Answer:
Step-by-step explanation:
The length of the ladder is the length of the hypotenuse of the right triangle formed. Since the height up the building is based on the distance the ladder is from the base of the building, and that distance is x, then the height up the building is x + 7. So what we have is a right triangle with one leg measuring x, the other leg measuring x + 7, and the hypotenuse measuring 13. Set up using Pythagorean's Theorem:
[tex]13^2=(x+7)^2+x^2[/tex] and do some simplifying. The left side is easy since 13-squared is 169; the right side not so much. We first have to expand that set of parenthesis by multiplying x + 7 by itself twice to get a second degree polynomial:
[tex](x+7)(x+7)=x^2+14x+49[/tex] and now we have:
[tex]169=x^2+14x+49+x^2[/tex] which simplifies down a bit to
[tex]169=2x^2+14x+49[/tex]
The only way to solve this for x, the height up the side of the building, is to factor. In order to do that, everything has to be on one side of the equals sign, setting the whole messy thing equal to 0:
[tex]2x^2+14x+49-169=0[/tex] and
[tex]2x^2+14x-120=0[/tex]. Begin by factoring out a 2:
[tex]2(x^2+7x-60)=0[/tex] and then factor the remaining quadratic using whatever method you are currently using in class to solve for x. Doing this will give that
x = -12 and 5. Since a side length will never be negative, we determine that x = 5 which is the distance between the bases of the buildings, and the height up the building where the ladder hits it is 12.
The transportation department predicts that about 800,000 cars will be registered in a certain state by year 2012. Their license plates are made using and two letters followed by and three digits from 0 to 9. Will there be enough possible arrangements?
Answer:
There won't be enough arrangement
Step-by-step explanation:
Given
[tex]Letters = 2[/tex]
[tex]Digits= 3[/tex]
[tex]Cars = 800000[/tex]
Required
Determine if the possible arrangement will be enough
The 2 letters can be selected from any of the 26 alphabets without restriction.
So, the selection of letters is:
[tex]Letters = 26 * 26[/tex]
The 3 digits can be selected from any of the 10 digits without restriction.
So, the selection of digits is:
[tex]Digits = 10*10*10[/tex]
The total arrangement is:
[tex]Total = Letters * Digits[/tex]
[tex]Total = 26*26*10*10*10[/tex]
[tex]Total = 676000[/tex]
By comparison:
[tex]Total < Cars[/tex]
i.e.
[tex]676000 < 800000[/tex]
Hence, the arrangement will not be enough
What is the length of the hypotenuse?
Answer:
13 cm
Step-by-step explanation:
[tex] \sqrt{ {12}^{2} + {5}^{2} } = \sqrt{169 } = 13[/tex]
[tex]245 \div 7[/tex]
Answer:
35
Step-by-step explanation:
[tex]245[/tex] ÷ [tex]7[/tex] :-
[tex]245[/tex] ÷ [tex]7 = 35[/tex]
Find the value of x, when log 10x + log 2 = log 60
Answer:
x = 3
Step-by-step explanation:
log 10x + log 2 = log 60
Subtract log 2 from each side
log 10x + log 2 -log 2 = log 60 - log 2
log 10x = log 60 - log 2
We know that log a - log b = log (a/b)
log 10 x = log (60/2)
log 10x = log 30
We know log a = log b that a = b
10x = 30
Divide by 10
10x/10 = 30/10
x =3
A computer downloads a 48 kilobyte file in 5 seconds. At this rate, how long will it take the computer to download a file that is 120 kilobytes?
Answer:
12,5
Step-by-step explanation:
First, you need to find how many kilobytes do you download every seconds.
You simply divide 48 kilobyte / 5 seconds and you get 9,6 kB/s.
Now you know that your download speed is this you can find the amount of time needed for downloading 120 kilobytes.
You simply divide [tex]\frac{120 kilobytes}{9,6 kilobytes/s} = 12.5 s[/tex].
12,5 seconds.
what is the equivalent decimal to 3/3
Answer:
answer is 1
Step-by-step explanation:
3 and 3 gets cancel .when you divide the same number answer is always 1
find the volume of 2 and 1/2 1 and 1/2 and 3
To find the volume multiply all 3 numbers together.
2 1/2 x 1 1/2 = 3 3/4
3 3/4 x 3 = 11 1/4
The volume is 11 and 1/4 cubic units
Write the equation of the line through (8,-2); m = 0
ANSWER ASAP PLEASE!!
Answer:
y = -2
Step-by-step explanation:
The formula for point-slope is as follows:
y - y1 = m(x - x1)
We are given the slope, m, or 0, and we are given the point (8, -2), which we can substitute into the point (x1, y1):
y + 2 = 0(x - 8)
y + 2 = 0
y = -2
What do I put In the empty boxes .
hey! please help i’ll give brainliest
Answer:
Answer is A
Step-by-step explanation:
smart
Answer:
i. A government by the people is the answer.
Step-by-step explanation:
Hope it helps you:)
Guys l forgot how to do this l knew how to buy can someone please remind me what to do asap pleasee
12 POINTS HELLPP
IM TAKING A TESTTT ASAPP
Answer: i would say 550 miles or 1,100 miles
Step-by-step explanation:
Hunter did not want to spend more than 150$ for a flight from Reno to Los Angeles. Write the inequality that models this situation and determine the first two possible solutions
Answer:
[tex](a)\ x < 150[/tex]
[tex](b)\ x = 149; x = 148[/tex]
Step-by-step explanation:
Given
[tex]Amount = 150[/tex] --- not more than
[tex]x \to[/tex] spending
Solving (a): Represent as an inequality
Not more than means <
So, the inequality is:
[tex]Spending < Amount[/tex]
[tex]x < 150[/tex]
Solving (b): The first two possible solutions
These are the numbers closest to 150 i.e. 149 and 148
Hence, [tex]x = 149; x = 148[/tex]
Luis compra 126 celulares a $268 por cada uno. Cada celular fue vendido a $325 ¿Cuánto dinero gano Luis?
Answer:
Ganancia total= $7.182
Step-by-step explanation:
Dada la siguiente información:
Luis compra 126 celulares a $268 por cada uno. Cada celular fue vendido a $325.
Primero debemos calcular cuanto gana con cada celular:
Ganancia unitaria= 325 - 268
Ganancia unitaria= $57
Ahora, la ganancia total:
Gnanacia total= 57*126
Ganancia total= $7.182
Point B has coordinates (3,2). The x-coordinate of point A is −6. The distance between point A and point B is 15 units. What are the possible coordinates of point A?
Answer:
Distance between two points= √(x2-x1)²+(y2-y1)²
D= 15units
Let "k" be the y-coordinate of A
A(-6,k)
B(3,2)
15= √(3--6)²+(2-k)²
Taking square of both sides to eliminate the square root.
15²=(9)²+(2-k)²
225=81+4-4k+k²
k²-4k - 140=0
Using Quadratic Formula to evaluate
k= 14 or k=-10
The Possible coordinates of A are
(-6,14) or (-6,-10)
A person is skateboarding to their local skate shop to pick up some sick rims. They skate at 8 miles per hour. The store is 2.5 miles away. How long will it take them to get to the store in hours?
Answer: 0.3125 hours
Step-by-step explanation:
The formula for time taken to cover a distance is:
= Distance / Speed
Distance = 2.5 miles
Speed = 8 miles per hour
Time taken = 2.5 / 8
= 0.3125 hours
In minutes this is:
= 0.3125 * 60 mins
= 19 mins approx
If the relationship between the independent and dependent variables is discovered to be false after another (third) variable is considered, that relationship between the independent and dependent variables is called
Answer:
"Spurious relationship" is the correct answer.
Step-by-step explanation:
A word always used to characterize a statistical association among two values, which purports to be directly connected, sometimes by coincidences or because of the function of such an intermediate step third factor after careful review, seems to have been, is defined as Spurious.Misconduct whatsoever amongst two factors which would also be produced by a third factor is a Spurious relationship.The relationship between the independent and dependent variables in this case can be referred to as: spurious relationship.
What is a Spurious Relation?A spurious relationship can be described as a statistical association between two variables, which are claimed to be directly connected to each other, and may in fact, just be a coincidence or may have been connected together by an intermediate or third factor when carefully examined.
Therefore, the relationship between the independent and dependent variables in this case can be referred to as: spurious relationship.
Learn more about spurious relationship on:
https://brainly.com/question/25093000
Edward has a box of following Skittles: 5 red, 4 green, 6 orange, 3 purple, and 7 yellow. He wants to know what the probability of choosing a red Skittle, eating it, and then choosing a yellow Skittle is. Which expression below shows Edward how to correctly find the probability of this situation? Skittles Original O 7/25 x 4/25 5/25 x 7/25 5/25 x 7/24 05/24 x 7/24
Answer:
Let's add the total skittles to get our outcome:
25 in total.
5(red skittles)/25(total skittles in all)
7(yellow skittles)/24(total skittles in all NOW since you took a red skittle)
So therefore your expression is:
5/25 x 7/24
PLs, help quickly please I will give brainliest
9514 1404 393
Answer:
outcomes (top to bottom): SS, SG, GS, GG
all probabilities are 0.25
Step-by-step explanation:
Each outcome is identified by the labels on the ends of the corresponding tree branch, in order left-to-right. The top one is SS, for example, and the next one down is SG. Continuing down the tree, the outcomes are GS and GG.
Each letter has a probability of 1/2, so any pair of letters will have a probability of (1/2)(1/2) = 1/4 = 0.25.
__
This method of identifying outcomes and their probabilities can ensure that you find all outcomes. The sum of probabilities should be 1.00 if the tree is properly constructed.
if the family chooses to give you a 20% tip and the tax rate is 8.5% how much will they pay in total??
Enter cost and tip percent to get a tip amount and total dinner amount. ... how many people? ... Calculate a tip or gratuity and get the total amount to pay. ... If you are splitting the cost at a restaurant among several people you can divide by the ... To calculate a gratuity or tip on any calculator it is a simple multiplication.
Answer:
Step-by-step explanation:
ill mark brainliest for correct answer
Answer:
Solution given:
[tex]\frac{1}{5}(6+3+1)²[/tex]
[tex]\frac{1}{5}(10)²[/tex]
[tex]\frac{1}{5}100[/tex]
=20 is a required answer.
Renee wrote the pattern shown below. What is the rule for following Renee's pattern? 23, 47, 95, 191 A. multiply by 2 B.multiply by 2, add 1 C.multiply by 2, add 2 D.multiply by 2, subtract 1
Answer:
B. Multiply by 2, add 1
explanation:
23× 2 = 46 + 1 = 47
47 × 2 = 94 + 1 = 95
95 × 2 = 190 + 1 = 191
2
Angle 1 and angle 2 are complementary. If m21
36°, what is m_2?
m2 =
Answer:
54
Step-by-step explanation:
Complementary angles add up to equal 90
If ∠1 and ∠2 are complementary angles then ∠1 + ∠2 = 90
if ∠1 = 36 then 36 + ∠2 = 90
90 - 36 = 54
Hence, ∠2 = 54
X^2 +14x+13=0 solve for X
X=13,1
I hope this helped :)
help me plzzz plzzzzd
Answer:
C
Step-by-step explanation:
Answer:
D should be the right answer
Step-by-step explanation:
for the other choices the grammar doesn't sound quite right to me
A population of beetles is modeled by the equation b(t) = 3,000 (2)t where t represents the number of weeks since the population was first measured?
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]b(t) = 3000 * 2^t[/tex]
The question is incomplete;
A possible question could be to calculate the initial amount of beetle
An exponential function is represented as:
[tex]f(x) = ab^x[/tex]
Where
[tex]a \to Initial\ amount[/tex]
By comparison:
[tex]a = 3000[/tex] --- The initial number of beetles
Another question could be to solve for f(t), after a certain number of weeks (say 3)
Substitute 3 for t in: [tex]b(t) = 3000 * 2^t[/tex]
[tex]b(3) = 3000 * 2^3[/tex]
[tex]b(3) = 3000 * 8[/tex]
[tex]b(3) = 24000[/tex]
Help me plzzzzzzzzzzzzz
Answer:
The area of a circle.
Step-by-step explanation:
Can I get brainiest please
In the diagram, a∥b and b∥c. Find the values of x. PLEASEEE HELP
The order of the answers doesn't matter.
================================================
Explanation:
a || b means the two lines a and b are parallel
If a || b and b || c, then a || c by the transitive property. Think of it like chaining pieces together.
Since a || c, this means the alternate exterior angles |5x+15| and 100 are congruent, or the same measure.
Solve for x
|5x+15| = 100
5x+15 = 100 or 5x+15 = -100
5x = 100-15 or 5x = -100-15
5x = 85 or 5x = -115
x = 85/5 or x = -115/5
x = 17 or x = -23
The value of x is 17.
What is alternate exterior angle?When a transversal intersects two or more lines, alternate exterior angles are produced. These angles are created on the various transversal sides' outer edges.
Any two parallel lines that cross a transversal produce a few pairs of angles with the transversal. In the area inside the parallel lines, interior angles are generated, whilst alternative external angles are created in the area outside the parallel lines.
Given:
<1 = 5x + 15
<2 = 100
Using alternate exterior angle
5x + 15 = 100
5x = 100- 15
5x = 85
x= 85/5
x= 17
Hence, the value of x is 17.
Learn more about alternate exterior angle here:
https://brainly.com/question/2279752
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If the quadrilateral below is a trapezoid, find the missing measures.
PLEASE HELP
Answer:
101°
46°
Step-by-step explanation:
The sum of angle C and angle F should be 180°as they are parallel.
Hence, angle C ;
Angle C + angle F = 180°
Angle C + 79° = 180°
Angle C = 180° - 79°
Angle C = 101°
Sum of angle in Trapezoid = 360°
Hence,
C + D + E + F = 360°
101° + 134° + E + 79° = 360°
314° + E = 360°
E = (360 - 314)°
E = 46°
Need help fast pleasee??
Answer:
Option 3.) f(-3) = g(-3), since that x-value of the point of intersection
Hope this helps!