Answer:
If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B
If Marguerite rents for 1 week, it will cost her the same at either company
h(x) = 5x - 5
Step-by-step explanation:
Marguerite wants to rent a carpet cleaner. Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. The following functions represent the rate structures of the two rental companies: x = the number of weeks Company A f(x) = 15(7x) Company B g(x) = 100x + 5 The function h(x) = f(x) – g(x) represents the difference between the two rate structures. Determine which statements about h(x) and about renting a carpet cleaner are true. Check all that apply. If Marguerite rents for 2 weeks, it will cost her more if she rents from Company B. If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B. If Marguerite rents for 1 week, it will cost her the same at either company. If Marguerite rents for 1 week, it will cost her more if she rents from Company A. h(x) = 5x – 5 h(x) = 5x + 5
Answer: Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. In one week there are 7 days, therefore in x weeks the cost of rentals are given below:
For company A: f(x) = 15(7x)
For company B: g(x) = 100x + 5
h(x) = f(x) – g(x) represents the difference between the two rate structures.
h(x) = f(x) - g(x) = 15(7x) - (100x + 5)
h(x) = 105x - 100x - 5
h(x) = 5x - 5
If Marguerite rents for 2 weeks:
The cost for company A = 15(7x) = 15(7 × 2) = $210
The cost for company B = 100x + 5 = 100(2) + 5 = 200 + 5 = $205
If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B
If Marguerite rents for 1 weeks:
The cost for company A = 15(7x) = 15(7 × 1) = $105
The cost for company B = 100x + 5 = 100(1) + 5 = 100 + 5 = $105
If Marguerite rents for 1 week, it will cost her the same at either company
Answer:
If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B.
h(x) = 5x + 5
those are the answers on edge
Step-by-step explanation:
6. Find d.
Please help
Answer:
Step-by-step explanation:
The first thing we are going to do is to fill in the other angles that we need to solve this problem. You could find ALL of them but all of them isn't necessary. So looking at the obtuse angle next to the 35 degree angle...we know that those are supplementary so 180 - 35 = the obtuse angle in the small triangle. 180 - 35 = 145. Within the smaller triangle we have now the 145 and the 10, and since, by the Triangle Angle-Sum Theorem all the angles have to add up to equal 180, then 180 - (10 + 145) = the 3rd angle, so the third angle is 180 - 155 = 25. Now let's get to the problem. If I were you, I'd draw that out like I did to keep track of these angles cuz I'm going to name them by their degree. In order to find d, we need to first find the distance between d and the right angle. We'll call that x. The reference angle is 35, the side opposite that angle is 12 and the side we are looking for, x, is adjacent to that angle. So we will use the tan ratio to find x:
[tex]tan(35)=\frac{12}{x}[/tex] Isolating x:
[tex]x=\frac{12}{tan(35)}[/tex] so
x = 17.1377 m
Now we have everything we need to find d. We will use 25 degrees as our reference angle, and the side opposite it is 12 and the side adjacent to it is
d + 17.1377, so that is the tan ratio as well:
[tex]tan(25)=\frac{12}{d+17.1377}[/tex] and simplifying a bit:
[tex]d+17.1377=\frac{12}{tan(25)}[/tex] and a bit more:
d + 17.1377 = 25.73408 so
d = 8.59, rounded
Solve by the quadratic formula: x^2= 6x-4
Answer:
3 [tex]\pm[/tex] [tex]\sqrt{5}[/tex].
Step-by-step explanation:
x^2 = 6x - 4
x^2 - 6x + 4 = 0
Now, we can use the quadratic formula to solve.
[tex]\frac{-b\pm\sqrt{b^2 - 4ac} }{2a}[/tex], where a = 1, b = -6, and c = 4.
[tex]\frac{-(-6)\pm\sqrt{(-6)^2 - 4 * 1 * 4} }{2 * 1}[/tex]
= [tex]\frac{6\pm\sqrt{36 - 4 * 4} }{2}[/tex]
= [tex]\frac{6\pm\sqrt{36 - 16} }{2}[/tex]
= [tex]\frac{6\pm\sqrt{20} }{2}[/tex]
= [tex]\frac{6\pm2\sqrt{5} }{2}[/tex]
= 3 [tex]\pm[/tex] [tex]\sqrt{5}[/tex]
x = 3 [tex]\pm[/tex] [tex]\sqrt{5}[/tex].
Hope this helps!
Please help me to solve this . Thank you so much .
And if possible , could you explain the answer too ?
Base on the diagram , state
a) The point which is 2 cm from R and 4 cm from P
b) The point which is more than 2 cm from R and 4 cm from T
c) The location of a moving point X in the diagram such that it is less than 4 cm from P and more than 2cm from R
d) The location of a moving point Y in the diagram such that YR < 2 cm and YP < 4 cm
e)The location of a moving point Z in the diagram such that ZT > 4 cm , ZP > 4 cm and ZR > 2 cm
Answer:
a) N
b) L
c) area I
d) area II
e) area VI
Step-by-step explanation:
a) the points that are 2cm from R are Q, N, M, S. Then, points that are 4cm from P are K, N, R. So, the only one point that works for both is N.
b) the points that are >2cm from R are P, K, L, T. We do not count those are exactly 2cm from R. Then, points that are 4cm from T are R, M, L. Ans is L.
c) <4cm from P, are area I and II. Then area that are >2cm from R are I, VI, and V. So, the only area that works for both is I.
d) <2cm from R, are areas II, III, and IV. Then, <4cm from P, are areas I and II. So, the only one works for both is area II.
e) >4cm from T, are areas I, II, III, VI. Then, >4cm from P, are III, IV, V, VI. Finally, >2cm from R, are areas I, VI, V. The only one that works for all three conditions is area VI.
Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions: 2ab-6a+5b+___ Please include an explanation too!
Answer:
[tex]2ab - 6a + 5b - 15[/tex]
Step-by-step explanation:
Given
[tex]2ab - 6a + 5b + \_[/tex]
Required
Fill in the gap to produce the product of linear expressions
[tex]2ab - 6a + 5b + \_[/tex]
Split to 2
[tex](2ab - 6a) + (5b + \_)[/tex]
Factorize the first bracket
[tex]2a(b - 3) + (5b + \_)[/tex]
Represent the _ with X
[tex]2a(b - 3) + (5b + X)[/tex]
Factorize the second bracket
[tex]2a(b - 3) + 5(b + \frac{X}{5})[/tex]
To result in a linear expression, then the following condition must be satisfied;
[tex]b - 3 = b + \frac{X}{5}[/tex]
Subtract b from both sides
[tex]b - b- 3 = b - b+ \frac{X}{5}[/tex]
[tex]- 3 = \frac{X}{5}[/tex]
Multiply both sides by 5
[tex]- 3 * 5 = \frac{X}{5} * 5[/tex]
[tex]X = -15[/tex]
Substitute -15 for X in [tex]2a(b - 3) + 5(b + \frac{X}{5})[/tex]
[tex]2a(b - 3) + 5(b + \frac{-15}{5})[/tex]
[tex]2a(b - 3) + 5(b - \frac{15}{5})[/tex]
[tex]2a(b - 3) + 5(b - 3)[/tex]
[tex](2a + 5)(b - 3)[/tex]
The two linear expressions are [tex](2a+ 5)[/tex] and [tex](b - 3)[/tex]
Their product will result in [tex]2ab - 6a + 5b - 15[/tex]
Hence, the constant is -15
From the top of a vertical cliff 75.0m high, forming one bank of a river, the angles of depression of the top and bottom of a vertical cliff which forms the opposite bank are 22° and 58° respectively. Determine the height of the second cliff and width of the river
Answer:
a. 46.9 m b. 56.1 m
Step-by-step explanation:
a. Width of the river
The angle of depression of the bottom of the second vertical cliff from the first vertical cliff = angle of elevation of the top of the first vertical cliff from the bottom of the second vertical cliff = 58°.
Since the height of the vertical cliff = 75.0 m, its distance from the other cliff which is the width of the river, d is gotten from
tan58° = 75.0 m/d
d = 75.0/tan58° = 46.87 m ≅ 46.9 m
b. Height of the second cliff
Now, the difference in height of the two cliffs is gotten from
tan22° = h/d, since the angle of depression of the top of second cliff from the first cliff is the angle of elevation of the top of the first cliff from the second cliff = 22°
h = dtan22° = 18.94 m
So, the height of the second cliff is h' = 75.0 - h = 75.0 m - 18.94 m = 56.06 m ≅ 56.1 m
I NEED HELP WITH THIS! I need to pass...
Answer: A) The log parent function has negative values in the range.
Step-by-step explanation:
The domain of y = ln (x) is D: x > 0
The domain of y = [tex]\sqrtx[/tex][tex]\sqrt x[/tex] is D: x ≥ 0
The range of y = ln (x) is: R: -∞ < y < ∞
So the only valid option is A because the range of a log function contains negative y-values when 0 < x < 1.
Find the area ratio of a regular octahedron and a tetrahedron regular, knowing that the diagonal of the octahedron is equal to height of the tetrahedron.
Answer:
[tex]\frac{4}{3}[/tex]
Step-by-step explanation:
The area of a regular octahedron is given by:
area = [tex]2\sqrt{3}\ *edge^2[/tex]. Let a is the length of the edge (diagonal).
area = [tex]2\sqrt{3}\ *a^2[/tex]
Given that the diagonal of the octahedron is equal to height (h) of the tetrahedron i.e.
a = h, where h is the height of the tetrahedron and a is the diagonal of the octahedron. Let the edge of the tetrrahedron be e. To find the edge of the tetrahedron, we use:
[tex]h=\sqrt{\frac{2}{3} } e\\but\ h=a\\a=\sqrt{\frac{2}{3} } e\\e=\sqrt{\frac{3}{2} }a[/tex]
The area of a tetrahedron is given by:
area = [tex]\sqrt{3}\ *edge^2[/tex] = [tex]\sqrt{3} *(\sqrt{\frac{3}{2} }a)^2=\frac{3}{2}\sqrt{3} *a^2[/tex]
The ratio of area of regular octahedron to area tetrahedron regular is given as:
Ratio = [tex]\frac{2\sqrt{3}\ *a^2}{\frac{3}{2} \sqrt{3}*a^2} =\frac{4}{3}[/tex]
Please help fast! 25 points and brainliest!!
Let f(x) = 36x5 − 44x4 − 28x3 and g(x) = 4x2. Find f of x over g of x
Answer:
The answer is
9x³ - 11x² - 7xStep-by-step explanation:
f(x) = 36x^5 − 44x⁴ − 28x³
g(x) = 4x²
To find f(x) / g(x) Divide each term of f(x) by g(x)
That's
[tex] \frac{f(x)}{g(x)} = \frac{ {36x}^{5} - {44x}^{4} - {28x}^{3} }{ {4x}^{2} } \\ \\ = \frac{ {36x}^{5} }{ {4x}^{2} } - \frac{ {44x}^{4} }{ {4x}^{2} } - \frac{ {28x}^{3} }{ {4x}^{2} } \\ \\ = {9x}^{3} - {11x}^{2} - 7x[/tex]
Hope this helps you
Answer:
9x³ - 11x² - 7x
Step-by-step explanation:
guy abpove is right or bwlowe
What the answer now
Answer:
57°
Step-by-step explanation:
There is a right angle at the point of tangency, so the angle of interest is the complement of the one given:
m∠K = 90° -m∠J = 90° -33°
m∠K = 57°
The graphed line shown below is y = negative 2 x minus 8. Which equation, when graphed with the given equation, will form a system that has infinitely many solutions? y = negative (2 x + 8) y = negative 2 (x minus 8) y = negative 2 (x minus 4) y = negative (negative 2 x + 8)
Answer: A y = -(2x+8)
Step-by-step explanation:
The first line is y=-2x-8
Thus, the answer that simplifies to y = -2x-8 is the answer.
a) y=-(2x+8)
Distribute
y=-2x-8
Because it works, no need to try the others.
Hope it helps <3
Answer:
[tex]\boxed{y = -(2x + 8)}[/tex]
Step-by-step explanation:
For the two lines to have infinite [tex]\infty[/tex] solutions, the two equations must be the same.
First equation : y = -2x - 8
A. y = -(2x + 8)
y = -2x - 8 correct
B. y = -2(x - 8)
y = -2x + 16 incorrect
C. y = -2(x - 4)
y = -2x + 8 incorrect
D. y = -(-2x+8)
y = 2x - 8 incorrect
y = -2x - 8 and y = -(2x + 8) when graphed are the same, they intersect at infinite points and there are infinite solutions.
A cube has a side length of 5 cm. Determine the surface area of the largest pyramid that will fit inside the cube. Round if necessary.
Answer:
The surface area of the pyramid is 80.9 cm²
Step-by-step explanation:
The side length, s of the cube is given as 5 cm
Therefore, the largest pyramid that can fit into the cube will have a base side length, s = The side length of the cube = 5 cm
The height, h of the largest pyramid = The height of the cube = 5 cm.
The surface area of a pyramid = Area of base, A + 1/2 × Perimeter of base, P × Slant height, S
The slant height of the pyramid = √(h² + (s/2)²) = √(5² + (5/2)²) = (5/2)×√5
The perimeter of the base = 4×5 = 20 cm
The area of the base = 5×5 = 25 cm²
The surface area of a pyramid = 25 + 1/2×20×(5/2)×√5 = 80.9 cm².
The surface area of a pyramid = 80.9 cm².
Triangle ABC has vertices at A(2,5), B(4,11) and C(-1,6). Determine the angles in this triangle.
I need this solved using vectors please
Answer:
The angles are
∠A = 90°, ∠B = 26.56°, ∠C = 63.43°
Step-by-step explanation:
We have that the angles of a vector are given as follows;
[tex]cos\left ( \theta \right ) = \dfrac{\mathbf{a\cdot b}}{\left | \mathbf{a} \right |\left | \mathbf{b} \right |}[/tex]
Whereby the vertices are represented as
A= (2, 5, 0), B = (4, 11, 0), C = (-1, 6, 0),
AB =(4, 11, 0) - (2, 5, 0) = (2, 6, 0) , BA = (-2, -6, 0)
BC = (-1, 6, 0) - (4, 11, 0) = (-5, -5, 0), CB = (5, 5, 0)
AC = (-1, 6, 0) - (2, 5, 0) = (-3, 1, 0), CA = (3, -1, 0)
θ₁ = AB·AC
a·c = a₁c₁ + a₂c₂ + a₃c₃ = 2×(-3) + 6×1 = 0
Therefore, θ₁ = 90°
BA·BC = (-2)×(-5) + (-6)×(-5) = 40
[tex]{\left | \mathbf{}BA \right |\left | \mathbf{}BC \right |}[/tex] = (√((-2)² + (-6)²)) × (√((-5)² + (-5)²)) = 44.72
cos(θ₂) = 40/44.72 = 0.894
cos⁻¹(0.894) =θ₂= 26.56°
CA·CB = 5×3 + 5×(-1) = 10
[tex]{\left | \mathbf{}CA \right |\left | \mathbf{}CB \right |}[/tex] = (√((3)² + (-1)²)) × (√((5)² + (5)²)) = 22.36
10/22.36 = 0.447
cos(θ₃) = 0.447
θ₃ = cos⁻¹(0.447) = 63.43°.
Jane exchanged £100 for 216 Swiss francs. After buying a meal and a present to take home,she had 70 francs left.How much is this in £?
Answer:
£32.4
Step-by-step explanation:
£100 = 216 Swiss francs
x = 70 francs
70 x 100=7000/216=32.4
At the shop near the beach, ice cream is offered in a cone or in a cylindrical cup as shown
below. The ice cream fills the entire cone and has a hemisphere on top. The ice cream
levelly fills the cylindrical cup.
radius of cone= 3 cm
radius of cylinder= 4.5 cm
height of cone = 10 cm
height of cylinder = 5 cm
Determine how much more ice cream the larger option has. Show your work. ( 19)
Answer:
B
Step-by-step explanation:
first correct answer gets best marks
Answer:
the answer would be x is less than 6.
Step-by-step explanation:
the reason why it would not be x is less than or equal to 6 is that the circle is not filled in.
Answer:
B
Step-by-step explanation:
x≤6
We can see from the graph that it starts from 6 and goes to 5, 4, 3, 2.
Hope this helps ;) ❤❤❤
dentify which of these types of sampling is used: random, systematic, convenience, stratified, or cluster. To determine her air qualityair quality, MirandaMiranda divides up her day into three parts: morning, afternoon, and evening. She then measures her air qualityair quality at 33 randomly selected times during each part of the day. What type of sampling is used?
Answer:
The sampling method used is a stratified sampling method
Step-by-step explanation:
sampling is the selection of a predetermined representative subpopulation from a larger population, to estimate the characteristics of the whole population.
Stratified sampling: Here, the total population are divided into subcategories (strata) before sampling is done. The strata are formed based on some common characteristics. In our example, the times of the day (morning, afternoon and evening) has widely varying atmospheric conditions which will add biases to the measurement of air quality. For example, the air in the morning if compared to the afternoon in an industrial area may be purer because of minimal industrial activity, hence effective comparison will be made by stratification.
the angle of elevation of the top of a tree from a point 27m away on the same horizontal ground as the foot on the tree is 30 degrees .find the height of the tree.
Answer:
The height of the tree = 15.59m
Step-by-step explanation:
let's make the height of the tree = x
tan30=x/27
x = 27 x tan30
x = 15.59m
The real numbers $x$ and $y$ are such that \begin{align*} x + y &= 4, \\ x^2 + y^2 &= 22, \\ x^4 &= y^4 - 176 \sqrt{7}. \end{align*}Compute $x - y.$
You get everything you need from factoring the last expression:
[tex]x^4-y^4=-176\sqrt7[/tex]
The left side is a difference of squares, and we get another difference of squares upon factoring. We end up with
[tex]x^4-y^4=(x^2-y^2)(x^2+y^2)=(x-y)(x+y)(x^2+y^2)[/tex]
Plug in everything you know and solve for [tex]x-y[/tex]:
[tex]-176\sqrt7=(x-y)\cdot4\cdot22\implies x-y=\boxed{-2\sqrt7}[/tex]
Answer:
-2sqrt(7)
Step-by-step explanation:
Solution:
From the third equation, $x^4 - y^4 = -176 \sqrt{7}.$
By difference of squares, we can write
\[x^4 - y^4 = (x^2 + y^2)(x^2 - y^2) = (x^2 + y^2)(x + y)(x - y).\]Then $-176 \sqrt{7} = (22)(4)(x - y),$ so $x - y = \boxed{-2 \sqrt{7}}.$
What is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y + 1 = 0?
4 x + y + 6 = 0
4 x + y - 6 = 0
4 x - y - 6 = 0
Answer:
The answer is
4x + y - 6 = 0Step-by-step explanation:
Equation of a line is y = mx + c
where m is the slope
c is the y intercept
4x + y + 1 = 0
y = - 4x - 1
Comparing with the above formula
Slope / m = - 4
Since the lines are parallel their slope are also the same
That's
Slope of the parallel line is also - 4
Equation of the line using point ( 1 , 2) is
y - 2 = -4(x - 1)
y - 2 = - 4x + 4
4x + y - 2 - 4
We have the final answer as
4x + y - 6 = 0Hope this helps you
Solve with long division method 31/27
Answer:
1.148 repetent
Step-by-step explanation:
hope this helps
Can somebody plz help me 15-[7+(-6)+1]^3
Answer:
7.
Step-by-step explanation:
15 - [7 + (-6)+ 1]^3
Using PEMDAS:
= 15 - [ 7-6+1]^3
Next work out what is in the parentheses:
= 15 - 2*3
Now the exponential:
= 15 - 8
= 7.
Step-by-step explanation:
Hi,
I hope you are searching this, right.
=15[7+(-6)+1]^3
=15[7-6+1]^3
=15[2]^3
=15-8
=7...is answer.
Hope it helps..
Please answer this in two minutes
The graph of g(x) resembles the graph of f(x)=x^2, but it has been changed. Which of these is the equation of g(x)?
Answer:
A.
Step-by-step explanation:
Anwer A has the following equation:
[tex]g(x)=\frac{3}{5}x^2-3[/tex]
In this equation, we can calculated the intercept replacing x by 0, as:
[tex]g(x)=\frac{3}{5}0^2-3=-3[/tex]
if this is the answer, the graph of g(x) should be through the point (0,-3) and that happens.
Additionally, the roots of the equations are calculated replacing g(x) by 0 and solving for x, so:
[tex]0=\frac{3}{5}x^2-3\\x_1=\sqrt{5}=2.236\\x_2=-\sqrt{5}=-2.236[/tex]
It means that the graph of g(x) should be through the points (2.236,0) and (-2.236,0) and that happens too.
So, the answer is A, [tex]g(x)=\frac{3}{5}x^2-3[/tex]
Solve for $x$, where $x > 0$ and $0 = -21x^2 - 11x + 40.$ Express your answer as a simplified common fraction.[tex]Solve for $x$, where $x \ \textgreater \ 0$ and $0 = -21x^2 - 11x + 40.$ Express your answer as a simplified common fraction.[/tex]
Answer:
[tex]\large \boxed{\sf \ \ \dfrac{8}{7} \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
The solutions are, for a positive discriminant:
[tex]\dfrac{-b\pm\sqrt{\Delta}}{2a} \ \text{ where } \Delta=b^2-4ac[/tex]
Here, we have a = -21, b = -11, c = 40, so it gives:
[tex]\Delta =b^2-4ac=11^2+4*21*40=121+3360=3481=59^2[/tex]
So, we have two solutions:
[tex]x_1=\dfrac{11-59}{-42}=\dfrac{48}{42}=\dfrac{6*8}{6*7}=\dfrac{8}{7} \\\\x_2=\dfrac{11+59}{-42}=\dfrac{70}{-42}=-\dfrac{14*5}{14*3}=-\dfrac{5}{3}[/tex]
We only want x > 0 so the solution is
[tex]\dfrac{8}{7}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
If 18% of q is 27 , what is 27% of 2q
In this problem, there are two parts. We will need to find what q is if 18% of q is 27, and what 27% of 2q is.
First, let's set up and solve the equation for 18% of q is 27.
18 / 100 = 27 / q
100q = 486
q = 4.86
Next, we'll find the value of 2q.
2(4.86) = 9.72
Finally, we'll set up a proportion and solve for 27% of 2q.
27 / 100 = x / 9.72
100x = 262.44
x = 2.6244
If 18% of q is 27, then 27% of 2q is 2.6244 (round to tenths/hundredths place as needed).
Hope this helps!! :)
Answer:
81Step-by-step explanation: Let's first find the value of q
[tex]18/100 \times q = 27\\\frac{18q}{100} = \frac{27}{1}\\18q = 2700\\\frac{18q}{18} = \frac{2700}{18} \\q= 150.\\[/tex]
Now we can find 27% of 2q
[tex]27 \% \times 2q = \\27 \% \times 2(150)\\\frac{27}{100} \times 300\\\\= \frac{8100}{100} \\= 81[/tex]
1.) Which movie had the Lower Q3 as shown in the box plot?
Movie A
Movie B
Both about the same
Q3, or third quartile, is visually located at the right edge of the box. Movie A shows to have a smaller Q3 value as it is to the left of Q3 for movie B.
The side lengths of a triangle are 9, 12, and 15. Is this a right triangle?
Answer:
Yes, this is a right triangle.Step-by-step explanation:
Hypotenuse always have the highest number than base and perpendicular.
Hypotenuse ( h ) = 15
Base ( b ) = 9
Perpendicular ( p ) = 12
Let's see whether the given triangle is a right triangle or not
Using Pythagoras theorem:
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
Plugging the values,
[tex] {15}^{2} = {12}^{2} + {9}^{2} [/tex]
Evaluate the power
[tex]225 = 144 + 81[/tex]
Calculate the sum
[tex]225 = 225[/tex]
Hypotenuse is equal to the sum of perpendicular and base.
So , we can say that the given lengths of the triangle makes a right triangle.
Hope this helps..
Best regards!!
Answer:
[tex]\boxed{Yes.}[/tex]
Step-by-step explanation:
To solve this equation, we can use the Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex], where [tex]a[/tex] and [tex]b[/tex] are regular side lengths and [tex]c[/tex] is the hypotenuse.
The hypotenuse is the longest side of a triangle and is assigned to the [tex]c[/tex]-variable.The other two side lengths can be assigned to either [tex]a[/tex] or [tex]b[/tex] because of the commutative property: [tex]a + b = b + a[/tex].Now, just substitute the side lengths into the formula and solve!
[tex]9^2 + 12^2 = 15^2[/tex] Simplify the equation by taking each value to its power.
[tex]81 + 144 = 225[/tex] Simplify by adding like terms.
[tex]225 = 255[/tex]
Therefore, this is indeed a right triangle.
Triangle A B C is shown with its exterior angles. Angle B A C is (p + 4) degrees and angle A C B is 84 degrees. Exterior angle X B C is (3 p minus 6 degrees).
What is the measure of ∠XBC?
m∠XBC = m∠BAC + m∠BCA
3p – 6 = p + 4 + 84
3p – 6 = p + 88
2p – 6 = 88
2p = 94
m∠XBC =
°
Answer: 135
Step-by-step explanation:
took it on edg2020
Answer:
135
Step-by-step explanation:
Just took the test and got it right
Pls help I need help with 12
Answer:
B. 14
Step-by-step explanation:
22/x = 11/(21-x)
462 - 22x = 11x
462 = 33x
x = 14
Answer: The value of x is 14, answer choice B
Let y be the other line segment connected to x
Using proportions:
[tex]\dfrac{11}{22}=\dfrac{y}{x}[/tex]
Cross multiply and simplify
[tex]22y=11x[/tex]
[tex]y=\dfrac{1}{2}x[/tex]
We know that x and y add to 21, so we can create the following equation:
[tex]x+y=21[/tex]
Substitute y=(1/2)x
[tex]x+\dfrac{1}{2}x=21[/tex]
Simplify by adding like terms
[tex]\dfrac{3}{2}x=21[/tex]
Divide both sides by 3/2
[tex]x=14[/tex]
Let me know if you need any clarifications, thanks!
When deriving the quadratic formula by completing the square, what expression can be added to both sides of the equation to create a perfect square trinomial?
Answer:
According to steps 2 and 4. The second-order polynomial must be added by [tex]-c[/tex] and [tex]b^{2}[/tex] to create a perfect square trinomial.
Step-by-step explanation:
Let consider a second-order polynomial of the form [tex]a\cdot x^{2} + b\cdot x + c = 0[/tex], [tex]\forall \,x \in\mathbb{R}[/tex]. The procedure is presented below:
1) [tex]a\cdot x^{2} + b\cdot x + c = 0[/tex] (Given)
2) [tex]a\cdot x^{2} + b \cdot x = -c[/tex] (Compatibility with addition/Existence of additive inverse/Modulative property)
3) [tex]4\cdot a^{2}\cdot x^{2} + 4\cdot a \cdot b \cdot x = -4\cdot a \cdot c[/tex] (Compatibility with multiplication)
4) [tex]4\cdot a^{2}\cdot x^{2} + 4\cdot a \cdot b \cdot x + b^{2} = b^{2}-4\cdot a \cdot c[/tex] (Compatibility with addition/Existence of additive inverse/Modulative property)
5) [tex](2\cdot a \cdot x + b)^{2} = b^{2}-4\cdot a \cdot c[/tex] (Perfect square trinomial)
According to steps 2 and 4. The second-order polynomial must be added by [tex]-c[/tex] and [tex]b^{2}[/tex] to create a perfect square trinomial.
Answer: D
Step-by-step explanation:
EDGE 2023