Select the correct answer.
A solution to a quadratic function, f, is given below.
-3-51
Which statement is true about the given function?
O
The other solution to function fis 3 - 5i.
The other solution to function fis 3 + 5i.
Function f has no other solutions.
The other solution to function fis-3 + 5i.

Answer:

4

6

y=4x+6

Step-by-step explanation:

check the attached file

Step-by-step explanation:

Hope u get it x=3×3

x=9

It didn't include in the photo

Evaluating the expression a² + b ÷ 3 for each set of given values we have

The expressions are evaluated using substitution as done below

for a = 4, b=3

substituting the the values of a and b

= a² + b ÷ 3  

= 4² + 3 ÷ 3

= 16 + 1

= 17

For a=2, b=21

substituting the the values of a and b

= a² + b ÷ 3

= 2² + 21 ÷ 3

= 4 + 7

= 11

For a = 3, b = 6

substituting the the values of a and b

=  a² + b ÷ 3

=  3² + 6 ÷ 3

= 9 + 2

= 11

substituting the values yielded the results as 17, 11 and 11

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The function f(t) = 2cos (∏/4 t) lowest at (4,-2), (12,-2),(20,-2). The points are pl0ted in the graph.

What is a function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given function is  f(t) = 2cos (∏/4 t).

f(t) will be lowest when cos (∏/4 t) is lowest.

The value of cosine lies between -1 to 1.

When cos (∏/4 t) = -1, f(t) has lowest value.

Solve the equation cos (∏/4 t) = -1

cos (∏/4 t) = -1

∏/4 t =cos ⁻¹ (-1)

∏/4 t = (2n + 1)∏

t = (2n + 1)4  where n is a whole number.

The value of the function is lowest at t = 4, 12, 20.

The lowest points are (4,-2), (12,-2),(20,-2) etc.

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Answer: (4, -2) (12,-2)

Step-by-step explanation:

The combination of streamers and balloons at the Party Palace will be 21 and 34, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Marisol necessities to buy Somewhere around 55 party enrichments. The Party Castle charges $0.50 per beautiful decoration and $0.25 per expansion, including the charge.

Let 'x' be the number of decorative streamers and 'y' be the number of balloons. Then the equations are given as,

0.50x + 0.25y = 19           ...1

x + y = 55                         ...2

From equations 1 and 2, then we have

0.50x + 0.25(55 - x) = 19

0.25x = 5.25

x = 21

The value of y is given as,

21 + y = 55

y = 34

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The Error checking button provides an automatic means of checking for mathematical errors within formulas of a worksheet.

The modeling process begins with the framing of a conceptual model that shows the relationships between the various parts of the problem being modeled.

Arrows pointing from the selected cell to cells that depend on the selected cell are generated by using the Trace dependents button of the Formula Auditing group.

nodes in an influence diagram represent part of the model

The Trace Precedents button, located in the Formula Auditing group, creates arrows pointing to the selected cell from cells that are part of the formula in that cell

The Error checking button provides an automatic means of checking for mathematical errors within formulas of a worksheet.

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Answer:

Choice D : x > - 1

Step-by-step explanation:

Left hand side (LHS) of the inequality can be siimplified

[tex]2\left(x-3\right)-5x = 2x - 6 - 5x = -3x -6\\\\[/tex]

Inequality becomes

[tex]-3x-6 < x-2[/tex]

Move x to the left side and -6 to the right side:

[tex]-3x - x < -2 + 6\\\\-4x < 4\\\\[/tex]

Multiply both sides by -1(the inequality sign changes to >)

[tex]4x > -4\\\\[/tex]

Divide both sides by 4:
[tex]x > -1[/tex]

The number line corresponding to this is the fourth choice

a) The maximum height of the rock is of: 5.50 metres.

b) The time that the rock was in the air is of: 2.12 seconds.

c) The distance which the rock landed is of: 12.72 meters.

The height of the projectile is modeled using a quadratic function, as follows:

y = -4.905t² + v(0)sin(60)ºt + h(0).

The parameters are given as follows:

Considering the values of these parameters, the function is given as follows:

y = -4.905t² + 10.39t.

The coefficients are given as follows:

a = -4.905, b = 10.39, c = 0.

The maximum height is obtained as the y-coordinate of the vertex, as follows:

Hmax = -(10.39² - 4(4.905)(0))/(4(-4.905)) = 5.50.

The rock hits the ground when:

y = 0.

Hence:

-4.905t² + 10.39t = 0

t(-4.905t + 10.39) = 0.

4.905t = 10.39

t = 10.39/4.905

t = 2.12 seconds.

The horizontal distance is given as follows:

x = v(0)cos(60º)t

Hence:

x = 12 x 0.5 x 2.12 = 12.72 meters.

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Answer:

Graph A

Step-by-step explanation:

Given piecewise function:

[tex]f(x)=\begin{cases}9+x, \;\;\:\:x\leq3\\x^2+3,\;\;x > 3\end{cases}[/tex]

To graph the given piecewise function:

The line  y = 9 + x  is a straight line with a positive gradient.  

It crosses the x-axis at (-9, 0) and crosses the y-axis at (0, 9).

Therefore, the only graph that shows the line  y = 9 + x  is the first graph.

The composition of A and B represents by the set A o B = {(2,2),(4,0)}

What is a set of ordered pair?

An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.

Given sets are

A = {(1,2), (-3,0), (4,7)}

B = {(2,1), (0,3), (4,-3)}

The inputs of B are 2, 0, and 4.

The outputs of B are 1, 3, and -3.

The inputs of A are 1, -3, and 4.

The outputs of A are 2, 0, and 7.

The composition can be written as A o B = A(B(x)

A(B(2)) = A(1) = 2

A(B(0)) = A(3) = not valid [Since 3 is not an input of A].

A(B(4)) = A(-3) = 0

The composition is {(2,2), (4,0)}.

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The dimensions that could be the measurements of a similar triangle are; base = 7.8 cm and height = 18 cm

Two triangles are said to be similar provided that they have the same ratio of corresponding sides and an equal pair of corresponding angles.

Now, we are given the side lengths of the triangle as a base length of 3.9 cm and a height of 9 cm.

Thus, this means that a similar triangle will have same ratio of side lengths. Thus;

If new height is h and new base is b, then we have;

9/h = 3.9/b

Thus,

h/b = 9/3.9

If we multiply the right side top and bottom by 2, then we have;

h/b = 18/7.8

18 and 7.8 cm could be similar dimensions.

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Answer:

≈20.35°

Step-by-step explanation:

height = 8

hypotenuse =23

angle is x

sin(x) =8/23

[tex]sin^{-1} (\frac{8}{23} )[/tex] ≈20.35°

x is about ≈20.35°

The ramp makes an angle of approximately 20.86 degrees with the ground.

Given that there is a truck with a ramp at a height of 8 feet the size of the ramp is 23 feet,

we need to find the angle ramp make with the ground.

To find the angle that the ramp makes with the ground, we can use the sine function.

The sine of an angle is equal to the opposite side divided by the hypotenuse in a right triangle.

In this case, the opposite side is the height of the ramp (8 feet), and the hypotenuse is the length of the inclined portion of the ramp (23 feet).

Let's calculate the angle:

sin(angle) = opposite/hypotenuse

sin(angle) = 8/23

To find the angle, we need to take the inverse sine (or arcsine) of both sides of the equation:

angle = arcsin(8/23)

We can find the approximate value of the angle:

angle ≈ 20.86 degrees

Therefore, the ramp makes an angle of approximately 20.86 degrees with the ground.

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The percent of increase Maria walked if found as the 50%.

The formula for the percentage increase is given as;

Percent increase = Increase / original number x 100

original number = 20 miles

Increase = 30 miles - 20 miles

Increase = 10 miles

So,

Percent increase = 10 / 20 x 100

Percent increase = 50%

Thus, the percent of increase Maria walked if found as the 50%.

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The correct question is-

9) Maria walked 20 miles yesterday. Today she walked 30 miles. What was the percent of increase Maria walked?

Answer: It's not possible for a positive, even integer to have a specific shape, such as the shape of a 4. This is because integers are abstract mathematical concepts that represent whole numbers and do not have any physical properties, such as shape. Additionally, even integers are simply integers that are divisible by 2, and do not have any specific shape associated with them.

If you're asking about a specific number that has the shape of a 4, such as the number "4" written in a specific way, it's important to note that the value of a number does not depend on its physical appearance. For example, the number 4 written as "4" and the number 4 written as "IV" (the Roman numeral for 4) are both the same number, and have the same value.

Answer:

-2

Step-by-step explanation:

The complete answer for the verbal expression into an algebraic inequality is  [tex]\frac{n}{-3} +5 \geq 12[/tex] .

What are inequality?

In arithmetic, the relationship between 2 values that are not equal is outlined by inequalities. difference means that not equal. Generally, if 2 values don't seem to be equal, we tend to use “not equal (≠)”.

Main body:

First, let's call "a number": n

"The quotient" means we are dividing.

Therefore, "the quotient of a number and -3" can be written as:

n÷ -3

now we need to add 5 to the expression ,

[tex]\frac{n}{-3} +5[/tex]

The quotient of a number and -3 plus 5 is at least 12.

so the expression found out till is equal to at least 12 which means sign used is " ≥"

Hence , the complete answer is  [tex]\frac{n}{-3} +5 \geq 12[/tex] .

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All the possible rational zeros of h(x) are given as follows:

±1/7, ± 5/7 ± 1, ± 5.

The rational zero theorem states that all the possible rational zeros of a function are given by plus/minus the factors of the constant by the factors of the leading coefficient.

The parameters for this function are given as follows:

The factors are given as follows:

Then the zeros are given as follows:

±1/7, ± 5/7 ± 1, ± 5.

As:

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The correct statement about histograms is given as follows:

d. All of these choices are true.

An histogram is a graph that shows the number of times each element of x was observed.

Each element is said in case that the histogram can represent element by element, but in the case of distribution with a wider range of possible output values, the histogram is divided into classes, and then the histogram shows the number of observations that were observed for each class, which cover the complete range of observations, meaning that the histogram is a summary of interval data.

The above paragraph, in case the histogram covers a wide range of data, means that all the statements in this problem are correct, and thus option d is correct.

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P-Value for the hypothesis test will be of z = 1.9065

The P-value for conducting the right-tailed test H0 : μ = 3 versus HA : μ > 3 is the probability that we would observe a test statistic greater than t* = 2.5 if the population mean

μ really were 3. Recall that probability equals the area under the probability curve. The P-value is therefore the area under a tn - 1 = t14 curve and to the right of the test statistic t* = 2.5. It can be shown using statistical software that the P-value is 0.0127

The P-value, 0.0127, tells us it is "unlikely" that we would observe such an extreme test statistic t* in the direction of HA if the null hypothesis were true. Therefore, our initial assumption that the null hypothesis is true must be incorrect. That is, since the P-value, 0.0127, is less than

α

= 0.05, we reject the null hypothesis H0 : μ = 3 in favor of the alternative hypothesis HA : μ > 3.

Note that we would not reject H0 : μ = 3 in favor of HA : μ ≠ 3 if we lowered our willingness to make a Type I error to α = 0.01 instead, as the P-value, 0.0254, is then greater than

α= 1.9065.

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The gallons after 8 hours will be 3400 gallons.

Expression refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

Numbers, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations.

In this case, the reactor coolant tank is being filled with coolant at the rate of 400 gallons per hour with t>0 measure in hours.

Therefore, the gallons after 8 hours will be:

= 200 + 400(8)

= 200 + 3200

= 3400 gallons.

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The equation to model on this situation is :

                   0.6 = (0.75x + 0.9)/(x + 3)

Noemi makes bracelets averaging $0.60 per bead, so we need to write an equation that models this average bead cost. This can be found by dividing the total bead cost by the number of beads used.

1. The total cost of a bead can be found by multiplying the price of each type of bead by the number used and adding these values ​​together.

So:

Total Cost = 0.75x + 3*0.3

                  = 0.75x + 0.9

2. Total number of beads = x + 3

3. Thus, the average cost is:

        (0.75x + 0.9)/(x + 3)

4. Using the value of the average cost per bead given to us ($0.60), we can now write up the full equation:

                      0.6 = (0.75x + 0.9)/(x + 3)

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The equation of line passes through the points (1, -4) and (4, 5) will be;

⇒ y = 3x - 7

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;

Two points on the line are (1, -4) and (4, 5).

Now,

Since, The equation of line passes through the points (1, -4) and (4, 5)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (5 - (-4)) / (4 - 1)

m = 9 / 3

m = 3

Thus, The equation of line with slope 3 is,

⇒ y - (-4)= 3 (x - 1)

⇒ y + 4 = 3x - 3

⇒ y = 3x - 3 - 4

⇒ y = 3x - 7

Therefore, The equation of line passes through the points (1, -4) and (4, 5) is given as;

⇒ y = 3x - 7

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Answer:

Below

Step-by-step explanation:

If you turn it sideways and use the y-axis portion as the base (4)  , you can see height = 5

Area = 1/2 * b * h =    1/2 *  4 *5 = 10 units^2

The angle of rotation is 90 degrees.

What is a square?

In a square, all the sides are equal in length and all the angles are right angles (90 degrees). The center of a square is the point that is equidistant from all four vertices, and it is also the point of intersection of the diagonals of the square.

The angle of rotation about the center that maps AB to BC is 90 degrees.

If we rotate the square about its center, the sides of the square will rotate to new positions. For example, if we rotate the square 90 degrees counterclockwise (as specified in the question), side AB will rotate to the position of side BC.

The angle of rotation that maps AB to BC is the angle through which the square was rotated.

Hence, the angle of rotation is 90 degrees.

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(a)     [tex]p_{n} =p_{n-1}-0.4p_{0} +n[/tex]

(b)       [tex]n = {\frac{p_{n-1} -p_{n} }{0.4p_{0}} }[/tex]

Given,

         Initial salmon population [tex]p_{0}=5000[/tex]

         Extraction rate = 40% per year

(a) Formula for recursion,

         For the first year,

                [tex]p_{1} =p_{0} -0.4p_{0}+n[/tex]

         For the second year,

                [tex]p_{2} =p_{1} -0.4p_{0} +n[/tex]

         For the n'th year,

               [tex]p_{n} =p_{n-1}-0.4p_{0} +n[/tex]

(b) The value of n,

        From the above equation,

                [tex]p_{n} =p_{n-1}-0.4p_{0} +n[/tex]

                  [tex]n = {\frac{p_{n-1} -p_{n} }{0.4p_{0}} }[/tex]

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Each year, 40% of the salmon population is extracted from a farming pond.

a. The recursion to describe Pn is Pn = 0.6 Pn-1 + N.

b. The value of N is 3000.

According to the recursion equation, the quantity of fish at the start of the nth year. Pn, is equal to 0.6 times the quantity at the start of the year before, Pn-1, plus the constant quantity of wild salmon that is restocked every year, N.

b. We can set the recursion equation equal to the initial population of 5000 fish in order to get the value of N that ensures the quantity of fish stays constant at the start of each year. Now we have the equation.

0.6Pn-1 + N = 5000. Solving for N gives us N = 3000.

Therefore, a. Pn = 0.6 Pn-1 + N. b.  3000.

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Division problem with quotient of 3 and a remainder of 28 are-

The given data is-

To estimate:

division problem?

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The expression [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex] as a single fraction is [tex]\frac{9a-11}{20}[/tex]

What is algebraic expression ?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

According to question

⇒     [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex]

⇒   taking LCM of 4, 5 = 20

now [tex]\[\frac{4(4+6a)-5(1+3a)}{20}[/tex]

⇒ (16 +24a - 5 - 15a)/20

⇒ ((24a - 15a) - (16-5))/20

⇒ (9a - 11)/20

hence, the expression  [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex] as a single fraction is [tex]\frac{9a-11}{20}[/tex]

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option D

Given;

larger cube edge length  -  3x+2 units

smaller cube edge length -  2x-1 units

We know that  volume of a cube  = (Edge of the cube)3

volume of larger cube = (3x+2 )³

                                     =27x³+8 +54x²+36x

volume of smaller cube=(2x-1)³

                                        =8x³-1 -12x²+6x

Volume difference = volume of larger cube -volume of smaller cube

volume difference =( 27x³+8+54x²+36x)-(8x³- 1 - 12x²+6x)

                                = 19x³+9+66x²+30x

                                 =19x³+66x²+30x+9

Hence volume of larger cube is greater by (19x³+66x²+30x+9)

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Answer:

Step-by-step explanation:

Angle E = W =119 degree

Angle V = 360-105-59-119

Angle V = 77

As DEFG = VWXY

There for D = V

So angle D = 77

Angle G = 360 -77-59-119

Angle = 105

Answer:

119 degree

Step-by-step explanation:

Any similar polygons have:

1- congruent corresponding angles

2- proportional corresponding sides

Here the question asking about measure of angle E.

The easiest way to find the corresponding angles by comparing the polygons names DEFG and VWXY, the 1st letter in both are D and V, that means these two angles are corresponding and congruent. Same for the 2nd letter in both are E and W, that means angle E is congruent to angle W which is 119 degree.

Done

Answer:

-11

Step-by-step explanation:

4c - 3   Substitute -2 for c

4(-2) - 3

-8 - 3

-11

Answer:

-11

Step-by-step explanation:

We are given the value of c, so we just need to plug it in. We can do this by replacing "c" with "-2" in our given expression.

4c - 3 ⇒ 4(-2) - 3

Now, we can simplify this.

-8 - 3 = -11

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