Answer:
irrational
Step-by-step explanation:
what are rational numbers ?
every number that can be expressed as a/b, with a and b being integer numbers, and b different to 0.
the square root of any number that is not a squared rational number is then an irrational number.
I am not sure, if the expression here is
sqrt(13) + 4
or
sqrt(13 + 4), which would then be sqrt(17).
but in both cases we are creating the square root of a not- squared rational number.
neither 13 nor 17 are the result of a multiplication of a rational number with itself.
in fact, 13 and 17 are prime numbers with no other factors than either 1 or themselves.
so, both, sqrt(13) and sqrt(17) are irrational numbers.
adding or subtracting rational numbers to irrational numbers result again in irrational numbers.
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We are asked to find out if [tex]\pmb{\sqrt{13} +4}[/tex] is rational or irrational.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Irrational numbers cannot be expressed as fractions (in [tex]\pmb{\cfrac{p}{q}}[/tex] form).So, can we write [tex]\pmb{\sqrt{13} +4}[/tex] as a fraction? We can write 4 as a fraction, but we cannot write [tex]\pmb{\sqrt{13}}[/tex] as a fraction, because this number has infinitely many digits after the decimal point, and they never repeat; there's no pattern at all!
And even if we add 4, which is a rational number, to [tex]\pmb{\sqrt{13}}[/tex], we'll still get an irrational number.
Thus, [tex]\pmb{\sqrt{13}+4}[/tex] is irrational.
Hope it helps you out! :D
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The square below represents one whole.
Express the shaded area as a fraction, a decimal, and a percent of the whole.
The shaded area expressed as a fraction, a decimal, and a percent of the whole is 23/100, 0.23 and 23% respectively
Fractions, Decimals and PercentagesFrom the question, we are to express the shaded area as a fraction, a decimal, and a percent of the whole.
In the diagram, there are 100 total squares and 23 of them are shaded
Expressing the shaded area as a fraction, we get
[tex]\frac{23}{100}[/tex]
Expressing the shaded area as a decimal, we get
[tex]\frac{23}{100}[/tex] = 0.23
Expressing the shaded area as a percent , we get
[tex]\frac{23}{100}\times 100\%[/tex] = 23%
Hence, the shaded area as a fraction, a decimal, and a percent of the whole is 23/100, 0.23 and 23% respectively
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If the cost of 3 notebooks is 30.30, then find the cost of 15 such notebooks.
Answer:
If the cost of 3 notebooks is 30.30, we can infer the cost of one notebook is 10.10.
Step-by-step explanation:
[tex]10.10 * 15 = x[/tex]
[tex]10.10 * 15 = 151.5[/tex]
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We are asked to find the cost of 15 notebooks, given that the cost of 3 notebooks is 30.30.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
First of all, we need to find the cost of 1 notebook.So we divide the cost of three notebooks (30.30) by 3:
[tex]\star~\large\pmb{30.30\div3}[/tex]
[tex]\star~\large\pmb{10.10}[/tex]
That's the cost of 1 notebook. Now, multiply that times 15 (we're asked to find the cost of 15 notebooks).
[tex]\star~\large\pmb{10.10\times15}[/tex]
This gives us:
[tex]\star~\large\pmb{151.5}[/tex]
That's the cost of 15 notebooks if the cost of one notebook is 10.10.
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WILL MARK BRAINLIEST 50 POINTS Find the area of the regular pentagon if the apothem is 7 ft and a side is 10 ft. Round to the nearest whole number.
175 ft2
350 ft2
35 ft2
70 ft2
Answer:
175 ft^2
Step-by-step explanation:
split the pentagon into 5 triangles with base length 10ft and height 7ft. each triangle then has an area of 10 * 7 * 1/2 = 35 ft^2
then the pentagon has an area 35*5 = 175 ft^2
F. In what order should items weighing
51 pounds, 40 pounds, 48 pounds,
and 44 pounds be stacked if you want
them in order from heaviest to lightest?
Answer:
51 pounds, 48 pounds, 44 pounds and 40 pounds in that chronological order.
im lost can someone help?
In triangle ABC, AP is an angle bisector of angle BAC. What is the length of PC? Round you answer to the nearest whole number.
A) 6 B) 7 C) 8 D) 9
Answer:
D) 9
Step-by-step explanation:
x = ½ × 13 = 6.5
y = ½ × 5 = 2.5
6.5 + 2.5 = 9
So the length of PC is 9
HOPE THIS HELPS AND HAVE A NICE DAY <3
Determine whether each triangle with sides of given length is a right triangle. justify your answer
7 yd, 5 yd, 9 yd
10 ft, 24ft, 26 ft
The triangles with the side lengths 10 ft, 24ft, 26 ft, is a right triangle while a triangle with side lengths of 7 yd, 5 yd, 9 yd is NOT based on the Pythagorean theorem.
What is a Right Triangle?A triangle is said to be a triangle based on the Pythagorean theorem, if the square of the longest side equals the sum of the squares of the other smaller sides of the triangle.
9² = 7² + 5²
81 = 74 (NOT TRUE), therefore, the triangle with the side lengths 7 yd, 5 yd, 9 yd, is not a right triangle.
26² = 10² + 24²
676 = 676 (TRUE), therefore, the triangle with the side lengths 10 ft, 24ft, 26 ft, is a right triangle.
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If we changed the 3 to a 0 in the equation, what would happen to the graph?
A function assigns the values. The function will move down by 3 units.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The graph of the function is given below. Now if 3 is replaced by a 0, then the y-intercept of the function will become zero while keeping the slope the same. Therefore, the function will move down by 3 units.
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Given that 24w = 14ten .Find the unknown base
Answer:
w = 5
Step-by-step explanation:
24w = (14)10
2w + 4 = 10 + 4
2w = 10
w = 5
I need help solving this problem system of equations
Answer:
y= -6
Step-by-step explanation:
-4x and 4x are canceled out. -2y+8y= 6y. -12-24=-36
You are left with 6y=-36 . Divide from both sides and -36/6 is -6. So, y=-6.
Hope this helped.
Select the correct answer. Which expression is equivalent to the complex number 10 + 3i?
The expression that is equivalent to the complex number 10 + 3i is (4+7i)-2i(2+3i)
Complex numbersComplex numbers are square root of negative numbers. They are expressed as a + bi
Using the expression
(4+7i)-2i(2+3i)
Expand
4 + 7i - 4i -2i(3i)
4 + 3i - 2(-3)
4 + 6 + 3i
10 + 3i
Hence the expression that is equivalent to the complex number 10 + 3i is (4+7i)-2i(2+3i)
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Draw and set up the integrals for the area enclosed by the y–axis, the curve y = (x + 1)1/2 and y = 2. Compute one of them.
Region II only please
If the definitions of type I and type II regions is the same as in the link provided, then as a type I region the integration domain is the set
[tex]R_{\rm I} = \left\{(x,y) \mid 0 \le x \le 3 \text{ and } \sqrt{x+1} \le y \le 2\right\}[/tex]
and as a type II region,
[tex]R_{\rm II} = \left\{(x,y) \mid 0 \le x \le y^2-1 \text{ and } 1 \le y \le 2\right\}[/tex]
where we solve y = √(x + 1) for x to get x as a function of y.
A. The area of the type I region is
[tex]\displaystyle \iint_{R_{\rm I}} dA = \int_0^3 \int_{\sqrt{x+1}}^2 dy \, dx = \int_0^3 (2 - \sqrt{x+1}) \, dx = \boxed{\frac43}[/tex]
B. The area of the type II region is of course also
[tex]\displaystyle \iint_{R_{\rm II}} dA = \int_1^2 \int_0^{y^2-1} dx \, dy = \int_1^2 (y^2-1) \, dy = \boxed{\frac43}[/tex]
I've attached a plot of the type II region to give an idea of how it was determined. The black arrows indicate the domain of x as it varies from the line x = 0 (y-axis) to the curve y = √(x + 1).
If the given figure is sliced through points J. K. and L, which best describes the shape of the resulting cross-section?
A
OA parallelogram
OB. trapezoid
OC. rectangle
OD. triangle
The shape of the resulting cross-section will be equal to the trapezoid.
What is a trapezoid?A trapezoid is a quadrilateral having four sides whose two sides are parallel to each other and the other two sides are nonparallel to each other.
As it is given in the question the figure is sliced through points J. K. and When the shape is sliced from the given points it will create the trapezoidal shape that will have two parallel sides and the other two sides are Non-parallel
Therefore the shape of the resulting cross-section will be equal to the trapezoid.
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Answer:
Trapezoid
Step-by-step explanation:
I got it right on Edmentum
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A rectangle has a height of m+8m+8m, plus, 8 and a width of
2m^3+m^2+3m2m 3 +m 2 +3m2, m, cubed, plus, m, squared, plus, 3, m. Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
Answer:
it is 18
Step-by-step explanation:
write a Pythagorean triplet whose smallest member is 6
Answer:
6, 8, 10
Step-by-step explanation:
Where:
a = 6
b = 8
c = 10
Pythagorean theorem: [tex]a^2 + b^2 = c^2[/tex]
[tex]6^2 + 8^2 = c^2[/tex]
[tex]36 + 64 = c^2[/tex]
[tex]100 = c^2[/tex]
c = [tex]\sqrt{100}[/tex]
c = 10
what is the area of the figure?
Answer:
area = 62ft
Step-by-step explanation
so you section the polygon into a big rectangle and 2 small rectangles
the area of the small rectangle will be 2ft x 3ft which will be 6 ft, and as there are 2 of them the area of it will be 12ft
the area of the big rectangle will be 10ft x 5ft, as 8ft - 3ft is 5ft so 5x10=50ft
now add the areas you got, 50+12 which is 62ft
hope this helps:)
Find the slope and the y-intercept of the following linear equation. 5. 3x + 2y = 14
The slope and y-intercept of the equation are - 3 / 2 and 7 respectively.
How to find slope and y-intercept?The slope and y-intercept of an equation can be easily found using slope intercept equation.
y = mx + b
where
m = slopeb = y-interceptTherefore,
3x + 2y = 14
2y = -3x + 14
y = -3 / 2 x + 7
Therefore,
slope = - 3 / 2
y-intercept = 7
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what is the median of the data set represented by the box plot shown below? 38,45,50,60,75
Answer:
50
Step-by-step explanation:
The diameter of a circle is 94 cm.
By first calculating the radius, work
out the area of the circle.
2
Give your answer in cm² to 1 d.p.
[tex]\huge\boxed{Formula: r= \frac{d}{2}}[/tex]
Substitute the values according to the formula.
[tex]r=\frac{94}{2}[/tex]
[tex]\large\boxed{r=47 \: cm}[/tex]
Now, let's find the area.
[tex]\huge\boxed{Formula:a= \pi{r}^{2}}[/tex]
So, we'll have to multiply π, 47 and 47.
Substitute the values according to the formula.
[tex]a= \pi{47}^{2}[/tex]
[tex]a= 6939.778172 \: {cm}^{2}[/tex]
[tex]\large\boxed{a= 6939.8 \: {cm}^{2}(1 \: d.p)}[/tex]
Hence, the area of the given circle is 6939.8 square centimeters.
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We are asked to find the radius & area of the circle.
To find the [tex]\star\bf{radius}\star[/tex], we divide the diameter by 2:
[tex]\star~\bf{94\div2}[/tex]
[tex]\star~\bf{Radius=47}\star[/tex]
Now that we have the radius, let's compute the area! :)
///\\\///\\\///\\\///\\\///\\\////\\\///\\///\\\///\\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\//\\\//\\
Calculating the Area
We can work out the area of a circle by using this formula:
[tex]\star\boxed{\pmb{A_{(circle)}=\pi r^2}}\star[/tex]
Where
[tex]\dag[/tex] A=Area of a circle
[tex]\dag[/tex] [tex]\pi =3.14...[/tex]
[tex]\dag[/tex] r=radius
Have you noticed the [tex]\large\pmb{^2}[/tex] next to r? This tells us that we should multiply the radius times itself.
Now it's time to substitute the values:
[tex]\star~\large\pmb{A=3.14\times47^{2}}\star[/tex]
Let's simplify it. The acronym PEMDAS will help us, and we won't make any mistakes in the Order of Operations! :)
Here's what it stands for:
P=Parentheses
E=Exponents
M=Multiplication
D=Division
A=Addition
S=Subtraction
2 is an exponent.
So what do you think we should do first?
[tex]\square[/tex] Square 47.
[tex]\square[/tex] Multiply 3.14 times 47 and then square.
That's right, we should square 47 first. :)
[tex]\star~\large\pmb{A=\pi \times2209}}\star[/tex]
Now, according to PEMDAS, we should multiply pi times 2209; after multiplying, we obtain:
[tex]\star~\large\pmb{A=6936.8\:cm^2}\star[/tex]
Remember, the area of any shape is measured in units squared.
[tex]\ddot\bigstar[/tex] Remember this...
[tex]\fbox{\bf{The\;area\;of\;any\;shape\;is\;measured\;in\;units\;squared}}[/tex]
Hope this helps you out! :D
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[tex]\bigstar\footnotesize\pmb{M^ar_ib^el\;Peri}[/tex]
Review the graph of complex number z.
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is at (negative 3, 1).
What is the modulus of z?
2
2StartRoot 2 EndRoot
3
StartRoot 10 EndRoot
Answer:
√10Step-by-step explanation:
[tex]\text {modulus of z } = =\sqrt{\left( -3\right)^{2} +\left( 1\right)^{2} } =\sqrt{9+1} =\sqrt{10}[/tex]
Answer:
square root of 10
Step-by-step explanation:
Determine u-x and o-x from the given parameters of the population and the sample.size. round the answer to the nearest thousandth where appropriate u=27 o=5 n=14
The u-x and o-x from the given parameters of the population and the sample size will be u =28 and standard deviation is 5.
How to calculate the values?From the information given about the population and sample mean, the values include:
u=27 o=5 n=14
The standard deviation will be:
= 5/✓14
= 5/3.74
= 1.34
Therefore, u-x and o-x from the given parameters of the population and the sample size will be u =28 and standard deviation is 1.34.
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answer question below.
The speed of the Elvira is 6.545 miles per hour. Then the speed of the Altheia will be 0.545 miles per hour.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
Let the speed of the Elvira be x. Then the speed of the Altheia will be (x - 6).
Let the distance between the coffee shop and Elvira's house be d.
Then the distance between the coffee shop and Altheia's house will be (3.6 - d).
Then we have
x = d / 0.5 ...1
(x - 6) = (3.6 - d) / 0.6 ...2
In solving the equations 1 and 2, we have
x = 6.545 and d = 3.2725 miles
Then the speed of the Elvira is 6.545 miles per hour. Then the speed of the Altheia will be 0.545 miles per hour.
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Suppose y varies inversely with x, and y = 49 when x = 17. What is the value of x when y = 7 ?
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{\underline{y} varies inversely with \underline{x}}}{y=\cfrac{k}{x}}\qquad \textit{we also know that} \begin{cases} y=49\\ x=17 \end{cases} \\\\\\ 49=\cfrac{k}{17}\implies 833=k~\hfill \boxed{y=\cfrac{833}{x}} \\\\\\ \textit{when y = 7, what is "x"?}\qquad 7=\cfrac{833}{x}\implies x=\cfrac{833}{7}\implies x=119[/tex]
Please solve these questions!! preferrably today since the quarter locks today!!
Answer:
131
Step-by-step explanation:
Write two numbers that multiply to the value on top and add to the value on bottom.
-84
17
Two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.
What is multiplication?Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. Multiplication essentially means the repeated addition.
The two given numbers are -84 and 17.
We need to write two numbers that multiply to the value on top (-84) and add to the value on the bottom (17).
If we multiply 21 and -4, we get the product as -84.
That is, 21×(-4)=-84
If we add 21 and -4, we get the sum as -17.
That is, 21+(-4)=21-4=17
Therefore, two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.
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A wooden roller is 1 m long and 8 cm in diameter. Find it's mass in grams if 1cm³ of the wood has a mass of 0.7 g
Answer:
1120π grams
==> 3518.58 grams using value of π = 3.14159 or
==> 3520 grams using value of π = 22/7
Step-by-step explanation:
Volume of a cylinder = πr²l where r is the radius of the base and h is the length of cylinder
The diameter of the cylinder, d = 8cm and radius = d/2 = 4cm
Length = 1 meter = 100 cm
Here, volume V = π.4².100 = π x 16 x 100 = 1600π cm³
Since 1 cm³ has a mass of 0.7gm total mass
M = 0.7V = (0.7)1600π =1120π gm
Using the ratio 22/7 for pi we get
M = 1120 x 22/7 = 3520 g
If we use the more accurate value of π as 3.14159 then we get
M = 1120 x 3.14.159 = 3518.58 g which is more accurate
What is true of the function g(x) = -2x² + 5?
O g(x) is the multiplication of g and x.
O-212 +5 is the input of the function.
The variable x represents the independent variable.
The variable g represents the input of the function.
Answer:
C.) The variable x represents the independent variable
Step-by-step explanation:
The variable "x" is the independent variable because that is the value that we can manipulate. We cannot manipulate the dependent variable because it is determined by the independent variable. In that case, "y" would be the dependent variable because its value is dependent on what "x" is.
A.) is incorrect because g(x) symbolizes the input of the variable "x" into the g function.
B.) is incorrect because "x" is the input.
D.) is incorrect because "x" is the input.
can someone help me with this worksheet please!!!!
(1) The missing term in the sequence, a₁₂ = 0.8.
(2) The missing term in the sequence, a₈ = 102.5.
(3) The missing term in the sequence, a₈ = 111.
(4) The missing term in the sequence, a₁₂ = -19.
(5) The missing term in the sequence, a₁₂ = 94.
(6) The missing term in the sequence, a₆ = 40.
(7) The missing term in the sequence, a₃₆ = -52.
(8) The missing term in the sequence, a₂₁ = -58.
Missing term of the sequenceThe missing term in the sequence is determined as follows;
Tₙ = a + (n - 1)d
1.0 a₄ = 18.4 and a₅ = 16.2, a₁₂ = ?T₄ = a + 3d
18.4 = a + 3d ---(1)
T₅ = a + 4d
16.2 = a + 4d ---(2)
subtract (1) from (2)
-2.2 = d
18.4 = a + 3(-2.2)
a = 25
a₁₂ = a + 11d
a₁₂ = 25 + 11(-2.2)
a₁₂ = 0.8
2.0 a₂ = 57.5 and a₅ = 80, a₈ = ?a₂ = a + d
57.5 = a + d -- (1)
a₅ = a + 4d
80 = a + 4d --- (2)
solve (1) and (2)
d = 7.5
a = 50
a₈ = a + 7d
a₈ = 50 + 7(7.5)
a₈ = 102.5
3.0 a₁₀ = 141 and a₁₃ = 186, a₈ = ?a₁₀ = a + 9d
141 = a + 9d --- (1)
a₁₃ = a + 12d
186 = a + 12d --- (2)
Subtract (1) from (2)
d = 15
a = 6
a₈ = a + 7d
a₈ = 6 + 7(15)
a₈ = 111
4.0 a₂₂ = -49 and a₂₅ = -58, a₁₂ = ?a₂₂ = a + 21d
-49 = a + 21d ---- (1)
a₂₅ = a + 24d
-58 = a + 24d --- (2)
subtract (1) from (2)
d = -3
a = 14
a₁₂ = a + 11d
a₁₂ = 14 + 11(-3)
a₁₂ = -19
5.0 a₄ = -2 and a₈ = 46, a₁₂ = ?a₄ = a + 3d
-2 = a + 3d --- (1)
a₈ = a + 7d
46 = a + 7d ---- (2)
Subtract (1) from (2)
d = 12
a = -38
a₁₂ = a + 11d
a₁₂ = -38 + 11(12)
a₁₂ = 94
6.0 a₉ = 64 and a₁₂ = 88, a₆ = ?a₉ = a + 8d
64 = a + 8d --- (1)
a₁₂ = a + 11d
88 = a + 11d --- (2)
Subtract (1) from (2)
d = 8
a = 0
a₆ = a + 5d
a₆ = 0 + 5(8)
a₆ = 40
7.0 a₂₀ = -4 and a₂₃ = -13, a₃₆ = ?a₂₀ = a + 19d
-4 = a + 19d ---- (1)
a₂₃ = a + 22d
-13 = a + 22d --- (2)
Subtract (1) from (2)
d = -3
a = 53
a₃₆ = a + 35d
a₃₆ = 53 + 35(-3)
a₃₆ = -52
8.0 a₂₈ = 5 and a₃₃ = 50, a₂₁ = ?a₂₈ = a + 27d
5 = a + 27d ---- (1)
a₃₃ = a + 32d
50 = a + 32d --- (2)
Subtract (1) from (2)
d = 9
a = -238
a₂₁ = a + 20d
a₂₁ = -238 + 20(9)
a₂₁ = -58
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Right triangle ABC is reflected over AC, then dilated by a scale factor of Two-thirds to form triangle DEC. Which statements about the two triangles must be true? Select three options.
△ABC ~ △DEC
∠B ≅ ∠E
3BC = 2EC
3DE = 2AB
3m∠A = 2m∠D
2m∠A = 3m∠D
The triangle △ABC and △DEC are similar to each other. Then the correct option is A, B, and D.
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
Right triangle ABC is reflected over AC.
Then dilated by a scale factor of Two-thirds to form triangle DEC.
The triangle △ABC and △DEC are similar to each other.
△ABC ≅ △DEC
The dilation is 2/3. Then we have
DE / AB = 2 / 3
3AB = 2DE
∠B ≅ ∠E = 90
There is no effect of dilation on angle.
Then the correct option is A, B, and D.
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Answer:
A. △ABC ~ △DEC
B. ∠B ≅ ∠E
D. 3DE = 2AB
Step-by-step explanation:
got it right on edge 23
PLEASE HELP!!!!!!!!!!!!!!!!!!! I'll NAME BRAINLIEST!!!!!!!!!!!!!!!!!A moving-van rental company uses the polynomial 110 + 0.65(m – 200) to calculate the rental charges if a customer drives a van more than 200 miles in one day. In the polynomial, m is the total number of miles that the customer drove the van during the day. Use the Distributive Property to write an equivalent expression for the total cost of renting the van and driving it more than 200 miles in one day.
Answer:I think it would be 84 + 0.45m + 108.
Which simplified could be 0.45m + 192.
hope this helps!
Step-by-step explanation: