Dahlia is simplifying (3 t) Superscript 4 using these steps:
(3 t) Superscript 4 = 3 t times 3 t times 3 t times 3 t = 3 times 3 times 3 times 3 times t times t times t times t
Although Dahlia is correct so far, which step could she have used instead to simplify the expression (3 t) Superscript 4?
(3 t) Superscript 4 = 3 t Superscript 4
3 Superscript 4 Baseline t = 81 t
4 (3 t) = 12 t
3 Superscript 4 Baseline t Superscript 4 Baseline = 81 t Superscript 4
Answer:
D would be the answer
Step-by-step explanation:
Took the test got it correct <33 good luck
A University has three student residences which are located at points (−6, 12) (0,0) (3,9). The University wants to build a tennis court an equal distance from all three residences. Determine the coordinates of the tennis court. What is the distance from a residence to the court to the nearest 10th of a metre? (1unit=40m).
Answer:
a. (-3, 6)
b. 268.3 m
Step-by-step explanation:
a. Determine the coordinates of the tennis court.
Let (x,y) be the coordinates of the tennis court. Since we have equal distances from the tennis court to each residence, we have using the equation for distance between two points (x₁,y₁) and (x₂,y₂), d = √[(y₂ - y₁)² + (x₂ - x₁)²]. Using the first two residences, (-6, 12) and (0,0) as (x₂,y₂) and (x, y) = (x₁,y₁), So,
d = √[(12 - y)² + (-6 - x)²]
d = √[(12 - y)² + (6 + x)²]
d = √[(144 - 24y + y² + 36 + 12x + x²]
d = √x² + y² + 12x - 24y + 180
d² = x² + y² + 12x - 24y + 180 (1)
Also, with (x₂, y₂) = (0,0) we have
d = √[(0 - y)² + (0 - x)²]
d = √[( - y)² + (- x)²]
d = √[y² + x²]
d = √[x² + y²]
d² = x² + y² (2)
Also, with (x₂, y₂) = (3,9) we have
d = √[(9 - y)² + (3 - x)²]
d = √[(81 - 18y + y² + 9 - 6x + x²]
d = √(x² + y² - 6x - 18y + 90)
d² = x² + y² - 6x - 18y + 90 (3)
Substituting (2) into (1), we have
d² = x² + y² + 12x - 24y + 180 (1)
d² = d² + 12x - 24y + 180 (1)
d² - d² = 12x - 24y + 180
12x - 24y + 180 = 0
12x - 24y = -180
dividing through by 12, we have
x - 2y = -15 (4)
Substituting (2) into (3), we have
d² = x² + y² - 6x - 18y + 90 (3)
d² = d² - 6x - 18y + 90 (3)
d² - d² = - 6x - 18y + 90
- 6x - 18y + 90 = 0
- 6x - 18y = -90
dividing through by -6, we have
x + 3y = 15 (5)
Subtracting (5) from (4), we have
x - 2y = -15 (4)
-
x + 3y = 15 (5)
-5y = -30
y = -30/-5
y = 6
substituting y = 6 into (4), we have
x - 2y = -15
x - 2(6) = -15
x - 12 = -15
x = 12 - 15
x = -3
So, the coordinates of the tennis court is (-3, 6)
b. What is the distance from a residence to the court to the nearest 10th of a metre? (1unit=40m).
Using equation (2),
d² = x² + y² (2) where x and y are the coordinates of the tennis court, and x = -3 and y = 6
So,
d² = x² + y²
d² = (-3)² + (6)²
d² = 9 + 36
d² = 45
d = √45 units
Since 1 unit = 40 m,
d = √45 × 40 m
d = 6.708 × 40 m
d = 268.33 m
d ≅ 268.3 m to the nearest tenth of a metre
A triangle has base 8 3/8 feet and height 6 3/4 feet. Find the area of the triangle as a mixed number.
Answer:
First you convert the mixed numbers into improper fraction
[tex]8\frac{3}{8} = \frac{67}{8} \\\\6 \frac{3}{4} = \frac{27}{4}[/tex]
Solution
[tex]A=\frac{\frac{27}{4} + \frac{67}{8} }{2}[/tex]
[tex]A=\frac{\frac{54 + 67}{8} }{2}[/tex]
[tex]A\frac{\frac{121}{8} }{2}[/tex]
[tex]A=\frac{121}{8}[/tex] * [tex]\frac{1}{2}[/tex]
[tex]A= \frac{121}{16}[/tex]
[tex]A= 7 \frac{9}{16}[/tex]
Step-by-step explanation:
Marcus earns $13.00 per hour by walking the neighbor's dogs. He walked the dogs for
four hours. How much money will he have at the end of the day?
Answer:
$52.00
Step-by-step explanation:
if he makes 13.00 per hour, for four hours, you just times 13 by 4 to get 52.
Answer:
52
Step-by-step explanation:
Multiply 13 and 4 to get $52.
The triangles below are similar. Find the measure of ∠B and ∠F
Answer:
∠ B = 45°, ∠ F = 22°
Step-by-step explanation:
Since the triangles are similar then corresponding angles are congruent, so
∠ B = ∠ E = 45°
∠ F = ∠ C = 22°
tina works 15 hours a week (monday to friday). last week she worked 3 1/2 hours on monday, 4 hours on tuesday, 2 1/6 hours on wednesday and 1 1/2 on thursday. how many hours did she works on fridays
Answer:
Tina worked [tex]3 \frac{5}{6}[/tex] hours on Friday.
Step-by-step explanation:
To solve for how many hours Tina worked on Friday you have to add up all the hours worked then subtract that from 15 hours to get the remainder.
Step 1 : Add up all the hours worked so far.
[tex]3\frac{1}{2}[/tex] + 4 + [tex]2\frac{1}{6}[/tex] + [tex]1\frac{1}{2}[/tex] = ?
We need to turn these mixed numbers into improper fractions first so we can add. Let's turn them all into sixths.
[tex]3 \frac{3}{6}[/tex] + 4 + [tex]2\frac{1}{6}[/tex] + [tex]1 \frac{3}{6}[/tex] = [tex]11\frac{1}{6}[/tex]
Allright, so now we know that Tina already worked 11 and 1/6 hours already, so we subtract that from 15 to find how many hours she worked on Friday.
Step 2 : Subtract [tex]11\frac{1}{6}[/tex] from 15.
15 - [tex]11\frac{1}{6}[/tex] = [tex]3 \frac{5}{6}[/tex]
Therefore Tina worked [tex]3 \frac{5}{6}[/tex] hours on Friday.
Hope this helps, please mark brainliest if possible. Have a great day.
Leo will create a mural consisting of five
vertical stripes of different colors. If Leo has
eight different colors from which to choose,
and the order of the stripes matter, in how
many ways can he complete his mural?
Answer:
he got 8 different colors to choose from for the first stripe. he has to choose from 7 for the second (one choose less bc he alrdy took one color)
that alone makes 56 different ways for just two stripes.
he will use 5 stripes in total, so the calculation is:
8*7*6*5*4 = 6720
(8!-3! would also work with the calculator 8! uses all the naturalnumbersfrom 1 to 8 and multiplies them)
Which of the following is equal to √16x4?
A. 32 B. 64 C. √16/4 D. √16•√4
Given :-
√16 × 4 .To Find :-
The value of the expression .Answer :-
We know that , if ,
=> √{ab}
It can be written as ,
=> √a × √b ,
Therefore ,
=> √{ 16 × 4 }
=> √16 × √4
Option D is correct !
Steven earns extra money babysitting. He charges $31.25 for 5 hours and $43.75 for 7 hours.
.
Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and
y represent the amount he charges.
The equation is y =?
Given:
Steven charges $31.25 for 5 hours and $43.75 for 7 hours.
To find:
The equation that represents the relationship.
Solution:
Let x represent the number of hours Steven babysits and y represent the amount he charges.
Then the two points on the function are (5,31.25) and (7,43.75). So, the equation of the line that passes through these two points is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-31.25=\dfrac{43.75-31.25}{7-5}(x-5)[/tex]
[tex]y-31.25=\dfrac{12.5}{2}(x-5)[/tex]
[tex]y-31.25=6.25(x-5)[/tex]
On further simplification, we get
[tex]y-31.25=6.25(x)-6.25(5)[/tex]
[tex]y-31.25=6.25x-31.25[/tex]
[tex]y=6.25x-31.25+31.25[/tex]
[tex]y=6.25x[/tex]
Therefore, the required equation for the given situation is [tex]y=6.25x[/tex].
what is the anser for 194*33333
(the answer is) = 6466602
franklin races bikes. in his city there are 4 lengths of race tracks. The chart shows the race tracks and each tracks length in miles
A. 1/4
B. 3/2
C. 1 3/4
D. 4/4
Franklin races 3 laps in the same lane. the total distance he raced is more than 4 1/2miles
which track does franklin race on?
Answer:
Step-by-step explanation:
1/4
Which function represents the graph below?
Answer:
answer is A. you can see each intervals slowly to know this
If j + m=5, what is the value of 50j + m)?
Answer:250
Step-by-step explanation:
j+m=5
50(j+m)=50x5=250
Answer:
If you mean 5(j + m) and j + m = 5 then you answer is 6j + 6m = 5.
If you mean 50j + m and j + m = 5 then there is no solution.
Step-by-step explanation:
j + m = 5
5(j + m)
5(j + m) + j + m = 5
5j + 5m + j + m
6j + 6m = 5
What is the measure of an angle if it is fourteen times its own complement?
Answer:
Let the measure of the complementary angle be x so that the measure of the other angle is 14x. The total measure of the angles is 180 degrees.
What is the solution to the equation 3(x - 1) – 2(2x + 1) = 8(x - 1)?
A 21-inch rope is to be cut into two pleces so that one piece is 8 inches longer than twice the other. How long is each piece, if a=2, b= 8, and I=21
smaller plece
in
larger plece
Answer:
4 1/3 inches Smaller piece
16 2/3 inches Larger piece
Step-by-step explanation:
x + (2x + 8) = 21
3x + 8 = 21
3x = 13
x = 13/3
x = 4 1/3 inches Smaller piece
2x + 8 = 8 2/3 + 8
2x + 8 = 16 2/3 inches Larger piece
Lisa uses 2 pieces of copper wire, each 9 feet long, for
each robot she builds. If she started with a 500-yard roll
of copper wire, which of the following represents the
number of yards of wire left on the roll after 'Lisa built r
robots? (3 feet = 1 yard)
Answer:
yards of wire left on the roll = 500 - r(3)
Step-by-step explanation:
9 feet = 3 yards we need to find how much wire is left on the roll after she builds a certain amount of robots. she uses 9 feet or 3 yards per robot so we have to multiply the amount of robots (r) by 3 yards and subtract that from 500 yards or the total amount of wire she has and that gives us the total amount of wire she has left. Hope this helps.
Find the distance between the line segment with end points (-3,5) and (1,5)
Answer:
[tex]\displaystyle d = 4[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Identify
Point (-3, 5)
Point (1, 5)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(1- -3)^2+(5- 5)^2}[/tex][√Radical] (Parenthesis) Subtract: [tex]\displaystyle d = \sqrt{4^2+0^2}[/tex][√Radical] Simplify: [tex]\displaystyle d = \sqrt{4^2}[/tex][√Radical] Evaluate: [tex]\displaystyle d = 4[/tex]For which equations does the fraction 13 make the equation true? A 6x __=3 B 6x__=2 C 7x__=7/21 D 8x__=3 1/3
Answer:
B. 6 x 1/3 = 2
Step-by-step explanation:
2 is 1/3 of 6
So multiplying 6/1 (6) bu 1/3 :
6/1 * 1/3 = 6 / 3 = 2
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
draw the image of triangle ABC after a translation along vector v
(just saying the points' ordered pairs is fine :) )
Answer:
[tex]A'=(1, 9), \\B'=(6,9),\\C'=(1,4)[/tex]
Step-by-step explanation:
Notice how [tex]\vec{v}[/tex] has a tail at (8,4) and a head at (2,2), which means the x-coordinate is translated 6 units to the left and the y-coordinate is translated 2 units down.
If [tex]\triangle ABC[/tex] were to be translated along this vector, its vertices should follow the vector.
Therefore, the new points of [tex]\triangle ABC[/tex] will be 6 units to the left of their initial x-coordinate and 2 units below their initial y-coordinate.
[tex]A(7, 11)\implies A'(1, 9), \\B(12, 11)\implies B'(6, 9), \\C(7, 6)\implies C'(1, 4)[/tex]
i keep getting this Q wrong can someone help me solve it :)
Answer:
Can I have your points because you stole it
my precious points
your answer is helpless
PLEASE HELP ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPp
Answer:
M1=44 M2=136 M3=44 M4=136
Step-by-step explanation:
M3= 44 so M1=44 due to opposite angles being equal
then if two of the angles add to 88
360-88= 272
divide 272 by 2 as M2 and M4 are equal
272/2=136
Answer:
m∠1 = 44°
m∠2 = 136°
m∠4 = 136°
Step-by-step explanation:
m∠1 explanation:
I got it from m∠3 since they're both congruent
m∠2 explanation:
Since we already have the measure of 3 and 1, we can easily add both of the measures (44 + 44 = 88°) then subtract it from 360° (total) = 272°
Then since both measures (2 and 4) are congruent (measuring the exact same length and angle) we can divide 272° ÷ 2 = 136°
m∠4 explanation:
I got it from m∠2 since they're both congruent
Which expressions are equivalent to the on below select all that apply 9x
Answer:
B and D
Step-by-step explanation:
Multiplying exponents just adds them.
Answer:
B + D
Step-by-step explanation:
Two sides of a triangle have lengths 4 and 7. Which of the following can NOT be the length of the third side?
Answer:
3 < x < 11
Step-by-step explanation:
triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side
if 'x' is the third side then:
x + 4 > 7
7 + 4 > x
therefore, 'x' must be greater than 3 and less than 11
The value of the third side should be < 11 so, it cannot be 11, the correct option is C.
What is a Triangle?A triangle is a polygon with three sides, three vertices and three angles.
The two sides of a triangle are 4 and 7
According to the property of sides of a triangle, The measure of the third side of a triangle is always less than the sum of the two sides.
The sum of the sides is 4+7 = 11
Let the third side be x
then,
x < 11
The x cannot be 11.
The missing options are
A. 4
B. 7
C. 11
D. 5
To know more about Triangle
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Tilly and her mom made a rectangular dog run. They used 26 one-yard long pieces of fencing. They put 6 pieces of fencing on one side. How many pieces did they put on the next side?
Write a function to describe the following scenario.
The temperature of a hot steak starts at 140° F and decreases at 5° F per minute. What will the temperature be of this steak after a certain number of minutes?
y= ? - ?x
Answer:
Below.
Step-by-step explanation:
Temperature after 1 minute = 140 - 5(1)
Temperature after 2 minutes = 140 - 5(2)
Temperature after 3 minutes = 140 - 5(3),
- and so on.
So the function is
y = 140 - 5x.
The temperature of the steak after a certain number of minutes can be described as the function
y = 140 - 5x
What is a linear equation?A linear equation with one variable has the standard form Cx + D = 0. In this case, the variable is x and C are coefficient, while D is a constant.
How to solve this problem?Let the certain number of minute is x.
Since the temperature decreases at 5° F per minute, then after x minutes, it will decrease 5x.
Initial temperature = 140° F
Then the present temperature, y = 140 - 5x.
Therefore, the temperature of the steak after a certain number of minutes can be described as the function
y = 140 - 5x
Learn more about temperature here -
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Simplify the expression below. (x^5)(x^2)
A. x^2
B. x^5
C. x^7
D. x^10
[tex]\longrightarrow{\green{C.\: {x}^{7}}}[/tex]
Step-by-step explanation:
[tex]( {x}^{5} )( {x}^{2} ) \\\\ = {x}^{5 + 2} \\\\ = {x}^{7} \\\\ (∵ {a}^{m} \times {a}^{n} = {a}^{m + n} )[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]
A 4.5 m long pipe rests against a 2 m high
tank. One end of the pipe is on the ground
3 m from the base of the tank. How much
of the pipe overhangs the tank?
4.5 m
Bm
3 m
help me please lol
Answer:
0.89 m is the answer
Step-by-step explanation:
the wall, the ground and portion of pipe form a right angle triangle with pipe portion being the hypotenuse.
for a right triangle
[tex]{hypotenuse}^{2} = {base}^{2} + {height}^{2} [/tex]
here we have base = 3m and height = 2m.
thus
[tex] {h}^{2} = {3}^{2} + {2 }^{2} \\ = 9 + 4 \\ = 13 \\ h = \sqrt{13} [/tex]
portion of pipe overhanging = 4.5 - sqrt (13)
= 4.5 - 3.61
= 0.89 m
Leeza is making labels in the shape of parallelograms each label has an area of 18 square centimeters and a base of 6 centimeters. What is the height of each labe
Answer:
3cm
Step-by-step explanation:
A parallelogram is quadrilateral that has two pairs of parallel sides. The opposite sides equal in length
Area of a parallelogram = base x height
18cm² = 6cm x height
height = 18cm² / 6cm = 3cm
HELP HELP HELP TODAY IS THE DEADLINE
C, 3 units translated to the left due to the +3 inside the bracket, vertically reflected on the x-axis as it is negative outside the bracket and translation 1 unit up because of the +1 outside the brackets.