Answer:
2.1 x 10^8
Step-by-step explanation:
2.1*10^8
The first number can not exceed ten so just count how many decimal place it would be and that should be the power.
Cristian put a large rock on the bottom of the terrarium he made for his pet turtle. The rock is a right rectangular prism 10\text{ cm}10 cm10, start text, space, c, m, end text wide by 12\text{ cm}12 cm12, start text, space, c, m, end text long. The rock displaces 1800 \text{ cm}^31800 cm 3 1800, start text, space, c, m, end text, cubed of water. How high is the rock?
Answer:
The height of the rock is 15 mm.
Step-by-step explanation:
Given : Cristian put a large rock on the bottom of the terrarium he made for his pet turtle.
To find : How high is the rock?
Solution :
The rock is a right rectangular prism 10 cm wide by 12 cm long.
Let the height be 'h'.
The volume of the right rectangular prism is [tex]V=L\times B\times H[/tex]
i.e. [tex]V=10\times 12\times h[/tex]
[tex]V=120h[/tex]
The rock displaces 1800 cm³ of water.
i.e. The volume of the right rectangular prism is equal to the rock displaces of water.
So, [tex]120h=1800[/tex]
[tex]h=\frac{1800}{120}[/tex]
[tex]h=15[/tex]
Therefore, the height of the rock is 15 mm.
The exact answer is going to be equal to 15mm
Hope this helped
The angles in a triangle are such that one angle is 100 degrees more than the smallest angle, while the third angle is 2 times as large as the smallest angle. Find the measures of all three angles.
Answer:
The measure of the three angles are 120°, 20° and 40°
Step-by-step explanation:
Let
x ----> the measure of the first angle
y ---> the measure of the second angle (smallest angle)
z ---> the measure of the third angle
Remember that
The sum of the angles in a triangle must be equal to 180 degrees
so
[tex]x+y+z=180[/tex] ----> equation A
[tex]x=y+100[/tex] -----> equation B
[tex]z=2y[/tex] ------> equation C
solve the system by substitution
substitute equation B and equation C in equation A
[tex](y+100)+y+(2y)=180[/tex]
solve for y
[tex]4y+100=180[/tex]
[tex]4y=180-100[/tex]
[tex]4y=80[/tex]
[tex]y=20\°[/tex]
Find the value of x
[tex]x=y+100[/tex] ---- [tex]x=20+100=120\°[/tex]
Find the value of z
[tex]z=2y[/tex] ----> [tex]z=2(20)=40\°[/tex]
therefore
The measure of the three angles are 120°, 20° and 40°
Answer:
Step-by-step explanation:
120,20 and 40
I need help on this questionnnn
Answer:
E(-5, - 6) D(5,-6) C(0,0)
Step-by-step explanation:
The strategy here is run then rise/fall
For example: for E, you run back - 5, then fall - 6
If 2/3 = x/y, then which of the following must be true?
O (2 + x)/3 = (x + 2)/y
3/2 = x/y
(2 + 3)/3 = (x + y)/y
(2 + 1)/3 = (x + 1)/y
Correct option is third [tex]\frac{2+3}{3}=\frac{x+y}{y}[/tex]
Solution:Given that:
[tex]\frac{2}{3}=\frac{x}{y}[/tex]
Need to check which of the expression from given four expressions will be true.
Let's first try to eliminate wrong options.
If we observe carefully, we can say that option 2 that is [tex]\frac{3}{2}=\frac{x}{y}[/tex] is not correct as [tex]\frac{x}{y}[/tex] must be equal to [tex]\frac{2}{3}[/tex] and not [tex]\frac{3}{2}[/tex]
Lets now modify given expression that is:
[tex]\frac{2}{3}=\frac{x}{y}[/tex]
On adding 1 to both sides we get
[tex]\frac{2}{3}+1=\frac{x}{y}+1[/tex]
[tex]=>\frac{2+3}{3}=\frac{x+y}{y} \text { which is same as third option. }[/tex]
Hence correct option is third one that is [tex]\frac{2+3}{3}=\frac{x+y}{y}[/tex]
9. Sales tax is 7.596. How much did Tammy's lunch cost before tax If the tax on it was $0.727 Define a variable and write an equation. Solve the
equation and check your solution.
Answer:
Cost of Tammy's lunch box before tax = $9.571
Step-by-step explanation:
Let the cost of Tammy's lunch box before tax be =$ [tex]x[/tex]
Sales tax charged = $0.727
Sales tax rate =7.596%
Sales tax charged in terms of will be = 7.596% of the Original cost of lunch box[tex]=7.596\% \ of\ x =0.07596\ x[/tex]
So, we have,
[tex]0.07596\ x=0.727[/tex]
Dividing both sides by [tex]0.07596[/tex]
[tex]\frac{0.07596\ x}{0.07596}=\frac{0.727}{0.07596}[/tex]
∴ [tex]x=9.571[/tex]
∴ Cost of Tammy's lunch box before tax = $9.571
What is the discriminant of the quadratic equation 0 = -х2 + 4х – 2?
Answer:
8
Step-by-step explanation:
The discriminant of ax² + bx + c = 0 is b² − 4ac.
Here, a = -1, b = 4, and c = -2.
b² − 4ac
(4)² − 4(-1)(-2)
16 − 8
8
The students want to make care packages for unhoused people for the winter season. They would like to put 5 boxes of tissues into each care package. If they have 450 boxes pack, how many tissue boxes will they need to complete the boxes?
Answer:
2250
Step-by-step explanation:
From my understanding you have 450 packs to make and you need to put 5 tissue boxes in each one so we would just simply multiply 450 packages by 5 tissue boxes each package and get 2250
Staghorn Coral is a type of branching Coral. It can add as much as 0.67 foot to its branches each year. Find how much a staghorn Coral can grow in 5 years?
A Staghorn Coral can grow as much as 3.35 feet in 5 years under ideal conditions, assuming it grows at a fixed rate of 0.67 foot per year.
Explanation:The question asks us to find out how much a Staghorn Coral, a type of branching coral, can grow in 5 years. Each year, the coral can potentially increase its size by 0.67 foot. To figure this out, we would use multiplication, a basic arithmetic operation.
First, we need to multiply the annual growth rate (0.67 foot) by the number of years (5). So, 0.67 * 5 equals 3.35 feet. This signifies that the Staghorn Coral can grow as much as 3.35 feet over the course of five years under optimal conditions.
Therefore, a Staghorn Coral can potentially add 3.35 feet to its branches during a 5 year span if it grows at the rate of 0.67 foot per year.
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y=-8x – 37
x+3y=4
Substitution method
Answer:
(- 5, 3 )
Step-by-step explanation:
Given the 2 equations
y = - 8x - 37 → (1)
x + 3y = 4 → (2)
Substitute y = - 8x - 37 into (2)
x + 3(- 8x - 37) = 4 ← distribute and simplify left side
x - 24x - 111 = 4
- 23x - 111 = 4 ( add 111 to both sides )
- 23x = 115 ( divide both sides by - 23 )
x = - 5
Substitute x = - 5 into (1) for corresponding value of y
y = - 8(- 5) - 37 = 40 - 37 = 3
Solution is (- 5, 3 )
Answer:
x = -5, y = 3 or you can write it as (-5, 3).
Step-by-step explanation:
y=-8x – 37
x+3y=4
From the second equation x = 4 - 3y, so substituting in equation 1:
y = -8(4 - 3y) - 37
y = -32 + 24y - 37
-23y = -69
y = 3
Now plug y = 3 into equation 1:
3 = -8x - 37
-8x = 40
x = -5.
What has a remainder of 2 when divided by 11?
Answer:
2Step-by-step explanation:
2 : 11 = 0 + r(2)
11 is 0 times in 2. The remainder of this division is 2.
Answer:
Answer. This is pretty tricky—if we have 2 divided by 11, the remainder is actually 2. The remainder is 2 because the quotient is 0 (11 goes into 2 zero times).
Step-by-step explanation:
What are the two basic qualifications to vote in the United States?
Answer:
Here are 3
Step-by-step explanation:
Are a U.S. citizen.
Meet your state's residency requirements.
Are 18 years old on or before Election Day.
The sixth-graders at Sarah's school got to choose between a field trip to a museum and a field trip to a factory. 70% of the sixth-graders picked museum. If there are 100 sixth graders in all at Sarah's school, how many sixth-graders went on the trip to the museum?
Please Show your work and or explain.
The problem involves applying the concept of percentage. By using the given data, we find that 70 sixth graders went on the museum trip.
Explanation:The subject of this problem is percentage and its application in a real-world situation. The problem stated that 70% of the sixth graders chose to go to the museum. As there are 100 sixth graders, to calculate the number of students who went on the museum trip, you would use the formula percentage/100 x total number.
So, 70/100 x 100 = 70 sixth graders. Hence, 70 sixth-graders from Sarah's school went on the field trip to the museum.
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How would I solve this frequency chart?
Answer:
The number of students who have a test score in the interval 71-80 is 13.
Step-by-step explanation:
Given:
The frequency chart which show the cumulative numbers of students test scores.
Now, to find the number of students who score in the interval 71-80, we will look in the frequency chart. In the chart score range of 65-80 the cumulative number of students are 13. As the 71 to 80 comes in between the score range 65-80 and there are 13 students who scored in this range.
Therefore, the number of students who have a test score in the interval 71-80 is 13.
What are the solution(s) of x2-4-0?
Of
X=-4 or x = 4
O x=-2 or x = 2
Ox=2
O X=4
o
Answer:
For [tex]x^2 - 4 = 0[/tex], x = 2, or x = - 2.
Step-by-step explanation:
Here, the given expression is :
[tex]x^2 - 4 = 0[/tex]
Now, using the ALGEBRAIC IDENTITY:
[tex]a^2 - b^2 = (a-b)(a+b)[/tex]
Comparing this with the above expression, we get
[tex]x^2 - 4 = 0 = x^2 - (2)^2 = 0\\\implies (x-2)(x+2) = 0[/tex]
⇒Either (x-2) = 0 , or ( x + 2) = 0
So, if ( x- 2) = 0 ⇒ x = 2
and if ( x + 2) = 0 ⇒ x = -2
Hence, for [tex]x^2 - 4 = 0[/tex], x = 2, or x = - 2.
Answer:
x = -2 or x = 2Step-by-step explanation:
[tex]x^2-4=0\qquad\text{add 4 to both sides}\\\\x^2-4+4=0+4\\\\x^2=4\iff\sqrt{x^2}=\sqrt4\\\\|x|=2\Rightarrow x=\pm2[/tex]
What is the value of x?
Enter your answer in the box.
Answer:
x = 27
Step-by-step explanation:
The given angles are vertical angles and congruent, thus
5(x - 4) = 4x + 7, that is
5x - 20 = 4x + 7 ( subtract 4x from both sides )
x - 20 = 7 ( add 20 to both sides )
x = 27
An ice cream store sells 3drinks, in 4sizes, and 8 flavors. In how many ways can a customer order a drink?
Simplify if possible.
a/b xy+xy−2 1/2 xy
Answer:
xy/2
Step-by-step explanation:
use m a t h w a y
C)
9 square units
12 square units
The diameter of Jim's circular flower bed is 10 feet. What is the area, in square feet, of Jim's flower bed?
Answer:
Option C. [tex]25\pi\ ft^{2}[/tex]
Step-by-step explanation:
The complete question is
The diameter of Jim’s circular flower bed is 10 feet. What is the area, in square feet, of Jim’s flower bed?
A) 10π
B) 20π
C) 25π
D) 100π
we know that
The area of a circle (Jim's circular flower bed) is equal to
[tex]A=\pi r^{2}[/tex]
where
r is the radius of the circle
we have
[tex]r=10/2=5\ ft[/tex] ----> the radius is half the diameter
substitute
[tex]A=\pi (5)^{2}[/tex]
[tex]A=25\pi\ ft^{2}[/tex]
The sum of 11 and m is greater than -23.
Answer: m=34
Step-by-step explanation:
11+m=-23
add 23 on both sides
m=34
PLZ HURRY!!!!!
A plan uses a certain amount of fuel based on the number of miles it travels, as shown in the table below. What equation represent the below situation? Miles Traveled, m 0 30 60 90 120 Gallons of Fuel, g 0 156 312 468 624 Question 4 options: m= 30g g = 30m m = 5.2g g = 5.2m
Answer:
I think that the answer is A
Step-by-step explanation:
Please help on implicit differentiation problem.
Answer:
[tex]\frac{ d^{2} y}{dx^{2} } = -10[/tex]
Step-by-step explanation:
Concept : We have to differentiate the given equation twice and then put the values of x and y at the given point.
The given point is (2,-5).
Given xy - y = -5
Differentiating both sides,
[tex] x \times \frac{dy}{dx} + y - \frac{dy}{dx}[/tex] = 0
Substitute (x,y) as (2,-5)
[tex]2 \times \frac{dy}{dx} -5 - \frac{dy}{dx}[/tex] = 0
[tex]\frac{dy}{dx} = 5[/tex]
Differentiating again, we get
[tex]\frac{dy}{dx} + x \times \frac{ d^{2} y}{dx^{2} } + \frac{dy}{dx} - \frac{ d^{2} y}{dx^{2} } = 0[/tex]
Substitute values of x , y and \frac{dy}{dx} ,
[tex]5 + 2 \times \frac{ d^{2} y}{dx^{2} } + 5 - \frac{ d^{2} y}{dx^{2} } = 0[/tex]
[tex]\frac{ d^{2} y}{dx^{2} } = -10[/tex]
put the values in order from least to greatest |-1/4|, |6/10|,|6.25|,|-.5|
Answer:
abs(-1/4), abs(-0.5), abs(6/10), abs(6.25).
Step-by-step explanation:
abs(-1/4)=1/4=0.25
abs(6/10)=6/10=3/5=0.6
abs(6.25)=6.25
abs(-0.5)=0.5
-----------------------------------
abs(-1/4)=0.25 is the smallest, then comes abs(-0.5)=0.5, next comes abs(6/10), finally, comes abs(6.25).
Write a linear expression in simplest form to represent total field goal points scored in the first two quarters.
1st quarter= 2x-6
2nd quarter = x+2
Answer:
Part A) The linear expression that represent the total field goal points scored in the first two quarters is (3x-4)
part B) The linear expression that represent the total points scored in the game is [tex]6x-1[/tex]
Step-by-step explanation:
Part A) we know that
To find out the total field goal points scored in the first two quarters, sum the field goal points scored in the first quarter plus the field goal points scored in the second quarter
we have that
1st quarter= 2x-6
2nd quarter = x+2
therefore
[tex](2x-6)+(x+2)[/tex]
Group terms
[tex](2x+x)+(-6+2)[/tex]
Combine like terms
[tex]3x-4[/tex]
therefore
The linear expression that represent the total field goal points scored in the first two quarters is (3x-4)
Part B) we know that
To find out the total points scored in the game, sum the field goal points scored in the first quarter, plus the field goal points scored in the second quarter plus the field goal points scored in the third quarter, plus the field goal points scored in the fourth quarter, plus the total free throw points.
we have that
1st quarter= 2x-6
2nd quarter = x+2
3rd quarter=2x
4th quarter=x-6
Free throw points =9
therefore
[tex](2x-6)+(x+2)+2x+(x-6)+9[/tex]
Group terms
[tex](2x+x+2x+x)+(-6+2-6+9)[/tex]
Combine like terms
[tex]6x-1[/tex]
therefore
The linear expression that represent the total points scored in the game is [tex]6x-1[/tex]
Blue string 5/4 inches long. If the length of blue string is 5/2 times the length of a piece of green string, what is the length of the piece of green string
Answer:
cdsnvj;vs
Step-by-step explanation:
A slow pitch softball diamond is actually a square 62ft on a side. How far is it from home to second base?
The distance from home to second base in a slow pitch softball diamond is approximately 87.68 feet. This calculation is achieved through the use of the Pythagorean theorem, which utilizes the square lengths of the diamond sides to calculate the diagonal path between the bases.
Explanation:The distance from home to second base in a slow pitch softball diamond can be calculated using the Pythagorean theorem, as the path forms a right triangle. The side lengths of the diamond are 62 ft, so we can use these as the legs of our right triangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, it's a^2 + b^2 = c^2, where c is the distance we want to find.
So, the calculation will be √((62ft)^2 + (62ft)^2). Simplifying this gives √(3844ft^2 + 3844ft^2), which is √7688ft^2. Which gives us approximately 87.68 ft. So, the distance from home to second base is approximately 87.68 feet.
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To find the distance from home to second base on a slow pitch softball diamond, use the Pythagorean theorem to calculate the diagonal of the square. With each side being 62 feet, the distance comes out to approximately 87.7 feet.
How to Find the Distance from Home to Second Base
In a slow pitch softball diamond, the bases form a square with each side measuring 62 feet.
We must compute the diagonal for the square in order to get the distance between home plate and second base.
This can be done using the Pythagorean theorem.
Step-by-Step Solution
Label the sides of the square. Each side is 62 feet.
Recall the Pythagorean theorem formula: a² + b² = c², where 'a' and 'b' are the legs of a right triangle, and 'c' is the hypotenuse (which, in this case, is the diagonal).
Here, both 'a' and 'b' are 62 feet because the square’s sides are equal.
→ Substitute the values into the formula: 62² + 62² = c²
→ Calculate the squares: 3844 + 3844 = c²
→ Combine the values: 7688 = c²
→ Take the square root to find 'c': c = √7688
The diagonal (distance from home to second base) is approximately 87.7 feet.
Therefore, the distance from home to second base is about 87.7 feet.
You buy two types of fish at the local market. You need 1.5 pounds of tilapia and
1 pound of cod. Tilapia costs $3.88 per pound and cod costs $3.53 per pound.How much is your fish purchase ?
Answer:
$9.35
Step-by-step explanation:
Tilapia: 1.5 * $3.88 = $5.82
Cod: 1 * 3.53 = $3.53
$3.53 + $5.82 = $9.35
Answer:
9.35
Step-by-step explanation:
3.88/2= 1.94 for every half pound of tilapia
1.94+3.88+3.53=9.35
Express the ratios as a fraction without reducing.
a. 6:13
b. 7:40
C. 45 : 36
d. 37 : 43
Answer:
A) 6/13 B) 7/40 C) 45/36 D) 37/43
Step-by-step explanation:
8,653,972 rounded to the ten-thousands is
8,653,972 rounded to the ten-thousands is 8,650,000.
Hope this helps!
8,653,972 rounded to the ten thousand is
8,650,000
Jadas family has completed 30% of a trip. They have traveled 15 miles. How far is the trip
Answer:67.5 miles left
Step-by-step explanation:
15×30%= 4.5 then do 15×4.5= 67.5
The required distance of the trip is given as, 50 miles.
Jadas family has completed 30% of the trip. They have traveled 15 miles. How far is the trip is to be determined.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
Let the distance for the trip be x,
According to the question,
30% of x = 15
x = 15 / 30%
x = 1500 / 30
x = 50 miles
Thus, the required distance of the trip is given as, 50 miles.
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2x-y=23 & x-9=-1 by substitution
Answer:
x=8, y=-7. (8, -7).
Step-by-step explanation:
2x-y=23
x-9=-1
-----------------
x=-1+9=8
x=8
-------------
2(8)-y=23
16-y=23
y=16-23=-7
x=8, y=-7. (8, -7).