determine whether the point (1,5) is a solution to the system of equations g(x)=3x+2 f(x)=|x-1|+1. Explain your reasoning.
Answers
Mark Brainliest Please
Answer:
(0, 1) so (1,5) is not the solution and reason is given below
Step-by-step explanation:
To find the solution to these 2 functions, we just set up an equation where they're equal to each other:
3x+2 = |x-1|+1
Then, isolate the absolute value:
3x+1 = |x-1|
Now, to get rid of the absolute value sign, we can set the right-hand side to be the positive or negative version of itself.
First, let's set it to the negative version of itself:
3x+1 = -x+1
4x = 0
x = 0
Then, let's set it to the positive version of itself:
3x+1 = x-1
2x = -2
x = -2
We can now plug the x as 0 and -2 into any of the 2 equations above to find the solution for y:
3(0)+1 = 1, so the first solution will be (0, 1)
3(-2)+2 = -4.
You might be tempted to say that -4 is the y value for the 2nd solution, but notice that |x-1| will never be less than 0, so that would not work. Therefore, x = -2 isn't a solution either, which means it's an extraneous solution.
In conclusion, the solution to these equations is (0, 1).
Related Questions
Which relation represents a function ?
Answers
Answer:
The third choice
Step-by-step explanation:
a relation is a function if an input has at most one output for a given input
Choices 1, 2 and 4 are not functions as they have two different outputs for the same input. (See the red ovals)
Help me fast 50 points!!!!!!!!
Answers
Answer:
30
Step-by-step explanation:
There are 14 data points on the plot
The median is the middle value, which is between the 7th and 8th data points
Since it is even, we find the average of the 7th and 8th data points
Add the 7th and 8Th data points values and divide by 2
( 30+30)/2 = 60/2 = 30
The median is 30
Answer:
30
Step-by-step explanation:
Middle numbers are 30 and 30 so you add them and then divide by two:
[tex]\frac{30 + 30}{2}[/tex] = [tex]\frac{60}{2}[/tex]= 30
An object dropped from a height of 500 feet has a height, h(t), in feet after t seconds have elapsed, such that h(t)=500−16t^2. Express t as a function of height h, and find the time to reach a height of 100 feet
Answers
Step-by-step explanation:
the answer is in the above image
Estimate: 4/5 - 1/2
Answer:
Need help ASAP..
Answers
Answer:
3/10
Step-by-step explanation:
Find the LCM of 5 and 2.
LCM = 10
[tex]\frac{4}{5} - \frac{1}{2} = \frac{8 - 5}{10} = \frac{3}{10}[/tex]
Answer:
[tex]\frac{3}{10}[/tex]
Step-by-step explanation:
5 = 5 × 1
2 = 2 × 1
LCM = 2 × 5
10
[tex]\frac{2(4)}{2(5)} -\frac{5(1)}{5(2)}[/tex]
[tex]\frac{8}{10} -\frac{5}{10}[/tex]
[tex]\frac{3}{10}[/tex]
Please help me with my math question?
Answers
Answer:
150 mL
Step-by-step explanation:
270 - 120 = 150
Hope this helps!
Is my answer correct?
Answers
9514 1404 393
Answer:
yes
Step-by-step explanation:
By the "rule of 72", the amount will be doubled in 72/I years, where I is the annual interest rate in percent. That is, it can be estimated to take 72/4 = 18 years to double the $240 investment to $480. It would take another 18 years to double it again to $960. So, to achieve a balance of $1500 will be expected to take more than 36 years. The only reasonable answer choice is the one you have selected.
__
The exact solution is ...
log (1500/240)/log(1 +0.04) ≈ 46.72 years ≈ 47 years.
Can any one help?
Solve the following equations:
Answers
Answer:
2- x=16/3 or 5.3
4- x=8
Step-by-step explanation:
yeah
find the coordinate for the mid point of the segment with the points given (-16,0)(0,-16)
(-8,-8)
(8,0)
(8,8)
Answers
Answer:
(-8,-8)
Step-by-step explanation:
Coordinates of a midpoint:
The coordinates of the midpoint of a segment is given by the mean of the coordinates of the endpoints.
In this question:
Endpoints (-16,0) and (0,-16).
x-coordinate:
[tex]\frac{-16+0}{2} = -8[/tex]
y-coordinate:
[tex]\frac{0-16}{2} = -8[/tex]
Then:
(-8,-8)
simplify 15 to the power of 18 over 15 to the power of 3
Answers
Answer:
15^18/(15^3)=15^15
Step-by-step explanation:
rule for quotients of similar bases with different exponents is:
(a^c)/(a^b)=a^(c-b)
15^18/(15^3)=15^15
What is the first term in the sequence for which d = -2 and a7 = 3?
A. -6
B. 12
C. 15
D. -12
Answers
Answer:
First term is 15
Step-by-step explanation:
Given data:
[tex]a_{7} =3\\d=-2[/tex]
Now,
[tex]a+6d=3.....(1)\\a_{n} =a+(n-1)d\\\\\\From equation (1)\\a+6(-2)=3\\a-12=3\\a=12+3\\a=15[/tex]
Therefore first term a =15
Correct option is (c)
In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third angle is 80° more than the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180° to find the measure of each angle. what is the measure of the first angle?
Answers
Answer:
The measure of the first angle is 50°.
Step-by-step explanation:
Let the three angles be a, b, and c.
The measure of the first angle is twice the measure of the second angle. In other words:
[tex]a=2b[/tex]
The measure of the third angle is 80° more than the measure of the second angle. In other words:
[tex]c=b+80[/tex]
And since the interior angles of a triangle must equal 180°:
[tex]a+b+c=180[/tex]
Substitute a and c:
[tex](2b)+b+(b+80)=180[/tex]
Combine like terms:
[tex]4b+80=180[/tex]
Subtract 80 from both sides:
[tex]4b=100[/tex]
And divide both sides by four:
[tex]b=25^\circ[/tex]
So, the measure of the second angle is 25°.
Since the measure of the first is twice the second, the measure of the first angle is 50°.
(And since the measure of the third is 80° than the second, the measure of the third angle is 105°.)
Solve the quadratic equation numerically (using tables of x- and y- values).
x2 + 7x+ 12 = 0
x= -1 or x = -1
x= -3 or x = -3
x = -4 or x = -3
x = 2 or x = -1
Answers
Answer:
x2 + 7x + 12 = 0
Step-by-step explanation:
(x + 4) (x + 3)
x + 4 = 0 or x + 3 = 0
x = - 4 or x = - 3
Someone please help me?
Answers
4 1/2 inches is 4 inches and 1.27 cm.
4 times 1
8 over 9 equal
Answers
Step-by-step explanation:
4*1 = 4
this indicates multiplication
8/9 = 0.88888888888 which when simplified would go back to 8/9 or .889
8 "over" 9 indicates division!
What is the range of function g?
g(x) = /x-1+2
A. y > 1
B. y > 2
C. y <2
D. y <1
Answers
Answer:
Option B
Step-by-step explanation:
Equation of the function is,
[tex]g(x)=\sqrt{x-1}+2[/tex]
Parent function of the given function 'g' is,
[tex]h(x)=\sqrt{x}[/tex]
By translating the parent function 'h' n=by 1 unit horizontally left and 2 units upwards we get the function 'g'.
That means function 'g' starts from a point (1, 2).
Range of the function 'g' will be all the values of y ≥ 2.
Option B is the answer.
Answer:
Range of the function 'g' will be all the values of y ≥ 2.
Step-by-step explanation:
Can someone please help me?
Answers
Answer:
A
Step-by-step explanation:
to find the inverse, there are two steps
1-interchange x and y
2-solve for y
so y=x+1/x
interchange to get x=y+1/y
and solving for y we multiply both sides by y to get xy=y+1
subtract both sides by y yielding xy-y=1
factor out y to get y(x-1)=1
then divide to get y=1/x-1
Which is the decimal expansion of the following 1/5
Answers
Answer:
Decimal expansion of 1/5 = 0.2
Can someone help asap!!?
Answers
Answer:
1: B. 2: 6n^6+9n^5+4n^2-4n. 3: D. 4: 6b^2-15b-9. 5: 48x^2-4x-4
Step-by-step explanation:
1.
A trinomial is a polynomial with three terms. The expression 7v^2 +2v +2 has 3 terms.
2.
A polynomial in standard form has its powers listed from highest power to lowest power. The terms are 6n^6, 4n^2, 9n^5, and -4n. Remove the bottom numbers to find 6, 2, 5, and 1. Next, put them in order. 6, 5, 3, 1. Then, re-add the bottom numbers. 6n^6+9n^5+4n^2-4n.
3. A sixth degree polynomial is one with a sixth degree power. So, the answer is either C or D. Next, let's look at the terms. The expression here has 4 terms. So, the answer is D.
4 and 5:
To solve expressions in this form, (a+b)(c+d), turn the expression into an equivalent one, ac+ad+bc+bd. Plug in the numbers (with a negative mark if its -a or a-b) into that expression to get your answer.
4 simplifies out into 6b^2+3b-18b-9, which can be simplified into 6b^2-15b-9
5 simplifies out into 48x^2+12x-16x-4, which can be simplified into 48x^2-4x-4.
Researchers at a medical school conducted a study to test the effectiveness of a new drug for lowering cholesterol. The 52 subjects who volunteered for the study were each given a randomly generated number. Subjects with an odd number were given the new drug, while those with an even number were given a placebo. Cholesterol levels before and after the treatment were measured for each subject, and the differences were computed.
This study is an example of ______________ study. The difference in cholesterol level is _____________ the variable. The treatment with drug or placebo is the ____________ variable.
Answers
Answer:
1. An Experimental
2. Dependent
3. Independent
Step-by-step explanation:
Considering the description of how the research was carried out, it can be concluded that This study is an example of AN EXPERIMENTAL study. This because the researcher is trying to study the effectiveness of a new drug for lowering cholesterol
The difference in cholesterol level is the DEPENDENT variable. This is because the difference in cholesterol level is what the researcher wants to determine.
The treatment with a drug or placebo is the INDEPENDENT variable. This is because this is what the researcher manipulates to determine the difference in cholesterol level which is the dependent variable in this experimental study.
What to numbers multiply to -38 and add to 17
Answers
Answer:
-2 and 19
Step-by-step explanation:
Answer:
19 and -2
Step-by-step explanation:
19 * -2 = -38
19 + -2 = 17
Hope this helps
A researcher collects demographic data on the marital status of the study subjects. The variable is measured as the number of years married on a scale of 0-75. What would be the most appropriate measure of central tendency
Answers
Answer:
Probably "Median"
The mode doesn't really make sense,
and "mean" would probably be skewed by people who get divorced quickly
I would suggest "Median" the number of years that 1/2 of the couples are above and 1/2 below
Step-by-step explanation:
The height of a triangle is 8 m more than twice the length of the base . The area of the triangle is 21 m^2 find the height of the triangle
Answers
Answer:12
Step-by-step explanation:cumquat
I am desperate please help.
Answers
Answer:
63.69 meters
Step-by-step explanation:
the total perimeter of two identical semi-circular = 100+100 = 200m
d = p/π = 200/3.14 = 63.69
Write the equation of the line that passes through the points (-7,8) and (-1,-5).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.
Answers
Answer:
y + 7 = -13/6(x-8)
and
y + 1 = -13/6(x+5)
Step-by-step explanation:
1. Find the slope using [tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex].
-5-8/-1+7 = -13/6
2. Plug the slope into the point-slope form, [tex]y-y_{1}=m\left(x-x_{1}\right)[/tex].
y - y1 = -13/6(x-x1)
3. Plug in one of the points to get the answer.
y + 7 = -13/6(x-8)
y + 1 = -13/6(x+5)
Solve for b. b= V [?] 12 5 b Pythagorean Theorem: a2 + b2 = c2 Enter
Answers
[tex]\huge\bold{Given:}[/tex]
Length of the perpendicular "[tex]a[/tex]" = 5.
Length of the hypotenuse "[tex]c[/tex]" = 12.
[tex]\huge\bold{To\:find:}[/tex]
The length of the missing side ''[tex]b[/tex]".
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
The length of the missing side (base) "[tex]b[/tex]" is [tex]\boxed{√119}[/tex].
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
Using Pythagoras theorem, we have
[tex]({perpendicular})^{2} + ({base})^{2} = ({hypotenuse})^{2} \\ \\⇢ {a}^{2} + {b}^{2} = {c}^{2} \\\\ ⇢ {5}^{2} + {b}^{2} = {12}^{2} \\ \\⇢25 + {b}^{2} = 144 \\ \\⇢ {b}^{2} = 144 - 25 \\ \\⇢ {b}^{2} = 119 \\ \\⇢b = \sqrt{119} [/tex]
[tex]\sf\blue{Therefore,\:the\:length\:of\:the\:missing\:side\:"b"\:is\:√119.}[/tex]
[tex]\huge\bold{To\:verify :}[/tex]
[tex] {5}^{2} + { \sqrt{119} }^{2} = {12}^{2} \\\\ ⇝25 + 119 = 144 \\ \\⇝144 = 144 \\ \\⇝L.H.S.=R. H. S[/tex]
Hence verified. ✔
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]
What is the mode of the data set shown below?
{2, 4, 5, 6, 8, 2, 5, 6}
A. 2
B. 5
C. 6
D. 2, 5, and 6
Answers
Answer:
D
Step-by-step explanation:
The mode is the value that appears most often in the number set for this set the most common numbers are 2, 5, and 6.
Answer:
d
Step-by-step explanation:
all show up 2 times
One side of a triangle is 3 times longer than the shortest side and the third side is 4 centimeters longer than the shortest side. The perimeter of the triangle is 64.
How long is the shortest side of the triangle?
Answers
Answer:
First side is: 12cm
Second side is: 36cm
Third side is: 16cm
Step-by-step explanation:
Let x represent the shorter side
Then 3x represents the second side, and
x + 4 represents the third side.
Perimeter of three sides:
P = x + 3x + (x + 4)
Perimeter is 64, so
64 = x + 3x + (x + 4)
64 = 5x + 4
60 = 5x
12 = x
First side is x: 12cm
Second side is 3x: 3(12) = 36cm
Third side is x + 4: 12 + 4 = 16cm
Graph the line.
y=3x
Answers
Answer:
desmos(dot)com/calculator/gv8jsoui4w
Step-by-step explanation:
Create a table of appropriate x values e.g. x = 2 and substitute into y=3x which will be y=3*2 meaning y=6 at the point x=2. Repeat with different x values until you have enough points to draw a straight line.
Which of the following illustrates the truth value of the given conditional statement?
p. 10 > 7
q. 10 > 5
p-~q
Answers
Answer:
T T → T
Step-by-step explanation:
Given :
p = 10 > 7
q = 10 > 5
Evaluating if the statements are true :
p = 10 > 7, This is TRUE, Because 10 is truly greater Than 7
q = 10 > 5, This is TRUE, Because 10 is truly greater Than 5
The statements are both True statements :
p = True ; q = True
True and True = True
T & T = T
T T → T
If repetition of digits is allowed, how many different ways 5-digit codes are possible with the condition that the first digit should be a multiple of 3 and the last digit cannot be zero.
a. 17496.
b. 27000.
c. 18000.
d. 30000.
Answers
Answer:
b) 27,000
Step-by-step explanation:
3 × 10 × 10 × 10 × 9 = 27000
'3' because the first digit can only be 3,6, or 9
'9' because the last digit cannot be zero, leaving only 9 options
