The approximate value of the account after 5 years will be $6778.
Given that,
Mario put $6,000 into a savings account that accrues interest at a rate of 5% per year.
The amount is given by,
A= p(1 + r)^t
P = 6000
R = 5%
T= 2.5 years
R = Rate of Interest
T= Time
P = Principal Amount
By substituting we get,
A= p(1 + r)^t
A = 6000(1 + 0.05)^2.5
A = 6000(1.05)^2.5
A = 6000 * 1.129
A = 6778.35
As a result, the account will roughly be worth $6778 after five years.
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What is the equation of the line that passes through the point (-2,14) and is perpendicular to the line with the following equation? y= -2/5 x-1
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{5}}x-1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-2}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{5}{-2}\implies \cfrac{5}{2}}}[/tex]
so we're really looking for the equation of a line whose slope is 5/2 and it passes through (-2 , 14)
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{14})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{14}=\stackrel{m}{ \cfrac{5}{2}}(x-\stackrel{x_1}{(-2)}) \implies y -14= \cfrac{5}{2} (x +2) \\\\\\ y-14=\cfrac{5}{2}x+5\implies {\Large \begin{array}{llll} y=\cfrac{5}{2}x+19 \end{array}}[/tex]
an oil paint set cost $45 more than an easel . an easel cost $129 what is the total cost of the oil paint set and the easel
At a candy store, Eva bought 2 pounds of jelly beans and 2 pounds of gummy worms for $26.
Meanwhile, Mimi bought 3 pounds of jelly beans and 2 pounds of gummy worms for $31. How
much does the candy cost per pound?
start with
m: cost per pound for Jelly Beans
n: cost per pound for Gummy Worms
Answer:
cost per pound for Jelly Beans is 5$
cost per pound for Gummy Worms is 8$
Mr.Customs is correcting the class’s math homework on customary units. Which of the following measurements is reasonable?
A.)a pencil is 12 feet long
B.)the back porch is 12 inches wide
C.)the 3rd hole in the golf course is is 123 miles long
D.)the distance from New York to California is 2,250 miles
The reasonable measurement is D.)the distance from New York to California is 2,250 miles
Measurement:
Measurement is the process of comparison of an unknown quantity with a known or standard quantity.
Given,
Mr. Customs is correcting the class’s math homework on customary units. Here we need to find which of the following measurements is reasonable.
By looking at the given options,
A) a pencil is 12 feet long - This one is wrong because the measuring unit of pencil is cm.
B) the back porch is 12 inches wide - For this one we have to use the feet or meter scale.
C) the 3rd hole in the golf course is is 123 miles long - Here this one we have to use either cm or mm.
Therefore, option (D) the distance from New York to California is 2,250 miles is a reasonable statement.
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The cost of 4kg of kale and 1.5 kg of beetroot is 12.20
The cost of 5kg of kale and 2kg of beetroots is 15.40 work out the cost of 1kg of beetroot and 1kg of kale
The cost of 1 kg of beetroot and 1 kg of kale are 1.39 units and 2.53 units respectively
How to find the cost of beetroot and Kale?The cost of 4kg of kale and 1.5 kg of beetroot is 12.20. The cost of 5kg of kale and 2kg of beetroots is 15.40.
The cost of 1kg of beetroot and 1kg of kale can be found as follows:
Therefore,
let
x = cost of 1kg of beetroot
y = cost of 1 kg of Kale
Therefore, using equation,
1.5x + 4y = 12.20
2x + 5y = 15.40
x = 12.20 / 1.5 - 4y / 1.5
x = 8.13 - 2.67y
Hence,
5y = 15.40 - 2(8.13 - 2.67y)
5y = 15.40 - 16.26 + 5.34y
5y = -0.86 + 5.34y
5y - 5.34y = -0.86
- 0.34y = - 0.86
y = - 0.86 / - 0.34
y = 2.52941176471
y = 2.53
1.5x = 12.20 - 4(2.53)
1.5x = 12.20 - 10.12
1.5x = 2.08
x = 2.08 / 1.5
x = 1.38666666667
x = 1.39
Therefore,
cost of 1kg of beetroot ≈ 1.39
cost of 1 kg of Kale = 2.53
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A store sold towels that cost $5 each at 15% less than the cost. The overhead was 20% of the cost of each towel. What was the selling price of each towel? How much more than $150 did the owner lose if 95 towels were sold?
If the overhead was 20% of the cost of each towel. The selling price of each towel is 5.88.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.
Suppose the selling price of a towel is x, according to the given condition,
5 = x - 15% of x
5=x-0.15x
5=0.85 x
x=5/0.85
x=5.88
Thus, if the overhead was 20% of the cost of each towel. The selling price of each towel is 5.88.
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- 4x + 7y = 3
x-intercept:
y-intercept:
Answer:
X intercept: (-3/4 , 0)
Y intercept: (0 , 3/7)
Step-by-step explanation: The x intercept is a coordinate whenever y is 0. The y intercept is a coordinate whenever x is 0. So to find the x intercept you put 0 in place of Y and you solve for x. So you get x=-3/4.
You do the same thing to find Y, but you put 0 instead of x and you get y=3/7.
PLEASE HELP, I WILL GIVE BRAINLY!!!
Compare the scenarios to determine which represents a greater speed. Explain your choice including a written description of each scenario. Be sure to include the rates in your explanation.
For every 50 y, there is 1 hour
at track practice, steve works out doing lunges on a path that is 110 yards long. if steve can cover 22 in with each lunge, how many lunges will it take to cover the path?
Answer:
It will take 5 lunges to cover the path.
Step-by-step explanation:
Path length = 110
1 lunge = 22 yards
110/22 = 5
5 lunges = 22x5 = 110 yards
Help! Solve this for the points
What is the product?
2y 4y-12
y-3 2y+6
O
تان
10
4y
y-3
4y
y+3
The product of the given polynomials is 4y/(y + 3).
We are given two polynomials. A polynomial is a mathematical statement that is composed of the sum of powers in one or more variables multiplied by coefficients. The polynomials are in rational form. A rational number is created by dividing an integer by an integer. The first polynomial is 2y/(y - 3). The second polynomial is (4y - 12)/(2y + 6). We need to find the product of these two polynomials. Let the product be represented by the variable "P".
P = [2y/(y - 3)]×[(4y - 12)/(2y + 6)]
P = [2y/(y - 3)]×[4(y - 3)/2(y + 3)]
P = [2y]×[2/(y + 3)]
P = 4y/(y + 3)
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To get in condition for running on the track team, Paul began by running 2 miles.
mile farther than he ran the day before. How far will Paul run on Day 7?
Every day after that, he ran
4
OA. 6 miles
OB. 6 miles
OC. 7 miles
OD. 8 miles
[tex]\sqrt{3^2+27}+2^3+\sqrt[3]{64}[/tex]
[tex]\boldsymbol{\sf{\sqrt{3^2+27}+2^3+\sqrt[3]{64} }}[/tex]
Calculate 3 to the power of 2.
[tex]\boldsymbol{\sf{\sqrt{9+27}+2^3+\sqrt[3]{64} }}[/tex]
Add 9 and 27.
[tex]\boldsymbol{\sf{\sqrt{36}+2^3+\sqrt[3]{64} }}[/tex]
Find the square root of 36.
[tex]\boldsymbol{\sf{6+2^3+\sqrt[3]{64} }}[/tex]
Calculate 2 to the power of 3.
[tex]\boldsymbol{\sf{6+8+\sqrt[3]{64} }}[/tex]
Add 6 and 8.
[tex]\boldsymbol{\sf{14+\sqrt[3]{64} }}[/tex]
Calculate [tex]\sqrt[3]{64}[/tex]
[tex]\boldsymbol{\sf{14+4=18}}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ 18}[/tex]
Step by step explanation:[tex] \: \: \: \: \: \: \: \bold{\sqrt{9 + 27} + 2 {}^{3} + \sqrt[3]{64} }[/tex]
To solve this problem, the first thing we have to do is simplify 3² to 9, since it multiplies 2 times 3 to give us 9.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \bold{ \sqrt{36} + {2}^{3} + \sqrt[3]{64} }[/tex]
Then we must add 9 + 27 to give us a result of 36.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{6 + {2}^{3} + \sqrt[3]{64} }[/tex]
Now we must multiply again but this time we are going to multiply 2 times 6 since 6 × 6 is equal to 36.
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{6 + 8 \: + \sqrt[3]{64} }[/tex]
Now we must again multiply 3 times 2 to give us 8.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{6 + 8 + 4}[/tex]
Then we must add 6 + 8 + 4.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{14 + 4}[/tex]
Before finishing we know that we got 14, now we must add 14 + 4 to give us a result of 18.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{18}[/tex]
Rpt: The result is 18.
The closed right circular cylindrical can of the smallest surface area whose volume is
250 π cm3 has a radius of _____ cm and a height of _____ cm
The closed right circular cylindrical can of the smallest surface area whose volume is 250π cm³ has a radius of 5cm and a height of 10 cm.
Let r and h be the radius and height of the cylinder respectively.
Volume, V= πr²h
Given,
Volume = 250 π
Now, we can solve by:
⇒ 250 π = πr²h
⇒ r²h=250
⇒ h= 250/r²
We know that,
Surface area, A = 2πr²+2πrh
⇒ A = 2πr²+ 2πr(250/r²)
⇒ A = 2πr²+ (500π/r)
Differentiating the above equation,
dA / dr = 4πr+500π(-1/r²)
For A to be maximum or minimum, dA/dr = 0
⇒ 4πr-500(π/r²) = 0
⇒ 4πr - 500π / r² = 0
⇒ 4πr³ -500π/ r² = 0
⇒ π (4r³ -500) = 0
⇒ 4r³ - 500 = 0
⇒ r = ∛125
⇒ r = 5
Putting value of r = 5, we get,
h = 250/(5)² = 10
By second derivative test,
d²A/dr² = 4π-500π(-2/r³)
At r= 5,
d²A/dr² = 4π+1000(π/r³) > 0 .
Therefore, It is a local minimum.
Ans: Radius = 5 and Height = 10
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Solve the equation for y.
2
у - 2/3x= -6
Answer:
[tex]y=1\frac{1}{3}x-3[/tex]
Step-by-step explanation:
Isolate y to find the value of y
2y-2/3x=-6
+2/3x. +2/3x
2y=2/3x-6
/2. /2. /2
y=4/3x-3
Hopes this helps please mark brainliest
pls help me how do I round 9.4725 to the nearest cent with no dollar sign
Rounding off 9.4725 to the nearest cent will give 9.5
Rounding Off NumbersRounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths. When rounding money to the nearest cent, look at the number to the right of the full cents. In this case, that number is 9. If the number is five or more, increase the cents by 1. If the number is four or less, keep the cents the same. Because 9 is more than 5, $3.299 rounds to $3.30.
Applying same principle or concept here, we can round off 9.4725 to the nearest cent to give 9.5.
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How many Pieces of ribbon .6m long can be cut from 13.2m ribbon?
I think is is 22
because it is asking how many times can .6m go into 13.2m of ribbon? If you start with 20x.6 you will get 12. Then you add on another one and get 12.6. Finally add one more to get 13.2m ribbon which would make the answer 22. You can also divide 13.2m divided by .6m and get 22.
Hopefully this helped you guys. If you guys want more answers please give me those 5 Stars and Give me a thanks to show you appreciation.
Over all the Answer is 22
Have a great day (:
Giving 50 points!!
Question: Determine whether the dilation from figure K to K’ is an enlargement or a reduction
Answer:
enlargement
Step-by-step explanation:
observe from the figure [tex]OK=x<x+5=7=OK'[/tex]
since [tex]OK<OK'[/tex], then the dilation is an enlargement.
Answer:
Step-by-step explanation:
defsfvbrfdv
If x is a positive, even integer and 2x + 8 < 22, how many possible values of x are there?
There are 7 possible positive integers that satisfy the inequality.
InequalityIn Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
We can find the positive values of x in the given inequality.
2x + 8 < 22
2x < 22 - 8
2x < 14
x < 7
The solution shows that x < 7
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Can anyone solve this for me?
Answer:
8°
Step-by-step explanation:
For the acute angles in a right triangle,
[tex]sin(90-\theta)=cos\theta[/tex]
Given expression is:
[tex]cos(7x)=sin(4x+2)\\sin(90-7x)=sin(4x+2)\\90-7x=4x+2\\88=11x\\x=8^o[/tex]
To check our answer, determine the measures of the other angles in a right triangle.
[tex]A1=90^o\\A2=8^o\\A3=90-8=82^o[/tex]
The smallest angle is 8°
7x+y=5 equations answer
Answer:
[tex]x=\frac{5}{7} -\frac{y}{7}[/tex]
Step-by-step explanation:
You move all terms that dont contain x
to the right side and solve.
Hope this helps! :))
What is the equation of this graphed line
The equation of the graphed line is written as: y = 2x + 2.
How to Find the Equation of a Graphed Line?The equation of a graphed line can be determined by calculating the slope of the line, m = rise/run, and determining the y-intercept value, b, which is the point at which the line intersects the y-axis.
Using two points on the graphed line in the diagram attached below, (-4, -6) and (2, 6):
Slope (m) = change in y / change in x = (-6 - 6) /(-4 - 2)
Slope (m) = -12/-6
Slope (m) = 2
The line cuts the y-axis at y = 2. The y-intercept of the line, b = 2.
Wrote the equation of the graphed line by substituting m = 2 and b = 2 into y = mx + b:
y = 2x + 2.
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A car travels 37 km in 25 minutes.
What is its average speed in km/h?
Give your answer rounded to 1 decimal place.
Answer:
88.8 km/h
Step-by-step explanation:
What is the slope of the line passing through the points (-1, 0) and (0, - 7)?
Answer:
1/-7
Explanation:
rise/run so up 1 down 7
What does b represent in the equation of a line in the form y = mx + b?The y-intercept
The value of x when y = 0
The slope
The x-intercept
Answer:
The y intercept
Step-by-step explanation:
Is the absolute value of -3 less than, greater than, or equal to -7
The statements are true "3 is less than 7, and the absolute value of 3 is less than the absolute value of 7".
What is absolute value?Absolute value is defined as the magnitude or size of a number, no negatives are allowed.
The distance a number is from 0 on the number line is known as the absolute value of the number.
For example, |5| is 5 because it is 5 units away from 0. Also, |-5| is also 5 because -5 is 5 units from 0.
The absolute value of a number is how distant it is from zero. The standard procedure to represent absolute value is to use a number line to estimate the exact distance the number is from zero.
As per the option, 3 is less than 7 is true.
The absolute value of 3 is less than the absolute value of 7 is true.
Thus, the statements are true "3 is less than 7, and the absolute value of 3 is less than the absolute value of 7".
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The question seems to be incomplete the correct question would be
Which statements about 3 and 7 are true? Choose ALL the correct answers.
3 is less than 7.
3 is greater than 7.
The absolute value of 3 is less than the absolute value of 7.
The absolute value of 3 is equal to the absolute value of 7.
The absolute value of 3 is greater than the absolute value of 7.
Simplity (34)-1
1/34
1/3-4
-34
33
Option-A is correct, when the The exponential term is (3⁴)⁻¹ which is in the division.
Given that,
The exponential term is (3⁴)⁻¹
We have to find the the exponential term which is correct from the option.
The multiplicative inverse of the base raised to a power with the opposite sign of the given power is a negative exponent. In plain English, we write the number's reciprocal and solve it just like positive exponents. For instance, (3/2)² can be used to represent (2/3)⁻². We are aware that an exponent indicates the degree of multiplication a number has undergone.
Take the term,
(3⁴)⁻¹
1/3⁴
Therefore, Option-A is correct, when the The exponential term is (3⁴)⁻¹ which is in the division.
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Mrs. Sharma is making treats for a tea party later this week, and she has up to 6 eggs to use for this purpose. A batch of scones requires 3 eggs and a batch of miniature tarts requires 2 eggs.
The eggs that will remain after Sharma is making treats for a tea party is 1.
How to calculate the value?From the information, Mrs. Sharma is making treats for a tea party later this week, and she has up to 6 eggs to use for this purpose a batch of scones requires 3 eggs and a batch of miniature tarts requires 2 eggs.
In this case, the eggs remaining will be:
= Total eggs - Eggs used
= 6 - (3 + 2)
= 6 - 5
= 1
There'll be 1 egg remaining.
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Complete question
Mrs. Sharma is making treats for a tea party later this week, and she has up to 6 eggs to use for this purpose. A batch of scones requires 3 eggs and a batch of miniature tarts requires 2 eggs. How many eggs will be left?
50 Points!!! Explain the difference between consecutive interior angles, corresponding interior angles, and co-interior angles.
Answer:
Co-interior angles or Consecutive interior angles are the two angles that are on the same side of the transversal. Co-interior angles are the interior angles and it sums up to 180 degrees. It means that the sum of two interior angles, which are on the same side of transversal is supplementary. Co-interior angles resemble like in “C” shape and both the angles are not equal to each other. The co-interior angle is also known as the consecutive interior angles or the same side interior angles.Co-interior Angles
Co-interior Angle Theorem and Proof
Statement:
If the transversal intersects the two parallel lines, each pair of co-interior angles sums up to 180 degrees (supplementary angles).
Proof:
Co-interior Angles Proof
Let us consider the image given above:
In the figure, angles 3 and 5 are the co interior angles and angles 4 and 6 are the co-interior angles.
To prove: ∠3 and ∠5 are supplementary and ∠4 and ∠6 are supplementary.
Given that, a and b are parallel to each other and t is the transversal.
By the definition of linear pair,
∠1 and ∠3 form the linear pair.
Similarly, ∠2 and ∠4 form the linear pair.
By using the supplement postulate,
∠1 and ∠3 are supplementary
(i.e.) ∠1 + ∠3 = 180
Similarly,
∠2 and ∠4 are supplementary
(i.e.) ∠2 + ∠4 = 180
By using the corresponding angles theorem, we can write
∠1 ≅∠5 and ∠2 ≅ ∠6
Thus, by using the substitution property, we can say,
∠3 and ∠5 are supplementary and ∠4 and ∠6 are supplementary.
Hence, the co-interior angle theorem (consecutive interior angle) is proved.
The converse of this theorem is “if a transversal intersects two lines, such that the pair of co-interior angles are supplementary, then the two lines are parallel”.
The football team has a total of 28 jerseys. There are 10 medium-sized jerseys. What percent of the jerseys are medium-sized jerseys?
The percentage of jerseys that were medium-sized jerseys is 35.71%
What is Percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
Given data ,
Total number of jerseys the football team has = 28 jerseys
Total number of jerseys that were medium sized = 10
So ,
Percentage of jerseys that were medium sized =
( Total number of jerseys that were medium sized / Total number of jerseys ) x 100
Percentage of jerseys that were medium sized = ( 10 / 28 ) x 100
= ( 5 / 14 ) x 100
= 7.14285 x 5
= 35.71 %
Therefore , the percentage of jerseys that were medium sized = 35.71%
Hence , the percentage of jerseys that were medium-sized jerseys is 35.71%
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