Answer:
The other sides equal 9cm also because a square has four equal sides.
L=9cm * W=9cm =A
A=81 cm
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
NEED HELP WITH THIS PLEASE. Just show me how please.
Given:
The quadratic equation is:
[tex]-5x^2-3x-2=0[/tex]
To find:
The discriminant of the given equation and the number of real solutions.
Solution:
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then the value of discriminant is:
[tex]D=b^2-4ac[/tex]
If D<0, then the quadratic equation has no real roots or two imaginary roots.
If D=0, then the quadratic equation has two equal real roots.
If D>0, then the quadratic equation has two distinct real roots.
We have,
[tex]-5x^2-3x-2=0[/tex]
Here, [tex]a=-5,b=-3,c=-2[/tex]. So, the discriminant of the given equation is:
[tex]D=(-3)^2-4(-5)(-2)[/tex]
[tex]D=9-40[/tex]
[tex]D=-31[/tex]
Since D<0, therefore the number of real solutions is 0.
Hence, the value of the discriminant is -31 and the number of real solutions is 0.
Please don't troll!!!!!!!
Answer:
Ben = $ 41
Kaden = $ 31
Step-by-step explanation:
Let initially Ben has $ p and then Kaden has $ (p - 10).
After that
Ben has= $ (p + 4)
Kaden has = $ (p- 10 + 4) = $ ( p - 6)
According to the question,
[tex]p- 6 = \frac{7}{9}\times (p+4)\\\\9 p- 54 = 7 p + 28 \\\\2 p = 82\\\\p =41[/tex]
Initially Ben has $ 41 and Kaden has $ 31.
The length of the missing sides
Answer:
length-14cm width-7cm
Step-by-step explanation:
To work out the sides, you can use 2l+2w=42. Since the length is twice the width, this becomes 2(2w)+2w=42.
This can be expanded to 4w+2w=42 or 6w=42.
From there, we can divide both sides by 6 to isolate w, meaning w=7.
Since the length is twice the width, it is given by l=2×7 or l=14.
**This question involves writing and solving algebraic equations from worded questions, which you may wish to revise. I'm always happy to help!
The average temperature of Kopikoville was reported to be - 23° last year. This year, the average temperature of Kopikoville rose by 6°. Which of the following is true about this year's average temperature of Kopikoville? A. This year's average temperature of Kopikoville is - 29°. B. This year's average temperature of Kopikoville is - 17°. C. This year's average temperature of Kopikoville is 17°.
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?
Which theorem would be used to write 15x + 12 + 117 = 180 in the diagram below?
a. Alternate Interior Angles Theorem
b. Corresponding Angles Theorem
c. Consecutive Exterior Angles Theorem
d. Vertical Angles Theorem
Answer:
C. Consecutive Exterior Angles Theorem states that if the transversal passes through the two parallel lines then any two exterior angles are congruent
Answer:
B
Step-by-step explanation:
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!
How do you get 21/2?
Answer:
10 1/2
Step-by-step explanation:
/ = divide
21 divided by 2 is 10 remainder 1 ~ 10 1/2 as a mixed number
21/2 as a improper fraction
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
15 pages in 2 days ___ in 1 day
Answer:
7.5 pages.
Step-by-step explanation:
You divide 15 by 2 to work out 1 day.
Answer:
7.5 pages in 1 day
Step-by-step explanation:
In order to find the answer, you would need to do is divide 15 with two since every two days 15 pages are completed, and you would therefore get your answer which is 7.5. If you want to check your answer then simply multiply 7.5 with 2.
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
Alt Test 7 -6 -5 -4 -3 -2 -1 2 3 1 Le 6 N . 1 -Z -3 -4 รา -6 In this graph, the y-intercept of the line is The equation of the line is y= y X
Answer:
[tex]{ \tt{y = y {}^{x} }} \\ y - intercept : { \tt{y = {y}^{0} }} \\y = 1[/tex]
What is the point of intersection to the system below?
2x - 3y = 5
3x +3y = 5
Answer:
Solution: {x = 2, y = -1/3}
Step-by-step explanation:
On observation, we see that the y-terms are equal and opposite in sign, therefore to solve the system, we add the two equations.
2x-3y = 5 ..........(1)
3x+3y = 5............(2)
(1) + (2)
2x - 3y + 3x + 3y = 5+5
5x = 10
x = 2 .......(3)
Substitute (3) in (2) and solve for x
3x+3y = 5 .....(2)
3(2) + 3y = 5
3y = 5-6 = -1
y = -1/3 .......(4)
assemble (3) and (4) to give the answer
Solution: {x = 2, y = -1/3}
The blue dot is at what value on the number line?
Answer:
The blue dot is at 3.
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.
Which number is the EXPONENT? 4^2 = 16 *
Answer: 4
Step-by-step explanation:
The exponent in the given number [tex]4^{2}=16[/tex] is 2.
What is exponent?
An exponent refers to the number of times a number is multiplied by itself.
For example, [tex]3^{4}[/tex] means we are multiplying 3 four times. Here the base is 3 and exponent is 4.
According to the question
We have a number
[tex]4^{2} =16[/tex]
Here, we are multiplying 4 two times. So, the base is 4 and the exponent is 2.
Hence, the exponent in the given number [tex]4^{2}=16[/tex] is 2.
Learn more about the exponent here:
https://brainly.com/question/5497425
#SPJ2
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 :)
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
Simplify fully
a) 8c²d^5 ÷ 2c³d³
b) 9a³b^5 ÷ 3ab²
Answer:
A) 8d^2/3c
B) 3a^2b^3
Step-by-step explanation:
Answer:
Step-by-step explanation:
In exponent division, if base are same , subtract the exponents.
[tex]\frac{a^{m}}{a^{n}}=a^{m-n} , m>n\\\\ \frac{a^{m}}{a^{n}}= \frac{1}{a^{n-m}}, m<n[/tex]
a) 8c²d⁵ ÷ 2c³d³ = [tex]\frac{8}{2}* \frac{d^{5-3}}{c^{3-2}}= 4*\frac{d^{2}}{c}= \frac{4d^{2}}{c}[/tex]
b) 9a³b⁵ ÷ 3ab² = [tex]\frac{9}{3}* a^{3-1}*b^{5-2} = 3a^{2}b^{3}[/tex]
plsssssssssssss help
Answer:
SSS (Side side side)
Step-by-step explanation:
If x= 3 what is the value of 50 - 2x?
50 - 2x; x = 3
____________________
50 - 2(3)
= 50 - 6
= 44
(a+b)(a-b)=? Đây là hằng đẳng thức nào?
Answer:
không
Step-by-step explanation:
Answer:
(a + b)(a - b) = a² - b²
Step-by-step explanation:
(a + b)(a - b) = a (a - b ) + b (a - b )
= a² - ab + ba - b² [ ab = ba ]
= a² - ab + ab - b² [ ab - ab = 0 ]
= a² - b²
Sketch the graph of y = (x + 3)2 – 4 and identify the axis of symmetry.
Answer: Thought I’d return the favor and help u with this question! But anyways, the axis of symmetry is at x = -3.
Explanatio: This can be found by looking at the basic form of vertex form:
y = (x - h)^2 + k
In this basic form the vertex is (h, k). By looking at what is plugged into the equation, it is clear that h = -3 and k = -4. This means the vertex is at (-3, -4).
It is a fact that the axis of symmetry is a vertical line of x = (vertex value of x). So we can determine that the axis of symmetry is at x = -3
i hope this helps u
simplify the following equation 32m : 2km
Step-by-step explanation:
the answer is in the image above
express 42 base 7 in base 10
Answer:
correct 42 in bsae 10 is 60
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
Simplify........................
Answer:
The answer is 3.
[tex]\longrightarrow{\purple{3}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \frac{(6a + b)(a + b) - 7b(a + b)}{2 {a}^{2} - 2 {b}^{2} } [/tex]
[tex] \\= \frac{(a + b)(6a + b - 7b)}{2( {a}^{2} - {b}^{2}) } [/tex]
[tex] \\= \frac{(a + b)(6a + b - 7b)}{2(a + b)(a - b)} [/tex]
[tex] \\= \frac{6a - 6b}{2(a - b)} [/tex]
[tex] \\= \frac{6(a - b)}{2(a - b)} [/tex]
[tex] \\= 3[/tex]
( OR )
[tex] \frac{(6a + b)(a + b) - 7b(a + b)}{2 {a}^{2} - 2 {b}^{2} } [/tex]
[tex] \\= \frac{6 {a}^{2} + 6ab + ab + {b}^{2} - 7ab - 7 {b}^{2} }{2( {a}^{2} - {b}^{2} )} [/tex]
[tex] \\= \frac{6 {a}^{2} - 6 {b}^{2} + 7ab - 7ab }{2( {a}^{2} - {b}^{2} )} [/tex]
[tex] \\= \frac{6 {a}^{2} - 6 {b}^{2} }{2( {a}^{2} - {b}^{2} )} [/tex]
[tex] \\= \frac{6( {a}^{2} - {b}^{2} )}{2( {a}^{2} - {b}^{2} )} [/tex]
[tex] \\= \frac{6}{2} [/tex]
[tex] \\= 3[/tex]
Note:[tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex]
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♬}}}}}[/tex]
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:
Name the polygon with seven sides_____
a polygon with seven sides is called a heptagon
Answer:
Hyptagon
Step-by-step explanation:
In geometry, a heptagon is a seven-sided polygon or 7-gon.
The heptagon is sometimes referred to as the septagon, using "sept-" (an elision of septua-, a Latin-derived numerical prefix, rather than hepta-, a Greek-derived numerical prefix; both are cognate) together with the Greek suffix "-agon" meaning angle.