Determine if the lengths of the sides of a triangle create a 'right, acute, or obtuse' triangle.
Answers
ANSWER
These three side lenghts form a right triangle
EXPLANATION
If the triangle is a right triangle, the side lenghts must satisfy the Pythagorean theorem. In a right triangle, the hypotenuse is always the longest side. Therefore, if it is a right triangle, the sum of the squares of the shorter sides must be equal to the square of the longest side:
[tex]\begin{gathered} 74^2=70^2+24^2 \\ 5476=4900+576 \\ 5476=5476 \end{gathered}[/tex]Therefore, this is a right triangle.
Related Questions
Solve the equation for all solutions in the interval. Write each answer in radians.
Answers
We are given a problem regarding trigonometric identities and asked to resolve for theta.
[tex]4\sec \theta-\sqrt[]{3}=\sqrt[]{3}+7\sec \theta[/tex]Recall that:
[tex]\sec \theta=\frac{1}{\cos \theta}[/tex]Therefore, we have:
[tex]\begin{gathered} \frac{4}{\cos\theta}-\sqrt[]{3}=\sqrt[]{3}+\frac{7}{\cos\theta} \\ \text{ We add }\sqrt[]{3}\text{ and subtract }\frac{7}{\cos\theta}\text{ from both sides to get:} \\ \frac{4}{\cos\theta}-\frac{7}{\cos\theta}=2\sqrt[]{3} \\ -\frac{3}{\cos\theta}=2\sqrt[]{3} \\ \text{Multiply both sides by }\cos \theta\text{ and divide both sides by }2\sqrt[]{3}\text{ to get:} \\ \cos \theta=-\frac{3}{2\sqrt[]{3}}=-\frac{\sqrt[]{3}}{2} \\ \theta=\cos ^{-1}(-\frac{\sqrt[]{3}}{2})=150^o \\ \end{gathered}[/tex]In radians, we have:
[tex]\frac{150\pi}{180}=\frac{5\pi}{6}[/tex]Here is a lkmeat equation: y=1/4x+5/41. Are (1, 1.5) and (12,4) solutions to the equation? A. Both (1, 1.5) and (12,4) are solutions to the equation.B. Neither (1, 1.5) and (12,4) are solutions to the equationC. (1, 1.5) is a solution to the equation but (12,4) is not.D. (12,4) is a solution to the equation but (1, 1.5) is not.Explain your reasoning
Answers
The equation is as follows:
[tex]y=\frac{1}{4}x+\frac{5}{4}[/tex]1. Are (1, 1.5) and (12,4) solutions to the equation?
[tex]\begin{gathered} 1.5=\frac{1}{4}\cdot1+\frac{5}{4} \\ 1.5=1.5 \\ (1,1.5)\text{ is a solution } \\ 4=\frac{1}{4}\cdot12+\frac{5}{4} \\ 4=3+\frac{5}{4} \\ 4\ne4.25 \\ (12,4)\text{ is not a solution} \\ \end{gathered}[/tex]The answer is C
(1, 1.5) is a solution to the equation but (12,4) is not.
Lorrie places a 25-foot ladder against the side of a building with the bottom of the ladder 7 feet from the base of the building. How high up the wall does the ladder reach?The ladder reaches feet up the wall
Answers
Let's use a diagram to represent the question below
using Pythagoras theorem we can find how high up the ladder reaches the wall.
[tex]\begin{gathered} x^2=25^2-7^2 \\ x^2=625-49 \\ x^2=576 \\ x=\sqrt[]{576} \\ x=24\text{ ft} \end{gathered}[/tex]The ladder reaches 24 ft up the wall.
both numbers in table have one digit and 3 digit what is the relationship between the values represented in these digits
Answers
the first one is: The value of 1 in carmen's number is 3 times the value the value of the 1 in michelles's number
and the second is:
lucia and jared each have a sibling with cystic fibrosis, but neither lucia nor jared nor their parents have the disease. calculate the probability that if this couple has a child, the child will have cystic fibrosis. what would be the probability if a test revealed that jared is a carrier but lucia is not? explain your answers.
Answers
The probability that a test revealed that Jared is a carrier but Lucia is not is 1/4
Mendel discovered that genes are inherited as separate, paired units, one from each parent. Its application of mathematics to illuminate observations of natural phenomena.
Given that lucia and jared each have a sibling with cystic fibrosis, but neither lucia nor jared nor their parents have the disease
Mendel theory is a technique used to estimate the probability of getting specific characteristics.
Lucia and Jared have a probability of both carrier and non carrier
If both of them are non carrier then the children born to their family have no chances of getting disease.
If any one of them is carier, then there is a chance of getting one child as a carrier. That is ¼ or the ratio is 1:4
If both of them are carriers then the ratio will be 1:2:1
If Jared is carrier then the probability will be ¼
Therefore the probability if a test revealed that jared is a carrier but lucia is not is ¼
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which equation best describes the line that passes thru (-4,7) with a slope of 3?
Answers
Answer:
[tex]y = 3x + 19[/tex]
Step-by-step explanation:
[tex]7 = 3( - 4) + b[/tex]
[tex]7 = - 12 + b[/tex]
[tex]b = 19[/tex]
which of the following number sentences illustrates the associative property of multiplication (3×8)×6=3×(8×6). 2×(1×9)=(2×1)×(2×9). 1×15=15. 8×9=9×8.
Answers
Answer:
(A)(3×8)×6=3×(8×6)
Explanation:
Definition: A set S is said to be associative under the operation x if the following holds:
[tex]\begin{gathered} \forall a,b,c\in S \\ a\times(b\times c)=(a\times b)\times c \end{gathered}[/tex]Therefore, the number sentence that illustrates the associative property of multiplication is:
[tex]\mleft(3\times8\mright)\times6=3\times\mleft(8\times6\mright).[/tex]The correct choice is A.
Geometry. Please help I’ll make it Brainliest
Answers
Answer:
I don't know
Step-by-step explanation:
I do not know
Answer:
75 degrees
Step-by-step explanation:
i attached a photo where i solved for all the angles sorry its messy since i did it on ms paint
quadrilateral EFGH is a rectangle solve for x, if FJ =3x-10 and JH=8x-40
Answers
In the quadrilateral shown, the diagonal FH is divided at the point J into line segments FJ and JH.
The lines FJ and JH are bisected by the line segment EG.
Hence, line FJ equals line JH. Therefore;
[tex]\begin{gathered} FJ=JH \\ 3x-10=8x-40 \\ \text{Collect all like terms,} \\ -10+40=8x-3x \\ 30=5x \\ \text{Divide both sides by 5} \\ 6=x \end{gathered}[/tex]The answer is x = 6
Hello I know this looks like a big list but I was just showing the directions it gave at the very top as you see. I need help with 17 or 18.
Answers
As given by the question
(17)
There are given that the equation
[tex]\sin (3\theta)=1[/tex]Now,
From the general solution for the given equation
[tex]3\theta=\frac{\pi}{2}+2\pi n[/tex]Then,
Solve above solution
So, divide by 3 on both side of the equation
[tex]\begin{gathered} 3\theta=\frac{\pi}{2}+2\pi n \\ \frac{3\theta}{3}=\frac{\frac{\pi}{2}+2\pi n}{3} \\ \theta=\frac{\pi}{6}+\frac{2\pi n}{3} \end{gathered}[/tex]Hence, the value of the given equation is shown below:
[tex]\theta=\frac{\pi}{6}[/tex]Consider AABC with vertices A(-2, -3) and B(-6, -6) and C(-8, 5).a) Draw AABC on graph paper. Is this a right triangle? JUSTIFY your answer.b) Reflect AABC across AC to create AA'B'C'. Find the location of B'. What kind oftriangle is ABB'C:? JUSTIFY your answer.
Answers
Given data:
The graph of the given points is shown below.
The slope of the line passing through A(-2, -3) and B(-6, -6).
[tex]\begin{gathered} m=\frac{-6-(-3)}{-6-(-2)} \\ =\frac{-3}{-4} \\ =\frac{3}{4} \end{gathered}[/tex]The slope of the line passing through B(-6, -6) and C(-8, 5).
[tex]\begin{gathered} m^{\prime}=\frac{5-(-6)}{-8-(-6)} \\ =-\frac{11}{2} \end{gathered}[/tex]The slope of the line passing through A(-2, -3) and C(-8, 5).
[tex]\begin{gathered} m^{\doubleprime}=\frac{5-(-3)}{-8-(-2)} \\ =\frac{8}{-6} \\ =-\frac{4}{3} \end{gathered}[/tex]The product of the slope of line passing through AB and line passing through AC is,
[tex]\begin{gathered} m\times m^{\doubleprime}=\frac{3}{4}\times(-\frac{4}{3}_{}) \\ =-1 \end{gathered}[/tex]Thus, the line passing through AB and line passing through AC are perpendicular.
please help 10 points
Answers
Answer:
3/3
Step-by-step explanation:
Divide by 2 each time to find the simplest form until they can't be divided into a whole number. 24÷2=12÷2=6÷2=3
12÷2=6÷2=3
If the measure of arc BC is 182 degrees and the measure of arc AC is 78 degrees, what is the measure of angle 1?Answer choice:A)52 degreesB)91 degreesc)104 degreesD)78 degrees
Answers
Given:
There are given that the arc of BC is 182 degrees and the measure of arc AC is 78 degrees.
Explanation:
To find the value of the angle of 1, we need to use the circle properties:
So,
From the properties:
[tex]1=\frac{(BC-AC)}{2}[/tex]Then,
Put the values into the above formula:
So,
[tex]\begin{gathered} 1=\frac{(BC-AC)}{2} \\ 1=\frac{(182-78)}{2} \\ 1=\frac{104}{2} \\ 1=52 \end{gathered}[/tex]Final answer:
Hence, the correct option is A.
a small auditorium can seat 320 people. which inequality best represents the number of people, p, who can sit at the audtorium
Answers
Given:
Number of people the auditorium can seat = 320 people
Let's dtetrmine the inequality that best represents the number of people who can sit at the auditorium.
Here, the greatest number of people that can sit at the auditorium is 320 people, from the list of inequalities given, the best inequality which represents the number of, P, who can sit at the auditorium is: p < 321
This means that the number of people, p, must be less than 321.
ANSWER:
p < 321
y = x^2 - 6x + 5 find vertex
Answers
The formula to get the vertex of a quadratic is:
[tex]x=-\frac{b}{2a}[/tex]When we obtain this x- value, we would substitute in the equation to get the corresponding y-value.
In the given quadratic equation,
[tex]y=x^2-6x+5[/tex]a = 1 and b = -6 , so
[tex]undefined[/tex]what are the terms a0, a1, a2, and a3 of the sequence {an}, where an equals a) 2n 1? b) (n 1)n 1? c) n/2? d) n/2 n/2?
Answers
When a[tex]_{n}[/tex] = [tex]2^{n}[/tex]+ n, a₀ = 1, a₁ = 3, a₂ = 6, and a₃ = 11
When a[tex]_{n}[/tex] = n^(n+1)!, a₀ = 0, a₁ = 2, a₂ = 2⁶, and a₃ = 3²⁴
When a[tex]_{n}[/tex] = [n/2], a₀ = 0, a₁ = 1/2, a₂ = 1, and a₃ = 3/2
When a[tex]_{n}[/tex] = [n/2] + [n/2], a₀ = 0, a₁ = 1, a₂ = 2, and a₃ = 3/2
Number sequence
A number sequence is a progression or a list of numbers that are directed by a pattern or rule.
Here,
a₀, a₁, a₂, and a₃ are terms of a sequence
from option a, a[tex]_{n}[/tex] = [tex]2^{n}[/tex]+ n
⇒ a₀ = 2⁰+ 0 = 1+0 = 1
⇒ a₁ = 2¹+ 1 = 2+1 = 3
⇒ a₂, = 2²+ 2 = 4+2 = 6
⇒ a₃ = 2³+ 3 = 8 +3 = 11
from option b, a[tex]_{n}[/tex] = n^(n+1)!
⇒ a₀ = 0^(0+1)! = 0
⇒ a₁ = 1^(1+1)! = 2² = 2
⇒ a₂, = 2^(2+1)! = 2^(3)! = 2⁶ [ ∵ 3! = 6 ]
⇒ a₃ = 3^(3+1)! = 3^(4)! = 3²⁴ [ ∵ 4! = 24 ]
from option c, a[tex]_{n}[/tex] = [n/2]
⇒ a₀ = [0/2] = 0
⇒ a₁ = [1/2] = 1/2
⇒ a₂, = [2/2] = 1
⇒ a₃ = [3/2] = 3/2
from option d, a[tex]_{n}[/tex] = [n/2] + [n/2]
⇒ a₀ = [0/2] + [0/2] = 0
⇒ a₁ = [1/2] + [1/2] = 1/2 + 1/2 = 1
⇒ a₂, = [2/2] + [2/2] = 1 + 1 = 2
⇒ a₃ = [3/2] + [3/2] = 6/4 = 3/2
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The Complete Question is -
What are the terms a₀, a₁, a₂, and a₃ of the sequence {a[tex]_{n}[/tex]}, where a[tex]_{n}[/tex] is where a[tex]_{n}[/tex] equals
a. [tex]2^{n}[/tex] + n b. n^(n+1)!
c. [n/2] d. [n/2] + [n/2]
May you please help me with this? I dont understand it
Answers
Answer:
The correct option is:
n/26 = 25
Explanation:
Given that:
25 . 26 = n
n is the product of 25 and 26
Then dividing n by either of 25 or 26 results to the number left.
n/25 = 26
and
n/26 = 25
When dividing decimals, what place value should our quotients go to (if necessary)?
Answers
Quotients are the results of division
Now, the place value is entirely dependent on the comparism between the divisor and the dividend
Let us use the numerator and denominator for easy understanding
If they are of the same value, in case of 0.56/0.28 for example
The place value here will be in the units
So what we are saying is that the place value is dependent on the values that we are dividing and how big of a magnitude they compare to each other
If g (p) = 25-6p, then g (-2)=?
Answers
= 25 + 12
= 37
1) What is the slope of the line below y.
Answers
From th given graph, the line is passing through the points,
[tex]\begin{gathered} (x_1,y_1)=(1,2) \\ (x_{2,}y_2)=(4,1) \end{gathered}[/tex]The expression to calculate the slope of a line passing through two points is,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute values in the above expression.
[tex]\begin{gathered} m=\frac{1-2}{4-1} \\ =\frac{-1}{3} \end{gathered}[/tex]Thus, the slope of the line y is -1/3.
4. Find the value of x for which ABCD must be a parallelogram.(15x + 2)°(9x+20)°
Answers
Given:
We're given a four-sided figure.
Value of ∠ADB = 9x + 20
Value of ∠DBC = 15x + 2
To find:
The value of x for which ABCD must be a parallelogram.
Step-by-step solution:
For ABCD to be a parallelogram, Alternate angles (Z angles) should be equal:
Thus,
∠ADB = ∠DBC
9x + 20 = 15x + 2
18 = 6x
x = 3
Final answer:
Thus we can say that the value of x should be 3 for ABCD to be a parallelogram.
(6X-12)°
88°
(3X+21) •
Answers
Answer: no alike terms
Step-by-step explanation:
6x+12+3x+21+88
Combine Like Terms:
=6x+12+3x+21+88
=(6x+3x)+(12+21+88)
=9x+121
Answer:
=9x+121
a department store chain is expanding into a new market, and is considering 22 different sites on which to locate 6 stores. assuming that each site is equally likely to be chosen, in how many ways can the sites for the new stores be selected? a) 53,721,360 b) 154 c) 74,613 d) 132 e) 28 f) none of the above.
Answers
In 53,721,360 ways can the sites for the new stores be selected.
A department store chain is expanding into a new market. It is considering 22 different sites on which to locate 6 stores. Let us assume each site is equally likely to be chosen.
We can find number of ways by multiplying the amount of possibility each store can have.
The store 1, it can be placed on 22 sites. The Store 2 can be placed on 21 sites (since store 1 is already on site 1). The Store 3 can be placed on 20 sites. Store 4 which has 19sites. store 5 which has 18 sites. And store 6 which has 17 sites.
Therefore the number of ways the sites for the new stores be selected is:
C = 22 × 21 × 20 × 219 × 18 × 17
C = 53,721,360 possibilities
Thus, the sites for the new stores be selected in 53,721,360 ways.
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How would you find 5^-3
Answers
So to calculate 5 with an exponent of 3, you can write 5, 3 times with a multiplication symbol between them like so: 5 · 5 · 5 When we multiply them together, we get the answer to 5 with an exponent of 3.
KIdentify any vertical, horizontal, or oblique asymptotes inthe graph of y=f(x). State the domain of f (interval notation).42-+12QQIdentify any vertical asymptotes. Select the correchoice below and, if necessary, fill in the answerboxes to complete your choice.OA. There is only one vertical asymptote. Itsequation is(Type an equation.)B. There are two vertical asymptotes. Theequation of the leftmost one is x=-6and the equation of the rightmost one isx=6(Type an equation.)OC. There are no vertical asymptotes.Identify any horizontal or oblique asymptotesSelect the correct choice below and, if necessary.fill in the answer box to complete your choice.OA. The function has a horizontal asymptotewhose equation is(Type an equation.)OB. The function has an oblique asymptotewhose equation is,(Type an equation.)C. The function has neither a horizontal noran oblique asymptote
Answers
the function has a horizontal asymptote whose equation is y = -3 (option A)
[tex]\begin{gathered} In\text{ interval notation:} \\ Domain\text{ = \lparen-}\infty,\text{ -6\rparen }\cup\text{ \lparen-6, 6\rparen }\cup\text{ \lparen6, }\infty) \end{gathered}[/tex]Explanation:Given:
A graph of a rational function
To find:
a) if the graph has a horizontal or oblique asymptote
b) domain of f
A horizontal asymptote is a line that is not part of the function of the graph.
From the graph, there is a horizontal dashed line between y = -2 and y = -4.
None of the graphs touches this line. This is the horizontal asymptote. The equation at the asymptote is y = -3 (midpoint between -2 and -4)
Hence, the function has a horizontal asymptote whose equation is y = -3
The domain is the input of the function (x values). Since the function is not given, we will use the vertical asymptote to determine the domain.
The vertical asymptotes are x = -6 and x = 6
The domain of the function is all real numbers except x = -6 and x = 6
[tex]\begin{gathered} In\text{ interval notation:} \\ Domain\text{ = \lparen-}\infty,\text{ -6\rparen }\cup\text{ \lparen-6, 6\rparen }\cup\text{ \lparen6, }\infty) \end{gathered}[/tex](2) Name the type of polyhedron that can be assembled from this net. *
Answers
The type of polyhedron that can be assembled from this net is a triangular prism because if you assemble this net you get a figure like this
1. A map has a scale of 2cm=2m. What is the scale factor? 2. And a map has a scale of 4in=3ft. What is the scale factor? Please help it is due tomorrow and I will give brainliest and bunch of points and step by step please or no brainliest.
Answers
The scale factors of the maps are 1 cm per m and 1 in per 0.75 ft, respectively
How to determine the scale factors of the maps?Scale factor of map 1
The scale is given as
A scale of 2 cm = 2m
Write out the scale
So, we have
2 cm = 2/2 m
Divide both sides of the scale by 2
So, we have the following equation
2/2 cm = 2/2 m
Evaluate the quotient
So, we have the following equation
1 cm = 1 m
The above means that the scale is 1 cm scale measurement represents 1 m actual measurement
Scale factor of map 2
The scale is given as
A scale of 4 in = 3 ft
Write out the scale
So, we have
4 in = 3 ft
Divide both sides of the scale by 4
So, we have the following equation
4/4 in = 3/4 ft
Evaluate the quotient
So, we have the following equation
1 in = 0.75 ft
The above means that the scale is 1 inch scale measurement represents 0.75 m actual measurement
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How to check and solve
-10=√x+6
Answers
The value of x is 4 . We can solve it by squaring both sides.
What are linear equations?An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Ax+By=C represents a two-variable linear equation in its standard form. As an illustration, the conventional form of the linear equation 2x+3y=5 It is rather simple to locate both intercepts when an equation is stated in this way (x and y). For the purpose of resolving systems involving two linear equations, this form is also highly helpful.
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The perimeter of an ICU ward that is rectangular in shape is 274 feet. The width is 37 feet less than the length. Find the length of the ward
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
rectangular ward:
perimeter = 274 ft
width = lenght - 37ft
Step 02:
lenght of the ward:
perimeter = 2*w + 2*l
274 = 2*(l - 37) + 2*l
274 = 2l - 74 + 2l
274 + 74 = 4l
348 / 4 = l
87 = l
The answer is:
The lenght of the ward:
Enter your answers in the boxes to correctly complete this statement. 74. 94×103=
because the number 10³ has
zeros when it is written without an exponent
Answers
74. 94×10³= 74940 because the number 10³ has zeros when it is written without an exponent.
Using scientific notation, it's found that the number in standard notation is represented by:
74. 94 × 10³= 74940
Using scientific notation, you can write extremely large or extremely small numbers. When a number between 1 and 10 is multiplied by a power of 10, the result is expressed in scientific notation as variety.
Scientific notation for the following number is:
[tex]a \times 10^{b}[/tex]
In this problem, the amount is given by:
= 74. 94 × 10³
Hence, applying the multiplication, we have that:
74. 94 × 10³ = 74. 94 × 1000 = 74940
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