Answer:
If a parallelogram has at least one 90 degree angle then its opposite angle is equal and also = 90 degrees.
The 2 remaining opposite angles add up to 180 degrees and since they must be equal, they must be 90 degrees each.
So, we have a quadrilateral with four 90 degree angles and is therefore a rectangle OR it could possibly be a square.
Step-by-step explanation:
Answer: one right angle property
One of the sides of a rectangle has length 7. Which of the following points, paired with (6,5), will make a side of this length?
Answer:
B (6,12)
Step-by-step explanation:
The distance from point A (6,5) to point B should be 7.
A- (6,5)-> (7,5) is 1 unit right
B- (6,5)-> (6,12) is 7 units up
C- (6,5)-> (6,7) is 2 units up
D- (6,5)-> (12,5) is 6 units up
What is the remainder in the synthetic division problem below?
Answer: 9
Step-by-step explanation:
Answer:
the remainder is 9
Step-by-step explanation:
find the remainder in the synthetic division
1 4 6 -1
Take down the first number 4 as it is. then multiply it with divisor 1 and put it below 6. then add it and do the same till we get remainder
1 4 6 -1
0 4 10
--------------------------------
4 10 9 -> Remainder
So the remainder is 9
If m∠CBD = 40°, find m∠CAD.
A) 30°
B) 40°
C) 50°
D) 60°
E) None of the above
The triangles cross the center of the circle CAD is the same as CBD.
The answer is B) 40 degrees.
A triangular city lot bounded by three streets has a length of 300 feet on one street, 250 feet on the second, and 420
feet on the third. Find the approximate measure of the largest angle formed by these streets.
Answer:
The approximate measure of the largest angle formed by these streets is [tex]99.2\°[/tex]
Step-by-step explanation:
we know that
Applying the law of cosines
[tex]c^{2}=a^{2}+b^{2} -2(a)(b)cos(C)[/tex]
In this problem we have
[tex]a=300\ ft[/tex]
[tex]b=250\ ft[/tex]
[tex]c=420\ ft[/tex] ----> is the greater side
substitute and solve for angle C
[tex]420^{2}=300^{2}+250^{2} -2(300)(250)cos(C)[/tex]
[tex]176,400=152,500 -150,000cos(C)[/tex]
[tex]cos(C)=[152,500-176,400]/150,000[/tex]
[tex]cos(C)=-0.1593[/tex]
[tex]C=arccos(-0.1593)=99.2\°[/tex]
Solve for the varaiables shown in the steps simplifying the expression below:
25 ⋅ 84
16
=
25 ⋅ (2a)4
24
=
25 ⋅ 2b
Answer:
a=3
b=12
c=13
Step-by-step explanation:
(see attached)
The value of 'a' is 3, 'b' is 12, and 'c' is 13 and this can be determined by using the arithmetic operations.
Given :
Expression - [tex]\dfrac{2^5\times 8^4}{16}=\dfrac{2^5\times (2^a)^4}{2^4}=\dfrac{2^5\times 2^b}{2^4}=2^c[/tex]
The value of a, b, and c can be determined by following the below calculations:
[tex]\dfrac{2^5\times 8^4}{16}=\dfrac{2^5\times (2^a)^4}{2^4}[/tex]
Further, simplify the above expression:
[tex]\dfrac{2^5\times (2^3)^4}{2^5}=\dfrac{2^5\times (2^a)^{4}}{2^4}[/tex]
the above equation holds good when the value of 'a' is 3.
[tex]\dfrac{2^5\times 8^4}{2^4}=\dfrac{2^5\times 2^b}{2^4}[/tex]
Further, simplify the above expression:
[tex]\dfrac{2^5\times 2^{12}}{2^5}=\dfrac{2^5\times 2^b}{2^4}[/tex]
the above equation holds good when the value of 'b' is 12.
[tex]\dfrac{2^5\times 2^{12}}{2^5}=2^c[/tex]
Further, simplify the above expression.
[tex]\dfrac{2^{17}}{2^4}=2^c[/tex]
[tex]2^{13}=2^c[/tex]
the above equation holds good when the value of 'c' is 13.
For more information, refer to the link given below:
https://brainly.com/question/20595275
A solution of the equation f(x)=g(x) is the same as
Answer:
The solution of the equation f (x) = g (x) is the same as the coordinates of the intersection.
Exaple in the attachment.
f(x) = g(x) → x = -2, y = -1 or x = -1 and y = 0 or x = 1 and y = 2.
A package of ground beef costs $6.98. The price per pound is $3.86. How many pounds of ground beef are in the package? Round to the nearest hundredth.
A. 1.81
B. 1.80
C. 1.72
D. .27
Answer:
B. 1.81
Step-by-step explanation:
Simply divide [tex]\frac{6.98}{3.86}[/tex] to get [tex]1.8082...[/tex].
This is closer to [tex]1.81[/tex] than it is to [tex]1.80[/tex], so that is how it is rounded.
Then, you have your answer.
find the volume of a trianglular prism that has a triangular base of 14 and and a height of 17 with a prism height of 5 leave your answer in a0 cubic units WILL GIVE BRAINLIEST!
Answer:
Exact Form:
1190/ 3
Decimal Form:
396. 6
Mixed Number Form:
396 2 /3
Step-by-step explanation:
Final answer:
The volume of the triangular prism with a triangle base of 14 units and height of 17 units and a prism height of 5 units is 595 cubic units.
Explanation:
To find the volume of a triangular prism, we need to first find the area of the base triangle and then multiply it by the height of the prism. The formula for the volume of a triangular prism is given by V = (base area) imes (prism height). However, we need to be clear about what the given 14 and 17 represent. Assuming they stand for base and height of the triangle, respectively, the area of the base triangle is A = (1/2) imes base imes height = (1/2) imes 14 imes 17. Multiplying this area by the prism height of 5 units gives us the volume of the prism.
Calculating the base area: A = (1/2) imes 14 imes 17 = 119 square units. The volume is then V = 119 imes 5 = 595 cubic units. Therefore, the volume of the triangular prism is 595 cubic units.
Radio listeners were asked to call in and pick their two favorite rodents the listeners had 4 choices woodchuck prairie dog beaver and chipmunk which of the following is the complete list of the possible pairs of rodents
Answer:
WoodChuck-Prairie Dog
WoodChuck-Beaver
WoodChuck-Chipmunk
PrairieDog-Beaver
PrairieDog-Chipmunk
Beaver-Chipmunk
Answer:
A chipmunk and a beaver
Will give brainiest and 10 Points, NEED ANSWER ASAP!
Find the total area of the Regular Pyramid.
L.A=
Answer:
The total area is [tex]16\sqrt{3}\ units^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the regular pyramid is equal to the area of its four triangular faces
Each face is an equilateral triangle
so
Applying the law of sines
The surface area is equal to
[tex]SA=4[\frac{1}{2}b^{2}sin(60\°)][/tex]
we have
[tex]b=4\ units[/tex]
[tex]sin(60\°)=\frac{\sqrt{3}}{2}[/tex]
[tex]SA=4[\frac{1}{2}(4)^{2}\frac{\sqrt{3}}{2}][/tex]
[tex]SA=16\sqrt{3}\ units^{2}[/tex]
Answer:
16 sqrt 3
Step-by-step explanation:
What is the measure of angle A
What is the measures of angle B
Answer: 72and 108
Step-by-step explanation: that is the correct answer don’t be a fool
The population of a small town is decreasing exponentially at a rate of 14.3% each year. The current population is 9,400 people. The town's tax status will change once the population is below 6,000 people. Create an inequality that can be used to determine after how many years, t, the town's tax status will change, and use it to answer the question below.
Answer:
After 2.9 years the town's tax status will change
The towns tax status change within the next 3 years
Step-by-step explanation:
The question below is
Will the towns tax status change within the next 3 years ?
Let
y -----> the population of a small town
t ----> the number of years
we have a exponential function of the form
[tex]y=a(b)^{t}[/tex]
where
a is the initial value
b is the base
In this problem
[tex]a=9,400\ people[/tex]
[tex]b=100\%-14.3\%=85.7\%=85.7/100=0.857[/tex]
substitute
[tex]y=9,400(0.857)^{t}[/tex]
Remember that
The town's tax status will change once the population is below 6,000 people
so
The inequality that represent this situation is
[tex]9,400(0.857)^{t}< 6,000[/tex]
Solve for t
[tex](0.857)^{t}< 6,000/9,400[/tex]
Apply log both sides
[tex](t)log(0.857)< log(6,000/9,400)[/tex]
[tex]-0.067t< -0.1950[/tex]
Multiply by -1 both sides
[tex]0.067t > 0.1950[/tex]
[tex]t > 2.9\ years[/tex]
so
After 2.9 years the town's tax status will change
therefore
The answer is
Yes, the towns tax status change within the next 3 years
the town's tax status will change a little over 7 years from the current time, assuming the rate of population decline remains constant.
To find out after how many years the population of the town would decrease to below 6,000 people, we start with the current population and apply the annual exponential decrease. The population decreases at a rate of 14.3% each year, which means the remaining population each year is 85.7% (100% - 14.3%) of the previous year. Starting with a population of 9,400 people, we need to solve for t in the inequality 9400 × (0.857)^t < 6000. We take the natural logarithm of both sides to solve for t:
ln(9400 × (0.857)^t) < ln(6000)
t × ln(0.857) < ln(6000) - ln(9400)
t > (ln(6000)-ln(9400)) / ln(0.857)
Using a calculator, we find that:
t > 7.17
Therefore, the town's tax status will change a little over 7 years from the current time, assuming the rate of population decline remains constant.
Can sumone plzhelp..Apply the distributive property to factor out the greatest common factor of all three terms .
9a-18b+21c=
Answer:
3(3a - 6b + 7c )
Step-by-step explanation:
The greatest common factor of 9, 18 and 21 is 3
Factor out 3 from each term
9a - 18b + 21c
= 3(3a - 6b + 7c) ← in factored form
Answer:
3(3a - 6b + 7c)
Step-by-step explanation:
Write each term as a multiplication of its factors. Then see which factors are in common to all terms.
9a - 18b + 21c =
= 3 * 3 * a - 2 * 3 * 3 * b + 3 * 7 * c
The common factors are shown below in bold:
= 3 * 3 * a - 2 * 3 * 3 * b + 3 * 7 * c
The only common factor is 3.
Now use the distributive property to factor out a 3.
= 3(3 * a - 2 * 3 * b + 7 * c)
Now multiply each term in parentheses again.
= 3(3a - 6b + 7c)
Deshawn won 95 pieces of gum playing hoops at the county fair. At school he gave four to every student in his math class. Write an expression for how many pieces of gum deshawn has now.
Answer:
x = 95 - 4y
Step-by-step explanation:
Let the pieces he has now be a variable x
The number of students in his class be y
According to the question he gave every student 4 pieces in the class
The pieces he gave to everyone become 4y.
Note that 4 here means he had given four to each
and as he had won 95 pieces at the fair in the starting,
therefore the equation becomes:-
x = 95 - 4y....
What are the coordinates of P?
Answer: THIRD OPTION.
Step-by-step explanation:
Given the trapezoid in the figure, you know the coordinates of two points:
(0,c) and (a,b)
You can observe that the point (a,b) and the point P have the same x-coordinate, because both points are "a" units from the origin.
Then, the x-coordinate of P is:
[tex]x=a[/tex]
Now, in order to find the y-coordinate of the point P, you need to remember that when the line touches the x-axis, the value of "y" is equal to zero. Therefore, the y-coordinates of the point P is:
[tex]y=0[/tex]
Then the answer is:
[tex](a,0)[/tex]
compute the probability of tossing a six-sided die and getting a 7
Which are harder in geometry? Theorems or proofs? Explain why
The difficulty between theorems and proofs in geometry is subjective. Theorems are proven true statements, while proofs are the logical processes used to establish the truth of theorems. Students may find one harder than the other depending on their individual abilities and understanding.
In the study of geometry, students often ask which are harder: theorems or proofs. To address this, it's important to understand the nature of both. A theorem is a statement that has been proven to be true through a logical sequence of statements, starting from agreed-upon assumptions, known as axioms. The Pythagorean Theorem, for instance, states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This theorem provides a consistent and reliable outcome as long as the arithmetic is carried out correctly.
On the other hand, a proof is the process by which a theorem is shown to be true. Proofs involve a series of logical deductions from accepted principles and previously proven theorems. They are essentially the 'work' or argument that establishes the truth of a theorem. In any proof, each step must logically follow from the previous ones based on established geometric postulates and existing theorems. Therefore, a proof can be viewed as a bridge that connects the basic assumptions of geometry to the theorem being proven.
Whether theorems or proofs are harder is subjective and depends on the student's strengths. Some students find memorizing theorems challenging, while others may struggle with the logical sequence and creativity required to craft proofs. Nonetheless, the study of geometry contributes valuable reasoning skills and knowledge that connects fundamental truths of mathematics to practical applications in the real world, like engineering and physics.
question 2-5 please
Answer:
1. [tex]m=1\frac{1}{14}[/tex]
2. undefined
3. [tex]-6[/tex].
4. [tex]2\frac{1}{3}[/tex].
5. [tex]2[/tex].
6. [tex]\frac{7}{2}[/tex]
Step-by-step explanation:
1. The required line passes through [tex](3,0),(-11,-15)[/tex]. The slope of the line joining the points [tex](x_1,y_1),(x_2,y_2)[/tex] is given by the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] or [tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]
Either of them yields the same result.
Substitute [tex]x_1=3,y_1=0,x_2=-11,y_2=-15[/tex] into the first formula to get,
[tex]m=\frac{-15-0}{-11-3}[/tex] [tex]\implies m=\frac{-15}{-14}=\frac{15}{14}[/tex]
You can write this as a mixed number to obtain:
[tex]\implies m=1\frac{1}{14}[/tex]
2. The given line passes through [tex](4,-8),(4,13)[/tex].
Observe that the first coordinates are the same for both points. This implies that, the line is vertical.
The slope of all vertical lines are undefined.
3. The average rate of change of the function [tex]y=f(x)[/tex] on the interval [tex][a,b]\:\:or\:\:a\le x\le b[/tex] is given by:
[tex]ARC=\frac{f(b)-f(a)}{b-a}[/tex].
The given function is [tex]f(x)=x^2-4x[/tex]
[tex]f(-2)=(-2)^2-4(-2)=12[/tex]
[tex]f(4)=(4)^2-4(4)=0[/tex]
[tex]ARC=\frac{f(4)-f(-2)}{4--2}[/tex].
[tex]ARC=\frac{0-12}{6}=-6[/tex].
4. The given function is [tex]f(x)=2^x-1[/tex]
[tex]f(0)=2^0-1=0[/tex]
[tex]f(3)=2^3-1=7[/tex]
[tex]ARC=\frac{f(3)-f(0)}{3-0}[/tex].
[tex]ARC=\frac{7-0}{3}=2\frac{1}{3}[/tex].
5. From the graph
[tex]f(3)=7,f(0)=1[/tex]
[tex]ARC=\frac{f(3)-f(0)}{3-0}[/tex].
[tex]ARC=\frac{7-1}{3}[/tex].
[tex]ARC=\frac{6}{3}=2[/tex].
6. The given equation is :
[tex]2y-7x=-4[/tex]
Add [tex]7x[/tex] to both sides.
[tex]2y=7x-4[/tex]
Divide through by 2.
[tex]y=\frac{7}{2}x-2[/tex]
Compare this function to [tex]y=mx+b[/tex]
The slope is [tex]m=\frac{7}{2}[/tex]
What is the area of this composite shape?
Answer:
51 in² is the area of the shape.
Step-by-step explanation:
Note that there is a triangle, as well as a Parallelogram.
First, solve for the measurement for the Parallelogram. The Parallelogram has sides that measure 6 in. & 7 in. respectively.
Note the measurement of the left length, which is 13. The right length is 7. To solve for the length of the triangle, subtract the two:
13 - 7 = 6
The triangle length is 6.
To solve for the triangle width, subtract the part from the total:
6 - 3 = 3
The triangle width is 3.
Note that the area of the triangle is found using the formula: Area = 1/2base x height (or length x width). Plug in the corresponding numbers to the corresponding variable.
A = 1/2(3)(6)
A = (3)(3)
A = 9
The triangle's area is 9 in².
Solve for the area of the parallelogram:
6 x 7 = 42
The parallelogram's area = 42 in².
Add the two measurements together:
42 + 9 = 51
51 in² is the area of the shape.
~
The above composite shape can be divided into :
● A Rectangle with Length 7 in. and Width 6 in.
● A Right angled Triangle with base 3 in. and height 6 in.
Let us first find the Area of Rectangle :
We know that - Area of a Rectangle is given by : Length × Width
[tex]:\implies[/tex] Area of Rectangle = (7 × 6) in²
[tex]:\implies[/tex] Area of Rectangle = 42 in²
Now, Let us find the Area of Right angled Triangle :
[tex]\mathsf{We\;know\;that - Area\;of\;a\;Triangle\;is\;given\;by : \dfrac{1}{2} \times base \times height}[/tex]
[tex]\implies \mathsf{Area\;of\;Right\;angled\;Triangle = \dfrac{1}{2} \times 3 \times 6\;(in^2)}[/tex]
[tex]:\implies[/tex] Area of Right angled Triangle = (3 × 3) in²
[tex]:\implies[/tex] Area of Right angled Triangle = 9 in²
Area of the Composite shape :
● Area of Rectangle + Area of Right angled Triangle
[tex]:\implies[/tex] Area of the Composite shape = (42 + 9) in²
[tex]:\implies[/tex] Area of the Composite shape = 51 in²
What is the value of y?
114/
ОА. 33
ОВ. 66°
Ос. 57°
D. 1140
Answer:
с. 57°
Step-by-step explanation:
The measure of the exterior angle of a triangle is equal to sum of the opposite interior angles
114 = y+y
114 = 2y
Divide by 2
114/2 = 2y/2
57 =y
57° is the value of y.
What are the properties of triangles?A triangle has three sides, three angles, and three vertices. The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle. The sum of the length of any two sides of a triangle is greater than the length of the third side
Given
The measure of the exterior angle of a triangle is equal to the sum of the opposite interior angles
114 = y+y
114 = 2y
Divide by 2
114/2 = 2y/2
57 =y
To know more about the properties of triangles refer to :
https://brainly.com/question/17228179
#SPJ2
all about easy points here
Answer:
90
Step-by-step explanation:
The formula for right triangular prisms is simple; 1/2 × a × b × c. So simply plug in your numbers (doesn't matter the order you plug in).
1/2 × 12 × 5 × 3 = 90
Answer:90
Step-by-step explanation:
solve the system of equations by substitution: y = x - 2
x+y=12
Step-by-step explanation:
y = x - 2
x + y = 12
Substitute the first expression for y into the second equation.
x + (x - 2) = 12
2x - 2 = 12
2x = 14
x = 7
Now plug into either equation to find y.
y = 7 - 2
y = 5
So the solution is (7, 5).
Me.stewart teaches three science classes her students are freshman and sophomores her student data are shown in relative frequency table
Answer:
the answer is that D is false
Step-by-step explanation:
the relative frequency chart shows that 0.35 of her total freshman and sophomores take biology (Bottom left corner of the chart).
Answer: D
Step-by-step explanation: Apex said so
what is 7.45 divided by .5
Answer: 14.9
I have to write this in order to have enough characters.
7.45 divided by 0.5 equals 14.9. This is calculated by converting the divisor 0.5 to a whole number and doing the same operation on the dividend, then performing the division.
Explanation:Dividing Decimals
To find what 7.45 divided by 0.5 is, one approach is to think of 0.5 as one-half, so you are essentially finding out how many halves there are in 7.45. Another way to approach this is to manipulate the numbers to make the division easier. Since 0.5 is equivalent to the fraction 1/2, dividing by 0.5 is the same as multiplying by 2 (which is the reciprocal of 0.5). Here are the steps to perform the division:
Therefore, 7.45 divided by 0.5 equals 14.9.
Learn more about Dividing Decimals here:https://brainly.com/question/29279046
#SPJ2
6R=4R-20? Answer pls!
Answer: r = -10
Step-by-step explanation:
Move variable to the left , collect like terms, then divide both sides by 2.
Answer:
r = -10
Step-by-step explanation:
Your equation is 6r = 4r - 20
To solve this equation, find out r's value.
To do that, you must get r alone on one side of the equation
6r = 4r - 20
[Subtract 4r from both sides]
2r = -20
[Now divide both sides by 2]
r = -10
So, the answer to this equation is r = -10
I hope this helps! :)
Divide 500 in the ratio 3:1:4
Answer:
Step-by-step explanation:
You need an x value to determine what number to multiply that will give you three numbers that are in the ratio of 3:1:4
Let the number = x
Set the equation up as 3x + x + 4x = 500
3x + x + 4x = 500 Combine the left
8x = 500 Divide both sides by 8
x = 500/8 Divide by 8.
x = 62.5
So 3x = 3*62.5 = 187.5
1x = 1 * 62.5 = 62.5
4x = 4 * 62.5 = 250 The total should be 500
Answer:
{187.50, 62.50, 250}
Step-by-step explanation:
Add up the numbers in the ratio: Add up 3, 1 and 4. We get 8.
Then we divide up 500 into eight parts, each 62.5.
The ratio we are to follow is 3:1:4.
3 parts of 62.5 each comes out to 187.5;
1 part of 62.5 each comes out to 62.5; and
4 parts of 62.5 each comes out to 250.
If we have done this correctly, these 3 results add up to 500:
187.50
62.50
250
-------------
500
So, 500 divided up in the ratio 3:1:4 is {187.50, 62.50, 250}
Consider the two points A(9.7) and B(5,2).
What is the ratio of the vertical change from A to B to the horizontal change from A to B? In other words, what is the
slope?
What the answer
Answer:
The slope is [tex]m=\frac{5}{4}[/tex] or [tex]m=1.25[/tex]
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]A(9,7)\ B(5,2)[/tex]
Substitute the values
[tex]m=\frac{2-7}{5-9}[/tex]
[tex]m=\frac{-5}{-4}[/tex]
[tex]m=\frac{5}{4}=1.25[/tex]
chris runs 2.3 miles every day of the week, except sunday. on sunday he only runs 2 miles. how many miles will he run in 2 weeks?
Answer:
He will run 31.6 miles in two weeks.
Step-by-step explanation:
6 days a week = 2.3 miles
6 days · 2 weeks = 12 days total running 2.3 miles
1 day a week = 2 miles
1 day · 2 weeks = 2 days total running 2 miles
(12 · 2.3) + (2 · 2)
27.6 + 4
31.6 miles
A man 1.5 metres tall standing on top of a mountain 298.5m high observes the angles of depressions of two flying boats D and C to be 28 and 34 degrees respectively. Calculate the distance between the boats.
Pls I need urgent answer plss
Answer:
119.45 meters
Step-by-step explanation:
This question can be solved using one of the three trigonometric ratios. The height mentioned is 298.5 + 1.5 = 300 m and the angle of depression is 28 degrees for Boat D and 34 degrees for Boat C. It can be seen that the required distance is given by x feet, which is the distance between the two boats. This forms two right angled triangle, as it can be seen in the diagram. The perpendicular is given by 300 m, the base is the unknown, and the angles 28 degrees for boat A and 34 degrees for boat B is is given, as shown in the attached diagram. Therefore, the formula to be used is:
tan θ = Perpendicular/Base (For the distance between the mountain and Boat D)
Plugging in the values give:
tan 28 degrees = 300/d.
d = 300/tan 28.
d = 564.22 m (to the nearest hundredth).
tan θ = Perpendicular/Base (For the distance between the mountain and Boat C)
Plugging in the values give:
tan 34 degrees = 300/c.
c = 300/tan 34.
c = 444.77 m (to the nearest hundredth).
The difference between d and c will be x, i.e. that distance between the boats. So 564.22 - 444.77 = 119.45 meters (to the nearest hundredth).
Therefore, the boats are 119.45 meters apart from each other!!!
To calculate the distance between the two boats, we can use the concept of angles of depression and trigonometry. The distance to boat D is calculated using the tangent function with the angle of depression and the height of the observer. The same process is used to find the distance to boat C. The distance between the boats is then the difference between these two distances.
Explanation:To calculate the distance between the two boats, we can use the concept of angles of depression. Let's consider the boat D first. The angle of depression is the angle that the line of sight makes with the horizontal when looking down. In this case, the angle of depression for boat D is 28 degrees. Similarly, the angle of depression for boat C is 34 degrees.
Now, let's use trigonometry to find the distances. We can use the tangent function, which is the opposite side divided by the adjacent side. The opposite side represents the height difference between the observer and the boat, while the adjacent side represents the distance between the observer and the boat.
For boat D, we have:
tan(28 degrees) = opposite/adjacent
opposite = 1.5 m (height of the observer)
adjacent = distance between the observer and boat D
distance between the observer and boat D = 1.5 m / tan(28 degrees)
We can use the same process to find the distance between the observer and boat C:
distance between the observer and boat C = 1.5 m / tan(34 degrees)
Therefore, the distance between the boats is the difference between the distance to boat D and the distance to boat C.
Match each function with the corresponding function formula when h(x) = 5 - 3x and g(x) = -3 x + 5. 1. k(x) = (3g + 5h)(x) 2. k(x) = (h - g)(x) 3. k(x) = (g + h)(x) 4. k(x) = (5g + 3h)(x) 5. k(x) = (3h - 5g)(x) 6. k(x) = (5h - 3g)(x)
Answer:
1. k(x) = (3g + 5h)(x) = -24x+40
2. k(x) = (h - g)(x) = 0
3. k(x) = (g + h)(x) = -6x+10
4. k(x) = (5g + 3h)(x) = -24x+40
5. k(x) = (3h - 5g)(x) = 6x-10
6. k(x) = (5h - 3g)(x) = 10-6x
Step-by-step explanation:
Given
h(x) = 5 - 3x
and
g(x) = -3 x + 5
1. k(x) = (3g + 5h)(x)
3*g(x) = 3(-3 x + 5)
=> -9x+15
5*h(x) = 5(5 - 3x)
=>25-15x
(3g + 5h)(x)=3*g(x)+5*h(x)
= -9x+15+25-15x
=-9x-15x+15+25
=-24x+40
2. k(x) = (h - g)(x)
(h - g)(x) = h(x) - g(x)
= 5 - 3x -(-3 x + 5)
=5-3x+3x-5
= 0
3. k(x) = (g + h)(x)
(g+h)x = g(x) + h(x)
= -3 x + 5 + 5 - 3x
= -6x+10
4. k(x) = (5g + 3h)(x)
5*g(x) = 5(-3 x + 5)
=-15x+25
3*h(x) = 3(5 - 3x)
=15-9x
(5g + 3h)(x) = 5*g(x) + 3*h(x)
= -15x+25+15-9x
= -15x-9x+25+15
=-24x+40
5. k(x) = (3h - 5g)(x)
(3h - 5g)(x) = 3*h(x)-5*g(x)
=15-9x-(-15x+25)
=15-9x+15x-25
=-9x+15x+15-25
=6x-10
6. k(x) = (5h - 3g)(x)
5*h(x)-3*g(x) = 25-15x - (-9x+15)
= 25-15x+9x-15
= 25-15-15x+9x
=10-6x
Answer:
1. k(x) = (5g + 3h)(x) ---------------- 5. k(x)=40-5(3^x)-9x
2. k(x) = (3h - 5g)(x) ---------------- 6. k(x)=5(3^x)-9x-10
3. k(x) = (3g + 5h)(x) ---------------- 1. k(x)=40-3^x+1-15x
4. k(x) = (5h - 3g)(x) ----------------- 3. k(x)=10+3^x+1-15x
5. k(x) = (h - g)(x) ----------------- 2. k(x)=3^x-3x
6. k(x) = (g + h)(x) ----------------- 4. k(x)=10-3^x-3x