Using the Pythagorean theorem we can find the height of the triangle:
height = √(14^2 - 12^2)
height = √(196 - 144)
height = √52
height = 7.2
The answer would be 7.2 centimeters.
C. 7.2 centimeters
How do you calculate the Pythagorean theorem?a 2 + b 2 = c 2. This is known as Pythagorean equation, named after the ancient Greek thinker Pythagoras. This relationship is useful because if 2 sides of the right triangle are known, the Pythagorean theorem could be used to determine the length of the 3rd side. Referencing the above diagram, if. a = 3 and b = 4
Using the Pythagorean theorem we can find the height of the triangle:
height = √(14^2 - 12^2)
height = √(196 - 144)
height = √52
height = 7.2
The answer would be 7.2 centimeters.
Learn more about Pythagorean equation here https://brainly.com/question/9373923
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Complete the solution the equation. Find the value of y when x equals 15 .
Three students solve a challenge math problem. Every day, the number of students who solve the problem doubles. There are 384 students enrolled in the class. If the number of students who solve the problem continues to increase at this rate, how long will it take until all of the students enrolled in the class solve the problem? Write an equation for the number of students who solved the problem, S= number of days since the first students solved the problem, D= the correct solution
OK, so this is assuming we are considering that the first three kids to solve ARE NOT in the first day.
So we have 3 kids and it doubles
Day 1 : 6
Day 2 : 12
Day 3 : 24
Day 4 : 48
Day 5 : 96
Day 6 : 192
Day 7: 384
So it should take 7 days or a week to solve all the problems.
The equation:
(3 * 2)^x = 384
Answer:
It will take 7 days for all the class to complete the problems.
Step-by-step explanation:
We are given that 3 students solve math problems everyday.
Also, the number of students doubles each day.
So, we get the pattern,
Days (S) Number of students
1 3 = 3
2 3 × 2 = 3 × 2¹
3 3 × 2 × 2 = 3 × 2²
4 3 × 2 × 2 × 2 = 3 × 2³
5 3 × 2 × 2 × 2 × 2 = 3 × 2⁴
6 3 × 2 × 2 × 2 × 2 × 2 = 3 × 2⁵
As, there are total 384 students in the class.
We get the equation as, [tex]3(2)^S=384[/tex]
On solving, we have,
[tex]3(2)^S=384[/tex]
i.e. [tex]2^S=\frac{384}{3}[/tex]
i.e. [tex]2^S=128[/tex]
i.e. [tex]S\log 2=\log 128[/tex]
i.e. [tex]S\times 0.301=2.107[/tex]
i.e. [tex]S=\frac{2.107}{0.301}[/tex]
i.e. S = 7
Hence, it will take 7 days for all the class to complete the problems.
What’s the actual distance = yards?
The legend says 1 inch = 30 yards.
Multiply the total inches by 30 yards:
4 inches x 30 yards = 120 total yards.
Answer:
1 inch = 30 yards
If you’re trying to figure out how many yards is 4 inches, you multiply 30 by 4. Your answer should be 120 yards
Amara needs 4545 kilograms of meat to feed her 22 pet dragons each day. Each pet dragon eats the same amount of meat.
How many kilograms of meat does Amara need to feed 44 pet dragons each day?
Answer:9090
it is simple you just need to multiply by 2
Answer:
9090
Step-by-step explanation:
meat to feed 22 pet dragons per day=4545
meet to feed 44 pet dragons per day=?
as number of pet dragons have doubled
so amount of feed will also be doubled
hence
meet to feed 44 pet dragons per day=4545*2=9090
You work at a fruit market. Bananas cost 50¢ a pound. A customer hands you a bunch of bananas that weighs 3 pounds. How much should you charge for the bunch of bananas?
Answer: I should charge 150¢ for the bunch of bananas.
Step-by-step explanation: Given that I work at a fruit market and bananas cost 50¢ a pound.
A customer hands me a bunch of bananas that weighs 3 pounds.
We are to find the price that I should charge for the bunch of bananas.
We will be using the UNITARY method to solve the given problem.
Also, we know that
100 ¢ = $1.
Cost of 1 pound of bananas = 50¢
Therefore, the cost of 3 pounds of bananas is given by
p = (50 × 3)¢ = 150¢ = $1.50.
Thus, I should charge 150¢ for the bunch of bananas.
Write a polynomial function with zeros -7, -1, 4
Answer:
(x+7)(x+1)(x-4)
Step-by-step explanation:
A zero is is the x-intercept of the function. It is also known as the root. From the equation, the zero or root comes from the factors. When the factors are set equal to 0, we solve for x and the zero is the result. We will reverse this by taking the opposite value of the zero and placing into a factor expression. Remember the factor has the form x+a.
-7: x+7
-1: x+1
4: x-4
We write them together. (x+7)(x+1)(x-4). With more information we could find the leading coefficient and so forth.
The speed of an Arabian horse is "4x + 2" miles per hour slower than a thoroughbred horse with a speed of "25x − 5" miles per hour. Find a single expression that represents the speed of an Arabian horse. A) 21x − 3 B) 21x − 7 C) 29x − 3 D) 29x − 7
PLS AWNSER THIS WERE GOING TO LEEVE AT 855
Answer:
B) 21x-7
Step-by-step explanation:
Let A = speed of Arabian horse and T = speed of thoroughbred.
Then
A = T – (4x + 2)
A = T – 4x - 2 Remove parentheses
A = 25x - 5 - 4x – 2 Combine like terms
A = 21x - 7
Identify the slope of the line shown in the graph below: slope = -1
Slope = 0
Slope = undefined
Slope = 1
Answer:
slope is undefined
Step-by-step explanation:
Answer:
Undefined
Step-by-step explanation:
The line is going straight down which means it cannot be negative or positive.
If you try to make the equation(y=mx + b), when you try to find the slope, you can't because (rise/run), there is no run. It is just a rise.
This means you cannot define the slope of the line.
Marjorie baked 100 cupcakes for a bake sale. She sold each cupcake for $0.50. The function P(c) = 0.50c represents the amount, in dollars, that she earned from the bake sale by selling c cupcakes. What domain and range are reasonable for the function?
Answer:
The answer in the procedure
Step-by-step explanation:
we have
P(c)=0.50c
where
P(c) ---> is the amount in dollars that Marjorie earned from the bake sale
c ----> is the number of cupcakes
The domain of the function are the number of cupcakes sold
so
The domain is the interval -----> [0,100]
All positive integers greater than or equal to 0 and less than or equal to 100
Find the range
For c=0
P(0)=0.50(0)=$0
For c=100
P(0)=0.50(100)=$50
The range is the interval -----> [0,50]
All real numbers multiples of 0.50 greater than or equal to 0 and less than or equal to 50
The domain for the function is c ≥ 0, and the range is P(c) ≥ 0.
Domain: The domain for the function P(c) = 0.50c, where c represents the number of cupcakes sold, would be all non-negative integers since Marjorie cannot sell a negative number of cupcakes. So, the domain is c ≥ 0.
Range: The range for the function would be all the possible earnings that Marjorie can make from selling cupcakes. Since each cupcake is sold for $0.50, the earnings can be any non-negative real number. Therefore, the range is P(c) ≥ 0.
Find the area of a triangle whose two sides are 12 inches and 14 inches long, and has a perimeter of 34 inches
Answer:
The simple answer: 48
Step-by-step explanation:
Finding the area of a triangle in most cases is simple, multiply the two sides that are not the hypotenuse (the noticeably longer side) then divide the product by two. In this case the perimeter is included because you are given one side and the hypotenuse. With simple 12+14=26 and 34-26=8 you have the other side you need. So 12 times eight equals 96 divide that by two and you have the answer 48.
please help and explain thanks
Answer: Woops I meant 2 cannot be repeated because x-values cannot be the same. So it is C.
A function CAN have the same y-values such as (3,4) and (6,4). But a function CANNOT have the same x-values like (7,10) and (7,1) because it would be a straight line.
Which quantity is proportional to 45⁄3? Check all that are true. 90⁄10 90⁄6 15⁄1 135⁄6 30⁄1
To solve this, turn everything into decimals. Once you've done that, it reads this way:
Which quantities are proportional to 15?
9
15 -- aka 90/6
15 -- aka 15/1
22.5
30
The only provided quantities that are proportional are 90/6 and 15/1.
what are the factors of 5
Answer:
5 & 1
Step-by-step explanation:
Factors are numbers that, when multiplied, will give the number that is given in the question. In this case:
5 * 1 = 5
5 & 1 are factors
~
Answer:
5= 1,5 so easy question
pls someone should kindly help me with this
Answer: a = 1, a = [tex]{\bold{-\dfrac{119}{125}}[/tex]
Step-by-step explanation:
In order to have the same root, the discriminant cannot be irrational.
Case 1: Discriminant = zeroCase 2: Discriminant = perfect square(a + 3)x² - (11a + 1)x + a = 2(a - 5)
(a + 3)x² - (11a + 1)x + a = 2a - 10
(a + 3)x² - (11a + 1)x + a - 2a + 10 = 0
(a + 3)x² - (11a + 1)x - (a - 10) = 0
a = a+3 b = -(11a+1) c = -(a - 10)
Case 1:
b² - 4ac = 0
[-(11a + 1)]² - 4(a + 3)[-(a - 10)] = 0
121a² + 22a + 1 + 4a² - 28a - 120 = 0
125a² - 6a - 119 = 0
Use any method to solve the quadratic equation. I chose to use the factoring method.
125a² - 6a - 119 = 0
125a² - 125a + 119a - 119 = 0
125a(a - 1) + 119(a - 1) = 0
(125a + 119)(a - 1) = 0
125a + 119 = 0 and a - 1 = 0
a = [tex]-\dfrac{119}{125}[/tex] and a = 1
Check:
(a + 3)x² - (11a + 1)x + a = 2(a - 5)
((1) + 3)x² - (11(1) + 1)x + (1) = 2((1) - 5)
4x² - 12x + 1 = -8
4x² - 12x + 9 = 0
(2x + 3)² = 0
x = [tex]-\dfrac{3}{2}[/tex]
Case 2: I am not sure how to do this one
[tex]ax^2+bx+c=0\\\\if\ \Delta=b^2-4ac>0\ then\ two\ solutions\qquad x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\if\ \Delta=b^2-4ac=0\ then\ one\ solution\\if\ \Delta=b^2-4ac<0\ then\ no\ real\ solution[/tex]
--------------------------------------------
[tex](a+3)x^2-(11a+1)x+a=2(a-5)\qquad\text{use distributive property}\\\\(a+3)x^2-(11a+1)x+a=2a-10\qquad\text{subtract 2 from both sides and add 10 to both sides}\\\\(a+3)x^2-(11a+1)x-a+10=0\\\\\Delta=[-(11a+1)]^2-4(a+3)(-a+10)\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\\Delta=(11a)^2+2(11a)(1)+1^2+(-4a-12)(-a+10)\\\\\Delta=121a^2+22a+1+4a^2-40a+12a-120\\\\\Delta=125a^2-6a-119[/tex]
[tex]\text{One solution if}\ \Delta=0.\\\\\Delta=0\iff125a^2-6a-119=0\\\\\Delta_a=(-6)^2-4(125)(-119)=36+59,500=59,536\\\\\sqrt{\Delta_a}=\sqrt{59,536}=244\\\\a_1=\dfrac{-(-6)-244}{2(125)}=\dfrac{-238}{250}=\dfrac{-238:2}{250:2}=-\dfrac{119}{125}\\\\a_2=\dfrac{-(-6)+244}{2(125)}=\dfrac{250}{250}=1\\\\Answer:\ \boxed{a=-\dfrac{119}{125}\ or\ a=1}[/tex]
i need help hurry plz? what the meaning of y and x intercept in the problem and tell me the answer of the last question
Answer:
For the first picture, the y-intercept is the height the pebble was dropped from. The x-intercept is the amount of seconds it took for the pebble to hit the ground.
For the second picture, the y-intercept is the height of the soccer ball (ground level). The x-intercept is the amount of seconds it took for the soccer ball to hit the ground.
Ryan has 4 cups of grape juice and Kelsey has 7 cups of lemonade they want to combine what they have to make punch how many 1/2 cup servings of punch can they make
Answer:
5.5 servings
Step-by-step explanation:
4+7=11
11/2=5.5 sevings
7.3 back side help me
Answer:
11. x=4.5
12. x=16
13. x=15
14. x=15
15. x=10
EH=9
16. Corry is 6 feet tall.
17. The Ferris Wheel is 15 m tall.
18. The mural is 150 inches long.
19. A 15 foot ladder would touch the building at a height of 10 feet.
Step-by-step explanation:
11. x/7.5=6/10
Simplifying the fraction on the right side of the equation:
x/7.5=3/5
Solving for x: Multiplying both sides of the equation by 7.5:
7.5(x/7.5)=7.5(3/5)
x=1.5(3)
x=4.5
12. x/20=(27-15)/15
x/20=12/15
Simplifying the fraction on the right side of the equation:
x/20=4/5
Solving for x: Multiplying both sides of the equation by 20:
20(x/20)=20(4/5)
x=4(4)
x=16
13. x/6=(14-4)/4
x/6=10/4
Simplifying the fraction on the right side of the equation:
x/6=5/2
Solving for x: Multiplying both sides of the equation by 6:
6(x/6)=6(5/2)
x=3(5)
x=15
14. x/20=12/(12+4)
x/20=12/16
Simplifying the fraction on the right side of the equation:
x/20=3/4
Solving for x: Multiplying both sides of the equation by 20:
20(x/20)=20(3/4)
x=5(3)
x=15
15. [(x+5)+9]/(x+5)=12/6
(x+5+9)/(x+5)=2
(x+14)/(x+5)=2
Solving for x: Multiplying both sides of the equation by (x+5):
(x+5)(x+14)/(x+5)=(x+5)2
x+14=2(x+5)
Eliminating the parentheses applying the distributive property:
x+14=2(x)+2(5)
Multiplying:
x+14=2x+10
Grouping the x's on the right side of the equation: Subtracting x both sides of the equation:
x+14-x=2x+10-x
Subtracting:
14=x+10
Solving for x: Subtracting 10 both sides of the equation:
14-10=x+10-10
4=x
x=4
EG=x+5→EG=4+5→EG=9
EH/HF=EG/GD
Replacing the known values:
EH/9=9/9
EH/9=1
Solving for EH: Multiplying both sides of the equation by 9:
9(EH/9)=9(1)
EH=9
16. Corry's height / Corry's shadow = Giraffe's height / Giraffe's shadow
Replacing the given values:
Corry's height / 4 feet = 18 feet / 12 feet
Simplifying the fraction on the right side of the equation:
Corry's height / 4 feet = 3/2
Solving for Corry's height: Multiplying both sides of the equation by 4 feet:
4 feet (Corry's height / 4 feet) =4 feet (3/2)
Corry's height = 2 feet (3)
Corry's height = 6 feet
17. Ferris Wheel's height / Ferris Wheel's shadow =
Man's height / Man's shadow
Replacing the given values:
Ferris Wheel's height / 20 m = 1.8 m / 2.4 m = 18/24
Simplifying the fraction on the right side of the equation:
Ferris Wheel's height / 20 m = 3/4
Solving for Ferris Wheel's height: Multiplying both sides of the equation by 20 m:
20 m (Ferris Wheel's height / 20 m) =20 m (3/4)
Ferris Wheel's height = 5 m (3)
Ferris Wheel's height = 15 m
18. Mural's length / Mural's width =
Photographer's length / Photographer's width
Replacing the given values:
Photographer's length / 120 inches = 5 inches / 4 inches = 5/4
Solving for Photographer's length: Multiplying both sides of the equation by 120 inches:
120 inches (Photographer's length / 120 inches) = 120 inches (5/4)
Photographer's length = 30 inches (5)
Photographer's length = 150 inches
19. Height 15-foot ladder touch the building / 15 feet =
Height 9-foot ladder touch the building / 9 feet
Height 15-foot ladder touch the building / 15 feet = 6 feet / 9 feet = 6/9
Simplifying the fraction on the right side of the equation:
Height 15-foot ladder touch the building / 15 feet = 2/3
Solving for Height 15-foot ladder touch the building: Multiplying both sides of the equation by 15 feet:
15 feet (Height 15-foot ladder touch the building / 15 feet) = 5 feet (2/3)
Height 15-foot ladder touch the building = 5 feet (2)
Height 15-foot ladder touch the building = 10 feet
What is the slope of this linear function?
y=−4x−9
Answer:
The slope of the given linear function is -4.
Step-by-step explanation:
We have been given the linear equation [tex]y=-4x-9[/tex]
The slope intercept form of a line is given by [tex]y=mx+b[/tex]
Here, b is y-intercept and m is the slope.
On comparing, the given equation with the slope intercept form, we get
b = -9
m = -4
It means that the y-intercept is -9 and the slope of the line is -4.
Therefore, the slope of the given linear function is -4.
Solve the following subtraction problems. Remember to borrow as necessary.
a. 5 lb. – 2lb. 5 oz.
b. 17 T. 13 lb. 3 oz. – 9 T. 20 lb. 9 oz.
c. 68 lb. 13 oz. – 30 lb. 15 oz.
Answer:
a. 2 lb 11 oz, b. 7 T 1,992 lb 12 oz , c. 38 lb 14 oz
Step-by-step explanation:
The first thing we need to understand is the conversions.
1 T = 2,000 lb
1 lb = 16 oz
Knowing this, there are many ways to find out the answer, please see below the one I used; I converted all measure units to oz, subtracted the amounts, and finally converted the units back to their original ones.
a. 5 lb or (16 oz*5) - (2 lb or (16 oz*2) + 5 oz) = 80 oz - 37 oz = 43 oz = 2 lb 11 oz
b. (17 T or (2,000 lb*17) + 13 lb + 3 oz) - (9 T or (2,000 lb*9) + 20 lb + 9 oz) = (34,013 lb or (16 oz *34,013) + 3 oz) - (18,020 lb or (16 oz *18,020) + 9 oz) = 544,213 oz - 288,329 oz = 255,884 oz = 7 T 1992 lb 12 oz
c. (68 lb or (16 oz*68) + 13 oz) - (30 lb or (16 oz*30)+15) = 1,117 oz - 495 oz = 622 oz = 38 lb 14 oz
Answer:
A. 2 pounds 11 ounces
B. 7T 1,992 pounds 12 ounces
C. 38 pounds and 14 ounces
what is the estimate of 8.36
Answer:
You can estimate to the nearest 10th.
Example:8.4
Step-by-step explanation:
Each individual letter of the word "Washinton" is placed on a paper,and all 10 pieces of paper are placed in a hat. if one letter is selected at random from the hat,find the probability that the letter "k" is selected.
when f(x) = x-7/2 , what is the value of (f^0 f^-1) (3)
Answer:
[tex](f o f^{-1})(3) = 3[/tex]
Step-by-step explanation:
[tex]f(x) = \frac{x-7}{2}[/tex]
We need to find (fof^-1)(3)
First we find f^-1(x)
Replace f(x) with y
[tex]y = \frac{x-7}{2}[/tex]
Now replace x with y and y with x
[tex]x = \frac{y-7}{2}[/tex]
Multiply by 2 on both sides
2x = y -7
Now add 7 on both sides
2x + 7 = y
Replace y with f^-1(x)
f^-1(x) = 2x+ 7
Now we find (fof^-1)(3)
[tex](f o f^{-1})(3) = f(f^{-1}(3))[/tex]
First we find f^-1(3)
f^-1(x) = 2x+ 7
f^-1(3) = 2(3) + 7 = 6 + 7 = 13
Now we plug in 13 for x and find out f(13)
[tex]f(x) = \frac{x-7}{2}[/tex]
[tex]f(13) = \frac{13-7}{2}= 3[/tex]
So , [tex](f o f^{-1})(3) = f(f^{-1}(3))= 3[/tex]
Dawn is packing cookies she puts 5 cookies in each package if she has 7,414 cookies how many packages can she make
Answer:
Dawn can make 1482 packages
Step-by-step explanation:
for each package Dawn need 5 cookies so for 7414 cookies she can make
7414 ÷ 5 = 1482.8
so she can make 1482 packages.
Andrew has 9.39 but he needs 15.00 to make a purchase how much more does he need.
Answer:
5.61
Step-by-step explanation:
just subtract 9.39 from 15.00
A jaguar can run 40 miles per hour while a giraffe can run 32 miles per hour. If they both run for 4 hours, how much farther will the jaguar run?
How do you write this as an equation?
The jaguar will run 32 miles farther than the giraffe after both run for 4 hours, calculated using the equation: Distance = Speed x Time.
To calculate how much farther the jaguar will run compared to the giraffe, we can start by writing an equation for the distance each animal travels. Distance is equal to speed multiplied by time, which can be expressed as:
D = s *t
For the jaguar traveling at 40 miles per hour for 4 hours, the distance would be:
D_jaguar = 40 miles/hour*4 hours = 160 miles
For the giraffe traveling at 32 miles per hour for 4 hours, the distance would be:
D_giraffe = 32 miles/hour *4 hours = 128 miles
To find out how much farther the jaguar runs, subtract the distance run by the giraffe from the distance run by the jaguar:
Additional distance = D_jaguar - D_giraffe = 160 miles - 128 miles = 32 miles
The jaguar will run 32 miles farther than the giraffe.
The quotient of 12 times an unknown number and 13 is 6 what is the unknown number?
Answer:
unknown number is 13/2
Step-by-step explanation:
Let unknown number be 'x'
given that quotient of 12 times x and 13 is 6
i.e. 12 x/13 =6
multiply 13 both sides
12x = 6 * 13
divide 12 on both sides
x= (6*13)/12
x=13/2
The stem and leaf plot below displays a set of data recorded in the North Pole.
Stem:
-3, -2, -1, 0, 1, 2, 3
Leaf:
5,2,2,1,0,7,7,7,5,3,2,0,-9,-6,-4,-1,-1,0,3,6,1,2,5
Which box plot closely resembling the data set within the stem and leaf plot, represents a data set with outliers?
Answer:
plot B
Step-by-step explanation:
-3
-2 goes with 5,2,2,1,0
-1 goes with 7,7,7,5,3,2,0
0 goes with -9,-6,-4,-1,-1,0,3,6
1 goes with 1,2
2 goes with 6
3
This means there should be no data in our box and whisker plot until a whisker starts at -25. This eliminates plot A
We will also stop our last whisker at 26 . This eliminates plot C
We have 23 data points. So the median point is 12
The 12th point is -10
The middle of our box should be at -10 This eliminates plot D
Our answer is plot B
what is the equation 19−6(−k−2)?
Answer:
6k+31
Step-by-step explanation:
19-6( -k -2)
= 19 +6k+12
=6k+31
find o(30) where o(n) =2n-1
Answer:
o(30) = 59
Step-by-step explanation:
o(30) means we want to let n = 30 in our function
o(n) =2n-1
o(30) = 2*30 -1
o(30) = 60 -1
o(30) = 59
j^2 over 2j times 2j over 3g
Answer:
D
Step-by-step explanation:
given [tex]\frac{j^2}{2j}[/tex] × [tex]\frac{2j}{3g}[/tex]
the 2j on the denominator of the first fraction cancels with the 2j on the numerator of the second fraction, leaving the expression in simplified form as
= [tex]\frac{j^2}{3g}[/tex] → D