Answer: (1,2)
Step-by-step explanation:
You must:
- Multiply the first equation by 3.
- Add both equations.
- Solve for the variable left. In this case will be x.
Then:
[tex]\left \{ {{39x +3y = 45} \atop {-9x - 3y = -15}} \right.\\------\\ 30x=30\\x=1[/tex]
Substitute x=1 into any of the original equtions and solve for y:
[tex]13(1)+y=15\\y=2[/tex]
The solution is: (1,2)
Answer:
The solution of the system of equation is (1 , 2)
Step-by-step explanation:
The system of equation is:
* 13x + y = 15 ⇒ (1)
* -9x - 3y = -15 ⇒ (2)
- By using elimination ⇒ we must make on of the
two variables in the two equations has the same value
with different sign
- So we will multiply equation (1) by 3 to eliminate y
∴ 3(13x) + 3(y) = 3(15)
∴ 39x + 3y = 45 ⇒ (3)
- Now add (2) and (3)
∴ 39x + -9x = 45 + -15
∴ 30x = 30 ⇒ ÷ 30 both sides
∴ x = 1
- Substitute the value of x in equation (1) or (2)
- Lets use (1)
∴ 13(1) + y = 15
∴ 13 + y = 15 ⇒ subtract 13 from both sides
∴ y = 15 - 13
∴ y = 2
∴ The solution of the system of equation is (1 , 2)
The layer cake has both vanilla and chocolate frosting. What percent of the surface area of the cake (not including the bottom) is chocolate? Round your answer to the nearest tenth of a percent. The radius is 6 in height for vanilla is 4 in height for chocolate is 4 in
Answer:
Step-by-step explanation:
2
Find the missing sides.
Answer:
Part 3)
[tex]x=6\ units[/tex]
[tex]y=3\ units[/tex]
Part 4) [tex]x=18\sqrt{2}\ units[/tex]
Step-by-step explanation:
Part 3)
step 1
Find the value of x
In the right triangle of the figure we know that
The cosine of angle of 30 degrees is equal to the adjacent side to angle of 30 degrees divide by the hypotenuse
so
[tex]cos(30\°)=\frac{3\sqrt{3}}{x}[/tex]
and remember that
[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]
substitute
[tex]\frac{\sqrt{3}}{2}=\frac{3\sqrt{3}}{x}[/tex]
Simplify
[tex]x=(2*3)=6\ units[/tex]
step 2
Find the value of y
In the right triangle of the figure we know that
The sine of angle of 30 degrees is equal to the opposite side to angle of 30 degrees divide by the hypotenuse
so
[tex]sin(30\°)=\frac{y}{x}[/tex]
and remember that
[tex]sin(30\°)=\frac{1}{2}[/tex]
substitute
[tex]\frac{1}{2}=\frac{y}{6}[/tex]
[tex]y=6/2=3\ units[/tex]
Part 4) Find the value of x
Applying the Pythagoras Theorem
[tex]x^{2} =18^{2} +18^{2} \\ \\x^{2} = 324+324\\ \\x^{2}=648\\ \\x=\sqrt{648}\ units[/tex]
Simplify
[tex]x=18\sqrt{2}\ units[/tex]
Winona got her hair cut for $21. She left a 15% tip for the hair stylist. What is the total amount of money Winona paid?
Answer:
$24.15
Step-by-step explanation:
What you do is you take 15% and make it into a decimal which is .15.
Then you times it by $21. 21*.15=3.15.
You then take the $3.15 and add it to $21 to get
$24.15 as your answer.
Winona left a 15% tip for her $21 haircut, resulting in a tip of $3.15. When added to the cost of the haircut, it means she paid a total of $24.15.
Explanation:The question is asking us to find out how much Winona paid in total for her haircut, including a 15% tip. To find the amount of the tip, we can multiply the cost of the haircut (which is $21) by 15% (or 0.15 in decimal form): $21 * 0.15 = $3.15. To find the total amount Winona paid, we simply add the cost of the haircut to the tip: $21 + $3.15 = $24.15. So, Winona paid a total of $24.15 for her haircut.
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Simplify the irrational number 75; then estimate it to two decimal places.
Answer:
[tex]5\sqrt{3}[/tex] OR [tex]8.69[/tex]
Step-by-step explanation:
Let's first simplify [tex]\sqrt{75}[/tex].
5 and 15 multiply to get 75. 5 and 3 multiply to get 15. Since we have a pair of fives and a three leftover, we can write [tex]\sqrt{75}[/tex] as:
[tex]5\sqrt{3}[/tex]
Now, let's find the answer in decimal form. We know that:
[tex]8^2=64[/tex] and [tex]9^2=81[/tex]
With that information, we know that the answer has to be between 8 and 9.
Divide 75 by 8: [tex]\frac{75}{8}=9.375[/tex]
Take the average of that answer and 8: [tex]\frac{9.375+8}{2}=\frac{17.375}{2}=8.6875[/tex]
This answer we got is extremely close to the exact answer of [tex]\sqrt{75}[/tex], which is [tex]8.66025403...[/tex]. Since we are estimating, the answer above will do just fine.
Question 10 Unsaved
A real estate agent made a scatter plot with the size of homes, in square feet, on the x-axis and the homeowner's property taxes on the y-axis. The variable have a strong linear correlation and the equation for the least squares regression line is yˆ=0.392x+638.118.
Based on the equation, what should the agent expect the property tax to be for a 2,400-square foot home in the area?
Question 10 options:
$2,464.12
$1,578.92
$1,190.94
$940.80
[tex]y = 0.392x + 638.118 \\ x = 2400 \\ y = (0.392 \times 2400) + 638.118 \\ y = 1578.92[/tex]
hope u understand
Here's a graph of linear function. Write the equation that describes that function. Express it in slope-intercept form.
the y intercept is -3 because its touching (0,-3).
The graph goes right one and down five so the slope is -5
y=mx + b
y= -5x -3
Write the equation for the inverse of y = cos 2x
Answer:
Inverse = (arcos x) / 2.
Step-by-step explanation:
y = cos 2x
2x= arcos y
x = (arcos y) / 2.
Inverse = (arcos x) / 2.
The equation for the inverse of y = cos 2x is obtained by switching the x and y variables and solving for y, resulting in y = arccos (x) / 2.
Explanation:The inverse of a function switches the roles of the x and y variables, so the first step to finding the inverse of y = cos 2x is to switch the x and y in the equation, giving us x = cos 2y. Now, we simply solve for y. The equation x = cos 2y is equivalent to 2y = arccos (x) where arccos is the inverse cosine function. Therefore, the final answer is y = arccos (x) / 2. This is the equation for the inverse of y = cos 2x.
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A hot air balloon descended 99.6 meters in 12 seconds . What was the balloons average rate of descent in meters per second ?
8.6 meters per second
You scored a 95% on your math quiz.The quiz was out of 60 points.How many points did you get
A rectangular prism has a volume of 729ft^3. The length width and height are the same. What is the length of each side
Answer:
9 feet
Step-by-step explanation:
If each side is the equivalent, each side of the prism is the cube root of 729
Cube root of 729 is 9
Each side is 9 feet long
Find the value of C so that (x-3) is a factor of the polynomial p(x)
In general, you have that [tex](x-x_0)[/tex] is a factor of a polynomial [tex]p(x)[/tex] if and only if [tex]p(x_0)=0[/tex]
So, we want [tex]p(3)=0[/tex]. We have
[tex]p(3) = -3^3+ 9c -4\cdot 3 +3 = -27+9c-12+3 = 9c-36[/tex]
So, we have
[tex]p(3) = 0 \iff 9c-36 = 0 \iff x = \dfrac{36}{9} = 4[/tex]
Answer:
c = 4
Step-by-step explanation:
Given that (x - 3) is a factor of p(x) then x = 3 is a root and p(3) = 0
p(3) = - (3)³ + c(3)² - 4(3) + 3 = 0, hence
- 27 + 9c - 12 + 3 = 0
9c - 36 = 0 ( add 36 to both sides )
9c = 36 ( divide both sides by 9 )
c = 4
Please answer this question only if you know it!
Answer:
d. 90°, 90°
Step-by-step explanation:
Both angles intercept 180° arc WZ. They are half the measure of the intercepted arc, hence both are 90°.
where Q and R are polynomials and the degree of R is less than the degree of B.
Answer:
see explanation
Step-by-step explanation:
[tex]\frac{a(x)}{b(x)}[/tex]
= [tex]\frac{2x^2-5x+6}{x-3}[/tex]
= 2x + 1 + [tex]\frac{9}{x-3}[/tex]
quotient q(x) = 2x + 1 and remainder r(x) = 9
Find the sum of the series 14+11+8+5........-82
The sum of this finite arithmetic series is -1122.
The sum of the arithmetic series 14+11+8+5...-82 is -1122. This is obtained by identifying the number of terms in the series, the first term, the last term and the common difference, then substitifying these values into the sum formula for an arithmetic series.
Explanation:The series provided is an arithmetic series, where each term decreases by 3 from the previous one. The formula to find the sum of an arithmetic series is S = n/2 * (a + l) where S is the sum of the series, n is the number of terms, a is the first term, and l is the last term.
In this case, the difference between consecutive terms is -3, the first term a = 14, and the last term l = -82. We find the number of terms by using the relation, l = a + (n-1)*d where d is the common difference. By substituting the given values, we can find that n = 33 terms. Substituting these values into the sum formula gives: S = 33/2 * (14 - 82) = -1122.
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What are the period and amplitude of the function?
Question 1 options:
period: 5; amplitude: 3
period: 5; amplitude: 4.5
period: 6; amplitude: 3
period: 6; amplitude: 4.5
➷ The period is the distance from one part of the function to the same part of it.
In this case, the period is 5
The amplitude is the half the distance from the largest and smallest value
3 + 6 = 9
9/2 = 4.5
In this case, the amplitude is 4.5
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Draw a number line and mark all described points on it. Numbers that are both larger than –2 and smaller than 3.
To mark the points on a number line that are both larger than -2 and smaller than 3, you would mark off the points at -1, 0, 1, and 2 on this line.
Explanation:To draw a number line and mark all points that are both larger than -2 and smaller than 3, follow these steps:
Draw a straight horizontal line. This is your number line. Mark an arbitrary point as 0, the origin. To the left and right of 0, begin to mark off equal intervals representing integers. Choose a numbering system where points to the right of 0 are positive and those to the left are negative. Your description requires numbers that are larger than -2 and smaller than 3. So you would mark off the points -1, 0, 1, and 2 on the number line. Learn more about Number Line here:
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To mark all points larger than -2 and smaller than 3 on a number line, draw a straight line with equal intervals, labeling -2 and 3, and shade in the area between them. For constructing a histogram, divide the data range into intervals, then draw and label bars on the y-axis to reflect the count of data points within each interval.
Explanation:
To draw a number line and mark all points that are both larger than –2 and smaller than 3, begin by drawing a horizontal line. Use a ruler to keep the line straight. Place tick marks at regular intervals, and label them with numbers from less than -2 to greater than 3, ensuring that -2 and 3 are clearly marked on the line. The numbers larger than -2 but smaller than 3 will be between these two points. Shade this region to indicate all the numbers that meet the condition.
Next, if you need to construct a histogram, you first need a set of data to work with. Once you have your data, determine the range of data and divide this range into five to six intervals. On the horizontal axis, or the x-axis, represent these intervals. Then, count how many data points fall within each interval. On the vertical axis, or the y-axis, draw bars for each interval with heights corresponding to the number of data points in each interval. Use your ruler for precision and label the axes to show the scale.
I REALLY NEED SOMEONES HELP ON THIS PLEASE!! I NEED THIS DONE TODAY!
Error analysis: Describe the error in the way the product of the two binomials is set up and/or solved. Please be specific. (Image is listed below)
Solve the problem in the question above correctly. Please show your work!
[tex]\huge\boxed{\text{The $5$ needs to be negative.}}[/tex]
Since the first binomial is [tex](x-5)[/tex], the [tex]5[/tex] is negative and must be that way when using the table.
Here's the corrected table:
[tex]\begin{array}{c|c|c|}\multicolumn{1}{c}{}&\multicolumn{1}{c}{3x}&\multicolumn{1}{c}{1}\\\cline{2-3}x&3x^2&x\\\cline{2-3}-5&-15x&-5\\\cline{2-3}\end{array}\\\\\\3x^2+x-15x-5\\3x^2-14x-5[/tex]
Since the sample size is always smaller than the size of the population, the sample meana. must always be smaller than the population meanb. must be larger than the population meanc. must be equal to the population meand. can be smaller, larger, or equal to the population mean
Answer:
d. can be smaller, larger, or equal to the population mean
Step-by-step explanation:
The mean of the sample will depend upon which values are selected from the population to form the sample.
The sample mean can be any value below, above or equal to the population mean.
However, as more and more samples are taken and their means found, the mean of the sample means will approach the population mean.
Answer:
It can be smaller, larger, or equal to the population mean.Step-by-step explanation:
We know that the sample size is smaller than the size of the population, because it's a subset that must represent the population.
However, that doesn't mean the sample mean has to be smaller than the population mean, actually this stats can be smaller, equal or larger, it depends on another factors.
Therefore, the right answer is the last choice
It can be smaller, larger, or equal to the population mean.What is the value of x in the equation 3(2x + 4) = −6? (4 points)
−3
1
12
19
3(2x+4)=-6 6x+12=-6
- 12. -12
6x = -18
÷6. ÷6
x= -3
Answer:
-3
Step-by-step explanation:
3(2x+4)= -6
6x+12= -6
6x= -18
x= -3
3. Find the quotient of 5/31 divided by 15/23. Reduce your answer to the lowest fraction.
Answer:
The answer is 23/93
Step-by-step explanation:
In order to divide two fractions, we can flip the second one and multiply.
5/31 ÷ 15/23
5/31 × 23/15 = 23/93
WILL GIVE BRAINLIEST
Plz help me.... : /
Answer:
(-7 , 3)
Step-by-step explanation:
3x^2 + 12x = 63 //Subtract 63 on both sides.
3x^2 + 12x - 63 = 0 //Common factor 3.
3(x^2 + 4x - 21) = 0 //Divide both sides by 3.
(x^2 + 7x - 3x - 21) = 0
x(x + 7) - 3(x + 7) = 0
(x + 7) (x - 3) = 0
x = -7 and 3
Solution: (-7, 3)
Jodie wants to buy a shirt regularly priced at $20. The shirt is on sale for 15% off the regular price. Which equation can be used to determine s , the sale price of the shirt, not including tax? A s = 20 – (20)(0.15) B s = 20 – (20 + 0.15) C s = 20(0.15) D s = 20 + 0.15
Answer:
it's A
Step-by-step explanation:
you toke the price and times it by the decimal of the discount
Answer:
0.150 x $20 = $ 3.00.
Step-by-step explanation:
You want to buy something that costs $20, and it's on sale for 15% off. What is the item's sale price?
First, convert the 15% to a real mathematical number. For percents, this is always done by dividing the 15% by 100%, or 15% / 100% = 0.150.
Second, find out what 15% of $20 is. This is the amount of the sale discount. This is always found by mulitplying 0.150 by the item's cost $20. So for this sale, you'll save $ 3.00 on this item.
This means, the cost of the item to you is $17.00$
What is the distance to the earth’s horizon from point P?
Answer:
156.7 miles.
Step-by-step explanation:
The radius and the tangent at the point of contact form a right angle so we can apply the Pythagoras theorem:
( 3959 + 3.1)^2 = x^2 + 3959^2
x^2 = 3962.1^2 - 3959^2
x^2 = 24555.41
x = 156.7 miles.
The solution is : 156.7 miles is the distance to the earth’s horizon from point P.
What is distance?The distance between two points is the length of the line joining the two points. Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.
here, we have,
from the given diagram, we get,
The radius and the tangent at the point of contact form a right angle so we can apply the Pythagoras theorem:
( 3959 + 3.1)^2 = x^2 + 3959^2
x^2 = 3962.1^2 - 3959^2
x^2 = 24555.41
x = 156.7 miles.
Hence, The solution is : 156.7 miles is the distance to the earth’s horizon from point P.
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A two gallon container had all of its dimensions tripled. How many gallons does the new container hold?
When the dimensions of a two gallon container are tripled, the container can hold up to 54 gallons of liquid, since the volume will increase 27 times.
Explanation:The question is about how a two gallon container can hold when all of its dimensions are tripled. In mathematics, when dimensions of a cube (or a rectangular prism, which the container can be assumed to be) are increased proportionally, the volume, which is proportional to the cube of the dimensions, increases by the cube of that same factor.
In this case, the dimensions of the container have all been tripled (a three-fold increase) which results in the volume of the space inside the container increasing by 3³ = 27 times. Therefore, the two gallon container, when its dimensions are tripled, can hold 2 gallons x 27 = 54 gallons. It's important to understand this is a principle of geometry and works irrespective of the units of measurement used (gallons, liters, cubic centimeters, etc.)
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The circumference of a circle is 28pi inches. What is the length of the radius of this circle?
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=28\pi \end{cases}\implies 28\pi =2\pi r\implies \cfrac{28\pi }{2\pi }=r\implies 14=r[/tex]
Line q goes through points (-3,3) and (-5,-3). At what point does line q cross the y-axis ?
Answer:
(0,12)
Step-by-step explanation:
To write the equation of a line, calculate the slope between points (-3,3) and (-5,-3). After, substitute the slope and a point into the point slope form. Then convert to the slope intercept form to identify the y-intercept.
[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{3--3}{-3--5}= \frac{6}{2}=3[/tex]
Substitute m = 3 and the point (-3,3) into the point slope form.
[tex]y - y_1 = m(x-x_1)\\y -3 = 3(x--3)\\y-3 = 3(x +3)\\y-3=3x + 9\\ y = 3x + 12[/tex]
This means that it crosses at (0,12) since b - 12 for y=mx+b.
Answer:(0,12)
Step-by-step explanation:
A man spends 80% of his salary and saves the rest. He saves $1080 a month. Find his salary
I need 7,714 solar panels to power my new workshop. If each box contains 24 panels, about how many boxes should I purchase? Choose the best estimate.
If you need 7, 714 solar panels, and 1 box contains 24 panels then you'll need:
7, 714/24 = 321.4167
This answer estimated can be 321. So yuh might need 321 panels.
ANSWER = 321 PANELS
Answer:300
Step-by-step explanation:
If you need 7, 714 solar panels, and 1 box contains 24 panels then you'll need:
7, 714/24 = 321.4167
This answer estimated can be 321. So yuh might need 321 panels.
ANSWER = 321 PANELS
But the best estimate is 300 pannels
Let f(x)=6/−2+2e^−0.3x . What is f(−4) ?
DID THE TEST
ANSWER: 1.3
Answer:
[tex]f(-4)=1.3[/tex]
Step-by-step explanation:
we have
[tex]f(x)=\frac{6}{-2+2e^{-0.3x}}[/tex]
we know that
f(-4) is the value of the function for x=-4
substitute x=-4 in the function
[tex]f(-4)=\frac{6}{-2+2e^{-0.3(-4)}}[/tex]
[tex]f(-4)=\frac{6}{-2+2e^{1.2}}[/tex]
[tex]f(-4)=1.3[/tex]
Answer:
1.94
Step-by-step explanation:
We substitute -4 into as x in the equation, but first what is e?
e is a term that represents the base of a natural logarithm and is a irrational number, its called Euler's number. e is equivalent to:
[tex]e=2.718[/tex]
We can substitute -4 into the equation
[tex]=6/(-2+2*(2.718^(-0.3*-4)))[/tex]
[tex]=6/(-2+2*(2.718^(1.2)))[/tex]
[tex]=6/(-2+2*2.54)[/tex]
[tex]=6/(3.09)[/tex]
[tex]=1.94
Therefore f(-4)=1.94
Which values of k would the product of k/3 times 12 be greater than 12? A. For any valu of k less than 1 but greater than 0. B. For any value of k less than 3 but greater than 1,. C. For any value of k equal to 3. D. For any value of k greater than 3
Answer:
k > 3
Option D
For any value of k greater than 3
Step-by-step explanation:
We ara dealing with an inequality
(k/3)*12 > 12
Dividing by 12 each side
(k/3)*12/12 > 12/12
(k/3) > 1
Multiplying by three
3*(k/3) > 3*1
k > 3
Answer:
k > 3
Option D
For any value of k greater than 3
Step-by-step explanation: