Answers
1. a = 68
b = 112
c = 68
2. a = 127
3. a = 35
b = 40
c = 35
d = 70
4. a = 20
b = 70
c = 20
d = 70
e = 110
5. a = 90
b = 90
c = 42
d = 48
e = 132
6. a = 70
b = 55
c = 25
Related Questions
What is the recursive formula for this geometric sequence?
-3, -21, -147, -1029, ...
Answers
Answer:
Step-by-step explanation:
First of all the first term is a1 and that's equal to -3
Every term is multiplied by 7
So the recursive formula is
an = 7*a_(n-1)
a2 = 7*a_(1 -1)
a2 = 7*-3
a2 = - 21
Now try a_4
a_4 = 7*a_3
a_3 = -147
a_4 = 7*(-147)
a_4 = -1029
100 students are interviewed to see which of biology, chemistry or physics they prefer. 42 of the students are girls. 5 of the girls like biology best. 4 of the boys prefer physics. 13 out of the 21 who prefer chemistry are girls. What percentage of the students prefer biology?
Answers
Answer:
A total of 51 people prefer biology, 51%
Step-by-step explanation:
Girls: 42
Boys: 58
Biology: 5 girls and 46 boys(100-42=58, 58-[4+8]=46)
Physics: 4 boys and 24 girls(42-[5+13])
Chemistry: 13 girls and 8 boys(21-13=8)
I think this is the answer...
Find the TWO integers whos product is -12 and whose sum is 1
Answers
Answer:
[tex] \rm Numbers = 4 \ and \ -3.[/tex]
Step-by-step explanation:
Given :-
The sum of two numbers is 1 .
The product of the nos . is 12 .
And we need to find out the numbers. So let us take ,
First number be x
Second number be 1-x .
According to first condition :-
[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]
Hence the numbers are 4 and -3
Answer:
[tex] \displaystyle( {x}_{1} , y_{1}) =( - 3,4)\\ (x _{2}, y_{2}) = (4, - 3)[/tex]
Step-by-step explanation:
we are given two conditions
two integers whos product is -12two integers whos sum is 1let the two integers be x and y respectively according to the first condition
[tex] \displaystyle xy = - 12[/tex]
according to the second condition:
[tex] \displaystyle x + y = 1[/tex]
now notice that we have two variables therefore ended up with a simultaneous equation so to solve the simultaneous equation cancel x from both sides of the second equation which yields:
[tex] \displaystyle y = 1 - x[/tex]
now substitute the got value of y to the first equation which yields:
[tex] \displaystyle x(1 - x) = - 12[/tex]
distribute:
[tex] \displaystyle x- {x}^{2} = - 12[/tex]
add 12 in both sides:
[tex] \displaystyle x- {x}^{2} + 12 = 0[/tex]
rearrange it to standard form:
[tex] \displaystyle - {x}^{2} + x + 12 = 0[/tex]
divide both sides by -1:
[tex] \displaystyle {x}^{2} - x - 12 = 0[/tex]
factor:
[tex] \displaystyle ({x} + 3)(x - 4) = 0[/tex]
by Zero product property we acquire:
[tex] \displaystyle {x} + 3 = 0\\ x - 4= 0[/tex]
solve the equations for x therefore,
[tex] \displaystyle {x}_{1} = - 3\\ x _{2} = 4[/tex]
when x is -3 then y is
[tex] \displaystyle y _{1}= 1 - ( - 3)[/tex]
simplify
[tex] \displaystyle y _{1}= 4[/tex]
when x is 4 y is
[tex] \displaystyle y _{2}= 1 - ( 4)[/tex]
simplify:
[tex] \displaystyle y _{2}= - 3[/tex]
hence,
[tex] \displaystyle( {x}_{1} , y_{1}) =( - 3,4)\\ (x _{2}, y_{2}) = (4, - 3)[/tex]
the salesperson recieved $2,800 commission on her 35% share of the total commission on the sale of a property that was sold for $160,000. What was the commission rate?
Answers
Answer:
5%
.35x = 2800
x = 8000
p(160,000)=8000
p=.05 = 5%
Step-by-step explanation:
A concert hall has 25,350 seats. There are 78 rows of seats in the hall each row has the same number of seats how many seats are in each row?
Answers
Answer:
There are 325 seats in each row
Step-by-step explanation:
78 × 325 = 25,350
In ∆ABC if AB = 6 cm , BC = 8cm, AC = 10 cm then value of ∠B is ________
Answers
Answer:
90 degrees
Step-by-step explanation:
B is the corner and angle opposite of the side AC.
so, AC is becoming side c, and the other two are a and b (it does not matter which is which).
we use the enhanced Pythagoras formula for general triangles
c² = a² + b² - 2ab×cos(C)
in our example the angle C is named B.
but other than that we simply calculate
10² = 6² + 8² - 2×6×8×cos(B)
100 = 36 + 64 - 96×cos(B)
100 = 100 - 96×cos(B)
0 = -96×cos(B)
cos(B) = 0
=>
B = 90 degrees
__1. What is the other term for Q3?
2. What measure of position is divided into four equal parts?
3. How many equal parts is the quartile divided into?
4. How many percentile is equivalent to Q1?
5. What is the other term for Median?
_6. What is the equivalence of D2 to Percentile?
7. What measure of position is divided into 10 equal parts?
_8. What measure of position is divided into 100 equal parts?
9. What is the decile equivalence of P80?
10. What quartile is equivalent to P75?
Answers
Answer:
1. The third quartile
2. The quartile
3. Four
4. 25
5. The second quartile, Q₂
6. 20th percentile
7. Decile
8. Percentile
9. D₈
10. The third quartile, Q₃
Step-by-step explanation:
1. The other term(s) for Q₃ is third quartile (or upper quartile). It is the mid point between the distribution's largest number and the median
2. The measure of position divided into four equal parts is the quartile
3. The quartile is the division of the data at three points (Q₁, Q₂, and Q₃) into four equal parts equal parts
4. Q₁, which is the first quartile is equivalent to the 25th percentile
5. The other term for the median is the second quartile, Q₂
6. D₂ which is the second decile (a decile divides the data into 10 equal parts) is equivalent to 20th percentile
7. The decile, D, divides a given data into 10 equal parts
8. The percentile divides a given data into 100 equal parts
9. The decile equivalent to P80, which is the 80th percentile, is D₈
10. The quartile equivalent to P75, which is the 75th percentile or the three quarter mark point of the data is equivalent to the the third quartile, Q₃
ABC ~ DEF
What is the value for x, the length of side BC?
Answers
Answer:
17.5
Step-by-step explanation:
as the triangles are similar, when oriented in the same direction they have the same angles, and the lengths of all sides of DEF are the lengths of the sides of ABC but multiplied by the same scaling factor f for all sides.
so, we see that
A ~ D
B ~ E
C ~ F
and therefore
AB ~ DE
BC ~ EF
CA ~ FD
that means
DE = AB × f
EF = BC × f
FD = CA × f
we know DE and AB.
so,
4 = 10 × f
f = 4/10 = 2/5
and now we know
EF = 7 = BC × f
BC = 7/f = (7/1) / (2/5) = (5×7)/(2×1) = 35/2 = 17.5
Answer:
17.5
Step-by-step explanation:
Find the equation of tangent to circle x^2+y^2 = 3 which makes angle of 60 ° with x-axis.
Answers
Step-by-step explanation:
hope it helps thnak you
brainliest pls ❤
In a county containing a large number of rural homes, 60% of the homes are insured against fire. Four rural homeowners are chosen at random from this county, and x are found to be insured against fire. Find the probability distribution for x.
Answers
Answer:
[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}[/tex]
Step-by-step explanation:
Given
[tex]p = 60\%[/tex]
[tex]n = 4[/tex]
Required
The distribution of x
The above is an illustration of binomial theorem where:
[tex]P(x) = ^nC_x * p^x *(1 - p)^{n-x}[/tex]
This gives:
[tex]P(x) = ^4C_x * (60\%)^x *(1 - 60\%)^{n-x}[/tex]
Express percentage as decimal
[tex]P(x) = ^4C_x * (0.60)^x *(1 - 0.60)^{n-x}[/tex]
[tex]P(x) = ^4C_x * (0.60)^x *(0.40)^{4-x}[/tex]
When x = 0, we have:
[tex]P(x=0) = ^4C_0 * (0.60)^0 *(0.40)^{4-0}[/tex]
[tex]P(x=0) = 1 * 1 *(0.40)^4[/tex]
[tex]P(x=0) = 0.0256[/tex]
When x = 1
[tex]P(x=1) = ^4C_1 * (0.60)^1 *(0.40)^{4-1}[/tex]
[tex]P(x=1) = 4 * (0.60) *(0.40)^3[/tex]
[tex]P(x=1) = 0.1536[/tex]
When x = 2
[tex]P(x=2) = ^4C_2 * (0.60)^2 *(0.40)^{4-2}[/tex]
[tex]P(x=2) = 6 * (0.60)^2 *(0.40)^2[/tex]
[tex]P(x=2) = 0.3456[/tex]
When x = 3
[tex]P(x=3) = ^4C_3 * (0.60)^3 *(0.40)^{4-3}[/tex]
[tex]P(x=3) = 4 * (0.60)^3 *(0.40)[/tex]
[tex]P(x=3) = 0.3456[/tex]
When x = 4
[tex]P(x=4) = ^4C_4 * (0.60)^4 *(0.40)^{4-4}[/tex]
[tex]P(x=4) = 1 * (0.60)^4 *(0.40)^0[/tex]
[tex]P(x=4) = 0.1296[/tex]
So, the probability distribution is:
[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}[/tex]
PLEASE HELP I WILL GIVE BRAINLY
If y varies directly with x and
y = 56 when x = 8, find y if x = 4.
First, find the direct variation equation.
y = [ ? ]x
Answers
Answer:
y = 7x and y = 28
Step-by-step explanation:
Given y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 56 when x = 8 , then
56 = 8k ( divide both sides by 8 )
7 = k
y = 7x ← equation of variation
When x = 4
y = 7 × 4 = 28
Q14SIMPLIFY THE EXPRESSION 6ab of2adivided by12x12ab+14a-a
Answers
Answer:
25
Step-by-step explanation:
6ab of 2a ÷ 12 × 12ab + 14a - a
= 6ab * 2a ÷ 12 × 12ab + 14a - a
= 12a²b ÷ 144ab + 13a
= 12*a*a*b / 144*a*b + 13*a
= a/12 + 13*a
= 1/12 + 13
= 1/25
Determina el centro,radio y gráfica de la circunferencia:(x+2)2 + (y-3)2=121
Answers
Answer:
La ecuación genérica para un círculo centrado en el punto (a, b), de radio R, es:
(x - a)^2 + (x - b)^2 = R^2
Entonces si miramos a nuestra ecuación:
(x + 2)^2 + (y - 3)^2 = 121
Tendremos el centro en:
(-2, 3)
el radio está dado por:
R^2 = 121
R = √121 = 11
La gráfica de esta circunferencia se puede ver en la imagen de abajo.
HELP PLEASE I NEED COOR!!!!!
y−5=43(x−5)
Answers
Answer:
y=43x-210
Step-by-step explanation:
Distribute 43
then add five on each side
you get y=43x-210, 43 and 210 cannot be sipilified so that is the answer.
Answer:
y=43x-210
Step-by-step explanation:
Distribute 43 through the parenthesis.
y-5=43x-215
Move the constant to the right and change its sign.
y=43x-215+5
Calculate sum.
y=43x-210
Hope i helped :)
Determine the equations of the straight lines
passing through the following pairs of points.
1)(2,-2) and (3, 4)
2)(-3, -2) and (1,2)
3)(4,6) and (5,2)
4)(5,8) and (7, 1)
Answers
Answer:
1). 6x - 14 2). y = 1x + 1 3). y = -4x + 22 4).y = -7/2x + 51/2
Step-by-step explanation:
1). y2 - y1 / x2 - x1 4 - (-2) / 3-2 = 6
y = 6x + b 4 = 6(3) + b 4 = 18 + b -14 = b
y = 6x - 14
2). 2 - (-2) / 1 - (-3) = 1
y = 1x + b 2 = 1(1) + b 2 = 1 + b 1 = b
y = 1x + 1
3). 2 - 6 / 5 - 4 = -4
y = -4x + b 6 = -4(4) + b 6 = -16 + b 22 = b
y = -4x + 22
4). 1 - 8 / 7 - 5 = -7/2
y = -7/2x + 51/2
-3x - 3y = 3, -5x + y =13
System of Equations
Answers
Answer:
([tex]\frac{-7}{3}[/tex], [tex]\frac{4}{3}[/tex])
Step-by-step explanation:
Hi there!
We are given the following system of equations:
-3x-3y=3
-5x+y=13
and we need to find the solution (the point at which the 2 lines intersect)
let's solve this by substitution, where we will set one variable equal to an expression containing the other variable, and then substitute that expression into the other equation to solve for the variable that the expression from earlier contains, and then use the value of the solved variable to find the value of the first variable
in the second equation, add 5x to both sides to isolate y by itself
y=5x+13
now substitute 5x+13 as y in -3x-3y=3
-3x-3(5x+13)=3
do the distributive property
-3x-15x-39=3
combine like terms
-18x-39=3
add 39 to both sides
-18x=42
divide both sides by -18
x=[tex]\frac{-7}{3}[/tex]
now we need to find y
remember: y=5x+13
substitute [tex]\frac{-7}{3}[/tex] as x in y=5x+13
y=5([tex]\frac{-7}{3}[/tex])+13
multiply
y=[tex]\frac{-35}{3}[/tex]+13
add
y=[tex]\frac{4}{3}[/tex]
So the answer is x=[tex]\frac{-7}{3}[/tex], y=[tex]\frac{4}{3}[/tex]. As a point, it's ([tex]\frac{-7}{3}[/tex], [tex]\frac{4}{3}[/tex])
Hope this helps! :)
Try Again
Alvin is 7 years older than Elga. The sum of their ages is 79. What is Elga's age?
39 уга
years old
?
Answers
Answer:
36 years
Step-by-step explanation:
Let
x = Elga's age
Alvin's age = x + 7
Sum of their ages = 79
Sum of their ages = Alvin's age + Elga's age
79 = (x + 7) + x
79 = x + 7 + x
79 = 2x + 7
79 - 7 = 2x
72 = 2x
x = 72/2
x = 36
Elga's age = x = 36 years
Alvin's age = x + 7
= 36 + 7
= 43 years
Help please-- Given circle O below, if arc GH and arc HJ are congruent, what is the measure of chord line HJ?
Answers
Answer:
the answer is D
Step-by-step explanation:
Hope this helps :)
The Venn diagram shows three types of numbers: odd (O), even (E), and prime (P).
Circles O and P overlap, and circle P also overlaps with circle E.
Which is represented by Ø?
Answers
Answer:
Null set
Step-by-step explanation:
Odd(0)
Even (E)
Prime (P)
Answer:
Its A since the other person didnt say it
Step-by-step explanation:
One circle has a circumference of 12π cm. Another circle has a circumference of 32π cm. What is the ratio of the radius of the smaller circle to the radius of the larger circle?
Options:
A: 3:8
B: 8:3
C: 1:3
D: 3:1
Answers
3:8
The ratio of small circle
12:32
If we divide both of them by 4 we get 3:8
Factorize (a+b)²-4ab
Answers
Answer:
(a - b)²
Step-by-step explanation:
(a + b)² - 4ab
= a² + 2ab + b² - 4ab
= a² - 2ab + b²
= (a - b)²
simplify the following radical expression -7√2 + 10 √2
Answers
Answer:
3√2
Step-by-step explanation:
* means multiply
-7√2 + 10 √2
take √2 out of the expression
√2 (-7 + 10)
√2 (3)
3√2
Determine the measure of <0
20.21°
0.005
73.74°
16.26°
Answers
Answer:
16.26°
Step-by-step explanation:
1. tanΘ= 7/24
2.[tex]tan^-1(\frac{7}{24} ) =[/tex]Θ
3. Θ = 16.26°
The Ramos family drove to their family reunion. Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours. After lunch, they drove at a constant rate of 45 miles per hour for 2 hours. How many total miles did the Ramos family drive? Miles
Answers
Answer:
ok so first they drove 55 for 3 hours so
55*3=165
and then they drove 45 for 2 hours
45*2=90
165+90=255
so in total they drove 255 miles
Hope This Helps!!!
The solution is : 255 miles total miles did the Ramos family drive.
What is speed?Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
Speed = Distance/ Time.
here, we have,
given that,
The Ramos family drove to their family reunion. Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours. After lunch, they drove at a constant rate of 45 miles per hour for 2 hours.
we get,
Journey before lunch:
Speed = 55 mph
Time = 3 hrs
distance = 55*3 = 165 miles.
Journey after lunch:
Speed = 45 mph
Time = 2 hrs
distance = 45 * 2 = 90 miles
Total miles driven
= distance traveled before lunch + distance traveled after lunch
= 165 miles + 90 miles
= 255 miles
Therefore, the Ramos family drove 255 miles in total.
To learn more on speed click:
brainly.com/question/28224010
#SPJ2
Y=2/7 -7 y=-x+2 What is the solution for this system of equations?
Answers
Answer:
(61/7, -47/7)
Step-by-step explanation:
Given: y=2/7 -7
y=-x+2
Rewrite the top equation ( y=2/7 -7
y = -47/7
y = -x + 2
Because both equations are equal to y, we can rewrite it again.
-47/7 = -x + 2
Add x to both sides
x + (-47/7) = 2
Add 47/7 to both sides.
x = 47/7 + 2/1
x = 61/7
As stated in the beginning, y is equal to -47/7
Hope you understand!
I had block the instructions but basically it said State what additional information is required in order to know that the triangles in the image below are congruent for the reason given.
Answers
Answer:
Segment XY congruent to Segment IJ is required.
Step-by-step explanation:
It's asking for Side-Angle-Side postulate and you already have a side and an angle. WX=HI and <x=<I. Order matters, so the angle should be directly between the first set of segments and the second.
Seo-Yun organizó una fiesta. Comprar 50 recuerditos para regalar y les dio 3 recuerditos a cada uno de sus invitados conforme llegaban a la fiesta.
Escribe una fórmula explícita para la sucesión.
g(n)=
Answers
Answer: nose
Step-by-step explanation:
Nas funções f(x) = -3x+9; f(x) = 2x-4 e f(x) = 5x-5, caso construamos seus respectivos gráficos, informe respectivamente os pares ordenados correspondentes aos zeros da função, ou seja, os pares ordenados que indicam onde os gráficos interceptam a abscissa (eixo "X") e a ordenada (eixo y ou f(x)) de cada uma das três funções.Leitura Avançada
{(3,0) e (0,9)}; {(2,0) e (0,-4)}; {(1,0) e (0,-5)}
{(3,0) e (0,9)}; {(2,0) e (0,4)}; {(1,0) e (0,5)}
{(3,0) e (0,9)}; {(2,0) e (0,-4)}; {(1,0) e (0,5)}
{(3,0) e (0,-9)}; {(2,0) e (0,-4)}; {(1,0) e (0,-5)}
Answers
1st option
{(3,0) e (0,9)}; {(2,0) e (0,-4)}; {(1,0) e (0,-5)}
see screenshot
sorry btw, no hablo espanol
Consider the equation 6x +7=3x � 5. Which of the following possible first steps would prevent having to deal with fractions when solving the equation?
Answers
Answer:
D. I or II only
Step-by-step explanation:
By a small online search, I've found that the equation is:
6x + 7 = 3x - 5
And the options are:
I. Combining the 6x and 3x terms
II. Combining the 7 and 5
III. Dividing both sides of the equation by 6
A. I only
B. II only
C. III only
D. I or II only
E. I or II or III
So, let's solve the equation in such a way that we can prevent the use of fractions:
6x + 7 = 3x - 5
We can use I and II, combining one in each side, so we get (so we use I and II at the same time)
6x - 3x = -5 - 7
solving these, we get:
(6 - 3)*x = -12
3*x = -12
and -12 is divisible by 3, so if we divide in both sides by 3, we get:
x = -12/3 = -4
x = -4
So we avoided working with fractions, and we used I and II.
Then the first step could be either I or II (the order does not matter)
Then the correct option is:
D. I or II only
Expansion (2x-3y+4z)^2
Answers
Answer:
Step-by-step explanation:
(a+b+c)²=a²+b²+c²+2ab+2bc+2ca
(2x-3y+4z)²=(2x)²+(-3y)²+(4z)²+2(2x)(-3y)+2(-3y)(4z)+2(4z)(2x)
=4x²+9y²+16z²-12xy-24yz+16zx
We know that,
→ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
Now Putting 2x = a, -3y = b and 4z = c , we get
→ (2x - 3y + 4z)²
→ (2x)² + (- 3y)² + (4z)² + 2 × 2x × (- 3y) + 2 × (- 3y) × 4z + 2 × 4z × 2x
→ 4x² + 9y² + 16z² - 12xy - 24yz + 16zx
Arranging according to the like terms, we get
→ 4x² - 12xy + 16zx + 9y² - 24yz + 16z²
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