Answer:
Approximately 8.6
Step-by-step explanation:
The length of a rectangle is five times its width. if the perimeter of the rectangle is 96 ft , find its area.
The width of the rectangle is 8 ft and the length is 40 ft. Therefore, the area of the rectangle is 320 square feet.
Explanation:To find the dimensions of the rectangle, let's use variables. Let the width of the rectangle be x. Since the length is five times the width, the length would be 5x. The perimeter of a rectangle is equal to twice the sum of its length and width. Therefore, we can set up the equation 2(5x + x) = 96 to find the width.
Simplifying the equation, we have 12x = 96. Dividing both sides by 12, we get x = 8. So the width of the rectangle is 8 ft.
Now, we can calculate the length by multiplying the width by 5. The length would be 5(8) = 40 ft. The area of a rectangle is equal to its length multiplied by its width. Therefore, the area of this rectangle is 8 ft * 40 ft = 320 square feet.
Tonya is twice Kevin's age. In three years, Tonya will be 17. And in another three years, Uncle Rob will be three times Tonya’s age.
How old is Kevin and Uncle Bob
17-3 = 14 ( Tonya's age now)
14/2 = 7 ( Kevin's age)
14*3 = 42 ( Uncle Bob's age)
Find the amount (future value) of the ordinary annuity. (round your answer to the nearest cent.) $1500/semiannual period for 8 years at 2.5%/year compounded semiannually
0. 135 written as a fraction
Explains how to write 0.135 as a fraction.
0.135 written as a fraction is 135/1000.
The following list shows the items and prices for a restaurant order. Calculate the total amount if there is a 7% tax and the customer leaves a 20% gratuity. 1 appetizer: $7.39 2 entrees: $16.99 each 1 dessert: $5.29 2 drinks: $2.30 each a. $65.82 b. $65.10 c. $54.85 d. $40.60
If m<1 = 7x + 6 and m<2 = 8x - 6, find the value of x so that p is perpendicular to q
Answer:
x = 12
Step-by-step explanation:
Given: [tex]\angle 1=7x+6[/tex]
[tex]\angle 2=8x-6[/tex]
∠1 and ∠2 form by two intersection line p and q.
p is perpendicular to q.
Therefore, ∠1 = ∠2 = 90°
So, 7x + 6 = 90°
7x = 84
x = 12
8x - 6 = 90°
8x = 96
x = 12
7x + 6 = 8x - 6
x = 6 + 6
x = 12
So, we get x=12 from all three equations.
hence, The value of x is 12
The perimeter of a square garden is to be at least 20 ft but no more than 32 ft. find all possible values for the lengths of its sides using a compound inequality
Answer:
Answer in pic
Step-by-step explanation:
What is 19.2×108 minutes in hours? 1.152×1011 h 3.200×109 h 1.152×107 h 3.200×107 h
Which of the following shows the numbers ordered from least to greatest?
A)0.004, 0.07, 0.6, 0.32
B)0.004, 0.6 0.07, 0.32
C)0.004, 0.07, 0.32, 0.6
D)0.004, 0.32, 0.07, 0.6
What's the parabola in vertex for for (-5,0) and has a vertex (-2,1)
hello :
the parabola's equation is : f(x) = a(x+2)²+1
but ; f(-5) = 0
0 = a(- 5+2)²+1
9a+1=0.....a= -1/9
f(x) = (-1/9)(x+2)²+1
help me ............
3 1/2 x 2 = 7
4 2/3 x 2 = 9 1/3
7 + 9 1/3 = 16 1/3 yards
Calculate the area of the figure below using the following information:
Area of triangle ABC = 23.85 square units
Area of triangle ACD = 29.4 square units
Area of triangle AED = 26.25 square units
The area of the Figure ABCDE is ______ square units.
Answer:
Area of pentagon ABCDE = 23.85 + 29.4 + 26.25 = 79.5 unit²
Step-by-step explanation:
Area of pentagon ABCDE is sum of area of triangles ABC, ACD and ADE
Area of pentagon ABCDE = Area of ΔABC +Area of ΔACD + Area of ΔADE
Area of ΔABC = 23.85 unit²
Area of ΔACD = 29.4 unit²
Area of ΔAED = 26.25 unit²
Area of pentagon ABCDE = Area of ΔABC +Area of ΔACD + Area of ΔADE
Area of pentagon ABCDE = 23.85 + 29.4 + 26.25 = 79.5 unit²
Which transformation will be equivalent to rotating a figure 180° counterclockwise?
A) reflecting over the line y = x.
B) reflecting over the line y = -x.
C) reflecting over the x-axis and the y-axis.
D) translating left 3 units and down 5 units.
If we have given coordinates of the image are in form (h,k).
The resulting coordinates of image rotation of 180° around the origin would be (-h,-k).
We have rule (h,k) ---> (-h,-k).
We can see that x-coordinate is being multiplied by -1 and then y-coordinate is also being multiplied by -1.
Above rule could be break into two parts.
(h,k) ---> (-h,k) ----> (-h,-k).We can see in first step, (h,k) ---> (-h,k) is being reflecting over the x-axis and
in second step (-h,k) ----> (-h,-k) is being reflecting over the y-axis.
Therefore, correct option is C) reflecting over the x-axis and the y-axis.The transformation which is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise is reflecting over the [tex]x[/tex]-axis and [tex]y[/tex]-axis. Therefore, the [tex]\fbox{\begin\\\ \bf option (C)\\\end{minispace}}[/tex] is correct.
Further explanation:
Consider a coordinate in the form [tex](a,b)[/tex] where [tex]a[/tex] and [tex]b[/tex] are real numbers.
If [tex]a[/tex] and [tex]b[/tex] are positive then the point [tex](a,b)[/tex] lies in the first quadrant.
If we rotate the coordinate [tex](a,b)[/tex] [tex]180^{\circ}[/tex] counterclockwise then the coordinates become [tex](-a,-b)[/tex].
The coordinate [tex](-a,-b)[/tex] lies in the third quadrant.
If we reflect the coordinate [tex](a,b)[/tex] about the [tex]x[/tex]-axis then the coordinates become [tex](a,-b)[/tex].
The coordinate [tex](a,-b)[/tex] lies in the fourth quadrant.
If we reflect the coordinate [tex](a,-b)[/tex] about the [tex]y[/tex]-axis then the coordinates become [tex](-a,-b)[/tex].
The coordinate [tex](-a,-b)[/tex] lies in the third quadrant.
This implies that rotating a figure [tex]180^{\circ}[/tex] counterclockwise is equivalent to transformation of reflecting over [tex]x[/tex]-axis and reflecting over [tex]y[/tex]-axis.
Option (A)
In option (A) it is given that reflection about the line [tex]y=x[/tex] is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise.
If we reflect the coordinate [tex](a,b)[/tex] about the line [tex]y=x[/tex] then the coordinates become [tex](b,a)[/tex].
This is not same as rotating the figure [tex]180^{\circ}[/tex] counterclockwise.
Therefore, the option (A) is incorrect.
Option (B)
In option (B) it is given that reflection about [tex]y=-x[/tex] is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise.
If we reflect the coordinate [tex](a,b)[/tex] about the line [tex]y=-x[/tex] then the coordinates become [tex](-b,-a)[/tex].
This is not same as rotating the figure [tex]180^{\circ}[/tex] counterclockwise.
Therefore, the option (B) is incorrect.
Option (C)
In option (C) it is given that reflection about [tex]x[/tex]-axis and [tex]y[/tex]-axis is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise.
If we reflect the coordinate [tex](a,b)[/tex] about [tex]x[/tex]-axis and [tex]y[/tex]-axis then the coordinates become [tex](-a,-b)[/tex].
This is same as rotating the figure [tex]180^{\circ}[/tex] counterclockwise.
Therefore, the option (C) is correct.
Option (D)
In option (D) it is given that shifting a point [tex]3[/tex] units left and [tex]5[/tex] units down is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise.
If we shift the point [tex](a,b)[/tex], [tex]3[/tex] units left and [tex]5[/tex] units down the coordinate is [tex](a+3,b-5)[/tex].
This is not same as rotating the figure [tex]180^{\circ}[/tex] counterclockwise.
Therefore, the option (D) is incorrect.
Therefore, the [tex]\fbox{\begin\\\ \bf option (C)\\\end{minispace}}[/tex] is correct.
Learn more
1. Learn more about the rotation of the triangle about the origin https://brainly.com/question/7437053.
2. Learn more about when a triangle is rotated about the origin https://brainly.com/question/2992432.
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Geometry
Keywords: Transformation, rotation, reflection, clockwise, geometry, counterclockwise, -axis, - axis, coordinates, graph, origin, line, degrees, translation, symmetry.
4.5/17 - x = 3/8 solve
Answer:
The value of the equation is [tex]x=\frac{-15}{136}[/tex] Or [tex]x=-0.1102[/tex].
Step-by-step explanation:
Consider the provided equation.
[tex]\frac{4.5}{17}- x =\frac{3}{8}[/tex]
We need to solve the provided equation for x.
Add x to both side.
[tex]\frac{4.5}{17}- x+x=\frac{3}{8}+x[/tex]
[tex]\frac{4.5}{17}=\frac{3}{8}+x[/tex]
Subtract 3/8 from both sides.
[tex]\frac{4.5}{17}-\frac{3}{8}=x[/tex]
[tex]x=\frac{4.5}{17}-\frac{3}{8}[/tex]
[tex]x=\frac{36-51}{136}[/tex]
[tex]x=\frac{-15}{136}[/tex]
Or
[tex]x=-0.1102[/tex]
Hence, the value of the equation is [tex]x=\frac{-15}{136}[/tex] Or [tex]x=-0.1102[/tex].
Solve the quadratic equation by taking square roots. Allow for imaginary solutions. Enter your answer in simplest form. Equation: 5x (squared) - 5 = -17
Which two expressions could be used to solve this problem?
Roberto ordered 4 pepperoni pizzas, 2 mushroom pizzas, and 3 cheese pizzas for his party. He paid the same price for each pizza. The total cost was $90. How much did each pizza cost?
Choose exactly two answers that are correct.
A.
4 × 2 × 3
B.
90 – 24
C.
90 ÷ 9
D.
90 obelus divided by(4 + 2 + 3)
What is the slope of the equation y = -x + 4
Summer paints a room that has 400 square feet of wall space in 2.5 hours. at this rate, how long will it take her to paint a room with 720 square feet of wall space?
A limousine service determines that its per-mile cost is $.36 and that it incurs $48 in miscellaneous expenses for each reservation.The service charges $3.56 per mile. What number of miles represents the break-even point?
What are the solutions to the equations |x-10|-4=2x
Completely factor the expression.
w^2 - 15w + 54
A minor league baseball team plays 117 games in a season. if the team won 13 more than 3 times as many as they lost. how many wins and losses
The distance formula is d=r/t. how long will it take (in hours) to travel 100 miles at a rate of 22mph? Show all work.
divide the distance ( 100 miles) by the speed ( 22 mph) to get the time
100/22 = 4.545454 hours (Round to 4.5 hours ?)
if you need hours and minutes multiply 0.545454 by 60 to get the minutes
4 hours 32.7 ( round to 33) 4 hours and 33 minutes
If a(x)=3x+1 and b(x)=
The answer is C. [1, ∞] on edge
Including a 8 %8% sales tax, an inn charges $ 135$135 per night. Find the inn's nightly cost before the tax is added.
number 4 I have absolutely no idea how to do. I generally understand finding distance on the coordinate plane but this has really confused me. Please help.
The area of a rectangle is 72 cm². The length of the rectangle is 6 cm longer than the width.
What is the width of the rectangle?
2 cm
6 cm
8 cm
10 cm
Answer:
6cm
step-by-step explanation
just dived each number bye 72 to find 12 witch we would get 6cm
Triangle MRN is created when an equilateral triangle is folded in half. What is the value of y?
A. 2√3 units
B. 4 units
C. 4√3 units
D. 8 units
we know that
If Triangle MRN is created when an equilateral triangle is folded in half
then
[tex]RM=\frac{1}{2}*MN[/tex]
[tex]MN=6+2=8\ units[/tex]
so
[tex]RM=\frac{1}{2}*8=4\ units[/tex]
Applying the Pythagorean Theorem in triangle MRN
[tex]MN^{2}=NR^{2}+RM^{2}[/tex]
we have
[tex]MN=8\ units[/tex]
[tex]RM=x=4\ units[/tex]
[tex]NR=y[/tex]
substitute
[tex]8^{2}=y^{2}+4^{2}[/tex]
solve for y
[tex]y^{2}=8^{2}-4^{2}[/tex]
[tex]y^{2}=48[/tex]
[tex]y=\sqrt{48}=4\sqrt{3}\ units[/tex]
therefore
the answer is the option C
[tex]4\sqrt{3}\ units[/tex]
Answer:
The correct option is C.
Step-by-step explanation:
It is given that triangle MRN is created when an equilateral triangle is folded in half.
It means original equilateral is triangle MNO and NR is a perpendicular bisector. The side length of the triangle is
[tex]MO=NO=MN=MS+SN=2+6=8[/tex]
Since NR is a perpendicular bisector, therefore
[tex]RM=\frac{MO}{2}=\frac{8}{2}=4[/tex]
Using Pythagoras property in triangle MNR,
[tex]MR^2+NR^2=MN^2[/tex]
[tex]4^2+y^2=8^2[/tex]
[tex]y^2=64-16[/tex]
[tex]y=\sqrt{48}[/tex]
[tex]y=4\sqrt{3}[/tex]
Therefore option C is correct.
When is it necessary to use three points to name an angle? If CP bisects and DPB , what is the measure of angle CPB?
In geometry, three points are used to name an angle when there are multiple angles that share the same vertex. If CP bisects angle DPB, angle CPB is divided into two equal angles, and the measure of angle CPB is half of the measure of angle DPB.
Explanation:In geometry, it is necessary to use three points to name an angle when there are multiple angles that share the same vertex. By using three points, we can clearly identify which angle we are referring to. In this case, if CP bisects angle DPB, it means that angle CPB is divided into two equal angles, and CP is one of the dividing lines. Therefore, the measure of angle CPB is half of the measure of angle DPB.
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Find the value of x for which l is parallel to m. The diagram is not to scale.
a. 31
b. 62
c. 93
d. 149