11 pieces can be cut frοm the 4 yards οf fabric.
In math, what is a fractiοn?An element οf a whοle is a fractiοn. The quantity is mathematically represented as a quοtient, where the numeratοr and denοminatοr are split in half. Bοth are integers in a simple fractiοn. A fractiοn can be fοund in either the numeratοr οr the denοminatοr οf a cοmplex fractiοn. The numeratοr οf an apprοpriate fractiοn is less than the denοminatοr.
1 yard = 36 inches (since 1 yard is equal tο 3 feet and 1 fοοt is equal tο 12 inches)
Sο, 4 yards οf fabric = 4 x 36 = 144 inches οf fabric.
If each piece is 13 inches lοng, we can find the number οf pieces by dividing the tοtal length οf fabric by the length οf each piece:
Number οf pieces = Tοtal length οf fabric / Length οf each piece
Number οf pieces = 144 / 13
Number οf pieces ≈ 11.08
Since we cannοt have a fractiοn οf a piece, we must rοund dοwn tο the nearest whοle number. Therefοre, 11 pieces can be cut frοm the 4 yards οf fabric.
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Exercise 1: 1) Suppose we have to select a manager, assistant manager, and night manager from a list of 11 people. How many ways can this be done
one number is less than 3 times another if their sum is increased by 5 the result is 25 find the number
Answer:
Let's use algebra to solve the problem.
Let x be the first number.
Let y be the second number.
From the problem, we can set up two equations:
"One number is less than 3 times another":
x = 3y - - - (Equation 1)
"Their sum is increased by 5 the result is 25":
x + y + 5 = 25
x + y = 20 - - - (Equation 2)
Now we have two equations with two unknowns. We can use substitution or elimination to solve for one of the variables.
Using substitution:
From equation 1, we know that x = 3y. We can substitute this into equation 2 to eliminate x:
3y + y = 20
4y = 20
y = 5
Now we can substitute this value of y back into equation 1 to find x:
x = 3y
x = 3(5)
x = 15
Therefore, the first number is 15 and the second number is 5.
Work 1.1.8 The president of South Africa, Mr Cyril Ramaphosa, announced that there will be an inflow of R10 billion investment in South Africa in the following year. Use the multiplier formula to calculate the eventual change in aggregate expenditure due to this R10 billion injection. The marginal propensity to save (mps) is 0,4. Remember to show all formulas and calculations!
Using the multiplier formula, the eventual change in aggregate expenditure due to the inflow of R10 billion into South Africa and using the marginal propensity to consume (MPC) is R6 billion.
What is the multiplier formula?The multiplier formula is used to compute the amount of new income generated from the flow of extra income.
The multiplier formula uses the MPS (marginal propensity to save) to compute the multiplier as follows:
M = 1 / MPS
The marginal propensity to save gives the proportion of income that will be saved.
The marginal propensity to save (MPS) = 0.4
M = 1 / MPS
M = 1/0.4)
= 2.5
Change in aggregate expenditure = R25 billion (2.5 x R10 billion)
Thus, we expect the aggregate expenditure in South Africa to increase by R25 billion following the inflow of R10 billion investment.
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Write two numbers that multiply to the value on top and add to the value on bottom.
Submit Answer
42
-13
Answer:
-6 and -7
Step-by-step explanation:
-6 + -7 = -13
-6 * -7 = 42
twelve cans of dog food cost $16.80. How much is one can?
Answer: 1.4
Step-by-step explanation: Just divide.
16.80 divided by 12, is 1.4(0). And if you multiply 1.4 by 12 you get 16.8(0)
intelligence test scores refered to as intelligent quotient or IQ scores are based on characteristics such as verbal skills,abstruct reasoning power, numerical ability and spatial visualization.if plotted on a graph the distribution of IQ scores approximates a normal curve with a mean of about 100. an IQ scores above 115 is considered superior studies of "intellectually gifted" children have generally defined the lower limit of their IQ scores at 140: approximately 1% of the population have IQ scores above this limit.find the standard deviation of this distribution?
The standard deviation of the distribution is given as follows:
[tex]\sigma = 17.2[/tex]
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean of the distribution of IQ scores is given as follows:
[tex]\mu = 100[/tex]
X = 140 is the 99th percentile, as approximately 1% of the population have IQ scores above this limit, hence when X = 140, Z = 2.327, meaning that the standard deviation is obtained as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.327 = \frac{140 - 100}{\sigma}[/tex]
[tex]2.327\sigma = 40[/tex]
[tex]\sigma = \frac{40}{2.327}[/tex]
[tex]\sigma = 17.2[/tex]
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Creative Minds Bookstore decided to donate an overstock of
children’s books to some local elementary schools. They gave
two-fifths of the load to Sunshine Elementary. One-third of the
remaining books were donated to Lincoln Elementary. Two-thirds
of the books left were then given to Vineyard Middle School with
the last 16 books donated to the local library. How many books
were donated all together and how many books did each school
receive?
The answer will be as follows after answering the supplied question equation (8/15)x = (8/15)(34.29) 18.29 books Vineyard Middle School
What is equation?A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that shows the equivalence of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.
Let's tackle this problem with algebra.
Let's call the total number of books contributed "x".
According to the issue, Creative Minds Bookstore donated two-fifths of the books to Sunshine Elementary. Sunshine Elementary received (2/5)x books as a result.
That leaves (3/5)x books to be donated to other schools and libraries.
That leaves (7/15)x books available for donation to the library.
Given that the library acquired 16 books, we may conclude:
(7/15)x = 16
Calculating x:
x = (16)(15/7) = 34.29 (rounded to two decimal places) (rounded to two decimal places)
(2/5)x = (2/5)(34.29) 13.72 books at Sunshine Elementary
(1/5)x = (1/5)(34.29) 6.86 books at Lincoln Elementary
(8/15)x = (8/15)(34.29) 18.29 books Vineyard Middle School
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Help, please? lol its for like homework or whatev. helpppp!!
There are 3 teaspoons in a tablespoon. There are 10 16 times more teaspoons in a cup. How many teaspoons are in a cup?
One large jar and two small jars together can hold 8 ounces of jam. One large jar minus one small jar can hold 2 ounces of jam.
A matrix with 2 rows and 2 columns, where row 1 is 1 and 2 and row 2 is 1 and negative 1, is multiplied by matrix with 2 rows and 1 column, where row 1 is l and row 2 is s, equals a matrix with 2 rows and 1 column, where row 1 is 8 and row 2 is 2.
Use matrices to solve the equation and determine how many ounces of jam are in each type of jar. Show or explain all necessary steps.
Please help me solve it through matrices, not by equations. There's a certain way to solve this, I'm just confused on this specific way by using matrices.
There are 2 ounces of jam in the large jar and 2/3 ounce of jam in each small jar.
Describe Matrix?In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Matrices are commonly used to represent and manipulate linear transformations and systems of linear equations.
The elements of a matrix are typically denoted by lowercase letters with subscripts, such as aij or bij, where i and j refer to the row and column indices, respectively. For example, a 3x3 matrix might look like this:
| a11 a12 a13 |
| a21 a22 a23 |
| a31 a32 a33 |
This matrix has three rows and three columns, and the element in the first row and second column is denoted by a12.
Matrices can be added, subtracted, multiplied, and divided, and these operations follow specific rules that are defined in matrix algebra. For example, to add or subtract two matrices of the same size, we simply add or subtract the corresponding elements. To multiply two matrices, we multiply the rows of the first matrix by the columns of the second matrix and sum the products.
Let's represent the number of ounces of jam in the large jar as "L" and the number of ounces of jam in each small jar as "S". Then we can write the system of equations:
1L + 2S = 8
1L - 1S = 2
We can write this system in matrix form as:
[1 2; 1 -1][L;S] = [8;2]
To solve for L and S, we can use matrix algebra to isolate [L;S]:
[L;S] = [1 2; 1 -1]⁻¹ [8;2]
First, we need to find the inverse of the coefficient matrix [1 2; 1 -1]. The inverse is:
[1 -2; 1 1]/3
So we can substitute this into our equation:
[L;S] = [1 -2; 1 1]/3 [8;2]
[L;S] = [2;2/3]
So there are 2 ounces of jam in the large jar and 2/3 ounce of jam in each small jar.
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The complete question is:
Need help with short problem 2
The transpose matrix of A is the one written below.
[tex]\left[\begin{array}{ccc}3&2&0\\0&3&4\\0&0&3\end{array}\right][/tex]
How to get the transpose matrix?Here we are given the matrix A, and we want to find the transpose matrix A^t.
To do so, just leave the elements in the diagonal as they are in the original matrix, and then do a "reflection" of the other elements along the diagonal line. So the elements with equal subindices stay where they are, and the others are reflected along them.
Then the new matrix will be:
[tex]\left[\begin{array}{ccc}3&2&0\\0&3&4\\0&0&3\end{array}\right][/tex]
That is the transpose matrix, where the diagonal is still "3, 3, 3" but the other elements changed.
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1. What is a reasonable distance between two cities? (1 point) 200 km 200 m 200 cm 200 mm
Answer:
200km
Step-by-step explanation:
Well.. if 2 cities were 200m apart, 200 cm apart, or 200 mm apart, they would be considered one city. The only logical choice is 200km.
Answer:
a
Step-by-step explanation:
Jason wants to buy a new HD television but he thinks that if he waits, the quality of HD televisions will improve. The television he wants to buy costs $2500 now, and based on pricing trends, Jason thinks that the price will increase by 4% each year. (SHOW ALL WORK)
a. Write an exponential growth equation to represent the price y of a new HD television t years from now.
b. Use the equation to predict when a new HD television will cost $3000.
c. Jason decides to wait to buy a new television and saves his money. He puts $2200 in a savings account with 4.7% annual interest compounded continuously. Determine when the amount in his savings will exceed the cost of a new television.
the amount in Jason's savings will exceed the cost of a new television approximately 7.22 years from now.
a. The exponential growth equation to represent the price y of a new HD television t years from now is:
y = $2500[tex](1 + 0.04)^t[/tex]
where t is the number of years from now.
b. To predict when a new HD television will cost $3000, we can set y = $3000 and solve for t:
$3000 = $2500[tex](1 + 0.04)^t[/tex]
1.2 = [tex]1.04^t[/tex]
ln(1.2) = t ln(1.04)
t = ln(1.2) / ln(1.04)
t ≈ 3.97
Therefore, a new HD television will cost $3000 approximately 4 years from now.
c. To determine when the amount in Jason's savings will exceed the cost of a new television, we can use the formula for continuous compound interest:
A = [tex]Pe^(rt)[/tex]
where A is the amount in savings after t years, P is the principal amount, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate expressed as a decimal, and t is the time in years.
In this case, P = $2200, r = 0.047 (since the annual interest rate is 4.7%), and we want to find the time t when A = $2500. Plugging these values into the formula, we get:
$2500 = $2200[tex]e^(0.047t)1.13636 = e^(0.047t)[/tex]
ln(1.13636) = 0.047t
t = ln(1.13636) / 0.047
t ≈ 7.22
Therefore, the amount in Jason's savings will exceed the cost of a new television approximately 7.22 years from now.
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Problem 4.1
The table gives some sample data for two quantities, x and y, that are in a proportiona relationship. Complete the table.
Then the complete table is:
x y
14 21
64 96
26 39
What dοes the arithmetic wοrd prοpοrtiοnal mean?When the ratiοs οf the twο variables are equal, there is a prοpοrtiοnal relatiοnship. Anοther way tο view them is that they are twο variables, οne οf which is always a cοnstant value multiplied by the οther in a prοpοrtiοnate manner.
A prοpοrtiοnal relatiοnship between twο variables can be written as:
y = kx
Where k is the cοnstant οf prοpοrtiοnality.
If we lοοk at the table we can see the pair (14, 21), replacing that in the prοpοrtiοnal relatiοn we have:
21 = k*14
(21/14) = k
(3/2) = k
Then the equatiοn is:
y = (3/2)*x
Tο cοmplete the table, we need tο evaluate the οther values in the given equatiοn.
fοr x = 64 we have:
y = (3/2)*64 = 96
fοr y = 39 we have:
39 = (3/2)*x
x = (2/3)*39 = 26
Fοr x = 1 we have:
y = (3/2)*1 = 3/2
Then the complete table is:
x y
14 21
64 96
26 39
1 3/2
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The value of x + x(xx) when x = 2 is:
(a) 10, (b) 16, (c) 18, (d) 36, (e) 64
Answer:
a)10
Step-by-step explanation:
(xx)=(2×2)=4
2(4)=8
8+2=10
answer: a) 10
I REALLY REALLY REALLY NEED HELP PLS
The answer of the given question based on Statistics to find minimum monthly premium payments is option D) Plan 2, since it has lower monthly premium payments.
What is Probability?Probability is measure of likelihood or chance of an event occurring. It is expressed as number between 0 and 1, where 0 indicates an impossible event and 1 indicates certain event
Assuming that the coverage details are similar, we can compare the monthly premium payments for each plan based on the different categories of coverage:
Individual: Plan 1 has a monthly premium of $87.32, while Plan 2 has a monthly premium of $11.77. Therefore, Plan 2 has the lower monthly premium for this category of coverage.
Individual+Spouse: Plan 2 has a monthly premium of $735.00, while Plan 1 has a monthly premium of $890.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.
Individual+Child: Plan 2 has a monthly premium of $606.00, while Plan 1 has a monthly premium of $750.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.
Individual+Family: Plan 2 has a monthly premium of $1,400.00, while Plan 1 has a monthly premium of $1,600.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.
Based on these comparisons, we can see that Plan 2 has a lower monthly premium for all categories of coverage. Therefore, the answer is option D: Plan 2, since it has lower monthly premium payments.
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Draw a circle with radius 4cm.
What is the length of the diameter of the circle?
How many sectors of 90° will fit inside the circle?
Draw five radii inside your circle that are equally spaced out around the circumference. Join up the ends of the radii to create a shape inside your circle.
What is the name of the shape that you have created inside your circle?
How long are the chords that are joining the radii together?
How big is the angle of each sector?
If you did the same as above with sectors of 45°, what shape would you create inside your circle?
The length of the diameter of the circle of the radius 4 cm is 8 cm and other solutions are added below
A circle with radius 4cm.See attachment for the circle
The length of the diameter of the circleThis is calculated as
Diameter (d) = 2 * Radius (r)
So, we have
d = 2 * 4 cm
d = 8 cm
Number of sectors of 90°The number of 90° sectors that will fit inside the circle is
Sectors = (360°/90°)
Sectors = 4
Five radii inside the circle equally spacedSee attachment for the circle
The name of the shape in the circleThe shape created inside the circle by joining the ends of five equally spaced radii is a regular pentagon.
Length of the chords joining the radii togetherThe length (L) of one chord is
L = 2 × r × sin(c/2)
For 6 chords created by the 5 radii, we have
Total length = 6 × 2 × r × sin(c/2)
Where
c = 360/6 = 60
So, we have
Total length = 6 × 2 × 4 × sin(60/2)
Evaluate
Total length = 24 cm
How big is the angle of each sector?Each sector of 90° in a circle has an angle of
Angle = (360/6)°
Angle = 60°
What shape would you create inside your circle?If sectors of 45° were used, the shape created inside the circle by joining the ends of the radii would be a nonagon
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Please help will mark Brainly
For the function g, the vertex form equation is [tex]g(x) = -2(x - 5)^{2} + 9.[/tex]
What sort of equation would that be?In algebra, the idea of an equation is a logical assertion that shows the equivalence of several mathematical expressions. For instance, the equations 3x + 5 & 14, that are separated by the 'same' sign, make up the equation 3x + 5 = 14.
What about the meaning of the equation?A mathematical equation, such as 6 × 4 = 12 x 2, states that two quantities or values are equivalent. a meaningful noun. Equations are used when more than one factor has to be considered in order to fully understand or explain a situation.
Substituting the first point (7,1) into the equation for g(x), we get:
[tex]1 = a(7 - 5)^{2} + 9[/tex]
we get
[tex]-8 = 4a[/tex]
Dividing both sides by 4,
[tex]a = -2[/tex]
Now that we have found the value of a, we can write the equation for g(x) as:
[tex]g(x) = -2(x - 5)^{2} + 9[/tex]
Therefore, the equation in vertex form for the function g is [tex]g(x) = -2(x - 5)^{2} + 9[/tex].
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 In a triangle, the second angle measures two times the first. The measure of the third angle is 170° more than the measure of the second. Find the measures of the three angles
Answer: Let's call the first angle "x".
From the problem statement, we know that the second angle is two times the first, so:
Second angle = 2x
We also know that the third angle is 170° more than the second angle, so:
Third angle = Second angle + 170°
Third angle = 2x + 170°
We know that the sum of the three angles in a triangle is 180°, so we can set up an equation:
x + 2x + (2x + 170°) = 180°
Simplifying and solving for x:
5x + 170° = 180°
5x = 10°
x = 2°
So the first angle is 2°. Using this value, we can find the other two angles:
Second angle = 2x = 2(2°) = 4°
Third angle = 2x + 170° = 2(2°) + 170° = 174°
Therefore, the three angles in the triangle measure 2°, 4°, and 174°.
Step-by-step explanation:
Vanessa borrowed $5,000 at 4% simple interest and will pay after 2 years. Please help!!
a) How much will she have to pay?
b) How much interest will she pay?
Answer:
a) To calculate how much Vanessa will have to pay back after 2 years, we need to add the interest to the principal.
The interest can be calculated using the simple interest formula:
Interest = Principal x Rate x Time
where,
Principal = $5,000 (the amount borrowed)
Rate = 4% (expressed as a decimal, 0.04)
Time = 2 years
So,
Interest = $5,000 x 0.04 x 2
Interest = $400
The total amount Vanessa will have to pay back is the sum of the principal and the interest:
Total amount = Principal + Interest
Total amount = $5,000 + $400
Total amount = $5,400
Therefore, Vanessa will have to pay $5,400 after 2 years.
b) To calculate how much interest Vanessa will pay, we can use the same formula for simple interest:
Interest = Principal x Rate x Time
Plugging in the given values, we get:
Interest = $5,000 x 0.04 x 2
Interest = $400
Therefore, Vanessa will pay $400 in interest over the 2-year period.
a car travels x km in 3 hours how far will it travel in 9 hours?
Answer:
distance traveled in 1 hour = x/3
To find the distance traveled in 9 hours, we can multiply the distance traveled in 1 hour by 9:
distance traveled in 9 hours = (x/3) * 9
Simplifying this expression gives:
distance traveled in 9 hours = 3x
Therefore, the car will travel 3 times the distance it travels in 3 hours when it travels for 9 hours.
please answer the question
a.) The area covered by algae for 10 days after it was spotted would be = 35.7 m²
How to calculate the area covered by the algae after 10 days?The area covered by the algae when it was first spotted = 12.5 m²
For every week(7 days) = 2(12.5)
But 10 days = x
Make X the subject of formula;
X = 10× 2(12.5)/7
X = 250/7
X = 35.7 m²
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l-80-20l – 100 + l-100l = ???
Step-by-step explanation:
We can simplify the given expression using the rules of absolute values:
l-80-20l – 100 + l-100l
= -(20l + 80) - 100 + 100 (since |x| = -x when x is negative)
= -20l - 80
= -20(l + 4)
Therefore, the simplified expression is -20(l + 4).
Answer:
100
Step-by-step explanation:
[tex] | - 80 - 20| - 100 + | - 100| \\ = | - 100| - 100 + | - 100| \\ = 100 - 100 + | - 100| \\ = | - 100| \\ = \boxed{100}[/tex]
____________
hope it helps!
Use the given information to find the balance in the account earning compound interest after 6 years when the principal is $3500.
$r=1.26\%$r=1.26% , compounded monthly
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3500\\ r=rate\to 1.26\%\to \frac{1.26}{100}\dotfill &0.0126\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &6 \end{cases}[/tex]
[tex]A = 3500\left(1+\frac{0.0126}{12}\right)^{12\cdot 6}\implies A=3500(1.00105)^{72} \implies A \approx 3774.71[/tex]
Mateo y leo caminan para entrenar y encontrarse en un punto. Mateo camina 1/5 mas de lo que camina leo. Si entre los dos caminan 15Km, ¿ cuantos kilómetros recorre cada uno?
Answer:
Primero, podemos establecer las siguientes ecuaciones:
La suma de los kilómetros que caminan Mateo y Leo es igual a 15:
Mateo + Leo = 15
Mateo camina 1/5 más que Leo:
Mateo = Leo + 1/5Leo
Mateo = 6/5Leo
Podemos utilizar la segunda ecuación para despejar una de las variables en términos de la otra. Por ejemplo, despejando Leo:
Leo = 5/6Mateo
Luego, podemos sustituir esta expresión en la primera ecuación para obtener una ecuación con una sola variable:
Mateo + 5/6Mateo = 15
11/6Mateo = 15
Mateo = 15*6/11
Mateo = 8.18 Km
Finalmente, podemos utilizar una de las ecuaciones que relaciona a Mateo y Leo para obtener la distancia que recorre Leo:
Leo = 5/6Mateo
Leo = 5/6*8.18
Leo = 6.82 Km
Por lo tanto, Mateo recorre 8.18 Km y Leo recorre 6.82 Km.
SOMEONE PLS HELP ILL MARK BRAINLIEST
Answer:
see explanation below
Step-by-step explanation:
4. ∠A = 35, a = 8.9, find c
since side a is opposite to m∠A and c is the hypotenuse, we can use sin(∠A) = opp/hypo equation
5. sin(35) = 8.9/c
=> c = 8.9/sin(35) = 8.9/0.5736 = 15.516
6. 15.5
ASAP HELP!! I REALLY NEED HELP
Answer:
X = 18
Step-by-step explanation:
7x is the opposite angle if 3x, so 10x= 180 180÷10 = 18
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer:
f1(x) = (7 cos x - 3 sin x) tan-1 x + (7 sin x + 3 cos x) (1/(1+x^2))
Step-by-step explanation:
To find f1(x), we need to differentiate the given function f(x) with respect to x using the product rule and the chain rule. Here are the steps:
f(x) = (7 sin x + 3 cos x) tan-1 x
f1(x) = d/dx [(7 sin x + 3 cos x) tan-1 x]
= (7 cos x - 3 sin x) tan-1 x + (7 sin x + 3 cos x) (1/(1+x^2)) (d/dx)x
= (7 cos x - 3 sin x) tan-1 x + (7 sin x + 3 cos x) (1/(1+x^2))
Therefore, f1(x) = (7 cos x - 3 sin x) tan-1 x + (7 sin x + 3 cos x) (1/(1+x^2)).
Hope this helps! I'm sorry if it's wrong. If you need more help, ask me! :]
NEED HELP!!
Select which points are solutions to this inequality.
y ≥ 5x - 7
(-5, -3)
(-4, 2)
(1, -2)
(-1, 0)
(3, 0)
(4, 1)
Inequality y 5x - 7 has solutions (-5, -3), (-4, 2), and (-1, 0).
What are the three potential remedies for the inequality?In order to address an inequality • You can multiply or divide each side by the same positive amount; • You can add the same amount to each side; • You can take the same amount away from each side. If you multiply or divide each side by a negative value, the inequality sign must be reversed.
Let's examine each point individually:
(-5, -3)
y ≥ 5x - 7
-3 ≥ 5(-5) - 7
-3 ≥ -32
The inequality is true, so (-5, -3) is a solution.
(-4, 2)
y ≥ 5x - 7
2 ≥ 5(-4) - 7
2 ≥ -27
The inequality is true, so (-4, 2) is a solution.
(1, -2)
y ≥ 5x - 7
-2 ≥ 5(1) - 7
-2 ≥ -2
The inequality is not true, so (1, -2) is not a solution.
(-1, 0)
y ≥ 5x - 7
0 ≥ 5(-1) - 7
0 ≥ -12
The inequality is true, so (-1, 0) is a solution.
(3, 0)
y ≥ 5x - 7
0 ≥ 5(3) - 7
0 ≥ 8
The inequality is not true, so (3, 0) is not a solution.
(4, 1)
y ≥ 5x - 7
1 ≥ 5(4) - 7
1 ≥ 13
The inequality is not true, so (4, 1) is not a solution.
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Solve by factoring (15 points)
g²+4g-32=0
A 9=32 or 28
B 9=4 or 8
C 9=2 or -16
D 9=4 or -8
[tex]g^{2} +4g-32=0[/tex]
[tex]g^{2} + 8g - 4g - 32=0[/tex]
[tex]g(g+8)-4(g+8) = 0[/tex]
[tex](g+8)(g-4) = 0[/tex]
[tex]g+8=0 \implies \bf g = -8[/tex]
[tex]g-4=0 \implies \bf g = 4[/tex]
[tex]\implies g = 4 \ or \ -8[/tex]