Answer:
0.5%=0.5/100
0.5/100×8=0.04
find all the zeros of the[tex]y = x^2 - x - 20[/tex] quadratic function
TO find the zeros of a quadratic function we should factorize the function
[tex]x^2-x-20=(x-)(x+)[/tex]So we have to find numbers that multiplied are -20 and added are -1. So we get -5 and 4
[tex]x^2-x-20=(x-5)(x+4)[/tex]
so the zeros of the function are 5 and -4
Lerato begins a new cycling programme with 2 km on the first day. Each day, he will increase his cycling by 500 m. How many kilometres will he cycle on day 30 of his programme?
He will cover total 247.5 kilometers on day 30 of his programe .
What is arithmetic progression ?When there are identical differences between every two next words, the series is known as an arithmetic progression (AP). There is a chance to find a formula for the nth term of the AP using this kind of development. The series 2, 6, 10, 14, etc., for instance, is an example of an arithmetic progression (AP) because it follows a pattern in which each number is acquired by adding 4 to the preceding word. Nth term in this series equals 4n-2.
Given that :Lerato begins a new cycling programme with 2 km on the first day. Each day, he will increase his cycling by 500 m.
The formula to find Sum of an arithmetic progression is
S = [tex]\frac{n}{2}[2a+(n-1)d][/tex]
here , a = 2km
n = 30
d = 0.5km
S =[tex]\frac{30}{2}[2(2)+(30-1)0.5][/tex]
S = 247.5 km
He will cover total 247.5 kilometers on day 30 of his programe
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helppppppppppppppppppypyppyoyoyoyoy
We are to solve using completing the square:
1/4x² + x + 1/4 = 0
Let's collect like terms:
1/4x² + x = -1/4
Divide both sides by the coefficient of x-squared:
x² + 4x = -1
Take half of the coefficient of x, square it, then add to both sides:
x² + 4x + 4 = -1 + 4
factor the left side of the equation:
(x + 2)² = 3
Take the root of both sides;
x + 2 = ±√3
Add 2 to both sides:
x = ±√(3) - 2
x = -2 + √3 or x = -2 - √3
herefore, the correct option is B, which is x = -2 + √3 or x = -2 - √3
3. A rectangle that is 2 cm by 3 cm has been scaled by a factor of 5. What are the dimensions of the new rectangle?
New width: 10 cm, new length: 15 cm
Or new width 15 and new length 10
1) Since this rectangle, has been scaled up by a factor k=5 (since 5 >1 then the rectangle has been enlarged)
2) Then we can write the following about their new dimensions:
w = 2 x 5 = 10
l = 3 x 5 = 15
3) So the answer is 10 x 15
Although there is a popular belief that herbal remedies such as Ginkgo biloba and Ginseng may improve learning and memory in healthy adults, these effects are usually not supported by well-controlled research (Persson, Bringlov, Nilsson, and Nyberg, 2004). In a typical study, a researcher
obtains a sample of n = 16 participants and has each person take the herbal supplements every day for 90 days. At the end of the 90 days, each person takes a standardized memory test. For the general popula-tion, scores from the test form a normal distribution with a mean of μ = 50 and a standard deviation of σ = 12. The sample of research participants had an average of M = 54. a. Assuming a two-tailed test, state the null hypoth-esis in a sentence that includes the two variables being examined.
b. Using the standard 4-step procedure, conduct a two-tailed hypothesis test with α = .05 to evaluate the effect of the supplements
Using the z-distribution to test the hypothesis, we have that:
a) The null hypothesis is [tex]H_0: \mu = 50[/tex].
b) The p-value of the test is greater than 0.05, hence we do not reject the null hypothesis, meaning that the supplements did not have the intended effect.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that the mean was different, hence:
[tex]H_0: \mu = 50[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the mean was different, hence:
[tex]H_1: \mu \neq 50[/tex]
What is the test statistic?The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.In the context of this test, the parameters are given as follows:
[tex]\overline{x} = 54, \mu = 50, \sigma = 12, n = 16[/tex]
Hence the test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{54 - 50}{\frac{12}{\sqrt{16}}}[/tex]
z = 1.33.
What is the p-value and what is the conclusion?Considering a two-tailed test, as we are testing if the mean is different of a value, with z = 1.33, the p-value of the test is of 0.1835, which is greater than 0.05, meaning that we do not reject the null hypothesis and the supplement did not change the mean.
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3.656 X 10^-5 written in standard form
To write 3.656 X 10^-5 in standard form 0.00003656
What is Standard Form ?
A mathematical item's canonical, normal, or standard form refers to how the object is typically expressed mathematically in both mathematics and computer science. It is frequently the one that offers the most straightforward illustration of the thing while yet enabling distinctive identification.
Move the decimal in the number that many spaces to the right when multiplying a number by 10 to the power of a positive exponent
(for example, (10)^3)).
For example, 4.5x(10)^3=4500.
Move the decimal in the number (the absolute value of) that many spaces to the left when multiplying a number by 10 to the power of a negative exponent
(for example, (10)^4)).
For example, (4.5x10)^4=(0.00045)
Move the decimal five spaces to the left for (3.656x 10)^-5:
0.00003656
Hence , 0.00003656 is Standard form of (3.656x 10)^-5
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Complete.
:14=15:21
Someone please answer how to solve
Answer:
The missing number is 10Step-by-step explanation:
Given ratiox : 14 = 15 : 21Multiply both sides by 14 to find the missing value:
x = 14*15/21 x = 10A scientist is working with two different concentrations of hydrochloric acid (HCI). One bottle is
80% HCI, and the other is 50% HCI. For their experiment they need 1 liter of 70% HCI.
How many liters of the 80% solution do they need?
How many liters of the 50% solution?
The liters of 80% material is 2/3 liters.
The liters of the 50% solution is 1/3 liters.
How to illustrate the information?Based on the information, the scientist is working with two different concentrations of hydrochloric acid (HCI).
Let x = volume of 80%
Let 1 -x =volume of 50%
Therefore, the expression to illustrate the information will be:
80x + 50 × (1 - x) = 70
80x + 50 - 50x = 70
30x = 70 - 50
30x = 20
Divide
x = 20/30
x = 2/3
Therefore there are 2/3 liters of 80% material
The liters for the 50% solution will be 2/3 subtracted from 1. The 2/3 implies that for the 80% material. This will be:
= 1 - 2/3
= 1/3
There are also 1/3 liters of 50% material.
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Give an example of each survey question type below that would relate to an organic produce farmer.
a) Dichotomous
b) Multiple choice
c) Rating scale
d) Completion
e) Open-ended
Examples of each survey question that relates to organic farm produce are as follows;
a) Dichotomous
Do you prefer organic farm produce?
Yes/No
b) Multiple choice
How many of your colleagues make use of organic farm produce
OneTwoThreeFourFivec) Rating scale
On a scale of 1 to 5, with 10 being happiest, how happy are you about our customer service?
1, 2, 3, 4, 5
d) Completion
Eating organic produce _______ improve my health
Will
Will not
e) Open-ended
Tell us why you prefer organic farm produce ___________
What is a statistical survey?A survey involves the administration of questions or the examination of a process that is aimed at obtaining data with regards to a service, process or product.
a) Dichotomous questions are questions that can have only two possible responses. Such questions are used in a survey in which the two possible responses are stated such as Agree/Disagree, Yes/No, Fair/Unfair, True/False, or Cold/Hot. Based on the definition of the responses, the opinion of the responder is made clear
An example of a dichotomous question asked with respect to organic farm produce is 'Do you prefer organic farm produce?'
The possible responses are; Yes/No
b) Multiple choice survey question
Multiple choice questions provide the opportunity for a respondent to have more options to choose a response from. The multiple choice questions also allow researcher to obtain detailed information on the subject.
An example of multiple choice question is as follows;
How many of your colleagues make use of organic farm produce
OneTwoThreeFourFivec) Rating Scale
In rating scale survey questions the respondents are asked to select a rating of their experience in a response that offers a rating such as 1 to 10 or 1 to 100
An example of a rating scale question in a survey is as follows;
On a scale of 1 to 5, with 10 being happiest, how happy are you about our customer service?
1, 2, 3, 4, 5
d) Completion
Completion type question assesses the level of cognition on a subject matter
Example;
Eating organic produce _______ improve my health
WillWill note) Open–ended
Open–ended questions gives respondents the latitude to express themselves with regards to the question in written text in a detailed or in a brief response.
Example;
Tell us why you prefer organic farm produce ___________
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Pierce is making a rectangular frame for a photo collage that has a perimeter of 72.2 inches. The length of the frame is 20.3 inches.
Write an equation to find the width of the frame, x.
Enter the correct equation in the box.
An equation to find the width of a rectangular frame with perimeter 72.2inches and length 20.3 inches is given by 2( 20.3 + x ) = 72.2 .
As given in the question,
Pierce is making a rectangular frame for a photo collage.
Perimeter of a rectangular frame is equal to 72.2 inches.
Length of the rectangular frame is equal to 20.3 inches
Perimeter of the rectangle = 2(length + width) __(1)
Let x inches be the width of the frame
Equation with x width of the frame is given
2(20.3 + x) = 72.2
Therefore, an equation to find the width of a rectangular frame with perimeter 72.2inches and length 20.3 inches is given by 2( 20.3 + x ) =72.2.
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what is the inequality of 1< x <5 on a number line.
When we write an inequality in the form:
[tex]1We are indicating the both are true: x is greater than 1 and x is less than 5. This means that x is between 1 and 5 (not including neither ends).In a number line, we can draw it, mark the endpoints (1 and 5) and then we highlight the parts at which the x is, which is in the middle:
Notice that we marked the endpoints as empty dots, which indicates that the endpoints are not included in the interval.
Jaxon was taking his boat out around the lake. The boat is able to drive for 18 minutes for every gallon of gas. Jaxon has 8 gallons of gas in his boat so he bought another 12 gallons. How long can the boat run for now? (In minutes)
Answer:
hi
Step-by-step explanation:
i dot no because i dot spak in english because im frach
Factor the trinomials:
1) [tex]x^2 -2x-2[/tex]
2)[tex]x^2-6x+4[/tex]
Given that equation
1) [tex]x^{2} - 2x - 2[/tex] using the general quadratic equation, x = 1
2)[tex]x^{2} -6x -4[/tex] using the general quadratic equation, x= [tex]\frac{6 - \sqrt{20} }{2}[/tex]
According to the question, given that
1) [tex]x^{2} - 2x - 2[/tex]
2)[tex]x^{2} -6x -4[/tex]
this equation cannot be factored but using general quadratic equation. we solved it easily.
When asked to solve a quadratic equation that you just can’t seem to factor (or that just doesn’t factor), you have to employ other ways of solving the equation, such as by using the quadratic formula. The quadratic formula is the formula used to solve for the variable in a quadratic equation in standard form.
Given a quadratic equation in standard form ax2 + bx + c = 0,
[tex]x = \frac{- b - \sqrt{b^{2} - 4 ac } }{2a}[/tex] and [tex]x = \frac{- b + \sqrt{b^{2} - 4 ac } }{2a}[/tex]
solve [tex]x^{2} - 2x - 2[/tex] = 0, you first say that a = 1, b = –2, and c = 2. The a, b, and c terms simply plug into the formula to give you the values for x:
1) [tex]x^{2} - 2x - 2[/tex]
[tex]x = \frac{- (-2) + \sqrt{(-2)^{2} - 4 (1)(1) } }{2(1)}[/tex]
[tex]x = \frac{2 + \sqrt{4 -4} }{2}[/tex]
x = [tex]\frac{2}{2}[/tex]
[tex]x = 1[/tex]
and [tex]x = \frac{- (-2) - \sqrt{(-2)^{2} - 4 (1)(1) } }{2(1)}[/tex]
[tex]x = \frac{2 - \sqrt{4 -4} }{2}[/tex]
x = [tex]\frac{2}{2}[/tex]
[tex]x = 1[/tex]
equation [tex]x^{2} - 2x - 2[/tex] and x= 1
2)[tex]x^{2} -6x -4[/tex]
solve [tex]x^{2} - 6x - 4[/tex] = 0, you first say that a = 1, b = –6, and c = 4. The a, b, and c terms simply plug into the formula to give you the values for x:
[tex]x^{2} -6x -4[/tex]
[tex]x = \frac{- (-6) + \sqrt{(-6)^{2} - 4 (1)( 4) } }{2(1)}[/tex]
[tex]x = \frac{6 + \sqrt{36 - 16} }{2}[/tex]
x = [tex]\frac{6 \sqrt{20} }{2}[/tex]
and [tex]x = \frac{- (-6) - \sqrt{(-6)^{2} - 4 (1)(4) } }{2(1)}[/tex]
[tex]x = \frac{6 - \sqrt{36 - 16} }{2}[/tex]
x = [tex]\frac{6 - \sqrt{20} }{2}[/tex]
equation [tex]x^{2} - 6x + 4[/tex] and x= [tex]\frac{6 - \sqrt{20} }{2}[/tex]
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M2 U2 Practice 6
Given: the equation of line lis y = -x +4
Write the equations of the lines passing through the point (6,7) that are (a) perpendicular to line I, and (b) parallel to
line l.
Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines. Parallel lines can also be said to meet at infinity.
What formula should you use to represent the line that passes through the given points?How to determine a line's equation from two points:
Using the slope formula, determine the slope.
To find the y-intercept (b), use the slope and one of the points.
You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of the line (y = mx + b).
y = -x/3 + 5 is the equation that depicts the line that crosses through the coordinates (-6, 7) and (-3, 6).
3 Answers What is the slope of the line passing through (- 7 2 and 6 7? by Certified Tutors
The slope of the equation would be nine.
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10. A blood alcohol content (BAC) of 0.08 g/100 mL means
Tanisha earns $3,000 per month
after taxes. She saves $720. What
percent of her budget is savings?
Answer:
[tex]{ \tt{\% savings = \frac{savings}{total \: income} \times 100\%}} \\ \\ { \tt{ = \frac{720}{3000} \times 100\%}} \\ \\ = { \tt{24\%}}[/tex]
Answer:
24%
Step-by-step explanation:
[tex]\boxed{\sf Percent=\left(\dfrac{Value}{Total\:value}\right) \times 100}[/tex]
Given information:
Value (savings) = $720Total value (earnings) = $3,000Substitute the given values into the formula and solve for percent:
[tex]\begin{aligned}\implies \textsf{Percent} & =\dfrac{720}{3000} \times 100\\\\& = \dfrac{720\times 100}{3000} \\\\& = \dfrac{72000}{3000} \\\\& = \dfrac{72}{3} \\\\& = 24\% \end{aligned}[/tex]
Therefore, 24% of Tanisha's budget is savings.
Aidan scored 390 points in 20 games what is his scoring rate in points per game?
Answer:
19.5
Step-by-step explanation:
Kara categorized her spending for this month into four categories: Rent, Food, Fun, and Other. The amountsshe spent in each category are pictured here.Food$289Rent$361Other$433Fun$217What percent of her total spending did she spend on Rent? Answer to the nearest whole percent.
Total expenses = $289 + $361 + $433 + $217 = $1300
Percentage of money spent on rent:
(Money spent on rent)/(Total expenses) = $361/$1300 = 0.2777 ≈ 28%
Therefore 28% of total expenses are for rent
The formula to show the height and time an object is in the air is given byh(t) = -16t2 + 48t + 50 where h(t) is the height of an object and t is the timein seconds. Find how long the object is in the air before it hits the ground.
The formula to show the height and time an object is in the air :
[tex]h(t)=-16t^2+48t+50[/tex]when the object hits the ground the height will become 0
so, put h(t) = 0
and simplify :
[tex]\begin{gathered} h(t)=-16t^2+48t+50 \\ 0=-16t^2+48t+50 \\ -16t^2+48t+50=0 \end{gathered}[/tex]Simplfy the equation by using discrimination rule :
The general form of quadratic equation is : ax² + bx + c
and the roots are express a s :
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]On compare the given equation with the general equation we get :
a = -16, b = 48 and c = 50
Substitute the value and simplify :
[tex]undefined[/tex]Choose the expression that is equivalent to a fraction with six raised to the negative third power in the numerator and the quantity three raised to the negative second power times six squared end quantity in the denominator and the entire fraction is cubed.
three raised to the sixth power divided by six raised to the fifteenth power
three squared divided by six raised to the fifth power
negative three raised to the sixth power divided by six raised to the fifteenth power
negative three squared divided by six raised to the fifth power
The value of the expression in the options is (a) three raised to the sixth power divided by six raised to the fifteenth power
How to determine the equivalent expression of the expression?The expression is given as
A fraction with six raised to the negative third power in the numerator and the quantity three raised to the negative second power times six squared end quantity in the denominator and the entire fraction is cubed.
Rewrite the expression properly
So, we have
[6^-3/(3^-2 x 6^2)]^3
Apply the law of indices to the expression
So, we have
[6^-3/(3^-2 x 6^2)]^3 = [6^(-3 - 2)/(3^-2)]^3
Evaluate the difference
[6^-3/(3^-2 x 6^2)]^3 = [6^-5/(3^-2)]^3
Apply the change of power rule
[6^-3/(3^-2 x 6^2)]^3 = [3^2/6^5]^3
Evaluate the product of exponents
[6^-3/(3^-2 x 6^2)]^3 = 3^6/6^15
In words, the result is (a) three raised to the sixth power divided by six raised to the fifteenth power
Hence, the value of the expression is (a)
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The retail cost of a TV is 10% more than its wholesale cost. Therefore, the retail cost is
The retail cost is
times the wholesale cost.
Answer:
1.1
Step-by-step explanation:
You want the multiplier of the wholesale cost that makes the retail cost be 10% more.
MultiplierThe retail cost is said to be ...
retail cost = (wholesale cost) + 10% × (wholesale cost)
= (wholesale cost) × (1 +10%)
= (wholesale cost) × 1.10
The retail cost is 1.10 times the wholesale cost.
DERMarissa VasquezDATEArcs and ChordsLGEBRA Find the value of x in each circle.1.2.KN384x+10=384x=284x + 10X=7M70°LР4. OR = OS(5x - 1)°3..109°A
SOLUTION
Given the question in the image, the following steps can be used to get x
Step 1: Explain the concept of equal arcs in a circle
If a circle is divided into arcs, then each arc is a minor arc and they all sum up to be equal to the total angles in the circumfference of the circle which is 360 degrees.
Step 2: Explain the breakdown of the minor arcs in the circle
It can be seen that the minor arcs divided the circle into three parts which are two equal arcs and a 70 degrees arc. This implies that:
[tex]x+x+70=360^{\circ}_{}[/tex]Step 3: Find x
[tex]\begin{gathered} x+x+70=360 \\ 2x=360-70 \\ 2x=290 \\ x=\frac{290}{2} \\ x=145^{\circ} \end{gathered}[/tex]Hence, the value of x in the given circle is 145 degrees
What is the quotient of 2.538\times 10^92.538×10
9
and 2.7 \times 10^22.7×10
2
expressed in scientific notation?
IF U DON"T KNOW THE ANSWER DON"T ANSWER & work it out plss
The quotient of 2.538 ×10^9 and 2.7×10^2 expressed in scientific notation is : 0.94 × 10^6.
Scientific notationGiven:
2.538 × 10^ 9 and 2.7 × 10^ 2
We have to first of all formulate before determining the scientific notation
(2.538 × 10^ 9) ÷ (2.7 × 10^2)
Rewrite as fraction
2.538 × 10^9 ÷ 2.7 × 10^2
simplify
2.538 ÷ 2.7 × 10^ 9-2
= 2.538 ÷ 2.7 × 10^7
Convert the fraction to decimal
0.94 × 10^7
Now let express it in scientific notation
Scientific notation = 94 × 10^6
Therefore the scientific notation is 94 × 10^6.
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The correct question is:
What is the quotient of 2.538 ×10^9 and 2.7×10^2 expressed in scientific notation
Find the sum of the first 31 terms of the following series, to the nearest integer. 4, 11,18,... 4,11,18,...
The sum of the first 31 terms of the arithmetic series is 114.
What is arithmetic series?
In mathematics, arithmetic series is the sequence of the number whose common difference between the two consecutive number is always constant. And the sum of the series is depend on the first term as well as on the last term.
According to the question, the given series is an arithmetic series. In the common difference is same.
The given series is:
4, 11, 18,....4, 11, 18,....4, 11, 18,....
To know the sum of the given series, first calculate the sum of the first three numbers. And later multiply by ten.
Using standard formula for the sum of the arithmetic series:
[tex]S_{3} =\frac{(first term + last term)}{2} = \frac{4+18}{2} =11[/tex]
Therefore to calculate the sum of the 31 terms:
s(31 terms) = 10(11) + first term = 110 + 4 = 114
Hence, the sum of the first 31 terms of the arithmetic series is 114.
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a wood cutter has 1/4 + 2/4 + 3/4 of wood And goes to the store and buys 1/4 + 2/4 + 3/4 And adds all of his wood up.
Answer: I believe the answer is 3.
Step-by-step explanation:
a wood cutter has 1/4 + 2/4 + 3/4 So we add those up to get 6/4.
Then he buys the same amount again which would make 12/4.
We are not done probably, so we MUST simplify.
how many times can 4 fit into 12? 3! so we have whole number 3 and since 4 fit into 12 3 times perfectly all we have is 3
THE GILBERTS PURCHASED A CAR. IF THE TOTAL COST, INCLUDING A 5% SALES TAX, WAS $14,512, FIND THE COST OF THE CAR BEFORE TAX
The cost of the car the Gilberts purchased before tax is $13,820.52.
What is the cost before tax?Tax is a compulsory amount that is levied on a good or service by the government. A sales tax is a tax that is levied on the purchase of a good and service. Taxes increase the cost of a good or service.
The equation that can be used to determine the cost of the car after tax is:
(1 + sales tax) x cost before tax = cost after tax
(1 + 0.05) x c = $14,512
1.05c = $14,512
In order to determine the value of c, divide both sides of the equation by 1.05:
c = $14,512 / 1.05
c = $13,820.52
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Sam is installing a walkway around a rectangular flower patch in his garden. The flower patch is 12 feet long and 6 feet wide. The width of the walkway is x feet.
Sam created function A to represent the total area taken up by the flower patch and walkway by multiplying the functions modeling the new total length and width.
What does represent in this function?
A.
the area of the walkway along the width of the flower patch
B.
the total area of the walkway
C.
the total area of the flower patch
D.
the area of the walkway along the length of the flower patch
The function represents the area of the walkway along the width of the flower patch.
What is function?Rule, or law that establishes the link between an independent variable and a dependent variable is known as function.
Functions can be found everywhere in mathematics, and they are essential for building physical connections in the sciences.
The German mathematician Peter Dirichlet initially offered the contemporary definition of function in 1837.
The total area taken up by the flower patch and walkway by multiplying the functions modeling the new total length and width represents the area of the walkway along the width of the flower patch.
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Your cousin gave you $13.78 with which
to buy a present. This covered 2/3 of the
cost. How much did the present cost?
The cost of the present is $20.67
Given,
The cost of the present = x
Amount given by cousin = $13.78
Amount given by cousin is 2/3 of x.
That is,
13.78 = 2/3 of x
Lets find x
13.78 = 2/3 × x
13.28 = 2x/3
Multiply with 3 on both sides
13.78 × 3 = (2x/3) × 3
We get,
41.34 = 2x
Divide 2 on both sides
That is,
41.34/2 = 2x/2
We get,
x = 20.67
Here, x is the cost of the present
Therefore, the cost of the present is $20.67
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point a of a triangle is at 2, to point via that a reflection of a point across the X axle a c is 5 unit directly to the left of the point B what are the triangles Dimensions you may you wish to plot the point on your own piece of graph paper
From the question;
Point A is at (2,2)
Point B is the reflection of point A across the x-axis;
The rule for reflection across the x-axis is;
[tex](x,y)\rightarrow(x,-y)[/tex]So, point B will be;
[tex]A(2,2)\rightarrow B(2,-2)[/tex]The point C is 5 units directly left of point B;
So, point C will be;
[tex]\begin{gathered} (x,y)\rightarrow(x-5,y) \\ B(2,-2)\rightarrow C(2-5,-2) \\ B(2,-2)\rightarrow C(-3,-2) \end{gathered}[/tex]Therefore, the coordinates of the Points A, B and C are;
[tex]\begin{gathered} A(2,2) \\ B(2,-2) \\ C(-3,-2) \end{gathered}[/tex]Shown as;
So, the length AB is;
[tex]AB=2-(-2)=4[/tex]The length BC is;
[tex]undefined[/tex]HELP ASAP 30 POINTS 9TH GRADE MATH. WILL GIVE BRAINIEST IF CORRECT
Solve.
Question 1.
-4x + 17 ≥ 9.
Question 2.
| 5 + z | + 3 = 10.
Question 3.
Match to the correct one
5y + 2 = 5y + 8. 1. All real numbers
2 (y + 4) = 2y + 8. 2. No solutions
5y + 2 = 2y + 8 3. Infinity many solutions.
Question 4.
Solve for x.
x - 4 ≥ 5. SHOW YOUR WORK.
question 5.
solve for x.
12x = 4 (2x -3) - 12.
SHOW YOUR WORK.
Question 7.
Solve for x
3(x + 2) = 3x + 2
For the given problems we have:
1) The solution of the inequality is:
x ≤ 2
2) The absolute value equation has two solutions:
z= 2
z = -12
3) The correct matches are:
5y + 2 = 5y + 8 this has no solutions2*(y + 4) = 2y + 8 this has infinite solutions5y + 2 = 2y + 8 This has a single solution.How to solve the different operations?Remember that solving means to isolate the variable in one side of the expression.
1) We have the inequality:
-4x + 17 ≥ 9
-4x ≥ 9 - 17
x ≤ -8/-4
x ≤ 2
This is the solution of the inequality.
2) We have the absolute value function:
|5 + z| + 3 = 10
|5 + z| = 10 - 3 = 7
We can decompose this into:
5 + z = 7
5 + z = -7
Then the two solutions are:
z = 7 - 5 = 2
z = -7 - 5 = -12
3) The correct matches here are:
5y + 2 = 5y + 8 this has no solutions, these are parallel lines.2*(y + 4) = 2y + 8 this has infinite solutions (all real numbers).5y + 2 = 2y + 8 This has a single solution.Learn more about inequalities:
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