[tex]\begin{gathered} Vertex\colon\: (-3,-10) \\ Vertex\: form\: equation\colon\: f(x)=(x+3)^2-10 \end{gathered}[/tex]

**1) ** In order to convert from the standard version to the vertex form we'll need to find the vertex of that parabola:

We can find the vertex, using these formulas:

[tex]\begin{gathered} x=h=-\frac{b}{2a}=\frac{-6}{2}=-3 \\ k=(-3)^2+6(-3)-1=9-18-1=9-19=-10 \\ V(-3,-10) \end{gathered}[/tex]So this is the vertex of that parabola at point (-3,-10)

**2) **Now, note that the coefficient *a *= 1, and with the vertex, we can now rewrite that equation into the vertex form:

* *

What’s the slope I need help

**Answer:**

-8/3

**Step-by-step explanation:**

You want the **slope of the line** shown in the **graph**.

Whether counting grid squares on the graph, or using the slope formula, it is convenient to choose two points on the grid where the line crosses the intersection of grid lines.

It appears, the line passes through grid points (1, 4) and (4, -4). Using the slope formula, we find the slope of the line to be ...

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

m = (-4 -4)/(4 -1) = -8/3

**The slope of the line is -8/3**.

The slope is the ratio of "rise" to "run" for the line. From the two points we see where the line crosses grid intersections, we have a "rise" of -1 from y=4 to y=-4, and a "run" of 3 from x=1 to x=4.

rise/run = **-8/3 = slope of the line**

you deposit $3,300 in account with an annual interest of 3.3% for 20 years. what is the amount of money you'll have at the end of the 20 years?

Given data:

The given principal is P=$3,300.

The given rate of interest is r=3.3%.

The given time is t=20 years.

The expression for the final amount of money is,

[tex]A=P+\frac{P\times r\times t}{100}[/tex]Substitute the given values in the above expression.

[tex]\begin{gathered} A=(3,300)+\frac{3,300\times3.3\times20}{100} \\ =3,300+2,178 \\ =5,478 \end{gathered}[/tex]Thus, the final amount after 20 years is **5,478.**

Please answer this question with an explanation. Thank you. :)

The rate is **positive** because she is withdrawing funds from her account. So, **Option C **is the correct option.

The** momentum **of a variable is represented by the rate of change, which is used to mathematically describe the percentage change in value over a defined** period** of time.

Jessica's savings account balance is plotted against the number of months.

Rate of withdrawal from her account is given as:

Amount in Savings account/Number of months

= 1000/10

= 100 dollars/month

Therefore, Jessica is withdrawing 100 dollars per month from her savings account.

As a result, the rate is** positive** because she is taking money out from her account. **Option C** is thus the right option.

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A table is on sale for $589, which is 24% less than the regular price.

What is the regular price?

$589 x 24% = $141.36

$589 + $141.36 = $730.36

Regular price was $730.36

$589 + $141.36 = $730.36

Regular price was $730.36

The slope of a line which passes through the vertex and the y-y− intercept of the quadratic equation x^2 + 10x - 5x

2

+10x−5 is

The **slope **of the line passing through the y **intercept **and the vertex of the **quadratic **x²+10x-5 is 5.

The provided **quadratic equation **is,

y = x²+10x-5

The **vertex **of a quadratic equation,

(-b/2a, -D/4a)

Where,

a = 1,

b = 10,

c = -5,

D = (b²-4ac)

D = (10²-4(-5)(1))

D = 100+20

D = 120,

Putting all the values to find the vertex of the equation,

(-10/2,-120/4)

(-5,-30)

So, the **vertex **are now known,

To find the **y intercept,** putting x = 0 and solving the equation for y,

y = (0)²+10(0)-5

y = -5

The y intercept is,

(0,-5)

If there are two points on the line, let say (a,b) and (c,d), then the **slope **of the line is,

M = (d-b)/(c-a)

Now, we know two points,(-5,-30) and (0,-5).

We can now find the slope of line,

M = (-5+30)/(0+5)

M = 25/5

M = 5

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can someone please help me find the value of x to this equation

**SOLUTION**

This is a right-triangle problem.

We will use the SOHCAHTOA principle.

In this triangle, we will relate the opposite side and the hypotenuse side to get the value of x. That will be the CAH relationship.

[tex]\begin{gathered} \cos \theta=\frac{adjacent}{hypotenuse} \\ \cos \theta=\frac{5}{18} \\ \cos \theta=0.27778 \\ \theta=\cos ^{-1}(0.27778) \\ \theta=73.872^o \\ \theta=73.87^o \end{gathered}[/tex]**The final answer is 73.87 degrees.**

Can somebody please help me right now??? i’m stuck and i need help with this bad

**Answer:**

**Step-by-step explanation:**

The answer is B!

Answer To this question so that we can move onto the next question so that we can get done with all this homework so we can go play

We need to transform a number that is written in scientific notation to the standard notation. For that we have to move the dot to the right, because the exponent of the power is positive, every time we do that we will subtract one from the exponent. When there is no more dot we will add zeros. This is done below:

[tex]\begin{gathered} 2.07\cdot10^5 \\ 20.7\cdot10^4 \\ 207\cdot10^3 \\ 2070\cdot10^2 \\ 20700\cdot10 \\ 207000 \end{gathered}[/tex]**The correct answer is 207,000.**

In the expression below, what operation should be done first?

4 + 8 ÷ 2

**Answer:**

**Division**

**Step-by-step explanation:**

Using the tool PEMDAS, you will see the order that you must complete an equation in, P=Parenthesis E=Exponents M=Multiplication D=Division Addition S=Subtraction

A shirt costs ₹(a2 –ab -b2 ) , a pair of trousers cost ₹(2a2 +8ab-2b2 ) and a pair of shoes cost ₹(a2 –3ab+4b2 ) .After collecting these three items from the store, Ranjan paid ₹(2a+b )2 .What balance will Ranjan receive from the cashier ?

The **balance **Ranjan will **receive** from the cashier is ₹ 0

Based on the information given, we have that;

shirt costs ₹(a² –ab -b² ) pair of trousersNow, expand the bracket for the **payment**, we have;

(2a+b )²

(2a +b) (2a + b)

Multiply through

4a² + 2ab + 2ab + b²

Add like terms

4a² + 4ab + b²

Now, let's add the amount for the items bought

a² –ab -b² + 2a² +8ab-2b² + a² –3ab + 4b²

add like terms

4a² + 4ab + b²

Now, subtract the amounts

4a² + 4ab + b² - 4a² + 4ab + b²

₹ 0

Hence, the **balance **is ₹ 0

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work out the sale has been decreased

20% of 120

The current amount of the** sale** is 96

The sale is 120

It was decreased by 20%

20/100 × 120

= 0.2 × 120

= 24

The amount of the current sale is

120-24

= 96

Hence the amount of the current **sale **which is calculated by subtracting 24 from 120 is 96

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please hurry. I need help on all three questions. please show working clearly.

I do not know the answer to the 3rd question

please look at screenshots

When the linear correlation coefficient is 1 there is a perfect positive linear relation between the **two variables.** Scatter diagram would contain points that all** lie on a line **with a positive slop.

A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively linked, the value either** rises or falls **together.

A correlation coefficient is a metric that expresses a correlation, or a statistical link between two variables, in **numerical terms**. Two columns of a specific data set of observations, sometimes referred to as a sample, or two parts of a multivariate random variable with a known distribution may serve as the variables.

The strength and direction of the linear links between two sets of **variables** are evaluated using correlation coefficients. Use Pearson's correlation coefficient if both variables are regularly distributed; otherwise, use **Spearman's correlation coefficient**.

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A man realizes he lost the detailed receipt from the store and only has the credit card receipt with the after-tax total. If the after-tax total was $1,253.07, and the tax rate in the area is 7.1%, what was the pre-tax subtotal?

To answer this question, we can proceed as follows:

1. We have that the after-tax total was $1,253.07.

2. We have that the tax rate in the area is 7.1%.

3. Then to find the pre-tax subtotal, we can proceed as follows:

[tex]7.1\%=\frac{7.1}{100}=0.071[/tex]Therefore, we have:

[tex]x+0.071x=1253.07[/tex]4. Finally, we need to add the like terms as follows:

[tex]1.071x=1253.07[/tex]And using technology, we can divide both sides by 1.071:

[tex]\begin{gathered} \frac{1.071}{1.071}x=\frac{1253.07}{1.071} \\ \\ x=1170 \\ \end{gathered}[/tex]**Therefore, the pre-tax subtotal is ****$1,170****.**

Find the slope between the points with coordinates

(-2,3) and (4, 5).

**Answer:**

1/3 or 2/6

**Step-by-step explanation:**

you just plug the coordinates into a calculator and look at the rise over run.

I need help on this also could you check if the first 3 questions are correct

We have two parallel lines intersected by other line.

We have to relate the angles.

We will take the angle with measure 17° as reference (red angle).

The angle <1 has a measure that is supplementary to the red angle, as <1 is supplementary to the <4, which is a corresponding angle to the red angle.

[tex]m\angle1=180-17=163\degree[/tex]It has no direct relationship with the red angle.

The angle <2 is supplementary to <1, so it will have the same measure as the red angle (m<2 = 17°).

The relationship with the red angle is that they are alternate exterior angles.

Angle <3 has no direct relationship with the red angle. As it is vertical with <1 it has the same measure (m<3 = 163°) and is supplementary to the red angle.

Angle <4 and the red angle are corresponding angles.

They have the same measure, so they are congruent.

Angle <5 and the red angle form a linear pair, so they are supplementary. The measure of <5 is then m<5 = 163°.

Angle <6 and the red angle are vertical angles, so they have the same measure.

Angle <7 and the red angle form a linear pair, so they are supplementary. The measure of <7 is then m<7 = 163°.

**Answer:**

**Angle <1:**

**Measure = 163°**

**Relationship: No name for relationship and supplementary.**

**Angle <2:**

**Measure = 17°**

**Relationship: Alternate exterior and congruent.**

**Angle <3:**

**Measure = 163°**

**Relationship: No name for relationship and supplementary.**

**Angle <4:**

**Measure = 17°**

**Relationship: Corresponding and congruent.**

**Angle <5:**

**Measure = 163°**

**Relationship: Linear pair and supplementary.**

**Angle <6:**

**Measure = 17°**

**Relationship: Vertical and congruent.**

**Angle <7:**

**Measure = 163°**

**Relationship: Linear pair and supplementary.**

Select the correct figures

The correct answer is the figure

Which of the following best describes AD?17D17сA. MedianB. AltitudeC. Perpendicular bisectorD. Angle bisector

The median of a triangle is a line segment joining a vertex to the midpoint of the opposite side thus bisecting that side.

Hence, Median best describes the line.

**Option A is the correct option,**

Translate to a system of equations and solve:Priam has a collection of nickels and quarters, with a total value of $9.30. The number of nickels is six less than three times the number of quarters. How many nickels and how many quarters does he have?

The value of a nickel is 5 cents

The value of the quarter is 25 cents

Since Priam has a total of 9.30 dollars = 930 cents, then

[tex]5n+25q=930[/tex]Simplify the equation by dividing all terms by 5

[tex]\begin{gathered} \frac{5n}{5}+\frac{25q}{5}=\frac{930}{5} \\ n+5q=186\rightarrow(1) \end{gathered}[/tex]Since he has 6 nickels less than 3 times the quarters, then

[tex]n=3q-6\rightarrow(2)[/tex]Substitute n in equation (1) by equation (2)

[tex](3q-6)+5q=186[/tex]Add the like terms on the left side

[tex]\begin{gathered} (3q+5q)-6=186 \\ 8q-6=186 \end{gathered}[/tex]Add 6 to both sides

[tex]\begin{gathered} 8q-6+6=186+6 \\ 8q=192 \end{gathered}[/tex]Divide both sides by 8

[tex]\begin{gathered} \frac{8q}{8}=\frac{192}{8} \\ q=24 \end{gathered}[/tex]The number of quarters is 24

Substitute q by 24 in equation 2 to find n

[tex]\begin{gathered} n=3(24)-6 \\ n=72-6 \\ n=66 \end{gathered}[/tex]The number of nickels is 66

**He has 66 nickels and 24 quarters**

solve the triangle. round to the nearest tenth A B 16 14 С

[tex]\text{Answer : }\theta\text{ = 41. 2 degr}ees[/tex]

According the question

Side AC of the triangle = 16

Side BC = 14

The opposite side of the triangle is AC = 14

The adjacent side of the triangle is BC = 16

Using SOH CAH TOA

[tex]\begin{gathered} \text{Tan }\theta\text{ = }\frac{opposite}{\text{adjacent}} \\ \text{Tan }\theta\text{ = }\frac{14}{16} \\ \text{Tan }\theta\text{ = 0.875} \\ \theta\text{ = arc tan of 0.875} \\ \theta=tan^{-1}(0.875) \\ \theta\text{ = 41. 18 degre}es \\ To\text{ the nearest tenth} \\ \theta\text{ = 41.2 degre}es \end{gathered}[/tex][tex]k(x) = 3(2) {}^{x} - 8[/tex]. Is the function linear, quadratic, exponential or neither?

An exponential function is defined as a function of the form:

[tex]f(x)=a(b)\placeholder{⬚}^x+c[/tex]where a, b and c are constants.

We notice that the function given has this form, **therefore the function given is an exponential function.**

A circle has a center at (4, -7) and a radius of 4 units. What is the equation of this circle?

O (4)² + (y + 7)² = 16

O (x + 4)² + (y + 7)² = 4²

O(x-4)² + (y - 7)² = 16

O(x + 4)² + (y - 7)² = 4²

the equation for the circle with radius, r = 4 units and center =(4,-7)

will be (x-4)² + (y+7)² = (4)².

When the center and radius of a **circle** are known, how do you determine its equation?

Use the formula (x-a) ² + (y-b) ² = r ² to determine a **circle's** equation when you are aware of its radius and center. Here, stands for the **circle's** center, and is its radius. This equation is essentially a variant way of writing the general equation for a **circle**.

In this question,

we are given the center of our **circle** to be,

(4,-7) ≈ (a,b)

thus we are given,

a = 4

and b = -7

and we are given the radius to be 4units

substituting these values in the above equation,

(x-4)² + (y-(-7))² = (4)²

= (x-4)² + (y+7)² = (4)²

Hence the equation for the **circle** with radius, r = 4 units and center =(4,-7)

will be (x-4)² + (y+7)² = (4)².

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a salad dressing recipe calls for 3/4 cup of olive oil for every 1/2 cup of vinegar is needed for 2 cups of olive oil?

the answer is 1 1/4 cups of vinegar

the answer is 1 1/4 cups of vinegar

Step-by-step explanati

Find the image of D (0, -2) after the composition of translations

(x, y) → (x+10, y − 8) and (x, y) → (x − 7, y + 15).

The **ordered pair **that represents the image of the point after the transformation is (3, 5)

The **ordered pair **of the **point **is given as

D = (0, 2)

The above **point **is an ordered pair on a **coordinate plane**

The sequence of **transformations **of the points is given as

(x, y) → (x+10, y − 8) and (x, y) → (x − 7, y + 15).

When the above **transformations **are applied on the point, we have:

So, we have the following equation

(x, y) → (x + 10 - 7, y − 8 + 15)

Evaluate the sum and the difference

So, we have the following equation

(x, y) → (x + 3, y + 7)

Recall that

D = (0, -2)

So, we have

D' = (0 + 3, -2 + 7)

Evaluate

D' = (3, 5)

Hence, the **image **of **point **D is (3, 5)

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Describe in extension each of the following sets:a) A is the set of positive integers less than 8.C) C is the set of digits of the number 12353888D) D is the set of courses you are enrolled in.

a. All positive integers are greater than 0,

we can express this as a set which positive integers less than 8, A = {1, 2, 3, 4, 5, 6, 7}.

This is a **Finite Set.**

b. The number 12353888 has a set of digits, 1, 2, 3, 5 and 8 and can be expressed as C = {1, 2, 3, 5, 8}

This is also a **Finite Set.**

c. The set of courses you are enrolled depends on the number of courses. We can express this as

D = {course1, course2, course3, ...}

This is **Universal Set.**

Evaluate 14xy if x=−23 and y=35 . Write your answer as a fraction in simplest form.

**Answer: -11270**

**Step-by-step explanation:**

14xy = -11270 x=-23 y=35

14(-23)(35) = -11270

The table below represents the snacks that Sidney and Erica purchased at the movies last month. Write a system of equations to determine the price of each candy and each drink.

**SOLUTION:**

**Case**: System of equations

**Given**: A table of value of snacks and drinks for Sidney and Erica

**Required**: Write a system of equations to determine the price of each candy and each drink.

**Method**:

Step 1: Assume the price of snacks be represented by s and drinks by d

Step 2: Equation for Sidney

[tex]\begin{gathered} 2s+1d=13.50 \\ 2s+d=13.50.........equation(1) \end{gathered}[/tex]Step 3: Equation for Erica

[tex]\begin{gathered} 3s+1d=12.85 \\ 3s+d=12.85.......equatiion(2) \end{gathered}[/tex]**Final answer:**

The system of equations is:

[tex]\begin{gathered} 2s+d=13.50 \\ 3s+d=12.85 \end{gathered}[/tex]Jena's income is $3800 a month, and she plans to budget 13 of her income for savings and 16 of her income for groceries.

What fraction of her income does she plan to spend each month on these two items together?

The **fraction** of Jena's income does she plan to spend each month on these two items **together** is 1/2

Amount of Jena's income spent on **savings** = 1/3 × $3800

= 1266.666666666666

Approximately,

= $1,266.67

Amount of Jena's income spent on groceries = 1/6 × $3800

= 633.3333333333333

Approximately,

= $633.33

Amount spent on the two items = $1,266.67 + $633.33

= $1900

Fraction of **Jena's income** spent on the two items = 1/3 + 1/6

= (2+1) / 6

= 3/6

= 1/2

So therefore, Jena spent 1/2 of her **income** on savings and groceries.

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solve x=y+4, where x=3

if x=3 we get

[tex]3=y+4\rightarrow y=3-4=-1[/tex]Please help which best explains an effect of the Diaspora on Jewish people?

The BEST explanation of the effect of the **Diaspora** on Jewish people is d) They developed **new rituals** to accommodate the loss of the Temple.

Some of the new **rituals** developed by the **Diaspora Jews** included:

The **Diaspora** did not affect the Jewish people by dividing their homeland, making the destroyed **Temple of Jerusalem** the center of their religiosity, or making Rabbis insignificant.

Thus, the **Diaspora** affected the Jewish people in Option D.

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Question Completion with Answer Options:a) Their homeland was divided into Israel and Judah.

b) The Temple of Jerusalem became the center of religious activity.

c) Rabbis no longer served as significant religious leaders.

d) They developed new rituals to accommodate the loss of the Temple.

Select the correct operator for the following exponential expression.(-2)^4 ? 2^4 A. C. =
1. Mike is busy writing letters in (he) ____ study.2. We can do (we) ____ shopping before lunch. 3. She is writing a letter to (she) ___ friend.4. Jack is playing with____ (he) toys.5. He is ashamed of (he)___mistake.6. This idea of (they)____ is quite interesting.7. Ann is late for (she)____classes as usual.8. She makes all (she) ____ clothes herself.9. This document is (he) ____. There is (he) ____ name on it10. The puppy is playing with ____ (it) tail.
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