Enter the number that belongs in the green box
A triangle with an area of 370 square inches
has a height that is 6 less than 8 times its
base. Find the base and height, in inches, of
the triangle.
Base=
Height=
Answer:
Step-by-step explanation:
Area of triangle = 1/2 (base × height)
Given, area of a triangle is 192 sq ins. and its height is 8 ins less than its base.
Then, let base = b, height = b-8
Hence, 1/2 (b)*(b-8) = 192
Above equation; “times 2”,
(b)*(b-8) = 384
b^2 - 8b - 384 = 0
(b+16)(b-24)=0
I need the answer pls, answer fast I am I s choool
Answer:
Hello! answer: D. 180
Step-by-step explanation:
What you do for these is find the surface area for each face separately then add them up so...
for the sides its 18 for the top and bottom it's 48 for the front and back it's 24 so now we add all 6 up so... 18 + 18 + 48 + 48 + 24 + 24 = 180 Hope that helps!
Answer:
180 in²
Step-by-step explanation:
To wrap the given box, we need to find the total surface area of the figure.
TSA of cuboid = 2 (lb + bh + hl)
= 2 { (6*8) + (8*3) + (3*6) }
= 2 ( 48 + 24 + 18 )
= 2 * 90
= 180 in²
A certain disease has an incidence rate of 0.3%. If the false negative rate is 6% and the false positive rate is 4%, compute the probability that a person who tests positive actually has the disease.
The probability that a person who tests positive actually has the disease is 0.012%
How to determine the probability?From the question, we have the following parameters that can be used in our computation:
Incidence rate = 0.3%False negative rate = 6%False positive rate = 4%The probability that a person who tests positive actually has the disease is represented as
Probability = Incidence rate * False positive rate
Substitute the known values in the above equation, so, we have the following representation
Probability = 0.3% * 4%
Evaluate the products
Probability = 0.012%
Hence, the probability is 0.012%
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Write a simplified expression that represents the perimeter of the triangle.
What is the perimeter of x=8?
A simplified expression that represents the perimeter of the triangle is 3 x + 12. The perimeter if x = 8 is 36.
Given, three sides of a triangle are given in terms of x
Side 1 is given as x units
Side 2 is given as ( x + 5 ) units
Side 3 is given as ( x + 7 ) units
We have to find a simplified expression that will represent the perimeter of the triangle with the given sides.
Perimeter of a triangle with sides a, b and c = a + b + c
This implies the perimeter of a triangle is equal to the sum of all the three sides
Perimeter of given triangle
= x + ( x + 5 ) + ( x + 7 )
= 3 x + 12
Hence, we get the perimeter of the triangle as 3 x + 12
To find the perimeter if the value of x is 8
Substitute the value of x as 8 in the above obtained equation of perimeter of triangle
=> Perimeter = 3 ( 8 ) + 12 = 24 + 12 = 36
Therefore, we get a simplified expression that represents the perimeter of the triangle as 3 x + 12 and the perimeter if x = 8 as 36.
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Find the surface area of this triangular promise correct unit
The surface area of the triangular prism would be =324,000cm²
How to calculate the triangular surface area of the given prism?To calculate the surface area of the triangular prism the formula that should be given would be as follows:
Surface area of triangular prism;
Surface area of triangular prism;= bh+(b1+b2+b3)l
where:
base length = 20cm
height = 15cm
length = 18cm
SA = 20×15(20+15+25)×18
= 300×60×18
= 324,000cm²
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karen wants to find the area of the isosceles triangle ABC. she knows that the base of the triangle (side CB) is equal to 8 squares. she also knows the height, or altitude, of the triangle is equal to 4.
Answer:
16 squares
Step-by-step explanation:
The area of an isosceles is \(\frac{bh}{2}\)
\(8 \cdot 4 = 32\\32 \div 2 = 16\)
Hope this helped!
Answer:
area = 16 unit ²
Step-by-step explanation:
given:
base = 8
height = 4
req'd : area of a triangle
area of isoceles triangle = 1/2 * b * h
= 1/2 * 8 * 4
= 16 unit²
There are 5 different pairs of gloves, where left and right are distinguishable. Select 4 of the 10 gloves. (a) How many are there to select 2 pairs of gloves? (b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
Answer:
(a) How many are there to select 2 pairs of gloves?
10 ways
(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
130 ways
Step-by-step explanation:
For the above questions we apply that combination formula
(a) How many are there to select 2 pairs of gloves?
There are 5 pairs of gloves according to the question above, hence:
5C2 = 5!/2! × (5 - 2)!
= 5!/2! × 3!
= 5 × 4 × 3 × 2 × 1/2 × 1 × 3 × 2 × 1
= 10 ways.
Therefore, there are 10 ways to select 2 pairs of gloves
(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
i) A way to select 4 gloves out of 10 gloves =
10C4 = 10!/4! ×(10 - 4)!
= 10!/ 4! × 6!
= 210 ways
ii) In order for 2 of the 4 gloves selected to be a pair, note that we have 5 pairs of gloves hence:
5 × 2⁴
= 80 ways.
Therefore, the number of ways which we can select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.) = 210 ways - 80 ways
= 130 ways
A customer buys a different book for a selling price of 38$.The book is discounted 25%.The customer must pay 6% sales tax on the disocounted price of the book.How much does the customer pay for the book including tax.
Answer:
$30.21
Step-by-step explanation:
Tamika has $800 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $482.62.
She buys 3 bicycle reflectors for $10.84 each and a pair of bike gloves for $24.49.
She plans to spend some or all of the money she has left to buy new biking outfits for $52.93 each.
Which inequality can be used to determine o, the maximum number of outfits Tamika can purchase while staying within her budget?
The inequality that can be used to determine x, the number of outfits Tamika can purchase is; 539.63+ 52.93x ≤ 800
The given parameters are:
Budget = $800
New bicycle = $482.62
3 bicycle reflectors = $10.84 each
Pair of a bike gloves = $24.49.
New biking outfits = $52.93each.
Let the number of new biking outfits be x So, we have;
New bicycle + 3 . price of bicycle reflectors + Pair of a bike gloves + New biking outfits <= Budget
This gives;
482.62 + 3( 10.84) + 24.49+ 52.93x ≤ 800
This gives;
539.63+ 52.93x ≤ 800
Solve the inequality;
52.93x ≤ 260.37
Divide by 52.93
x ≤ 4.91
Hence, the inequality is 539.63+ 52.93x ≤ 800
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Mr. Santor cuts 1/2 of a piece of construction paper. He uses 1/6 of the piece to make a flower. What fraction of the sheet of paper does he use to make the flower?
Answer:
1/12
Step-by-step explanation:
1/2 multiplied by 1/6 equals 1/12
-1/3 = r -3/4 what is r?
Answer:
5/12 = r
Step-by-step explanation:
-1/3 = r - 3/4
+3/4 +3/4
5/12 = r
What is the value of 5^4/5^6
1/25
1/5
5
25
Answer:
1/25
Step-by-step explanation:
5^4/5^6
Since we are dividing exponents with the same base, we subtract the exponents
5^( 4-6)
5^-2
We know that a^-b = 1/a^b
1/5^2
1/25
A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a
Answer:
53\(x_{123}\) == 134 cf
Step-by-step explanation:
A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a
The height of the building is approximately 78.63 meters.
The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.
Draw a diagram of the situation described in the problem to get a better understanding of the problem. The diagram would have a right-angled triangle with angle of elevation of 66° at the bottom left vertex and another angle of elevation of 53° at the bottom right vertex. The object on top of the building is at the vertex of the triangle. Point M and I on the diagram are points on the horizontal line of sight and on the ground respectively. We can label the diagram with the following values:Angle of elevation from point A = 66°Angle of elevation from point P = 53° Length of line segment AM = h Length of line segment MP = x Length of line segment IP = y Length of line segment MT = 50m. We'll use these values to calculate the length of h, which is the height of the building.Use the tangent ratio to find x:tan 66° = h / x => x = h / tan 66°. Use the tangent ratio to find y:tan 53° = h / y => y = h / tan 53°.We know that x + y = 50, so substituting the expressions for x and y from step 3 gives:h / tan 66° + h / tan 53° = 50h = 50 tan 66° tan 53° / (tan 53° + tan 66°) ≈ 78.63 m.Therefore, the height of the building is approximately 78.63 meters.
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7.56x11 i need halp im brain ded
Answer:
83.16
Step-by-step explanation:
just use a calculator for proof :)
Answer:
83.16
Step-by-step explanation:
To solve this problem, let's use the standard base of cross-multiplying. Even though 11 is a bigger number than 7.56, we are going to put 7.56 on top because it has more number placements. Now let's write this out and solve:
7.56
x 11
For now I am going to remove the decimals so that it doesn't get fonfusing while we are solving.
756
+7560
8316
Now we can bring the decimal back by counting how many placements were behind the decimal. There are two, so we count two decimal places forward from the end of the answer to look like this:
83.16
I hope that this helps.
Write the direct variation function given that y varies directly with x, and y = 1.5 when x = 5.
Answer:
y=0.3x
Step-by-step explanation:
Formula = \(K=\frac{y}{x}\)
y α x
y = kx
Where k is the constant of proportionality.
When y = 1.5; x = 5;
We substitute these known values in the equation,
y = kx
1.5 = k5
Dividing both sides of the equation by 5 to find the value for k, we have
1.5/5= k0.3/5
Therefore,
K = 0.3
Having found the value of k,
We substitute this value into the relationship
y = kx
Therefore we have,
y = 0.3x.
The direct variation function is therefore,
y = 0.3x.
[RevyBreeze]
Answer:
y= 0.3x
Step-by-step explanation:
Since y varies directly as x, use the direct variation equation, y = kx.
1.5 = k(5) Substitute 1.5 for y and 5 for x.
k = 0.3 Solve for k.
Write the direct variation function by using the value for k.
y = 0.3x Substitute 0.3 for k in y = kx.
Enter a positive value for d that makes this statement true: 34×d is less than 34 but greater than zero HELP PLSS FASTT
Answer:
0.5 (any number between 0 and 1)
Step-by-step explanation:
34 * 0.5 = 17
34 > 17 > 0
Solve the quadratic equation by factoring. x2+3x−18=0 Enter the exact answers.
The question is given below as
\(x^2+3x-18=0\)Step 1:We will look for two factors we will multiply together to get -18 and the same two factors that will add up together to +3
\(\begin{gathered} The\text{ factors of 18 are} \\ 1,-1,2,-2,3,-3,6,-6,-9,9,18,-18 \end{gathered}\)Since -18 is a negative value
Then, the two factors must have different signs because of the sign pattern below
\(\begin{gathered} -\times-=+ \\ +\times-=- \\ +\times+=+ \end{gathered}\)The two factors are
\(\begin{gathered} +6,-3 \\ +6\times-3=-18 \\ +6-3=+3 \end{gathered}\)Step 2: Substitute the factors in the equation below
\(\begin{gathered} x^2+3x-18=0 \\ x^2+6x-3x-18=0 \\ x(x+6)-3(x+6)=0 \\ (x-3)(x+6)=0 \end{gathered}\)Step 3: Equate both factors to zero
\(\begin{gathered} (x-3)=0,(x+6)=0 \\ x=0+3,x=0-6 \\ x=3,x=-6 \end{gathered}\)Hence,
The final answer are x =3 and x = -6
(need help 35 points)
Answer:
x=7
Step-by-step explanation:
Set up as proportion and cross multiply:
x/6 = 42/36
x=7
two numbers are in the ratio 4:1 Their sum is 60 find the largest number
Answer:
48
Step-by-step explanation:
You want the largest of two numbers in the ratio 4 : 1 that have a sum of 60.
LargestThe largest of the two numbers will be 4/(4+1) = 4/5 of their total.
(4/5)(60) = 48
The largest of the numbers is 48.
__
Additional comment
The smaller number is 12. So, you have 48:12 = 4:1, and 48+12=60.
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Algebra Question
Let v = (-7,6,-6) and w = (-5,-3,-6) be vectors in R^3. Find the orthogonal projection of v onto w.
Answer:
Projection on w: (-54/14, -159/70, -159/35)
I have the correct answer but I don't know how they got it.
The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).
To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:
proj_w(v) = (v⋅w) / (w⋅w) * w
where ⋅ denotes the dot product.
Calculating the dot product of v and w:
v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53
Calculating the dot product of w with itself:
w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70
Now, substituting these values into the formula, we have:
proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)
Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).
In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.
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Find the tangent of the smaller acute angle in a right triangle with side lengths 5, 12, and 13.
Write your answer as a fraction.
The tangent of the smaller acute angle is ____?_______
The tangent of the smaller acute angle in a right triangle is tanФ = 0.42.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
Given, A right triangle with side lengths 5, 12, and 13.
tanФ = 5/12.
tanФ = 0.42.
Ф = tan⁻¹(0.42).
Ф = 22.8°.
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What is 9 times 9
It’s so hard
Which of the following represent a linear inequality in open-sentence form? (Select all that apply.) 2x + 8 = 10y 2x - 7y > 10 8 + x > 5 3 < 5
Answer:
8 + x bigger then 5
Good luck!!
Which line segments have a positive slope PLS FAST!! THANKS!!
find the volume of the figure below. pls show solution:)
Answer:
294pi
Step-by-step explanation:
1/3*pi*r^2*h=V
1/3*pi*49*18=V
V=294pi
what is the area of the circle below?
The area of the circle shown above is equal to: A. 1,520.5 cm².
How to calculate the area of a circle?Mathematically, the area of a circle can be calculated by using the following mathematical expression:
Area of a circle, A = πr²
Where:
r represents the radius of a circle.
By substituting the radius into the formula for the area of a circle, we have the following;
Area of a circle, A = πr²
Area of a circle, A = 3.14 × 22²
Area of a circle, A = 1,520.5 cm².
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Graph the following features: Slope = − 2 −2 Y-intercept = 3 3
Answer: graphed and attached
Step-by-step explanation:
to graph a y intercept and slope, first find the y intercept on the graph and place your point. here the y intercept is 3, so (0, 3) because x=0 at a y intercept.
next use slope to find your next point. slope of -2 is the same as -2/1 or down -2 and right +1. so from your y intercept of 3, go down -2 and right 1 and place your point (1, 1). do this again for a 3rd point at (2, -1).
graph is attached.
Write x^2 - 8x + 10 in the form
(x + a)^2 + B
\(x^2-8x+10=x^2-8x+16-6=(x-4)^2-6\)
the diffrence of two numbers is 1 and their product is 56
Answer: I hope this is helpful please mark me brainlist
Step-by-step explanation:
inspection, two numbers whose sum is -1 and whose product is -56 are -8 and 7.
Answer: the answer is 8 and 7.