The solution for x ≥ 0 and x ≥ -5 is [-5, ∞), in the interval notation.
The interval notations are used to represent numbers between two numbers excluding or including the numbers as per the use. We use the following four interval notations:
[a, b] ⇒ All numbers between a and b including both a and b.
(a, b) ⇒ All numbers between a and b excluding both a and b.
(a, b] ⇒ All numbers between a and b excluding a but including b.
[a, b) ⇒ All numbers between a and b including a but excluding b.
We are asked to write the solution for x ≥ 0 and x ≥ -5 in the interval notation.
We first write each inequality in interval notation:
x ≥ 0 ⇒ x are all numbers greater than 0 including 0. This can be written in the interval notation as [0, ∞). We don't include ∞ as it is indeterminant.
x ≥ -5 ⇒ x are all numbers greater than -5 including -5. This can be written in the interval notation as [-5, ∞). We don't include ∞ as it is indeterminant.
Now, we are asked to solve for x ≥ 0 or x ≥ -5. Since it is 'or', we take unions of the two sets, that is the solution is:
[0, ∞) ∪ [-5, ∞) = [5, ∞).
Therefore, the solution for x ≥ 0 and x ≥ -5 is [-5, ∞), in the interval notation.
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Create diagrams to represent the possible cases for common tangents between two circles. Your diagram can be created using multimedia sources or drawn by hand. They should not be copied and pasted from a website. Explain why your diagrams satisfy the given criteria.
No Common Tangents (10 points)
Diagram:
Justification:
The diagram to represent the possible cases for common tangents between two circles is as shown in the attachment.
How to Create Common Tangents?
A tangent line to a circle is defined as a line that touches the circle at exactly one point, never entering the circle's interior.
1. When one circle is in between another and one circle does not touch the other one, then tangent is not possible.2. When one circle is in between another and one circle touches the other one at a point inside the circle, then only one tangent is possible.3. When one circle intersects the other one, then two tangents are possible.4. When one circle touches the other one at a point outside, then three tangents are possible.5. When one circle neither intersects the other one nor inside the other one, then four tangents are possible.Thus, the diagram to represent the possible cases for common tangents between two circles are as attached below.
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Find the measure of the angles indicated
Both angles have a measure of 125°.
How to find the measure of the angles?
Assuming the two horizontal lines are parallel, we know that the measure of the two indicated angles must be the same one.
Then:
-1 + 14x = 12x + 17
Now we need to solve this for x:
14x - 12x = 17 + 1
2x = 18
x =18/2 = 9
Now that we know the value of x we can replace it in any of the expressions for the angles:
-1 + 14*9 = 125°
Both angles have a measure of 125°.
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Which of the following represents x = 1/3y written in general form?
The general form of the given equation is 3x-y=0.
The given equation is [tex]x=\frac{1}{3}y[/tex].
We need to write the given equation in a general form.
What is a general form of an equation?The general form of any equation contains the degree of variables in decreasing order. The general form of a linear equation is ax + b = 0.
That is, [tex]3x=y[/tex]
[tex]3x-y=0[/tex].
Hence, the general form of the given equation is 3x-y=0.
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if a football player passes a football 4 feet off the ground with the velocity of 36 feet per second, how long will it take the football to hit the ground? Use the equation h=-16t^2+36t+4
The ball will hit the ground after 2.355 secs
Velocity of an objectThe velocity of an object the change of displacement with respect to time.
Given the function that represents the height of football ground
h(t) = -16t^2+36t+4
The ball will hit the ground at the point where the height h(t) = 0
Substitute
-16t^2+36t+4 = 0
16t^2-36t-4 =0
4t^2-9t-1= 0
Factorize
t = 9/8 + √97/8
t = 9/8 + 1.23
t = 2.355secs
Hence the ball will hit the ground after 2.355 secs
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The number y of objects a machine produces is proportional to the time x (in minutes) that the machine runs. The machine produces five objects in four minutes.
a. Write an equation that represents the situation.
Hellllppp me please!!!!!!!!!!!
The equation that represents the situation will be 4y = 5x.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The number y of objects a machine produces is proportional to the time x (in minutes) that the machine runs.
The machine produces five objects in four minutes.
Let y be the number of objects and x be the number of the minutes.
Then the equation that represents the situation will be
y = (5/4)x
4y = 5x
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Lea wants to save money on a new computer. At the store near her, the computer she wants is listed at a regular price of $400.00.
On Saturday, the store will have a sale and discount the computer by 30%.
Shoppers who buy a computer that same Saturday before 9:00 a.m. will also receive an additional 10% off the sale price.
How much will Lea pay, without tax, when she buys the computer that Saturday before 9:00 a.m.?
Answer:
Step-by-step explanation:
you take 30% and 10% and turn them into decimal like so:
30/100=0.3
10/100=0.1
400.00(0.3)=120.00
120(0.1)=12
5. Try It #5
If f(x) is a linear function, with f(2)=-11, and f(4)=-25, find an equation for the function in slope-intercept form.
The function in slope-intercept form is mathematically given as
f(x)=14x+154
What is an equation for the function in slope-intercept form.?
Parameters
f(2)=-11,
f(4)=-25
Generally, the equation for the slope is mathematically given as
[tex]m=\frac{-25+11}{2-}[/tex]
m=7
In conclusion, the line equation
y-2=7(x-+11)
y as subject
y=14x+154
f(x)=14x+154
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3 men build a wall in 2 days.
How long will it take
a) 1 man
b) 2 men?
Please show working
Answer:
Step-by-step explanation:
Big clever stuff 100 men in 1 second tick tick boom
Find the area of the shaded regions.
Answer:
Area = 84.8 cm²
Step-by-step explanation:
It appears that the line BO is equal to the radius. It also looks like the missing region is equal to 1/4 of the entire area. Therefore, to find the area of the shaded region, you need to (1) find the area of the entire circle and then (2) find the area of 3/4 of the circle.
Area of Circle:
r = 6 cm
A = πr²
A = π(6 cm)²
A = π(36 cm²)
A = 113 cm²
Area of Shaded Region:
Area (Entire Circle) x 3/4 = Area (Shaded Region)
113 cm² x 3/4 = 84.8 cm²
Carissa pays $2.10 each day for lunch. her money is in an account that is deducted each time she buys a lunch. there are 6 days until the end of the school year and her account has $12.75 in it. how much money will she get back at the end of the year?
Answer:
15¢
Step-by-step explanation:
$12.75 - 6 × $2.10 = $12.75 - $12.60 = $0.15
Answer: 15 cents
Tiger Biscuits factory planing to produce 10,000 units in Month Standard time per 200 units is 8 hours! the Company pays. Rs. 40 per her.
The total cost or amount that Tiger Biscuits will pay will be Rs 16000.
How to calculate the cost?From the information given, the factory is planing to produce 10,000 units and the standard time per 200 units is 8 hours.
The time taken to produce 10000 units will be:
= (10000/200) × 8
= 400 hours.
The amount that the company will pay will be:
= 400 × Rs 40
= Rs 16000
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Two digit natural number whose sum is 5
When the tens place digit is x write in terms of x
The value of the given 2 digits number when the tens place digit is x write in terms of x is; 10x + y
How to find a two digit number?
We are given that the sum of a two digit number is 5.
Now, if the number is xy, then we can say that;
x + y = 5
Since x is the tens place digit, then we can say that the value of x is 10x and as such the value of the 2 digits is written as;
10x + y
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A student can pitch a fast ball at 65 miles per hour. Convert this
speed to yards per second.
O 95.33 yd/sec
O 132.95 yd/sec
O 31.77 yd/sec
O 21.67 yd/sec
Answer:
31.77 yd/sec
Step-by-step explanation:
Conversions:
1 mile = 1760 yards1 hour = 3600 secondsGiven:
[tex]\sf 65\:miles\:per\:hour=65\:miles/hour=\dfrac{65\:miles}{hour}[/tex]
Therefore, to convert 65 mph to yards per second:
[tex]\implies \sf \dfrac{65\:miles}{hour}=\dfrac{65 \times 1760\:yards}{3600\:seconds}=31.777...\:yd/s[/tex]
Answer:
c.) 31.77... yd/sec
Explanation:
Given: 1 hours → 65 miles
Conversions:
(i) 1 hour = 60 minutes = 3600 seconds
(ii) 1 miles = 1760 yards
Then,
1 hour = 3600 seconds65 miles = (1760 × 65) = 114400 yards Speed:⇒ distance/speed
⇒ 114400/3600
⇒ 31.77777...
⇒ 31.77 yd/sec
What is the range of Y = l0g8X?
O all real numbers less than 0
O all real numbers greater than 0
O all real numbers not equal to 0
all real numbers
Step-by-step explanation:
all real numbers not equal to 0
all real numbers
Step-by-step explanation:
[tex]What \ is\ the \ range \ of \ y = log_8x?\\x > 0 \ or\ x\in(0;\infty).\\Answer: \ all \ real \ numbers \ greater\ than \ 0.[/tex]
Simplify the following expression as a
monomial:
-8a8
———-
-2a7
Answer:
4a
Step-by-step explanation:
-8 / -2 = 4
a^8/a^7 = a^(8 - 7) = a
Answer: 4a
Given: AD∥BC and AB∥CD
Prove: AD≅BC and AB≅CD
Answer:
BC || AD and AB || CD (given)
∠BCA ≅ ∠DAC 2. As alt.interior angles with parallel lines
∠BAC ≅ ∠DCA 3. As alt.interior angles with parallel lines
AC ≅ AC (identity)
△ABC ≅ △CDA (ASA)
AB = CD (CPCT C)
Please help me with this geometry question, Im pretty sure you need to use SAS congruence rule
Congruent triangles are two or more triangles with the same length of sides and measure of internal angles. Thus the required proof is as shown below:
From the given diagram, it can be observed that:
AB = AC (similar property of two lines)
AC = AE (similar property of two lines)
Also,
m<A is a common angle to ΔABC and ΔADE
So that it can be concluded that;
ΔABC ≅ ΔADE (Side-Angle-Side property)
Thus since ΔABC ≅ ΔADE are congruent, then;
BC = DE (corresponding sides of congruent triangles)
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See below for the proof that sides BC and DE are congruent
How to prove the side lengths?The given parameters are:
AC = AE
AB = AD
∠BAD = ∠EAC
By the definition of congruence, side lengths marked with I are congruent and side lengths marked with II are congruent
From the attached figure, we have the following marks:
In triangle ABC,
AB = I and AC = II
In triangle ADE,
AD = I and AE = II
This means that two corresponding sides of ABC and ADE are congruent.
Since both triangles have a congruent angle, then the last corresponding sides are also congruent
i.e. BC = DE
Hence, sides BC and DE are congruent
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Find a 95% confidence interval for the mean amount of time spent on this ride. Round the values in your confidence interval to two decimal places. The 95% percent confidence interval is
95% confidence interval is 1.96
A confidence interval is defined as the range of values that we observe in our sample and for which we expect to find the value that accurately reflects the population.
For 95% confidence interval, we will keep 95% area in the center and will divide the remaining area equally on both sides.
From Standard Normal table, P(-1.96 < Z < 1.96) = 0.95, i.e., there is a 95% probability that a standard normal variable, Z, will fall between -1.96 and 1.96.
Hence 95% percent confidence interval is 1.96
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Hassan wants to ride his bicycle 26.8 miles this week. He has already ridden 6 miles.
If he rides for 4 more days, what is the average number of miles he would have to ride
each day to meet his goal?
AnsTHE OTHER GUY GOT IT RIGHT SORRY I DID THE MATH WRONG :( Step-by-step explanation:
Answer:
5.2 miles
Step-by-step explanation:
Distance left to ride = 26.8miles - 6 miles = 20.8 miles
There are 4 days left, so on average,
Hassan has to ride:
[tex] \frac{20.8}{4} \\ = 5.2mi[/tex]
Juan wants to change the shape of his vegetable garden from a square to a rectangle, but keep the same area so he can grow the same amount of vegetables. The rectangular garden will have a length that is 2 times the length of the square garden, and the width of the new garden will be 16 feet shorter than the old garden.
Answer:
The answer is 32
Step-by-step explanation:
A group of students and workers entering a metro station were asked whether they were riding the bus or the subway. The two-way table shows their answers.
How many people were polled?
A. 48
B. 69
C. 118
D. 166
please help me with math
The area of triangle BMN is 124.7 square centimeter.
What are similar triangles?Similar triangles are triangles that their corresponding angles are equal and the ratio of their corresponding lengths are equal. They are often similar When at least Two angles are equal or The ratio of any corresponding lengths are same.
Analysis:
AB = AC = BC = 50cm
AH = AC/2 = 50/2 = 25cm
From Δ ABH, using Pythagoras theorem to find BH.
[tex](BH)^{2}[/tex] = [tex](AB)^{2}[/tex] - [tex](AH)^{2}[/tex]
[tex](BH)^{2}[/tex] = [tex]50^{2}[/tex] - [tex]25^{2}[/tex]
[tex](BH)^{2}[/tex] = 2500 - 625
[tex](BH)^{2}[/tex] = 1875
BH = [tex]\sqrt{1875}[/tex] = 43.3cm
ΔBMN and BHC are similar,
so, BM/BH = MN/HC
BM/43.3 = 12/25
25BM = 12 X 43.3
BM = 519.6/25 = 20.78cm
Area of ΔBMN
= 1/2(MN)(BM) = 1/2 x 12 x 20.78 = 124.7 square centimeter
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Using a table of values, determine the solution to the equation below to the nearest fourth of a unit.
2-5x=2x - 3
=
OA. X 0.75
OB. x= -0.75
OC. x 1.25
OD. x= -1.25
2
The solution to the equation below to the nearest fourth of a unit is 0.75
Solving linear equationGiven the linear equation below expressed as:
2-5x=2x - 3
Collect the like terms
-5x - 2x = -3- 2
-7x = -5
Divide both sides by -7 to have:
-7x/-7 = -5/-7
x = 5/7
x = 0.75
Hence the solution to the equation below to the nearest fourth of a unit is 0.75
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9r-4(-5r-5)<-9r+10+5
Five little girls taken in couples weigh 129 pounds, 125 pounds, 124 pounds, 123 pounds, 122 pounds, 121 pounds, 120 pound, 118 pounds, 116 pounds and 114 pounds on a weighing machine. What was the weight of each one of the five little girls if taken separately
The weight of each one of the five little girls if taken separately is 242.4 lb.
Weight of each girl when taken separatelyThe weight of each girl can be determined from the average weight of the girls.
Weight of each girl = (Total weight) / number of girls
W = (129 + 125 + 124 + 123 + 122 + 121 + 120 + 118 + 116 + 114)/5
W = 1,212/5
W = 242.4 lb
Thus, the weight of each one of the five little girls if taken separately is 242.4.
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Prove that the triangles formed due to the diagonal of rectangle are congruent to one another
A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle.The triangles formed due to the diagonal of the rectangle are congruent to one another.
What is a rectangle?A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
For the given rectangle ABCD, the length of the diagonals AC and BD can be written as,
AC = √(x² + y²)
BD = √(x² + y²)
Now, the triangles formed due to the diagonals AC and BD are ΔABC and ΔBCD. Also, for ΔABC and ΔBCD we can write,
∠ABC = ∠BCD = 90°
AB = CD = x {Oppsite sides of the rectangle are equal}
BC = AD = y {Oppsite sides of the rectangle are equal}
Hence, the two triangles are equal. Therefore, the triangles formed due to the diagonal of the rectangle are congruent to one another.
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Jackrabbits are capable of reaching speeds up to 40 miles per hour. How fast is this in feet per second? (Round to the nearest whole number.)
-8√147x simplify do you know how to answer this?
Answer:
-56√3x
Step-by-step explanation:
√147 = 7√3
-8(7√3x)
-56√3x
A recipe calls for 11 tablespoons of sugar and 22 teaspoons of salt. How many
teaspoons of salt are needed for just one tablespoon of sugar?
On the double number line below, fill in the given values, then use multiplication or
division to find the missing value:
It will require 2 tablespoons of salt for just 1 tablespoon of sugar for the combination.
What are word problems?Word problems are a systematic approach used in mathematics for solving real-life cases by determining unknown values.
From the given information:
If it takes 11 tablespoon + 22 teaspoon to make 1 recipe.i.e.
11 tablespoon of sugar + 22 teaspoon of salt = 1 recipe
Then it will require 2 tablespoons of salt for just 1 tablespoon of sugar.
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Given the function g(x) = x^2 - 5x which statement is not correct ?
Hello,
g(x) = x² - 5x
g(-3) = (-3)² - 5 × 3 = 9 - 15 = - 6 ≠ 24 ⇒ not correct
g(-1) = (-1)² - 5 × (-1) = 1 - 5 = -4 ⇒ correct
g(5) = 5² - 5× 5 = 25 - 25 = 0 ⇒ correct
g(7) = 7² - 5 × 7 = 49 - 35 = 14 ⇒ correct