Answer:
The equivalent expression to 9(15) is 9(10+5).
Step-by-step explanation:
this is equivalent to 910 because 27 x 10 = 30 x 9 = 270.
this is also equal to 9(15) to 9(10+5)
An expression is defined as a set of numbers, variables, and mathematical operations. The expression that is equivalent to 9/10÷2/3 is (9×3)/(10×2).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The expression is equivalent to 9/10÷2/3, can be written as,
[tex]\dfrac9{10} \div \dfrac23\\\\\\= \dfrac{\frac{9}{10}}{\frac23}\\\\\\= \dfrac{9\times 3}{10 \times 2}[/tex]
Thus, the expression that is equivalent to 9/10÷2/3 is (9×3)/(10×2).
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What is the greatest number of right angles a triangle can contain?
O A. O
O
B. 3
O c. 1
OD.2
SUBMIT
Answer:
1
Step-by-step explanation:
Only 1 right angle can be in any triangle.
1000(1+0,05 )^4 *x=1500
The answer is supposed to be x=ln(1.5)/4ln(1.0125)
I'm currently at 4log¹'⁰¹²⁵(1.0125)=log¹'⁰¹²⁵(1.5)
What did I do wrong?
The correct answer is [tex]\( x = \frac{\ln(1.5)}{4\ln(1.05)} \).[/tex]
Let's analyze the given equation step by step:
Given the equation [tex]\( 1000(1+0.05)^4 \cdot x = 1500 \)[/tex], we want to solve for [tex]\( x \).[/tex]
First, simplify the left side of the equation by calculating
[tex]\( (1+0.05)^4 \):\( (1+0.05)^4 = (1.05)^4 \).[/tex]
Now, the equation becomes:
[tex]\( 1000 \cdot (1.05)^4 \cdot x = 1500 \).[/tex]
Next, divide both sides by [tex]\( 1000 \cdot (1.05)^4 \) to isolate \( x \):[/tex]
[tex]\( x = \frac{1500}{1000 \cdot (1.05)^4} \).[/tex]
Simplify the right side by dividing 1500 by 1000:
[tex]\( x = \frac{1500}{1000} \cdot \frac{1}{(1.05)^4} \),[/tex]
[tex]\( x = 1.5 \cdot \frac{1}{(1.05)^4} \).[/tex]
Now, to express [tex]\( x \)[/tex] in terms of natural logarithms, we take the natural logarithm of both sides:
[tex]\( \ln(x) = \ln(1.5 \cdot \frac{1}{(1.05)^4}) \).[/tex]
Using the property of logarithms that [tex]\( \ln(ab) = \ln(a) + \ln(b) \)[/tex], we can split the right side:
[tex]\( \ln(x) = \ln(1.5) - \ln((1.05)^4) \).[/tex]
Applying the power rule of logarithms, [tex]\( \ln(a^b) = b\ln(a) \)[/tex], we get:
[tex]\( \ln(x) = \ln(1.5) - 4\ln(1.05) \).[/tex]
To solve for [tex]\( x \)[/tex], exponentiate both sides to remove the natural logarithm:
[tex]\( e^{\ln(x)} = e^{\ln(1.5) - 4\ln(1.05)} \),[/tex]
[tex]\( x = e^{\ln(1.5)} \cdot e^{-4\ln(1.05)} \),[/tex]
[tex]\( x = 1.5 \cdot \frac{1}{e^{4\ln(1.05)}} \),[/tex]
[tex]\( x = 1.5 \cdot \frac{1}{(e^{\ln(1.05)})^4} \),[/tex]
[tex]\( x = 1.5 \cdot \frac{1}{(1.05)^4} \).[/tex]
Now, we have arrived back at the expression we had for [tex]\( x \)[/tex] earlier:
[tex]\( x = 1.5 \cdot \frac{1}{(1.05)^4} \).[/tex]
To find the numerical value of [tex]\( x \)[/tex], we can use the expression involving natural logarithms:
[tex]\( x = e^{\ln(1.5) - 4\ln(1.05)} \).[/tex]
This is equivalent to:
[tex]\( x = \frac{e^{\ln(1.5)}}{e^{4\ln(1.05)}} \),[/tex]
[tex]\( x = \frac{1.5}{1.05^4} \).[/tex]
Finally, to express [tex]\( x \)[/tex] as a single logarithm, we can use the change of base formula for logarithms:
[tex]\( x = \frac{\ln(1.5)}{\ln(1.05^4)} \),[/tex]
[tex]\( x = \frac{\ln(1.5)}{4\ln(1.05)} \).[/tex]
This is the correct expression for [tex]\( x \)[/tex] in terms of natural logarithms. The mistake in the original attempt was likely in the manipulation of the logarithms, where the properties of logarithms were not correctly applied. The correct step is to use the quotient rule of logarithms, [tex]\( \ln(\frac{a}{b}) = \ln(a) - \ln(b) \)[/tex], and the power rule, [tex]\( \ln(a^b) = b\ln(a) \)[/tex], to arrive at the correct expression for [tex]\( x \).[/tex]
What are the solutions of x^2-2x+5=0
Answer:
1 + 2i and 1 – 2i
If the area of a triangle with a base measuring 22 feet is 93.5 square feet, find its height
Answer:
I think it is 8.5
Step-by-step explanation:
The height of the triangle is 8.5 feet
To find the height of a triangle when the area and the base are known, we use the formula Area = 1/2 x base x height, where A is the area, b is the base, and h is the height. Given that the area of the triangle is 93.5 square feet and the base measures 22 feet, we can rearrange the formula to solve for h: h = 2 × Area/Base
h = 2×93.5/22
h=187/22
h = 8.5 feet
Therefore, the height of the triangle is 8.5 feet.
evie had 3/8 gallon of blue pint, 1/4 gallon of red, and 2/5 of green paint. How paint does she have in all?
Answer: 1 1/40.
Step-by-step explanation:
PLEASE HELP
The total cost f(x), in dollars, for renting a moving van for a week and driving it x miles is shown below:
f(x) = 90 + 0.13x
What is the value of f(200), and what does f(200) represent?
Answer:
f(200) =116
f(200) is the cost to rent the moving van and drive it 200 miles
Step-by-step explanation:
f(x) = 90 + 0.13x
Let x = 200
f(200) = 90+ .13(200)
=90+26
=116
f(200) is the cost to rent the moving van and drive it 200 miles
Skylar is filling a barrel with water. The graph shows the relationship between time in minutes and the gallons of water in the barrel. Write an inequality showing the times there will be more than 10 gallons in the barrel. Explain your answer.
Answer:
t>15
Step-by-step explanation:
what is two thirds times negative one
Answer:
-1/3
Step-by-step explanation:
2/3 times -1 is -1/3
It is -2/3 or negative two thirds
8 divided by 6040 fill in the blank
Answer:
0.00132450331
Step-by-step explanation:
just divide lol
To solve 8 divided by 6040, perform the division, resulting in approximately 0.0013245.
To solve the problem of 8 divided by 6040, follow these steps:
1. Recognize this as a division problem: 8 ÷ 6040.2. Since 8 is smaller than 6040, the quotient will be less than 1.3. Perform the division by dividing 8 by 6040: 8 ÷ 6040 ≈ 0.0013245Therefore, 8 divided by 6040 equals 0.0013245.What is the quotient for the equation above?
Answer:
The correct answer is 32.5
Charles earns an annual salary of $61,870. If he is paid weekly, much would his pay be each week?
A box in the shape of a rectangular prism has a volume of 72 cubic feet. The box has a length of x feet, a width of (x − 1) feet, and a height of (x + 9) feet. Find the dimensions of the box.
72 = l . w . h
72 = x . (x - 1) . (x + 9)
72 = (x² - x) . (x + 9)
72 = x³ + 9x² - x² - 9x
72 = x³ + 8x² - 9x
0 = x³ + 8x² - 9x - 72
0 = x² (x + 8) - 9 (x + 8)
0 = (x² - 9)(x + 8)
0 = (x - 3)(x + 3)(x + 8)
x = 3 or x = -3 or x = -8
so, x = 3
length = x = 3
width = x - 1 = 2
height = x + 9 = 12
Final answer:
To find the dimensions of the rectangular prism, set up an equation using the volume formula and solve for x. The dimensions of the box are 3 feet, 2 feet, and 12 feet.
Explanation:
To find the dimensions of the box, we need to set up an equation using the volume formula for a rectangular prism. The volume of a rectangular prism is given by V = length x width x height.
So, we have the equation x(x - 1)(x + 9) = 72.
Simplifying this equation, we get x³ + 8x² - 9x - 72 = 0.
Using factoring or synthetic division, we find that x = 3 is a solution to the equation. Therefore, the length of the box is 3 feet, the width is 2 feet, and the height is 12 feet.
Please help me out! I will mark brainliest!!!
Answer:A. 36
Step-by-step explanation:2x+16=×+20 x=4
4+8=12. 4+20=24
12+24=36
The students at Porterville Elementary sold raffle tickets, each for the same price, for a fundraiser. The equation below shows how much money was raised with t tickets sold. $1,530 = $17t
Roberto has 1 3/4 pies he wants to give to two friends. Show two ways he could split the pies between the friends
Answer:
7/8
Step-by-step explanation:
Simplify the following:
(1 + 3/4)/2
Put 1 + 3/4 over the common denominator 4. 1 + 3/4 = 4/4 + 3/4:
(4/4 + 3/4)/2
4/4 + 3/4 = (4 + 3)/4:
((4 + 3)/4)/2
4 + 3 = 7:
(7/4)/2
7/4×1/2 = 7/(4×2):
7/(4×2)
4×2 = 8:
Answer: 7/8
Sarah walks 3.1 kilometers on Monday and 1.35 kilometers on Tuesday. On Wednesday she walks 2.4 times as far as she walked on the previous two days combined. How far does Sarah walk on Wednesday?
Answer:10.68
Step-by-step explanation:
3.1 + 1.35 = 4.45 4.45 × 2.4 = 10.68
Answer:
10.68
Step-by-step explanation:
i worked it out on a piece of paper but this is my answer
Point X (-3, -2) is translated using the rule (x, y) = (x+3, y + 4), then reflected over the x-axis. What is
the coordinate of X”?
(a) (0,2)
(c) (-2,0)
(b) (0,-2)
(d) (2,0)
The resulting coordinate of X is (0, -2)
TransformationGiven the coordinate point X (-3, -2). If the coordinate is translated using the rule (x, y) = (x+3, y + 4), the resulting coordinate will be (-3+3, -2+4) = (0, 2)
If the result is reflected over x-axis, hence the resulting coordinate will be (0, -2)In conclusion, the resulting coordinate of X is (0, -2)
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After translation and reflection, the coordinate of X" is (0, -2).
Explanation:To find the coordinate of X" after a translation and reflection, we need to first apply the translation rule to point X (-3, -2). Using the rule (x, y) = (x+3, y + 4), we add 3 to the x-coordinate and add 4 to the y-coordinate:
x' = -3 + 3 = 0
y' = -2 + 4 = 2
After the translation, the new coordinates are (0, 2). To reflect over the x-axis, we change the sign of the y-coordinate, giving us the final coordinate of X" as (0, -2).
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Two sides of a triangle measure 5 inches 6 inches. jason says the triangle wust be scalene is jason correct?
Answer:
He is incorrect
If there was 2 sides of 6 inches, the base can be 5 inches and it could be an isoscles triangle
Step-by-step explanation:
He is incorrect, the third side could be 5.
Doubling the radius of a sphere increases the surface area by a factor of ?
Answer:
4π(2r)² = 4π(4r²) = 4(4πr²)
Doubling the radius of a sphere increases the surface area by a factor of 4.
The correct factor is 4. Doubling the radius of a sphere increases the surface area by a factor of 4.
To understand why the surface area increases by a factor of 4 when the radius is doubled, let's consider the formula for the surface area of a sphere, which is given by:
[tex]\[ A = 4\pi r^2 \][/tex]
where A is the surface area and [tex]\( r \)[/tex] is the radius of the sphere.
Now, if we double the radius, the new radius becomes [tex]\( 2r \)[/tex]. Substituting this into the formula for surface area, we get:
[tex]\[ A_{\text{new}} = 4\pi (2r)^2 \][/tex]
[tex]\[ A_{\text{new}} = 4\pi \cdot 4r^2 \][/tex]
[tex]\[ A_{\text{new}} = 16\pi r^2 \][/tex]
To find out how much the surface area has increased, we take the ratio of the new surface area to the original surface area:
[tex]\[ \text{Factor of increase} = \frac{A_{\text{new}}}{A} \][/tex]
[tex]\[ \text{Factor of increase} = \frac{16\pi r^2}{4\pi r^2} \][/tex]
[tex]\[ \text{Factor of increase} = 4 \][/tex]
Therefore, when the radius of a sphere is doubled, the surface area increases by a factor of 4.
I need help ASAP!! Please no decimals
Answer:
-3/4 is plotted 3 little tabs left of 0
5/4 is plotted 1 little tab right of 1
A science class has a total of 34 students. The number of females is 16 less than the number of males. How many males and how many females are in the class?
Answer:
25 and
9
Step-by-step explanation:
Let the number of males be A and that of females be B
Total number of students = 34
Number of females B = A - 16
Remember males and females = 34
That’s
A + B = 34
We now have two equations
Equation one:B = A - 16
Equation two: A + B = 34
Substitute A - 16 for B in equation 2
We have,
A + B = 34
A + A - 16 = 34
2A - 16 = 34
Add 16 to both sides
2A - 16 + 16 = 34 + 16
2A = 50
Divide both sides by 2
2A/2 = 50/2
A = 25
Now put 25 as A in any of the equations to get B
Using equation one , we have
B = A - 16
B = 25 - 16
B = 9
There are 25 males and 9 females in the class
what is the answer to the equation: 7x + 4x +2
1. Collect like terms
(7x + 4x) + 2
2. Simplify
11x + 2
Please take a look and help if you can!
Answer:
see explanation
Step-by-step explanation:
1
The area of a rectangle = length × width
2
To find the width, divide the area by the length
3
width = [tex]\frac{area}{length}[/tex] = [tex]\frac{3x^2+9x}{3x}[/tex]
To simplify divide each term on the numerator by 3x
= [tex]\frac{3x^2}{3x}[/tex] + [tex]\frac{9x}{3x}[/tex] = x + 3 ← width
The bake stars picked 907 apples last weekend at local orchard. They made caramel apples and sold them in the bakery in trays of 6. How many trays of caramel apples did they have to sell and how many apples were left over?
Answer:
151 trays, 1 left over
Step-by-step explanation:
907/6 = 151 remainder 1
The Bake Stars could sell 151 trays of caramel apples with 1 apple left over.
The Bake Stars picked 907 apples and sold them in trays of 6.
To determine how many trays they can sell, divide the total number of apples by the number of apples in each tray:
907 apples / 6 apples per tray = 151 trays with 1 apple remaining (since 907 = 151 * 6 + 1).
9-4b+(8+7b+5c) what is the answer to this
Answer:
17+3b+5c
Step-by-step explanation:
9-4b+(8+7b+5c)
9-4b+8+7b+5c
9+8-4b+7b+5c
17+3b+5c
The city of Arachna has a spider population that has been doubling every year. If there are about 100,000
spiders this year, how many will there be 4 years from now?
Answer:
1,600,000
Step-by-step explanation:
100,000x2x2x2x2
Answer:160000
Step-by-step explanation:
,
What is a equivalent expression for 5times v+6
Answer:
5v +30
Step-by-step explanation:
[tex]5(v + 6) \\ = 5v + 5 \times 6 \\ = 5v + 30[/tex]
Slide the green dot from 0 to plot the number at the correct
location.
Plot V5
Plot the numbers on the number line.
V5, V8, V13
Which inequalities are true? Check all that apply
0 V5 <3
V8 > 3
V8 < 513
013 = 3.6
2.2< V5 <2.3
3.6 > 3> 3.7
The true inequalities are √5 < 3, 2.2 < √5 < 2.3, and 3.6 > √13 > 3.7. The false inequalities are √8 > 3 and √13 = 3.6. The truth value of √8, √13 is inconclusive due to the incomplete expression. These comparisons highlight the relative magnitudes of square roots in the given range of numbers.
The given numbers √5, √8, and √13 can be compared using various inequalities to determine their relative magnitudes. First, √5 is less than 3, as √5 is approximately 2.24. However, √8 is not greater than 3, as it is approximately 2.83, rendering the second inequality false.
The inequality √8, √13 is incomplete, making it impossible to determine its truth value without a specific comparison operator. Moving on, √13 is not equal to 3.6; in fact, it is approximately 3.61, making the statement false.
On the other hand, the range-based inequality 2.2 < √5 < 2.3 holds true, as √5 is approximately 2.24, falling within the given range. Similarly, the range-based inequality 3.6 > √13 > 3.7 is true since √13 is approximately 3.61, falling within the specified range.
In summary, √5 < 3, 2.2 < √5 < 2.3, and 3.6 > √13 > 3.7 are true inequalities, while √8 > 3, √13 = 3.6, and √8, √13 are inconclusive or false based on the provided information. These comparisons highlight the relative sizes of square roots within the given numerical context.
In ΔPQR, the measure of ∠R=90°, the measure of ∠Q=38°, and RP = 72 feet. Find the length of PQ to the nearest tenth of a foot.
Answer:74
Step-by-step explanation:
Since RP is 72, you would divide 72 by 2. The quotient you would get is 36. So then Q=38, you would add 36+38 and get 74.
Answer:
116.9FT
Step-by-step explanation:
Factor the quadratic expression completely
8x2 – 18x – 5 =
Final answer:
To factor the quadratic expression 8x² – 18x – 5 completely, one finds factors of the coefficient product (–40) that sum to the x coefficient (–18). These factors are -20 and +2, which are used to rewrite and group the middle term, allowing us to factor by grouping into (4x + 1)(2x – 5).
Explanation:
To factor the quadratic expression 8x2 − 18x − 5 completely, we need to find two binomials that when multiplied together give us the original quadratic expression. This process generally involves finding two numbers that multiply to give us the product of the coefficient of x2 term (8) and the constant term (-5) and also add to give the coefficient of the x term (-18).
The product of the coefficient of x2 and the constant term is -40 (8 × -5). We need to find factors of -40 that will add up to -18. After testing several combinations of factors, we see that -20 and 2 work since -20 + 2 = -18. Now we rewrite the middle term using these two numbers:
8x² − 20x + 2x − 5
Next, we group the terms to facilitate factoring by grouping:
=(8x² − 20x) + (2x − 5)
Now we factor out the common factors from each group:
=4x(2x − 5) + 1(2x − 5)
At this point, we have a common binomial factor (2x − 5) that can be factored out:
=(4x + 1)(2x − 5)
This is the expression factored completely.