The solution of the simultaneous equations using target matrix are; x = 51/37 and y = 33/37
How to use matrix to solve simultaneous equations?The target variable is defined as the variable whose values are modeled and predicted by other variables.
We are given the simultaneous equations as;
5x - y = 6
2x + 7y = 9
In matrix form, it is expressed as;
5 -1 6
2 7 9
row 2 = row 2 + row 1 * 7
This gives us;
37 0 51
Thus;
x = 51/37
Plugging in 51/37 for x in eq 1 gives;
5(51/37) - y = 6
Multiply through by 37 to get;
5*51 - 37y = 37*6
255 - 37y = 222
-37y = 222 - 255
y = 33/37
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what is the solution set of x+4/2x-1 <0
Answer: x=1/3
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
3x−1<0
Step 2: Add 1 to both sides.
3x−1+1<0+1
3x<1
Step 3: Divide both sides by 3.
3x/3 <1/3
x/1/3
First try was incorrect
Hall is baking a pie. The radius of the pie is 17 inches. What is the
area of the pie?
Use 3.14 for pi and round your answer to the nearest tenth.
label required
Answer:
907.5
Step-by-step explanation:
Formula to find the area of a circle: πr²
πr² = 3.14 x 17²
= 3.14 x 289
= 907.46
≈ 907.5
Hope this helps :)
Help please I give brainliest
Answer:
interest is $105
total is $455
Step-by-step explanation:
350 * .03 = 10.5
10.5*10 = 105
interest is 105
350 +105 = 455
Interest earned: $105
The balance of the account: $455
(I just need one more brainliest then I get the rank ACE)
The accompanying data set lists the numbers of children of world leaders. Use the data to construct a frequency distribution using six classes and to create a frequency polygon. Describe any patterns.
LOADING... Click the icon to view the data set.
Step-by-step explanation:
bla bla bla.....................
pls help me...........
Answer:
3,480
Step-by-step explanation:
After 4 years she had to repay 3,480, i did this one before and got it right hope it helped have a nice day!
[tex]\color{plum}\tt\bold{(b) \: \$3480 }[/tex]
Steps to derive correct option :Money Maria borrowed = $3000
Percentage of simple interest per annum = 4%
Time she took to repay the money she borrowed = 4 years
We know that :
[tex]\color{hotpink}\tt \: Simple \: interest = \color{plum}\frac{principal \times rate \times time}{100} [/tex]
In this case :
Principal = $3000
Rate = 4%
Time = 4 years
Which means. the simple interest :
[tex] = \tt \frac{3000 \times 4 \times 4}{100} [/tex]
[tex] = \tt \frac{48000}{100} [/tex]
[tex]\color{plum} =\tt\$ 480[/tex]
Thus, the interest she has to pay = $480
We know that :
[tex]\color{hotpink}\tt \: Amount \color{plum}= principal + interest[/tex]
Then, the Amount Maria has to pay :
[tex] =\tt 3000 + 480[/tex]
[tex]\color{plum} =\tt \$3480[/tex]
Thus, the amount Maria has to repay after 4 years = $3480
Therefore, the correct option is (b) $3480
1.99 ÷ 3 =
2. 125 ÷ 5 =
3. 288 ÷ 36=
4. 540 ÷ 12=
5. 999 ÷ 111=
pls answer ngayon ko na po ito ipapasa explain the answer
What type of chart would best be used for continuous data?
Group of answer choices
Pareto chart
Histogram
Dot plot
Pie chart
Ralph receive money from his family members for his graduation. He decides he wants to spent no more than $120 on movies to bring with him to college.
What is the slope of the red and blue line
Answer:
red=-1/4 blue= 4/1
Step-by-step explanation:
rise/run
Given quadrilateral ABCD, find the values for x and y.
x = 4, y = 6
x = 34, y = 56
x = 1067, y = 223
x = 627, y = 1109
Answer:
x = 4, y = 6
Step-by-step explanation:
Consider the triangle BEC.
∠BEC=112 (vertically opposite angles)
∠EBC=∠ECB (BEC is an isosceles triangle)
All the angles in a triangle add up to 180, so:
∠BEC+∠EBC+∠ECB=180
112+(7x+6)+(7x+6)=180
14x=180-112-6-6
x=56/14=4
Consider the triangle CED
∠CED=68 (lies on a straight line with 112, angles on a straight line add up to 180)
∠EDC=∠ECD (CED is an isosceles triangle)
All the angles in a triangle add up to 180, so:
∠CED+∠EDC+∠ECD=180
68+(9y+2)+(9y+2)=180
18y=180-68-2-2
y=108/y=6
The value of x and y for quadrilateral ABCD is at x = 4 and y = 6. Option A is correct.
What are quadrilaterals?A closed quadrilateral has four sides, four vertices, and four angles. It is a form of a polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
Given quadrilateral ABCD,
Consider the ΔBEC.
∠BEC = 112 (vertically opposite angles)
∠EBC=∠ECB
ΔBEC is an isosceles triangle because BE = EC.
the sum of angles of a triangle is 180°,
∠BEC + ∠EBC + ∠ECB = 180°
112 + (7x + 6) + (7x + 6) = 180°
14x = 180 - 112 - 6 - 6
x = 56/14
x = 4
Consider the ΔCED
∠CED = 68
lies on a straight line with 112°, and angles on a straight line add up to 180°.
∠EDC = ∠ECD
ΔCED is an isosceles triangle because DE = CE.
the sum of the angles of a triangle is 180°
∠CED + ∠EDC + ∠ECD = 180°
68 + (9y + 2) + (9y + 2) = 180°
18y = 180 - 68 - 2 - 2
y=108/18
y = 6
Hence values of x = 4 and y = 6.
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find the sum of (x^2+6x-5)+(2x^2+15)
Answer:
3x²+6x+10 is your answer
Step-by-step explanation:
(x^2+6x-5)+(2x^2+15)
open bracket
x²+6x-5+2x²+15
add or subtract common
3x²+6x+10
The area of a triangle varies jointly with the lengths of its base and height. A triangle with a base of 10 ft and a height of 4 ft has an area of 20 square ft. Find the area of a triangle with a base of 3 ft and a height of 8 ft.
Answer:
12 square ftStep-by-step explanation:
base = 3ft. and height = 8ft. area of triangle = 1/2 ×base × height = 1/2 ×3 × 8 = 24 /2 = 12 square ft. MARK ME AS BRAINLISTPLZ FOLLOW MEIn a store the number of dogs is 12 times greater than 3 times of cats. If there are 21 dogs in the store, how many cats are in the store?
Answer:
If you really meant that the number of dogs is 12 greater than 3 times the number of cats then:
3 cats
Step-by-step explanation:
21= number of dogs
c = number of cats
21 = 12 + (3c)
3c = 9
c = 3
Which data set is the most spread from its mean?
14, 26, 24, 28
22, 16, 18, 36
22, 28, 20, 22
21, 19, 27, 25
Answer:
Tha mean is 23 which means there is no answer:)
14, 26, 24, 28: still 23
22, 16, 18, 36:STILL 23
22, 28, 20, 22: 23
21, 19, 27, 25: STILL 23
Answer:
the answer is B
Step-by-step explanation: each number on a c and d is 7-5 away from 23 but b has 36 which is 13 away from 23 and in all is the farthest plz mark brainlest
I need to know how to work fractions word problems like Leon's older brother is 4 3/4 feet tall. Leon is 1/3 foot shorter than his brother. How tall is Leon?
Answer:
4 5/12 feet tall
Step-by-step explanation:
Find the LCM first. The LCM is the lowest common multiple between the two denominators. The LCM in this problem is 12, so you multiply each fraction until the denominators equal 12
4 3/4 -> 4 9/12
1/3 -> 4/12
Now it's much easier to solve. 4 9/12 - 4/12 = 4 5/12 feet tall
pls guys tell me the answer pls
Answer:
Height = 7m
Step-by-step explanation:
Hope that helps!
Answer:
7m
Step-by-step explanation:
There are more than one answer help me and I give brainilest
Answer:
Equivalent to a), b), and d). It is NOT equivalent to c).
Step-by-step explanation:
6m + 12 is also equivalent to a) 3(2m+4) because when you distribute, it's 6m + 12. It is also equivalent to b) 3m + 8 + 4 + 3m because if you add them together, you get 6m + 12. It is not equivalent to c) but is do d) 4m + 2(m + 6) cause you use the distributive property then add. I hope this helped and please mark brainliest!
Simon mixes dried fruits and nuts to make a trail mix that he sells at the farmer's market. The dried fruits cost $6 per pound. The nuts cost
$2 per pound. It costs Simon $40 to make 12 pounds of trail mix.
Which system of equations can be used to find the number of pounds, x, of dried fruits and the number of pounds, y, of nuts that Simon used
to make 12 pounds of trail mix?
Answer:
d
Step-by-step explanation:
Find the surface area of the rectangular prism. 8 yd 3 yd 3 yd pls help
Answer:
114
Step-by-step explanation:
add the areas of all 6 faces
the formula is A= 2(l*w)+2(l*h)+2(h*w)
A=2(8*3)+2(8*3)+2(3*3)=114
answer: 114yd^2
is 8.2 and 5.15 proportional
if f(x)= x/2-3 and g(x) = 2x^2+x-6, find (f+g)(x)
Answer:
2x² + 3x/2 - 9
Step-by-step explanation:
(f+g)(x) = f(x) + g(x)
= x/2 - 3 + 2x² + x - 6
= 2x² + x/2 + x -3 -6
= 2x² + 3x/2 - 9
4x-5y=11 and 8x-5y=27
Answer:
y = -1 , x = 4
Step-by-step explanation:
(4x - 5y = 11) x8
(8x - 5y = 27) x4
32x - 40y = 88
- - -
32x - 20y = 108
[0. 20y = -20] divide both by 20
y = -1
8x - 5y = 27
8x - 5(-1) = 27
8x = 27 + 5
8x = 32 ( divide both by 8)
x = 4
<CEB and BED are adjacent angles ehat is the side common to the two angles?
Step-by-step explanation:
<CEB and < BED are adjacent angles then
The common side to the two angles is
EB
A ray can intersect a circle in __________.
1. a line segment
2. a line
3. a ray
4. a point
Answer:
a line segment.
Step-by-step explanation:
a line segment
A ray can intersect a circle at points on the circumference. Option D is correct.
The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²
where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.
Here,
A ray can intersect a circle at a maximum of two points,
The line which intersects the circle at two points is called the secant to the circle, and the line that intersects the circle at one point is called the tangent two the circle.
Thus, a ray can intersect a circle at points on the circumference. Option D is correct.
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[tex] \sqrt{25} [/tex]
pls help i just want the answer T-T.
Answer:
5
Step-by-step explanation:
what is 2x2x2x2+2+2+2divitide by 6
Answer:
3.6 repeating or 3 and 2/3
Step-by-step explanation:
I did the work on a calculator.
Answer:
f be it is right
Step-by-step explanation:
okay that is it
what is the area of 5m, 17m, 8m, and 5m, the shape is a kite
Answer:
It can't be a kite. A kite has 2 pairs of equal sides.
Step-by-step explanation:
How many terms are in the expression below?
17 – (5n = 4) + 8%
Answer: 4
Step-by-step explanation:
(Can someone please answer my math question)
If a man is driving at a rate of 50 km per hour, how many kilometers will he travel in 30 minutes? A. 25 km B. 30 km C. 150 km D. 180 km
Answer:
A. 25 km
Step-by-step explanation:
1 hour = 60 minutes
30 minutes is a half of an hour, therefore
50 / 2 = 25
Answer:
a, 25km
Step-by-step explanation:
i dont need brainliest but thx
im jamming to rick astley right now its so fun
Suppose a subdivision on the southwest side of Denver, Colorado, contains 1,500 houses. The subdivision was built in 1983. A sample of 120 houses is selected randomly and evaluated by an appraiser. If the mean appraised value of a house in this subdivision for all houses is $228,000, with a standard deviation of $8,500, what is the probability that the sample average is greater than $229,500?
Answer:
0.0268 = 2.68% probability that the sample average is greater than $229,500
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Single house:
The mean appraised value of a house in this subdivision for all houses is $228,000, with a standard deviation of $8,500, which means that [tex]\mu = 228, \sigma = 8.5[/tex]
Sample:
Sample of 120, so, by the central limit theorem, [tex]n = 120, s = \frac{8.5}{\sqrt{120}} = 0.7759[/tex]
What is the probability that the sample average is greater than $229,500?
This is 1 subtracted by the pvalue of Z when X = 229.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{229.5 - 228}{0.7759}[/tex]
[tex]Z = 1.93[/tex]
[tex]Z = 1.93[/tex] has a pvalue of 0.9732
1 - 0.9732 = 0.0268
0.0268 = 2.68% probability that the sample average is greater than $229,500