Answer: 2.5 mi/hr. 7.5/3= 2.5
Step-by-step explanation:
Grayson's retirement party will cost $60 if he invites 10 guests. If there are 86 guests, how much will Grayson's retirement party cost? Solve using unit rates.
Answer:
Grayson's party will cost $516.
Step-by-step explanation:
Start with putting a unit rate for money per person
60/10
Divide by 10
6/1 (6$ per person)
Then multiply by 86 (# of guests attending)
86 x 6 = 516
Use the graph of the function to find its domain and range. Write the domain and range in interval notation.
I’m not sure if I did it right
Answer:
you did it right!
Step-by-step explanation:
Vartan was paid $25,000 for a cell phone app that he wrote and wants to invest it to save for his son’s education. He wants to put some of the money into a bond that pays 4% annual interest and the rest into stocks that pay 9% annual interest. If he wants to earn 7.4% annual interest on the total amount, how much money should he invest in each account?
Find the length of the missing side. Leave your answer in the simplest radical form.
Length of the missing side. Leave your answer in the simplest radical form b= root of 69 feet
Pythagorean theorem:
Pythagorean theorem is the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2
The Pythagorean Theorem is tremendously useful. In many realistic scenarios it is possible to measure a and b with ease, but it is often difficult to measure c. For instance, c might pass through a lake or private property or might be up in the air! We'll do a few example puzzles in class together to show you how this works.
Nonetheless, the Pythagorean Theorem still presents a substantial limitation to utility. Specifically, it requires that the angle between a and b is 90 degrees. If the angle is not 90 degrees, the Pythagorean Theorem doesn't help.
This is where the Law of Cosines comes in. The Law of Cosines allows us to find c even when the angle between a and b is not 90 degrees. Check out this applet which illustrates the relationship between a2 and b2 and c2 that also takes into account the angle C (note the angle is capital C to distinguish it from lower case c, the side opposite angle C) between the legs a and b.
Adjust the blue dots in the triangle on the right right side of the screen to see the relationship. At the outset, when angle C is 90 degrees, a2+b2 is exactly equal to c2. However, when you move any of the three vertices of the triangle, note that the equality is not maintained. The problem is that angle C becomes not 90 degrees.
Now ,
a= 10
c= 13
b=?
a2 + b2 = c2
[tex]10^{2} +b^{2} = 13^{2} \\\\100+ b^{2} = 169\\\\b^{2} = 169-100\\\\b=\sqrt{69}[/tex]
Length of the missing side. Leave your answer in the simplest radical form
b= root of 69 feet
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solve for y 3x-7y=21
A. y=-3/7x+21
B. y=3/7x-21
C. y=3/7x-3
D. y=-3/7x+3
Answer:
Y = 3/7x-3
Step-by-step explanation:
I don't have an explanation other than the fact I put this into a calculator and this is what it gave me.
47=
\,\,-\frac{x}{11}+43
−
11
x
+43
Answer:
x=−44
Step-by-step explanation:
Rewrite the equation as
−x11+43=47.−x11+43=47
Move all terms not containing
x
to the right side of the equation.
−x11=4
Multiply both sides of the equation by
−11.−11(−x11)=−11⋅4
Triangle ABC is an equilateral triangle. Use the figure to find the value of x
The value of x in the equilateral triangle is 10
The equilateral triangle's three characteristics are: Equal on all three sides. The three angles are identical. Three symmetry lines may be seen in the figure. Additionally, each inside angle is identical (60 degrees).
A unique isosceles triangle with three equal sides is called an equilateral triangle. The formulas that we take into account most frequently for a triangle are: Dimensions of an equilateral triangle , the equilateral triangle's circumference, Equilateral triangle's height
An equiangular triangle's area can be calculated using the following formula:
If A=√3a2/4, then ABC's perimeter 3a
where a is the triangle's side length.
In equilateral triangle, the sum of the 3 angles are 180°.then the angle of each side is 60°
From the given data,
(7x-10)°=60°
7x=60+10
7x=70, x=10
Hence the value of x is 10
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Write a slope-intercept equation for a line that passes through (7,0) and (-5,3).
Answer:
y = -1/4x + 7/4
Step-by-step explanation:
m = (y2-y1)/(x2-x1)
m = (3 - 0)/(-5 - 7) = 3/(-12) = -1/4
using m = -1/4, y = 0 , x = 7
y = mx + b
0 = -1/4(7) + b
0 = -7/4 + b
b = 7/4
y = -1/4x + 7/4
please help
please hurry
From the given table, the relationship that is an inverse variation is the fourth relationship with (1, -2) and (3, -6).
What is an inverse variation?An inverse variation refers to when the values of x and y move in opposite directions.
For instance, when x increases, y decreases. The decrease will have to be constant however which is why the fourth relationship is an inverse variation.
When x increases by 1, the value of y decreases by 2.
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Simplify the following (1/7x+3/8) + (2x - 1/8)
50 POINTS!!!!
Answer the questions by drawing on the coordinate plane below.
(a) Draw the image of ∆ABC under the dilation with scale factor 3 and the origin as the center of dilation. Label the image ∆A'B'C'. Make sure to include the coordinates of A’, B’, and C’.
(b) Draw the image of ∆DEF under the dilation with scale factor -1/2 and the origin as the center of dilation. Label the image ∆D'E'F'. Make sure to include the coordinates of D’, E’, and F’.
Using dilation rules, the dilated triangle is given at the end of the answer. The coordinates of the vertices are as follows:
A'(-6,6), B'(-3,0), C'(3,6).
What is the rule for a dilation?To dilate a figure by a factor of a, each coordinate of each vertex of the image is multiplied by a, that is, the following rule is applied:
(x,y) -> (ax, ay).
The coordinates of the vertices of ABC are given as follows:
A(-2,2), B(-1,0), C(1,2).
After a dilation with a scale factor of 3, the coordinates of the vertices of A'B'C' will be given as follows:
A'(-6,6), B'(-3,0), C'(3,6).
These coordinates are derived multiplying the coordinates of A, B and C by 3.
The image of the triangle is given at the graph at the end of the answer.
For the image of triangle DEF, each of the coordinates of D, E and F will be multiplied by -1/2 to generate the dilated triangle.
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Which sequence of transformations can joseph perform to show that figure A and figure B are congruent
Step-by-step explanation:
If rigid transformations can be used to map two shapes onto one another, they are said to be congruent (a sequence of one or more rotations, translations, and reflections). Any series of rigid transformations performed on a triangle results in a congruent triangle.
Let's now analyze rigid transformation.
An isometry, also known as a rigid transformation of the plane, preserves length. Reflections, translations, rotations, and combinations of these three transformations are all considered "rigid transformations".
Example: Congruent shapes include, for instance, the right angle triangle and its preimage.
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VIEW IMAGE
9. The parent or basic absolute value function, f (x)= xl, is transformed to become
1
g(x)= -lal. Which of the following are true about f (x) and g(x)?
The domain of both f (x) and g (x) are all real numbers.
II The graphs of each function are vertical reflections of each other.
III The axis of symmetry of the graphs of both functions is x = 0.
The range of both f (x) and g (z) are all real numbers.
Both [tex]f(x)[/tex] and [tex]g(x)[/tex] have real domains.
What is domain?
The domain is all x-values or function inputs, and the range is all y-values or function outputs. When looking at a graph, the domain is all of the graph's values from left to right. The range includes all of the graph's values from bottom to top.
Here, the options
(I) The domain of both [tex]f(x)[/tex] and [tex]g(x)[/tex] are all real numbers,
(II) The axis of symmetry of the graphs of both functions is [tex]x=0[/tex]
are correct.
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The prom committee is decorating the venue for prom and wants for prom and wants to hang lights above the diagonals of the rectangular room. If DH=44.5, EF=39, and m angle GHF=128 degrees, find GE and m
The length of diagonal GE is 89 units
What is a quadrilateral?
quadrilateral is a plane mathematical closed figure consist of four side and four edges. There are 7 types of quadrilateral.
Trapezium, Parallelogram, Rectangle, Rhombus, Square, Kite.
It is given that :
length of side EF = 39 units
and, DH = 44.5 units
It is known that :
Diagonals of a Rectangle
A rectangle has 2 congruent diagonals, that is the two diagonals are equal to each other.
The diagonals of a rectangle bisects each other into equal segments.
The diagonals of the rectangular room are:
DF and GE
Thus:
DF = GE
DH = 1/2(DF)
44.5 = 1/2(DF)
DF = 2(44.5)
DF = 89
Therefore :
DF = GE = 89
GE = 89 units
Thus, The length of diagonal GE is 89 units.
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Rosita paid $32.08, including tax, for her family to eat dinner at a restaurant. She wants to tip a whole dollar amount that is close to 20%. What is a reasonable tip that Rosita should leave?
Answer:
$6
Step-by-step explanation
$32 is the total(100%)
in order to find what she needs to tip, you have to divide by 5 because 100% / 5=20%
now, to find 20% of 32, you divide 32 by 5.
32 you can just round to 30, so that you can divide it by 5.
30/5=$6
you could've rounded the total up to 35, but 30 was closer, therefore $6 was the closest whole number tip rosita could've left.
hope this helps
A flag measures 475 feet by 220 feet. Find its area answer
Answer:104,500
Step-by-step explanation:
Area = l × w= 475 × 220= 104500 feet2
Can a table 9 feet wide (legs folded) fit through a rectangular doorway 4 feet by 8
Yes , it is possible to fit a table 9 feet wide through a rectangular doorway 4 feet by 8.
The Pythagorean theorem states, "In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides." The sides of this triangle were called the perpendicular, the base, and the hypotenuse. Here, the hypotenuse is on the opposite side of the 90° angle, so it is the longest side. The sides of a right triangle (a, b, c, etc.) with positive integer squared values are put into the equation, also known as the Pythagorean triple. which is given by [tex]c^2=a^2+b^2[/tex] here “a” is the perpendicular, “b” is the base, “c” is the hypotenuse.A table with folded legs can pass through a rectangular door at an angle of 45°, forming a triangle to which the Pythagorean theorem can be applied.
Let the two sides of the door be the two sides of triangles a and b, then
[tex]c^2=4^2+8^2\\c^2=16+64\\c^2=80\\c=8.94[/tex]
Conclusion: Using the Pythagorean theorem, we know that an 8.94 foot table can pass through the door. And we know that 8.94 ≈ 9
Hence , a 9-feet table can pass through a rectangular door.
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Which expression is equivalent to the image below.
Answer:
t - s
------------
t + s
Step-by-step explanation:
To solve a problem like this you need to flip the denominator and multiply
Step 1: Write the equation
s
1 - ------
t
--------------
s
1 + -------
t
Step 2: Flip it and multiply
s t
1 - ------ × 1 + -------
t s
Step 3: Multiply Across
s t -s + t t - s
1 - ------ × 1 + ------- = -------------- or ---------------
t s t + s t + s
I hope this helps!
Type an equation for the following pattern.
Evaluate the function /(x) = 5x²+2x for the given value of x. Simplify your answer.
h(-4)
Answer:
h(-4) = 72
Step-by-step explanation:
Given:
h(x) = 5x² +2x
Evaluate the function h(x) = 5x²+2x for x=-4 means to
find h(-4) by substituting x with -4:
h(-4) = 5·(-4)² +2·(-4)
h(-4) = 5·16 -2·4
h(-4) = 5·16 -2·4
h(-4) = 80 -8
h(-4) = 72
Find the area of a quadrilateral formed by the points of intersection of the graphs f(x) = (x − 3)(x + 1) and g(x) = 4x − 2x^2 + 6 and the points of extrema of f(x) and g(x).
Answer:
24
Step-by-step explanation:
The extrema is halfway between the roots, so for f(x), it has coordinates (1, f(1)) = (1, -4).
For g(x), we can rewrite it as -2(x²-2x-3) = -2(x-3)(x+1). We can see that the extrema has coordinates (1, 8).
Finding the intersection,
[tex](x-3)(x+1)=-2(x-3)(x+1) \\ \\ 3(x-3)(x+1)=0 \\ \\ x=-1, 3 \\ \\ x=-1 \implies f(x)=g(x)=0 \\ \\ x=3 \implies f(x)=g(x)=0[/tex]
So, we need to find the quadrilateral with vertices (1,-4), (1,8), (-1,0), and (3,0).
We observe this is a kite with diagonals of lengths 4 and 12. So, using the formula for the area of a kite, the area is 24.
What is the 7 1/2 divided by 1 9/10 in the simplest form
Answer:
3 18/19
Step-by-step explanation:
7 1/2 ÷ 1 9/10 =
= 15/2 × 10/19
= 150/38
= 75/19
= 3 18/19
simplify 20/64 into simplest form
Answer:
Ahmm I guess it is
[tex] \frac{5}{16} \\ [/tex]
Step-by-step explanation:
Cuz I did like
[tex] \frac{20}{64} = \frac{20}{64} \div \frac{2}{2} = \frac{10}{32} = \frac{5}{16} \\ \\ \\ \\ \frac{20}{64} = \frac{20}{64} \div \frac{4}{4} = \frac{5}{16 \\ \\ \\ \\ \\ \\ } [/tex]
so I guess it's correct
Select the correct answer.
Which function defines (g. f)(z)?
f(z)
g(z)
log(5z)
5z + 4
OA
(9. f)(z)
OB.
(g-f)(z): = 5x + 4+ log(5z)
OC (g. f)(z) = 5z log(5z) +4
OD. (g. f)(z) = 5z - 4-log(5z)
5z log(52) + 4log(5z)
Answer: A. (g•f)(x)= log(5x) ( 5x + 4)=5x log(5x) + 4log(5x)
Step-by-step explanation:
Hope this helps :)
the length of a rectangle is 5 feet longer than the width if the perimeter is 94 feet find the length and width of the rectangle
The length and width of the rectangle with the given perimeter are 26ft and 21ft respectively.
What is the length and width of the rectangle?The perimeter of rectangle is expressed as;
P = 2( l + w )
Given the data in the question;
Let 'x' represent the width of the rectangle.
Width w = xLength = x+5Perimeter = 94ftPlug these values into the equation above.
P = 2( l + w )
94 = 2( (x+5) + x )
94 = 2x + 10 + 2x
94 = 4x + 10
4x = 94 - 10
4x = 84
x = 84/4
x = 21
Hence;
Width of the rectangle = x = 21ft
Length of the rectangle = x+5 = 21+5 = 26ft
Therefore the length and width of the rectangle with the given perimeter are 26ft and 21ft respectively.
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14x-3y=-2
4x + 5y = 14
solve each system of equations by elimination
Answer:
x = [tex]\frac{16}{41}[/tex]
y =[tex]\frac{102}{41}[/tex]
Step-by-step explanation:
To use elimination I need either the x terms to be inverses of each other or the y terms to be inverses of each other. There are a number of ways to do this. I am going to focus on the y's. If I multiple the first equation through by 5 and the second equation through by 3. I will make equivalent equations that will allow the y terms to be eliminated.
14x - 3y = -2
5(14x - 3y) =5(-2)
70x - 15y = -10
4x + 5y = 14
3(4x + 5y) = 3(14)
12x +15y =42
Add together the 2 bold equations above
70x - 15y = -10
12x + 15y = 42
82x = 32 Divide both sides by 82
x = [tex]\frac{32}{82}[/tex] = [tex]\frac{16}{41}[/tex]
Plug this in either equation to solve for y
y = [tex]\frac{102}{41}[/tex]
If the polygons are similar, write similar on the blank. If they are not similar, write not similar on the blank. Consider all angles are congruent. First square is 5 by 7 by 5 by 7, the second square is 2.5 by 3.5 by 2.5 by 3.5
The circle graph on the right shows the uses of corn production. Use this graph to answer the question. What percent of corn production is used for ethanol or exports?
Answer:
37%
Step-by-step explanation
Reading the graph we see:
The percent of corn production is used for ethanol is 18%
The percent of corn production is used for exports is 19%
Answer the question:
The percent of corn production used for ethanol OR exports is the sum of the two 18%+19% = 37%
Solve for x 8x + 12 = 2x - 18
Answer:
[tex] \sf \Large x=−5 [/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
8x+12=2x−18
Step 1: Subtract 2x from both sides.
8x+12−2x=2x−18−2x
6x+12=−18
Step 2: Subtract 12 from both sides.
6x+12−12=−18−12
6x=−30
Step 3: Divide both sides by 6.
6x/6 = −30/6
x=−5
Step-by-step explanation:
8x + 12 = 2x -18
8x - 2x = -18 - 12
6x = -30
6x/6 = -30÷6
x = - 5
Please help me please please please!!!!
Step-by-step explanation:
total number of people are 40
take teach takeaway category and divide it by 40
eg)3÷40 / 11÷40
since there are 360⁰ in a circle, multiply your answer by 360 to get your angle
(3÷40)×360 = a
(11÷40)×360 = b
(9÷40)×360 = c
(2÷40)×360 = d
(15÷40)×360 = e
those are your angles. use a protractor to measure the angles
note : if all your angles add up to 360 the you've done everything correctly
