Answer:
4:1
Step-by-step explanation:
the angle of elevation of the top of a tower from a point 42 metres away from it's base on level ground is 26 degrees. find the height of the tower.
Answer:
20.485 Meters
Step-by-step explanation:
So first you wanna draw a diagram. Start with the tower, then on the ground to the left (or right) draw a point. The point will be labeled as 42 m away from the tower. Now draw a line from that point to the top of the tower. This makes your triangle, and that angle you just drew that touches the point is 26 degrees.
Now, since you have a right triangle you can use trig. You know an angle and a side. Specifically, relative to the 26 degree angle you know the adjacent angle and want the opposite, which is the tower. So opposite and adjacent is tangent. So you set up tan(26) = o/42 where o is the opposite side.
So solving you get o = 20.485 meters
pada hari kantin sebanyak 800 naskah kupon telah dijual,harga senaskah kupon masing masing rm 30 dan rm 50 .jumlah wang diperoleh hasil daripada jualan kupon ialah rm30000.berapa naskah kupon rm30 dan rm50 yang telah dijual?
Answer:
Step-by-step explanation:
On the day of the canteen, 800 coupons were sold, the price of each coupon was RM 30 and RM 50 respectively. The amount of money earned from the sale of coupons was RM30000. How many copies of RM30 and RM50 coupons were sold?
Let:
RM 30 = x
RM 50 = y
x + y = 800 - - - (1)
30x + 50y = 30000 - - - (2)
From (1)
x = 800 - y
Put x = 800 - y in (2)
30(800 - y) + 50y = 30000
24000 - 30y + 50y = 30000
24000 + 20y = 30000
20y = 30000 - 24000
20y = 6000
y =
y=x+2 y=-x +8 What is the solution for this system of equations?
Answer:
x = 3 y = 5
Step-by-step explanation:
y=x+2
+ y=-x +8
2y = 10
y = 5
y = -x + 8
5 = -x + 8
x = 3
PLS HELP ASAP
WHICH IS THE RIGHT ASNWER OF THE FUNCTION PICTURED BELOW? A,B,C,D?
Answer:
Step-by-step explanation:
C looks right
as shown in the graphs :P
Find the TWO integers whos product is -12 and whose sum is 1
Answer:
[tex] \rm Numbers = 4 \ and \ -3.[/tex]
Step-by-step explanation:
Given :-
The sum of two numbers is 1 .
The product of the nos . is 12 .
And we need to find out the numbers. So let us take ,
First number be x
Second number be 1-x .
According to first condition :-
[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]
Hence the numbers are 4 and -3
Let integers be x and x-1
ATQ
x+x-1=1[tex]\\ \sf\longmapsto 2x-1=1[/tex]
[tex]\\ \sf\longmapsto 2x=1+1[/tex]
[tex]\\ \sf\longmapsto 2x+2[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{2}{2}[/tex]
[tex]\\ \sf\longmapsto x=1[/tex]
Now
[tex]\\ \sf\longmapsto x-1=1-1=0[/tex]
The integers are 1 and 0But
Integers can be x and 1-x as their sum is 1
[tex]\\ \sf\longmapsto x(1-x)=-12[/tex]
[tex]\\ \sf\longmapsto x- x^2=-12[/tex]
[tex]\\ \sf\longmapsto x^2-x-12=0[/tex]
[tex]\\ \sf\longmapsto x^2-4x+3x-12=0[/tex]
[tex]\\ \sf\longmapsto x(x-4)+3(x-4)=0[/tex]
[tex]\\ \sf\longmapsto (x-4)(x+3)=0[/tex]
[tex]\\ \sf\longmapsto x=4,-3[/tex]
A condition statement is logically equivalent to a biconditional statement. true or false
Answer:
true
Step-by-step explanation:
Because a logically equivalent is the same as biconditional statement
Step-by-step explanation:
hello the answer is true, you can check but it's obviously true
Solve for x. Round to the nearest tenth, if necessary.
According to the rational root theorem which of the following are possible roots for the function below x^4-29x^2+100
Hello,
The rational roots may be all divisors of 100
+1,-1,+2,-2,+4,-4,+5,-5,+10,-10,+20,-20,+25,-25,+50,-50,+100,-100
f(x)=x^4-29x^2+100
f(5)=5^4-29*5^2+100=0 : 5 is a root
f(-5)=(-5)^4-29*(-5)²+100=0 : -5 is a root
f(2)=2^4-29*2²+100=0 : 2 is a root
f(-2)=(-2^)^4-26*(-2)²+100= 0 : -2 is the last root.
Find each measure
Please help me
Answer:
1. m∠CGB=120
3. m∠AGD=90
5. m∠CGD=150
2. m∠BGE=60
4. m∠DGE=30
6. m∠AGE=120
Step-by-step explanation:
Sorry that they are out of order.
Answer:
1. m∠CGB=120°
2.m∠BGE=60°
3.m∠AGD=90°
4.m∠DGE=30°
5.m∠CGD=150°
6.m∠AGE=120°
Step-by-step explanation:
My work is scatterbrained so I'm not gonna be any help if I give an explanation.
Find the length of side AB.
Give your answer to 1 decimal place.
12 cm
62°
A
B
Hey there!
To solve this problem, we will be using Trigonometric Ratio. Trigonometry is always helpful when it comes to finding a missing side with specific measure/angle.
1. Cosine Ratio
Currently, there are 6 Trigonometric Ratios. But we will be talking about Cosine Ratio instead since it is what we will be using in your question! Cosine Ratio is defined as adjacent to hypotenuse or adjacent/hypotenuse. You know what adjacent and hypotenuse are right? If not then head to the next topic!2. Adjacent and Hypotenuse
Adjacent is basically the base of a triangle. It is basically drawn from right angle to any measure/angles. Hypotenuse is the longest side of a right triangle. It is also an opposite side of right angle.Hope you understand this topic! If not, feel free to ask!
3. Solve The Problem
Since our adjacent is length AB but we don't know its exact value. What we have to do is to determine AB as any variables which I will determine AB as "x". Next, we have the value of hypotenuse which is 12 cm. Then we also know the Cosine Ratio which is adjacent to hypotenuse.Therefore, the equation for the problem is:
[tex] \large{cos62 \degree = \frac{x}{12} }[/tex]
*cos is the short form of cosine*
At this part, we need a calculator to find the value of cos62 degrees. That's because it is not a degree like 0, 30, 45, 60 and 90 which can be found without a calculator.
When we put cos62 in a calculator, make sure to put it in degree mode since a calculator has two modes which are degree and radian.
When we put cos62 in, we should get 0.46947156... Because you want a one decimal place, we round the value up to the nearest tenth as we get 0.5 because 6 is greater than 5 and should be rounded up and not down. That makes the equation to:
[tex] \large{0.5 = \frac{x}{12} }[/tex]
Oh well! Finally to the equation part. Whenever you have to solve the equation that has decimal numbers in it, the best way to deal with decimal numbers is to make them into a whole number or integer. But how? Simply multiply the whole equation by 10. Because 0.5×10 is 5 thus 0.5 becomes an integer after multiplying 10.
[tex] \large{0.5 \times 10 = \frac{x}{12} \times 10} \\ \large{5 = \frac{10x}{12} }[/tex]
10x/12 can be simplified again.
[tex] \large{5 = \frac{5x}{6} }[/tex]
Then we isolate x-value by multiplying 6 the whole equation.
[tex] \large{5 \times 6 = \frac{5x}{6} \times 6} \\ \large{30 = 5x} \\ \large{x = 6}[/tex]
Huh, that's awkward! We want the answer in a 1 decimal place but seems like the answer for this is 6. Why? Well that is not an exact answer, but more like an approximation. Because the value of cos62 degree is actually a repeating decimal and doesn't have exact value.
When we put the equation cos62 = x/12 in the equation and solve. It appears that the the answer is 5.63365875. Because we round up to nearest tenth, it gives an approximation to 5.63365875 instead.
Hence, the equation and value above is just a rounded to the whole number from 5.63365875.
Because you want a one place decimal. Hence,
4. Final Answer
The length AB is 5.6 (rounded to nearest tenth)- (For 10 points!)
Alfred draws candles randomly from a pack containing 4 colored candles of the same shape and size. There are 2 red candles, 1 green candle, and 1 blue candle. He draws 1 candle and then draws another candle without replacing the first one. Find the probability of picking 1 red candle followed by another red candle, and show the equation used.
(don't joke around please?? /gen)
Answer:
The probability of picking 1 red candle followed by another red candle is 16.66%.
Step-by-step explanation:
Since Alfred draws candles randomly from a pack containing 4 colored candles of the same shape and size, and there are 2 red candles, 1 green candle, and 1 blue candle, and he draws 1 candle and then draws another candle without replacing the first one, to find the probability of picking 1 red candle followed by another red candle, the following calculation must be performed:
2/4 x 1/3 = X
0.5 x 0.333 = X
0.16666 = X
Therefore, the probability of picking 1 red candle followed by another red candle is 16.66%.
Answer:
1/6
Step-by-step explanation:
2/4 x 1/3 = 1/6
need help w this question thanksss!
Given:
A figure of a circle.
To find:
The value of x.
Solution:
Central angle theorem: According to this theorem, the central angle on an arc is twice of the subtended angle on that arc.
Using the central angle theorem, we get
[tex]x=2\times 35^\circ[/tex]
[tex]x=70^\circ[/tex]
Therefore, the value of x is 70 degrees.
2. Resolve into factors.
a) 8x3 + y3
Answer:
(2x + y)(4x² - 2xy + y²)
Step-by-step explanation:
8x³ + y³ ← is a sum of cubes and factors in general as
a³ + b³ = (a + b)(a² - ab + b²) , then
8x³ + y³
= (2x)³ + y³
= (2x + y)((2x)² - 2xy + y²) , that is
(2x + y)(4x² - 2xy + y²)
express 3 as a percent of 5
Answer:
0.15
Step-by-step explanation:
first get three percent:
3/100 = 3%
then use of operation:
3% of 5;
= (3/100) * 5
Answer:
60%
Step-by-step explanation:
To change a fraction to a percentage, multiply the fraction by 100% , then
[tex]\frac{3}{5}[/tex] × 100% = [tex]\frac{3(100)}{5}[/tex] = [tex]\frac{300}{5}[/tex] = 60%
What is the inverse of the function f(x)=4x+8?
To find the inverse of a function, we switch out every x for a y and vice-versa.
Original: y = 4x + 8
Flipped: x = 4y + 8
Now, we solve for y again to put this equation into slope-intercept form.
x = 4y + 8
4y = x - 8
y = 1/4x - 2
h(x) = 1/4x - 2
Hope this helps!
find the missing side plzzz helpppp
Answer:
10*30 = 300, 300 is the answer
Step-by-step explanation:
Answer:
Step-by-step explanation:
The lines indicates that all side are 10 cm and the white shape is a rhombus
the biggest figure is a rectangle: its angles are 90 degrees
so the triangles have the angles : 90 30 60
so, we have that theeir side are
5 cm and 5√3 cm
perimeter = (10 + 5√3)* 2 + 10 = 20 + 10√3 + 10 = 30 + 10√3 = 10(3 + √3) cm
A = (10 + 5√3)* 5 = 50 + 25√3 = 25(2+√3) cm^2
Area of the two triangle = 5 * 5√3 = = 25√3 cm^2
if we want know the perimeter and the area of the white figure, we have
perimeter = 40 cm
area = 50 + 25√3 - 25√3 = 50 cm^2
A water storage tank has the shape of a cylinder with diameter 14 ft. It is mounted so that the circular cross-sections are vertical. If the depth of the water is 12 ft, what percentage of the total capacity is being used
Answer:
"85.7%" is the right answer.
Step-by-step explanation:
According to the question,
The total capacity of water tank will be:
⇒ [tex]v_1=A\times 14[/tex]
The total volume of water will be:
⇒ [tex]v_2=A\times 12[/tex]
Now,
The percentage of total capacity will be:
= [tex]\frac{100\times v_2}{v_1}[/tex]
= [tex]\frac{v_2}{v_1}\times 100[/tex]
By putting the values, we get
= [tex]\frac{A\times 12}{A\times 14}\times 100[/tex]
= [tex]85.7[/tex]%
In 90 minutes, John can run 30 laps around the track. Determine the number of laps he can run per hour.
Answer:
in 90 minutes he ran 30 laps
there is 60 minutes in a hour so the fraction would be
2/3 so we have to multiply this by 30
2/3*30=20
He can run 20 laps in a hour
Hope This Helps!!!
they help me ? is the last someone please
Convert 43.81 ounces to grams
16 ounces = 1 pound
1 kilogram ≈ 2.2 pounds
Round your answer to the nearest hundredth
Answer:
1241.99
Step-by-step explanation:
1241.993 grams is the original answer but rounded to the nearest hundred is 1241.99
How would the domain and range of the function y = one-fourth x minus 6 be determined? Explain.
Answer:
Domain = ( -∞ , ∞ )
Range = ( ∞ , ∞ )
Step-by-step explanation:
A function is given to us and we need to find the domain and range of the given function .
The function :-
[tex]\rm \implies y = \dfrac{1}{4}x - 6 [/tex]
Definitions :-
Range :- The range is the set of all valid y values .Domain :- All real numbers except where the expression is undefined.In this case, there is no real number that makes the expression undefined. Therefore the domain will be :-
Domain :-
[tex]\rm Domain = ( -\infty , \infty ) [/tex]
or
[tex]\rm Domain = \{ x | x \in \mathbb{R} \}[/tex]
Range :-
[tex]\rm Range = ( -\infty , \infty ) [/tex]
or
[tex]\rm Range = \{ y | y \in \mathbb{R}\} [/tex]
Answer:
Create a table or a graph of the function. The domain represents all input values and the range represents all output values. The domain and range contain all real numbers.
Step-by-step explanation:
Two cars started from a point and traveled in opposite directions; each
car has traveled some miles as shown on the number line. Find the
distance between the two cars.
[tex] \frac{6}{11} - \frac{ - 7}{11} [/tex]
[tex] \frac{6 - ( - 7)}{11} [/tex]
[tex] \frac{6 + 7}{11} [/tex]
[tex] \frac{13}{11} [/tex]
Classwork Let's tick (V) the correct answer.
a) The terms of expression 5x2 – 3xy are (i) 5x² and 3xy (ii) x and xy (iii) 5x2 and - xy
Answer:
Option i
Step-by-step explanation:
The given expression is , 5x² - 3xy .
We can clearly see that there are two terms in the expression , 5x² and 3xy .
Therefore option (i) is correct .
What're solutions for X^+4x-9=5x+3
Answer:
GUCCI GANG
Step-by-step explanation:
GUCCI GUCCCIII GAAAANNNGGGG
Answer:
x=-3 and x=4
Step-by-step explanation:
I assume you mean x^2 in the first part,
x^2 + 4x -9 = 5x +3
x^2 -x -12 =0
x -4
x +3
-----------------------
(x-4)(x+3) = x^2 -x -12 = 0
that gives us
x=4 and x=-3 are solutions
Cláudio pode ir de sua casa a escola andando três km para o Norte, 2 para o oeste, um para o sul, quatro para o leste e, finalmente, 2 para o sul ponto para ir de sua casa a escola em linha reta, Cláudio deve andar: a) 1 km para o sul b) 2 Km para o leste c) 3 km para o oeste d) 4 km para o Norte e) 5 km para o leste
Answer:
b) 2 Km para o leste
Step-by-step explanation:
1. 2 km N
2. 2 km W
3. 1 km S
4. 4 km E
5. 2 km S
Sul e Norte:
(1.) 2 km N + (3.) 1 km S + (5.) 2 km S = 2 km - 1 km - 2 km = 0
Este e Oeste:
(2.) 2 km W + (4.) 4 km E = -2 km + 4 km = 2 km E
Veja imagem abaixo.
Solve the following linear quadratic system of equations algebraically.
y=^2+3x-2
y+3=5x
Answer:
[tex]x=1[/tex]
[tex]y=2[/tex]
Step-by-step explanation:
[tex]y=x^2+3x-2[/tex] , [tex]y+3=5x[/tex]
Replace all occurrences of [tex]y[/tex] in [tex]y+3=5x[/tex] with [tex]x^2+3x-2.[/tex]
[tex](x^2+3x-2)+3=5x[/tex]
[tex]y=x^2+3x-2[/tex]
Add [tex]-2[/tex] and 3.
[tex]x^2+3x+1=5x[/tex]
[tex]y=x^2+3x-2[/tex]
Subtract 5x from both sides of the equation.
[tex]x^2+3x+1-5x=0[/tex]
[tex]y=x^2+3x-2[/tex]
Subtract 5x from 3x.
[tex]x^2-2x+1=0[/tex]
[tex]y=x^2+3x-2[/tex]
Rewrite 1 as [tex]1^2[/tex].
[tex]x^2-2x+1^2=0[/tex]
[tex]y=x^2+3x-2[/tex]
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
[tex]2x=2[/tex] · [tex]x[/tex] · [tex]1[/tex]
[tex]y=x^2+3x-2[/tex]
Rewrite the polynomial.
[tex]x^2-2[/tex] · [tex]x[/tex] · [tex]1[/tex] [tex]+[/tex] [tex]1^2=0[/tex]
[tex]y=x^2+3x-2[/tex]
Factor using the perfect square
trinomial rule [tex]a^2-2ab+b^2=(a-b)^2,[/tex]
where a = x and b = 1.
[tex](x-1)^2=0[/tex]
[tex]y=x^2+3x-2[/tex]
Set the [tex]x-1[/tex] equal to 0.
[tex]x-1=0[/tex]
[tex]y=x^2+3x-2[/tex]
Add 1 to both sides of the equation.
[tex]x=1[/tex]
[tex]y=x^2+3x-2[/tex]
Replace all occurrences of [tex]x[/tex] in
[tex]y=x^2+3x-2[/tex] with 1.
[tex]y=(1)^2+3(1)-2[/tex]
[tex]x=1[/tex]
[tex]y=2[/tex]
If a^2 -b^2 =12 and a-b=4 what is the bay of a +b
Answer:
a+b = 3
Step-by-step explanation:
a = b+4
a^2 = (b+4)(b+4) = b^2 + 8b +16=-b^2 = 12
8b=-4
b = - 1/2
a = 3.5
Find the area of the triangle whose vertices are (2, 3); (-1, 0); (2, -4)...
[Also show the steps of the solution]
Please answer correctly, it's really urgent!
Answer:
Area = 14.5
Step-by-step explanation:
Let's label the given coordinates A, B, C;
Thus;
A = (2, 3)
B = (-1, 0)
C = (2, -4)
From the coordinate geometry formula, the formula for area of a triangle with 3 vertices is;
Area = [Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)]/2
Area = [2(0 - (-4)) + (-1)(-4 - 3) + 2(3 - (-4))]/2
Area = 29/2
Area = 14.5
(g) (2 sin 60°)(3 kos 60°) + 3 tan 30°
Answer:
[tex](2 \ sin 60)(3\ cos 60) +3\ tan 30\ =\ \frac{5\sqrt3}{2}[/tex]
Step-by-step explanation:
[tex](2 \ sin 60)(3 \ cos 60) + 3\ tan 30\\\\= (2 \times \frac {\sqrt3}{2}) (3 \times \frac{1}{2})+ (3 \times \frac{1}{\sqrt3})\\\\=(\sqrt{3}\ \times \frac{3}{2})+ \frac{3}{\sqrt3}\\\\=\frac{3\sqrt3}{2}+\frac{3}{\sqrt3}\\\\=(\frac{3\sqrt3}{2} \times \frac{\sqrt3}{\sqrt3})+(\frac{3}{\sqrt3} \times \frac{2}{2})\\\\=\frac{3\times (\sqrt3)^2}{2\sqrt3}\ + \ \frac{6}{2 \sqrt3}\\\\=\frac{3 \times 3}{2 \sqrt3} +\frac{6}{2 \sqrt3}\\\\=\frac{9+6}{2\sqrt3}\\\\=\frac{15}{2\sqrt3} \times \frac{\sqrt3}{\sqrt3}\\\\[/tex]
[tex]=\frac{15 \sqrt3}{2 \times (\sqrt{3})^2}\\\\=\frac{15 \sqrt 3}{2 \times 3}\\\\=\frac{5\sqrt3}{2}[/tex]
find the value of x to the nearest tenth
7
Step-by-step explanation:
To solve this you need to use trigonometry:
1. Identify the sides. In this case, x is opposite and 10 is adjacent.
2. Identify which part of SOHCAHTOA you need to use. In this case, you need to use TOA.
3. Form your equation. In this case, x = tany x A
4. Substitute numbers into your equation. In this case, x = tan35° x 10
5. Calculate this equation using a scientific calculator. In this case the answer is 7.
