Answer:
[tex]D=\sqrt{10}=3,16...[/tex]
Step-by-step explanation:
[tex]A(x_{1},y_{1})[/tex]
[tex]B(x_{2};y_{2})[/tex]
[tex]D=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
[tex]A(-6,2)[/tex]
[tex]B(-9;1)[/tex]
[tex]D=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
[tex]D=\sqrt{[-9-(-6)]^{2}+(1-2)^{2}}[/tex]
[tex]D=\sqrt{[-9+6]^{2}+(1-2)^{2}}[/tex]
[tex]D=\sqrt{[-3]^{2}+(-1)^{2}}[/tex]
[tex]D=\sqrt{9+1}[/tex]
[tex]D=\sqrt{10}=3,16...[/tex]
Answer:
The distance between -6.2 and -9.1 is 2.9.
Step-by-step explanation:
Given : Two numbers -6.2 and -9.1.
To find : What is the distance between the numbers ?
Solution :
Let A=-6.2
B=-9.1
The distance between two number is [tex]d=|B-A|[/tex]
Substitute the values,
[tex]d=|-9.1-(-6.2)|[/tex]
[tex]d=|-9.1+6.2|[/tex]
[tex]d=|-2.9|[/tex]
[tex]d=2.9[/tex]
Therefore, The distance between -6.2 and -9.1 is 2.9.
there is a 6 degree drop in temperature over the past hour. If it is 55 degrees now, what was the temperature an hour ago?
Answer:
61
Step-by-step explanation:
if it dropped 6 degrees, you would add 6 to the current temperature to get 61 (55+6=61)
Answer:
61 degrees
Step-by-step explanation:
it is 55 degrees now. it had dropped 6 degrees in an hour. since it went down and subtracted 6 degrees, we would have to do the other order of operation which in this case is addition. 55 plus 6 is 61. ( message me if you need more help)
A roll of material is (x + 2) metres wide. Annie buys (x + 3) metres of the material and Bronwyn buys 5 metres of the material.
a) Write an expression, in terms of x, for the area of each piece of material purchased.
b) If Annie has bought more material than Bronwyn, write an expression for how much more she has than Bronwyn.
c) Factorise and simplify this expression.
d) Find the width of the material if Annie has 5m^2 more than Bronwyn.
e) How much material does each person have? Explain.
The problem involves determining the area of material purchased, comparing the quantities, and solving for the width given certain conditions. After setting up and solving the equations, it was found that the width of the material is 3 metres and the total amounts of material purchased by Annie and Bronwyn are 4 and 15 square metres respectively.
To solve the problems related to the area of material purchased by Annie and Bronwyn, follow these steps:
Area of material: Given the width of the material is (x + 2) metres, Annie buys (x + 3) metres long and Bronwyn buys 5 metres long. The area for each piece of material purchased is the product of the width and length. So, Annie's material area is (x + 2)(x + 3) square metres, and Bronwyn's material area is 5(x + 2) square metres.
More material: To express how much more material Annie has than Bronwyn, subtract Bronwyn's area from Annie's area, which gives us ((x + 2)(x + 3) - 5(x + 2)) square metres.
Factorisation: The expression for how much more material Annie has than Bronwyn can be factorized as (x + 2)(x - 2) square metres after simplifying.
Width of material: If Annie has 5 square metres more material than Bronwyn, we solve the equation (x + 2)(x - 2) = 5. Solving this quadratic equation gives x = 1, the width of the material is therefore 3 metres.
Total material: With x = 1, Annie purchases 4 square metres (since 3 x 1 + 3) and Bronwyn purchases 15 square metres (since 5 x 3). So, Annie has 4 square metres of material and Bronwyn has 15 square metres.
Lauren visits the park every 3 days and goes to the library every 10 days. If Lauren gets to do them both. On the same day again
Answer:
On the 30th day
Step-by-step explanation:
What are the factors of 10?
10,20,30,40,50
What are the factors of 3?
3,6,9,12,15,18,21,24,27,30
Which numbers are the same on both?
(Hint which is the first number on both factors :))
Lauren will visit both the park and the library on the same day again after 30 days. This is because the least common multiple (LCM) of 3 and 10 is 30.
Explanation:The subject of this question is Mathematics, particularly dealing with the concept of least common multiple (LCM). The question is asking when will Lauren visit the park and the library on the same day again. Given that Lauren goes to the park every 3 days and the library every 10 days, the day when she'll do both again is the least common multiple of 3 and 10.
The least common multiple (LCM) is the smallest multiple that is exactly divisible by every member of a set of numbers. In this case, we need to determine the LCM of 3 and 10. The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ... The multiples of 10 are 10, 20, 30, 40, .... As we can see, the smallest number that appears in both lists is 30. Therefore, Lauren will visit both the park and library on the same day again after 30 days.
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Multiply the binomials (3x-5) (x-10)
Helpp
Answer: The answer would be 3x^2-35x+50
Answer:
3x^2-35x+50 is the answer
Step-by-step explanation:
If you use the FOIL method this will be a breeze.
In science class, Savannah measures the temperature of a liquid to be
24 Celsius. Her teacher wants her to convert the temperature to degrees Fahrenheit. What is the temperature of Savannah's liquid to the nearest degree Fahrenheit?
Answer:
75.2 °F
Step-by-step explanation:
(24°C × 9/5) + 32 = 75.2°F
the formula F=ma means that the force on an object is equal to its mass times the acceleration. Solve F=ma for m
Answer:
Step-by-step explanation:
F = m / a
cross multiply
m = F /a
To solve F=ma for mass, divide both sides by acceleration to get m=F/a. For a wagon of 55 kg accelerating at 0.0255 m/s², the calculated force is 1.4025 newtons.
Explanation:To solve the formula F=ma for mass (m), you need to isolate the variable m. This is done by dividing both sides of the equation by acceleration (a), thus the rearranged formula becomes m = F/a. When we apply this to a practical example, if a wagon with mass 55 kg accelerates at a rate of 0.0255 m/s², the force on the wagon can be calculated using the same formula. By substituting the values into the formula, the force F is found as F = 55 kg × 0.0255 m/s², which equals 1.4025 newtons (N).
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What is the answer to this
Answer: The answer would be 2 1/2
Step-by-step explanation:
first you convert the mixed number into an improper fraction which would be 25/8
then you multiply 4/5 with 25/8
which equals 100/40
finally you simplify and you get 2 1/2
Answer:
so first you would make 3 1/8 into a number like the frist one then change them into common denominators then multilpy.I hope it helps
Write all the numbers up to 30 that have an equal number of odd and even factors
Answer: 2, 6, 10, 14, 18, 22, 26, 30 have an equal number of odd and even factors.
Step-by-step explanation:
Since they want the same number of even and odd factors for numbers 1-30 then we can list the factors of only even numbers from 1-30
List factors of even numbers 1-30
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30
2) 1,2
4) 1,2,4
6) 1, 2, 3 6
And so forth for the rest of the numbers
you will notice that you add 4 each time untill you get to thirty which are numbers that have an equal number of odd and even factors.
How much interest is earned on an investment of $12,000 at 2.9% compounded daily for eight years
Answer:
$3,113,34
Step-by-step explanation:
The formula for calculating compound interest is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where
A=the future total value, i.e, the money you will have after t years.
P=the initial deposit.
r=the annual interest rate.
n=the number of times that interest is compounded per year.
t=the number of years the money is saved.
In our case
A is unknown and we will have to calculate it with the formula.
P=$12,000
r=2.9%=0.029
n=365 because the interest is compounded daily and there are 365 days in a year
t=8 years
Applying the formula we get
[tex]A=12,000(1+\frac{0.029}{365})^{365\times8}[/tex]
[tex]A=12,000(1+\frac{0.029}{365})^{2,920}[/tex]
[tex]A=12,000(1.000079)^{2,920}[/tex]
So A=15,113.336
This is the amount of money you would have after 8 years.
Subtracting the initial deposit from this amount we obtain the interest earned I
I=15,113.336-12,000=3,113.336
Rounded to the nearest hundreth
I=$3,113,30
Reggie knows how to make 5 different entrees, 4 dif-
ferent side dishes, and 6 different desserts. How many
distinct complete meals, each consisting of an entrée, a
side dish, and a dessert, can Reggie make?
F. 16
G. 26
H. 72
J. 120
K. 144
Reggie can make 120 distinct complete meals, each consisting of an entrée, a side dish, and a dessert.
This is a rather simple and straightforward question.
If Reggie can make
5 Entrees
4 Side dishes
6 Desserts,
Then she can make 5 × 4 × 6 different distinct dishes.
5 × 4 × 6 = 120
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What is the domain of the function f(x) = 2x + 5?
O A.
all real numbers except 2
O B. all real numbers
O c. all real numbers except 5
OD. all positive real numbers
There is no value that x cannot be for linear equations.
Thus, the domain is ALL REAL NUMBERS.
CHOICE B.
Answer:
B all real numbers
Step-by-step explanation:
A point, beginning at (0,0), undergoes the following composition of translation. Write an ordered pair for the points final position. T<5,-7> and then T<-6,2>
Answer:
(-1,-5)
Step-by-step explanation:
Starting at (0,0), we perform the first translation:
T<5,-7> implies that we move the point 5 units to the right (in the x (horizontal) direction), and 7 units DOWN in the y <vertical) direction.
From there we do the second translation: T<-6,2>
which means: 6 units to the left (in the horizontal direction) which takes us to "-1" for the x value, and 2 units up (vertical) which takes us to -5 for the y value.
Therefore the new location is (-1,-5)
what is the decimal equivalent to 8/3
a 2.6
b 0.375
c2.6666666666666
d8.3
Answer:
C. 2.6666666666666
Step-by-step explanation:
You can estimate.
We know that 3 * 2 = 6.
So, we know that The decimal is at least 2.
We can cancel out B and D.
2.6 * 3 = 7.18
So, we can cancel out A.
Just to make sure, let's try C.
2.6666666666666 * 3 = 7.999999...
This is the closest answer to 8.
So, our answer is C.
C. 2.6666666666666
A store sells 4 cans of fruit cocktail for $10.What is the price of 7 cans of fruit cocktail?
Answer:
17.5
Step-by-step explanation:
so 4 cans is 2.5$ each so i did 2.5 times 7 to see how much it would be for 7 cans
To find the cost of 7 cans of fruit cocktails, you first determine the price per can at $2.50 by dividing the cost for 4 cans ($10) by 4. Multiplying the price per can by 7 gives the total cost, which is $17.50.
Explanation:To find the price of 7 cans of fruit cocktails when 4 cans are sold for $10, we need to calculate the price per can and then multiply by the desired number of cans.
Step-by-step calculation:
First, determine the price per can by dividing the total price by the number of cans: 4 cans for $10 results in $10 ÷ 4 = $2.50 per can.Next, multiply the price per can by the number of cans desired: 7 cans × $2.50 per can = $17.50.Therefore, 7 cans of fruit cocktails will cost $17.50.
[{8 + 113 • 5] - 8 + 11
Answer:
[8 + 113 • 5] - 8 + 11 =
[8 + 565] - 8 + 11 =
573 - 8 + 11 = 576
A ladder leaning against the side of a building touches the building at a point 12 meters from the ground. If the foot of the ladder is 18 meters from the base of the building, what is the slope of the ladder?
Answer:
The slope of the ladder to the building is 2/3
Step-by-step explanation:
* Lets explain how to find the the slope of the ladder
- A ladder leaning against the side of a building touches the building
at a point 12 meters from the ground
* That means the height of the ladder (h) from the ground is 12 m
- The foot of the ladder is 18 meters from the base of the building
* That means the horizontal distance (d) on the ground between the
ladder and the building is 18 m
- The slope of the ladder (m) , the height of the ladder (h) and the
horizontal distance on the ground from the base of the ladder to
the base of the building (d) can form a right triangle
∵ The slope of the ladder = the vertical distance/horizontal distance
∵ The vertical distance h is 12 meters
∵ the horizontal distance d is 18 meters
∴ The slope of the ladder [tex]m=\frac{12}{18}=\frac{2}{3}[/tex]
∴ The slope of the ladder to the building is 2/3
Answer:
2/3
Step-by-step explanation:
Its just as easy as it looks. Its 12/18, or Rise 12 and Run 18.
Solving would get you 2/3, so your slope is 2/3
Find the least
common denominator
3/5+4/7
Answer:
35
Step-by-step explanation:
5*1=5 5*2=10 5*3=15 5*4=20 5*5=25 5*6=30 5*7=357*1=7 7*2=14 7*3=21 7*4=28 7*5=35In the diagram shown below is it given (known) that FB and EH intersect at A and ZEAG is right. Give
two different angles that are both supplementary to ZFAH. What must be true of these two angles?
Answer:
Angle HAB and Angle FAE are congruent angles
Step-by-step explanation:
we know that
Two angles are supplementary if their sum is equal to 180 degrees
In this problem
m∠FAH+m∠HAB=180° ----> by a linear pair
Remember that
A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. A linear pair of angles must add up to 180 degrees
m∠FAH+m∠FAE=180° ----> by a linear pair
therefore
m∠HAB=m∠FAE -----> by vertical angles
Angle HAB and Angle FAE are congruent angles
Answer:
<HAB is congruent with <FAE
NO CAP
help on question 32 please
Answer:
90
Step-by-step explanation:
The mean is measured as
mean = [tex]\frac{score}{count}[/tex]
After 5 tests the mean is 84, that is
[tex]\frac{score}{5}[/tex] = 84 ( multiply both sides by 5 )
score = 420
let the sixth test score be x, then
[tex]\frac{420+x}{6}[/tex] = 85 ( multiply both sides by 6 )
420 + x = 510 ( subtract 420 from both sides )
x = 90
Require to score 90 on the sixth test
Help please fast
Question 17
Answer:
I think the answer may be 12 minutes
Answer:
I think it is 12 mins
The volume, V, of the right circular cone with radius r.
and height h, shown below, can be found using the
formula V= { ar?h. A cone-shaped paper cup has a
volume of 142 cubic centimeters and a height of
8.5 centimeters. What is the radius, to the nearest
centimeter, of the paper cup?
Answer:
radius^2 = 3 * Volume / (PI * height)
radius^2 = 3 * (142 cc / 3.14159265 * 8.5)
radius^2 = 3 * (142 cc / 26.703537525 )
radius^2 = 15.9529425493
radius = 4.0 cm
Step-by-step explanation:
Final answer:
The radius of a cone-shaped paper cup with a volume of 142 cubic centimeters and height of 8.5 centimeters is approximately 4 centimeters when rounded to the nearest centimeter.
Explanation:
To determine the radius of a paper cup that is a right circular cone with a given volume, we will use the formula for the volume of a cone V = (1/3) πr²h. The volume, V, is provided as 142 cubic centimeters, and the height, h, is 8.5 centimeters.
Rearrange the formula to solve for the radius, r, as follows:
Divide both sides by π and 8.5 to isolate ¹⁄₃r² on one side.
Multiply both sides by 3 to get rid of ¹⁄₃.
Take the square root of both sides to solve for r.
Once we have the value of r, we round it to the nearest centimeter as the question asks for an approximation to the nearest whole number.
Let's perform the calculation:
V = (1/3)πr²(8.5) => 142 = πr²(8.5/3)
142 = (π × 8.5/3)r²
142 / (π × 8.5/3) = r²
r² ≈ 142 / (3.14159 × 8.5/3)
r² ≈ 15.91549431
r ≈ √15.91549431 ≈ 3.99 cm
Round r to the nearest centimeter: r ≈ 4 centimeters
x+109 and x+89 what is x they need to be the same number when finished
Answer:
DNE (dose not exist)
Step-by-step explanation:
what you would do is just set both functions equal to each other and then solve for x. so set x+109=x+89. then get you numbers on one side and your x's on one side. so subtract x from on side getting x-x+89=109 now you subtract 89 from both sides getting x-x=109-89 getting 0= 20 0 dosen not = 20 so you would have zero there is no value that you could plug in for x to get them both equal
0.5,7/16,0.75,19/48 order least to greatest
Answer:
19/48, 7/16, 0.5, 0.75
Step-by-step explanation:
12. Snowfall At 8:00 A.M., you measure the depth of snow in your backyard to be
4 inches. At 6:00 P.M., you measure the snow depth to be 19 inches. What is the
average rate of change in the snow depth?
10
Answer: The answer would be 1.5
Step-by-step explanation: From 8-6 it is 10 hours. Then you go from 4 inches to 19 inches. So every 10 hours is 15 inches more of snow. If you divide 15 by 10 then it is 1.5
Which inequality represents all the solutions of 8(6x − 7) < 5(9x − 4)?
Answer:
The inequality that represents the solution of 8(6x − 7) < 5(9x − 4) is x < 12.
Step-by-step explanation:
Given 8(6x − 7) < 5(9x − 4)⇒ 48x - 56 < 45x - 20⇒ 48x - 45x < -20 + 56
⇒3x< 36 ⇒ x<36/3 ⇒ x<12.
Inequalities help us to compare two unequal expressions. The correct option is B.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The given inequality can be solved as,
8(6x − 7) < 5(9x − 4)
48x − 56 < 45x − 20
48x − 45x < 56 − 20
3x < 36
x < 36/3
x < 12
Hence, the inequality that represents all the solutions of 8(6x − 7) < 5(9x − 4) is x < 12.
The complete question is:
Which inequality represents all the solutions of 8(6x − 7) < 5(9x − 4)? A. x > 12 B. x < 12 C. x > 20 D. x < 20
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2⋅(36⋅3−5) . evaluate
Answer:
[tex]206[/tex]
[tex]2 \times |108 - 5|=\\ 2 \times 103 = \\ 206 [/tex]
Answer: 206
Answer:
Answer is = 6
Step-by-step explanation:
Trinity is going to the movies with some friends and will pay for her own ticket plus her own and her friends' small popcorns. Her total cost is given by the following expression: 8.5 + 6x What does the 6x represent?
A. The total cost of the small popcorns
B. The amount of small popcorns she is buying
C. The total cost
D. The cost of the ticket
Answer:
A. The total cost of the small popcorns
Step-by-step explanation:
Let us suppose Trinity is going to the movies with [tex]x[/tex] number of friends, we know she will pay for only her own movie ticket hence cost of movie ticket will be a constant (say [tex]a[/tex]) for her expense and cost of popcorn will be price of one popcorn (say [tex]b[/tex]) multiplied by number of friends.
considering the situation, her expense will be given by the function-
[tex]f(x) = a + bx[/tex]
comparing this with the given function [tex]8.5 + 6x[/tex], [tex]6x[/tex] will be the total cost of small popcorns.
Give an equation for a line perpendicular to the line y=0. Is there more than one such line? Explain.
Check the picture below.
sure, since y = 0 is a line, in essence the x-axis really, that goes to infinity, so we can draw an infinite amount of perpendicular lines on it all the way.
The equation for a line perpendicular to the line y=0 is x=a, where a is the x-coordinate of the point where the line intersects the x-axis. There are infinitely many lines that are perpendicular to the line y=0. For example, the line x=3.
Explanation:The equation for a line perpendicular to the line y=0 is simply the equation for a vertical line passing through any point on the x-axis. A vertical line is defined by the equation x = a, where a is the x-coordinate of the point where the line intersects the x-axis.
Since the line y=0 is also the x-axis, any vertical line passing through a point on the x-axis will be perpendicular to it. Therefore, there are infinitely many lines that are perpendicular to the line y=0.
For example, the equation for a line perpendicular to y=0 passing through the point (3,0) would be x=3.
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solve for x: x² - 14x + 49/x² - 49 = 3/17
Answer:
x = 10
Step-by-step explanation:
Begin by factorising the numerator/ denominator of the left side
x² - 14x + 49 = (x - 7)² ← perfect square
x² - 49 = (x - 7)(x + 7) ← difference of squares
Thus left side becomes
[tex]\frac{(x-7)^2}{(x-7)(x+7)}[/tex] → x ≠ ± 7
Cancel (x - 7) on numerator/denominator, leaving
[tex]\frac{x-7}{x+7}[/tex]
Returning to the equation, that is
[tex]\frac{x-7}{x+7}[/tex] = [tex]\frac{3}{17}[/tex] ( cross- multiply )
17(x - 7) = 3(x + 7) ← distribute both sides
17x - 119 = 3x + 21 ( subtract 3x from both sides )
14x - 119 = 21 ( add 119 to both sides )
14x = 140 ( divide both sides by 14 )
x = 10
A movie cost 3,254, 107 to produce what digit is in th hundred thousands place
Answer:5
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
3 million
2 hundred thousand
5 ten thousand
4 thousand
1 hundred
0 ten
7 one