Solve 2x2 – 3x = 12 using the quadratic formula.

9514 1404 393

Answer:

  f(x) = (x -4)(x -1)

Step-by-step explanation:

If 'a' is a zero of the function, then (x -a) is a factor. The two zeros mean the factored form of the quadratic is ...

  f(x) = (x -4)(x -1)

__

The expanded form will be ...

  f(x) = x² -5x +4

log₉(x - 7) + log₉(x - 7) = 1

2 log₉(x - 7) = 1

log₉(x - 7) = 1/2

Take the base-9 antilogarithm of both sides; in other words, make both sides powers of 9:

[tex]9^{\log_9(x-7)} = 9^{1/2}[/tex]

[tex]9^{1/2}[/tex] can also be written as √9 = 3, and [tex]b^{\log_b(a)}=a[/tex], so the equation reduces to

x - 7 = 3

Solve for x :

x = 10

Answer:

The answer is 155.

Step-by-step explanation:

We can find the remaining parts of the triangle angles.

Answer:

...

Step-by-step explanation:

seeee the above picture

Answer:

you didn't feature any graphs for me to choose from

Answer:

2[(x^2 + 7)(x + 5)]

Step-by-step explanation:

Note that the ratio of the first and second terms is the same as that between the third and fourth terms. So this cubic will factor by grouping, but first we can separate out the common scalar factor 2...

2x3+10x2+14x+70=

2(x3+5x2+7x+35)

2((x3+5x2)+(7x+35))

2(x2(x+5)+7(x+5))

2(x2+7)(x+5)

Answer:

The answer is D. 2[(x2 + 7)(x + 5)]

Step-by-step explanation:

Answer:

25.13 cm

Step-by-step explanation:

Perimeter ( circumference ) of a circle = 2πr

Given,

The circle is 8 cm wide

which means,

The diameter (d) of the circle is 8 cm.

Radius (r) of the circle = d/2

= 8/2

= 4

Radius = 4 cm

Putting the value in the formula;

2πr

= 2 (22/7) (4)

= 25.13 cm (approx)

Answer:

i think 3

Step-by-step explanation:

Answer: [A] 2

Step-by-step explanation:

100% on edge 2023

Answer:

f(x) = 2x + 1, g(x) = 3x - 2 and fg(x) = 5

Step-by-step explanation:

Answer:

175

Step-by-step explanation:

so, the LCM is the combination of the longest chains of the prime factors in every number.

40 : 2, 2, 2, 5

1400 / 40 = 35

35 : 5, 7

but LCM(35, 40) = 2×2×2×5×7 = 280

and not 1400.

what is missing ?

1400 / 280 = 5

aha, another prime factor 5 is missing to get 1400.

x : 5, 5, 7

so, x = 5×5×7 = 175

LCM(175, 40) = 2×2×2×5×5×7 = 1400

Option 4

Verification:-

[tex]\\ \sf\longmapsto x-7y=-49[/tex]

[tex]\\ \sf\longmapsto 7-7(8)=-49[/tex]

[tex]\\ \sf\longmapsto 7-56=-49[/tex]

[tex]\\ \sf\longmapsto -49=-49[/tex]

And

[tex]\\ \sf\longmapsto 10x+9y=142[/tex]

[tex]\\ \sf\longmapsto 10(7)+9(8)=142[/tex]

[tex]\\ \sf\longmapsto 70+72=142[/tex]

[tex]\\ \sf\longmapsto 142+142[/tex]

Hence verified

Answer:

4.

Step-by-step explanation:

1. 8x - y = 48

9x + 10y = 142

8(7) - 8 = 48

9(7) + 10(8) = 143

No

2. 9x - y = 55

8x + 10y = 140

9(7) - 8 = 55

9(7) - 10(7) = -24

No

3. x-6y=-41

8x + 9y = 127

7 - 6(8) = -41

8(7) + 9(8) = 128

No

4. x-7y=-49

10x + 9y = 142

7 - 7(8) = 49

10(7) + 9(8) = 142

Yes

Answer:

101 is the answer of the question

Answer:

101 degrees

Step-by-step explanation:

First you add all the percentages

39 + 28 + 30 + 3 = 100%

To find the number of degrees of basketball you multiply 28% by 360 because it’s a circle.

28/100 * 360 = 10,080/100 = 100.8 ~ 101

Answer:

The numbers are 18 and 25

Step-by-step explanation:

Given

[tex]\bar x_1 = 14[/tex]     [tex]n_1 = 17[/tex]

[tex]\bar x_2 = 13[/tex]     [tex]n_2 = 15[/tex]

[tex]a - b = 7[/tex] --- the difference of the 2 numbers

Required

Find a and b

We have:

[tex]\bar x = \frac{\sum x}{n}[/tex] -- mean formula

So, we have:

[tex]\bar x_1 = \frac{\sum x_1}{n_1}[/tex]

[tex]14 = \frac{\sum x_1}{17}[/tex]

Cross multiply

[tex]\sum x_1 = 14 * 17[/tex]

[tex]\sum x_1 = 238[/tex]

When the two numbers are removed, we have:

[tex]\bar x_2 = \frac{\sum x_2}{n_2}[/tex]

[tex]13 = \frac{\sum x_2}{15}[/tex]

Cross multiply

[tex]\sum x_2 = 13 * 15[/tex]

[tex]\sum x_2 = 195[/tex]

The two numbers that were removed are:

[tex]a + b = \sum x_1 - \sum x_2[/tex]

[tex]a + b = 238 - 195[/tex]

[tex]a + b = 43[/tex]

Make a the subject

[tex]a= 43 - b[/tex]

We have:

[tex]a - b = 7[/tex]

Substitute [tex]a= 43 - b[/tex]

[tex]43 - b - b = 7[/tex]

[tex]43 - 2b = 7[/tex]

Collect like terms

[tex]2b = 43 - 7[/tex]

[tex]2b = 36[/tex]

Divide by 2

[tex]b = 18[/tex]

Substitute [tex]b = 18[/tex] in [tex]a= 43 - b[/tex]

[tex]a = 43 - 18[/tex]

[tex]a = 25[/tex]

Answer:

a) 0.1287 = 12.87% probability the sample will contain exactly 8 defective drives

b) 0.2092 = 20.92% probability the sample will contain more than 8 defective drives.

c) 0.6621 = 66.21% probability the sample will contain less than 8 defective drives.

d) The expected number of defective drives in the sample is 6.6

Step-by-step explanation:

For each DVD, there are only two possible outcomes. Either it is defective, or it is not. The probability of a DVD being defective is independent of any other DVD, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A company that produces DVD drives has a 12% defective rate.

This means that [tex]p = 0.12[/tex]

Let X represent the number of defectives in a random sample of 55 of their drives.

This means that [tex]n = 55[/tex]

a. What is the probability the sample will contain exactly 8 defective drives?

This is [tex]P(X = 8)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 8) = C_{55,8}.(0.12)^{8}.(0.88)^{47} = 0.1287[/tex]

0.1287 = 12.87% probability the sample will contain exactly 8 defective drives.

b. What is the probability the sample will contain more than 8 defective drives?

This is:

[tex]P(X > 8) = 1 - P(X \leq 8)[/tex]

In which:

[tex]P(X \leq 8) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)[/tex]

Then

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{55,0}.(0.12)^{0}.(0.88)^{55} = 0.0009[/tex]

[tex]P(X = 1) = C_{55,1}.(0.12)^{1}.(0.88)^{54} = 0.0066[/tex]

[tex]P(X = 2) = C_{55,2}.(0.12)^{2}.(0.88)^{53} = 0.0244[/tex]

[tex]P(X = 3) = C_{55,3}.(0.12)^{3}.(0.88)^{52} = 0.0588[/tex]

[tex]P(X = 4) = C_{55,4}.(0.12)^{4}.(0.88)^{51} = 0.1043[/tex]

[tex]P(X = 5) = C_{55,5}.(0.12)^{5}.(0.88)^{50} = 0.1450[/tex]

[tex]P(X = 6) = C_{55,8}.(0.12)^{6}.(0.88)^{49} = 0.1648[/tex]

[tex]P(X = 7) = C_{55,7}.(0.12)^{7}.(0.88)^{48} = 0.1573[/tex]

[tex]P(X = 8) = C_{55,8}.(0.12)^{8}.(0.88)^{47} = 0.1287[/tex]

So

[tex]P(X \leq 8) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) = 0.0009 + 0.0066 + 0.0244 + 0.0588 + 0.1043 + 0.1450 + 0.1648 + 0.1573 + 0.1287 = 0.7908[/tex]

[tex]P(X > 8) = 1 - P(X \leq 8) = 1 - 0.7908 = 0.2092[/tex]

0.2092 = 20.92% probability the sample will contain more than 8 defective drives.

c. What is the probability the sample will contain less than 8 defective drives?

This is:

[tex]P(X < 8) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)[/tex]

With the values we found in b.

[tex]P(X < 8) = 0.0009 + 0.0066 + 0.0244 + 0.0588 + 0.1043 + 0.1450 + 0.1648 + 0.1573 = 0.6621[/tex]

0.6621 = 66.21% probability the sample will contain less than 8 defective drives.

d. What is the expected number of defective drives in the sample?

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

In this question:

[tex]E(X) = 55(0.12) = 6.6[/tex]

The expected number of defective drives in the sample is 6.6

Answer:

D. 157

Step-by-step explanation:

4(x^2+3)-2y

4(6^2+3)-2(-1/2) add in given values

4(39)+1.     start with parentheses

156+1.        combine like terms

157.            answer

Answer:

D. 157

Step-by-step explanation:

Hi there!

We want to find the value of the expression 4(x²+3)-2y is when x=-6 and y=-1/2

Let's first simplify the expression, as that will likely make it easier

Distribute 4 to both x² and 3

4x²+12-2y

That's the expression

Substitute -6 as x into the expression

4(-6)²+12-2y

Raise (-6) to the second power

4*36+12-2y

Multiply 36 by 4

144+12-2y

Add 12 and 144 together

156-2y

Now the expression is 156-2y

But remember that we know that y=-1/2, and we haven't substituted it into the expression yet

Substitute -1/2  as y into the expression

156-2(-1/2)

Multiply

156+2/2

Simplify

156+1

Add

157

Hope this helps!

Answer:

Substitute in the values of both given coordinates & form 2 equations:

[tex]\left \{ {{A(2)+B(-1)=1} \atop {A(-3)+B(-2)=1}} \right. \\\\=\left \{ {{2A-B=1} \atop {-3A-2B=1}} \right.[/tex]

Find the value of B from the equation 2A - B = 1:

[tex]2A-B=1\\-B=1-2A\\B=2A-1[/tex]

Substitute in the B-value to the other equation:

[tex]-3A-2B=1\\-3A-2(2A-1)=1\\-3A-4A+2=1\\-7A=1-2\\-7A=-1\\A=\frac{-1}{-7} =\frac{1}{7}[/tex]

Find the B-value using the equation from before:

[tex]B=2A-1=2(\frac{1}{7})-1=\frac{2}{7} -\frac{7}{7} =-\frac{5}{7}[/tex]  

Therefore the equation Ax + By = 1 would equal:

[tex]\frac{1}{7} x-\frac{5}{7} y=1[/tex]

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

May August

95 100

72 80

78 95

50 65

89 85

92 98

75 70

90 96

65 87

The appropriate test is a paired t test :

d = difference between May and August

d = (-5, -8, -17, -15, 4, -6, 5, -6, -22)

The hypothesis :

H0 : μd = 0

H1 : μd ≠ 0

The test statistic :

T = dbar / (Sdbar/√n)

Where, dbar and Sdbar are the mean and standard deviation of 'd' respectively.

Using calculator :

dbar = - 7.777 ; Sdbar = 9.052

Test statistic = - 7.777 / (9.052 /√9)

Test statistic = - 2.577

The Pvalue, df = n - 1 = 9 - 1 = 8

Pvalue(-2.577, 8) = 0.0327

At α = 0.05

Pvalue < α ; WE reject the H0 ; and conclude that there has been a change in score

Answer:

The answer is "-310840".

Step-by-step explanation:

[tex]\begin{array}{l} P'(x) = 2x - 1198\\ \\ \frac{{dP}}{{dx}} = 2x - 1198\\ \\ dP = \left( {2x - 1198} \right)dx\\ \\ \int {dP} = \int\limits_0^{380} {\left( {2x - 1198} \right)dx} \\ \\ P = \left( {2\frac{{{x^2}}}{2} - 1198x} \right)_0^{380}\\ \\ P = {380^2} - 1198 \times 380 = 144400-455240=-310840\\ \end{array}[/tex]

Answer:

More points are needed to determine the correlation.

Answer:

its d

Step-by-step explanation:

;)

Answer:

Determination of type of error arising from the situations

Situation       Type of Error

1.                    Nonresponse

2.                   Bad sampling method

3.                   Question wording

4.                   Undercoverage

Step-by-step explanation:

Types of errors:

a. question wording means that the manner a question is worded elicits some particular responses, which may not accurately reflect reality.

b. undercoverage occurs when some elements of the target population is not represented on the survey frame.

c. processing error arises from data processing

d. bad sampling method is caused by the voluntariness of those who choose to respond.

e. response error is caused by a questionnaire that requires framing improvements, misinterpretation of questions by interviewers or respondents, and errors in respondents' statements.

f. nonresponse error arises as a result of incomplete information or partial response.

g. random sampling error arises from the limited sample size when compared with the population size.

Answer:

D

Step-by-step explanation:

The answer is D.

Answer:

2160

Step-by-step explanation:

because c is 15 and d is 12 therefore d² is 144 and 144x15 is 2160

Answer:

2160

Step-by-step explanation:

Substitute

[tex](15)(12) {}^{2} [/tex]

[tex]15 \times 144 = 2160[/tex]

Answer:

The number is 30.

Step-by-step explanation:

Let the number be x

so

x + (130% of x) = 69

x + 13x/10 = 69

or, (10x + 13x)/10 = 69

or, 23x = 690

or, x = 690/23

so, x = 30

Answer: 30

Step-by-step explanation:

its correct on rsm

Answer:

-  x³ - 2x² + 3 - 1 / x

Step-by-step explanation:

(4x³ - 8x² + 12x - 4) / (-4x)

-  x³ - 2x² + 3 - 1 / x

Answer:

F(x) = 45*x - (5/2)*x^2 + C

Step-by-step explanation:

Here we want to find the antiderivative of the function:

f(x) = 45 - 5*x

Remember the general rule that, for a given function:

g(x) = a*x^n

the antiderivative is:

G(x) = (a/(n + 1))*a*x^(n + 1) + C

where C is a constant.

Then for the case of f(x) we have:

F(x) = (45/1)*x^1 - (5/2)*x^2 + C

F(x) = 45*x - (5/2)*x^2 + C

Now if we derivate this, we get:

dF(x)/dx = 1*45*x^0 - 2*(5/2)*x

dF(x)/dx = 45 - 5*x

Answer: 4.25

Step-by-step explanation:

2.5/100 = 0.025

0.025 × 170 = 4.25

but the question there is any goats in 2.5 cm ??

that is impossible

Answer:

D. 212 degrees Fahrenheit and 100 degrees Celsius.

Step-by-step explanation:

The boiling point of water in Celsius is 100.

The way to calculate Celsius to Fahrenheit:

F = (C × 9/5) + 32

So we plug in 100 for C.

F = (100 × 9/5) + 32

F = 180 + 32

F = 212

Therefore, the numbered pair is 212 degrees F and 100 degrees  C.

Answer:

√45 or 3√5

Step-by-step explanation:

Answer:

192

Step-by-step explanation:

geometric mean theorem :

with p and q being the segments of the Hypotenuse, then

h = x = sqrt(p×q)

p = 144

q = 400-144 = 256

h = x = sqrt(144×256) = 12×16 = 192