Answer:
• Let's first assign identifications to the equations given:
[tex]{ \rm{8x + 9y = {}^{ - }3 \: - - - \{equation \: (a) \} }} \\ { \rm{6x + 7y = 1 - - - \{equation \: (b) \}}} \\ [/tex]
• There are various methods to solve this system of equation, namely;
Graphical methodSubstitution methodElimination methodCalculus (Calculator synthetic method)1. Graphical method
→ You'll have to draw a graph, demacate it very well following the suitable scale.
→ Get values to plot from both equation (a) and equation (b).
→ Draw respective lines of each equation. The point of intersection of the lines is the answer of the values of x and y.
→ It'll be in coordinate format i.e; (x, y)
2. Substitution method
→ Lemme first consider equation (a)
[tex]{ \rm{8x + 9y = {}^{ - }3 }}[/tex]
• make x the subject of the equation (a):
[tex]{ \rm{8x = - 3 - 9y}} \\ \\ { \rm{x = \frac{ - 3}{8} - \frac{9}{8}y }} \: { \rm{- - - \{equation \: (c)}} \}[/tex]
→ Considering equation (b) next
[tex]{ \rm{6x + 7y = 1}}[/tex]
• substitute x in equation (b) with x in equation (c)
[tex]{ \rm{6( \frac{ - 3}{8} - \frac{9}{8}y ) + 7y = 1 }} \\ \\ { \rm{ - \frac{9}{4} - \frac{27}{4} y + 7y = 1}} \\ \\ { \rm{ \frac{1}{4} y = \frac{13}{4} }} \\ \\ { \underline{ \rm{ \: \: y = 13 \: \: }}}[/tex]
• then find x using equation (c)
[tex]{ \rm{x = \frac{ - 3}{8} - \frac{9}{8} y }} \\ \\ { \rm{x = \frac{ - 3}{8} - \frac{9}{8} (13)}} \\ \\ { \underline{ \rm{ \: \: x = - 15 \: \: }}}[/tex]
3. Elimination method:
→ Here, we have to align the equations so that if we use addition or subtraction operations we remain with one term giving us zero [ eliminated ]
→ Multiply equation (a) by 6 and multiply equation (b) by 8. In order to eliminate x
→ Then we subtract equation (a) with equation (b)
[tex]{ \underline{ \rm{ - \binom{6(8x + 9y = - 3)}{8(6x + 7y = 1)} }}} \\ { \rm{ 0x \: - 2y = - 26 }} \\ \\ { \rm{ - 2y = - 26}} \\ \\ { \underline{ \rm{ \: \: y = 13 \: \: }}}[/tex]
• find x using equation (c)
[tex]{ \rm{x = \frac{ - 3}{8} - \frac{9}{8} y}} \\ \\ { \underline{ \rm{ \: \: x = - 15 \: \: }}}[/tex]
4. Calculator synthetic method:
→ To use this method, you must have a scientific calculator.
→ If you have it, follow the steps below;
Go to mode (press it 3 times until you see "EQN" )Press 1 or any number below the "EQN". It'll display "Unknowns" with 2 and 3 below it. 2 → Two equations system. 3 → 3 equations system.According to our question, it is a two equations system, press 2It'll display a, b and c [ a is the coefficient of x, b is the coefficient of y, c is the constant]For a1 press 8 then press "equal sign", b1 press 9, then equal sign, c1 press -3 then equal sign.Follow the same procedure for a2, b2 and c2Automatically, It will display the answersAnswer: x = -15, y = 13
³√27 x 1000
What is the answer and show me working out please?
<3
if you don't understand please ask in the comment section
Which line contains the points (1,-2) and (-3,2)?
A. Y= -x+1
B. Y= -x-1
C. Y= 1/2x-1
D. Y= -1/2x+1
Answer: y = -x1 - 1
Step-by-step explanation:
Do both points satisfy this equation?:
(1,-2): -2 = -1 -1 Yes
(-3,2): 2 = -(-3)-1 [or 3-1=2] Yes
The line contains the points (1,-2) and (-3,2) is Y= -x-1. The correct option is B.
What is coordinate geometry?A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that the points are (1,-2) and (-3,2). The equation of the line will be the line which satisfies the given points.
Y= -x-1
At points (1,-2),
Y= -x-1
-2=-1-2
-2=-2
At point(-3,2).
Y =-x-1
2=3-1
2 = 2
The line Y= -x-1 is passing through the points (1,-2) and (-3,2). The correct option is B.
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what is the equation
of a line perpendicular
to y=3/4x+12 that passes
through (12,3)
Answer:
y = -4/3 x + 19
Step-by-step explanation:
y = 3/4x + 12
Slope of this line = 3/4 and the slope of the perpendicular line: - 4/3
Point: (12,3)
y-intercept: 3 - (- 4/3)(12) = 3 + 16 = 19
y = - 4/3x + 19
3.7% of 35 is what number?
Answer:
1,295
Step-by-step explanation:
35 - 100%
x - 3,7%
x= 35*3,7:100=1,295
Question 11
Solve for x.
willl give brainliest
Answer:
79
Step-by-step explanation:
360⁰-44⁰=316
4x = 316
316/4=79
X=79
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In the given figure, 4x and 44° forms linear pair
so , they are supplementary angles of each other, that is :
[tex]4x + 44 = 180[/tex][tex]4x = 180 - 44[/tex][tex]4x = 136[/tex][tex]x = 34 \degree[/tex]your clients bust measurement is 32 inches. if you will draft the bodice pattern using the metric system, what is its equivalent to centimeters
Answer: 81.28 centimeters
1 inch = 2.54 centimeters
Multiply
32 x 2.54 = 81.28
Answer: 81.28 centimeters
Step-by-step explanation: Since there are 2.54 centimeters in an inch, there are 2.54 x 32 = 81.28 centimeters in 32 inches! Hope this helps!
Which example represents a 25% increase? Group of answer choices The attendance at the local high school drama for Friday evening was 400. On Saturday, the attendance was 550. The price of gas Monday was $2.00 per gallon. On Tuesday, the price gas was $2.25 per gallon. Terri's grade on her math test was 50%. She was able to retake the test and score a 75%. Steve caught 8 fish on Friday. On Saturday, he was able to catch 10 fish.
Ques 8 From the graph the solution of the equations y = −2x and y = x +6 y=x+6 is
Answer:
the first option if you are looking for where they intercept
Step-by-step explanation:
what is 9 + 10 - 11 + 23 and 12
APPLY
39. Make Sense and Persevere A company
manufactures cell phone cases. The length
of a certain case must be within 0.25 mm of
125 mm, as shown (figure is not to scale). All
cases with lengths outside of this range are
removed from the inventory. How could you
use an absolute value inequality to represent
the lengths of all the cases that should be
removed? Explain.
An absolute value inequality is used to represent the situation given that
cases with values above and below the allowance are to be removed.
The absolute value inequality for the situation is; |x - 125| ≥ 0.25.Reason:
The given parameter are;
Length of a case x ≤ 125 + 0.25
Length of a case x ≥ 125 - 0.25
Required:
Represent the cases that are to be removed using absolute inequality.
Solution:
The given inequalities sign can be rearranged to give the cases to be
removed as follows;
x ≥ 125 + 0.25
∴ x - 125 ≥ 0.25...(1)
x ≤ 125 - 0.25
x - 125 ≤ -0.25
Multiplying both sides by (-1) gives;
-1×(x - 125) ≥ (-1) × -0.25 = 0.25
-(x - 125) ≥ 0.25...(2)
Therefore;
The given that a case with difference (x - 125) ≥ 0.25 or when (x - 125) is
negative -(x - 125) ≥ 0.25 should be removed, using absolute inequality, we
have;
|x - 125| = (x - 125) when x > 125
|x - 125| = -(x - 125) when x < 125, and (x - 125) is negative
Which gives; A case with length |x - 125| ≥ 0.25 should be removed.
The absolute value inequality that represents the lengths of all the cases
that should removed is therefore;
|x - 125| ≥ 0.25Learn more here:
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Tia received $7.55 in change in quarters and dimes. There
were 38 coins in all. How many of each kind did she
receive?
Answer: 25 quarters and 13 dimes
Step 1: Setup Coin Value and Coin Total Equation:
Coin Value Equation → 0.1d + 0.25q = $7.55 where d = dimes and q = quarters
Coin Total Equation → d + q = 38
Step 2: Rearrange Coin Total Equation in terms of dimes (d)
d = 38 - q ← Revised Coin Total Equation
Step 3: Plug in our Revised Coin Total Equation for d into our Coin Value Equation:
0.1(38 - q) + 0.25q = $7.55
0.1(38) - 0.1(q) + 0.25q = $7.55
3.8 - 0.1q + 0.25q = $7.55
3.8 + (0.25 - 0.1)q = $7.55
3.8 + 0.15q = $7.55
Step 4: Subtract 3.8 from each side of the equation to isolate q
3.8 - 3.8 + 0.15q = $7.55 - 3.8
0.15q = 3.75
Step 5: Divide each side of the equation by 0.15 to isolate q
0.15q/0.15 = 3.75 /0.15
q = 25
Step 6: Using our value for q, Solve for d using our Coin Total Equation:
d + 25 = 38
Subtracting 25 from both sides, we get d + 25 - 25 = 38 - 25
d = 13
Summarizing our word problem, we see that 25 quarters and 13 dimes add up to $7.55
According to a U.S. news poll, 38% of students in the class of 2013 had done an internship during their time as an undergraduate student. Dana is interested in finding out whether students at her university had an internship rate that was higher than the national average. She obtained a list of 25 randomly selected students from the population of all students at her university by requesting this information from the university’s institutional research office. She collected the responses and calculated that the proportion for her university was 43%. Which one of the following statements about the z-test is correct?
It is not safe to use the z-test for p, since the sample is not a random sample from the entire population (or cannot be considered as one).
It is not safe to use the z-test for p, since n * (1 ? po) is not large enough.
It is safe to use the z-test for p.
It is not safe to use the z-test for p, since n * po is not large enough.
A national poll by the Institute for College Access and Success showed that in 69% of college graduates from public and nonprofit colleges in 2013 had student loan debt. Dr. Blackman wanted to find out if her public nonprofit university had a lower proportion of students who graduated with student loan debt in 2013.
For this survey, the null hypothesis was that the proportion of students with graduated with student loan debt equals 69% and the alternative hypothesis is that the proportion with student loan debt does not equal 69%. The significance level for this test was 0.05.
The results of the hypothesis test of the new survey showed a p-value of 0.039.
Which of the following statements is correct? Check all that apply.
The results were statistically significant.
The results were not statistically significant.
The null hypothesis should be rejected.
The null hypothesis should be accepted.
The null hypothesis cannot be rejected.
Answer: The null hypothesis should be accepted and The results were not statistically significant
Step-by-step explanation:
Please help!!
!!!!!!!!!!!!!!!
Step-by-step explanation:
SSS
side- side- side
when all 3 sides are congruent, then the triangles is congruent.
ML and NP are given.
MP is shared (so, definitely even the same side).
and PL and NM are parallel.
so, all 3 sides are covered.
Multiply the following
Provide in standard form :)
Answer:
x^3 + 4x^2 - 7x - 10
Step-by-step explanation:
[tex]((x-2)(x+1))(x+5)[/tex] [tex]((x-2)(x+1))(x)+((x-2)(x+1)(5)[/tex] [tex]x^3 - x^2 -2x + 5x^2-5x-10[/tex] [tex]x^3+4x^2-7x-10[/tex]Can someone help me!
if something cost $4.90 due to a 14% discount what is the original price
What is the slope of the line that passes through the points (10,5) and (9,5)? Write
your answer in simplest form.
hope you like my answer 15
Here is the screenshots for my question
I need help pleaseee
Answer:
its too small, i cant read it, sorry
Step-by-step explanation:
Please help! 10 points to solve it!
Suppose that NASA wants to launch a probe to study Mercury. It will take the probe 150 days to travel the 96,562,000 miles that planet.
How many miles per day does the probe need to travel? Round to the nearest hundredth, if needed.
Answer:
643746.67
Step-by-step explanation:
Simply divide 96,562,000 by 150 and round to nearest hundredth.
Answer:
yes he is right: )
Step-by-step explanation:
please mark me brainliest because i'm not a nerd..... no offence.
PLEASE HELP WILL GIVE BRAINLIEST AND 5 STARS AND A THANKS DUE IN 1 HOUR!~
Answer:
-7
Step-by-step explanation:
Answer:
check explanation
Step-by-step explanation:
the slope between two points can be defined as the change in y over the change in x. Consider (0, 11) as your first point and (1,4) as your second point.
To find the slope, do:
(y2 - y1) / (x2 - x1) = slope
(4 - 11) / (1 - 0) = slope
-7/1 = slope
26 past due! last question!! ty for all you guys' help!!
Answer:
Slope = 3/2, or 1.5
Step-by-step explanation:
Pick out the lattice points ( points that intersect the graph markings)
I see 2 points, ( 3, 1), and ( 5, 4)
Slope = Δy/xΔ = 4 - 1/5 - 3 = 3/2
Slope is 3/2, or 1.5
-Chetan K
science-fiction book is 180 pages long. She has read 135 pages so far. Brooke has read _____% of the book.
180-135=45
45/180 ×100
25%
Brainlyest goes to the right answer
What is the value of the expression
(
44
+
6
2
)
4
2
4
2
(44+6
2
)
?
Answer:
Step-by-step explanation:
(44+62)4242(44+62)
=44(62+62)4242
=44(124)4242
=5456*4242
=23,144,352.
What's the missing side of this triangle
Answer:
20.25inches
Step-by-step explanation:
Using the Pythagorean theorem,
h^2=7^2 +19^2
h^2=410
h=sqr 410=20.25inches
Finding the price of a 17,100 truck with a 5% sales tax.
Round to the nearest cent when necessary
Answer:
17,955
Step-by-step explanation:
5% turns into 0.05 multiply the numbers 0.05 and 17100 you end up with 855 then add both since sales tax INCREASES the price and the final answer should be 17,955.
Answer:
17,955.
Step-by-step explanation:
5% divide by 100 = 0.05
0.05 times 17100 = 855
855 + 17100 and the final answer should be 17,995
Evaluate the expression 90 = [(82 - 77).91
Answer:
See below.
Step-by-step explanation:
Since there is an equal sign, this is not an expression. It is an equation. If you evaluate the right side, you'll see that it is a false equation since both sides are not equal to each other. Also, there is a bracket missing.
90 is not equal to 4.55.
Maybe it is meant to be the following expression:
90 + [(82 - 77).91] = 90 + 5(0.91) = 90 + 4.55 = 4.55
Or maybe this one:
90 - [(82 - 77).91] = 90 - 5(0.91) = 90 - 4.55 = 85.45
) vis directly proportional to x. If y = 60 when x = 120. Find the value of y when x =
50.
Answer: 100
Step-by-step explanation:
x = 2y
50 = 2y
so 50/2 = 25
25 = y
Evaluate using suitable identity:
c). 98²
Step-by-step explanation:
★ Solution :-[tex]\sf \longmapsto 98^2[/tex]
[tex]\sf \longmapsto (a - b)^2 = a^2 - 2ab + b^2[/tex]
Here,
a = 100b = 2[tex]\sf \longmapsto (100 - 2)^2 = 100^2 - 2(100)(2) + 2^2[/tex]
[tex]\sf \longmapsto 100^2 - 2(100)(2) + 2^2[/tex]
[tex]\sf \longmapsto 10000 - 400 + 4[/tex]
[tex]\sf \longmapsto 9606[/tex]
pls help i need this
Answer:
[tex]21x^3-2x^2-66x+27[/tex]