Answer:
5. To find the time in which the loan of N3,900 at the rate of 5% yields N585, we can use the formula for simple interest:
I = P * r * t
where I is the interest, P is the principal (the amount borrowed), r is the interest rate (as a decimal), and t is the time (in years).
Plugging in the given values, we get:
585 = 3900 * 0.05 * t
Solving for t, we get:
t = 3 years
Therefore, it will take 3 years for the loan to yield N585 in interest.
6. To find the time it will take for the simple interest on N70,000 at the rate of 7% to be N20,000, we can again use the formula for simple interest:
I = P * r * t
Plugging in the given values, we get:
20000 = 70000 * 0.07 * t
Solving for t, we get:
t = 4 years
Therefore, it will take 4 years for the simple interest on N70,000 at the rate of 7% to be N20,000.
7. To find the time it takes for N300 to amount to N390 at the rate of 3%, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
where A is the final amount, P is the principal (the initial amount), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).
Plugging in the given values, we get:
390 = 300 * (1 + 0.03/1)^(1*t)
Simplifying, we get:
1.3^t = 1.3
Taking the logarithm of both sides, we get:
t = log(1.3) / log(1.3)
t ≈ 1.82
Therefore, it takes approximately 1.82 years for N300 to amount to N390 at the rate of 3%.
8. To find the rate percent per annum for a simple interest of N80 on N5600 in 1 year, we can use the formula for simple interest:
I = P * r * t
Plugging in the given values, we get:
80 = 5600 * r * 1
Solving for r, we get:
r = 0.0143 or 1.43%
Therefore, the rate percent per annum is 1.43%.
9. To find the year in which N5100 will yield an interest of N170 at the rate of 2 1/2 per annum, we can use the formula for simple interest:
I = P * r * t
Plugging in the given values, we get:
170 = 5100 * 0.025 * t
Solving for t, we get:
t = 2/3 years
Since the question asks for the year, we need to add 2/3 years to the current year. Assuming the current year is 2021, we get:
2021 + 2/3 ≈ 2022.67
Therefore, N5100 will yield an interest of N170 at the rate of 2 1/2 per annum in the year 2022.
10. To find the rate per annum at which N4,600 will yield an interest of N230 for 2 years, we can again use the formula for simple interest:
I = P * r * t
Plugging in the given values, we get:
230 = 4600 * r * 2
Solving for r, we get:
r = 0.025 or 2.5%
Therefore, the rate per annum is 2.5%.
11. To find the time it takes for N8100 to yield an interest of N729 at the rate of 9% per annum, we can use the formula for simple interest:
I = P * r * t
Plugging in the given values, we get:
729 = 8100 * 0.09 * t
Solving for t, we get:
t = 1 year
Therefore, it takes 1 year for N8100 to yield an interest of N729 at the rate of 9% per annum.
12. To find the rate of interest per annum for an interest of N23 on N2300 for 2 years, we can use the formula for simple interest:
I = P * r * t
Plugging in the given values, we get:
23 = 2300 * r * 2
Solving for r, we get:
r = 0.005 or 0.5%
Therefore, the rate of interest per annum is 0.5%.
I want you to help me solve the variable equations of questions 3
Answer:
[tex]\huge\boxed{\sf x = -24}[/tex]
Step-by-step explanation:
Given equation:[tex]\displaystyle -\frac{1}{2} x - 4 =8\\\\Add \ 4 \ to \ both \ sides\\\\-\frac{1}{2} x = 8+4\\\\-\frac{1}{2} x = 12\\\\Multiply \ both \ sides \ by \ -2\\\\-\frac{1}{2} x \times \ -2 = 12 \times -2\\\\\boxed{x = -24}\\\\\rule[225]{225}{2}[/tex]
Answer:
[tex]\boxed{\mathtt{1) \ x=4}}[/tex]
[tex]\boxed{\mathtt{2) \ x=2}}[/tex]
[tex]\boxed{\mathtt{3) \ x=-24}}[/tex]
Step-by-step explanation:
[tex]\textsf{For these problems, we are asked to solve for x in each equation.}[/tex]
[tex]\textsf{We should use similar steps for each of them.}[/tex]
[tex]\large\underline{\textsf{For Number 1:}}[/tex]
[tex]\textsf{We should first begin by adding 2 to both sides of the equation.}[/tex]
[tex]\mathtt{8x=32}[/tex]
[tex]\textsf{Now, divide by 8.}[/tex]
[tex]\boxed{\mathtt{1) \ x=4}}[/tex]
[tex]\large\underline{\textsf{For Number 2:}}[/tex]
[tex]\textsf{Let's begin by subtracting 5 from both sides of the equation.}[/tex]
[tex]\mathtt{-x=-2}[/tex]
[tex]\textsf{Now, divide by -1.}[/tex]
[tex]\boxed{\mathtt{2) \ x=2}}[/tex]
[tex]\large\underline{\textsf{For Number 3:}}[/tex]
[tex]\textsf{Beginning Number 3, let's multiply by -2 to both sides of the equation.}[/tex]
[tex]\mathtt{x+8=-16}[/tex]
[tex]\textsf{Now, subtract 8 from both sides of the equation.}[/tex]
[tex]\boxed{\mathtt{3) \ x=-24}}[/tex]
trey paid 42 dollars for 2/3 ton of concrete. he wants to know the price of 3 tons of concrete.
Answer:
To find the price of 3 tons of concrete, we need to use a proportion:
If 2/3 ton of concrete costs $42, then 1 ton of concrete costs:
$42 ÷ (2/3) ton = $42 × (3/2) = $63
Therefore, 3 tons of concrete will cost:
$63 × 3 = $189
So Trey would need to pay $189 for 3 tons of concrete.
You have a 5" by 7" photo that you would like to have enlarged to fit an 7.5" by 10.5" frame. Would the two photographs be similar? Explain your answer using Similarity Transformations.
The photos are similar because the enlarged photo is 1.5 times the size of the original photo.
What is meant by similarity transformations?
Similarity transformations turn items in space into similar objects. If two items have the same shape or have the same shape as their mirror images, they are said to be similar. More specifically, by uniformly scaling (enlarging or decreasing), maybe with additional translation, rotation, and reflection, one can be created from the other. This indicates that one object may be properly aligned with the other object by rescaling, moving, and reflecting it. When two things are comparable to one another, one is consistent with the outcome of a specific uniform scaling of the other.
Here the initial dimension of the photo is 5" by 7" and after enlarging it has dimensions 7.5" by 10.5".
The scale factor is = 7.5/5 = 10.5/7 = 1.5
Since the scale factor is constant for all sides, the pictures before and after enlargement are similar.
Therefore the photos are similar because the enlarged photo is 1.5 times the size of the original photo.
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if you put 25 ml of concerete in a glass how much water should be added
Answer:
50ml of water should be added
SUN The temperature of the Sun's surface is about 5.5×10^3
degrees Celsius. The temperature of the Sun's core is about 2.7×10^3
times hotter than the surface. What is the approximate temperature of the Sun's core? (In Celsius) PLEASE BE QUICK!!
According to the given information, the approximate temperature of the Sun's core is [tex]1.485*10^{7}[/tex]degrees Celsius.
The Sun is a massive ball of gas that generates heat and light through nuclear fusion at its core. The temperature of the Sun's core is much hotter than its surface temperature, and this difference in temperature is responsible for the Sun's energy output.
The temperature of the Sun's surface is approximately [tex](5.5*10^{3})[/tex] degrees Celsius, which is also known as the photosphere. However, the temperature at the Sun's core is estimated to be about [tex](2.7*10^{3})[/tex] times hotter than the surface temperature. This is because the core is the site of intense nuclear fusion reactions that convert hydrogen into helium and release huge amounts of energy in the form of heat and light.
To find the approximate temperature of the Sun's core, we can start with the temperature of the Sun's surface, which is given as [tex](5.5*10^{3})[/tex] degrees Celsius. We need to multiply this by the factor of [tex](2.7*10^{3})[/tex] to get the temperature of the core.
The approximate temperature of the Sun's core
= [tex](5.5*10^{3}) * (2.7*10^{3})[/tex]
=[tex]14.85*10^{6}[/tex]degrees Celsius
= [tex]1.485*10^{7}[/tex] degrees Celsius (in scientific notation)
Therefore, the approximate temperature of the Sun's core is [tex]1.485*10^{7}[/tex]degrees Celsius.
This extremely high temperature is necessary to sustain the nuclear reactions that power the Sun's energy output. The high temperature and pressure in the core create the ideal conditions for nuclear fusion to occur, which releases energy that eventually makes its way to the surface of the Sun and out into space in the form of light and heat.
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Noa flies a drone in a circular path around an object that is 210 meters west and 150 meters south of her
position. The drone's path takes it over a point that is 170 meters east and 190 meters north of her.
Find an equation for the drone's path. (Assume Noa is located at the origin, with the horizontal axis running
east-west and the vertical axis running north-south)
The drone's path follows the equation________
When the drone passes due north of Noa's position, it will be ___________ feet north of
her (round your answer to three decimal places).
We can solve this problem using the standard equation of a circle:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is the radius.
Since Noa is at the origin, the center of the circle is the midpoint between the object and the point where the drone passes:
h = (210 - 170)/2 = 20
k = (190 - 150)/2 = 20
The radius is the distance between the center and the point where the drone passes:
r = √((170 - 20)² + (190 - 20)²) = √(150² + 170²) = √(62500) = 250
So the equation of the drone's path is:
(x - 20)² + (y - 20)² = 250²
When the drone passes due north of Noa's position, its x-coordinate is 20, so we can substitute that into the equation:
(20 - 20)² + (y - 20)² = 250²
y - 20 = ±√(250²)
y = 20 ± 250
y ≈ -230 or y ≈ 270
So the drone will be approximately 230 feet north of Noa's position.
A quality control inspector randomly selects 5 calculators to inspect from 22 calculators. How many ways could the inspector select?
Answer:
22 cakculator is write answer
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The sοlutiοns tο the inequality are x values greater than 5.
A number line frοm negative 3 tο 3 in increments οf 1. An οpen circle is at 5 and a bοld line starts at 5 and is pοinting tο the right.
-6x - 5 < 10 - x and -6x + 15 < 10 - 5x are cοrrect representatiοns οf the inequality –3(2x – 5) < 5(2 – x).
Tο sοlve the inequality -3(2x - 5) < 5(2 - x), we can start by distributing the negative 3 and the pοsitive 5 οn the right side:
-6x + 15 < 10 - 5x
Then, we can simplify by mοving all the x terms tο οne side and all the cοnstant terms tο the οther side:
-x < -5
Finally, we can divide bοth sides by -1, remembering tο reverse the inequality sign:
x > 5
Therefοre, the sοlutiοns tο the inequality are x values greater than 5. The representatiοns οf this sοlutiοn οn a number line are:
A number line frοm negative 3 tο 3 in increments οf 1. An οpen circle is at 5 and a bοld line starts at 5 and is pοinting tο the right.
A number line frοm negative 3 tο 3 in increments οf 1. An οpen circle is at negative 5 and a bοld line starts at negative 5 and is pοinting tο the left.
Hοwever, οnly the first representatiοn is cοrrect, since the secοnd representatiοn shοws the sοlutiοns tο x < -5, which is the οppοsite inequality tο the οne we fοund.
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Harriet is cultivating a strain of bacteria in a petri dish. Currently, she has 103 bacteria in the dish. The bacteria divide every two hours such that the number of bacteria has doubled by the end of every second hour. How many bacteria will Harriet have in the dish at the end of 6 hours?
A.
1024
B.
103
6
C.
603
D.
103
8
Step-by-step explanation:
Since the number of bacteria in the petri dish doubles every two hours, after 2 hours, Harriet will have 103 x 2 = 206 bacteria.
After another 2 hours (i.e., 4 hours from the beginning), the number of bacteria will double again to become 206 x 2 = 412 bacteria.
After another 2 hours (i.e., 6 hours from the beginning), the number of bacteria will double once more to become 412 x 2 = 824 bacteria.
Therefore, Harriet will have 824 bacteria in the dish at the end of 6 hours. Answer: A. 1024 (rounded to the nearest whole number).
15. Many people swimming in a pool experience pain in their ears if they dive to the
bottom. Why is this?
A. Pressure increases as the depth of the water column above them increases.
B. The area of the pool is wider where it's deeper.
C. Pressure decreases as the depth of the water column above them increases.
D. The vapor pressure at the surface is removed.
Answer:
The answer is Ahope this helps
Divide 1/20 divide by 5 enter your answer in the box as a fraction in simplest form
Answer:
honestly don't know but you got this bro {=•=}
Solve the problem. This is for my practice test.
The bearing of the plane to the nearest degree is 357°, which is answer choice (c).
What is vector addition?
Vector addition is the operation of adding two or more vectors together into a vector sum. The so-called parallelogram law gives the rule for the vector addition of two or more vectors. For two vectors, the vector sum is obtained by placing them head to tail and drawing the vector from the free tail to the free head.
To find the bearing of the plane, we need to determine the direction in which it is traveling with respect to the true north. To do this, we need to use vector addition to combine the velocity of the plane with the velocity of the wind.
Let's break down the velocity vectors into their north-south and east-west components, using positive directions to the north and east.
The airspeed of the plane is 213 mph due south, so its velocity vector can be written as:
Vp = (0, -213)
The wind velocity is 16 mph at a direction of 52.0°. We can find its components using trigonometry:
Vw,x = 16 cos(52.0°) = 10.91 mph to the east
Vw,y = 16 sin(52.0°) = 12.18 mph to the south
So the wind velocity vector is:
Vw = (10.91, -12.18)
To find the total velocity vector of the plane relative to the ground, we can add the velocity vectors of the plane and the wind:
Vtot = Vp + Vw
Vtot = (0 + 10.91, -213 - 12.18)
Vtot = (10.91, -225.18)
The direction of the total velocity vector, measured from true north, can be found using the arctangent function:
θ = arctan(Vtot,x / Vtot,y)
θ = arctan(10.91 / -225.18)
θ ≈ -2.8°
Since the result is negative, this means the direction is to the left of true north. We can convert this to a bearing by adding 360° to get the positive equivalent:
θ = 360° + θ
θ ≈ 357.2°
Therefore, the bearing of the plane to the nearest degree is 357°, which is answer choice (c).
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A steel rod of mass 25kg is melted down to create ball bearings of radius 4mm. One kilogram of this steel has a volume of 150[tex]cm^3[/tex]. How many ball bearings could be made from this steel rod?
Therefore, approximately 110,294 ball bearings of radius 4mm can be made from the steel rod.
What is volume?Volume is the amount of space that a three-dimensional object occupies. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet. The volume of an object can be calculated by multiplying its length, width, and height, or by using a specific formula for the shape of the object, such as the formula for the volume of a sphere, cylinder, or cone. Volume is an important concept in mathematics, physics, engineering, and many other fields, and it is used to describe the size and shape of objects, as well as their capacity, density, and other properties.
Here,
To solve this problem, we need to determine the total volume of the steel rod and then calculate how many ball bearings of radius 4mm can be made from this volume. First, we need to calculate the volume of the steel rod. We are given that one kilogram of the steel has a volume of 150 cm³. Therefore, the total volume of the steel rod is:
25 kg * 150 cm³/kg = 3750 cm³
Next, we need to calculate the volume of one ball bearing of radius 4mm. The formula for the volume of a sphere is:
V = (4/3)πr³
Substituting r = 4mm = 0.4cm, we get:
V = (4/3)π(0.4)³ = 0.034 cm³ (rounded to three decimal places)
To find the number of ball bearings that can be made from the steel rod, we divide the total volume of the steel rod by the volume of one ball bearing:
3750 cm³ / 0.034 cm³ ≈ 110,294
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can someone please help me
Find the area of each shaded region.
Round the answer to two decimal places.
please show work
Answer:
7) S=6.28 yd A=12.57 [tex]yd^{2}[/tex]
8) S=99.48 ft A=945.1 [tex]ft^{2}[/tex]
9) S=21.99 in A=43.98 [tex]in^{2}[/tex]
Step-by-step explanation:
7)
S=r θ
S=4([tex]\frac{90\pi }{180}[/tex])........................................plug in values
S=4([tex]\frac{\pi }{2}[/tex])...........................................simplify
S=6.28 yd...................................solve and round
A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ
A=[tex]\frac{1}{2}[/tex]([tex]4^{2}[/tex])([tex]\frac{90\pi }{180}[/tex]) ....................................plug in values
A=[tex]\frac{1}{2}[/tex](16)([tex]\frac{\pi }{2}[/tex]) .....................................simplify
A=12.57 [tex]yd^{2}[/tex]...................................solve and round.
8)
S=r θ
S=19([tex]\frac{300\pi }{180}[/tex]).........................................plug in values
S=19([tex]\frac{5\pi }{3}[/tex]).............................................simplify
S=99.48 ft........................................solve and round
A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ
A=[tex]\frac{1}{2}[/tex]([tex]19^{2}[/tex])([tex]\frac{300\pi }{180}[/tex]) ....................................plug in values
A=[tex]\frac{1}{2}[/tex](361)([tex]\frac{5\pi }{3}[/tex]) .....................................simplify
A=945.1 [tex]ft^{2}[/tex].......................................solve and round.
9)
S=r θ
S=4([tex]\frac{315\pi }{180}[/tex]) ............................................plug in values
S= 4( [tex]\frac{7\pi }{4}[/tex])..............................................simplify
S=21.99 in..........................................solve and round
A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex])θ
A=[tex]\frac{1}{2}[/tex]([tex]4^{2}[/tex])([tex]\frac{315\pi }{180}[/tex]) ....................................plug in values
A=[tex]\frac{1}{2}[/tex](16)( [tex]\frac{7\pi }{4}[/tex])......................................simplify
A=43.98 [tex]in^{2}[/tex]....................................solve and round.
need help with This Math
Since line GF = line JK and < G = <J ; the minor arcs, the major arcs of the both circle are also similar and equal.
What is the major and minor arc of a circle?The minor arc of the given circle above can be defined as the part of the circle that is less than 180°. This is represented by <HGF in the first circle( with a red ink).
The major arc of the given circle above can be defined as the part of a circle that is greater than 180°. Thus is represented by <IJK in the second circle (with black ink).
Therefore in conclusion, there is a established similarity between the two circles since line GF = line JK and < G = <J, thus making their minor and major acre to be equal too.
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Please help
please click on the documents that's attached...
Please show work
The factored form of trinomial equation 10m² + 29mn + 10n² is (5m + 2n)(2m + 5n).
What is the difference between factoring and expanding polynomials?The parenthesis must be dropped in order to expand the equation. One need just multiply the value outside the value, which is 2 to each of the values inside the parenthesis, to arrive at an equation without parentheses. The opposite of factoring out, which entails adding parenthesis to an equation, is expanding, which entails removing parentheses from an equation.
The given trinomial equation is 10m² + 29mn + 10n².
Multiply the coefficients of the first and last term that is:
(10)(10) = 100
Now factor the term using two factors to make the given middle term, here the factor of 100 are 4 and 25.
Now, rewrite the equation with the factors as follows:
(10m² + 4mn) + (25mn + 10n²)
= 2m(5m + 2n) + 5n(5m + 2n)
Factor out the common binomial factor (5m + 2n):
(5m + 2n)(2m + 5n)
Hence, the factored form of 10m² + 29mn + 10n² is (5m + 2n)(2m + 5n).
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Marbles are divided among Tom, Gary, and Mary in the ratio 2:3:5, respectively. If Tom gets 30 marbles, how many do Gary and Mary receive?
Answer:
Gary would have 45 and Mary would have 75
Which transformations would take Figure A to Figure B?
simplity: 2x3 + 3y3 + 5x3 + 4y
7x³ +3y³ +4y
Simplify the expression by Removing parentheses and brackets by multiplying factors, use the exponent rule to remove grouping if the term contains exponents, combine like terms by adding or subtracting coefficients and combine the constants.
Answer: The answer is 7x^3 + 3y^3 + 4y. Or in simpler terms choice A is correct
Step-by-step explanation:
The following scenario represents a proportional relationship.
John's last paycheck was $450 for 40 hours of work.
What is the constant of proportionality?
Enter your answer in the box.
We can say that after answering the offered question Therefore, the proportionality constant of proportionality in this scenario is 11.25.
what is proportionality?Proportionate relationships are those that have the same ratio every time. For example, the average number of apples per tree defines how many trees are in an orchard and how many apples are in an apple harvest. Proportional refers to a linear relationship between two numbers or variables in mathematics. When the first quantity doubles, the second quantity doubles as well. When one of the variables decreases to 1/100th of its previous value, the other falls as well. When two quantities are proportional, it means that when one rises, the other rises as well, and the ratio between the two remains constant at all values. The diameter and circumference of a circle serve as an example.
In this case, we may use the following formula to calculate the proportionality constant:
proportionality constant = output/input
where the output is John's pay and the input is the number of hours he worked.
As a result, the proportionality constant is:
Paycheck/hours worked = proportionality constant
proportionality constant = 450/40
proportionality constant = 11.25
As a result, the proportionality constant in this scenario is 11.25.
In this case, we may use the following formula to calculate the proportionality constant:
proportionality constant = output/input
where the output is John's pay and the input is the number of hours he worked.
As a result, the proportionality constant is:
Paycheck/hours worked = proportionality constant
proportionality constant = 450/40
proportionality constant = 11.25
Therefore, the constant of proportionality in this scenario is 11.25.
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Find the square root of 8!/70
Answer:
We can write 8! as:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
To simplify the square root of 8!/70, we can first simplify the denominator:
8!/70 = (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)/70
= (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)/(2 x 5 x 7)
= (8 x 6 x 4 x 3 x 2 x 1)/2
= 8 x 6 x 4 x 3 x 1
= 576
Now, we can write the original expression as:
sqrt(8!/70) = sqrt(576/1)
= sqrt(576)
= 24
Therefore, the square root of 8!/70 is 24.
painting outside of a cylinder and finding the amount of paint. cylinder will be used without the top
Approximately 9.42 units of paint would be required to paint the outside of a cylinder with a radius of 3 meters and a height of 5 meters, without the top.
how to calculate the amount of paint?To calculate the amount of paint required to paint the outside of a cylinder, you will need to find the surface area of the cylinder. Since the cylinder is without a top, we only need to find the lateral surface area.
formula of surface area
Lateral Surface Area = 2πrh
when r is the cylinder's radius, h is its height, and is a constant value roughly equivalent to 3.14.
Once you have calculated the lateral surface area of the cylinder, you can use the following formula to find the amount of paint required:
Amount of Paint = Lateral Surface Area / Coverage per unit of paint
where coverage per unit of paint refers to the area that can be covered by one unit of paint. This will depend on the type of paint you are using and its thickness.
For example, if the cylinder has a radius of 3 meters and a height of 5 meters, the lateral surface area would be:
Lateral Surface Area = 2πrh
Lateral Surface Area = 2 x 3.14 x 3 x 5
Lateral Surface Area = 94.2 square meters
If the coverage per unit of paint is 10 square meters, the amount of paint required would be:
Amount of Paint = Lateral Surface Area / Coverage per unit of paint
Amount of Paint = 94.2 / 10
Amount of Paint = 9.42 units of paint
Therefore, approximately 9.42 units of paint would be required to paint the outside of a cylinder with a radius of 3 meters and a height of 5 meters, without the top.
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select all that are equal to 6^4 (6^5)
Given GH = 3x - 2, HI = 7x - 4, 2
and GI = 8x + 10, find x
The value of x is 8 when GH is 3x-2, HI is 7x-4 and GI is 8x+10. It forms a straight line.
What is segment addition?Segment addition is a concept in geometry that states that given three collinear points A, B, and C, with B between A and C, the length of AB added to the length of BC will give the length of AC. This can be expressed algebraically as:
AB + BC = AC
According to question:We can use the fact that GH + HI = GI (by the segment addition postulate) and substitute the given expressions to get:
(3x - 2) + (7x - 4) = 8x + 10
Simplifying the left side by combining like terms, we get:
10x - 6 = 8x + 10
Subtracting 8x from both sides, we get:
2x - 6 = 10
Adding 6 to both sides, we get:
2x = 16
Dividing by 2, we get:
x = 8
Therefore, x = 8.
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what is 5% of $26.50
Answer:1.325
Step-by-step explanation:
The population of a town was 821 in 1970. The population has been growing at a rate of 11% each year. What is the population of the town in the year 1995? i have 30 minutes until the quiz is submitted
The pοpulatiοn οf the tοwn in the year 1995 was apprοximately 4,262.
Hοw tο determine the percentage grοwth rate?The grοwth factοr (b) is given as: b = 3.76
The grοwth factοr (b) is greater than 1.
We can sοlve this prοblem by using the fοrmula fοr expοnential grοwth:
[tex]P(t) = P0(1 + r)^t[/tex]
where:
P0 is the initial pοpulatiοn (821 in 1970)
r is the annual grοwth rate (11% οr 0.11)
t is the number οf years since the initial pοpulatiοn (25 years frοm 1970 tο 1995)
Substituting the given values, we get:
[tex]P(25) = 821(1 + 0.11)^25\\\\P(25) = 821(1.11)^25[/tex]
Using a calculatοr tο evaluate this expressiοn:
P(25) ≈ 4,261.9
Therefοre, the pοpulatiοn οf the tοwn in the year 1995 was apprοximately 4,262.
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A rectangular pyramid has a height of 5 units and a volume of 50 units3. Shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. Which statement explains whether Shannon is correct?
A rectangular prism in which BA = 10 and h = 5 has a volume of 150 units3; therefore, Shannon is correct
A rectangular prism in which BA = 30 and h = 5 has a volume of 150 units3; therefore, Shannon is correct
A rectangular prism in which BA = 10 and h = 5 has a volume of 50 units3; therefore, Shannon is incorrect
A rectangular prism in which BA = 30 and h = 5 has a volume of 50 units3; therefore, Shannon is incorrect
Answer:
B (A rectangular prism in which BA = 30 and h = 5 has a volume of 150 units3; therefore, Shannon is correct)
Step-by-step explanation:
I took the test!
The solution is,: A rectangular prism in which BA = 30 and h = 5 has a volume of 150 units^3; therefore, Shannon is correct
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
step 1
Find the area of the base of the rectangular pyramid
we know that:
The volume of the rectangular pyramid is equal to:
V = 1/3 * bh
where
B is the area of the base
H is the height of the pyramid
we have
V= 50
h = 5
substitute and solve for B
we get,
b= 30
step 2
Find the volume of the rectangular prism with the same base area and height
we know that
The volume of the rectangular prism is equal to
V = bh
we have
b = 30
h = 5
substitute
V = 30 * 5 = 150 unit^3
therefore
The rectangular prism has a volume that is three times the size of the given rectangular pyramid. Shannon is correct
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what does 2(-3+5) + 7× (-4) + (-1) equal?
Answer:
-25
Step-by-step explanation:
= 2*(2) - 28 - 1
= 4 - 29
= -25
Given:-
[tex] \tt \: 2(- 3+5 ) + 7× (-4) + (-1) = ?[/tex][tex] \: [/tex]
Solution:-
[tex] \tt \: 2(- 3+5 ) + 7× (-4) + (-1) [/tex][tex] \: [/tex]
[tex] \tt \: 2( 2 ) - 28 - 1[/tex][tex] \: [/tex]
[tex] \tt \: 4 - 29[/tex][tex] \: [/tex]
[tex] \boxed{ \: \tt \pink{-25 }\: \: } [/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━
hope it helps! :)
I will mark you brainiest!
Given that QRVTSU is a regular hexagon, what are the lengths of QR and ST ?
A) 37
B) 28
C) 14
D) 10
Answer:
QR & ST = 37
Step-by-step explanation:
Because this is a regular hexagon, all the sides are equal.
Thus, since the length of QR = the length of ST, we can set the equations for both sides equal to each other and solve for y:
[tex]3y+19=6y+1\\3y+18=6y\\18=3y\\6=y[/tex]
Now, we can plug in 6 for y into any of the two equations to find the length of both QR and ST:
[tex]QR=3(6)+19\\QR=18+19\\QR=37[/tex]
Find the distance between the pair of points.
N(-3,-11), P(-3,-2)
d=
(Simplify your answer. Type an exact answer, using radicals as needed.)
The distance between the two points N(-3, -11) and P(-3, -2) is 9 units.
How to find the distance between the pair of points.Given the points
N(-3,-11) and P(-3,-2)
To find the distance between two points, we can use the distance formula:
d = √((x2 - x1)²+ (y2 - y1)²)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using this formula, we can find the distance between the two points N(-3, -11) and P(-3, -2) as follows:
d = √((-2 + 11)²+ (-3 + 3)²)
This gives
d = √9²+ 0²)
So, we have
d = √81
Evaluate
d = 9
Therefore, the distance between the two points N(-3, -11) and P(-3, -2) is 9 units.
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