Final answer:
The expression for the total number of autographs Jackson has after getting 3 more is 'n + 3', where 'n' represents the original number of autographs.
Explanation:
Jackson currently has n autographs in his autograph book. Since he obtained 3 more autographs yesterday, we can express the total number of autographs he now has by creating a simple algebraic expression. You add the number of new autographs to his original count. The expression that represents the total number of autographs in Jackson's book now is n + 3.
A van travels 168 miles on 14 gallons of gas,At this rate,how many gallons will it need to travel 252 miles?
A.) 21 gallons
B.)9.3 gallons
C.)20 gallons
D.)23 gallons
Answer:
The answer would be A.) 21 gallons.
Step-by-step explanation:
1.) The first thing you need to do is see how many miles per gallon the van is using by doing 168/14= 12.
2.) Then, you would apply this to the amount need to travel by doing 252/12= 21, meaning the answer is in fact A.) 21 gallons.
To find out how many gallons of gas a van would need to travel 252 miles, given that it travels 168 miles on 14 gallons, you can use a simple ratio and proportion calculation. This yields that the van would need 21 gallons to travel 252 miles.
Explanation:The subject here is the mileage of a van, which is a problem of ratio and proportion. Given that the van travels 168 miles on 14 gallons of gas, we can find out how much it would need to travel 252 miles. We set up the proportion as follows:
168 miles / 14 gallons = 252 miles / X gallons
To find X (the unknown), we cross multiply:
168 * X = 252 * 14
After solving this equation, we find that X equals 21. Therefore, the van would need 21 gallons to travel 252 miles.
Learn more about ratios and proportions here:https://brainly.com/question/31776433
#SPJ3
Which is an equation in point-slope form for the lines that passes though the points (-1,4) and (3,-4)
I don't know if this is the equation you need. But here it is.
Y - 4 = -2 (x + 1)
how do i determine ordered pairs from a word problem?
Find CH and EH! Quickly please!!
1. Determine the angle, to the nearest degree, of C if tan C = 5.1323
2. Determine the angle, to the nearest degree, of B if cos B = 0.8954
Answer:
C = 79, B = 26 degrees
Step-by-step explanation:
tan C = 5.1323
To find C you use your calculator . Press tan-1 ( or it might be arctan) then the value 5.1323 Then ENTER.
C = 79 degrees to nearest degree.
cos B = 0.8954
B = 26 degrees
The nearest degree, of C =79 degrees
The nearest degree, of B = 26 degrees
tan C = 5.1323
To find C you use your calculator. Press tan-1 ( or it might be arctan) then the value 5.1323 Then
C = 79 degrees to nearest degree.
cos B = 0.8954
B = 26 degrees.
What is the angle of trigonometric functions?
The angle of the trigonometric function is the angle given by the ratio of the trigonometric functions. Trigonometry involves studying the relationship between angles and the sides of a triangle. Angle values range from 0 to 360 degrees. The important angles of trigonometry are 0 °, 30 °, 45 °, 60 °, 90 °, 180 °, 270 °, and 360 °.
The angle at which the vertex is at the origin and one side is on the positive x-axis. Can take positive or negative dimensions and can be larger than 360 °
Learn more about trigonometry here: https://brainly.com/question/24349828
#SPJ2
Wanda started walking along a path 27 seconds before Dave. Wanda walked at a constant rate of 3 feet per second. Dave walked along the same path at a constant rate of 4.5 feet per second. Graph the system of linear equations. How long after Dave starts walking will he catch up with Wanda?
Answer:
Wanda and Dave will catch each other in 54 seconds after Dave starts walking.
Step-by-step explanation:
Let Wanda and Dave catch each other when x be the time after Dave starts walking and y be the distance covered by them
It is given that Wanda started walking along a path 27 seconds before Dave and the constant speed of Wanda is 3 feet per second.
[tex]speed=\frac{distance}{time}[/tex]
[tex]3=\frac{y}{x+27}[/tex]
[tex]y=3(x+27)[/tex]
[tex]y=3x+81[/tex] .... (1)
The constant speed of Dave is 4.5 feet per second.
[tex]4.5=\frac{y}{x}[/tex]
[tex]y=4.5x[/tex] .... (2)
Equate equation (1) and (2).
[tex]3x+81=4.5x[/tex]
[tex]81=1.5x[/tex]
Divide both sides by 1.5.
[tex]\frac{81}{1.5}=x[/tex]
[tex]54=x[/tex]
Therefore, Wanda and Dave will catch each other in 54 seconds after Dave starts walking.
u need question problem 2 to solve problem 3
Answer:
You are correct
Step-by-step explanation:
Start with 1 1/2. This can be made into an improper fraction which is 3/2
Now multiply both top and bottom of 3/2 by 5
(3*5)/(2 * 5) = 15 / 10
16/10 is just slightly bigger than 15/10
The fraction is grather than 1 if the numerator is greater than denominator.
The fraction is less than 1 if the numerator is less than denominator.
The fraction is equal 1 if the numerator is equal the denominator.
----------------------------------------------------------------------------------
[tex]a.\ \text{greater than 1:}\ \dfrac{4}{3},\ \dfrac{7}{5};\ \dfrac{16}{10}\\\\b.\ \text{less than 1:}\ \dfrac{1}{3};\ \dfrac{12}{15};\ \dfrac{3}{10};\ \dfrac{3}{5}\\\\c.\ \text{equal to 1:}\ \dfrac{3}{3}[/tex]
[tex]\dfrac{16}{10}=\dfrac{10+6}{10}=\dfrac{10}{10}+\dfrac{6}{10}=1+\dfrac{6}{10}=1\dfrac{6}{10}=1\dfrac{6:2}{10:2}=1\dfrac{3}{5}\\\\3\text{ is greater than half of 5.}\ \text{Therefore}\ \dfrac{3}{5}>\dfrac{1}{2}.\\\\\text{Therefore}\ \dfrac{16}{10}>1\dfrac{1}{2}.\\\\OTHER:\\\\\dfrac{16}{10}=1\dfrac{6}{10}\\\\1\dfrac{1}{2}=1\dfrac{1\cdot5}{2\cdot5}=1\dfrac{5}{10}<1\dfrac{6}{10}\\\\OTHER\\\\\dfrac{16}{10}=1\dfrac{6}{10}=1.6\\\\1\dfrac{1}{2}=1.5\\\\1.6>1.5\Rightarrow\dfrac{16}{10}>1\dfrac{1}{2}[/tex]
How many zero will be in product (6x5)x the power of 10 3
To solve for the number of zeros in the product of (6x5) x 10³, one should first multiply the whole numbers (6x5) to get 30. Then, append as many zeros as the power of 10, which in this case is 3. So, we append three 0's to 30 which yields 30000. This gives us four zeros in total.
Explanation:The problem (6x5) x 10³ refers to a multiplication involving whole numbers and a power of ten. Our task is to find out how many zeros will be in the resulting product.
Step 1: Multiply the whole numbers. 6x5 equals 30.
Step 2: When multiplying by a power of ten, you add as many zeros to the end of the number as there are in the exponent of ten. So, in this case, as it is power of ten to the power of 3 (10³), we would add three 0's.
Final result: 30000.
So, the product (6x5) x 10³ will have four zeros.
Learn more about Multiplication with Powers of Ten here:https://brainly.com/question/2707839
#SPJ3
Quinn returned home one summer's day to find it sweat-inducingly hot! He turned the air conditioner on and fell asleep. The room's temperature decreased by 0.5 ∘ Celsius each minute, and Quinn woke up 60 minutes later when it was 10 ∘ Celsius.
The initial room temperature was -20 degrees Celsius.
Explanation:The temperature in the room decreases by 0.5 degrees Celsius per minute.
After Quinn slept for 60 minutes, the room's temperature became 10 degrees Celsius.
We can calculate the initial room temperature by subtracting the total decrease in temperature from the final temperature:
Initial temperature = Final temperature + (Rate of temperature decrease * Time)
Initial temperature = 10 + (-0.5 * 60) = 10 + (-30) = 10 - 30 = -20 degrees Celsius
Therefore, the initial room temperature was -20 degrees Celsius.
Final answer:
The final temperature of the room after 60 minutes of the air conditioner being on is -20°C.
Explanation:
In this question, we are given the initial temperature of the room and the rate at which the temperature decreases. We are also given the time period for which the air conditioner was on. We need to determine the temperature after the given time period.
Given: Initial temperature = 10°C, Rate of temperature decrease = 0.5°C/min, Time period = 60 min.
To calculate the final temperature, we need to multiply the rate of temperature decrease by the time period and subtract this value from the initial temperature.
Final temperature = Initial temperature - (Rate of temperature decrease * Time period) = 10°C - (0.5°C/min * 60 min) = 10°C - 30°C = -20°C.
The number of one inch-cubes that will fit into a box that is 9 inches wide, 14 inches long, and one inch high is what?
Point Y is the midpoint of segment XZ. If XY = 2(3x +1) and YZ = 5x + 22, find the value of x. x = 20 x = 24 x = 18 x =11
Answer:
x = 20
Step-by-step explanation:
To find the midpoint of a segment, add the lengths and divide by 2
If y is the midpoint the 2 parts have to be equal.
XY = YZ
2(3x+1) = 5x+22
Distribute
6x+2 = 5x+22
Subtract 5x from each side
6x-5x +2 = 5x-5x+22
x+2 =22
Subtract 2 from each side
x+2-2=22-2
x=20
Answer:
x=20
Step-by-step explanation:
Have a nice day!!!
GIVING 15 POINTS!!!!!!! Jose is going to the store to buy candles. Small candles cost $3 each and large candles cost $5 each. He needs to buy at least 25 candles, and he can spend no more than $120. Which represents a viable solution for the number of small candles, S, and large candles, L, Jose can buy?
A. (6,24)
B.(8,16)
C.(13,8)
D.(18,11)
Answer:
D
Step-by-step explanation:
B,C don't have enough candles and a cost too much.
Answer:
D. (18,11)
Step-by-step explanation:
The last option is the one that makes the most sense for Jose. Jose needs to buy small and large candles. Small candles are $3 while large candles are $5. His budget is $120 and he needs at least 25 candles. If Jose picks option D, he would be able to buy:
18 small candles = 54
11 large candles = 55
Therefore,
18 + 11 = 29 candles
54+ 55 = $109
It costs Edgar $2.65 one way to ride the bus to work. He uses the bus to go to and from work fourdays per week. He buys a bottle of water that costs $1.45 on his way to work each day. How muchdoes it cost Edgar to ride the bus and buy water for one week?
Answer:
Ambitious
In this case, you have to multiply the price of the one way journey ($2.65) by 8 (as this is the number of individual journeys made in one week. It's gives you $21.20. As he has 1 bottle of water at $1.45 each day for four days, you have to multiply these together, giving you $5.80 You then have to add together $21.20 and $5.80, giving you $27. Therefore, it costs Edgar $27 a week
Step-by-step explanation:
Answer:
$27.00
Step-by-step explanation:
To ride the bus to and from work costs
2* 2.65 = 5.30 for 1 day
He rides the bus 4 days a week
4 * 5.30 = 21.20 for 4 days
He buys a bottle of water on the way to work 4 days a week
4 * 1.45 = 5.80 for 4 days
Cost to ride the bus = bus fare for 4 days + water for 4 days
= 21.20 + 5.80
= 27.00
4 (2*2.65+ 1.45) = 27
How many radians is -135°?
Answer:
[tex]-135\degree=-\frac{3}{4}\pi\: radians.[/tex]
Step-by-step explanation:
This question demands that we convert from a degree measure to a radian measure.
To convert from a degree measure to radians, multiply by [tex]\frac{\pi}{180\degree}[/tex].
That is [tex]-135\degree=-135\degree \times \frac{\pi}{180\degree}[/tex].
This can be simplified by canceling out the common factors to get,
[tex]-135\degree=-3\times45\degree \times \frac{\pi}{4\times 45\degree}[/tex].
This will give us,
[tex]-135\degree=-\frac{3}{4}\pi\: radians.[/tex]
Answer:
- 3pi over 4
Step-by-step explanation:
evaluate the following expression 3(7 -5) + 8(9 +2)
Answer:
The answer to your expression is 94.
Step-by-step explanation:
Given Expression -> 3 ( 7 - 5 ) + 8 ( 9 + 2 )
Order of Operations Parenthesis -> 3 ( 2 ) + 8 ( 11 )
Multiplcation Left to Right -> 6 + 8 ( 11 )
Multiplcation Left to Right -> 6 + 88
Addition -> 94
Final answer:
To evaluate the expression 3(7 - 5) + 8(9 + 2), we first solve the expressions within parentheses, then multiply, and finally add the results to get the answer, which is 94.
Explanation:
To evaluate the expression 3(7 - 5) + 8(9 + 2), we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).
Then we add the results of the multiplications: 6 + 88.
So, the expression 3(7 - 5) + 8(9 + 2) evaluates to 94.
The radius of a circle in 3 units
The area and the circumference of the circle are 28.26 square units and 18.84 units
Finding the area and the circumference of the circle
From the question, we have the following parameters that can be used in our computation:
Radius, r = 3 units
The area and the circumference of the circle are calculated using
Area = πr²
Circumference = 2πr
Substitute the known values into the equation
Area = 3.14 * 3² = 28.26
Circumference = 2 * 3.14 * 3 = 18.84
Hence, the area and the circumference of the circle are 28.26 square units and 18.84 units
Question
The radius of a circle in 3 units
Find the area and the circumference of the circle
I need help with this question show steps! Quickly please!
use both points to find the slope
[tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{-13-3}{9-(-3)}[/tex]
[tex]\frac{-16}{12} =\frac{-4}{3} =slope[/tex]
Now, to find b, plug in one of the points in y=mx+b
3=[tex]\frac{-4}{3}[/tex](-3)+b
3=4+b
b= -1
therefore, your final equation should be,
y=[tex]\frac{-4}{3}[/tex]x-1
What are the solutions of -1/2x + 4 = x+1
[tex]-\dfrac{1}{2}x+4=x+1\qquad\text{multiply both sides by 2}\\\\-x+8=2x+2\qquad\text{subtract 8 from both sides}\\\\-x=2x-6\qquad\text{subtract 2x from both sides}\\\\-3x=-6\qquad\text{divide both sides by (-3)}\\\\\boxed{x=2}[/tex]
Question:
1. What is the value of x? Show your work to justify your answer. (2 points)
2. What is the value of the exterior angle? Show your work to justify your answer. (2 points)
Answer:
x=56 and the exterior angle is 116
Step-by-step explanation:
We will call the unknown angle in the triangle y. Angle y and the angle (2x +4) form a straight line so they make 180 degrees.
y + 2x+4 =180
Solve for y by subtracting 2x+4 from each side.
y + 2x+4 - (2x+4) =180 - (2x+4)
y = 180-2x-4
y = 176-2x
The three angles of a triangle add to 180 degrees
x+ y+ 60 = 180
x+ (176-2x)+60 = 180
Combine like terms
-x +236=180
Subtract 236 from each side
-x+236-236 = 180-236
-x = -56
Multiply each side by -1
-1*-x = -56*-1
x=56
The exterior angle is 2x+4. Substitute x=56 into the equation.
2(56)+4
112+4
116
James completed 4 math problems in 6 minutes. At that rate, how many would he be able to complete in 1 hour?
The lengths of two sides of a triangle are 3 and 7. What is one possible length of the third sides
List 3 values that would make this inequality true. 3n < 18
explain how you can use sss sas asa or aas with the definition of congruent triangles to complete a proof
Answer:
SSS - This means side side side. You must have 3 congruent sides in both triangles to prove them congruent.
SAS - This means side angle side. You must have 2 sides and an included angle in both triangles to prove them congruent.
ASA - This means angle side angle. You must have 2 angles and an included side in both triangles to prove them congruent.
AAS - This means angle angle side. You must have 2 angles and a side in both triangles to prove them congruent.
NOTE: included basically means in between.
the values in the table represent a linear function. what is the common difference of the arithmetic sequence x: 1 2 3 4 5 y: 11 25 39 53 67
Answer:
common difference: 14
Step-by-step explanation: You have to find out what number it takes to add to the number to get the following number. ex 11+14=25 25+14=39 etc
Answer:
The common difference of the arithmetic sequence is 14.
Step-by-step explanation:
The arithmetic sequence is defined as
x: 1 2 3 4 5
y: 11 25 39 53 67
The common difference of the arithmetic sequence is
[tex]d=\frac{y_2-y_1}{x_2-x_1}[/tex]
Consider any two points, i.e.,(1,11) and (2,25).
[tex]d=\frac{25-11}{2-1}[/tex]
[tex]d=\frac{14}{1}[/tex]
[tex]d=14[/tex]
Therefore the common difference of the arithmetic sequence is 14.
the ratio of width to length of the united states flag is 10:19. If the width of the flag of Emerson's School is 4 ft , what is the length?
Answer: The length of the united states flag is [tex]2\frac{2}{19}\ feet[/tex]
Step-by-step explanation:
Since we have given that
Ratio of width to length of the united states flag is 10:19
So, Let the length of the united states flag be 10x
Let the width of the united states flag is 19x
As we have the width of the flag of Emerson's school = 4 feet.
According to question,
[tex]19x=4\\\\x=\frac{4}{19}[/tex]
So, our length of the united states flag will be
[tex]10x=10\times \frac{4}{19}\\\\=\frac{40}{19}\\\\=2\frac{2}{19}\ feet[/tex]
Hence, the length of the united states flag is [tex]2\frac{2}{19}\ feet[/tex]
Final answer:
To find the length of the flag, you can set up a proportion using the given ratio of width to length. Solve for the unknown length by cross-multiplying and dividing. The length in feet is found by multiplying the width of Emerson's School flag by the ratio and dividing by 10.
Explanation:
To find the length of the United States flag, you can set up a proportion using the given ratio of width to length. The ratio is 10:19, and the width of Emerson's School flag is 4 ft. First, write the proportion using the length as the unknown value: 10/19 = 4/L. To solve for L, cross-multiply and divide: 10L = 4 * 19. Divide both sides by 10 to find the length:
L = (4 * 19) / 10.
Multiply 4 and 19, then divide by 10 to get the length in feet.
L= 7.6
You take out a cash advance of $2,790.00 on a credit card with a 3.5% cash advance fee and a 13.5% APR. What is the amount due by the end of the month? $2,920.14 $3,277.48 $2,821.39 $2,887.65
Answer:
The answer is $3277.48
Step-by-step explanation:
An Annual Percentage Rate or APR is calculated by taking into account the interest rate on a credit card (or another borrowed sum) and any other charges such as an annual fee or arrangement fee.
So the first step here is to calculate the 3.5% cash advance fee on cash advance of $2790.00.
$2790.00 × 3.5%
2790 × (3.5 ÷ 100)
2790 × 0.035
$97.65
Now APR is calculated on the sum of cash advance and cash advance fee, i.e.,
13.5% × (2790 + 97.65)
13.5% × 2887.65
( 13.5 ÷ 100 ) × 2887.65
0.135 × 2887.65
$389.83
The total amount due at the end of the month is sum of Cash advance, Cash advance fee and APR
$2790 + $97.65 +$389.83 = $3277.48
3.277.48
this a a short answear
what is the cost of renting a car for 4 days at $17.59 per day and driving 237 miles at 19¢ per mile
Answer: $58.40 Multiply 4 times 17.59 and add 237 times 0.19
Final answer:
The total cost of renting a car for 4 days at $17.59 per day and driving 237 miles at 19¢ per mile would be $115.39.
Explanation:
To calculate the cost of renting a car for 4 days:
For the rental cost, we multiply the daily rental rate by the number of days:
Rental cost=Number of days × Daily rental rate
Cost of renting the car for 4 days = 4 days x $17.59 per day = $70.36
Next, to find the cost of driving 237 miles, we multiply the distance driven by the cost per mile:
Cost of driving=Distance driven × Cost per mile
Cost of driving 237 miles at 19¢ per mile = 237 miles x $0.19 = $45.03
Total cost = Cost of renting + Cost of driving = $70.36 + $45.03 = $115.39
I need help figuring this out (#9)
there are 60 minutes in 1 hr.
every 10 minutes the factory makes 15 bears.
so 10+10+10+10+10+10 is 1 hr, and is really 15+15+15+15+15+15 bears, namely 90 per hour.
every day, the factory does that for 8 hours straight, so namely they make 90 * 8 teddy bears, or 720 per day.
let's make a table of bears per day
1 day............................... 720(1)
2 days............................ 720(2)
3 days............................ 720(3)
4 days............................ 720(4)
x days............................ 720(x)
so the amount of bears they make say "A" is per day is A = 720x.
what would be the fewest days to make 5000?
well, whatever 720x is, it has to be either 5000 exactly OR more, not less, then
5000 ⩽ 720x.
and dividing both sides by 720 we get about 6.94 ⩽ x.
so we can conclude that whole days, it'll be 7, since 6.94 is about 7 days, but rounded up to whole days it'll be 7 days.
In a parallelogram WXYZ , W and X are adjacent interior angles the measure of X is three times the measure of W which equation gives the exact measure of W
Answer:
The required equation is [tex]\angle W+3\angle W=180^{\circ}[/tex].
Step-by-step explanation:
Given information: WXYZ is a parallelogram, W and X are adjacent interior angles and measure of X is three times the measure of W.
According to the properties of parallelogram, the two adjacent interior angle are supplementary angle and their sum is 180 degrees.
[tex]\angle W+\angle X=180^{\circ}[/tex] .... (1)
It is also given that the measure of X is three times the measure of W.
[tex]\angle X=3\angle W[/tex]
Substitute this value in equation 1.
[tex]\angle W+3\angle W=180^{\circ}[/tex]
[tex]4\angle W=180^{\circ}[/tex]
[tex]\angle W=45^{\circ}[/tex]
Substitute this value in equation 1.
[tex]\angle W=135^{\circ}[/tex]
Therefore the required equation is [tex]\angle W+3\angle W=180^{\circ}[/tex].
Write an equation to represent the situation.
Mrs. Davis bought one pair of pants and two polo shirts for each of her three children. She had $3.09 left after purchasing the clothing items for her children.
Item : polo shirt pants sweater jacket
Price ($) : $9.99 $12.99 $15.99 $19.99
Let m represent the amount of money Mrs. Davis initially had to spend on each of her three children.
Answer:
3(m - 32.97) = 3.09
Step-by-step explanation:
She started with m money for each of the three children.
A pair of pants costs $12.99. Each polo shirt costs $9.99.
A pair of pants and 2 polo shirts cost
$12.99 + 2 * $9.99 = $12.99 + $19.98 = $32.97
For each child, she had m money and spent $32.97.
For each child, she had m - 32.97 money left.
For the three children, the amount of money left was 3(m - 32.97).
We are told that for the three children, the amount of money left is $3.09.
That means that 3(m - 32.97) must equal $3.09.
The equation is:
3(m - 32.97) = 3.09