Write the equation for a parabola that has x-intercepts (−4.5, 0) and (−2.8, 0) and y-intercept (0, 37.8).

Answer:

[tex]{{$log_{b} \left(x\right)$}}\div( 1 + {{log_{b} \left(n\right)}})[/tex]  =  [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex]

[tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex] =  [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(nb\right)}})[/tex]   =   [tex]{{$log_{nb} \left(x\right)$}}[/tex]

Step-by-step explanation:

i) [tex]$\log_{nb} x[/tex]   =  [tex]{{$log_{b} \left(x\right)$}}\div( 1 + {{log_{b} \left(n\right)}})[/tex]  =  [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex]

ii) therefore simplifying i) we get

    [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex] =  [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(nb\right)}})[/tex]   =   [tex]{{$log_{nb} \left(x\right)$}}[/tex]

iii) Hence the equation is proved.

To determine if a quadrilateral is a parallelogram, we need to compare the lengths of the sides and the measures of the angles.

A quadrilateral is a parallelogram if and only if both pairs of opposite sides are equal in length and both pairs of opposite angles are congruent. To find the values of x and y that make the quadrilateral a parallelogram, we need to compare the lengths of the sides and the measures of the angles.

For example, if we have a quadrilateral with sides x, y, z, and w, we can check if it is a parallelogram by comparing x and z and y and w. If x = z and y = w, then the quadrilateral is a parallelogram.

Similarly, we can check the angles by comparing the measures of opposite angles. If the measures of the opposite angles are equal, then the quadrilateral is a parallelogram.

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The values of x and y that make the quadrilateral a parallelogram are [tex]\(x = 114^\circ\)[/tex] and [tex]\(y = 66^\circ\)[/tex].

In a parallelogram, opposite angles are congruent. Therefore, if one angle measures [tex]\(66^\circ\)[/tex], its opposite angle must also measure [tex]\(66^\circ\).[/tex] Similarly, if another angle measures [tex]\(114^\circ\)[/tex], its opposite angle must also measure [tex]\(114^\circ\)[/tex].

Let's denote the measures of the angles as follows:

- Angle opposite to x is [tex]\(114^\circ\)[/tex]

- Angle opposite to y is [tex]\(66^\circ\)[/tex]

Since the opposite angles are congruent, we have:

[tex]\[ x = 114^\circ \]\[ y = 66^\circ \][/tex]

Therefore, the values of x and y that make the quadrilateral a parallelogram are [tex]\(x = 114^\circ\)[/tex] and [tex]\(y = 66^\circ\)[/tex].

Answer:

Step-by-step explanation:

Least common number for 9 and 12 is 36

36/9=4

36/12=3

4 packs of hot dogs and 3 packs of buns

Answer:

The correct answer is B. 87°

Step-by-step explanation:

Let's recall that the interior angles of a triangle add up to 180°,

therefore, we have:

∠x + 28 + 65 = 180

∠x = 180 - 65 -28

∠x = 180 - 93

∠x = 87°

The correct answer is B. 87°

Answer:

17.56

Step-by-step explanation:

The amount of tax withheld from Ed Employee's weekly earnings is approximately $36.02.  Option D is the right choice.

To calculate the amount of tax withheld, we need to determine the applicable tax rate based on the employee's weekly earnings and the number of exemptions claimed.

Given:

- Weekly earnings: $544.00

- Number of exemptions claimed: 2

First, let's find the applicable tax rate from the provided table based on the weekly earnings. The table provides tax rates for various income ranges.

Since the weekly earnings fall between $540 and $560, we can interpolate to find the tax rate corresponding to this range.

From the table:

- For earnings between $540 and $560, the tax rate is between $19.81 and $17.56.

Using linear interpolation:

[tex]\[ \text{Tax rate} = \$19.81 - \left( \frac{560 - 544}{560 - 540} \times (\$19.81 - \$17.56) \right) \]\[ = \$19.81 - \left( \frac{16}{20} \times ( \$19.81 - \$17.56 ) \right) \]\[ = \$19.81 - \left( \frac{4}{5} \times \$2.25 \right) \]\[ = \$19.81 - \$1.80 \]\[ = \$18.01 \][/tex]

Now, to find the tax withheld:

[tex]\[ \text{Tax withheld} = \text{Tax rate} \times \text{Number of exemptions} \]\[ = \$18.01 \times 2 \]\[ = \$36.02 \][/tex]

Therefore, the amount of tax withheld from Ed Employee's weekly earnings is approximately $36.02.  Option D is the right choice.

Question:-

Ed Employee has weekly earnings of $544.00 and he claims 2 exemptions. How much tax is withheld?

A. $19.81

B. $17.56

C. $18.73

D. $36.02

Answer:

3/-3 basically -1

Step-by-step explanation:

do the y2-y1 / x2-1 formula and put the coordinates in and that is:

3-0 / -13- -10

or

3/-3

or -1

BTW: if the numerator and denominator are both negative,

Answer:

Step-by-step explanation:

(-10,0) and (-13,3)

Slope m = (y2 - y1)/(x2 - x1)

y2 = 3, y1 = 0, x2 = -13, x1 = -10

: m = (3 - 0)/(-13 + 10)

m = 3/-3

m = -1

Slope m = -1

Answer:

Therefore,

[tex]6r-r++(15-r)+23-6 = -3r+137[/tex] i.e

[tex]6r-r+8(15-r)+23-6[/tex]    and

[tex]-3r+137[/tex] are Equivalent .

Step-by-step explanation:

To Check:

[tex]6r-r+8(15-r)+23-6[/tex] and

[tex]-3r+137[/tex] is Equivalent or Not

Solution:

Consider,

[tex]6r-r+8(15-r)+23-6[/tex]  

Step 1 . Apply Distributive Property , A(B+C)=AB+AC we get

[tex]6r-r+8\times 15-8\times r+23-6[/tex]  

[tex]6r-r+120-8r+23-6[/tex]  

Step 2 . Combining Like Terms i.e r terms and the numbers we get

[tex]6r-r-8r+120+23-6[/tex]  

[tex]-3r+137[/tex]  

Which is Equivalent to the given expression

[tex]-3r+137[/tex]

Therefore,

[tex]6r-r+8(15-r)+23-6= -3r+137[/tex]   i.e

[tex]6r-r+8(15-r)+23-6[/tex]      and

[tex]-3r+137[/tex]                  ..........are Equivalent .

Answer:

40.625 miles covered in 2.5 hours

Step-by-step explanation:

Given that [tex]16 \frac{1}{4} [/tex]

miles was ran in one hour, then to find miles run in 2.5 hours, we just have to multiply:

[tex]16 \frac{1}{4} [/tex]

by [tex]2 \frac{1}{2} [/tex]

This means that miles run in 2½ hours

[tex] = 16 \frac{1}{4} \times 2 \frac{1}{2} [/tex]

[tex] = \frac{65}{4} \times \frac{5}{2} [/tex]

[tex] = \frac{325}{8} [/tex]

[tex] = 40 \frac{5}{8} = 40.625[/tex]

Therefore 40.625 miles will be run in 2.5 hours.

Answer: C

Step-by-step explanation: simply apply the distributive property to each half of the expression to be left with terms that can be combined.

(8x + 16y)/2 = 4x + 8y

4(x - y) = 4x - 4y

(4x + 8y) + (4x - 4y) = 4x + 4x + 8y - 4y

= 8x + 4y => C

Answer:

[tex]\frac{8x+16y}{2}+4(x-y)=\frac{2*4x+2*8y}{2}+4*x-4*y\\\\=\frac{2*(4x+8y)}{2}+4x-4y\\\\=4x+8y+4x-4y=8x+4y[/tex]

Step-by-step explanation:

Answer:

x - 5.19 or x = -2.67 is the correct answer.

Step-by-step explanation:

Here, the given quadratic equation is:  [tex]2x^2- 5x-28=0[/tex]

To solve it by : Completing The Square

Step : 1  Make the coefficient of leading variable x² as  1.

Divide whole equation by 2,we get:

[tex]x^2- \frac{5}{2} x-14=0\\\implies x^2- \frac{5}{2} x = 14[/tex]

Step 2: Find the coefficient of x in the equation and DIVIDE it by 2 to HALF THE VALUE

Here, the coefficient of x = (-5/2)

Dividing ot by 2, we get the value =  (-5/4)

Step 3: ADD THE SQUARE of the found value on BOTH sides.

And USE: [tex](a - b)^2 = a^2 + b^2 - 2ab[/tex]

[tex]x^2- \frac{5}{2} x = 14 \implies x^2- \frac{5}{2} x + (\frac{5}{4} )^2= 14 + (\frac{5}{4} )^2\\\implies (x -\frac{5}{4})^2 = 14 + \frac{25}{16} = \frac{224 + 25}{16} = \frac{249}{16} \\\implies (x -\frac{5}{4})^2 = \frac{249}{16} = (\frac{15.7}{4})^2\\ \implies (x -\frac{5}{4})^2 = (\frac{15.7}{4})^2[/tex]

Step 4: TAKE ROOT ON BOTH SIDES, we get:

[tex](x -\frac{5}{4})^2 = (\frac{15.7}{4})^2\\\implies (x -\frac{5}{4}) = \pm (\frac{15.7}{4})\\\implies x = (\frac{15.7}{4}) +(\frac{5}{4}) = 5.19\\or, x = - (\frac{15.7}{4}) +(\frac{5}{4}) = -2.67\\[/tex]

So, either x - 5.19 or x = -2.67

The correct answer is B) [tex]$1606.42[/tex]. The balance after Anna writes check  is

 [tex]$1606.42[/tex].

To solve this problem, we need to follow the transactions in Anna's checking account to determine the balance after check #1620 is written. Let's assume that the initial balance before any transactions is $0.00.

 Let's check each option:

A) [tex]$1536.24[/tex][tex]- $1452.77 = $83.47[/tex] (This cannot be the correct balance after check #1620 because it does not match the balance after check #1612.

B)[tex]$1606.42 - $1452.77 = $153.65[/tex] (This is the amount spent on groceries, indicating that the balance after check #1612 is correct and no additional funds were withdrawn by check #1620.)

 C)[tex]$1734.81[/tex][tex]- $1452.77 = $282.04[/tex] (This would mean an additional $282.04 was withdrawn after the groceries purchase, which is not possible since we are looking for the balance after one check, #1620.)

 D) [tex]$1760.61[/tex][tex]- $1452.77 = $307.84[/tex] (This would also mean an additional amount was withdrawn, which is not possible for the same reason as option C.) Therefore, the only logical balance that matches our calculations after check #1620 is option B) $1606.42, which implies that check #1620 did not change the balance from what it was after check #1612. This means that check #1620 was for the same amount as the groceries purchase ($153.65), which brought the balance back to $1606.42 after the groceries were bought

Answer:

Top Left

Step-by-step explanation:

Shaded circle means it will be Greater than or equal to or Less then or equal to. The answwers are less that or equal to 75 so s is less than or equal to 75

Answer:

It is s less than and equal to 75

Step-by-step explanation:

I say that because on 75 ther is a full circled dot instead of open dot.

Answer:

Step-by-step explanation:

We have parallel lines.

Angles 1 and 2 are alternate angles.

With parallel lines, alternate angles are congruent.

Therefore

[tex]m\angle1=m\angle2[/tex]

[tex]m\angle1=2x+20,\ m\angle2=3x+10\\\\2x+20=3x+10\qquad\text{subtract 20 from both sides}\\\\2x+20-20=3x+10-20\\\\2x=3x-10\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\2x-3x=3x-3x-10\\\\-x=-10\qquad\text{change the signs}\\\\x=10\\\\m\angle1=2(10)+20=20+20=40[/tex]

L = length

W = width

L = 2(2W + 8)

W = 2W

Perimeter: 96 = 4W + 16 + 2W

96 = 6W + 16

80 = 6W

13.33 = W

Plug this into the equation:

2(13.33) + 8

26.67 + 8 or 34.67 = L

Answer:

-10

Step-by-step explanation:

2-12 =

-12+2 = -10

Answer:20$

Step-by-step explanation:

Answer:

You earn $20.

Step-by-step explanation:

35 divided by 7 is 5.

5 times 4 is 20.

Step-by-step explanation:

To find fg(x), you first open up the g.

This will make f(6x+5). How you substitute 6x + 5 for the x in the f.

This means you get 2(6x+5)+4

Which equals 12x+14

Answer:

Sorry I can't read it :(

Answer:15pq

Step-by-step explanation:

The correct expression is 15pq.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:

Constant: A constant is a fixed numerical value.

Variable: A variable is a symbol that doesn't have a fixed value.

Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.

Coefficient: A coefficient is a number that is multiplied by a variable in an expression.

Given:

(3p)(5q).

=3p * 5q

=15 pq

Hence, the simplified expression is 15 pq.

Learn more about expression here:

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The rate change of interval for the given table is Constant , so the function a linear function.

Step-by-step explanation:

A linear function is defined as a function which yields a line in a graph and the rate of change(constant) is called as slope.

Since the rate is constant, then function will result in a straight line.

From the given table the slope m=1 and it changes constantly.

The linear equation formula is y=mx+c.

where m is the slope and c is the y-intercept.

The linear equation for the given table is y=x+1.

∴ The rate change of interval for the given table is Constant , so the function a linear function.

If the graph for a function has any shapes other than a straight line then it doesn't have a constant slope and it will be a non-linear function.

the answer to your question is 7

Answer:

4x + 3

Step-by-step explanation:

(-6 + 7) - ( -4x - 2)

1 - ( -4x -2 )

distribute the negative sign to the parenthesis

( remember a negative plus a negative equals a positive )

1 + (4x + 2)

Answer: 4x + 3

Answer:

Step-by-step explanation:

It's unclear, but if is the question

12x-7=8

then

x=[tex]\frac{5}{4}[/tex]

Answer:

[tex]\huge{\boxed{x=\pm\dfrac{5}{4}}[/tex]

Step-by-step explanation:

[tex]12|x|-7=8\qquad\text{add 7 to both sides}\\\\12|x|-7+7=8+7\\\\12|x|=15\qquad\text{divide both sides by 12}\\\\\dfrac{12|x|}{12}=\dfrac{15}{12}\\\\|x|=\dfrac{15:3}{12:3}\\\\|x|=\dfrac{5}{4}\iff x=\pm\dfrac{5}{4}[/tex]

Answer:

The answer is B ⅚ because there's only one out of 6 chance that the spinner will land on 6.

A graph tracking Mr. Gomez's account balance over time would include a horizontal line indicating the $15 threshold for bank notices. Payments or withdrawals dropping the balance to this level would be highlighted, showing when notices are sent.

Suppose the bank sent Mr. Gomez a notice whenever the amount in his account dropped to $15 or less. To visualize how the graph in the example would change with this information, first, we should understand that the account's balance is being tracked over time. Typically, a graph representing an account balance over time would have time on the horizontal axis and the account balance on the vertical axis.

If a notice is sent whenever the account drops to $15 or less, this adds a conditional behavior to the graph.

Specifically, there would be a horizontal line at the $15 mark indicating this threshold. When Mr. Gomez makes payments or withdrawals that drop the account balance to this level or below, it could be highlighted or represented differently (using a different color or pattern) on the graph to indicate when the bank sent a notice. Therefore, the primary change to the graph is the visual representation of these notices being sent at or below the $15 mark.

Mr. Gomez will receive a notice from the bank whenever the amount in his checking account falls below $20.

The inequality is x < 20, which means that the amount in Mr. Gomez's account (represented by x) must be less than $20 for him to receive a notice from the bank.

The graph of the inequality is shaded to the left of 20 (shown by the open circle) because any number less than 20 satisfies the inequality.

Let x represent the amount in Mr. Gomez's checking account.

The bank sends a notice when the account drops below $20, so we can express this mathematically as x < 20.

Graph the inequality on a number line. Since 20 is not included in the solution, we use an open circle at 20.

Shade the region to the left of 20 because any number in that region is less than 20 and satisfies the inequality.

Question:-

Mr. Gomez gets a notice from the bank when the amount in his checking account drops below $20. For what amounts will Mr. Gomez receive a notice from the bank? Use words and symbols to represent the situation. Let x represent the amount in Mr. Gomez's account. When x is less than $20, the bank will send a notice. x<20 Graph the inequality to show all of the solutions.

Why is the graph in the example shaded to the left?

Marissa walked her dog 1/10 mile on saturday and 55/100 mile on sunday. how far did she walk her dog in all?​

Marissa walked [tex]\frac{65}{100}[/tex] miles altogether on saturday and sunday

Given that, Marissa walked her dog

From given information,

[tex]\text{Miles walked on saturday } = \frac{1}{10} \text{ mile }\\\\\text{Miles walked on sunday } = \frac{55}{100} \text{ mile }[/tex]

We have to find the distance walked in all

[tex]\text{Total distance } = \text{Miles walked on saturday + Miles walked on sunday }[/tex]

Substituting the values we get,

[tex]\text{Total distance } = \frac{1}{10} + \frac{55}{100}[/tex]

Make the denominators same for easier calculations by taking L.C.M of 10 and 100

Prime factors of 10 = 2 x 2 x 5

Prime factors of 100 = 2 x 2 x 5 x 5

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 5, 5

Multiply these factors together to find the LCM

LCM = 2 x 2 x 5 x 5 = 100

[tex]\text{Total distance } = \frac{1}{10} + \frac{55}{100}[/tex]

[tex]\text{Total distance } = \frac{1 \times 10}{10 \times 10} + \frac{55}{100}\\\\\text{Total distance } = \frac{10}{100} + \frac{55}{100}\\\\\text{Total distance } = \frac{10+55}{100} = \frac{65}{100}[/tex]

Thus she walked [tex]\frac{65}{100}[/tex] miles altogether on saturday and sunday

Answer:

y = 10

Step-by-step explanation:

The question is a simple equation and ought to be 3y/5 = 6 ( in stead of 3/5y=6)

Multiply through by the lowest common multiple (LCM) of denominator (which equals 5)

5 × 3y/5 = 6 × 5

3y = 30

Divide through by 3

3y/3 = 30/ 3

y = 10

Therefore, y = 10

Check

3y/5 = 6

y = 10

3(10)/5 = 6

30/5 = 6

6 = 6

Answer:

[tex]g(x) = 5^{x} -10[/tex]

Step-by-step explanation:

See the attached figure which represents the problem.

At first we should know the rules of translation

1) {f(x) + a} is f(x) shifted up (a) units

2) {f(x) – a} is f(x) shifted down (a) units

3) {f(x + a)} is f(x) shifted left (a) units.

4) {f(x – a)} is f(x) shifted right (a) units.

The given function : [tex]f(x) = 5^{x}[/tex]

As shown on the attached graph the function g(x) is below f(x)

Which mean f(x) is shifted down.

by comparing two points with the same x-coordinate like (1,5) and (1,-5)

So, the difference will be = 5 - (-5) = 10

by applying the second rule and substitute with a = 10

g(x) = f(x) - 10

[tex]g(x) = 5^{x} -10[/tex]

Answer:

D option

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

50% chance for spin one to be gray and 50% chance for spin two to be blue. Put them together for that order and you get 25%.

Answer:

Let's Take 8 sections and in which 6 are grey and 2 are blue.

The probability that the first spin lands on blue = 2/8 = ¼

The probability that the second spin lands on gray = 6/8 = ¾

 The probability that the first spin lands on blue and the second spin lands on gray is

(¼)(¾) = 3/16

These events are independent, so you can just multiply the probabilities

Good evening

Answer:

x > 1

Step-by-step explanation:

 2/3x-1/6>1/2  if we multiply both sides by 6 we will get

4x - 1 > 3 ⇔ 4x > 4 ⇔ x > 1

look at the photo below for the graph.

:)