Answer:
d = 15
Step-by-step explanation:
(-5, 4), (4, -8)
(x₁, y₁) (x₂, y₂)
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(4 - (-5))² + (-8 - 4)²
d = √(4 + 5)² + (-12)²
d = √(9)² + (-12)²
d = √81 + 144
d = √225
d = 15
I hope this helps!
Find the equation in slope intercept
Answer:
y=-1/4x+4
Step-by-step explanation:
The graph starts on 4 so that is your y-intercept
Use slope formula to get the slop (y2-y1 over x2-x1)
Use 2 coordinates for formuls (In your case (0,4) and (4,3))
3-4=-1 4-0=4
slope is -1/4
y= -1/4x+4
Add the 2 polynomials:
(-77x²¹ +
2
·x² + x
3
+[52*+
1
-
Answer:
Step-by-step explanation:
In the diagram ray MO bisects the measurement of
Simplify.
2x-4
²-8+12
O
O
O
-6
x+6
x-6
-
x-2
²-82+12
The simplified value of (2x - 4)² is 4x² - 16x + 16.
First, let us understand the algebraic identities;
Algebraic identities are equations in which the left hand side of the equation is identically equal to the right hand side of the equation.
Some of the identities are:
(a + b)² = a² + 2ab + b²(a - b)² = a² - 2ab + b², etc.We are given (2x - 4)².
Use the identity (a - b)² = a² - 2ab + b² to expand to the given expression.
So, a = 2x and b = 4.
Put it into the identity, we will get;
Therefore,
(2x - 4)² = (2x)² - 2 * 2x * 4 + (4)² = 4x² - 16x + 16
Thus, the simplified value of (2x - 4)² is 4x² - 16x + 16.
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Caroline was comparing the price of salmon at two stores. At SuperGrocery B, 3
pounds of salmon costs $24.63. The table below represents the total cost, in dollars
and cents, y, that it costs for a pounds of salmon at SuperGrocery A.
SuperGrocery A
Pounds (z) Total Cost (y)
2
$23.70
2.5
$29.63
3.5
$41.48
4.5
$53.33
How much more expensive is it, per pound, to buy salmon at
SuperGrocery A than at SuperGrocery B?
By the concept of basic arithmetic, it is $3.64 more expensive per pound, to buy salmon at Super Grocery A than at Super Grocery B.
What is meant by basic arithmetic?The area of mathematics known as arithmetic deals with the study of numbers and the numerous operations that can be performed on them. The four fundamental arithmetic operations in mathematics are addition (finding the sum), subtraction (finding the difference), multiplication (finding the product), and division (finding the quotient). These operations can be applied to all real numbers. The usage of fundamental arithmetic operations is the focus of the field of mathematics known as arithmetic.
At Super grocery B, 3 pounds of Salmon cost = $ 24.63
So, 1 pound will cost = $ 24.63/ 3
= $ 8.21
At Super grocery A, 2 pounds of Salmon cost = $ 23.70
So, 1 pound will cost = $23.70/ 2
= $ 11. 85
To buy salmon at SuperGrocery A than at SuperGrocery B expense per pound is given by
= $11.85 - $ 8.21
$ 3.64
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If q is 2.00 what is the distance from C to A?
Answer: 4.00
Step-by-step explanation:
If the q is 2.00 A to C is double the q. So, 2.00x2= 4.00.
Answer:
AC = 4.00Step-by-step explanation:
Given is a parallelogram.
One of the properties of a parallelogram is its diagonals bisect each other.
It gives us:
AC = 2qAC = 2*2.00 = 4.00what is the total change in the cats weight for all 3 months?
The total change in the cats weight for all 3 months is -0.5 pounds.
How to find the total change?Since we have 3 months which is from April to June, Now let add up the change in weight in pounds so as to find the total change
Let x represent the total change
x = -0.7 + 0.5 + (- 0.3 )
x = -0.5 pounds
Therefore the -0.5 pound is the change in weight.
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WILL GIVE BRAINLIEST !!
A helicopter lifts 75m vertically into the air and then comes back down to the ground.
a) What is the distance of the helicopter’s flight?
b) What is the displacement of the helicopter’s flight? Show your work
Distance is the total length covered by an object.
Displacement is the distance between the final point and the initial point.
The distance of the helicopter's flight is 150 m
The displacement of the helicopter's flight is zero.
What is displacement?Displacement is the distance between the final point and the initial point.
We have,
A helicopter lifts 75m vertically into the air and then comes back down to the ground.
Distance is the total length covered by an object.
Distance of the helicopter's flight.
= 75m + 75m
= 150 m
Displacement of the helicopter's flight.
= Final point - Initial point
= 0 - 0
= 0
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On an architect's blueprint, 1 inch corresponds to 4 feet. Find the length of a wall represented by a line 1 inches long on the blueprint
The length of wall in real life is 4 feet.
Given that on an architect's blueprint, 1 inch corresponds to 4 feet.
In this architect's plan, a wall represented by a line 1 inches long on the blue print.
So, the length of wall in real life is = 4 feet.
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Answer:
4ft
Step-by-step explanation:
If 1 inch corresponds to 4 ft on the blueprint. The ratio is 1 inch on the blue print for every 4 ft in real life.
Line x is the perpendicular bisector of segment ZY
what does b=
Based on the definition of perpendicular bisector, the value of b = 5.
What is a Perpendicular Bisector?A perpendicular bisector can be described as any line that bisects another line segment at right angles.
This means, the measure of the angles at the point of bisection are right angles (90 degrees).
Therefore:
12b + 30 = 90 [definition of perpendicular bisector]
Solve for b
12b + 30 - 30 = 90 - 30
12b = 60
Divide both sides by 12
12b/12 = 60/12
b = 5
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Sets A, B, and C are subsets of the universal set U.
These sets are defined as follows:
U= {f, g, h, p, q, r, x, y, z}
A= {f, g, p, q}
B= {g, h, q, x, y}
C={ p, q, x, y, z}
Find (A' u B) ∩ C'.
Write your answer in roster form or as Ø.
=====================================================
Explanation:
Unfortunately the U from "universal set" and the union symbol look almost identical.
What I'll do to avoid confusion is to let E represent the set of everything we care about, aka universal set.
E = {f, g, h, p, q, r, x, y, z}
Feel free to use other notation if it makes better sense to you.
From this set, we'll erase items that are found inside set A = {f, g, p, q}
So we go from this
E = {f, g, h, p, q, r, x, y, z}
to this
A' = {h, r, x, y, z}
Everything found in here is guaranteed to not be inside set A.
------------------------
The next step is to union set A' with set B. This is where we combine those two sets into a larger set of items. Toss out any duplicates. Each unique letter is to be listed once.
A' u B = {h, r, x, y, z} U {g, h, q, x, y}
A' u B = {h, r, x, y, z, g, h, q, x, y}
A' u B = {g, h, q, r, x, y, z}
It's recommended you sort the items in a consistent fashion.
Set this result aside for now, and come back to it later.
------------------------
Go back to the set of everything, aka universal set.
E = {f, g, h, p, q, r, x, y, z}
Cross off stuff found in set C, so we guarantee to form the opposite or complement set C'
C' = set of everything NOT found in C
C' = erase "p,q,x,y,z" from set E
C' = {f, g, h, r}
------------------------
To recap we found
A' u B = {g, h, q, r, x, y, z}C' = {f, g, h, r}Intersect those sets by looking at what they have in common. This is the overlapped region between the sets.
The three items in common are: {g, h, r} which forms the final answer.
Find the value of z and z + 45.
angles:
(z+45)
55
78
Z
74
92≤x≤9? I need help with this fast thankyou
Answer:
yes
Step-by-step explanation:
because 4
Answer:
Step-by-step explanation:
average rate of change
[tex]=\frac{25-(-10)}{9-2} \\=\frac{35}{7}\\=5[/tex]
Examine the worked examples. Then, answer the questions.
Alessa's car uses 2 gallons of gas to drive 45 miles. How many miles can
Alessa's car drive using 15 gallons of gas?
Let m represent the number of miles and g represent the gallons of gas.
m=
11 L
m=
m=
Write an equation in the form y = kx for the number of
miles in terms of the gallons of gas.
(15) Substitute the value for the given quantity.
Evaluate the right hand side of the equation.
Alessa's car can drive
miles using 15 gallons of gas.
Answer: if you multiply you will end up with 675
Step-by-step explanation:
Complete the model to find-9 + 3 Show your work
Answer:
Answer is 0. If you have to owe someone 9 dollars and they give you nine back it is 0. You can also rearrange the problem to 9-9 (same thing) which is 0
X
0
123
4
f(x)
36
54
81
121.5
182.25
کے
Using the given table, what are the y-values of the table?
Using the given table, the y-values are 36, 54, 81, 121.5, and 182.25.
We are given a table. Mathematical tables are collections of numbers that represent the outcome of a computation with varied arguments. The table has two columns and five rows. The first column shows the x-values. The second column shows the f(x) values. We know that y = f(x). So, the second column shows the y-values. The y-value is the vertical value in a pair of coordinates. It denotes how high or low the point is. In an ordered pair of coordinates, the y-coordinate is always written second (x, y). The five rows show the data points with corresponding x-values and y-values.
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Emory walks one lap on the
track every 7 minutes. Madison
walks one lap on the track every
8 minutes. How many minutes
will pass before they meet on
track at the same time?
Answer: 56 minutes
Step-by-step explanation:
7 = 7, 14, 28, 35, 42, 49, 56
8 = 8, 16, 24, 32, 40, 48, 56
7 and 8 have 56 in common so it would take them 56 minutes
Paula stands on the side of a river and sights the opposite bank at an angle of depression of 7 degrees. if Paula is 5.5 feet tall, approximately how wide is the river, to the nearest foot?
The width of the river to the nearest foot will be 45 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Paula remains on a waterway and sights the contrary bank at a point of the wretchedness of 7 degrees.
If Paula is 5.5 feet tall.
Let 'w' be the width of the river. Then the width of the river will be given as,
tan 7° = 5.5 / w
0.12278 = 5.5 / w
w = 44.79
w ≈ 45 feet
The width of the river to the nearest foot will be 45 feet.
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4 yd.
3 yd.
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
yards
Answer:
5 yds
Step-by-step explanation:
i am assuming that 4 yd and 3 yd are the legs
so
to find the hypotenuse you square both legs add them and then take the square root of that
so
4^2 + 3^2 = c^2
16 + 9 = c^2
25 = c^2
c = 5
the final side is 5
what is the sum of 3x and -3x + 4?
You can afford a $1100 per month mortgage payment. You've found a 30 year loan at 8% interest.
a) How big of a loan can you afford?
b) How much total money will you pay the loan company?
c) How much of that money is interest?
a) $149911.84 can be afforded
b) $39600 is the total money you will pay the loan company
c) $246088.16 is the interested amount
What is interest ?The cost of borrowing money is called interest, and it is typically stated as a percentage, such as an annual percentage rate (APR).Lenders may charge interest to borrowers for using their funds, or borrowers may charge interest to lenders for using their funds.Interest is frequently regarded as simple interest (based on the principal amount) or compound interest (based on principal and previously-earned interest).Credit cards, mortgages, auto loans, personal loans, savings accounts, and penalty assessments are all frequently linked with interest.The macroeconomic policy set by the Federal Reserve's federal funds rate has a significant impact on interest rates.Calculation
Given,
d=$1100
N= 30 years
r = 8% or 0.08
a) Loan amount that can be afforded
[tex]=\frac{d[1- (1+\frac{r}{k})^{-Nk} }{\frac{0.08}{12} }[/tex]
[tex]=\frac{1100[1- (1+\frac{0.08}{12})^{-30*12} }{\frac{0.08}{12} }[/tex]
= $149911.84
b) Total money you pay = d×N×k
=1100×30×12
=$39600
c) Interest paid = Total money paid – loan amount
⇒39600–14911.84 = $246088.16
Hence,
a) $149911.84 can be afforded
b) $39600 is the total money you will pay the loan company
c) $246088.16 is the interested amount
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PLEASE HELP EXTRA POINTS select all true statements
Answer: C
PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!
f(x) = √3x
g(x) = 3x + 2
Find (4) (2). Include any restrictions on the domain.
Option A is correct. The value of function (f/g)(x) is found to be [tex]\sqrt[3]{3x}[/tex]/(3x+2) where the condition is that x ≠ -2/3.
What exactly is a function composition?In mathematics, function composition is an operation in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
What is the sum of two functions?The new function obtained by performing f first and then g is the combination of two functions g and f.
Given:
f(x) = [tex]\sqrt[3]{3x}[/tex]
g(x) = 3x + 2
(f/g)(x) = [tex]\sqrt[3]{3x}[/tex]/(3x+2)
Also, the denominator should not be equal to 0.
So, 3x + 2 ≠ 0
x ≠ -2/3
Therefore, the value of function is found to be [tex]\sqrt[3]{3x}[/tex]/(3x+2) where the condition is that x ≠ -2/3. So, Option A is correct
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19 is what percent of 500?
Answer:95
step by step explanation
See question in screenshot below.
The equation of the transformation of the exponential function y = 2ˣ in the form y = A·2ˣ + k, obtained from the simultaneous found using the points on the graph is y = (-2)·2ˣ + 3
What is an exponential equation?An exponential equation is an equation that has exponents that consists of variables.
The given equation is y = 2ˣ
The equation for the transformation is; y = A·2ˣ + k
The points on the graphs are;
(0, 1), (1, -1) and (2, -5)
Plugging the x and y-values to find the value A and k gives the following simultaneous equations;
When x = 0, y = 1, therefore;
1 = A·2⁰ + k = A + k
1 = A + k...(1)
When x = 1, y = -1, which gives;
-1 = A·2¹ + k
-1 = 2·A + k...(2)
Subtracting equation (1) from equation (2) gives;
-1 - 1 = 2·A - A + k - k
-2 = A
1 = A + k, therefore;
1 = -2 + k
k = 2 + 1 = 3
k = 3
Which gives;
y = -2·2ˣ + 3 = 3 - 2·2ˣ
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Franks’s annual salary is $80000. About 25% of her salary is deducted for taxes.
How much tax is deducted?
Explain.
If 3 workers complete a certain task in 12 days, how many workers are needed to finish the same task in 4 days?
A total of 9 workers are needed to finish the same task in 4 days
How to determine the number of workers?From the question, we understand that:
3 workers can complete a certain task in 12 days
This means that
3 workers = 12 days
The proportionality constant is then calculated as
Proportionality constant = Number of workers x Number of days
Substitute the known values in the above equation So, we have the following equation
Proportionality constant = 3 * 12
Evaluate
Proportionality constant = 36
When the number of days is 4, we have
Days = 4
So, we have
Proportionality constant = Number of workers x Number of days
This gives
36 = Number of workers x 4
Divide both sides by 4
Number of workers = 9
Hence, the number of workers is 9
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Which parabola will have one real solution with the line y=x-5?
The equation of the parabola that has one real solution with the line y = x - 5 is y = x² + 7·x + 4
What is the standard form of the equation of a parabola?The standard form of the equation of a parabola is y = a·x² + b·x + c
The equation of the line is; y = x - 5
The parabola that has one real solution with the line is given by the parabola that is equal to both (x - 5) and the equation for the parabola;
Analyzing the quadratic equations of the parabolas with the equation y = x - 5, gives;
y = x² + x - 4 = x - 5x² + x - 4 - x + 5 = 0
x² + 1 = 0
x² = -1
x = ±√(-1) (Complex solution)
y = x² + 2·x - 1 = x - 5x² + x + 4 = 0
The discriminant, b² - 4·a·c is 1² - 4 × 1 × 4 = -15 < 0 (Complex solution)
x² + 6·x + 9 = x - 5x² + 5·x + 14 = 0
The discriminant, b² - 4·a·c is 5² - 4 × 1 × 14 = -31 < 0 (Complex solution)
x² + 7·x + 4 = x - 5x² + 6·x + 9 = 0
The discriminant, b² - 4·a·c is 6² - 4 × 1 × 9 = 0 One real solution;The quadratic equation that gives one real solution with the equation y = x - 5 is therefore;
y = x² + 7·x + 4
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A group of 16 people is choosing a chairperson and vice-chairperson. They put all 16 people's names into a hat. The first name drawn becomes chair. The second name drawn becomes vice-chair. How many possible combinations of chair and vice-chair are there?
Based on the number of people present, the total number of combinations of Chairperson and Vice Chairperson is 240 combinations.
How to carry out Probability combinations?In order for us to find out the total possible combinations, we will use the formula as:
Total possible combinations = Number of possible chairpersons * Number of possible vice chairpersons
We are given that;
Number of possible chairpersons = 16
Number of possible vice chairpersons = 15 (This is because a chairperson is chosen first and leaves 15 people.)
Thus, we can say that;
Total possible combinations = 16 * 15
Total possible combinations = 240 combinations
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A cube box is 20 cm x 20 cm x 20 cm. What is the surface area of the largest size sphere that can fit in this box? Leave your answer in terms of pi.
The surface area of the largest size sphere that can fit in this box is 400π
What is the surface area of the sphere?
The surface area of a sphere is the space that the sphere's outer surface occupies. A sphere is a circle in three dimensions. A circle is a two-dimensional (2D) shape, whereas a sphere is a three-dimensional (3D) shape, which is the difference between the two.
Here, we have
The diameter of the biggest sphere will be equal to the side of the sphere.
radius = 20/2
= 10
The surface area of the sphere = 4πr²
=4π(10)²
= 400π
Hence, the surface area of the largest size sphere that can fit in this box is 400π.
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