ΔABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin. It is then reflected across the line y = -x. What are the coordinates of the vertices of the image?
Answer:
A(0, -3) ; B(3, -2) and C(1, -1).
Step-by-step explanation:
Given : ΔABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin.
To find : What are the coordinates of the vertices of the image.
Solution : We have given
Vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise.
By the rotation rule of 180° clockwise : (x ,y) →→ ( -x ,-y).
Then vertices would be
A(-3, 0) →→ A(3, 0)
B(-2, 3) →→ B(2, -3)
C(-1, 1) →→ C(1, -1).
Reflection y = -x then
A(0, -3) ; B(3, -2) and C(-1, 1).
Therefore, A(0, -3) ; B(3, -2) and C(1, -1).
Newer stocks can be bought for $8 each, while older stocks can be bought for $4 each. The total cost, in dollars, of 10 stocks is represented by the expression 8s+4(10-s), where s represents the number of new stocks bought. how does changing the value of s change the value of the term 4(10-s)?
A.) For values of s less than 10, the term 4(10-s) will be negative; for values of s greater than 10, the term will be negative; for values of s equal to 10, the term will equal 0.
B.) For values of s less than 10, the term 4(10-s) will be negative; for values of s greater than 10, the term will be positive; for values of s equal to 10, the term will equal 0.
C.) For values of s less than 10, the term 4(10-s) will be positive; for values of s greater than 10, the term will be positive; for values of s equal to 10, the term will equal 0.
D.) For values of s less than 10, the term 4(10-s) will be positive; for values of s greater than 10, the term will be negative; for values of s equal to 10, the term will equal 0.
For the points M(-2,3), N(4,5), P(1,6) and Q(4,-3), what is the relationship between MN and PQ?
evaluate the expression (18-6)÷(11-5), if possible
What does the end behavior look like of the graph of the function f(x)=-8x^4-2x^3+x?
I know what the graph itself looks like but I have trouble explain its end behavior.
Thank you.
1. Write the expression in simplified radical form. Show your work. 3 – 2√11/ 2 +√11
The longer leg of a right triangle is 4cm longer than the shorter leg the hypotenuse is 8 cm longer than the shorter find the side lengths of the triangle
The side lengths of the triangle are 8 cm, 12 cm, and 16 cm
To solve for the side lengths of the right triangle, we can use the Pythagorean Theorem, which states that for any right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, this is written as a^2 + b^2 = c^2.
Let's denote the shorter leg of the triangle as x. Then, according to the problem, the longer leg is x + 4 cm and the hypotenuse is x + 8 cm. Plugging these expressions into the Pythagorean Theorem, we have:
x^2 + (x + 4)^2 = (x + 8)^2
Expanding and simplifying the equation:
x2 + x2 + 8x + 16 = x2 + 16x + 64
2x2 + 8x + 16 = x2 + 16x + 64
x2 - 8x - 48 = 0
Solving this quadratic equation for x, we find:
x = 8 cm (shorter leg)
x + 4 = 12 cm (longer leg)
x + 8 = 16 cm (hypotenuse)
Therefore, the side lengths of the triangle are 8 cm, 12 cm, and 16 cm
Mrs. Sage will print a copy of the class alphabet book for each student. The book is formatted in1/2 pages with a title page, a page for each letter and an end page. If there are 70 students, how many reams of paper will Mrs. Sage need for the books?
Dimitri deposited 60% of his paycheck into a savings account be deposited $41.67 what was the total of his check
write an equation of the line, in slope intercept form, that passes through the given point and has the given slope. point:(8,-8), slope:3
Find the next term of the following sequence.
25, 10, 4,
The given sequence is 25, 10, 4.
Notice that this is a geometric sequence because here we have equal common ratio.
So, common ratio : r = [tex] \frac{a_{2}}{a_{1}} [/tex]
= [tex] \frac{10}{25} [/tex]
= 0.4
So, each term is 0.4 times of it's previous term.
Hence, to get the next term of this sequence, multiply 0.4 with the third term 4.
So, fourth / next term = 4* 0.4 =1.6
Hence, next term of this sequence is 1.6.
Hope this helps you!
Answer:
Step-by-step explanation:
the answer is 8/5 i just did it on my quiz and got it right.
PLEASE HELP ME DO NOT HELP IF YOU DO NOT KNOW HOW TO DO IT
The state of Colorado had roughly the shape of a rectangle that is 3.8 x 10^2
2.8 x 10^2 miles high. What is the approximate area of Colorado? hint: the area of the rectangle is a product of its length and width.
Jade wants to buy a $200,000 term life insurance policy. She is 34 years old. Using the premium table, what is her annual premium for a 10 year policy?
The premium of $200,00 term life insurance policy is $1,202
What is Annual premium?Annualized premium is the total amount paid in a year's time to keep the life insurance policy in force. The annualized premium amount of a life insurance policy does not include taxes and rider premiums.
Given, Jade wants to buy a $200,000 term life insurance policy. She is 34 years old.
Jade wants to buy a $200,000 term life insurance policy. She is 34 years old.
Since, Jade is female.
Using table for 10-year policy: We will see the column of female.
Annual premium of life insurance per $1000 for 10-years policy term of 34-years old female = $6.01
For $1000 life insurance premium = $6.01
For $1 life insurance premium = $0.00601
For $20000 life insurance premium = 200000 x 0.00601
For $20000 life insurance premium = $ 1,202
Therefore, The premium of $200,00 term life insurance policy is $1,202
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How many 3 letter "words" can be created from the letters abcdefg when 1. repetition allowed,?
You know, this question "functions" just as well as the Kardashians. Not at all, at least to my brain! I definitely need help with this.
Can someone please explain this in a way my dumb brain would understand? WHY does 2 - (-8) = 10? Shouldn't it be decreasing to -6?
The reasoning is because you are subtracting 2. If you were to be adding 2, then it would be -6.
Since you are subtracting 2 it = 10.
Glad to help a Senior mod out.
Thanks, Plip.
If the intercepts of a line are (a,0) and (0,b), what is the slope of the line?
Show how you solved it.
5377 people/km^2= how many people/m^2 ?
Answer:
0.005377 people/m²
Step-by-step explanation:
5377 people/km² can written as
5377 × [tex]\frac{people}{km^2}[/tex]
Now we have to find the value in [tex]\frac{people}{meter^2}[/tex]
Since 1 km = 1000 meter.
So 5377 × [tex]\frac{people}{km^2}[/tex] = 5377 × [tex]\frac{people}{(1000)^2met^2}[/tex]
= [tex]\frac{5377}{(1000)^2}[/tex] people per met²
= [tex]\frac{5377}{(1000000)}[/tex]
= 0.005377 people/m²
A checkers board is 8 squares long and 8 squares wide. The area of each square is 14 square centimeters. Estimate the perimeter of the checkers board to the nearest tenth of a centimeter.
Area of each square = 14 sq. cm.
length of each square = sqrt(14) = 3.7 cm
length of one side = 8 x 3.7 = 29.6 cm
Perimeter of the checker board = 4 x 29.6 = 118.4 cm
The perimeter of the checker board 118.4 cm
Area of each square = 14 sq. cm.
What is the length?
The square root of area is the length of one side
[tex]length of each square =\sqrt{14} = 3.7 cm[/tex]
[tex]length of one side = 8 * 3.7 = 29.6 cm[/tex]
What is the formula for perimeter of square?Perimeter (P) =4 (length of side a)
[tex]P=4a[/tex]
[tex]Perimeter of the checker board = 4 *29.6 = 118.4 cm[/tex]
Therefor we get the perimeter of the checker board 118.4 cm
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There are 20 girls on the basketball team. of these, 17 are over 16 years old, 12 are taller than 170 cm, and 9 are both older than 16 and taller than 170 cm. how many of the girls are older than 16 or taller than 170 cm?
Final answer:
By using the principle of inclusion-exclusion, we calculate that all 20 girls on the basketball team are either over 16 years old or taller than 170 cm, as the sum of the individual criteria minus the intersection equals the total number of girls on the team.
Explanation:
To determine how many of the girls on the basketball team are either over 16 years old or taller than 170 cm, we can use the principle of inclusion-exclusion. According to the information provided, there are 20 girls on the team in total, of which 17 are over 16 years old, 12 are taller than 170 cm, and 9 satisfy both criteria. The principle of inclusion-exclusion states that the number of elements in the union of two sets is equal to the sum of the sizes of each set minus the size of their intersection.
Using this principle:
Number of girls over 16 years old: 17
Number of girls taller than 170 cm: 12
Number of girls who are both over 16 and taller than 170 cm: 9
The calculation would be as follows:
17 (over 16) + 12 (taller than 170 cm) - 9 (both) = 20
Therefore, there are 20 girls on the team who are either older than 16 or taller than 170 cm.
If you are dealt two cards successively (with replacement of the first) from a standard 52-card deck, find the probability of getting a heart on the first card and a diamond on the second.
Katie jogged 2.4 miles on Monday, 3.7 miles on Tuesday, and 2.9 miles on Wednesday. How many miles did Katie jog on Thursday if she jogged a total of 12.1 miles for the four days
Help please I’ll mark you brainliest
A survey was taken on pet ownership. 750 people were covered on the first day of the survey. The number tripled every subsequent day. Find the total number of people surveyed in 6 days
A. 265100
B. 265200
C. 273000
D. 265700
To find the total number of people surveyed in 6 days with numbers tripling each day starting with 750, we calculate the number for each day and sum them up, giving a total of 273000 people surveyed.
To calculate the total number of people surveyed in 6 days if 750 people were covered on the first day and the number tripled every subsequent day. We will use an exponential growth formula to find the answer.
On Day 1: 750 people.
On Day 2: 750 × 3 = 2250 people.
On Day 3: 2250 × 3 = 6750 people.
On Day 4: 6750 × 3 = 20250 people.
On Day 5: 20250 × 3 = 60750 people.
On Day 6: 60750 × 3 = 182250 people.
To find the total number of people surveyed over the 6 days, we add up the total number of people surveyed each day:
750 + 2250 + 6750 + 20250 + 60750 + 182250 = 273000 people.
Therefore, the correct answer is C. 273000.
Jessie is completing a mental rotation experiment. her reaction time will be fastest when the objects are rotated: 120 degrees. 180 degrees. 240 degrees. 60 degrees.
HELP MEH PLEZ! When the county fair opened its gates, 68 people entered the fairgrounds. After one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. After two hours, there
The equation representing the number of people, y, at the fair x hours after the gates open:
y = 68 * 1.5^(x-1)
Initial number of people: 68 (given)
Growth factor per hour: 1.5 (given)
Number of hours since gates opened: x
The equation uses the following logic:
Start with the initial number of people (68).
Multiply by the growth factor (1.5) to account for the increase after the first hour.
Since the growth factor applies after each hour, raise it to the power of (x-1) to account for the total number of times it's applied after x hours. This is because the first hour's growth is already accounted for in the initial number.
Therefore, the equation y = 68 * 1.5^(x-1) accurately represents the number of people at the fair x hours after opening.
Complete question:
When the county fair opened its gates, 68 people entered the fairgrounds. After one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. After two hours, there were 1.5 times as many people on the fairgrounds as the previous hour. If this pattern continues, write the equation representing the number of people, y, at the fair x hours after the gates open.
If sin theta = 3/5 and cos theta <0 find tan theta
Suppose you had d dollars in your bank account. You spent $12 but have at least $51 left. How much money did you have initially? Write and solve an inequality that represents this situation.
A.
d+12 51; d 75
B.
d + 12 51; d 75
C.
d-12 51; d 63
D.
d-12 > 51; d > 63
a fishing lake was stocked with 300 bass. Each year, the population decreases by 25. the population of bass in the lake after x years is represented by the function f(x)=300-25x
The function f(x)=300-25x represents the decline of population in a fishing lake that was initially stocked with 300 bass. Each year, the population reduces by 25. For instance, after 4 years, the number of bass left in the lake would be 200.
Explanation:The question is about a fishing lake that was initially stocked with 300 bass. As per the information given, the population of bass in the lake decreases by 25 each year. Therefore, if we let x represent the number of years, then every year, the number of bass decreases by 25x. This relationship is represented by the algebraic function f(x)=300-25x.
To provide a practical understanding, suppose you want to calculate the number of bass remaining after 4 years. You just substitute '4' in place of x in the equation. Hence, f(4) = 300 - 25 * 4 = 300 - 100 = 200. So, after 4 years, there would be 200 bass remaining in the lake.
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John buys big ice-cream cylindrical Jar and sells it for $1 each ice-cream cone.
Each cone has around 30 cubic cm of ice-cream in it.
Jar has diagonal 20 cm. and its height is 3 times of width.
If he sells the whole jar, and He originally bought it for $7 does he make profit out of selling the jar?
John can make a profit by selling ice cream from the cylindrical jar. After calculating the volume, he would earn approximately $15.70 in revenue, and by deducting the initial cost ($7), he makes a profit of around $8.70.
To determine if John will make a profit by selling the entire ice-cream cylindrical jar, we first need to calculate the volume of the jar to find out how many cones he can fill. The jar has a diagonal of 20 cm and a height that is three times its width. Assuming the width is 'w' and height is '3w', we can use the Pythagorean theorem with the jar's diagonal to find 'w', since the diagonal forms a right triangle with the width and height of the cylinder.
The formula for the Pythagorean theorem is diagonal^2 = width^2 + height^2, which gives us 20^2 = w^2 + (3w)^2. Solving for 'w', we get w = 4 cm and height = 12 cm. The volume 'V' of the cylinder is given by V = π * radius^2 * height, which gives us V = π * 2^2 * 12, therefore, V = 48π cm^3. Then, we divide the jar's volume by the volume of each ice cream cone to find the number of cones, 48π cm^3 / 30 cm^3/cone ≈ 5π cones.
Given that John sells each cone for $1, the total revenue from selling all the ice-cream cones would be approximately $5π. Since π is approximately 3.14, his total revenue would be about $15.70. Subtracting the initial cost of the jar ($7), we find that John would make a profit of approximately $8.70.
Therefore, John will indeed make a profit out of selling the jar of ice cream.