Answer:
slope 1
Step-by-step explanation:
change in y over cahnge in x
The slope of the line that passes through the points -10,9 and -12,7 is 1.
What is a slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is defined as the ratio of the rise to the run.
Given that the line passes through the points -10,9 and -12,7. The slope of the line will be calculated as,
The slope of the line is calculated by the formula given below,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 7 - 9 ) / ( -12 + 10)
Slope = ( -2 / -2 )
Slope = 1
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An arrangement of marbles has 12 marbles in the first row and 10 rows in all. In each successive row one marble is added.What is the explicit rule for this situation, and how many marbles will be in the 10th row?Drag and drop the answers into the boxes to match the situation.Explicit ruleNumber of marbles in the 10th rowAn = 11 + 11n, An = 12 + n, An = 11 + n, An = 12 + 10n, 19, 20, 21,
The explicit rule for the number of marbles in 10th row is An= 12+ n-1.
Step-by-step explanation:
Total number of rows = 10 rowsThe number of marbles in the 1st row = 12 marblesOne marble is added to each successive rowTherefore, for the remaining 9 rows out 10 rows ⇒ 9 marbles are added.
The number of marbles in the 10th row = 12+9 = 21 marbles.The explicit rule is An = 12 + n-1For n= 10, then
⇒ A10 = 12 + (10-1)
⇒ A10 =12+9 = 21
Answer:
A(n)=11+n
Step-by-step explanation: took test
What's the common denominator for 3/8 and 3/10?
Which number is farther from 0: -7 or 5
Answer:
-7
Step-by-step explanation
A sports team is throwing an end-of-season party at the fitness club. The costs associated with the party include a $150 flat fee for the room rental and a $14 per person charge for the Italian buffet. An 18% tip must be added to the cost of the food. Express the total cost for the party as a function of the number of people attending
Answer:
[tex]c(x)=150+16.52x[/tex]
With x being the number of people attending the party, and c(x) the cost in dollars.Explanation:
The total cost is comprised of three costs, namely the flat fee for the room rental ($150), the charge person for the Italian buffet ($14 per person), and the tip (18% added to the cost of the food). With this you can build your equation:
[tex]Total\text{ }cost=$150+$14x+18\%\times (14x)[/tex]
Where x respresents the number of people attending the party.
Convert 18% to its decimal form, which is 0.18 and simplify the equation:
[tex]Total\text{ }cost=$150+$14x+0.18\times (14x)=150+14x+2.52x\\ \\ Total\text{ }cost=150+16.52x[/tex]
Hence, calling the function c(x), it is:
[tex]c(x)=150+16.52x[/tex], with x being the number of people attending the party, and c(x) the cost in dollars.
The function which representing the total cost of party is [tex]150+16.52x[/tex]
Total cost :Let us consider that number of people who attending part be x.
The room rental amount is $150.
The charge of the Italian buffet for per person = $14
For x number of people [tex]=14x[/tex]
Since, 18% tip added to the cost of the food.
Tip cost [tex]=14x*\frac{18}{100} =2.52x[/tex]
Total cost of the party [tex]=150+14x+2.52x=150+16.52x[/tex]
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a:b=5:3 find the value of 3a+4b:5a+2b
Yo sup??
a:b=5:3
a/b=5/3
a=5x
b=3x
3a+4b:5a+2b
=15x+12x:25x+6x
=27x:31x
=27:31
Hope this helps.
Answer:
Step-by-step explanation:
a:b=5:3 the value of 3a+4b:5a+2b
(3*5)+(4*3):(5*5)+(2*3)
15+12:25+6
=27:31
15 inches increased by 20%
Answer:
18
Step-by-step explanation:
15 + Percentage increase =
15 + (20% × 15) =
15 + 20% × 15 =
(1 + 20%) × 15 =
(100% + 20%) × 15 =
120% × 15 =
120 ÷ 100 × 15 =
120 × 15 ÷ 100 =
1,800 ÷ 100 =
18
A system of equations consists of two lines. line one passes through (-1,3) and (0,1). the other line passes through (1,4) and (0,2). determine if the pair has no solution, one solution, or an infinite number of solutions.
Final answer:
The two lines have different slopes, with the first line having a slope of -2 and the second line having a slope of 2. Since the slopes are different, the two lines intersect at exactly one point, indicating that there is one solution.
Explanation:
To determine if two lines have no solution, one solution, or an infinite number of solutions, we need to find the slopes of each line. If the slopes are different, the lines intersect at one point, indicating one solution. If the slopes are the same, but they have different y-intercepts, the lines are parallel and there is no solution. If the slopes and y-intercepts are the same, the lines coincide and there are an infinite number of solutions.
For the first line through (-1,3) and (0,1), the slope can be calculated using the formula slope (m) = (y2 - y1) / (x2 - x1). Plugging in the values, we get:
m = (1 - 3) / (0 + 1) = -2
The second line passes through (1,4) and (0,2). Using the same formula:
m = (2 - 4) / (0 - 1) = 2
Since the slopes of the two lines are different, they will intersect at exactly one point, indicating one solution.
The system of equations has one solution since the lines intersect at a single point, confirming a unique solution.
To determine if the system of equations has no solution, one solution, or an infinite number of solutions, we need to analyze the slopes and y-intercepts of the two lines.
Step 1:
Calculate the slope of each line using the formula [tex]\(m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\).[/tex]
For the first line passing through (-1,3) and (0,1):
[tex]\[ m_1 = \frac{{1 - 3}}{{0 - (-1)}} = \frac{{-2}}{{1}} = -2 \][/tex]
For the second line passing through (1,4) and (0,2):
[tex]\[ m_2 = \frac{{2 - 4}}{{0 - 1}} = \frac{{-2}}{{-1}} = 2 \][/tex]
Step 2:
Calculate the y-intercept for each line using the slope-intercept form [tex]\(y = mx + b\)[/tex], where (b) is the y-intercept.
For the first line:
[tex]\[ 1 = -2 \cdot 0 + b_1 \][/tex]
[tex]\[ b_1 = 1 \][/tex]
For the second line:
[tex]\[ 2 = 2 \cdot 0 + b_2 \][/tex]
[tex]\[ b_2 = 2 \][/tex]
Step 3: Compare the slopes and y-intercepts.
Since the slopes are different (-2 for the first line and 2 for the second line), the lines are not parallel. Therefore, they will intersect at exactly one point, resulting in one solution for the system of equations.
Conclusion:
The system of equations has one solution.
What number 0.2% of 50?
Answer:
0.2% of 50 = [tex]0.1[/tex]
Step-by-step explanation:
0.2% of 50
We have to find 0.2% of 50
[tex]50*0.2*\frac{1}{100}[/tex]
[tex]50*\frac{2}{10}* \frac{1}{100}[/tex]
=[tex]\frac{5*2}{100}[/tex]
=[tex]\frac{10}{100}\\\\ \frac{1}{10}\\\\0.1[/tex]
The 0.2% of 50 is 0.1
Answer:
0.1
Step-by-step explanation:
What is the area and perimeter of a heart
Area of the heart is 178.5 cm² and Perimeter is 51.4 cm
Step-by-step explanation:
Step 1:Total area of heart = Area of the square + 2 × area of the semi circle
Step 2:Calculate the area of the square where side = 10 cm
⇒ Area of the square = side² = 10² = 100 cm²
Step 3:Calculate the area of the 2 semicircles where radius = 10/2 = 5 cm
⇒ Area of the semicircle = 1/2 × π × r²
⇒ Area of the 2 semicircles = 2 × 1/2 × π × r² = 3.14 × 5² = 78.5 cm²
Step 4:⇒ Total area of the heart = 100 + 78.5 = 178.5 cm²
Step 5:Calculate the perimeter of the heart = length of 2 sides of the square + 2 × perimeter of the semicircle (since there are 2 semicircles)
⇒ Perimeter = 10 + 10 + 2 × π × r (since perimeter of semicircle = πr)
⇒ Perimeter = 20 + 2 × 3.14 × 5 = 20 + 31.4 = 51.4 cm
The area and Perimeter values of the figure are 178.5 cm² and 51.4 cm
How to calculate the Area and Perimeter of the figureThe area of the square portion
side length²We have;
Area of square = 10² = 100cm²Area of the Semicircle:
radius = 10/2 = 5 cmArea of Semicircle = 0.5×πr²
Area of Semicircle = 39.25
Since, we have 2 similar Semicircles :
2 × 39.25 = 78.5 cm²Total Area = 100 + 78.5 = 178.5 cm²
2.)
The Perimeter of the figure ;
For the 2 Semicircles ;
Perimeter = πrPerimeter = 31.4 cm
Perimeter of the square ;
2 × side length = 2(10) = 20Total Perimeter = 20 + 31.4 = 51.4 cm
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Which function is not linear?
tof
Select one:
O a. f(x)=5/x
O b. f(x)=3x4
O c. f(x)=-7x
O d. f(x)=5
Answer:
f(x)=-7x is the only one linear
Step-by-step explanation:
I'm wondering if this is mistake or not with your question, but if you graph each function, all but one graph is linear.
[tex] {x}^{2} - 5x + 6 = 0 \: \: the \: numbers \: a \: lies \: between \: the \: roots[/tex]
Answer:
x is either 2 or 3
Step-by-step explanation:
[tex] {x}^{2} - 5x + 6 = 0 [/tex]
(x-3)×(x-2) = 0
x- 3 = 0 ➡x = 3
x -2 = 0➡ x = 2
Normal Distribution
Using the graph as a reference, select all
statements that are true about a normal distribution
of data.
Normal distributions are symmetrical about
the mean, m.
The total area under the curve is 100.
Ninety-five percent of the data lies within 1
standard deviation of the mean.
The probability that an event is within 1
standard deviation above the mean is 34%.
All data sets are normally distributed
Answer:
1 and 4.
Step-by-step explanation:
i just did it
find the equation of the line that passes through the point (2,6) and with a slope of 3
using yinterstep form
slope intercept form: y=mx+b
y=3x+6
y=3(2)+6
y=6+6
y=12
Consider the line segment shown on the coordinate plane. What are the coordinates of midpoint AB?
A- (-1, 1/2)
B- (1, 1/2)
C - (1, -1)
D-(1,2)
Three runners run along a 1.5 mile trail one Saturday morning. The graph shows the runners’ locations starting at 9:00 a.m.
who runs fastest?
Caedin runs fastest (he has the highest speed)
Step-by-step explanation:
The question in this problem is "who runs fastest": this means that the problem is asking us "which runner has the greatest speed?"
The speed of a body is a scalar quantity defined as
[tex]v=\frac{d}{t}[/tex]
where
d is the distance covered by the body
t is the time elapsed
In order to calculate the distance covered by each runner, we have to sum the length of all the pieces of motion, regardless of their direction.
From the graph, we observe that:
- Andy moves from x = 0 to x = 1.25 miles, so the distance covered is d = 1.25 miles. Since the time taken is 10 minutes, his speed is
[tex]v=\frac{1.25}{10}=0.125 mi/min[/tex]
- Berta moves from x = 0.5 miles to x = 1.15 miles, so the distance covered is
d = 1.15 - 0.5 = 0.65 miles
The time taken is 10 minutes, so her speed is
[tex]v=\frac{0.65}{10}=0.065 mi/min[/tex]
- Finally, Caeding moves first from x = 1.5 miles to x = 0, so he covers a distance of
[tex]d_1 = 1.5 mi[/tex]
Then he also moves from x = 0 to x = 1.0 miles, so he covers an additional distance of
[tex]d_2=1.0 mi[/tex]
So the total distance is
[tex]d=d_1+d_2=1.5+1.0=2.5 mi[/tex]
And since the time taken is 10 minutes, the speed is
[tex]v=\frac{2.5}{10}=0.25 mi/min[/tex]
Therefore, Caedin has the highest speed.
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From 45 ft to 92 ft?
Answer:47
Step-by-step explanation:
Answer:
47 feet
Step-by-step explanation:
92 feet-45 feet= 47 feet
Answer is 47 feet
A right triangle has a base of 12 yards and a height of 7 yards. If you were to construct a similar but not congruent right triangle with a base of 26 yards, what would be the height of your new triangle rounded to the nearest tenth?
To find the height of a new right triangle similar to the original with a base of 26 yards, use the ratio of sides from the original triangle (7/12) to set a proportion. Solve the proportion to get the new height as 15.2 yards (or 45.5 feet).
Since the triangles are similar, the ratio of their corresponding sides must be the same. To find the height of the new triangle with a base of 26 yards, we set up a proportion using the corresponding sides of the original triangle:
7 yards / 12 yards = height / 26 yards
By cross-multiplying and solving for the unknown height, we get:
7 yards * 26 yards = height * 12 yards
182 y = height * 12 yards
height = 182 / 12 yards
height = 15.1666667 yards
Since 1 yard = 3 feet, we convert the height to feet:
15.1666667 yards * 3 feet/yard = 45.5 feet
Therefore, the height of the new right triangle is approximately 15.2 yards or 45.5 feet when rounded to the nearest tenth of a foot.
What is the measure of angle ABC 4x+2, angle DBE, 5x-13, angle CBE angle ABD
The values are [tex]m\angle \mathrm{ABC}=62^{\circ}[/tex], [tex]m\angle \mathrm{DBE}=62^{\circ}[/tex], [tex]m\angle \mathrm{CBE}=118^{\circ}[/tex] and [tex]m\angle \mathrm{ABD}=118^{\circ}[/tex]
Explanation:
It is given that [tex]\angle \mathrm{ABC}=4x+2[/tex] and [tex]\angle \mathrm{DBE}=5x-13[/tex]
The image having these measurements is attached below:
The angles ABC and DBE are vertically opposite.
Since, vertically opposite angles are equal, [tex]\angle \mathrm{ABC}=\angle \mathrm{DBE}[/tex]
Equating the values, we have,
[tex]\begin{aligned}4 x+2 &=5 x-13 \\2+13 &=5 x-4 x \\15 &=x\end{aligned}[/tex]
Thus, the value of x is 15. Let us substitute x in the equation to find [tex]\angle \mathrm{ABC}[/tex] and [tex]\angle \mathrm{DBE}[/tex]
Thus,
[tex]\begin{aligned}\angle A B C &=4(15)+2 \\&=60+2 \\&=62\end{aligned}[/tex]
Thus, [tex]m\angle \mathrm{ABC}=62^{\circ}[/tex]
Also, substituting x = 15 in [tex]\angle \mathrm{DBE}[/tex]
We have,
[tex]\begin{aligned}\angle DBE &=5(15)-13 \\&=75-13 \\&=62\end{aligned}[/tex]
Thus, [tex]m\angle \mathrm{DBE}=62^{\circ}[/tex]
Hence, the measure of [tex]\angle \mathrm{ABC}=62^{\circ}[/tex] and [tex]\angle \mathrm{DBE}=62^{\circ}[/tex]
To find the measure of [tex]\angle \mathrm{CBE}[/tex] and [tex]\angle \mathrm{ABD}[/tex]:
Since, the angles in a straight line add up to 180°
To find [tex]\angle \mathrm{CBE}[/tex], let us add the angles and equals to 180°
[tex]\angle \mathrm{CBE}+\angle \mathrm{DBE}=180[/tex]
Substituting the value of DBE, we have,
[tex]\angle \mathrm{CBE}+62=180[/tex]
Subtracting both sides by 62,
[tex]\angle \mathrm{CBE}=118[/tex]
Thus, the measure of [tex]\angle \mathrm{CBE}[/tex] is 118°
Since, [tex]\angle \mathrm{CBE}[/tex] and [tex]\angle \mathrm{ABD}[/tex] are vertically opposite, they are equal.
Thus, [tex]\angle \mathrm{ABD}=118[/tex]
Thus, the measure of [tex]\angle \mathrm{ABD}[/tex] is 118°
Hence, the values of the angles are [tex]m\angle \mathrm{ABC}=62^{\circ}[/tex], [tex]m\angle \mathrm{DBE}=62^{\circ}[/tex], [tex]m\angle \mathrm{CBE}=118^{\circ}[/tex] and [tex]m\angle \mathrm{ABD}=118^{\circ}[/tex]
Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x-3)?
Which point is an x-intercept of the quadratic function
f(x) = (x + 6)(x - 3)? THE ANSWER IS D.
15 POINTS!
IMAGE ATACHED
Answer:
Step-by-step explanation:
T think its the 3rd option down
Answer:
b
Step-by-step explanation:
ILL MARK YOU BRAINLIEST IF YOU ANSWER CORRECTLY
Write in scientific notation: 0.0042
A) 42 x 10^-2
B) 4.2 x 10^-4
C)4.2 x 10^-3
D).42 x 10^-4
---------------------------------------------------
write in standard notation:6.12 x 10^3
A)6120
B)612
C) 61,200
D)61.2
Answer:
Scientific Notation:
4.2 × 10^-3
E-Notation:
4.2e-3
Engineering Notation:
4.2 × 10^-3
Real Number:
0.0042
Step-by-step explanation:
What is 3/4 times 8/9 equal
Answer:
2/3
Step-by-step explanation:
photomath bud
i believe the answer is 2/3
Amy has a collection of marbles in three sizes, small, medium, and large. She has five times as many small marbles as medium marbles. The number of large marbles is two more than three times the number of medium marbles.
Let x represent the number of medium marbles Amy has. Write an algebraic expression to represent the number of small marbles she has.
Write an algebraic expression to represent the number of large marbles she has.
If Amy has a total of 560 marbles, how many of each size does she have? Show your work.
Answer:
Amy has 310 small marbles, 62 medium marbles and 188 large marbles.
Step-by-step explanation:
i) Let the number of small marbles be x
ii) let the number of medium marbles be y
iii) let the number of large marbles be z
iv) Amy has 5 times as many small marbles as medium marbles therefore we can write 5y = x
v) the number of large marbles is two more than than three times the number of medium marbles therefore we can write
z = 3y + 2
vi) Amy has a total of 560 marbles therefore we can write x + y + z = 560
vii) Therefore from i) we can write x = 5y
viii) using vii) and v) in vi) we can write
x + y + z = 5y + y + 3y + 2 = 560
ix) Therefore 9y = 558 .... therefore y = [tex]\frac{558}{9}[/tex] = 62
x) Therefore from i) we get x = y [tex]\times[/tex] 5 = 62 [tex]\times[/tex] 5 = 310
xi) Therefore z = (3 [tex]\times[/tex] 62) + 2 = 188
Amy has 310 small marbles, 62 medium marbles and 188 large marbles.
Mark spent $79 on 3 shirts and a package of socks. If each shirts cost $24, how much did the package of socks cost?
Answer:7
Step-by-step explanation:
Gotta get rid of the shirts so 24x3 shirts is 72 and 79-72=7 which is the socks price
Answer:$7
Step-by-step explanation:3 Shirts at $24 each 24×3=$72 then subtract $72- from total cost for shirts and socks $72-$79=$7✔
How many integers between 10 and 50 (inclusive) meet the following conditions? 1. The sum of the digits is odd. 2. The number is a perfect square.
a) 3
b) 4
c) 5
d) 6
There are only a handful of perfect squares in the given range: 16, 25, 36, and 49
The sum of their digits wil be odd if one digit is odd and the other is even, which is the case for 16, 25, and 49. So the answer is A.
There are 5 pennies for every 6 quarters in Ahmed's pocket. Could Ahmed have a total of 30 coins in his pocket? Explain
Ahmed cannot have total of 30 coins in his pocket
Solution:
Given that,
There are 5 pennies for every 6 quarters in Ahmed's pocket
We are asked if Ahmed can have a total of 30 coins in his pocket
From given,
5 pennies for every 6 quarters
Therefore, ratio is:
penny : quarter = 5 : 6
Total = 5 + 6 = 11
Then the total number of coins must be multiple of 11
But 30 is not a multiple of 11
Therefore, Ahmed cannot have total of 30 coins in his pocket
No, Ahmed cannot have a total of 30 coins in his pocket.
Explanation:Yes, Ahmed could have a total of 30 coins in his pocket.
To determine how many quarters and pennies Ahmed could have, we can set up a ratio.
The ratio of pennies to quarters is 5:6.
Let the number of quarters be represented by 6x, where x is a positive integer. Then, the number of pennies would be 5x.
To find out if Ahmed could have a total of 30 coins, we need to solve the equation 6x + 5x = 30.
Combining like terms, we obtain 11x = 30. By dividing both sides of the equation by 11, we find that x = 2.7272 (repeating).
Since x must be a positive integer, we can conclude that Ahmed cannot have a total of 30 coins in his pocket.
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You deposit $7500 in an account that pays 5.2% interest compounded continuously. Find the balance after 10 years.
Answer:$3900
Step-by-step explanation:
If the width of a rectangle is 8 less than the length and the perimeter is 32, find the dimensions of the rectangle
Answer:
length = 12
width = 4
Step-by-step explanation:
Width = w
Length = l
w = l-8
l-8 + l-8 + l + l = 32
4l - 16 = 32
4l = 48
length = 12
width = 4
A metal worker makes a box from a 15inch by 20inch piece of tin by cutting a square with a side length x out of each corner and folding up the sides
a) write expressions for length width and height of the box
b) write a polynomial for the volume of the box
Answer:
a) Length = (20 - 2x) inches
Width = (15 - 2x) inches
b) Volume = (20 - 2x)(15 - 2x)x cubic inches.
Step-by-step explanation:
A metalworker makes a box from 15 inches by 20 inches piece of tin by cutting a square with a side length x out of each corner and folding up the sides.
a) So, the length of the box will become (20 - 2x) inches.
And, the width of the box will become (15 - 2x) inches.
b) The volume of the box will be = (Length × Width × Height)
= (20 - 2x)(15 - 2x)x cubic inches. (Answer)
There are 4000 sheets of paper in 8 reams. Which of the following expresses the ratio of sheets of paper to reams in simplest form?
A.
1 to 500
B.
1:500
C.
4000 to 8
D. 500 to 1
500 : 1 expresses the ratio of sheets of paper to reams in simplest form ⇒ D
Step-by-step explanation:
The given is:
There are 4000 sheets of paperThere are 8 reamsWe need to find the ratio between the sheets of paper to the reams in simplest form
∵ The number of the sheets is 4000
∵ The number of the reams is 8
→ sheet : ream
→ 4000 : 8
to simplify the ratio divide the two terms by the same number
∵ 4000 ÷ 2 = 2000 and 8 ÷ 2 = 4
∵ 2000 ÷ 2 = 1000 and 4 ÷ 2 = 2
∵ 1000 ÷ 2 = 500 and 2 ÷ 2 = 1
∴ 4000 and 8 can be divided by 8 to get the simplest form
of the ratio
→ sheet : ream
→ 4000 ÷ 8 : 8 ÷ 8
→ 500 : 1
∴ The ratio of sheets to reams is 500 : 1
500 : 1 expresses the ratio of sheets of paper to reams in simplest form
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