Answer: 5/8
Step-by-step explanation:
A 10 meter long ladder rests against a vertical wall so that the distance between the foot of the ladder and the wall is 2 meter. Find the angle the ladder makes with the wall and height above the ground at which the upper end of the ladder touches the wall. Round your answer to the nearest hundredth of a degree if necessary.
Answer:
1. The angle ladder makes with the wall is 11.54°
2. The height above the ground at which the upper end of the ladder touches the wall is 9.80 m
Step-by-step explanation:
∠A is what we are trying to find. Also AC is the length we are trying to find, as well.We see that the side opposite of ∠A and the hypotenuse (side opposite of 90 degree angle) of the triangle are known. The ratio that relates these two sides are SINE.
We know,
[tex]sin(angle)=\frac{opposite}{hypotenuse}[/tex]
Thus we can write:
[tex]sin(A)=\frac{2}{10}\\sin(A)=\frac{1}{5}[/tex]
To find ∠A, we take the inverse sine of [tex]\frac{1}{5}[/tex]. Our answer is:
[tex]sin(A)=\frac{1}{5}\\A=sin^{-1}(\frac{1}{5})\\A=11.54[/tex]
Thus the angle ladder makes with the wall is 11.54°
Second part of the question asks for the height above the ground at which the upper end of the ladder touches the wall, this is the length of AC.
Given the angle we found, we see that the side AC is adjacent of the angle and we also know the hypotenuse. The ratio that relates these 2 sides is COSINE.
We know,
[tex]cos(angle)=\frac{adjacent}{hypotenuse}[/tex]
Thus, we can write:
[tex]cos(11.54)=\frac{AC}{10}[/tex]
Cross multiplying and solving for AC, gives us:
[tex]cos(11.54)=\frac{AC}{10}\\AC=10*cos(11.54)\\A=9.80[/tex]
Thus, the height above the ground at which the upper end of the ladder touches the wall is 9.80 m
what is the value of p in the linear equation 24 p + 12 - 18 p
Answer:
P= -2 NEGATIVE 2
Step-by-step explanation:
Answer:
B. -2
Step-by-step explanation:
The numbers of days of rain per month in Seattle, for a period of twelvre
months, are
18, 14, 16, 14, 12,9, 5, 0, 7, 13, 18, 17
What is the range of the data values?
Answer:
18
Step-by-step explanation:
will mark brainliest :) please answer if 100% positive. thank you
Clyde ran 3 1/3 miles on Friday. On Saturday, he ran 4 2/7 times that distance. How far did Clyde run on Saturday?
Answer:
100/7 miles
Step-by-step explanation:
So 3 1/3 can be written as 10/3 and 4 2/7 can be written as 30/7. So multiplying, we get 300/21 which can be simplified to 100/7.
Abbie recorded the temperatures at which two oils freeze: Oil Temperature Cottonseed oil −48.1 °C Coconut oil 24.8 °C Which statement about the temperatures at which these oils freeze is true? Coconut oil freezes at a higher temperature than cottonseed oil because 24.8 °C < −48.1 °C. Coconut oil freezes at a lower temperature than cottonseed oil because 24.8 °C < −48.1 °C. Coconut oil freezes at a higher temperature than cottonseed oil because 24.8 °C > −48.1 °C. Coconut oil freezes at a lower temperature than cottonseed oil because 24.8 °C > −48.1 °C.
Answer:
The correct answer is option (C).
Coconut oil freezes at a higher temperature than cottonseed oil because 24.8 > -48.1
Step-by-step explanation:
We have been given the freezing temperatures of cottonseed oil and coconut oil. The freezing temperature of cottonseed oil is -48.1 degree celsius and the same for coconut oil is 24.8 degree celsius.
We are supposed to compare the two freezing temperatures. We know that 24.8 is higher than -48.1, therefore, we can conclude that freezing temperature of coconut oil is higher than the freezing temperature of cottonseed oil because 24.8 is more than -48.1. Thus, correct answer is option (C).
Answer:
C
Step-by-step explanation:
what is m+4(2m-3)=-3
Answer:
m = 1
Step-by-step explanation:
distribute and simplify the left side of the equation
m + 8m - 12 = - 3
9m - 12 = - 3 ( add 12 to both sides )
9m = 9 ( divide both sides by 9 )
m = 1
Fill in the blank plz
Step-by-step explanation:
a. Given => m∠5 = 40°
b. Given => m∠2 = 140°
c. Same Side Interior Angle Theorem => The same side interior angles must add up to 180°, which in this case, it does. m∠4 and m∠2 are alternate interior angles, and so there measurements are the same. 180 - 140 = 40
d. Both angles are part of the "same-side interior angles", which means that there measurements should add up to 180°. Note that m∠5 = 40°, and m∠2 = 140° (Given). Set the equation
m∠5 + m∠2 = 180
Plug in the number for each angle
40 + 140 = 180
180 = 180 (True).
e. It is proven that the above measurements are congruent with their corresponding parts. This means that a || b through Converse of Same Side Interior angle Theorem.
~
PLEASE HELP!!!!!!
Which number(s) below belong to the solution set of the inequality? Check all that apply.
“X + 22 < 32”
A. 5
B. 71
C. 10
D. 15
E. 8
F. 0
A
E
And
F
They all add up to under 32.
the permitir of the garden is (6x+2) units. Find the length of the missing side .
Answer: ? = x + 1
Step-by-step explanation:
The perimeter of the garden is x + 3x + 1 + x + ?
The perimeter of the garden is also (6x + 2)
Therfore:
x + 3x + 1 + x + ? = 6x + 2
Collect like terms:
5x + 1 + ? = 6x + 2
Subtract 5x from both sides:
1 + ? = x + 2
Subtract 1 from both sides:
? = x + 1
You cannot find ? as a number, only in terms of x.
What is the slope of the line represented by the equation 6y-14x=5
Answer:
14/6
Step-by-step explanation:
To find the slope, we can put it into slope intercept form. So 6y=14x+5. So y=14/6+5/6.
Lipids are made of fatty acids and glycerides. All fatty acids contain a
A. Carboxyl group
B. Water molecule
C. Hydroxyl group
D. Triglyceride
Answer:
D. triglyceride:
Step-by-step explanation:
lipids are a groups of organic molecules, that are insoluble, that contain fatty acids, triglyceride, phospholipids, and sterols.
Sam purchased 3 games for $140 after a discount of 30%. What is the original price
The original price of the three video games before the discount was $200.
Sam purchased 3 video games for a total of $140 after receiving a 30% discount. To find the original price of the games before the discount, we need to divide the sale price by the percentage that Sam actually paid (100% - discount percentage).
The discount percentage is 30%, so Sam paid 100% - 30% = 70% of the original price. Since 70% is the same as 0.70 in decimal form, we can set up the equation:
$140 = original price * 0.70
To determine the original price, divide $140 by 0.70:
Original price = $140 / 0.70
Original price = $200
Therefore, the original price of the three video games before the discount was $200.
Marisa painted 1/2 of her bedroom in 3/4 of a hour at this rate how long will it take her to paint the entire room
Answers
3/8 of an hour
8/3 of an hour
4/6 of an hour
6/4 of an hour
At the same rate, it would take Marisa 6/4 of an hour to paint the entire room. This is a ratio problem, specifically dealing with rates and proportional relationships.
Explanation:Since Marisa painted 1/2 of her room in 3/4 of an hour, to paint the entire room would take double that time. When you double 3/4, you get 6/4. Therefore, at the same rate, Marisa would need 6/4 of an hour to paint the entire room.
This problem is a basic ratio problem related to rates and proportional relationships, common topics in middle school math. The rate in this case is painting speed, half a room per 3/4 of an hour. Thus, when we double the room space to be painted (from half a room to a full room) we should also double the required time.
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12 = n/-3 + 10
what is the value of n
Answer: n = -6
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
12= −1/3n +10
Step 2: Flip the equation.
−1/3n +10=12
Step 3: Subtract 10 from both sides.
−1/3n +10−10=12−10
−1/3n =2
Step 4: Multiply both sides by 3/(-1).
(3/−1) x (-1/3n) = (3/-1) x (2)
n=−6
need some help, thanks :)
Answer:
x=24 in
Step-by-step explanation:
We can use proportions to solve this problem
5 15
------ = -------------
8 x
Using cross products
5 * x = 8 *15
Divide by 5
5x/5 = 8*15/5
x = 8*3
x =24
A survey at your school found that 792 in 1,220 students have a cell phone. What percent of the a poinp students in school have a cell phone? Round to the nearest hundredth where necessary
Answer: 100/1220*792= 64.9 have cell phones.
Step-by-step explanation:
Answer:
The percentage of students with cell phone is 64.92%
Step-by-step explanation:
Given
Sample Size = 1,220
Number of student with cell phones = 792
Required
Percentage of students with cell phone
To calculate the percentage of students with cell phone, we take a ratio of the number of students with cell phone to the sample size.
Mathematically, this is represented as
[tex]Percentage = \frac{Students-with-cell-phone}{Sample Size}[/tex]
By Substitution,
[tex]Percentage = \frac{792}{1220}[/tex]
[tex]Percentage = 0.64918032786[/tex]
[tex]Percentage = 64.918032786[/tex]%
[tex]Percentage = 64.92[/tex]% Approximated to nearest hundredth
Hence, the percentage of students with cell phone is 64.92%
At a pizzeria, the ratio of pizzas topped with meat to pizzas topped with vegetables was 4:3 on Saturday. The pizzeria made a total of 84 pizzas that day. How many of those pizzas were topped with vegetables?
A. 12
B. 36
C. 48
D. 63
Answer:
Option B is correct
36 pizzas were topped with vegetables
Step-by-step explanation:
Let x be the number.
As per the statement:
At a pizzeria, the ratio of pizzas topped with meat to pizzas topped with vegetables was 4:3 on Saturday.
The ratio of pizza topped with meat to pizzas topped with vegetables = 4 : 3
then;
the number of pizza topped with meat = 4x
and
the number pizza topped with vegetables = 3x
It is also given that the pizzeria made a total of 84 pizzas that day.
[tex]\text{Total Pizzas} = \text{Number of pizzas topped with meat}+ \text{Number of pizzas topped with vegetables}[/tex]
Substitute the given values we get;
[tex]84 = 4x+3x[/tex]
Combine like terms;
[tex]84= 7x[/tex]
Divide both sides by 7 we get;
12 = x
The pizza were topped with vegetables = 3x = 3(12) = 36
therefore, 36 pizzas were topped with vegetables
Answer:
The correct answer is option B.
Step-by-step explanation:
The ratio of pizzas topped with meat to pizzas topped with vegetables was 4:3 on Saturday.
Let the pizza's topped with meat be 4x
Let the pizza's topped with vegetable be 3x
Total pizzeria made a Saturday = 84
4x + 3x = 84
7x = 84
x = [tex]\frac{84}{7}=12[/tex]
Pizza's topped with meat = 4x = 4 × 12 = 48
Pizza's topped with vegetable = 3x = 3 × 12 = 36
12 pizzas were topped with vegetables.
linar equations 2xty=5
2xty=5 is not linear.
Plz help me thank you guys so much!!!!! oops part of my face is also in the pics just ignore that
1) All three are right A.K.A 4
4) The answer is also 4).
Tickets to the zoo cost $4 for children, $5 for teenagers and $6 for adults. In the high season, 1200 people come to the zoo every day. On a certian day, the total revenue at the zoo was $5300. For every 3 teenagers, 8 children went to the zoo. How many teenagers went to the zoo?
a.
100 teenagers
c.
300 teenagers
b.
200 teenagers
d.
400 teenagers
Answer:
300 teenagers
Step-by-step explanation:
6a + 5t + 4c = 5300
a + t + c = 1200
(8/3)*t = c
6a+4c+5t = 5300
a+c+t = 1200
3c-8t = 0
a = 100
c = 800
t = 300
Answer: c is the right answer
Step-by-step explanation:
3×3=?
[tex]3 \times 3 = 8[/tex]
Hey there!
Say that you have 3 books in 3 rows on shelves in the library [tex]Row1:3[/tex][tex]Row2:3[/tex][tex]Row3:3[/tex][tex]3,6,9[/tex][tex]3+3+3[/tex][tex]3+3= 6[/tex][tex]6+3 = 9[/tex][tex]3*3\neq 8[/tex][tex]3*3= 9[/tex] So, the correct answer should be: [tex]\boxed{9}[/tex]Good luck on your assignment and enjoy your day!
~[tex]LoveYourselfFirst:)[/tex]
On Monday Kennedy spent $2 on lunch. On Tuesday she spent $1 on a snack on Wednesday, her sister gave her $3. Graph the integers on the number line.
Answer:
-2, -1, 3.Step-by-step explanation:
Money per day:On Monday: $2 on lunch.
On Tuesday: $1 on a snack.
On Wednesday: her siter gave her $3.
Now, before we graph the integers, first you need to think about those number and their meaning. If the number represents debt or expenses, then it must be a negative number. But, if the number represents money received, then it must be a positive number.
So, we have the following integer: -2, -1, 3.
If we graph these integers, it would be like the images attached shows.
What is the 15th term of the sequence an =-3n+50
Answer:
[tex]a_{15}[/tex] = 5
Step-by-step explanation:
to find the 15th term substitute n = 15 into the nth term formula
[tex]a_{15}[/tex] = (- 3 × 15 ) + 50 = - 45 + 50 = 5
To find the 15th term, enter n = 15 into the nth term formula.
What is the Sequence?A list of numbers in a specific order is called a sequence. A term is the name given to each number in a sequence. A sequence has a place for each phrase (first, second, third and so on). Consider the sequence 5, 15, 25, 35, for instance. Each number in the series is referred to as a word. You should be familiar with the following four main categories of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences.
Sets of numbers that adhere to a pattern or norm are known as number sequences. It is referred to as an arithmetic sequence if the rule is to add or remove a number each time. It is referred to as a geometric sequence if the rule is to multiply or divide by the same integer each time.
A term is the name given to each number in a series. A sequence is a list of objects that is in order in mathematics (or events). Similar to a set, it has members (also called elements, or terms). The length of the sequence is the number of ordered elements (potentially infinite)
Detailed explanation:
Substitute n = 15 into the nth term formula to discover the 15th term.
a15= (- 3 × 15 ) + 50 = - 45 + 50 = 5
a15= 5
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Solve the elimination. 5x+7y=-1 4x-2y=22
[tex]\left\{\begin{array}{ccc}5x+7y=-1&\text{multiply both sides by 2}\\4x-2y=22&|\text{multiply both sides by 7}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}10x+14y=-2\\28x-14y=154\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad38x=152\qquad\text{divide both sides by 38}\\.\qquad \boxed{x=4}\\\\\text{Put the value of x to the first equation:}\\\\5(4)+7y=-1\\20+7y=-1\qquad\text{substract 20 from both sides}\\7y=-21\qquad\text{divide both sides by 7}\\\boxed{y=-3}\\\\Answer:\ \boxed{x=4\ and\ y=-3\to(4,\ -3)}[/tex]
Rachel has 30 pounds of a mixture of candy that sells for $1.00/lb. If lollipops sell for $0.95/lb and caramel candies sell for $1.10/lb. How many pounds of lollipops are in the mixture?
Answer:
20 lbs
Step-by-step explanation:
you are designing a mix of 4 songs to play on your mp3 player while you exercise you have 25 mp3’s that you consider appropriate for the purpose how many different sequences of 4 songs can you devise?
A. 24
B. 12,650
C. 13,800
D. 303,600
E. 390,625
Which is the approximate solution for the system of equations x+5y=10 and 3x+y=1?
Step-by-step explanation:
Given system of equations :
x+5y=10 and 3x+y=1.
Let us solve the system of equation by substitution.
Solving second equation 3x+y=1 for y first.
3x+y=1.
Subtracting 3x from both sides, we get
3x-3x+y=1-3x
y = 1-3x.
Substituting y=1-3x in first equation x+5y=10, we get
x+ 5(1-3x) = 10.
x + 5 -15x =10
-14x +5 = 10.
Subtracting 5 from both sides, we get
-14x +5-5 = 10-5
-14x =5
Dividing by -14 on both sides, we get
-14x/-14=5/-14
x= -0.36.
Plugging x=-0.36 in second equation y=1-3x, we get
y = 1-3(-0.36) = 1+1.08 = 2.08.
Therefore, approximate solution is (-0.36, 2.08).Answer:
A (–0.3, 2.1)
Step-by-step explanation:
factor the expression completely. 8y - 36
Answer:
[tex]4(2y-9)[/tex]
Step-by-step explanation:
To begin factoring the expression [tex]8y-36[/tex], we use the GCF or greatest common factor. The greatest common factor is the greatest number that will divide into two or more values. We start to find it by factoring each term:
[tex]8y: 2*4*y[/tex]
[tex]-36: -1*4*9[/tex]
We notice the only common factors is 4.
We write in the form 4(____+_____). We find the inside of the parenthesis by dividing each term by 4.
[tex]\frac{8y}{4} =2y[/tex]
[tex]\frac{-36}{4} =-9[/tex]
4(2y-9)
Given a circle with measures of (C, d, and r) and a circle with measures of (C', d', and r'), what is r' if C/C' = 0.75 and d = 6.0?
A) 2
B) 4
C) 8
D) 12
Answer:
B
Step-by-step explanation:
All circles are similar and therefore proportional. C/C' is the ratio of Circle C to Circle C'. Since it is 0.75, this means that C is 75% of C'. We know that radius of C will also be 75% of the radiuc of C'. We can the radius because we know the diameter of Circle C is 6. The radius is therefore 3. 3 is 75% of 4. So r/r' or 3/4=0.75. r/ must be 4.
Answer: B) 4
Step-by-step explanation:
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