What is the sum of the x-intercepts of the function below?

f(x) = 3x² - 11x - 4

O 3 2/3
O -1 1/3
O 1 1/3
O-3 2/3

Answer:

The correct answer would be D

Given that Neil retrieved 3470 grams of soil, and the average soil density on mars is 3.93 g/cm^3, we can make the equation of 3470/3.93 to get 882.951654, or ~882.95

Answer:

5(-2m - 4) is equivalent to 10m + 20.

Answer:

D) 10m+20

Step-by-step explanation:

To solve for this, we have to solve -5(-2m-4).

To do this, distribute (multiply) -5 to both of the numbers in the parathesis:

-5x-2m

=10m

-5x-4

=20

10m+20

So, D is the correct answer.  Hope this helps :)

Answer: 50°

Step-by-step explanation: Sum of all Angles in a triangle is 180°

Answer:

square root of x.

If the area is "x" the length must be the square root of x because all sides of a square are equal and the square root of x times itself equals x

The ratio of the areas is 4:7.

If two trapezoids are similar, then their corresponding sides are proportional. The ratio of the corresponding diagonal is given as 1:7, so let us assume that the ratio of the corresponding bases is also 1:7.

Let the bases of the trapezoids be a and 7a, and let the heights be h1 and h2 respectively. We can use the formula for the area of a trapezoid, which is:

Area = (1/2) × (sum of bases) × height

The area of the larger trapezoid is:

A2 = (1/2) × (a + 7a) × h2 = 4a × h2

The area of the smaller trapezoid is:

A1 = (1/2) × (a + 7a) × h1 = 4a × h1

We know that the corresponding diagonal is in the ratio of 1:7, which means that the corresponding sides are also in the ratio of 1:7. This implies that the corresponding heights are in the same ratio, i.e., h1:h2 = 1:7.

Therefore, we can write h1 = (1/7)h2. Substituting this into the expression for A1, we get:

A1 = 4a × h1 = 4a × (1/7)h2 = (4/7)A2

So the ratio of the areas of the smaller trapezoid to the larger trapezoid is:

A1 : A2 = (4/7) : 1

Therefore, the ratio of the areas of the two similar trapezoids is 4:7.

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A graph titled "Monthly Sales and Advertising Costs" has advertising costs (1,000 dollars) on the x-axis and sales (1,000 dollars) on the y-axis. The line goes through points (6.4, 117) and (6.6, 120) with a slope of 15.

The slope of the trend line represents the rate of change of the data. In this case, the slope is positive, which means there is a positive correlation between advertising costs and sales. For every $1,000 increase in advertising costs, the sales increase by $15,000. So, the correct statements are:

1. The slope represents the rate of change of the data.
2. Sales increase $15,000 as ads increase by $1,000.
3. A positive slope infers a positive correlation.

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Answer:

C = (-3/2, 1)

r = 25

Step-by-step explanation:

4x² + 12x + 4y² - 8y = 87        divide both sides by 4

x² + 3x + y² - 2y = 87/4           rearrange the equation

(x² + 3x + h) + (y² - 2y + k) = 87/4 + h + k       complete the square

h = (3/2)² = 9/4

k = (-2/2)² = 1

(x² + 3x + 9/4) + (y² -2y + 1) = 87/4 + 9/4 + 1

(x² + 3x + 9/4) + (y² -2y + 1) = 25

(x + 3/2)² + (y - 1)² = 25

r² = 25

r = √25 = 5

C = (h, k) = (-3/2, 1)

The state income tax owed on a $70,000 per year salary is $ $3,684.

To compute the state income tax payable on a $70,000 per year wage, we must first estimate how much of the salary falls into each progressive tax band and then calculate the tax owed for each range.

The first $2,000 in earnings is taxed at 2%:

This portion's tax = $2,000 x 0.02 = $40

The following $7,000 in earnings (from $2,001 to $9,000) is taxed at 5%:

This portion's tax = $7,000 x 0.05 = $350

The remainder of your income beyond $9,000 is taxed at 5.4%:

This portion's tax = ($70,000 - $9,000) x 0.054

= $61,000  x 0.054

= $ 3294

Now, the total amount of tax owed = 40 + 350 + 3294

= $ 3,684.

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Correct question:

A certain state uses the following progressive tax rate for calculating individual income tax:

Income Range ($)          Progressive Tax Rate

0-2000                                   2%

2001-9000                               5%

9001 and up                         5.4%

Calculate the state income tax owed on a $70,000 per year salary.

tax = $[?]

Round your answer to the nearest whole dollar amount

The volume of the composite figure is 123 cm³

From the image shown, we can see that the composite is made up of a cone and a rectangular prism.

The volume of a rectangular prism is expressed as;

V = lwh

Such that the parameters are;

Substitute the values

Volume, V = 5 × 1 × 12

Multiply the values

Volume = 60 cm³

The formula for the volume of a cone is expressed as;

Volume = πr²h/3

Substitute the values

Volume = 3 × 3² × 7/3

Multiply the values

Volume = 63 cm³

Then, the total volume = 63 + 60 = 123 cm³

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The value of measure of the smallest angle in this triangle is, 40 degree

Since,

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Here, The measure of three angles of triangle are given;

⇒ (x²+34)°, (6x+4)°, and (10x+10)°.

Hence,

(x²+34)°+(6x+4)°+(10x+10)°=180°

x²+16x+48=180

x²+16x-132=0

Using splitting middle term method, we get

x²+22x-6x-132=0

x(x+22)-6(x+22)=0

(x+22)(x-6)=0

x-6=0

x=6

Therefore, the value of of measure of the angle in this triangle is,

⇒ x² + 34 = 6² + 34 = 36 + 34 = 70

⇒ (6x + 4) = 6 × 6 + 4 = 40

⇒ (10x + 10) = 10 × 6 + 10 = 70°

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Step-by-step explanation:

The mean is: 48

The median is: 49.5

The Mode is: 74

The Range is: 51

The mean is increased by: 1.09

The median is increased by: 0.5

The mode is: 74

The Range is: 51

The least-squares regression line's equation is thus: f(x) = -1,246.78x + 10,381.72

The line for which the sum of the squares of the residuals is as tiny as it can be is known as the least square regression line, or LSRL for short. M=rsysx, where r is the dataset's correlation coefficient, provides the LSRL's slope.

n = 4

∑x = 10

∑y = 38,862.38

∑xy = 337,655.08

∑x² = 30

b = (4337,655.08 - 1038,862.38) / (4 × 30 - 10²) = -1,246.78

a = (38,862.38 - (-1,246.78) × 10) / 4 = 10,381.72

Based on this, least-squares regression line's equation is thus: f(x) = -1,246.78x + 10,381.72

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The equation that belongs to the same function family as the graph shown below is given as follows:

C. h(x) = 2(5)^x.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

The graphed function is a decreasing exponential function, belonging to the exponential function family.

Hence the correct option is given by option C, as it is the only exponential function among the options given.

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[tex]V = \pi(3)^2(21)[/tex] is the equation that shows the volume of the given cylinder.

The following formula may be used to determine a cylinder's volume:

[tex]V=\pi r^2h[/tex]

Where r is the radius of the cylinder's base, h is its height and is a mathematical constant that denotes the ratio of a circle's circumference to its diameter.

We must first determine the radius of the cylinder's base in order to utilize this formula to calculate the fulgurite's volume. The radius is equal to half of the base's diameter, or 3 inches since we know it to be 6 inches.

When we enter the values we are aware of into the formula, we obtain:

[tex]V = \pi(3)^2(21)[/tex]

Therefore, the expression that represents the volume is [tex]V = \pi(3)^2(21)[/tex]

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It cost $8,428.80

The first step to solving this problem is to find the area of the deck in square yards. We can do this by multiplying the length by the width:

Area of the deck = Length x Width = 8 yards x 12 yards = 96 square yards

Next, we can find the total cost of building the deck by multiplying the area by the cost per square yard:

Total cost = Area of the deck x Cost per square yard

Total cost = 96 square yards x $87.85 per square yard

Total cost = $8,428.80

Therefore, it cost $8,428.80 to build Ryan's backyard deck.

Answer:

In the point (4,-2) abscissa is positive and ordinate is negative. So, it lies in fourth quadrant.

The correct option is E. The population mean is less than 125. As, 125 is does not comes in the interval of 135 to 160, the interval tends to refute the claim that the population mean is less than 125.

The 90% confidence interval for the mean of the population is computed to be 135 to 160. This means that we are 90% confident that the true population mean falls within this range.

Since 125 is not within the interval of 135 to 160, the interval tends to refute the claim that the population mean is less than 125.

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The surface area of a triangular prism can be found by the formula SA = 2(Ab) + Ph. The volume can be found by V = Ab × h.

We have,

to find the volume and surface area of a triangular prism:

To calculate the surface area of a triangular prism, one must sum the areas of all its faces. This can be done by computing the area for each component of the prism and then combining them; utilizing the formulas:

SA = 2(Ab) + Ph

Where SA stands for Surface Area, Ab is the Area of the base (triangle), P representing the Perimeter of the base (triangle) and h denoting the Height of the triangular prism.

Moreover, to ascertain the volume of a triangular prism, the equation is:

V = Ab × h

in which V stands for Volume, Ab is still the Area of the triangular base and h is representing the Height of the triangle that comprises the prism.

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The percentage of the students that do not like to travel out of state like camping is 34%. The Option B is correct.

Given that:

The number of students who do not like to travel out of state and like camping = 38

The total number of students who do not like to travel out of state is 112.

The percentage of non-travelers who like camping will be calculated as:

= (Number of non-travelers who like camping / Total number of non-travelers) x 100%

= (38 / 112) x 100%

= 0.33928571428 * 100%

= 33.93%.

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The value that is equivalent to 5(22 − 9 · 2) − 2( 3 · 2 + 4) + 7 is 7

From the question, we have the following parameters that can be used in our computation:

5(22 − 9 · 2) − 2( 3 · 2 + 4) + 7

Evaluate the expressions in bracket

So, we have

5(22 − 9 · 2) − 2( 3 · 2 + 4) + 7 = 20 − 20 + 7

Evaluate the sum and the difference

So, we have

5(22 − 9 · 2) − 2( 3 · 2 + 4) + 7 = 7

Hence, the soluton is 7

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Answer:

Step-by-step explanation:

This is the difference of squares.  There is no GCF to take out.

The first term is a "perfect square" and so is the second term

You can take the square root of both terms perfectly

[tex]\sqrt{4w^{2} }[/tex] = 4w

√1 = 1

format for factors:

(√ of 1st term + √ of 2nd term)(√ of 1st term - √ of 2nd term)

The order of + and minus doesn't matter which parenthesis it goes in

factor:

(4w+1)(4w-1)

The required sides are solved to get

2. angle EFG = 160 degrees

4. angle EHG = 200 degrees

5. arc length of EHG = 200 degrees

6. arc length of FEG = 280 degrees

In the problem it is given that angle EDF = angle FDG = 80 degrees.

Knowing that intercepted arc and the central angle are equal we have that

2. angle EFG = 80 degrees + 80 degrees = 160 degrees

4. angle EHG = 360 - angle EFG

= 360 - 160

= 200 degrees

5. arc length of EHG = angle EHG = 200 degrees

6. arc length of FEG

= 360 - 80

= 280 degrees

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[tex]\sin( x )=\cfrac{\stackrel{opposite}{6}}{\underset{hypotenuse}{16}} \implies \sin( x )=\cfrac{3}{8}\implies x=\sin^{-1}\left( \cfrac{3}{8} \right)\implies \boxed{x\approx 22^o} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{16}\\ a=\stackrel{adjacent}{x}&\leftarrow \textit{Joel's shadow}\\ o=\stackrel{opposite}{6} \end{cases}[/tex]

[tex](16)^2= (x)^2 + (6)^2\implies \boxed{6^2+x^2=16^2}\implies x^2=16^2-6^2 \\\\\\ x=\sqrt{16^2-6^2}\implies x=\sqrt{220}\implies \boxed{x\approx 14.83}~ft[/tex]

Make sure your calculator is in Degree mode.

The classifications that must be the according to the figure are:

For RSUT

For XVWY

For ABCD

A rectangle is a four sided polygon otherwise known as a quadrilateral that has other properties such as

For ABCD, the third property mentioned here is failing as the diagonals are not equal.

Other figures makes us the desired properties of a rectangle

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Errors that pertain to anything in the research process except sample size are known as option b. non-sampling error.

Non-sampling errors are errors that occur in the research process other than those related to sample size. These errors can arise at any stage of the research process, including data collection, data processing, analysis, and interpretation. Examples of non-sampling errors include errors in data entry or coding, selection bias, measurement bias, interviewer bias, and response bias. Non-sampling errors can have a significant impact on the accuracy and validity of research findings and should be carefully controlled and minimized to the extent possible.

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let's firstly convert the mixed fraction to improper fraction.

[tex]\stackrel{mixed}{2\frac{5}{8}}\implies \cfrac{2\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{21}{8}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} gallons&miles\\ \cline{1-2} \frac{21}{8} & 147\\[1em] 1& m \end{array} \implies \cfrac{\frac{21}{8}}{1}~~=~~\cfrac{147}{m}\implies \cfrac{21}{8}=\cfrac{147}{m} \\\\\\ 21m=(8)(147)\implies m=\cfrac{(8)(147)}{21}\implies m=56[/tex]

The possible numbers of minutes Jim will run today is  represented by the inequality: 42 ≤ t ≤ 6x

If Jim runs at least 7 laps today, then the minimum number of minutes he will run is 7 laps x 6 minutes/lap = 42 minutes.

To find the maximum number of minutes he will run, we need to consider the possibility that he runs more than 7 laps.

Let's say he runs x laps in total, where x is greater than or equal to 7. Then the total number of minutes he will run is n laps x 6 minutes/lap = 6n minutes.

Therefore, the possible numbers of minutes Jim will run today can be represented by the inequality: 42 ≤ t ≤ 6x

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Part(a),

The amount added to the account each year will be £98.

Part(b),

After two years, there will be £1602.86 in the account.

a) Apply the basic interest formula to determine how much is added to the account annually:

I = Prt

where I stands for interest, P for principal, r for the interest rate expressed as a decimal per year, and t for the period of time in years.

P = £1400, r = 0.07, and t = 1 in this instance (since we are calculating the interest for one year). When these values are added to the formula, we obtain:

I = 1400 × 0.07 × 1 = £98

Therefore, £98 is added to the account each year.

b) The interest earned in the first year must be added to the principal to determine the balance in the account after two years, and the interest earned in the second year must be determined using the same formula:

Year 1: Interest = £98, Total amount = £1400 + £98 = £1498

Year 2: Interest = 1498 × 0.07 × 1 = £104.86, Total amount = £1498 + £104.86 = £1602.86

Therefore, after two years, there will be £1602.86 in the account.

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