If log3⁡⁡(4y−1)=log3⁡⁡(2y+7), what is the value of y?

Enter your answer as a number, rounded to one decimal place, if necessary, like this: 42.5

Answer-

Area of the kite is 14.0 sq.units

Solution-

[tex]\text{Area}_{WXYZ}=\text{Area}_{WXY}+\text{Area}_{WZY}[/tex]

From the graph, in the triangle WXY

Base = WY=4 units,

Height = 3 units

[tex]\text{Area}_{WXY}=\dfrac{1}{2} \cdot base\cdot height=\dfrac{1}{2} \cdot 4\cdot 3=6\ sq.unit[/tex]

From the graph, in the triangle WZY

Base = WY=4 units,

Height = 4 units

[tex]\text{Area}_{WZY}=\dfrac{1}{2} \cdot base\cdot height=\dfrac{1}{2} \cdot 4\cdot 4=8\ sq.unit[/tex]

[tex]\therefore \text{Area}_{WXYZ}=6+8=14\ sq.units[/tex]

Option (b) 4(3-x)+6x=3x+12+2x is the equation that has the solution x = all real numbers because it simplifies to an identity, which is true for any value of x.

Among the given equations, the one that has the solution x = all real numbers is essentially an identity, meaning that for any value of x you plug into the equation, the equation will hold true. To determine which equation is an identity, each equation must be simplified.

Let's take option (b) as an example:

4(3−x)+6x=3x+12+2x

4∙3 - 4∙x + 6∙x = 3∙x + 12 + 2∙x

12 - 4∙x + 6∙x = 3∙x + 12 + 2∙x

12 + 2∙x = 5∙x + 12

12 - 12 + 2∙x - 2∙x = 5∙x - 2∙x + 12 - 12

0 = 3∙x - 3∙x

After simplifying, we end up with 0 = 0, which is an identity and is true for all values of x, hence this is the equation where x is all real numbers.

Answer:

c.7 and d.5

Step-by-step explanation:

Given the following equation :

[tex]x^{2}-6x+40=6x+5[/tex]

This equation is equivalent to the following equation :

[tex]x^{2}-6x+40=6x+5[/tex]

[tex]x^{2}-6x+40-6x-5=0[/tex]

[tex]x^{2}-12x+35=0[/tex]

Given an equation [tex]ax^{2}+bx+c=0[/tex] we can find the solutions using the quadratic equation (x1 and x2 are the solutions) :

[tex]x1=\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex]

[tex]x2=\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]

Using this equations :

[tex]x^{2}-12x+35=0[/tex]

[tex]a=1\\b=-12\\c=35[/tex] ⇒

[tex]x1=\frac{-(-12)+\sqrt{(-12)^{2}-4.(1).(35)}}{2.(1)}=7[/tex]

[tex]x2=\frac{-(-12)-\sqrt{(-12)^{2}-4.(1).(35)}}{2.(1)}=5[/tex]

Given the two solutions x1 and x2 we can write the equation :

[tex]ax^{2}+bx+c=0[/tex] ⇒ [tex]a.(x-x1).(x-x2)=0[/tex] ⇒

[tex]x^{2}-12x+35=0[/tex] is equivalent to

[tex](x-7).(x-5)=0[/tex]

The solutions for this equation are 7 and 5.

Therefore, c.7 and d.5 are the solutions for this exercise.

The decimal form of the given percent 203% is 2.03

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction. The word "percent" means "per hundred." So, whenever you see a number with a percent sign (%), you can imagine it as a fraction,

Percent is from the Latin adverbial phrase per centum meaning “by the hundred.” The Latin phrase entered English in the 16th century.

Example: 10% means 10 out of every 100. So if 10% of 500 people have ice cream, then 50 people have ice cream.

Given that, what is decimal form for the 203 percent,

Since, the percent is any number in its 100th part,

Therefore, 203% = 203/100

Since, it is 100 in the denominator,

The decimal will be put after two digits in the numerator,

Therefore,

203% = 203/100 = 2.03

Hence, the decimal form of the given percent 203% is 2.03

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Answer:

abc(a + b + c)

That's your answer!!!

Answer: The answer is C on Quizizz.

Step-by-step explanation:

Answer: 704 feet

Step-by-step explanation: speed of car is V= 60 miles per hour

First convert the speed from miles per hour to feet per second .

[tex]V=\frac{60\times 5280}{60\times 60} \frac{ft}{s} = 88 \frac{ft}{s}[/tex]

Now Length of tunnel , L= speed of car x time taken

Therefore [tex]L=88\times 8 feet=704 feet[/tex]

Answer:

{y | y > –4}

Step-by-step explanation:

The range of f(x) = (3/4)^x - 4 is (-∞, -4].

The range of the function f(x) = (3/4)^x - 4 can be determined by finding the minimum and maximum values that the function can reach.

Putting it all together, the range of f(x) is (-∞, -4].

Answer:

17 cars

Step-by-step explanation:

Mike collects toy cars. He decides to put all of his toy cars in a line so that he can count them.

It is given that 9th car in the line ends up being exactly at the middle of the line.

This statement shows that before and after the middle car there were 8 cars.

So the cars in the line is 8 + 1(middle) + 8 = 17 cars

Mike have total 17 cars.

Final answer:

To confirm that a transformation is not a rigid motion, use a protractor to check for any changes in angles within a shape post-transformation. If the angles have changed, the transformation is not rigid. Corresponding side length changes further confirm this.

Explanation:

To confirm that a transformation is not a rigid motion using a protractor, you must look for changes in the shape's size or the angles between any two adjacent sides. A rigid motion, also known as an isometry, will preserve distances and angles between all points on a shape. Therefore, if after a transformation, using a protractor shows that the angles within the shape have changed, or that the corresponding sides are not congruent, then the transformation is not a rigid motion.

For example, if you have a triangle and apply a transformation, such as dilation or shearing, the new angles can be measured with a protractor. If they are different from the original triangle's angles, this confirms the transformation was not a rigid motion. Additionally, if the distances between corresponding points on the figure have changed, which you can measure with a ruler, this also confirms that the transformation is not rigid.

The time it takes the rock to reach the canyon floor is after 3.99seconds

The intercept is the point where the axis is equal to zero. Give the quadratic equation that represents the height h (in feet) of an object t seconds after it is dropped expressed as:

h = -16t² + 255

The rock reaches the ground when h(t) = 0. Substitute

h = -16t² + 255

h = -16t² + 255 = 0
16t² = 255
t² = 255/16
t² = 15.9375

t = 3.99seconds

Hence the time it takes the rock to reach the canyon floor is after 3.99seconds

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To find two numbers a and b whose sum a + b is 0 and whose difference a - b is 2, we can set up a system of equations and solve for the values of a and b.

To find two numbers a and b whose sum a + b is 0 and whose difference a - b is 2, we can set up a system of equations:

a + b = 0

a - b = 2

We can solve this system by adding the two equations:

(a + b) + (a - b) = 0 + 2

2a = 2

a = 1

Substituting the value of a back into one of the equations, we find that b = -1.

Therefore, the two numbers are 1 and -1.

The simplification form  of the expression 15x+14y+3x+7y is 18x + 21y option (D) 18x + 21y is correct.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

15x+14y+3x+7y

After simplification,

Adding like terms:

= 18x + 21y

Thus, the simplification form  of the expression 15x+14y+3x+7y is 18x + 21y option (D) 18x + 21y is correct.

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We can calculate for the slope of the line using the formula:

m = (y2 – y1) / (x2 – x1)

From the given values:

m = (4,000 – 10,000) ft / (15 – 0) min

m = -400 ft/min

This means that the altitude is decreasing by 400 ft per minute.

> The slope is –400 . This means that the helicopter descends 400 ft each minute.

Answer: Option 'C' is correct.

Step-by-step explanation:

Since we have given that

Cost for 5 weeks i.e. 15 classes = $108

Cost of per class is given by

[tex]\frac{108}{15}=7.2[/tex]

Cost for 8 weeks i.e. 24 classes = $125

Cost of per class is given by

[tex]\frac{125}{24}=5.21[/tex]

Amount of saving of per class by taking the 8 week class is given by

[tex]7.2-5.21=\$1.99[/tex]

Hence, Option 'C' is correct.

The principle being demonstrated is known as the Symmetric Property, which holds that if an equation or statement is valid, then its switched or flipped version will also be true.

The question refers to a fundamental property in mathematics called the Symmetric Property. The Symmetric Property states that if an equation or statement is true, then its mirror or flipped version will also hold true. In this case, if LM = JK, then under Symmetric Property, it must be true that JK = LM.

For instance: If 5 = 2 + 3, then 2 + 3 = 5.

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When a system has one answer or in other words, the graphs of the equations intersect one time, the system is called a consistent system of linear equations and therefore the equations are independent.

When a system has no solution meaning, the graphs of the equations don’t interconnect at all, the system is known to be an inconsistent system of linear equations and the equations are independent.

So therefore, the answer is yes.

The first factor has a degree of 7, the second has a degree of 6, and the third has a degree of 5. The product has a degree of 7, the highest among them.

To determine the degree of each polynomial in the expression[tex]2a^7 - 16a^6 + 18a^5[/tex], we need to understand that the degree of a polynomial is the highest exponent of the variable in that polynomial.

The first factor is[tex]2a^7[/tex]. Here, the highest exponent of the variable 'a' is 7. So, the degree of the first factor is 7.

The second factor is[tex]-16a^6[/tex]. In this case, the highest exponent of 'a' is 6. So, the degree of the second factor is 6.

The third factor is [tex]18a^5[/tex]. Here, the highest exponent of 'a' is 5. So, the degree of the third factor is 5.

Now, to find the degree of the product of these three factors when added together, we need to find the highest degree among them. In this case, the highest degree is 7 (from the first factor). Therefore, the product has a degree of 7.

In summary:

The first factor has a degree of 7.

The second factor has a degree of 6.

The third factor has a degree of 5.

The product has a degree of 7.

These degrees reflect the highest power of 'a' in each term of the polynomial expression.

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