Write the phrase as a mathematical expression. Use x as the variable.
4 times the sum of 2 times a number and 7

Answer:

f(x)=x²-3x-10

Step-by-step explanation:

[tex]f(x) = x {}^{2} - 3x - 10 \\ to \: find \: x \: intercept \:o r \: zero \: substitute \: f(x) = 0\: \\ 0 = x {}^{2} - 3x - 10 \\ x {}^{2} - 3x - 10 = 0 \\ x {}^{2} + 2x - 5x - 10 = 0 \\ x(x + 2) - 5x - 10 = 0 \\ x(x + 2) - 5(x + 2) = 0 \\ (x + 2).(x - 5) = 0 \\ x + 2 = 0 \\ x - 5 = 0 \\ x = - 2 \\ x = 5[/tex]

therefore the zeros of the equation are x₁=-2,x₂=5

From the straight line AB and CD with point M as midpoint of both lines, AM = BM = 3.2 cm and CM = DM = 2 cm

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

m as the midpoint of both ab and cd, hence:

AM = BM = AB/2 = 6.4/2 = 3.2 cm

CM = DM = CD/2 = 4/2 = 2 cm

From the straight line AB and CD with point M as midpoint of both lines, AM = BM = 3.2 cm and CM = DM = 2 cm

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Answer:

[tex]6[/tex]

Step-by-step explanation:

The gist of modular arithmetic in a nutshell: the numbers [tex]a[/tex] and [tex]b[/tex] are considered to be congruent by their modulus [tex]m[/tex] if [tex]m[/tex] is a divisor of their difference.

In mathematics: [tex]a \equiv_{m} b \Leftrightarrow (a - b) \vdots m[/tex]

Exemplifying this: [tex]6 \equiv_{7} -1[/tex] because [tex]6 - (-1) = 6 + 1 = 7[/tex], [tex]7 \vdots 7[/tex].

Let us have following equivalences: [tex]a \equiv_{m} b[/tex] and [tex]c \equiv_{m} d[/tex], then:  [tex](a - b) \vdots m[/tex] and [tex](c - d) \vdots m[/tex] by definition.

Properties:

1. [tex]a + c \equiv_{m} b + d \Leftrightarrow ((a + c) - (b + d)) \vdots m \Leftrightarrow (a + c - b - d) \vdots m \Leftrightarrow ((a - b) + (c - d)) \vdots m[/tex].

2. [tex]a - c \equiv_{m} b - d \Leftrightarrow ((a - c) - (b - d)) \vdots m \Leftrightarrow (a - c - b + d) \vdots m \Leftrightarrow ((a - b) - (c - d)) \vdots m[/tex].

3. [tex]ac \equiv_{m} bd \Leftrightarrow (ac - bd) \vdots m \Leftrightarrow (ac - bc - bd + bc) \vdots m \Leftrightarrow (c(a - b) + b(c - d)) \vdots m[/tex].

4. What if we have [tex]a \equiv_{m} b[/tex] twice? If we abide by property 3, we can come to the conclusion that [tex]a^2 \equiv_m b^2[/tex]. It is fair enough that there is room for the equivalence [tex]a^n \equiv_{m} b^n[/tex].

[tex]3^{51} = (3^3)^\frac{51}{3} = 27^{17} \equiv_{7} (-1)^{17} \equiv_{7} -1 \equiv_{7} 6[/tex].

We used property 4.

Keep in mind that any remainder cannot be a negative number.

Therefore, the remainder equals [tex]6[/tex].

Answer:

[tex](-\infty, -1)\ \cup\ (0, 2)[/tex]

Step-by-step explanation:

So if you expand out the two binomials (k-2)(k+1), you'll get: [tex]k^2+k-2k-2[/tex]. which simplifies to: [tex]k^2-k-2[/tex]. Multiplying this by the k gives you: [tex]k^3-k^2-2k[/tex]. As you can see the degree is odd, this means that this polynomial will have two opposite end behaviors. And as you can see the leading coefficient is positive, meaning that this function will go towards positive infinity as k goes towards positive infinity. Also we if look at the original equation given, it's in factored form, with the zeroes as k=0, k=2, and k=-1. So given this we can draw a simple graph to see when the value of the equation is negative. If you look at the graph I drew you'll see that it's negative from (-infinity, -1) and then negative from (0, 2)

Answer:

18 and 72

Step-by-step explanation:

the smaller part can be assigned as x while the larger will be 4x. Both numbers need to add up to 90, giving the equation: 4x+x = 90

Solve:

4x+x = 90

5x = 90

x = 18

4x = 72

The percent by volume of the resulting solution is 10L by 93 percent

The resulting solution = sum of the volumes of both solutions

Resulting solution = 6L × 33 percent + 4L × 60 percent

Resulting solution = 10 L × 93 percent

This is so because both solutions add up to form the resulting solution

Thus, the percent by volume of the resulting solution is 10L by 93 percent

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Answer:

The highest number that divides each of the two or more numbers is the HCF or Highest Common Factor.

Step-by-step explanation:

Example: What is the HCF of {12,42,14}

Answer: The HCF is 2 as the biggest number they can all be divided by is 2. {12,42,14} = {2^2*3,2*3*7,2*7} The factors in each number is 2.

The statement that's true about the triangle is that WXY + YXZ = 180°.

It should be noted that in the question, the options are related to a linear pair.

According to the linear pair, when a line cuts another line at a point, then the sum of the adjacent angles formed at the point will be 180°.

Therefore, WXY + YXZ = 180°.

The correct option is C.

The complete question is:

Which statement regarding the diagram is true?

m∠WXY = m∠YXZ

m∠WXY < m∠YZX

m∠WXY + m∠YXZ = 180°

m∠WXY + m∠XYZ = 180°

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Answer: the total area with the extension S≈82,3 foot²,  S>S'.

Step-by-step explanation:

D₁=8 foot    D₂=10 foot    a wide extension = 4 foot.

1) Let the total area with the extension S is the area of the circular table S₁

plus a wide extension S₂.

Considere S₁:

[tex]R_1=\frac{D_1}{2} \\R_1=\frac{8}{2} \\R_1=4 foot.\\S_1=\pi* R_1^2\\S_1=\pi *4^2\\S_1=16*\pi \\S_1\approx50,3\ foot^2.\\[/tex]

[tex]S_2=8*4\\S_2=32 \ foot^2.[/tex]

[tex]S\approx50,3+32\\S\approx82,3 \ foot^2.[/tex]

2)\ Considere S':

[tex]R_2=\frac{D_2}{2} \\R_2=\frac{10}{2} \\R_2=5 \ foot.\\S'=\pi *R^2\\S'=\pi *5^2\\S'=25*\pi \\S'\approx78,5\ foot^2.[/tex]

S>S'.

Good luck an' have a nice day!

Answer:

16 to the power of 5

y to the power of 4

(7a) to the power of 3 or 7 times a to the power of 3

Answer:

area = 78

Step-by-step explanation:

Area of triangle = 1/2  x  base  x  perpendicular height

                            ⇒ 1/2  x  13  x  12

                            ⇒ 78 units²

Answer:

(x - 4)^2 + (y + 1)^2=9

Step-by-step explanation:

The equation of a circle can be written using a kinda of fill-in-the-blank method if you know the coordinates of the center and the radius.

If the center is (h,k) and the radius is r, then fill in those given numbers into:

(x-h)^2 + (y-k)^2 =r^2

The center of your circle is (4, -1).

Fill in 4 for the h, -1 for the k and 3 for the r.

(x-4)^2+(y- -1)^2= 3^2

Simplify.

(x-4)^2+(y+1)^2=9

[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]

What is [tex]\bf{\bigg(\dfrac{2}{5}\bigg)^2[/tex]?

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

When we have a fraction that is raised to a specific power, we raise both the numerator and the denominator to that power.

[tex]\bf{\dfrac{2^2}{5^2}}=\dfrac{4}{25}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Answer:}[/tex]

                    [tex]\bf{=\dfrac{4}{25}[/tex]

[tex]\boxed{\bf{aesthetic \not101}}[/tex]

Answer:

55

Step-by-step explanation:

To find the average you add up all numbers given then divide by the amount of numbers there were. The mean, or average, of the original 5 people was 13 since their ages added was 65, which you divide by 5 for 13. The new mean once the 6th person entered the room was 20. So, you do 6 [number of people] times 20 [average] to get 120. Taking 65 [added amount of original ages of the 5 people] away from 120 [the new added up ages of all 6 people], you get 55. This means 55 would be the 6th person's age.

Sorry if the explanation is confusing!

Call the total ages of the 6 people, x

To calculate the mean age of 6 people, we take the total age (x) and divide by the amount of people (6)

So, x : 6 = 20

-> The total ages of the 6 people are 20 x 6 = 120

We can calculate the 6th person's age by taking 120 and minus the total age of the other 5

-> 120 - (13+12+13+15+12) = 55

So, the 6th person's age is 55.

Answer:

  a) 2.5

  b) 6.25

Step-by-step explanation:

For similar figures, the ratio of any corresponding linear dimensions is the same. The ratio of areas is the square of that.

The ratio of linear dimensions, larger to smaller, is ...

  (30 yd)/(12 yd) = 2.5

Perimeter is a linear dimension, the sum of side lengths. The ratio of perimeters is 2.5.

The ratio of areas, larger to smaller, is the square of the scale factor for side lengths:

  (2.5)² = 6.25

The ratio of the areas of the larger to smaller figure is 6.25.

Answer:

===========

Let the number of apples in each bag is x, then the number of bags is 20/x.

Since the number of apples in each bag is greater than one and number of bags is greater than one, we have the following conditions:

The factors of 20 between 1 and 20 are:

The possibilities are:

The table below is a quadratic function.

A quadratic function is an Algebraic function with the power of its variable as 2.

This function normally has three algebraic terms, the x-square term, the x-term and the constant term.

Analysis:

The X-column values increases from -2 to 1, while the f(x) column which is the y-column increase from -9, until it gets to 1, where the value falls to -5.

A typical behavior of an inverted-v curve which is a quadratic curve.

If it were a linear function, as x values increase, y value would either keep increasing or decreasing, it does not change its orientation.

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The angle of y in the triangle is 30 degrees.

∠O = 180 - 30 - 70 (angles in a triangle)

∠O = 180 - 100(angles in a triangle)

∠O = 80°

Using vertically opposite angle principle and sum of angle in a triangle,

80 + y + 70 = 180

180 - 150 = y

y = 30 degrees

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Answer:

ok so we can just add 20 + 45 then divide by 2

20+45=65/2=32.5

32.5

Hope This Helps!!!

The solution is x=3/4

How can we solve given equation?

First, we will solve like terms. Then shift constant to other side and keep x on the same side to get the value of x.

We can solve given equation as shown below:

5/2-3x-5+4x=-7/4

(5-10)/2+x=-7/4

-5/2+x=-7/4

x=5/2-7/4

x= (10-7)/4

x=3/4

Hence, the solution is x=3/4.

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Answer:

5/6

Step-by-step explanation:

The numbers on a six-sided die are as shown:

1, 2, 3, 4, 5, 6

The even numbers are:

2, 4, 6

The numbers greater than 3 are:

3, 4, 5, 6

Both lists together are:

2, 3, 4, 5, 6

Because 5 out of 6 numbers satisfy these conditions, the probability of satisfying these conditions is 5/6.

The value of x will be equal to 33.94 units.

Trigonometry is the branch of mathematics that set up a relationship between the sides and angle of the right-angle triangles.

Given that:-

Given that the radius of the circle is 12 units which are PO = 12 and OR = 12, QR = x , ∠O = 60 So ∠Q = 30.

First, we will calculate the Length OQ by angle property in triangle OQR.

[tex]Sin 30=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]Sin 30 = \dfrac{12}{OQ-12}[/tex]

[tex]\dfrac{1}{2}=\dfrac{12}{OQ-12}[/tex]

OQ - 12 = 24

OQ = 36

Now applying the Pythagorean theorem in the triangle OQR.

H² = P² + B²

36² = 12² + x²

x² = 1296 - 144

x = √1152

x = 33.94

Therefore the value of  x will be equal to 33.94 units.

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Using the Central Limit Theorem, the standard deviation of the sampling distribution of sample means would be of 0.86.

It states that the standard deviation of the sampling distribution of sample means is given by:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\sigma = 6.8, n = 63[/tex].

Hence:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

[tex]s = \frac{6.8}{\sqrt{63}}[/tex]

s = 0.86.

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Marta’s equation has a positive y-intercept, but the scatterplot shows a negative correlation.

The scatter plot is a manner in which data is presented as dots on a cartesian axes, The line of best fit is a description of the data that is presented in the scatter plot.

Hence, Marta is incorrect because Marta’s equation has a positive y-intercept, but the scatterplot shows a negative correlation.

Missing parts;

Marta believes that the equation of the line of best fit for the scatterplot below is y=-5/9x+23/9. Which statement best summarizes why Marta is likely incorrect?

Marta’s equation has a positive y-intercept, but the scatterplot suggests a negative y-intercept.

Marta’s equation has a positive y-intercept, but the scatterplot shows a negative correlation.

Marta’s equation has a negative slope, but the scatterplot suggests a negative y-intercept.

Marta’s equation has a negative slope, but the scatterplot shows a positive correlation.

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Answer:

c.) 38

Step-by-step explanation:

[tex]\sum\limits_{n=3}^6 a_n[/tex]   means "summation of the all the elements starting from the 3rd element to the 6th element".

The 3rd element in the series is 14, and the 6th element is 5; we have to add these and all the elements between them together.

∴    [tex]\sum\limits_{n=3}^6 a_n[/tex]    =  14 + 11 + 8 + 5

                   = 38

Step-by-step explanation:

There cannot be such a question because the difference of half of the big number and the small number will automatically be zero, but we can find it with the equation I circled on the paper I gave you. achievements

Step-by-step explanation:

I assume

SR = 2x + 23

RQ = x + 21

if that is true, then the situation is completely simple :

14 = (2x + 23) + (x + 21) = 3x + 44

3x = -30

x = -10

SR = 2×-10 + 23 = -20 + 23 = 3

RQ = -10 + 21 = 11

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = -10 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex] \qquad \tt \rightarrow \: SR + RQ = SQ[/tex]

[tex]\qquad \tt \rightarrow \: 2x + 23 + x + 21 = 14[/tex]

[tex]\qquad \tt \rightarrow \: 3x + 44 = 14[/tex]

[tex]\qquad \tt \rightarrow \: 3x = 14 - 44[/tex]

[tex]\qquad \tt \rightarrow \: 3x = - 30[/tex]

[tex]\qquad \tt \rightarrow \: x = - 10[/tex]

Now,

[tex] \qquad \tt \rightarrow \: SR = 2x + 23 [/tex]

[tex] \qquad \tt \rightarrow \: SR = 2(-10) + 23 [/tex]

[tex] \qquad \tt \rightarrow \: SR =-20+ 23 [/tex]

[tex] \qquad \tt \rightarrow \: SR = 3 \:\: units [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

3

Step-by-step explanation:

Start with the amount that he wants to pay with gigabytes and subtract the amount of his bill without gigabytes.

58.50-46.50=12

 Then divide that amount by the price of each gigabyte to determine how many gigabytes he can use while staying in budget.

12/4=3

Answer: 3

Inequalities help us to compare two unequal expressions. The gigabytes of data that Elijah should use while staying within his budget is 3 gigabytes.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Given that Elijah pays a flat cost of $46.50 per month and $4 per gigabyte. He wants to keep his bill at $58.50 per month. Therefore, we can write the inequality for this condition as,

$46.50 + $4(x) ≤ $58.50

46.50 + 4x ≤ 58.50

4x ≤ 58.50 - 46.50

4x ≤ 12

x ≤ 12/4

x ≤ 3

Hence, the gigabytes of data that Elijah should use while staying within his budget is 3 gigabytes.

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Answer: 5

Step-by-step explanation:

By the inscribed angle theorem.

[tex]\frac{9}{15}=\frac{2x-1}{3x}\\\\27x=30x-15\\\\-3x=-15\\\\x=5[/tex]