The two lines 4x + 5y = 10 and 5x - 4y = 28 are perpendicular to each other as they have slopes that are negative reciprocals of each other.
What is a slope?The slope is generally defined as the rate of change of the y-axis with respect to the x-axis.
We know we can determine if two lines are parallel or perpendicular to each other by their slope.
If they are parallel they will have the same slope and if they are perpendicular they will have slopes that are negative reciprocals of each other.
Given are two lines 4x + 5y = 10 and 5x - 4y = 28.
We know the equation of a line is y = mx + b.
∴ 4x + 5y = 10 can be written as 5y = -4x + 10 Or y = -(4/5)x + 5/2.
And 5x - 4y = 28 can be written as -4y = -5x + 28 Or y = (5/4)x - 7.
Thus we can conclude that these two lines are perpendicular to each other as (-4/5) is the negative reciprocal of (5/4).
learn more about slopes here :
https://brainly.com/question/3605446
#SPJ5
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.
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
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
To learn more about the perimeter of square visit:
https://brainly.com/question/25092270
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.
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
What are the solutions to the inequality? Graph the solutions. x/5 greater than or equal to -2
Help please I’ll mark you brainliest
For the points M(-2,3), N(4,5), P(1,6) and Q(4,-3), what is the relationship between MN and PQ?
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.
Describe the cross section
Answer:
D. Square
Step-by-step explanation:
A cross section is the shape that we get when we cut the object.
Here the given object is a cube.
It is cut straight through the middle.
Imagine a cube cut through the middle, when we look at the same on the top, we get square.
Since in a cube all the sides are equal.
Therefore, we get square when we cut the cube straight through the middle.
Answer: D. Square.
The cross-section of the shape in the image is a square.
Here's why:
The shape in the image is a cube.
A cube has six square faces.
When you cut a cube through the middle along any of its axes, the resulting cross-section will always be a square.
Therefore, the answer is D. square.
Graph f(x)=34x+2. Use the line tool and select two points to graph the line.
we have
[tex]f(x)=\frac{3}{4}x+2[/tex]
To graph the linear equation find the intercepts
we know that
The x-intercept is the value of x when the value of the function is equal to zero
The y-intercept is the value of the function when the value of x is equal to zero
so
Find the y-intercept
for [tex]x=0[/tex]
[tex]f(x)=\frac{3}{4}*0+2=2[/tex]
the y-intercept is the point [tex](0,2)[/tex]
Find the x-intercept
for [tex]f(x)=0[/tex]
[tex]0=\frac{3}{4}x+2[/tex]
Multiply by [tex]4[/tex] both sides
[tex]0=3x+8[/tex]
[tex]x=-\frac{8}{3}=-2.667[/tex]
the x-intercept is the point [tex](-2.667,0)[/tex]
Plot the intercepts to graph the line
The answer in the attached figure
Answer:
the answer is (-2,0) and (0, 2)
Good luck!
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.
1. Write the expression in simplified radical form. Show your work. 3 – 2√11/ 2 +√11
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).
Write the fraction 29 over 7 as a repeating decimal
1.17 - 0.07a + (-3.92a)
Answer:
The simplified form of the given expression is [tex]1.17-3.99a[/tex].
Step-by-step explanation:
The given expression is
[tex]1.17-0.07a+(-3.92a)[/tex]
The given expression can be written as
[tex]1.17-0.07a-3.92a[/tex]
Now, combine the like terms.
[tex]1.17+(-0.07a-3.92a)[/tex]
[tex]1.17+(-3.99a)[/tex]
[tex]1.17-3.99a[/tex]
Therefore the simplified form of the given expression is [tex]1.17-3.99a[/tex].
evaluate the expression (18-6)÷(11-5), if possible
Which expression is equivalent to square root of 9x^2?
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
the set of ____ contains all the whole numbers amd their opposite
If sin theta = 3/5 and cos theta <0 find tan theta
7x=2x-35
A. 7
B.5
C.-5
D.-7
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
Dimitri deposited 60% of his paycheck into a savings account be deposited $41.67 what was the total of his check
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
Learn more about annual premium here:
https://brainly.com/question/9834518
#SPJ6
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.
using radicals, write an expression for the expression y 1/2
Elliott purchased shares of Microsoft in 2008 for $28 per share. He plans to sell them as soon as the price rises 20%. At what price will he sell his shares?
Since we are to find the price when it is risen 20%, therefore the fractional increase must be 0.20 of the original, therefore:
amount increased = $28 * 0.20 = $5.60
So the selling price must be:
selling price = $28 + $5.60 = $33.60
Final answer:
Elliott will sell his Microsoft shares at a price of $33.60 each after a 20% price increase from his initial purchase price of $28 per share.
Explanation:
The question concerns the calculation of a future selling price of shares after a certain percentage increase. To find the selling price after a 20% increase on Elliott's initial purchase price of $28 per share, we first calculate the 20% increase, which is 0.20 × $28 = $5.60. Next, we add this increase to the original purchase price to determine the selling price: $28 + $5.60 = $33.60 per share. Therefore, Elliott plans to sell his shares when their price reaches $33.60 each.
Determine which equations below, when combined with the equation 3x-4y=2, will form a system with no solutions. Choose all that apply.
A) 2y = 1.5x - 2
B) 2y = 1.5x - 1
C) 3x + 4y = 2
D) -4y + 3x = -2
Answer: D,B,B,C,D,A,C,B,D, (A-D)
ALL TEST ANSWERS
Step-by-step explanation:
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.