Answers
The possible values of x for the given triangle ABC are 0.75<x<8.
What is the triangle inequality theorem?The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.
Given that, m∠A < m∠B < m∠C.
a) From triangle ABC,
BC<AC<AB
2x+3<6x<5x+8
Now, 2x+3<6x
Subtract 2x on both the sides of an inequality, we get
3<4x
Divide 4 on both the sides of an inequality, we get
0.75<x
Here, 6x<5x+8
Subtract 5x on both the sides of an inequality, we get
x<8
So, possible values of x are 0.75<x<8
b) From triangle ABC,
BC<AC<AB
3x+1<4x+8<7x+2
Now, 3x+1<4x+8
Subtract 3x on both the sides of an inequality, we get
1<x+8
Subtract 8 on both the sides of an inequality, we get
-7<x
Here, 4x+8<7x+2
Subtract 4x on both the sides of an inequality, we get
8<3x+2
Subtract 2 on both the sides of an inequality, we get
6<3x
Divide 3 on both the sides of an inequality, we get
2<x
So, possible values of x are -7<x<2
Therefore, the possible values of x for the given triangle ABC are 0.75<x<8.
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Related Questions
What is the smallest natural number value
for n if the solution for √56n is also a
natural number?
Answers
Answer:
2√14
Step-by-step explanation:
√56 = √4 × √14
which is
2√14
Why is triangle always 180 degrees?
Answers
Triangle is always 180 degrees because the sum of all angles in a triangle is 180 degrees. This is known as the "Triangle Angle Sum Theorem." The theorem states that the sum of all angles in a triangle is equal to 180 degrees.
1. A triangle is a three-sided polygon with three angles.
2. The sum of the three angles in any triangle must be 180 degrees.
3. This is known as the Triangle Angle Sum Theorem.
4. The Triangle Angle Sum Theorem states that the sum of the angles in a triangle must equal 180 degrees.
5. It does not matter which angles the triangle has, the sum will always equal 180 degrees.
6. This theorem is based on the fact that the sum of the angles in any triangle is equal to two right angles or 180 degrees.
7. The Triangle Angle Sum Theorem can be proven by drawing a triangle, and then measuring and adding the three angles.
8. The sum of the three angles will always equal 180 degrees.
9. Therefore, triangle is always 180 degrees.
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Under his cell phone plan, Gabriel pays a flat cost of $52.50 per month and $5 per gigabyte. He wants to keep his bill under $75 per month. Write and solve an inequality which can be used to determine 9, the number of gigabytes Gabriel can use while staying within his budget.
Answers
Find the slope of a line parallel to the line whose equation is 10x+6y=_96
Answers
Answer:
Slope=-3.333/2.000=-1.667
X-intercept= -13/5 = -2.60000
Y-intercept= -13/3 = 14.33333
Josh has 27 signed baseballs. He places the baseballs equally on 3 shelves. How many baseballs are on each shelf?
Answers
Answer:
9
Step-by-step explanation:
27 divided by 3 equal 9
2+2/3x=3/7 rewritten no fractions
Answers
Answer:
x = 3.1 as a decimal or x = 28/9 as a fraction
Step-by-step explanation:
Is 45/20 equal to 225%
Answers
Answer:
Yes, it would be 225%.
Step-by-step explanation:
If 20/20= 100% you can evenly take out 200% because there is 45/20.
That leaves you with the 5/20.
5/20= 25%.
If we add those two percentages 200% + 25%= 225%.
I hope that made sense lol, have a great day!
Rafael and his sister bought snacks at a discount store for movie night. Rafael got 3 boxed candies and 1 bag of chips for $3. 82. His sister got 2 bags of chips and 1 boxed candy for $2. 69. Find the cents for each item find the cost of each item
Answers
The cost of each box of candy is 31 cents and the cost of each bag of chips is 69 cents.
To find the cost of each box of candy, we first need to find the total cost for all items. We know that Rafael and his sister spent a total of $3.82 + $2.69 = $6.51 on snacks. Since Rafael bought 3 boxes of candy and 1 bag of chips, and his sister bought 2 bags of chips and 1 box of candy, there were a total of 3 + 2 = 5 bags of chips and 3 + 1 = 4 boxes of candy bought.
To find the cost of each box of candy, we divide the total cost for all boxes of candy by the number of boxes of candy: $6.51 / 4 = $1.63 or 163 cents. To find the cost of each bag of chips, we divide the total cost for all bags of chips by the number of bags of chips: $6.51 / 5 = $1.30 or 130 cents.
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PLS HELP!!!! WILL GIVE BRAINLIEST!!! EDGE. PERFORMANCE TASK STEP FOUR
Answers
5W = 24D is the expression that represents the change in the rate of dosage as per the weight.
What is an expression?A mathematical expression is a sentence that includes numbers, variables, or both. The equal symbol is never used in expressions. Here are a few phrases as examples. A mathematical statement stating the equality of two expressions is known as an equation.
Given the relation between dosage and the weight of a medicine
Children's Fever Medicine
(given every 4-6 hours, as needed)
Weight: 24 lbs 36+ lbs 48+lbs 60+lbs 72+ lbs
Dosage: 5 mL 7.5 mL 10 mL 12.5 mL 15 mL
ratio of weught and dose
24/5 = 36/7.5 = 48/ 10 = 60/12.5 = 75/15
=> 4.8 = 4.8 = 4.8 = 4.8 = 4.8
Since weight is directly proportional to the dosage
let W be the weight of the child and D be the Dose of the medicine
Thus, Relation between them:
=>W/D = 24/5
=> 5W = 24D
Therefore, The formula that describes the change in dosage rate in relation to weight is 5W = 24D.
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What is the solution of 7x =- 63?
Answers
The answer to 7^2 is 49. This means that 7 is multiplied by itself two times. To solve the given problem following steps should be followed :
Step 1: To calculate the value of 7 power 2, we need to use the exponentiation operator (^).
Step 2: The operator is written as 7^2, which is read as "seven to the power of two".
Step 3: We can calculate the value of 7 power 2 by multiplying 7 by itself 2 times.
Step 4: 7 × 7 = 49
Therefore, 7 power 2 = 49.
An expression known as "power" is defined as the process of repeatedly multiplying a value or integer. An is often a power where n is the exponent and an is the base.
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what is the y-intercept of a line that passes through the points (2, -2.5) and (4, -2)?
Answers
Answer:
Step-by-step explanation:
To find the y-intercept, we can use the slope-intercept form of a linear equation which is y = mx + b, where m is the slope of the line, and b is the y-intercept.
Since the line passes through the points (2, -2.5) and (4, -2), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
To find the slope(m) we can use the rise over the run formula ,
m = (y2 - y1) / (x2 - x1) = (-2 - (-2.5)) / (4 - 2) = -0.5
then we can substitute the values in point-slope form
y - (-2.5) = -0.5 (x - 2)
And now we can use x = 0,
y = -0.5(0-2) -2.5 = 1.5
so the y-intercept of the line is 1.5
-x+3y=6 in slope intercept form pls i need to know!!!
Answers
Answer:
[tex]\sf \bf y = \dfrac{1}{3}x + 2[/tex]
Step-by-step explanation:
Slope intercept form: y = mx + bWhere m is slope and b is y-intercept.
To write in slope intercept form isolate y.
To isolate y, first add 'x' to both sides,
-x + 3y = 6
3y = x + 6
Now, divide the entire equation by 3,
[tex]\sf \dfrac{3y}{3}=\dfrac{1}{3}x + \dfrac{6}{3}\\\\\\[/tex]
[tex]\sf \boxed{\bf y = \dfrac{1}{3}x + 2}[/tex]
What is the quotient of 1. 782 x 109 and 8. 1 x 106 expressed in scientific
notation?
Answers
The quotient of 1.782 × 10⁹ and 8.1 × 10⁶ in scientific notation is 2.2 × 10². The result is obtained by using the quotient rule.
What are the rules for exponents?Several rules for exponents are
Product rule → aⁿ × aˣ = aⁿ⁺ˣQuotient rule → aⁿ / aˣ = aⁿ⁻ˣPower of a product rule → (ab)ⁿ = aⁿ × bⁿPower of a quotient rule → (a/b)ⁿ = aⁿ / bⁿPower of a power rule → (aⁿ)ˣ = aⁿˣZero rule → a⁰ = 1Find the quotient of 1.782 × 10⁹ and 8.1 × 10⁶!
Dividing the first number by the second using the quotient rule, it would be
= (1.782 × 10⁹) / (8.1 × 10⁶)
= (1.782/8.1) × (10⁹/10⁶)
= 0.22 × 10⁹⁻⁶
= 0.22 × 10³
In scientific notation, we should write a.b × 10ⁿ, where 1 ≤ a < 10 and n is an integer.
So,
0.22 × 10³ = 2.2 × 10²
Hence, the result of 1.782 × 10⁹ divided by 8.1 × 10⁶ in scientific notation is 2.2 × 10².
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The length of one diagonal of a rhombus is 4 times the length of the other diagonal. Write an expression that represents the perimeter of the rhombus. Let d be the length of the shorter diagonal.
Answers
The expression that represents the perimeter of the rhombus is 2d√17
How to determine the expression that represents the perimeter of the rhombus?
From the question, we have the following parameters that can be used in our computation:
The length of one diagonal of a rhombus is 4 times the length of the other diagonal.
This means that
Length 1 = 4 * Length 2
From the question, we have
Let d be the length of the shorter diagonal.
This means that
Length 1 = 4d
Length 2 = d
The perimeter of the rhombus from the diagonals is calculated as
P = 2√(Length 1² + Length 2²)
Substitute the known values in the above equation, so, we have the following representation
P = 2√((4d)² + d²)
Evaluate the exponents
P = 2√(16d² + d²)
So, we have
P = 2√(17d²)
Evaluate the exponents
P = 2d√17
Hence, the perimeter is 2d√17
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Rene makes $38,000 per year and pays about 35% of
his gross monthly income in federal and state taxes.
He wants to find an apartment to rent. Estimate how
much he can afford to pay for rent each month. Then
determine how much money he will have after taxes
and rent are paid.
PLEASE HELP
Answers
After the taxes and rent, the remaining amount in his gross pay is $5,700
The term gross income is defined as also known as gross pay when it’s on a paycheck is an individual’s total earnings before taxes or other deductions.
Here we have given that Rene makes $38,000 per year and pays about 35% of his gross monthly income in federal and state taxes.
And as we all know that If you live in a metropolitan city, your HRA is equivalent to 50% of your basic salary.
Therefore, the remaining amount in his hand is calculated as,
=> $38000 - [35% of income + 50% of income]
Here the 35% of income is
=> 38000 x 35/100
=> 380 x 35
=> 13300
Similarly, the 50 percent of the income is
=> 38000 x 50/100
=> 380 x 50
=> 19000
Then the remaining amount is calculated by apply the values on it, then we get,
=> $38000 - [$13300 + $19000]
=> $3800 - $32300
=> $5700
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I need help with this question. :Probability and Statistics thanks
Answers
The number of possible combinations of 4 digit codes would be 72.
What are permutation and combination?A permutation is an arrangement of things where order matters, AB and BA are two different permutations.
The combination is a selection of things where order does not matter, AB and BA are the same combinations.
Given, I am creating a 4 digit code with the numbers 1 to 10.
Now, From 1 to 10 there are (10 - 1 + 1 ) = 10 and we are taking 4 numbers at a time.
Therefore the number of combinations of 4 digit codes would be,
[tex]^9C_4\times2![/tex]. As the number consists of two digits.
= [9!/(9 -2)!×2!]×2!.
= 9!/7!.
= 72 possible ways.
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The 19th and 15th term of an AP are -5 and -7 1/2 repectively. What i the um of the firt 20 term
Answers
The sum of first 20 terms of the AP will be -206.25
As in AP, let us assume that the "a" be the first term and 'd' be the common difference.
So, the value of nth term can be determined by using formula: a_n=a+(n-1)d, where, n = number of terms, and d = common difference.
So, the value of 19th terms = a+(19-1)d = a+18d = -5 -----(i)
And the value of 15th term = a+(15-1)d = a+14d = -7(1/2) ----(ii)
Now subtracting (ii) from (i),
We will get,
4d = 2(1/2)
=>4d = 2.5
=>d = (2.5/4) = 0.625
Now putting value of "d" in (i)
We will get,
a+(18*0.625) = -5
a=-5-11.25 = -16.25
We have, the formula for finding the sum of terms:
Sum of terms can be determined by using formula:
Sum = (n/2) × [2a + (n-1)d]
Here, n = 20, a = -16.25, d = 0.625
We will get sum of first 20 terms as:
[tex](n/2)\times [2a + (n-1)d]\\(20/2) \times [2 \times -16.25+(20-1)0.625]\\[/tex]
10[-32.5+11.875]
=10(-20.625) =-206.25
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Ericka was solving an exponential equation, and upon finishing, she realized her answer was incorrect when she substituted -5 back into her original equation. Identify Ericka’s mistake.
Answers
Ericka’s mistake is in ''Step 2.''
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Ericka was solving an exponential equation, and upon finishing, she realized her answer was incorrect when she substituted -5 back into her original equation.
Now,
Since, Ericka was solving an exponential equation.
Clearly, The equation is,
⇒ 5 ⁹ˣ⁺⁶ = 25³ˣ ⁻ ²⁴
Step 1;
⇒ 5 ⁹ˣ⁺⁶ = 25³ˣ ⁻ ²⁴
⇒ 5 ⁹ˣ⁺⁶ = 5 ² ⁽³ˣ ⁻ ²⁴⁾
Step 2;
⇒ 9x + 6 = 2 (3x - 24)
So, Ericka’s mistake is in Step 2.
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What is the length of the short side of one of the 30 60 90 triangles?
Answers
Remembering the ratio of 1: 3: 2 and understanding that the smallest side length is always opposite the shortest angle (30°) and the longest side length is always opposing the greatest angle (90°) can help you recall the 30-60-90 triangle principles.
According to the 30-60-90 triangle theorem, the hypotenuse is twice as long as the shorter leg. Additionally, the sides of this particular triangle have a ratio of 1:2: [tex]\sqrt{3}[/tex].
A 30-60-90 triangle can have three sides, and if you only know one, you can use shortcuts to discover the other two. The three scenarios you encounter when performing these computations are as follows:
You are aware of the short leg (the side across from the 30-degree angle). To find the hypotenuse, multiply the length by two. The long leg can be calculated by multiplying the short side by the square root of 3.You are aware of the hypotenuse. To get the short side, divide the hypotenuse by two. To determine the long leg, multiply this response by the square root of 3.You are aware of the long leg (the side across from the 60-degree angle). To determine the short side, divide this side by the square root of 3. To find the hypotenuse, multiply that amount by two.To know more about the 30 60 90 triangles on brainly : brainly.com/question/11751274
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Questions with Bounds:
1) Andy Mann is building a garden fence out of planks. The planks are 10cm wide to the nearest cm. He needs to make 75 m of fencing altogether, correct to the nearest meter. How many planks does he need to order to make sure he has enough to complete the fence?
Answers
A total of 785 planks Andy Mann needs to order to make sure he has enough to complete the fence.
As the planks are 10cm wide to the nearest cm.
The total length of the fencing is = 75 m
From above, we can conclude that,
Range of the planks' lengths: 9.5 cm <= Plank's length < 10.5 cm
Range of fencing needed: 74.5 m <= Fence length < 75.5 m
We should consider the worst-case scenario where all the planks are 9.5 cm.
To complete the job, he only needs 74.5 m in total.
So, the total number of planks needed for completing the Job will be
= (74.5 * 100) / 9.5 = (7.84210*100) = 784.210
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The base of an open rectangular box is of length (2x + 5) cm and width x cm.
The area of this base is 58 cm².
The height of the open box is (x - 2) cm.
I have attached a pic
(I already did part (a) and (bi) and you may use the answers to help you do the (bii) question)
+ the answer for (bi) if you can’t see it, it is 4.28 and -6.78
This is the question:
b) (ii) Hence calculate the volume of the box, stating the units of your answer.
Answers
The volume of the box is 58 cm³. Therefore, the units of the answer are cm³.
What is volume?Volume is the measure of the amount of 3-dimensional space occupied by an object or substance. It is usually measured in cubic units, such as cubic centimeters (cm3) or cubic meters (m3). Volume is an important concept in mathematics, physics, chemistry, and engineering, and is used to calculate the amount of material needed for a given project.
The volume of the box can be calculated by multiplying the area of the base with the height of the box. The area of the base is 58 cm² and the height of the box is x - 2 cm. Therefore, the volume of the box can be expressed as:
Volume = 58 cm² x (x - 2 cm)
= 58 cm³
The volume of the box is 58 cm³. Therefore, the units of the answer are cm³.
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Pop is on sale at Save-U-Lots. Which pack has the lowest cost per unit?
A. 6- pack for $2. 49
B. 12-pack for $3. 99
C. 24-pack for $5. 49
Answers
In the case of a 24-pack for $5. 49, the cost of the unit is the lowest.
The cost per item is nothing to the amount of money invested in buying one item.
As we have 3 different scenarios:
Case A. 6- pack for $2. 49
As here. cost of 6 packs is $2.49, so for determining the cost of one pack we will divide $2.49 by 6.
So, the cost of 1 pack will be = 2.49/6 = 0.415 $/pack
B. 12-pack for $3. 99
As here. cost of 12 packs is $3.99, so for determining the cost of one pack we will divide $3.99 by 12.
So, the cost of 1 pack will be = 3.99/12 = 0.3325 $/pack
C. 24-pack for $5. 49
As here. cost of 24 packs is $4.49, so for determining the cost of one pack we will divide $5.49 by 24.
So, the cost of 1 pack will be = 5.49/6 = 0.22875 $/pack
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What are the 3 ways to find x-intercept?
Answers
The three ways of finding the x-intercept are:
Using a Graph of a Line.Using the Equation of the Line.Using the Quadratic Formula.By looking at the equation, we may determine the y-intercept when the equation is expressed in the slope-intercept form (y=mx+b). The y-intercept is the value of b. This is due to the fact that the y-intercept occurs when the x value is 0. Y = B when x = 0, since mx = 0 at this point.
We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.
The formula for the x-intercept is y = 0: The x-intercept(s) can be determined by factoring or by employing the quadratic formula because ax2 + bx + c=0.
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Jane is building a fence around her garden. For every 4 feet of fencing, the cost is 36 Complete the table below showing the length of the fence and the cost.
Answers
The Complete is showing the length of the fence and the cost.
Length of fencing 4 6 7 9 10
Cost: 36 54 63 81 90
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
Length of fencing 4 6 7 x 10
Cost: 36 y z 81 w
Now, Using proportion
4/ 36 = 6/y
4y = 36(6)
y = 54
and, 4/36 = 7/z
4z = 36 (7)
z = 63
and, 4/36 = x /81
x = 9
and, 4/36 = 10/w
360 = 4w
w= 90
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Morgan collects toy horses. she has 34 in her collection. she got 23 horses for her birthday. she dropped a box and broke 5 of them. how many toy horses does she has now
Answers
Answer:
34 + 23 = 57
57 - 5 = 52
Therefore, she has 52 toy horses.
Spiral Review
99
15. Roberto paid $35. 75 for dinner at a restaurant, plus an additional $7. 15
tip. What percent of the bill did he pay as a tip? Round to the nearest
percent, if necessary.
Answers
Roberto paid 16.7% of the bill as a tip.
To find the percent of the bill Roberto paid as a tip, you can use the formula: (tip / total bill) x 100 = tip percentage
In this case, the tip was $7.15 and the total bill was $35.75 + $7.15 = $42.90. We know the formula to calculate percentage share of an item to total items.
Plugging these values into the formula:
(7.15 / 42.90) x 100 = 16.7 %
Roberto paid 16.7% of the bill as a tip, rounded to the nearest percent.
Thus, we know Roberto paid 16.7% of the bill as a tip.
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Mrs. Johnson lets her students choose between two word problems:
Problem A: If you are digging for dinosaurs and need to fence off your dig site, what's the biggest site you can fence off with 40 ft. of fence?
Problem B: What is the largest area you can create with 20 inches of rope?
Mrs. Johnson finds a significant majority of her students chose to work Problem A. Which of the following is the most likely reason more students chose Problem A instead of Problem B?
Answers
The reason to choose problem B over A is simple - it is more relatable to them.
Problem A involves dinosaurs, which may be more interesting to students than the abstract concept of creating an area with rope. Additionally, the use of feet as a unit of measurement in Problem A may be more familiar to students than inches.
Finding a number that represents the quantity of anything is called measurement. An accepted quantity that is used to represent a physical quantity is called a measurement unit. Let's learn about some of the standard units used to measure physical quantities.
The inch, foot, yard, and mile are the fundamental units of length and distance measurement in the English system. The rod, furlong, and chain are additional length units.
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When a space shuttle returns from a mission, the last part of its descent to the ground
must be between 17 degrees and 19 degrees with the horizontal (ZZ). If the pilot of
space shuttle Pioneer plans to descend from 11,700 feet (UH) at an angle of 18
degrees (ZZ) from the runway, determine the horizontal distance from the landing site
(ZU) at which the pilot must begin the descent.
Use the diagram to determine the measure of the sought side.
Answers
Answer:
please see the followings,
11700 ÷ tan 18 = ZU
Is 12 16 20 a right triangle?
Answers
No, 12 16 20 is not a right triangle. In order to be a right triangle, one side must be the same as the square root of the sum of the squares of the other two sides. In this case, the hypotenuse (side 20) is not equal to the square root of 12^2 + 16^2 which is 20.
No, 12 16 20 is not a right triangle. To determine whether or not something is a right triangle, we need to use the Pythagorean Theorem. This theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is side 20, and the other two sides are 12 and 16. When we calculate the square root of 12^2 + 16^2, we get 20, which does not match the length of the hypotenuse. Therefore, 12 16 20 is not a right triangle.
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What's the longest UK number 1?
Answers
The person who has the most number 1 in UK is Elvis Presley. He has a total of 21 number 1 which is the highest in history.
The UK Singles Chart is a chart which numbers musician on the basis of their songs and their sales and streams it was created in 1969. The records and statistics listed here, however, date back to 1952 .
The song which charted the charts was Old Town Road which was recently remixed and launched by Lil Nas X.
Elvis Aaron Presley or more commonly known as Elvis, was an American singer and actor. He dubbed the "King of Rock and Roll", and is now regarded as one of the most significant cultural figures of the 20th century.
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