Answer
It will take 3 hours to get to your cousin's house.
Explanation
Firstky, note that Speed is given as
[tex]\text{Speed =}\frac{Dis\tan ce}{Time}[/tex]For this question, we are told that the distance to your cousin's house is 150 miles.
The speed is an average rate of 50 miles per hour.
We are then asked to calculate how long it will take to get to your cousin's house.
Speed = 50 miles/hour
Distance = 150 miles
Time = ?
[tex]\begin{gathered} \text{Speed = }\frac{Dis\tan ce}{Time} \\ 50=\frac{150}{Time} \\ \text{Cross multiply} \\ 50\times Time=150 \\ \text{Divide both sides by 50} \\ \frac{50\times Time}{50}=\frac{150}{50} \\ \text{Time = 3 hours} \end{gathered}[/tex]Hope this Helps!!!
Choose the best initial step in solving the following system by substitution.
2x + 3y = –12
6x + y = 18
Answers:
1.Solve the first equation for x.
2.Solve the first equation for y.
3.Solve the second equation for x.
4.Solve the second equation for y.
Answer:
I think you have to first solve the first equation for y.
Answer choice: 3.
Step-by-step explanation:
Hope this helps! :)
Which equation has the solution x= 9? Select each correct answer. 4 + 5x = 18 0 24 - 2x – 13 DE O +7=8 – 0 3x + 2 = 25 81 si - 3 = 6 3 = V 2x - 3= 15
Equations with solution x = 9 are:
81/x - 3 = 6
2x - 3 = 15
Explanation:To determine the equation whose result ives x = 9, we need to solve each of the equation in the question
a) 4 + 5x = 18
5x = 18 - 4
5x = 14
x = 14/5
This is not x = 9 (option is wrong)
b) 24 - 2x = 13
24 - 2x + 2x = 13 + 2x
24 = 13 + 2x
24 - 13 = 2x
11 = 2x
x = 11/2
This is not x = 9 (option is wrong)
c) x/3 + 7 = 8
x/3 = 8 - 7
x/3 = 1
x = 3(1) = 3
This is not x = 9 (option is wrong)
d) 3x + 2 = 25
3x = 25 - 2
3x = 23
x = 23/3
This is not x = 9 (option is wrong)
e) 81/x - 3 = 6
81/x = 6 + 3
81/x = 9
81 = 9x
x = 81/9
x = 9
This equation has the sloution x = 9
f) 2x - 3 = 15
2x = 15 + 3
2x = 18
x = 18/2
x = 9
This equation has the sloution x = 9
x = -4z - 19
y= 5x + z - 4
-5y - z = 25
Answer:
x = 1, y = -4, z = -5
Step-by-step explanation:
Solve the following system:
{x = -4 z - 19 | (equation 1)
{y = z + 5 x - 4 | (equation 2)
{-z - 5 y = 25 | (equation 3)
Express the system in standard form:
{x + 0 y + 4 z = -19 | (equation 1)
{-(5 x) + y - z = -4 | (equation 2)
{0 x - 5 y - z = 25 | (equation 3)
Swap equation 1 with equation 2:
{-(5 x) + y - z = -4 | (equation 1)
{x + 0 y + 4 z = -19 | (equation 2)
{0 x - 5 y - z = 25 | (equation 3)
Add 1/5 × (equation 1) to equation 2:
{-(5 x) + y - z = -4 | (equation 1)
{0 x + y/5 + (19 z)/5 = -99/5 | (equation 2)
{0 x - 5 y - z = 25 | (equation 3)
Multiply equation 2 by 5:
{-(5 x) + y - z = -4 | (equation 1)
{0 x + y + 19 z = -99 | (equation 2)
{0 x - 5 y - z = 25 | (equation 3)
Swap equation 2 with equation 3:
{-(5 x) + y - z = -4 | (equation 1)
{0 x - 5 y - z = 25 | (equation 2)
{0 x + y + 19 z = -99 | (equation 3)
Add 1/5 × (equation 2) to equation 3:
{-(5 x) + y - z = -4 | (equation 1)
{0 x - 5 y - z = 25 | (equation 2)
{0 x + 0 y + (94 z)/5 = -94 | (equation 3)
Multiply equation 3 by 5/94:
{-(5 x) + y - z = -4 | (equation 1)
{0 x - 5 y - z = 25 | (equation 2)
{0 x + 0 y + z = -5 | (equation 3)
Add equation 3 to equation 2:
{-(5 x) + y - z = -4 | (equation 1)
{0 x - 5 y + 0 z = 20 | (equation 2)
{0 x + 0 y + z = -5 | (equation 3)
Divide equation 2 by -5:
{-(5 x) + y - z = -4 | (equation 1)
{0 x + y + 0 z = -4 | (equation 2)
{0 x + 0 y + z = -5 | (equation 3)
Subtract equation 2 from equation 1:
{-(5 x) + 0 y - z = 0 | (equation 1)
{0 x + y + 0 z = -4 | (equation 2)
{0 x + 0 y + z = -5 | (equation 3)
Add equation 3 to equation 1:
{-(5 x) + 0 y + 0 z = -5 | (equation 1)
{0 x + y + 0 z = -4 | (equation 2)
{0 x + 0 y + z = -5 | (equation 3)
Divide equation 1 by -5:
{x + 0 y + 0 z = 1 | (equation 1)
{0 x + y + 0 z = -4 | (equation 2)
{0 x + 0 y + z = -5 | (equation 3)
Collect results:
Answer: {x = 1, y = -4, z = -5
how does y sqaured eqaul 169
Answer:
13
Step-by-step explanation:
A number squared is just a number multiplied by itself.
13 x 13 is 169.
Answer is 13.
Hope this helps!
P.S, Brainliest, please, thanks!
Is √3 rational?
I’m trying to figure out is the question above rational
Answer:
The square root of 3 is an irrational number if that's what you were asking
a high school has 48 players on the football team. the summary of the players' weights is given in the box plot. approximately, what is the percentage of players weighing greater than or equal to 232 pounds?
The proportion of players weighing more than or equatable to 220 pounds is 50%.
What is termed as the quartile?The dataset is divided into four groups by dividing the data into three points: lower quartile, midpoint, and upper quartile.The quartiles, along with the data set's minimum and maximum values, divide a collection of observations in to the four sections, each chosen to represent 25% of the observations.Based on the information provided
There are 48 players in total.
Based on the box plot;
158 pounds is the minimum weight.
Q1 = 185, which represents 25% of the information below 185 pounds.
The second quartile Q2 = 220 pounds, which represents 50% of the information below 220 pounds.
The third quartile (Q3) = 232, representing 75% of the information below 232 pounds.
248 pounds is the maximum weight.
In this case, 220 is the middle number and represents the median.
50% of the information are located on both the left and right sides of the median.
As a result, the proportion of players weighing more than or equatable to 220 pounds is 50%.
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WILL GIVE BRAINLY
PLS ANSWER QUICK
Use properties to evaluate [tex]-5x14 ÷ \frac{3}{4} x 15[/tex]
A. -350
B. -1400
C. 350
D. 1400
The expression has a value of -1400 when evaluated
How to evaluate the expression?From the question, the expression is represented as
-5 x 14 ÷ 3/4 x 15
Start by evaluating the product of -5 and 14
So, we have the following equation represented as
-5 x 14 ÷ 3/4 x 15 = -70 ÷ 3/4 x 15
Next, we rewrite the quotient as products
So, we have the following equation represented as
-5 x 14 ÷ 3/4 x 15 = -70 x 4/3 x 15
Divide 15 by 3
So, we have
-5 x 14 ÷ 3/4 x 15 = -70 x 4 x 5
Continue by evaluating the product of -70 and 4
So, we have the following equation
-5 x 14 ÷ 3/4 x 15 = -280 x 5
Lastly, we have
-5 x 14 ÷ 3/4 x 15 = -1400
Hence, the value of the expression is -1400
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PLEASE HELP FASTTT ILL MARK BRAINLIEST
Answer:
[tex]2\sqrt{2}[/tex]
Doing RSM I see... lol gl. (tell me if this is wrong, I'll correct it if it is) :]
Step-by-step explanation:
h(6)=2
g(2) = [tex]\sqrt{2\\}[/tex]
f(sqrt2) = [tex]2\sqrt{2}[/tex]
:]
division of fractions and mixed numbers in the real world the local preservation group is cleaning up a 3 3/5 km hiking trail twelve members sign up to help. to make the work easier, the leader of the group splits the trail into equal sections, one for each member. what length of trail is each member responsible for cleaning?
The length of trail is each member responsible for cleaning is 0.3.
Given,
In the real world the local preservation group is cleaning up a 3 3/5 km hiking trail twelve members sign up to help.
To find the length of trail is each member responsible for cleaning.
(Division of fractions)
Now, According to the question:
Based on the given condition
= [tex]3\frac{3}{5}[/tex] ÷ 12
= 18/5 ÷ 12
Convert into decimal
= 3.6 x 1/12
= 0.3
Hence, The length of trail is each member responsible for cleaning is 0.3.
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rearrange the following so g is the main subject:
f+4(g-h)=x
Answer:
g=x-f+4h/4
Step-by-step explanation:
change of subject of formula
f+4(g-h)=x
f+4g-4h=x
4g-4h=x-f
4g=x-f+4h
g=x-f+4h/4
rate as brainliest
Solve for X.
Help please!!!
Answer:
x=17
Step-by-step explanation:
2x-3+3x+8=90
5x=85
x=17
:]
Congruent triangles
Please answer this question
A.Congruent triangles)
Suppose Alex wants to kick a ball over a 10-foot fence. Assuming that gravity has no effect, at what angle would he have to kick the ball if he were standing 6 feet away from the fence?
a.
36.9°
c.
53.1°
b.
59.0°
d.
31.0°
You would take Alex's distance from the fence, which is 10 feet, and the length of the fence to get the angle.
Finding the angle using the right triangle's trig formulas, sine, cosine, or tangent
neighboring side = 6 feet
obverse side = 10 feet
employ a tangent because
[tex]tan^{-1}\frac{opposite}{adjacent} = tan^{-1}\frac{10}{6} = 59.0[/tex]
About Right triangle's
The formula for a right triangle's area, perimeter, and hypotenuse length are all included in the formula for a right triangle.
In geometry, there are several figure kinds that are distinguished from one another by their unique characteristics. A triangle is one of the shapes they frequently use. A triangle is a closed, three-sided polygonal shape. It has three vertices and three sides that contain the triangle's three interior angles. A triangle's three inner angles always add up to 180 degrees.
Equilateral, isosceles, scalene and right-angled triangles are the most typical triangle types we examine. The right triangle formula, commonly known as the right-angled triangle formulae, will be discussed in this section.
Any interior angle that is 90 degrees in length is said to be in a right triangle. It should be remembered that only one of the three angles may be a right angle because the total interior angle of a triangle is 180 degrees.
Continue reading: Right Angle Triangle
The triangle is referred to as an isosceles right-angled triangle if the other two angles are equal, or 45 degrees each. A scalene right-angled triangle, on the other hand, results from the other two angles being uneven.
Trigonometry is where right-angled triangles are used the most frequently. In reality, trigonometry's foundation is the relationship between its angles and sides.
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In a solar system, two comets pass near the sun, which is located at the origin. Comet E is modeled by quantity y plus 16 end quantity squared over 400 plus x squared over 144 equals 1 and Comet H is modeled by quantity y plus 13 end quantity squared over 144 minus x squared over 25 equals 1 comma where all measurements are in astronomical units.
Part A: What are the vertices for the path of Comet E? Show your work. (4 points)
Part B: Which comet travels closer to the sun? Give evidence to support your answer. (5 points)
Part C: What key feature does the sun represent for both comets? Give evidence to support your answer. (6 points)
The vertices of the path of the comet E are; (-12,0) and (+12,0) as it is moving an elliptical path.
What are the vertices of the path of the comet E?Comet 'E' is modeled by
((y + 16)²)/400 + (x²)/144 = 1
This is an equation of an ellipse. So, the path traveled by Comet E will be an elliptic path.
Comparing with the equation of ellipse;
((y - k)²)/(b²)+ ((x - h) ²)/(a ²) = 1
whose; Centre is (h,k) and Vertex is (h±a, 0)
On Comparing Centre (h, k), h= 0 and k = -16,
a²=144
a = 12
b²=400
b=20
So, Centre (0, -16),
The Vertex (-12,0) and (+12,0)
So, the vertices of the path of the comet E are; (-12,0) and (+12,0).
Part B: The path of Comet H has been modeled as; a horizontal hyperbola.
Thus, The Comet H travels closer to the sun.
Part C: The sun represents the one of the foci of both the Comet E and Comet H.
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12. x=lyl with inputs x = 1, x = 2, and x
3
If x=lyl with inputs x = 1, x = 2, and x = 3 then y = ±1, y = ±2, and y = ±3.
To solve this problem we have to learn about the modulus operator and absolute value.
What is absolute value?
Absolute value is the distance of a number from zero.
Example: for -12, the distance from 0 is 12. Therefore 12 is the absolute value of -12.
What is the mod operator?
A Mod operator is a mathematical device that converts all types of integers into a positive integer or it finds the absolute value.
Now, we have to find values.
x=lyl Or, 1 = |y| or, we can say the absolute value of y is 1. y may be ±1x=lyl Or, 2 = |y| or, we can say the absolute value of y is 2. y may be ±2x=lyl Or, 3 = |y| or, we can say the absolute value of y is 3. y may be ±3To know more about absolute values visit,
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Alvin's
age Is three times Elga's age. The sum of their ages Is 96. What Is Elga's age?
years old
Answer: Elga is 16 years old
Step-by-step explanation: so first you divide 96 by 2 and get 48, 48 divided by 3=16,
please mark brainliest if this helps :)
Work Shown:
x = Elga's age
3x = Alvin's age since he is 3 times older
x+3x = 4x = sum of their ages
4x = 96
x = 96/4
x = 24 is Elga's age
3x = 3*24 = 72 is Alvin's age
Check: 24+72 = 96 which confirms the answer.
Is it possible for consecutive interior angles to be congruent?
No, It is not possible for consecutive interior angles to be congruent.
If the transversal line crosses the two lines as parallel to one another, the consecutive interior angles are supplementary rather than congruent and add up to 180 degrees.
Parallel internal angles are additional (the consecutive interior angles postulate) External angles that follow each other are supplemental (the consecutive exterior angles theorem) Congruent alternate interior angles (the alternate interior angles theorem)
What are consecutive interior angles?The pair of non-adjacent internal angles that are located on the same side of the transversal are referred to as consecutive interior angles. The term "consecutive" describes events that take place side by side. On the internal side of a transversal, two consecutive interior angles are situated next to one another.
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PLEASE HELP ME ! due tonight , Will make you a brainlist if you give me the correct answer .
Answer:
y=3/2x+3
Step-by-step explanation:
gradient is dy/dx
so up 3 and across 2
3/2
crosses at 3
Answer:
y=-3/2x+3
Step-by-step explanation:touches y axis at 3 and negative 3/2 slope
solve the following equation 23 + 23 = 5y + 11
Answer:
7
Step-by-step explanation:
Since 23 + 23 = 46
We just have to multiply 5 by something. 11 + 5 x 7 = 46
Y is = 7
btw im in middle school
your answer could be 72
i did a lot of math
and if you have what y means to me its y = 3 so i did 5*3
Eric orders 3 large cheese pizzas. There is a $2 delivery fee for each pizza. He pays a total of $42. Which equation can be used to find the price, r, of each pizza?
we have that he paid 4 dollars due the delivery. So each pizza costs
[tex]\frac{38}{2}=19[/tex]so the equation to find the price r is
[tex]r=\frac{42-4}{2}[/tex]Math To Do, -Ready
Interactive Practice: Work with Scientific Notati
-) Multiply. Write your answer using scientific notation.
(2 × 10 ) × (3.1 × 10¹⁰) = ||
X ?
6.2 × [tex]10^{11}[/tex] is the result after multiplying the terms (2 × 10 ) × (3.1 × 10¹⁰).
We are provided with the equation mentioned below:
(2 × 10 ) × (3.1 × 10¹⁰) equation 1
We were asked to multiply the terms mentioned in the above equation using scientific notation. The steps to simplify the above mentioned equation are written below;
(2 × 10 ) × (3.1 × 10¹⁰)
Separately write similar terms first as shown below,
= ( 2 × 3.1 ) × ( [tex]10^{1}[/tex] × [tex]10^{10}[/tex] )
Now multiply the similar terms as written below;
= 6.2 × [tex]10^{(1 + 10)}[/tex]
Add powers of 10, we get
= 6.2 × [tex]10^{11}[/tex]
Thus, the solution of the given equation is 6.2 × [tex]10^{11}[/tex].
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please help asap
during a snow storm the temperature drops from 0 degress f to - 12 degress f in 3 hour. on averge by how many degress is the temperature changing per hour?
A, -4f
B. 12f
C. 15f
D. -9f
The average change per hour is: -4 F/h
So the temperature decreases by 4 degrees Fahrenheit each hour.
How to get the average change in temperature?
To get the average change in degrees per hour, we need to take the quotient between the change in temperature and the number of hours in which this happens.
We know that initially the temperature is 0F
The final temperature is -12F
and this happens on an interval of 3 hours, then the average change per hour is:
(-12F - 0F)/3h = -12F/3h = -4 F/h
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Draw the graph of each circle given its equation below.
Step 1:
First, write the general equation of a circle
[tex]\begin{gathered} (x-a)^a+(y-b)^2=r^2 \\ r\text{ is the radius} \\ (a,\text{ b) is the center} \end{gathered}[/tex]Step 2:
Question 1
[tex]\begin{gathered} x^2+y^2\text{ = 121} \\ x^2+y^2=11^2 \\ \text{radius r = 11} \\ \text{center = (0 , 0)} \end{gathered}[/tex]Question 2
[tex]\begin{gathered} (x-2)^2+y^2\text{ = 64} \\ (x-2)^2+y^2=8^2 \\ \text{Center = (2, 0)} \\ r\text{ = 8} \end{gathered}[/tex]Question 3
[tex]\begin{gathered} (x\text{ + }\frac{3}{2})^2\text{ + (y + }\frac{5}{8})^2\text{ = 36} \\ (x\text{ + }\frac{3}{2})^2\text{ + (y + }\frac{5}{8})^2\text{ = }6^2 \\ \text{Center = (-}\frac{3}{2}\text{ , -}\frac{5}{8}) \\ r\text{ = 6} \end{gathered}[/tex]Question 4
[tex]\begin{gathered} (x-1)^2+(y+7)^2\text{ = 9} \\ (x-1)^2+(y+7)^2\text{ = }3^2 \\ \text{Center = (1, -7)} \\ r\text{ = 3} \end{gathered}[/tex]Question 5
[tex]\begin{gathered} (x+8)^2+(y-3)^2\text{ = 7} \\ (x+8)^2+(y-3)^2\text{ = (}\sqrt[]{7})^2 \\ \text{Center = (-8, 3)} \\ \text{radius r = }\sqrt[]{7} \end{gathered}[/tex]
A restaurant customer left $1.05 as a tip. The tax was 8% and the tip was 15% of the cost including tax.
a. Which information is not needed to compute the bill after tax and tip?
b. What was the total bill?
well, the bill was actually "x", which oddly enough is the 100%, but we also know that the tip was $1.05 and that's 15% of the whole bill plus tax.
so if we know that 1.05 is 15% of "x", what the dickens is "x"?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 1.05 & 15\\ x& 100 \end{array} \implies \cfrac{1.05}{x}~~=~~\cfrac{15}{100} \\\\\\ 105=15x\implies \cfrac{105}{15}=x\implies 7=x[/tex]
well, as you can see, we know the tax was 8%, but, it doesn't really matter if it had been 25% or who knows, so long we know that 1.05 is 15% of the whole smack.
Angel buys cookies and lemons at the store.
He pays a total of $29.80.
He pays a total of $6.25 for the cookies.
• He buys 5 bags of lemons that each cost the same amount.
How much does each bag of lemons cost?
The cost of each bag of lemons is $4.71
Let y represent the cost of lemon
Angel pays $29.80 for both the cookies and lemon
He pays a total of $6.25 for the cookies
He buys 5 bags of lemons
The equation can be expressed as
6.25 + 5y= 29.80
collect the like terms
5y= 29.80-6.25
5y= 23.55
divide by the coefficient of y which is 5
y= 23.55/5
y= 4.71
The result of y from the equation is 4.71
Hence each bag of lemon costs $4.71
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A water treatment plant needs to maintain the ph of the water in the reservoir at a certain level. To monitor this, they take 2 oz. Of water at 37 locations every hour, measure the ph at each of those locations, and find their average. If the ph level of the reservoir is ok, the results at each location will have varying results, with an average ph of 8. 5 and a standard deviation of 0. 22. If the ph level of the reservoir is ok, what is the probability that the sample average is less than 8. 42?.
P(X < 8.4)
= P(Z < (8.4 - 8.5) / (0.22 / sqrt(37)))
= P(Z < -2.76 ) = 0.0029
So the probability is 0.0029
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The larger of two numbers is 1 more than 3 times the smaller. Their sum is 65. Find the numbers.
The larger number is 49 and the smaller number is 16.
What are the numbers?The first step is to form a linear expression that represents the larger number.
Let the smaller number be represented with y
The larger number is represented with this linear expression : 1 + 3y
The sum of the two numbers : 1 + 3y + y = 65
Take the following steps to determine the value of the smaller number:
Combine similar terms: 65 - 1 = 3y + y
Add similar terms together: 64 = 4y
Divide both sides by 4: y = 64 / 4
y = 16
Larger number = 1 + 3(16)
1 + 48 = 49
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Write as an inequality. Do not solve.
Yellow Cab charges a flat rate of $3.00 plus $0.50 per mile. Raven
has $20.00 to spend on a cab ride. Write an inequality that expresses how
many miles Raven can travel under her limit.
The product of 8 and y is less than 21.
Raven can travel 5.71 miles or less under her limit.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions. If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.
Let x b the number of miles Raven travels, we can write an expression relating the amount he spends. So there:
3.00 + 0.50= 3.50
Consider that total cost per mile be less than equal to the amount the Raven can spend:
3.50x ≤ 20
We can determine x;
x ≤ 5.71
Therefore, Raven can travel 5.71 or less under her limit.
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At Simba Travel Agency, the price of a climbing trip to Mount Kilimanjaro includes an initial fee plus a constant fee per meter.
F represents the fee (in dollars) for climbing d meters.
F=110+0.12d
What is the increase in price for every 100 meters climbed?
Answer:
$12
Step-by-step explanation:
You want to know the price increase per 100 meters if the fee for climbing d meters is ...
f = 110 + 0.12d
Rate of changeThe rate of change indicated by the coefficient of d in the equation is 0.12 for each unit of d. Then the amount of change for 100 units of d is ...
0.12(100) = 12
The price increases by $12 for every 100 meters climbed.
<95141404393>
Simplify to create an equivalent expression 10+4(−8q−4)
Answer:
-32q-6
Step-by-step explanation:
Please look at the attachment! Hope this helps! ~~
Answer : -0.3125 + q + 0.5
1) Distribute
10 - 32q - 16
2) Divide all terms by -32
-0.3125 + q + 0.5