Answer:
leg = 18
hypotenuse = 18 sqrt(2)
Step-by-step explanation:
We know that sin theta = opp side / hypotenuse
sin 45 = 18 / hyp
hyp sin 45 = 18
hyp = 18 / sin 45
hyp = 18 sqrt(2)
Since this is an isosceles triangle ( the two angles are the same measure), the two legs have to be the same length
leg = 18
the lengths of the other leg and the hypotenuse
is 18 units and 18[tex]\sqrt{2}[/tex]units respectively.
Answer:
Solution given:
Let <C=<B=45°
AB=18 units
BC=?
AC=?
again
By using
By usingspecial right triangle ratios
sin C=opposite/hypotenuse=AB/AC=18/AC
Sin 45=18/AC
AC=18/sin45
AC=hypotenuse=18[tex]\sqrt{2}[/tex]units
again
Tan A=opposite/adjacent=BC/AB=BC/18
Tan45=BC/18
BC=Tan45*18
BC=length of another leg=18 units.
Samuel played a video game. He gained some points, lost 87 points, and
finished with less than 320 points, Which of the following inequality
represents the given situation?
A.) n-87 < 320
B.) N + 87 < 320
C.) N-87 = 320
D.) n +87= 320
Answer:
A
Step-by-step explanation:
The correct inequality that represents the given situation is: A.) n - 87 < 320.
How to explain the equationThe situation states that Samuel played a video game and gained some points. Let's represent the points he gained as 'n'.
Next, it is mentioned that he lost 87 points. To represent this in the inequality, we subtract 87 from the initial points gained, which gives us 'n - 87'.
Finally, the situation specifies that Samuel finished with less than 320 points. This means that the final score, represented by 'n - 87', is less than 320.
This inequality represents that the initial points gained by Samuel (n) minus 87 points is less than 320 points, indicating that his final score is less than 320 points after losing 87 points.
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What is a counterexample to this claim? Dividing a number by 2 always results in a smaller number.
Given:
Dividing a number by 2 always results in a smaller number.
To find:
The counterexample to the given claim.
Solution:
If 0 is divided by is divided by any non-zero real number [tex]a[/tex], then
[tex]\dfrac{0}{a}=0[/tex]
Let us consider the unknown number be 0. Then dividing a number by 2, we get
[tex]\dfrac{0}{2}=0[/tex]
Here, the result is not a smaller number because [tex]0=0[/tex].
Therefore, the counterexample to the given claim is "Dividing 0 by 2".
Answer:
-1
Step-by-step explanation:
can i get some help. did it 3 times and still not sure.
Answer:
18
Step-by-step explanation:
The height of the cone is 8, and the diameter is 3. This means that the radius is 3/2, or 1.5. We can plug everything into the formula (using 3 for pi):
[tex]\frac{3(1.5)^2(8)}{3}[/tex]
We can cancel out the 3 from the numerator and the denominator, so we are left with 1.5^2 times 8. 1.5 squared is equal to 2.25, and 2.25 times 8 is equal to 18.
f(x) = x2 + 3x + 2 is shifted 2 units left. The result is g(x). What is g(x)?
Answer:
[tex]g(x) = x^2+7x+12[/tex]
Step-by-step explanation:
If we are given a function f and we want to shift it a units horizontally, the resulting function will be f(x - a), where a positive a is a shift rightwards and a negative a is a shift leftwards.
We have the function:
[tex]f(x)=x^2+3x+2[/tex]
And we want to shift it two units to the left.
Since we want to shift it two units to the left, a = -2. Therefore, our new function, let's call it g, must be f(x - (-2)) or f(x + 2). Substitute:
[tex]g(x) = f(x+2)=(x+2)^2+3(x+2)+2[/tex]
Simplify. Expand:
[tex]g(x) = (x^2+4x+4)+(3x+6)+2[/tex]
Combine like terms. Hence:
[tex]g(x) = x^2+7x+12[/tex]
C=-(251x3+281)+3X251-(1-281)
Answer:
-1
Step-by-step explanation:
=-251x3+281 +251x3-1+281
=-1
An experiment consists of rolling a six sided die to select a number between between 1 and 6 and drawing a card at random from a set of 10 cards numbered 1,2,3,...10. Which event definition corresponds to exactly one outcome of the experiment?
Answer:
Man this is confusing
Step-by-step explanation:
Which of the following could be the first step in solving the equation below ? 5 ^ x = 21
Answer:
D
Step-by-step explanation:
usually when your variable is an exponent you always take the log of both sides.
The possible first step of solving the equation is log 5^x = log 21
How to determine the first step?The equation is given as:
5^x = 21
Take the logarithm of both sides of the equation
log 5^x = log 21
The above represents the possible first step of solving the equation
Hence, the possible first step of solving the equation is log 5^x = log 21
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What is the quotient of the synthetic division problem below, written in polynomial form?
-1| 1 7 15 9 7
Answer:
Step-by-step explanation:
If we have 5 terms to the right of the -1 outside the box thing, that means that our original polynomial is a 4th degree (the degree is one lower than the number of terms in order to allow for the constant which has no variable). Set up the synthetic division as shown in the problem. The rule is to bring down the first term, the 1 to the right of the box, multiply it by the number outside, -1, and put that product up under the next number in line inside the box. Like this:
-1 | 1 7 15 9 7
-1
1
Now add straight down, multiply the sum by -1 and put that product up under the next term in line, the 15:
-1 | 1 7 15 9 7
-1 -6
1 6
Then add straight down again, multiply the sum by -1 and put that product up under the next term in line, the 9:
-1 | 1 7 15 9 7
-1 -6 -9
1 6 9
Then do the same thing. Add straight down, multiply the sum by -1 and put the product up under the next term in line, the 7:
-1 | 1 7 15 9 7
-1 -6 -9 0
1 6 9 0 7
This is the final result. The last number, the 7 is the remainder, but the rest of it makes up what we call the depressed polynomial and is a polynomial that is one degree less than the degree we started with. So this depressed polynomial is a 3rd degree. The numbers are the coefficients on the x terms:
[tex]1x^3+6x^2+9x+0R7[/tex] or more simply stated:
[tex]x^3+6x^2+9xR7[/tex]
What are the x-intercepts of the parabola?
A: (4.5, 0) and (5, 0)
B: (0, 4.5) and (0, 5)
C: (0, 5) and (0, 4)
D: (5, 0) and (4, 0)
Answer:
D: (5, 0) and (4, 0)
Step-by-step explanation:
The x-intercepts of a parabola are the points where the parabola intersect the x-axis (horizontal axis). Therefore, the y-value of the x-intercepts are always 0. Since coordinates are written (x, y), we can immediately eliminate answers B and C.
Next, we look at the x-coordinates of where the parabola intersects the x-axis. We can see clearly that the parabola crosses the x-axis at [tex]x=4[/tex] and [tex]x=5[/tex]. Therefore, the x-intercepts of the given parabola are (4, 0) and (5, 0).
1. 80 = -10b
2. 6 = 2n
3. -16r = 32
1.
2.
3.
Answer:
1. - 8
2. 3
3. - 2
Step-by-step explanation:
1.
80 = - 10b
- 10b = 80
b = 80 / - 10
b = - 8
2.
6 = 2n
2n = 6
n = 6 / 2
n = 3
3.
- 16r = 32
r = 32 / - 16
r = - 2
Which graph represents the function f(x) = √x+3 – 1?
Answer:
look at the png below
Step-by-step explanation:
HELP QUICK PLEASE!
Given: AC BD and AD BC
B
D
What postulate could prove DCA ACDB
O Side-Side-Side
O Side-Angle-Side
Angle-Side-Angle
Angle-Angle-Side
Answer:
Step-by-step explanation:
Side - side - side. In fact the two triangles have the side CD in common
Select the relationship that does represent a function.
Answer:
c
Step-by-step explanation:
What is the area of the label on a soup can that is 8 inches high and has a diameter of 4 inches? Round to the nearest hundredth. Assume the label wraps around the entire height of the can and does not overlap. SHOW WORK..
Answer:
Area of label = 100 inch² (Approx.)
Step-by-step explanation:
Given:
Height of label = 8 inches
Diameter of label = 4 inches
Find:
Area of label
Computation:
Design of label = Rectangle
So,
Width of label = 2πr
Width of label = 2(3.14)(4/2)
Width of label = 2(3.14)(2)
Width of label = 12.56 inches
Area of label = Height of label x Width of label
Area of label = 12.56 x 8
Area of label = 100.48
Area of label = 100 inch² (Approx.)
Daniel paid interest of 1,020 in 5years at12%per annum on a loan. Hw much did he borrow
Line ab and cd (if presented in the picture) are straight lines. Find x (the pictures are not scaled)
Answer:
[tex]x + 2x + 34 + 20 = 180 [/tex]
Answer:
x=42
Step-by-step explanation:
Statement Reason
1. m∠AOB = 180° — Def. of straight ∠
2. m∠AOE + m∠EOF + m∠FOB = m∠
AOB —- Parts − whole Postulate
3. x + 2x+34° + 20° = 180° —- Substitution
4. x = 42°. —- Algebra
This is statement and reason! (no problem rsm people)
The length of a boat in scale drawing is 8 in. Find the length of the actual
boat if the scale is 1 in = 3 ft.
A)24 in
B.)24 ft
C.) 8 ft
D.) 11 in.
Answer:
B. 24 ft
Step-by-step explanation:
1 in = 3ft
8 in must equal 24 ft since 8 in x 3 ft is 24 ft. So, B.
The length of the boat will be equal to 24 ft.
What is the scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.
Given that:-
The length of a boat in scale drawing is 8 in. Find the length of the actual boat if the scale is 1 in = 3 ft.The actual length will be calculated as follows:-
1 in = 3 ft.
8 in = 8 x 3 ft
8 in = 24 ft.
Therefore the length of the boat will be equal to 24 ft.
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What is the value of x that makes the given equation true?
2(x−8)=x+5x
a x=-4
b x=-16
c x=-2
d x=0
Answer:
x = -4
Step-by-step explanation:
2(x−8)=x+5x
Distribute
2x - 16 = x+5x
Combine like terms
2x-16 = 6x
Subtract 2x from each side
2x-16 = 6x-2x
-16 = 4x
Divide by 4
-16/4 = 4x/4
-4 =x
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
[tex]\sf{2(x-8)=x+5x }[/tex] [tex]\sf{2x-16=6x }[/tex] [tex]\sf{2x-6x=16 }[/tex] [tex]\sf{-4x=16 }[/tex] [tex]\sf{ x=\dfrac{16}{-4} }[/tex] [tex]\sf{x=-4 }[/tex][tex]\sf{ }[/tex]
Please help me with this question please and thank you ❤️
Answer:
x = -1
Step-by-step explanation:
3x - 1/9 (27) = 18
3x - 3
Divide both sides be 3
x = -1
Answer:
x = 7
Step-by-step explanation:
to solve this equation we are given the value of y which 27. just substitute 27 for y in the equation :
3x - 1/9(27) = 18
3x - 3 = 18
3x = 21
x= 7
please I really need help with this
Answer:
24
Step-by-step explanation:
(1+25) - (16)(1/8)
26 - 2
24
Cheers
Answer:
24
Step-by-step explanation:
(1+5^2) -16 ( 1/2)^3
PEMDAS
Parentheses first
Exponents in the parentheses
(1+25) -16 ( 1/2)^3
Then add in the parentheses
(26) -16 ( 1/2)^3
Then exponents
(26) -16 ( 1/8)
Then multiply
26 - 2
Then subtract
24
Carol wants to build a fence around her
garden to prevent rabbits from eating the
plants. The fencing costs $15 per metre.
How much will it cost to enclose a square
garden with an area of 81 m2?
(Hint: Area of a square = 5?, perimeter of a
square = 4s)
Answer:
540$
Step-by-step explanation:
9x9 = 81
9 + 9 + 9 + 9 = 36
36 x 15 =540
Find the value of x.
A. 70
B. 30
C. 65
D. 40
Answer:
Option (A)
Step-by-step explanation:
From the figure attached,
By applying triangle sum theorem in ΔBCP,
m∠CBP + m∠CPB + m∠BCP = 180°
15° + 20° + m∠BCP = 180°
m∠BCP = 145°
m∠ACB + m∠BCP = 180° [Linear pair of angles are supplementary]
m∠ACB + 145° = 180°
m∠ACB = 35°
Since, ∠ACB is the inscribed angle and AB is the intercepted arc.
Therefore, m(arc AB) = 2m(∠ACB)
m(arc AB) = 2 × 35°
= 70°
Therefore, Option (A) is the correct option.
F={(-1, 2), (3, 2), (4,2), (0, 2)} Is Fa function and why/why not?
Answer:
yes it is a function A
Step-by-step explanation:
How many index laws are there?
Answer:
There are three laws of indices.
aint the answer for this 10 just let me if im wrong
Answer:
Yup
Step-by-step explanation:
What is the measure of n
Answer:
n = [tex]\sqrt{32}[/tex]
Step-by-step explanation:
The 2 right triangles inside the larger right triangle are similar , so corresponding sides are in proportion
[tex]\frac{8}{n}[/tex] = [tex]\frac{n}{4}[/tex] ( cross- multiply )
n² = 32 ( take the square root of both sides )
n = [tex]\sqrt{32}[/tex]
Which expression is equivalent to 6(3n-4)?
1)9n-10
2)18n-24
3)18n-4
4) 3n-24
Answer:
[tex]18n - 24[/tex]
Step-by-step explanation:
[tex]6(3n - 4) = 18n - 24[/tex]
Answer:
18n-24
Step-by-step explanation:
6(3n-4)
Open the brackets .......
(6×3n)-(6×4)
=18n_24
Can someone help me with this math homework please!
Answer:
The graph for a member's yearly cost for total game tokens purchased would have a y-intercept of (0, 60). However, the nonmember's yearly cost would have a different y-intercept of (0,0). This is because the member's yearly cost has a yearly initial fee of $60, while as the nonmember yearly cost doesn't include an inital fee. Also, the graph for the nonmember's yearly cost would be steeper than the member's graph because the slope 1/5 is greater than 1/10.
Hope this helps (●'◡'●)
The fractions 1/10 and 1/5 convert to 0.1 and 0.2 respectively.
So the equations y = (1/10)x+60 and y = (1/5)x are the same as y = 0.1x+60 and y = 0.2x in that order.
We see that the nonmember cost graph is steeper since the slope 0.2 is larger than 0.1; the further we move away from 0, the steeper the slope. A steeper slope means that you pay more per token. This is the unit cost.
Specifically, you would pay 0.20-0.10 = 0.10 more dollars per token if you are a nonmember compared to if you are a member.
---------------------------
Also, notice that the y intercepts of y = 0.1x+60 and y = 0.2x are 60 and 0 in that order. The members pay an up front fee of $60 before they can buy any tokens. Nonmembers don't have to pay an upfront cost.
Visually, the graph for the members will be much higher up compared to the nonmembers graph. Both lines are increasing, but the members graph is increasing less overall. At some point, the two lines intersect. After this point, it makes more sense to be a member.
What is the volume of the cylinder below?
A. 196pi units3
B. 784pi units3
C. 98pi units 3
D. 112pi units 3
Answer:
196π units^3
Step-by-step explanation:
The volume of a cylinder is:
πr^2h
SINCE, there is no given pi, the formula will be:
r^2h
Use the formula on the given dimensions:
r^2h
= (7^2) 4
= (49) 4
= 196
So we could just leave the final answer as:
196π
The real volume will be solved once π is given.
I hope I helped!
The volume of the cylinder given is 196 π, Option A is correct.
The volume of the cylinder is given by V=πr²h
Where r is radius of cylinder and h is the height of the cylinder.
V is the volume
r=7
h=4
Now plug in these values in volume formula.
V=π(7)².4
=π.49.4
V=196π
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need help asap pleaseeeeeeeeeeeeeeeeeeeeeeeeeee
PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
9514 1404 393
Answer:
4a. 177
4b. 248
5a. 27
5b. 9
5c. 12
Step-by-step explanation:
4.a) x is 3/4 of 1/2 of all, so is 3/8 of all.
x = 3/8·472
x = 177
b) x is 2/5 of 2/3 of all, so is 4/15 of all.
x = 4/15·930
x = 248
__
5.Elaine gave her grandmother 3/4 of 48 = (3/4)(48) = 36 of the flowers. Then Elaine had 48 -36 = 12 flowers left.
Her grandmother gave 1/4 of 36 flowers = (1/4)(36) = 9 of the flowers to her neighbor. Elaine's grandmother has 36 -9 = 27 flowers now.
Elaine's grandmother has 27 flowersthe neighbor has 9 flowersElaine has 12 flowers