Answer:
the Answer is 60 miles.
Step-by-step explanation:
The current of the river is towards city B; hence, the reason the ferry moves faster from town A to B than when coming back from town B to A. The distance between both towns is 60m.
Let
[tex]s \to[/tex] speed in still water
[tex]d \to[/tex] distance between both cities
The given parameters are:
[tex]t_{AB} =2[/tex] -- from A to B
[tex]t_{BA} =1.5[/tex] -- from B to A
[tex]s_c = 5mph[/tex] -- speed of the current
Speed is calculated as:
[tex]Speed = \frac{Distance}{Time}[/tex]
The speed (s) from town A to town B is:
[tex]s = s_c + \frac{d}{t_{AB}}[/tex] --- i.e. speed of the current + speed in still water from A to B
[tex]s = 5 + \frac{d}{2}[/tex]
Multiply through by 2
[tex]2s = 10 + d[/tex]
Make d the subject
[tex]d = 2s - 10[/tex]
The speed (s) from town B to town Ais:
[tex]s = -s_c + \frac{d}{t_{BA}}[/tex] --- i.e speed in still water from B to A - . speed of the current
[tex]s = -5 + \frac{d}{1.5}[/tex]
Multiply through by 1.5
[tex]1.5s = -7.5 + d[/tex]
Make d the subject
[tex]d = 1.5s + 7.5[/tex]
So, we have:
[tex]d = 1.5s + 7.5[/tex] and [tex]d = 2s - 10[/tex]
Equate both values of d
[tex]2s - 10 = 1.5s + 7.5[/tex]
Collect like terms
[tex]2s - 1.5s= 10 + 7.5[/tex]
[tex]0.5s= 17.5[/tex]
Divide both sides by 0.5
[tex]s = 35[/tex]
Substitute [tex]s = 35[/tex] in [tex]d = 1.5s + 7.5[/tex] to calculate distance (d)
[tex]d =1.5 *35 + 7.5[/tex]
[tex]d =52.5 + 7.5[/tex]
[tex]d =60[/tex]
The distance between town A and B is 60m.
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What is the sine value of 2 pi over 3? negative 1 over 2 1 over 2 negative square root 3 over 2 square root 3 over 2
Answer:
[tex]\large\boxed{\sin\dfrac{2\pi}{3}=\dfrac{\sqrt3}{2}}[/tex]
Step-by-step explanation:
[tex]\sin\dfrac{2\pi}{3}=\sin\bigg(\pi-\dfrac{\pi}{3}\bigg)\\\\\text{use}\ \sin(x-y)=\sin x\cos y-\sin y\cos x\\\\=\sin\pi\cos\dfrac{\pi}{3}-\sin\dfrac{\pi}{3}\cos\pi\\\\\text{use the table from the attachment}\\\\\sin\pi=0\\\\\cos\dfrac{\pi}{3}=\dfrac{1}{2}\\\\\sin\dfrac{\pi}{3}=\dfrac{\sqrt3}{2}\\\\\cod\pi=-1\\\\\text{subtitute:}\\\\=(0)\left(\dfrac{1}{2}\right)-\left(\dfrac{\sqrt3}{2}\right)(-1)=\dfrac{\sqrt3}{2}[/tex]
The value of sin 2π/3 will be;
⇒ √3 / 2
What is Mathematical expression?The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.
Given that;
The expression is,
⇒ sin 2π/3
Now,
Since, The expression is,
⇒ sin 2π/3
⇒ sin 2×180/3
⇒ sin 120°
⇒ sin (90 + 30)°
⇒ cos 30°
⇒ √3 / 2
Thus, The value of sin 2π/3 = √3 / 2
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What is the equation that passes through (4, 3) and (2, -1)?
Y = 2x - 5
y = 4x -13
y = 6x+4
y = 1/2 x -2
Answer:
y = 2x - 5
Step-by-step explanation:
We are to find the equation of line the line which passes through the points (4, 3) and (2, -1).
Finding the slope:
Slope = [tex]\frac{3-(-1)}{4-2} =2[/tex]
Substituting the coordinates of one of the given points and slope in the standard form of an equation to find the y intercept.
[tex]y=mx+c[/tex]
[tex] -1 = 2 (2) + c \\\\ c = - 5 [/tex]
So the equation of the line would be [tex]y=2x-5[/tex]
Answer: first option.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
To find "m", we need to substitute the coordinates of the points (4, 3) and (2, -1) into this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We can identify that:
[tex]y_2=-1\\y_1=3\\x_2=2\\x_1=4[/tex]
Then:
[tex]m=\frac{-1-3}{2-4}\\\\m=2[/tex]
To find "b" we must substitute the slope and one of the given points into [tex]y=mx+b[/tex] and solve for "b". Then, this is:
[tex]3=2(4)+b\\\\3-8=b\\\\b=-5[/tex]
Therefore, the equation of this line is:
[tex]y=2x-5[/tex]
How many roots does the polynomial function, y = (x + 4)(x-2)(x+7) have?
A. 3
B. 1
C. 2
D. A
Answer:
A. 3Step-by-step explanation:
The polynomial y = (x + 4)(x - 2)(x + 7) has 3 roots.
y = 0 ⇒ (x + 4)(x - 2)(x + 7) = 0 ⇔ x + 4 = 0 ∨ x - 2 = 0 ∨ x + 7 = 0
x + 4 = 0 subtract 4 from both sides
x = -4
x - 2 = 0 add 2 to both sides
x = 2
x + 7 = 0 subtract 7 from both sides
x = -7
The polynomial function y = (x + 4)(x - 2)(x + 7) has three distinct roots: -4, 2, and -7.A. 3
The polynomial function y = (x + 4)(x - 2)(x + 7) has three distinct roots, which can be found by setting y to zero and solving for the values of x that make the function equal to zero. When you set y to zero, the equation becomes 0 = (x + 4)(x - 2)(x + 7), and the roots are x = -4, x = 2, and x = -7. Hence, the correct answer to the question of how many roots the polynomial function has is:
A. 3
Find the geometric means in the following sequence.
-9,?,?,?,?,-9,216
Select one:
a. -144, -576, -2,304, -9,231
b. 36, 144, 576, 2,304
c. -720, -1,080, -1,440, -1,800
d. -36, -144, -576, -2,304
Answer:
Last choice. d.
Step-by-step explanation:
We are given the first term and the sixth term.
The first term is [tex]a_1=-9[/tex].
The sixth them is [tex]a_6=a_1r^5=-9216[/tex].
Let's solve for the common ratio, r.
[tex]-9r^5=-9216[/tex]
Divide both sides by -9:
[tex]r^5=1024[/tex]
Take the fifth root of both sides:
[tex]r=1024^{\frac{1}{5}}[/tex]
[tex]r=4[/tex]
So the common ratio is 4.
[tex]a_1=-9[/tex]
[tex]a_2=-9(4)=-36[/tex]
[tex]a_3=-9(4)^2=-144[/tex]
[tex]a_4=-9(4)^3=-576[/tex]
[tex]a_5=-9(4)^4=-2304[/tex]
[tex]a_6=-9(4)^5=-9216[/tex]
Is 36 a perfect square?
Answer:
yes
Step-by-step explanation:
6 times 6 = 36
Answer: Yes
Step-by-step explanation: Yes, it is a perfect square of 6. 6 x 6 = 36.
wh as t is a prime numbers
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers
Step-by-step explanation:
Final answer:
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. Prime numbers have many interesting properties and applications in mathematics.
Explanation:
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, it is a number that is only divisible by 1 and itself.
For example, the numbers 2, 3, 5, and 7 are prime numbers because they have no divisors other than 1 and themselves. On the other hand, the number 4 is not prime because it is divisible by 1, 2, and 4.
Prime numbers have many interesting properties and applications in mathematics, including their role in number theory and cryptography.
The length of a rectangular is 7/10 ft .and the width is 1/5ft what is the perimeter
[tex]\huge\boxed{1 \frac{4}{5}\ \text{ft}}[/tex]
Explanation:Change [tex]\frac{1}{5}[/tex] so that is has a common denominator. [tex]\frac{1*2}{5*2}=\frac{2}{10}[/tex]
Make an equation. [tex]\frac{7+7+2+2}{10}[/tex]
Add. [tex]\frac{14+4}{10}[/tex]
Add. [tex]\frac{18}{10}[/tex]
Divide both sides by 2. [tex]\frac{9}{5}[/tex]
Convert to a mixed number. [tex]1 \frac{4}{5}[/tex]
Answer:
1 4/5 ft.
Step-by-step explanation:
Change 7/10 into 70
Change 1/5 into 20
( It will be easier to find perimeter this way )
Formula: P=2(l+w)
P=2(l+w)=2·(70+20)=180
Then, you change the 180 back into a fraction to get 1 4/5.
Pat needs boards that are one half foot long. Which equation shows how many one half foot pieces he can get from a four foot long board
Answer:
4/.5 = 8
Step-by-step explanation:
You can solve this by adding up .5 8 times to equal 4. Another way to look at it is that you have 4 individual pieces that are a foot long and you decide to split all of them in half. Let me know if you have any other questions.
Answer:
The equation that shows that is the division between 4 and 0.5 as:
[tex]\frac{4}{0.5}[/tex]
Step-by-step explanation:
First, it is necessary to know that one half foot is equivalent to 0.5 foot.
We can solve this using a rule of three in which we know that 1 piece has one half foot long, then 4 foot long how many pieces have. This is:
1 board ----------- 0.5 foot
X ------------ 4 foot
Where X is the number of pieces that he can get from a four foot long board.
Solving for X, we get:
[tex]X = \frac{4*1}{0.5} = \frac{4}{0.5}[/tex]
So, the equation that shows how many one half foot pieces he can get from a four foot long board is:
[tex]X=\frac{4}{0.5}[/tex]
AB || CD. Find the measure of
Step-by-step explanation:
solve the equation:
5x-10=4x+20
Answer:
The correct answer is option B. 140
Step-by-step explanation:
From the figure we can see that,
AB ║ CD
To find the value of x
From the figure we can see that,
<CFE = <BEF [Alternate interior angles are equal]
4x + 20 = 5x - 10
5x - 4x = 20 + 10
x = 30
To find the measure of <BEF
m<BEF = 5x - 10
= (5*30) - 10
= 150 - 10
= 140°
Therefore the correct answer is option B. 140
Which graph is the graph of the function f(x) = | x-1/4 | +4
Answer:
Step-by-step explanation:
David, if the problem came with possible answer choices, you need to share those choices.
The graph of f(x) = | x-1/4 | +4 stems from the graph of y = |x|, the absolute value function. Draw this function; its vertex is at (0, 0) and it's v-shaped, opening upward.
First, translate this graph 1/4 unit to the right. Second, translate the resulting graph 4 units upward. Done.
Answer: A for plato users or edmentum
Step-by-step explanation:
simplify 30 (1/2 x -2) + 40 (3/4 y - 4)
Answer:
10(3/2x-22+3y)
Step-by-step explanation:
One-third of Sharon's land has
farm animals. One-fifth of the farm
animals are chickens. Which
model shows what fraction of
Sharon's land has chickens?
Which of the following functions is shown in the graph below?
y = (x - 1)^2 + 2
y = -2(x - 1)^2 + 2
y = 2(x + 1)^2 + 2
y = (x + 1)^2 + 2
#2
Step-by-step explanation:
it is opening downwards so the number multiplying the function must be negative (in this case it is -2)
Answer:
y = -2(x - 1)² + 2
Step-by-step explanation:
recall that the vertex form of a quadratic equation is :
y = a(x - h)² + k, where (h, k) is the coordinate of the vertex (i.e maxima point)
from the graph we can see that the vertex is at x = 1, y = 2
hence the answers that are valid would have h = 1 and k = 2
right away by observing the answers, we can see that the last 2 choices have h = (-1) and so these are NOT the answers.
To decide between the first 2 choices, we observe from the given graph, that when x=0, y=0.
The only choice which satisfies this is the 2nd option
Proof:
for y = -2(x - 1)² + 2, when x = 0,
y = -2(0 - 1)² + 2
y = -2(- 1)² + 2
y = -2(1) + 2 = -2 + 2 = 0 (Proven to be valid)
Sanity check: check the first choice
y = (x - 1)² + 2
when x = 0,
y = (0- 1)² + 2
y = 1 + 2 ≠ 0 (not the answer)
Two forces of 7 newtons and 11 newtons act on a body at an angle of 60° to each other. Find the magnitude of the resultant force to the nearest whole number.
Answer:
16 N
Step-by-step explanation:
If the 7 N force is at 0°, and the 11 N force is at 60°, then the components of the resultant force are:
Fₓ = 7 cos 0° + 11 cos 60° = 12.5
Fᵧ = 7 sin 0° + 11 sin 60° ≈ 9.53
The magnitude of the resultant force is:
F = √(Fₓ² + Fᵧ²)
F ≈ 15.7
Rounded to the nearest whole number, the magnitude is 16 N.
Suppose S and T are mutually exclusive events find P(S or T) if P(S)=1/3 and P(T)=5/12
Answer:
P(S or T)= 3/4
Step-by-step explanation:
Given:
S and T are mutually exclusive events
find P(S or T)
P(S or T)= P(S) + P(T)
= 1/3 +5/12
=4+5/12
=9/12
=3/4 !
Answer:
The value of P(S or T) is 3/4.
Step-by-step explanation:
It is given that S and T are mutually exclusive events. It means intersection of S and T is 0.
[tex]S\cap T=0[/tex]
[tex]P(S\cap T)=0[/tex]
We need to find the value of P(S or T). It means we have to find the probability of union of S and T.
[tex]P(S\cup T)=P(S)+P(T)-P(S\cap T)[/tex]
Substitute the given values in the above formula.
[tex]P(S\cup T)=\frac{1}{3}+\frac{5}{12}-(0)[/tex]
[tex]P(S\cup T)=\frac{4+5}{12}[/tex]
[tex]P(S\cup T)=\frac{9}{12}[/tex]
[tex]P(S\cup T)=\frac{3}{4}[/tex]
Therefore the value of P(S or T) is 3/4.
what is the rate of change from x = pi x = 3pi/2
Answer: 3/2 (simplified: 1.5)
Step-by-step explanation:
X=pi
X=3pi/2
Remove pi from both equations because pi will cancel out each other then you will be left with the equation 3/2. So therefore the rate of change would be 3/2 simplified would be 1.5
What is the simplified expression for 4^4 x 4^3/4^5
What is the length of the side opposite
3 units
4 units
5 units
6 units
0
Answer:
A. 4 units
Step-by-step explanation:
Answer: B: 4 units
Step-by-step explanation:
the guy above me almost got it, lol, love u
A die rolled. The set of equally likely outcomes is {1,2,3,4,5,6}. Find the probability of rolling an odd number.
Answer:
3/6 or 50%
Step-by-step explanation:
The probability of rolling an odd number from the dice numbered, {1,2,3,4,5,6} is 3/6.
6 numbers in all.
3 odd numbers.
3 even numbers.
Therefore, 3/6 or 50%.
1. Evaluate cos-1 (tan (0))
Answer:
pi/2
Step-by-step explanation:
Arccos(tan(0))
Arccos( 0) since tan(0)=0
Arccos(0)=pi/2 since cos(pi/2)=0 and the restricted domain of cosine is [0,pi].
Answer:
1
Step-by-step explanation:
First of all go one step at a time. Find tan(0). For this question, you can use your calculator.
Tan(0) = 0 That's because the opposite side has a length of 0 and the tangent's definition is
Tan(x ) = opposite side / adjacent side. The opposite side and the adjacent side are part of the same length. There is no real opposite side.
=========
Now you are down to cos-1(0)
If you put that into your calculator like this
2nd Function
cos-1(
0
)
=
You will get 1
Find the sum.
2x
x2 - 6x + 9 + x2 + 2x - 15
Answer:
[tex]\large\boxed{x^2-6x+9+x^2+2x-15=2x^2-4x-6}[/tex]
Step-by-step explanation:
[tex]x^2-6x+9+x^2+2x-15\qquad\text{combine like terms}\\\\=(x^2+x^2)+(-6x+2x)+(9-15)\\\\=2x^2-4x-6[/tex]
if sin(x-3)° / cos(2x+6) = 1, then the value of X is
Answer:
x = 29° + n·120° . . . or . . . 261° +n·360° . . . . for any integer n
Step-by-step explanation:
Multiplying by the denominator, the equation becomes ...
sin((x -3)°) = cos((2x+6)°)
The sine and cosine are equal when ...
(x -3) + (2x +6) = 90 + n·360 . . . . . for any integer n
3x +3 = 90 + n·360 . . . . . . . . . collect terms
x +1 = 30 +n·120 . . . . . . . . . . . .divide by 3
x = 29 + n·120 . . . . . . . . . . . . . . subtract 1
__
The sine and cosine are also equal when ...
(x -3) -(2x +6) = 90 + n·360
-x -9 = 90 +n·360
x = -99 -n·360
Since n can be any integer, this can also be written as ...
x = 261 + n·360
Possible values of x include {29, 149, 261, 269} +n·360 for any integer n.
_____
The graph shows solutions to sin(x-3)-cos(2x+6)=0, which has the same solutions as the given equation.
Help me with question 4 and 5
How would you do number 12 and 15?
Answer:
[tex]x_1=x_2=-\dfrac{2}{3}[/tex]
Step-by-step explanation:
For the quadratic equation [tex]ax^2+bx+c=0[/tex] the discriminant is defined as
[tex]D=b^2-4ac[/tex]
and the quadratic formula for the roots gives us two roots:
[tex]x_1=\dfrac{-b-\sqrt{D}}{2a}[/tex]
and
[tex]x_2=\dfrac{-b+\sqrt{D}}{2a}[/tex]
For the equation [tex]9x^2 +12x+4=0[/tex] use quadratic formula to find roots:
[tex]D=12^2-4\cdot 9\cdot 4=144-144=0[/tex]
So,
[tex]x_1=x_2=\dfrac{-12\pm \sqrt{0}}{2\cdot 9}=-\dfrac{12}{18}=-\dfrac{2}{3}[/tex]
SEE PHOTO. Based on the diagram, all of the following are true except...
A) cos38 = 24/x
B) sin52 = 24/x
C) cos38 = x/34
D) cos52 = x/24
Answer:
Option D) cos52 = x/24
Step-by-step explanation:
In this problem angle of 38 degrees and angle of 52 degrees are complementary angles
so
38°+52°=90°
therefore
cos(38°)=sin(52°)
we know that
see the attached figure with letters to better understand the problem
In the triangle ABD
cos(38°)=24/x ----> The cosine of angle of 38 degrees is equal to divide the adjacent side to angle of 38 degrees by the hypotenuse
Remember that
cos(38°)=sin(52°)
so
sin(52°)=24/x
In the right triangle ABC
cos(38°)=x/34 ----> The cosine of angle of 38 degrees is equal to divide the adjacent side to angle of 38 degrees by the hypotenuse
In the right triangle ABD
Applying the Pythagoras Theorem
[tex]BD=\sqrt{x^{2}-576}\ units[/tex]
[tex]cos(52\°)=(\sqrt{x^{2}-576})/x[/tex]----> The cosine of angle of 52 degrees is equal to divide the adjacent side to angle of 52 degrees by the hypotenuse
If WZYX is equal to PMLN describes two quadrilaterals, which other statement is also true? I NEED THIS ANSWER ASAP
A.WXYZ equal to LMNP
B.WXYZ equal to NPML
C.WXYZ equal to PNLM
D.WXYZ equal to MLNP
Answer:
C.WXYZ equal to PNLM
Step-by-step explanation:
Look at the given statement, WZYX is equal to PMLN.
WZYX is equal to PMLN. W corresponds to P.
WZYX is equal to PMLN. Z corresponds to M.
WZYX is equal to PMLN. Y corresponds to L.
WZYX is equal to PMLN. X corresponds to N
Now look in the choices. The letters must correspond like they do above.
W must correspond to P.
WXYZ equal to P...
X must correspond to N.
WXYZ equal to PN...
Y must correspond to L.
WXYZ equal to PNL...
Z must correspond to M.
WXYZ equal to PNLM
Answer: C.WXYZ equal to PNLM
Answer: C.WXYZ equal to PNLM
–7x + 8y = 1
4x – 8y = 20
What is the y-coordinate of the solution for this system?
A. –1
B. –6
C. 1
D. 6
PLEASE HELP, i got 7 but thats not one of the answers
[tex]\bf \begin{cases} -7x+8y=1\\ 4x-8y=20 \end{cases}\qquad \qquad \stackrel{\textit{using elimination}}{ \begin{array}{llll} -7x~~\begin{matrix} +8y \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~=1\\ ~~4x~~\begin{matrix} -8y \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~=20\\ \cline{1-1}\\ -3x~\hfill =21 \end{array}}[/tex]
[tex]\bf x=\cfrac{21}{-3}\implies \blacktriangleright x=-7 \blacktriangleleft \\\\\\ \stackrel{\textit{substituting in the 2nd equation}}{4(-7)-8y=20}\implies -28-8y=20\implies -8y=48 \\\\\\ y=\cfrac{48}{-8}\implies \blacktriangleright y = -6 \blacktriangleleft[/tex]
The solution to the system is (x, y) = (-2.2, -1.8) the y-coordinate of the solution is -1, the correct option is A.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that;
The equations;
–7x + 8y = 1
4x – 8y = 20
Now,
To solve this system of equations, we can use the elimination method. We can multiply the first equation by 2 and add it to the second equation to eliminate y:
-14x + 16y = 2 +4x - 8y = 20
-10x = 22
x = -2.2
Now that we have x, we can substitute it into either equation to solve for y. Let’s use the first equation:
-7x + 8y = 1 -7(-2.2) + 8y = 1 15.4 + 8y = 1 8y = -14.4 y = -1.8
Therefore, the solution to the system of equations will be (x, y) = (-2.2, -1.8) the y-coordinate will be -1.
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A girls' track team must run 3 miles on the first day of practice and 6 miles every day after that. The boys' team must run 5 miles every day of practice. The coach will order new javelins at the end of the day that each girl's total mileage surpasses each boy's. How many total miles will each girl have run by the time the coach orders the new equipment?
Answer:
The 4th day so 21 miles the girls would have to run
Step-by-step explanation:
Answer:
Each girl would have ran a total of 21 miles and boys would have ran a total of 20 miles by the end of the fourth day before the couch order new javelins.
Step-by-step explanation:
Girls track team
First day of practice=3 miles
Days afterwards= 6 miles
Boys track team
Everyday= 5 miles
coach will order new javelins at the end of the day that each girl's total mileage surpasses each boy's.
First day
Each girl total mileage= 3 miles
Each boy total mileage= 5 miles
Second day
Each girl total mileage= 3miles+6miles=9 miles
Each boy total mileage=5 miles+5 miles= 10 miles
Third day
Each girl total mileage= 3+6+6=15 miles
Each boy total mileage=5+5+5=15 miles
Fourth day
Each girl today mileage= 3+6+6+6=21 miles
Each boy total mileage=5+5+5+5= 20 miles
Difference=girls-boys
=21-20= 1 mile
The fourth day is the day each girl's total mileage(21 miles) surpasses each boy's total mileage(20 miles) with a total of 1 mile
Write the slope-intercept form of the equation that passes through the point (-3, 5) and is perpendicular to the line y = 1/5x + 10 y = 5x + 10 y = -1/5x + 22/5 y = 1/5x + 28/5 y = -5x - 10
Answer:
y = -5x - 10Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\=========================[/tex]
[tex]\text{We have}\ y=\dfrac{1}{5}x+10\to m_1=\dfrac{1}{5}\\\\\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{5}}=-5.\\\\\text{Put the value of a slope and the coordinates of the point (-3, 5)}\\\text{to the equation}\ y=mx+b:\\\\5=-5(-3)+b\\5=15+b\qquad\text{subtract 15 from both sides}\\-10=b\to b=-10\\\\\text{Finally:}\\\\y=-5x-10[/tex]
Could Triangle JKL be congruent to Triangle XYZ? Explain.
Answer:
Im pretty sure its C
Step-by-step explanation:
because when u line up the the right angles u see the hypotenuse and leg of another triangle is the same
The given triangles are not congruent since the hypotenuse of one triangle is equal to the length of leg of another triangle.
What is congruency?Congruent triangles are triangles having both the same shape and the same size.Types of congruencies are SSS, SAS, AAS, ASA, RHS.How to find whether ΔJKL and ΔXYZ are congruent?For two triangles two be congruent, we need to check the the equality of corresponding sides and angles.Here the hypotenuse of ΔJKL is 10 units and one side(not the hypotenuse) of ΔXYZ is 10So the corresponding sides of the triangles are not equal.
So the triangles are not congruent.
So, option C is correct.
Find more about "Congruency" here: brainly.com/question/2938476
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