if mnp has vertices at m (-5,-7) , N (7,-2) andcp (2,10) is mnp isoscles?
Answers
now, clearly the longest side is MP, and for a triangle to be an isosceles, it has to have two equal sides, so two sides must be twins.
since MP is the longest one, that only leaves out NP and NM, are they twins?
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &N&(~ 7 &,& -2~) % (c,d) &P&(~ 2 &,& 10~) \end{array}\\\\\\ % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ NP=\sqrt{[2-7]^2+[10-(-2)]^2}\implies NP=\sqrt{(2-7)^2+(10+2)^2} \\\\\\ NP=\sqrt{(-5)^2+12^2}\implies NP=\sqrt{25+144}\implies \boxed{NP=13}[/tex]
and now let's check NM
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &N&(~ 7 &,& -2~) % (c,d) &M&(~ -5 &,& -7~) \end{array}~~~ \\\\\\ NM=\sqrt{[-5-7]^2+[-7-(-2)]^2}\\\\\\ NM=\sqrt{(-5-7)^2+(-7+2)^2} \\\\\\ NM=\sqrt{(-12)^2+(-5)^2}\implies NM=\sqrt{144+25}\implies \boxed{NM=13}[/tex]
ΔMNP IS isosceles.
Related Questions
Which description best describes the graph?
A graph is shown. A straight line begins at the upper left side of the coordinate plane and moves down towards the right side. The line crosses the y-axis at y equals 3 and the x-axis at x equals 1.5
Linear increasing
Linear decreasing
Nonlinear increasing
Nonlinear decreasing
Answers
As the x-values increase, the y-values decrease; this means it is a decreasing graph.
The graph shows a straight line with a constant rate of change, so it is linear.
Answer:
B. Linear decreasing
Step-by-step explanation:
We are given that,
The graph of the function is passing through the points (0,3) and (1.5,0).
Then, the rate of change is [tex]m=\frac{0-3}{1.5-0}=\frac{-3}{1.5}=-2[/tex]
So, the function is represented by a straight line with constant rate of change -2.
Thus, the function is a linear function.Moreover, as the value of x is increasing, we see that the value of y is decreasing.
So, the function is a decreasing function.Hence, option B is correct.
Given f(x)=x2+14x+40 .
Enter the quadratic function in vertex form in the box.
f(x)=
Answers
the quadratic function in vertex form is--------------> y=a*(x-h)²+k
we have
f(x)=x²+14x+40
y=x²+14x+40
We can convert to vertex form by completing the square on the right hand side
y-40=x²+14x
y-40-49=x²+14x-49------> subtract 49 on BOTH sides to preserve the equality
y-40=(x²+14x+49)-49
y=(x²+14x+49)-49+40---------> y=(x+7)²-9
the answer is
the quadratic function in vertex form-----------> y=(x+7)²-9
the vertex is the point (-7,-9)
Answer: f(x) = (x+7)^2 -9
Step-by-step explanation:
I know that this is late but hopefully it will help someone else.
Place the indicated product in the proper location on the grid.
(3a + 2c )(9a 2 - 6ac + 4c 2 )
Answers
27a^3+8c^3
Explanation.
In this question you are expected to expand (3a+2c)(9a^2-6ac+4c^2
(3a+2c)(9a^2-6ac+4c^2
=(3a×9a^2 )-(3a×6ac)+(3a×4c^2 )+(2c×9a^2 )-(2c×6ac)+(2c×4c^2 )
27a^3-18a^2 c+12ac^2+18a^2 c-12ac^2+8c^3
27a^3+8c^3
The expansion of the expression, (3a+2c)(9a^2-6ac+4c^2) is 27a^3+8. This is what the question requires.
Answer:
The product of [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)=8c^3+27a^3[/tex]
Step-by-step explanation:
Given: Polynomial [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)[/tex]
We have to place the indicated product in the proper location o the grid.
Consider the given product [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)[/tex]
Using distributive property, Multiply each term of first bracket with each term of last bracket, we have,
[tex]=3a\cdot \:9a^2+3a\left(-6ac\right)+3a\cdot \:4c^2+2c\cdot \:9a^2+2c\left(-6ac\right)+2c\cdot \:4c^2[/tex]
Apply plus-minus rule [tex]+\left(-a\right)=-a[/tex] , we have,
[tex]=3\cdot \:9a^2a-3\cdot \:6aac+3\cdot \:4ac^2+2\cdot \:9a^2c-2\cdot \:6acc+2\cdot \:4c^2c[/tex]
Simplify, we have,
[tex]=27a^3-18a^2c+12ac^2+18a^2c-12ac^2+8c^3[/tex]
Adding similar terms, we have,
[tex]=8c^3+27a^3[/tex]
Thus, The product of [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)=8c^3+27a^3[/tex]
Location on grid is as shown below
Someone help with math?
Answers
The table shows the height of an object, h(t), in meters after t seconds. Use your calculator to find the quadratic function. Find the approximate time, to the nearest hundredth of a second, after which the object will reach its maximum height.
Answers
.. h(t) = -4.9t^2 +23.4t +120
The maximum height is reached at t=-23.4/(2(-4.9)) ≈ 2.39 seconds.
Round each number to the nearest hundred and estimate the sum.
1,841 + 964
2,900
2,800
2,700
2,600
Answers
964 ≈ 1000 (nearest hundred}
1,841 + 964 ≈ 1800 + 1000 = 2800 (Answer B)
Answer:
The answer is 2,800 (B)
Good Luck :)
Find the area of the shaded polygons:
Answers
now, notice, is really just a large triangle in red, with a base of 4 and a height of 3 units, and two smaller triangles below it, one has a base 1 and a height of 1, and the other has a base of 3 and a height of 1.
so just get the area of each, sum them up, and that's the shaded area.
The total area of the figure is 8 square units.
How to find the area?
Remember that the area of a triangle is equal to its height times its base over 2.
In the image we can see 3 triangles, the larger one has a height of 3 units and a base of 4 units, so its area is:
A = 3*4/2 = 6 square units.
The bottom left triangle has a base of 1 unit and a height of 1 unit, so its area is:
A' = 1*1/2 = 0.5 square units.
The bottom right triangle has a base of 3 units, and a height of 1 unit, so its area is:
A'' = 1*3/2 = 1.5 square units.
The total area is:
A + A' + A'' = (6 + 0.5 + 1.5) square units = 8 square units.
If you want to learn more about area, you can read:
https://brainly.com/question/24487155
3x - 5y = 17 y = -7 Solve by substitution.
Answers
.. 3x -5(-7) = 17
.. 3x +35 = 17
.. 3x = -18
.. x = -6
The solution is (x, y) = (-6, -7).
Find all solutions in the interval [0, 2π).
sec2x - 2 = tan2x
a) No solution
b) x = pi/3
c) x = pi/4
d) x = pi/6
Answers
sec²x - 2 = tan²x--------> equation 1
and we know
identity-----------> tan²x=sec²x-1------------> equation 2
I substitute 2 in 1
sec²x - 2 = sec²x-1----------> -2=-1---------> no solution
the answer is the option a) No solution
Explanation:
sec²x - 2 = tan²x
tan²x=sec²x-1
sec²x - 2 = sec²x-1
-2=-1
there is no solution
what is the factored form of the expression? w^2 + 12w + 36
Answers
Answer:
[tex](w+6)^2[/tex] is the factored form of the given expression.
Step-by-step explanation:
The given expression is:
[tex]w^2+12w+36[/tex]
Simplifying the above given expression, we get
[tex]w^2+6w+6w+36[/tex]
[tex]w(w+6)+6(w+6)[/tex]
[tex](w+6)(w+6)[/tex]
[tex](w+6)^2[/tex]
Which is the required factored form of the given expression.
A rectangular box contains 336 cubic inches. If it is 12 inches long and 7 inches wide, how deep is it?
Answers
Your answer is 4 inches deep :))
Hope this helps
Choose the graph that matches the following system of equations: 2x + y = −1 3x + 2y = −6
Select one:
a. picture of coordinate plane with line y equals negative 2x plus 1 and line y equals 3 halves x minus 6. They intersect at 2, negative 3
b. picture of coordinate plane with line y equals negative 2x minus 1 and line y equals negative 3 halves x minus 3. They intersect at 4, negative 9
c. picture of coordinate plane with line y equals 2x minus 1 and line y equals negative 3x minus 3. They intersect at negative 0.4, negative 1.8
d. picture of coordinate plane with line y equals negative 2x minus 1 and line y equals 3 halves x plus 6. They intersect at negative 2, 3
Answers
Firstly, we express both equations with y on the left hand side since all choices are in that form:
[tex]y=-2x-1[/tex]
[tex]y=- \frac{3}{2}x-3 [/tex]
Knowing these, we can immediately rule out options a, c, and d since they have the wrong equations. This will leave us with option b.
You can verify if the point of intersection provided in option b is true by plugging in the values of x and y to both equations (you will find that it is indeed true).
ANSWER: b. picture of coordinate plane with line y equals negative 2x minus 1 and line y equals negative 3 halves x minus 3. They intersect at 4, negative 9.
Answer:
B
Step-by-step explanation:
Got it right on the test
Hope this helps :)
How many 12 inch sections can you get out of 9 foot calculator?
Answers
1 foot = 12 inches.
Therefore doing the conversion:
(12 inch) * (1 foot / 12 inch) = 1 foot.
The number of sections is:
N = (9 feet) / (1 foot) = 9
Answer:
you can get out 9, 12 inch sections of 9 foot calculator
Question 2(Multiple Choice Worth 2 points)
(10.06 MC)
Compare the functions shown below:
f(x) = 4 sin (2x − π) − 1
g(x)
x y
−1 6
0 1
1 −2
2 −3
3 −2
4 1
5 6
h(x) = (x − 2)2 + 4
Which function has the smallest minimum y-value?
f(x)
g(x)
h(x)
Both f(x) and g(x) have the same minimum y-value.
Answers
Answer:
1. f(x)=4 sin (2 x-π)-1
=4 sin [-(π-2 x)] -1
= -4 sin 2 x -1
-1 ≤ sin 2 x ≤1
f(x) is minimum, when, sin 2 x=1
= -4 × 1 -1
= -5→Minimum value of f(x).
2. Minimum y value of g(x) by looking at the table is ,
g(x)=-3→Minimum
3. h(x)=(x-2)²+4
As, (x-2)², will yield always a positive value.
So, minimum of h(x), will be at , x=2
h(2)=(2-2)²+4=4→Minimum
Among the three function given, f(x) has minimum y -value,equal to -5.
Option A: f(x)
The angle of depression from D to F measures 10°. If DE = 300 m, find DF. Round your answer to the nearest tenth.
304.6 m
1,910.2 m
1,727.6 m
1,701.4 m
Answers
Answer:
Option C) 1727.6 m
Step-by-step explanation:
Given that the angle of depression from D to F measures 10°.
Also given that DE =300 m.
Since 10 is angle of depression, we can visualize a right triangle with hypotenuse DF=300 m and EF, DE two legs.
In the right triangle DEF, the angle opposite 10 is the side DE[tex]\frac{DF}{DE} =\frac{hypotenuse}{opposite side}= cosec 10\\\\DF =300 cosec 10 = 1727.6 m[/tex]
by Using trignometric ratios
Printer paper is sold in packages of 500 sheets. of a printing job uses 1 3/4 packages of paper how may sheets is that
Answers
[tex]1 \dfrac{3}{4} \text { package of papers = } 500 \times 1 \dfrac{3}{4} [/tex]
[tex]1 \dfrac{3}{4} \text { package of papers = } 500 \times \dfrac{7}{4} [/tex]
[tex]1 \dfrac{3}{4} \text { package of papers = } 875 \text { sheets}[/tex]
The printing job that uses 1 3/4 packages of printer paper requires 875 sheets.
To determine how many sheets of paper are used in a printing job that uses 1 3/4 packages of paper, follow these steps:
First, understand that 1 package contains 500 sheets of printer paper.Next, convert the mixed number 1 3/4 to an improper fraction. This is done by multiplying the whole number (1) by the denominator (4) and adding the numerator (3), giving us 7/4.Now, multiply the number of packages (7/4) by the number of sheets per package (500):7/4 * 500 sheets = (7 * 500) / 4 = 3500 / 4 = 875 sheets.
Therefore, the printing job uses 875 sheets of paper.
Find the length of the hypotenuse of a right triangle with legs of lengths 9 and 12 If necessary round your answer to two decimal places
Answers
[tex] {x}^{2} = {9}^{2} + {12}^{2} \\ {x}^{2} = 81 + 144 = 225 \\ x = \sqrt{225} = 15[/tex]
hope this helps
quick computing company produces calculators they have found that the cost c(x),of making calculators is a quadratic function in terms of x the company also discovers that it costs $45 to produce 2 calculators, $143 to produce 4 calculators, and 869 to produce 10 calculators FIND THE TOTAL COST OF PRODUCING 1 CALCULATOR
Answers
Answer:
$23
Step-by-step explanation:
We will use a quadratic regression to solve this.
Using a graphing calculator, put the number of calculators into the first list (x) and the cost to produce into the second list (y).
Next we run the quadratic (x^2) regression. Doing this gives us an equation in the form
y = ax²+bx+c. The values we are given for a, b and c are
a = 8.9999999999; b = -4.999999999999; c = 18.999999999
These can be rounded to a = 9, b = -5 and c = 19. This gives us the equation
y = 9x²-5x+19
Substituting 1 in place of x, we have
y = 9(1²)-5(1)+19 = 9(1)-5+19 = 9-5+19 = 4+19 = 23
Determine if x + 3 is a factor of -3x^3+6x^2+6x+9, and how do you know?
Answers
-3(x^3 - 2x^2 - 2x - 3)
If x + 3 is a factor, what is inside the brackets should be 0 when x = - 3 It is not. There is only one real root and that is when (x - 3) is equated to 0. Just to show the root is +3, the graph is included.
Each chef at "sushi emperor" prepares 151515 regular rolls and 202020 vegetarian rolls daily. on tuesday, each customer ate 222 regular rolls and 333 vegetarian rolls. by the end of the day, 444 regular rolls and 111 vegetarian roll remained uneaten. how many chefs and how many customers were in "sushi emperor" on tuesday?
Answers
.. 15c -2q = 4
.. 20c -3q = 1
we find that c=2 and q=13 are common solutions.
There were 2 chefs and 13 customers on Tuesday.
_____
It looks like this is better solved using proportions, since the ratio of roll production is different than the ratio of roll consumption. There can only be one solution.
.. (15c-4)/(20c-1) = 2/3 . . . . the ratio of rolls produced is the same as the ratio of rolls consumed
.. 3(15c -4) = 2(20c -1)
.. 45c -12 = 40c -2
.. 5c =10
.. c = 2 . . . . there were 2 chefs
They produced 30 rolls, of which 4 were left and the remaining devoured 2 at a time. Hence there were
.. (30 -4)/2 = 13 customers.
Answer:
There were 2 chefs and 13 customers.
Step-by-step explanation:
Bailey writes 5 + 8 on the left-hand side of a paper and then writes 4 + 9 to the right of it. Which symbol should Bailey write between the two sets of numbers to show they have the same sum
a. +
b. –
c. ≠
d. =
Answers
13 = 13
ANSWER: D) =
The equals sign should be in between because the numbers on each side add up to the same number.
Hope this helps! :)
How do I solve this?
Answers
.. (-3/2)x^2 +0x +3
to the pattern of
.. ax^2 +bx +c
and you can see that
.. a = -3/2 . . . b = 0 . . . c = 3
____
Because a is negative, the parabola opens down. Because it opens down, the vertex is the high point, the maximum.
____
The y-intercept is always c. Here c=3, so the y-intercept is (0, 3).
____
The axis of symmetry is given by
.. x = -b/(2a)
.. x = -0/(2*(-3/2)) = 0
____
Because the y-intercept is on the axis of symmetry, it is the vertex.
.. vertex = (0, 3)
____
Put x=±2 in the equation and evaluate.
.. y = (-3/2)*(±2)^2 +3
.. = (-3/2)*4 +3
.. = -6 +3 = -3
The two points are (-2, -3) and (2, -3).
How many feet are in 100 meters if 1 meter is 1.09 yards? Will mark brainliest if you include clear steps. Thank you!
Answers
[tex]\bf 100~\underline{m}\cdot \cfrac{1.09~\underline{yd}}{\underline{m}}\cdot \cfrac{3~ft}{\underline{yd}}\implies \cfrac{100\cdot 1.09\cdot 3~ft}{1}\implies 327~ft[/tex]
notice, we use the ratio, and whichever unit you want cancelled, you simply flip the ratio to have it cancelled, if the "m" is atop and you need that cancel, use the ratio with the "m" at the bottom, m/m = 1, and so they cancel out, and so on.
If someone can answer this, you are BEYOND SMARTT!!! But tell me how to do it too!!!!
Answers
we know that at t = 0, the height of the rock is 16
choices H and I do not have a value of 16 at t = 0.
H: h(0) = -5.2(0)² + 24(0) - 12 = -12
I: h(0) = -4.2(0)² + 26(0) - 20 = -20
so we are left with F and G
if we take choice F and plug in t = 1
h(1) = -4.7(1)² - 25(1) + 16 = -13.7
if we take choice G and plug in t = 1
h(1) = -4.7(1)² + 25(1) + 16 = 36.3
only choice G works for us since it has 36.3 at t = 1
you could have also put these points in a graphing calculator and then use the quadratic regression feature to get an equation that will model this data
Polynomials are closed under the operation of subtraction.
Which statement best explains the meaning of closure of polynomials under the operation of subtraction?
A. When any two polynomials are subtracted, the coefficients of like terms are always subtracted.
B. When any two polynomials are subtracted, the result is always a polynomial with negative coefficients.
C. When any two polynomials are subtracted, the result is always a polynomial.
D. When any two polynomials are subtracted, the result is always a monomial or a binomial.
Answers
A polynomial is an expression consisting of variables and coefficients, that involves the operations of addition, subtraction, multiplication .
polynomials are closed under the operations of addition, subtraction, and multiplication.
Polynomials will be closed under an operation if the operation produces another polynomial.
The statement that best explains the meaning of closure of polynomials under the operation of subtraction is
option C. When any two polynomials are subtracted, the result is always a polynomial.
A plane begins to descend from a height of 202 meters. The plane decreases in altitude at an average rate of 1.8 meters per second. Which function can be used to find the altitude of the plane in meters x seconds since it started. Show work please!
Multiple choice :
F. t(x) = 202- 1.8x
G. t(x) -1.8 (x + 202)
H. t(x) = 202 + 1.8x
I. t(x) = 1.8 ( x + 202)u
Answers
All altitudes are in meters.
After 1 second, it is at 202 - 1.8
After 2 seconds, it is at 202 - 1.8 * 2
After 3 seconds, it is at 202 - 1.8 * 3
etc.
After x seconds, it is at 202 - 1.8 * x
202 - 1.8 * x is the same as 202 - 1.8x
Answer: F. t(x) = 202 - 1.8x
Twice the sum of two consecutive integers equals 42
Answers
Let's assume n the first integer
n+1 the greater
n+(n+1)=2n+1 is odd but 42 (universel answer in Robots IE) is even!!!!
Not answer!
The histogram shows the number of hours volunteers worked one week.
What percent of the volunteers worked 8 to 11 hours or 16 to 19 hours?
Enter your answer in the box.
%
Answers
Answer: 45%
Step-by-step explanation:
From the given histogram, The number of volunteers worked 8 to 11 hours = 5
The number of volunteers worked 16 to 19 hours = 4
The number of volunteers worked 8 to 11 hours or 16 to 19 hours =5+4=9
Total number of volunteers = 4+2+5+4+4+1=20
The percent of volunteers worked 8 to 11 hours or 16 to 19 hours is given by :-
[tex]\frac{9}{20}\times100=45\%[/tex]
Hence, the percent of the volunteers worked 8 to 11 hours or 16 to 19 hours =45%
Dan measures an object to the nearest fourth inch. He records the length as 4 1/4 inches. Geri measures the same object the nearest half inch. Could Dan and Geri get the same measurement? Explain.
Answers
Dan and Geri cannot get the same measurement for whatever object it is that Dan has measured. (They may get the same measurement on other objects.)
Elliot and Katy both bought the same lunchbox for $6. Elliot lives in Oklahoma and pays 4.5% in sales tax, while Katy lives in South Carolina and pays 6% in sales tax. How much more did Katy pay in sales tax than Elliot? A.$0.09 B.$0.27 C.$0.63 D.$0.36
Answers
Elliot pays a total of $0.27 in tax
Katy pays a total of $0.36 in tax
[tex]0.36 - 0.27 = 0.09[/tex]