The sides of the triangle are (d) 12√2, 12√2, 24
How to determine the side lengths?The given parameters are:
Hypotenuse = 24Angle = 45-45-90 degree anglesIn a 45-45-90 degree angle triangle, we have:
Hypotenuse = Opposite√2 and Hypotenuse = Adjacent√2
This means that:
Opposite =Adjacent
So, we have:
24 = Adjacent√2
Divide both sides by √2
Adjacent = 24/√2
Evaluate
Adjacent = 12√2
This means that:
Opposite = 12√2
Hence, the sides of the triangle are (d) 12√2, 12√2, 24
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What is the value of x?
(Round your answer to
the nearest tenth.)
Answer:
x ≈ 8.7
Step-by-step explanation:
given 2 secants from an external point to the circle, then
the product of the external part of one secant and the entire secant is equal to the product of the external part of the other secant and the entire secant , that is
6(6 + x) = 4(4 + 18) ← distribute parenthesis on both sides
36 + 6x = 4 × 22 = 88 ( subtract 36 from both sides )
6x = 52 (divide both sides by 6 )
x ≈ 8.7 ( to the nearest tenth )
Can anyone help me solve this?
Answer:9
Step-by-step explanation:
Use the pythagorean theorem. [tex]a^{2}+b^{2}=c^{2}[/tex]
We know both a and c, so it becomes
[tex]4^{2}+b^{2}=\sqrt{97}^{2}[/tex]=
16+b^2=97=
97-16=b^2=
81=b^2=
9=b
PLEASE HELPPP ITS WORTH 20 points!!!
Answer:
tanD =4/7
Step-by-step explanation:
tanD = P/B
Where P=4 and B=7
So;
tanD=4/7
HELLPPPPP ASAAPPPP.
please help with math
Find the slope of the line graphed below.
to get the equation of any straight line, we simply need two points off of it, let's use the ones provided in the picture below.
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{-7}{2}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-\cfrac{7}{2}}(x-\stackrel{x_1}{1}) \\\\\\ y-4=-\cfrac{7}{2}x+\cfrac{7}{2}\implies y=-\cfrac{7}{2}x+\cfrac{7}{2}+4\implies y=-\cfrac{7}{2}x+\cfrac{15}{2}[/tex]
What is the length of EF? (Giving 45 points, please hurry!)
3x² - 12x +9=0 using quadratic formula
Answer:
The quadratic equation 3x² - 12x + 9 = 0 has two real roots when solved:
x₁ = 1 and x₂ = 3
Step-by-step explanation:
✍ An equation of type ax² + bx + c = 0, can be solved, for example, using the quadratic formula:
[tex]\boldsymbol{x=\dfrac{-b\pm\sqrt{b^{2}-4ac } }{2a} }[/tex]
either
[tex]\boldsymbol{x=\dfrac{-b\pm\sqrt{\Delta} }{2a} }[/tex]
where
[tex]\bf{\Delta=b^{2}-4ac }[/tex]
Identify the coefficients
a = 3, b = -12 and c = 9
Calculate the discriminant value
Δ = b² - 4ac
Δ = (-12)² - 4.3.9 = 144 - 12.9
Δ = 144 - 108 = 36
Enter the values of a, b and the discriminant value in the quadratic formula
[tex]\boldsymbol{x=\dfrac{-b\pm\sqrt{\Delta } }{2a} }[/tex]
[tex]\boldsymbol{x=\dfrac{-(-12\pm\sqrt{36} }{2\cdot3 } }[/tex]
[tex]\boldsymbol{x=\dfrac{(12\pm\sqrt{36} }{6 } \ ==== > \ (Solution \ general) }[/tex]
As we can see above, the discriminant (Δ) of this equation is positive (Δ> 0) which means that there are two real roots (two solutions), x₁ and x₂.
[tex]\boldsymbol{x_{1}=\dfrac{-12-\sqrt{36} }{6}=\dfrac{12-6}{6}=\dfrac{6}{6}=1 \ === > (First \ solution) }[/tex]
To find x₁, just choose the positive sign before the square root. Later,
[tex]\boldsymbol{x_{1}=\dfrac{12+\sqrt{36} }{6}=\dfrac{12+6}{6}=\dfrac{18}{6}=3 \ === > (Second \ solution) }[/tex]
) The gym teacher divided a class into four teams with 7 students per team. How many students are in the class?
Answer:
28 students
Step-by-step explanation:
7 times 4 = 28
there are are seven students in 4 teams, so that means there are 4 groups of seven, and you multiply them together to get how many students in the class
Answer:
28
Keyword(s):
divided, four, 7, per team, how many
Step-by-step explanation:
7 × 4 = 28
Nathan has 40 coins.Of coins,1/5 are nickels,1/5 are dimes,and the rest are quarters.What Is the ratio of Nathan’s nickels to dimes to quarters?
The ratio of Nathan's nickels to dimes to quarters is 4 : 4 : 17.
What is the ratio ?Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained within other value(s).
Number of dimes = 1/5 x 40 = 8 Number of nickels = 1/5 x 40 = 8 Number of quarters = 40 - 8 - 8 = 34The ratio = 8 : 8 : 34 = 4 : 4 : 17
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Solve each equation.
1. x+6=4
2.x- -4 = -6
3.2(x-1)=-200
4.2x+-3=-23
Step-by-step explanation:
1) x+6 =4
x. =4-6
x. =-2
2) x-(-4) =-6
x+ 4. =-6
x. =-6-4
x. =-10
3)2(x-1)=-200
2x-2 =-200
2x. = -200+2
2x. = -198
x. = -198/2
x. = -99
4)2x+(-3) =-23
2x-3. =-23
2x. =-23+3
2x. =-20
x. =-20/2
x. = -10
f(x) = 5 + 4x2, then f(3) =
Step-by-step explanation:
To answer this, we need to plug in 3 as x in the equation f(x) = 5 + 4x².
That would look like this: f(3) = 5 + 4(3)²
f(3) = 5 + 4(3)²
f(3) = 5 + 36
f(5)=41
Therefore, the answer is 41.
I hope this helps!! :)
for each sequences, find the first 4 term and the 10th term the sequences are
(a) n^2+3
(b)2n^2
Answer:
see explanation
Step-by-step explanation:
to find the first 4 terms substitute n = 1, 2, 3, 4 into the sequence rule
to find the 10th term substitute n = 10 into the rule
(a)
a₁ = 1² + 3 = 1 + 3 = 4
a₂ = 2² + 3 = 4 + 3 = 7
a₃ = 3² + 3 = 9 + 3 = 12
a₄ = 4² + 3 = 16 + 3 = 19
a₁₀ = 10² + 3 = 100 + 3 = 103
(b)
a₁ = 2(1)² = 2(1) = 2
a₂ = 2(2)² = 2(4) = 8
a₃ = 2(3)² = 2(9) = 18
a₄ = 2(4)² = 2(16) = 32
a₁₀ = 2(10)² = 2(100) = 200
There are two pieces of wires, each of length 66 cm. One wire is bent into a square and the other wire is bent into a circle. Find (a) the area of the square, (b) the area of the circle.
Answer:
Area of Circle = 346.5 cm².
Area of square = 272.25 cm ² .
Step-by-step explanation:
So , 2πR = 66
2 × 22 / 7 × R = 66
R comes out is 21/2 cm .
Area of Circle = 22/7 × 21/2 × 21/2 = 33×21/2
= 693 / 2 = 346.5 cm².
If bent into the shape of a square ;
4 a = 66
a = 33/2 . ( Side of a square )
Area of square = a ² = 33×33/4 = 1089/4
= 272.25 cm ² .
8- Determine the midpoint of a line segment with the endpoints (8, 0) and
(4,6)
A. (3,6)
B. (7,3)
C. (6,3)
D. (7.6)
Can someone help pls ?
Answer:
C. (6, 3)
Step-by-step explanation:
Use the midpoint formula!
Midpoint Formula
[tex]\text{midpoint} = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]
x₁, x₂ ... x-coordinates of the endpoints
y₁, y₂ ... y-coordinates of the endpoints
Given endpoints:
(8, 0)
(4, 6)
Points are in form (x, y).
Now let's substitute the variables in the formula with our values.
[tex](\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]
[tex](\frac{8 + 4}{2}, \frac{0+ 6}{2})[/tex]
[tex](\frac{12}{2}, \frac{6}{2})[/tex]
[tex](6, 3)[/tex]
(6, 3) is our midpoint!
Which of the following functions best models the data represented by the scatterplot shown below?
A: y=160x-100
B: y=2^x+12
C: y=8x^2+10
D: y=25x+20
Answer:
C: y = 8x^2 + 10.
Step-by-step explanation:
It looks close to being a parabola so I think it is probably a function in x^2.
Try 8x^2 + 10
Checking against the plot
When x = 5 , y = 8(5)^2 + 10 = 210 , and on graph its 200
Calculating y for other values:
When x = 7, y = 8(7)^2 + 10 = 402, and on graph y = 400.
When x = 11, y = 978 , and on graph = 1000.
When x = 17, y = 2322, and on graph y = about 2350.
Which equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17)?
Answer: y - 17 = -2(x-7)
Step-by-step explanation:
point-slope form: y - y1 = m(x - x1)
m = y2-y1/x2-x1
= 9+17/-6-7
= 26/-13
= -2
y1 = -17
x1 = 7
y - 17 = -2(x-7)
The equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y = -2x - 3
What is the general equation of a straight line?The general equation of a straight line is-
y = mx + c
where, m is the gradient and is given by y₂ - y₁/x₂ - x₁
and, c is the value where the line cuts y-axis.
Now it is given that the line passes through points (−6,9) and (7,−17)
Therefore we have,
x₁ = -6, y₁ = 9, x₂ = 7, y₂ = -17
So, the slope m of the line is given as,
m = (y₂ - y₁)/(x₂ - x₁)
Put the values,
m = (-17 - 9)/(7 - (-6))
m = -26/7+6
m = -26/13
m = -2
Thus, the equation parallel to the line will be given as:
y - y₁ = m(x - x₁)
y - 9 = -2{x - (-6)}
y - 9 = -2(x + 6)
y = -2x - 12 + 9
y = -2x - 3
Thus, the equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y = -2x - 3
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Move point C so that ∠BAC and ∠CAD form a pair of supplementary angles, or angles whose sum is 180°. Record each of the angle measurements for this case.
The recorded angle measurements of ∠BAC and ∠CAD could be 110° and 70°, vice versa.
What are supplementary angles?Supplementary angles are a pair of angles that always sum up to 180°. These angles can either;
adjacent non-adjacent. Adjacent supplementary anglesAdjacent supplementary are angles with a common vertex and arm.
Non-adjacent supplementary anglesNon- adjacent supplementary angles are angles without a common vertex or arm.
∠BAC and ∠CAD are adjacent supplementary angles because they have a common vertex, A, and a common arm AC.
They add up to 180°.
∠ BAC = 110° and ∠CAD = 70°
Hence, the angles could be 110° and 70°.
Note, this is an overview as the question is not complete.
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Answer: When the two angles are supplementary, m∠BAC = m∠CAD = 90° and m∠DAB = 180°.
Step-by-step explanation: Edmentum Answer
Question in the picture 1-5
how to understand next steps what will be anyone give me explains
Step-by-step explanation:
remember a few things :
a × -1 = -a
-a × -1 = a
-1 × -1 = 1
1 × a = a
therefore,
-1 × -1 × a = 1 × a = a
and finally
c × (a + b) = c×a + c×b
so, we can say
(1 - 5) = -1 × -1 × (1 - 5) =
= -1 × (-1×1 + -1×-5) = -1 × (-1 + 5) =
= -1 × (5 - 1) = -(5 - 1)
Which graph can be used to find the solution(s) to x2 – 4x + 4 = 2x + 1 + x2?
The solution to the equation x² – 4x + 4 = 2x + 1 + x² is x = 2.5 and the graph is shown in the picture.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have an equation:
x² – 4x + 4 = 2x + 1 + x²
After solving:
-4x + 4 = 2x + 1
6x = 3
x = 1/2 = 0.5
Thus, the solution to the equation x² – 4x + 4 = 2x + 1 + x² is x = 2.5 and the graph is shown in the picture.
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What is x in the figure?
im not sure I'd need to see the figure
these box plots show daily low temperatures for a sample of days in two different towns which statment is the most appropriate comparison of the centers
The correct statement about the center of both box plots is: the median for Town A, 30° is greater median for Town B, 25°
What is the correct statement?A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. The two lines are known as whiskers. The end of the first line represents the minimum number and the end of the second line represents the maximum number.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile.
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To identify the most efficient model for a windmill, Gandalf Engineering Company designs the windmill shown. The design consists of four right triangles arranged equally around point O such that point O is the midpoint of BF¯¯¯¯¯ and DH¯¯¯¯¯¯.
Deductive Reasoning is the practice of arriving at a mathematical conclusion by simply analyzing the facts using the knowledge of the related concepts.
What is the proof that ∠A ≅ ∠E?Looing at ΔOAB and ΔOEF
It is clear that
OB = OF (O is the midpoint)
∠OBA = ∠OFE = 90°
Therefore
∠AOB = ∠EOF (Vertically Opposite Angles)
⇒ ΔOAB ≅ ΔOEF and
∠ A ≅ ∠E.
QED
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2. Mikaela counted 2 more turtle nests
on a North Carolina beach than
Diego. If Mikaela counted 38 turtle
nests, which equation could you use
to find the number of turtle nests
Diego counted?
A 2x = 38
B x÷2=38
C x - 2 = 38
D x + 2 = 38
A ball is kicked upward with an initial velocity of 52 feet per second. The ball's height, h (in feet), from the ground Is
modeled by h= -16t^2 +52t where t is measured in seconds. How much time does the ball take to reach its highest
point? What is its height at this point?
Check the picture below.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+52}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 52}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (52)^2}{4(-16)}\right) \implies \left( - \cfrac{ 52 }{ -32 }~~,~~0 - \cfrac{ 2704 }{ -64 } \right)[/tex]
[tex]\left( \cfrac{13}{8}~~,~~\cfrac{169}{4} \right)\implies \underset{\stackrel{\uparrow \hspace{3em}}{seconds\qquad }}{\stackrel{\stackrel{\qquad feet}{\hspace{3em}\downarrow }}{\left( 1\frac{5}{8}~~,~~42\frac{1}{4} \right)}}[/tex]
Reflect the shape A in the line y
=
y
(-5, 6)
(4,3)
(-3, 1)
-8-7 -6 -5 -4 -3 -2 -1
4 5 6 7 8
-1
-2
-3
-4
-5
-6
-7
-8
What are the coordinates of the vertices
of the image?
A
00
8
7
6
LO
5
4
3
2
-
1
Đ
1
-2
3
-X.
2
(-5,6)
Step-by-step explanation:
Which set of values could be the side lengths of a 30-60-90 triangle?
OA. (6,6 2,12}
OB. (6,6√3, 12)
OC. (6, 12, 12√√3}
D. (6, 12, 12 √2)
The correct answer is option B which is the set of values that could be the side lengths of a 30-60-90 triangle are (6,6√3, 12).
What is the right-angled triangle?A triangle has three angles of 30-60 and 90 degrees in which the two sides are perpendicular to each other.
The three sides of the triangle will be calculated by applying the Pythagorean theorem:-
The sum of the square sides will be equal to the square of the third side.
For sides (6,6√3, 12)
12² = 6² + (6√3)²
144 = 36 + (36 x 3)
144 = 36 + 108
144 = 144
Therefore the correct answer is option B which is the set of values that could be the side lengths of a 30-60-90 triangle (6,6√3, 12).
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My sister needs help on this question and I am too lazy to figure this out please help ASAP
The question was: Which figure has exactly one line of symmetry?
Answer:
its the Pentagon, the other shaps have 2 lines if symmetry
Mrs. Yamaguchi's class weighed the potatoes that they grew in their garden and recorded the data on a table. Determine how many dots are above each data value in a line plot of this data.
Weights of Potatoes (in pounds)
1
4
3
8
5
8
1
2
5
8
1
2
1
2
3
4
1
4
1
8
3
4
1
2
3
8
1
2
3
4
3
8
The value
1
8
will have
Choose...
dots above it.
The value
1
4
will have
Choose...
dots above it.
The value
3
8
will have
Choose...
dots above it.
The value
1
2
will have
Choose...
dots above it.
Using a dot plot, it is found that the number of dots of each point are given as follows:
The value [tex]\frac{1}{8}[/tex] will have one dot above it.The value [tex]\frac{1}{4}[/tex] will have two dots above it.The value [tex]\frac{3}{8}[/tex] will have three dots above it.The value [tex]\frac{1}{2}[/tex] will have five dots above it.The value [tex]\frac{5}{8}[/tex] will have two dots above it.The value [tex]\frac{3}{4}[/tex] will have three dots above it.What does a dot plot shows?The dot plot shows the number of times each measure appears in the data-set.
In this problem, one measure has a value of 1/8, hence:
The value [tex]\frac{1}{8}[/tex] will have one dot above it.
Two measures have a value of 1/4, hence:
The value [tex]\frac{1}{4}[/tex] will have two dots above it.
Three measures have a value of 3/8, hence:
The value [tex]\frac{3}{8}[/tex] will have three dots above it.
Five measures have a value of 1/2, hence:
The value [tex]\frac{1}{2}[/tex] will have five dots above it.
Two measures have a value of 5/8, hence:
The value [tex]\frac{5}{8}[/tex] will have two dots above it.
Three measures have a value of 3/4, hence:
The value [tex]\frac{3}{4}[/tex] will have three dots above it.
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Answer:
1 2 3 5 2 3
Step-by-step explanation:
expression equivlant (x+5)^2
Answer:
(x+5) (x+5)
Step-by-step explanation:
it's just (x+5)^2 twice