The two cars are 5 kilometers far apart from each other.
What is Pythagoras theorem?
The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Given that;
Two cars leave the same parking lot, with one heading north and the other heading east.
After several minutes, the northbound car has traveled 3 kilometers, and the eastbound car has traveled 4 kilometers.
Now,
The straight path is find by using the Pythagoras theorem as;
Straight path = √3² + 4²
= √9 + 16
= √25
= 5 km
Therefore,
The two cars are 5 kilometers far apart from each other.
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What is the biconditional statement that corresponds to “congruent angles are angles with the exact same measure”
Two angles are congruent if and only if they have the same measure.
Given,
“Congruent angles are angles with the exact same measure”
To define the Biconditional Statement:
Now,
What is Biconditional Statement ?
If two angles have the same measure, then the angles are congruent and if two angles are congruent, then the angles have the same measure.
"If two angles are congruent, then they have the same measure."
P = two angles are congruent.
Q = they have the same measure.
Hence, Two angles are congruent if and only if they have the same measure.
or: P if and only if Q, this is biconditional.
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Use the graph to estimate the x- and y-intercepts of this function and describe where the function is positive and negative.
Answer:
the graph you want is
Step-by-step explanation:
Dakota Lane purchased a car stereo for
$279.99. If he made a 35% down pay-
ment, how much did he finance?
A $189.99
C
$181.99
1
B $244.99
D $98.99
A
∠A and
∠
B
∠B are supplementary angles. If
m
∠
A
=
(
4
x
−
16
)
∘
m∠A=(4x−16)
∘
and
m
∠
B
=
(
x
+
1
)
∘
m∠B=(x+1)
∘
, then find the measure of
∠
B
∠B.
Answer:
a
Step-by-step explanation:
what in the hell type of question is that need more easy work not alien work, But just put (B/)
find the lcm:- x⁴+x³-x²-x, x⁴-x and 4x²-4.
The LCM of both the factors x⁴+x³-x²-x, x⁴-x and 4x²-4 is discovered to be x(x+1)²(x-1).
Explain LCM.The LCM of any two numbers is the value that is evenly divisible by the two given numbers. Least Common Multiple is an abbreviation for Least Common Multiples. It's also known as the Least Common Divisor (LCD).
What exactly is an LCM example?The smallest integer that is a multiple of two or more numbers is known as the LCM. For instance, the LCM of 4 and 6 is 12, and the LCM of 10 and 15 is 30.
The two given expressions are:
x⁴+x³-x²-x, x⁴-x and 4x²-4
Let us simplify both these factors.
x⁴+x³-x²-x = x(x³ + x² -x -1)
= x(x+1)(x+1)(x-1)
= x(x+1)²(x-1)
4x²- 4 = 2²(x+1)(x-1)
Multiplying each factor with the highest power,
4x²- 4 = 2²x(x+1)²(x-1)
= 4x(x+1)²(x-1)
Thus x(x+1)²(x-1) is the least common factor of both factors.
As a result, it is discovered that the LCM of x⁴+x³-x²-x, x⁴-x and 4x²-4. is x(x+1)²(x-1).
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The principal would like to assemble a committee of 5 students from the 15-memberstudent council. How many different committees can be chosen?
SOLUTION
The question involves combination since it only deals with the selection without arrangement.
Hence the formula to use is
[tex]^nC_r=\frac{n!}{(n-r)!r}[/tex]For this question, we have
[tex]\begin{gathered} n=15,r=5 \\ ^nC_r=\frac{n!}{(n-r)!r} \\ \text{becomes } \\ ^{15}C_5=\frac{15!}{(15-5)!5!} \end{gathered}[/tex]Simplifying the last expression we obtained
[tex]\begin{gathered} ^{15}C_5=\frac{15!}{10!5!} \\ =\frac{15\times14\times13\times12\times11\times10!}{10!\times5!} \\ =3003 \end{gathered}[/tex]Therefore,
The number of committees to be chosen is 3003
Jackie's grandfather gave her $250 for her birthday. Jackie asked her mother to save it for her and only
give her $10 each week. The amount of money remaining each week can be found using the function
A(t) 250-10t, where t is the number of weeks since her birthday.
What are the domain and range of the function for this situation?
A)Domain: 0 sts 250, te Z
Range: 0 ≤ A(t) ≤ 25, where A(t) = 250-10t
B)Domain: tER
Range: A(t) € R
C)Domain: 0 st s 25, te Z
Range: 0 ≤ A(t) ≤ 250, where A(t) = 250 - 10t
D)Domain: t≥ 0, tez
Ranne: Aft) > 0. where A(t)= 250 - 10r
The domain and range of the function for this situation include:
C. Domain: 0 ≤ t ≤ 25,
Range: 0 ≤ A(t) ≤ 250, where A(t) = 250 - 10t
What is a domain?A domain is a collection of potential input values. All input values visible on the x-axis make up the graph's domain. The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range for a relation.
A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
For her birthday, Jackie's grandfather gifted her $250. Jackie pleaded with her mother to set aside money for her and limit her weekly checks to $10. The function can be used to determine how much money is left each week.
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find h from 3-h/V
help
By "undoing" the common logarithm by exponentiating both sides with base 10 to obtain [H+] = 10pH. "Solution A" has a hydrogen ion concentration of [H+] = 105.6 0.0000025 = 2.51 106 M.
How can I determine H value?The number of articles for which an author has been cited at least that many times by other writers is used to compute the h-index. For instance, a scientist with an h-index of 17 has at least 17 papers to their credit, each of which has been mentioned at least 17 times.
At pH 7, [H+] = [OH-] = 1 x 10-7 M, the molarity of acidic H+ ions matches the molarity of basic OH- ions.
The pH of threeThe pH scale is logarithmic, which means that an increase or decrease in an integer number will result in a tenfold change in concentration. A pH of 3 is ten times more acidic than a pH of 4, for instance. Similar to how a pH of 3 is 100 times more acidic than a pH of 5, so is a pH of 5. A pH of 11 is also ten times more basic than a pH of 10, for example.
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My number is three different digits, the sum of the digits is equal to 3x5, the hundreds digit is the only odd digit, i'm greater than 30x9 and less than 50x9
Answer: 735
Step-by-step explanation:
find the circumference and area if its 56 cm
If the diameter of the circle is 56cm² then the circumference of the circle is 176cm and the area of the circle is 2464cm².
How do you determine a circle's area?A circle's area is equal to pi times the radius squared (A = πr). Discover how to apply this formula to determine a circle's area given its diameter.
Area of Circumference: What Does It Mean?The length of a circle's outline is referred to as its circumference, while the length of a form with straight sides is referred to as its perimeter. Circle circumference equals 2πr.
The circle has a 56 cm diameter, determine its circumference and area.Diameter of the circle =56cm
Radius of circle =56/2 =28cm
Therefore,
Circumference of circle
=2πr
=2*22/7*28
=176 cm²
Also,
Area of circle
=πr
=(22/7)*28*28
=2464cm²
Hence the circumference of the circle is 176cm² and the area of the circle is 2464 cm².
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Note: The question is incomplete in the portal. Here is the total question,
Question: Find the circumference and area of the circle if its diameter is 56 cm.
Low flow showerheads use 2 1/2 gallons of water per minute. If family members shower a total of 2 1/3 hours per week, how much water does the family use for showers each week? Write an expression that represents the problem. Then solve the problem
The expression that represents the situation is (5/2)x = y and the family uses 350 gallons of water for each week.
First, we convert the given fractions into improper fractions as follows;
2 1/2 = 5/2
2 1/3 = 7/3
As the showerhead uses 5/2 gallons of water per minute an expression for this situation can be given as;
(5/2)x = y
Here x is the amount of time in minutes and y represents the gallons of water used by the family each week
As the family uses the showerhead for 7/3 hours per week, we first convert the hours into minutes as follows;
(7/3) × 60 = 140 minutes
Now substituting this value in the equation (5/2)x = y;
(5/2)x = y
(5/2)140 = y
y = 350 gallons
Therefore, 350 gallons of water is used by the family per week.
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it is estimated that the world's population is growing at a rate of 1.14% per year. On January 1st 2014 the population was 7.23 billion a) Find the expected population on January 1st 2020
The most appropriate choice for growth and depreciation will be given by:
Population on 1st January 2020 is 7.74 billion
What is growth and depriciation?
The increase in the value of a product over a period of time is called growth.
If V is the value after n years and [tex]V_0[/tex] is the present value r is r% per annum.
[tex]V=V_0(1 + \frac{r}{100})^n[/tex]
The decrease in the value of a product over a period of time is called depriciation.
If V is the value after n years and [tex]V_0[/tex] is the present value r is r% per annum.
[tex]V=V_0(1 - \frac{r}{100})^n[/tex]
Population on 1st January 2014 = 7.23 billion
Rate of growth of population = 1.14%
Population on 1st January 2020
[tex]7.23(1 + \frac{1.14}{100})^6\\7.23(1+0.0114)^6\\7.23(1.0114)^6\\[/tex]
[tex]7.74[/tex] billion
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Mila bought stock in a company two years ago that was worth x dollars. During the first year that she owned the stock, it decreased by 35%. During the second year the value of the stock decreased by 32%. Write an expression in terms of a that represents the value of the stock after the two years have passed.
Mila bought stock in company two years ago that was worth x dollars. During first year that she owned the stock, it decreased by 35%. During second year the value of the stock decreased by 32%, an expression in terms of a that represents the value of the stock after the two years have passed is 2x+0.67.
What do you mean by percentage?It is not always obvious from the context what a % is in relation to because of inconsistent usage. The typical meaning of a "10% rise" or "10% decline" in a quantity is that this refers to the quantity's starting value. As an illustration, the new price of a $200 item would be $220 if the price increased by 10%, or $20. The final price is equal to 100% of the starting price (100% + 10% = 110%).
Other instances of % changes include:
If a quantity is increased by 100%, the final amount will be 100% more than the original amount (100% of initial + 100% of increase = 100% of initial). The quantity has therefore doubled.
If an amount is increased by 800%, the final sum will be nine times as large as the original (100% + 800% = 900% = 9 times as large).
When something is reduced by 60%, the final sum equals 40% of the original (100% - 60% = 40%).
A reduction of 100% results in a final value of 0% (100% - 100% = 0%).
In general, if a quantity is changed by x percent, the final amount will be 100 + x percentage of the original amount, or (1 + 0.01x) times the original amount.
x-35%+x-32%
⇒[tex]x-\frac{7}{20} +x-\frac{8}{25}[/tex]
⇒[tex]2x+(\frac{-175-160}{500})[/tex]
⇒2x+0.67
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Suma:
1) 21+(-45)-67-100+234=
2)76-43+222-21-78-44+99-345=
Answer:
1. 43
2. -123
What is the equation of the line that passes through the point (5,−5) and has a slope of 1/5
Answer:
y= 1/5x -6
Step-by-step explanation:
Use point-slope form (could be wrong name): y-y1= slope(x-x1)
Substitute in the numbers: y-(-5)= 1/5(x-5)
Distribute: y+5= 1/5x-1
Solve for final answer: y= 1/5x -6
PS write 1/5 as [tex]\frac{1}{5}[/tex]
In a city, the people use
approximately 4,140,000,000
pounds of burgers in a year.
Write this number in scientific
notation.
Answer: [tex]4.14 \times 10^9[/tex]
Explanation:
Place the decimal point between the first two digits to get 4.14
Now ask yourself: How many places must we move the decimal point to go from 4.14 back to 4,140,000,000?
The answer is 9 places to the right.
This means we'll have 9 as the exponent over the 10
[tex]4,140,000,000 = 4.14 \times 10^9[/tex]
H
3. A scale drawing of a rectangular park is 9 inches wide and 12 inches long. The scale used is
1 inch = 18 feet. What is the area of the actual park in square feet?
Answer: Area = 34992 square feet
Step-by-step explanation:
W = (9*18)
L = (12*18)
Area = W*L
Therefore, Area = 34992, and don't forget square feet
63 divided by 7 x 3 - 4
Step-by-step explanation:
Dmas divide multiple add subtract
divide 63 by 7 = 9 then multiply by 3 = 27 then subtract by 4 27-4 = 23
your awnser is 23
The value of the expression is -1.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
63 ÷ 7 x 3 - 4
Using PEMDAS rule of operation.
We multiply first.
So,
= 63 ÷ 21 - 4
Using the division.
= 63/21 - 4
= 3 - 4
= -1
Thus,
The value of the expression is -1.
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Graph the linear equation, 64 Points!!!
The graph for the three selected points can be found in the photos section. Good luck!
Halp Brainliest to correct answer
Answer:
A. The total number of hours it takes to make dresses and skirts each month
Step-by-step explanation:
By multiplying the amount of time to make an item by the amount of items made, you get the total amount of time spent on making those items. Therefore the total time spent making dresses is 8x, and the total time spent making skirts is 3y, which means that the total time to make both is 8x+3y.
15. Write an equation that goes through point (-6, 8) and has a y-intercept of -4.
Answer:
y = -2x - 4
Step-by-step explanation:
First, substitute the known values into the slope-intercept form, y = mx + b, where m represents the slope of the line and b represents the y-coordinate of the point of intersection of the line and the y-intercept. We are given that the graph has a y-intercept of -4, so substitute -4 for b. The graph contains the point (-6, 8), so substitute -6 for x and 8 for y.
8 = -6m - 4
12 = -6m
m = -2
Finally, substitute -2 for m and -4 for b to write the equation of the line in the form, y = mx + b.
y = -2x - 4
A mortician works 45 hours a week. 15 hours are spent doing paperwork. Another mortician works 25 hours a week and spends 8 hours, 20 minutes on paperwork. Which mortician spends the greater fraction of time working on paperwork? Why?
The two mortician spent equal fraction on time working to paperwork
Comparing FractionsIn the given question, we have two mortician that work different hours.
The first mortician worked 45 hours a week and spent 15 hours doing paperwork.
The second mortician worked 25 hours a week and spent 8.33 hours on paper work.
Let's compare the ratios and find which mortician had a greater fraction on paperwork.
Mortician A
[tex]\frac{15}{45}= 0.3[/tex]
Mortician B
[tex]\frac{8.333}{25} = 0.3[/tex]
From the calculation above, both mortician spent equal ratio of time doing paperwork.
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Please help me I really need help. ILYSM THANK YOU :)
How many pounds of apples will he get if he goes to David’s orchard?
The pounds of apples that he get if he goes to David’s orchard is 20 pounds.
How to calculate the pounds of apples?Let the assumed amount with him be $40.
It should be noted that for David's orchard, the first ten pounds are $2 per round and each additional round is $1 per pound.
Therefore, the expression to illustrate this will be:
($2 × 10) + ($1 × r)
where r = additional pounds
Therefore,
($2 × 10) + ($1 × r) = $40
20 + r = 40
r = 40 - 20
r = 20
He will get 20 pounds.
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Dorothy wants to purchase a car. She reviewed her budget and can comfortably afford a car payment of $490 per month. She has good credit and anticipated being able to secure a 4-year loan at 4% interest.What is the maximum cost she should pay for a car to stay within her budgeted monthly amount?
$21702.
$19762.
$16185.
$10386.
The maximum cost Dorothy should pay for the car to stay within her monthly budget amount is $23,518.84. See the explantion below.
What is a budget?A budget is a financial plan that takes into account both income and costs. In other words, it's a projection of how much money you'll make and expend over a specific time period, such as a month or a year.
The calculation that justified the above amount is solved as follows:
Given that:
Rate = 4%
Time = 4 years
The monthly payment is $490, to determine the amount (maximum) in 4 years, we use the Compound Interest formula:
A = P (1+ (r/n)ⁿᵇ
Where:
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
b = number of time periods elapsed
A = P (1 + (0.04/1)^(1x4)
A = P (1.04)⁴ in four years
Hence, given that the monthly payment over the four-year period is $490, we say:
P [(1.04)⁴] /12 x4 = 490
⇒ P (1.04)⁴ = 490 x 48
P = (490 x 48)/1.1699
P = 20104.2824173
P [tex]\approx[/tex] 20,104
The maximum amount payable hence
= 20,104 (1.04)⁴
A = 23518.837
A [tex]\approx[/tex] 23,518.84
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The table represents a quadratic function. Write an equation of the function in standard form
-4-2 02
f(x) -3 0 10
X
https://tex.z-dn.net/?f=y%3D%5Cboxed%7B-%5Cdfrac%7B1%7D%7B4%7D%7D%5Cleft(x-%5Cboxed%7B-2%7D%5C%3A%5Cright)%5E2%2B%5Cboxed%7B4%7D
Jack and Jill took a trip to Grandma’s house. It took them 8 hr to get to Grandma’s house but on their way back home they took the scenic route, which is 20 mi longer. If their speed going home was 10 mi/hr less than their speed going to Grandma’s house, and if it took them 10 hr to get home, how far did they travel going to Grandma’s and what was their average speed on the trip there?
Answer:
Let s be the distance to Grandma’s and v the speed they went to get to Grandma’s.
So s=8v, because it took them 8 hours to get there.
Coming back they travelled s+20 miles. Since s=8v we can write this as 8v+20 miles.
Their speed was reduced by 10mph so that’s v-10. It took them 10 hours to return so:
8v+20=10(v-10); 8v+20=10v-100; 120=2v
so v=60mph. This is their average speed going to Grandma’s.
(not 100% sure but give it ago)
Question 8 options:
4x-3
x=2
4(2)-3
The
property is used here.
Answer:
the property is used here in 4(2)-3
The required property that is used is the substitution of values in the variable.
Given that,
A simplification of the expression is given we have to determine which property is used in the simplification,
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
As in the simplification shown that the variable x is substitute by the constant value 2, so this property can be stated as the substitution property.
Thus, the required property that is used is the substitution of values in the variable.
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if w=20 compute the value of
12w^12 over 60w^10
Answer: 80
Step-by-step explanation:
12(20)^12
/
60(20)^10
= 80
Fill in the blanks below with the correct units. (a) Boris's bed is about 7 long. (b) Ivanna's 5 year old cat weighs about 9 . (c) Today, Kira drank a total of 7 of water.
(a) Boris's bed is about 7 inches long
(b) Ivanna's 5 year old cat weighs about 9 kg.
(c) Today, Kira drank a total of 7 liters of water.
What are Units of Measurement?Units of measurement give standards so that the numbers from our measurements refer to the same thing.
Measurement is to find a number that shows the amount of something. A measurement unit is a standard quantity used to express a physical quantity.
(a) Boris's bed is about 7 inches long
The inch is a commonly used customary unit of length
(b) Ivanna's 5 year old cat weighs about 9 kg.
Kilogram is a unit of measurement used to measure much heavier objects.
(c) Today, Kira drank a total of 7 liters of water.
A liter is a metric unit of volume primarily used to measure liquids. .
Hence inches, Kilograms and liters are the units for respective blanks of a, b and c.
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find the equation that is perpendicular to the line 8x-6y=-5 and passes through (1,-3)
pls help omg its 2am and i need to get this done by tomorrow
The equation of the perpendicular line in slope intercept form is
y = (-3/4)x - 9/4.
What is the slope?The slope is defined as the rate of change of the y-axis with respect to
x-axis.
We know equation of a line in slope intercept form is y = mx + b, where slope = m and y-intercept = b.
We also know that perpendicular lines have a slope that is negative reciprocal of each other.
Given line is 8x - 6y = -5.
-6y = - 8x - 5.
-y = (-8/6)x - 5/6.
-y = (-4/3)x - 5/6.
y = (4/3)x + 5/6.
∴ Slope(m) = 4/3.
So, the line which is perpendicular has a slope(m) = -3/4 with points (1,-3).
∴ - 3 = (-3/4)(1) + b.
- 3 = -3/4 + b.
b = 3/4 - 3.
b = -9/4.
∴ The equation of the line is y = (-3/4)x - 9/4.
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