Answers
Answer:
120 cm³Step-by-step explanation:
First we have to find out area of the base
[tex]s = \frac{a + b + c}{2} [/tex]
[tex] = \frac{5 + 12 + 13}{2} [/tex]
[tex] = \frac{30}{2} [/tex]
[tex] = 15[/tex]
Area of base = [tex] \sqrt{s(s - a)(s - b)(s - c)} [/tex]
[tex] = \sqrt{15(15 - 5)(15 - 12)(15 - 13)} [/tex]
[tex] = \sqrt{15 \times 10 \times 3 \times 2} [/tex]
[tex] = \sqrt{5 \times 3 \times 5 \times 2 \times 3 \times 2} [/tex]
[tex] = 2 \times 3 \times 5[/tex]
[tex] = 30 \: {cm}^{2} [/tex]
Now, let's find the volume of triangular pyramid
[tex] = \frac{1}{3} \times a \times h[/tex]
[tex] = \frac{1}{3} \times 30 \times 12[/tex]
[tex] = 120 \: [/tex] cm³
Hope this helps..
best regards!!
Related Questions
Find an exact value. tangent of seven pi divided by twelve
Answers
(
7
π
12
)
=
−
(
2
+
√
3
)
Explanation:
tan
(
7
π
12
)
=
tan
(
π
−
5
π
12
)
= #-tan((5pi)/12)
=
−
tan
(
3
π
12
+
2
π
12
)
=
−
tan
(
π
4
+
π
6
)
Now using
tan
(
A
+
B
)
=
tan
A
+
tan
B
1
−
tan
A
tan
B
=
−
tan
(
π
4
)
+
tan
(
π
6
)
1
−
tan
(
π
4
)
tan
(
π
6
)
=
−
1
+
1
√
3
1
−
1
×
1
√
3
Multiplying numerator and denominator by
√
3
=
−
√
3
+
1
√
3
−
1
=
−
(
√
3
+
1
)
2
(
√
3
−
1
)
(
√
3
+
1
)
=
−
3
+
1
+
2
√
3
3
−
1
=
−
(
2
+
√
3
Answer: negative 2 minus radical 3
Step-by-step explanation:
We can use the tangent half-angle formula to find the exact value of tangent of 7π/12:
tan(θ/2) = ±√[(1-cosθ)/1+cosθ)]
Here, θ = 7π/6, and cos(7π/6) = -sqrt(3)/2.
Substituting these values, we get:
tan(7π/12) = ±√[(1-(-sqrt(3)/2))/(1+(-sqrt(3)/2))]
= ±√[(2+sqrt(3))/(2-sqrt(3))]
Multiplying the numerator and denominator by (2+sqrt(3)), we get:
= ±√[(2+sqrt(3))^2/(4-3)]
= ±√[(2+sqrt(3))^2]
= ±(2+sqrt(3))
Since 7π/12 lies in the second quadrant, and tangent is negative in the second quadrant, the exact value of tangent of 7π/12 is - (2+√3)
4 1/3 b+b=6b–10.4 efvnabvkjaebv
Answers
Answer: The value of b= 15.6
Step-by-step explanation:
The given equation: [tex]4\dfrac{1}{3}b+b=6b-10.4[/tex]
To find : Value of b.
Since, we can write [tex]4\dfrac{1}{3}=\dfrac{13}{3}[/tex]
So, the given equation becomes [tex]\dfrac{13}{3}b+b=6b-10.4[/tex]
[tex]\Rightarrow\dfrac{13b+3b}{3}=6b-10.4\Rightarrow\dfrac{16b}{3}=6b-10.4[/tex]
Subtract 6b from both sides , we get
[tex]\Rightarrow\dfrac{16b}{3}=6b-10.4\\\\\Rightarrow\dfrac{16b-18b}{3}=-10.4\\\\\Rightarrow\dfrac{-2b}{3}=-10.4\\\\\Rightarrow b=-10.4\times\dfrac{-3}{2}\\\\\Rightarrow\ b= 15.6[/tex]
hence, the value of b= 15.6
Reiko drove from point A to point B at a constant speed, and then returned to A along the same route at a different constant speed. Did Reiko travel from A to B at a speed greater than 40 miles per hour?
(1) Reiko's average speed for the entire round trip, excluding the time spent at point B, was 80 miles per hour.
(2) It took Reiko 20 more minutes to drive from A to B than to make the return trip.
Answers
Answer:
no
Step-by-step explanation:
it was slower the way there and if he was going 40 it would have taken the same time to get there as it would have to go back
Answer:
Yes.
Step-by-step explanation:
Reiko's average speed was 80 miles per hour. That is more than 40 miles per hour. Even if it took him longer to drive from A to B, his speed would still be more than 40 miles per hour to have the average speed be 80 miles per hour.
Hope this helps!
Solve the equation using the distributive property and properties of equality. One-half (x + 6) = 18 What is the value of x? 6 7 and one-half 14 and one-half 30
Answers
Answer:
The value of x is 30.
We have to find the value of x in the given equation.
Using distributive property
We have,
[tex]1/2(x+6)=18\\a.(b+c)=a.b+a.c\\1/2(x+3)=18\\1/2x=15\\x=3[/tex]
other are also solve by this methode;)
The required solution of the expression [tex]1/2(x+6) = 18[/tex] is 30.
To solve the equation using the distributive property and properties of equality. One-half (x + 6) = 18 and value of x to be determined.
The equation is the well-organized link of the variables of two expressions that contain equal between them.
distributive properties are used to evaluate the math problem easily by distributing numbers to the numbers present in parenthesis. eg, if we apply the distributive property of multiplication to solve the expression
a( b + c ) = a.b + a.c
[tex]1/2(x+6) = 18[/tex]
Using distributive property a( b + c ) = a.b + a.c
[tex]1/2.x+1/2*6 = 18\\1/2x+3=18\\1/2x=18-3\\1/2x=15\\x=2*15\\x=30\\[/tex]
Thus, The required solution of the expression [tex]1/2(x+6) = 18[/tex] is 30.
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What is the first step to circumscribe a circle around a triangle? a Find the diameter b Find the angle bisectors c Find the perpendicular bisectors d Draw the circle
Answers
Answer:
Step 1-Construct the perpendicular bisector of one side of the triangle.
Step 2-Construct the angle bisector of another side of the triangle.
Explanation:
A circumscribed circle is the circle that passes through all three vertices of the triangle. The center of the circumscribed circle is the circumcenter of the triangle, the point where the perpendicular bisectors of the sides meet
Please answer this question now
Answers
Answer:
b=9.96≅10
Step-by-step explanation:
b^2=a^2+c^2−(2ac)cos(64)
b=√6²+11²-2(6*11)cos64
b=9.96≅10
look at the pattern below.How should the tird shape be labeled
Answers
Answer:
You havent showed us the pattern
PLEASE HELP!!!
A calculator was used to perform a linear regression on the values in the table. The results are shown to the right of the table.
Image attached
Answers
Answer: C
explanation: a p e x
Explanation:
Start with the template they give, which is y = ax+b. From here, replace 'a' with -2.9 and b with 13.5 to get the answer y = -2.9x + 13.5
The r and r^2 values aren't used to form the regression line. Instead, they are ways to see how good a fit we have. Since r is fairly close to -1, this means we have a really strong negative correlation. All of the points are close or around the same straight line with a negative slope (that slope being -2.9).
Please help.. I'm really confused tbh
Answers
X axis is the horizontal axis and y is the vertical.
On a graph, quandrant 1 is the upper right side which requires both x and y to be positive.
Quadrant 2 is upper left, which is negative x and positive y.
Quandrant 3 is lower left, which is negative x and y.
Quadrant 4 is lower right, which is positive x and negative y.
X< 0 is negative and y > 0 is positive.
This matches quadrant 2
The answer is B.
You are in a panic! You forgot to buy your little brother a birthday present. You start with $60 in your wallet. You buy him several toys, t, that are $5 each. You know have $45 leftover. How many toys did you buy your little brother for his birthday? (set up the equation)
Answers
Answer: 3 toys
Step-by-step explanation:
equation will be 60 - 5 x t = 45
solving it we get
5 x t = 60 - 45 = 15
=> t = 15/5 = 3
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP(25 points)
Answers
Answer: I hope it helps :)
x=6 , y=6√3x =23√3 , y=23u =12 , v= 6a =18√2 , b =18x = 13 , y= 13Step-by-step explanation:
1.
[tex]Hypotenuse =x\\Opposite =y \\Adjacent =6\\\alpha = 6\\Let's\: find\: the \:hypotenuse\: first\\Using SOHCAHTOA\\Cos \alpha = \frac{adj}{hyp} \\Cos 60 = \frac{6}{x} \\\frac{1}{2} =\frac{6}{x} \\Cross\:Multiply\\x = 12\\Let's\: find\: y\\Hyp^2=opp^2+adj^2\\12^2=y^2+6^2\\144=y^2+36\\144-36=y^2\\108=y^2\\\sqrt{108} =\sqrt{y^2} \\y=6\sqrt{3}[/tex]
2.
[tex]Opposite =x\\Hypotenuse = 46\\Adjacent =y \\\alpha =60\\Using \: SOHCAHTOA\\Sin \alpha =\frac{opp}{adj} \\Sin 60=\frac{x}{46}\\\\\frac{\sqrt{3} }{2} =\frac{x}{46} \\2x=46\sqrt{3} \\x = \frac{46\sqrt{3} }{2} \\x =23\sqrt{3} \\\\Hyp^2=opp^2+adj^2\\46^2=(23\sqrt{3} )^2+y^2\\2116=1587+y^2\\2116-1587=y^2\\529=y^2\\\sqrt{529} =\sqrt{y^2} \\y = 23[/tex]
3.
[tex]Hypotenuse = u\\Opposite =6\sqrt{3} \\Adjacent = v\\\alpha =60\\Sin\: 60 = \frac{6\sqrt{3} }{u} \\\frac{\sqrt{3} }{2} =\frac{6\sqrt{3} }{u} \\12\sqrt{3} =u\sqrt{3} \\\\\frac{12\sqrt{3} }{\sqrt{3} } =\frac{u\sqrt{3} }{\sqrt{3} } \\u = 12\\Hyp^2=opp^2+adj^2\\12^2= (6\sqrt{3} )^2+v^2\\144=108+v^2\\144-108=v^2\\36 = v^2\\\sqrt{36} =\sqrt{v^2} \\\\v =6[/tex]
4.
[tex]Hypotenuse = a\\Opposite =18 \\Adjacent = b\\\alpha =45\\Tan \alpha = opp/adj\\Tan \:45 =18/b\\1=\frac{18}{b}\\ b = 18\\\\Hyp^2=Opp^2+Adj^2\\a^2 = 18^2+18^2\\a^2=324+324\\a^2=648\\\sqrt{hyp^2} =\sqrt{648}\\ \\a =18\sqrt{2}[/tex]
5.
[tex]Hypotenuse = 13\sqrt{2}\\ Opposite =x\\Adjacent = y\\\alpha =45\\Sin\:\alpha = opp/hyp\\Sin 45=x/13\sqrt{2}\\ \\\frac{\sqrt{2} }{2} =\frac{x}{13\sqrt{2} } \\2x=26\\2x/2=26/2\\\\x = 13\\\\Hyp^2=opp^2+adj^2\\(13\sqrt{2})^2=13^2+y^2\\ 338=169+y^2\\338-169=y^2\\169=y^2\\\sqrt{169} =\sqrt{y^2} \\13 = y[/tex]
Sarah serves at a restaurant and makes 20% of what she sells as tips. Her base salary is $10.20an hour. Each hour she sells an average of $60 of food and drinks. She also makes time and a half when she works over 8 hours during a single shift. Her work week contains three 10-hour shifts, one 5-hour shift, and one 11-hour shift. Using the same income deductions as stated in the previous question, what is Sarah’s annual gross income and annual net income.
Answers
Sara works 46 hours per week
9 hours are overtime and 37 hours are regular time
pay rate at time and a half: 10.20∗1.5=15.30
regular hours plus overtime pay
37∗10.20=377.40
9∗15.30=137.70
Income due to tips
Total hours worked∗60per hour∗20%
46∗60∗.20=552
Weekly Income=Hourly income + tips
Weekly Income=377.40+137.70+552.00
Weekly Income=1067.10
Annual income=Weekly income∗52
Annual income=55489.20
30 POINTS!! Write the slope-intercept form of the equation for the line.
Answers
Answer:
B. [tex]y = -\frac{3}{10}x + \frac{1}{2}[/tex]
Step-by-step explanation:
Well slope-intercept form is [tex]y = ax + b[/tex].
Let's start with the slope.
In this case, finding the slope is easy.
It should have a negative slope.
So we can cross out answer choices A. and C.
Also, we can cross out D. because it just makes no sense, -10/3, if you start from the y-intercept and go down 10 and across 3, yeah that's
not the slope.
So we can cross out D.
The only answer choice left is B.
We can tell the y-intercept is 1/2 because like come on so B is the correct answer.
B. [tex]y = -\frac{3}{10}x + \frac{1}{2}[/tex]
Looking at the graph, we can figure out our y-intercept or b simply by looking at the line to see where it intersects the y-axis.
So, we can see that the line intersects the y-axis at 1/2 or 0.5
That means, our y-intercept or b is 1/2 (0.5).
Now, to find out the slope of the line, we can pick two pairs of coordinates on the line and plug it into the slope equation to figure out the slope.
Let's use the two coordinate pairs: (-5, 2) and (0, 1/2).
Plug it in.
1/2 - 2 = - 1.5
0 - - 5 = 5
-1.5/5 = -0.3
Convert it into a fraction: -0.3 = -3/10
Thus, our slope intercept form for this line is: y = -3/10 + 1/2
can u help me spot the sequence
Answers
Answer:
Hey mate... I don't know the first three... But mayb I can help u in last one.
Step-by-step explanation:
The answer is : 2: 6: 18: 54: 162: 426
I can see the pattern by multiplying.. As from 3
2x3=6 :6x3=18 :18x3= 54 :54x3=162 :162x3=426
So I guess this is the ans
Hope it helped u!
29, 40, 53
75, 96, 135
Explanation:
5, 8, 13, 20, 29, 40, 53
Keep adding odd number
5+3 => 8 + 5 => 13 + 7 => 20 + 9 => 29 => 29 + 11 => 40 + 13 => 53
3, 12, 27, 48, 63, 78, 93
3 x 4 = 12
3 x (4 + 5)= 27
3 x (9+7)= 48
3 x (16+9) = 75
3 x (21 + 11) = 96
3 x (32 + 13) = 135
What are the solutions to the quadratic equation x^2 – 16 = 0?
Answers
Answer:
x=4
Step-by-step explanation:
x²-16=0
x²=0+16
x²=16
x=√16
x=4
Write an algebraic expression yo find the number of seconds in n minutes
Answers
Answer:
60n seconds
Step-by-step explanation:
In 1 min, there are 60 seconds
So,
1 min = 60 secs
For n minutes, it becomes:
=> 60n seconds
An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 634" by 412" on the drawing, how large is the bedroom?
Answers
and the answer should be 18 x 27. The answers were reversed.
Step-by-step explanation:
basically you can do (6x4) + 3 = 27
and (4x4) + 2 = 18.
A ratio shows us the number of times a number contains another number. The real size of the bedroom is 2536' by 1648'.
What is a Ratio?A ratio shows us the number of times a number contains another number.
Given that architectural drawing lists the scale as 1/4" = 1'. Therefore, we can write the scale ratio as,
1/4" = 1'
1" = 4'
Now, given that the bedroom measures 634" by 412" on the drawing. Therefore, the real dimensions of the bedroom are,
634" = 634 × 4' = 2536'
412" = 412× 4' = 1648'
Hence, the real size of the bedroom is 2536' by 1648'.
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A painter can paint a building in 15 days and a coworker can do the same job in 10 days. If the first painter starts and 3 days later the coworker joins in to help finish the job, how many days does it take to paint the building?
Answers
Answer: 7.8 days
Step-by-step explanation:
Painter can get the job done in 15 days so gets [tex]\dfrac{1}{15}[/tex] of the job done in 1 day.
Coworker can get the job done in 10 days so gets [tex]\dfrac{1}{10}[/tex] of the job done in 1 day.
Together, they get [tex]\dfrac{1}{15}+\dfrac{1}{10}[/tex] of the job done in 1 day.
Painter worked for 3 days so completed [tex]\dfrac{1}{15}(3)=\dfrac{1}{5}[/tex] of the job.
That leaves a remaining of [tex]1-\dfrac{1}{5}=\dfrac{4}{5}[/tex] of the job to be completed.
Let x represent the number of days it will take them to work together.
Painter + Coworker = Together
[tex]\dfrac{1}{15}(x)\quad +\quad \dfrac{1}{10}(x)\quad =\quad \dfrac{4}{5}[/tex]
Multiply by 30 to eliminate the denominator:
[tex]\dfrac{1}{15}(x)(30) +\ \dfrac{1}{10}(x)(30) = \dfrac{4}{5}(30)[/tex]
Simplify and solve for x:
2x + 3x = 24
5x = 24
[tex]x=\dfrac{24}{5}[/tex]
x = 4.8
Remember that Painter worked 3 days alone in addition to the 4.8 days they worked together.
So the total time to paint the building is 3 + 4.8 = 7.8
changing fraction to percentage
Answers
Answer:
Hello There!
`~~~~~~~~~~~~~~~~~~`
You added no fraction so i thought you wanted the definition
Convert Fractions to Percents. Divide the top of the fraction by the bottom, multiply by 100 and add a "%" sign.
Hope this helped you. Brainliest wouldbe nice!
Try using a calculator
Divide the top of the fraction by the bottom, Then multiply the result by 100 and read off the answer
Example: 4/5 =x/100
4*100= 5x
400=5x
400/5=x
80=x
80/100 = 80%
:)
Three years after a company was founded, its assets were $11,283,500. Ten years after being founded, its assets had grown to $21,794,600. During that period of time, at what rate did the company's assets grow per year?
Answers
Answer:
$1,051,110Step-by-step explanation:
Given
Step one:
Company's initial asset value = $11,283,500
Company's final asset value = $21,794,600
Step two
we can calculate the company's asset appreciation after 10 years as
$21,794,600- $11,283,500= $10,511,100
Step three
Hence, the growth rate of the company's asset value per year can be expressed as = $10,511,100/10= $1,051,110
A double-blind experiment was conducted to evaluate the success of a Zika virus vaccine. What is the purpose of keeping treating physicians unaware of
the treatment status of the experimental subjects?
To eliminate grounds for malpractice suits
To ensure subjects were assigned randomly to treatments
To remove a possible source of bias
To make sure nobody is injured
To avoid the placebo effect
Answers
To remove a possible source of bias
Step-by-step explanation:
If the test subjects know they are part of an experiement, this could cause them to think that it worked and it could either lead to untruthful answers or the test subjects tricking themselves to think that the vaccine worked
Write an expression for the volume and simplify your answer. 3x x+1 x+4
Answers
Answer:
volume=3x³+15x²+12x
Step-by-step explanation:
v= l*w*h =(3x )(x+1) (x+4)
v=3x(x²+5x+4)
volume=3x³+15x²+12x
For water to be a liquid, its temperature must be within 50 Kelvin of 323 Kelvin. Which equation can be used to determine the minimum and maximum temperatures between which water is a liquid? |323 – 50| = x |323 + 50| = x |x – 323| = 50 |x + 323| = 50
Answers
Answer:
Mark as BRAINLIEST plz
|x-323|<50: answer
Step-by-step explanation :
For water to be a liquid, the temperature must be within 50 Kelvin of 323 K.
So, the range of the temperature of water will lie between 50 kelvin more than 323 kelvin and 50 kelvin less than 323.
The equation that can be used to determine the maximum temperature at which water is a liquid can be given by : x < 323 + 50
The equation that can be used to determine the minimum temperature at which water is a liquid can be given by : x > 323 - 50
So the resultant equation can be written as :
|x-323|<50
The solution of inequality equation is | x - 323 | < 50
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the temperature of the water be = x Kelvin
Now , the equation will be
For water to be in the liquid state, the temperature must be within 50 kelvin (K) of 323 K
So , the value of the temperature of water will lie between 50 kelvin more than 323 kelvin and 50 kelvin less than 323
Substituting the values in the inequality equation , we get
For maximum temperature ,
x should be 50 more than 323 and
For minimum temperature ,
x should be 50 less than 323
So ,
The inequality relation is
x > 50 + 323 be equation (1)
x < 323 - 50 be equation (2)
So , the modulus function is expressed as
It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.
Therefore , the value is | x - 323 | < 50
Hence , The solution of inequality equation is | x - 323 | < 50
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what are the lengths for x and y
Answers
Answer:
They are both equal to 7.07
Step-by-step explanation:
Using SohCahToa to find x you use the opposite and the hypotenuse if you use the 45 degree angle.
Now you use sin(45)=x/10
x=7.07
Now using SohCahToa to find y you use hypotenuse and adjacent, if using the 45 degree angle.
Now you use cos(45)=y/10
y=7.07
Answer: side y=7.1
side x= 7.1
Step-by-step explanation:
[tex]sin(45)=\frac{x}{10}[/tex]
[tex]x=7.07...[/tex]
[tex]cos(45)=\frac{y}{10}[/tex]
[tex]y=7.07...[/tex]
What is 651 minus -13? Please with explanation.
Answers
Answer:
664
Step-by-step explanation:
651 - - 13
Negative times negative is positive.
651 + 13
Add.
664
Answer:
664
Step-by-step explanation:
651 - (-13)
Do the keep , change , change method
So , it will be :
651 + 13 = 664
Hope this helps and plsss plss amrl as brianliest and THNXX :)
If you flip a coin three times in the air, what is the probability that tails lands up all three times? A. 1/2 B. 1/8 C. 1/4 D. 1/6
Answers
Answer: A) 1/2
Step-by-step explanation:
Answer:
If you flip a coin three times in the air, what is the probability that tails lands up all three times?
Step-by-step explanation:
1/2
Determine the equation for the total cost of snow tubing, the rest of the chart:
8 . 20
10 . 25
PLEASE HELP ASAP!!! *grade 9 work* best answer gets brainliest :)
Answers
Step-by-step explanation:
Notice how you get the same value each time when you divide the cost by the number of downhill rides
5/2 = 2.5 10/4 = 2.5 15/6 = 2.5Moreover when the downhill rides grow by 2 the total cost grows by 5
so we can state :
n+2 ⇒c+50+2 ⇒ 0+5 0+6 ⇒0+ (3*3)To complet the chart we can use the proportionaliyu relation:
2⇒520⇒ Cc = [tex]\frac{20*5}{2}[/tex]= 50so 20 goes with 50
same method:
2⇒525⇒ C C = [tex]\frac{25*5}{2}[/tex] =62.5so 25 goes with 62.5
What is the least number of colors you need to correctly color in the sections of the pictures so that no two touching sections are the same color?
Answers
Answer:
2
Step-by-step explanation:
Polygons on either side of a common edge need to be colored differently, so 2 colors are needed, as a minimum. Polygons of the same shape do not share an edge, so all can be colored the same color.
What true bearing is WSW equivalent to?
Answers
Answer:
S 67.50° W
Step-by-step explanation:
A rectangle has a perimeter of 35.8 inches and a base of 12.6 inches. What is the height?
Answers
Answer:
Height is 5.3 inches.
Step-by-step explanation:
2* base + 2*height = 35.8
2*12.6 + 2h = 35.8
h = (35.8 - 2(12.6) / 2
= (35.8 - 25.2) /2
= 10.6 / 2
= 5.3 inches.
Answer:
5.3inStep-by-step explanation:
The formula of a perimeter of a rectangle:
[tex]P=2(l+w)[/tex]
l - length
w - width
We have
[tex]P=35.8in\\l=12.6in[/tex]
Substitute:
[tex]35.8=2(12.6+w)[/tex] divide both sides by 2
[tex]\dfrac{35.8}{2}=\dfrac{2(12.6+w)}{2}[/tex]
[tex]17.9=12.6+w[/tex] subtract 12.6 from both sides
[tex]17.9-12.6=12.6-12.6+w\\\\5.3=w\to w=5.3\ (in)[/tex]