15. Which table correctly lists the x- and y-values for the equation 5x + y = 14?


A.
x
–1
0
1
y
21
28
7
B.
x
–1
0
1
y
19
14
9
C.
x
–1
0
1
y
9
14
19
D.
x
–1
0
1
y
–5
0
5

The perimeter of a rectangle with sides of 14 ft and 8 ft is 44 ft.

The perimeter of a rectangle is calculated by adding all its sides. For a rectangle with sides of 14 ft and 8 ft, the perimeter is found by adding twice the length and twice the width:

Perimeter = 2(length + width)
Perimeter = 2(14 + 8) = 2(22) = 44 ft

The only option that is a triangle from the given options is; 4cm, 8cm, 10 cm

A triangle is a plane shape with three sides which could all be equal or have 2 equal or have no equal sides.

Now, we know a triangle to be one if the sum of two smallest sides is greater than the longest side.

Thus, only option B can B a triangle because the sum of 4cm and 8cm is 12 cm which is greater than 10 cm.

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Answer:

B. & E.

Step-by-step explanation:

First, to find your slope, put your line into slope-intercept form.

[tex]y=mx+b\\[/tex]

[tex]3x-4y=7\\-4y=-3x+7\\y=\frac{3}{4} x-\frac{7}{4}[/tex]

Your slope is [tex]\frac{3}{4}[/tex].

Now, you can find the y-intercept of your parallel line by plugging your given point and your slope into point-slope form.

[tex]y-y1=m(x-x1)\\y-(-2)=\frac{3}{4} (x-(-4))\\y+2=\frac{3}{4} (x+4)\\y+2=\frac{3}{4} x+3\\y=\frac{3}{4} x+1[/tex]

Your y-intercept is 1.

If you notice, answer choice E is equivalent to one of our steps in converting it to point-slope form. Therefore, E is one of your answers.

The equation of your parallel line is:

[tex]y=\frac{3}{4} x+1[/tex]

B is also a correct answer.

If you put B into slope-intercept form, you get the following:

[tex]3x-4y=-4\\-4y=-3x-4\\y=\frac{3}{4} x+1[/tex]

This, of course, is equivalent to the parallel line which we already found, so we know it is parallel.

Answer:

[4, 1]

Step-by-step explanation:

Here we have four rows and one column, so the order of A + B is [4, 1].

Answer:

D.

Step-by-step explanation:

The data is symmetric for Shop A but not for Shop B ( note the values 10 and 11 for Shop B which are a lot lower than the other values).

Mean for Shop A and Median for Shop B.

Answer:

The correct option is B.

Step-by-step explanation:

The number of lattes sold daily by two coffee shops is shown in the table.

The data set for shop A is

55, 52, 56, 48, 57, 30, 45, 41

Arrange the data in ascending order.

30, 41, 45, 48, 52, 55, 56, 57

Mean of shop A is

[tex]Mean=\frac{\sum x}{n}=\frac{30+41+45+48+52+55+56+57}{8}=48[/tex]

[tex]Median=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{48+52}{2}=50[/tex]

The data set for shop B is

45, 42, 57, 48, 11, 10, 46, 43

Arrange the data in ascending order.

10, 11, 42, 43, 45, 46, 48, 57

Mean of shop A is

[tex]Mean=\frac{\sum x}{n}=\frac{10+11+42+43+45+46+48+57}{8}=37.75[/tex]

[tex]Median=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{43+45}{2}=44[/tex]

Both data distribution are not symmetric, so it is better to describe the centers of distribution in terms of median for both coffee shops. Therefore the correct option is B.

Answer:

Mary: 16

Kevin: 22

Ahmed: 88

Step-by-step explanation:

This could be written as the following formula.

Mary + Kevin + Ahmad = 126

and we know that

Mary + 6 = Kevin

Kevin * 4 = Ahmed

so Ahmed = (Mary + 6) * 4

When filling this in you get

Mary + Mary + 6 + (Mary + 6) * 4 = 126

Mary + Mary + 6 + 4Mary + 24 = 126

6Mary + 30 = 126

6Mary = 96

Mary = 16

So Mary served 16 orders.

Using the earlier formulas you get

Kevin = Mary + 6 = 16 + 6 = 22

Ahmed = Kevin * 4 = 22 * 4 = 88.

Now we just need to double check it.

Mary + Kevin + Ahmad = 16 + 22 + 88 = 126. Which matches what it should be.

Answer:

-2

Step-by-step explanation:

Within the provided points list for the graph, there is the coordinate (1, -2). Hence, by definition of a function and how to read graphs, f(1) is -2.

In this scenario, you're being asked to read the value of f(1) from a given graph. The line passing through the listed points is irrelevant provided one of the plotted points has an x-coordinate of 1. You directly read this from the graph - not calculate it or interpolate it. The list of points you've provided includes (1, -2), so, in your case, f(1) = -2. This is exactly how you would refer to the y-value at x=1 on a visual graph.

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Answer:

1. Length when found = length at birth + (age when found × growth each year); 2. 6.3 yr

Step-by-step explanation:

1. The word equation

Length when found = length at birth + (age when found × growth each year)

2. The calculations

                            5 m = 2.6 m + (age when found × 0.38 m/yr)  

Do the multiplication first (PEMDAS)

                            5 m = 2.6 m + 0.38 × age when found m/yr

Subtract 2.6 m from each side of the equation

                           2.4 m = 0.38 × age when found m/yr

Divide each side by 0.38 m/yr

                           6.3 yr = age when found

The killer whale is 6.3 yr old.

Answer:

Wrong

Step-by-step explanation:

The student is wrong. Two angles are coterminal if and only if the difference between their measures is a multiple of 360°.

The difference between the angles 180° and –180° is 360°, and they are coterminal. Therefore the student is WRONG.

Answer:

The student is wrong. Two angles are coterminal if and only if the difference between their measures is a multiple of 360°.

The difference between the angles 180° and –180° is 360°, and they are coterminal. Therefore the student is WRONG.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]p\%=\dfrac{p}{100}\\\\14\%=\dfrac{14}{100}=0.14\\\\3540\%=\dfrac{3540}{100}=35.40=35.4\\\\14\%\ of\ 3540\%\ of\ 35\to(0.14)(35.4)(35)=173.46[/tex]

The end behavior of the function y = 10x9 – 4x is such that as x approaches infinity, y approaches infinity, and as x approaches negative infinity, y approaches negative infinity. This is because the degree of the polynomial is odd and the leading coefficient is positive.

The end behavior of a polynomial function describes what happens to the function values (y-values) as x approaches infinity and negative infinity. In your function, y = 10x9 – 4x, the highest power of x is 9, and it's coefficient is positive.

According to the rules of end behavior, if the degree (highest power) of the polynomial is odd, and the leading coefficient (the number in front of the highest power) is positive, as x approaches positive infinity, y also approaches positive infinity, and as x approaches negative infinity, y approaches negative infinity.

In simpler terms, this means that the graph of your function starts in the third quadrant (bottom-left) and ends in the first quadrant (top-right). Hence, the end behavior of this function can be described as: as x approaches infinity, y approaches infinity; and as x approaches negative infinity, y approaches negative infinity.

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Answer: C

Step-by-step explanation: the answer is C on edge :)

Answer:

[tex]x_{1}=\frac{+3+\sqrt{5} }{2}\\\\x_{2}=\frac{+3-\sqrt{5} }{2}[/tex]

Step-by-step explanation:

Using:

[tex]x=\frac{-b+-\sqrt{b^{2}-4*a*c} }{2*a}[/tex]

we will have two solutions.

x^2-3x+1=0

So, a=1   b=-3  c=1

[tex]x_{1}=\frac{+3+\sqrt{-3^{2}-4*1*1} }{2*1}\\\\x_{2}=\frac{+3-\sqrt{-3^{2}-4*1*1} }{2*1}[/tex]

We have two solutions:

[tex]x_{1}=\frac{+3+\sqrt{5} }{2}\\\\x_{2}=\frac{+3-\sqrt{5} }{2}[/tex]

The answer is in the picture below! :)

|

V

The graph shows the solutions:

x1 = -3    ⇒  x + 3 = 0

x2 = 1     ⇒  x - 1 = 0

x3 = 5     ⇒  x - 5 = 0

The polynomial follows:   y = (x + 3)(x - 1)(x - 5)

.

Answer:

y= (x+3) (x-1) (x-5)

Step-by-step explanation:

The graph crosses the x axis at the points -3,1,5

These are also called the zeros

f(x) =k (x-a) (x-b) (x-c) .....

where a,b,c,... are the zeros of the function and k is a constant

f(x) = k * (x--3) (x-1) (x-5)

f(x) = k(x+3) (x-1) (x-5)

To help determine the value of k

Take another point  at x = 0, we know the value is positive

f(0) = k(3) (-1) (-5)

f(0) = k(15)

That means k must be greater than 0  Looking at the graph, it should be around 1

f(x) = (x+3) (x-1) (x-5)

Answer:

Is a Mean, Median and Mode

Is also a summary statistics that presents the center point or typical value off a dataset.

Answer is attached in the image provided.

Answer: B. Rhombus.

Step-by-step explanation: B. Rhombus is the answer because a rectangle has 2 pairs of equal sides. A pentagon has 5 sides. A trapezoid doesn’t have all equal sides. A rhombus is like a squished square.

The sum of the geometric series is approximately 435.4, according to the formula for geometric series summation.

To find the sum (Sn) of a geometric series, you can use the formula:

[tex]\[ Sn = \frac{{a_1 \cdot (1 - r^n)}}{{1 - r}} \][/tex]

Where:

[tex]- \( a_1 \) is the first term\\- \( r \) is the common ratio\\- \( n \) is the number of terms[/tex]

Given:

[tex]\( a_1 = 0.28 \)\( a_5 = 362.88 \)\( r = 6 \)[/tex]

We need to find [tex]\( n \)[/tex]. Since [tex]\( a_5 \)[/tex] is the fifth term, we can use the formula for the nth term of a geometric series:

[tex]\[ a_n = a_1 \cdot r^{(n-1)} \][/tex]

Substitute the values we have:

[tex]\[ 362.88 = 0.28 \cdot 6^{(5-1)} \]\[ 362.88 = 0.28 \cdot 6^4 \]\[ 362.88 = 0.28 \cdot 1296 \]\[ 362.88 = 363.648 \][/tex]

So, [tex]\( n = 5 \).[/tex]

Now, plug the values into the sum formula:

[tex]\[ S_5 = \frac{{0.28 \cdot (1 - 6^5)}}{{1 - 6}} \]\[ S_5 = \frac{{0.28 \cdot (1 - 7776)}}{{-5}} \]\[ S_5 = \frac{{0.28 \cdot (-7775)}}{{-5}} \]\[ S_5 = \frac{{-2177}}{{5}} \]\[ S_5 = -435.4 \][/tex]

Since the sum of a series cannot be negative, the correct answer is option:

a. 435.4

Answer:

(x^2)/3 + 4

Step-by-step explanation:

4 more means add four and the quotient of x squared and 3 shows that x squared must be divided by three before added to 4

please mark brainliest :)

The two lines are parallel, which means they never touch, cross or meet.

Answer: No solution

Answer:

no solution

Step-by-step explanation:

Answer:

=2.83 the second option

Step-by-step explanation:

Using the trigonometric ratios we can find the sides of the triangle with the acute angles.

In the triangle provided we will use COSINE

Cos ∅=adjacent/hypotenuse

Let us substitute with the values in the question into the formula.

Tan 45 =2/x

x=2/Cos 45

=2.83 units

Answer: SECOND OPTION.

Step-by-step explanation:

You can use the following identity:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

In this case:

[tex]\alpha=45\°\\adjacent=2\\hypotenuse=x[/tex]

Therefore, in order to calculate the value of "x", you need to substitute values into [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex] and solve for "x".

This is:

[tex]cos(45\°)=\frac{2}{x}\\\\xcos(45\°)=2\\\\x=\frac{2}{cos(45\°)}\\\\x=2\sqrt{2}[/tex]

[tex]x[/tex]≈[tex]2.83[/tex]

Answer:

[tex] 27^{\frac{1}{5}} = \sqrt[5]{27} [/tex]

Step-by-step explanation:

Rule of exponents:

[tex] a^{\frac{1}{n}} = \sqrt[n]{a} [/tex]

Apply the rule to this case:

[tex] 27^{\frac{1}{5}} = \sqrt[5]{27} [/tex]

Step-by-step explanation:

x - y = 7...eqn 1

x^2 + y = 125...eqn 2

making y the subject of the formula in eqn 1

=> y = x -7...eqn 3

subst for y from eqn 3 in eqn 2

=> x^2 + x-7 = 125

=> x^2 + x - 132 = 0

=> (x + 12) (x -11) =0

x = 11 or -12

when x = 11, y = 4

when x = -12, y = -19

Answer:

The largest numbers is either -12 or 11

Step-by-step explanation:

Let the numbers be a and b and a be the largest number.

The difference of two numbers is 7

        a - b = 7 ------------------------- eqn 1

The sum of the smaller number and the square of the larger number is 125

        a² + b = 125 ------------------------- eqn 2

eqn 1 + eqn 2

       a² + a - 132 = 0

       ( a + 12 ) (a - 11) = 0

        a = -12 or a  = 11

So the largest numbers is either -12 or 11

Answer:

204 in^3

Step-by-step explanation:

The volume of the base square is V=lwh.

When we substitute our givens, it becomes V=6(4)(2). This equals 48 in^3.

The volume of the triangle is V=.5lwh.

When we substitute our givens, it becomes V=.5(6)(4)(15-2). This equals 156 in^3.

When we add 48 and 156, we get 204 in^3.

Hope this helps :)

The question appears to be about finding the midpoint of segment AH, which involves dividing the segment into two equal parts, either by measurement or by averaging the coordinates of A and H if available.

The question seems to be asking about identifying the midpoint of a line segment in a geometric construction. However, the provided text alludes to various geometric proofs and theorems, rather than directly providing information about finding midpoints.

To find the midpoint of segment AH, one would need to measure the length of AH and then divide it by 2 to find the center point. If the points A and H are on a coordinate plane, the midpoint can be found by calculating the average of the x-coordinates and the y-coordinates of the endpoints A and H. Without specific coordinates or measurements, a more detailed answer cannot be provided.

The midpoint of AH is (0, 4).

Let's assign coordinates to the points A and H to make it easier to calculate the midpoint. Suppose A is at (x1, y1) and H is at (x2, y2).

The formula for finding the midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) is:

[tex]M = \left( \frac{x1 + x2}{2}, \frac{y1 + y2}{2} \right)[/tex]

If we assume A is at (0, 0) and H is at (0, 8) (since H is directly 'below' A on a vertical line), the coordinates are as follows:
A = (0, 0)
H = (0, 8)

Now, applying the midpoint formula:

[tex]M = \left( \frac{0 + 0}{2}, \frac{0 + 8}{2} \right) = (0, 4)[/tex]

Answer:

[tex]3-\sqrt{11}[/tex]

Step-by-step explanation:

If you want rational coefficients then you would want the conjugate of any irrational zero given.

The question is equivalent to what is the conjugate of [tex]3+\sqrt{11}[/tex].

The conjugate of [tex]3+\sqrt{11}[/tex] is [tex]3-\sqrt{11}[/tex].

In general, the conjugate of a+b is a-b

or the conjugate of a-b is a+b.

Or maybe you like this explanation more:

Let [tex]x=3+\sqrt{11}[/tex]

Subtract 3 on both sides:

[tex]x-3=\sqrt{11}[/tex]

Square both sides:

[tex](x-3)^2=11[/tex]

Subtract 11 on both sides:

[tex](x-3)^2-11=0[/tex]

Use difference of squares to factor. I apply [tex]u^2-v^2=(u-v)(u+v)[/tex].

[tex]([x-3]-\sqrt{11})([x-3]+\sqrt{11})=0[/tex]

So you have either

[tex][x-3]-\sqrt{11}=0[/tex] or [tex][x-3}+\sqrt{11}=0[/tex]

Solve both for x-3 and then x.

Add sqrt(11) on both sides for first equation and subtract sqrt(11) on both sides for second equation:

[tex]x-3=\sqrt{11}[/tex] or [tex]x-3=-\sqrt{11}[/tex]

Add 3 on both sides:

[tex]x=3+\sqrt{11}[/tex]  or [tex]x=3-\sqrt{11}[/tex]

Answer:

the answer is C.

Step-by-step explanation:

ANSWER

[tex]x = - \frac{2}{9} [/tex]

EXPLANATION

The given equation is :

[tex] \frac{2}{5}(x - 2) = 4x[/tex]

We multiply both sides by [tex] \frac{5}{2} [/tex]

[tex] \frac{5}{2} \cdot\frac{2}{5}(x - 2) = 4x \times \frac{5}{2} [/tex]

We simplify to obtain:

[tex]x - 2 = 10x[/tex]

Group similar terms to obtain:

[tex] - 2 = 10x - x[/tex]

Simplify the right hand side.

[tex] - 2 = 9x[/tex]

Divide both sides by 9.

[tex] \frac{ - 2}{9} = \frac{9x}{9} [/tex]

[tex] - \frac{2}{9} = x[/tex]

Or

[tex]x = - \frac{2}{9} [/tex]

The second choice is correct

The solution for [tex]x[/tex] is [tex]x = -\frac{2}{9}[/tex].

To solve the equation [tex]\frac{2}{5} (x - 2) = 4x[/tex], we need to perform the following steps:

Distribute the Fraction:
We start by distributing [tex]\frac{2}{5}[/tex] to both terms inside the parentheses:
[tex]\frac{2}{5}x - \frac{2}{5} \cdot 2 = 4x[/tex]
This simplifies to:
[tex]\frac{2}{5}x - \frac{4}{5} = 4x[/tex]

Isolate the Variable:
Next, we want to get all terms involving [tex]x[/tex] on one side. We can do this by subtracting [tex]\frac{2}{5}x[/tex] from both sides:
[tex]-\frac{4}{5} = 4x - \frac{2}{5}x[/tex]

Now, we can combine the [tex]x[/tex] terms on the right:
[tex]4x - \frac{2}{5}x = \left(4 - \frac{2}{5}\right)x = \left(\frac{20}{5} - \frac{2}{5}\right)x = \frac{18}{5}x[/tex]
Thus, we have:
[tex]-\frac{4}{5} = \frac{18}{5}x[/tex]

Solve for x:
Now, we want to solve for [tex]x[/tex] by multiplying both sides of the equation by the reciprocal of [tex]\frac{18}{5}[/tex], which is [tex]\frac{5}{18}[/tex]:
[tex]x = -\frac{4}{5} \cdot \frac{5}{18} = -\frac{4}{18} = -\frac{2}{9}[/tex]

Given the multiple-choice options of [tex]\frac{2}{9}[/tex], [tex]9[/tex], [tex]-\frac{2}{9}[/tex], and [tex]-\frac{9}{2}[/tex], the correct answer is negative 2 over 9.

Answer:

180

Step-by-step explanation:

180-120 = 60 this is one of all the congruent angles

of the top of my head i know a regular triangle has three 60 degree angles meaning it is 60*3 = 180

Answer:

You would click (1,-5)

Step-by-step explanation:

The absolute minimum is the lowest point of the graph.

In all graphs, if it says minimum, it almost certainly means that lowest point, and if there are more than one, you would simply click on those.

It does not matter how many points there are, only that they are the lowest.

Therefore, it would be 1,-5.

Answer:

Step-by-step explanation:

If you accept that this is a function or even a relationship then and is connected then the minimum should be (1,-5).  

Answer:

Option D. is the answer.

Step-by-step explanation:

Option A.

From the table we can see that for the value of x = 3, there are two values of y (14 and 19).

Which is not possible for a function. It should be one to one.

So option A is not a function.

Option B.

In this option again we have two values of y = 0, -5 for the value of x = 3.

For a function values of x and y should be one to one.

Therefore, it's not a function.

Option C.

Here for x = -1, there are two values of y (y = -11 and 5).

Therefore, it's not a function.

Option D.

In the given graph we find that there are different values of y for every value of x.

Therefore, Option D is the answer.

The discriminant of the quadratic function f(x) = 25x² - 10x + 1 is equal to zero. Hence, the graph of this function has only one x-intercept.

The student is asking for the value of the discriminant of the quadratic function f(x) = 25x² - 10x + 1 and the number of x-intercepts the function has. In a quadratic function ax²+bx+c, the value of the discriminant, denoted as D, is calculated using the formula D = b² - 4ac. In this case, a = 25, b = -10, and c = 1.

Therefore, the discriminant D = (-10)² - 4(.25)(1) = 100 - 100 = 0. The quadratic equation will have exactly one root if the discriminant is zero.

Thus, "the graph of the function f(x) = 25x² - 10x + 1 has one x-intercept".

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The value of the discriminant is 0, and the graph of \(f\) has one repeated x-intercept.

1. The value of the discriminant [tex](\(\Delta\))[/tex] of the quadratic function [tex]\(f(x) = 25x^2 - 10x + 1\)[/tex] is [tex]\(b^2 - 4ac\),[/tex] where a, b and c are coefficients in the quadratic equation [tex]\(ax^2 + bx + c = 0\)[/tex].

2. The number of x-intercepts the graph of \(f\) has is determined by the discriminant:

  - If [tex]\(\Delta > 0\)[/tex], there are two distinct x-intercepts.

  - If [tex]\(\Delta = 0\)[/tex], there is one repeated x-intercept (the graph touches the x-axis but does not cross it).

  - If [tex]\(\Delta < 0\)[/tex], there are no x-intercepts (the graph does not intersect the x-axis).

1. Calculate [tex]\(\Delta\)[/tex]: In the given function [tex]\(f(x) = 25x^2 - 10x + 1\)[/tex], [tex]\(a = 25\),[/tex] [tex]\(b = -10\),[/tex]and [tex]\(c = 1\)[/tex]. Plug these values into the discriminant formula: [tex]\(\Delta = b^2 - 4ac\).[/tex]

[tex]\[\Delta = (-10)^2 - 4(25)(1) = 100 - 100 = 0\][/tex]

2. Analyze the number of x-intercepts based on \(\Delta\):

  - Since [tex]\(\Delta = 0\)[/tex], there is one repeated x-intercept.

Therefore, the value of the discriminant is 0, and the graph of \(f\) has one repeated x-intercept.

Answer:

33 feet

Step-by-step explanation:

We can draw a triangle in this situation.

Note:

The height of the tree is the side "opposite" of the 35 angle. The squirrel's distance of 47 feet from the base of the tree is the side "adjacent" to the angle.

Which trig ratio relates "opposite" and "adjacent"?

It is Tan

Thus we can write and solve (let height of tree be h):

[tex]Tan(35)=\frac{h}{47}\\h=Tan(35)*47\\h=32.91[/tex]

To the nearest foot, the height of tree is about 33 feet