Maria is 7 years older than her brother Robert and in 2 years her age will be four times what Robert’s age was three years ago. Find their present ages.

Since only the first term has ax for coefficients the GCF cant be -3ax^5.

The GCF would be -3a

Factor -3a out of all the terms:

-3a(2x^7)-3a(-4a^5)-3a(a^4)

Now factor -3a out of the equation for the final answer:

-3a(2x^7-4a^5+a^4)

Answer:

  A.  congruent; proportional; similar

Step-by-step explanation:

As soon as you see the scale factor is not 1, you know the figures are similar and dimensions are proportional. None of the transformations we study (translation, rotation, dilation, reflection) changes any angles. They remain congruent.

Answer:

  (-√10)/10

Step-by-step explanation:

The trig identity that relates the sine and the tangent is ...

  sin(x) = ±tan(x)/√(1 + tan(x)²)

For your given value of tan(x), this evaluates to ...

  sin(x) = ±(1/3)/(√(1 + (1/3)²) = ±1/√10 = (±√10)/10

The given value of the tangent function is positive, so the sine and cosine functions have the same sign (both are negative in this case).

So, your sine function is ...

  sin(x) = (-√10)/10

_____

You can derive the above relationship using SOH CAH TOA.

  Tan = Opposite/Adjacent

You are given the value of the tangent function as 1/3, so it is convenient to assign Opposite = 1 and Adjacent = 3. Then Hypotenuse is found using the Pythagorean theorem as ...

  Hypotenuse = √(Opposite² + Adjacent²) = √(1² + 3²) = √10

Now, the sine is ...

  Sin = Opposite/Hypotenuse = 1/√10

Rationalizing the denominator, this is ...

  Sin = (√10)/10

__

Now, you need to take into account the quadrant of the angle. Tangent is positive and Cosine is negative in the 3rd quadrant, where the Sine is also negative. Then your sine value is ...

  sin(x) = (-√10)/10

Answer:

If a scatter plot has no association then it's ordered pairs have no predictable pattern.

Step-by-step explanation:

Answer:

[tex]y=2\cdot4^x\\y=4\cdot\left(\frac{1}{2}\right)^x[/tex]

Step-by-step explanation:

We're given both the y-intercept and a point on the graphs of both functions, so our work her is largely just substituting x and y values in the general form of the equation for an exponential function.

For the first one, we can start by using the point (0, 2) to solve for a:

[tex]y=a\cdot b^x\\2=a\cdot b^0\\2=a[/tex]

Next, we can use that a-value and the second point to solve for b:

[tex]y=2\cdot b^x\\128=2\cdot b^3\\64=b^3\\4=b[/tex]

This gives us the equation [tex]y=2\cdot4^x[/tex] for the first function.

We can repeat the same process for the second function. Solving for a:

[tex]y=a\cdot b^x\\4=a\cdot b^0\\4=a[/tex]

And then for b, using the point (2, 1):

[tex]1=4\cdot b^2\\\frac{1}{4}=b^2\\\frac{1}{2}=b[/tex]

This gives us the general equation [tex]y=4\cdot\left(\frac{1}{2}\right)^x[/tex]

To write an exponential function in y = a · bx form that represents the given situations, substitute the given points into the equation to find the values of a and b.

To write an exponential function in the form y = a · bx that represents the given situations:

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Answer:

The numbers are 4 and 5

Step-by-step explanation:

Let

x------> the smaller number

x+1----> the bigger number

we know that

[tex]\sqrt{x}=(x+1)-3[/tex] ----> equation that represent the situation

solve for x

[tex]\sqrt{x}=(x-2)[/tex]

squared both sides

[tex]x=(x-2)^{2}\\x=x^{2}-4x+4\\x^{2}-5x+4=0[/tex]

using a graphing calculator to solve the quadratic equation

see the attached figure

the solution is

[tex]x=4[/tex]

[tex]x+1=5[/tex]

The consecutive numbers are 4 and 5 in which the square root of the smaller number is 3 less than the bigger number

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the smaller number and y the larger number, hence:

y = x + 1  (1)

Also:

[tex]\sqrt{x} =y-3[/tex]   (2)

From equation 1 and 2:

x = 4, and y = 5

The consecutive numbers are 4 and 5

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Answer:

3^2+7*4~  Addition should be last

Step-by-step explanation:

Parenthesis        ----- Addition is second to last in order of operations

Exponents                    

Multiplication

Division

Addition

Subtraction

Given the problem 3² + 7 × 4, the last operation that should be performed is addition due to the rules dictated by the order of operations (PEMDAS).

In the given problem, 3² + 7 × 4, the operation that should be performed last is addition. This is due to the rule of the order of operations, often remembered by the acronym PEMDAS which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Therefore, in this expression, you first perform the exponentiation (3²), then multiplication (7x4), and add the results last.

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Answer:

  $1710.00

Step-by-step explanation:

The total bill was ...

  (after-tax total) = (pre-tax subtotal) + 6.1% · (pre-tax subtotal)

  (after-tax total) = (pre-tax subtotal) · 1.061

Divide by the coefficient on the right to find the value of the variable on the right.

  (pre-tax subtotal) = (after-tax total)/1.061 = $1814.31/1.061 = $1710.00

The pre-tax subtotal was $1710.00.

Answer:

Step-by-step explanation:1703.64

Answer:

[tex](x+2)^2+(y-1)^2=25[/tex]

Step-by-step explanation:

The equation of a circle with center at (h,k) and radius r, is given by

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Since the given circle contains the point (-5,-3) and it is centered at (-2,1), we can determine the radius of the circle using the distance formula;

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

This implies that;

[tex]r=\sqrt{(-2--5)^2+(1--3)^2}[/tex]

[tex]r=\sqrt{(-3)^2+(4)^2}[/tex]

[tex]r=\sqrt{9+16}[/tex]

[tex]r=\sqrt{25}[/tex]

[tex]r=5[/tex]

We now substitute (h,k)=(-2,1) and r=5 into the formula to obtain;

[tex](x+2)^2+(y-1)^2=5^2[/tex]

[tex](x+2)^2+(y-1)^2=25[/tex]

Here is a step by step tutorial!

The solution of expression 1/12÷36 is 1/432

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

1/12÷36

Express the expression properly

So, we have

1/12 ÷ 36

NExt, we rewrite it as quotient

so, we have the following representation

1/12 ÷ 36 = 1/12 * 1/36

So, we have

1/12 ÷ 36 = 1/432

Hence, the solution is 1/432

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5/6=f/15

15•5=6•f

75=6•f

75/6=f

12.5=f

The flag pole is 12.5 ft tall

¶

. |

__& ____|

Answer:

  The flagpole is 12.5 ft tall.

Step-by-step explanation:

The ratio of object height to shadow length is ...

  (teen height) : (teen shadow) = (5 ft) : (6 ft) = 5 : 6

so the height of an object is 5/6 the length of its shadow. Then the height of the flagpole is ...

  (5/6) · (15 ft) = 12.5 ft

_____

A suitable scale drawing can show you the answer.

Answer:

The relation is not a function

Step-by-step explanation:

∵ {(-7 , -7) , (-7 , -8) , (-1 , 4) , (6 , 5) , (10 , -1)}

* The relation is a function if every x-coordinate has only

  one image of y-coordinate, that means x-coordinate

  can not appear more than one time in the order pairs of relation.

* Ex: {(2 , -3 , (2 , 1)} ⇒ not function because 2 has

        two values of y -3 and -1

        means 2 appears twice in the relation so it's not a function

∵ -7 appears twice in the relation (-7 has 2 values of y -7 and -8)

∴ The relation is not a function

Answer:

It is not a function.

Step-by-step explanation:

We have given the relation.

{(-7, -7), (-7, -8), (-1, 4), (6, 5), (10, -1)}

We have to find whether  It is a function or not.

A function is a relation that assigns each input a single output.

This relation is not a function.

Because one input -7  has two outputs -7 and -8.

It is not a function.

Answer:

(5/6) cup carbonated water

Step-by-step explanation:

We can easily solve this problem by applying a rule of three.

4 cups of orange juice    ------------------------  2/3 cup carbonated water

5 cups of orange juice    ------------------------  x

x = (5/4)*2/3 cup carbonated water

x = (10/12) cup carbonated water

x = (5/6) cup carbonated water

x = 0.8333 cup carbonated water

Answer:

  w = 0, x = 3, y = 2, z = 1

Step-by-step explanation:

You can use each equation to write an expression that will substitute into the next equation.

  y = 8 -2x . . . . from the first equation

  8 -2x + 3z = 5 . . . . . substituted into the second equation

  z = (-3 +2x)/3 . . . . . solved for z

  (-1 +2/3x) +2w = 1 . . . . . substituted into the third equation

  w = (2 -2/3x)/2 . . . . . solved for w

  5(1 -1/3x) +3x = 9 . . . . . substituted into the last equation

  4/3x = 4 . . . . . simplified, 5 subtracted

  x = 3 . . . . . . . . multiply by 3/4

  w = 0 . . . . . . . .value of x substituted into equation for w

  z = 1 . . . . . . . . value of x substituted into equation for z

  y = 2 . . . . . . . .value of x substituted into equation for y

The solution is (w, x, y, z) = (0, 3, 2, 1).

To find the solution to each variable, we can use the method of substitution or elimination. Let's solve the system of equations using the method of elimination. We can solve this system using any method of our choice, such as substitution or elimination.

To find the solution to each variable, we can use the method of substitution or elimination. Let's solve the system of equations using the method of elimination.

Multiplying the first equation by 3, the second equation by 2, the third equation by 3, and the fourth equation by 2, we get:

Now, if we add the first and fourth equation together, we eliminate the x variable:

(6x + 3y) + (10w + 6x) = 24 + 18
9y + 10w = 42

Next, we can subtract the second equation from the third equation to eliminate the z variable:

(3z + 6w) - (2y + 6z) = 3 - 10
-2y - 3z + 6w = -7

Now we have a system of equations with only two variables, y and w:

We can solve this system using any method of our choice, such as substitution or elimination.

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Answer:

where are the pictures

Step-by-step explanation:

Answer:

There isn't one

Step-by-step explanation:

√q differs from √(q+1) by 1 only when q=0. The difference gets smaller as q gets larger.

___

Here, q=7x. The same logic applies.

The equation 5x+8-7x=-4x+1 has exactly one solution

Option B is correct

The given equation is:

5x  +  8  -  7x   =  -4x  +  1

Simplify both sides of the equation

5x  -  7x  +  8  =  -4x  +  1

-2x   +  8   =  -4x  +  1

Collect like terms

-2x  +  4x  =  1  -  8

2x  =   -7

Divide both sides by 2

[tex]\frac{2x}{2} =\frac{-7}{2} \\\\x=-3.5[/tex]

As seen above, the equation has exactly one solution

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Final answer:

The equation 5x+8-7x=-4x+1 simplifies to 2x = -7, which means that there is exactly one solution for x, which is x = -7/2. The correct option is:  B)exactly one solution

Explanation:

To determine how many solutions the equation 5x+8-7x=-4x+1 has, let's first simplify and solve for x:

Combine like terms on the left side: (5x - 7x) + 8 = -2x + 8.

Bring the term involving x from the right side to the left: -2x + 8 + 4x = 1.

Combine like terms involving x: (4x - 2x) + 8 = 1, which simplifies to 2x + 8 = 1.

Subtract 8 from both sides: 2x = 1 - 8, which simplifies to 2x = -7.

Divide by 2 to solve for x: x = -7/2.

Since we have found a single value for x, the equation has exactly one solution.

Answer:

  3 5/26

Step-by-step explanation:

You can work this a couple of ways.

1. Find the total number of siblings for the current students (25×3), add the new number of siblings (8) and students (1), then recompute the average.

  (25×3 + 1)/(25 +1) = 83/26 = 3 5/26

___

2. Find the difference of the number of siblings from average, and divide that difference by the new total number of students. This will be the change in the average.

  difference from average = 8 -3 = 5

  difference divided by new student total = 5/26

  new average = 3 + 5/26 = 3 5/26

Answer:

The answers for your two problems, can be found below in the attached images.

Problem 1

Graph

The graph was plotted using a calculator. We can see that the graph opens up.

f(x) = x^2 + 4x +3

Vertex

The vertex is the minimum point of the equation

In this case  Vertex (V) = (-2,-1)

Axis of symmetry

The x axis corresponding to the vertex component

x = -2

y intercept

Interception with the y-axis

From the first attached image, we can see that they y intercept occurs

at x = 0, y = 3  

(0,3)

Problem 2

Graph.

The graph was plotted using a calculator. We can see that the graph opens up.

f(x) = 2x^2 + 3x +1

Vertex

The vertex is the minimum point of the equation

In this case  Vertex (V) = (-0.75,-0.125)

Axis of symmetry

The x axis corresponding to the vertex component

x = -0.75

y intercept

Interception with the y-axis

From the second attached image, we can see that they y intercept occurs

at x = 0, y = 1  

(0,1)

Answer:

  90.04 °F

Step-by-step explanation:

Evaluate the expression.

  (9×10) + (4×.01) = 90 + .04 = 90.04

Answer:

  zero

Step-by-step explanation:

Assuming your intended side lengths are {7 cm, 10 cm, 18 cm}, the sum of the short sides is not long enough to connect to the ends of the long side. No triangle can be formed.

To write a percent as a decimal- move the decimal point two places to the left and divide by 100.

Explanation:

Lets take an example.

We have to convert 25% into decimals.

So, we will divide 25 by 100 , [tex]\frac{25}{100} =0.25[/tex]

Here, we can see that we have moved the decimal to two places on the left side.

Answer:

Move the decimal point two places to the left

Divide by 100

Step-by-step explanation:

To write a percent as a decimal, there are two possible options, and they are the same thing.

The first one is moving the decimal point two places to the left. For example, 25% =0.25.

The second one is dividing by 100. 25% = 25/100 = 0.25.

So the answers are:

Move the decimal point two places to the left

Divide by 100

Answer:

The student assumed he was asked to factor

(a^2 - b^2)

Which is equal to

= (a+b)*(a-b)    (His response)

But, he was asked to simplify

(a^2 + b^2)

Which has imaginary roots, and can be factored as:

(b +ai)(b-ai)

Answer:

No. No.

Step-by-step explanation:

The sum of interior angles of a triangle is always 180°. The given angles cannot form a triangle.

The sum of interior angles of a triangle is always 180°. The given angles cannot form a triangle.

Answer: No

Step-by-step explanation:

Answer:

  zero

Step-by-step explanation:

In order for sets A and B to have the same sum of elements, that sum of elements must be the same for each set, and half the sum of elements of the original set.

The sum of elements of the set {1, 2, 3, ..., 42} is an odd number (903), so there cannot be two sets with the same sum that have that total.

Answer:

Step-by-step explanation:

you have to change it into a x and keep change flip and

1/5 / 3/7

1/5 * 7/3 then x

To divide two fractions, you should flip the second fraction to get its reciprocal, then multiply the first fraction with this reciprocal. For instance, in dividing 3/5 by 4/7, you flip 4/7 to get 7/4, then multiply 3/5 by 7/4 to obtain 21/20.

To divide two fractions, you will need to follow a few simple steps. Firstly, you need to flip or find the reciprocal of the second fraction (the one that you are dividing by). Secondly, you will multiply the first fraction (the one being divided) by the reciprocal of the second fraction. This process can also be remembered as 'copy, flip, multiply'.

For example, if we have to divide 3/5 by 4/7, first we flip 4/7 to get 7/4. Then we multiply 3/5 by 7/4. The result is 21/20.

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Answer:

Option D. 103°

Step-by-step explanation:

we know that

The length of the sides and the measurement of the internal angles of the figure do not vary after the translation, therefore the two figures are congruent.

The measure of angle Z after the translation is 103°

Translation in geometry does not change the size, shape, or angle measures of a figure, hence the measure of angle Z will remain the same after the transformation.

The question asks about the measure of angle Z after figure WXYZ is translated up 3 units and 4 units to the right to create figure WXYZ'. A translation in geometry is a transformation that moves every point of a figure or a space by the same distance in a given direction. Since a translation does not affect the size, shape, or the measure of the angles of a figure, the measure of angle Z will remain the same after the transformation. Therefore, if the original measure of angle Z was 58, 77, 96, or 103 degrees, it will be the same after the translation. As no specific value was given for angle Z before the transformation, we can assume that the measure of angle Z after this transformation will be the same as it was prior to the transformation.

Answer:

Step-by-step explanation: