5x² + 2x - 3 < 0
5x² + 2x < 3
x² + 2/5 x < 3/5
Complete the square on the left side:
x² + 2/5 x + 1/25 - 1/25 < 3/5
(x + 1/5)² - 1/25 < 3/5
(x + 1/5)² < 16/25
Take the square root of both sides, keeping in mind that √(x²) = |x| for all x.
√((x + 1/5)²) < √(16/25)
|x + 1/5| < 4/5
This means
-4/5 < x + 1/5 < 4/5
-1 < x < 3/5
A rectangle has a length of 2x+1 and a width of 3x-2.
Write an expression for the area of the rectangle.
Answer:
(2x+1)x(3x-2)
Step-by-step explanation:
area of rectangle = length * width
length = 2x+1
width = 3x-2
area = (2x+1) x (3x-2)
A 40 -inch board is to be cut into three pieces so that the second piece is 4 as long as the first piece and the third piece is 5 times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces.
Answer:
4*4=16 INCHES FOR THE SECOND PIECE. 5*4=20 INCHES FOR THE LONGEST PIECE.
Step-by-step explanation:
x = 20 inch, the length of the first piece
What is mathematical expression?
A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
given,
Total length = 40 inch
let first piece be = x inch
second piece = 4 times of first piece = 4x inch
third piece = 5 times of first piece = 5x inch
So,
x + 4x + 5x = 200
10x = 200
x = 200/10
x = 20
Therefore, the length of the first piece is 20 inch
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Factors are the numbers used to multiply. True False
Answer:
True
Step-by-step explanation
Write an equation in point-slope form of the line that passes through the given point and with the given slope m. (-9,6); m = 6 The equation of the line is (Simplify your answer. Type your answer in point-slope form.)
Answer:
y = -54 + 60
Step-by-step explanation:
multiply 6 and -9 to get -54 (6)(-9) = -54
then subtract -54 from 6 to get 60 6 - (-54) = 60
then put it in equation form as, b = 60, and x = -54
y = -54 + 60
plz mark brainliest
The equation of line passes through the points (-9, 6) will be;
⇒ y = 6x + 60
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point on the line is (-9, 6).
And, The slope = 6
Now,
Since, The equation of line passes through the point (-9, 6).
And, Slope of the line is,
m = 6
Thus, The equation of line with slope 6 is,
⇒ y - 6 = 6 (x - (-9))
⇒ y - 6 = 6 (x + 9)
⇒ y - 6 = 6x + 54
⇒ y = 6x + 54 + 6
⇒ y = 6x + 60
Therefore, The equation of line passes through the points (-9, 6) will be;
⇒ y = 6x + 60
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Alan Jeff and Lucy all take their pets to the same vet. The pets are a dog a cat and a rabbit. The names of the pets are Blackie bandit and Moe. Read the clues to determine the kind of pet each owner has and the name of the pet. Mark the correct boxes on the grid to show your answers.
Answer:
i need at least a pick of the problom
Step-by-step explanation:
Answer:
huh?
Step-by-step explanation:
help me please i’ll give u a cookie
Answer:
the answer is B
Step-by-step explanation:
i just did this.
Jamie borrowed $361.75 from his uncle,
who has agreed to charge him a monthly
simple interest rate of 2.5%. Jamie pays
his uncle back in 7 months.
Answer:
Jamie will pay back a total of 370.79
Step-by-step explanation:
361.75 x 1.025
Simple interest is not compounded so just multiply the borrowed amount by
1 + .025
He pays 370.28125.
What is Simple Interest?Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.
Given:
Jamie borrowed = $361.75
Simple interest = 2.5%
As, Simple interest is not compounded.
so,
361.75 x 1.025
=370.28125
Hence, he pays 370.28125.
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sixteen people wore white socks. The ratio of those who wore white socks to those who wore black socks 1:2. How many people wore black socks?
Answer:
It should be 32.
Step-by-step explanation:
If a1=2 and an=an-1+5 then whats the value of a5
Answer:
a5=10
Step-by-step explanation:
a1=2 a2=4 a3=6 a4=8 a5=10
The value of the 5th term of the arithmetic sequence will be 22.
What is an arithmetic sequence?A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.
The value of the first term is 2. Then the value of the 5th term is calculated as,
a₂ = a₁ + 5
a₂ = 2 + 5
a₂ = 7
a₃ = a₂ + 5
a₃ = 7 + 5
a₃ = 12
a₄ = a₃ + 5
a₄ = 12 + 5
a₄ = 17
a₅ = a₄ + 5
a₅ = 17 + 5
a₅ = 22
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Multiply 3/5 by 10/21 Express your answer in simplest form
Answer:
2/7
Step-by-step explanation:
Answer:
3/5 * 10/21= 2/7
Pls help - Solve for x
Answer:
-3
3x/(x^2+6x) = 1 is this the qstn?
if so then the ans is -3
The population of New Town is increasing by 6% a year.
If the population was 19613 on January 1st, 2000, what was it on January 1st, 2020?
Give your answer to the nearest 100 people.
Answer:
After population (A) = 62,902 (Approx)
Step-by-step explanation:
Given:
Current population (P) = 19613
Number of years (n) = 2020 - 2000 = 20 year
Rate of growth (r) = 6% = 0.06
Find:
After population (A)
Computation:
[tex]After\ population (A) = Current\ population (P)[1+r]^n \\\\After\ population (A) = 19613[1+0.06]^{20} \\\\After\ population (A) = 19613[1.06]^{20} \\\\After\ population (A) = 62,901.548[/tex]
4 1/8÷2 3/4 convert the mixed numbers to improper fractions
Answer:
Check picture
Step-by-step explanation:
9514 1404 393
Answer:
1 1/2
Step-by-step explanation:
[tex]\dfrac{4\dfrac{1}{8}}{2\dfrac{3}{4}}=\dfrac{\left(\dfrac{4\cdot8+1}{8}\right)}{\left(\dfrac{2\cdot4+3}{4}\right)}=\dfrac{\left(\dfrac{33}{8}\right)}{\left(\dfrac{11}{4}\right)}=\dfrac{\left(\dfrac{33}{8}\right)}{\left(\dfrac{22}{8}\right)}=\dfrac{33}{22}=\dfrac{3}{2}[/tex]
Then the improper fraction 3/2 can be written as the mixed number 1 1/2.
(4 1/8) / (2 3/4) = 1 1/2
_____
Comment on division of fractions
Fractions can be divided several ways. Two ways that are commonly taught are "invert and multiply", or "match denominators". Here, we have used the second of these methods.
If we were to "invert and multiply", the computation would be ...
(33/8)(4/11) = (33/11)(4/8) = 3(1/2) = 3/2
Instead, we multiplied 11/4 by 2/2 to make it be 22/8, so having a denominator of 8 matching that of the numerator. Then the value of the compound fraction is the ratio of the numerators:
(33/8)/(22/8) = 33/22 = (3/2)(11/11) = 3/2
This is for 11th grade math
Two shooters, Rodney and Philip, practice at a shooting range. They fire 100 rounds each at separate targets. The targets are marked with circles and each bullet hitting a particular circle gets them a particular number of points. 60 rounds are selected at random. The sample mean scores of Rodney and Philip are 8 and 10, respectively. And, their variances are 0.25 and 0.50, respectively The standard error of the difference between their mean scores is ______________ (Round your answer to two decimal places.) The 95% confidence interval for the difference between the mean scores Rodney and Philip is ________ _____________: (Enter a minus sign if your answer is negative. Round your answer to two decimal places.)
Answer:
A) SE = 0.1118
B) 95% Confidence interval is;
-2.22 < μ1 - μ2 < -1.78
Step-by-step explanation:
We are given;
Sample size; n = 60
Sample mean 1; x1 = 8
Sample mean 2; x2 = 10
Variance 1; v1 = 0.25
Variance 2; V2 = 0.5
Now,
Standard deviation is given by the formula ;
σ = √variance
Thus;
σ1 = √0.25
σ1 = 0.5
σ2 = √0.5
σ2 = 0.7071
Formula for standard error of mean is;
SE = σ/√n
Thus;
SE1 = 0.5/√60
SE1 = 0.06455
SE2 = 0.7071/√60
SE2 = 0.0913
The standard error of the difference between their mean scores would be;
SE = √[(SE1)² + (SE2)²]
SE = √(0.06455² + 0.0913²)
SE = 0.1118
Formula for 95% confidence interval is;
(x1 - x2) - ((Z_α/2) × SE) < μ1 - μ2 < (x1 - x2) + ((Z_α/2) × SE)
Where Z_α/2 is the critical value. At confidence interval of 95%, we have a critical value of 1.96 from tables.
Thus, plugging in the relevant values, we have;
(8 - 10) - (1.96 × 0.1118) < μ1 - μ2 < (8 - 10) + (1.96 × 0.1118)
-2.22 < μ1 - μ2 < -1.78
Hello, I wanted to leave you this photograph of mathematics that I think will be very useful to some of you, observe it
Answer:
yes
Step-by-step explanation:
Answer:
thank you
Step-by-step explanation:
:)
this is the last question i need help on! i will mark brainlessttt :)thanks
Answer:
A.3
Step-by-step explanation:
Since the lines are parallel that angle is 90 same as the other. So you plug in all your answers to see with one gives you 90 that being 3 because 30(3)=90.
Uma caixa contém 40 bolinhas de jogo de tênis, sendo 10 verde, 14 azuis e 16 vermelhas. Retirando uma bola ao acaso da caixa, qual a probabilidade desta bola ser vermelha? Assinale a alternativa correta, que representa a probabilidade desta situação.
qual dessas quatro e a resposta .
14 / 40
15 / 40
16 / 40
17 / 40
Answer:
p = 15/40
Step-by-step explanation:
Since the total number of marbles is 40, that is our size of the sample. there are 16 red ones on that sample, so the probability of extracting a red marble from the box is given by the ratio of successes divided the total number of marbles:
p = 15/40
The following table shows the height of a plant at different ages.
Age (in weeks)
3
7
10
Height (in centimeters)
12
35
60
Is the height of the plant proportional to its age?
Choose 1 answer:
А
Yes
B
No
Answer:
the answer to this question would be A
1 5/16 divided by 7/12
please i need in under 20 mintute quick
Answer:
its been over twenty minutes. did you figure it out ?
A proposed change in income tax suggests charging 20% on a person's income up to $30,000 and then 40% on any
income above that. If a person has an income of $47,000, what will be their income tax under the proposal?
Give your answer in dollars to the nearest dollar. Do not include commas or the dollar symbol in your answer.
Provide your answer below
Answer:
If you get tax you should know the details of the what the tax is FOR
Step-by-step explanation:
Not enough details in question
Answer:
Step-by-step explanation:
Since the person earns over $30,000, they will be charged 20% on $30,000 plus 40% on ($47,000−$30,000)=$17,000. Hence the total amount of tax that they'd need to pay under the proposal is
Total Income Tax=$30,000×20%+$17,000×40%=$30,000×20100+$17,000×40100=$6,000+$6,800=$12,800.
A factory that manufactures screws is performing a quality control experiment. Each object should have a length of no more than 19 centimeters. The factory believes that the length of the screws exceeds this value and measures the length of 65 screws. The sample mean screw length was 19.04 centimeters. The population standard deviation is known is known to be 0.19 centimeters. What is the null hypothesis and what is the alternative hypothesis?
Answer:
Step-by-step explanation:
Ok
Answer:
A factory that manufactures bolts is performing a quality control experiment. Each object should have a length of no more than 11 centimeters. The factory believes that the length of the bolts exceeds this value and measures the length of 76 bolts. The sample mean bolt length was 11.09 centimeters. The population standard deviation is known to be 0.29 centimeters.
What is the test statistic ?
What is the -value?
Does sufficient evidence exist that the length of bolts is actually greater than the mean value at a significance level of
Rewrite the following using the GCF and the distributive property
:32 + 54
Answer:
GCF: 2
Step-by-step explanation:
GCF: 2
(2*16) + (2*27)
PLEASE HELP ASAP
Prove that triangles PQR and RSQ are congruent.
Given:
PQ = RS, and
Answer:
Step-by-step explanation:
ok so lets assume that line PQ and RS and QR and PS are parallel lines cut by a transeversal. To prove this you can do it in a couple of different ways the one way i know is that if you assume these are parralel then you can uses the alternate interior anges to prove that measure of QSP and SQR then by logic you know that PQS + SQR = RSQ+QSP which symplifies to PQR = RSQ
A researcher wanted to determine the prevalence of type 2 diabetes among persons living with HIV in Ojai, a small town in California. He developed a survey questionnaire and mailed to 600 residents of Ojai. The survey asked participants several questions including whether their doctor or health care professional ever told them that they had diabetes. All 600 residents completed the survey and the researcher considered their sample a random sample of the 2,500 total residents of 3 Ojai. The following data was compiled from the survey. The prevalence of diabetes in the sampled survey was 6%. The researcher wanted to compare the prevalence of diabetes by smoking status. In their survey, they found that among 230, who were smokers, 157 reported diabetes and among the remaining nonsmokers, 50 reported diabetes.
Construct a two by two table using the data given above. Be sure to label the cells and margins.
Diabetes
Yes No
Smoking Yes a b
No с d
Total
Answer:
Step-by-step explanation:
Given that:
There are 600 residents in the survey.
And results gathered identify that among 230 who were smokers, 157 are reported to have diabetes and among the remaining nonsmokers, 50 reported diabetes.
The objective is to construct a two by two table from the given data:
Diabetes
Yes No Total
Smoking
Yes 157 230 - 157
= 73 230
No 50 370 - 50 600 - 230
= 320 = 370
Total 157 + 50 320+ 73
= 207 = 393 600
A grocery store sells bananas for $0.59 per pound. On Wednesdays, the store offers a 10% discount to senior
citizens. Create a function f (x) which models the amount, in dollars, a senior citizen would pay for 2 pounds
of bananas on Wednesday
Answer:
2
Step-by-step explanation:
f(x)= 0.90(0.59*2)
A grocery store sells bananas for $0.59 per pound. On Wednesdays, the store offers a 10% discount to senior citizens. We need to create a function f(x) which models the amount in dollars, a senior citizen would pay for 2 pounds
What is a simple Equation?
A mathematical equation which represents the relationship of two expressions on either side of the sign.
The 10% discount will make it so the senior citizens will pay 90% of the price.
90%=0.90
Also we need to know that 0.59*2 means how much money per pound the bananas cost.
So when you put it together, you should get f(x)=0.90(0.59*2)
The function f (x)=0.90(0.59*2) which models the amount, in dollars, a senior citizen would pay for 2 pounds of bananas on Wednesday
So the required function is f(x)=0.90(0.59*2)
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Robert bought a 6 pack of cans of iced tea for $2.70. About how much is the unit cost for each can of iced tea?
Answer:
.45$
Step-by-step explanation:
2.70 ÷ 6
Answer:
$0.45
Step-by-step explanation:
If 6 cans of iced tea costs $2.70,
1 can would cost ($2.70 ÷ 6)
How much mixed spice will she need for 6 spice
Answer:
who
Step-by-step explanation:
There are 20 students in a class and 70% of these students passed their Biology test.
What number of these students passed their test? Round your answer to the nearest whole
number if necessary.
Answer:
The answer is 14 students.
Step-by-step explanation:
70% of 20 = 14