The perimeter of the triangle ABC is [tex]10+\sqrt{10}[/tex] [tex]units[/tex].
The given parameters:
Triangle ABC = Isosceles triangleThe length of AC = 3-(-2) = 5 unit
The length of AC = length of BC = 5 unit
The length of BC is calculated by applying Pythagoras theorem as follows;
[tex]BC^2=(4-1)^2+(3-2)^2[/tex]
[tex]BC^2=3^2+1^2[/tex]
[tex]BC^2=10[/tex]
[tex]BC=\sqrt{10}[/tex]
The perimeter of the triangle ABC is calculated as follows;
[tex]P=AB+AC+BC[/tex]
[tex]P=5+5+\sqrt{10}[/tex]
[tex]P=10+\sqrt{10[/tex] [tex]units[/tex]
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“for each expression find value that could be added as a constant term to make each expression a perfect square” these are two separate questions please help
Step-by-step explanation:
here you go hopefully it helps
The width of the desk is 7 in. The perimeter of the desk is 63 in. What is
the length of the desk?
The formula to find the perimeter of a rectangle is as follows:
[tex]P=2l+2w[/tex]
[tex]l[/tex] = length[tex]w[/tex] = widthSolving the QuestionWe're given:
[tex]w[/tex] = 7 inches[tex]P[/tex] = 63 inchesWe are solving for [tex]l[/tex]⇒ Plug the given information into the perimeter formula and solve for l:
[tex]P=2l+2w\\63=2l+2(7)\\63=2l+14\\49=2l\\l=24.5[/tex]
AnswerTherefore, the length of the desk is 24.5 inches.
Factorise
x2 + 11x + 30
What is the answer
Answer:
it's 13x+30
Step-by-step explanation:
A manufacturer sells mirrors in the shapes of squares. The smallest size mirror the manufacturer sells has an area of 4 ft ^2. The largest size mirror has an area of 9 ft^2.
which graph represents the possible side lengths of the mirror sold by the manufacturer.
The domain of the graph of the that represents the side length of the mirror is 2 ≤ x ≤3
How to determine the graph?The given parameters are:
Shape = SquareSmallest area = 4ft²Largest area = 9ft²The area (y) of a square of side length x is:
y = x²
Make x the subject
x = √y
When y = 9, we have:
x = √9 = 3
When y = 4, we have:
x = √4 = 2
This means that the domain of the graph of the that represents the side length of the mirror is 2 ≤ x ≤3
See attachment for the graph
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Line contains points a,b, and c from left to right. ac =60 bc 2times ab
Answer:
AB=20, BC=40
Step-by-step explanation:
Let AB be x
Therefore, ATQ:
x+2x=60
x=60/3=20
AB=20
And BC =2(AB)
So BC=2*20=40
What is the range of the function y=√x+5?
O y≥-5
O y≥0
O yz√√5
O y≥5
It's not clear what is under the square root. Is it solely the x only?
In other words, is the equation this: [tex]y = \sqrt{x}+5[/tex] ?
If so, then the range is y≥5 because y = 5 is the smallest possible output. In other words, we can have y = 5 or y > 5. I recommend using a tool like Desmos to graph and verify.
-----
OR is the +5 also under the square root?
Is the equation this? [tex]y = \sqrt{x+5}[/tex]
If so, then the range would be y≥0
The smallest output possible of a square root function is 0. We cannot get negative outputs. This explains how y = 0 is the smallest output. So y = 0 or y > 0, or in short, y≥0
The solution is, the range of the function y=√x+5 is y∈(∞,∞) is Range, from the given options y≥0.
What is range ?The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
here, we have,
we know that,
Range of a function is defined as those values of y, for which x is Defined.
The given function is
y=√x+5
Squaring both sides
we get,
y² = x+5
or, x = y²- 5
x is defined for ,all Real values of y.
For any real y,we get defined value of x.
That is , y ∈ R
→→y∈(-∞,∞)⇒Range
Hence, The solution is, the range of the function y=√x+5 is y∈(∞,∞) is Range, from the given options y≥0.
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If f(x)= 5x-1 and g(x)=3x+2, find f(g(x)).
Pls help me!!
Answer:
15x+9
Step-by-step explanation:
f(g(x))
=f(3x+2)
=5(3x+2)-1
=15x+9
Write the coordinates of the vertices
after a reflection over the line y = -4.
Answer:
--------------------------- HeyA --------------------------
Explanation :
- GiveN :
C( 8 , -4 ) , D( 9 , -4 ) , E( 9 , 1 ) & F( 8 , 1 ) are the vertices of the given rectangle.Reflection in the line y = k :
P( x , y ) ----------------------P'( x , 2k - y )
C( 8 , -4 ) ----------------------C'( 8 , -4 ) D ( 9 , -4 ) ----------------------D' ( 9 , -4 ) E ( 9 , 1 ) ----------------------- E' ( 9 , -9 )F ( 8 , 1 ) ----------------------- F' ( 8 , -9 ) C' ( 8 , -4 ) , D'( 9 , -4 ) , E' ( 9 , -9 ) & F'( 8 , -9 ) are the coordinates of the vertices after a reflection over the line y = -4 .-----------------HappY LearninG <3 -----------------
Which of the following terms appear in the expansion of (x + y) 10? The letter a
in each term represents a real constant
A. axbys
B. ays
c. axy
D. axs
What is the area, measured in square centimeters, of the green shape
pictured below? Do not include units in your answer.
Answer:
21
Step-by-step explanation:
To find the area of a parallelogram, we can split this shape up into a rectangle and two right triangles.
The rectangle:
The rectangle has dimensions of 4 by 3 centimeters therefore the area would be 4*3=12 cm squared
two right triangles:
The area of a triangle is 1/2 base * height, but since there are two triangles it would just be the base times the height. The base is 3 cm and the height is 3 so 3*3=9
Next, we add the two areas together: 12+9 = 21
Can someone help me with this and pls explain how u did it if you’re able to I don’t need an explanation but it would be appreciated I’ll give brainliest if it’s correct
[tex]\huge{\green}\fcolorbox{blue}{cyan}{\bf{\underline{\red{\color{red}Answer}}}}[/tex]
To find :-
The value of x
Given :-
Here 2 angles are given
142°, and (3x + 22)°
Solution :-
We can see here the 2 lines intersect each other.
And the angle is formed
Since the angles are just opposite to each other so they are equal.
142° = (3x + 22)° {vertically opposite angles}
[tex]142 - 22 = 3x \\ 120 = 3x \\ \frac{120}{3} = x \\ 40 = x[/tex]
Result :-
The value of x is 40°.
please help me asap!!
8. Compare the function g(x) modeled by the graph and the functionf (x) =
21x + 2) + 3.
True or false. Explain.
a) f(x) has a greater y intercept
b) g(1) > f(-1)
c) f(x) increases at a faster rate than g(x)over interval [0, 3).
Answer:
a) false
b) true
c) true
Step-by-step explanation:
Part (a)The y-intercept of a function is the point when x = 0
⇒ f(0) = 2|0 + 2| + 3
= 2|2| + 3
= 4 + 3
= 7
From inspection of the graph, the y-intercept of g(x) is (0, 7)
Therefore, the y-intercepts of f(x) and g(x) are the same.
"f(x) has a greater y-intercept" → false
Part (b)
From inspection of the graph, g(1) = 6
⇒ f(-1) = 2|-1 + 2| + 3
= 2|1| + 3
= 2 + 3
= 5
Therefore, g(1) > f(-1) → true
Part (c)The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
From inspection of the graph:
g(0) = 7
g(3) = 4
[tex]\textsf{average rate of change of g(x)} \implies \dfrac{4-7}{3-0}=-1[/tex]
f(0) = 7 (from part (a))
f(3) = 2|3 + 2| + 3
= 2|5| + 3
= 10 + 3
= 13
[tex]\textsf{average rate of change of f(x)} \implies \dfrac{13-7}{3-0}=2[/tex]
Function g(x) decreases over [0, 3] at the rate of -1
Function f(x) increases over [0, 3] at the rate of 2
Therefore, "f(x) increases at a faster rate than g(x) over interval [0, 3]" is true
**Please see the attached graph for reference**
The interval [0, 3] is shaded in grey
f(x) is shown in red
The added 2 points are f(-1) and g(1)
HELP PLEASE HELP PLEASE
Answer:
D 1/4
Step-by-step explanation:
Your question is a problem in reading comprehension. It tells you its own answer.
x is always 1/4
SOMEBODY HELP ME PLSSS
Answer:
5.88*10^12
Step-by-step explanation:
You have to move the decimal place over 12 times and to the left, so it's positive.
Ahab jumped 2 times in 4 minutes. at that rate, how many times would he jump in 9 hours?
Answer: 270
Step-by-step explanation: 20 mins = 10 jumps now 20x3 is 60 which is an hour so in an hour he would have jumped 30 times and if you times 30 with 9 you would get 270 hence your answer
How do I do step by step
Answer:
1.1
Step-by-step explanation:
Write out a long division problem! Since you can't have a decimal in the divisor, multiply both numbers by 10. This will leave you with 39.6÷36. Now all you have to do is follow the steps and end up with an answer of 1.1
A pack of red pens can be divided into equal shares among 3, 5, 6 and 9 teachers with no pen left over?
Answer:
90 red pens
Step-by-step explanation:
we need to find the least common multiple of the numbers 3 , 5 , 6 , 9
6 = 2 × 3
9 = 3²
then
LCM(3,5,6,9) = 2×5×3² = 2×5×9 = 90
The number 90 can be divided into 3 ,5 ,6 ,9 with no remainder
Therefore the pack must have 90 pens or a multiple of 90
For example 180 , 270 ...
A prism is completely filled with 270 cubes that have edge length of 13
in.
What is the volume of the prism?
Answer:
593190 cubic inches
Step-by-step explanation:
to solve this equation you must first find out the volume of one cube
that can be modeled by 13*13*13 or more simply 13^3
13^3 = 2197
then you multiply that to 270
2197 * 270 = 593190
that is your answer
I need help ASAP please
Data were recorded for a car’s fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour (mph). Scatterplot A displays the relationship between the car’s speed and fuel efficiency. Two transformations of the data are shown in scatterplots B and C. Scatterplot B displays the relationship between the car’s speed and the natural log of the fuel efficiency. Scatterplot C displays the relationship between the natural log of the car’s speed and the natural log of the fuel efficiency.
Which scatterplot best represents the relationship between a car’s speed and its fuel efficiency?
A linear model would best represent the relationship because scatterplot A is fairly linear.
An exponential model would best represent the relationship because scatterplot B is fairly linear.
A power model would best represent the relationship because scatterplot C is fairly linear.
A linear model would best represent the relationship because scatterplot C is fairly linear.
Answer:
A power model would best represent the relationship because scatterplot C is fairly linear.
Step-by-step explanation:
I think that is the answer but I am not sure between option 2 and 3. I would eliminate linear models for this graph for sure.
I hope I helped you a little!
Have a nice day! :)
Triangle LMN was dilated to create L’M’N. The coordinates of the pre-image and the image are shown in the table belowL(0,4) M(0.8) N(5.10) L’(0,10) M’(0,20) N’(12.5,25) find the scale favor that used in the dilation record your answer on the gird
Answer:
L'M'N' is scaled by 2.5
Step-by-step explanation:
10 / 4 = 2.5
20 / 8 = 2.5
salaries of 38 college graduates who took a statistics course in college have a mean, x, of $69,800. assuming a standard deviation, o, of $16,094, constructs a 95% confidence interval for estimating the population mean u.
Answer:2,652,400
Step-by-step explanation:
SOMEONE PLEASE HELP
Describe how the variable h and the variable k of the general formula for a cube root function effects the graph. The general formula is y=a^3sqrt x-h+k
Using translation concepts, it is found that the variable h shifts the function horizontally while the variable k shifts the function vertically.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The cube root function is given by:
[tex]y = \sqrt[3]{x}[/tex]
The translated function is given by:
[tex]y = \sqrt[3]{x - h} + k[/tex].
The variables work as follows:
Variable h is in the domain, hence it changes the function horizontally.Variable k is in the range, hence it changes the function vertically.More can be learned about translation concepts at https://brainly.com/question/4521517
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A scientist studying earth's rotation determines that a specific location on earth's equator travels about 40,000 kilometers in one day. What is the approximate speed of the location, in miles per hour, due to earth's rotation
Answer:
Step-by-step explanation:
Discussion
The first thing you have to do is convert km to miles
Formula
1 mile = 1.6 km
x mile = 40000 km Cross Multiply
Solution
1.6*x = 1 * 40000 Divide by 1.6
x = 40000/1.6
x = 25000 miles
Answer Part 1
The distance covered is 25000 miles
Discussion Part 2
That's the distance covered in a day. Now we need to convert that to speed. The time (in hours) for 1 day is 24 hours.
Givens
d = 25000 miles
t = 24 hours
s = ?
Solution
s = d/t
s = 25000 / 24
s = 1041.66 miles per hour
Answer: 1041.66 is what is to be entered as your answer
(x - 2)2 + (y +13)2 = 150
Center:
Radius:
Answer:
Center: (2, -13)
Radius: 5√6
Explanation:
Equation: (x - 2)² + (y +13)² = 150
Circle Formula:
(x - h)² + (y - k)² = r²
where (h, k) is the center points, r is radius
Rewrite the equation:
(x - (2) )² + (y - (-13))² = (√150)²
Identify following's:
h = 2, k = -13, radius = √150 = 5√6
What is the answer to this question: 100 + 100?
Answer:
200
Step-by-step explanate
100+100 = 200
used a calculator
The astronauts of Expedition 28 on the international Space Station spend 15 weeks in space. Convert the time to minutes.
4) Find the area of a
rectangular poster (in cm²)
that is 95 cm by 45 cm.
PLS HELPPPP
Answer:
I think it is 4275cm square.
Answer:
Area= 4275cm
Step-by-step explanation:
The area formula for a rectangle is length x width so if we plug in the numbers and multiply we get 4275 as our product.
A rectangular prism has a length of 4 in., a width of 2 in., and a height of 2 1/2 in.
The prism is filled with cubes that have edge lengths of 1/2 in.
How many cubes are needed to fill the rectangular prism?
Enter your answer in the box.
Answer:
160
Step-by-step explanation:
Each cube is 1/2 inch, so there will be 2 cubes in each 1 inch of length. The dimensions of the prism in terms of the number of cubes are ...
length: 4 in ⇒ 4×2 = 8 cubes
width: 2 in ⇒ 2×2 = 4 cubes
height: 2 1/2 in ⇒ (2 1/2)×2 = 5 cubes
Then the number of cubes required to fill the prism is ...
8 × 4 × 5 = 160 . . . . cubes
The volume of the prism is equivalent to that of 160 1/2-inch cubes.
What is the correct answer for the problem 3.12 x 4.0
Hi Brielle the correct answer to your question is 3.12 x 4.0 = 12.48
12.48
Your answer should be 12.48 I hope that helps you