The correct option that defines repeating decimals correctly is Option B;
a decimal that has a recurring sequence of numbers that follow a pattern.
What is a Repeating Decimal?A repeating decimal is also called a recurring decimal and it is a decimal representation of a number whose digits are periodic and the infinitely repeated portion is not zero.
From the above definition, it means that the correct option that defines repeating decimals correctly is Option B.
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A square is drawn below.
What is the value of x?
(2x + 15)°
(6x-45°) .
Answer:
2x+15 =6x-45 [Alternate Angles]
or, 15+45 =6x-2x
or, 60 =4x
or 60/4 =x
or 15 = x
# x=15
What is the Length of CG
Answer: 32
Step-by-step explanation:
Since [tex]\overline{FG} \parallel \overline{AC}[/tex], we know that by the corresponding angles theorem, [tex]\angle BFG \cong \angle BAC[/tex] and [tex]\angle BGF \cong \angle BCA[/tex].
Thus, [tex]\triangle BFG \sim \triangle BAC[/tex] by AA.
It follows that since corresponding sides of similar triangles are proportional,
[tex]\frac{36+90}{90}=\frac{CG+80}{80}\\ \\\frac{126}{90}=\frac{CG+80}{80}\\\left(\frac{126}{90} \right)(80)=CG+80\\112=CG+80\\CG=\boxed{32}[/tex]
Question 2 Determine if (x-3) is a factor to the polynomial P(x) = 2x³ +5x²-28x - 15. (3 marks)
Answer:
(x - 3) is a factor of P(x)
Step-by-step explanation:
if (x - 3) is a factor of P(x) then P(3) = 0
P(3) = 2(3)³ + 5(3)² - 28(3) - 15
= 2(27) + 5(9) - 84 - 15
= 54 + 45 - 99
= 99 - 99
= 0
since P(3) = 0 then (x - 3) is a factor of P(x)
A scale model of a building is 3 inches tall. If the building is 90 feet tall, find the scale of the model.
The scale model of a building 3 inches tall if the building is 90 feet tall is 2:5
Scaling of measurementScaling is the way of enlarging or reducing the image of an object.
Given scale model of a building is 3 inches, if the building is 90feet tall, to write the scale;
Convert both measures to same units
Since 1 feet. = 12 in
90 feet = 90/12 in = 7.5 in
Take the ratio
3 : 7.5 = 30: 75
Reduce to lowest term
30: 75 = 2 : 5
Hence the scale model of a building 3 inches tall if the building is 90 feet tall is 2:5
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|2/13t-11|-10=-16
solve for t
[tex]\left|\dfrac{2}{13}t-11\right|-10=-16\\\\\left|\dfrac{2}{13}t-11\right|=-6\\\\x\in\emptyset[/tex]
A motorboat travels 464 kilometers in 8 hours going upstream and 644 kilometers in 7 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Rate of boat in still water ______km/h
Rate of current: _______ km/h
Let's say you are paddling at 5mph and the current is 3 mph. Going upstream, you are going 2 mph and downstream, 8 mph.
8(b - c) = 464
7(b + c) = 644
b - c = 58
b + c = 92
Adding the two together
2b = 150
b = 75
75 - c = 58
c = 17
The boat's speed is 75 mph and the current's speed is 17 mph.
A rectangular prism has a length of 7 m, a height of 5 m, and a volume of 140 m3. What is the width?
Which steps are correct? Check all that apply.
Substitute the known values into the formula:
140 = 7(w)(5).
Substitute the known values into the formula:
7 = 140(w)(5).
Substitute the known values into the formula:
5 = 7(w)(140).
Solve for the unknown: w = 4 m.
Solve for the unknown: w = 7 m.
Solve for the unknown: w = 2 m.
The question is incomplete because it was not properly and correctly arranged
Complete Question:
A rectangular prism has a length of 7 m, a height of 5 m, and a volume of 140 m³. What is the width? A prism has a length of 7 meters, width of w, and height of 5 meters.
Which steps are correct? Check all that apply.
a) Substitute the known values into the formula: 140 = 7(w)(5).
b) Substitute the known values into the formula: 7 = 140(w)(5).
c) Substitute the known values into the formula: 5 = 7(w)(140).
d) Solve for the unknown: w = 4 m.
e) Solve for the unknown: w = 7 m.
f) Solve for the unknown: w = 2 m.
Answer:
a) Substitute the known values into the formula: 140 = 7(w)(5).
d) Solve for the unknown: w = 4 m.
Step-by-step explanation:
The steps that are correct are Options a) and d). This is because:
Step 1
The volume of a rectangular prism is calculated as:
Volume of a rectangular prism = Length (l) × Width(w) × Height(h)
The unit of the volume or a rectangular prism is in cubic metres (m³)
In the question, we are asked to find the unknown value which is the width and we were given the following known values:
Length = 7 m,
Height = 5 m
Volume = 140 m³
Step 2
Solve for the unknown value( Width)
Volume of a rectangular prism = Length (L) × Width(W) × Height(H)
140m³ = 7m × Width(m) × 5m
140m³ = 35m² × Width(m)
Width(w) = 140m³ ÷ 35m²
Width(w) = 4m
Hence, the unknown Width(w) = 4m
From the above explanation we can see that the correct steps is Option a) and Option d)
Answer:
Step-by-step explanation:
Volume of rectangular prism= Length x width x height
V=L x W x H
140=7 x W x 5
140= 35 x w
W= 140/35
W= 4
help asap please
Which of the points shown below are on the line given by the equation y = x + 4? Check all that apply
A) -1, 3
B) 2, 6
C) -2, -2
D) 2, 4
The points on the line are points B and D
How to determine the points on the line?The equation is given as:
y = x + 4
The above means that the output value is 4 more than the input value
Using the above rule, the points that satisfy the equation are:
B) 2, 6 and D) 2, 4
This is so because:
6 = 2 + 4
4 = 2 + 2
Hence, the points on the line are points B and D
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a) What is the population of interest? Approximately, how many people are in the population of interest? (Recall, the definition of a population is: The collection of all outcomes, responses, measurements, or counts that are of interest.)
b) What is the best data collection method to use for the study (explain)? (Recall, data collection methods are: Observation, Survey, Experiment, Simulation).
c) For one of the three studies, a census is possible. Determine which one and then explain why a census is possible for that study and is not possible for the other two studies. (A census means that we are able to collect data from every unit in the population. Most of the time the population is too large for a census to be feasible)
d) For the two studies where a census is not possible, how many people, students, or cars would you sample out of the population? What sampling technique would you use (see section 1.3)? (Explain your reasoning)
The What is the population of interest are:
GMC students People who own Cars in Macon, GA.People who eat oatmeal in Georgia.The data collection method according to the group below
SurveySurveyExperiment What is the statistical studies about?The best data collection method for the first one oatmeal and GMC students is survey because the population is large and opinions may differ.
The best data collection method for the cars is Experiment as one needs to study the cars that pass the red lights
For one of the three studies, a census is possible in the first one because the study population is the Georgia which is very large.
For the two studies the one that a census is not needed is GMC students and cars at red light because the population is not too big.
Based on the study I will use 500 people, 200 students, or 300 cars and the sampling technique would be Systematic sampling, Simple random sampling and Judgmental/purposive sampling.
A Simple random sampling is known to be the easiest method of selecting a sample as every member is known to have an equal chance of being selected in the sample.
See the other part of the question below
Write a reply
Consider the following statistical studies:
1. A study (in Georgia) of the effect of eating oatmeal on lowering cholesterol.
2. A study of current GMC students next career move after graduating or transferring from GMC.
3. A study of how many cars run the red light at a certain intersection in Macon, GA.
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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:
Eleanor is working her way through school. She works two part-time jobs for a total of 24 hours a week. Job A pays $5.80 per hour, and Job B pays
$7.40 per hour. How many hours did she work at each job the week that she made $158.40.
Step-by-step explanation:
a = hours at job A
b = hours at job B
a + b = 24
a = 24 - b
5.8a + 7.4b = 158.4
note we can use the a = 24 - b identity in the second equation :
5.8×(24 - b) + 7.4b = 158.4
139.2 - 5.8b + 7.4b = 158.4
1.6b = 19.2
b = 12 hours
a = 24 - b = 24 - 12 = 12 hours
she worked 12 hours on job A and 12 hours on job B.
The sum of two polynomials is 8d5 – 3c3d2 + 5c2d3 – 4cd4 + 9. If one addend is 2d5 – c3d2 + 8cd4 + 1, what is the other addend?
6d5 – 2c3d2 + 5c2d3 – 12cd4 + 8
6d5 – 4c3d2 + 3c2d3 – 4cd4 + 8
6d5 – 4c3d2 + 5c2d3 – 12cd4 + 8
6d5 – 2c3d2 – 3c2d3 – 4cd4 + 8
By subtracting the given addend to the sum, we see that the other addend is:
[tex]6d^5 - 2c^3d^2 + 5c^2d^3 - 12cd^4 - 8[/tex]
How to get the other addend?
We know that the sum of two polynomials is:
[tex]8d^5 - 3c^3d^2 + 5c^2d^3 - 4cd^4 + 9[/tex]
One of the addends is:
[tex]2d^5 - c^3d^2 + 8cd^4 + 1[/tex]
To get the other addend, we can subtract the given addend to the sum:
[tex]8d^5 - 3c^3d^2 + 5c^2d^3 - 4cd^4 + 9 - (2d^5 - c^3d^2 + 8cd^4 + 1)\\\\6d^5 - 2c^3d^2 + 5c^2d^3 - 12cd^4 - 8[/tex]
Then we can conclude that the other addend is:
[tex]6d^5 - 2c^3d^2 + 5c^2d^3 - 12cd^4 - 8[/tex]
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√y18
please solve this one for me with explication
Answer: [tex]y^9[/tex]
This is the same as saying y^9
===================================================
Explanation:
When we apply the square root to the expression [tex]a^{2b}[/tex], we end up with [tex]a^b[/tex]
[tex]\sqrt{a^{2b}} = a^b[/tex]
The exponent 2b divides in half to get b
Based on that rule, we can then say:
[tex]\sqrt{y^{18}} = y^{18/2} = y^9[/tex]
Suppose a normal distribution has a mean of 38 and a standard deviation of 2. What is the probability that a data value is between 36 and 43? Round your answer to the nearest tenth of a percent.
Answer:
[tex]P(36 < X < 43)\approx83.5\%[/tex]
Step-by-step explanation:
Use a TI-84 to calculate the probability
[tex]P(\text{Lower} < X < \text{Upper})=\text{normalcdf}(\text{Lower},\text{Upper},\mu,\sigma)\\\\P(36 < X < 43)=\text{normalcdf}(36,43,38,2)\approx0.8351\approx83.5\%[/tex]
What value correctly fills in the blank so that the expressions are equivalent?
18+45 = x (2+5)
A 2
B O3
C 07
D 9
Answer:
D, x = 9
Step-by-step explanation:
[tex]x\left(2+5\right)=63[/tex]
=> divide both side by 7
[tex]\frac{x\left(2+5\right)}{7}=\frac{63}{7}[/tex]
x=9
Answer:
D) 9
Step-by-step explanation:
Given :
⇒ 18 + 45 = x (2 + 5)
=============================================================
Simplify both sides :
⇒ 18 + 45 = x (2 + 5)
⇒ 63 = 7x
⇒ 7x = 63
=============================================================
Divide both sides by 7 :
⇒ 7x/7 = 63/7
⇒ x = 9
Line segment AB with endpoints A (5, 8) and B (7, 8) is translated 2 units down and 2
units left. Identify the coordinates of the endpoints of the translated line segment?
A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of objects. The coordinates of the translated line segment will be A' (3,6) and B' (5,6).
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
Since AB is a line segment the changes will occur on both the coordinates, therefore, if the line segment is translated 2 units down and 2 units left, the coordinates will be,
A = (5,8) → 2 units down ⇒ (5, 8-2) → 2 units left ⇒ (5-2, 8-2) = (3, 6)
B = (7,8) → 2 units down ⇒ (7, 8-2) → 2 units left ⇒ (7-2, 8-2) = (5, 6)
Hence, the coordinates of the translated line segment will be A' (3,6) and B' (5,6).
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what would be the answer to this ?
Solve. 5x=15
Interpretation 1:
[tex]5x = 15 \\ [/tex]
Divide both sides by 5:
[tex]\implies \boxed{x = 3}[/tex]
(Which is the final answer.)
[tex]\huge\mathfrak\colorbox{white}{}[/tex]
Interpretation 2:
[tex] 5^{x}=15[/tex]
Take logarithm to the base 5 on both sides:
[tex]\implies log_5(5^{x})=log_5(15)\\\implies x=log_5 (15) \\\implies x= \frac{ln(15)}{ln(5)} \\\implies \boxed{x≈1.683} [/tex]
(Which is a thing too!)
[tex]\huge\mathfrak\colorbox{white}{}[/tex]
P. S.: Now please don't tell me that this is a PhD level question and this is referring to the Knuth's Up-Arrow Notation. Which translates the question into something like: [tex]^{5}x=15[/tex]
Answer:
x = 3Step-by-step explanation:
what would be the answer to this ?
Solve.
5x=15
x = 15 : 5
x = 3
--------------
check
5 * 3 = 15
the answer is good
The cost of a ticket to the circus is $22.00 for children and $46.00 for adults. On a certain day, attendance at the circus was 1,400 and the total gate revenue was $52,400. How many children and how many adults bought tickets?
The number of children and adults who bought the tickets at the circus was 500 and 900 respectively.
How to write and solve equation?let
x = number of childreny = number of adultsx + y = 1400
22x + 46y = 52,400
From equation (1)
x = 1400 - y
Substitute into (2)
22(1400 - y) + 46y = 52,400
30,800 - 22y + 46y = 52,400
- 22y + 46y = 52,400 - 30,800
24y = 21,600
y = 21,600 / 24
y = 900
substitute y into
x + y = 1400
x + 900 = 1400
x = 1400 - 900
x = 500
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The number of children's ticket that was bought is 500.
The number of adult's ticket that was bought is 900.
What is the linear equation that represents the question?a + b = 1400 equation 1
22a + 46b = 52,400 equation 2
Where:
a - number of children's ticket b = number of adult's ticketWhat is the number of adult's ticket?Multiply equation 1 by 22
22a + 22b = 30800 equation 3
Subtract equation 3 from equation 2
21,600 = 24b
b = 21,600 / 24
b = 900
What is the number of children's ticket?Subtract 900 from 1400
1400 - 900 = 500
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The total area of town C and town D is 120,000 square miles. The area of town C is 30,000 square miles more than that of town D. Find the area land of each town.
Answer:
Find the area land of each town.
Let x be the area of town D
then, x+ 30000 is the area of town C
we know that,
the total area of town C and town D is 120,000 square miles.
x+x+30000=120000
2x= 90000
x=45000
Area of town D= 45000 square miles
Area of town C= 45000+30000= 75000 square miles.
Choose two number sentences below that equal 39:
A) 71 - 32
B) 49 - 20
C) 85 - 46
D) 50 - 29
Which is an x-intercept of the continuous function in the table ? (0, - 6); (3, 0); (- 6, 0) O (0, 3)
An x-intercept of the continuous function in the table is (-1, 0)
Intercept of a lineThe x-intercept of a line is the point where the line crossed the x-axis or the point where the value of y is zero.
From the table, the x-intercept are all the point where the value of f(x) is zero. Hence the Which is an x-intercept of the continuous function in the table is (-1, 0)
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find the midpoint of the line segment between the points (11, -5) and (-3, -7)
Answer:
(4, -6)
Step-by-step explanation:
(x1+x2)/2 + (y1+y2)/2 = midpoint
(11+-3)/2 = 8/2 = 4. x = 4
(-5 + -7)/2 = -12/2. y = -6
4, -6 is the midpoint
give brainliest please! hope this helps :)
Given u = −8i − 3j and v = −12i − 7j, what is projvu?
−4.845i − 1.819j
−7.275i − 4.244j
−7.886i − 2.957j
−11.828i − 6.900j
Answer:
(b) -7.275i -4.244j
Step-by-step explanation:
The projection of vector u onto vector v is the product of the unit vector v, the magnitude of vector u, and the cosine of the angle between them.
__
The dot product gives the product of the magnitudes of the two vectors and the cosine of the angle between them. To find the projection, we must divide the dot product by the magnitude of v and multiply by the unit vector in the direction of v.
[tex]proj(u,v)=(\vec{u}\cdot\vec{v})\cdot\dfrac{\vec{v}}{|\vec{v}|^2}=\dfrac{((-8)(-12)+(-3)(-7))(-12\vec{i}-7\vec{j})}{(-12)^2+(-7)^2}\\\\=\dfrac{-(96+21)(12\vec{i}+7\vec{j})}{144+49}=-\dfrac{117}{193}(12\vec{i}+7\vec{j})\approx\boxed{-7.275\vec{i}-4.244\vec{j}}[/tex]
if the volume of a cube is 27cm³ what are the dimensions of the cube
Answer:
3 cmStep-by-step explanation:
if the volume of a cube is 27cm³ what are the dimensions of the cube
Cube Volume = l³
we use the inverse formula
∛V = l
so
∛27 =
3 cm
Graph the function y = 4x4 – 8x2 + 4. Which lists all of the turning points of the graph?
(0, 4)
(–1, 0) and (1, 0)
(–1, 0), (0, 4), and (1, 0)
(–4, 0), (–1, 0), (0, 4), and (1, 0)
A function assigns the values. The correct option is C.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
If we plot the function, y = 4x⁴ - 8x² + 4, then it can be observed that the lists all of the turning points of the graphs are (–1, 0), (0, 4), and (1, 0).
Hence, the correct option is C.
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The sides of a triangle measure 10 feet, 13 feet, and 17 feet.
How would you explain to a friend that the triangle is not a right triangle?
Step-by-step explanation:
if the squares of the two shorter sides add up to the square of the hypotenuse, the triangle contains a right angle
bbc
10 squared = 100
13 squared = 169
17 squared = 289
100 + 169 = 269 NOT 289 so
there is no right angle and so its not a right triangle
A rain drop hitting a lake makes a circular ripple.. if the radius, in inches,, grows as a function of time in minutes according to R(t)=20sqrt(t+2), find the area of the ripple as a function of time. What is the area of the circular ripple at t=2?
Answer:
Step-by-step explanation:
Area A(t) = πR² = π x 400 (t + 2) = 400π (t + 2)
A(2) = 400π (2 + 2) = 1600π = 5026.5 in²
Simplify 5/8+9/2+(-4/5)+7/8+(-5/2)+7/5
please answer
Help me plsss helpppppppppp
Step-by-step explanation:
this is very easy u can do urself
how to find the value of x and z
Answer:
z = 86 °
and, x = 2
Step-by-step explanation:
We know that a straight line is a 180 degree-angle. So, we know that
94 + z must equal 180, because they are the only two angles that make up the straight line.
from this information, (that 94 + z = 180) we can easily find z.
(this is typically an intuitive method of subtracting 94 from 180)
94 + z = 180
-94 -94
z = 86 °
-- we know that the relation between z and (10x + 74) must also be equal to 180, as they make up a straight line
if z = 86, then we can know that (10x + 74) must be equal to
(10x + 74) + 86 = 180
- 86 -86
(10x + 74) = 94
10x + 74 = 94
- 74 - 74
10 x = 20
÷ 10 ÷ 10
x = 2
so, z = 86 °
and, x = 2
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