Identifying the Factored Form of a Trinomial Which expression is the factored form of x2 – 7x + 10?

The unknown number is equal to 2100.

In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:

Let the variable n represent the unknown number.

"when divided by 3, I am 700."

n/3 = 700  ...equation 1.

n = 700(3)

n = 2100.

"when divided by 7, I am 300."

n/7 = 300 ....equation 2.

n = 300(7)

n = 2100.

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Final answer:

A sphere has no vertices as it is a three-dimensional shape with a continuous curved surface, unlike a cube which has distinct edges and flat faces.

Explanation:

The question "how many vertices does a sphere have?" can be answered quite simply. A sphere is a perfect three-dimensional shape where every point on the surface is equidistant from the center. Unlike a cube, which has flat faces and edges, a sphere has a continuous curved surface. Consequently, a sphere does not have any vertices, edges, or faces. Vertices are points where edges intersect, and since a sphere has no edges or flat faces, it cannot have vertices.

Answer:

The diameter is 36 inches

Step-by-step explanation:

The volume of a sphere is

[tex] \frac{4}{3} \pi {r}^{3} [/tex]

The given sphere has volume

[tex]7776\pi {in}^{3} [/tex]

We can now equate the formula to the given volume and solve for r.

[tex]\frac{4}{3} \pi {r}^{3} = 7776\pi[/tex]

[tex] {r}^{3}= 7776\pi \times \frac{3}{4\pi} [/tex]

[tex] {r}^{3} = 5832[/tex]

[tex]r = \sqrt[3]{5832} [/tex]

[tex]r = 18[/tex]

The diameter of the sphere is twice the radius.

Hence

[tex]diameter = 2 \times 18 = 36in[/tex]

When the given system of equations is added together, it simplifies to '0=8', which is a contradiction. Therefore, the system of equations has no solution.

You can simply add the two equations together. Adding the two equations eliminates the variables x and y:

(2/3x - 2/3x) + (y - y) = 6 + 2

This simplifies to 0 = 8, which is a contradiction. Therefore, this system of equations has no solution. That means the correct answer is D. 'No solution'.

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Ricardo will calculate the total amount he will pay for the 50 tool sheds by multiplying the quantity (50 sheds) by the cost per shed ($40), which equals $2,000.

To calculate the total amount Ricardo will pay for the 50 tool sheds he received, he needs to multiply the number of sheds by the cost per shed. Since each shed costs him $40, the calculation to find the total cost is as follows:

Multiply the quantity of tool sheds by the cost per shed: 50 sheds imes $40 per shed.

Calculate the product to find the total cost: 50 imes $40 = $2,000.

Therefore, Ricardo will pay a total of $2,000 for the 50 tool sheds.

The standard form of the equation of the circle with the radius of 12 and center at the origin is,

⇒ x² + y² = 144

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

the radius of circle is, 12 and center at the origin.

Now, We know that;

Standard form of circle with center origin and radius r is,

⇒ x² + y² = r²

Here, r = 12

Hence, The standard form of the equation of the circle with the radius of 12 and center at the origin is,

⇒ x² + y² = 12²

⇒ x² + y² = 144

Thus, The standard form of the equation of the circle with the radius of 12 and center at the origin is,

⇒ x² + y² = 144

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After selling 6 out of 21 granola bars, the store has 15 left. Following a shipment of 42 granola bars, the store will have a total of 57 granola bars in stock.

To find out how many granola bars the store will have in stock after the shipment, we should first calculate how many granola bars are left after the sales by subtracting the number sold from the initial stock. They started with 21 granola bars and sold 6, so they have 21 - 6 = 15 granola bars left. Then, we add the number of granola bars in the shipment arriving tomorrow to the number they currently have in stock. They will receive 42 granola bars in the shipment, so the total will be 15 + 42 = 57 granola bars in stock after the shipment arrives.

Final answer:

To choose the correct box-and-whiskers plot for Jaime's discussion group scores, we must calculate the five key statistics and match them with a plot displaying those exact values, factoring in the majority of scores in the 70-89 range.

Explanation:

To determine which box-and-whiskers plot correctly displays Jaime's discussion group scores, we need to calculate five key statistics: the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and the maximum. These statistics help us create an accurate box plot representation of the dataset.

First, we organize the scores in ascending order: 62, 69, 73, 73, 78, 79, 81, 93. From here, we can identify the minimum (62) and maximum (93) scores directly. The median score will be the average of the fourth and fifth scores since we have an even number of observations, which is (73+73)/2 = 73. The lower quartile (Q1) is the median of the lower half of the data, which would be (69+73)/2 = 71. The upper quartile (Q3) is the median of the upper half of the data, which is (79+81)/2 = 80.

Now that we have all the necessary statistics, we can select the box plot that matches these values. Jaime's scores are mostly within the 70-89 range, reflecting a majority of C and B grades, with a few scores in the 60-69 and 90-100 ranges, which correspond to D/F and A ranges respectively. The correct box-and-whiskers plot will show a box ranging from Q1 (71) to Q3 (80), a median line at 73, a whisker extending to the minimum score of 62, and another whisker extending to the maximum score of 93.

Sarah must score at least 44 on her third test in order to have an average of at least 80.

To find out what score Sarah must make on her third test in order to have an average of at least 80, we can set up an equation. The average of her three test scores can be calculated by adding up her scores and dividing by 3:

Average = (98 + 98 + x) / 3

We want the average to be at least 80, so we can solve the equation for x:

(98 + 98 + x) / 3 ≥ 80

Simplifying the equation, we get:

196 + x ≥ 240

Subtracting 196 from both sides, we have:

x ≥ 44

Therefore, Sarah must score at least 44 on her third test in order to have an average of at least 80.

Sarah needs to score at least a 44 on her third test to have an average of at least 80 across her three test scores.

Sarah has grades of 98 and 98 on her first two tests and wants to have an average of at least 80 after her third test. To calculate the minimum score Sarah must make on the third test to achieve her goal, we use the formula for the average of three numbers, which is (test1 + test2 + test3) / 3. In Sarah's case, the average after three tests should be at least 80.

Let's represent the third test score as 'x'. Thus, the equation to find 'x' becomes:

(98 + 98 + x) / 3 ≥ 80

Combining the scores of the first two tests gives us:

(196 + x) / 3 ≥ 80

By multiplying both sides by 3 to eliminate the denominator, we have:

196 + x ≥ 240

Subtract 196 from both sides to solve for x:

x ≥ 240 - 196

x ≥ 44

Therefore, Sarah must score at least a 44 on her third test to achieve an average of 80.

To simplify the expression 4/7 * 5/9, the equivalent expression is 20/63.

To simplify the expression 4/7 * 5/9, we can multiply the numerators together to get the new numerator and multiply the denominators together to get the new denominator. So, the expression becomes 20/63. Therefore, none of the options listed are equivalent to 4/7 * 5/9.

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None of the options a, b or c are equivalent to the expression 4/7*5/9. The correct expression must simplify to 20/63.

The question is asking to find out which of the provided expressions is equivalent to the expression 4/7*5/9. The correct option should yield the same result as the original expression when calculated. The expression 4/7*5/9 simplifies to 20/63.

Let's check the provided options:

The provided information about relative frequencies is irrelevant for this question.

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The shortest distance they travel to return to starting point is 9.43 miles.

Since, two joggers run 8 miles north and then 5 miles west.

According to question , a right triangle is formed. and hypotenuse of right triangle represent the shortest distance between starting point to final point.

Apply Pythagoras theorem,

             Shortest distance, [tex]=\sqrt{8^{2}+5^{2} } =\sqrt{64+25}=\sqrt{89}=9.43miles[/tex]

Thus, They travel 9.43 miles to return to their starting point.

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[tex] \lim\limits_{x\to11}\dfrac{\sqrt{x+5}-4}{x-11}=\lim\limits_{x\to11}\dfrac{(\sqrt{x+5}-4)(\sqrt{x+5}+4)}{(x-11)(\sqrt{x+5}+4)}\\\\=\lim\limits_{x\to11}\dfrac{(\sqrt{x+5})^2-4^2}{(x-11)(\sqrt{x+5}+4)}=\lim\limits_{x\to11}\dfrac{x+5-16}{(x-11)(\sqrt{x+5}+4)}\\\\=\lim\limits_{x\to11}\dfrac{x-11}{(x-11)(\sqrt{x+5}+4)}=\lim\limits_{x\to11}\dfrac{1}{\sqrt{x+5}+4}=\dfrac{1}{\sqrt{11+5}+4}\\\\=\dfrac{1}{\sqrt{16}+4}=\dfrac{1}{4+4}=\dfrac{1}{8}\\\\Answer:\ d.\ \dfrac{1}{8} [/tex]

Trinomial [tex]a^2 + a - 20[/tex] with factors (a + 5)(a - 4)
Trinomial [tex]a^2 - 9a + 20[/tex] with factors (a - 4)(a - 5)
Trinomial [tex]a^2 - 8a - 20[/tex] with factors (a - 10)(a + 2)
Trinomial [tex]a^2 - 12a + 20[/tex] with factors (a - 10)(a - 2)

To match the trinomials with their factors, we can factor each trinomial and compare the factors given:
1. Factorizing trinomial [tex]a^2 + a - 20:[/tex]
The factors are (a + 5)(a - 4).
This matches with the pair (a - 4)(a + 5).
2. Factorizing trinomial [tex]a^2 - 9a + 20:[/tex]
The factors are (a - 4)(a - 5).
This matches with the pair (a - 4)(a - 5).
3. Factorizing trinomial [tex]a^2 - 8a - 20[/tex]:
The factors are (a - 10)(a + 2).
This matches with the pair (a - 10)(a + 2).
4. Factorizing trinomial [tex]a^2 - 12a + 20:[/tex]
The factors are (a - 10)(a - 2).
This matches with the pair (a - 10)(a - 2).
Therefore, the correct matches are:
- Trinomial [tex]a^2 + a - 20[/tex] with factors (a + 5)(a - 4)
- Trinomial [tex]a^2 - 9a + 20[/tex] with factors (a - 4)(a - 5)
- Trinomial [tex]a^2 - 8a - 20[/tex] with factors (a - 10)(a + 2)
- Trinomial [tex]a^2 - 12a + 20[/tex] with factors (a - 10)(a - 2)