Answer:
One triangle
Step-by-step explanation:
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Verify the length sides of triangle
Applying the triangle inequality theorem
1) 3+5 > 6 ---> is true
2) 3+6 > 5 ---> is true
3) 5+6> 3----> is true
therefore
One triangle can be drawn with the given lengths
With side lengths of 3 inches, 5 inches, and 6 inches, only one triangle can be drawn as these dimensions meet the triangle inequality theorem, allowing for the creation of one unique triangle.
Explanation:The question is about determining if a triangle can be constructed with given side lengths. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the third side. In this case, the side lengths are 3 inches, 5 inches, and 6 inches.
Adding the lengths of the two shorter sides, 3 inches + 5 inches = 8 inches, which is greater than the length of the longest side, 6 inches. This means a triangle with these side lengths can be drawn. However, it is important to note that the lengths provided can only create one unique triangle, since the lengths are fixed and there can't be another triangle with different angles with the same side lengths.
Therefore, with side lengths of 3 inches, 5 inches, and 6 inches, exactly one triangle can be drawn.
The sum of two numbers is zero. When 13 times the smaller number is added to 8 times the larger, the result is 2. Find the two numbers.
Answer:
x = (2/5); y = (-2/5)
Step-by-step explanation:
x + y = 0
13x + 8y = 2
Multiply so the "x" variables are opposite with the same absolute value.
(-13) x + y = 0 (-13) ⇒ -13x - 13y = 0
(1) 13x + 8y = 2 (1) ⇒ 13x + 8y = 2
Add the two equations.
(13x - 13x) + (8y - 13y) = (2 - 0)
-5y = 2
Divide both sides by -5
y = [tex]-\frac{2}{5}[/tex]
Plug the value of "y" into either equations.
x + [tex](-\frac{2}{5})[/tex] = 0
Add [tex]\frac{2}{5}[/tex] to both sides.
x = [tex]\frac{2}{5}[/tex]
7+ 2x divided by 5= 13
Answer:
[tex]x=29[/tex]
Step-by-step explanation:
Given equation :
[tex]\frac{(7+2x)}{5} =13[/tex]
Making the terms of 'x' to one side and constants to the other.
[tex](7+2x)=13*5[/tex]
[tex]7+2x=65[/tex]
[tex]2x=65-7[/tex]
[tex]2x=58[/tex]
[tex]x=\frac{58}{2}[/tex]
[tex]x=29[/tex]
So, the value of 'x' is 29.
Answer:
x = 29
Explanation:
7 + 2x / 5 = 13
Multiply both sides by 5
7 + 2x / 5 = 13 · (5) = (13) · (5)
7 + 2x = 65
Simplify both sides of the equation
2x + 7 = 65
Subtract 7 from both sides
2x + 7 − 7 = 65 − 7
2x = 58
Divide both sides by 2
2x / 2 = 58 / 2
x = 29
Which expression represents the number 13,809 written in expanded form?
A 13+80+9
B 13,000+800+90
C9+1,300+80
B 3,000+10,000+9+800
Answer:
The answer is b or d, but most likely d.
Answer:
B. 13,809 = 3,000+10,000+9+800
Step-by-step explanation:
13,809 = 10,000 + 3000 + 800 + 9
24 miles out of 32 miles express ratio as fraction
Answer:
Step-by-step explanation:
That would be:
24 miles 3
------------- = ------ with no units of measurement
32 miles 4
Are 3 (4x-2) and 12x-2 equivalent
Final answer:
The expression 3 (4x-2) is not equivalent to 12x-2, as it simplifies to 12x-6, not 12x-2.
Explanation:
The expression 3 (4x-2) is not equivalent to 12x-2 because when we distribute the 3 across the terms inside the parenthesis of the first expression, we get 12x-6, not 12x-2.
To show this step-by-step:
Multiply 3 by 4x to get 12x.
Multiply 3 by -2 to get -6.
Combine these to get 12x-6.
As a result, 3 (4x-2) simplifies to 12x-6, and this is not equal to 12x-2 unless we are considering a special case where x equals to a value that makes -6 equal to -2, which generally isn't the case.
what is the imaginary part of the number 9?
Answer:
0iStep-by-step explanation:
The imaginary number has form:
a + bi
a - real part
bi - imaginary part
i - imaginary unit (i = √-1)
We have the number 9.
9 is a real part
An imaginary part is equal 0.
Therefore the imaginary part of number 9 is 0i.
help me ................ i don't have time
The angle measure of m∠ACB (x°) is 39°.
Step-by-step explanation:
Let us name the joining points as ABC and ABC forms triangle with extended lines. (refer the image)
We have to find the value of m∠ACB = x°.
the given data,
m∠A=68°.
m∠B =107°.
To find m∠CAB,
Let us consider that AB is a line traversed by a line C intersecting at A. (refer diagram)
Using the theorem of corresponding angles theorem, when a line intersects another line, then the angles opposite each other is equal to each other.
m∠A=m∠CAB.
m∠CAB =68°.
To find m∠ABC,
Let us consider AB is a line.(refer diagram)
Using the straight line proof, the total of angles in a straight line is 180°.
Thus m∠ABC+m∠B=180°.
m∠ABC+107°=180°.
m∠ABC=180°-107°.
m∠ABC=73°.
Finally we have to find the value of x° that is m∠ACB.
Using the interior angles proof, the sum of interior angles of triangle is 180°.
⇒m∠ABC+m∠CAB+m∠ACB=180°.
73°+68°+m∠ACB=180°.
141°+m∠ACB=180°..
m∠ACB=180°-141°.
m∠ACB=39°.
Thus the angle measure of m∠ACB (x°) is 39°.
Ethan had $8 more than Dakota. Ethan then gave 1/4 of his money to Dakota. The ratio of money Ethan had to the money Dakota had became 5:2. How much money did Ethan five to Dakota?
Final answer:
To find how much money Ethan gave to Dakota, we need to set up and solve an equation based on the given conditions, include the initial difference of $8, the 1/4 transfer of funds, and the resulting 5:2 ratio of their money.
Explanation:
Ethan had $8 more than Dakota. When he gave 1/4 of his money to Dakota, the ratio of Ethan's money to Dakota's became 5:2. To solve this, let's assume Dakota originally had D dollars and Ethan had D + 8 dollars. After giving away 1/4 of his money to Dakota, Ethan would have 3/4 of D + 8, and Dakota would have D plus 1/4 of D + 8.
The new ratio of Ethan's money to Dakota's money is 5/2, leading us to the equation 3/4(D + 8) / (D + 1/4(D + 8)) = 5/2. Solving this equation will not only give us the initial amounts of money each person had but also allow us to calculate the exact amount Ethan gave to Dakota, which is the 1/4 of Ethan's original money.
Trying to prepare a budget. Chester has done research and found that he spends an average of $120 on his phone/internet/cable service, $277 on his electric bill, and
$299 on his health insurance premium. If he earns $2800 per month, estimate the amount of money he will have after paying these bills each month.
After adding his phone/internet/cable, electric bill, and health insurance premium costs, Chester spends $696 on bills each month. With monthly earnings of $2800, he therefore should have around $2104 left over after paying these bills.
Explanation:To figure out how much money Chester will have left after paying his bills, you first have to add up all his bills. So, he pays on average $120 for his phone/internet/cable service, $277 for his electric bill, and $299 for his health insurance premium.
To add these together: 120 + 277 + 299 = $696. This is the total amount Chester pays for his bills each month.
Now, subtract this total from Chester's monthly earnings. So, Chester earns $2800 per month, and his bills total $696. So, 2800 - 696 = $2104. Therefore, Chester will have around $2104 left each month after paying these bills.
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Dakota bought 2 scarves and 1 hat for $13. Kristina bought 1 scarf and two hats for $14. What was the price for one hat and one scarf?
Answer:
The price for one hat was $5 and the price for one scarf was $4
Step-by-step explanation:
Let
x ----> the price for one scarf in dollars
y ----> the price for one hat in dollars
we know that
Dakota bought 2 scarves and 1 hat for $13
so
[tex]2x+y=13[/tex] ----> equation A
Kristina bought 1 scarf and two hats for $14
so
[tex]x+2y=14[/tex] ----> equation B
Solve the system by elimination
Multiply by -2 both sides equation B
[tex]-2(x+2y)=-2(14)[/tex]
[tex]-2x-4y=-28[/tex] ----> equation C
Adds equation A and equation C
[tex]2x+y=13\\-2x-4y=-28\\---------\\y-4y=13-28\\-3y=-15\\y=5[/tex]
Find the value of x
substitute the value of y in any equation
equation B
[tex]x+2(5)=14\\x=14-10\\x=4[/tex]
therefore
The price for one hat was $5 and the price for one scarf was $4
Let f(x) = x2 – 3x - 7. Find f(-3).
O 11
Answer:
plug -3 as x to find f(-3)
Step-by-step explanation:
A portrait without its frame has a height 1.5 times its width w, in inches. Its frame is 2 in. wide all along its perimeter. What is an expression for the area of
the framed portrait in terms of w?
A. 1.5W2 + 5W + 4
B. 1.5w2 + 8w + 8
C. 1.5w2 + 8.5w + 16
D. 1.5w2 + 10w + 16
Answer:
The correct answer is A. 1.5w² + 5w + 4
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Height of the portrait = 1.5 times its width in inches
Frame = 2 inches all along its perimeter
2. What is an expression for the area of the framed portrait in terms of w?
Let's recall that the area of a rectangle is length or height * width.
A = height * width
Now, we can replace in terms of w:
A = 1.5w * w
But we need to add the 2 inches of the frame, this way:
A = (1.5w + 2) * (w + 2)
A = 1.5w² + 2w + 3w + 4
A = 1.5w² + 5w + 4
The correct answer is A. 1.5w² + 5w + 4
Final answer:
The expression for the area of the framed portrait in terms of w is 1.5w^2 + 8w + 8.
Explanation:
To find the expression for the area of the framed portrait, we need to consider the dimensions of both the portrait and the frame. Let's assume the width of the portrait is w inches. According to the given information, the height of the portrait without the frame is 1.5 times the width, so the height is 1.5w inches.
To calculate the dimensions of the framed portrait, we need to add 2 inches to the width and height for the frame. The width of the framed portrait is w + 2 inches, and the height is 1.5w + 2 inches.
The area of the framed portrait is equal to the product of its width and height. Therefore, the expression for the area, in terms of w, is (w + 2) * (1.5w + 2). When we simplify this expression, we get 1.5w2 + 8w + 8.
At every company meeting, the president speaks for 20 minutes and then takes questions from her employees. Let q represent the number of minutes she spends answering questions and t represent the total number of minutes the meeting lasts. Complete the equation that represents the relationship between q and t.t=?
Answer:
T. T = 2q
Step-by-step explanation:
20t : q
40t : 2q
You just times the values
Which quantity is proportional to 40⁄8?
Check all that are true.
A. 120⁄24
B. 10⁄5
C. 120⁄36
D. 5⁄1
E.
20⁄4
Answer:
A and D and E is the answer.
Step-by-step explanation:
13 1/6- 3 4/5=
13 1/6- 3 4/5=
[tex]13\frac{1}{6}-3\frac{4}{5}=(13*6+1)/6-(3*5+4)/5=79/6-19/5=(395-114)/30=\\ \\=281/30=9\frac{11}{30}[/tex]
Hey there! Since my last answer got reported and deleted because I messed it up, here is a second answer for you!
Answer:
Exact form : 281/30
Decimal form : 9.36 (please a line over the six to represent that the six is repeating itself. It will look like this...9.3666666666...)
Mixed Number form : 9 11/30
Step-by-step explanation: Convert the mixed number to improper fractions, then find the LCD (Least Common Denomintor) and then combine.
Hope this helps you out.
If it takes 930 kg of food to feed a pair of elephants for 3 days how much food would u need to feed them for a week?
Answer:
2170 kg
Step-by-step explanation:
since there are 7 days in a week first you calculate the days
930 plus 930 equals 1860 which can feed a pair of elephants for 6 days
then since in one day it takes 310 kg then add 1860 plus 310
and then you get 2170
so, you need 2170 kg of food to feed a pair of elephants in a week
2. a. How could you distinguish between traveling west at 5 miles per hour and
traveling east at 5 miles per hour without using the words "east" and "west"
b. Four people are cycling. They each start at the same point. (0 represents their
starting point.) Plot their finish points after five seconds of cycling on a number line!
• Lin cycles at 5 meters per second
• Diego cycles at -4 meters per second
• Elena cycles at 3 meters per second
Answer:
Traveling east 5miles/hour can be represented as; traveling 45 degrees from south at 5 miles per hour .
Traveling west 5miles/hour can be represented as;
Traveling 45 degrees from south towards the north
The second part is on the attached file
Step-by-step explanation:
You will declare variables before you start solving the questions
Answer:
Step-by Traveling east 5miles/hour can be represented as; traveling 45 degrees from south at 5 miles per hour .
Traveling west 5miles/hour can be represented as;
Traveling 45 degrees from south towards the north
The second part is on the attached filey-step explanation:
Perpendicular to 3y=x-4 and passes through the point (-2,1)
Answer:
The equation is [tex]y=-3x-5[/tex]
Step-by-step explanation:
We are given;
The equation of a line 3y = x-4 A point (-2,1)Assuming the question requires we determine the equation of a line perpendicular to the given line and passing through the point given.
Step 1: Determine the slope of the given line
To determine the slope from an equation requires we write the equation in the form, y = mx + c, where m will be the gradient.
In this case;
[tex]3y = x - 4\\ y = \frac{1}{3}x-\frac{4}{3}[/tex]
Therefore, the slope is [tex]\frac{1}{3}[/tex]
Step 3: Determine the slope of the line in question
We know that the product of the slope of two perpendicular line is -1
That is;
m₁ × m₂=-1
Thus;
1/3 × m₂ -1
Hence; m₂ = -3
Step 3: Determine the equation of the line in question;
We have its slope, m₂ = -3
A point (-2, 1)
Taking another point (x,y)
Thus;
[tex]\frac{y-1}{x--2}=-3\\y-1 =-3(x+2)\\y-1 = -3x-6\\y=-3x-5[/tex]
Therefore, the required equation is [tex]y=-3x-5[/tex]
The equation of the line perpendicular to the line and passing through the point is y = -3x - 5
Equation of a lineGiven the equation 3y = x - 4
Find the slope of the line
y = 1/3 x - 4/3
The slope of the line is 1/3 and the slope of the line perpendicular is -3
Substitute the point (-2, 1) and the slope into equation
y - y1 = m(x-x1)
y - 1 = -3(x+2)
y - 1 = -3x - 6
y = -3x - 5
Hence the equation of the line perpendicular to the line and passing through the point is y = -3x - 5
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Find the numerical value of sin(a)cos(a) if sin (a)-cos (a) = 0.6
The value of sin(a)cos(a) = 0.32
Step-by-step explanation:
Step 1: Given details are sin(a) - cos(a) = 0.6
Step 2: Square the given equation on both sides.
⇒ (sin(a) - cos(a))² = (0.6)²
⇒ sin²a + cos²a - 2 sin(a)cos(a) = 0.36
⇒ 1 - 2 sin(a)cos(a) = 0.36 since sin²a + cos²a=1
⇒ - 2 sin(a)cos(a) = - 0.64
⇒ 2 sin(a)cos(a) = 0.64
⇒ sin(a)cos(a) = 0.32
The rectangular prism shown has a surface area of 488 square inches. What is the length of the prism?
Answer:
length of the prism = 244 - (width x height) / width + height)
Step-by-step explanation:
Let length be a and width be b and height be c
2 (a * b) + 2 (b* c) + 2 (a * c) = 488
2ab+ 2bc + 2ac = 488
ab + bc + ac = 244
ab + ac = 244 - ac
a (b + c) = 244-ac
a = 244-bc / b + c
Therefore the length of the prism = 244 - (width x height) / width + height)
Answer:
teh answer is 14
Step-by-step explanation:
use teh equation for surface are
A=2(lw+hl+wh)
plug in the values
488=2(6*8+6*x+x*8)
to get x=14
which is the length
THIS IS CORRECT CAUSE I HAD TO DO IT FOR CLASS AND I GOT IT RIGHT BTW. :)
two numbers that multiply to -14 and add to -5
The solution is 2 and -7.
To find two numbers that multiply to -14 and add to -5, we can set up a system of equations based on the properties of multiplication and addition of numbers with different signs.
Let x and y be the two numbers we are looking for, with the following conditions:
x * y = -14 (Multiplication condition)
x + y = -5 (Addition condition)
Using the addition rules, we know that if we have two numbers with opposite signs, the sign of the larger (absolute value) number will dictate the sign of the result. Similarly, the multiplication rules tell us that two numbers with different signs will give a product with a negative sign.
Applying these principles, we can guess that one number is positive and the other negative since their product is -14. We also know that the number with the greater absolute value must be negative since their sum is -5. We can begin by listing pairs of factors of 14 (since the product is -14) keeping the sign in mind:
1 and -14
-1 and 14
2 and -7
-2 and 7
From this list, the pair that adds up to -5 is 2 and -7. Hence, the two numbers are 2 and -7.
1 Which set of ordered pairs does not represent a function?
1 {(1, 10), (3, 18), (5, 26), (7, 34), (9, 42)
2 {(2, 10), (3, 20), (4, 15), (5,5), (6,25)
3 {(0,8), (5,4), (10,0), (15, 4), (20,8)
4 {(9, 1), (6,2), (3, 3), (6,4), (9,5)}
Answer: it’s D
Step-by-step explanation:
I completed it
The relation set - {(9, 1), (6,2), (3, 3), (6,4), (9,5)}
does not represent the function.
What is a function?An expression in mathematics defines a relationship between one variable (the independent variable, x) and another variable (the dependent variable, y). For example -
f(x) = 4x + 6
Given are the set of ordered pairs as given in the question.
It can be clearly seen that the relation set -
{(9, 1), (6,2), (3, 3), (6,4), (9,5)}
does not represent the function as for x = 6, there are two possible values of [y] given, which is not possible.
Therefore, the relation set - {(9, 1), (6,2), (3, 3), (6,4), (9,5)}
does not represent the function.
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Evaluate the equation: x+3=18
Answer:
x=15
Step-by-step explanation:
x+3=18
x+3-3=18-3
x+0=15
x=15
Which pair shows equivalent expressions?
(Look at picture)
Answer:
-2x - 10 = -2(x + 5)
Step-by-step explanation:
-2x - 10 is already simplified, but in order to understand the solution, we need to simplify -2(x + 5) in order to show that it is an equivalent expression:
-2(x + 5) = -2x - 2(5)
Further simplify:
-2x - 10
This proves that -2x - 10 = -2(x + 5) is an equivalent expression.
There are 12 inches in 1 foot. The height of Rachel door is 7 feet Find the height in inches
Answer:
84 Inches
Step-by-step explanation:
so 12 inches are in 1 foot. 12 x 7+84
Answer: 84 in
Step-by-step explanation: since there are 12 inches in a foot multiple 12 by the number of feet.
what is 2 divideed by 8
Answer: 0.25
Step-by-step explanation:
A car traveling on the taconic parkway travels 84 miles in two hours.
Answer:
The speed of the car is 42 mph.
Step-by-step explanation:
Speed = distance / time. 84 / 2 = 42
what is 15/5 as a mixed number
Answer:
3
Step-by-step explanation:
Answer: 3
Step-by-step explanation:
15 divided by 5 is 3. Which means that 15/5 is 3.
PLEASE ANSWER QUICKLY!
The number of bagels sold daily for two bakeries is shown in the table:
Bakery A Bakery B
45 48
52 42
51 11
48 45
57 57
30 10
55 43
46 46
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.
Mean for both bakeries because the data is symmetric
Mean, because the distribution is symmetric for both bakeries
Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric
Mean for Bakery B because the data is symmetric; median for Bakery A because the data is not symmetric
Answer:
Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric, as can be observed from the stem and leaf frequency plot.
Step-by-step explanation:
CALCULATIONS FOR BAKERY A
Considering the data for Bakery A
45 52 51 48 57 30 55 46
Calculating Mean for Bakery A
[tex]Mean=\frac{Sum\:of\:terms}{Number\:of\:terms}[/tex]
Sum of terms = 45 + 52 + 51 + 48 + 57 + 30 + 55 + 46 = 384
Number of terms = 8
As
[tex]Mean=\frac{Sum\:of\:terms}{Number\:of\:terms}[/tex]
[tex]Mean=\frac{302}{8}[/tex]
[tex]Mean=48[/tex]
Calculating Median for Bakery A
As the median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.
As the data for Bakery A is
45 52 51 48 57 30 55 46
Ordering the data from least to greatest, we get:
30 45 46 48 51 52 55 57
As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:
[tex]Median=\frac{\left(48+51\right)}{2}=\frac{99}{2}=49.5[/tex]
Getting a Plot and Leaf Plot for Bakery A
Plot and leaf plot is generally a unique table-like diagram which displays the frequency distribution of a data set. Plot and leaf plot is a visual aid that supports us in recognizing frequency classes and the center of the distribution where most of the data gets clustered around.Data for Bakery A in ascending order
30 45 46 48 51 52 55 57
STEM LEAF
3 0
4 5 6 8
5 1 2 5 7
CALCULATIONS FOR BAKERY B
Considering the data for Bakery B
48 42 11 45 57 10 43 46
Calculating Median for Bakery B
[tex]Mean=\frac{Sum\:of\:terms}{Number\:of\:terms}[/tex]
Sum of terms = 48 + 42 + 11 + 45 + 57 + 10 + 43 + 46 = 302
Number of terms = 8
[tex]Mean=\frac{302}{8}=37.75[/tex]
Calculating Median for Bakery B
[tex]Median=\frac{\left(43+45\right)}{2}=44[/tex]
Getting a Plot and Leaf Plot for Bakery B
Data for Bakery B in ascending order
10 11 42 43 45 46 48 57
STEM LEAF
1 0 1
2
3
4 2 3 5 6 8
5 7
So, from the above observation, we can conclude that Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric, as can be observed from the stem and leaf frequency plot.
Keywords: symmetric distribution, mean, media
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Answer:
Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric, as can be observed from the stem and leaf frequency plot.
Help please **attachment**
Answer:
i think the answer is c but im not sure
Step-by-step explanation: