Answer:
x>-4
Step-by-step explanation:
-6x + 5 – 4x < 45
Combine like terms
-10x + 5 < 45
Subtract 5 from each side
-10x + 5 – 5 < 45-5
-10x< 40
Divide each side by -10, remembering to flip the inequality
-10x/-10 >40/-10
x >-4
Point P is on segment AB such that AP:PB is 4:5. If A has coordinates (4,2), and B has coordinates (22,2), determine and state the coordinates of P.
The coordinates of P are (12, 2).
Solution:
Given data:
[tex](x_1, y_1)= A (4, 2)[/tex] and [tex](x_2, y_2)=B(22, 2)[/tex]
P(x, y) is the point on the line segment AB.
AP : PB = m : n = 4 : 5.
That is m = 4 and n = 5.
Section formula:
[tex]$P(x, y)=\left(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n}\right)[/tex]
[tex]$P(x, y)=\left(\frac{4\times 22 + 5\times 4}{4+5}, \frac{4\times 2 + 5\times 2}{4+5}\right)[/tex]
[tex]$P(x, y)=\left(\frac{88 + 20}{9}, \frac{8+10}{9}\right)[/tex]
[tex]$P(x, y)=\left(\frac{108}{9}, \frac{18}{9}\right)[/tex]
P(x, y) = (12, 2)
Hence the coordinates of P are (12, 2).
Explain how the product 1\2 ×1\3 relates to the model
Final answer:
The product 1/2 x 1/3 equals 1/6, which can be visualized using a two-dimensional model where a rectangle is divided into halves and then thirds, resulting in 1/6 of the total area.
Explanation:
The product 1/2 times 1/3 can be understood through a two-dimensional model. If you take a rectangle and divide it into 2 equal parts, taking 1/2 of the whole, and then divide one of those halves into 3 equal parts, taking 1/3 of that half, you will have 1 out of the 6 equal parts of the original rectangle, which is 1/6, the product of 1/2 and 1/3.
To visualize this process, imagine a bar or a piece of chocolate that is first divided down the middle, and then one of those halves is divided into 3 equal pieces.
Taking one of these smaller pieces represents 1/6 of the original chocolate bar. In mathematical terms, when we multiply fractions, we multiply the numerators ( 1 times 1) to get the numerator of the product, and the denominators (2 times 3) to get the denominator of the product, yielding 1/6 as the answer. This demonstrates the first partial product principle, where in this case the third vector (1/3) is multiplied by the scalar product of 1/2.
An engineer scale model shows a building that is 3 inches tall. If the scale is 1 inch = 600 feet, how tall is the actual building in feet ?
Answer:
1800ft tall
Step-by-step explanation:
What is the slope of (3, 3) and (-6, -3)
Answer:
m=2/3
Step by Step Explanation:
x1,y1= 3,-6
x2,y2=3,-3
m={-3-3} (Fraction Form)
{-6-3}
Refine:
m={2}{3}
Answer:
Slope = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Step 1: Identify x1, x2, y1, y2
Slope Formula: [tex]\frac{y2-y1}{x2-x1}[/tex]
(x1, y1) -> (3, 3)
(x2, y2) -> (-6, -3)
Step 2: Plug into the formula
Slope = [tex]\frac{-3 - 3}{-6 - 3}[/tex]
Slope = [tex]\frac{-6}{-9}[/tex]
The top negative sign and the bottom negative sign cancel to make a positive number.
Slope = [tex]\frac{-6}{-9}[/tex]
Slope = [tex]\frac{6}{9}[/tex]
The top and bottom can be simplified by a factor of 3.
Slope = [tex]\frac{6}{9}[/tex]
Slope = [tex]\frac{6/3}{9/3}[/tex]
Slope = [tex]\frac{2}{3}[/tex]
Answer: Slope = [tex]\frac{2}{3}[/tex]
Eliza bought a meal that cost $12.00. She tipped the waiter 25%of that amount . How much was the tip ?
The question is about calculating a tip which is 25% of a meal cost of $12.00. The tip is calculated by multiplying the total cost of the meal by the tip percentage, converted into decimal form. The answer is $3.00.
Percentage is a mathematical concept used to express a portion of a whole as a fraction of 100. It is a versatile tool in various fields, including finance, statistics, and everyday calculations. To calculate a percentage, you divide a part by the whole and then multiply by 100. Percentages are commonly used to represent proportions, express changes, and compare values, making them vital for analyzing data, understanding discounts, and determining growth rates. In essence, percentages simplify the representation of relative quantities and are fundamental in both practical and academic mathematics.
The subject of the question is Mathematics, specifically Percentage. The student is being asked to calculate 25% of $12.00, which is the cost of Eliza's meal. To calculate the tip, multiply the total meal cost by the percentage of the tip. Here's how we can do it:
Convert the percentage into a decimal: 25% is equal to 0.25 in decimal form.Multiply the total cost of the meal by the decimal: $12.00 * 0.25 = $3.00So the tip Eliza left for the waiter was $3.00.
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10. The length of the hypotenuse of a 30°-60°-90° triangle is 16. What is the perimeter?
64+8 square root 3
24+8 square root 3
16+64 square root 3
8+24 square root 3
Answer:
24+8 square root 3
Step-by-step explanation:
The ratio is x : x radical 3 : 2x
hypotenuse= 2x= 16
x =8
x square root 3 = 8 square root 3
16+8=24
I need help with problem 27
Answer:
0+7-4=3
Step-by-step explanation:
They started with none, hence the 0. "Gained" typically means addition, so you add seven. "Lost" is a signal word for subtraction, so subtract zero. It comes out to 4.
Is (1, 10) a solution to this system of equations?
y = 9x + 1
y = x + 9
Final answer:
The point (1, 10) satisfies both given equations when substituting x with 1 and y with 10, therefore it is a solution to the system of equations.
Explanation:
To determine if the point (1, 10) is a solution to the given system of equations, we must substitute x with 1 and y with 10 into each equation and see if the equations hold true.
For the first equation y = 9x + 1, substituting gives us:
10 = 9(1) + 1
10 = 9 + 1
10 = 10
This is true, so (1, 10) satisfies the first equation.
For the second equation y = x + 9, substituting gives us:
10 = 1 + 9
10 = 10
This is also true, so (1, 10) satisfies the second equation as well.
Since (1, 10) satisfies both equations, it is indeed a solution to the system of equations.
Let's determine if the point (1, 10) is a solution to the given system of equations by substituting the x and y values from the point into both equations.
The system of equations is:
1. \( y = 9x + 1 \)
2. \( y = x + 9 \)
We are given the point (1, 10), where x = 1 and y = 10.
We'll substitute these values into each equation to check for equality.
First, let's substitute x = 1 and y = 10 into the first equation:
\( y = 9x + 1 \) becomes \( 10 = 9(1) + 1 \), simplifying to \( 10 = 9 + 1 \), which further simplifies to \( 10 = 10 \).
The first equation is satisfied with x = 1 and y = 10.
Next, we'll substitute x = 1 and y = 10 into the second equation:
\( y = x + 9 \) becomes \( 10 = 1 + 9 \), simplifying to \( 10 = 10 \).
The second equation is also satisfied with x = 1 and y = 10.
Since the point (1, 10) satisfies both equations, we can conclude that (1, 10) is indeed a solution to the given system of equations.
Solve the equation:
x² – 2x² – 15x=0
Answer: x=0, x²=0
Step-by-step explanation:
Answer:
x=3 and x=5/2
Step-by-step explanation:
The prism is completely filled with 1750 cubes that have edge length of 15 ft.
What is the volume of the prism?
The volume of the prism = 14 ft³
Solution:
Number of cubes in the prism = 1750
Edge length of each cube (a) = [tex]\frac{1}{5}[/tex] ft
To find the volume of each cube:
Volume of each cube = a³
[tex]$=\left(\frac{1}{5} \right)^3[/tex]
Volume of each cube [tex]$=\frac{1}{125} \ \text{ft}^3[/tex]
To find the volume of the prism:
Volume of the prism = Volume of each cube × Number of cubes
[tex]$=\frac{1}{125} \ \text{ft}^3\times 1750[/tex]
= 14 ft³
The volume of the prism = 14 ft³
3/4, find the surface area
Answer:
1,350 cm^2
Step-by-step explanation:
It's a cube so all faces/bases are the same.
15 × 15 = 225
225 × 6 = 1,350
What’s the area of this?
Answer:
25.5
Step-by-step explanation:
[tex]A_{t} = \frac{1}{2} * (6 + 3) * (5 + 2) = 31.5\\\\A_{r} = 2 * 3 = 6\\\\A = A_{t} - A_{r} = 31.5 - 6 = 25.5[/tex]
a ladder 20 feet long leans against a building, forming an angle of 71° with the level ground. To the nearest foot, how high up the wall of the building does the ladder touch the building?
The wall is 18.79 feet high from the ground.
Data;
Length of ladder = 20ftangle of elevation = 71 degreeslength of the wall = ?Trigonometric RatioTo solve this problem, we need to use trigonometric ratio SOHCAHTOA in which we can find the missing side.
if we draw an illustration of this question, we would get
hypothenuse = 20ftangle = 71 degreesopposite = ?Using the sine angle ratio,
[tex]sin\theta=\frac{opposite}{hypothenuse}\\sin71=\frac{x}{20}\\ x=20sin71\\x=18.79ft[/tex]
The wall is 18.79ft high
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To calculate the height the ladder reaches on the wall, we use sine function and find it to be approximately 19 feet.
To find out how high up the wall the ladder touches the building when a 20-foot ladder forms an angle of 71° with the level ground, we can use trigonometry. Specifically, the sine function relates the opposite side to the hypotenuse in a right triangle. The ladder represents the hypotenuse, and the height reached on the wall is the opposite side.
Using the formula:
sin(angle) = opposite/hypotenuse
For this problem:
sin(71°) = height / 20 feet
Now we solve for height:
height = 20 feet × sin(71°)
We can calculate this using a calculator:
height ≈ 20 feet × 0.945
height ≈ 18.9 feet
To the nearest foot, the ladder reaches approximately 19 feet up the wall.
What are period and amplitude for the function
PLEASE ANSWER BOTH QUESTIONS I WILL GIVE You the
Answer: Period: 4. Amplitude: 3
Step-by-step explanation: The period is how long it takes for one cycle of the function (one up and down). In this graph, one cycle ends at 4.
The amplitude is how far away the extremes of the graph are from the midline. This graph is a total of 6 units tall, making the amplitude 3. (I usually find total graph height and divide by 2.)
Which cone has a volume of 24pie cm³? Need this done asap!
Step-by-step explanation:
volume of a cone is given by
[tex] \frac{\pi {r}^{2}h }{3} [/tex]
1st cone,
B= 25π cm²
πr²=25π
r²=25
r=5
Here, volume = π(5)²×3.5/3
=29.1π cm³
2nd cone,
r=3cm
Here, volume = π(3)²×6.5/3
= 19.5π cm³
3rd cone,
r= 4cm
Volume = π(4)²×4.5/3
=24π cm³
4th cone,
B=4π cm²
r²=4
r=2
volume = π(2)²×7.5/3
= 10π cm³
So, the third cone has vol 24π cm³
2. The number of years that Elijah has been on the soccer team is 2 less than 5 times the number of years that Deaundre
has. In total, the boys have been on the soccer team for 10 years. How long has Elijah been on the soccer team?
The Elijah have been on the soccer team for 8 years.
Step-by-step explanation:
Let,
The number of years that Deaundre have been on the soccer team "x".The number of years that Elijah have been on the soccer team = 2 less than 5 times the number of years that Deaundre.The number of years that Elijah have been on the soccer team = 5x - 2.Given that,
The boys have been on the soccer team for 10 years.
Number of years of Deaundre + Number of years of Eliijah = 10 years.
x + (5x-2) = 10
Keep x terms on one side and constants on another side to solve for x value :
6x = 10+2
6x = 12
x = 12/6
x = 2
The Deaundre have been on the soccer team for 2 years.
Substitute x=2 in (5x-2) to find the number of years of Elijah,
5(2)-2 = 8 years.
Therefore, the Elijah have been on the soccer team for 8 years.
Which of the following statements are true of the parabola shown?
1. It has a directrix of x = -4.
2. It opens to the left.
3. It has a vertex at the origin.
4. The axis of symmetry is the y-axis.
5. It has a focus at (4, 0).
True statements are:
It has a directrix of x = - 4.It has a focus at (4, 0).Step-by-step explanation:
We have the following statements to check on whether it's right or wrong:
1. It has a directrix of x = -4:
According to figure , parabola directrix is at -4 i.e. at x = -4 , Therefore this statement is true!
2. It opens to the left:
In figure, Parabola opens to right not left , Therefore this statement is wrong!
3. It has a vertex at the origin:
Vertex of Parabola is at what points not shown in figure. Therefore this statement cannot be confirmed as true.
4. The axis of symmetry is the y-axis:
Axis of symmetry for above parabola is x-axis as it cuts parabola into two equal halves , y-axis doesn't do this ! Therefore this statement is wrong!
5. It has a focus at (4, 0):
Parabola focus is at [tex]F(4,0)[/tex] on x-axis . And so, Therefore this statement is true!
1. True it has a directrix of x = -4; 2. False it opens to the left; 3. False it has a vertex at the origin; 4. True the axis of symmetry is the y-axis; 5. True it has a focus at (4, 0).
In this parabola, the given statements can be evaluated as follows:
1. Directrix : The given directrix is x = -4. The directrix of a parabola is a vertical line that is equidistant from all points on the parabola. In this case, the directrix is to the left of the origin, so it's possible that the parabola opens to the right.
2. Direction of Opening : The parabola cannot open to the left because the given directrix is to the left of the origin. Parabolas open towards their focus or away from their directrix. Since the directrix is to the left, the parabola opens to the right.
3. Vertex : The vertex is the point where the parabola changes direction. The origin (0, 0) is not the vertex in this case, as the parabola opens to the right.
4. Axis of Symmetry: The axis of symmetry is a vertical line that passes through the vertex and divides the parabola into two equal halves. Since the parabola opens to the right, its axis of symmetry is the y-axis.
5. Focus : The focus is a point inside the parabola that is equidistant to the vertex and the directrix. The focus should indeed be to the right of the vertex, and at a distance of 4 units, based on the given directrix
x = -4.
Mathematically, the equation of a parabola that opens to the right, with its vertex at the origin, is of the form:
[tex]\[x^2 = 4py\][/tex]
Given that the directrix is x = -4, the distance from the origin to the directrix is 4 units. So, the equation becomes:
[tex]\[x^2 = 16y\][/tex]
The focus is at a distance of p units from the vertex, where [tex]\(p = 4\)[/tex], so the focus is at (4, 0).
In summary, the given parabola opens to the right, has a vertex at the origin, its axis of symmetry is the y-axis, and its focus is at (4, 0), with a directrix of x = -4.
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About 8% of the U.S. population catches the flu each season. Assuming everyone has equal probability of catching the flu, about what are the odds of catching the flu in a given season?
1 in 8
1 in 12
1 in 18
1 in 80
Answer:
The correct answer is B. 1 in 12.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Percentage of the U.S. population that catches the flu each season = 8%
8% = 8/100
2. Assuming everyone has equal probability of catching the flu, about what are the odds of catching the flu in a given season?
Let's review together each of the possible answers given:
A. 1 in 8 = 1/2 = 0.125 = 12.5%, this is not the percentage given.
B. 1 in 12 = 1/12 = 0.083 = 8.3%, if we round to 8%, this is the percentage given.
C. 1 in 18 = 1/18 = 0.056 = 5.6%, this is not the percentage given.
D. 1 in 80 = 1/80 = 0.0125 = 1.25%, this is not the percentage given.
The correct answer is B. 1 in 12.
what is y= -3/2x + 4 in standard form
Answer:
2y + 3x = 8
Step-by-step explanation:
Step 1: Add 3/2x to both sides
y + 3/2x = -3/2x + 4 + 3/2x
y + 3/2x = 4
Step 2: Multiply both sides by 2
(y + 3/2x)*2 = 4*2
2y + 3x = 8
Answer: 2y + 3x = 8
Evaluate n/6 + 2 when n = 12
Answer:
[tex]\frac{(12)}{2} +2\\6+2=8\\8[/tex]
Hope this helped
Answer:
4
Step-by-step explanation:
n/6 + 2 when n = 12
n/6 + 2
Replace n with 12
Therefore,
n/6 + 2 = 12/6 + 2
= 2+2
=4
I hope this was helpful, please rate as brainliest
what is the unit price of a 16-ounce box of cereal that sells for $2.48?
Answer:
0.155
Step-by-step explanation:
Answer:
$0.15 per ounce
Step-by-step explanation:
2.48/16 = 0.155
HELP PLEASE !!!!!!!!!!!!!!
A triangular prism has a volume of 350 cubic meters. If the dimensions are tripled what is the volume of the new
prism?
Answer:
9450 m³
Step-by-step explanation:
(S1/S2)³ = V1/V2
3³ = V1/350
New Volume = 27 × 350
= 9450 m³
The graphed line can be expressed by which equation?y+2=23(x+2) y−2=34(x−1) y−1=−34(x−2) y−2=34(x−2)
For this case we have that by definition, the equation of a line in the point-slope form is given by:
[tex]y-y_ {0} = m (x-x_ {0})[/tex]
Where:
[tex](x_ {0}, y_ {0}):[/tex]It is a point through which the line passes
m: It is the slope of the line
According to the graph we have that the line goes through the following points:
[tex](x_ {1}, y_ {1}) :( 4,2)\\(x_ {2}, y_ {2}): (- 2, -2)[/tex]
We found the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-2-2} {- 2-4} = \frac {-4} {- 6} = \frac {2} {3}[/tex]
We choose a point:
[tex](x_ {0}, y_ {0}): (-2, -2)[/tex]
The equation of the line is:
[tex]y - (- 2) = \frac {2} {3} (x - (- 2))\\y + 2 = \frac {2} {3} (x + 2)[/tex]
ANswer:
[tex]y + 2 = \frac {2} {3} (x + 2)[/tex]
Option A
ted, sam, and jack can do a piece of work in 15, 12 and 20 days respectively. they started the work together, but jack left after 2 days. in how many days will the remaining work be completed by ted and sam?
Answer:
the answer was 24
Step-by-step explanation:
A spinner with four equal quadrants labeled A, B, C, and D is spun. What is the theoretical probability of the spinner NOT landing on the letter C?
Answer:
3/4, 75% chance
Step-by-step explanation:
you have four in total, three of which are not c, so you have a three out of four chance of NOT picking c. 3/4 as a percentage is 75%
Answer:
25%
Step-by-step explanation:
On MobyMax its 25%
The total cost of a boat rental includes the price per hour plus the cost of one full tank of gas. The table below represents the boat rental fees.
No. Of Hours 2 4 6 8
Rental Fee $92$150$208 $266
What is the cost for a full tank of gas?
A. $58
B. $266
C. $34
D. $29
Answer:
C. $34
Step-by-step explanation:
$58 is added every 2 hours so you just subtract that from $92 since $92 is the price of 2 hours and a full tank of gas.
$9.60 for 4 pounds i need help
hey bro, what do you mean by this question?
do you want to convert 9.60 dollars into pounds? if so then right now the exchange rate for dollars to pounds is 0.80. So you will do this (0.80)(9.60)=7.68
If you mean pounds like how much something weighs then all you need to do is just divide 9.60 by 4 = 2.4 which means $2.4 per pound.
Solve the system of linear equations using elimination. −2x − y = 3 −9x − y = 17
A) (2, 1) B) (2, −1) C) (−2, 1) D) (−2, −1)
Answer:
x = -2 , y = 1
Step-by-step explanation:
Solve the following system:
{-2 x - y = 3 | (equation 1)
-9 x - y = 17 | (equation 2)
Swap equation 1 with equation 2:
{-(9 x) - y = 17 | (equation 1)
-(2 x) - y = 3 | (equation 2)
Subtract 2/9 × (equation 1) from equation 2:
{-(9 x) - y = 17 | (equation 1)
0 x - (7 y)/9 = -7/9 | (equation 2)
Multiply equation 2 by -9/7:
{-(9 x) - y = 17 | (equation 1)
0 x+y = 1 | (equation 2)
Add equation 2 to equation 1:
{-(9 x)+0 y = 18 | (equation 1)
0 x+y = 1 | (equation 2)
Divide equation 1 by -9:
{x+0 y = -2 | (equation 1)
0 x+y = 1 | (equation 2)
Collect results:
Answer: {x = -2 , y = 1
Answer:
C) (−2, 1)
Step-by-step explanation:
y=x^2-10x-2
Find the equation of the axis of symmetry