Answer:
Length = 16 yds
Width = 13 yds
Step-by-step explanation:
P = 2w + 2l
l = w + 3
58 = (2w + 2(w + 3))
58 = 4w + 6
52 = 4w
w = 13
L = w + 3
= 13 + 3
= 16
The length and width of the rectangle are 16,13yd.
The Length and Width of the rectangle can be found as:
Given:The length of the rectangle is 3yds longer than the width which means length = w+3
and the perimeter is given by 58yd
Let W be the width and L be the length
We know that the perimeter of a rectangle is 2(L+w)
The perimeter of a rectangle is defined as the sum of all the sides of a rectangle
By simplifying we get2(w+w+3)=58
2(2w+3)=58
2w=29-3
w=13
then the length of the rectangle will be w+3
13+3 = 16
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can someone help me?
Answer:
think of each T in the original equation as an empty box, like this:
P( ) = 2( )² + ( ) - 7
when it says p(some number), it means replace all Ts in the equation with that number.
P( 0 ) = 2( 0 )² + ( 0 ) - 7 = 0 + 0 - 7 = -7
do the same for the rest <:)
for the second part, it's the same concept: every T is replaced with what's inside the parentheses.
so P( -t ) = 2( -t )² + ( -t ) - 7 = 2t² - t - 7
and so on and so forth.
Use 8a+16c.
What is the value of the expression when a = –5 and c = –1? Enter your answer in the box.
To eliminate the × terms and solve for y in the fewest steps by which constants should be equations be multiplied by before adding the equations together
To eliminate the y terms and solve for x in the fewest steps, you can multiply the equations by appropriate constants so that the coefficients of the y terms in Both equations have the same magnitude but opposing signs. So to eliminate the y terms and solve for x in the fewest steps, you should multiply the first equation by 2 and the second equation by 3x
In this instance, you can do the following steps:
Start with the original equations:
Equation 1: 2x + 3y = 8
Equation 2: 3x - 2y = 4
To eliminate the y terms, multiply Equation 1 by 2 and Equation 2 by 3:
Multiply Equation 1 by 2:
2(2x + 3y) = 2(8)
4x + 6y = 16
Multiply Equation 2 by 3:
3(3x - 2y) = 3(4)
9x - 6y = 12
Now, add the two modified equations together to eliminate the y terms:
(4x + 6y) + (9x - 6y) = 16 + 12
4x + 9x + 6y - 6y = 28
13x = 28
Finally, solve for x by dividing both sides of the equation by 13:
x = 28/13
Therefore, to eliminate the y terms and solve for x in the fewest steps, you should multiply the first equation by 2 and the second equation by 3x
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The probable question may be:
To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? The first equation should be multiplied by 2 and the second equation by 3. x.
An indoor running track is 200 meters in length. During a 3,000-meter race, runners must complete 15 laps of the track. An electronic timing device records the amount of time it takes each runner to complete a lap for every lap in the race. These are called lap times. The histograms below display the lap times for both Stefano and Alex, runners in the 3,000-meter race.
2 histograms. A histogram titled Alex apostrophe s 3,000 meter race lap times has lap times (seconds) on the x-axis, and frequency on the y-axis. 35 to 36, 1; 36 to 37, 5; 37 to 38, 4; 38 to 39, 4; 39 to 40, 1. A histogram titled Stefano apostrophe s 3,000 meter race lap times has lap times (seconds) on the x-axis, and frequency on the y-axis. 32 to 33, 1; 34 to 35, 1; 36 to 37, 1; 37 to 38, 4; 38 to 39, 5; 39 to 40, 1; 40 to 41, 2.
Using the histograms, which of the following is a correct comparison?
Neither runner had a lap time between 35 and 36 seconds.
Alex’s lap times show less variability than Stefano’s lap times.
The median lap time for both runners is in the 38–39 interval.
Both runners’ highest number of lap times in the 37–38 interval.
The true statement based on the histogram is
There were no lap times between 35 and 36 seconds.
The correct option is (A).
What is Histogram?A histogram is a graphical representation that organizes a group of data points into user-specified ranges.
Given:
indoor running track is 200 meters in length.
Also, a 3,000-meter race, runners must complete 15 laps of the track.
As, there no data for interval 35-36.
So, there were no lap times between 35 and 36 seconds.
Hence, The interval from 37 to 38 seconds saw the most lap times.
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Answer:
B. Alex's lap times show less variability than Stefano's lap times.
Step-by-step explanation:
A can't be right because Alex has a lap time between 35 and 36 seconds.
C can't be right because the median lap time for Alex isn't 38-39.
D can't be right because both runners have a higher frequency on lap times other than 37-38.
so it has to be B.
5(b)
Joe has a bucket containing 1370cm³ of water measured to the nearest 10 cm³.
Joe Says
"If I tip my bucket of water in the cuboid container, it will never overflow"
Is Joe correct?
You must explain your answer
If the side length is greater than 11.11 cm then it will not overflow.
Otherwise, it will overflow.
If Joe tips the bucket of water in a cuboid container and the water is not overflowing then the cuboid container must be of volume greater than 1370 cm³.
We find the cube root of 1370 cm³.
[tex]\sqrt[3]{1370} \approx11.11[/tex]
Then the cuboid container should have a side of length greater than 11.11 cm.
Here the statement "If I tip my bucket of water in the cuboid container, it will never overflow" is correct or wrong based on the information that the container has a side length lesser or greater than 11.11 cm.
If the side length is greater than 11.11 cm then it will not overflow.
Otherwise, it will overflow.
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Identify a pair of overlapping congruent triangles in the
diagram. Then use the given information to write a proof
to show that the triangles are congruent.
Proof
Given: AC = BC, LA = LB
Answer:
overlapping congruent triangles:
ΔACE ≅ ΔBCD
Proof:
given: AC ≅ BC, angle A ≅ angle B
angle ACB ≅ angle BCA by the reflexive property
ΔACE ≅ ΔBCD by the ASA triangle congruence property
BC and DE are tangents to this circle. Work out the size of angle 0. Give reasons for your answer. A 52° B O D 27° E 0 C Not drawn accurately BC and DE are tangents to this circle . Work out the size of angle 0 . Give reasons for your answer . A 52 ° B O D 27 ° E 0 C Not drawn accurately
Answer:
Θ = 39°
Step-by-step explanation:
OA = OB ( radii of the circle ) , then
Δ AOB is isosceles with base angles congruent , that is
∠ ABO = ∠ BAO = 52°
the exterior angle of a triangle is equal to the 2 opposite interior angles.
∠ DOB is an exterior angle of the triangle , so
∠ DOB = ∠ ABO + ∠ BAO = 52° + 52° = 114°
the angle between a tangent and the radius at the point of contact is 90°, then
∠ OBC = ∠ ODE = 90°
the sum of the 4 interior angles of quadrilateral OBCD = 360°
∠ OBC + ∠ DOB + ∠ ODC + ∠ BCD = 360°
90° + 114° + (90 + 27)° + Θ = 360°
90° + 114° + 117° + Θ = 360°
321° + Θ = 360° ( subtract 321° from both sides )
Θ = 39°
9. Solve for x: Please explain
Answer:
since the triangle has a line on 2 sides, it means that it is equal. Also, every triangle has 180 degrees so the missing degree is 70
Step-by-step explanation:
Figured it out
Answer:
x = 70°
Step-by-step explanation:
Since 2 sides are marked as congruent then the triangle is isosceles with 2 base angles being congruent , both 55°
the sum of the 3 angles in the triangle = 180° , so
x + 55° + 55° = 180°
x + 110° = 180° ( subtract 110° from both sides )
x = 70°
The image of ΔABC after a reflection across Line E G is ΔA'B'C'.
2 triangles are shown. Line E G is the line of reflection. Line segment D D prime has a midpoint at point F. Line segment C C prime has a midpoint at point G. Points B and B prime share a point. Angle C G F is a right angle.
Which triangle must be a right triangle and why?
ΔA'B'C' is right because it is the image of ΔABC.
ΔADC is right because AA' intersects AC at A.
ΔBCC' is right because B lies of the line of reflection.
ΔBGC is right because Line E G is perpendicular-to CC'.
ΔDGC is right because Line E G is perpendicular-to CC', Option D is the correct answer.
What is Reflection ?Reflection along a line is plotting a new object as a mirror image of the original object .
It is given that the there are two Triangles , ABC and A'B'C' as an image.
The figure is attached with the answer.
D is the mid point of the line joining BB'
As the line of reflection is always perpendicular to the object and the image.
And as it is given that C G F is a right angle.
Therefore triangle DGC is right angled triangle , (the option given in the question is incorrect ) , Line E G is perpendicular-to CC'.
Option D is the correct answer.
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Answer:
D
Step-by-step explanation:
8.
36.2
22.3
- 30-
33
Find the value of x.
(Round answer to the nearest tenth when necessary)
44.6
33.2
Answer:
36.2
Step-by-step explanation:
Assuming that the dotted line is a perpendicular bisector, we can say that it splits the side that is 30 units long into 2 sets of 15 units. Then, we can use the pythaogrean theorem to solve (Leg A is 33 and Leg B: 15). a^2+b^2=c^2
33^2+15^2=c^2
1089+225=c^2
1314=c^2
Square root of 1314 = square root of c^2
36.2 aapproximately c
What is the nth term rule of the linear sequence below?
27, 25, 23, 21, 19, ...
Answer:
Step-by-step explanation:
Comment
This is an arithmetic series. It has the following givens.
a = 27 The first term
d = - 2 The difference between one term and the one behind it.
n = quite small
Tn = a + (n - 1)*d
tn = 27 - 2n + 2
tn = 29 - 2n
f(x)=x+2 g(x)=x-4
(f g)(x) =
O2x-2
O²-8
02-2x-8
Ọ x2+2x-8
Solve for (f g)(x)
Step-by-step explanation:
please mark me as brainlest
The new function (fog)x will be x - 2.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
To find (f g)(x), we need to evaluate f(g(x)).
First, we need to find g(x):
g(x) = x - 4
Next, we substitute g(x) into f(x):
f(g(x)) = f(x - 4)
Now we can simplify:
f(x - 4) = (x - 4) + 2
f(g(x)) = x - 2
Therefore, (f g)(x) = x - 2.
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There are x boys in a class. If the
number of girls are 3x + 1, how many
boys and girls are in the class
altogether.
Answer:
4x+1
Step-by-step explanation:
3x+x+1=4x+1
Which transformation would be a horizontal reflection and a dilation of scale factor ½ of the L shape?
The transformation which would be a horizontal reflection and a dilation of scale factor ½ of the L shape is as in the attached image.
What is horizontal reflection and dilation?The term horizontal reflection with respect to transformation in mathematical context simple means that the shape is reflected over the vertical axis(y-axis as mirror). The dilation of a scale factor of ½ simply means that the shape reduces to half it's original size.
Hence, it follows that the attached image represents the transformation.
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80 pupils in a sports centre are surveyed. the pupils can only use the swimming pool and the gym. 32 pupils use the swimming pool. 43 pupils use the gym. 19 pupils use neither the swimming pool nor the gym. find the probability to select a pupil that uses the swimming pool but not the gym.
[tex]\frac{18}{80}[/tex] is the probability of pupil that uses the swimming pool but not the gym.
It is given that:
Total students are 80
32 pupils use the swimming pool
43 pupils use the gym
19 pupils use neither the swimming pool nor the gym
To know the pupils who use both add 32+43 = 75
75-61= 14 pupils use both
32-14 = 18 pupils use only the swimming pool
43-18= 29 pupils use only the gym
Hence, [tex]\frac{18}{80}[/tex] is the probability of pupil that uses the swimming pool but not the gym.
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+
Carla babysits and tutors to make extra money. She babysits for $5 an hour and tutors for $10 an hour.
She can only work at most 15 hours a week. She wants to go on a trip with her friend and needs to
make $95 dollars this week to cover the cost of the trip. Write a system of inequalities to represent this
situation.
The system of inequalities to represent this situation will be x + y ≤ 15 and 5x + 10y ≤ 95.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Carla babysits and tutors to make extra money.
She babysits for $5 an hour and tutors for $10 an hour.
She can only work at most 15 hours a week.
Likewise, she wants to go on a trip with her friend and needs to make 95 dollars this week to cover the cost of the trip.
Then the system of inequalities to represent this situation will be
Let x be the number of babysits hours and y be the number of tutor's hours.
x + y ≤ 15
5x + 10y ≤ 95
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help grade 5 math please only answer if you know and if it’s right ill mark brainliest and please fast extra points who explain it
Answer:
[tex]\frac{42}{8}[/tex]
Step-by-step explanation:
7/8 <> 0.875
0.875 * 6 = 5.25
5.25 <> 42/8
(<> is used to show decimal to fraction and vice versa [the other way around])
w and x are whole numbers
w>60
x<50
Work out the smallest possible value of x-z
Using the given information, the smallest possible value of x - z is 12
Evaluating an expressionFrom the question, we are to determine the smallest possible value of x - z
From the given information,
w and x are whole numbers
and
w > 60
x < 50
∴ w = 61, 62, 63, 63, 65, ...
x = 49, 48, 47, 46, 45, ...
Then,
The smallest possible value of x - z is
x - z = 61 - 49
x - z = 12
Hence, the smallest possible value of x - z is 12
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4 kg 2 dag when converted in g gives you?
Answer:
4020 grams
Step-by-step explanation:
4kg=4000g
2 dag= 20g
Total: 4000g + 20g = 4020g
Answer:
4020 grams
Step-by-step explanation:
1 kg = 1000 g
1 dag = 10 g
4 x1000= 4000
2 x 10 = 20
4000 + 20
Last week, you went to the water park with friends on Monday, Wednesday, and Friday. If you stayed at the water park 3.5 hours each of those days, how many hours did you spend at the water park last week?
A. 15 hours
B. 9 hours
C. 5.5 hours
D. 10.5 hours
Answer: D. 10.5 hours
Step-by-step explanation:
3 days, 3.5 hours each
3.5 * 3 = 10.5 hours
Answer:
D. 10.5
Step-by-step explanation:
3.5 x 3 = 10.5
Write and solve a proportion to complete the statement. Round to the nearest hundreth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help
The conversion of the following units are done below.
6 km = 3.72 miles2.5 L = 0.65 gallons90 lb = 40.5 kgWhat is conversion?Conversion means to convert the same thing into different units.
We know the following unit's conversion.
1 km = 0.62 miles
6 km = 3.72 miles
1 L = 0.26 gallons
2.5 L = 0.65 gallons
1 lb = 0.45 kg
90 lb = 40.5 kg
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(PLEASE HELP!) A rectangular photograph measures 24x19 cm. It is mounted on a card of size such that there is a 2 cm border all around. For the purposes of this question take the length of the photograph to be 24 cm.
If one of the borders must be 2 cm in width, determine the width of a possible length and width so that the inner and outer rectangles are similar.
Answer: The card is 28 cm by 23 cm
Check out the diagram below
Explanation:
I added 4 cm to each dimension of the "24 x 19". Why 4 instead of 2? Because we're effectively adding two copies of "2 cm" to each of the original length and width. Along the horizontal component, we have the left and right boundaries. Along the vertical component, we have the top and bottom boundaries. The diagram hopefully clears up any confusion you may have.
How many solutions does the following equation have?
7(y+3)=5y+8
A. No Solution
B. Exactly One Solution
C. Infinitely many solutions
Answer:
B. Exactly One Solution
Step-by-step explanation:
Given:
[tex]7(y+3)=5y+8[/tex]
Expand the brackets:
[tex]\implies 7y + 21 = 5y + 8[/tex]
Subtract 21 from both sides:
[tex]\implies 7y + 21-21 = 5y + 8-21[/tex]
[tex]\implies 7y=5y-13[/tex]
Subtract 5y from both sides:
[tex]\implies 7y-5y=5y-13-5y[/tex]
[tex]\implies 2y=-13[/tex]
Divide both sides by 2:
[tex]\implies \dfrac{2y}{2}=\dfrac{-13}{2}[/tex]
[tex]\implies y=-\dfrac{13}{2}[/tex]
Therefore, the equation has exactly one solution.
Matt is trying to measure the height of a tree using
trigonometry. He is having trouble because of the
terrain around the tree. The horizontal distance
from the tree to Matt's eyes is 120 feet. The angle
of depression from the horizontal is 30°. Matt's
angle of sight to the top of the tree is 23°. What is
the height of the tree? (Round to the nearest foot.)
The height of the tree will be 18.35 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Matt is trying to measure the height of a tree using trigonometry.
He is having trouble because of the terrain around the tree.
The horizontal distance from the tree to Matt's eyes is 120 feet.
The angle of depression from the horizontal is 30°.
Matt's angle of sight to the top of the tree is 23°.
The diagram is given below.
Let x be the height of tree and AM be h.
The value of (h + x) will be
tan 30° = (x + h) / 120
x + h = 69.288
Then the value of h will be
tan 23° = h / 120
h = 50.94 feet
Then the height of the tree will be
⇒ h + x – h
⇒ 69.29 - 50.94.
⇒ 18.35 feet
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Find the variance of the given
data rounded to the nearest
hundredth.
3, 4, 5, 7, 10, 12, 15
Σ (x - mean)²
n
0²
0²
=
=
[?]
Enter
Answer:
17.14
Step-by-step explanation:
You have the data values {3, 4, 5, 7, 10, 12, 15}
To find the mean, [tex]\frac{3+4+5+7+10+12+15}{7} =8[/tex], yay a whole number, my favorite.
Then, [tex](3-8)^2+(4-8)^2+(5-8)^2+(7-8)^2+(10-8)^2+(12-8)^2+(15-8)^2=120[/tex].
Since n=7, σ^2≈[tex]17.14[/tex]
Let f(x)=6/-2+2e^-0.3x. what is f(4)? enter your answer rounded to the nearest tenth
The value of the function f(x)=6/-2+2[tex]e^{-0.3x}[/tex] at x=4 after rounded to the nearest tenth is -2.4.
Given Function of x : f(x)=6/-2+2[tex]e^{-0.3x}[/tex]
The given function showing the relationship between x and f(x) is f(x)=6/-2+2[tex]e^{-0.3x}[/tex] where e is exponential and we have to find the value of f(4) by just putting the value of x=4 in the given function and round to the nearest tenth means replacing a number with an approximate value.
f(4)=6/-2+2[tex]e^{-0.3*4}[/tex] ( The value of e is 2.7812)
f(4)=-3+2[tex]e^{-1.2}[/tex]
f(4)=-3+2*0.30119 (The value of [tex]e^{-1.2}[/tex] is 0.30119)
f(4)=-3+0.60238
f(4)=-2.3972
Round -2.3972 to tenth is -2.4.
Hence the value of function of at x=4 is -2.4.
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The value of f(4) is -4.3.
The function is a relation between two different sets X and set Y which are in one-one or many-one relation. Here set X is called as the domain and set Y is called as the codomain.
For example: f(x)=3x+9
To get the value of the function at any point of x, we have to put the number in the function to get its function value.
For example the value of f(x) in above function at x=a will be f(a)=3a+9
Similarly given function in the question
[tex]f(x)=\frac{6}{-2+2e^{-0.3x}}[/tex]
to get the value of f(x) at x=4 put the value of x in the function,
[tex]f(x)=\frac{6}{-2+2e^{-0.3*4}}[/tex]
⇒[tex]f(x)=\frac{6}{-2+2e^{-1.2}}[/tex]
⇒f(x)=-4.3
Therefore the value of f(4) is -4.3.
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Find the simplified product. b-5/2b X b^2+3b/b-5
The simplified product of [tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5}[/tex] is [tex]\frac{(b+3)}{2}[/tex]
How to simplify a product?The products can be simplified as follows;
Multiplying fraction,
[tex]\frac{x}{y} . \frac{a}{b} = \frac{xa}{yb}[/tex]
Therefore,
[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)}[/tex]
Hence,
Let's reduce the fraction by dividing
[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)}[/tex]
Therefore,
[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)} = \frac{(b(b+3))}{2b}[/tex]
Hence,
[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)} = \frac{(b(b+3))}{2b} = \frac{b+3}{2}[/tex]
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Answer:
A, b+3/2
Step-by-step explanation:
Which of the following objects is considered to be one-dimensional because it ha length but no width or height?
A. Line segment
B. Point
C. Triangle
D.Cube
Which of the following is equivalent to
(16 3/2)^1/2 ?
O 6
O 8
O 12
O 64
Step-by-step explanation:
[tex] = { ({16}^{ \frac{3}{2} } )}^{ \frac{1}{2} } [/tex]
[tex] = { ({( {2}^{4}) }^{ \frac{3}{2} } )}^{ \frac{1}{2} } [/tex]
[tex] = {2}^{4 \times \frac{3}{2} \times \frac{1}{2} } [/tex]
[tex] = {2}^{ \frac{12}{4} } [/tex]
[tex] = {2}^{3} [/tex]
[tex] = 2 \times 2 \times 2[/tex]
[tex] = 8[/tex]
The answer is B.
can someone please help and explain its due in a littleee
Answer:
slope = 3
y-intercept: -4
explanation on how to graph given in step-by-step explanation
Step-by-step explanation:
y=3x-4 is given in slope-intercept form which is y=mx+b where m is the slope and b is the y-intercept (when x = 0)
So the first coordinate that is easy to graph is the y-intercept since it's just (0, b) or in this case (0, -4). So that's the first point you graph. Now from here you can use the slope to graph all the other points. The slope is 3, which essentially means every time x increases by 1, the y-value increases by 3. So from the y-intercept (0, -4) you're going to go one unit to the right and three units up which should give you the coordinates (1, -1). Then from that coordinate go one unit to the right and three units up which should get you (2, 2) then from that coordinate go one unit to the right and three units up which should get you to (3, 5). Now go back the y-intercept (0, -4) and instead of going to the right 1 and up 3 you're going to do the inverse and instead go left 1 and down 3. So from (0, -4) go to the left one unit and down 3 units which should get you to (-1, -7). And now with all these points plotted draw a line through all of them
