Answer:
52.94 miles per unit
Step-by-step explanation:
The unit rate is found by dividing miles per time
90 miles /1.7 unit
52.94117647 miles per unit
PLEASE HELP ME !! Carter has 3 statues of various sizes in his garden. Statue A is one foot taller than statue B. Statue is one-half of a foot taller than statue B. A) write an algebraic expression for the total combined height of statue A and c. (equations for statues A and C) B) If the total combined height of the 3 statues is 10 feet, find the height of statue B in inches.
Answer:
Step-by-step explanation:
In combining like terms, what do these equations equal?
1: 5+6(2x+3)-2x
2: 3(4x+8) + 3(2x-6)
3: (32-8x)
____
4
4: 24x+18
____
6
If you can, please explain it! Thanks!
Answer:
Look below. The answers are bolded!
Step-by-step explanation:
1. 10x + 23
5+6(2x+3)-2x
Distribute first!
5 + 12x + 18 -2x.
Now you can combine like terms.
23 + 10x
2. 18x + 6
3(4x+8) + 3(2x-6)
Distribute first!
12x + 24 + 6x - 18
Now you can combine like terms.
18x + 6
3. -2x + 8
(32-8x)
____ ___
4
Divide 32 and -8x by 4.
32/4 = 8
-8x/4 = -2x
-2x + 8
4. 4x + 3
24x+18
______
6
Divide 24x and 18 by 6
24x/6 = 4x
18/6 = 3
4x + 3
Each year, the number of students taught by Mr. Wright increases by 2. The first year, he taught 18 students. The total number of students taught after 25 years can be represented using the expression . How many students has Mr. Wright taught in 25 years?
450
500
1,050
2,100
Answer:
Mr. Wright taught 1,050 students in 25 years.
Step-by-step explanation:
Given,
The number of students Mr. Wright taught = 18,
Also, every year the number of student is increased by 2,
So, in second year, the number of students = 18 + 2 = 20,
In third year = 20 + 2 = 22,
In fourth year = 22 + 2 = 24,
.............., so on,
Hence, we get an A.P. that shows the given situation,
18, 20, 22, 24, ............. till 25 years.....
First term, a = 18,
Common difference, d = 2,
And, number of terms, n = 25,
Hence, the total number of students that have been taught by him are,
[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]
[tex]S_{25}=\frac{25}{2}[36+(25-1)2][/tex]
[tex]=\frac{25}{2}[36+24\times 2][/tex]
[tex]=\frac{25}{2}[36+48][/tex]
[tex]=\frac{25}{2}(84)[/tex]
[tex]=\frac{2100}{2}[/tex]
[tex]=1050[/tex]
Third option is correct.
A rectangle has an area (x2-17x+72) square units.Since the area of a rectangle is determined using the formula, A= lw, what could be the length and width of the rectangle
Answer:
length: 9
width: 8
Step-by-step explanation:
you would need to factorise the equation in order to work out the length and width of the rectangle
so to factorise x^2 -17x +72, you will need to numbers that multiply to make 72 and add to make -17
the numbers are -9 and -8
so the factorised equation is (x-9)(x-8)
if you equate it to 0 you get 9 and 8 as values for x
since the length is longer than the width
the length is 9 and the width is 8
Find the value of
[tex] {x}^{i} [/tex]
for all x belongs to Real Numbers and i = √(-1).
Answer: cis (ln x) ; x > 0
Step-by-step explanation:
[tex]x^i[/tex]
[tex]= e^{ln(x^i)}[/tex]
[tex]=e^{i \ln(x)}[/tex]
= cos (ln x) + i sin (ln x)
AKA: cis (ln x)
NOTE: I found this following formula which you may find useful:
[tex]A^i = x + iy[/tex]
Gabe Amodeo, a nuclear physicist, needs 60 liters of a 60% acid solution. He currently has a 50% solution and a 70% solution. How many liters of each does he need to make the needed 60 liters of 60% acid solution? Gabe needs 30 liters for a 50% solution .
He also needs a ___ for a 70% solution . whats __?
Answer:
Gabe needs 20 liters of the 40% solution.
He also needs 40 liters of the 70% solution.
Step-by-step explanation:
Equation:
acid + acid = acid
0.40x + 0.70(60-x) = 0.60*60
40x + 70*60 - 70x = 60*60
-30x = -10*60
x = 20 liters
Gabe needs 20 liters of the 40% solution.
He also needs 40 liters of the 70% solution.
On a car trip Sam drove m miles Kara drove twice as many miles as Sam and Darin drove 20 fewer miles than Kara in terms of m many miles did Darin drive
Answer:
Darin drove '2m - 20' miles.
Step-by-step explanation:
We are given that Sam drove 'm' no. of miles.
As, it is also given that Kara drove twice as many miles as Sam. Therefore we get that Kara drove '2m' no. of miles.
Now, it is given that Darin drove 20 miles fewer than Kara .i.e. Darin drove '2m - 20' no. of miles.
Hence, in terms of m, Darin drove '2m - 20' miles.
3 is what percent of 12
Answer:
25%
Step-by-step explanation:
The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
The percentage of 3 in 12 is 25%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
3 and 12.
The percentage of 3 in 12.
= 3/12 x 100
= 1/4 x 100
= 25%
Thus,
The percentage of 3 in 12 is 25%.
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Sin (3pi/4) =_____ please help!!!
[tex]sin\frac{3}{4}\pi=sin(\pi-\frac{\pi}{4})=sin\frac{\pi}{4}=\frac{\sqrt2}{2}[/tex]
How many centimeters are in 7 feet, given that 1 inch = 2.5 centimeters?
Answer:
210 cm
Step-by-step explanation:
We need to convert 7 ft to cm
We know that 1 ft = 12 inches
7 ft * 12 inches/1 ft = 84 inches
We know that 1 inch = 2.5 cm
( 1 inch is really 2.54 cm but you question says 2.5 cm)
84 inches * 2.5 cm/1 inch = 210 cm
a train travels 160 km in 2 h what is the trains average speed in km/h
Answer:
80km/h
Step-by-step explanation:
we know that the train is 160 km in 2 hours we need to find how much is in 1 hour you divide 160÷2= 80 so it means that there is 80 km in 1 hour which is "80 km/h"
triple of a number x decreased by one
Answer:
3x-1
Step-by-step explanation:
if you triple x, you multiply x 3 times
The green line below
Answer:
A D E are all true. The others are false and should not be checked.
Step-by-step explanation:
A crosses the x axis at (- 2.5,0)
B is false. The line does not go through (0,0) which is the origin.
C is false. The green line is not perpendicular to anything.
D is true. It crosses the y axis at (0,5)
E is true. It is on the xy plane.
F is false. It is not parallel to either axis.
Elise took out a payday loan for $500 due in 2 weeks that charges an $80 fee. What is the periodic interest rate of the loan?
The periodic interest rate of Elise's payday loan is calculated by dividing the $80 fee by the $500 borrowed, resulting in a rate of 16% for the 2-week period.
To calculate the periodic interest rate of Elise's payday loan, we need to consider the fee charged as the interest for the period of the loan, since the loan is due in 2 weeks, which is a half-month period. Elise is being charged an $80 fee on a $500 loan, and this fee represents the interest for the loan's term.
Therefore, we can calculate the periodic interest rate by dividing the interest by the principal and the number of periods.
Here's the calculation:
Interest (Fee) = $80
Principal (Amount borrowed) = $500
Periodic interest rate = Interest / Principal
Periodic interest rate = $80 / $500 = 0.16 or 16%
Since the period is 2 weeks, we could express this interest rate on a monthly basis if needed by scaling the bi-weekly rate to a monthly rate. However, the loan terms only mention a 2-week period, so the periodic interest rate for the loan's duration is 16%.
"If parallel lines have a transversal, then corresponding angles are congruent."
On the fence, lines A and B are parallel and line C is a transversal. How many pairs of corresponding angles are available on the picture to use to prove the theorem? Which given pair of angles can be used?
A) 2 pairs; ∠5 and ∠1;
B) 2 pairs; ∠5 and ∠7;
C) 4 pairs; ∠2 and ∠4
D) 4 pairs; ∠3 and ∠5;
Answer:
Option C. 4 pairs; ∠2 and ∠4
Step-by-step explanation:
we know that
In the figure
[tex]m<6=m<1[/tex] -----> by corresponding angles
[tex]m<3=m<7[/tex] -----> by corresponding angles
[tex]m<5=m<8[/tex] -----> by corresponding angles
[tex]m<2=m<4[/tex] -----> by corresponding angles
therefore
Are available [tex]4[/tex] pairs of corresponding angles
The answer is the option C
(((FIND THE MEASUREMENT INDICATED IN EACH PARALLELOGRAM)))
Help please
Thanks
Answer:
LM=12
V =90
Step-by-step explanation:
4. If it is a parallelogram, the two sides have to be equal.
2x-6 = x+3
Subtract x from each side
2x-x -6 = x+3-x
x-6 =3
Add 6 to each side
x-6+6 = 3+6
x=9
LM =2x-6
= 2*9 -6
= 18-6
= 12
5.
<U + < T = 180 Adjacent corners in a parallelogram are supplementary
11x+2 + 12x-6 = 180
Combine like terms
23x -4 = 180
Add 4 to each side
23x-4+4 = 180+4
23x = 184
Divide by 23
23x/23 = 184/23
x=8
<V = <T Opposite corners in a parallelogram are equal.
<V = 12x-6
<V = 12(8) -6
<V = 96-6
<v =90
The question involves solving algebra and geometry problems related to parallelograms, focusing on transformations, coordinates, and area calculations to find the equation for y.
Explanation:The student is asked to solve a series of algebra and geometry problems related to the properties of a parallelogram. These include finding coordinates, proving algebraic expressions, computing distances, and determining areas. The goal is to find the equation for y given a series of transformations and conditions on a square that becomes a parallelogram. Important concepts include the area of a parallelogram, vector addition using the parallelogram rule, and the determinant relating to a change of basis in vectors.
For example, part (e) involves finding the area of the parallelogram by computing twice the area of triangle PQO, using PQ as the base of the triangle. Solving for y in part (f) by setting this area equal to 1 involves understanding the effects of transformation on geometrical shapes and employing algebra to arrive at the desired equation.
help me!! need help!!!!! 10 minutes due!
Answer:
3
Step-by-step explanation:
The slope is 3 because the equation is y=mx+b. If you add in the terms m=3 and b=0. It is y=3x. M is the slope, so the slope is 3!
Your parents are renting an apartment for you when you go away to college. An annual contract is $502.00/month with a 2-month penalty if you break the lease. The month-to-month contract is $615.00/month. How much is the difference in payments if you stay the whole year?
Answer:
The month-to-month contract will cost an extra $1356.
Step-by-step explanation:
"An annual contract is $502.00/month with a 2-month penalty if you break the lease."
If you stay the whole year, and you pay $502 per month, you pay 12 * $502 = $6024 for the entire year.
"The month-to-month contract is $615.00/month."
If you stay the entire year, you pay 12 * $615 = $7380.
The difference is $7380 - $6024 = $1356
Point M is the midpoint of AB. The coordinates of point A are (-7,2) and the coordinates of M are (-2,2). What are the coordinates of point B?
Answer:
(-9/2,2)
Step-by-step explanation:
Midpoint equals (x1+x2)/2, (y1+y2)/2
Answer:
(-9/2,2)
Step-by-step explanation:
An equation that expresses a mathematical rule or relationship is a ___.
proportion
conversion factor
formula
ratio
Answer:
formula
Step-by-step explanation:
3rd option is correct which is formula.
What is a formula ?
A mathematical relationship or rule which expressed only in symbols and which is the connection between two or more variable.
What is the correct option ?An equation that expresses a mathematical rule or relationship is a formula.
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Harvey the wonder hamster can run 3 1/6 km in 1/4 hour harvey runs at a constant rate what is his average speed in kilometers per hour
Find the value of x such that PQ = QRwhere P, Q and Rare the pints (2, 5), (x, -3) and (7, 9) respectively.
Answer: x = 12.5
Step-by-step explanation:
P = (2, 5)
Q = (x, -3)
R = (7, 9)
[tex]d_{PQ}=d_{QR}[/tex]
[tex]d_{PQ}=\sqrt{(2-x)^2+(5+3)^2}, \quad d_{QR} = \sqrt{(x-7)^2+(-3-9)^2}[/tex]
[tex]\sqrt{(2-x)^2+(5+3)^2} = \sqrt{(x-7)^2+(-3-9)^2}[/tex]
[tex](2-x)^2+(5+3)^2 = (x-7)^2+(-3-9)^2[/tex]
[tex]4-4x+x^2+64 = x^2-14x+49+144[/tex]
[tex]4x+68 = -14x+193[/tex]
[tex]10x+68 = 193[/tex]
[tex]10x= 125[/tex]
x = 12.5
2t + 15 = 40 – 3t please solve
Answer:
t=5
Step-by-step explanation:
Add 3t to the other side to cancel it out
2t+3t+15=40
Subtract 15 to the other side to cancel it out
2t+3t=40-15
Simplify
5t=25
t=5
What is the geometric mean of 5 and 4
Answer:
[tex]2\sqrt{5}[/tex]
Step-by-step explanation:
Geometric mean of two numbers of the square root of their product:
[tex]\sqrt{20}=\sqrt{4\cdot5}=2\sqrt{5}[/tex]
The geometric mean of 5 and 4 is [tex]2\sqrt{5}[/tex].
What is the geometric mean of two numbers?The Geometric mean of the two numbers formula is defined as the square root of the product of 2 numbers.
The following formula is used to calculate the geometric mean;
[tex]\rm Geometric \ mean = \sqrt{a \times b}[/tex]
Where a is the first term and b is the second term.
Therefore,
The geometric mean of 5 and 4 is;
[tex]\rm Geometric \ mean = \sqrt{a \times b}\\\\a=5 \ and \ b=4\\\\\rm Geometric \ mean = \sqrt{5 \times 4}\\\\\rm Geometric \ mean = \sqrt{20}\\\\\rm Geometric \ mean = 2\sqrt{5}[/tex]
Hence, the geometric mean of 5 and 4 is [tex]2\sqrt{5}[/tex].
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Which inequality best represents that ice cream at −3°C is cooler than ice cream at 1°C?
A. −3°C > 1°C
B.−3°C < 1°C
C. 1°C > 3°C
D. 1°C < −3°C
Answer: Choice B
"ice cream at -3 degrees C is cooler than ice cream at 1 degree C"
-3 is smaller than 1
-3 < 1
Keep the order the same even though 1 > -3 is also possible, but fortunately this isn't listed.
These triangles are similar. find Y and X
It these triangles are similar, then the sides of the triangles are in proportion:
[tex]\dfrac{y}{10}=\dfrac{y+4}{15}[/tex] cross multiply
[tex]15y=10(y+4)[/tex] use distributive property
[tex]15y=10y+40[/tex] subtract 10y from both sides
[tex]5y=40[/tex] divide both sides by 5
[tex]\boxed{y=8}[/tex]
[tex]\dfrac{x}{4}=\dfrac{6}{8}[/tex] cross multiply
[tex]8x=(4)(6)[/tex]
[tex]8x=24[/tex] divide both sides by 8
[tex]\boxed{x=3}[/tex]
How do I do this please dumb this down
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept fprm is
y = mx + b ( m is the slope and b the y-intercept )
y = [tex]\frac{5}{4}[/tex] x - 4 is in this form
with m = [tex]\frac{5}{4}[/tex] and b = - 4
Plot the point (0, - 4)
using the slope add 5 to the y-coordinate and 4 to the x-coordinate
(0, - 4 ) → (0 + 4, - 4 + 5) → (4, 1) ← point on the line
Plot the points (0, - 4) and (4, 1) and draw a straight line through them to obtain a sketch of the graph
Jian’s family sells honey from beehives. They collected 3,311 ounces of honey from the beehives this season. They will use the honey to completely fill 4-ounce jars or 6-ounce jars. Jian’s family will sell 4-ounce jars for $5 each or 6-ounce jars for $8 each. Jian says if they use only 4-ounce jars, they could make $4,140 because 3,311 / 4 =827 R3. That rounds up to 828, and 828 multiplied by $5 is $4,140. Part A-Explain the error that Jian made when finding the amount of money his family could make if they use only 4-ounce jars. Enter your explanation in the space provided. Part B- Explain how to determine the money Jian’s family could make if they use only 6-ounce jars. Include the total amount of money and the total number of 6-ounce jars in your explanation. Enter your answers and your explanation in the space provided.
Answer:
A. Jian rounded the number of 4-ounce jars to 828 which is wrong. There are only 827 jars that can be completely filled.
B. Total number of 6-ounce jars = 551
Total money earned from 6-ounce jars = $4408
Step-by-step explanation:
A. Jian's family's collection = 3311 ounces
Number of 4-ounce jars = [tex]\frac{3311}{4}[/tex]
= 827.75
Jian rounded it to 828 which is wrong. There are 827 jars that can be completely filled.
Cost per 4-ounce jar = $5.
Total cost = 827 × 5 = 4135
B. Now, number of 6-ounce jars = [tex]\frac{3311}{6}[/tex]
= 551.83
≅ 551 jars
Cost per 6-ounce jar = $8
Total cost = 551 × 8 = 4408
A jet plane can travel 567 miles per hour. How many mile can it travel in 4hour
Answer: 2268 miles
Step-by-step explanation: 1 hour = 567 miles
4 hours= n miles
multiply 567 miles by four hours
= 2268 miles
Answer:
2304
Step-by-step explanation:
567 x 4
Mr. Geyer dog weighs 32.01 pounds if he goes on a die and loses 5.89 pounds how much will he weigh
Answer: 27.12
Step-by-step explanation:
32.01
-5.89
27.12