Answer:
-7/3
Step-by-step explanation:
-7 2/3=-23/3
5 1/3=16/3
-----------------
16/3+(-23/3)
16/3-23/3
-7/3
Final answer:
To express 5 1/3 plus (-7 2/3), separate and add the integers to get -2, then add the fractions to find -1/3, resulting in the final expression -2 1/3.
Explanation:
To express the sum of 5 1/3 and (-7 2/3) as the sum of its integer and fractional parts, we need to perform the following steps:
First, separate the integers from the fractions: 5 + 1/3 and -7 + (-2/3).Now, add the integers: 5 + -7 = -2.Next, add the fractions: 1/3 + (-2/3). Recall that subtracting a negative is the same as adding a positive, so this becomes 1/3 - 2/3 = -1/3.Combine the integer and fractional results to get the final expression: -2 1/3.Our intuition about addition and subtraction of fractions can be helpful in visualizing the mixing of different pie pieces to form a whole, and understanding how changing the sign affects the direction of the operation.
If there are 5 apples and you take away 3. How many apples do you have?
Answer:
2
Step-by-step explanation:
ling pedaled hard.she traveled 80 km in 2.5 hours.what was her average speed in km per hour?
36km per hour
Step-by-step explanation:
If Charlie has a total of 103 marbles how many of each size does he have
four times the area of the curved surface of a cylinder is equal to 6 times the sum of the areas of its bases. if its height is 12 cm find its curved surface area
Answer:
Step-by-step explanation:
Curved surface Area = 2πrh
Area of its bases = 2πr²
6* Area of its bases = 4 * Curved surface Area
6 * 2πr² = 4 *2πrh
r² / r = 4 * 2* π*12 / 6 * 2 * π { substituting h =12 cm}
r = 4*2
r = 8 cm
Curved surface Area = 2πrh
= 2 * 3.14 * 12 * 8
= 602.88 Sq. cm
Answer:
603.42
Step-by-step explanation:
Curved Surface Area = 2πrh sq.cm
Area of the base = πr² sq. cm
Sum area of the base = πr² + πr² = 2πr² sq.cm
A.T.Q
4(2πrh) = 6x2πr²
8πrh = 12πr²
2h = 3r
r = 8 cm
Curved Surface Area = 2πrh
2x22/7x8x12
4224/7
603.42
People at the state fair were surveyed about which type of
lemonade they preferred. The results are shown below.
Pink lemonade: 156 males, 72 females
Yellow lemonade: 104 males, 48 females
Answer:
Step-by-step explanation:
You would require the table with the number of males and females who prefer either pink or yellow lemonade at the state fair.
Pink Lemonade Yellow Lemonade TOTAL
Male 156 104 260
Female 72 48 120
TOTAL 228 152 380
P(pink lemonade | female) = 72 / (48 + 72) = 72 / 120 = 0.6
P(pink lemonade) = (156 + 72) / (156 + 72 + 104 + 48) = 228 / 380 = 0.6
Therefore, The event "prefers pink lemonade" and "female" are independent because P(pink lemonade | female) = P(pink lemonade) = 0.6
Answer:
P(pink lemonade | female) = P(pink lemonade) = 0.6.
Step-by-step explanation:
y =( x + 3) 2 - 1 identify the vertex
Answer:
Step-by-step explanation:
The vertex is of the form (h, k). The general equation of a quadratic in vertex form is
[tex]y=(x-h)^2+k[/tex]
where h is the x coordinate of the vertex and k is the y coordinate of the vertex. The important thing to remember is that the "x -" part of the formula is constant, it doesn't change. So if our expression inside the parenthesis is
(x + 3), it is understood to be (x - (-3)) which indicates movement to the left. The "+ k" part is not taken literally. If we have a + 2 at the end of our equation we are moving up 2; if we have a -1 at the end, we are moving down 1. Our vertex then is located at (-3, -1)
Henry, Brian and Colin share some sweets in the ratio 4:5:4. Henry gets 56 sweets. How many more sweets does Brian get over Colin?
Both Henry and Colin have a ratio of 4, so Colin gets the same amount as Henry, so we know Colin has 56.
Brian's ratio is 5, so for every 4 Colin gets, brian gets 5 ( 1 more).
Divide Colin's quantity by 4 :
56/4 = 14
Brain gets 14 more.
If someone has 16 dollars left bus used 3/7 of it how much money did they have
Answer:
$37.33 dollars
Step-by-step explanation:
16 x 7/3= 112/3
d=37.33
based on the graph, what would be the slope for the line of best fit of scatter plot? A. 0 B. 1/2 C. 1 D.1 1/2 E. 2
Answer:
c
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
rise over run 4/4=1
is (-7,2), (4,-6), (2,-2), (-3,9), (0,11), (4,0) a function
PLEASE MARK BRAINLIEST!
Answer:
Yes, because there are no repeated input values.
Step-by-step explanation:
*This would not be a function IF any input value (x-value) was repeated. In functions, x-values CANNOT be repeated, but y-values CAN be repeated.
I hope this helps!
- sincerelynini
A certain region currently has wind farms capable of generating a total of 2200 megawatts (2.2 gigawatts) of power. Assuming wind farms can generate 25% of their capacity, how much energy, in kilowatt-hours, can the region's wind farm generate in one year?
Given that the average household in the region uses about 10,000 kilowatt-hours of energy each year, how many households can be powered by these wind farms?
Answer:
The correct answer is A. 4,818'000,000 kilowatt-hours per year and B. 481,800 households.
Step-by-step explanation:
1. Let's review the information provided to us for solving the questions:
Power capacity of the wind farms = 2,200 Megawatts or 2.2 Gigawatts
2. Let's resolve the questions A and B:
Part A
Assuming wind farms typically generate 25% of their capacity, how much energy, in kilowatt-hours, can the region's wind farms generate in one year?
2,200 * 0.25 = 550 Megawatts
550 Megawatts = 550 * 1,000 Kilowatts = 550,000 Kilowatts
Now we calculate the amount of Kilowatts per hour, per day and per year:
550,000 Kw generated by the farms means that are capable of produce 550,000 kw per hour of energy
550,000 * 24 = 13'200,000 kilowatt-hours per day
13'200,000 * 365 = 4,818'000,000 kilowatt-hours per year
Part B
Given that the average household in the region uses about 10,000 kilowatt-hours of energy each year, how many households can be powered by these wind farms?
For calculating the amount of households we divide the total amount of energy the wind farms can generate (4,818'000,000 kilowatt-hours) and we divide it by the average household consumption (10,000 kilowatt-hours)
Amount of households = 4,818'000,000/10,000 = 481,800
Find the value of x. Plz hurry
Answer:
x = 12
Step-by-step explanation:
both (x+5) and (2x-7) are corresponding angles formed by an intersection between a transversal and 2 parallel lines.
hence they are equal in value
x+5 = 2x-7
x - 2x = -7 - 5
-x = -12
x = 12
Answer: x=12
Step-by-step explanation:
How do you solve 15.00 - 6.24
Answer:
8.76
Step-by-step explanation:
Simplifying
15.00 + -6.24 = b
Combine like terms: 15.00 + -6.24 = 8.76
8.76 = b
Solving
8.76 = b
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '-1b' to each side of the equation.
8.76 + -1b = b + -1b
Combine like terms: b + -1b = 0
8.76 + -1b = 0
Add '-8.76' to each side of the equation.
8.76 + -8.76 + -1b = 0 + -8.76
Combine like terms: 8.76 + -8.76 = 0.00
0.00 + -1b = 0 + -8.76
-1b = 0 + -8.76
Combine like terms: 0 + -8.76 = -8.76
-1b = -8.76
Divide each side by '-1'.
b = 8.76
Simplifying
b = 8.76
Liza is driving to her sister's house 360 miles away. After 4 hours, Liza is 2 3 of the way there.
How many more hours
does Liza have to drive?
A. 3
B. 2
C.11
_
2
Liza is driving to her sister's house 360 miles away. After 4 hours, Liza is 2/3 of the way there. How many more hours does Liza have to drive?
Answer:
Liza need to drive 2 more hours to reach her sister house
Solution:
Given that Liza is driving to her sister's house 360 miles away
So total distance = 360 miles
After 4 hours, Liza is 2/3 of the way there.
[tex]\frac{2}{3} r d \text { of total distance }=\frac{2}{3} \times 360=240[/tex]
So Liza has covered 240 miles in 4 hours
Let us find the speed
The relation between distance and speed is given as:
[tex]speed = \frac{distance}{time}[/tex]
[tex]speed = \frac{240}{4} = 60[/tex]
Thus speed = 60 miles per hour
Assuming speed is same throughout the journey, let us calculate the time taken to complete remaining distance
Remaining distance = 360 - 240 = 120 miles
Now distance = 120 miles and speed = 60 miles per hour
[tex]time taken = \frac{distance}{speed}\\\\time taken = \frac{120}{60} = 2[/tex]
Thus Liza need to drive 2 more hours to reach her sister house
solve this inequality 6(x-5)>3(x-1)
Answer:
x>9
Step-by-step explanation:
Open parenthesis:
6x-30>3x-3
Move all like terms to one side:
6x-3x>30-3
3x>27
x>9
geometry math thanks if you help
Answer: Option B.
Step-by-step explanation:
For this exercise it is important to remember that, by definition, a relation is a function if and only if each input value has an unique output value.
The input values are the values of the variable "x" and the output values are the values of the variable "y".
You can observe in the table shown in the picture, that the input value -2 has two different output values:
[tex]x=-2,y=3\\\\x=-2,y=-13[/tex]
Notice that the input vale -1 has two different output values too:
[tex]x=-1,y=-1\\\\x=-1,y=-9[/tex]
Therefore, based on this, you can conclude that the information given in the table is a relation but not a function.
What are the solutions to the equation
[tex] |x - 8| + 2 = 20[/tex]
Answer:
Solutions are -10 and 26
Step-by-step explanation:
( - the abolute sign I'm using
( x - 8 ) + 2 = 20
( x - 8 ) = 18
x - 8 = 18 (postive case)
x - 8 + 8 = 18 + 8
x = 26
( x - 8 ) = 18
x - 8 = -18 (negative case)
x - 8 + 8 = -18 + 8
x = -10
What is 11/20 as an decimal
Answer:
0.55 would be the decimal form
Step-by-step explanation:
9:
Which expressions equivalent to 3−83−4?
Select all that apply.
A
3−12
B
3−4
C
32
D
132
E
134
F
1312
The question asks for equivalent expressions to 3-8/3-4. After clarifying and simplifying the expression, we determined that the equivalent expressions are 3-12 (A) and 13/12 (F).
Explanation:The question is asking us to determine which expressions are equivalent to 3−83−4. First, let's clarify this expression. The symbols − and − can stand for subtraction or negative signs, making the expression ambiguous. However, we can interpret this as a subtraction problem with mixed numbers, which would be processed as 3 minus 8 thirds minus 4. Converting the mixed numbers to improper fractions, we get: 3−(8/3)−4 which simplifies to (9/3)−(8/3)−(12/3). This simplifies to 1/3−(12/3), or 1/3− 4, which then further simplifies to −(⅔).
When we look for equivalent expressions, we have the following options:
A) 3−12 is correct because it is the simplified form of 3 minus 8/3 minus 4, which is −3 1/3.B) 3−4 is incorrect because it simplifies to −1, which is not the same as −3 1/3.C) 3² is incorrect as this represents 3 squared, or 9, which is not the same as −3 1/3.D) 13² is incorrect because it represents 1/3 squared, which is 1/9, not the same as −3 1/3.E) 13´ could be construed as 13 to the power of 4 or 1/3 to the power of 4, but both interpretations are incorrect.F) 13⅜ is correct because it represents 1/3 minus 8/3 minus 4, which is −3 1/3.
The height of a wooden pole, h, is equal to 15 feet. Ataut wire is stretched from a point on the ground to the top of the pole. The
distance from the base of the pole to this point on the ground, b. is equal to 8 feet.
The question is incomplete. Here is the complete question:
The height of a wooden pole, h, is equal to 15 feet. A taut wire is stretched from a point on the ground to the top of the pole. The distance from the base of the pole to this point on the ground, b. is equal to 8 feet. What is the length of the wire?
Answer:
Length of wire = 17 feet
Step-by-step explanation:
Given:
The height of the wooden pole is, [tex]h=15\ ft[/tex]
The distance from the base of the pole to this point on the ground is, [tex]b=8\ ft[/tex]
Let the length of the wire be 'l'.
Now, consider the triangle formed by the pole, the base, and the wire. The length of the wire is the slant length and hence the hypotenuse of the triangle.
Using Pythagorean theorem, we can find the hypotenuse.
[tex](Hypotenuse)^2=(height)^2+(base)^2\\l^2=h^2+b^2[/tex]
Plug in the given values and solve for 'l'. This gives,
[tex]l^2=15^2+8^2\\\\l^2=225+64\\\\l^2=289\\\\l=\sqrt{289}\\\\l=\pm17[/tex]
As length can never be negative, we ignore the negative result.
Therefore, the length of the wire is 17 feet.
if (x-a) is a factor of (x^3-4x^2-4x+7), what is the value of the remainder?
Answer:
0
Step-by-step explanation:
When any number or expression is divided by one of its factors, the remainder is zero.
Find an equation of the line. Write the equation using function notation.
Through (3,-3); perpendicular to 4y=x-8
The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:
[tex]y = -4x+9[/tex]
Step-by-step explanation:
Given equation of line is:
[tex]4y=x-8[/tex]
We have to convert the given line in slope-intercept form to find the slope of the line
So,
Dividing both sides by 4
[tex]\frac{4y}{4} =\frac{x-8}{4}\\y = \frac{1}{4}x-\frac{8}{4}\\y = \frac{1}{4}x-2[/tex]
Let m1 be the slope of given line
Then
[tex]m_1 = \frac{1}{4}\\[/tex]
Let m2 be the slope of line perpendicular to given line
As we know that produt of slopes of two perpendicular lines is -1
[tex]m_1.m_2 = -1\\\frac{1}{4} . m_2 = -1\\m_2 = -1*4\\m_2 = -4[/tex]
The slope intercept form of line is given by:
[tex]y = m_2x+b[/tex]
Putting the value of slope
[tex]y = -4x+b[/tex]
to find the value of b, putting (3,-3) in equation
[tex]-3 = (-4)(3) + b\\-3 = -12 +b\\b = -3+12\\b = 9[/tex]
Putting the value of b in the equation
[tex]y = -4x+9[/tex]
Hence,
The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:
[tex]y = -4x+9[/tex]
Keywords: Equation of line, slope
Learn more about equation of line at:
brainly.com/question/4837736brainly.com/question/4805611#LearnwithBrainly
Final answer:
The result is the equation f(x) = -4x + 9 in function notation.
Explanation:
To find the equation of a line that is perpendicular to another and passes through a given point, follow these steps:
First, determine the slope of the given line. The equation given is 4y = x - 8. To put this in slope-intercept form, divide everything by 4 to get y = ⅔x - 2. The slope (m) of this line is ⅔.To find the slope of a line perpendicular to this one, take the negative reciprocal of ⅔, which is -4.Now, using the point-slope form of a line equation, which is y - y1 = m(x - x1) where (x1, y1) = (3, -3) and m = -4, we get:Therefore, the equation of the line in function notation is f(x) = -4x + 9.
Two of the angles in a triangle measure 18° and 72°. What is the measure of the third angle?
Final answer:
To find the third angle of a triangle, add the two known angles and subtract from 180 degrees. In this case, the third angle measures 90 degrees since the sum of the two given angles is 90 degrees.
Explanation:
When determining the measure of the third angle in a triangle, we utilize the fundamental property that the sum of all angles in a triangle equals to 180 degrees. Given that two of the angles measure 18° and 72°, we can find the third angle by subtracting the sum of these two angles from 180°.
The calculation is as follows:
Add the two known angle measures: 18° + 72° = 90°.Subtract this sum from the total sum of angles in a triangle: 180° - 90° = 90°.Therefore, the measure of the third angle in the triangle is 90 degrees.
Describe the transformations of the graph of y=x that will produce the graph of
y = -(x + 2)2 +3.
The graph of y = x is transformed by a reflection about the x-axis, a horizontal translation to the left by 2 units, and a vertical translation upward by 3 units to produce the graph of y = -(x + 2)^2 + 3.
Explanation:The given equation is y = -(x + 2)^2 + 3, and we need to describe the transformations of the graph of y = x that will produce this graph.
The first transformation is the reflection about the x-axis, which is indicated by the negative sign in front of the original equation. This flips the graph upside down.
The second transformation is the horizontal translation to the left by 2 units, which is indicated by the addition of 2 inside the parentheses. This shifts the graph 2 units to the left.
The third transformation is the vertical translation upward by 3 units, which is indicated by the addition of 3 to the entire equation. This moves the graph 3 units up.
Set up a right triangle model for this problem and solve by using a calculator. Follow the models above,
A photographer stands 60 yards from the base of a lighthouse and observes that the angle between the
ground and the top of the lighthouse is 41", How tall is the lighthouse?
Question:
Set up a right triangle model for this problem and solve by using a calculator. Follow the models above,
A photographer stands 60 yards from the base of a lighthouse and observes that the angle between the ground and the top of the lighthouse is 41° How tall is the lighthouse?
Answer:
The height of lighthouse is 52.2 yards
Solution:
Given that photographer stands 60 yards from the base of a lighthouse and observes that the angle between the ground and the top of the lighthouse is 41 degree
The diagram is attached below
Consider a right angled triangle ABC
AB is the height of the lighthouse
BC is the distance between the base of a lighthouse and Photographer
As per given, BC = 60 yards
Angle between the ground and the top of the lighthouse is 41 degree
Angle ACB = 41 degree
To find: height of lighthouse i.e AB = ?
We know that,
[tex]tan(\angle ACB) = \frac{Perpendicular}{Base}[/tex]
Here Base is BC and perpendicular is AB
[tex]\tan 41^{\circ}=\frac{A B}{B C}[/tex]
Substituting the values,
[tex]\begin{aligned}&\tan 41^{\circ}=\frac{A B}{60}\\\\&0.8692=\frac{A B}{60}\\\\&A B=0.8692 \times 60=52.157 \approx 52.2\end{aligned}[/tex]
Thus the height of lighthouse is 52.2 yards
Write a two column proof.
can someone please help me with these questions?
I have been struggling and have lots of other work.
Happy New Years everyone! Enjoy with your family and friends
Answer:
this should be correct.
h(x)=x^2-4x+1 find axis of symmetry
Answer:
the answer is x=2
I used math-way
What is the value of the sum?
Drag and drop the answer into the box to match the sum with its value.
-3/8 + 5/16
A: -11/16
B: -1/16
C: 1/16
D: 1/4
E: 11/16
Answer:
-1/16
Step-by-step explanation:
On a particular airline, bags checked in must weigh less than 50 pounds. Betty packed 32 pounds of clothes and five gifts that weigh the same amount. Which inequality can be used to find the possible weight, w, of each gift.
(A) x + 32 < 50
(B) 5x + 32 < 50
(C) 5 + x + 32 < 50
(D) x/5 + 32 < 50
Answer:
5x + 32 < 50
Step-by-step explanation:
On a particular airline, bags checked in must weigh less than 50 pounds. Betty packed 32 pounds of clothes and five gifts that weigh the same amount.
If each gift weighs w pounds, then the weight of five gifts will be 5w pounds and an additional 32 pounds of clothes will make it total (32 + 5w) pounds.
Now, this total weight has to be less than 50 pounds.
Therefore, the inequality equation that can be used to find the possible weight of each gift, w is
5x + 32 < 50 (Answer)
what is the total number of 0.3 pound meatballs Thomas can make with 8.1 pounds of meat?