Given:
The gradient of the line passing through A(2,3), B(k,7) is [tex]\dfrac{2}{3}[/tex].
To find:
The value of k.
Solution:
The gradient or slope of a line is:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The gradient of the line passing through A(2,3), B(k,7) is [tex]\dfrac{2}{3}[/tex]. So,
[tex]\dfrac{2}{3}=\dfrac{7-3}{k-2}[/tex]
[tex]\dfrac{2}{3}=\dfrac{4}{k-2}[/tex]
On cross multiplication, we get
[tex]2(k-2)=4(3)[/tex]
[tex]2k-4=12[/tex]
[tex]2k=12+4[/tex]
[tex]2k=16[/tex]
Divide both sides by 2.
[tex]k=\dfrac{16}{2}[/tex]
[tex]k=8[/tex]
Therefore, the value of k is 8.
Solve for x. Thank you
Answer:
20
Step-by-step explanation:
Let the angle at the left corner is A, so the angle at the rIght corner should be (180-90-A) = (90-A).
In the left triangle:
tanA = 8√5/16 = √(5)/2
Thus,
cotA = 1/tanA = 2/√5
In the right triangle:
tan(90-A) = 8√5/x
cotA = 8√5/x [tan(90-x) = cotx]
2/√5 = 8√5/x
x = 20
pls help and explain answer!!
At a certain point in time, a physicist measures the
speed of a falling object to be 17.6 feet per second.
What is the equivalent speed in miles per hour?
(5280 feet = 1 mile)
Answer:
0.003 miles per hour
Step-by-step explanation:
Well since 5280 feet gives 1 mile den convert 17.6 feet per sec to miles per hr
Dr. Comeaux decides to conduct a survey of her class to determine whether the number of breaks is sufficient for a three-hour class period. She assigns each of her 40 students a number and arbitrarily selects 20 using a computer program. Using the language of research methodology, Dr. Comeaux's sample is both a representative and a(n) _____ sample.
Answer:
Random and Representative.
Step-by-step explanation:
According to the Question,
Given That, Dr. Comeaux decides to conduct a survey of her class to determine whether the number of breaks is sufficient for a three-hour class period. She assigns each of her 40 students a number and arbitrarily selects 20 using a computer program. Using the language of research methodology, Dr. Comeaux's sample is both a Representative and Random sample.Which statements are true about the result of simplifying this polynomial?
+ (8 + 9t) – (t2 + 4)(+2 – 3t)
The simplified expression has four terms.
The simplified expression is a polynomial.
The simplified expression has a constant term.
The simplified expression is cubic.
a
The simplified expression is a trinomial.
Answer:
The simplified expression has four terms.
The simplified expression has a constant term.
The simplified expression is cubic.
The simplified expression is a trinomial.
The statements that are true about the result of simplifying this polynomial are:
b. The simplified expression is a polynomial.
c. The simplified expression has a constant term.
What are polynomials?Sums of terms of the form k x xⁿ, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. A description of polynomials.
All other options are false. As it is not cubic because it is degree 4, and it does not have four terms as it has five terms. And it is not trinomial as it has five terms, not three.
The full solution is;
t³(8 + 9t) - (t² + 4)(2 - 3t)
8t³ + 9t⁴ - (2t² - 3t³ + 8 - 12t)
8t³ + 9t⁴ - 2t² + 3t³ - 8 + 12t
9t⁴ + 11t³ - 2t² + 12t - 8
Therefore, the correct options are a, and b.
To learn more about polynomials, refer to the below link:
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Find the nth term...-1,5,11,17
Answer:
23
Step-by-step explanation:
you just add 6 to every one
The following table shows a direct variation.
3 y
15 5
18 6
27 9
Answer:
Yes, it shows direct variation
Step-by-step explanation:
Given
The above table
Required
Is it a direct variation?
The constant of variation (k) is:
[tex]k = y/x[/tex]
For each pair x and y, we have:
[tex]k = 5/15 = 1/3[/tex]
[tex]k = 6/18 = 1/3[/tex]
[tex]k =9/27 = 1/3[/tex]
Since the calculate constant have the same value for all pair or x and y, then the table shows direct variation
Answer:1
Step-by-step explanation:3/3=1
Given EH = 12 and EG = 20 , find FJ.
Answer:
10
Step-by-step explanation:
If you look at it 20 is from EG so if FJ is half of EG then FJ is half of 20
solve: 3( − 3) − 5 >− 3 − 6
(show your work)
x>3 is the answer
Step-by-step explanation:
[tex]3( x− 3) − 5x >− 3x − 6 \\ 3x - 9 - 5x > - 3x - 6 \\ 3x - 9 - 5x + 5x > - 3x - 6 + 5x \\ 3x - 9 > 2x - 6 \\ 3x - 9 - 2x > 2x - 6 - 2x \\ x - 9 > - 6 \\ x - 9 + 9> - 6 + 9 \\ x > 3[/tex]
Solve the inequality -10w _< 20
Step-by-step explanation:
-10w< 20w< 20/-10w< -2hope it helps
stay safe healthy and happy...a cone with base radius 7 cm and a volume of 308cm^3 find the vertical height of the cone
Answer: Using the formula
V=πr2h
3
Solving for h;
h=3V
πr2=3·308
π·72≈6.00241cm
Step-by-step explanation:
Mathematics can help me with
Answer:
Fabric Cloaks
21 6
7 2
14 4
Step-by-step explanation:
To represent the situation, we can write a ratio using the information 21 sq meters per 6 wizard cloaks. we can write:
21 sq m/ 6 cloaks
and simplify both the numerator and denominator by dividing each by 3:
7 sq m/ 2 cloaks
We can already fill out the second row because, from the ratio above, we can say 2 cloaks use 7 sq m.
For the next row, we need the number of cloaks, or the denominator to be 4. So, we need to multiply both the top and the bottom by two to get:
14 sq m/ 4 cloaks
This means 4 cloaks need 14 sq m.
The function shown is a composition of the functions g(x) and h(x) .
f(x)=2x√+8−7
Which of the following shows a possible decomposition of the function f(x) ?
Distribute an amount of Rs. 200 between Raheem and Usman such that Raheem
gets RS 50 more than twice as much as Usman gets .
Answer:
50 and 150
Step-by-step explanation:
Raheem- (2x+50)
Usman- x
(2x+50)+x=200
3x+50=200
3x=150
x=50
plug in the numbers
What is the answer to this question
Answer:
48 units
Step-by-step explanation:
Pls ans this question step by step not only ans if it will help me than I will thanks uu comment uu pls ansme
Answer:
-2x+7
Step-by-step explanation:
Describe fully the single transformation that maps a onto shape b
Answer:
Reflected over y-axis
Sabe-se que EF = xcm , GH = (x + 6) cm , RS = 16 cm e NP = 28 cm . Sabendo que EF ,GH , RS ,e NP São, nessa ordem, segmentos proporcionais, determine o valor de x .
Answer:
The value of x is 8 .
Step-by-step explanation:
It is known that EF = x cm , GH = (x + 6) cm , RS = 16 cm and NP = 28 cm . Knowing that EF ,GH , RS , and NP are, in that order, proportional segments, determine the value of x .
As EF, GH, RS and NP are in proportion
So,
EF : GH = RS : NP
[tex]\frac{x}{x+6}=\frac{16}{28}\\\\7 x = 4 (x + 6)\\\\7 x = 4 x + 24 \\\\3 x = 24 \\\\x = 8[/tex]
What is the point-slope equation of a line with slope -3 that contains the point
(-8,-4)?
O A. y+ 4 = -3(x+8)
B. y+ 4 = -3(x-8)
C. y-4 = -3(x-8)
O D. y- 4 = -3(x+ 8)
Answer:
y + 4 = -3(x + 8)
Step-by-step explanation:
y + 4 = -3(x + 8)
Find the product
(7x^2y^3)(3x^5y^8)
Step-by-step explanation:
First, we put the expressions in multiplication form:
(7x2y3)×(3x5y8)(7x2y3)×(3x5y8)
We multiply like terms:
(7x2×3x5)(y3×y8)(7x2×3x5)(y3×y8)
We multiply the coefficients and add the exponents:
21x2+5y3+821x2+5y3+8
Solving, we obtain:
21x7y11
Hello!
[tex]\large\boxed{21x^7y^{11}}}[/tex]
(7x²y³)(3x⁵y⁸)
Multiply by ADDING exponents with the same base:
(7 * 3) (x² * x⁵) (y³ * y⁸)
21 * x² ⁺ ⁵ * y³ ⁺ ⁸
Simplify:
21 * x⁷ * y¹¹
21x⁷y¹¹
The rocket that carried the Curiosity Rover to Mars traveled at a speed of 21,000 miles per hour. What is this speed to the nearest mile per second?
6 miles per second
350 miles per second
1,260,000 miles per second
75,600,000 miles per second
Answer:
6 mps to the nearest mps.
Step-by-step explanation
The rocket that carried the Curiosity Rover to Mars traveled at a speed of 21,000 miles per hour. What is this speed to the nearest mile per second?
1 hr = 3600 sec
Since an hour is 3600 seconds (i.e., 60 x 60), you simply need to divide that number by 3600
→ 21000 mph = 21000 ÷ 3600 mps = 5 5/6 mps →
ANSWER : 6 mps to the nearest mps.
Answer:
Believe the other person
Step-by-step explanation:
I got a 100%, and also got this question.
Jul 02, 10:37:22 AM
Drag the numbers below to put them in order from least to greatest:
9.58 9.558 9.62 9.7 9.691 9.592
Answer: 9.558, 9.58, 9.592, 9.62, 9.691, 9.7
Step-by-step explanation:
Answer:
9.7 9.58 9.62 9.558 9.592 9.691
[tex]factories : - \\ \\ p {}^{2} + 8p - 84[/tex]
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: (p - 6)(p + 14) }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] {p}^{2} + 8p - 84[/tex]
[tex] = {p}^{2} + 14p - 6p - 84[/tex]
Taking [tex]p[/tex] as common from first two terms and [tex]6[/tex] from last two terms, we have
[tex] = p(p + 14) - 6(p + 14)[/tex]
Taking the factor [tex](p+14)[/tex] as common,
[tex] = (p - 6)(p + 14)[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Mystique35 }}{\red{❦}}}}}[/tex]
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹27 for a book kept for seven days, while Susy paid ₹21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Answer:
Ji Gud afternoon.
I'm fine
what about you madam.
Hope u r fine and stay safe and healthy
a solid cylinder has radius x cm and height (7x÷2) cm .the surface area of a sphere with radius R cm is equal yo the total surface area of the cylinder . find an expression for R in terms of x
Answer:
[tex]R=(\sqrt{11} )\frac{x}{2}[/tex]
Step-by-step explanation:
The expression for the radius of the sphere will be R = (3/2)x.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that a solid cylinder has a radius x cm and height (7x÷2) cm .the surface area of a sphere with a radius R cm is equal to the total surface area of the cylinder.
The expression will be solved as:-
SA ( sphere) = 4πR²
SA (cyl) = 2πr² + 2πrl
SA (cyl) = 2πx² + 2πx ( 7x / 2)
SA (cyl) = 2πx² + 7πx²
SA ( sphere) = SA (cyl)
4πR² = 2πx² + 7πx²
R² = 9πx² / 4π
R = √(9x²/4)
R = ( 3 / 2 )x
Therefore, the expression for the radius of the sphere will be R = (3/2)x.
To know more about an expression follow
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Find the measure of the missing angle using the triangle angle sum theorem
Answer:
m∠60
Step-by-step explanation:
30 + 90 = 120
180-120=60
Answer:
x = 60°
Step-by-step explanation:
A triangle is equal to 180°
Make an equation and solve:
30° + 90° + x = 180°
120° + x = 180°
x = 180° - 120°
x = 60°
what is the measure of angle D?
Answer:
57
Step-by-step explanation:
Can someone help with 11 & 13
[tex]11. \: we \: know \: that \\ \frac{sum \: of \: all \: quantities}{number \: of \: quantities} = mean \\ => \frac{7 + 11 + 13 + 6 + 8 + x}{6} = 8 \\ = > \frac{45 + x}{6} = 8 \\ = > 45 + x = 8 \: \times 6 \\ = > 45 + x = 48 \\ = > x = 48 - 45 \\ = > x = 2 \\ \\ 12. we \: know \: that \\ \frac{sum \: of \: all \: quantities}{number \: of \: quantities} = mean \\ => \frac{2 + 5 + 1.3 + 2.2 + x}{5} = 1.8 \\ = > \frac{10.5 + x}{5} = 1.8 \\ = > 10.5 + x = 5 \times 1.8 \\ = > 10.5 + x = 9 \\ = > x = 9 - 10.5 \\ = > x = - 1.5 \\ [/tex][/tex]
This is the answer.
Hope it helps!!
step below. Question 1 Hexagon AGHBGHCGHD GHEGHFGH is a reflected image of hexagon ABCDEF. The midpoints of the sides of hexagon ABCDEF are also shown. Drag the line of reflection, Għ until the image coincides with the preimage. At this location, if the preimage flips about the line of reflection, it will flip onto itself. In how many different positions can you place GHso the image reflects onto the preimage in this manner? Describe the different positions. Be sure to pass the line of reflection through both vertices and midpoints before answering.
Answer:
Hexagon AGHBGHCGHDGHEGHFGH coincides with hexagon ABCDEF when GH passes through the midpoints of opposite sides; that is, it is a perpendicular bisector of the two sides. HexagonAGHBGHCGHDGHEGHFGH also coincides with hexagon ABCDEF when the line of reflection joins a pair of vertices opposite one another on the hexagon. There are three perpendicular bisectors and three pairs of opposite vertices. In all, there are six lines of reflection that will map the hexagon back onto itself.
Step-by-step explanation:
Rewrite the expression as a simplified expression containing one term.
Answer:
-(cos α)/(sin α)
= -cot α
Step-by-step explanation:
use trigonometric identities
LAST QUESTION SOMEONE HELP PLEASE QUICK
Answer:
27%
Step-by-step explanation:
Answer:
p(j)=27% is correct answer
