Answer:
$4.05
Step-by-step explanation:
We must divide 4 by 8. We get 0.5. 0.5 stands for $0.5. Then we add 0.5 to 4, which equals $4.05.
Hope this helped :)
find the equation of the sides of an isosceles right angled triangle whose vertex is (-2,3) and the base is on the line x=0
Answer:
[tex]\large \boxed{y = x + 5; y = -x + 1}[/tex]
Step-by-step explanation:
This is an isosceles right triangle, so triangles ABD and CBD are congruent.
∠ ABD = ∠CBD = 45°
The slope of BC = tan(45°) = 1, and
The slope of BA = tan(-45°) = -1.
1. Equation of BC
The point-slope formula for a straight line is
y - y₁ = m(x - x₁)
x₁ = -2; y₁ = 3; m = 1
Substitute the values
[tex]\begin{array}{rcl}y - 3 & = & 1(x - (-2))\\y - 3 & = & x + 2\\y & = & x + 5\\\end{array}\\\text{The equation for the line is $\large \boxed{\mathbf{y = x + 5}}$}[/tex]
2. Equation of BA
x₁ = -2; y₁ = 3; m = -1
Substitute the values
[tex]\begin{array}{rcl}y - 3 & = & -1(x - (-2))\\y - 3 & = & -1(x + 2)\\y - 3 & = & -x - 2\\y & = & -x +1\\\end{array}\\\text{The equation for BA is $\large \boxed{\mathbf{y = -x + 1}}$}[/tex]
An isosceles right triangle has two equal length legs and the hypotenuse side as its base
The equation of the sides of the isosceles right triangle are;
x = 0 (equation of the base)
y = 1 - x
y = x + 5
The reason for arriving at the above equations are as follows:
The given parameters of the isosceles right triangle are:
The coordinate of the vertex of the triangle = (-2, 3)
The base of the triangle, x = 0
The required parameter:
The equation of the sides of the isosceles triangle
Strategy:
Define the terms and relate the given information with the given term definitions
Solution:
The base of an isosceles triangle is the side that form the equal base angles with the two equal sides of the triangle
In an isosceles right triangle, the two equal sides of the right triangle are the legs of the right triangle, and therefore, the base of the triangle is the hypotenuse side
The base angles of an isosceles right triangle, [tex]\theta _b[/tex] = 45°
The altitude of the triangle, y = (0 - (-2) = 2
The altitude is a perpendicular bisector of the base, therefore;
[tex]tan(\theta _b) = \dfrac{Altitude}{\dfrac{1}{2} \times Base \ length }[/tex]
Therefore;
[tex]Base \ length = \dfrac{Altitude}{\dfrac{1}{2} \times tan(\theta _b)}[/tex]
We get:
[tex]\mathbf{Base \ length} = \dfrac{2}{\dfrac{1}{2} \times tan(45^{\circ})} \mathbf{= 4~}[/tex]
The coordinate of the midpoint of the base is the horizontal line from the vertex to the base, and therefore, the coordinate of the midpoint of the base is x = 0, and y = 3 = (0, 3)
The base is 4 units long and half the base length = 4/2 = 2 units
The coordinates of vertex at the base is given by adding or subtracting 2 from the y-coordinates of midpoint of the base as follows;
Vertex coordinates at the base = (0, 3 + 2) = (0, 5), and (0, 3 - 2) = (0, 1)
The slope, m₁, of the side, s₁, with endpoints (-2, 3), and (0, 1), is found as follows;
m₁ = (1 - 3)/(0 - (-2)) = -1
Therefore, the equation of the side s₁ is (y - 1) = -1·(x - 0), which gives;
y = -x + 1
The slope, m₂, of the side, s₂, with endpoints (-2, 3), and (0, 5), is found as follows;
m₂ = (5 - 3)/(0 - (-2)) = 1
Therefore, the equation of the other side s₂ is (y - 5) = 1·(x - 0), which gives;
y = x + 5
The equation of the sides are; x = 0 (given), y = 1 - x, and y = x + 5
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TRIGNOMETRY:
Faisal is 30m from a flagpole. The angle of elevation of its top is 12.4° and the angle of depression of the bottom is 2.1°. Find the height of the flagpole, correct to 3 significant figures.
Answer:
7.698 m
Step-by-step explanation:
From the question,
Faisal's distance to the flagpole = 30 m
angle of elevation of its top = 12.4°
angle of depression of its bottom = 2.1°
Thus, the height of the flagpole is divided into two parts. Let the upper part be represented by x and the lower part by y.
From the triangle of the upper part (elevation), we have;
tan 12.4° = [tex]\frac{x}{30}[/tex]
x = 30 × tan 12.4°
= 30 × 0.2199
= 6.597 m
From the triangle of the lower part (depression), we have;
tan 2.1° = [tex]\frac{y}{30}[/tex]
y = 30 × tan 2.1°
= 30 × 0.0367
= 1.101 m
The height of the flagpole = x + y
= 6.597 + 1.101
= 7.698 m
The height of the flagpole is 7.698 m.
The population of big cats in Africa is increasing at a rate of 5% per year. At the
beginning of 2004 the population was 10 000. (a) Write down the population of
big cats in Africa at the start of 2005. (b) Find the population of big cats at the
beginning of 2010. (c) Find the number of years, from the beginning of 2004, it
will take the population of big cats to exceed 50,000.*
Answer:
a) 10,500 big cats
b) 13,401 big cats
c) 33 years
Step-by-step explanation:
Hi, to answer this question we have to apply an exponential growth function:
A = P (1 + r) t
Where:
p = original population
r = growing rate (decimal form; 5/100= 0.05)
t= years
A = population after t years
Replacing with the values given:
a) At 2005, 1 year passed since 2004 (t=1)
A = 10,000 (1+ 0.05)^1
A = 10,500 big cats
b)
At 2010, 6 years passed since 2004 (2010-2004= 6)
A = 10,000 (1+ 0.05)^6
A = 13,401 big cats
c)
50,000 < 10,000 (1+ 0.05)^t
Solving for t:
50,000/10,000 < 1.05^t
5 < 1.05^t
log 5 < log 1.05^t
log 5 < t ( log 1.05)
log 5 / log 1.05 < t
32.9 years < t
33 years = t
Feel free to ask for more if needed or if you did not understand something.
what is the equation of the line perpendicular to 2x-3y=13 that passes through the point (-6,5)?
Answer:
y = (-3/2)x - 4
Step-by-step explanation:
Recall that a line perpendicular to a given line has a slope which is the negative reciprocal of the given line. The given line can be re-written as -3y = -2x + 13, or
y = (2/3)x - 13/3
and so the slope of a line perpendicular to this given line is -3/2.
Then the desired equation, in point-slope form, is
y - 5 = (-3/2)(x + 6) (This is in point-slope form.)
Alternatively,
2y - 10 = -3(x + 6) = -3x - 18, or
2y = 10 - 3x - 18, or
2y = -3x - 8, or y = (-3/2)x - 4 (This is in slope-intercept form.)
1 1/3 x 1 1/2 x 1 1/5
Answer:
7
Step-by-step explanation:
!..........................
Step-by-step explanation:
[tex](1\frac{1}{3} )(1\frac{1}{2} )(1\frac{1}{5} )\\(\frac{4}{3} )(\frac{3}{2} )(\frac{6}{5} )\\(\frac{2}{1} )(\frac{1}{1} )(\frac{6}{5} )\\\frac{12}{5}[/tex]
In the second step I made them all into simple fractions, just because that's easier.
In the third step I did a bit of cancelling to simplify everything as much as possible.
Answer:
[tex]\frac{12}{5}[/tex]
solve by cross multiplication method 2x-7y=-10 and 3x+2y-10=0
Answer:
x=2
y=2
Step-by-step explanation:
Is the graph increasing decreasing or constant A ,B or C
Answer:
A.) constant
Step-by-step explanation:
The graph has a horizontal line that is neither increasing nor decreasing; therefore it is constant.
The given graph is constant because the line is parallel to the x axis, option A is correct.
The equation of the given graph is y=3.
The equation y = 3 represents a horizontal line that cuts across the y-axis at a height of 3.
This line is parallel to the x-axis and remains at a constant level of y = 3 regardless of the value of x.
There is no change in the y-value as x varies, the graph is considered constant.
Hence, the graph is constant.
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Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!
Answer:
A
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
m(x) = 2(x + 4)² - 8 ← is in vertex form
with vertex = (- 4, - 8 ) → A
3x+-2=-2 will give brainiest if ya answer :D
Answer:
x=0
Step-by-step explanation:
3x+-2=-2
Add 2 to each side
3x+-2+2=-2+2
3x = 0
Divide by 3
3x/3 = 0/3
x = 0
How Do I Find The Answer To 320 = 3x + 16
｡☆✼★ ━━━━━━━━━━━━━━ ☾
320 = 3x + 16
-16 from both sides
304 = 3x
/3 on both sides
x = 304/3
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
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Jayne stopped to get gas before going on a road trip. The tank already had 4 gallons of gas in it. Which equation relates the total amount of gasoline in the tank, y, to the number of gallons that she put in the tank, x? y=4+x y = x − 4 y = 4 · x y = x ÷ 4
The required equation is, y = 4 + x.
Hence, The correct answer would be an option (A).
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Now, Jayne stopped for gas before embarking on a road trip.
There were already 4 gallons of gas in the tank.
Hence, As per the question, the required equation would be as:
⇒ y = 4 + x
Thus, This equation relates the total amount of gasoline in the tank, y, to the number of gallons that she put in the tank, x. The total amount of gasoline in the tank, y, is equal to the number of gallons that she put in the tank, x, plus the 4 gallons that were already in the tank.
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A pairs of fair dice is tossed . What is the probability of not getting a sum 5 or 9 ?
Answer:
28/36 or 7/9
Step-by-step explanation:
there are 36 possible answers
4 of them equal 5 (1+4, 2+3, 3+2, 4+1)
4 of them equal 9 (3+6, 4+5, 5+4, 6+3)
8-36 = 28
8.
How is the graph of y = 4(2)* - - 3 translated from the graph of y = 4(2)*?
3 units right
3 units down
3 units left
3 units up
Answer: 3 units up
Step-by-step explanation:
Find the circumference of the circle with the given radius or diameter. (Use 3.14 for it.)
diameter = 25 ft
a 39.25 ft
b. 78.5 ft
C. 490.63 ft
d. 1,962.5 ft
Answer:
B. 78.5 feet
Step-by-step explanation:
The circumference of a circle can be found using the following formula.
c=πd
We know that the diameter is 25 feet. We also know we are using 3.14 for pi.
d=25
π=3.14
Substitute these values into the formula.
c=3.14*25
Multiply the two numbers together
c=78.5
Add appropriate units. Circumference uses the same units as the diameter. The diameter is 25 feet, so the units are feet.
c=78.5 feet
The circumference of the circle is 78.5 feet, and the correct answer is B
The right answer is 78.5ft
please see the attached picture for full solution
hope it helps
good luck on your assignment
log base4 64=3 pls solve
Answer: 4^3 = 64
Step-by-step explanation:
Formula is [tex]a^c=b[/tex]
[tex]4^3=64[/tex]
Answer:
[tex]{4}^{3} = 64 \\ [/tex]
Step-by-step explanation:
[tex] log_{a}(c) = b \\ {a}^{b} = c[/tex]
Use the formula.
[tex] log_{4}(64) = 3[/tex]
[tex] {4}^{3} = 64[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
use the rencetangle to find this area
Answer:
The area of the triange is 20 feet. beacause the area of the rectangel is 40 feet.
Step-by-step explanation:
Solve the system of equations below algebraically.
2x + 3y = 6
- 5x+2y=4
Answer: The solution is (0,2)
Step-by-step explanation:
2x +3y = 6 We will solve the equations using the elimination method
-5x +2y= 4 but first we need to eliminate one of the variables and we will multiply the first equation by 5 and multiply the second equation by 2 to eliminate the x variable.
5(2x + 3y) =6(5) new equation : 10x +15y = 30
2(-5x + 2y) = 4(2) new equation ; -10x +4y =8
Now we have to new equations so we will eliminate the x term by adding
10x +15y = 30
-10x +4y =8
19y = 38 divide both sides by 19.
y= 2 Now using the solution for y plot it into one of the new equations and solve for x
10x + 15(2) = 30
10x + 30 = 30
-30 -30
10x = 0
x= 0
find the answer! 10 points to the first person!
Answer:
36
Step-by-step explanation:
This is a 30, 60 90 triangle, which means that there is a ration for calculating each side.
Which sampling would be appropriate to survey 120,000 people?
A) 12,000
B) 1,200
C) 120
D) 12
Answer: Id say b
Step-by-step explanation: a would be too high and a bit too detailed. Whereas c and d will be inaccurate.
Answer:
A. Twelve thousand
Step-by-step explanation:
cant specify my sources but please hit thank it would make my day :)
A store buys an item for $10. To earn a PROFIT of $25, what percent does 13 po
the store need to mark up the item? (Hint: if the profit is $25, they must
sell it for more than that...) *
Answer:
150%
Step-by-step explanation:
25-10= 15
15/10 = 1.5
1.5 = 150%
Please answer correctly !!!!!!! Will mark brainliest !!!!!!!!!
If a number is increased by 28 and then divided by 5, the result is 7.
The algebraic equation is
x + 28 divided by 5 =7.
what is x
x+28 / 5 = 7
Multiply both sides by 5:
x +28 = 35
Subtract 28 from both sides:
x = 7
A regular polygon has 12 sides. Work out the size of each interior angle.
Answer:
150°
Step-by-step explanation:
Measure of each interior angle of polygon
[tex] = \frac{(n - 2) \times 180 \degree}{n} \\ \\ = \frac{(12 - 2) \times 180 \degree}{12} \\ \\ = \frac{10 \times 180 \degree}{12} \\ \\ = 10 \times 15 \degree \\ \\ = 150 \degree[/tex]
In Evan's senior class of 240 students, 85% are planning to attend college after graduation. What is the probability that a senior is chosen at random not planning to attend college after graduation?
Answer:
36% ,hope this helps
Step-by-step explanation:
1) 100 - 85 = 15
2) 240 times 15 devided by:100
3) equals 36
4) 36 %
Kevin made cookies and brownies for the bake sale at school. He made 12 more cookies than brownies. He sold cookies for $1.50 and brownies for $2. He sold all of his food and made a total of $123. How many of each item did he sell? *
Answer:
He made 42 cookies and 30 brownies.
Step-by-step explanation:
Let c = number of cookies
Let b = number of brownies
"He made 12 more cookies than brownies."
The number of cookies is 12 more than the number of brownies.
c = b + 12
"He sold cookies for $1.50 and brownies for $2."
The money he made from selling cookies was 1.5c.
The money he made from selling brownies was 2b.
The total sales were $123
1.5c + 2b = 123
We have a system of equations.
c = b + 12
1.5c + 2b = 123
Substitute c of the second equation with b + 12
1.5(b + 12) + 2b = 123
1.5b + 18 + 2b = 123
3.5b = 105
b = 30
c = b + 12
c = 30 + 12
c = 42
He made 42 cookies and 30 brownies.
i only need answer to number 1 btw. My teacher said dont use trig ratios?? so im very lost.
x (y-z)+y (z-x) +z ( x-y)
Answer:
xy-xz+yz-yx+zx-zy hoped this helped a little
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
x (y-z)+y (z-x) +z ( x-y)
Simplify the bracket
xy -xz + yz - yx + zx - zy
combine the like terms
xy - yx -xz + zx + yz - zy
= 0
A car is going 50 miles per hour. A rate that describes this would have units of
Answer:
mph or miles per hour
Step-by-step explanation:
A rectangle with an area of 24 square inches is formed by cutting strips of equal width from a rectangular piece of paper. Find the dimensions of the new rectangle if the original rectangle measures 8 inches by 6 inches.
Answer: 4 inches by 6 inches or 8 inches by 3 inches.
Step-by-step explanation:
The area of a rectangle is A = W*L
where L is the width and L is the lenght.
Now, the original rectangle has a measure of 8 in by 6 in.
if 8in is the lenght and 6 in is the width.
We want to divide only one of those measures in equal parts, such that when we take the product of the end results is equal to 24 in.
If we divide the lenght by half (so both parts will have the same width as this did not change), we now have that the lenght is 8in/2 = 4in and the width is 6in.
Now the area is 4in*6in = 24in, which is the area that we where looking for.
We also could cut the width in half, and get the dimensions 8 inches by 3 inches.
1.) Mr. Taylor weighs 300 pounds. He went on the Subway diet and was guaranteed to lose 5 pounds per week. Write an equation that could be used to find how many weeks, w, it would take for him to weigh 150 pounds
2.)You have $60 and your sister has $120. You are saving $7 per week and she is saving $5 per week. How long will it take before you and your sister have the same amount of money?
Answer:
1.) 300 - 5w = 150
2.) 30 weeks
Step-by-step explanation:
w = weeks on the diet
if every week he's on the diet, that means that the weeks * 5 is how many pounds he loses. If he's on the diet one week then he loses 5 pounds. 2 weeks then 10 pounds... etc. But because he's losing punds the value is negative
He starts at 300 pounds so the y-intercept (starting value) would be 300
Finally, because he's looking to get to 150 pounds, that is the final value you're solving for
So this is your firat equation:
300 - 5w = 150
Then we are looking for when two different eqaution have the same value.
Your equation is: 60 + 7w
Her equation is: 120 + 5w
Your final equation is 60 + 7w = 120 + 5w
Solve for this by getting w on one side, and your plain old variable-less value on the other. Do this by subtracting 5w from each side, as well as 60.
Your equation is now 2w = 60
Then divide the whole equation by 2, and you get w = 30
