Equation1: y = 3x
Equation 2: x = -2y + 70
To solve this system, we will use the value of x of the second equation into the fist equation:
y = 3x = 3(-2y + 70) = -6y + 210
y = -6y + 210
y + 6y = 210
7y = 210
y = 210/7 = 30
y = 30
Now, we will tusethe value of y into the second equation to find the value of x:
x = -2y + 70 = -2(30)+80 = -60 + 70 = 10
x = 10
Answer:
x = 10
y = 30
Explain how you determine if a function is linear or non-linear if you are given a graph
A linear equation is used to represent a straight line in a graph, whereas non-linear equations are used to represent curves.
An equation is considered linear if it is in the form of y = mx+b where m is the slope of the equation and b is the y-intercept.
Notice how here, x can only be to the power of one. In here, the conditions are just simply m,b∈R.
Some examples include y = 5x+4, y = x−2, y = 0, and even some like
x = 1.
As you can see here, all of the following equations are represented using a straight line.
An equation is considered “non-linear” when it is not graphed using straight lines. Some examples include y = 3x2+1, y = 2x3−3, y = x5+43.
In conclusion, a linear equation will always be in the form of y = mx+b, where m is the slope of the equation, and b is the y-intercept of the equation.
Hence the answer is A linear equation is used to represent a straight line in a graph, whereas non-linear equations are used to represent curves.
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A caterer uses 4 pans of lasagna to serve 30 people. At this rate, how many pans of lasagna does the caterer use to serve 390 people?
A. 13
B. 52
C. 90
D. 98
What is the solution to the inequality below?1x1 < 5A. x < 5 or x>-5B. x>5 and x < -5C. x < 5 and x > -5D. x > 5 or x<-5
The Solution is given by:
[tex]\lvert x\rvert<5[/tex]This means that:
[tex]-5So it follows that:[tex]x<5\text{ and x>-5}[/tex]Hence option C is correct.
4. Find (1.1x + y)2.
Rewrite the division problem into a multiplication problem 1/4 ÷ 3/5
ANSWER
[tex]\text{ }\frac{1}{4}\cdot\text{ }\frac{5}{3}[/tex]EXPLANATION
We want to rewrite the division problem into a multiplication one.
To do this, we have to change the division sign to a multiplication sign, and then, we invert the fraction on the right.
That is:
[tex]\begin{gathered} \frac{1}{4}\div\frac{3}{5} \\ \Rightarrow\text{ }\frac{1}{4}\cdot\text{ }\frac{5}{3} \end{gathered}[/tex]That is the answer.
What congruence rule does the triangle follow? Please write the congruence statement triangle EFH is congruent to ________?
We can see here two triangles, and we can notice the following:
1. Since H is the midpoint of the segment EG, we can say that EH and HG are congruent segments.
2. Since these two triangles, namely, EFH and GFH share the same segment (HF), this side is also congruent to these two triangles.
3. Since EH is congruent to HG, and FH is congruent to itself, then EF is congruent to GF.
4. Angle E is congruent to angle G.
Therefore, we can say that:
Since we have that:
a. EF is congruent to GF
b. EH is congruent to GH
c. Angle E is congruent to angle G
We can conclude that the congruence rule, in this case, is SAS (Side-Angle-Side), because if two sides and the included angle are congruent to the corresponding parts of the other triangle, the triangles are congruent.
We also see that the three sides are congruent (and in this case, we can also conclude that the triangles are congruent by the rule SSS (side-side-side).
Likewise, we can also conclude that the triangle EFH is congruent to triangle GFH.
Where can I find L2 and L3 for a missing corresponding angles?
Answer:
Explanation:
Given:
<1=123.9°
<3=56.1°
Based on the given figure, the angles formed a straight line (Ex. <3 and <4). Angles on a straight line add up to 180°. So,
For <3 and <4:
We plug in what we know.
[tex]\begin{gathered} \angle3+\angle4=180 \\ 56.1+\angle4=180_{} \\ \text{Simplify and rearrange} \\ \angle4=180-56.1 \\ \angle4=123.9 \end{gathered}[/tex]For <2 and <1:
We plug in what we know.
[tex]\begin{gathered} \angle2+\angle1=180 \\ \angle2+123.9=180 \\ \angle2=180-123.9 \\ \angle2=56.1 \end{gathered}[/tex]Therefore, <2 = 56.1° while <4= 123.9°.
What is the volume of the following prism?this is a prism with a right triangle as the base. The width of the triangle is 8 inches and the height of the triangle is 8 inches. The height of the prism is 12 inches.A. 768 m³B. 150 m³C. 384 m³D. 374 m³
Given the following information
Volume of the prism=?
base of the prism= right triangle
volume of a prism with a right triangle as a base is given by
[tex]\frac{1}{2}*b*a*h[/tex]where
b= base of the triangle = 8
a= height of the triangle = 8
h= height of the prism=12
[tex]V=\frac{1}{2}8*8*12[/tex][tex]V=\frac{768}{2}[/tex][tex]V=384m^3[/tex](5x^5-y)^2 binomials to power
Answer:
The expansion of the expression gives;
[tex]=25x^{10}-10x^5y+y^2[/tex]Expansion:
Given the expression:
[tex](5x^5-y)^2[/tex]We want to expand;
[tex]\begin{gathered} (5x^5-y)^2 \\ =(5x^5-y)(5x^5-y) \\ =5x^5(5x^5-y)-y(5x^5-y) \\ =5x^5(5x^5)+5x^5(-y)-y(5x^5)-y(-y) \\ =25x^{10}-5x^5y-5x^5y+y^2 \\ =25x^{10}-10x^5y+y^2 \end{gathered}[/tex]Therefore, the expansion of the expression gives;
[tex]=25x^{10}-10x^5y+y^2[/tex]Point A is located at (2, 6), and point M is located at (−1, 8). If point M is the midpoint of segment AB, find the location of point B. a(5, 4) b(0.5, 7) c(0, 6) d(−4, 10)
ANSWER:
d. (−4, 10)
STEP-BY-STEP EXPLANATION:
The midpoint has the following definition:
[tex]\left(x_m,y_m\right)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)[/tex]We can calculate point B, using the following equations obtained taking into account the above:
[tex]\begin{gathered} x_m=\frac{x_1+x_2}{2} \\ \\ -1=\frac{2+x_2}{2} \\ \\ x_2+2=-2 \\ \\ x_2=-2-2=-4 \\ \\ \\ y_m=\frac{y_1+y_2}{2} \\ \\ 8=\frac{6+y_2}{2} \\ \\ y_2+6=16 \\ \\ y_2=16-6=10 \\ \\ \text{ Therefore, point B is located at \lparen-4, 10\rparen} \end{gathered}[/tex]The correct answer is: d. (−4, 10)
On a hot day, Gabrielle poured 1/8 of a bucket of water into a plastic wading pool. A few minutes later she added another 1/2 of a bucket. How much water did Gabrielle pour into the pool?
5/8 of a bucket of water
Explanation:Initial amount poured = 1/8 bucket of water
An addition of 1/2 bucket into the the pool
Total amount of water in the pool = 1/8 bucket of water + 1/2 bucket of water
[tex]\begin{gathered} \frac{1}{8}+\frac{1}{2},\text{ }LCM\text{ = 8} \\ \frac{1(1)\text{ +4(1)}}{8} \end{gathered}[/tex][tex]=\frac{1+4}{8}=\text{ 5/8}[/tex]Total water in the pool is 5/8 of a bucket of water
graph the line with the equation
we have the equation
y=-(1/2)x+7
Remember that
To graph a line we need al lest two points
so
Find the intercepts
step 1
Find the y-intercept (value of y when the value of x is zero)
For x=0
y=-(1/2)(0)+7
y=7
y-intercept is (0,7)
step 2
Find the x-intercept (value of x when the value of y is zero)
For y=0
o=-(1/2)x+7
(1/2)x=7
x=14
x-intercept is (14,0)
step 3
Plot the intercepts and join them to graph the line
using a graphing tool
see the attached figure
please wait a secon to draw the line
What percentage of the data values falls between the values pf 3 and 24 in the data set shown? 0 5 10 15 20 25 O 25% O 50% O 75% O 100%
The graph shown in the image is a box and whiskers plot.
The sides of the box are determined by the first and third quartiles of the sample.
The left side corresponds to the first quartile (Q₁), this value separates the bottom 25% of the sample from the top 75%
The right side corresponds to the third quartile (Q₃), this value separates the bottom 75% of the sample from the top 25%
The line inside the box represents the second quartile (Q₂), this value is also known as the Median of the sample and divides the bottom 50% from the top 50%.
The body of the box, i.e. the space between Q₁ and Q₃, is the interquartile range (IQR), this represents the mid 50% of the sample.
The left whisker links the first quartile with the minimum value of the sample.
The right whisker links the third quartile with the maximum
Josh bought a new scooter for $412. He plans to make equal payment of $42 each month until the scooter is paid in full. About how many payments will Josh make? 10 20 5 or 15
Data:
T=Total price of the scooter: $412
M=Every month he pays: $42
t= number of payments
[tex]t=\frac{T}{M}[/tex][tex]t=\frac{412}{42}=9.8\approx10[/tex]What formula do I use to get my answer? I’m getting 1/13, but my answer is incorrect. Thank you.
We will have the following:
First, the probability of getting the first t-shirt white will be:
[tex]p_1=\frac{4}{9}[/tex]And the probability of getting the second t-shirt white will be:
[tex]p_2=\frac{3}{8}[/tex]Now, the probability of getting the two white t-shirts one after the other will be:
[tex]\begin{gathered} p_3=p_1\ast p_2\Rightarrow p_3=\frac{4}{9}\ast\frac{3}{8} \\ \\ \Rightarrow p_3=\frac{1}{6} \end{gathered}[/tex]So, the probability of getting the two white t-shirts one after the other is 1/6.
what 6 numbers equals 15 with out using save number twice
What is the shape of the base of each prism? (The base is not alwaysthe bottom)?A=B=C=D =E=F=
A)
The base of the figure A is;
Here the base is in the shape of triangle.
A) Triangle
B)
12. Make an estimate and then divide as if the dividend was a whole number. Use the estimate to place your decimal.8.46 ➗3=Estimate: What partial quotients did you use? ___how to divide 3 into 8.46 dividing decimals?______________________Answer:
Given data:
The given expression is 8.46 ➗3.
The given expression can be written as,
Thus, the quotient is 2.82 which is in decimal.
Complete the proof. Given: CM LAB 3= 4 Prove: AMC BMC Use the information provided to complete a two-column proof.
Perpendicular Bisector Theorem:
In the shown figure, the line segment AB is bisected by line CM since it is given in the question.
[tex]CM\perp AB[/tex]Which simply means that the line CM bisected line AB at 90°.
So, that means we have two Right angled triangles, these are triangle AMC and BMC
This also means that the line CM is equal for both triangles since it is common to both.
What is the range of the given function?{(-2, 0), (-4,-3), (2, -9), (0, 5), (-5, 7)}Ox|x=-5, -4, -2, 0, 2)O lyly = -9, -3, 0, 5, 7)Oxx-9, -5, -4, -3, -2, 0, 2, 5, 7)O lyly = -9, -5, -4, -3, -2, 0, 2, 5, 7)
The range of the function is the values of y-coordinates of the ordered pairs
Since the function is
[tex]\lbrace(-2,0),(-4,-3),(2,-9),(0,5),(-5,7)\rbrace[/tex]Then the values of y-coordinates are
[tex]\lbrace0,-3,-9,5,7\rbrace[/tex]Then the range should be
[tex]\lbrace y:y=-9,-3,0,5,7\rbrace[/tex]The 3rd choice
can someone help me i wikll give 25 pints but i need it now PLS
Answer:
Its in the picture below
a) Form a suitable equation to show that x squared - 6x - 59 = 0b) Complete the square (x+p)squared-q= 0, and find the constants p and q.
Given:
There is a triangle given as
Required:
We want to find the sutiable form that show that
[tex]x^2+6x-59=0[/tex]and also complete the square
[tex](x+p)^2-q=0[/tex]and find the value of p and q
Explanation:
The area of triangle is
[tex]\begin{gathered} \frac{1}{2}(x+1)(x+5)=32 \\ \\ x^2+5x+x+5=64 \\ x^2+6x-59=0 \end{gathered}[/tex]hence proved for a
Now for second
[tex]\begin{gathered} x^2+6x+9-9-59=0 \\ (x+3)^2-68=0 \end{gathered}[/tex]now compare with
[tex](x+p)^2-q=0[/tex]we get
[tex]\begin{gathered} p=3 \\ q=68 \end{gathered}[/tex]Final answer:
p=3 and q=68
24. Which point is part of the solution for the system of inequalities graphed below? A. (-1,-2) B. (3,1) C. (1,-2) D. (-3,1)
The solution must be insige the red grind so we can see that the only point inside this area is the coordinate (-3, 1) so the answer is D
Savannah earned a score of 720 on Exam A that had a mean of 700 and a standarddeviation of 25. She is about to take Exam B that has a mean of 400 and a standarddeviation of 100. How well must Savannah score on Exam B in order to doequivalently well as she did on Exam A? Assume that scores on each exam arenormally distributed.
Answer:
480
Explanation:
First, we need to standardize the score on Exam A. It can standardize as
[tex]z=\frac{\text{ score}-\text{ mean}}{\text{ standard deviation}}[/tex]Replacing score = 720, mean = 700, and standard deviation = 25, we get
[tex]z=\frac{720-700}{25}=\frac{20}{25}=0.8[/tex]Then, to do equivalently well on exam B, we need a standard value equal to 0.8. So, the score can be calculated as
[tex]\text{ score = z\lparen standard deviation\rparen + mean}[/tex]Replacing z = 0.8, standard deviation = 100 and mean = 400, we get
[tex]\begin{gathered} \text{ score = 0.8\lparen100\rparen+400} \\ \text{ score = 80 + 400} \\ \text{ score = 480} \end{gathered}[/tex]Therefore, the answer is 480
You roll a six-sided dice.Event A: Roll a 6. Event B: Roll a prime number. Find P(A or B) . Express your answer as a fraction in simplest form.
The probability of rolling a 6 is:
[tex]P(A)=\frac{1}{6}[/tex]There are 3 prime numbers between 1 and 6: 2, 3 and 5. Therefore, the probability of rolling a prime number is:
[tex]P(B)=\frac{1}{3}[/tex]Therefore, the probability of rolling a 6 or a prime number is:
[tex]P(AorB)=\frac{1}{6}+\frac{1}{3}=\frac{1}{2}[/tex]Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph.
we have
f(x)=2x^4-4x^2
REmember that
The Leading Coefficient Test is the test which enables you to discover thebehavior of the graph in terms of rising and falling. This test utilizes the leading coefficientand whether the degree is odd or even to determine the behavior of the curves. The test goes as follows:
In this problem the leading coefficient is positive and even
sothe graph rises to the left and rises to the right.As smart phones have grown in popularity, regular cell phones have fallen out of favor. As a result, one electronics retailer estimates that 17% fewer regular cell phones will be sold every year. If the retailer sells 162,147 regular cell phones this year, how many will be sold 10 years from now?If necessary, round your answer to the nearest whole number.
Initially, the retailer sells 162,147 regular cell phones
The retailer stimates, that every year sales will fall a 17%
meaning that after one year, sales will be:
162,147 * (1-0.17) = 134582.01
then, after 2 years, sales will be:
134582.01 * (1-0.17) = 111703.0683
which is the same as
[tex]162147\mleft(1-0.17\mright)^2=111703.0683[/tex]in that way, we can create the following formula:
[tex]162147\cdot(1-0.17)^y[/tex]where y is time in years,
now, if we replace y = 10 we can obtain the solution we are looking for
[tex]162147\cdot(1-0.17)^{10}=25158.795[/tex]rounding to the nearest whole number: 25,159
3) Graph y=-3 (x - 2)2 + 3
The equation is:
[tex]y=-3(x-2)^2+3[/tex]So this is a parabola, so we can graph it with the vertex and the intercections with the x axis
So the vertex is in the coordinat (2,3) becuase of the transformation of -2 in the x axis and +3 in the y axis so the vertex is (2, 3)
now for the interception with the x axis we replace y = 0 and solve for x so
[tex]0=-3(x-2)^2+3[/tex]we open the parenthesis like:
[tex]undefined[/tex]Convert: 9 kilogramsmilligrams
Answer
9,000,000 milligrams
Step-by-step explanation
1 kilogram is equivalent to 1,000,000 milligrams. Using this conversion factor, the equivalence of 9 kilograms is found as follows:
[tex]\begin{gathered} 9\text{ kg }=9\text{ kg}{}\cdot\frac{1,000,000\text{ mg}}{1\text{ kg}} \\ \text{ SImplifying the units:} \\ 9\text{ kg }=9\cdot1,000,000\text{ mg} \\ 9\text{ kg}=9,000,000\text{ mg} \end{gathered}[/tex]Find the slope-intercept form of the line that satisfies the given conditions.x-intercept 8, y-intercept −3
Given:
A line satisfies the given conditions.
x-intercept 8, y-intercept −3
The x-intercept is the value of x when y = 0
The y-intercept is the value of y when x = 0
So, the given line passes through the points (8, 0) and (0, -3)
We will find the slope using the following formula:
[tex]$$slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}$$[/tex]Substitute with points:
[tex]m=\frac{-3-0}{0-8}=\frac{-3}{-8}=\frac{3}{8}[/tex]The slope-intercept form is: y = m * x + b
substitute m = 3/8 and b = -3
So, the answer will be, that the equation of the line is as follows:
[tex]y=\frac{3}{8}x-3[/tex]