Answer:
The correct answer is
For addition, Caulleen used the words total, sum, altogether, and increase. But we could also have used the words combine, plus, more than, or even just the word "and". For subtraction, Caulleen used the words, fewer than, decrease, take away, and subtract. We also could have used less than, minus, and difference.
Step-by-step explanation:
hope this helps u!!!
Complete the table.PLSSS HELP ILL GIVE BRAINLIEST.PLS PLS PLS PLS
Answer:
0, 22, 44, 66
Step-by-step explanation:
Given the equation for the model, [tex] d = 11t [/tex] , you can complete the table above by simply plugging in each value of "t" has given in the table to solve for "d".
*When t (seconds) = 0, distance (feet) would be:
[tex] d = 11(0) [/tex]
[tex] d = 0 [/tex]
*When t (seconds) = 2, distance (feet) would be:
[tex] d = 11(2) [/tex]
[tex] d = 22 [/tex]
*When t (seconds) = 4, distance (feet) would be:
[tex] d = 11(4) [/tex]
[tex] d = 44 [/tex]
*When t (seconds) = 6, distance (feet) would be:
[tex] d = 11(6) [/tex]
[tex] d = 66 [/tex]
HELP PLEASE! A Blue Jay wanted to store some acorns for the winter. If she hides 18 acorns per tree, she will be left with four acorns; if she hides 20 acorns per tree, there will be extra space for an additional four acorns (the number of trees is always the same). How many acorns is the Blue Jay going to store for the winter, and in how many trees?
Answer:
Step-by-step explanation:
Let
T = number of trees
A = number of acorns
Given:
A = 18T + 4 ...........................(1)
A = 20T -4 .........................(2)
Equate A from (1) and (2)
20T-4 = 18T+4
simplify and solve for T
20T - 18T = 4+4
2T = 8
T = 4 trees
A = 18T + 4 = 72+4 = 76 acorns, or
A = 20T - 4 = 80 - 4 = 76 acorns.
The measure of minor arc JL is 60°. Circle M is shown. Line segments M J and M L are radii. Tangents J K and L K intersect at point K outside of the circle. Arc J L is 60 degrees. What is the measure of angle JKL? 110° 120° 130° 140°
Answer:
angle JKL = 120 degrees
Step-by-step explanation:
Since arc JL is 60 degrees, the central angle is also 60 degrees.
Point K is the intersection of tanges at J and L, therefore KJM and KLM are 90 degrees.
Consider quadrilateral JKLM whose sum of internal angles = 360.
Therefore
angle JKL + angle KLM + angle LMJ + angle MJK = 360 degrees
angle JKL + 90 + 60 + 90 = 360
angle JKL = 360 - 90 - 60 -90 = 120 degrees
Answer:
120 degrees
Step-by-step explanation:
Since arc JL is 60 degrees, the central angle is also 60 degrees.
Point K is the intersection of tanges at J and L, therefore KJM and KLM are complementary or equal 90 degrees.
look at quadrilateral JKLM whose sum of internal angles = 360.
Therefore
angle JKL plus angle KLM plus angle LMJ plus angle MJK = 360 degrees
angle JKL + 90 + 60 + 90 = 360
what equals 1+1= Why can't I see any answers help i logged off etc is it just me?
Answer:
1 + 1 = 2
Step-by-step explanation:
^
Answer:
no , it's happening to everyone , even I can't see it .
expand(x+y2)2 plzzzzzzzzzzzzzzzz
Answer:
[tex](x + {y}^{2}) = {x}^{2} + 2x {y}^{2} + {y}^{4} [/tex]
Hope it helps!!❤❤Please mark me as the brainliest!!!Thanks!!!!
A study regarding the relationship between age and the amount of pressure sales personnel feel in relation to their jobs revealed the following sample information. At the 0.10 significance level, is there a relationship between job pressure and age.
(Round your answers to 3 decimal places.)
Degree of Job Pressure
Age (years) Low Medium High
Less than 25 25 27 20
25 up to 40 49 53 40
40 up to 60 59 59 52
60 and older 35 42 44
H0: Age and pressure are not related. H1: Age and pressure are related.
Reject H0 if X2 > .
X2=
(Click to select)Reject Do not reject H0. Age and pressure (Click to select)areare not related.
Answer:
Reject H0
Age and pressure are related
Step-by-step explanation:
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value. In the given scenario we reject the null hypothesis because job pressure and age are related to each other.
Find the length of AG
Answer:
[tex]AG=22[/tex]
Step-by-step explanation:
Follow the next steps:
[tex]\frac{A-B}{A-E} =\frac{B-C}{E-F} =\frac{C-D}{F-G} =\frac{A-C}{A-F} =\frac{B-D}{E-G} =\frac{A-D}{A-G}[/tex]
Let:
[tex]\frac{A-B}{A-E} =\frac{B-C}{E-F}\\ \\\frac{4}{A-E} =\frac{5}{10x}\\ \\Solving\hspace{3}for\hspace{3}A-E\\\\A-E=8x[/tex]
Now:
[tex]\frac{C-D}{F-G} =\frac{A-C}{A-F} \\\\\frac{2}{F-G} =\frac{9}{18x} \\\\Solving\hspace{3}for\hspace{3}F-G\\\\F-G=4x[/tex]
Hence:
[tex]A-G=(A-E)+(E-F)+(F-G)=22x[/tex]
Finally:
[tex]\frac{B-D}{E-G} =\frac{A-D}{A-G}\\\\\frac{A-D}{B-D} =\frac{A-G}{E-G}\\[/tex]
[tex]\frac{11}{7} =\frac{22x}{14x} \\\\\frac{11x^{2} }{7} -\frac{11}{7} =0\\\\[/tex]
Hence:
[tex]x=1\\x=-1[/tex]
Since it would be absurd for [tex]x=-1[/tex], the real solution is [tex]x=1[/tex]
Therefore:
[tex]AG=22[/tex]
Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year. How many years will it take for carbon–14 to decay to 10 percent of its original amount? The equation for exponential decay is At = A0e–rt.
Answer:
It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount
Step-by-step explanation:
The amount of Carbon-14 after t years is given by the following equation:
[tex]A(t) = A(0)e^{-rt}[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year.
This means that [tex]r = \frac{0.0124}{100} = 0.000124[/tex]
How many years will it take for carbon–14 to decay to 10 percent of its original amount?
This is t for which:
[tex]A(t) = 0.1A(0)[/tex]
So
[tex]A(t) = A(0)e^{-rt}[/tex]
[tex]0.1A(0) = A(0)e^{-0.000124t}[/tex]
[tex]e^{-0.000124t} = 0.1[/tex]
[tex]\ln{e^{-0.000124t}} = \ln{0.1}[/tex]
[tex]-0.000124t = \ln{0.1}[/tex]
[tex]t = -\frac{\ln{0.1}}{0.000124}[/tex]
[tex]t = 18569.2[/tex]
It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount
In a random sample of 40 refrigerators, the mean repair cost was $150. Assume the population standard deviation is $15.50. Construct a 99% confidence interval for the population mean repair cost. Then change the sample size to n = 60. Which confidence interval has the better estimate?
Answer: ($143.69, $156.31)
Step-by-step explanation:
Confidence interval to estimate population mean :
[tex]\overline{x}\ \pm z\dfrac{\sigma}{\sqrt{n}}[/tex]
, where [tex]\sigma[/tex] = population standard deviation
n= sample size
[tex]\overline{x}=[/tex] Sample mean
z= critical value.
As per given,
n= 40
[tex]\sigma[/tex] = $15.50
[tex]\overline{x}=[/tex] $150
Critical value for 99% confidence level = 2.576
Then, 99% confidence interval for the population mean:
[tex]150\pm(2.576)\dfrac{15.50}{\sqrt{40}}\\\\\Rightarrow\ 150\pm6.31 \ \ (approx)\\\\\Rightarrow(150-6.31,150+6.31)=(143.69,156.31)[/tex]
Hence, the required confidence interval : ($143.69, $156.31)
Look at the number pattern shown below:3 × 17 = 5133 × 167 = 5511333 × 1667 = 555111What will be 33333 × 166667?
Answer:
33333 x 166667 = 5555511111
I think that is the answer you wanted
Step-by-step explanation:
166667
x 33333
5555511111
Graph a line that contains the point (-7,-4)and has a slope of - 2/3
Hi there! :)
Answer:
Given the information, we can write an equation in slope-intercept form
(y = mx + b) to graph the line:
Plug in the slope for 'm', the y-coordinate of the point given for 'y', and the
x-coordinate given for 'x':
-4 = -2/3(-7) + b
-4 = 14/3 + b
Solve for b:
-12/3 = 14/3 + b
-12/3 - 14/3 = b
-26/3 = b
Therefore, the equation of the line is y = -2/3x - 26/3 (Graphed below)
Some points on the line include:
(-7, -4)
(-4, -6)
(0, -26/3)
(2, -10)
(5, -12)
A bag contains two red marbles, four green ones, one lavender one, four yellows, and six orange marbles. HINT [See Example 7.] How many sets of four marbles include one of each color other than lavender
Answer:
192
Step-by-step explanation:
There are a total of 15 marbles . When the lavender is left out 14 remain.
Using combinations we find that each of the four color marbles can be chosen in the following way.
2C1*4C1*4C1*6C1= 2*4*4*6= 192
We select one of the two red marbles , one of the four green marbles, one of the four yellow marbles, one of the 6 orange marbles leaving the lavender out.. We apply combinations and then multiply to get the answer.
when Charles eats Oreos , he likes to dunk 2 out of every 5 cookies in a cold glass of milk. if he eats a total of 15 Oreos , how many will he dunk ? how many will ge eat without dunking?
Answer: 6 with milk, 9 without
Step-by-step explanation:
2/5 of the cookies he eats are dunked. Thus, simply do 2/5, or .4*15 to get that 6 cookies are dunked, and 15-6 to get that 9 cookies are not dunked.
Hope it helps <3
Amber says that the data set is left-skewed because the box is farther to the left on the number line. (A) Is Amber correct? (B) Explain your reasoning.
Given the radius of a circle is 7 cm, what is the circumference?
Answer:
14π or 43.96
Step-by-step explanation:
C = 2πr and we know that r = 7 so C = 14π or 43.96.
PLEASE ANSWER FAST I WILL MARK BRAINLEIST AMD 20 POINTSBased on the figure below what is the value of X
Answer:
[tex]\boxed{9}[/tex]
Step-by-step explanation:
The two angles are complementary to each other.
That means they add up to 90 degrees.
[tex]5x+15+30=90[/tex]
[tex]5x+45=90[/tex]
[tex]5x=45[/tex]
[tex]x=9[/tex]
Answer:
x = 9
Step-by-step explanation:
So you know that the total is 90 degrees.
What you need to do is create an equation.
5x + 15 + 30 = 90
Then, solve the equation like this.
5x + 15 + 30 = 90
5x + 45 = 90
5x = 90 - 45
5x = 45
x = 45 ÷ 5
x = 9
Hope this helps! :)
Roberta sold goods costing $35,500, her expenses totaled $2,500 and her freight in totaled $750.
Her company's average stock of goods during the same period was $9,500.
The inventory turnover ratio for Roberta's company is
Answer:
Inventory turnover ratio is 3.74
explanation:
Inventory turnover is a ratio of the number of times a company's inventory is sold and replaced in a given period.
Inventory turn over ratio is calculated as ; Cost of goods sold ÷ Average stock of goods sold
= $35,500 / $9500
= 3.74
Suppose that you have $100. You have two options for investing your money.
Option 1: Increase by $10 each year
Year
Amount
1
100
110
Type:
a =
b =
Answer:
Option One:
type : linear growth
a : 120
b : 130
Option 2:
type: linear growth
d : 121
e : 133
Step-by-step explanation:
its right on EDG 2020
Option One:
type: linear growth
a: 120
b: 130
Option 2:
type: linear growth
d: 121
e: 133
What is linear and exponential growth?Linear growth occurs with the aid of including an equal amount in each unit of time. An exponential increase happens while a preliminary population will increase by the same percent or issue over the same time increments or generations.
What is the distinction between linear and exponential?Linear and exponential relationships vary within the way the y-values change whilst the x-values increase with the aid of a steady quantity: In linear dating, the y-values have identical variations. In an exponential relationship, the y-values have identical ratios.
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1. Manuel quiere fabricar banderitas chilenas para venderlas en los partidos de la selección nacional. Si se demora 1 hora en hacer 45 banderitas y trabaja 5 horas diarias. ¿Cuántos días se demorará en fabricar 1800 banderitas?
Answer:
[tex]\large \boxed{\text{Eight days}}[/tex]
Step-by-step explanation:
1. Calculate the hours
[tex]\text{Hours} = \text{1800 flags} \times \dfrac{\text{1 h}}{\text{45 flags}} = \textbf{40 h}[/tex]
2. Calculate the days
[tex]\text{Days} = \text{40 h} \times \dfrac{\text{1 da}}{\text{5 h}} = \text{8 da}\\\\\text{It will take $\large \boxed{\textbf{eight days}}$ to make 4500 flags.}[/tex]
Which pairs of angles are alternate exterior angles? select yes or no
A - No
B - No
C - Yes
D - Yes
.
C and D are alternate exterior angles
When randomly selecting an adult, let B represent the event of randomly selecting someone with type B blood. Write a sentence describing what the rule of complements below is telling us. P B or B = 1 Choose the correct answer below. A. It is impossible that the selected adult has type B blood or does not have type B blood. B. It is certain that the selected adult has type B blood. C. It is certain that the selected adult has type B blood or does not have type B blood. D. It is certain that the selected adult does not have type B blood.
Answer: The rule of complements is apprising us that, the person selected will.eithwr have a type B blood or will not have a type B blood
Step-by-step explanations:
Find explanations in the attachment
A catering company is catering a large wedding reception. The host of the reception has
asked the company to spend a total of $454 on two types of meat: chicken and beef. The
chicken costs $5 per pound, and the beef costs $ 7 per pound. If the catering company
buys 25 pounds of chicken, how many pounds of beef can they buy?
The answer is 47 pounds
Explanation:
1. First, let's calculate the amount of money that was spent on chicken
$5 per pound of chicken x 25 pounds = $125
2. Calculate the amount of money left to buy beef by subtracting the total spend on chicken to the total of the budget.
$454 (total) - $125 (chicken) = $329
3. Calculate how many pounds of beef you can buy with the money left by dividing the money into the price for one pound.
$329 / $7 = 47 pounds
A factory manufactures chairs and tables, each requiring the use of three operations: cutting, assembly, and finishing. The first operation can use at most 40 hours; the second at most 42 hours; and the third at most 25 hours. A chair requires 1 hour of cutting, 2 hours of assembly, and 1 hour of finishing; a table needs 2 hours of cutting, 1 hour of assembly, and 1 hour of finishing. If the profit is $20 per unit for a chair and $30 for a table, what is the maximum revenue? Round your answer to the nearest whole number. Do not include a dollar sign or comma in your answer.
Answer:
z(max) = 650 $
x₁ = 10 units
x₂ = 15 units
Step-by-step explanation:
That is a linear programming problem, we will use a simplex method to solve it
Formulation:
Let´s call x₁ number of chairs and x₂ number of tables then :
Item (in hours) cutting assembly finishing Profit ($)
Chairs (x₁) 1 2 1 20
Tables (x₂) 2 1 1 30
Availability 40 42 25
Objective Function
z = 20*x₁ + 30x₂ ( to maximize) subject to:
x₁ + 2x₂ ≤ 40
2x₁ + x₂ ≤ 42
x₁ + x₂ ≤ 25
x₁ , x₂ >= 0
Using excel or any other software we find:
z(max) = 650
x₁ = 10
x₂ = 15
The chairs and tables manufactured by the factory is an illustration of linear programming, where the maximum revenue is 674
Let x represent chairs, and y represent tables
So, the given parameters are:
Cutting:
Chairs: 1 hourTable: 2 hoursHour available: 40So, the constraint is:
[tex]\mathbf{x + 2y \le 40}[/tex]
Assembly:
Chairs: 2 hoursTable: 1 hourHour available: 42So, the constraint is:
[tex]\mathbf{2x + y \le 42}[/tex]
Finishing:
Chairs: 1 hourTable: 1 hourHour available: 25So, the constraint is:
[tex]\mathbf{x + y \le 25}[/tex]
The unit profit on the items are:
Chairs: $20Table: $30So, the objective function to maximize is:
[tex]\mathbf{Max\ z = 20x + 30y}[/tex]
And the constraints are:
[tex]\mathbf{x + 2y \le 40}[/tex]
[tex]\mathbf{2x + y \le 42}[/tex]
[tex]\mathbf{x + y \le 25}[/tex]
[tex]\mathbf{x,y \ge 0}[/tex]
Using graphical method (see attachment for graph), we have the following feasible points:
[tex]\mathbf{(x,y) = \{(10,15),\ (17,8),\ (14.67, 12.67)\}}[/tex]
Calculate the objective function using the feasible points.
[tex]\mathbf{z = 20 \times 10 + 30 \times 15}[/tex]
[tex]\mathbf{z = 650}[/tex]
[tex]\mathbf{z = 20 \times 17 + 30 \times 8}[/tex]
[tex]\mathbf{z = 580}[/tex]
[tex]\mathbf{z = 20 \times 14.67+ 30 \times 12.67}[/tex]
[tex]\mathbf{z = 673.5}[/tex]
Approximate
[tex]\mathbf{z = 674}[/tex]
Hence, the maximum revenue is 674
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Find the present value of an investment that is worth $19,513.75 after earning 3% simple interest for 512 years.
Answer:
$16,750.00
Step-by-step explanation:
Simple interest:
I = Prt
Value of an investment of value P over t years at r interest rate:
F = P + Prt
F = P(1 + rt)
19,513.75 = P(1 + 0.03 * 5.5)
1.165P = 19,513.75
P = 16,750
Answer: $16,750.00
The present value of the investment was $16,750 which is worth $19,513.75 after earning 3% simple interest for 512 years.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100
We have been given data as:
Rate of Interest (R) = 3% = 3/100 = 0.03
Time (T) = 512 years
Value of an investment of value P over t years at r interest rate:
A = P + Prt
A = P(1 + rt)
19,513.75 = P(1 + 0.03 × 5.5)
19,513.75 = 1.165P
1.165P = 19,513.75
P = 19,513.75/1.165
P = 16,750
Thus, the present value of the investment was $16,750 which is worth $19,513.75 after earning 3% simple interest for 512 years.
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The state of CT claims that the average time on death row is 15 years. A random survey of 75 death row inmates revealed that the average length of time on death row is 17.8 years with a standard deviation of 5.9 years. Conduct a hypothesis to test the state of CT's claim. What type of test should be run? t-test of a mean z-test of a proportion The alternative hypothesis indicates a right-tailed test left-tailed test two-tailed test Calculate the p-value. What is the decision? We reject the claim that the average time on death row is 15 years We fail to reject the claim that the average time on death row is 15 years
Answer:
a)The calculated value t = 4.111 > 1.9925 at 5 % level of significance
Null hypothesis is rejected
The claim that the average time on death row is not 15 years
b) The p-value is 0.000101<0.05
we reject Null hypothesis
The claim that the average time on death row is not 15 years
Step-by-step explanation:
Step(i):-
Sample size 'n' =75
Mean of the sample x⁻ = 17.8
standard deviation of the sample (S) = 5.9
Mean of the Population = 15
Null hypothesis:H₀:μ = 15 years
Alternative Hypothesis :H₁:μ≠15 years
Step(ii):-
Test statistic
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }=\frac{17.8-15}{\frac{5.9}{\sqrt{75} } }[/tex]
t = 4.111
Degrees of freedom
ν = n-1 = 75-1=74
t₀.₀₂₅ = 1.9925
The calculated value t = 4.111 > 1.9925 at 5 % level of significance
Null hypothesis is rejected
The claim that the average time on death row is not 15 years
P-value:-
The p-value is 0.000101<0.05
we reject Null hypothesis
The claim that the average time on death row is not 15 years
A bag contains a collection of distinguishable marbles. The bag has two red marbles, three green ones, one lavender one, two yellows, and two orange marbles. HINT [See Example 7.] How many sets of four marbles include exactly two green marbles
Answer:
63
Step-by-step explanation:
Given that;
The bag has two red marbles, n(red) =2
three green ones marbles, n(green) = 3
one lavender one marbles, n(lavender) = 1
two yellows marbles, n(yellow ) = 2
two orange marbles. n(orange) = 2
number of non green marbles = 2+1+2+2 = 7
The objective is to find out how many sets of four marbles include exactly two green marbles
Since sets of four marbles contain exactly two green marbles, then N(select 2 from 3 marbles and 2 from 7 marbles)
= [tex]^3C_2 \times ^{7}C _2[/tex]
= [tex]\dfrac{3!}{2!(3-2)!} \times \dfrac{7!}{2!(7-2)!}[/tex]
= [tex]\dfrac{3*2!}{2!} \times \dfrac{7*6*5!}{2!(5)!}[/tex]
= [tex]3 \times 7\times 3[/tex]
= 63
4. Simplify the following.
3
a. 2-X5-:11
3
x5
5
6
7
Answer:
[tex]1 \frac{1}{4} [/tex]Step-by-step explanation:
[tex]2 \frac{3}{7} \times 5\frac{5}{6} \div 11 \frac{1}{3} [/tex]
Convert the mixed number to an improper fraction
[tex] \frac{17}{7} \times \frac{35}{6} \div \frac{34}{3} [/tex]
To divide by a fraction, multiply the reciprocal of that fraction
[tex] \frac{17}{7} \times \frac{35}{6} \times \frac{3}{34} [/tex]
Reduce the number with the G.C.F 7
[tex]17 \times \frac{5}{6} \times \frac{3}{34} [/tex]
Reduce the numbers with the G.C.F 17
[tex] \frac{5}{6} \times \frac{3}{2} [/tex]
Reduce the numbers with the G.C.F 3
[tex] \frac{5}{2} \times \frac{1}{2} [/tex]
Multiply the fraction
[tex] \frac{5}{4} [/tex]
In mixed fraction:
[tex]1 \frac{1}{4} [/tex]
Hope this helps..
Good luck on your assignment...
NEED HELP AS SOON AS POSSIBLE which interval describes where the graph of the function is negative
Answer:
2 < x < ∞
Step-by-step explanation:
We want where the value of y is less than zero
The value of the graph is less than zero is from x=2 and continues until x = infinity
2 < x < ∞
Answer:
[tex]\boxed{2 < x < \infty}[/tex]
Step-by-step explanation:
The value of y should be less than 0 for the graph of the function to be negative.
In the graph, when it startes from x is 2 the value becomes less than 0 and it keeps continuing until x is equal to infinity.
[tex]2 < x < \infty[/tex]
Consider a triangle ABC like the one below. Suppose that B=36°, C= 62°, and b= 40. (The figure is not drawn to scale.) Solve the triangle.
Round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".
Answer:
A=82°
a= 67.4
c = 60.1
Step-by-step explanation:
For A
A+B+C =180°
A= 180-(B+C)
A= 180-(36+62)
A= 189-(98)
A= 82°
For a
a/sinA= b/sinB
a/sin82= 40/sin36
a= (40*sin82)/sin36
a=( 40*0.9903)/0.5878
a=67.39
Approximately = 67.4
For c
c/sinC= b/sinB
c= (sinC*b)/sinB
c= (sin62*40)/sin36
c =(0.8829*40)/0.5878
c = 60.08
Approximately = 60.1
What point lies on the line described by the equation below? Y+3=2 (x-1
Answer:
[tex]\boxed{(1, -3)}[/tex]
Step-by-step explanation:
[tex]y+3=2 (x-1)[/tex]
Put equation in slope-intercept form.
[tex]y=mx+b[/tex]
[tex]y=2(x-1)-3[/tex]
[tex]y=2x-2-3[/tex]
[tex]y=2x-5[/tex]
Let x = 1
[tex]y=2(1)-5[/tex]
[tex]y=2-5[/tex]
[tex]y=-3[/tex]
The point (1, -3) lies on the line.