By using the triangular inequality, we conclude that the other side must measure more than 3 inches and less than 13 inches.
Which values could the length of the third side take?
Remember that the triangular inequality says that the sum of any two sides on a triangle is larger than the other side of the triangle.
If we define the missing side of the triangle as x, then we must have:
5 + x > 8
8 + x > 5
8 + 5 > x
From the third inequality we get the upper bound:
13 > x.
From the first inequality we get the lower bound:
x > 8 - 5 = 3
Then:
3 < x < 13
This means that the other side of the triangle must measure more than 3 inches and less than 13 inches.
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Solve the following equation algebraically: Negative 16 = 16 x squared How many solutions does this equation have? Explain. a. Negative 1 = x squared; One solution because only -1 will satisfy the equation. b. Negative 1 = x squared; No real solution because there is no real number that, when squared, produces -1. c. 1 = x squared; Two solutions because the square root of 1 is positive 1 and negative 1. d. 1 = negative x squared; One solution because only -1 will satisfy the equation.
Answer:
The correct answer is b.
Step-by-step explanation:
[tex]16 {x}^{2} = - 16[/tex]
[tex] {x}^{2} = - 1[/tex]
No real solutions.
Select the correct answer.
One leg of a right triangle is 10 units, and its hypotenuse is 12 units. What is the length of the other leg?
A.
about 7 units
B.
about 15 units
C.
about 25 units
D.
about 122 units
E.
about 224 units
Drag the tiles to the correct boxes to complete the pairs.
Two parallel lines, a and b, cut by a transversal, forming 2 groups of 4 angles. Starting at top left of line a and moving clockwise, angles are 1, 2, 4, 3. Starting at top left of line b and moving clockwise, angles are 5, 6, 8, 7.
In the figure, line a and line b are parallel. Based on the figure, match each given angle with its congruent angles.
angles congruent to ∠1
angles congruent to ∠2
angles congruent to ∠7
angles congruent to ∠6
∠3,∠7,∠6
arrowRight
∠3,∠7,∠2
arrowRight
∠4,∠8,∠5
arrowRight
∠3,∠6,∠2
The answer to the drop down menu are:
Angles 3, 7, and 6 are congruent to angle 2.Angles 3, 7, and 2 are congruent to angle 6.Angles 4, 8, and 5 are congruent to angle 1.Angles 3, 6, and 2 are congruent to angle 7.What are congruent angles?Congruent angles are known to be two or more angles that are said to be similar or identical to one another. Thus, one can say that their measure of their angles is the same to each other.
Based on the above, the angles given able are congruent to the other angles because they are known to have the same angle (in terms of degrees and radians).
Therefore, The answer to the drop down menu are:
Angles 3, 7, and 6 are congruent to angle 2.Angles 3, 7, and 2 are congruent to angle 6.Angles 4, 8, and 5 are congruent to angle 1.Angles 3, 6, and 2 are congruent to angle 7.Learn more about Angles from
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Answer:
Hope this helps
Step-by-step explanation:
What is (-1,-4) reflected over the y axis
Answer:
(1,-4)
Step-by-step explanation:
What is the square root of 45
Erika is working on solving the exponential equation 50x = 17; however, she is not quite sure where to start. using complete sentences, describe to erika how to solve this equation.
hint: use the change of base formula: log base b of y equals log y over log b.
Erika is working on solving the exponential equation 50^x = 17; The solution is x = 0.7242.
What is logarithm?When you raise a number with an exponent, there comes a result.
Let's say you get
a^b = c
Then, you can write 'b' in terms of 'a' and 'c' using a logarithm as follows
[tex]b = \log_a(c)[/tex]
'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'
Erika is working on solving the exponential equation 50^x = 17;
however, she is not quite sure where to start.
The equation is
[tex]50^x = 17\\[/tex]
By taking the log both sides
[tex]log_a b = x\\\\a_x = b[/tex]
By using the base formula
[tex]log_0 y = \dfrac{logy}{log b}[/tex]
So, [tex]log_{50} 17= x\\\\[/tex]
[tex]x = \dfrac{log17}{log 50}[/tex]
x = 0.7242
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What is the diameter of a hemisphere with a volume of 458 ft³, to the nearest tenth
of a foot?
Answer:
12.0 ft
Step-by-step explanation:
what is the probability that the first marbles you choose is red and the second is blue
Answer:
2/9
Step-by-step explanation:
What is the slope of the line represented by the equation y + 3 = -4(x-5)?
OA. 3
OB. 4
O C. -3
OD. -4
Answer:
-4
Step-by-step explanation:
if you graph it, we can find out two points are 0,17 and 1,13
we can find the slope from rise/run
-4 is the slope of the line represented by the equation y + 3 = -4(x-5)
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The equation of the line is y + 3 = -4(x-5)
We have to find slope
Let us simplify the equation to slope intercept form to find slope
y+3=-4x+20
y=-4x+17
Hence, -4 is the slope of the line represented by the equation y + 3 = -4(x-5)
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What are the roots of the equatio
x² - x -42=0
[tex]x^2-x-42=0\\x^2+6x-7x-42=0\\x(x+6)-7(x+6)=0\\(x-7)(x+6)=0\\x=7 \vee x=-6[/tex]
Answer:
The roots are 7 and -6.
Keys:
[tex]ax^2+bx+c=0[/tex][tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex][tex]-(-a)^(^n^) = a^(^n^)[/tex][tex]\sqrt[n]{a}^n = a[/tex][tex]1^a = 1[/tex]When you see a ± in a quadratic equation, you will have multiple solutions; more than one.
Step-by-step explanation:
solve the main expression
[tex]x^2-x-42=0\\x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \left(-42\right)}}{2\cdot \:1}\\\rightarrow \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \left(-42\right)}\\=\sqrt{\left(-1\right)^2+4\cdot \:1\cdot \:42}\\\rightarrow \left(-1\right)^2\\=1^2\\=1\\\rightarrow 4\cdot \:1\cdot \:42\\=168\\=\sqrt{1+168}\\=\sqrt{169}\\=\sqrt{13^2}\\=13\\x_{1,\:2}=\frac{-\left(-1\right)\pm \:13}{2\cdot \:1}[/tex]
solve for x₁
[tex]\frac{-\left(-1\right)+13}{2\cdot \:1}\\=\frac{1+13}{2\cdot \:1}\\=\frac{14}{2\cdot \:1}\\=\frac{14}{2}\\=7[/tex]
solve for x₂
[tex]\frac{-\left(-1\right)-13}{2\cdot \:1}\\=\frac{1-13}{2\cdot \:1}\\=\frac{-12}{2\cdot \:1}\\=\frac{-12}{2}\\=-\frac{12}{2}\\=-6[/tex]
Use the definition of division to write the division problem as a multiplication problem, then simplify.
6/0=
Division problem 6/0 as a multiplication problem = 6×1/0
Simplified solution of the problem = ∞
What is division?The division is the process of repetitive subtraction. It is the inverse of the multiplication operation.
Given division problem,
6/0
Division is inverse of the multiplication
∴ 6/0 = 6×1/0
Now, simplifying
6 × 1/0 = 6 × ∞ = ∞
Hence, ∞ is the solution of the division problem 6/0 after converting it into multiplication problem 6 × 1/0.
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What is the y-intercept of the graph below?
Answer:
B
Step-by-step explanation:
the y- intercept is the point on the y- axis where the line crosses it
the line crosses the y - axis at (0, - 4 ) ← y- intercept
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Step-by-step explanation:
please mark me as brainlest
what is the surface area of a square based pyramid if the square side is 8 and the pyramid height is 12.
a) 266.39
b) 294.76
c) 525.51
d) 304
Answer:
A) 266.39
Step-by-step explanation:
Answer:
a) 266.39 unit^2.
Step-by-step explanation:
Area of the base = 8^2 = 64 .
There are 4 triangular sides.
To find the area of 1 side we need to know the slant height s of the triangle, This can be found using the Pythagoras Theorem
s^2 = 4^2 + 12^2 = 160
s = √160
So the area of 1 side = 1/2 * base * s
= 1/2 * 8 * √160
and
area of 4 sides
= 4 * 1/2 * 8 * √160
= 202.386
So the Surface area of the pyramid
= 64 + 202.386
= 266.386
use the drop down menus to complete the statements about the function p(x)=x(x-1)+1
Answer:
a=1
b=-1
c=1
value of discriminant =-3
quadratic function will intersect x-axis 0 times
Step-by-step explanation:
If you pull a card from a standard deck of 52 and then pull a second card without replacing the first card, you have about a ____ chance(round to nearest percent) of pulling out a face card, followed by on ace.
The probability that you pull a card from a standard deck of 52 and then pull a second card without replacing the first card is 2%
How to determine the probability?The given parameters are:
Cards = 52
Face card = 12
Ace = 4
The probability of selecting a face card is:
P(Face card) = 12/52
Now, there are 51 cards.
The probability of selecting an ace is:
P(Ace) = 4/51
The required probability is:
P = 12/52 * 4/51
Evaluate
P = 0.0181
Express as percentage
P = 1.81%
Approximate
P = 2%
Hence, the probability is 2%
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pleeeeeeeeeeeeeeeeas FAST !!!!! i need help if a/b = (-7/9)^8 / (-7/9)^6 find the value of (a/b)^2.
Answer:
(-7/9)^4 = 2401/6561
Step-by-step explanation:
The rules of exponents apply.
(a^b)/(a^c) = a^(b-c) . . . . . quotient rule
(a^b)^c = a^(bc) . . . . . . . . power rule
__
value of a/bThe first rule of exponents shown above helps us find the value of a/b.
[tex]\dfrac{a}{b}=\dfrac{\left(\dfrac{-7}{9}\right)^8}{\left(\dfrac{-7}{9}\right)^6}=\left(\dfrac{-7}{9}\right)^{8-6}=\left(\dfrac{-7}{9}\right)^2[/tex]
value of (a/b)^2The second rule of exponents shown above tells us how to find the square.
[tex]\left(\dfrac{a}{b}\right)^2=\left(\left(\dfrac{-7}{9}\right)^2\right)^2=\left(\dfrac{-7}{9}\right)^{2\times2}\\\\\boxed{\left(\dfrac{a}{b}\right)^2=\left(\dfrac{-7}{9}\right)^4=\dfrac{2401}{6561}}[/tex]
_____
Additional comment
Since -7 is always to an even power in these expressions, its sign can be ignored. The product of an even number of negative values is positive.
which of the following is the missing value in the table above?
Answer:
Answer is A 216
Step-by-step explanation:
252×6=1512
1512÷7=216
Which pairs of polygons are similar?
Select each correct answer.
Jhonny has 7 apples how manuy apples does jonny haves
Answer: 7 apples
Step-by-step explanation:
Considering it's the same person and you only had a typo?
How does his estimate compare to the actual product? It’s a good estimate. The actual product is 35. It’s a good estimate. The actual product is 40. It’s a bad estimate. The actual product is 60. It’s a bad estimate. The actual product is 120
Some ways through which the value of a thing be estimated are:
Given: 11.51 * 12.95, an estimated value of the individual numbers can be made out to be 12 * 13 respectively.
What is an Estimate?This refers to the rough calculation of the approximate value of a thing, usually a number.
In mathematical calculations, estimates are important as they are used to round off the value of numbers either to the nearest tenth, hundredth, thousandth, etc.
Hence, we can see that your question is incomplete, so I gave you a general overview of estimates to give you a better understanding of the concept.
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Help please!!!!!!! I'm so confused about this
Answer: I think the answer is A (4,6)
Step-by-step explanation:
Because point B is translated up you have to move the whole shape and pint D would end up at (4,6)
Graph the system of equations on graph paper to answer the question.
y =2/7x-7
y=-x+ 2
What is the solution for this system of equations?
Enter your answer in the boxes. HELPP
Answer:
(7,-5)
Step-by-step explanation:
See attached graph.
Ingrid Nilsen purchased a $4,000 hydroponic system for her garden. The down payment is 20%, and the
installment loan has an APR of 10% for 36 months. Find the a) down payment, b) amount financed, c) monthly
payment, d) total amount repaid, and e) finance charge.
The purchase of the hydroponic system by Ingrid Nilsen for $4,000 with a 20% down payment at 10% APR for 36 months, and the related calculations, are as follows:
a) down payment = $800.00 ($4,000 x 20%)
b) amount financed = $3,200 ($4,000 - $800)
c) monthly payment = $103.25
d) total amount repaid = $4,517
e) finance charge = $517
How is periodic payment computed?The amount of the periodic payment, finance charge, and total repayment can be computed using an online finance calculator as follows:
Data and Calculations:
Auto Price = $4,000
Loan Term = 36 months
Interest Rate = 10%
Down Payment = $800 ($4,000 x 20%)
Monthly Payment = $103.25
Total Loan Amount $3,200.00
Upfront Payment = $800.00 ($4,000 x 20%)
Total of 36 Loan Payments = $3,717. ($103.25 x 36)
Total Loan Interest = $517
Total Cost (price, interest, tax, fees) = $4,517
Thus, Ingrid Nilsen repaid a total of $4,517 with $517 in interest (finance charge).
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Jamiah bought two 125 ounce bags of flour for baking. He used up 32 ounces of flour to bake a batch of brownies. How much flour does Jamiah have now?
Answer: its 218
Step-by-step explanation: you just have to subtract 250 minus 32
Your password has 3 letters and 3 digits. no repeats are allowed. how many different passwords exist?
Answer:
a bunch
Step-by-step explanation:
Answer:
it is probably 9 or 12 I apologize apologise in advance if I'm wrong
Step-by-step explanation:
What is the orthocenter?
The midpoint of the base of the triangle
The point of intersection of the three medians
The point of intersection of the three altitudes
The orthocenter is the point of intersection of the three altitudes.
What is an orthocenter?An orthocenter can be defined as the point of intersection of altitudes which are perpendicular from the vertex to the opposite sides of a triangle.
Therefore, the orthocenter is the point of intersection of the three altitudes.
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Simplify the algebraic expression by combining like terms. -7x² +19x²
Simplify your answer.
1
F is a force of 3N pulling an object due north and F is a force of 5N pulling an object 60 east of north.
Determine the direction (measured clockwise from north) and magnitude of the resultant force.
2
The direction of the force is given as = 38.21⁰ while the magnitude is given as 7N
The magnitude of the resultant force is given as
Fr = [tex]\sqrt{F1^2+F2^2+2F1F2CosO}[/tex]
∅ = 60 degrees
= √3² + 5² + 2*3*5cos60
= √49
FR = 7N
How to solve for the direction of the force7cos∅ = 3 + 5cos∅
7cos ∅ = 3 + 2.5
cos∅ = 5.5/7
∅ = cos⁻¹0.7857
= 38.21⁰
Hence the direction of the force is = 38.21⁰
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Which of the sequences is an arithmetic sequence?
O A. 1, 8, 16, 24, 32, ...
OB. 3, 6, 9, 15, 24, ...
O C. 1, -2, 3, 4, 5, ...
OD. -3, -10,-17, -24, -31,...
The sequence which shows arithmetic sequence is -3, -10, -17, -24, -31, ....... so the correct option is Option D.
What is Arithmetic Sequence?
An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same.
Here, out of the given option option D follows the definition.
Difference between two consecutive term is equal.
-10 - (-3) = -10 + 3 = -7
-17 - (-10) = -17 + 10 = -7
-24 - (-17) = -24 + 17 = -7
-31 - (-24) = -31 + 24 = -7
Thus, the sequence which shows arithmetic sequence is -3, -10, -17, -24, -31, ....... so the correct option is Option D.
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