Answer:
d = 10.5, a₁ = - 3.5
Step-by-step explanation:
The n th term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₂ = 7 and a₄ = 28 , then
a₁ + d = 7 → (1)
a₁ + 3d = 28 → (2)
Subtract (1) from (2) term by term to eliminate a₁
2d = 21 ( divide both sides by 2 )
d = 10.5 ← common difference
Substitute d = 10.5 into (1)
a₁ + 10.5 = 7 ( subtract 10.5 from both sides )
a₁ = - 3.5 ← first term
Emma made a scale model of the Sam Houston's monument. The monument's actual height is 67 ft tall. Emma is using a scale where 1 inch is 10 ft. What is the height of Emma's model?
Answer: 6.7inch
Step-by-step explanation:
From the question, we are informed that Emma made a scale model of the Sam Houston's monument and that the monument's actual height is 67 ft tall but Emma is using a scale where 1 inch is 10 ft.
The height of Emma's model will therefore be 67ft divided by 10 since he's using a scale of 1:10. This will be:
= 67/10
= 6.7inch
Happy Paws charges $22.00 plus $4.50 per hour to keep a dog during the day. Woof Watchers charges $11.00 plus $5.75 per hour. Write an equation and solve it to find for how many hours the total cost of the services is equal. Use the variable h to represent the number of hours.
Answer:
Total amount charged by Happy Paws = 22 + 4.50h
Total amount charged by Woof Watchers = 11 + 5.75h
3.2 hours
Step-by-step explanation:
Total amount charged by Happy Paws = 22 + 4.50h
Total amount charged by Woof Watchers = 11 + 5.75h
22 + 4.50h = 11 + 5.75h
Collect like terms
22 + 11 = 4.5h + 5.75h
33 = 10.25h
Solve for h
33/10.25 = h
h = 3.22
does this graph represent a function? if yes why?
PLEASE HELP! WILL MARK BRAINLIEST
Simplify each and state the excluded values.
8x^3/12x^2+16
Answer:
Cancel the common factor of 8 and 12x²+6.
Tap for more steps...
4x³/6x²+3
Factor 3
out of 6x²+3.
4x³/3(2x²+1)
Step-by-step explanation:
Jenn wants to measure the height of a tree. She walks exactly 125 feet from the base of the
tree and looks up. The angle of elevation from the ground to the top of the tree is 33º. How
tall is the tree? Which equation would be used to solve this problem?
Answer:
[tex]81.2\:\mathrm{ft}[/tex]
Step-by-step explanation:
We can form a right triangle and use basic trig for a right triangle to solve this problem:
[tex]\tan33^{\circ}=\frac{h}{125}[/tex], where [tex]h[/tex] is the height of the tree.
Solving, we get:
[tex]h=125\cdot \tan 33^{\circ},\\h\approx \fbox{$81.2\:\mathrm{ft}$}[/tex].
what is x ? pleasee help !!!
Answer:
It is an unknown number but add 16 + 32 degrees and you get 48x degrees then multiply 48 X 72 degrees and you get 336 degrees.
Step-by-step explanation:
In Mr. Layden's class, three students
brought in their baseball card
collections. For their three
collections, the mode was 126 and
the range was 26. What are two
possibilities for the number of cards
in each student's collection?
Answer: 126, 126, 152
or
100, 126, 126
Step-by-step explanation:
The sum of 5 times one number, x, and 4 times a second number, y, is 87. If the sum of the two numbers is 20, find the two numbers. Pls hurry need it before schools is over
(hint will mark brainiest)
Step-by-step explanation:
We have 5x + 4y = 87 and x + y = 20.
=> 5x + 4y = 87 and 4x + 4y = 80.
5x + 4y = 87
- (4x + 4y = 80)
=> x = 7
Therefore (7) + y = 20, y = 13.
The answers are x = 7 and y = 13.
Please help me lol!!!!!!
Answer:
A
Step-by-step explanation:
HELP NEEDED HELP NEEDED!
Answer:
G. 8.625 [tex]ft^{2}[/tex]
Step-by-step explanation:
Area of first rectangle:
1.5 × 2.5 = 3.75 ftArea of second rectangle:
1.5 × 2.5 = 3.75 ftArea of triangle:
1.5 × 1.5 = 2.252.25 ÷ 2 = 1.125Put them together:
3.75 + 3.75 + 1.125 = 8.625 [tex]ft^{2}[/tex]I hope this helps!
help me plez There are 100 bolts in 5 bookcases.
What is the unit rate in bolts per bookcase?
2 bolts per bookcase
20 bolts per bookcase
50 bolts per bookcase
200 bolts per bookcase
Answer:
20 bolts per bookcase
Step-by-step explanation:
Paul volunteered at the senior center for 3 9/10 hours on Saturday and 5 1/6 hours on Sunday. How many hours did Paul volunteer at the senior center on both days?
Answer:
Saturday 3 9/10 hours = 60/10 = 6, 6 X 9 =54
3 hours 54 mins
Sunday 5 1/6 hours = 60/6 = 10, 10 X 1 = 10
5 hours 10 mins
3 hrs 54 mins + 5 hrs 10mins = 9 hrs 4 mins
Answer:9 4/10
Step-by-step explanation:
PLEASE HELP ME PLEASEEEEEEEEEEE
A triangle is inscribed in a square, as shown. Write a simplified function r in terms of x that represents the area of the shaded region.
This is the same as (1/2)x^2 because 1/2 = 0.5
We could rewrite that into [tex]\frac{x^2}{2}[/tex]
=========================================================
Explanation:
The base of the white triangle (aka unshaded region) is x, while the height is also x
The area of the white triangle is
A = 0.5*base*height
A = 0.5*x*x
A = 0.5*x^2
The area of the entire square is x*x = x^2. Subtract off the area of the white triangle to get the area of the two blue shaded regions combined
shaded region = (square area) - (white triangle area)
shaded region = (x^2) - (0.5x^2)
shaded region = x^2 - 0.5x^2
shaded region = 1x^2 - 0.5x^2
shaded region = (1-0.5)x^2
shaded region = 0.5x^2
So the white triangle occupies half of the square, while the blue shaded region occupies the remaining 50% of the square.
Because 0.5 = 1/2, we can write this as (1/2)x^2, but I think using decimals in this case is easier.
The sum of the angle measures of any triangle is 180°. If one angle of a triangle measures 35º and another angle measures 72º, what is the measure of the third angle?
Answer:
73°
Step-by-step explanation:
Start with 35° + 72° = 107°
Then 180° - 107° = 73°
Answer:
[tex]we \: knw \: that \: total \: angle = 180 \\ 35 + 72 + x = 180 \\ 107 + x = 180 \\ x = 180 - 107 \\ x = 73 \\ thank \: you[/tex]
solve h+9.7=-9.7 and show me the steps
Answer:
h = -19.4
Step-by-step explanation:
1. Take the constant on the left side of the equation by changing the positive to a negative ---> h = -9.7 -9.7
2. Solve the right side, and you have yuor answer. ---> h = -19.4
ben jogged 4 1/2 miles in 1 1/4 hours at a constant rate. how far did ben jog in one hour
(the answer on top)
Answer:
b is the answer
Step-by-step explanation:
4 1/2 divided by 1 1/4 = 3 3/5
The distance Ben jogged in one hour is 3 3/5 miles. The correct option is B. 3 3/5 miles
Distance, Rate, and TimeFrom the question, we are to determine how far Ben jogged in one hour. That is, how far he jogged per hour.
This means we should determine the rate
Using the formula,
Rate = Distance / Time
From the given information,
Distance = 4 1/2 miles
Time = 1 1/4 hours
∴ Rate = 4 1/2 ÷ 1 1/4
Rate = 3 3/5 miles/hour
Hence, the distance Ben jogged in one hour is 3 3/5 miles. The correct option is B. 3 3/5 miles
Learn more on Calculating Rate here: https://brainly.com/question/20654411
#SPJ2
2 equivalent rations for 6/5 ? please help !!!
What is the equation of the line that has a slope of 1/3 and goes through the point (6,−2)?
A. y = 1/3x − 4
B. y = 1/3x + 4
C. y = 1/3x − 8
D. y = 1/3x
Answer: A) y = 1/3x − 4
Step-by-step explanation:
Find the Equation Using Point-Slope Formula
slope: 1/3
point: (6, −2)
Use the slope 1 and a given point (6, −2) to substitute for [tex]x_1[/tex] and [tex]y_1[/tex] in the point-slope form
y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex]), which is derived from the slope equation m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
y − (−2) = 1/3 ⋅ (x − (6))
Simplify the equation and keep it in point-slope form.
y + 2 = 1/3 ⋅ (x − 6)
Solve for y.
1/3 ⋅ (x − 6).
Apply the distributive property.
y + 2 = 1 /3 x + 1 /3 ⋅ − 6
Combine 1/3 and x.
y + 2 = x/3 +1/3 ⋅ −6
Cancel the common factor of 3.
y + 2 = x /3 − 2
Move all terms not containing y to the right side of the equation.
Subtract 2 from both sides of the equation.
y = x/3 − 2 − 2
Subtract 2 from −2. x
y = x/3 − 4
Reorder terms.
y = 1/3x − 4
List the equation in different forms.
Slope-intercept form:
y = 1/3x − 4
Point-slope form:
y + 2 = 1/3 ⋅ (x − 6)
A real estate agency an agent salty house for 313,000. The commission rate is 4.5 for the real estate agency in the commission rate for the agent is 20% of the amount the real estate agent gets. How much did the agency make on the house? How much did the agent earn in comission
Answer:
313000/100 X 4.5 = 14085
14085/100 X 20 = 2817
14085 - 2817 = 11268
agency = 11268
agent = 2817
A bear cub walks
5/6 miles in 5/12
age
hours. What is its
speed in terms of miles per hour?
Answer:use math(way
Step-by-step explanation
It help
Answer: 2 miles per hour
Step-by-step explanation: Reduce the common factor which would be 5 and then you divide and you get 2
Please help me with this
Answer:
emily 37.44$ Andy 22.15$
Step-by-step explanation:
Andy needs 23 feet multiply 23 feet by 12 you get the amount of inches so 276 inches if the cost for 130 inches is 10.40 we need to increase this number proportionally to 276 So 130+113%=276.9 so 276. Now 10.40x113%=22.15.
Emily needs 13 yards, 13 yards is 39 feet, 39 feet is 468 inches, Now do same thing we did for Andy. 130+360%=468 exactly 10.40+360%=37.44
29% expressed as a fraction in simplest form is?
At the science fair, Adriana uses 8 fluid ounces of vinegar to make her volcano erupt. How many times can she make her volcano erupt with 1 quart of vinegar?
Answer:
4 times
Step-by-step explanation:
We known that 1 quart is equivalent to 32 fluid ounces
Suppose each eruption consumes 8 fluid of ounces, if we also assume that the amount of vinegar required per eruption is constant, then the number of times Adriana can make her volcano erupt is
n = 32 / 8
n = 4 times
Adriana can make her volcano erupt 4 times with 1 quart of vinegar
Find -0.5D D=[18. 16] [-14 -6]
Options are: A. [9 8] [-14 -6] B. [9 8] [7 3] C. [9. 8] [-7 -3] D. [-9 -8] [7 3]
Answer:
The correct answer is Option D: [-9 -8] [7 3]
Step-by-step explanation:
Given that
D = [18 16][-14 -6]
We have to find -0.5D
In order to find the required values of D we only have to multiply the individual elements with -0.5, this might change the signs of elements and reduce the magnitude.
So,
[tex]-0.5D = [-0.5*18\ \ -0.5*16][-0.5*-14\ \ \ -0.5*-6]\\-0.5D =[-9\ \ \ -8][7\ \ \ 3][/tex]
Hence,
The correct answer is Option D: [-9 -8] [7 3]
WILL MARK BRAINLIEST !!!! Which equation is an equation of a circle with a radius of 3 and its center is at (5, -2)?
(x - 5)² + (y + 2)² = 3
(x - 5)² + (y + 2)² = 9
(x + 5)² + (y – 2)² = 3
(x + 5)² + (y - 2)² = 9
Answer:
the first one
Step-by-step explanation:
Answer:
(x + 5)² + (y – 2)² = 3
Step-by-step explanation:
Calculate the pay for the following day of a
weekly time card given a wage of $13/hr.
Name
Week of:
Morning
In Out
Monday 08:00 12:00
Afternoon
In Out
12:45
17.30
pay = $[?]
Round your answer to the nearest hundredth.
Please help if you can.
Answer:
dfsfsffsfsdfsfsfsfsfsfsefsfsdfsff
Step-by-step explanation:sfsfsfsf
fsfsfdfdsfsdfsfsf
What is the surface area of a right cylinder which has a base with radius 9 units and has a height of 12 units
оооо
508.7 units squared
678.2 units squared
1,186.9 units squared
1,256.0 units squared
A Cinema has 240 seats. 144 seats were sold for the current movie. What percent of seats are empty?
1 I am thinking of a 6-digit number. • The sum of the digits is 38. • The number is under 600 000. What could my number be? Find twelve different possibilities.
Answer:
A 6 digit number can be written as:
abcdef
Where each letter represents a single digit.
We know that this number is smaller than 600,000, and we also know that:
a + b + c + d + e + f = 38
Now, we have a lot of variables, so we can play a little.
I will suppose that:
f = 6
e = 7
d = 3
c = 9
then we have:
a + b + 9 + 3 + 7 + 6 = 38
a´+ b + 25 = 38
a + b = 38 - 25 = 13
now let's suppose that b = 8
a + 8 = 13
a = 13 - 8 = 5
Then our number is:
589,376
This number is smaller than 600,000, and if we add the sum of the digits is 38.
Now we want to find 11 other numbers like this.
We can simply change the places of some of the digits, like:
598,376 (also meets the condition)
Where i just changed the positions of the 9 and the 8.
589,367 (also meets te condition)
Where i just changed the position of the 6 and 7.
Now just keep doing that, only take care that the number can not be larger than 600,000, so i will leave the first 5 fixed in that position.
589,673 (also meets the condition)
598,736 (also meets the conditions)
536,798 (also meets the conditions)
536,897 (also meets the conditions)
536,978 (also meets the conditions)
563,798 (also meets the conditions)
563,987 (also meets the conditions)
563,879 (also meets the conditions)
573,689 (also meets the conditions)
573,869 (also meets the conditions)