Answer:
(4, 2 )
Step-by-step explanation:
Given the 2 equations
3x + y = 14 → (1)
7x - 4y = 20 → (2)
Rearrange (1) making y the subject by subtracting 3x from both sides
y = 14 - 3x → (3)
Substitute y = 14 - 3x into (2)
7x - 4(14 - 3x) = 20 ← distribute parenthesis and simplify left side
7x - 56 + 12x = 20
19x - 56 = 20 ( add 56 to both sides )
19x = 76 ( divide both sides by 19 )
x = 4
Substitute x = 4 into (3) for corresponding value of y
y = 14 - 3(4) = 14 - 12 = 2
solution is (4, 2 )
Answer:
[tex]3x + y = 14 \\ y = 14 - 3x \\ substitute \: y \: into \: equation \: 2\\ 7x - 4(14 - 3x) = 20 \\ 7x - 56 + 12x = 20 \\ 19x = 76 \\ x = \frac{76}{19} =4 \\ y = 14 - 3( 4 ) = 2 \\ [/tex]
The center of the circle is located (3'8), and the circle has a radius that is 5 units long. What is the general form of the equation for the circle
9514 1404 393
Answer:
x² +y² -6x -16y +48 = 0
Step-by-step explanation:
Given:
circle center: (3, 8)circle radius: 5Find:
general form equation for the circle
Solution;
The standard form equation for the circle is ...
(x -h)² +(y -k)² = r² . . . . . circle with radius r centered at (h, k)
(x -3)² +(y -8)² = 5²
Subtracting 25 and expanding this will give the general form.
x² -6x +9 +y² -16y +64 -25 = 0
x² +y² -6x -16y +48 = 0
_____
Additional comment
"General form" of an equation is usually the form f(x,y) = 0, where f(x, y) is written in "standard form," with terms in lexicographical order and decreasing degree.
HELP
-5(2m-3)-4<81
I need the steps also well
Answer:
m>-7
Step-by-step explanation:
expand
-10m+15-4<81
-10m+11<81
collect like terms
-10m<81-11
-10m<70
m>-7
3p + 2q = 14
10p + 6q = 44
What is p and what is q
Answer:
p = 2 ; q = 4
Step-by-step explanation:
Given tbe equation :
3p + 2q = 14 - - - (1)
10p + 6q = 44 - - -(2)
What is p and what is q
This is a simultaneous equation ; using elimination method :
Multiply (1) by 6 and (2) by 2
18p + 12q = 84 - - - - (3)
20p + 12q = 88 - - - (4)
Subtract (3) and (4)
-2p = - 4
p = 4/2
p = 2
Put p = 2 in (1)
3p + 2q = 14
3(2) + 2q = 14
6 + 2q = 14
2q = 14 - 6
2q = 8
q = 8/2
q = 4
p = 2 ; q = 4
Suppose that the IQ of a randomly selected student from a university is normal with mean 115 and standard deviation 25. Determine the interval of values that is centered at the mean and for which 50% of the students have IQ's in that interval.
Answer:
The interval is [98,132]
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normal with mean 115 and standard deviation 25.
This means that [tex]\mu = 115, \sigma = 25[/tex]
Determine the interval of values that is centered at the mean and for which 50% of the students have IQ's in that interval.
Between the 50 - (50/2) = 25th percentile and the 50 + (50/2) = 75th percentile.
25th percentile:
X when Z has a p-value of 0.25, so X when Z = -0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 115}{25}[/tex]
[tex]X - 115 = -0.675*25[/tex]
[tex]X = 98[/tex]
75th percentile:
X when Z has a p-value of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 115}{25}[/tex]
[tex]X - 115 = 0.675*25[/tex]
[tex]X = 132[/tex]
The interval is [98,132]
Which of the following choices is the average speed of a tourist who traveled for 1 hour on a plane at 400 mph and 4 hours by car at 60 mph?
(average= total miles/total hours)
Answer:
128 mph
Step-by-step explanation:
1 hour = 400
4 hours = 240
240+400= 640
4+1 = 5
640/5=128
3.
If 9x = 27, what is the value of x?
Four times a number is 88 less than 6 times the number. Find the number.
Answer:
44
Step-by-step explanation:
Let x represent the number.
Create an equation, and solve for x:
4x = 6x - 88
-2x = -88
x = 44
So, the number is 44.
The number is 44.
To find the number.
What is arithmetic?science that deals with the addition, subtraction, multiplication, and division of numbers and properties and manipulation of numbers. Arithmetic is the basics of the abstract science of numbers and operations on them. The formula for any arithmetic sequence is this: an = a1 + d (n - 1).
Given that:
Let x represent the number.
Create an equation, and solve for x:
4x = 6x - 88
-2x = -88
x = 44
So, the number is 44.
Learn more about arithmetic here:
https://brainly.com/question/24163536
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From two points on the same level as the base of a tree, the angles of elevation to the top of the tree are found to be 24° and 46°. If the two points are 42 feet apart and on the same side of the tree, how tall is the tree? (Give your answer to the nearest tenth of an inch.)
Answer:
the answer is 32.8in.
Step-by-step explanation:
(sin 22)/42 = (sin 24)/x
x = 45.60
sin 46 = x/45.60
x = 32.80
32.8in.
hope it helped :)
mark me brainliest!
What is the length of an arc with a central angle of 2/3pi radians and a radius of 24 centimeters?
Use 3.14 for pi.
Enter your answer, as a decimal, in the box.
9514 1404 393
Answer:
50.24 cm
Step-by-step explanation:
Fill in the given numbers and do the arithmetic.
s = rθ
s = (24 cm)(2/3π) = (24 cm)(2/3)(3.14) = 50.24 cm
what is the sum of the geometric series 4∑ t=1 6t-1
Answer:
Hello friend kya in snap and p to Trisha
(URGENT!!) Which graph models the function f(x) = -4(2)x? (2 points)
Answer:
2nd Graph
Step-by-step explanation:
Bases off the graphs, you gave me, I assume your the equation is
[tex]f(x) = - 4(2) {}^{x} [/tex]
The parent equation of this function is
[tex]f(x) = b {}^{x} [/tex]
Let say x=0
Using the rules of exponets, the y value must be 1 so a critical point is
(0,1)
The function is multiplied by -4.
This means the function is stretched in the y direction by 4 and reflected over the x axis. So our new point will be
(0,-4).
The base 2 the function will get compressed by 1/2.
The best graph that represents this is the second graph
Ali is hiking on the hill, whose height is given by f(u,v)=n^2 e^((u+n)/(v+n)). Currently, he is positioned at point (3, 5). Find the direction at which he moves down the hills quickly. Take n =12
Answer:
[tex]<-144e^{0.88},7.47e^{0.88}>[/tex]
Step-by-step explanation:
We are given that
[tex]f(u,v)=n^2e^{\frac{u+n}{v+n}}[/tex]
Point=(3,5)
n=12
We have to find the direction at which he moves down the hills quickly.
[tex]f(u,v)=144e^{\frac{u+12}{v+12}}[/tex]
[tex]f_u(u,v)=144e^{\frac{u+12}{v+12}}[/tex]
[tex]f_u(3,5)=144e^{\frac{3+12}{5+12}}[/tex]
[tex]f_u(3,5)=144e^{\frac{15}{17}}=144e^{0.88}[/tex]
[tex]f_v(u,v)=144e^{\frac{u+12}{v+12}}\times (-\frac{u+12}{(v+12)^2})[/tex]
[tex]f_v(3,5)=144e^{\frac{15}{17}}(-\frac{15}{(17)^2}[/tex]
[tex]f_v(3,5)=-\frac{2160}{289}e^{\frac{15}{17}}=-7.47e^{0.88}[/tex]
[tex]\Delta f(3,5)=<f_u(3,5),f_v(3,5)>[/tex]
[tex]\Delta f(3,5)=<144e^{0.88},-7.47e^{0.88}>[/tex]
The direction at which he moves down the hills quickly=-[tex]\Delta f(3,5)[/tex]
The direction at which he moves down the hills quickly=[tex]<-144e^{0.88},7.47e^{0.88}>[/tex]
How many different committees can be formed from 12 teachers and 43 students if the committee consists of 3 teachers and 4 students?
The committee of 7 members can be selected in BLANK
different ways.
Answer:
27150200Step-by-step explanation:
Combination of 3 teachers out of 12:
12C3 = 12!/9!3! = 10*11*12/2*3 = 220Combination of 4 students out of 43:
43C4 = 43!/39!4! = 40*41*42*43/2*3*4 = 123410Total combinations:
220*123410 = 271502005
12
of the pupils in Year 9 say their favourite colour is red.
There are 240 pupils in Year 9.
How many students said red is their favourite colour?
Answer:
100
Step-by-step explanation:
I assume you mean [tex]\frac{5}{12}[/tex] of the students in Year 9.
Basically, first you need to work out 1/12 of the students, which is just 240 divided by 12, equals 20.
So, we know 1/12 of 240 is 20, therefore, in order to work out 5/12, we must do 20 x 5, which is 100.
is this right? PLEASE HELP ILL MARK
Answer:
yeah u r correct...hope it helps ..stay safe healthy and happy.convert 23/4 into mixed number
Please help. I'm stuck on this problem
Answer:
Step-by-step explanation:
[tex]h(t)=-16t^2+96t\\\\h(t)=-t(16t-96)[/tex]
[tex]96=2^5*3\\\\16=2^4\\\\h(t)=-t(2^5*3*t-2^4)=-2^4t(2^1*3*t-1)\\\\h(t)=-16t(6t-1)[/tex]
the b) part is easy do it!
Find the equation of the lines in problem 1 (0,0) slope =2.
Answer:
y = 2x
Step-by-step explanation:
Given that , the line passes through the point (0,0) and has a slope of 2. So here we can use the point slope form of the line as ,
[tex]\implies y- y_1 = m( x - x_1) \\\\\implies y - 0 = 2( x - 0 ) \\\\\implies y = 2(x) \\\\\implies \underline{\underline{y = 2x }}[/tex]
Please help!!!!
I’m using Plato
1 by 4 ^ 256 is equal to 4 and 1 by 4 ^ 64 will be root 4 so here the answer will be 4 into 4 root 4
there option 4 will be correct
Yuki bought a drop–leaf kitchen table. The rectangular part of the table is a 2–by–3–foot rectangle with a semicircle at each end, as shown.
Answer:
[tex](a)\ Area = 13.0695[/tex]
[tex](b)\ Area = 26.139[/tex]
Step-by-step explanation:
Given
The attached image
Solving (a): The area (one side up)
This is calculated as:
Area= Area of semicircle + Area of rectangle
So, we have:
[tex]Area = \pi r^2 + l *w[/tex]
Where:
[tex]l,w =2,3[/tex] --- the rectangle dimension
[tex]d = 3[/tex] --- the diameter of the semicircle
So, we have:
[tex]Area = \pi * (3/2)^2 + 2 * 3[/tex]
[tex]Area = \pi * 2.25 + 6[/tex]
[tex]Area = 2.25\pi + 6[/tex]
[tex]Area = 2.25*3.142 + 6[/tex]
[tex]Area = 13.0695[/tex]
Solving (b): Area when both leaves are up.
Simply multiply the area in (a) by 2
[tex]Area = 2 * 13.0695[/tex]
[tex]Area = 26.139[/tex]
a set of date consists of 225 observations. the lowest value of the data set is 2,403; the highest is
Answer:
8 classes
Step-by-step explanation:
Given
[tex]Least = 2403[/tex]
[tex]Highest = 11998[/tex]
[tex]n = 225[/tex]
Required
The number of class
To calculate the number of class, the following must be true
[tex]2^k > n[/tex]
Where k is the number of classes
So, we have:
[tex]2^k > 225[/tex]
Take logarithm of both sides
[tex]\log(2^k) > \log(225)[/tex]
Apply law of logarithm
[tex]k\log(2) > \log(225)[/tex]
Divide both sides by log(2)
[tex]k > \frac{\log(225)}{\log(2)}[/tex]
[tex]k > 7.8[/tex]
Round up to get the least number of classes
[tex]k = 8[/tex]
Which of the following is not true?
Answer:
C. m<c = 140°
Step-by-step explanation:
Let's analyse each of the given options:
A. m<a = 140° is TRUE
Rationale: angle a and 140° are vertical angles. Vertical angles are congruent.
B. m<b = 140° is TRUE.
Rationale: angle a and 140° are alternate interior angles. Alternate interior angles are congruent.
C. m<c = 140° is NOT TRUE.
Rationale: angle c and 140° are same side interior angles. Same side interior angles are supplementary.
D. m<d = 140° is TRUE.
Rationale: angle d and 140° are corresponding angles. Corresponding angles are congruent.
Convert 0.53 hectograms to centigrams.
53 centigrams
0.000053 centigrams
530 centigrams
5,3000 centigrams
Answer:
As for metric prefixes, "hecto" means hundred and "centi" means hundredth.
So, converting .53 hectograms to centigrams requires multiplying it by 10,000.
So, .53 hectograms * 10,000 equals 5,300 centigrams.
Source http://www.1728.org/convprfx.htm
Step-by-step explanation:
Find the measure of each angle whose degree measure is represented in terms of x in the given
triangle.
Please help :)
Answer:
Step-by-step explanation:
Answer:
That's barely readable! Anyway the solution is:
7x + 7x +2 +5x +7 = 180 degrees
19x + 9 = 180 degrees
19x = 171 degrees
x = 9
So the angles are:
7x = 63 degrees
7x + 2 = 65
5x + 7 = 52
Double check:
Since ALL 3 triangle sides add up to 180:
63 + 65 + 52 = 180 degrees
Step-by-step explanation:
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. text({)1, 1/4, 1/16, 1/64, 1/256, ... text(})
Answer:
[tex]T_n = \frac{1}{4^{n-1}}[/tex]
Step-by-step explanation:
Given
[tex]({)1, 1/4, 1/16, 1/64, 1/256, ... (})[/tex]
Required
The general term
The given sequence is geometric.
So first, we calculate the common ratio (r)
[tex]r = T_2/T_1[/tex]
So, we have:
[tex]r = 1/4 \div 1[/tex]
[tex]r = 1/4[/tex]
The function is then calculated using:
[tex]T_n =T_1 * r^{n-1}[/tex]
This gives
[tex]T_n =1 * 1/4^{n-1}[/tex]
[tex]T_n = \frac{1}{4^{n-1}}[/tex]
I need help! please!!
Answer:
r=8°.answerStep-by-step explanation:
95°=6r°+47{ vertically opposite angle are equal}95°-47°=6r°6r°=48°r=48/6r=8°hope it helps.stay safe healthy and happy.Answer:
8
Step-by-step explanation:
95°=6r°+47(being vertically opposite angle)
or,48°=6r
or,48=/6=r°
or,r=8°
7/3a - 8/5 +4/15a
Simplified
Answer:
13/5a - 8/5
Step-by-step explanation:
= 35/15a + 4/15a - 8/5
= 39/15a - 8/5
= 13/5a - 8/5
The simplified form of the given expression, "7/3a - 8/5 +4/15a" will be 13/5a - 8/5.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that the expression is,7/3a - 8/5 +4/15a.
We have to simplify the expression.
We have to apply the arithmetic operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
=7/3a - 8/5 +4/15a
= 35/15a + 4/15a - 8/5
= 39/15a - 8/5
= 13/5a - 8/5
Thus, the simplified form of the given expression, "7/3a - 8/5 +4/15a" will be 13/5a - 8/5.
Learn more about the expression here:
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Find the standard normal area for each of the following (Round your answers to 4 decimal places.): Standard normal area a.P(1.26 < Z < 2.16) b.P(2.05 < Z < 3.05) c.P(-2.05 < Z < 2.05) d.P(Z > .55)
Answer:
The correct answer is:
(a) 0.0884
(b) 0.0190
(c) 0.9596
(d) 0.2921
Step-by-step explanation:
(a)
= [tex]P(1.26<Z<2.16)[/tex]
= [tex]P(Z<2.16)-P(Z<1.26)[/tex]
= [tex]0.9846-0.8962[/tex]
= [tex]0.0884[/tex]
(b)
= [tex]P(2.05<Z<3.05)[/tex]
= [tex]P(Z<3.05)-P(Z<2.05)[/tex]
= [tex]0.9989-0.9798[/tex]
= [tex]0.0190[/tex]
(c)
= [tex]P(-2.05<Z<2.05)[/tex]
= [tex]P(Z<2.05)-P(Z<-2.05)[/tex]
= [tex]0.9798-0.0202[/tex]
= [tex]0.9596[/tex]
(d)
= [tex]P(Z>0.55)[/tex]
= [tex]1-P(Z<0.55)[/tex]
= [tex]1-0.7088[/tex]
= [tex]0.2912[/tex]
8) If 150% of a number is 75, then what is the 80% of that number?
A. 40
B. 50
C. 70
D. 85
Answer:
A. 40
Step-by-step explanation:
Answer:
A. 40
Step-by-step explanation:
75 ÷ 1.5 = 50 = original number
80% of 50 = 50 × 0.8 = 40
Mark looked at the statistics for his favorite baseball player, Jose Bautista. Mark looked at seasons
when Bautista played 100 or more games and found that Bautista's probability of hitting a home run
in a game is 0.173
If Mark uses the normal approximation of the binomial distribution, what will be the variance of
the number of home runs Bautista is projected to hit in 100 games? Answer choices are rounded
to the tenths place.
O 0.8
O 14.3
0 3.8
O 17.3
⭕ 17.3
#CARRYONLEARNING
[tex]{hope it helps}}[/tex]
