to solve the system of equations below, miguel isolated the variable y in the first equation and then substituted it into the second equation. what was the resulting equation?
Answers
Given the system of equations:
[tex]\begin{cases}5y=10x{} \\ x^2+y=36{}\end{cases}[/tex]Given that Miguel isolated the variable in equation 1 and then substituted it into the second equation.
Let's find the resulting equation.
Divide both sides in equation 1 by 5 to isolate the y-variable:
[tex]\begin{gathered} \frac{5y}{5}=\frac{10x}{5} \\ \\ y=2x \end{gathered}[/tex]Now, substitute 2x for y in the second equation.
We have:
[tex]x^2+2x=36[/tex]Therefore, the resulting equation is:
[tex]x^2+2x=36[/tex]ANSWER: B
[tex]x^2+2x=36[/tex]Related Questions
Jina is ordering 4 bags of cat food from Canada. Each bag has a mass of 2.5 kg. To determine the shipping costs, Jina needs to know the total weight in pounds. What is the weight of the cat food in pounds? USE 1kg=2.2lb AND DON'T ROUND ANY COMPUTATIONS.
Answers
Answer
22 lb
Step-by-step explanation
Given that 1 bag weighs 2.5 kg, then 4 bags will weigh:
[tex]4\times2.5\text{ kg}=10\text{ kg}[/tex]Using the conversion factor: 1 kg = 2.2 lb, 10 kg are equivalent to:
[tex]10\text{ kg}=10\text{ kg}\times\frac{2.2\text{ lb}}{1\text{ kg}}=22\text{ lb}[/tex]Answer:
22 pounds
Step-by-step explanation:
Jina is ordering 4 bags, each of them weighs 2.5 kgs. Let's first find each bag's weight in lbs:
[tex]2.5kg*2.2lb = 5.5 lbs[/tex]
Now, to find the total mass of cat food, let's multiply each bag's weight to the number of bags:
[tex]5.5lbs * 4 = 22 lbs[/tex]
Determine the value of x that would make lines a and b parallel. X=
Answers
If the two lines are parallel, the indicated angles formed by the transversal are Exterior Alternate Angles. Thus, they are equal to each other.
Hence, we can calculate the variable as
[tex]3y+53=7y-55[/tex]Solving by collecting like terms, we have
[tex]\begin{gathered} 3y-7y=-55-53 \\ -4y=-108 \end{gathered}[/tex]Dividing both sides by -4, we have
[tex]\begin{gathered} y=\frac{-108}{-4} \\ y=27 \end{gathered}[/tex]Hence, the value of y is 27.
What is the image of the point (4,0) after a rotation of 90° counterclockwise aboutthe origin?
Answers
To rotate a point 90º counterclockwise you have to invert the place fo the coordinates, for example:
(x,y) → (y,x)
Then you have to change the sign of the
Find the slope of the line between the points (3,-8)(2,-3)
Answers
Slope = -5
Explanations:The formula for calculating the slope of a line is expressed as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1, y1) and (x2, y2) are the coordinates of the line.
Given the coordinates (3,-8) and (2,-3), the slope of the line is expressed as:
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{-3-\left(-8\right)}{2-3} \\ m=\frac{-3+8}{-1} \\ m=\frac{5}{-1} \\ m=-5 \end{gathered}[/tex]Hence the slope of the line between the points (3,-8) and (2,-3) is -5
Please solve the problem step by step, to check my final answers.
Answers
We are asked to determine the future value and the time for a quarterly compounded interest. To do that we will use the following formula:
[tex]A=P(1+\frac{r}{400})^{4t}[/tex]Where:
[tex]\begin{gathered} A=\text{ future value} \\ P=\text{ initial value} \\ r=\text{ interest rate} \\ t=\text{ time} \end{gathered}[/tex]Part A. We are asked to determine the time in 7 years. To do that we will substitute the value of "t = 7" and "r = 2", we get:
[tex]A=4000(1+\frac{2}{400})^{(4)(7)}[/tex]Solving the operations:
[tex]A=4599.49[/tex]Therefore, in 7 years there will be the amount of $4599.49
Part B. We are asked to determine the time to get the amount of $5000. To do that we will substitute the value of "A = 5000", and we get:
[tex]5000=4000(1+\frac{2}{400})^{4t}[/tex]Now, we solve for "t". First, we divide both sides by 4000:
[tex]\frac{5000}{4000}=(1+\frac{2}{400})^{4t}[/tex]Now, we take the natural logarithm to both sides:
[tex]\ln(\frac{5000}{4000})=\ln(1+\frac{2}{400})^{4t}[/tex]Now, we use the following property of logarithms:
[tex]\ln x^y=y\ln x[/tex]Applying the property we get:
[tex]\operatorname{\ln}(\frac{5,000}{4,000})=4t\operatorname{\ln}(1+\frac{2}{400})[/tex]Now, we divide both sides by the natural logarithm and by 4:
[tex]\frac{1}{4}\frac{\ln(\frac{5000}{4000})}{\ln(1+\frac{2}{400})}=t[/tex]Solving the operations:
[tex]11.19=t[/tex]Therefore, the amount of 5000 will be obtained after 11.19 years.
marlo has a photogrph this is 5 inches wide and 7 inches tall.he wants to enlarge the photo to fit in a frame that is 32 inches tall.if the length and width will be scaled proportionally,what is the width of the frame for the enlarged photo?round to one decimal place.
Answers
Given: a photograph is 5 inches wide and 7 inches tall.
He wants to enlarge the photo to fit in a frame that is 32 inches tall.
So, the length and the width will be scaled proportionally
So, the scale factor = r= new length over the lod length
[tex]r=\frac{32}{7}[/tex]It must be the same ratio: new width to old width
Let the new wide = x
so,
[tex]\frac{x}{5}=\frac{32}{7}[/tex]solve for x:
[tex]x=\frac{32}{7}\cdot5=\frac{160}{7}=22\frac{6}{7}in[/tex]So, the answer will be: the new width = 22 6/7 inches
Which of the following would be a good name for the function that takes the pages in areading assignment and returns the time needed to ocomplete it A. Time(pages) B. Cost(time C. Time(cost) D. Pages(time) E Year(time) F Time(year)
Answers
A function is expressed as
f(
The seniors and juniors at sweet valley high school are going on a trip to Busch gardens. The seniors filled 12 Van's and 13 buses with 564 total students. The juniors filled 6 Van's and 13 buses with 492 students. How many students were in each van? in each bus?
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The seniors and juniors at sweet valley high school are going on a trip to Busch gardens. The seniors filled 12 Van's and 13 buses with 564 total students. The juniors filled 6 Van's and 13 buses with 492 students. How many students were in each van? in each bus?
step 1
Seniors
Let
x -----> number of students in vans
y -----> number of students in bus
we have
12x+13y=564
Juniors
6x+13y=492
solve the system of equations
Solve by graphing
the solution is the intersection point both graphs
see the attached figure
the solution is the point (12,32)
therefore
In each Vans there are 12 students and in each bus there are 32 studentsI just am having trouble solving the equation. Can you help me?
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Given:
[tex]h(x)=x^2-1[/tex]Required:
To calculate which option is correct
Explanation:
According to the formula for the average rate of change of the function:
[tex]\begin{gathered} \frac{\Delta y}{\Delta x}=(f^1(x_1)+f^1(x_2))\text{ divide by 2} \\ \\ So,\text{ -3}\leq x\leq1,\frac{\Delta y}{\Delta x}=\frac{-6+2}{2}=-2 \\ \\ it\text{ has a negative rate of change.} \end{gathered}[/tex]Required answer:
Option C
Each individual letter of the word Wisconsin is placed on a piece of paper, and all 9 pieces of paper are placed in a hat. If one letter is selected at random from the hat, find the probability that a consonant is selected.P(consonant)-(Type a fraction. Simplify your answer.)
Answers
GIVEN:
We are told that all the individual letters of the word WISCONSIN are placed on a piece of paper. Then all nine pieces of paper are placed in a hat.
Required;
Find the probability that a letter chosen at random is a consonant.
Step-by-step solution;
The probability of an event is given by the formula;
[tex]P[event]=\frac{number\text{ }of\text{ }required\text{ }outcomes}{number\text{ }of\text{ }all\text{ }possible\text{ }outcomes}[/tex]The number of all possible outcomes is the total number of letters that stands a chance of being selected, and that is 9. The number of required outcomes for this experiment is 6 (that is, 6 consonants).
Therefore, the probability of selecting a consonant by random is;
[tex]\begin{gathered} P[consonant]=\frac{6}{9} \\ \\ P[consonant]=\frac{2}{3} \end{gathered}[/tex]ANSWER:
The probability of selecting a consonant is;
[tex]P[consonant]=\frac{2}{3}[/tex]T+a/N=F I need to solve for a.
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What is the midpoint of line segment QP given Q(6, 3) and P(-6, -1).
Answers
Recall that given two points, the midpoint of a line segment is determined by the formula
[tex]\begin{gathered} M=\mleft(\dfrac{x_1 + x_2}{2},\; \dfrac{y_1 + y_2}{2}\mright) \\ \text{where} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are the two endpoints of the line segment} \end{gathered}[/tex]Substitute the following and we get
[tex]\begin{gathered} (x_1,y_1)=(6,3) \\ (x_2,y_2)=(-6,-1) \\ \\ M=\mleft(\dfrac{x_1 + x_2}{2},\; \dfrac{y_1 + y_2}{2}\mright) \\ M=\mleft(\dfrac{6 + -6}{2},\; \dfrac{3 + -1}{2}\mright) \\ M=\mleft(\dfrac{0}{2},\; \dfrac{2}{2}\mright) \\ M=(0,\; 1) \end{gathered}[/tex]Therefore, the midpoint of line segment is (0,1)
A rectangular swimming pool with a length of 18 meters and a width of 6 meters is surrounded by a concrete patio. The patio is a uniform 3 meters width around the entire pool. What is the area of the patio?
Answers
The area of the combined patio and swimming pool is
[tex]\begin{gathered} (18\text{ m}+3\text{ m})(6\text{ m}+3\text{ m}) \\ =(21\text{ m})(9\text{ m}) \\ =189\text{ m}^2 \end{gathered}[/tex]The area of the swimming pool is
[tex](18\text{ m})(6\text{ m})=108\text{ m}^2[/tex]Subtract the combined area to the area of the swimming pool and we get
[tex]189\text{ m}^2-108\text{ m}^2=81\text{ m}^2[/tex]Therefore, the area of the patio is 81 square meters.
use the graph to find when f(x)
Answers
x > -7
Explanations:For the graph g(x), select two points on the line
(-7, 4) and (-2, 8)
That is, x₁ = -7, y₁ = 4, x₂ = -2, y₂ = 8
The slope of the line is given as:
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = }\frac{8-4}{-2-(-7)} \\ m\text{ = }\frac{4}{5} \end{gathered}[/tex]The equation of a line is given as:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - 4 = }\frac{4}{5}(x-(-7)) \\ y\text{ - 4 = }\frac{4}{5}(x+7) \\ y-4=\frac{4}{5}x+\frac{28}{5} \\ y\text{ = }\frac{4}{5}x+\frac{28}{5}+4 \\ y\text{ = }\frac{4}{5}x\text{ + }\frac{48}{5} \\ y\text{ = }0.8x+9.6 \\ g(x)\text{ = 0.8x+9.6} \end{gathered}[/tex]For the graph f(x):
Select the points (-7, 4) and (-3, 2)
[tex]\begin{gathered} m\text{ = }\frac{2-4}{-3-(-7)} \\ m\text{ = }\frac{-2}{4} \\ m\text{ = -0.5} \end{gathered}[/tex]The equation of the line is:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - 4 = -0.5(x - (-7)} \\ y\text{ - 4 = -0.5(x + 7)} \\ y\text{ - 4 = -0.5x - }3.5 \\ y\text{ = -0.5x - 3.5 + 4} \\ y\text{ = -0.5x + 0.5} \\ f(x)\text{ = -0.5x + 0.5} \end{gathered}[/tex]f(x) < g(x)
-0.5x + 0.5 < 0.8x + 9.6
-0.5x - 0.8x < 9.6 - 0.5
-1.3x < 9.1
-x < 9.1 / 1.3
-x < 7
x > -7
The head of public safety notices that the average driving speed at a particular intersection averages 35 mph with a standard deviation of 7.5 mph. After a school speed limit sign of 20 mph is placed at the intersection, the first 40 cars travel past at an average speed of 32 mph. Using the .01 alpha level, was there a significant change in driving speed?figure the effect size
Answers
First, we have to define the system of hypothesis
[tex]\begin{gathered} H_0\colon\mu=35 \\ H_a\colon\mu\ne35 \end{gathered}[/tex]Then, we find the statistic test value
[tex]\frac{\sqrt[]{n}\cdot(\bar{x}-\mu)}{\sigma}[/tex]It's important to know that this situation models a standard normal distribution.
Replacing the given information, we have
[tex]\frac{\sqrt[]{40}\cdot|32-35|}{7.5}=\frac{|-3|\cdot\sqrt[]{40}}{7.5}=2.5[/tex]This value allows us to deduct that the null hypothesis can't be rejected because the test statistic is not greater than 2.57583, it's equal. It's important to consider that this value refers to 0.5% of the distribution (two tales).
Hence, there's no significant evidence to reject the null hypothesis.5. The custodians at school must sanitize all the desks in the building each night. If there are 3,500 desks in the entire school building and the custodians have cleaned 1,400 desks by the time Ms. Burlingame leaves at 3:30pm, what percent of the desks have the custodians cleaned?
Answers
The cleaned desks is 40%.
Given:
Total number of desks is, N = 3500.
Number of desks cleaned is, C = 1400.
The objective is to find the percentage of cleaned desks.
Consider the percentage as x.
Then, the equation can be represented as,
[tex]\begin{gathered} \frac{x}{100}\cdot3500=1400 \\ \frac{x}{100}=\frac{1400}{3500} \\ x=\frac{14}{35}\cdot100 \\ x=40 \end{gathered}[/tex]Hence, the percentage of cleaned desks is 40%.
Jason wants to dine at five different restaurants during a summer getaway. If two of nineavailable restaurants serve seafood, find the number of ways that at least one of theselected restaurants will serve seafood given the following conditions.a) The order of selection is important.b) The order of selection is not important.
Answers
Solution
Explanation:
If order is important, permutations can be used to find the number of ways the event can take place
Number of ways to select any 5 out of 8 in a particular order = 8P5
In this case, "at least one" is complement of "fewer than one" (that is 0). Thus, four restaurants that are not serving seafood can be chosen from five restaurants in
[tex]8P_5=6720[/tex]Number of restaurants serving seafood = 2 , Number of restaurants not serving seafood = 3
Number of selections in which all restaurants do not serve seafood = 5P3 = 20
Number of ways such that at least one of the selected restaurants will serve seafood = Total number of selections - Number of selections in which all restaurants do not serve seafood
[tex]6720-20=6700[/tex]some help and I need an answer asap explain it to me pls
Answers
a)
[tex]\begin{gathered} \frac{29}{4}\text{cups of yellow}\rightarrow\frac{29}{16}cups\text{ of blue } \\ 1\text{ yellow cup}\rightarrow\frac{29}{16}\div\frac{29}{4}=\frac{29}{16}\times\frac{4}{29}=\frac{4}{16}=\frac{1}{4}cups\text{ of blue paint} \end{gathered}[/tex]So therefore 1/4 cups of blue paint will be used for 1 cup of yellow paint.
b) So for this we will assume this relationship:
[tex]\begin{gathered} x=ky \\ \text{where k is the constant of proportionality:} \\ x=\frac{35}{8} \\ y=\frac{35}{2} \end{gathered}[/tex]So substituting the values of and y into the equation above:
[tex]\begin{gathered} \frac{35}{8}=k\times\frac{35}{2} \\ \frac{35}{8}\div\frac{35}{2}=k \\ \frac{1}{4}=k \\ \text{The constant of proportionality that relates the quantities x and y is:} \\ \frac{1}{4} \end{gathered}[/tex]can the given information be used to prove triangle ABC is congruent to triangle EDC explain your reasoning
Answers
SOLUTION:
Case: Congruence
Method:
Compare the triangles
[tex]\frac{15}{10}\equiv\frac{12}{8}\ne\frac{21}{12}[/tex]Final answer:
The scale factor is not consistent
Hence the given information cannot be used to prove triangle ABC is congruent to triangle EDC.
ground aller seconds is given by the equation (t) = 5 + 100t – 16t" . Here is a graph that represents h. 200 150 height above ground (feet) 100 50 1 7 2 3 4 5 6 time (seconds) a. How does the 5 in the equation relate to the graph? [Select] [Select] y-intercept b. W on mean in terms of the rocket? x-intercept maximum rate of change
Answers
Part A
The 5 in the equation is the intercept on the Vertical -axis, that is Y- intercept
I have the picture of the jersey and I will give it to you when we start :)
Answers
Print it :
$21 per jersey
x = number of jerseys
y = total cost
y= 21x
Top print
Setting up cost = $45
$18 per jersey
y= 45+18x
Equal both costs:
21x = 45 + 18x
Solve for x:
21x-18x =45
3x =45
x =45/3
x=15
when 15 jerseys are bought, both companies have the same cost.
If he bought more than 15 ( for example 20)
Print it = 21x = 21 (20)= 420
Top print = 45 +18 (20) = 405
Less than 15 jerseys ( ex: 10)
PRINT IT = 21 (10) = $210
TOP PRINT = 45+18(10) = $225
1.
When he buys more than 15 jerseys, he should choose TOP PRINT.
When he buys less than 15 jerseys, he should choose PRINT IT
2. set up one-off set up cost less than TOP PRINT = ex = 15
And a cost per shirt higher than TOP PRINT and less than PRINT IT = ex = 20 ( the slope value must be between 18 and 21 )
Factor the quadratic expressionx^2 + 5x - 14
Answers
Solution:
Given:
[tex]x^2+5x-14[/tex]Using the product-sum to factor the expression, the middle term is split;
[tex]\begin{gathered} x^2+7x-2x-14 \\ \\ Grouping\text{ the terms;} \\ (x^2+7x)(-2x-14) \\ \\ Factor\text{ out the terms;} \\ x(x+7)-2(x+7) \\ =(x-2)(x+7) \end{gathered}[/tex]Therefore, the factored term is;
[tex](x-2)(x+7)[/tex]
how do u graph the solutions for b>5
Answers
Given
We have already used the number line on which we have represented numbers as points on a line.
For b>5
A twelve-sised die with sides labeled 1 through 12 will be rolled once. Each number is equally likely to be rolled. What is the probability of rolling a number less than 4?
Answers
Explanation:
There are 3 posible outcomes with a number less than 4: 1, 2 & 3. This is the numerator
The total posible outcomes is 12. This is the denominator
Now we have to write and simplify the fraction:
[tex]\frac{3}{12}=\frac{1}{4}=0.25[/tex]Answer:
The probability of rolling a number less than 4 is 1/4
Study the diagram of circle L, where RS is tangent to circle L at point S.Also, RS = 24, RL = 26, and LS is a radius.What is the length of the radius, r?
Answers
From the figure given,
Where RS is perpedicular to the radius LS and L is the centre of the circle,
Given that
[tex]\begin{gathered} RS=24\text{ units} \\ RL=26\text{ units and } \\ LS=r\text{ units} \end{gathered}[/tex]The formula to find the value of r is the Pythagorean theorem, which is given as
[tex](\text{HYP)}^2=(OPP)^2+(\text{ADJ)}^2[/tex]Where
[tex]\begin{gathered} \text{HYP=RL}=26\text{ units} \\ OPP=RS=24\text{ units} \\ \text{ADJ=LS}=r\text{ units} \end{gathered}[/tex]Substitute the values into the formula of the Pythagorean theorem
[tex]\begin{gathered} (RL)^2=(RS)^2+(LS)^2 \\ 26^2=24^2+r^2 \\ 676=576+r^2 \\ \text{Collect like terms} \\ r^2=676-576 \\ r^2=100 \\ \text{Square root of both sides} \\ \sqrt[]{r^2}=\sqrt[]{100} \\ r=10\text{ units} \end{gathered}[/tex]Hence, the length of radius, r is 10 units
Reny establishes a loan for an $8,000 vacation package to Transylvania. The vacation company charges 5.5% simple interest. Reny plans to pay back the loan over 1.5 years.How much interest will Reny pay?
Answers
SOLUTION
We are asked how much interest will Reny pay after getting a loan of $8,000 at an interest rate of 5.5% for 1.5 years
We will apply the simple interest formula
[tex]\begin{gathered} I=\frac{P\times R\times T}{100} \\ \text{Where I = interest } \\ P=\text{ principal, that is loan collected = 8,000} \\ R=\text{interest rate = 5.5\%} \\ T\text{ = time in years = 1.5 years } \end{gathered}[/tex]Substituting the values we have
[tex]\begin{gathered} I=\frac{P\times R\times T}{100} \\ I=\frac{8000\times5.5\times1.5}{100} \\ I=80\times5.5\times1.5 \\ I=660\text{ dollars } \end{gathered}[/tex]Hence, the answer is $660
I’m confused and stuck in these 4 questions. Can you please help me?
Answers
Answer:
1. 32.2 square inches (A)
2. 21.4 inches (H)
3. 14.5 inches (I)
4. 15.2 square inches (E)
AHIE
Explanation:
1. Given the diameter of the closed paint can's lid as 6.4 inches, the radius(r) will be;
[tex]\text{radius(r) }=\frac{Diameter}{2}=\frac{6.4}{2}=3.2\text{ inches}[/tex]We can now go ahead and determine the area(A) of the closed paint can's lid using the below formula;
[tex]A=\pi\cdot r^2=3.14\cdot(3.2)^2=3.14\cdot10.24=32.2in^2[/tex]So the area of the closed paint can's lid is 32.2 inches squared (A)
2. Given the radius of the closed paint can as 3.4 inches, the can's circumference(C) can be determined using the below formula;
[tex]C=2\pi r=2\cdot3.14\cdot3.4=21.4\text{ inches}[/tex]So the circumference of the can is 21.4 inches (H)
3. Given the diameter(d) of the open paint can as 4.6 inches, then we can determine its circumference(C) using the below formula;
[tex]C=\pi d=3.14\cdot4.6=14.5\text{ inches}[/tex]So the circumference of the open paint can is 14.5 inches (I)
4. Given the diameter(d) of the open paint can's lid as 4.4 inches, the radius(r) will be;
[tex]r=\frac{d}{2}=\frac{4.4}{2}=2.2\text{ inches}[/tex]We can go ahead and determine the area(A) of lid using the below formula;
[tex]A=\pi\cdot r^2=3.14\cdot(2.2)^2=3.14\cdot4.84=15.2\text{ squared inches}[/tex]So the area of the lid is 15.2 square inches (E)
Find the final hourly wage if a $14.00 starting wage is increased by 5.5% each year for 10 years. The final hourly wage is $____Round your answer to the nearest cent.
Answers
Answer: $23.91
The exponential growth formula goes by:
[tex]y=a(1+r)^x[/tex]Where:
a = present value
r = rate
x = time
From the given, we know that:
a = $14.00
r = 5.5% = 0.055
x = 10
Substitute these to the equation:
[tex]\begin{gathered} y=a(1+r)^x \\ y=14.00(1+0.055)^{10} \\ y=23.9140 \\ y=23.91 \end{gathered}[/tex]Find the length of PQ. The endpoints are P(-2,-1) and Q(2,4)
Answers
Morgy, this is the solution:
Point P = (-2, -1)
Point Q = (2, 4)
Let's use the formula to calculate the distance, this way:
d = √(2 - -2)² + (4 - -1)²
d = √4² + 5²
d = √16 + 25
d = √41
d = 6.403
In consequence, the lenght of PQ is 6.403 units
use the function p=20g to find the value of p when g =8
Answers
To find the value of p when g = 8 you have to replace g = 8 into the equation, as follows
p = 20g
p = 20(8)
p = 160