slope of a line that is perpendicular to the line y=-3x is 1/3
What is slope of line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. where "m" represents a line's slope. So, the slope of a line is tanθ.
y=-3x
tanθ=slope = y/x= -3
Slope(M) of this equation is -3
Let the slope of its perpendicular line is m
As we know that the product of the slopes of perpendicular lines is -1
so,
M*m =-1
-3 * m= -1
m=1/3
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what is the answer for the discriminant of this equation and what are the values of k
For having a discriminant equal to or larger than zero we must have:
k ≤ 2 and k ≥ 10
How to get the possible values of k?
For a quadratic equation of the form:
y = a*x^2 + b*x + c
The discriminant is:
D = b^2 - 4ac
And the equation has real roots only if the discriminant is equal to or larger than zero.
Here our equation is:
x^2 + (k - 2)*x + (2k - 4) = 0
The discriminant is:
D = (k - 2)^2 -4*1*(2k - 4)
D = k^2 - 4k + 4 - 8k + 16
D = k^2 -12k + 20
The solutions of :
k^2 -12k + 20 = 0
are:
k = (+12 ± √( (-12)^2 - 4*1*20))/(2)
k = (+12 ± 8)/2
The two values of k are:
k = 20/2 = 10
k = 4/2 = 2
The possible values of k are:
k ≤ 2 and k ≥ 10
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5/If AB is 12, what is the
length of A' B'?
Answer:
8
Step-by-step explanation:
Corresponding sides of similar triangles are proportional, so:
[tex]\frac{A'B'}{12}=\frac{4}{6} \implies A'B'=8[/tex]
To rewrite y(t)=2*sin 4pi t+5*cos 4pi t in the form y(t)=Asin (wt+theta), solve for theta.
I will report if you do not answer
The required standard equation is given as y(t) = 5.39 sin(4πt + 0.379π).
Given that,
To rewrite y(t)=2×sin 4pi t+5×cos 4pi t in the form y(t)=Asin (wt+Ф).
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
Here
We know that.
Asin(α + β) = Asinαcosβ + Acosαsinβ,
Comparing it with the given equation,
Asinα = 5
Acosα = 2
Taking the ratio of the equation,
sinα/cosα = 5/2
tanα = 5/2
α = 0.379π
Now,
Asin0.379π = 5
A = 5 / sin0.379
A = 5.39
Now,
The standard form equation is given as, y(t) = 5.39 sin(4πt + 0.379π) where ω = 4π.
Thus, the required equation is given as y(t) = 5.39 sin(4πt + 0.379π).
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if the 5-day simple moving average was $54.27, what was the closing price on thursday?
Answer:
The correct answer is D.
Step-by-step explanation:
1. You add all 4 of the given closing prices with answer choice D ($56.24) Getting $271.35
2. Then divide the total of $271.35 by 5. which gives you $54.27.
meaning that your answer is D.
Sorry if this didn't help very much... Would appreciate a 5 star if it did :)
The function g is defined by the following rule.
g(x) = 5x-1
Complete the function table.
X
-2
1
4
5
X
g(x)
?
?
?
?
?
Step-by-step explanation:
You need to replace x in the equation with x in the table.
If AABC ADEF, and mzA = (x + 30)°, mzC = 45°, and m
A 15 degrees
B 45 degrees
C
50 degrees
D
80 degrees
Answer:
D. 80 degree
Step-by-step explanation:
According to the question:
[tex]\triangle ABC \cong \triangle DEF[/tex]
[tex] \rm m \angle A = (x + 30) \degree \\ \rm m \angle C = 45 \degree \\ \rm m \angle D = 80 \degree[/tex]
From above congruence we can conclude:
[tex] \rm m \angle A = m \angle D[/tex]
[tex] \therefore [/tex]
[tex] \rm m \angle A = 80 \degree[/tex]
40 POINTS AND BRAINLIEST
5.06 mid unit test Algebra 1.
Show all work!
Write the radical below in simplest radical form. Decimals not allowed
√175
2. √5/12
From the procedure, the simplest form of the radical is 5√7.
What is the basic form?A radical can also be called a surd. The surd is an irrational number. We say that it is irrational because it can not be expressed as a terminating decimal.
Now we have to look at the radical √175. We have to think of two numbers that we can multiply to obtain 175 and one of them would be a perfect square.
If we choose the numbers 7 and 25, we can write;
√175 = √7 * √25
Thus we have in the simplest radical form 5√7.
The expression √5/12 is already in the simplest form.
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Logan is selling dog tags to raise money for the dog rescue organization. Th e company that makes the tags charges a fl at fee of $348 plus $2 per tag. Logan plans to sell the tags for $5 each. a) Write an equation to show the total cost for the dog tags. b) Write an equation to show the revenue. c) How many dog tags must Logan sell in order to break even?
The equation for the total cost of the dog tags will be 348 + 2t.
The equation to show the revenue would be Revenue = 5t
The number of dog tags that Logan needs to sell to break even is 116 dog tags.
How to find the break even quantity?Assuming that the number of dog tags sold by Logan to raise money is represented by t, the total cost would be:
= Flat fee charge + Cost per tag x Number of tags
= 348 + 2t
The total revenue would be:
= Number of dog tags x Selling price per dog tag
= 5t
The breakeven point would be the point where total profit would be zero and so can be shown as:
0 = Sales - total cost
0 = 5t - (348 + 2t)
0 = 5t - 348 - 2t
3t = 348
t = 348 / 3
t = 116 tags
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Three undefined terms in mathematics: i. Point ii. Line iii. Plane the mathematical term parallel lines explicitly uses the undefined term(s). The mathematical term perpendicular lines explicitly uses the undefined term(s). The mathematical term line segment explicitly uses the undefined term(s).
Three mathematical terms with no definitions: (1) The terms (ii) and (iii) are correct., (2) The term (ii) is correct., (3) The term (i) and (ii) is correct.
What is parallel and perpendicular lines?
The definition of a parallel line is a pair of lines that never cross and always have the same distance between them. Lines that cross at right angles are referred to as perpendicular lines (90 degrees).
(1) The mathematical term parallel lines explicitly uses the undefined term(s).
The terms (ii) and (iii) are correct.
(2) The mathematical term perpendicular lines explicitly uses the undefined term(s)
The term (ii) is correct.
(3) The mathematical term line segment explicitly uses the undefined term(s).
The term (i) and (ii) is correct.
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Anyone who understands derivatives, please help.
Answer to part (A) is y = 42x+9
Answer to part (B) is 98
========================================================
Explanation:
Part (A)
Let's plug x = 0 into the 1st derivative of f(x)
[tex]f'(\text{x}) = \cos(\pi \text{x}) + \text{x}^5 + 6\\\\f'(0) = \cos(\pi *0) + (0)^5 + 6\\\\f'(0) = 1 + 0 + 6\\\\f'(0) = 7\\\\[/tex]
We'll use that later in the steps below, which show computing the derivative value of h(x) at x = 0.
[tex]h(\text{x}) = ( f(\text{x}) )^2\\\\h'(\text{x}) = 2( f(\text{x}) )*f'(\text{x}) \ \ \text{ ... chain rule}\\\\h'(0) = 2( f(0) )*f'(0)\\\\h'(0) = 2( 3 )*7\\\\h'(0) = 42\\\\[/tex]
This is the slope of the tangent line to h(x) at x = 0.
Now plug x = 0 into the h(x) function itself, without any derivatives applied.
[tex]h(\text{x}) = ( f(\text{x}) )^2\\\\h(0) = ( f(0) )^2\\\\h(0) = ( 3 )^2\\\\h(0) = 9\\\\[/tex]
This is the y intercept of the line, i.e. the b value.
We found that
m = 42 = slope of the tangentb = 9 = y intercept of the tangent lineWe go from y = mx+b to y = 42x+9 as the equation of the tangent line.
===================================================
Part (B)
In the previous part, we already calculated the first derivative. Differentiate that with respect to x to get the second derivative.
[tex]h'(\text{x}) = 2( f(\text{x}) )*f'(\text{x})\\\\h''(\text{x}) = \frac{d}{dx}\left[h'(x)\right]\\\\h''(\text{x}) = \frac{d}{dx}\left[2( f(\text{x}) )*f'(\text{x})\right]\\\\h''(\text{x}) = \frac{d}{dx}\left[2( f(\text{x}) )\right]*f'(\text{x})+2*f(\text{x})*\frac{d}{dx}\left[f'(\text{x})\right] \ \ \text{ ... product rule}\\\\h''(\text{x}) = 2f'(\text{x})*f'(\text{x})+2*f(\text{x})*f''(\text{x})\\\\h''(\text{x}) = 2\left(f'(\text{x})\right)^2+2*f(\text{x})*f''(\text{x})\\\\[/tex]
The second derivative is useful to determine where the function is concave up or concave down. And also to determine points of inflection.
The h''(x) function involves f''(x), so we'll need to find the second derivative of the f(x) function.
[tex]f'(\text{x}) = \cos(\pi \text{x}) + \text{x}^5 + 6\\\\f''(\text{x}) = \frac{d}{dx}\left[\cos(\pi \text{x}) + \text{x}^5 + 6\right]\\\\f''(\text{x}) = -\pi\sin(\pi \text{x}) + 5\text{x}^4\\\\[/tex]
Then plug in x = 0
[tex]f''(\text{x}) = -\pi\sin(\pi \text{x}) + 5\text{x}^4\\\\f''(0) = -\pi\sin(\pi *0) + 5(0)^4\\\\f''(0) = 0\\\\[/tex]
We have enough info to find h''(0) finally.
[tex]h''(\text{x}) = 2\left(f'(\text{x})\right)^2+2*f(\text{x})*f''(\text{x})\\\\h''(0) = 2\left(f'(0)\right)^2+2*f(0)*f''(0)\\\\h''(0) = 2\left(7\right)^2+2*3*0\\\\h''(0) = 98\\\\[/tex]
Side notes:
Refer back to the previous section when we found f'(0) = 7.The h''(0) is positive. It tells us that h(x) is concave up when x = 0.The sum of the measures of angle P and angle S is 140⁰.
• The measure in degrees of angle P is represented by the expression (5x + 30)º.
●
• The measure of angle S is 80°.
What is the value of x?
A 38
B 6
C 10
D 22
Answer: Value of x is B equals 6
Step-by-step explanation:
Which of these are equivalent to -11/-4? Choose ALL that apply.
-11 / 4
11 / (-4)
-11 / (-4)
-11/4
11/-4
-11/-4
The equivalent fraction for the given fraction -11/-4 is -11/(-4) and -11/-4.
Fraction.
Fraction means a number expressed as a quotient, in which a numerator is divided by a denominator.
Given,
Here we have the fraction -11/-4.
Now, we have to find the equivalent fraction of this fraction.
In order to find the equivalent fraction, we have to identify that the given term is reduceable or not.
If it is reduceable, then we have to simplify it to get the equivalent fraction.
But here the given fraction -11/-4 is not reduceable.
So, the next thing we have to do is to find the sign equivalent value for this one.
In the given fraction both the numerator and the denominator are in negative sign.
So, the equivalent fraction, must have both positive or both negative one.
Therefore, the equivalent fraction are -11/(-4) and -11/-4.
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What is the domain of the relationship graphed below Domain: {x|x € N} domain:
The domain of the relationship graphed, Domain: {x|x € N} is from -4 and ended at 4.
How to identify domain and range from co-ordinates?
If x,y be a co-ordinate pair then x is the domain and y is the range .
The domain of a function is the set of all possible inputs for the function.
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
Here
x starts from -4 and ended at 4.
domain is the set of natural numbers
Hence, the domain of the relationship graphed, Domain: {x|x € N} is from -4 and ended at 4.
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suppose a sample of a radioactive substance weighs 32 mg. One year later, the sample weighs 25.5 mg. What is the half-life of this substance? (round your answer to two decimal places.)
The half-life of this substance that weighs 32 mg and one year later, the sample weighs 25.5 mg will be 3.053 year.
What is half-life?The duration it takes for a given quantity to fall to half of its initial value is known as the half-life. The phrase can be used to refer to other types of decay, whether or not they are exponential, but it is most frequently used in connection with atoms going through radioactive decay. The amount of time needed for the reactant concentration to drop to half its initial value is known as the half-life of a reaction.
Here,
The initial weight of radioactive substance=32 mg
The final weight of radioactive substance=25.5 mg
Duration=1 year
The formula,
N(t)=N(0)*1/2^(t/t₁/₂)
25.5=32*1/2^(1/t₁/₂)
half-life, t₁/₂ = 3.053 year
The half-life of this substance, which weighs 32 mg, will be 3.053 years when the sample weighs 25.5 mg.
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Find the perimeter of the figure below.
8 cm
The given figure is pentagon, and the perimeter of pentagon is 47 cm.
What is pentagon and its perimeter?
The perimeter of a pentagon is the total length of the pentagon’s boundaries. Therefore, we can find the perimeter by adding the lengths of the five sides of the pentagon.
The length of side with radius = 2rsin(180/n)
Here, n = 5
length of side with r = 8 = 2*8sin(180/5)
=16 sin 32
=16 (0.58779)
=9.4
Perimeter is given as 5(length) = 47 cm.
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if an examination Nita scored 372 marks if she scored 62% marks find the maximum marks
If Nita scored 62% of the marks then the maximum marks of the examination was 600 .
In the question ,
it is given that,
the number of marks scored by Nita in the examination = 372 marks
percent of marks scored by Nita in the examination = 62% ,
let the maximum marks of the examination = "x" ,
So , according to the questions
372 = 62% of x
372 = 0.62 * x ....because 62% = 0.62
x = 372/0.62
x = 600
Therefore , If Nita scored 62% of the marks then the maximum marks of the examination was 600 .
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I will give brainliest to anyone who answer this right with a clear solution. Pls help ASAP. Thank you in advance.
Answer:
7.81
Step-by-step explanation:
x1= 1
x2= 6
y1= -4
y2= 2
31.The first one just has one minor error which is not putting a square root.
after putting the square root on [tex]\sqrt{61}[/tex] you will get an answer which is 7.81 units
the second one has an error in putting the correct values
32. the equation for distance is [tex]\sqrt{(x_2-x_1 )+(y_2-y_1)} }[/tex] however the values are inputted wrong as x2=6 and x1=1 but here x1 is taken as 2 which is the value of y2 and instead of inputting y2 as 2 it is written as 1 which is the value of x1
Comment if you still don't understand
Answer:
31. Omission of the square root sign in step 1.
32. Subtracting the y-value from the x-value in each parentheses in step 1.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
Given points:
A = (6, 2)B = (1, -4)Question 31The error was the omission of the square root sign in the first step of the calculation:
[tex]\textsf{Error}: \quad AB=(6-2)^2+(1-(-4))^2[/tex]
[tex]\textsf{Correction}: \quad AB=\sqrt{(6-2)^2+(1-(-4))^2}[/tex]
Correct calculation:
[tex]\begin{aligned}AB&=\sqrt{(6-1)^2+(2-(-4))^2}\\&=\sqrt{5^2+6^2}\\&=\sqrt{25+36}\\&=\sqrt{61}\\& \approx 7.8\end{aligned}[/tex]
Question 32The error was subtracting the y-value from the x-value in each parentheses in the first step of the calculation, rather than subtracting the x-values and the y-values separately:
[tex]\begin{aligned}\textsf{Error}: \quad AB&=\sqrt{(x_A-y_A)^2+(x_B-y_B)^2}\\ &=\sqrt{(6-2)^2+(1-(-4))^2}\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Correction}: \quad AB&=\sqrt{(x_A-x_B)^2+(y_A-y_B)^2}\\&=\sqrt{(6-1)^2+(2-(-4))^2\end{aligned}[/tex]
Correct calculation:
[tex]\begin{aligned}AB&=\sqrt{(6-1)^2+(2-(-4))^2}\\&=\sqrt{5^2+6^2}\\&=\sqrt{25+36}\\&=\sqrt{61}\\& \approx 7.8\end{aligned}[/tex]
Solve the equation by identifying the quadratic form. Use a substitute variable(t) and find all real solutions by factoring.
Type your answers from smallest to largest. If an answer is not an integer then type it as a decimal rounded to the nearest hundredth. When typing exponents do not use spaces and use the carrot key ^ (press shift and 6). For example, x cubed can be typed as x^3.
(x^2-1)^2+(x^2-1)-12=0
Step 1. Identify the quadratic form
Let t= Answer
. We now have:
t^2+t-12=0
Step 2. Factor
Factor this and solve for t to get t=Answer
and Answer
Step 3. Solve for x
We have solved for t now we need to use this value for t to help us solve for x. Revisit step 1 to remind you of the relationship between t and x. Type your real solutions (no extraneous) from smallest to largest.
x=___ and ___
The quadratic form of (x² - 1)² + (x² - 1) - 12 = 0 is (x² + 3)(x² - 4) = 0 and the roots are x = ± i√3 Or x = ± 2.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, (x² - 1)² + (x² - 1) - 12 = 0.
∴ x⁴ - 2x² + 1 + x² - 1 - 12 = 0.
x⁴ - x² - 12 = 0.
x⁴ + 3x² - 4x² - 12 = 0.
x²(x² + 3) - 4(x² + 3) = 0.
(x² + 3)(x² - 4) = 0.
Now (x² + 3) = 0 Or (x² - 4) = 0.
x² = - 3 Or x² = 4.
x = ± √-3 Or x = ± 2.
x = ± i√3 Or x = ± 2.
We can also solve this equation by assuming x² = t and substitute we will get the roots in terms of t and then we'll replace x² again in t.
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PLEASE HELP! I WILL NAME YOU THE BRAINLIEST! PLEASE PLEASE PLEASE!
Write the point-slope form of the equation of the line with slope −7/4 that passes through the point (−9, 2).
WORK DOES NOT NEED TO BE SHOWN!
A. y + 2= −7/4(x − 9)
B. y − 9= −7/4(x + 2)
C. y + 9 = −7/4(x − 2)
D. y − 2 = −7/4(x + 9)
Answer: D. Y-2 = -7/4(X+9)
Convert meters to centimeters. 4.5 m = X(
I ment middle not high...
Answer:
450 centimeters
Step-by-step explanation:
We know that,
1 meter = 100 centimeters
so 4.5 meters = 4.5*100 centimeters
=450 centimeters
Write an equation in point slope for the line that passes through the given points
(-4,6), (-2,22)
Answer:
y - 6 = 8(x + 4)
Step-by-step explanation:
The point-slope form is [tex]y-y_{1}=m(x-x_{1})[/tex], where y1 and x1 are any point on the line and m is the slope.
The formula for slope is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
By plugging in the points we have, we get: [tex]\frac{22-6}{-2-(-4)}=8=m[/tex]
We can use any of the two pairs of points to represent y1 and x1 so if we choose (-4,6), we get:
[tex]y-6=8(x-(-4))\\y-6=8(x+4)[/tex]
A quadratic function is defined by g(x) = 2x² + 12x + 1. Write this in the completed-square (vertex) form
and show all the steps.
The completed-square (vertex) form 2x² + 12x + 1 is 2(x+3)^2−17. Completing the Square is a technique to find maximum or minimum values of quadratic functions.
How to find completed-square ?Completing the square is a highly helpful technique or way to change a quadratic equation from also known as the "standard form," to its "vertex form,".
For some combinations of h and k, completing the square is a method for transforming a quadratic polynomial. In other words, the quadratic expression is completed by inserting a perfect square trinomial.
Finding the maximum or lowest values of quadratic functions can be done using the square method, sometimes known as "completing the square."
Use the form ax^2 + bx + c, to find the values of a, b, and c.
Consider the vertex form of a parabola.
a(x+d)^2+e
Find the value of d using the formula
d = b/2a.
d = 3
Find the value of e using the formula
e = c− b^2 / 4a.
e = −17
Substitute the values of a, d, and e into the vertex form 2(x+3)^2−17.
2(x+3)^2−17
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Which equation is true for the value b=10
Answer:
3(b-2)=24
Step-by-step explanation:
3b - 6 = 24
3b = 30
b= 10
a contractor needs to buy nails to build a house. the nails come in small boxes and large boxes. each small box has 50 nails and each large box has 350 nails. the contractor bought 3 more small boxes than large boxes, which altogether had 2950 nails. write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. define the variables that you use to write the system.
Seven huge boxes and two tiny boxes total were bought by the contractor.
A linear equation is defined as an algebraic equation of maximum degree 1 is a linear equation.
According to the question, a builder needs to purchase nails to construct a house.
Both small and large boxes of nails are provided. There are 50 nails in each small box and 350 in each large box.
The contractor purchased 5 more large than tiny boxes, hence it is assumed that he purchased a certain number of little boxes.
He purchased (x+5) huge cartons.
So, 50(x) + 350(x+5) = 2590.
50x + 350x + 1750 = 2590.
400x = 2590 - 1750.
400x = 840.
x = 2.1
The bulk of the boxes he bought is 7.
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Late assignment. Help ?
The rigid transformation of the pre-image ΔABC, that produces the image ΔDEF is option E as follows;
E. [tex]R_{(90^{\circ},\,(0,\, 0))}[/tex]
What is a rigid transformation?A rigid transformation is one in which the distances between each pair of points on the pre-image is preserved on the image, such that the pre-image and the image have the same size.
The coordinates of the vertices of ΔABC are;
A(-3, -3), B(-1, -4), C(-3, -4)
The coordinates of the vertices of ΔDEF are; D(-3, 3), E(-4, 1), F(-4, 3)
The formula for the rotation of a point (x, y) 90° clockwise about the origin is presented as follows;
Pre-image point [tex]{}[/tex] (Rotation 90° clockwise) Image point after rotation
(x, y) [tex]{}[/tex] ⇒ [tex]{}[/tex] (-y, x)
The points in the image ΔDEF of pre-image triangle ΔABC which corresponds to points on ΔABC are;
Vertex A in triangle ΔABC corresponds to vertex D on triangle ΔDEF
Vertex B in triangle ΔABC corresponds to vertex E on triangle ΔDEF
Vertex C in triangle ΔABC corresponds to vertex F on triangle ΔDEF
The transformation of (x, y) ⇒ (-y, x), (which is the transformation of a 90° clockwise rotation about the origin), on the vertices of ΔABC are;
A(-3, -3) [tex]\underset \longrightarrow {R_{(90^{\circ}, (0, 0)}}[/tex] D(-3, 3)
B(-1, -4) [tex]\underset \longrightarrow {R_{(90^{\circ}, (0, 0)}}[/tex] D(-4, 1)
C(-3, -4) [tex]\underset \longrightarrow {R_{(90^{\circ}, (0, 0)}}[/tex] F(-4, 3)
Therefore, the triangle ΔDEF can be obtained from the triangle ΔABC by a rotation of 90° clockwise about the origin.
The correct option is; E [tex]R_{(90^{\circ}, (0, \,0))}[/tex]
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The width of a plastic storage box is 2 ft longer then the height the length is a 5 ft longer than the height the volume is 216ft3
What is the formula for the volume of a rectangular prism?
What variable expressions represent the length height and width?
What equation represents the volume of the plastic storage box
Answer:
See belowStep-by-step explanation:
Let the dimensions are width - w, length - l and height - h.
Givenw = h + 2,l = h + 5,Volume = 216 ft³.SolutionFormula for volume:
V = lwhVariable expressions for length, height and width:
l = h + 5,h,w = h + 2Equation for the volume of this box:
V = lwhSubstitute the variables:
V = h(h + 2)(h + 5)or
h(h + 2)(h + 5) = 216Answer:
a) V = l × w × h b) l = (h + 5), w = (h + 2), h = h c) 216 = (h + 5)(h + 2)(h)Step-by-step explanation:
a) Formula we use,
→ V = l × w × h
b) The variable expressions are,
→ l = (h + 5)
→ w = (h + 2)
→ h = h
c) Forming required equation,
→ V = l × w × h
→ V = (h + 5)(h + 2)(h)
→ 216 = (h + 5)(h + 2)(h)
These are the required answers.
graph the equation. y=-4(x+2)^2-1
Hope this helps you with your question.
Answer:
Step-by-step explanation:
I did it on a graphing app
Janelys went shopping for a new pair a of pants. The listed price of the pair of pants
was $20, but the price with tax came to $21.40. Find the percent sales tax.
The percent sales tax on perchaging new pants is 7%. Percent is very useful for comparing two different things.
What is percent?
It is a figure or ratio stated as a fraction of 100 in mathematics. It is frequently represented by the percent sign, "%".
The formula to calculate the percent sales tax is as follows:
[tex]\textnormal{Percent sales tax}=\frac{\textnormal{Tax amount}}{\textnormal{Price without tax}} \times 100[/tex]
Total price of new pants with tax = $21.40
Price of new pants without tax = $20
The amount of tax on perchanging pants = $21.40 - $20 = $1.40
Now, calculate the percent tax.
[tex]\textnormal{Percent sales tax}=\frac{\textnormal{Tax amount}}{\textnormal{Price without tax}} \times 100\\\textnormal{Percent sales tax}=\frac{\$1.40}{\textnormal\$20}\times 100\\=7\%[/tex]
Hence, the percent sales tax on perchagin new pants is 7%.
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Coast Guard Station Able is located L=250 miles due south of Station Baker. A ship at sea sends an SOS call that is received by each station. The call to Station Able
indicates that the ship is located N55°E; the call to Station Baker indicates that the ship is located S60°E.
Use this information to answer the questions below.
(a) How far is each station from the ship?
The distance from Station Able to the ship is
miles.
(Do not round until the final answer. Then round to two decimal places as needed.)
The distance from Station Baker to the ship is
miles.
(Do not round until the final answer. Then round to two decimal places as needed.)
(b) If a helicopter capable of flying 200 miles per hour is dispatched from the nearest station to the ship, how long will it take to reach the ship?
minutes (Round to two decimal places as needed.)
The distance of each station from the ship is = 250 miles.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
with the help of the gievn statemnets with logical reasoning and unitary method we can solve our question-a= The distance of each station from the ship is = 250 miles.b= 200*250= 50000 mts.hence,The distance of each station from the ship is = 250 miles.
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Hi! I can’t figure out m<4 and m<5. Can anyone help me?
The measure of angle 4 is 35 degrees and the measure of angle 5 is 81 degrees
The sum of angles on a straight line is equal to 180 degrees
Then the equation will be
∠3 + 81 +∠4 = 180 degrees
Substitute the value of ∠3 in the equation
64 + 81 + ∠4 = 180
145 + ∠4 = 180
∠4 = 180 - 145
∠4 = 35 degrees
The sum of interior angles of the triangle is 180 degrees
∠4 + ∠5 + 64 = 180
Substitute the values in the equation
35 + ∠5 + 64 = 180
∠5 + 99 = 180
∠5 = 180 - 99
∠5 = 81 degrees
Hence, the measure of angle 4 is 35 degrees and the measure of angle 5 is 81 degrees
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