Answer:
(x - 10)(x + 8)
Step-by-step explanation:
x² - 2x - 80
Consider the factors of the constant term (- 80) which sum to give the coefficient of the x- term (- 2)
The factors are - 10 and + 8 , since
- 10 × 8 = - 80 and - 10 + 8 = - 2 , then
x² - 2x - 80 = (x - 10)(x + 8)
50 points! I would appreciate an explanation, I actually want to know how to do this. Thanks! :P
Answer:
1.
(a) The Domain is the set of inputs of the function.
Considering that the function takes a period of 3 weeks (21 days), the domain is [0, 21], once we can't evaluate what happens after the 21st day.
[tex]\text{Domain is } [0, 21][/tex]
Otherwise, it could be [tex][0, \infty)[/tex]
Note: We include 0 and 21.
Once the greatest balance was $400, it will not exceed $400, either it doesn't show negative values.
[tex]\text{Range is } [0, 400][/tex]
Note: We include 0 and 400.
(b)
Once the greatest balance was $400, when x=0, it seems that the y-value is half of $400, therefore, approximately $200. It also represents the initial value, the amount of money when she opened the account.
(c)
[tex]f(x)=B(d)[/tex]
[tex]B(12)=0[/tex]
(d)
It is in segment 4.
The balance equal to zero means that the y-value of the graph is zero, therefore in the x-axis.
At what rate per annum will N250 amount to N330 in 4 years.
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{8 \: \% \: }}}}}[/tex]Step-by-step explanation:
Given,
Principal ( P ) = N 250
Time ( T ) = 4 years
Amount ( A ) =N 330
Rate ( R ) = ?
First, finding the Interest :
According to definition of Amount ,
Amount = Principal + Interest
plug the values
⇒[tex] \sf{330 = 250 + I}[/tex]
Move i to left hand side and change it's sign
⇒[tex] \sf{ - I = 250 - 330}[/tex]
Calculate
⇒[tex] \sf{ - I = - 80}[/tex]
Change the signs of the both equation
⇒[tex] \sf{I = 80 }[/tex]
Interest = 80
Finding the rate :
Simple Interest = [tex] \sf{ \frac{PTR}{100} }[/tex]
plug the values
⇒[tex] \sf{80 = \frac{250 \times 4 \times R}{100} }[/tex]
Multiply the numbers
⇒[tex] \sf{80 = \: \frac{1000 \: R}{100} }[/tex]
Apply cross product property
⇒[tex] \sf{1000R = 100 \times 80}[/tex]
Multiply the numbers
⇒[tex] \sf{1000R = 8000}[/tex]
Divide both sides of the equation by 1000
⇒[tex] \sf{ \frac{1000R}{1000} = \frac{8000}{1000} }[/tex]
Calculate
⇒[tex] \sf{R = 8 \: \% \: }[/tex]
Thus, Rate = 8 %
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Let's learn about Principal , Interest , Time , Rate and Amount :
Principal = The money which is borrowed or deposited is called principal.Interest = The additional amount of money which is paid by borrower to the lender is called interest.Time = The duration of time for which principal us deposited or borrowed is termed as time period.Rate = The condition under which the insterest is charged is called rate.Amount = The sum of principal and Interest is called an amount.Hope I helped!
Best regards!!
Name the quadrants in which of the following points (3, 0) (-9,-3) lie.
Answer:
(3,0) lie between quadrants I and II. (-9, -3) lie in quadrant III
please help me on number 4!!
Answer: B) 5 inches
======================================================
Explanation:
1 ft = 12 in
9 ft = 108 in ... multiply both sides by 9
9 ft, 9.5 in = 108 in + 9.5 in = 117.5 in
The board's length of 9 ft, 9.5 inches is the same as 117.5 inches.
It's cut into sections of 11.25 inches, so we have (117.5)/(11.25) = 10.44 approximately which rounds down to 10.
Having 10 sections of length 11.25 inches each, takes up 10*11.25 = 112.5 inches so far. That leaves 117.5 - 112.5 = 5 inches as the remaining piece of the board.
Pls Answer A and B. You don’t need to explain. Thank you!!
If the amount of VAT paid for an item at 13% was Rs 390, at what price was the item sold?
Answer:
Step-by-step explanation:
Let the price of the item = Rs x
13% of x = 390
[tex]\frac{13}{100}*x=390\\\\\\x = 390*\frac{100}{13}\\\\\\[/tex]
x = Rs. 3000
simplify the following
Answer:
1) 11[tex]\sqrt{3}[/tex]
2) 2[tex]\sqrt{2}[/tex]
3) [tex]20\sqrt{3} + 15\sqrt{2}[/tex]
4) [tex]53 + 12\sqrt{10}[/tex]
5) -2
6) [tex]7\sqrt{2} - 5\sqrt{3}[/tex]
Step-by-step explanation:
1) 2[tex]\sqrt{12}[/tex] + 3[tex]\sqrt{48}[/tex] - [tex]\sqrt{75}[/tex]
=(2 × 2[tex]\sqrt{3}[/tex] )+ (3 × 4[tex]\sqrt{3}[/tex]) - 5[tex]\sqrt{3}[/tex]
= 4[tex]\sqrt{3}[/tex] + 12[tex]\sqrt{3}[/tex] - 5[tex]\sqrt{3}[/tex]
= 11[tex]\sqrt{3}[/tex]
2) 4[tex]\sqrt{8}[/tex] -2[tex]\sqrt{98}[/tex] + [tex]\sqrt{128}[/tex]
= (4 × 2[tex]\sqrt{2}[/tex]) - (2 × 7[tex]\sqrt{2}[/tex]) + 8[tex]\sqrt{2}[/tex]
= 8[tex]\sqrt{2}[/tex] - 14[tex]\sqrt{2}[/tex] +8[tex]\sqrt{2}[/tex]
= 2[tex]\sqrt{2}[/tex]
3) 5[tex]\sqrt{12\\}[/tex] - 3[tex]\sqrt{18} + 4 \sqrt{72} +2\sqrt{75}[/tex]
= 5× [tex]2\sqrt{3}[/tex] - 3×[tex]3\sqrt{2}[/tex] + 4×[tex]6\sqrt{2}[/tex] + 2×[tex]5\sqrt{3}[/tex]
= [tex]10\sqrt{3} - 9\sqrt{2} +24\sqrt{2} +10\sqrt{3}[/tex]
= [tex]20\sqrt{3} + 15\sqrt{2}[/tex]
4) [tex](2\sqrt{2} + 3\sqrt{5} )^{2}[/tex]
= [tex]8 + 12\sqrt{10} + 45[/tex]
= [tex]53 + 12\sqrt{10}[/tex]
5) [tex](1+\sqrt{3} ) (1-\sqrt{3} )[/tex]
= [tex]1 - 3[/tex]
= -2
6) [tex](2\sqrt{6} -1) (\sqrt{3} -\sqrt{2} )[/tex]
= [tex]2\sqrt{18}-2\sqrt{12} -\sqrt{3} +\sqrt{2}[/tex]
= 2×[tex]3\sqrt{2}[/tex] - 2×[tex]2\sqrt{3}[/tex] - [tex]\sqrt{3} + \sqrt{2}[/tex]
= [tex]6\sqrt{2} - 4\sqrt{3} -\sqrt{3} +\sqrt{2}[/tex]
= [tex]7\sqrt{2} - 5\sqrt{3}[/tex]
Hope the working out is clear and will help you. :)
Step-by-step explanation:
please I solved the question in the diagram above
Write down inequalities,that are satisfied by these sets of integers between -10 and 10
1,2,3,4,5,6,7,8,9,10
-3,-4,-5,-6,-7,-8,-9,-10
9,10
-10
Answer:
Below
Step-by-step explanation:
Notice that x is between 10 and -10 but takes only the values that are integers.
The inequalities:
● we can write an inequality that includes all these values.
● -10 《 x 《 10
This is a possible inequality
Multiply both sides by 2 and you will get a new one:
● -20 《 2x 《 20
You can multiply it by any number to generate a new inequality.
Or you can add or substract any number.
Express the following in scientific notation: 0.0000079
Answer:
7.9 * 10 ^-6
Step-by-step explanation:
Move the decimal 6 places to the left so there is one number before the decimal
0.0000079
7.9
The exponent is -6 ( negative because we moved it to the left)
7.9 * 10 ^-6
Answer:
Hey there!
7.9 × 10-6 is your answer.
Hope this helps :)
Could anyone help me with number 25 THANK YOU!!!
Answer:
ΔABC ~ ΔQPR by the Angle-Angle (AA) similarity theorem of two triangles
Step-by-step explanation:
The coordinates of the vertices are given as follows;
A = (1, 2), B =(9, 8), C = (1, 8)
P= (5, -3), Q = (-7, 6), R = (-7, -3)
The given dimensions of AB and PQ are 10, and 15 respectively
The, l lengths of the sides of triangles are found as follows;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
For segment BC, we have;
B =(9, 8), C = (1, 8)
(x₁, y₁) = (9, 8), (x₂, y₂) = (1, 8), substituting gives;
Length BC = 8
For length CA, C = (1, 8) A = (1, 2)
(x₁, y₁) = (1, 8)
(x₂, y₂) = (1, 2)
The length found by substituting the values for (x₁, y₁), (x₂, y₂) in the length equation gives; Length CA = 6
Given that length CA² + BC² = 8² + 6² = 64 + 36 = 100 = BA², we have by Pythagoras theorem, we have ΔABC is a right triangle
Similarly, for ΔQPR, we have;
Length QR, Q = (-7, 6), R = (-7, -3) = 9
Length PR, P= (5, -3), R = (-7, -3) = 12
QR² + PR² = 9² + 12² = 225 = 15² = PQ²
∴ ΔQPR is a right triangle
By comparing the ratio of the sides, we have;
cos(θ) = PR/PQ = 12/15 = 4/5, θ = cos⁻¹(4/5) = 36.9°
∠RPQ = 36.9°
sin(θ) = QR/PQ = 9/15 = 3/5
Similarly in triangle ΔABC, we have;
cos(θ) = BC/AB = 8/10 = 4/5
∠CBA = 36.9°
Therefore, ∠CBA ≅ ∠RPQ = 36.9°
Also ∠PRQ ≅ ∠BCA = 90° (Angle opposite hypotenuse side of right triangle
Therefore, ΔABC and ΔQPR are similar triangles by the Angle-Angle (AA) similarity theorem of two triangles.
A girl who normally gets A's didn't do the first assignment given on the first day of school and now has 0%. How many 95% grades will she need to achieve an average of 90% overall? The points for each assignment are based on what she scores.
Answer:
19 of 95% grades
Step-by-step explanation:
90= (0+95(x-1))/x
90x=0+95(x-1)
90x=95(x-1)
90x=95x-95
90x-95x=-95
-5x=-95
x=-95/-5
x=19
Estimate the correlation coefficient that would best describe the data below.
0.4
-0.4
0.9
-0.9
Answer:
Step-by-step explanation:
Draw a line through the data points with about half of the points on one side of the line and the other half on the other side. You'll see that there is a slight positive rise in the graph as we move from left to right, but the correlation is weak. Thus, 0.4 is the correct correlation coefficient in this case.
The correlation coefficient that would best describe the data give in the table is 0.4 which is a weak positive correlation.
CorrelationWhat is correlation?The statistical concept of correlation describes how closely two variables move in tandem with one another.
Types of correlation:(1) Positive correlation:The two variables are considered to have a positive correlation if they move in the same direction.When there is a complete positive correlation, the correlation coefficient is 1.(2) Negative correlation:We say there is a negative correlation between the variables when the 'y' variable tends to decrease as the 'x' variable increases.(3) No correlation:We claim there is no correlation between the two variables when there is no obvious connection between them.Description for the graph:As the graph is scattered in such a way that,if we draw a line from the centre, we can observe that as 'x' increases 'y' also increases so the relation is positive correlation.
But it is seen in the graph that these points are scattered, so this relation is weak. For positive weak correlation the value should be less than 0.5.
Therefore, the given graph shows positive weak correlation with value 0.4.
To know more about statistics, here
https://brainly.com/question/23724696
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The following expression is a polynomial: 4x + 5y True False
Answer: False. This expression is a monomial!
Answer:
false
Step-by-step explanation:
it is molonomial
David is selling floral arrangements. Each arrangement uses 1 vase and 12 roses. Each vase costs David $2.00. Let C be the total cost of the arrangement and r be the cost of 1 rose. Which equation should David use to find the total cost of each arrangement? C = 12r + 2 12 = C + 2r C = 2r + 12 12C = r + 12
Answer:
C = 12r + 2Step-by-step explanation:
To model the equation for the cost of Each Arrangement.
We need to itemize all parameters needed.
An arrangement consists of
1. one vase
2. twelve roses
Given that 1 vase cost $2 and
The cost of one rose is r
Let the total cost of the arrangement be C
Hence C is the cost of the vase plus the cost of 12 roses combined, this is given as
[tex]C = 12r + 2[/tex]
Jessie works at a car manufacturing plant. One day she installed a total of 46 axles, 2 in each car she worked on. She wants to know how many
cars she installed axles on. You can write an equation that relates the total number of cars, the total number of axles, and the number of axles
installed per car. This equation will have two known quantities and one unknown quantity.
Part A
Write an equation forj, the number of cars Jessie installed axles in.
BIŲ X, Font Sizes
EEE 를 를
!!!
Characters used: 0 / 15000
Answer:
Jessie instaled axels on 23 cars The equation: 2·j = 46Step-by-step explanation:
j - total number of cars she installed axles on
2 - number of axles she installed on one car
2·j - total number of axles she installed on
46 - total number of axles she installed on
2·j = 46 {divide both sides by 2}
j = 23The formula for centripetal acceleration, a, is given below, where v is the velocity of the object and r is the object's distance from the center of the circular path.
This is the same as writing v = sqrt(ar)
===========================================
Work Shown:
[tex]a = \frac{v^2}{r}\\\\ar = v^2\\\\v^2 = ar\\\\v = \sqrt{ar}\\\\[/tex]
I multiplied both sides by r to isolate the v^2 term, then I applied the square root to fully isolate v.
A family has four children. What is the probability that two children are girls and two are boys? Assume the the probability of having a boy (or a girl) is 50%.
Answer:The first issue one most notice is the words “at least” We are trying to find the probability of at least 2 girls.
The five possible outcomes for girls are 0,1,2,3,4. The odds of 1 girl out of 4 is .25 and the odds of 1 boy out of 4 is .25 (same as the odds of 3 out of 4 girls). Therefore the odds of 1 OR 3 girls must be .5 because 1 girl and 3 girls each has a .25 probability. If the probability of (1 OR 3 girls) equals .5, then the probability of 2 girls must be a different number.
The probability of 2 or more girls, is the sum of the probability of 4 girls (.06125)(—-.5 to the 4th power—— ), plus the probability of 3 girls (.25)——(the same as the probability of 1 boy)—- plus the probability of 2 girls. Since we know the probability of zero boys is .0625 (again, .5 to the 4th power) and the probability of 1 boy is .25 (the same as the probability of 3 girls )———then the probability of 2 girls is ((1 minus (the sum of the probability of 0 OR 1 boys) plus the (sum of the probability of 3 or 4 girls)), or 1-((.0625+.25)+(.0625+.25)), or .375. We had to derive the probability of two from the other known probabilities. Therefore .375+.25+.0625=.6875 is the probability of both AT LEAST 2 girls and also NO MORE than 2 boys. Notice this adds up to 1.375 because the probability of the central number 2 (i.e., .375) appears on both sides.
Select the correct answer.
Simplify the following expression.
(3x^2 - 11x - 4) – (x – 2) (2x + 3)
Answer choices
5x^2 - 12x - 10
x^2 - 10x + 2
x^2 + 10x - 2
x^2 – 12x – 10
Answer:
x^2 -10x+2
Step-by-step explanation:
(3x^2 - 11x - 4) – (x – 2) (2x + 3)
FOIL
(3x^2 - 11x - 4) – (2x^2-4x+3x-6)
Combine like terms
(3x^2 - 11x - 4) – (2x^2 -x-6)
Distribute the minus sign
3x^2 - 11x - 4 – 2x^2 +x+6
Combine like terms
x^2 -10x+2
The area of a triangle is 30
square inches. The height is
5 in. Find the base.
Answer:
12 inches
Step-by-step explanation:
A=1/2bh
30=1/2b5
(30*2)/5=b
B=12
simplify (b^4)^3 because the nun of the answers answer my question
Answer:
b^12
Step-by-step explanation:
(b^4)^3
We know that x^y^z = x^(y*z)
b^4^3 = b^*4*3) = b^12
Points A, B, and C are collinear. Point B is between A and C. Solve for x. Find x if BC = 2x+10, AC = x+21, and AB = 11.
the answer choices:
*0 *-4 *-11 *-1
Answer:
x = 0
Step-by-step explanation:
Since the points are collinear , then
AB + BC = AC , that is
11 + 2x + 10 = x + 21
2x + 21 = x + 21 ( subtract x from both sides )
x + 21 = 21 ( subtract 21 from both sides )
x = 0
A school system is reducing the amount of dumpster loads of trash removed each week. In week 5, there were 40 dumpster loads of waste removed. In week 10, there were 30 dumpster loads removed. Assume that the reduction in the amount of waste each week is linear. Write an equation in function form to show the amount of trash removed each week. A f(x) = −2x + 40. B f(x) = 2x + 40 C f(x) = −2x + 50 D f(x) = 2x + 50
Answer:
The answer is A f(x) = -2x + 40
Step-by-step explanation:
it has a negative 2 because the dumps are decreasing by 2 every week and x is the amount of weeks and + 40 because that is the amount you started with.
please do the steps Solve for d: 1/6d-8=5/8 2. Solve for x: 3x-4+5x=10-2z 3. Solve for c: 7(c-3)=14 4. Solve for m: 11(m/22+3/44)=87m+m 5. Solve for k: ck+5k=a
Answer:
d = 55.5
x = 1
c = 11
m = [tex]\frac{1}{122}[/tex]
k = [tex]\frac{a}{(c + 5)}[/tex]
Step-by-step explanation:
Sorry, the formatting is slightly hard to understand, but I think this is what you meant.
Q1.
[tex]\frac{1}{6}[/tex]d - 8 = [tex]\frac{5}{8}[/tex] x 2
Step 1. Simplify.
[tex]\frac{5}{8}[/tex] x 2 = [tex]\frac{5}{8}[/tex] x [tex]\frac{2}{1}[/tex] = [tex]\frac{10}{8}[/tex]
Step 2. Cancel out the negative 8.
[tex]\frac{1}{6}[/tex]d - 8 = [tex]\frac{10}{8}[/tex]
+ 8 to both sides (do the opposite: [tex]\frac{1}{6}[/tex]d is subtracting 8 right now, but to cancel that out, we will do the opposite of subtraction, i.e. addition)
[tex]\frac{1}{6}[/tex]d = [tex]\frac{10}{8}[/tex] + 8
Step 3. Simplify.
[tex]\frac{10}{8}[/tex] + 8 = [tex]\frac{10}{8}[/tex] + [tex]\frac{8}{1}[/tex] = [tex]\frac{10}{8}[/tex] + [tex]\frac{64}{8}[/tex] = [tex]\frac{74}{8}[/tex] = [tex]\frac{37}{4}[/tex]
Step 4. Cancel out the [tex]\frac{1}{6}[/tex].
[tex]\frac{1}{6}[/tex]d = [tex]\frac{37}{4}[/tex]
÷ [tex]\frac{1}{6}[/tex] from both sides (do the opposite: d is multiplied by [tex]\frac{1}{6}[/tex] right now, but to cancel that out, we will do the opposite of multiplication, i.e. division)
÷ [tex]\frac{1}{6}[/tex] = x 6
So....
x 6 to both sides
d = [tex]\frac{37}{4}[/tex] x 6 = [tex]\frac{37}{4}[/tex] x [tex]\frac{6}{1}[/tex] = [tex]\frac{222}{4}[/tex] = [tex]\frac{111}{2}[/tex] = 55.5
Step 5. Write down your answer.
d = 55.5
Q2.
3x - 4 + 5x = 10 - 2x × 3
Step 1. Simplify
3x - 4 + 5x = 3x + 5x - 4 = 8x - 4
10 - 2x × 3 = 10 - (2x × 3) = 10 - 6x
Step 2. Cancel out the negative 6x
8x - 4 = 10 - 6x
+ 6x to both sides (do the opposite - you're probably tired of reading this now - right now it's 10 subtract 6x, but the opposite of subtraction is addition)
14x - 4 = 10
Step 3. Cancel out the negative 4
14x - 4 = 10
+ 4 to both sides (right now it's 14x subtract 4, but the opposite of subtraction is addition)
14x = 14
Step 4. Divide by 14
14x = 14
÷ 14 from both sides (out of the [14 × x] we only want the [x], so we cancel out the [× 14])
x = 1
Step 5. Write down your answer.
x = 1
Q3.
7(c - 3) = 14 × 4
Step 1. Expand the brackets
7(c - 3) = (7 x c) - (7 x 3) = 7c - 21
Step 2. Simplify
14 x 4 = 56
Step 3. Cancel out the negative 21
7c - 21 = 56
+ 21
7c = 56 + 21
7c = 77
Step 4. Cancel out the ×7
7c = 77
÷ 7
c = 77 ÷ 7
c = 11
Step 5. Write down your answer.
c = 11
Q4.
11([tex]\frac{m}{22}[/tex] + [tex]\frac{3}{44}[/tex]) = 87m + m × 5
Step 1. Expand the brackets
11([tex]\frac{m}{22}[/tex] + [tex]\frac{3}{44}[/tex]) = (11 x [tex]\frac{m}{22}[/tex]) + (11 x [tex]\frac{3}{44}[/tex]) = ([tex]\frac{11}{1}[/tex] x [tex]\frac{m}{22}[/tex]) + ([tex]\frac{11}{1}[/tex] x [tex]\frac{3}{44}[/tex]) = [tex]\frac{11m}{22}[/tex] + [tex]\frac{33}{44}[/tex] = [tex]\frac{m}{2}[/tex] + [tex]\frac{3}{4}[/tex]
Step 2. Simplify.
87m + m x 5 = 87m + 5m = 92m
Step 3. Cancel out the add [tex]\frac{3}{4}[/tex]
[tex]\frac{m}{2}[/tex] + [tex]\frac{3}{4}[/tex] = 92m
- [tex]\frac{3}{4}[/tex]
[tex]\frac{m}{2}[/tex] = 92m - [tex]\frac{3}{4}[/tex]
[tex]\frac{m}{2}[/tex] = [tex]\frac{92m}{1}[/tex] - [tex]\frac{3}{4}[/tex]
[tex]\frac{m}{2}[/tex] = [tex]\frac{368m}{4}[/tex] - [tex]\frac{3}{4}[/tex]
[tex]\frac{m}{2}[/tex] = [tex]\frac{368m - 3}{4}[/tex]
Step 4. Cancel out the ÷ 4
[tex]\frac{m}{2}[/tex] = [tex]\frac{368m - 3}{4}[/tex]
x 4
2m = 368m - 3
Step 5. Cancel out the 368m
2m = 368m - 3
- 368m
-366m = - 3
Step 6. Cancel out the × -366
-366m = -3
÷ -366
m = [tex]\frac{-3}{-366}[/tex]
m = [tex]\frac{1}{122}[/tex]
Step 7. Write down your answer.
m = [tex]\frac{1}{122}[/tex]
Q5.
ck + 5k = a
Step 1. Factorise
ck + 5k = (c × k) + (5 × k) = (c + 5) x k = k(c + 5)
Step 2. Cancel out the × (c + 5)
k(c + 5) = a
÷ (c + 5)
k = a ÷ (c + 5)
k = [tex]\frac{a}{(c + 5)}[/tex]
Drag a vertex of the triangle to change its shape.
Double-click or double-tap a vertex or side to prevent it from
changing.
Problem: Construct a triangle with interior angle
measures of 60° and 75°.
What is the measure of the third angle?
O 30°
2C = 41°
O 45°
48°
9.2
10
50°
ZA = 49°
6.0 ZB = 90°
Answer:
The correct option is;
45°
Step-by-step explanation:
By angle sum theorem, we have that the sum of angles in a triangle = 180°
Therefore, we have;
When the interior angles of the triangle are constructed to be 60° and 75°, we have by the angle sum theorem;
The third angle + 60° + 75° = 180°
Which gives;
The third angle = 180°- 60° - 75° = 180°- 135° = 45°
The measurement of the third angle by the angle sum theorem will be 45°
The correct option is ∠third angle = 45°.
trigonometry help got one right need help with another
Answer:
B. [tex] \frac{HI}{GI} [/tex]
Step-by-step explanation:
The trigonometric ratio formula for tangent of any angle in a right triangle is given as:
tan(θ) = [tex] \frac{opposite}{adjacent} [/tex]
Note: it is the length of the side opposite to the θ, and the length of the side adjacent to θ.
Thus, in the right triangle given, ∆GHI,
θ = <G
The length of side the opposite <G = HI
The length of the side adjacent to <G = GI
Therefore, the equivalent of tan(<G) = [tex] \frac{HI}{GI} [/tex]
Please help me figure out the 3 answers for each letters. PLEASE will be marked as brainliest if correct:))
Answer:
Step-by-step explanation:
Our interval is 180 to 270 so that's quadrant III. In quadrant 3, both x and y are negative. If we set up our right triangle in this quadrant and label it accordingly with the values given for tangent theta, we find that the missing length is the hypotenuse. Solve for that using Pythagorean's Theorem. Doing that gives us that the hypotenuse is [tex]\sqrt{61}[/tex]. Now we can solve for your other identities. First,
[tex]cos(2\theta)=2cos^2\theta-1[/tex] (There are 3 identities for cos(2θ) and regardless of which one you pick, the answer will be the same every time...promise!)
Filling in now:
[tex]cos(2\theta)=2(\frac{-5}{\sqrt{61} })^2-1[/tex] and simplified a bit:
[tex]cos(2\theta)=2(\frac{25}{61})-1[/tex] and a bit more:
[tex]cos(2\theta)=\frac{50}{61}-\frac{61}{61}[/tex] giving us, finally:
[tex]cos(2\theta)=-\frac{11}{61}[/tex]
Now for b. We have an identity for the half angle of sin:
[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{1-cos\theta}{2} }[/tex] and filling in:
[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{1-(-\frac{5}{\sqrt{61} } )}{2} }[/tex] which simplifies a bit to:
[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{1+\frac{5}{\sqrt{61} } }{2} }[/tex] and a bit more to:
[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{\sqrt{61}+5 }{2\sqrt{61} } }[/tex] I'm not sure if this is the form you need it in, but this is the answer, as convoluted and crazy as it may look.
As for the cosine half-angle, the identity is the same, except there's a + sign in the numerator of the identity instead of a -, giving us the solution:
[tex]cos(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{\sqrt{61}-5 }{2\sqrt{61} } }[/tex]
Find the midpoint between two points on a number line if one of the points is at -7, and the other point is at 12.
A. 9.5
B. 5
C. -2
D. 2.5
Answer:
D
Step-by-step explanation:
The midpoint is the average of the 2 endpoints, that is
midpoint = [tex]\frac{-7+12}{2}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5 → D
Wrapping a Package It takes 70 inches of ribbon to make a bow and wrap the ribbon
round a box. The bow takes 32 inches of ribbon. The width of the box is 14 inches. What
the height of the box?
-14 in. -
First subtract the amount the bow takes from the total:
70 - 32 = 38 inches
The width is 14 on top and bottom so subtract 14 x 2 = 28 from 38:
38-28 = 10
Divide 10 by the 2 sides:
10/2 = 5
The height is 5 inches.
help me please asap!!
Answer:
136^3 cm
Step-by-step explanation:
Big square:
5 × 4 × 6 = 20 × 6 = 120
Small rectangle:
7 - 5 = 2
2 × 2 × 4 = 4 × 4 = 16
Both:
120 + 16 = 136
The volume of this figure is 136 cm^3.
Hope this helped.
Answer:
Below
Step-by-step explanation:
First you can find the front area and just multiply it by the length
Find the area of the small square
A = lw
= (2)(2)
= 4 cm^2
Find the area of the large square
A = lw
= (6)(5)
= 30 cm^2
Now just multiply the area of the two by the length
34 x 4 = 136 cm^3
Hope this helps!
The combined weight of three basset hounds is 185 pounds. The two smaller dogs weigh the same. The difference between the larger weight and the smaller weight is 20 pounds. How many pounds does the largest dog weigh?
Answer:
75 pounds
Step-by-step explanation:
(x) + (x) + (x+20) = 185
3x + 20 = 185
3x = 165
x = 55
Large dog = 55 + 20 = 75