Final answer:
To solve the system of equations, we first expressed x in terms of y from the first equation and substituted it into the second equation. After simplifying, we solved for y and then substituted back into the first equation to find x. The solution is x = 5/3, y = -1.
Explanation:
To solve the system of equations 3x = -5y and 6x - 7y = 17, one can use the method of substitution or elimination. We'll use elimination for this example. First, observe that the first equation can be rewritten to solve for x in terms of y:
3x = -5y
x = -5y/3
Let's substitute this expression for x into the second equation:
6(-5y/3) - 7y = 17
-10y - 7y = 17
-17y = 17
y = -1
Now substitute y back into the first equation to find x:
3x = -5(-1)
3x = 5
x = 5/3
The solution to the system of equations is x = 5/3, y = -1.
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y 2 + 5y Choose the constant term that completes the perfect square trinomial.
The constant term that completes the perfect square trinomial is 6.25.
Explanation:To complete the square for the given expression y² + 5y, we take half of the coefficient of the linear term (5/2) and square it to find the value to be added. Half of 5/2 is 5/4, and squaring it gives 25/16. Adding 25/16 to the expression yields a perfect square trinomial: y² + 5y + 25/16 = (y + 5/4)².
To write it in standard form, we convert 25/16 to 1.5625. Therefore, the constant term that completes the perfect square trinomial is 1.5625, or 6.25 when expressed as a decimal.
English is spoken as the first or primary language in 78 countries than Farsi is spoken as the first language. Together English and Farsi are spoke as a first language in 130 countries. In how many countries is English spoken as the first language? In how many countries is Farsi spoken as the first language.
Answer:
52
Step-by-step explanation:
130 (total)-78=52
what is the slope of a line that is perpendicular to the line that passes through (1,0) and is parallel to y=3x+5
[tex] - 30 = 2(x - 97)[/tex]
If c(x) = 2x^2 - 4x + 3
17. c(3a)
18. c(b^2)
Dora is purchasing a $162,000 home with a 30-year mortgage at 5.15%. What is her monthly principal and interest payment?
A. $829.23
B. $884.56
C. $807.81
D. $876.09
Answer:
Option B is the answer.
Step-by-step explanation:
The formula for EMI is :
[tex]\frac{p\times r\times (1+r)^{n} }{(1+r)^{n} -1}[/tex]
Here p = 162000
r =[tex]5.15/12/100=0.004292[/tex]
n = [tex]30\times12=360[/tex]
Now putting the values in the formula we get,
[tex]\frac{162000\times 0.004292\times (1+0.004292)^{360} }{(1+0.004292)^{360} -1}[/tex]
[tex]\frac{162000\times 0.004292\times (1.004292)^{360} }{(1.004292)^{360} -1}[/tex]
= $884.60 close to option B.
So, option B is the answer.
Bill had a salary of $48,000 last year. This year his salary is $49,920. What is the percent increase of Bill's salary?
greatest common factor of 3 in 10
The greatest common factor of 3 and 10 is 1.
Greatest common factorThe greatest common factor (GCF) of two or more numbers is the largest number that is a factor of all the numbers.
The greatest common factor (GCF) of 3 and 10 is 1. There are no common factors other than 1 that evenly divide both 3 and 10.
Because 3 and 10 do not have any common prime factors, The greatest common factor of 3 and 10 is 1.
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Jackets R us is having a 35% off sale at its outlet store this month.todd is figuring the sale price of a winter jacket normally priced at $89.99.
a. Estimate the sale price. Describe how you found your estimate.
b. calculate the amount that todd will pay for the jacket.
A Ferris wheel has a circumference of 440 feet. What is the approximate diameter of the Ferris wheel? Use 3.14 for pi
The ratio of girls to boys who participated in the geography bee was 5:4 there were 36 total students how many were boys
Answer:
There are 16 boys and 20 girls
The graph shows Susan’s distance from her office, in yards, as she runs errands, over time, in minutes.
For which values of t (time) is Susan’s distance from her office decreasing from 70 yd to 0 yd?
A.
from t = 0 to t = 6
B.
from t = 10 to t = 12
C.
from t = 16 to t = 22
D.
from t = 22 to t = 26
whats the answer ?????
A circle has a sector with are of (17/2)pi and a central angle of (17/90)pi radians. What is the area of the circle? Either enter an exact answer in terms of pi or use 3.14 pi and enter your answer as a decimal.
Answer:
17pi/2= R* 17pi/90
R=45
A=45^2 * pi
A=90 pi or 282.6
Step-by-step explanation:
A rectangle is 3 times as long as it is wide. The perimeter is 40 feet. Find the dimensions.
Victor and his three friends (4 people all together) are planning to split a pizza. They want to spend at most $5 per person. Find the maximum (at most) cost of the pizza they can order.
Tubas, trombones and French horns are bass instruments. Fully stretched out, the length of a tuba is 18 feet. The length of a trombone is 8 13/14, and the length of a French horn is 17 3/14. The tuba is how much longer than the French horn? And the French horn is how much longer than the trombone?
The length of the Tuba is 11/14 feet longer than the length of the French horn.
The length of the French is 8 ²/₇ feet longer than the length of a Trombone horn.
What is subtraction?It absolutely indicates subtracting something from a commodity, group, location, etc. Subtracting from an assemblage or a list of ways is known as subtraction.
Tubas, trombones, and French horns are bass devices. Fully pulled out, the measurement of a Tuba is 18 feet. The measurement of a trombone is 8¹³/₁₄ feet, and the measurement of a French horn is 17³/₁₄ feet.
The difference between the length of the Tuba and the French horn is given as,
⇒ 18 - 17 ³/₁₄
⇒ 18 - 241/14
⇒ (252 - 241) / 14
⇒ 11/14 feet
The difference between the length of the French and the Trombone horn is given as,
⇒ 17 ³/₁₄ - 8 ¹³/₁₄
⇒ 241/14 - 125/14
⇒ 116 / 14
⇒ 8 ²/₇ feet
The length of the Tuba is 11/14 feet longer than the length of the French horn.
The length of the French is 8 ²/₇ feet longer than the length of a Trombone horn.
More about the subtraction link is given below.
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Given a triangle with vertices U(6, −1), W(0, −5), and X(4, −9), and Y is the midpoint of segment UW and Z is the midpoint of segment WX comma what is the length of YZ?
Here we have to use the distance formula
Please see the image attached with the solution , for the figure
Firstly we have to find the length of line segment XU
and the triangle has a property that the length of line segment that connects the midpoint of the two sides is half the length of the third side.
It means here
Length of YZ = half the length of XU
So lets find the length of XU
[tex] \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}= \sqrt{(6-4)^2 +(-1+9)^2} =\sqrt{4+64} [/tex]
[tex] =\sqrt{68} [/tex]
[tex] =2\sqrt{17} [/tex]
Now the length of YZ = half of [tex] =2\sqrt{17} [/tex]
So length of YZ = [tex] =\sqrt{17} [/tex]
Mark raises guppies in an aquarium. He finds out that guppies reproduce very rapidly, and the number quadruples every month. He starts out with only 2 guppies, and the function y equals 2 times 4 to the x models the number of guppies he will have after x months. Which graph represents this function?
In this exercise we have to recognize the graphics given in the images and in this way identify which functions are being represented, in this way we have to:
[tex]y = 2 * (4 ^ x)[/tex]
What is the exponential function?The exponential function represents a dependency relationship. In this type of mathematical operation there is a variable (unknown) in the exponent and the real number (greater than zero and different than one) in the base.
So we know that the graphs are of exponential functions and their form is given by:
[tex]y=a^x[/tex]
With this form we have that the function of the graph is:
[tex]y = 2 * (4 ^ x)[/tex]
See more about exponencial function at brainly.com/question/21822047
Yvonne purchased a jacket at Right Price, and the lowest price on the tag was $4. This was the sale price, which was calculated by taking 75% off of the original price. What was the original price of Yvonne's jacket?
what rational number between 9.5 and 9.7
Angelo rode his bike around a bike trail that was 1/4 of a mile long. He rode his bike around the trail 8 times. Angelo said he rode his bike a total of 8/4 Miles. Teresa said he was wrong and that he actually rode 2 miles. Who is correct?
Which of the numbers 4, 5, or 6 is a solution of x+7>12
Chris visited the local Pizza Shack to purchase one pizza for each member of his Scout Troop. On arrival, he realised that he had mislaid the list he had made of the pizzas that had been requested. He knew that there were 32 people altogether and that all 3 vegetarians in the Troop wanted mushrooms only. He also remembered that the same number of people wanted just the chicken topping as wanted a plain pizza. Alex, a Young Leader, was able to help by recalling that: 12 people requested toppings that included chicken, 10 requested toppings that included pepperoni, 9 requested toppings that included mushroom, 1 person wanted all 3 toppings, 2 wanted chicken and pepperoni only, 2 wanted peperoni and mushroom only. What was the final order that Chris placed at Pizza Shack?
Hello,
Please, see the attached files.
Thanks.
The sketch shows two parallel lines cut by a transversal. Which pair of angles are alternate interior angles?
Answer:
angle 5 and angle 4
Step-by-step explanation:
BIG Nicks Moving Company unloaded 72% of the 300 boxes they delivered in 30 minutes. How many boxes did they unload each minute?
calculate the interquartile range of the following data set: 36, 54, 49, 39, 41, 48, 50
Answer:
14
Step-by-step explanation:
Simplify 8 over -3 divided by -4 over 9
Answer:
2/3
Step-by-step explanation:
you take the problem and write it down then flip the last fraction and multiply them together.
Over a 12 hour period the students estimate that 2,400 bees will leave the hive. How many bees should they expect to travel west?