Quick algebra 1 question for 10 points!

Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!

Answer: 88°

Step-by-step explanation:

We know that the ratio of ∠DCB : ∠ACD is 3:1. In other words, ∠DCB is [tex]\frac{3}{3+1}[/tex], or [tex]\frac{3}{4}[/tex] of the whole angle (i.e., ∠ACB), while ∠ACD is [tex]\frac{1}{4}[/tex] of the whole angle.

To easily find ∠ACB, which is the sum of both angles, we can add up all the angles of [tex]\triangle ABC[/tex] and set it equal to 180°.

[tex]m\angle A + m\angle B + m\angle ACB = 180\\75+53+m\angle ACB=180\\128+m\angle ACB=180\\m\angle ACB=52[/tex]

From here, we can calculate ∠BCD by multiplying the value of ∠ACB by three-fourths.

[tex]m\angle BCD = \frac{3}{4}(m\angle ACB)\\m\angle BCD = \frac{3}{4}(52)\\m\angle BCD = 39[/tex]

Similar to what we did to get the measure of ∠ACB, we can add up all the angles measures of [tex]\triangle DBC[/tex] to get the measure of ∠BDC.

[tex]m\angle B + m\angle BDC + m\angle BCD = 180\\53+m\angle BDC + 39= 180\\92+ m\angle BDC=180\\m\angle BDC = 88[/tex]

The measure of ∠BDC is 88°.

Answer:

Jamie is currently 15.

Step-by-step explanation:

The first four partial sums of the sequence are S₁ = 0.3010, S₂ = 0.9999, S₃ = 2.447, S₄ = 4.8569.

In this question,

A sequence is a set of things (usually numbers) that are in order. A partial sum is the sum of part of the sequence.

The sequence is [tex]a_{n} =log(n^{n}+1 )[/tex]

The first four partial sum S₁, S₂, S₃, S₄ can be calculated by substituting n = 1,2,3,4 in the sequence.

S₁ can be calculated as

S₁ = a₁

⇒ [tex]a_{1} =log(1^{1}+1 )[/tex]

⇒ [tex]a_{1} =log(1+1 )[/tex]

⇒ [tex]a_{1} =log(2 )[/tex]

⇒ [tex]a_{1} =0.3010[/tex]

Now, S₁ = 0.3010

S₂ can be calculated as

S₂ = a₁ + a₂

⇒ [tex]a_{2} =log(2^{2}+1 )[/tex]

⇒ [tex]a_{2} =log(4+1 )[/tex]

⇒ [tex]a_{2} =log(5 )[/tex]

⇒ [tex]a_{2} =0.6989[/tex]

Now, S₂ = 0.3010 + 0.6989

⇒ S₂ = 0.9999

S₃ can be calculated as

S₃ = a₁ + a₂ + a₃

⇒ [tex]a_{3} =log(3^{3}+1 )[/tex]

⇒ [tex]a_{3} =log(27+1 )[/tex]

⇒ [tex]a_{3} =log(28)[/tex]

⇒ [tex]a_{3} =1.4471[/tex]

Now, S₃ = 0.3010 + 0.6989 + 1.4471

⇒ S₃ = 2.447

S₄ can be calculated as

S₄ = a₁ + a₂ + a₃ + a₄

⇒ [tex]a_{4} =log(4^{4}+1 )[/tex]

⇒ [tex]a_{4} =log(256+1 )[/tex]

⇒ [tex]a_{4} =log(257 )[/tex]

⇒ [tex]a_{4} =2.4099[/tex]

Now, S₄ = 0.3010 + 0.6989 + 1.4471 + 2.4099

⇒ S₄ = 4.8569

Hence we can conclude that the first four partial sums of the sequence are S₁ = 0.3010, S₂ = 0.9999, S₃ = 2.447, S₄ = 4.8569.

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The difference between the mean times is about 2 times the absolute deviation of the data sets.

Given that the difference of the means is found.

The difference in the means is basically the absolute difference between the mean of two groups. It explains the mean of two groups. It explains how much difference that exists between the average between two groups.Calculating mean difference is significant during clinical trials where we have the experimental group and the control group. The mean absolute deviations is basically the variation of each data value from the mean. It tells us how much the values in a set of data differ from the mean value. It explains the reach of values in a data set. There is a relationship that exists between the difference of the mean absolute deviations.

Hence the difference between the mean times is about 2 times the absolute deviation of the data sets.

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The system of the linear systems of equation using substitution is;

3x-y=4

x+2y=6

from (2)

x = 6 - 2y

substitute into (1)

3x-y=4

3(6 - 2y) - y = 4

18 - 6y - y = 4

- 6y - y = 4 - 18

-7y = -14

y = 2

Substitute into

x+2y=6

x + 2(2) = 6

x + 4 = 6

x = 6 - 4

x = 2

2. 2x-y= -39

x+y= -21

From (2)

x = -21 - y

substitute into

2x-y= -39

2(-21 - y) - y = -39

-42 - 2y - y = -39

- 2y - y = -39 + 42

- 3y = 3

y = 3/-3

y = -1

substitute into

x+y= -21

x + (-1) = -21

x - 1 = -21

x = -21 + 1

x = -20

3. 2x+y =11

6x-5y =9

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Using limits, the correct option regarding the end behavior of the function is given by:

A. as x→∞, y→−∞ as x→−∞, y→−∞.

The end behavior is found calculating the limit of f(x) as x goes to infinity.

For this problem, the equation is given by:

[tex]f(x) = -x^6 - 6x^5 + 50x^3 + 45x^2 - 108x - 108[/tex]

Since x goes to infinity, we consider only the term with the highest exponent, hence the limits are given as follows:

[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} -x^6 - 6x^5 + 50x^3 + 45x^2 - 108x - 108 = \lim_{x \rightarrow -\infty} -x^6 = -(-\infty)^6 = -\infty[/tex]

[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} -x^6 - 6x^5 + 50x^3 + 45x^2 - 108x - 108 = \lim_{x \rightarrow \infty} -x^6 = -(\infty)^6 = -\infty[/tex]

Hence the correct option is:

A. as x→∞, y→−∞ as x→−∞, y→−∞.

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Answer:

336

Step-by-step explanation:

They can place 1 of 8 frags on the bottom.

Now they have 7 flags left.

They can place 1 of 7 flags in the middle.

Now they have 6 flags left.

The can place 1 of 6 flags on top.

8 × 7 × 6 = 336

Answer:

23 is the answer

Answer:

x = 4

Step-by-step explanation:

These triangles are similar by the AA Similarity Postulate.

12 + 4 = 16

(5x - 2)/12 = 6x/16 (3x/8)

Cross multiply: 8(5x - 2) = 12(3x)

40x - 16 = 36x

4x - 16 = 0

4x = 16

x = 4

Based on the logarithms given, the requirement to use one digit, and the figures to be produced, the right numbers are:

The log of a number gives 1 which is an integer so we can find numbers that when multiplied, produce a number that can be taken a log of. Those numbers are 2 and 4:

= 2 x 4

= 8

Log₈ = 1

Taking the log of a number to a decimal form leads to an irrational number. So, find numbers that when divided, will give a decimal:

= 6/5

= 1.2

Take a log of 7:
log₇ (1.2) will give an irrational number.

The remaining numbers ae 9, 3, and 1.

With the numbers 9,3 and 1, the log to produce a rational number is:
log₉3¹ = log₉9¹/² = 1/2

1/2 is a rational number.

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Answer:

[tex]\textsf{A. } y=3x^2+10x-8[/tex]

Step-by-step explanation:

We are given the information that a function has zeros at x = ⅔ and x = -4. In order to find the function that has those zeros, we can substitute the value of the zeros into each function. If the value of a function equates to zero with both values, then that is the function we are looking for.

..................................................................................................................................................

Standard Form of a Quadratic: ax² + bx + c = 0.

..................................................................................................................................................

[tex]\large \text{$y = 3x^2+10x-8 \implies 0=3x^2+10x-8$}[/tex]

[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=3\left(\dfrac{2}{3}\right)^2+10\left(\dfrac{2}{3}\right)-8\\\\\implies 0=3\left(\dfrac{4}{9}\right)+10\left(\dfrac{2}{3}\right)-8\\\\\implies 0=\not{3}\left(\dfrac{4}{\not{9}\ 3}\right)+\dfrac{20}{3}-8\\\\\implies 0=\dfrac{4}{3}+\dfrac{20}{3}-8\\\\\implies 0=\dfrac{24}{3}-8\\\\\implies 0=0\ \checkmark\end{minipage}}[/tex]    [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=3(-4)^2+10(-4)-8\\\\\implies 0=3(16)-40-8\\\\\implies 0=48-48\\\\\implies 0=0\ \checkmark\end{minipage}}[/tex]

..................................................................................................................................................

[tex]\large \text{$y = 2x^2-5x-12 \implies 0=2x^2-5x-12$}[/tex]

[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=2\left(\dfrac{2}{3}\right)^2-5\left(\dfrac{2}{3}\right)-12\\\\\implies 0=2\left(\dfrac{4}{9}\right)-\dfrac{10}{3}-12\\\\\implies 0=\dfrac{8}{9}-\dfrac{10}{3}-12\\\\\implies 0=\dfrac{8}{9}-\dfrac{10\times3}{3\times3}-\dfrac{12\times9}{9}\\\\\implies 0=\dfrac{8}{9}-\dfrac{30}{9}-\dfrac{108}{9}\\\\\implies0=-\dfrac{22}{9}-\dfrac{108}{9}\\\\\implies 0=-\dfrac{130}{9}\ \textsf{X}\end {minipage}}[/tex]    [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=2(-4)^2-5(-4)-12\\\\\implies 0=2(16)+20-12\\\\\implies 0=32+20-12\\\\\implies 0=40\ \textsf{X}\end{minipage}}[/tex]

..................................................................................................................................................

[tex]\large \text{$y = 2x^2+5x-12 \implies 0=2x^2+5x-12$}[/tex]

[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=2\left(\dfrac{2}{3}\right)^2+5\left(\dfrac{2}{3}\right)-12\\\\\implies 0=\dfrac{8}{9}\right)+\dfrac{10}{3}-12\\\\\implies 0=\dfrac{8}{9}\right)+\dfrac{10\times3}{3\times3}-\dfrac{12\times9}{9}\\\\\implies 0=\dfrac{8}{9}+\dfrac{30}{9}-\dfrac{108}{9}\\\\\implies0=\dfrac{38}{9}-\dfrac{108}{9}\\\\\implies 0=-\dfrac{70}{9}\ \textsf{X}\end{minipage}}[/tex]    [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=2(-4)^2+5(-4)-12\\\\\implies 0=2(16)-20-12\\\\\implies 0=32-32\\\\\implies 0=0\ \checkmark\end{minipage}}[/tex]

..................................................................................................................................................

[tex]\large \text{$y = 3x^2-10x-8 \implies 0=3x^2-10x-8$}[/tex]

[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=3\left(\dfrac{2}{3}\right)^2-10\left(\dfrac{2}{3}\right)-8\\\\\implies 0=3\left(\dfrac{4}{9}\right)-\dfrac{20}{3}-8\\\\\implies 0=\not{3}\left(\dfrac{4}{\not{9}\ 3}\right)-\dfrac{20}{3}-8\\\\\implies 0=\dfrac{4}{3}-\dfrac{20}{3}-\dfrac{8\times3}{3}\\\\\implies 0=-\dfrac{16}{3}-\dfrac{24}{3}\\\\\implies 0=-\dfrac{40}{3}\ \textsf{X}\end{minipage}}[/tex]    [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=3(-4)^2-10(-4)-8\\\\\implies 0=3(16)+40-8\\\\\implies 0=48+40-8\\\\\implies 0=80\ \textsf{X}\end{minipage}}[/tex]

..................................................................................................................................................

Therefore, the function whose zeros are ⅔ and -4 is [tex]y=3x^2+10x-8[/tex].

The table of values for y=1/2x-1 is completed as follows:

x               y

-2             -2

-1            -3/2

0               -1

1             -1/2

2                0

3              1/2

Exactly one value from the set of second components of the ordered pair is connected with each value from the set of first components of the ordered pairs in a relation known as a function.

Given function:  y=1/2x-1

For x = -2

Value of y = -2

For x = -1

Value of y = 1/2(-1)-1 = -3/2

For x = 0

Value of y = 1/2(0)-1 =-1

For x = 1

Value of y = 1/2(1)-1 = -1/2

For x = 2

Value of y = 0

For x = 3

Value of y = 1/2(3)-1 = 1/2

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The descriptive statistics for the above data is given as follows:
X = 12.5

A set of concise descriptive coefficients that describe a particular data set indicative of a whole or sample population is known as descriptive statistics.

For X (mean) = [tex]{\displaystyle X={\frac {1}{n}}\sum _{i=1}^{n}X_{i}[/tex]

= 300/24

= 12.5

For sample variance = [tex]s^2 = \frac{1}{n-1}\biggl[\, \sum_{i=1}^n X_i^2 - \frac{\Bigl(\,\sum\limits_{i=1}^n X_i\Bigr)^{\!2}}{n} \biggr][/tex]

= (1/(24-1) (4,900 - (300²/24)

= 50

Standard deviation s = √s²

= √50

= 7.0711

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The stock's current price  is  53.413455.

What is CAPM ?

The capital asset pricing model (CAPM) to know the value of the stock

[tex]Ke = rf + \beta ( r_{m} - r_{f} )[/tex]

risk free = 0.085

premium market =(market rate - risk free) = 0.045

beta(non diversifiable risk) 1.3

Ke = 0.085 + 1.3(0.045)

Ke = 0.14350

Now we need to know the present value of the future dividends:

D0 = 2.8

D1 = D0 × ( 1 +g ) = 2.8  = 2.8 * 1.23 = 3.444

D2 3.444 x 1.23 = 4.2361200

The next dividends, which are at perpetuity will we solve using the dividned grow model

[tex]\frac{divends}{return - growth} = Intrinsic value[/tex]

In this case dividends will be:

4.23612 x 1.07 = 4.5326484

return will be how return given by CAPM and g = 7%

plug this into the Dividend grow model.

[tex]\frac{4.5326484}{0.1435 - 0.07} = Intrinsic value[/tex]

value of the dividends at perpetity: 61.6686857

Finally is important to note this values are calculate in their current year. We must bring them to present day using the present value of a lump sum:

[tex]\frac{principal}{(1 + rate)^{time} } = PV[/tex]

[tex]\frac{3.444}{(1 + 1. 1435)^{1} } =PV[/tex]

3.011805859

[tex]\frac{4.23612}{( 1 + 0.1435)^{2} } = PV[/tex]

3.239633762

[tex]\frac{61.6686857}{(1 + 0.1435)^{2} } = PV[/tex]

47.16201531

We add them and get the value of the stock  is 53.413455.

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Answer:

m=-4

y-intercept=8

x-intercept=2

Step-by-step explanation:

Please see attachment.

y-intercept=8

The y-intercept is where the line crosses the y-axis.

x-intercept=2

The x-intercept is where the line crosses the x-axis.

m=-4

If you do not know how to find slope by looking at graph, use slope formula.

(y2-y1)/(x2-x1)

Choose 2 points. You may use the x and y intercepts.

(2,0) and (0,8)

(8-0)/(0-2)=8/-2=-4

Hope this helps!

The correct option is the thrid one, the first step is

-x+5= 6x-2

Here we have the system of equations:

y = -x + 5

y = 6x - 2

Now, the variable "y" should represent the same thing in both equations, then we can write:

-x + 5 = y = 6x - 2

If we remove the middle part, we get the equation that only depends on x:

-x + 5 = 6x - 2

This is the first step that we should use to solve the system of equations, which is the one in option 3.

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Answer:

y is equal to -16

Answer:

y = 8

Step-by-step explanation:

We can use proportions for this question since y varies directly with x. This means that if x changes, y changes along with the x, and vice versa.

When y = -8, x = 4, so the proportion will be -8 : 4.

We need to find the y when x is 4, so our equation will be:

-8 : 4 = y : -4

Since the proportion will be the same.

Next, we multiply the inner two numbers, and the outer two numbers, saying that the values are the same.

4y = 32

y = 8

So y = 8 will be our answer!

[tex]y = mx + n[/tex]

[tex]m = \frac{y - y}{x - x} = \frac{5 - ( - 1)}{ - 5 - ( - 3)} = \frac{6}{ - 2} = - 3[/tex]

[tex]y = - 3x + n \\ [/tex]

[tex]5 = - 3( - 5) + n \\ n = 5 - 15 = - 10[/tex]

[tex]y = - 3x - 10[/tex]

Answer: 120

Step-by-step explanation:

Answer:

B. 60°

Step-by-step explanation:

Angle 4 and angle 8 are equal. Find the measure of angle 4 to know the measure of angle 8.

∠4=∠8

180-120=60

∠4=60°

Since angle 4 equals 60 degrees, angle 8 also equals 60 degrees.

Hope this helps!

The linear function which represents the line given by the point-slope equation is (B) [tex]f(x)=\frac{1}{2} x+6[/tex].

To find the linear function which represents the line given by the point-slope equation:

Given: [tex]y-8=\frac{1}{2} (x-4)[/tex]

Distribute the right side:

[tex]y-8=\frac{1}{2} (x)-\frac{1}{2} 4\\y-8=\frac{1}{2} x-2[/tex]

Adds 8 on both sides:

[tex]y=\frac{1}{2}x-2+8\\y=\frac{1}{2}x+6[/tex]

Convert to function notation:

[tex]f(x)=y\\f(x)=\frac{1}{2} x+6[/tex]

Therefore, the linear function which represents the line given by the point-slope equation is (B) [tex]f(x)=\frac{1}{2} x+6[/tex].

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The complete question is given below:

Which linear function represents the line given by the point-slope equation y – 8 = y minus 8 equals start fraction one-half end fraction left-parenthesis x minus 4 right-parenthesis. (x – 4)?

A) F(x) = f(x) equals StartFraction one-half EndFraction x plus 4.X + 4

B) f(x) = f(x) equals StartFraction one-half EndFraction x plus 6.

C) X + 6 f(x) = f(x) equals StartFraction one-half EndFraction x minus 10.X –10

D) f(x) = f(x) equals StartFraction one-half EndFraction x minus 12.X – 12

The critical value is the z-score right at the edge of the rejection region option (A) is correct.

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

It is given that:

The z-score is right at the edge of the rejection region.

As we know, the rejection zone is the area in which we have sufficient data to reject the null hypothesis if our test statistic falls within it.

Thus, the critical value is the z-score right at the edge of the rejection region option (A) is correct.

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The volume of a solid is  [tex]\frac{26}{3} \pi[/tex].

Given

The given curves about the specified line. y = x + 1, y = 0, x = 0, x = 2; about the x-axis

Curve is y = x + 1

Line is y = 0

We have to find out the volume v of the solid obtained by rotating the region bounded by these curves.

If the region bounded above by the graph of f, below by the x-axis, and on the sides by x=a and x=b is revolved about the x-axis, the volume V of the generated solid is given by [tex]V = \pi \int\limits^b_a {(f(x))^{2} } \, dx[/tex]. We can also obtain solids by revolving curves about the y-axis.

Volume of a solid:

According to washer method:

[tex]V = \pi \int\limits^b_a {(f(x))^{2} } \, dx[/tex]

Using washer method, where a=0 and b=2, we get

V = [tex]\pi \int\limits^2_0 {(x+1)^{2} } \, dx[/tex]

= [tex]\pi[ \frac{(x+1)^{3} }{3} ]0 \ to \ 2[/tex]

= [tex]\pi [\frac{(3+1)^{3} }{3} -\frac{(0+1)^{3} }{3}][/tex]

= [tex]\pi [\frac{27}{3} -\frac{1}{3} ][/tex]

= [tex]\pi [\frac{26}{3}][/tex]

= [tex]\frac{26}{3} \pi[/tex]

Therefore the volume of a solid is  [tex]\frac{26}{3} \pi[/tex].

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Answer:

See below

Step-by-step explanation:

Using triangle side rule :  The sum of any two sides must be greater than the third side

.5<x<16.5

The range of possible sizes for side x for given triangle is 0.5<x<16.5.

In the given triangle, one side measures 8.5 units, other side is 8.0 units and third side is x units.

The length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides.

Here, the range of x is 8.5-8.0<x<8.5+8.0

0.5<x<16.5

Therefore, the range of possible sizes for side x for given triangle is 0.5<x<16.5.

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Answer:

D

Step-by-step explanation:

Pq=opp/hyp

(135+12)=180

Answer:

the answer is B

a 3d rectangle slided vertically can produce a 2d rectangle

The term that is not possible in the domain of a sequence is:

-5

The domain of a function is the set that contains all possible input values for the function. For a sequence, the domain is the set that contains all the indexed of the terms, starting at 0 and going until the nth term.

For example, suppose we have the following sequence: 3, 5, 7, ...

From what was explained above, which also can be visualized with the example, an index term of a sequence cannot be negative, hence the term that is not possible in the domain of a sequence is:

-5.

Which is the only negative number of the options.

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The p-value that would be given as the evidence would be given as p-value = 0.00002 and also P value = 0.00003

The sample size of the first sample = 100

x1 = success 0f 86%

We have to find the proportion of this = 0.86

The sample size of the second sample n2 = 100

x12 = success 0f 60%

We have to find the proportion of this = 60/100

= 0.6

The difference = 0.86-0.6= 0.26

Next we have to find the pooled proportion. This is taken given as p = (x1+x2)/(n1+n2) this gives us 0.73

Next we have to find the standard error

= √(p*(1-p)*(1/n1+ 1/n2)= 0.06279

Z stat = (0.26-0)/0.0628= 4.1411

From here the p value would have to be

p-value = 0.00002 and also

P value = 0.00003

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The amount of water that will serve the entire container exists 3/10 gallons.

An expression exists a sentence with a minimum of two numbers or

variables and at least one math function.

Given: 1 over 5 gallons of water serve 2 over 3 of the container.

(1/5) gallon / (2/3) container = x gallons / 1 container

cross-multiplying the above equation, we get

1/5 = (2/3)x

multiply both sides by the reciprocal of 2/3 = 3/2

(3/2) (1/5) = x = 3/10 gallons serve the total container

Each 1/10 of a gallon serve 1/3 of the container

So 3(1/10) gallons serve 3(1/3)bins

3/10 gallons serve a whole container.

The amount of water that will serve the entire bin container exists 3/10 gallons.

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The ratio illustrates that the values will be 3146.7945 gram, 9440.3835 gram, and 3968.93 grams.

It should be noted that 1 ounce is equivalent to 28.3495 gram.

Therefore, 111 ounces will be:

= 111 × 28.3495 gram

= 3146.7945 gram

333 ounces will be:

= 333 × 28.3495 gram

= 9440.3835 gram

140 ounces will be:

= 140 × 28.3495 gram

= 3968.93 grams

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