Answer:
RS = 2[tex]\sqrt{7}[/tex]
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
RS² + RT² = TS² , that is
RS² + 6² = 8²
RS² + 36 = 64 ( subtract 36 from both sides )
RS² = 28 ( take the square root of both sides )
RS = [tex]\sqrt{28}[/tex] = [tex]\sqrt{4(7)}[/tex] = 2[tex]\sqrt{7}[/tex] ≈ 5.3 ( to 1 dec. place )
If k is a non-zero constant, determine the vertex of the function y = x2 - 2kx + 3 in terms of k.
Answer:
Set y = 0, evaluate the quadratic at h=−b2a and solve for k.
k=9 I think..... I'm not completely sure but I think that's how it is
Answer:
[tex]\displaystyle \text{Vertex} = \left(k, 3-k^2\right)[/tex]
Step-by-step explanation:
We are given the quadratic equation:
[tex]y=x^2-2kx+3[/tex]
Where k is a non-zero constant.
And we want to determine the vertex of the parabola in terms of k.
The vertex of a parabola is given by the formulas:
[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = 1, b = -2k, and c = 3.
Find the x-coorinate of the vertex:
[tex]\displaystyle x=-\frac{(-2k)}{2(1)}=\frac{2k}{2}=k[/tex]
To find the y-coordinate, we substitute the value we acquired back into the equation. So:
[tex]\displaystyle \begin{aligned} y(k)&=(k)^2-2k(k)+3\\&=k^2-2k^2+3\\&=3-k^2\end{aligned}[/tex]
Therefore, our vertex in terms of k is:
[tex]\displaystyle \text{Vertex} = \left(k,3-k^2\right)[/tex]
I need help finding the distince.
Answer:
guessing that the area of the inner rectangle is 10m²
and the other rectangle is 16m*10m= 160m²
we can say that
(16-x) * (10-x) = 10
for the area of the inner rectangle
let's calculate the lefthand side of the equation
160 - 16x -10x + x² = 10
160 -26x +x² = 10
subtract 10 on both sides
150 -26x +x² = 0
rearrange
x² -26x + 150 = 0
looks like something we can throw the pq formula on to solve for x
with p = -26 and q = 150
[tex]x = - \frac{ - 26}{2} \frac{ + }{ - } \sqrt{( \frac{ - 26}{2})^{2} - 150 } [/tex]
[tex]x = 13 \frac{ + }{ - } \sqrt{169 - 150 } [/tex]
[tex]x = 13 \frac{ + }{ - } \sqrt{19 } [/tex]
[tex]x1 = 8.64[/tex]
[tex]x2 =17.36 [/tex]
we need to interpret this solutions
but to be sure on this, I need the unreadable text of the photographed problem
write the formula for the coefficient of quartile deviation
Step-by-step explanation:
How to Calculate the Semi Interquartile Range / Quartile Deviation. As the SIR is half of the Interquartile Range, all you need to do is find the IQR and then divide your answer by 2. Note: You might see the formula QD = 1/2(Q3 – Q1). Algebraically they are the same.
the sum of the digits of a two-digit number is 15. the unit digit is one less than the tens digit. find the number. let x be the tens digit. show the equation!
Answer: 87.
Step-by-step explanation:
Let x be the tens digit, then (x - 1) - unit digit.
x + x - 1 = 15
2x - 1 = 15
2x = 15 + 1
2x = 16
x = 16 ÷ 2
x = 8 - the tens digit.
8 - 1 = 7 - the units digit.
87 - the number.
The graph of the function f(x) = (x + 2)(x − 4) is shown. On a coordinate plane, a parabola opens up. It goes through (negative 2, 0), has a vertex at (1, negative 9), and goes through (4, 0). Which describes all of the values for which the graph is negative and increasing? all real values of x where x < −2 all real values of x where −2 < x < 4 all real values of x where 1 < x < 4 all real values of x where x < 0
Answer:
c
Step-by-step explanation:
all real values of x where 1 < x < 4
Answer:
c
Step-by-step explanation:
trust me
Select the correct answer from the drop-down menu. A vertical pole is supported by two ropes staked to the ground on opposite sides of the pole. One rope is 8 meters long, and the other is 7 meters. The distance between the stakes is 6 meters, and the height of the pole is meters.
Answer:
6.78 m
Step-by-step explanation:
Since the set up forms a triangle with length of ropes two sides of the triangle a = 8 m and b = 7 m respectively, the distance between them which is c = 6 m forms the third side of the triangle.
To find the height of the pole, we need to find the angle between any of the ropes and the ground. So, choosing the 8 m long rope side and using the cosine rule,
b² = a² + c² - 2accosФ where Ф is the angle opposite the 7 m long side which is also the angle between the 8 m long side and the ground.
So, making, Ф subject of the formula, we have
b² - (a² + c²) = 2accosФ
cosФ = [b² - (a² + c²)]/2ac
Ф = cos⁻¹{[b² - (a² + c²)]/2ac}
substituting the values of the variables into the equation, we have
Ф = cos⁻¹{[b² - (a² + c²)]/2ac}
Ф = cos⁻¹{[7² - (8² + 6²)]/2(8)(6)}
Ф = cos⁻¹{[49 - (64 + 36)]/96}
Ф = cos⁻¹{[49 - 100]/96}
Ф = cos⁻¹{-51/96}
Ф = cos⁻¹{-0.53125}
Ф = 122.09°
Since the height of the pole, h is a perpendicular bisector to the base of the triangle, and the 8 m long side form a triangle with it and the ground and the 8 m long side being the hypotenuse side of this triangle, we have that
sinФ = h/a where a = 8 m and Ф = 122.09° = the angle between the 8 m long side and the ground.
h = asinФ
substituting the values of the variables into the equation, we have
h = asinФ
h = (8 m)sin122.09°
h = 8 m × 0.8472
h = 6.78 m
Navin gave his brother 1/5 of his money and her sister 5/8 of the remainder. Navin remained with $12.00 (a) Calculate how much money he had at first.
Answer:
$40
Step-by-step explanation:
Fraction Navin gave his brother = 1/5
Remainder = 1 - 1/5
5/5 - 1/5 = 4/5
Fraction Navin gave his sister = 4/5 x 5/8 = 1/2
total amount Navin gave his siblings :
[tex]\frac{1}{5} + \frac{1}{2}[/tex]
[tex]\frac{2 + 5}{10}[/tex] = [tex]\frac{7}{10}[/tex]
Fraction that remains = 1 - 7/10
10/10 - 7/10 = 3/10
Let a = amount Navin has initially
3/10 x a = 12
a = (12 x 10) / 2 = $40
7. The Waltz family are planning to repave their driveway. The length of their driveway is 7 feet
longer than its width. The area of the driveway is 144 square feet. Write a quadratic equation in
standard form representing the area of the driveway.
Find the dimensions of the driveway in feet.
Width
Length =
Answer:
Dimensions Of The Driveway is Length=16 Feet & Width=9 Feet
Step-by-step explanation:
According To Question,We Have Given
Length of Driveway Is 7 feet longer than its Width
Let the Width be X Feet . So Length is (X+7)Feet
Area Of Driveway = 144 sq. Feet
X * (X+7) = 144
[tex]X^{2}[/tex]+7X=144
[tex]X^{2}[/tex]+16X-9X-144=0
X(X+16)-9(X+16)=0
X = -16 & +9 (Neglect -16 because Width=X, that Can Never be in Negative)
So X = +9
Now Put this value, We get Width = 9 Feet & Length =16 Feet
Write an equation that you could use to solve for X.
THE CORRECT EQUATION IS..
(8X+3)°=(7X+12)°
[BEING VERTICALLY OPPOSITE ANGLES ARE ALWAYS EQUAL ]
HOPE THIS HELPS YOU...
Answer:
8x + 3 = 7x + 12
8x -7x= 12-3
x=9
Which function vertex form is equivalent to f(x)=x^2+6x+3?
Answer:
y = (x + 3)² - 6
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given
f(x) = x² + 6x + 3
Using the method of completing the square
add/subtract ( half the coefficient of the x- term)² to x² + 6x
f(x) = x² + 2(3)x + 9 - 9 + 3
= (x + 3)² - 6 ← in vertex form
The blue dot is at what value on the number line?
Answer:
The blue dot is at 3.
Anyone know the answer?
Answer:
Determine AC with the pythagorean theorem, then you can find CD by subtracting AD.
with DC and BC, you can find BD. again, with the pythagorean theorem
Answer:
20
Step-by-step explanation:
Find AC
[tex]\sqrt{65^{2} -16^{2} } = 63[/tex]
Substract
63 - AD = 12
Find "?"
[tex]\sqrt{12^{2} +16^{2} } = 20[/tex]
Helpppppppppp what’s the angleeeee plz tell me tytytytyytyttytytytg
Answer:
looks like 154 degrees to me
Step-by-step explanation:
If x= 3 what is the value of 50 - 2x?
50 - 2x; x = 3
____________________
50 - 2(3)
= 50 - 6
= 44
The length of the base of an isosceles triangle is x. The length of a leg is 3x-4. The perimeter of the triangle is 97. Find x.
Answer:
x = 15
Step-by-step explanation:
Given that,
The length of the base of an isosceles triangle is x.
The length of a leg is 3x-4.
Perimeter, P = 97
An isosceles triangle has one base. The perimeter of a triangle is given by :
97=x+3x-4+3x-4
97 = 7x-8
97+8=7x
105 = 7x
x = 15
So, the value of x is 15.
I need help ASAP. Will give Brainliest.
Answer:
4,5
Step-by-step explanation:
Your welcome! :)
Good Luck!
Answer:
B is 4 and A is 5 --> 4,5
Step-by-step explanation:
Write the equation of the line that passes through (−3, 5) and (2, 10) in slope-intercept form.
Answer:
gradient =y2-y1÷x2-x1
=10-5÷2-(-3)
1
y-y1=m(x-x1)
y-5=1(x-(-3))
y=x+2
31/24 menos 5/8 cuanto es?
Answer:
31/24 menos 5/8 cuanto es 2/3
Step-by-step explanation:
=31/24- 5/8
=31-15/24
= 16/24
=2/3
Hence the final answer is 2/3
Help
Will
Give
Brainlist
Answer:
3.14 million
Step-by-step explanation:
10.676 - 7.536 = 3.14
To check
7.536 + 3.14 = 10.676
Answer:
3.14 million is the correct answer
petit high school has one thousand two hundred and fifty-two learners.the number of girls is three times more than the number of boys.how many girls are at petit high school
Answer:
939 girls
Step-by-step explanation:
Let us start by writing an equation. We can set the number of boys as x, and the number of girls as 3x since the number of girls is three times the number of boys:
Step 1, writing an equation:
[tex]1252=3x+x[/tex]
We will assume in this case, that the number of girls plus the number of boys adds up to the total number of learners at Petit High School
Step 2, solving the equation:
We can simplify the above equation and isolate the term containing x.
[tex]1252=4x\\x=313[/tex]
Step 3, determining values:
We know that we set # of boys as x and we have just solved for x. Therefore, there are 313 boys in the high school. We have set # of girls as 3x, so [tex]3*313=939[/tex] girls in the high schoolThere are [tex]\fbox{939}[/tex] girls at Petit High School.
I hope this helps! Let me know if you have any questions :)
Need answer to this maths question plssss
Answer:
The fourth angles is 105
Step-by-step explanation:
The sum of the angles of a quadrilateral is 360
3*85 = 225
Let the fourth angle be x
225 +x = 360
x = 360 -225
x =105
express 42 base 7 in base 10
Answer:
correct 42 in bsae 10 is 60
Write the equation of the line that passes through
the points (-1, 2) and (63) in slope-intercept form.
Step 1: Choose (21. Y1).
Answer:
y=63x+65
Step-by-step explanation:
What is the perimeter square above
A.882 square centimeters
B.42 square centimeters
C.441 square centimeters
D. 84 square centimeters
Answer:
option D
Step-by-step explanation:
length of a square = 21 cm
perimeter of a square = 4l
=4*21
=84 centimeters
Answer:
C
Step-by-step explanation:
The square looks like it has equivalent sides so
21 x 21 = 441 square centimeters
Shem will select a letter at random from the word “PROBABILITY”. Japhet will select a letter at random from the word “STATISTICS”. Who is more likely to pick the letter “I”?
Answer:
The answer to this situation would be that Japhet will be most likely to pick the letter “I.”
Step-by-step explanation:
First, calculate how many letters each word has:
P R O B A B I L I T Y - 11 Letters
S T A T I S T I C S - 10 Letters
Next, calculate how many “I”'s each letter has:
"Probability" has two “I”'s.
"Statistics" has two “I”'s.
Finally, divide the amount of “I”'s in the word by it's letter count:
"PROBABILITY" - 2 “I”'s / 11 Letters ≈ 18%
"STATISTICS" - 2 “I”'s / 10 Letters = 20%
So, Japhet would have the better probability to choose the letter “I.”
Hope this helps!
Consider the quadratic function that has x-intercepts of–1 and –7 and passes through the point (-2,-20). What is the
value of a in the factored form of this function?
1, 2,3,4?
In ΔOPQ, PQ = 14, QO = 13, and OP = 20. Which list has the angles of ΔOPQ in order from smallest to largest?
Answer:
The answer is A, that's the correct one
Which glide reflection describes the mapping ABC to DEF?
(x, y) (x + 6, y – 1) and reflected across x = 0
(x, y) (x + 6, y − 1) and reflected across y = 0
(x, y) (x, y + 6) and reflected across y = 0
(x, y) (x + 7, y) and reflected across x = 0
Answer:
Option (2)
Step-by-step explanation:
To get the transformation applied in triangle ABC to map triangle DEF we will apply the following rules.
If a point A of triangle ABC maps the point D of triangle DEF,
Coordinates of point A → (-4, -5)
Coordinates of point D → (2, 6)
First point A is shifted to quadrant (4) from quadrant (3),
Rule for the translation,
A(x, y) → A'(x + 6, y - 1)
A(-4, -5) → A'(2, -6)
Followed by reflection across x-axis (y = 0)
A'(x, y) → D(x, -y)
A'(2, -6) → D(2, 6)
Therefore, Option (2) will be the answer.
what are 2 consecutive odd integers whose sum is 36.
Two consecutive odd integers with a sum of 36 are 17 and 19.
Hope it helps you I'm from ph❤️
Answer:
Two consecutive odd integers with a sum of 36 are 17 and 19.
Step-by-step explanation:
hope i helped
how long will it take a 1500 W motor to lift a 300 kg piano to a sixth-story window 20 m above?
Answer:
39.24 sec
How long will it take a 1500 W motor to lift a 300 kg piano to a sixth-story window 20 m above? All tutors are evaluated by Course Hero as an expert in their subject area. Answer is t = 39.24 sec
Step-by-step explanation:
It will take the motor 39.2 seconds to lift the piano to the sixth-story window.
Given the following data;
Power = 1500 WattsMass = 300 kgHeight = 20 metersWe know that acceleration due to gravity is equal to 9.8 m/s².
To find how long it will take to lift the piano to the sixth-story window;
First of all, we would have to determine the gravitational potential energy required to lift the piano up.
Mathematically, gravitational potential energy is given by the formula;
[tex]G.P.E = mgh[/tex]
where:
G.P.E is the gravitational potential energy of an object.m is the mass of the object.g is the acceleration due to gravity.h is the height of the object.Substituting into the formula, we have;
[tex]G.P.E = 300*9.8*20[/tex]
G.P.E = 58,800 Joules
Next, we would determine the time using the following formula;
[tex]Time = \frac{Energy}{Power}[/tex]
Substituting the values into the formula, we have;
[tex]Time = \frac{58800}{1500}[/tex]
Time = 39.2 seconds.
Therefore, it will take the motor 39.2 seconds to lift the piano to the sixth-story window.
Find more on power, time and energy here: https://brainly.com/question/20488953