Answer:
(n -7)(4n + 8) = 0
Step-by-step explanation:
(a -b)² = a² - 2ab + b²
(2n - 5)² = 81
(2n)² - 2*2n*5 + 5² = 81
4n² - 20n + 25 = 81
4n² - 20n + 25 - 81 = 0
4n² - 20n - 56 = 0
4n² - 28n + 8n - 8*7 = 0
4n*(n -7) + 8*(n - 7) = 0
(n -7)(4n + 8) = 0
The goal for a fundraiser is $1,500. The school has raised 70% of the money. How much money has the school collected?
The school has collected $1050.
Madison brought $42.50 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1/4 as much as the sketchbook, and the sketchbook cost 2/3 the cost of the paint set. Madison had $4.00 left over after buying these items.
Answer:
Amount spent on each item is;
brush = $3.50
sketchbook = $14.00
paint set = $21.00
Completed question:
Madison brought $42.50 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1/4 as much as the sketchbook, and the sketchbook cost 2/3 the cost of the paint set. Madison had $4.00 left over after buying these items. How much is each item.
Step-by-step explanation:
Let x,y and z represent the price of brush, sketchbook and paint set respectively.
The brush was 1/4 as much as the sketchbook,
x = 1/4 × y
y = 4x ....1
the sketchbook cost 2/3 the cost of the paint set
y = 2/3 × z
3y = 2z
z = 3y/2
Substituting equation 1
z = 3(4x)/2 =6x
z = 6x ....2
Total amount spent = amount he brought - amount he left with(remainder)
= $42.50 - $4.00
= $38.50
Total amount spent = x+y+z = $38.50
x+y+z = 38.50
Substituting equation 1 and 2
x + 4x + 6x = 38.50
11x = 38.50
x = 38.50/11
x = 3.5
y = 4x = 4(3.5) = 14
z = 6x = 6(3.5) = 21
Amount spent on each item is;
brush = $3.50
sketchbook = $14.00
paint set = $21.00
Eliza solved a quadratic equation. Her work is shown below, with Step 2 missing.
What could Eliza have written as the result from Step 2?
(2 + 3)2 – 2 = 18
${z + 3)= 20
Step 1
Step 2
2 + 3 = 10
Step 3
I= -13 or 2 = 7 Step 4
Step 2: [tex]$(x + 3)^2 = 100$[/tex]. Step 3: [tex]$x + 3 = \pm 10$[/tex]. Step 4: [tex]$x = -13$[/tex] or [tex]$x = 7$[/tex]. The final answer is (C).
Given:
[tex]\frac{1}{5}(x+3)^2-2 & =18[/tex]
[tex]\frac{1}{5}(x+3)^2 & =20 \quad \text { Step } 1[/tex]
Step 2: To solve for (x+3), we isolate it by dividing both sides by [tex]$\frac{1}{5}$[/tex]:
[tex]\frac{1}{5}(x+3)^2 &= 20[/tex]
[tex](x+3)^2 &= 20 \times 5[/tex]
[tex](x+3)^2 &= 100[/tex]
Step 3: Take the square root of both sides to solve for x+3:
[tex]\sqrt{(x+3)^2} &= \pm \sqrt{100}[/tex]
[tex]x+3 &= \pm 10[/tex]
Step 4: Solve for x by subtracting 3 from both sides:
[tex]x &= -3 \pm 10[/tex]
[tex]x &= -13 \quad \text{or} \quad x = 7[/tex]
So, the complete step by step solution is:
Step 2:
[tex](x+3)^2 = 100[/tex]
Step 3:
[tex]x+3 = \pm 10[/tex]
Step 4:
[tex]x = -13 \quad \text{or} \quad x = 7[/tex]
Thus, the correct answer is (C).
Complete Question:
The median of this set of numbers is {20, 30, 40, 50, 60, 70, 80}
Milk & Cookies is an ice cream sandwich stand.
Use the following bar chart to find Milk & Cookies' total profit from July through September.
The total profit from July through September is -$1 if Milk & Cookies is an ice cream sandwich stand.
What is a bar chart?It is defined as the depiction of numerical data in a graph using a bar with space.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
As we can see in the bar graph,
Milk & Cookies is an ice cream sandwich stand.
Total profit from July through September = (+2) + (+2) + (-5)
= -$1
Thus, the total profit from July through September is -$1 if Milk & Cookies is an ice cream sandwich stand.
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Without the bar chart data, the exact total profit for Milk & Cookies' from July through September cannot be calculated. Normally, you would add the monthly profits to find the total profit for the quarter.
Explanation:To determine Milk & Cookies' total profit from July through September, we would need to examine the provided bar chart that lists profits for each month. However, since the actual bar chart data is not included in the question, we cannot calculate the exact total profit.
In a typical situation, you would add the profit of each month: Profit in July + Profit in August + Profit in September to find the total profit for that quarter.
If the total profits for July, August, and September are positive when added together, then Milk & Cookies has made a profit over these months.
If the sum is zero, the business broke even, and if the sum is negative, the business incurred a loss during that period. The profits from the bar chart are essential to conduct this analysis.
Jorge asked each of the 24 students in his class if they play a musical instrument. He also asked each
student if they play a sport. He gathered the following results:
. 6 students play both a musical instrument and a sport
. 3 students play neither a musical instrument nor a sport.
• 14 students in total play a sport.
Can you help Jorge organize the results into a two-way frequency table?
Plays a sport
Does not play a sport
Plays a musical instrument
Does not play a musical instrument
Final answer:
To organize the results into a two-way frequency table, fill in the known values and calculate the remaining values based on the total number of students.
Explanation:
To organize the results into a two-way frequency table, we can use the information given. First, we know that 6 students play both a musical instrument and a sport. We also know that 3 students play neither a musical instrument nor a sport. Furthermore, we know that a total of 14 students play a sport. From this information, we can fill in the table:
Plays a sport Does not play a sport
Plays a musical instrument 6 To be filled
Does not play a musical instrument To be filled 3
We can calculate the values for the empty cells by subtracting the known values from the total. So, the number of students who play a musical instrument but do not play a sport is 24 - (6 + 3 + 14) = 1. Likewise, the number of students who do not play a musical instrument but play a sport is 24 - (6 + 3 + 14) = 1.
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Sarah missed 9 questions on a quiz with 60 questions. What percent of questions did she get wrong?
If Sarah missed 9 questions on a quiz with 60 questions then 15% of questions did she get wrong
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that the number of questions in quiz are 60.
In that sarah missed 9 questions.
We need to find what percentage of questions did she get wrong.
x×60 =9
Now divide both sides by 60
x=9/60
x=0.15
Now multiply 0.15 with 100.
0.15×100
15%
Hence, 15% of the questions sarah get wrong.
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A survey was given to a random sample of 1350 residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. Of those surveyed, 26% of the people said they were in favor of the plan. Determine a 95% confidence interval for the percentage of people who favor the tax plan, rounding values to the nearest tenth.
Answer:
[tex]0.26 - 1.96\sqrt{\frac{0.26(1-0.26)}{1350}}=0.237[/tex]
[tex]0.26 + 1.96\sqrt{\frac{0.26(1-0.26)}{1350}}=0.283[/tex]
Rounded the 95% confidence interval would be given by (0.2;0.3)
Step-by-step explanation:
We know that the estimated proportion of people said they were in favor of the plan is [tex]\hat p=0.26[/tex]
We want to construct a confidence interval with 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
The confidence interval for the true proportion of interest is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
Replacing the info given we got:
[tex]0.26 - 1.96\sqrt{\frac{0.26(1-0.26)}{1350}}=0.237[/tex]
[tex]0.26 + 1.96\sqrt{\frac{0.26(1-0.26)}{1350}}=0.283[/tex]
Rounded the 95% confidence interval would be given by (0.2;0.3)
In ΔWXY, the measure of ∠Y=90°, WX = 7.9 feet, and XY = 6.7 feet. Find the measure of ∠X to the nearest tenth of a degree
Answer:
32
Step-by-step explanation:
The measure of ∠X is approximately 47.9 degrees to the nearest tenth of a degree.
To find the measure of ∠X in triangle WXY, you can use the trigonometric relationship of the tangent function.
Given that ∠Y is a right angle (90°), and you have the lengths of two sides, WX and XY, you can use the following relationship:
tan(∠X) = opposite/adjacent
In this case:
Opposite side to ∠X = WX
Adjacent side to ∠X = XY
So, you have:
tan(∠X) = WX / XY
tan(∠X) = 7.9 feet / 6.7 feet
Now, you can find ∠X by taking the arctan (inverse tangent) of this value:
∠X = arctan(7.9 / 6.7)
Using a calculator, you can find:
∠X ≈ 47.9 degrees (rounded to the nearest tenth of a degree)
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Part one: Sequence and Series
1)
Find the 29th term of the arithmetic sequence in which a=13 and d = -2.5
Answer:
- 57
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a + (n - 1)d
where a is the first term and d the common difference
Here a = 13 and d = - 2.5, thus
[tex]a_{29}[/tex] = 13 + (28 × - 2.5) = 13 - 70 = - 57
3. Which choice below would ensure that
quadrilateral IJKL is a trapezoid?
A. IJAJK
B. ĪJ | KL
C. IJ KL
D. KL=LI
K
La
Joaquin and Trisha are playing a game in which the lower median wins the game. Their scores are shown below. Joaquin's scores: 75, 72, 85, 62, 58, 91 Trisha's scores: 92, 90, 55, 76, 91, 74 Which supports the conclusion that Joaquin won the game?
Answer:
Step-by-step explanation:
Given
Joaquin's score is [tex]75,72,85,62,58,91[/tex]
and Trisha's score is [tex]92,90,55,76,91,74[/tex]
Arranging score in order of value we get
Joaquin's : [tex]58,62,72,75,85,91[/tex]
Trisha's : [tex]55,74,76,90,91,92[/tex]
as no of values is even therefore their median is
Joaquin's[tex]=\frac{72+75}{2}=73.5[/tex]
Trisha's [tex]=\frac{76+90}{2}=83[/tex]
Therefore median of Joaquin's is lower
Thus Joaquin wins the game
Answer:
the answer is A)
Step-by-step explanation:
took the test and got a 90
En un polinomio P(x,y), homogéneo y completo en "x" e "y", la suma de los grados absolutos de todos sus términos es 420. ¿Cuál es su grado de homogeneidad?
Answer:
the degree of homogeneity is 20.
Step-by-step explanation:
In a polynomial P (x, y), homogeneous and complete in "x" and "y", the sum of the absolute degrees of all its terms is 420. What is its degree of homogeneity?
A homogeneous polynomial is one in which all monomials have the same degree.
This is an example of a homogeneous polynomial of degree 4 (the degree of all monomials is 4):
x ^ 4 + 3x ^ 3y + 2x ^ 2y ^ 2 + xy ^ 3 + 8y ^ 4.
As you can see, the sum of the exponents of the variables x, y in each monomial is 4.
And the number of terms is 5, that is, it is the degree of homogeneity plus 1.
In relation to the sum of the absolute degrees of all monomials or terms it will be: 4 + 4 + 4 + 4 + 4 = 4 * 5 = 20.
In general, you can say that the sum of the absolute degrees in a homogeneous polynomial will be the degree of each monomial by the number of terms = degree * (degree + 1)
Calling n, the degree of our polynomial, it must be fulfilled:
n (n + 1) = 420
=> n ^ 2 + n = 420
=> n ^ 2 + n - 420 = 0
Factoring:
(n + 21) (n - 20) = 0
=> n = -21 and n = 20.
Only the positive value makes sense, therefore n = 20.
In other words, the polynomial is of the form (excluding the coefficients):
x ^ 20 + x ^ 19 y + x ^ 18 y ^ 2 + x ^ 17 y ^ 3 + .... x ^ 3 y ^ 17 + x ^ 2y ^ 18 + xy ^ 19 + y ^ 20
That polynomial has 21 terms.
So the sum of the degrees will be 20 * 21 = 420, as required in the statement.
Therefore, the degree of homogeneity is 20.
What is the radius of a circle whose equation is x2+y2+8x−6y+21=0?
2 units
3 units
4 units
5 units
Answer:
The Answer is 2 Units on edg 2020
Step-by-step explanation:
The radius of a circle whose equation is given is x²+y²+8x−6y+21=0 is; 2.
Radius of a circleThe given equation of the circle is;
x²+y²+8x−6y+21=0.Hence, by collecting like terms and subsequent factorisation by completing the square method, it follows that;
(x+4)² + (y-3)² -16 -9 +21 = 0.(x+4)² + (y-3)² = 4(x+4)² + (y-3)² = 2².By comparison of the equation above with the standard form equation of a circle, it follows that the radius of the circle is; 2
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you are a waiter at a restaurant, you did a wonderful job and your customers want to leave you a 20% tip. if their bill is $60, how much will your tip be?
Answer:
$12
Step-by-step explanation:
20% of $60 =
= 20% * $60
= 0.20 * $60
= $12
Least common multiples of 3v^7y^2x^5 and 24y^4x^5
Answer:
the answer is B
Step-by-step explanation:
Connor randomly chooses a card from a deck of numbered cards. the cards are numbered 1 through 10, and each number appears only one time. What is the probability that the card Connor chooses has a number on it that is even or divisible by 5?
1) 7/10
2) 3/5
3) 1/2
4) 4/5
Answer:
Probability that the card Connor chooses has a number on it that is even or divisible by 5 is (3/5) or 0.6.
Step-by-step explanation:
We are given that Connor randomly chooses a card from a deck of numbered cards. the cards are numbered 1 through 10, and each number appears only one time.
And we have to find the probability that the card Connor chooses has a number on it that is even or divisible by 5.
Let the Probability that card Connor chooses has a number on it that is even = P(A)
Probability that card Connor chooses has a number on it that is divisible by 5 = P(B)
Probability that card Connor chooses has a number on it that is even and divisible by 5 = [tex]P(A\bigcap B)[/tex]
Probability that card Connor chooses has a number on it that is even or divisible by 5 = [tex]P(A\bigcup B)[/tex]
Here, Even numbers are = {2, 4, 6, 8, 10} = 5
Numbers divisible by 5 = {5, 10} = 2
Also, Number which is even and also divisible by 5 = {10} = 1
Total numbers = 10
Now, Probability that card Connor chooses has a number on it that is even = [tex]\frac{5}{10}[/tex] = 0.5
Probability that card Connor chooses has a number on it that is divisible by 5 = [tex]\frac{2}{10}[/tex] = 0.2
Probability that card Connor chooses has a number on it that is even and divisible by 5 = [tex]\frac{1}{10}[/tex] = 0.1
Now, [tex]P(A\bigcup B) = P(A) +P(B) -P(A\bigcap B)[/tex]
= 0.5 + 0.2 - 0.1
= 0.6 = [tex]\frac{3}{5}[/tex]
Hence, probability that the card Connor chooses has a number on it that is even or divisible by 5 is 0.6.
Two homeroom classes at Eagletown Junior High charted the amount of time each student spent studying for their science final exam.
Answer:
(A)There are twice as many students in Homeroom B that spent 6 hours studying for their final science exam than in Homeroom A
Step-by-step explanation:
From the dot plot presented,
In Homeroom A, number of students who spent 6 hours studying for their science final exam =1
In Homeroom B, number of students who spent 6 hours studying for their science final exam =4
Therefore, the statement that "There are twice as many students in Homeroom B that spent 6 hours studying for their final science exam than in Homeroom A" is not supported from the dot plot.
The correct option is A.
so im really confused by this and could use some help.
Gorilla Weight (pounds) Plugged into 2b - 15 = 605 True or False? Sophia 318 George 417 Nancy 310 Hank 136 Paula 62 Gavin 24 2b- 15 =605.
Answer:
Nancy fits the equation.
Step-by-step explanation:
I think they're asking which gorilla fits the equation.
2b - 15 = 605
Add 15 to both sides
2b=620
Divide both sides by 2
b=310
The only gorilla who weighs 310 pounds is Nancy.
Answer:
Nancy
Step-by-step explanation:
Little Tommy built a train out of LEGOS. One-sixth of the train was made with blue blocks, 5/8 of the train was made with red blocks and the remaining five blocks were yellow.
How many LEGO blocks long was Tommy's train?
Answer:
24 blocks long
Answer:
24 blocks.
Step-by-step explanation:
[tex]\frac{1}{6} +\frac{5}{8} =5[/tex] blocks
[tex]\frac{8}{48} + \frac{30}{48}=\frac{38}{48}\\\\ \frac{48}{48} -\frac{38}{48} =\frac{10}{48}[/tex]
[tex]\frac{10}{48}[/tex] is 5 blocks
You can use ratios to find out how many blocks for each color now. (I'm too lazy)
Blue blocks: 4 blocks
Red blocks: 15 blocks
Yellow blocks: 5 blocks
4+15+5=24 blocks in total.
A rectangular pyramid has a volume of 1512 in ', a height of 12 in, and a base length of 21 in. What is the width of its base?
2 in
6 in.
12 in.
18 in.
The width of the base of the rectangular pyramid is 6 inches, which is found by rearranging and simplifying the formula for the volume of a pyramid using the given values for the pyramid's volume, height, and length.
Explanation:The student has asked about finding the width of the base of a rectangular pyramid with a known volume, height, and base length. To find the width (w), we use the formula for the volume of a pyramid: V = (1/3) × base area × height. The base area is the product of the base length (l) and width (w), so we can rewrite the equation as V = (1/3) × l × w × h, where
V is the volume of the pyramid,l is the length of the base,w is the width of the base,h is the height of the pyramid.Given that V = 1512 in³, h = 12 in, and l = 21 in, the equation becomes 1512 = (1/3) × 21 × w × 12. Simplifying, we find w = 1512 / (1/3 × 21 × 12), which calculates to 6 in. Hence, the width of the base of the pyramid is 6 inches.
Find the volume of a cone with a diameter of 11.5 inches and a height of 15.2 inches.
Answer:
The volume of a right circular cone is [tex]526\ \text{feet}^3[/tex].
Step-by-step explanation:
We have,
Diameter of a cone is 11.5 inches
Height of a cone is 15.2 inches
It is required to find the volume of a cone. The volume of a cone is given in terms of radius r and height h as :
d = 11.5 inches
Radius, r = 5.75 inches
[tex]V=\dfrac{1}{3}\pi r^2 h\\\\V=\dfrac{1}{3}\times 3.14\times (5.75)^2\times 15.2\\\\V=526\ \text{inches}^3[/tex],
So, the volume of a right circular cone is [tex]526\ \text{feet}^3[/tex].
Final answer:
To find the volume of a cone with a given diameter and height, use the formula V = (1/3)πr²h where r is the radius and h is the height.
Explanation:
Volume of a cone:
Given diameter = 11.5 inches, radius = 11.5 / 2 = 5.75 inches
Using the formula V = (1/3)πr²h, plug in radius = 5.75 inches and height = 15.2 inches
Calculate the volume: V = (1/3) × 3.142 × (5.75)² × 15.2 inches³
©
As an estimation we are told 5 miles is 8 km.
Convert 62.5 miles to km.
Answer:
100.584 KILOMETERS
Step-by-step explanation: cause i know it ❤
hope you get it right! love ya stranger
On conversion of 62.5 miles to kilometers we get 100.625 km.
To convert 62.5 miles to kilometers, use the conversion factor of 1 mile being equal to 1.61 kilometers to calculate that it is equivalent to 100.625 km.
To convert 62.5 miles to kilometers, you can use the fact that 1 mile is equal to 1.61 kilometers to set up a conversion ratio.
1 mile = 1.61 km
62.5 miles x 1.61 km/mile = 100.625 km
Rewrite the following equation in slope-intercept form
y + 8 = 1/8 (x+8)
Answer:
y=1/8x-7
Step-by-step explanation:
You have to get Y by itself so start out by subtracting 8 from both sides so you have y=1/8(x+8)-8.
Next simplify by distributing 1/8 to (x+8) which is 1/8+1.
Combine like terms and bam.
y=1/8x-7
PLLLZZ HELP!!!!
which of these describes a unique polygon?
1.A triangle with angles 30 degrees, 60 degrees, and 90 degrees
2. A triangle with side lengths 5 cm, 4 cm, and 3 cm
3. A quadrilateral with each side length 4 cm
4. A triangle with side lengths 7 cm and 8 cm and a 40-degree angle
Answer:
3. A quadrilateral with each side length 4 cm
Step-by-step explanation:
We need to understand what is a unique polygon?
It means all regular polygons with the same number of sides are similar.
1.A triangle with angles 30 degrees, 60 degrees, and 90 degrees
It is an right triangle, so the 3 sides are not simillar, so it is wrong
2. A triangle with side lengths 5 cm, 4 cm, and 3 cm
It is a triangle with the 3 sides are not simillar, so it is wrong
3. A quadrilateral with each side length 4 cm
It is an square with the 4 sides are simillar, so it is true
4. A triangle with side lengths 7 cm and 8 cm and a 40-degree angle
It is a triangle with the 3 sides are not simillar, so it is wrong
Hence, we choose 3.
A container is 24 m long, 9 m wide and 8 m high.
How many books can it hold if each book is 20 cm
long, 16 cm wide and 6 cm thick?
Answer:
900,000 books.
Step-by-step explanation:
The volume of the container = 24 * 9 * 8
= 1728 m^3
The volume of each book = 20*16*6 = 1920 cm^3
There are 100*100*100 = 1,000,000 cm^3 in 1 m^3.
So the number of books the container can hold
= (1728 * 1000000) / 1920
= 900,000.
El ancho de un jardìn de forna rectangular mide 40m y su diagonal 60m ¿Cuàl de las siguientes opciones nos indica la medida del largo del jardìn con dos decimales? A) 44,72 b) 44,55 c) 30,45
Answer:
La longitud del jardín es [tex]l \approx 44.72\,m[/tex]. (Opción A) (The length of the garden is [tex]l \approx 44.72\,m[/tex]) (Option A)
Step-by-step explanation:
El largo del jardín se calcula por el Teorema de Pitágoras (The length of the garden is now calculed by the Pythagorean Theorem):
[tex]l = \sqrt{(60\,m)^{2}-(40\,m)^{2}}[/tex]
[tex]l \approx 44.72\,m[/tex]
Answer:
A) x = 44,72 m
Step-by-step explanation:
A rectangular shape means two dimensions width (w) and length (l) and the internal angles are of 90⁰; therefore if we know one of its side, and a diagonal (d) we can calculate the other side, using Pytagoras Theorem, then:
x² + l² = d²
x² = d² - l² ⇒ x² = (60)² - (40)² ⇒ x² = 3600 - 1600
x² = 2000
x = √2000
x = 44,72 m
Use the divisibility rules to determine which of the following numbers 504 is divisible by. (Check all that apply.)
2
3
5
7
11
The number 504 is divisible by 2, 3, and 7 using the divisibility rules. It is not divisible by 5 as it does not end in 0 or 5, and not by 11 as the difference between the sum of alternating digits is not a multiple of 11.
To determine which numbers 504 is divisible by using the divisibility rules, we can examine each option provided:
2: A number is divisible by 2 if it is even, that is, if its last digit is 0, 2, 4, 6, or 8. Since 504 ends with a 4, it is divisible by 2.
3: A number is divisible by 3 if the sum of its digits is a multiple of 3. For 504, the sum of its digits is 5 + 0 + 4 = 9, which is a multiple of 3, so 504 is divisible by 3.
5: A number is divisible by 5 if its last digit is 0 or 5. Since 504 ends with a 4, it is not divisible by 5.
7: To determine divisibility by 7, there isn't a simple rule like there is for 2 or 5. However, through manual calculation or knowledge, we can confirm 504 is 7 times 72, and therefore, it is divisible by 7.
11: A number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is a multiple of 11 or 0. For 504, (5 - 0 + 4) = 9 which is not a multiple of 11, so 504 is not divisible by 11.
In conclusion, 504 is divisible by 2, 3, and 7.
What is the solution to the system of equations below y=1/2x-4andy=2x-9 (-2,-5) (-2,-3) (2,-3) (2,-13
The solution to the system of equations y = 1/2x - 4 and y = 2x - 9 is x = -2 and y = -5.
Explanation:To find the solution to the system of equations y = 1/2x - 4 and y = 2x - 9, we need to find the values of x and y that satisfy both equations. We can do this by finding the points of intersection between the two lines graphically or by solving the equations algebraically.
Graphically, we can plot the two lines on a graph and see where they intersect. The points of intersection are (-2, -5) and (2, -3).
Algebraically, we can set the two equations equal to each other and solve for x:
1/2x - 4 = 2x - 9
Now solve for x:
x = -2
Then substitute the value of x back into one of the original equations to find the value of y:
y = 1/2(-2) - 4 = -5
So the solution to the system of equations is x = -2 and y = -5.
Which expression is equivalent to 3(1 + x) + 7?
Answer:
3+3x+7 or 3x+10
Step-by-step explanation:
Answer:
3x+10
Step-by-step explanation:
3(1 + x) + 7
Distribute
3+3x+7
Combine like terms
3x+3+7
3x+10