-3/7)
Matt has c baseball cards, and Jen has 9 fewer than 5 times as many cards as Matt. Jen gives Matt 14 cards. How many cards does Jen have now?
Answer:
Jen has 5c -23 cards now
Step-by-step explanation:
Matt has c baseballs.
Jen has 9 fewer than 5 times as Matt.
Mathematically, what Jen has will be 5c -9 baseballs
Now, Jen gives Matt 14 cards. This means that she lost 14 of her cards and we are going to subtract.
The number of cards she has now is thus 5c-9-14 = 5c -23 cards
In a collection of 1050 flowers, 3/10 of them are red , 2/5 of them are
white and the rest are yellow. Find the no. of red, white and yellow flowers
Answer:
315 red flowers420 white flowers315 yellow flowersStep-by-step explanation:
1050 flowers
3/10 of them are red=> 3/10 *1050=3*105=315 red flowers
2/5, (or 4/10), are white =>4/10 * 1050=4*105=420 white flowers
=> 1050-(315+420)=1050-735=315 yellow flowers
I really need help
it’s very hard
Answer:
The angle ZLK has a value of 75 degrees.
Step-by-step explanation:
We can calculate this as:
[tex]m\angle MLZ+m\angle ZLK=m\angle MLK\\\\(x+66)+(x+86)=130\\\\2x+152=130\\\\2x=130-152\\\\x=-22/2=-11\\\\\\m\angle ZLK=x+86=-11+86=75[/tex]
We replace the angles values in the equation, as both angles that are formed with Z (MLZ and ZLK), when added, gives as the angle MLK. This allows us to calculate x. The value for x is -11.
Then, with the value for x we can calculate any of both angles.
17. The length of a swing is 2.1 m. If the length
of the arc that is made by the swing
4.4 m, calculate the angle swept by the
swing
Answer:
dose it tell you want angle the arc is at?
Step-by-step explanation:
Find the nth term -1 8 19 32 47
[tex]\bold{\text{Answer:}\quad \text{Recursive formula:}\ a_n=a_{-1}+2n+5}\\.\qquad \qquad \ \text{Explicit formula:}\ a_n=2n^2+3n-6[/tex]
Step-by-step explanation:
-1 → 8 = +9
8 → 19 = +11
19 → 32 = +13
32 → 47 = + 15
a₁ = -1
d = 2n + 5
Recursive formula is: the previous term plus the difference (d)
[tex]\large\boxed{a_n=a_{n-1}+2n+5}[/tex]
Explicit formula is the first term plus the product of d and n-1:
[tex]a_n=a_1+d(n-1)\\a_n=-1+(2n+5)(n-1)\\a_n=-1+2n^2-2n+5n-5\\\large\boxed{a_n=2n^2+3n-6}[/tex]
If x + y = 6 and xy = 3, then the value of | x − y | it is
Answer:
2√6
Step-by-step explanation:
x + y = 6
xy = 3
Square the first equation.
x² + 2xy + y² = 36
Subtract 4xy from both sides.
x² − 2xy + y² = 36 − 4xy
Factor.
(x − y)² = 36 − 4xy
Substitute.
(x − y)² = 36 − 4(3)
(x − y)² = 24
Take square root.
x − y = ±√24
x − y = ±2√6
Take absolute value.
|x − y| = 2√6
Which of the polygons listed below have at least four sides? Triangles Quadrilaterals Pentagons Hexagons Heptagons
Answer:
"Correct"
Triangles: Have three (3) sides
Quadriliaterals: QUAD being the key word means four (4)
"Incorrect"
Pentagons: Have five (5) sides
Hexagons: Have six (6) sides; key word being HEX
Heptagons: 7 sides (7)
Step-by-step explanation:
Simplify...
can I get help
Answer:
b ^ 8
Step-by-step explanation:
b^10 / b^2
Since the base is the same, we can subtract the exponents to do division
b^ (10-2)
b ^ 8
Answer:
c----[tex]\frac{b^{8} }{1}[/tex]
Step-by-step explanation:
wwhen you divide variables with exponents you need to subtract them.
in this case you are subtraction 2 from 10
[tex]\frac{b^{10} }{b^{2} }[/tex]
10-2
8
[tex]\frac{b^{8} }{1}[/tex]
A country has a total biocapacity of 6.21 ha/person, a biocapacity of grazing land of 0.85 ha/person, and a biocapacity of forest land of 2.53 ha/person. Calculate the percentage of biocapacity from grazing and forest land.
Answer:
3.38/6.21=54.428% (0.54428)
Step-by-step explanation:
biocapacity of grazing land of 0.85 ha/person+biocapacity of forest land of 2.53 ha/person
2.53+0.85=3.38
the percentage of biocapacity from grazing and forest land
3.38/6.21=54.428% (0.54428)
Please answer this question in two minutes
Answer:
work is shown and pictured
3. A bag has five blue marbles, seven red marbles and nine green marbles. Three marbles are drawn
without replacement. Determine the probability of drawing a green marble, then a blue marble,
and then another green marble. [7 marks/K]
Answer:
The probability is 9/266
Step-by-step explanation:
The first thing to do here is get the total number of marbles = 5 + 7 + 9 = 21 marbles
Now we are drawing the marbles without replacement, this means once a marble is drawn there is a decrease in the total number of marbles left.
The probability of drawing a green marble initially = number of green marbles/ total
number of marbles = 9/21 = 3/7
Now, we want to draw a blue marble
There are 5 blue marbles and we have already drawn one marble from the total. So the probability of drawing a blue marble would be 5/20 = 1/4
And lastly, another green marble
That would make 6 green marbles left and a total of just 19 left. So the probability at this point for green marbles = 6/19
Having and in probability means we multiply all
So this means the probability we are calculating is; 3/7 * 1/4 * 6/19 = 18/(28 * 19) = 9/(14 * 19) = 9/266
Help ASAP!!!!!! First gets brainliest
Answer:
So we are moving up 3 units
So we are moving to the right 2 units
Step-by-step explanation:
f(x-2) +3
y = f(x) + C C > 0 moves it up
So we are moving up 3 units
y = f(x + C) C < 0 moves it right
So we are moving to the right 2 units