Answer:
The numbers are 1 and 17
Step-by-step explanation:
The only factors of 17 are 1 and 17 since 17 is a prime number
1*17 =17
1+17 =18
The two numbers that multiply to 17 and add to 18 are 1 and 17.
To find two numbers that satisfy the conditions of multiplying to 17 and adding to 18, we can set up a system of equations based on these criteria.
Let the two numbers be x and y .
1. Set up the equations:
- [tex]\( xy = 17 \)[/tex] (product of the numbers)
- [tex]\( x + y = 18 \)[/tex] (sum of the numbers)
2. Solve the system of equations:
From x + y = 18, express y in terms of x :
[tex]\[ y = 18 - x \][/tex]
Substitute y = 18 - x into [tex]\( xy = 17 \)[/tex]:
[tex]\[ x(18 - x) = 17 \][/tex]
[tex]\[ 18x - x^2 = 17 \][/tex]
[tex]\[ x^2 - 18x + 17 = 0 \][/tex]
3. Find the roots of the quadratic equation:
Use the quadratic formula [tex]\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)[/tex], where a = 1 , b = -18, and c = 17:
[tex]\[ x = \frac{-(-18) \pm \sqrt{(-18)^2 - 4 \cdot 1 \cdot 17}}{2 \cdot 1} \][/tex]
[tex]\[ x = \frac{18 \pm \sqrt{324 - 68}}{2} \][/tex]
[tex]\[ x = \frac{18 \pm \sqrt{256}}{2} \][/tex]
[tex]\[ x = \frac{18 \pm 16}{2} \][/tex]
So, [tex]\( x = \frac{34}{2} = 17 \)[/tex] or [tex]\( x = \frac{2}{2} = 1 \)[/tex].
4. Determine the corresponding y values:
- If x = 17, then [tex]\( y = 18 - 17 = 1 \)[/tex].
- If x = 1 , then [tex]\( y = 18 - 1 = 17 \)[/tex].
Therefore, the two numbers that multiply to 17 and add to 18 are 1 and 17.
The numbers 1 and 17 satisfy the conditions of multiplying to 17 and adding to 18, providing a clear solution based on the given criteria of the problem.
A truck that can carry no more than 6600 lbs is being used to transport refrigerators and upright pianos. each refrigerator weighs 300 lbs and each piano weighs 425 lbs. what is an equation that shows how many refrigerators and how many pianos the truck could carry. will 10 refrigerators and 8 pianos overload the truck?
Answer:
(a). 300r + 425p ≤ 6,600
(b). No, it’s not considered overweight
Step-by-step explanation:
In this question, we are to write an equation that shows the number of refrigerators and pianos the truck could carry.
Let the number of refrigerators be r and the number of pianos be p
By using their individual weights, the equation is as follows;
300r + 425p ≤ 6,600
To the second question, we want to consider if 10 refrigerators and 8 pianos are overload.
To get this, we simply multiply the number of each by their individual weights;
That would be;
300(10) + 425(8) = 3000 + 3,400 = 6,400 lbs
This is not considered overweight as it is less than 6,600 lbs
What is the result of adding 17 to its opposite
The answer is zero (0), when you add any number to it's opposite you always get zero
An ice cream shop sells 6 different flavors, 4 toppings, and 3 types of cones. How many different combinations of two different flavors, one topping, and one cone are possible?
144
120
432
360
not enough information
Answer:
360 combinations
Step-by-step explanation:
To calculate the number of different combinations of 2 different flavors, 1 topping, and 1 cone, we are going to use the rule of multiplication as:
6 * 5 * 4 * 3 = 360
1st flavor 2nd flavor topping cone
Because first, we have 6 possible options for the flavor, then we only have 5 possible options for the 2nd flavor. Then, we have 4 options for the topping and finally, we have 3 options for the cone.
It means that there are 360 different combinations of two different flavors, one topping, and one cone are possible
Coll
4/15 version of 4/7 version of M4T2 Test Review
Created by Meena Frazier
Q1: What is the distance between (2, 3) and (-2, 7)? Round to the nearest tenth, if necessary.
Answer:
The answer to your question is 5.7
Step-by-step explanation:
Data
Point A = (2, 3)
Point B = (-2, 7)
Process
To find the distance between points A and B use the formula of the distance between two points, substitute and simplify.
Formula
dAB = [tex]\sqrt{(x2 - x1)^{2}+ (y2 - y1)^{2}}[/tex]
-Identify wich is the value of x1, y1, x2, y2
x1 = 2 y1 = 3 x2 = -2 y2 = 7
-Substittion
dAB = [tex]\sqrt{(-2 - 2)^{2} + (7 - 3)^{2}}[/tex]
-Simplification
dAB = [tex]\sqrt{(-4)^{2} + (4)^{2}}[/tex]
dAB = [tex]\sqrt{16 + 16}[/tex]
dAB = [tex]\sqrt{32}[/tex]
-Result
dAB = 5.65 ≈ 5.7
Suppose that $2000 is loaned at a rate of 11%, compounded semiannually. Assuming that no payments are made, find the amount owed after 5 years.
Do not round any intermediate computations, and round your answer to the nearest cent.
Answer:
The final value owed will be $3416.29.
Step-by-step explanation:
Since this is a compound interest problem we should use the apropriate formula given bellow:
M = C*(1 + r/n)^(n*t)
Where M is the final amount, C is the initial amount, r is the interest rate, t is the total time and n is the rate at which it is compounded. Since it's semiannually the value of n is 2 and we can use the formula to find the desired value.
M = 2000*(1 + 0.11/2)^(2*5)
M = 2000*(2/2 + 0.11/2)^(10)
M = 2000*(2.11/2)^(10)
M = 3416.29
The final value owed will be $3416.29.
Motor cortex and somatosensory cortex are _____.
A. organized in similar manner adjacent to each other, and are anatomically similar from one person to the next
B. dispersed along the ventral and dorsal, respectively
C. located on the left and right sides, respectively, of the cerebellum
D. located in the hypothalamus and hippocampus, respectively
E. located in the thalamus and hypothalamus, respectively
Answer: A) organized in similar manner adjacent to each other, and are anatomically similar from one person to the next.
The physical organization of the motor cortex and somatosensory cortex, which are located next to one another, is the same in every individual. Hence, Option A is correct.
What is the meaning of cortex?
The brain's cerebral cortex is located on the outside. It looks wrinkled because of the numerous folds on its surface. Numerous deep grooves, or sulci, and elevated regions, or gyri, make up the folds.
These folds increase the surface area of the cerebral cortex, which enables more nerve cells to handle significant amounts of information. A nerve cell's dendrites are the area where a chemical communication from another cell is received. The mass of the brain is roughly divided in half by the cerebral cortex.
There are between 14 billion and 16 billion nerve cells in each of the six layers that make up the cerebral cortex. The brain's gray matter, which is located in the outer layer, is made up of nerve cell bodies, including dendrites, the end of nerves.
Therefore, Option A is correct.
Learn more about cortex from here:
https://brainly.com/question/12993641
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Scientists can measure the depths of craters on the moon by looking at photos of shadows. The length of the shadow cast by the edge of a crater is 500 meters. The angle of elevation of the rays of the Sun is 55∘. Estimate the depth d of the crater to the nearest tenth.
Answer:714.1
Step-by-step explanation:
500 times tan(55)
We can use the tangent function from trigonometry to estimate the depth of the crater. The depth is approximately 714.1 meters when the length of the shadow is 500 meters and the angle of sun elevation is 55 degrees.
Explanation:To solve this problem, we can use trigonometry, specifically the tangent function. The tangent function of an angle in a right triangle is equal to the ratio of the opposite side over the adjacent side. Here, the shadow length of the moon's crater functions as the adjacent side, and the depth of crater is the side opposite to the angle.
So tangent(55°) = depth / 500 meters.
To find the depth, rearrange the equation to multiply both sides by 500: depth = 500 * tangent(55°).
Using a calculator, you'll find that the tangent of 55° is approximately 1.4281. So then your final depth equation would look like: depth = 500 meters * 1.4281. By doing this calculation, we find depth ≈ 714.05 meters, and rounding this to the nearest tenth, we have 714.1 meters. So the estimated depth of the crater is 714.1 meters.
Learn more about Crater Depth Calculation here:https://brainly.com/question/31053220
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X/6.5=0.1820
What is x equal to
Answer:
X = 1.183
Step-by-step explanation:
X/6.5=0.1820
Multiply each side by 6.5
X/6.5 * 6.5=0.1820*6.5
X = 1.183
For a regular 36-gon, what is the sum of measure of each interior angle?
Answer:
170°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2)
Here n = 36, thus
sum = 180° × 34 = 6120°
The size of each interior angle = [tex]\frac{6120}{36}[/tex] = 170°
Final answer:
The sum of the measures of each interior angle of a regular 36-gon is 6120 degrees.
Explanation:
For a regular 36-gon, or a polygon with 36 sides, we can calculate the sum of the measures of the interior angles using the formula ((n - 2) × 180°), where n is the number of sides. So for a regular 36-gon:
((36 - 2) × 180°) = (34 × 180°) = 6120°.
Therefore, the sum of the measures of each interior angle of a regular 36-gon is 6120 degrees.
Express in the form 1 : n 6 : 24
Answer: n=4
Step-by-step explanation: 1:4 = 6:24
A train covers a distance of 70 4/5 km in 1 hour. How much distance will it cover in 3 3/4 hours?
Answer:
the distance travelled in 3 3/4 hours is 37/8 km
what is the percent change of 10 feet to 6 feet
Answer:It would be a decrease of 40 percent
Step-by-step explanation:You go from 10/10 to 6/10 meaning you decrease by 4/10 and 4/10 is the same as 40/100 and anything over 100 is its percent value so you would be going down by 40%
Answer:
40 % decrease or -40%.
Step-by-step explanation:
The decrease is 10 - 6 = 4 feet.
% decrease = (4/10) * 100
= 0.4 * 100
= 40 % decrease.
Circle O is inscribed in square EFGH.
The circumference of circle Ois 20 centimeters.
Which of the following is closest to the perimeter
of square EFGH?
A. 27 cm
B. 24cm
C. 28.5cm
D. 24.5cm
Answer:
D) 25.5 cm
Step-by-step explanation:
Circumference = pi × d
20 = 3.14 × d
d = 6.3694267516
Diameter = length of one side
Perimeter of the square = 4s
4(6.3694267516)
25.4777070064 cm
From the options, closest is 25.5
(a)Nicole has a box of candies and will randomly choose one piece. The odds against choosing a lemon-flavored piece are . What is the probability of choosing a lemon-flavored piece?
Since the odds against choosing the lemon-flavored piece wasn't included, let us now assume that it is 2/5
Answer:
The Probability of choosing a lemon-flavored piece is 5/7
Step-by-step explanation:
Please kindly see the attached files for explanation
Write 0.06 as a fraction in
simplest form.
Answer:
[tex]\frac{3}{50}[/tex]
Step-by-step explanation:
Answer: 6/10
Step-by-step explanation:
the 6 is in the tenth place which means it is by ten
Find the solution by elimination method.
Please Help.
Answer:
I'm newbie here
Step-by-step explanation:
Elimination Method.
4x + 6/y = 15 → step 1
6x - 8/y = 14 → step 2
so,
4x + 6/y = 15 |×6|
6x - 8/y = 14 |×4|
24x + 6/y(6) = 90
24x - 8/y(4) = 56
24x + 36/y = 90
24x - 32/y = 56
____________ _
68/y = 34
68 = 34y
34y = 68
y = 2
subsitution y = 2 to..
4x + 6/y = 15
4x + 6/2 = 15
4x + 3 = 15
4x = 12
x = 3
So, for x is 3, and for y is 2
Answer:
x = 3, y = 2
Step-by-step explanation:
Multiply equation 1 by -6
-24x - 36/y = -90
Multiply equation 2 by 4
24x - 32/y = 56
Add the two equations:
-36/y - 32/y = -34
-68/y = -34
y = -68/-34
y = 2
4x + 6/2 = 15
4x = 15 - 3
4x = 12
x = 3
In a race that consisted of three parts the cycling part was 12 1/2 miles long the running part of the race was won for the distance of the cycling parking asking part of the race was won half the distance of the running part what was the entire distance in miles of the raie
Complete question is;
In a race that consisted of three parts, the cycling part was 12 1/2 miles long. The running part of the race was 1/4 the distance of the cycling part. The kayaking part of the race was 1/2 the distance of the running part. What was the entire distance, in miles of the race?
Answer:
Total distance of race = 17.1875 miles
Step-by-step explanation:
The 3 parts of the race are; cycling, running and kayaking.
The cycling distance was; 12½ miles
We are told that the running part was ¼ of the cycling distance. Thus;
Running distance = ¼ x 12½ = ¼ x 25/2 = 25/8 miles
Lastly, we are told that the kayaking part was ½ the distance of the running part. Thus;
Kayaking distance = ½ x 25/8 = 25/16
Thus,total distance of race = cycling distance + running distance + kayaking distance = 12½ + 25/8 + 25/16 = 17.1875 miles
A driver is currently at an elevation of -350 feet write an absolute value statement to express the drivers distance in feet from sea level then interpret the results written the context of the situation
Answer:
[tex]d = |h - 0\,ft|[/tex], The driver is 350 feet below sea level.
Step-by-step explanation:
The distance of the driver from the sea level is given by the following expression:
[tex]d = |h - 0\,ft|[/tex]
[tex]d = |-350\,ft-0\,ft|[/tex]
[tex]d = |-350\,ft|[/tex]
[tex]d = 350 \,ft[/tex]
The driver is 350 feet below sea level.
Answer:
Driver is 350 Below sea Level
Step-by-step explanation:
Driver has Elevation of -350 meters, negative indicates below sea level.
Therefore it can be inferred that the driver is 350 below sea level.
x² - 12x + 27? what is the factored form of this polynomial
Answer:
( x - 9 )( x - 3 )
Step-by-step explanation:
plz give brainliest
Saul decides to use the IQR to measure the spread of the data. Saul calculates the IQR of the data set to be 27 .
Saul asks Jasmine to check his work. Saul copies the data in numerical order from least to greatest for Jasmine.
25,30,50,50,50,50,56,n,250
What is the value of n that will make the IQR of the data set equal to 27?
N equals 78
The equation: (56+n)/2 - 40=27
Add 40 to 27=67
Multiply everything by 2 leaving you with 56+n=134
Subtract 56 from 134
Leaves you with n=78
If you plug it in you would get 67-40, which equals 27
The current cost of gourmet coffee Is $14 per pound At the corner market the cost has increased 10% Per year over the past few years What did the coffee cost 2 years before ?
Answer:
$11.57
Step-by-step explanation:
Let's call the price of the coffee two years ago by X.
The price increased 10% per year (that is, the price is multiplied by 1+0.1=1.1) over two years, so the current price is:
X * 1.10 * 1.10 = X * 1.21
If the current price is $14, we have that:
X * 1.21 = 14
X = 14/1.21 = 11.57
The price of the coffee two years ago was $11.57
4) A light is on the top of a 12 ft tall pole and a 5 ft 6 in tall person is walking away from the pole at a rate of 2 ft/sec. a. At what rate is the tip of the shadow moving away from the pole when the person is 25 ft from the pole? b. At what rate is the tip of the shadow moving away from the person when the person is 25 ft from the pole?
Final answer:
The rate at which the tip of the shadow is moving away from the pole when the person is 25 ft from the pole is 0 ft/sec. The rate at which the tip of the shadow is moving away from the person when the person is 25 ft from the pole is 0 ft/sec.
Explanation:
To solve for the rates at which the tip of the shadow is moving away from the pole and from the person, we can use similar triangles and related rates. Let's solve each part step by step:
a. Rate the tip of the shadow is moving away from the pole:
We have a right triangle formed by the pole, the person, and the tip of the shadow. Let x be the distance between the person and the tip of the shadow.
Since the person is moving away from the pole at a rate of 2 ft/sec, dx/dt = 2 ft/sec.
Using the similar triangles, we have:
(12 ft + 5.5 ft) / x = 12 ft / (x + 25 ft)
Simplifying the equation gives:
17.5x + 437.5 = 12x + 300
5.5x = 137.5
x = 25 ft
Now, let's differentiate both sides of the equation with respect to time t:
17.5 (dx/dt) = 12 (dx/dt) + 0
17.5 (dx/dt) - 12 (dx/dt) = 0
5.5 (dx/dt) = 0
dx/dt = 0 ft/sec
So, the rate at which the tip of the shadow is moving away from the pole when the person is 25 ft from the pole is 0 ft/sec.
b. Rate the tip of the shadow is moving away from the person:
Using the similar triangles, we have:
(12 ft + 5.5 ft) / x = 5.5 ft / 25 ft
Simplifying the equation gives:
17.5x = 137.5
x = 7.857 ft
Now, let's differentiate both sides of the equation with respect to time t:
17.5 (dx/dt) = 5.5 (dx/dt) + d(7.857)/dt
12 (dx/dt) = d(7.857)/dt
dx/dt = (d(7.857)/dt) / 12
dx/dt = (0 ft/sec) / 12
So, the rate at which the tip of the shadow is moving away from the person when the person is 25 ft from the pole is 0 ft/sec.
You are planning to use PERT for planning of your project. A task has pessimistic estimate of 24 days, most likely estimate of 15 days and optimistic estimate of 12 days. What is the mean using the PERT technique?
a.18 days
b.25.5 days
c.15 days
d.16 days
Answer: d.16 days
Step-by-step explanation:
Hi, using PERT technique we can calculate the mean by applying the next formula:
Mean = (a + 4m + b)/6
Where:
a = optimistic time
m = most likely time
b = pessimistic time
Replacing with the values given:
Mean = (12 +4 (15) + 24)/6
Solving
m = (12+ 60+24)/6
m= 96/6
m = 16 days
Feel free to ask for more if needed or if you did not understand something.
How many faces dose a triangular prisim have?
Answer:
the answer is 5
Step-by-step explanation:
YW
Answer:
There are 5 faces in a triangular prism
I hope this help. If I'm wrong/made any mistakes please let me know so that I can learn from it!
. A random sample of 80 jars of grape jelly has a mean weight of 568 g, with a standard deviation of 48.28 g. Construct a 99% confidence interval for , the true weight of a jar of jelly.
Answer:
The 99% confidence interval is (553.7523, 582.2477)
Step-by-step explanation:
The formula for the confidence interval is
[tex]CI=\bar{x}\pm z\frac{s}{\sqrt{n}}[/tex]
Where:
s = Standard deviation
z = t[tex]_{df}[/tex] since the population variance is unknown
df = Degrees of freedom
n = Sample count
Which gives
[tex]568 \pm t_{79}(0.05\%) \frac{48.28}{\sqrt{80} }[/tex]
= 568 [tex]\pm[/tex] 2.64×5.4
(553.7523, 582.2477)
That is there is a 99% chance that the mean weight of a jar of jelly is
553.75 < μ < 582.25.
The coastline of Canada stretches about 202 080 km. The British Columbia portion of the coastline is about 2/15 of the total coastline of Canada. How long is the coastline of British Columbia?
Given Information:
Coastline of Canada = 202080 km
Coastline of British Columbia = 2/15 of Coastline of Canada
Required Information:
How long is the coastline of British Columbia = ?
Answer:
Coastline of British Columbia is 26944 km long
Step-by-step explanation:
We are given the length of Coastline of Canada that is 202080 km
We also know that Coastline of British Columbia is 2/15 of the Coastline of Canada.
So,
Coastline of British Columbia = (2/15)*202080
Coastline of British Columbia = 26944 km
Therefore, the Coastline of British Columbia is about 26944 km.
Given triangle EFG shown below, state the value of the cosine of angle G the hypotenuse which is also side EG = 53 side EF = 45 side GF = 28 F is a right triangle
Answer:
[tex]cos(G)=\frac{28}{53}[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
In the right triangle EFG
[tex]cos(G)=\frac{GF}{EG}[/tex] ----> by CAH (adjacent side divided by the hypotenuse)
substitute the given values
[tex]cos(G)=\frac{28}{53}[/tex]
12.6 is what percent of 42?
What is the slope of the line that passes through the points (1, 2) and (-2, -13)?
Answer:
5
Step-by-step explanation:
To find the slope given two points, we use the formula
m= (y2-y1)/(x2-x1)
= (-13-2)/(-2 -1)
= -15/-3
=5
Answer:
The slope is 5
Step-by-step explanation:
Δ means the change in
slope = m = Δy/Δx = [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{2-(-13)}{1-(-2)}[/tex] = 15/3 = 5/1 = 5
Slope = 5
Flaky pastry can be made using flour and fat in the ratio 4 : 3. Jake makes some flaky pastry using 90 grams of fat. What weight of flour does he use?
Answer:
He use 120 grams of flour.
Step-by-step explanation:
Given:
Flaky pastry can be made using flour and fat in the ratio 4 : 3. Jake makes some flaky pastry using 90 grams of fat.
Now, to find the weight of flour he use in making flaky pastry.
Let the weight of flour be [tex]x.[/tex]
Weight of fat = 90 grams.
The ratio of flour and fat used in making flaky pastry is 4 : 3.
As, 4 is equivalent to 3.
Thus, [tex]x[/tex] is equivalent to 90.
Now, to solve using cross multiplication method:
[tex]\frac{4}{3} =\frac{x}{90} \\\\By\ cross\ multiplying\ we\ get:\\\\360=3x\\\\Dividing\ both\ sides\ by\ 3\ we\ get:\\\\120=x\\\\x=120\ grams.[/tex]
Therefore, he use 120 grams of flour.