using addition rules ,show how to add the two real numbers 7+(-14)
Answer:
Step-by-step explanation:
14+(−7)+7
Now −7 is the idea or the construct that is the complete opposite of 7, when it comes to additive regions. So, they would cancel out.
And we are left with
14.
What are the restrictions for y
X=10/5+y
Answer:
[tex]y\ne-5[/tex]
Step-by-step explanation:
So you have the equation:
[tex]x=\frac{10}{5+y}[/tex]. As you may know, you cannot divide by 0, so y has to be restricted in a way that the denominator is never equal to 0. So to find when y makes the denominator 0, simply set the denominator equal to 0, and solve for y. This gives you the equation: 5+y = 0, y=-5. So the y value CANNOT be equal to -5. Because it makes the denominator 0. so [tex]y\ne-5[/tex] would be the restriction.
Which function is graphed below?
The graphed rational function is:
[tex]f(x)= \frac{6}{x + 2}[/tex]
Which function is graphed below?Here we can see that we have a rational function of the form:
[tex]f(x) = \frac{q(x)}{p(x)}[/tex]
Now we notice two things, as x increases, we have a horizontal asymptote that tends to zero.
Then q(x) is a constant, let's say:
q(x) = k
We also can see that we have a vertical asymptote at x = -2, then:
p(x) = (x + 2)
So the rational function is:
[tex]f(x) = \frac{K}{x + 2}[/tex]
Now, notice that when x = 0, the curve intercepts the y-axis at y = 3, then if we evaluate the function in x = 0 we must get:
[tex]f(0) = 3 = \frac{K}{0 + 2} = \frac{K}{ 2} \\\\3*2 = K = 6[/tex]
Then the rational function is:
[tex]f(x)= \frac{6}{x + 2}[/tex]
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What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)? f(x) = 2x2 + x + 4 x g(x) –2 1 –1 3 0 5 1 7 2 9
The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is
[tex](\sqrt{2},\sqrt{-2} )[/tex] and [tex]((7+\sqrt{2)} ,(7+\sqrt{-2}))[/tex]
We have given that,
f(x) = 2x^2 + x + 4
x g(x)
-2 1
-1 3
0 5
1 7
2 9
What is a polynomial function?A polynomial function is a relation where a dependent variable is equal to a polynomial expression.
A polynomial expression is an expression including numbers and variables, where variables are raised to non-negative powers.
The general form of a polynomial expression is:
a₀ + a₁x + a₂x² + a₃x³ + ... + anxⁿ.
The highest power to a variable is the degree of the polynomial expression. When degree = 2, the function is a quadratic function.
When degree = 1, the function is a linear function.
How do we solve the given question?
The quadratic function is given to us:f(x) = 2x^2 + x + 4.
We need to determine the linear equation g(x).
Since it's a linear equation we use the two-point method to determine the equation.
What is the two-point?y-y₁ = ((y₂-y₁)/(x₂-x₁))*(x-x₁)
We take the points g(-2) =1, g(-1) = 3
g(x) - g(1) = ((g(-2)-g(-1))/(-2+1))*(x-1)or,
g(x) - 1 = ((-2-(-1))/(-2+1))*(x-1)or, g(x) - 1 = -1(-x+1)or,
g(x) = x - 1 + 1 = x
∴ g(x) = x , is the linear function g(x)
We are asked to find the solution to the system of equations f(x) and g(x).To find the solution we need to check what is the common solution to both f(x) and g(x).
For that, we equate f(x) and g(x).2x^2 + x + 4 = x or, 2x² - x +x- 4 = 0or, 2x^2 - 4 = 02(x^2-2)=0x^2-2=0[tex]x^2-\sqrt{2}=0[/tex][tex](x-\sqrt{2}) (x+\sqrt{2})=0[/tex][tex](x-\sqrt{2})=0 \\x=\sqrt{2} or x=-\sqrt{2}[/tex]g(-1) = 3(from the table)[tex]g(\sqrt{2})=\sqrt{2} \ and \ g(\sqrt{-2}) =-\sqrt{2}[/tex][tex]f(\sqrt{2}) = 2(\sqrt{2} )^2 + (\sqrt{2} ) + 3\\=2(2)+\sqrt{2} +3\\=7+\sqrt{2}[/tex][tex]g(-\sqrt{2} )= 2(\sqrt{-2} )^2 + (\sqrt{-2} ) + 3\\=2(2)+\sqrt{-2} +3\\=7+\sqrt{-2}[/tex]
The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is [tex](\sqrt{2},\sqrt{-2} )[/tex] and [tex]((7+\sqrt{2)} ,(7+\sqrt{-2}))[/tex]
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Angelica Reardon received a 4-year non-subsidized student loan of $17,000 at an annual interest rate of 6.1%. What are Angelica's monthly loan payments for this loan after she graduates in 4 years? (Round your answer to the nearest cent.) $
Answer:
$1503.08 per month
Step-by-step explanation:
Solve for Y
V = −4y + 4x
Answer:
Y=−4y/v +4x/v
Step-by-step explanation:
Divide each term in by v and simplify.
Select the correct answer.
Which statement best defines perpendicular lines?
A.
lines that lie in the same plane
B.
lines that intersect and form right angles
C.
lines that lie in the same plane and do not intersect
D.
lines that share a point
Answer:
c or b
Step-by-step explanation:
Answer:
Answer:B
Step-by-step explanation:
I did the test and got it right the person above help thx
In the rhombus below, if NL = 7 and KM = 8 find JL.
Answer:
JL = 14
Step-by-step explanation:
N represents the center of the rhombus
Then
N is the midpoint of the diagonal (line segment) JL
Then
JL = 2 × NL
= 2 × 7
= 14
47. A car travels at a constant speed of 50 miles per hour.
The distance the car travels in miles is a function of
time, t, in hours given by d(t) = 50t. Find the inverse
function by expressing the time of travel in terms of
the distance traveled. Call this function t(d). Find
t(180) and interpret its meaning.
Answer:
The inverse of the given function is [tex]$t(d)=\frac{d}{50}$[/tex]. The time taken to travel 180 miles is 3.6 hours.
Step-by-step explanation:
It is given that a car travels at a constant speed of 50 miles per hour. A function for distance traveled is also given as d(t)=50t.
It is required to find the inverse of the function by expressing the time travel in terms of distance traveled and also find t(180).
To find the inverse, express time traveled in terms of distance traveled using normal algebraic methods and then substitute 180 for t and explain its results.
Step 1 of 2
The given function is d(t)=50t.
Consider d(t) as d and t as t(d) and rewrite the equation.
The rewritten function is d=50 t(d)
Divide by 50 on both sides of the equation.
[tex]$$\begin{aligned}&d=50 t(d) \\&\frac{d}{50}=\frac{50 t(d)}{50} \\&t(d)=\frac{d}{50}\end{aligned}$$[/tex]
Step 2 of 2
Substitute 180 for $t$ in the simplified expression and interpret the results.
[tex]$$\begin{aligned}&t(d)=\frac{d}{50} \\&t(d)=\frac{180}{50} \\&t(d)=3.6\end{aligned}$$[/tex]
The time taken to travel 180 miles is 3.6 hours.
f is an even function. a = A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 2, 3. Column 2 is labeled f (x) with entries 4, 5, a, 7. g is an odd function b = A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 2, 3. Column 2 is labeled f (x) with entries b, 0, negative 3, negative 4.
The values of a and b are 4 and -3
How to solve for (a) and (b)?To solve for a, we make use of the function f(x).
x f(x)
2 4
0 5
2 a
3 7
Remove the x values 0 and 3
x f(x)
2 4
2 a
The above table implies that:
f(2) = 4 and f(2) = a
Substitute 4 for f(2) in f(2) = a
4 = a
Rewrite as:
a = 4
To solve for b, we make use of the function g(x).
x g(x)
2 b
0 0
2 -3
3 -4
Remove the x values 0 and 3
x g(x)
2 b
2 -3
The above table implies that:
f(2) = b and f(2) = -3
Substitute -3 for f(2) in f(2) = b
-3 = b
Rewrite as:
b = -3
Hence, the values of a and b are 4 and -3
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Complete question
Use the Symmetry of a Function to Find Coordinates
f is an even function g is an odd function
x f(x) x g(x)
2 4 2 b
0 5 0 0
2 a 2 -3
3 7 3 -4
Find a and b
Answer:
4, 3
Step-by-step explanation:
Given the function h of x equals three times the square root x plus 1 end root minus 2, which statement is true about h(x)? The function is increasing on the interval (–∞, –2). The function is decreasing on the interval (–3, ∞). The function is decreasing on the interval (–∞, –3). The function is increasing on the interval (–2, ∞).
The function is decreasing on the interval (–3, ∞). Therefore, the correct option is B.
How to illustrate the function?A linear function can be represented by a line. The standard form for this equation is: ax+b where,
a= the slope
b= the constant term that represents the y-intercept.
The domain of a function is the set of input values for which the function is real and defined.
Here, the function is decreasing on the interval (–3, ∞).
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Jillian had 2/9m of a cloth. she used 1/9m of it for sewing a blanket. how much of the cloth does she have remaining?
Hello,
2/9 - 1/9 = (2 - 1)/9 = 1/9
Help Me Asap Please And Thank You!
In this case using the elimination method is actually easier, but the question asks you to use substitution method so....
2x+y= -10
3x-y=0
1st equation: It is better to isolate 2x on both sides because the y is going to be positive no matter what, 2x+y=-10 => y=-2x-10
If you isolated 3x for the 2nd equation, the y will be negative, and you have to divide the whole equation by -1 to make it positive
Now we got y=-2x-10, lets substitute it in the 2nd equation and solve for x:
3x-(-2x-10) = 0
5x+10=0
5x=-10
x=-2
Now lets solve for y:
3(-2)-y=0
-6-y=0
y=-6
Lets see if the same is applicable for 1st equation
2(-2)+(-6)=-10
-10=-10
Yess!!
(-2,-6) is the solution
The answer to the question is explained at the beginning
Hope it helps!
How long should the ladder be if they want to use all the cable they have? Use the law of sines to find the length
Answer:
Step-by-step explanation:
can someone please help me
Answer: A
Step-by-step explanation:
Answer:
A
I solved on paper it took me 45 mins
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y < 3x + 2
y > 3x + 2
y < One-thirdx + 2
y > One-thirdx + 2
Answer:
y < 3x + 2
Step-by-step explanation:
We will be solving this in slope-intercept form, which is a form that gives us the slope and the y-intercept of the graph explicitly:
[tex]y=mx+b[/tex], m is the slope and b is the y-intercept
We are given that everything to the left of the resulting line is shaded, so we know that the inequality sign will be < (less than). That already eliminates the second and fourth options. We also know the y-intercept, or the point where the graph crosses the y-axis and x is 0. because it is given to us (2, which comes from the point (0,2)). To figure out the slope, we can use the formula since we are given two points [(-3, -7) and (0, 2)] the line passes through. The formula, which is mapped out below, tells us that the slope is just the difference in rise (vertical movement) divided by the difference in run (horizontal movement).
[tex]m=\frac{-7-2}{-3-0} =\frac{-9}{-3} =3[/tex]
Now we have all the information we need to find the inequality. The slope is 3, the y-intercept is 2, and the sign is <. The first inequality fits these criteria, meaning the correct linear inequality is y < 3x + 2
Tara makes donut topping by mixing sugar and 12 g of cinnamon. The tape diagram shows the ratio of sugar to
cinnamon.
Complete the table.
Here is the completed table:
Original Ratio Amount (g)
Sugar 3 18
Cinnamon 2 12
Total topping 5 30
How should the table be filled?Original ratio of Cinnamon = total topping - original ratio of sugar
5 - 3 = 2
Amount of Sugar = (12 x 3) / 2 =18g
Total toppings = 18 + 12 = 30g
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Can someone help please
Answer:
35.3
Step-by-step explanation:
please mark brainliest
Answer:
35.3
Step-by-step explanation:
Jim has 10 used books and 12 used DVD's to sell at a garage sale for $1.50 and $5.00 each respectively.
Let x be the number of books and y be the number of DVD's Jim ends up selling.
Which of the following systems of linear inequalities represents this situation if Jim wants to make at least $40.00?
a.)
x ≥ 10
y ≥ 12
1.5x + 5y ≥ 40
b.)
x ≤ 10
y ≤ 12
1.5x + 5y ≥ 40
c.)
x ≥ 1.5
y ≥ 5
10x + 12y ≥ 40
d.)
x ≤ 1.5
y ≤ 5
10x + 12y ≥ 40
Answer:
The correct system of inequalities is b.
Find the equation of the line that passes through (1,3) and is perpendicular to y = 1 − 2 x . Leave your answer in the form y = m x + c
Answer:
[tex]y = \frac{1}{2} x + \frac{5}{2} [/tex]
Step-by-step explanation:
Since the line with equation y = 1 - 2x has slope -2, we need to find the equation of the line with slope 1/2.
[tex]3 = \frac{1}{2} (1) + b[/tex]
[tex]3 = \frac{1}{2} + b[/tex]
[tex]b = \frac{5}{2} [/tex]
[tex]y = \frac{1}{2}x + \frac{5}{2} [/tex]
someone please help me slove this its due tmrw somebody help, i will give brainlisest answer please
Answer:
Question 5:
a) 65 degrees
b) 11
Question 6:
a) 15.6
b) 6.4
Question 7:
a) 10
b) 20
Question 8:
a) EF = 14.4
Question 9:
a) x = 6
b) y = 22.5
Step-by-step explanation:
Hi! having a bit of trouble with this one problem that I can't seem to solve correctly. This is an exponential and logarithmic equation problem, but I keep getting 1.74036... and apparently that isn't the answer. I'd appreciate the help!
The value of x from the given expression is 0.7558
Solving exponential equationsThe standard exponential equation is expressed as y = ab^x
Given the equation below
10^x +5 = 60
Subtract 5 from both sides
10^x = 60 - 5
10^x = 55
Take the log of both sides
log10^x = log55
x = log55/log10
x = 0.7558
Hence the value of x from the given expression is 0.7558
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look at image.........
Answer:
first of all its not d since the y intercept is negitive
then its not b since its sloping down
so the slop is either 7/5 or 5/7
since rise/run it has to be 7/5
Hope This Helps!!!
1. Nasim thinks of a number.
When he multiplies his number by 5 and subtracts 16 from the result, he gets the same
answer as when ads 10 to his number and multiplies that result by 3.
Find the number Nasim is thinking of.
Step-by-step explanation:
5x-16 = 3 (10+x)
=> x= 23
Find an equation of a line with slope -3/4 and that passes through P(-4,6) in standard, form.
Answer:
[tex]y = - \frac{3}{4}x + 3[/tex]
Step-by-step explanation:
the standard form of any straight line is:
y = m × x + c
where: y is the y value of the point
x is the x value of the point
m is the gradient/slope
SOLUTION
[tex]y = mx + c \\ 6 = - \frac{3}{4} ( - 4) + c \\ c = 3[/tex]
cos 0 = 8/17. Find tan 0.
tan is 15/8
How to determine the identitySince cos = adjacent/ hypotenuse
Adjacent = 8
Hypotenuse = 17
Let's find opposite
Using the Pythagoras theorem
Opposite ^2 = Hypotenuse^2 - adjacent^2
Opposite = [tex]\sqrt{17^2 - 8^2}[/tex]
Opposite = [tex]\sqrt{289 - 64}[/tex]
Opposite = [tex]\sqrt{225}[/tex]
Opposite = 15
Tan = opposite/ adjacent
Tan = 15/ 8
Thus, tan is 15/8
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Sec6A - tan6A = 1+3tan2A.sec2A
sec ^6 A−tan ^6A=(1+tan ^2A−tan ^2 A)(1+tan ^4
A+2tan ^2 A+tan ^2 A+tan ^4 A+tan ^4 A)
sec ^6 A−tan ^6 A=1+3tan ^2 A+3tan ^4A
L.H.S. = R.H.S.
Hence proved
Step-by-step explanation:
♡´･ᴗ･`♡
Help me asap find the area for each letter and find the surface area
Surface area of A = 50 square inches, S.A of B = 120 square inches, S.A of C = 60 square inches, S.A of D = 50 square inches, S.A of E = 60 square inches, S.A of F = 120 inches.
S.A of the box = 460 square inches.
What is a cuboid?A cuboid is a three dimensional solid shape made of 6 rectangles.
Analysis:
surface area of A = surface area of D which is the smallest from the diagram = 5 x 10 = 50 square inches
surface area of C = surface area of E = the second largest = 5 x 12 = 60 square inches
surface area of B = surface area of F = 10 x 12 = 120 square inches
surface area of shape = 2( 50 + 60 = 120) = 2(230) = 460 square inches.
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what would be 12% of 40
Hello,
Answer:
4,8
Step-by-step explanation:
what would be 12% of 40 ?
12% × 40 = 12/100 × 40 = 0,12 × 40 = 4,8
A 20-ft ladder leans against a building so that the angle between the ground and the ladder is 72 degrees. How high does the ladder reach on the building?
The height of the building is 19.02 feet, for a 20-ft ladder to lean against the building at an angle of 72 degrees.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Trigonometric ratio is used to show the relationship between the sides and angles of a right angle triangle.
Let h represent the height of the building, hence:
sin(72) = h/20
h = 19.02 feet
The height of the building is 19.02 feet, for a 20-ft ladder to lean against the building at an angle of 72 degrees.
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The height reached by the ladder of height 20-ft. inclined at 72° is approximately 19.02-ft.
How can the height reached by the ladder be found?Length of the ladder = 20 feet
Angle between the ground and ladder = 72°
Height reached by the ladder = Required
Solution:
From the definition of the sine of an angle, we have;
[tex]sin (\theta) = \mathbf{ \frac{opposite \: side}{hypotenuse}} [/tex]
The length of the ladder = The hypotenuse side = 20 ft.
The opposite side to the angle 72° = The height reached by the ladder
Which gives;
[tex]sin (72 ^ {\circ})= \frac{height \: reached}{20} [/tex]
Height = 20 × sin(72°) = 19.02
The height reached by the ladder on the building ≈ 19.02-ft.Learn more about the sine of angles here:
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