[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=\stackrel{adjacent}{12}\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{13^2-12^2}=b\implies \sqrt{25}=b\implies 5=b[/tex]
Answer:
5
Step-by-step explanation:
a^2 + b^2 = c^2
13 is the hypotenuse because it is the longest side.
12^2 + b^2 = 13^2
144 + b^2 = 169
subtract the 144 from both sides to isolate the variable you are solving for
b^2 = 25
Square root both sides to solve
b = 5
Need to find the value of y
Answer:
√55
Step-by-step explanation:
Notice that the small triangle in the bottom corner shares an angle with the overall triangle. Also, they are both right triangles. Therefore, they are similar triangles.
Notice that the large triangle at the top shares an angle with the overall triangle and is also a right triangle. Therefore it is also similar to the overall triangle and the smaller triangle.
Writing a proportion between the small and large triangles:
y / 11 = 5 / y
y² = 55
y = √55
45% as fraction in the simplest form
Answer:9/20
Step-by-step explanation: 45/100=9/20, 45÷5=9, 100÷5=20 both the denominater and the numerator are divisible by 5.
To write a percent as a fraction in lowest terms, first remember that a percent is a ratio that compares a number to 100. 45% can be written as the ratio 45 to 100 or 45/100. Notice however that 45/100 is not in lowest terms so we need to dive both the numerator and denominator by the greatest common factor of 45 and 100 which is 5.
45 ÷ 5 = 9
100 ÷ 5 = 20
Therefore, 45% can be written as the fraction 9/20.
Alison is playing a video game. At the end of each level, the player is given either a bag of gold or a magic wand.
Alison says that the probability of getting a bag of gold is 30%. To test this, she plays the game 50 times and calculates the relative frequency of each outcome.
Outcome Bag of Gold Magic Wand
Relative frequency 0.32 0.68
Select from the drop-down menus to correctly complete each statement.
The relative frequency of getting a bag of gold is
30%.
Alison's claim about the theoretical probability is likely to be
.
Further, this means that the theoretical probability of getting a magic wand is most likely
.
Outcome Bag of Gold Magic Wand
Relative frequency 0.32 0.68
The relative frequency of getting a bag of gold is .......... reasonably close
.32 is close to 30% so
Alison's claim about the theoretical probability is likely to be 2............true
Further, this means that the theoretical probability of getting a magic wand is most likely 3............1 - 30% = 70%
What is the approximate area of the triangle below?
a)72.8 sq. cm.
b)111.9 sq. cm.
c)142.0 sq. cm.
d)164.7 sq. cm.
Answer:
Option a)72.8 sq. cm.
Step-by-step explanation:
step 1
Find the measure of the third internal angle of the triangle
Remember that
the sum of the internal angles of a triangle must be equal to 180 degrees
so
95°+35°+A=180°
A=180°-95°-35°
A=50°
step 2
Applying the law of sines
Find the length side opposite to the angle of 35 degrees
14/sin(50°)=b/sin(35°)
b=[14/sin(50)]*sin(35)
b=10.48 cm
step 3
Applying the law of sines find the area of the triangle
A=(1/2)(14)(10.48)sin(95°)=73.10 cm²
therefore
The approximate area of the triangle below is 72.8 sq. cm
Answer:
72.8 sq. cm
Step-by-step explanation:
Given:
two angles and a side of a triangle that are 95°, 35° and 14 cm receptively
Area of triangle=?
Finding 3rd angle
=180-(95+35)
= 180-130
=50
Area of triangle can be calculated by using ASA i.e.
Area= a^2sinBsinC/2sinA
Putting values of a=14, B=95, C=35 and A=50, we get
Area= 14^2(sin95)(sin35)/2(sin50)
=98(0.74591)
=73.099
Closest option is a)72.8 sq. cm!
Fishing rods are discounted at 50% off the regular price of $25. How much money will be saved?
Answer:
$12.50
Step-by-step explanation:
Tell whether the lines for.the pair of equations are parallel, perpendicular, or neither y = - 4/5x + 3; 4x - 5y = -15
Answer:
The lines are neither parallel nor perpendicular
Step-by-step explanation:
The first step is to re-write the equations in slope-intercept form. The first equation is given as;
y = -4/5x + 3
This equation is already in slope-intercept form. Its slope is -4/5
The second equation is given as;
4x - 5y = -15
We solve for y;
-5y = -4x - 15
y = 4/5x + 3
The slope of the line is thus 4/5
Parallel lines have equal or identical slopes. The slopes of the two lines are not equal implying that the lines are not parallel. Two lines are said to be perpendicular if the product of their slopes is equal to -1.
The product of the slopes of the two lines is;
(-4/5) * (4/5) = -16/25 ≠ -1
The two lines are not perpendicular
By comparing the slopes of the given equations, y = -4/5x + 3 and 4x - 5y = -15, we find that they are negative reciprocals of each other, indicating that the lines are perpendicular.
To determine whether the given pair of equations represent lines that are parallel, perpendicular, or neither, we need to compare their slopes. The slope-intercept form of a line is y = mx + b, where m represents the slope and b represents the y-intercept.
The first equation is already in slope-intercept form: y = -4/5x + 3, so its slope is -4/5.
To put the second equation into slope-intercept form, we solve for y:
4x - 5y = -15
-5y = -4x - 15
y = (4/5)x + 3
The slope of the second line is 4/5.
Since the slopes of the two lines are negative reciprocals of each other, the lines are perpendicular.
3. What’s the answer to this question asap!
Because you are required to get a positive number of centimetres we use positive value of x.
[tex]
\mid6.75-x\mid<0.25 \\
6.75-x<0.25\Longrightarrow x>6.5
[/tex]
The answer is B: The length of a part must be greater than 6.5 cm.
How many solutions does the equation -2y+2y+3=3have?
Cancel 3 on both sides
-2y + 2y = 0
Simplify -2y + 2y to 0
0 = 0
Since both sides are equal, there are infinitely many solutions;
= Infinitely Many Solutions
I NEED HELP asap would be nice thanks
The Answer is B
Hope this helps :)
Simplify: |5-11|
16
-16
6
-6
Subtract 11 from 5 to get -6.
Because the equation is in between two vertical lines, this means the absolute value, which is a positive value, so -6 becomes positive 6.
The answer is 6
At an arcade there is a fee to purchase a game card. Any number of credits can then be added to the card at a constant cost per credit.Jude buys a card with 50 credits and it cost him 17. Audrey buys a card with 80 credits and it costs 26 how much would a card with 75 credits cost
Answer:
25 dollars
Step-by-step explanation:
To calculate the cost of a 75 credits card, we first find the cost per credit and the initial cost of the card, which are $0.18 and $8 respectively. The total cost is then $21.5.
Explanation:We know Jude bought a card with 50 credits for $17 and Audrey got one with 80 credits for $26. We can say that the cost per credit is constant. To find this cost per credit, we first need to calculate the difference between the costs and then divide the result by the difference in number of credits: So, cost per credit = (26-17) / (80-50) = 0.18. This implies for each credit the cost is 18 cents. For a 75 credit card, the price would be 75 * 0.18 = $13.5. However, this doesn't account for the initial cost to purchase the game card. If we say the initial cost is a flat fee included in the price Jude and Audrey paid, we need to subtract the total cost of the credits from their total spend to work this out: Jude’s initial cost = $17 - (50 * $0.18) = $8. Audrey’s initial cost = $26 - (80 * $0.18) = $8. As we supposed, initial cost is a constant of $8. Hence, the cost of a 75 credits card would include this initial cost: 75 credits would cost = $8 + 75 * $0.18 = $21.5.
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Cecile drew a 4-sided figure. It had 2 sides that were 3.4 centimeters long and 2 sides that were 3.3 centimeters long. It had at least 3 right angles. Which best describes the figure she drew?
square
rectangle that is not a square
quadrilateral that is not a parallelogram
trapezoid
answer would be the second one: Rectangle that is not a square
Answer:
B.Rectangle that is not a square.
Step-by-step explanation:
We are given that Cecile drew a 4-sides figure. it means a quadrilateral.It had 2 sides that were 3.4cm long and 2 sides that were 3.3 centimeters long.
We are given that a quadrilateral had atleast 3 right angles.
If a quadrilateral had 3 right angles then the IV angle of quadrialteral is also right angle.
In quadrlateral ABCD
[tex]\angle A=90^{\circ}[/tex]
[tex]\angle B=90^{\circ}[/tex]
[tex]\angle C=90^{\circ}[/tex]
[tex]\angle A+\angle B+\angle C+\angle D==360^{\circ}[/tex]
By angle sum property of quadrilateral
[tex]90+90+90+\angle D=360[/tex]
[tex]270+\angle D=360[/tex]
[tex]\angle D=360-270=90^{\circ}[/tex]
Hence, IV angle of quadrilateral is also right angle.
Given two sides of quadrilateral are equal and other two sides of quadrilateral are equal.Therefore, the given quadrilateral can be rectangle not square because in square four sides are of equal lengths.
Hence, the given quadrilateral can be rectangle but not square.Therefore, option B is correct.
Jaylen decided to buy a new digital camera that retails for $199. If the store is currently running a promotion on all cameras for 25% off, and the sales tax in her state is 6%, what is jaylen’s total at checkout ?
So 25% of $199 is $49.75. If you subtract the promotion off you get 199-49.75=149.25. Then the sales tax is 6% so you take the new cost $149.25 and multiply it by .06 which equals 8.955. so then you add on the tax so $149.25+8.955=$158.205. Your answer is $158.205 or approximately $158.21
Answer:
$94.61
Step-by-step explanation:
Tax is on reduced and not original price
Please include work in the answer.
The answer is 3. You would just match up the sides and combine the common things. 3z times z is 3z^2 because it would be the same number twice, not times two. Then 9 times 8 is 72. Z times 8 is 8z because it would be 8 times whatever number the variable was. Then lastly it’s 9 times 3 z. You’ll multiply the 9 times 3 to get 27. Then it would be 27z. 27z and 3z^2 cannot be added together because they are preforming different things. One is multiplying by the variable another is multiplying by 3 and the the variable to the 2nd power.
Triangle angle theorems
The value of x is?
what you do I set 45x equal to your two other angles since the sum of those two angles is equal to that angle outside the triangle.
so you have
45x=57+x+25x
combine like terms
45x=57+26x
then subtract 26x on both sides to get
19x=57
lastly divide by 19
x=3
Answer:
3 degrees
Step-by-step explanation:
To find the circumference of a circle multiply the diameter by?
Answer:
D. Pi
Step-by-step explanation:
Circumference=diameter*pi
Or
Circumference=2*pi*radius
From the equation, find the axis of symmetry of the parabola.
y = 2x2 + 4x - 1
a. X=3
C. X=-3
b. x=-1
X = 1
Answer:
B. x= -1
Step-by-step explanation:
axis of symmetry is: [tex]x=\frac{-b}{2a}[/tex]
[tex]x=\frac{-4}{2(2)} \\x=\frac{-4}{4}\\x=-1[/tex]
The axis of symmetry for the given parabola equation y = 2x²+ 4x - 1 is x = -1.
The axis of symmetry of a parabola in the form y = ax² + bx + c can be found using the formula x = -b/(2a). For the given equation y = 2x² + 4x - 1, we can identify a as 2 and b as 4. Substituting these values into the formula for the axis of symmetry gives us x = -4/(2²) = -1.
please help will give you brainliest
Answer:
Neither A or B
Answer: Option A
Step-by-step explanation:
Given two variables X and Z, it is said that there is a correlation between X and Z if both variables change together.
That is, if when the variable X increases the variabl Z increases also then there is a positive correlation
if when the variable X increases the variable Z decreases then there is a negative correlation.
Now observe the graphs that are shown in the image. Note that in both cases the points are scattered and there is no clear relationship between the variables. Therefore the correlation is zero in both cases
Examples of strong positive and negative correlations are shown in the attached image
Find the area of the triangle in terms of x
Answer:
4x + 16
Step-by-step explanation:
Area of a triangle is:
A = ½ bh
Here, b = x+4 and h = 8:
A = ½ (x + 4) (8)
A = 4x + 16
The area of the given triangle with sides 5x,8, and x+4 is 4x + 16.
We have given the diagram.
In the diagram we have,
base(b) = x+4 and height(h) = 8
We have to determine the area of the triangle
What is the area of a triangle?[tex]A = 1/2\times b\times h[/tex]
Where b is the base and h is the height of the triangle
Use the given values in the above formula we have,
[tex]A = 1/2(x + 4) (8)\\\\A = 4x + 16[/tex]
Therefore the area of the triangle is 4x + 16.
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HELPP!! In the 30-50-90 triangle below, side s has a length of and side q has a length of
Answer:
(B) is the homogeneous mixture
Evaluate the series 4+2+1+1/2+1/4 to s10
Answer:
The correct answer is 13.75
Step-by-step explanation:
4+2= 6
6+1=7
6+7= 13
13+1/2= 13.5
13.5+1/4= 13.75
Answer:
[tex]s_10=\frac{1023}{128}[/tex]
Step-by-step explanation:
4+2+1+1/2+1/4.....
WE need to find out the sum s10
first term is 4 and second term is 2
2/4 = 1/2
1/2= 1/2
1/2 / 1= 1/2
so common ratio is 1/2
The given series is geometric series
we use the sum formula for the geometric series
[tex]s_n= a\frac{(1-r^n)}{1-r}[/tex]
Where 'r' is the common ratio and 'a' is the first term
a= 4 and r= 1/2
Plug in the values in the sum formula'
[tex]s_n= 4\frac{(1-(\frac{1}{2})^n)}{1-(\frac{1}{2})}[/tex]
Given n=10
[tex]s_10= 4\frac{(1-(\frac{1}{2})^{10})}{1-(\frac{1}{2})}=\frac{1023}{128}[/tex]
Solve: a^2+4(3+a)
a=5
Answer:
57
Step-by-step explanation:
[tex] {a}^{2} + 4(3 + a)[/tex]
[tex] {5}^{2} + 4(3 + 5)[/tex]
[tex]25 + 12 + 20[/tex]
[tex]57[/tex]
Please help I’m confused!! I will mark brainliest
Hello There!
“A” 2g+17
“B” 18h-3
Have A Great Day!
Answer:
A) 2g + 17
B) 18h - 3
Step-by-step explanation:
Hello! The reasoning for A is 2 x g + 17 would be the algebraic expression for "the sum of 2 times g and 17.
the reasoning for B is the same reason as a it is the algebraic expression for "the product of 18 and h.
I hope this helped you good luck!
PLEASE GIVE A BRAINLIEST IT WOULD MEAN A LOT!
:)
When you went to sleep, the temperature was −2.8°C.
When you woke up, the temperature was 1.4°C.
Which expression and statement describes the situation?
A. 1.4<-2.8,so 1.4°C is cooler than −2.8°C.
B. -2.8>1.4,so −2.8°C is warmer than 1.4°C.
C. 1.4=1/2(-2.8),so 1.4°C is half as cold as −2.8°C
D. 1.4>-2.8,so 1.4°C is warmer than −2.8°C
D
The larger the number the warmer it is
Answer:
D
Step-by-step explanation:
solve the system of equations below. -3x+6y=9
5x+7y=-49
A. (1,-2)
B.(-2,-7)
C.(-7,-2)
D.(-2,1/2)
[tex]
-3x+6y=9 \\
5x+7y=-49 \\ \\
-15x+30y=45 \\
15x+21y=-147 \\ \\
51y=-102 \\
\underline{y=-2} \\ \\
-3x+6\cdot(-2)=9 \\
-3x-12=9 \\
-3x=21 \\
\underline{x=-7} \\ \\
\boxed{(-7, -2)}
[/tex]
The answer is C.
Hope this helps.
r3t40
Answer:
(-7, -2) is the correct answer
Function g can be thought of as a scaled version of f(x)=x^2. Write the equation for g(x).
To write the equation for g(x) which is a scaled version of f(x)=x^2, we can use the general form of a quadratic function y=a(x-h)^2+k. The value of a determines the scaling factor.
Explanation:To write the equation for g(x) which is a scaled version of f(x)=x^2, we can use the general form of a quadratic function y=a(x-h)^2+k. The value of a determines the scaling factor. Since g(x) is a scaled version of f(x), a is the scaling factor. Therefore, the equation for g(x) is g(x)=a(x-h)^2+k, where a is the scaling factor, h is the x-coordinate of the vertex of f(x), and k is the y-coordinate of the vertex of f(x).
The scaled version of the function f(x) = x^2 is g(x) = a * x^2, where a is the scale factor determining the graph's stretch or compression.
If the function g is considered a scaled version of f(x) = x^2, it means that g will also be a quadratic function, but with a constant factor that scales or stretches the graph of f. The general form of a scaled quadratic function is g(x) = a * x^2, where a is the scale factor.
This scale factor a could be any real number. It determines whether the graph of g is narrower or wider compared to f. For example, if a is greater than 1, the graph of g will be narrower; if 0 < a < 1, the graph will be wider; and if a is negative, the graph will be reflected over the x-axis.
The shed in Adam’s backyard is shown below. Which correctly describes the dimensions of the figures that make up the shed? a rectangular prism measuring 5 feet by 6 feet by 8 feet and a triangular prism with the dimensions of 3 feet by 5 feet by 8 feet a rectangular prism measuring 3 feet by 5 feet by 8 feet and a triangular prism with the dimensions of 5 feet by 6 feet by 8 feet a rectangular prism measuring 5 feet by 6 feet by 8 feet and a triangular prism with the dimensions of 3 feet by 5 feet by 6 feet a rectangular prism measuring 3 feet by 5 feet by 6 feet and a triangular prism with the dimensions of 5 feet by 6 feet by 8 feet
Answer:A
Step-by-step explanation:took the test
The correct option is a. A rectangular prism measuring 5 feet by 6 feet by 8 feet and a triangular prism with the dimensions of 3 feet by 5 feet by 8 feet describes the correct dimensions of the figures.
A rectangular prism has three dimensions: length, width, and height.
A triangular prism has three dimensions: the base of the triangular face, the height of the triangular face, and the length (or depth) of the prism.
Let's examine each option based on the given dimensions:
Option a is the correct answer. It logically fits the dimensions of the shed with a larger rectangular prism for the base and a reasonably proportioned triangular prism for the roof.
In figure, the dimensions of rectangular prism are 5 feet by 6 feet by 8 feet and the dimensions of triangular prism are 3 feet by 5 feet by 8 feet.
The complete question is
The shed in Adam’s backyard is shown below.
Which correctly describes the dimensions of the figures that make up the shed?
a. a rectangular prism measuring 5 feet by 6 feet by 8 feet and a triangular prism with the dimensions of 3 feet by 5 feet by 8 feet
b. a rectangular prism measuring 3 feet by 5 feet by 8 feet and a triangular prism with the dimensions of 5 feet by 6 feet by 8 feet
c. a rectangular prism measuring 5 feet by 6 feet by 8 feet and a triangular prism with the dimensions of 3 feet by 5 feet by 6 feet
d. a rectangular prism measuring 3 feet by 5 feet by 6 feet and a triangular prism with the dimensions of 5 feet by 6 feet by 8 feet
Determine the direction that this parabola opens y=x^2-6x
Answer:
the graph of the parabola opens upwards.
Step-by-step explanation:
For any quadratic equation of the form
[tex]ax ^ 2 + bx + c[/tex] is true that:
if the main coefficient "a" is negative then the graph of the parabola opens downwards.
If the main coefficient "a" is positive, the parabola opens upwards
In this case the parabola is [tex]y=x^2-6x[/tex]
Note that [tex]a=1[/tex] and [tex]a>0[/tex] therefore the graph of the parabola opens upwards.
Find x. Assume that segments that appear tangent are tangent.
a.
56
c.
32
b.
28
d.
20
Answer:
c. 32
Step-by-step explanation:
The problem states that we need to assume that segments that appear tangent are actually tangent. From the figure, the tangent segment is the one that measures [tex]x[/tex] while the radius measures 24. The key in this problem is that if a radius of a circle and a tangent line to that circle touch intersect at the same point, then they form a right angle there. Accordingly, we have a right triangle here, so using the Pythagorean theorem, we can find [tex]x[/tex]. Thus:
[tex]x=\sqrt{40^2-24^2} \\ \\ x=\sqrt{1600-576} \\ \\ \boxed{x=32}[/tex]
If angle PQR and angle RQS form a linear pair and angle PQR =5x+5 and angle RQS =11x-65 then angle PQR=?
Answer:
m<PQR = 80°
Step-by-step explanation:
Points to remember
Sum angles in a linear pair is 180
To find the value of x
It is given that, angle PQR and angle RQS are linear pairs, and
m< PQR =5x+5 and m<RQS =11x-65
m<PQR + m<RQS = 180
5x + 5 + 11x - 65 = 180
16x -60 = 180
16x = 180 + 60
16x = 240
x = 15
To find the value of angle PQR
m<PQR = 5x + 5
= 5*15 + 5
= 75 + 5 = 80
Therefore m<PQR = 80°