Answer:
see explanation
Step-by-step explanation:
Since (k, 3) lies on each of the lines, the point satisfies the equations.
Substitute x = k, y = 3 into each and solve for k
y = 3x + 1
3 = 3k + 1 ( subtract 1 from both sides )
2 = 3k ( divide both sides by 3 )
k = [tex]\frac{2}{3}[/tex]
-------------------------------------------------------
y = 4x - 2
3 = 4k - 2 ( add 2 to both sides )
5 = 4k ( divide both sides by 4 )
k = [tex]\frac{5}{4}[/tex]
--------------------------------------------------------
y = [tex]\frac{1}{2}[/tex] x
3 = [tex]\frac{1}{2}[/tex] k ( multiply both sides by 2 to clear the fraction )
k = 6
---------------------------------------------------------
2x + 3y = 4
2k + 3(3) = 4
2k + 9 = 4 ( subtract 9 from both sides )
2k = - 5 ( divide both sides by 2 )
k = - [tex]\frac{5}{2}[/tex]
The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equationh = -16t2 + h0, where h0 is the initial height of the object. Suppose a small rock dislodges from a ledge that is 255 ft above a canyon floor. Solve the equation h = -16t2 + 255 for t, using the quadratic formula to determine the time it takes the rock to reach the canyon floor.
Answer:
The time it takes the rock to reach the canyon floor is approximately 4 seconds.
Step-by-step explanation:
The equation representing the height h (in feet) of an object t seconds after it is dropped is:
[tex]h=-16t^{2}+h_{0}[/tex]
Here, h₀ is the initial height of the object.
It is provided that a small rock dislodges from a ledge that is 255 ft above a canyon floor.
That is, h₀ = 255 ft.
So, when the rock to reaches the canyon floor the final height will be, h = 0.
Compute the time it takes the rock to reach the canyon floor as follows:
[tex]h=-16t^{2}+h_{0}[/tex]
[tex]0=-16t^{2}+255\\\\16t^{2}=255\\\\t^{2}=\frac{255}{16}\\\\t^{2}=15.9375\\\\t=\sqrt{15.9375}\\\\t=3.99218\\\\t\approx 4[/tex]
Thus, the time it takes the rock to reach the canyon floor is approximately 4 seconds.
Answer:
t=4
Step-by-step explanation:
ed2020
Given the function f(x) = x + 7 What would the input have to be so that f(x) = 15?
I really need help with question.
Step-by-step explanation:
[tex]\huge{\purple{\underline{\underline{\bf{\pink{Answer}}}}}}[/tex]
in this we have given the value of f(x) = 15
[tex]f(x) = x + 7[/tex]
[tex]f(15) = 15 + 7[/tex]
[tex]f(15) = 22[/tex]
so this is ur answer
hope it helps .
Please answer it now
Answer:
8
Step-by-step explanation:
x+37+x+37+90 = 180
2x + 74 = 90
2x = 16
x = 8
Answer:
x=8°
Step-by-step explanation:
JI is a diameter and K is on the circumference of a circle.
∴∠JKI=90°
also KJ=KI=x(say)
tan (x+37)=y/y=1=tan 45
so x+37=45
x=45-37=8°
PLS HELP!! Consider the exponential functions f, g, and h, defined as shown. Determine which function or functions have each key feature. Drag the tiles to the correct boxes. Not all tiles will be used.
Answer:
1) increases on all interval of x = only g(x)
2) approaches an integer as x approaches -∞ = only f(x)
3) y-intercept at (0, 4) = only g(x)
4) x-intercept at (1, 0) = f(x) and h(x)
Step-by-step explanation:
1) The functions that increases on all interval of x are;
f(x) = -2(3)ˣ + 6 decreases on all interval of x
The function g(x) which is 4 × 4ˣ increases on all interval of x
The function h(x) is observed to be decreasing as x increases, therefore, the only function that increases on all interval of x = g(x)
2) The function that approaches an integer as x approaches -∞ = -2(3)ˣ + 6
-2(3)ˣ + 6 approaches 6 as x approaches -∞ which is only f(x)
3) The functions that have a y-intercept at (0, 4) is only g(x)
4) The function that have a x-intercept at (1, 0) are f(x) and h(x).
Answer:
A) f(x) and g(x)
B) only g(x)
C) All three functions
D) f(x) and h(x)
Step-by-step explanation:
In my uploaded image on the test I have gotten C) wrong but if you graph all three functions, you can see that all three functions have the same style of -∞
end behavior so I think that would be the most logical answer.
What is negative 14 minus 5
Answer:
-19
Step-by-step explanation:
(-14)
-5
-------
14+5=19
add the negative
-19
PLS HELP BRAINLIST AND A THANK YOU WILL BE REWARDED
Answer:
x=25
Step-by-step explanation:
you know that both angles equal the same degrees, so the bottom one is 150° so the other is also 150°. You already have 50° so all you need left is 100°. divide 100 by 4 and you get x=25
Simplify.
3^2+ (9-8/2)
Hi there! Hopefully this helps!
-----------------------------------------------------------------------------------------------------------
Answer: 14.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
First we calculate 3 to the power of 2 and get 9.
|
\/
9 + 9 - [tex]\frac{8}{2}[/tex] = 14.
Now we add 9 + 9 to get 18.
18 - [tex]\frac{8}{2}[/tex] = 14.
Then, we divide 8 by 2 to get 4.
18 - 4 = 14.
Then we subtract 4 from 18 to get.....You guessed it, 14!
Answer: 14
PEMDAS
P: Parentheses
E: Exponets
M: Multiplcaction
D: Divison
A: Addition
S: Subtraction
PEMDAS can also be known as Please Excuse My Dear Aunt Sally
P: [tex](9-8/2)[/tex]
E: [tex]3^2[/tex]
M: [tex]3*3[/tex]
D: [tex]8/2[/tex]
A: [tex]9+5[/tex]
S: [tex]9-8/2[/tex]
Multiply
E: [tex]3^2=3*3=9[/tex]
M: [tex]3*3=9[/tex]
Divide
D: [tex]8/2=4[/tex]
Subtract
S: [tex]9-4=5[/tex]
Add
A: [tex]9+5=14[/tex]
Answer: [tex]14[/tex]
The reason why we didn't use P to get our answer because it would of messed up the steps. So instead we separated it by dividing 8/2 in D and 9-4-5 for S.
Please Help Asap will give brainliest!!! M(9, 8) is the midpoint of side RS.The coordinates of S are (10, 10). What are the coordinates of R? No nonsense answers will report and give explanation plz.
the change in x is 1 and 2 in y respectively
the points are in order from r (x,y) to m (9,8) to s (10,10
if we take - 1 from x and 2 from y we will get r, or (8,6)
△ABCis reflected to form △A′B′C′. The vertices of △ABC are A(-1, 3), B(2, 4), and C(-5, 6). The vertices of △A′B′C′ are A′(3, −1), B′(4, 2), and C′(6, −5). Which reflection results in the transformation of △ABC to △A′B′C′? Reflection across the x-axis reflection across the y-axis reflection across y = x reflection across y=−x
Answer:
reflection across y = x
Step-by-step explanation:
Transformation is the movement of a point from its initial position to a new position. If a shape is transformed, all its point are also transformed. Types of transformation is reflection, rotation, transformation and dilation.
If a point is reflected across the x axis, the x coordinate is the same but the y coordinates is negated. If X(x, y) is reflected across the x axis the new point is X'(x, -y)
If a point is reflected across the y axis, the y coordinate is the same but the x coordinates is negated. If X(x, y) is reflected across the y axis the new point is X'(-x, y)
If a point is reflected across y = x, the x coordinate and y coordinates are interchanged. If X(x, y) is reflected across the y=x axis the new point is X'(y, x)
If a point is reflected across y = -x, the x coordinate and y coordinates are interchanged and both negated. If X(x, y) is reflected across the y=ix axis the new point is X'(-y, -x)
The vertices of △ABC are A(-1, 3), B(2, 4), and C(-5, 6). The vertices of △A′B′C′ are A′(3, −1), B′(4, 2), and C′(6, −5). The reflection of △ABC to form △A′B′C′ shows a reflection across x axis since the x and y coordinates are interchanged
Answer:
reflection across y = x
Step-by-step explanation:
does it matter in what order we divide our our prime factors explain
Answer:
No, it does not matter.
Step-by-step explanation:
In prime factorization there is only one way to be factored. Once these numbers are broken down, into prime numbers you will get the same result no matter what list of prime numbers you use and what order you use them in.
A 2 inch by 2 inch square has its area increased by 21 square inches producing a new square. How many inches long is a side of the new square?
Answer:
A 2 by 2 inch square has an area of 4 square inches.
If its area is increased by 21 inches, then its area equals 25 square inches.
To find the length of the side we take the square root of 25 square inches which is 5 inches.
Step-by-step explanation:
Determine the most precise name for KIET (parallelogram,rhombus,rectangle or square.) you must use slope or length. K(0,0) I(2,2) T(5,-5) E(7,-3)
Answer: rectangle.
Step-by-step explanation:
Given points: K(0,0) I(2,2) T(5,-5) E(7,-3)
Distance formula to find distance between [tex]A(a,b)[/tex] and [tex]B(c,d)[/tex]: [tex]AB=\sqrt{(d-b)^2+((c-a)^2}[/tex]
[tex]KI=\sqrt{(2-0)^2+(2-0)^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}\ units[/tex]
[tex]KT=\sqrt{(5-0)^2+(-5-0)^2}=\sqrt{25+25}=\sqrt{50}=5\sqrt{2}\ units[/tex]
[tex]TE=\sqrt{(7-5)^2+(-3+5)^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}\ units[/tex]
[tex]IE=\sqrt{(7-2)^2+(-3-2)^2}=\sqrt{25+25}=\sqrt{50}=5\sqrt{2}\ units[/tex]
i.e. KI = TE and KT= IE, so opposite sides equal.
It can be a parallelogram or rectangle. [if all sides are equal it would be square or rhombus]
[tex]IT=\sqrt{(5-2)^2+(-5-2)^2}=\sqrt{3^2+7^2}=\sqrt{9+49}=\sqrt{58}\ units[/tex]
[tex]KE=\sqrt{(7-0)^2+(-3-0)^2}=\sqrt{7^2+3^2}=\sqrt{9+49}=\sqrt{58}\ units[/tex]
IT= KE, i.e. diagonals are equal.
It means KIET is a rectangle.
The city plans a roadway to have trees every mile. If the path is miles long, how many trees will the city need?
30 trees
31 trees
32 trees
33 trees
Answer:
32
Step-by-step explanation:
the country would need 30 to 33 trees
6 points are place on the line a, 4 points are placed on the line b. How many triangles is it possible to form such that their verticies will be the given points, if a ∥b?
Answer: 96
Step-by-step explanation:
Ok, lines a and b are parallel.
We can separate this problem in two cases:
Case 1: 2 vertex in line a, and one vertex in line b.
Here we use the relation:
"In a group of N elements, the total combinations of sets of K elements is given by"
[tex]C = \frac{N!}{(N - K)!*K!}[/tex]
Here, the total number of points in the line is N, and K is the ones that we select to make the vertices of the triangle.
Then if we have two vertices in line a, we have:
N = 6, K = 2
[tex]C = \frac{6!}{4!*2!} = \frac{6*5}{2} = 3*5 = 15[/tex]
And the other vertex can be on any of the four points on the line b, so the total number of triangles is:
C = 15*4 = 60.
But we still have the case 2, where we have 2 vertices on line b, and one on line a.
First, the combination for the two vertices in line b is:
We use N = 4 and K = 2.
[tex]C = \frac{4!}{2!*2!} = \frac{4*3}{2} = 6[/tex]
And the other vertice of the triangle can be on any of the 6 points in line a, so the total number of triangles that we can make in this case is:
C = 6*6 = 36
Then, putting together the two cases, we have a total of:
60 + 36 = 96 different triangles
Pls Answer A and B. You don’t need to explain. Thank you!!
Write the following fractions as mixed number: 46/9, and 32/5
Answer:
[tex]5 \frac{1}{9}[/tex]
[tex]6 \frac{2}{5}[/tex]
Step-by-step explanation:
We can convert these improper fractions into mixed numbers by seeing how many times the denominator goes into the numerator.
In [tex]\frac{46}{9}[/tex], 9 goes into 46 5 times, with a remainder of 1. So:
[tex]5 \frac{1}{9}[/tex].
In [tex]\frac{32}{5}[/tex], 5 goes into 32 6 times with a remainder of 2, so:
[tex]6 \frac{2}{5}[/tex].
Hope this helped!
Answer:
5 1/9 and 6 2/5
Step-by-step explanation:
The simplest way to convert improper fractions into mixed fractions is by long division (see attached).
One leg of a right triangle measures 8 units and the hypotenuse measures 12 units. The perimeter of the triangle is irrational. True False
Answer:
TRUE
Step-by-step explanation:
Length of other leg [tex]= \sqrt {12^2 - 8^2} \\
= \sqrt {144 -64} \\
= \sqrt {80} \\
= 4\sqrt {5} \\[/tex]
Since, [tex] \sqrt 5[/tex] is an irrational number, hence Perimeter of triangle will also be irrational.
TRUE
Answer:
True.
Step-by-step explanation:
The length of the other side = sqrt ( 12^2 - 8^2)
= sqrt (144 - 64)
= sqrt ( 80) which is irrational so the perimeter is also irrational.
(The sum of a rational number and an irrational is irrational).
What is the asymptote of the function g(x) = 5⋅2^ 3x + 4 shown on the graph?
Answer:
y=4
Step-by-step explanation:
An exponential function of the form has a horizontal asymptote of .
The given function is .
The graph of the given function is shown in the attachment.
From the graph the horizontal asymptote is
A.) 170
B.) 300
C.)280
D.)155
Please help me
Answer:
Step-by-step explanation:
The formula for this is
∠G = 1/2(arcEH - arcHF)
We have angle G (5x - 10) and we have arcEH (195) so we have to solve for x to find the measure of arcEHF so we can add arcEH + arcHF = arcEHF
Filling in the formula with what we have:
[tex]5x-10=\frac{1}{2}(195-(8x+17))[/tex]
which simplifies down a bit to
[tex]5x-10=\frac{1}{2}(195-8x-17)[/tex] which simplifies down a bit more to
[tex]5x-10=\frac{1}{2}(178-8x)[/tex] Multiply both sides by 2 to get rid of the fraction and get:
2(5x - 10) = 178 - 8x which of course simplifies to
10x - 20 = 178 - 8x. Now add 8x to both sides and at the same time add 20 to both sides to get:
18x = 198 so
x = 11. Now we can find the measure of arcHF:
arcHF is 8x + 17, so arcHF is 8(11) + 17 which is 105°.
arcEH + arcHF = arcEHF so
195 + 105 = arcEHF so
arcEHF = 300°
12) Express in standard form :
a) 0.000000056 b) 56780000000 c) 1923.8
13) The diameter of a plant cell is 1.26 m and the length of a bacterium is 5.1 m. Compare their
diameters.
Answer:
part a)
Step-by-step explanation:
Solve for g.
-3+5+ 6g = 11 – 3g
g =
Answer:
g = 1
Step-by-step explanation:
-3 + 5 + 6g = 11 - 3g
Move the variables to one side and the numbers to the other:
9g = 9
Simplify:
g = 1
Answer:
g=1
Step-by-step explanation:
-3+5=2
2+6g=8
11-3g=8
makes sense that g will have to be 1
explain how the phrase oh heck another hour of algebra can help a student recall the trigonometric ratios
Answer:
its a mnemonic
Oh Heck Another Hour Of Algebra
(O = opposite side, H = hypotenuse ) = sine
(A = adjacent side, H = hypotenuse ) = cosine
(O = opposite side, A = adjacent ) = tangent
Maria has eight black marbles, fourteen clear marbles, and twelve blue marbles in a bag. If she picks two marbles at random, without replacement, what is the probability that she will select a blue marble first, then a clear marble?
Answer:
[tex]\boxed{0.15}[/tex]
Step-by-step explanation:
Part 1: Solve for the total amount of marbles
To solve for the probability of certain events, a population is needed to derive this information from. In order to find this population, add up the amounts of each marble.
8 + 14 + 12 = 34 marbles
Part 2: Determine the probabilities
Now, given the amounts of marbles, simply multiply the ratios of blue marbles to total marbles and the ratio of clear marbles to total marbles to get the combined probability.
[tex]\frac{12}{34}*\frac{14}{33} = \frac{28}{187} \approxeq 0.1497 \approxeq 0.15 * 100 = 15[/tex]
The probability of these events occurring simultaneously is 15%.
when symplified 9a-6b+a-b
Answer:
10a -7b
Step-by-step explanation:
9a-6b+a-b
Combine like terms
9a+a -6b-b
10a -7b
Answer:
10a-7b
Step-by-step explanation:
[tex]9a - 6b + a - b \\ 9a + a - 6b - b \\ 10a - 7b[/tex]
What is the volume of the following prism?
7 m
3
Š
6 m
Answer:
v = 63
Step-by-step explanation:
v = 1/2(7)(6)(3)
v = 63
the angle of elevation from the top of the tower from a point 100m away from the ground is fourty five degrees. what is the hieght of the tower in the nearest meter
Answer:
100m
Step-by-step explanation:
x=the height of the tower
100m=the distance from the tower
45 degrees the angle of elevation
Drawing a diagram allows you to see that you can form a 'right-angled triangle'.
Using trig. :
Tan 45=x/100m
multiply both sides by 100m
100m*tan 45=100m
Answer:
[tex]\Huge \boxed{\mathrm{100 \ meters}}[/tex]
Step-by-step explanation:
The base of the right triangle created is 100 meters.
The angle between the base and the hypotenuse of the right triangle is 45 degrees.
We can use trigonometric functions to solve for the height of the tower.
[tex]\displaystyle \mathrm{tan(\theta)=\frac{opposite}{adjacent} }[/tex]
Let the height be x.
[tex]\displaystyle \mathrm{tan(45)}=\frac{x}{100}[/tex]
Multiplying both sides by 100.
[tex]\displaystyle 100 \cdot \mathrm{tan(45)}=x[/tex]
[tex]100=x[/tex]
The height of the tower is 100 meters.
Can someone help me with this please it’s algebra 2
Answer:
7 8 9
Step-by-step explanation:
Which matrix represents the system of equations shown below?
3x-2y = 4
6x- y = 10
Answer:
B.
Step-by-step explanation:
First equation: the coefficients of x and y are 3 and -2, and the constant is 4.
So the first row should be [3 -2 4].
Second equation: the coefficients of x and y are 6 and -1, and the constant is 10. Hence, the second row should be [6 -1 10].
The cost of a daily rental car is as follows: The initial fee is $59.99 for the car, and it costs $0.30 per mile. If Joan's bill was $200.00 before taxes, how many miles did she drive? Please help!
Answer:
466.7 or 42.003 miles
Step-by-step explanation:
subtract 59.99 from 200.00. Then you have 140.01 and divide or multiply it by 0.30.
simplify 5 x 5^2 in index form
Answer:
5x(25)
Step-by-step explanation:
