4.8 inches is the height of a trapezoid with an area of 24 square inches if the two bases measure 4 inches and 6 inches.
Using the formula for the area of a trapezoid, which is:
Area = (1/2)(b1 + b2)h
In this formula, b1 and b2 are the lengths of the two bases of the trapezoid, and h is the height of the trapezoid. In our problem, we know that the area is 24 square inches, and the lengths of the two bases are 4 inches and 6 inches. We want to solve for h, the height of the trapezoid.
Plugging in the known values, we get:
24 = (1/2)(4 + 6)h
24 = (1/2)(10)h
24 = 5h
4.8 = h
Therefore, the height of the trapezoid is 4.8 inches.
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9. If XYZ LMN, what is the length of XZ?
Answer:
XZ = 21 cm
Step-by-step explanation:
since the triangles are congruent then corresponding sides are congruent, so
LN = XZ , that is
5x - 19 = 2x + 5 ( subtract 2x from both sides )
3x - 19 = 5 ( add 19 to both sides )
3x = 24 ( divide both sides by 3 )\
x = 8
then
XZ = 2x + 5 = 2(8) + 5 = 16 + 5 = 21 cm
What is 78=13n sovle for n
Answer:
Step-by-step explanation:
13n=78 /13
n= 6
Some students equally share 2 baskets of apples.Each basket has 12 apples. Write an algebraic expression to represent this situation. Then explain how you chose which variable and operation to use.
The algebraic expression to represent the given situation is 24/x where x is the number of students.
According to the question,
We have the following information:
Some students equally share 2 baskets of apples. Each basket has 12 apples.
Now, this situation can be presented to find the number of apples each student had.
Let's take the number to students to be x.
(x is the variable in this case.)
Number of apples one student had = total number of apples/number of students
Number of apples one student had = (2*12)/x
Number of apples one student had = 24/x
Hence, the algebraic expression to represent the given situation is 24/x where x is the number of students.
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Express y in the form axⁿ in the logarithm
[tex] log_{10}y + log_{10}x = 2[/tex]
Using the properties of logarithm we get the value y = 100x⁻¹ in the exponential form axⁿ
The given logarithmic equation is :
log ₁₀y + log ₁₀x = 2
Now we know that: 1 = log₁₀10
∴log ₁₀y + log ₁₀x = 2× log₁₀10
or, log ₁₀y + log ₁₀x = log₁₀10² (10 raised to the power 2)
or, log ₁₀y + log ₁₀x = log₁₀100
we know that log p+ log q = log pq
or, log ₁₀xy = log₁₀100
Now we take antilog on both sides of the equation:
or, xy = 100
or, y = 100 / x
or, y = 100x⁻¹
Problems that cannot be solved using the concept of basic exponents alone can be solved with a logarithm. Simply said, a logarithm is another way to talk about exponents.
A relatively simple way to remember this is that base remains the base in both forms and base does not remain solely with exponent in log form. Be aware that "b" is the base on both the left and right sides of the implies symbol, and that when an equation is written in log form, the base b and exponent x do not necessarily stay on the same side of the equation.
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When Richard turned 15, he deposited $1,500.00 in a savings account with an interest rate of 7% that is compounded daily. How much money will Richard have when he turns 27?
The amount of money that Richard will have when he turns 27 can be found to be $3, 474.26
How to find the amount compounded to?Convert the interest rate to a periodic rate which will be in days as the interest is compounded daily:
= 7% / 365 days a year
= 0.019178%
The number of periods is:
= (27 - 15) years x 365 days a year
= 4, 380 days
The money that Richard will have when he turns 27 is:
= 1, 500 x ( 1 + 0.019178%) ⁴³⁸⁰
= $3, 474.26
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a box of volume 252 m3 with a square bottom and no top is made of two different materials. the cost of the bottom is $40/m2 and the cost of the sides is $30/m2. find the dimensions of the box that minimize the total cost.
The dimensions of the box that minimizes the total cost is side of the square base is 7.23 m and height of the box is 4.82 m .
In the question ,
it is given that ,
the bottom of the box is = square ,
let the side of the square bottom be = "s" ,
so , the base area [tex]=[/tex] s²
let the height of the box [tex]=[/tex] h ,
Volume of the box = height × (base area)
So , the Volume of the box [tex]=[/tex] s²h
given that the volume of the box is 252 m³ , that means
s²h = 252
h = 252/s²
given that the Cost of bottom = $40 per m²
and the Cost of sides = $30 per m²
So , the total cost = 40s² + 30×(4sh)
substituting the value of h= 252/s² , we get
C = 40s² + 120s×252/s²
C = 40s² + 30240/s
to minimize the cost we differentiate with respect to s , and equating it to 0 ,
we get ,
80s - 30240/s² = 0
s³ = 30240/80
s³ = 378
s = 7.23
again differentiating C = 40s² + 30240/s with respect to s , and equating it to 0 ,
we get ,
d²C/ds² = 80 + (30240*2)/s³
at s=7.23 , d²C/ds² > 0
So , the minimum is at s = 7.23 ,
we have h = 252/(7.23)²
h = 4.82 .
Therefore , The dimensions of the box that minimizes the total cost is side of the square base is 7.23 m and height of the box is 4.82 m .
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A retaurant cutomer left $1. 65 a a tip. The tax wa 6% and the tip wa %15 of the cot including tax. What wa the total bill?
A retaurant cutomer left $1. 65 a tip. The tax was 6% and the tip was %15 of the cot including tax. Then the total bill is $13.31.
In the given question we have to find the total bill of the customer.
A retaurant cutomer left $1. 65 a a tip.
The tax was 6% and the tip was 15% of the cost including tax.
The tip was 15%(0.15) of the cost including tax.
Thus 0.15*X= 1.65
Divide both sides of the equation by 0.15.
x = 11
Now 6%(0.06) tax on meal at 11 is
11* 0.06 = 0.66
So the total bill cost = 6% tax on meal + 15% tip on meal+cost of meal
The total bill cost = $1.65 + $11+0.66
The total bill cost = 13.31
A retaurant cutomer left $1. 65 a tip. The tax was 6% and the tip was %15 of the cot including tax. Then the total bill is $13.31.
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Company A offers to sell you the newest smart phone for $35.50 a month for one year or $35.50 per 1/12 of a phone. Company B offers the same phone on a two year plan at $18.00 a month or $18.00 per 1/24 of a phone. Which company is selling the phone for less money?
From the equations , the company A is selling the phone for less money
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The equations for Company A :
The smart phone price per month = $ 35.50
The smart phone price for 1 year = $ 35.50 x 12
= $ 426
The price for 1/12 th of a phone = $ 35.50
The price for the entire phone = ( Price for 1/12 th of a phone ) x 12
= $ 35.50 x 12
= $ 426
Now , The equations for Company B :
The smart phone price per month = $ 18.00
The smart phone price for 2 year = $ 18.00 x 24
= $ 432
The price for 1/24 th of a phone = $ 18.00
The price for the entire phone = ( Price for 1/24 th of a phone ) x 24
= $ 432
Therefore , we can clearly see that price of the smart phone offered by Company A is lesser than price of the phone offered by Company B
And , $ 426 < $ 432
Hence , from the equations , the company A is selling the phone for less money
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Andrea earns $60 per day plus $4 for every sale she makes. On Wednesday, she wants to earn at least $128. Which best
describes the number of sales she needs to make to reach her goal?
at least 47 sales
at most 47 sales
at most 17 sales
at least 17 sales
Answer:
at least 17 sales
Step-by-step explanation:
On Wednesday she wants to earn 128.
Per day value = 60
128-60=68
She still needs to earn 68.
68 divided by 4=The number of sales needed to get 68 dollars=17
Thus she needs to make at least 17 sales, at most means maximum but she wants to earn AT LEAST 128 which means she wants more thus, answer is 4th option.
the sum of two-thirds of a number and twenty
(translating expressions)
Answer:
Step-by-step explanation:
(2/3)20
find the tension in each string and the acceleration of the 3-box system below if there is no friction
Tension in each string in the 3 - box system is T1 = m2 * f/m, T2 = m3 *f/m, a = f/m1+m2+m3.
In 3 - box system:
There are two tensions and two strings, let T1 and T2 be the tensions.
Let mass of boxes be m1,m2,m3
total mass m = m1+m2+m3
Acceleration a = force / m
a = f/m1+m2+m3
T1 = m2 * f/m
T2 = m3 * f/m.
Therefore Tension in each string in the 3 - box system is T1 = m2 * f/m, T2 = m3 *f/m, a = f/m1+m2+m3.
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given that sinx =3/5=x=90. evaluate (tan x+2cosx)
The value of (tanx+2cosx) = [tex]2\frac{7}{20}[/tex].
Given that
sinx = [tex]\frac{3}{5}[/tex]
sinx = [tex]\frac{opp}{hyp}[/tex]
Using the Pythagoras' theorem
[tex]hyp^{2} = opp^{2} + adj^{2} \\\\adj^{2} = 5^{2}- 3^{2} \\ \\= 25-9\\\\adj^{2} = 16\\ \\adj = \sqrt{16} \\[/tex]
adj = 4.
Now we have to find out tanx and cosx
[tex]tanx = \frac{opp}{adj}[/tex]
[tex]= \frac{3}{4}[/tex]
[tex]cosx = \frac{adj}{hyp}\\ \\= \frac{4}{5}[/tex]
Now we have to find out the given equation (tanx+2cox)
[tex]= \frac{3}{4} +2(\frac{4}{5})\\ \\= \frac{15+32}{20} \\\\= \frac{47}{20} \\\\or\\\\= 2\frac{7}{20}[/tex]
Hence the answer is the value of (tanx+2cosx) = [tex]2\frac{7}{20}[/tex].
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chart with the title 'average yearly earnings in the u.s. based on sex.' the blue line represents women's yearly average earnings. the red line represents men's yearly average earnings. the x-axis shows the years 1969, 1979, 1989, 1999, 2009, 2019. the y-axis shows the dollar amounts from 0 to 70,000 in increments of 10,000. in 1969, women earned 20,156 and men earned 32,241. in 1979, women earned 22,446 and men earned 37,622. in 1989, women earned 25,310 and men earned 36,855. in 1999, women earned 27,208 and men earned 37,701. in 2009, women earned 36,278 and men earned 47,127. in 2019, women earned 47,299 and men earned 57,456source: u.s. department of laborwhat is the relationship between the average yearly earnings of women and men? men continue to earn more than women. men work in higher skilled jobs where they earn more. women's earnings have increased in relation to men's earnings. women's earnings are lower because they take more time off.
The correct answer is Men continue to earn more than women.
The average yearly wages of men and women are different from one another. Men make more money than women do.
What is the annual salary?
Annual earnings may also be referred to as annual income or yearly income. It displays a person's earnings over a specific time period.
The yearly earning of a person or a corporation is calculated by dividing the monthly earnings by the number of months in a year.
Men continue to earn more than women under the situation mentioned above, hence their wages are higher. The red line is always above the blue line.
As a result, choice A is accurate which is men continue to earn more than women.
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Answer: C. women's earnings have increased in relation to men's earnings
Step-by-step explanation:
The chart shows that
Derek has $80 to spend on used books. Hardcover books cost $10 each, and paperbacks cost $20 each. Complete the equation which determines the number x of hardcover books and the number y of paperback books he can buy.
) a sector of a circle of radius 24 m has an area of 288 m2. find the central angle of the sector in radians.
The Central Angle of the sector in radians is 0.3184 π .
In the question ,
it is given that ,
the radius of the sector = 24 m
the area of the sector = 288 m²
we know that the Area of the sector of the circle is given by the formula
Area = πr²(θ/360)
Substituting the values , we get
288 = (3.14)*(24)²*(θ/360)
θ = (288*360)/((3.14)*(24)²)
θ = 1,03,680/1808.64
θ = 57.32°
converting the angle to radian ,
we get
θ = 57.32° × π/180 radian
= 0.3184 π
Therefore , The Central Angle of the sector in radians is 0.3184 π .
The given question is incomplete , the complete question is
A sector of a circle of radius 24 m has an area of 288 m² . find the central angle of the sector in radians .
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factorize:(sin alpha + cos alpha) ^ 2 - (sin alpha - cos alpha) ^ 2
After factorizing we get the value as:
4sinαcosα
Given,
we have the expression as:
(sinα + cosα)² - (sinα - cosα)²
open the brackets using the identity of:
(a+b)² = a²+b²+2ab
(a-b)² = a²+b²-2ab
now evaluate:
⇒ sin²α + cos²α + 2sinαcosα - (sin²α + cos²α - 2sinαcosα)
⇒ sin²α + cos²α + 2sinαcosα - sin²α - cos²α + 2sinαcosα
⇒ cancel the like terms
⇒ 2sinαcosα + 2sinαcosα
= 4sinαcosα
hence after factorization we get the value as 4sinαcosα
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Kenny has 2 red marbles and 4 black marbles which ration compares a part to a whole
The ratio which compares to be a whole is:
2/9
Given,
Kenny has 2 red marbles and 4 black marbles.
we are asked to determine the ratio which compares a part to whole.
Based on the given conditions, formulate:
2 ÷ (4+2+3)
Calculate the sum
2/6+3
calculate the sum:
2/9
hence ratio is:
2/9
Hence we get the ratio as 2/9.
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Helllppp 30 points pleases
Answer:
D
Step-by-step explanation:
Unit rates always compare quantities with different units
Ex. 10 km per 1 hour (10kph)
The perimeter of a park is 10 km . A wall is being constructed around it . If 4/5 of the wall has been constructed , how much part of the wall is incomplete
Perimeter of the park = 10km
Part of the wall's construction completed =
[tex] \frac{4}{5}th \: of \: perimeter [/tex]
=
[tex] \frac{4}{5} \times 10[/tex]
(cancel 5 and 10)
=
[tex] \frac{4}{1} \times 2[/tex]
= 8km
•.• Part of the wall left (to be constructed) = 10km - 8km = 2km
HOPE THIS HELPS YOU
you were asked to find the value of z such that 0.05 of the area lies to the right of z. see below for graphical and symbolic representations of the problem.
The value of z such that 0.05 of the area lies to the right of z is 1.64.
Given:
0.05 = 5%
The z score is calculated:
z = x - μ / σ
from the t table the value of z is:
= 1.64
More details is in the image uploaded.
Therefore the value of z such that 0.05 of the area lies to the right of z is 1.64.
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(1 point) a cylinder is inscribed in a right circular cone of height 2.5 and radius (at the base) equal to 7.5. what are the dimensions of such a cylinder which has maximum volume?
For the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.
As given in the question,
Height of the right circular cone = 2.5 units
And radius of right circular cone = 7.5 units
Let r be the radius of the cylinder and h be the height of the cylinder.
Volume of a cylinder 'V' = π r² h
Cylinder is inscribed in right circular cone
From origin edge cylinder is inscribed at x distance in right circular cone.
r = 7.5 - x
h = (2.5 /7.5) x
= x/3
V = π ( 7.5 - x )² ( x / 3)
⇒ V = π ( x² -15x + 56.25 ) (x/3)
⇒ V = (π /3)( x³ - 15x² + 56.25x)
For maximum volume ,
dV/dx = 0
dV/dx = (π/3)( 3x² -30x + 56.25)
(π/3) ≠ 0
⇒ 3x² -30x + 56.25 = 0
⇒ 3 ( x² -10x + 18.75) = 0
3 ≠ 0
⇒ x² -10x + 18.75 = 0
x = [ - (-10) ± √ (-10)² -4(1)(18.75)]/2(1)
⇒ x = [ 10 ± √ 100 -75]/2
⇒ x= ( 10 ± 5 ) / 2
⇒ x = 7.5 or 2.5
As r = 7.5 -x
Hence x ≠ 7.5
r = 7.5 -2.5
= 5 units
h = x/3
= 2.5/3
= 0.8333 units
Therefore, for the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.
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The radius of the earth is approximately 6400 km. The equator is the circle around the earth dividing it into the northern and southern hemisphere. (The center of the earth is also the center of the equator.) What is the length of the equator? (numerical answer only; no units)
The length of the equator is 40192 km.
How to find the length of the equator?The radius of the earth is approximately 6400 km. The equator is the circle around the earth dividing it into the northern and southern hemisphere.
Let's find the length of the equator as follows:
The length of the equator is the circumference.
Therefore,
L = 2πr
where
r = radiusL = 2 × 3.14 × 6400
L = 6.28 × 6400
L = 40192 km
Therefore, the equator which is the circle around the earth has a length of 40192 km.
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PLEASE HELP HURRY
Find the area of the figure below composed of a rectangle and a semicircle round to the nearest tenth place 8 10
The area of the composed rectangle and the semicircle is 92.56 square units.
Area of rectangle and semicircle
The formula for the Area of a Rectangle.
A = l × w.
where l refers length and w refers width of the rectangle
The area of a semicircle refers the half of the area of the circle. Therefore, the area of a semicircle is 1/2(πr²), where r is the radius.
Given,
Here we have the figure below composed of a rectangle and a semicircle And we need to find the area of this figure then round to the nearest tenth place.
Here we know the following values,
Length of the rectangle = 10
Width of the rectangle = 8
Diameter of the circle = 8
Through the given diameter we have identified the radius as 4.
Now, the area of the rectangle is calculated as,
A = 10 x 8
A = 80 square units.
Similarly, the area of the semicircle is
A = 1/2 (π x 4²)
A = 1/2 x π x 8
A = π x 4
We know the value of π = 3.14, then the area of the semicircle is,
A = 3.14 x 4
A = 12.56 square units.
Therefore, the are of the figure is,
Total area = area of rectangle + area of semicircle
Total area = 80 + 12.56
Therefore, the total area of the figure is 92.56 square units.
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Two parallel lines are cut by a transversal as shown below. Suppose m4=83°. Find m5 and m7
The angles found by the given figure are:
m∠5 = 97°
m∠7 = 97°
From the graph given we can get that the two parallel lines are cut by a transversal and:
m ∠4 = m∠2
m∠2 = 83°
hence, m∠2 + m∠5 = 180°
so,:
m∠5 = 180° - m∠2
= 180 - 83
= 97°
hence m∠5 = 97°
now, m∠7 = m∠5
since the vertical angles of two increasing lines are equal
so, m∠7 = 97°
Hence we get the two angles respectively.
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A child’s piggy bank has 3 times as many dimes as nickels. Altogether she has 3.85 how many dimes does she have
Step-by-step explanation:
d = number of dimes
n = number of nickels
one dime = $0.10
one nickel = $0.05
d = 3n
0.1×d + 0.05×n = 3.85
0.1×3n + 0.05×n = 3.85
0.3×n + 0.05×n = 3.85
0.35×n = 3.85
n = 3.85 / 0.35 = 11
d = 3n = 3×11 = 33
she has 33 dimes (and 11 nickels).
For a ride on a rental scooter, Boris paid a $2 fee to start the scooter plus 12 cents per minute of the ride. The total bill for Boris's ride was $10.52 . For how many minutes did Boris ride the scooter?
Answer: 119 minutes
Step-by-step explanation:
Which expression represents the total cost for mrs.Alvarez to rent skis for s days and poles for p days
At the ski shack, customers can rent,skis, snowboards, boots, and poles by the day Mrs.Alvarez is renting skis and poles she has a 18$ coupon off
which expression represents the total cost for Mrs.Alvarez to rent skis for s days and poles for p days
If the answer you asked is this:
48s+12p-18 the correct answer
Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio
A(-3,2), B(5,-4); 2 to 6
QUICK I NEED IT BEFOR# MONDAY
The ordered pair P within the line segment AB is (- 1, 1 / 2).
What is the location of an ordered pair within a line segment?
In this question we have a segment whose endpoints are known: A(x, y) = (- 3, 2), B(x, y) = (5, - 4), and in which we need to determine the location of point P such that the following relationship is known:
k = AP / PB
[tex]\overrightarrow {AP} = k \cdot \overrightarrow {PB}[/tex]
P(x, y) - A(x, y) = k · [B(x, y) - P(x, y)]
(k + 1) · P(x, y) = A(x, y) + k · B(x, y)
P(x, y) = [1 / (k + 1)] · A(x, y) + [k / (k + 1)] · B(x, y)
Where:
A(x, y), B(x, y) - Endpoints of the line segment.P(x, y) - Ordered pair of a line segment.k - Segment ratio.If we know that A(x, y) = (- 3, 2), B(x, y) = (5, - 4) and k = 1 / 3, then the location of the ordered pair is:
P(x, y) = [1 / (4 / 3)] · (- 3, 2) + [(1 / 3) / (4 / 3)] · (5, - 4)
P(x, y) = (3 / 4) · (- 3, 2) + (1 / 4) · (5, - 4)
P(x, y) = (- 9 / 4, 6 / 4) + (5 / 4, - 1)
P(x, y) = (- 9 / 4, 3 / 2) + (5 / 4, - 1)
P(x, y) = (- 1, 1 / 2)
The ordered pair P is (- 1, 1 / 2).
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Part A: The area of a square is (16x2 − 8x + 1) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points)
Part B: The area of a rectangle is (81x2 − 4y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)
The length of each side of the square is 4x - 1 while the area for the dimensions of the rectangle is (9x + 2y) by (9x - 2y) using the factorization methods of grouping and difference in two squares respectively.
Factorisation by grouping and difference in two squaresFactorization is the process of breaking down a number in which when multiplied together will arrive at the original number.
Part A: Given the area of square as 16x² - 8x + 1, applying factorization by grouping;
16x² - 8x + 1 = 16x² - 4x - 4x + 1 (group terms with common factors)
16x² - 8x + 1 = 4x(x - 1) - (4x - 1) (factor out the common factor in each group)
16x² - 8x + 1 = (4x - 1) × (4x - 1) (factor the common factor from the expression)
16x² - 8x + 1 = (4x - 1)²
Part B: For the area or rectangle given as 81x² - 4y², factorizing by the method of difference in two squares;
81x² - 4y² = 9²x² - 2²y² (express as squares)
81x² - 4y² = (9x)² - (2y)²
81x² - 4y² = (9x + 2y) × (9x - 2y)
Therefore, 4x - 1 is the length of one side of the square as all sides of a square are equal and (9x + 2y) by (9x - 2y) is the dimension of the rectangle using the factorization methods of grouping and difference in two squares.
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If you invest $200 into a savings account that earns 4% annual interest compounded continuously, how much money will you have after 21 years?
Answer:
$455.75
Step-by-step explanation:
Formula for compound interest:End amount = Starting amount x (1 + interest in decimal form)^length of time in years Starting amount: $200Interest rate as a decimal: 0.04 (4%/100)Length of time: 21 yearsEnd amount = 200.00(1 + 0.04)^(21) = $455.75