solve by substitution 3x+2y=-5, 2x-5y=-16
The solution to the system of equations is [tex]\(x = -3\)[/tex] and [tex]\(y = 2\).[/tex]
let's solve the system of equations using the substitution method.
Given:
1. [tex]\(3x + 2y = -5\)[/tex]
2.[tex]\(2x - 5y = -16\)[/tex]
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve equation 1 for [tex]\(x\):[/tex]
[tex]\[3x = -2y - 5\][/tex]
[tex]\[x = \frac{-2y - 5}{3}\][/tex]
Step 2: Substitute the expression for [tex]\(x\)[/tex]from step 1 into the other equation.
Substitute [tex]\(x = \frac{-2y - 5}{3}\)[/tex] into equation 2:
[tex]\[2\left(\frac{-2y - 5}{3}\right) - 5y = -16\][/tex]
Step 3: Solve for [tex]\(y\).[/tex]
[tex]\[ \frac{-4y - 10}{3} - 5y = -16 \][/tex]
[tex]\[ -4y - 10 - 15y = -48 \][/tex]
[tex]\[ -19y - 10 = -48 \][/tex]
[tex]\[ -19y = -38 \][/tex]
[tex]\[ y = 2 \][/tex]
Step 4: Substitute the value of [tex]\(y\)[/tex] into one of the original equations to solve for [tex]\(x\).[/tex]
Let's use equation 1:
[tex]\[3x + 2(2) = -5\][/tex]
[tex]\[3x + 4 = -5\][/tex]
[tex]\[3x = -9\][/tex]
[tex]\[x = -3\][/tex]
So, the solution to the system of equations is [tex]\(x = -3\)[/tex] and [tex]\(y = 2\).[/tex]
Complete question:
solve by substitution 3x+2y=-5, 2x-5y=-16
Monica is shopping for candy for her wedding and needs lollipops and gummy bears for a display she is making for the reception. Lollipops are $1 per pound and gummy bears are $0.75 per pound. She knows she wants to spend exactly $15 on candy. If she spent $9 on lollipops, which of the following is the number of pounds of gummy bears she purchased?
6 8 9 12
We have been given that she wants to spend exactly $15 on candy.
Also, she spent $9 on lollipops. It means she spent [tex]15-9= $6[/tex] on gummy bears.
Also, we have been given that the cost of gummy bears are $0.75 per pound.
Thus, in 1$ she can purchase [tex]\frac{0.75}{6}[/tex] pounds of gummy bears.
Hence, in $6, she can purchase
[tex]\frac{1}{0.75} \times 6\\ \\ =8[/tex]
Therefore, she purchased 8 pounds of gummy bears.
what is the factored form of the expression? 4x^2-81y^2
3+4(z+5)=31 please show the correct step by step and correct answer
Use a change of variables to find the indefinite integral xe^(x^2) dx
ABCD and DECF are both squares. If AC = 28 millimeters, what is the perimeter of DECF?
A six-sided die is thrown 50 times. the numbers of occurrences of each face are shown below. face 1 2 3 4 5 6 count 12 5 9 11 6 7 can you conclude that the die is not fair?
Sandra is traveling 19 mph on her bicycle. After 2 hours, how far will she have traveled?
Hey can you please help me posted picture of question
The function f(x)=2^x and g(x)=f(x)+k.If k=-5,what can be concluded about the graph of g(x)?
the graph of g(x) is shifted horizontally
a.5 units to the left of the graph of f(x)
b. 5 units to the right of the graph of f(x)
c.the graph is not shifted horizontally from the graph of f(x)
The graph of g(x) will be the same as the graph of f(x) shifted vertically downwards by 5 units because k=-5 represents a vertical shift, not a horizontal one. There is no horizontal shift involved.
When considering the functions [tex]f(x)=2^x[/tex]and g(x)=f(x)+k, with k=-5, we look at how the graph of g(x) compares to the graph of f(x).
Since the value of k is negative, it implies that a constant is being subtracted from the function f(x). This means that the graph of g(x) will not be shifted horizontally, but rather vertically downwards by 5 units.
Therefore, option c is the correct answer: the graph is not shifted horizontally from the graph of f(x).
Use the X method to find the solutions of 6x2 + 2x – 20 = 0. x = x =
The solutions of the given quadratic equations is 5/3 and -2
Given the quadratic function expressed as:
6x^2 + 2x – 20 = 0Factorizing the function we will have:
6x^2 + 2x – 20 = 0
3x^2 + x - 10 = 0
3x^2 +6x - 5x - 10 = 0
3x(x+2) 5(x+2) = 0
Group the function;
(3x-5)(x+2) = 0
Find the factors
3x- 5 = 0 and x + 2 = 0
x = 5/3 and -2
The solutions of the given quadratic equations is 5/3 and -2
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A person whose eye level is 1.5 meters above the ground is standing 75 meters from the base of the jin mao building in shanghai, china. the person estimates the angle of elevation to the top of the building is about 80º. what is the approximate height of the building
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The height of the building from the ground is 426.85 meters.
What is Tangent (Tanθ)?The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
As it is given that the angle of elevation from the person's view is 80°, while the distance between the person and the base of the building is 75 meters, therefore, using the trigonometric function the height of the building top from the person eye level is,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}\\\\\\Tan(80^o) = \dfrac{\text{Height of the building}}{75\ meters}\\\\\\\text{Height of the building} = 75 \times tan(80^o) = 425.35\ meters[/tex]
Now, we know the height of the building top from a person's eye level, and we also know the person's eye level as well, therefore, the height of the building can be written as,
[tex]\text{Height of the building} = 425.35 + 1.5 = 426.85\rm\ meters[/tex]
Hence, the height of the building from the ground is 426.85 meters.
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Cameroon corp. manufactures and sells electric staplers for $15.90 each. if 10,000 units were sold in december, and management forecasts 5% growth in sales each month, the dollar amount of electric stapler sales budgeted for february should be:
2 blue shirts
1 white shirt
1 red shirt
2 black slacks
1 white pair of pants
1 pair of jeans
1 pair of sandals
2 pairs of running shoes
Alex is on vacation and has the clothes listed above with her. She is trying to pick out an outfit. What is the probability she chooses a red shirt and a pair of jeans?
A) 0.01 B) 0.06 C) 0.08 D) 0.5
Determine whether the two figures are similar. If so, give the similarity ratio of the smaller figure to the larger figure. The figures are not drawn to scale
A. yes; 1:1:2
B. yes; 1:1:4
C. yes; 1:2:4
D. no
5% of all widgets are defective. there is a 30% chance that a widget was produced at the foo factory. if a widget was produced at the foo factory, then there is a 4% chance that the widget is defective.
a.) what is the probability that a widget was produced at the foo factory AND is defective?
b.) are "produced at the foo factory" and "defective" independent events? justify.
What is the domain of the function?
The domain of the function is (-∞, ∞).
Definition of function
A function is an expression that shows the relationship between variables as well as numbers.
The domain of a function is the set of all possible inputs for the function.
From the graph, the domain is the set of all x values, hence:
Domain = (-∞, ∞)
The domain of the function is (-∞, ∞).
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Adam charges 20$ to mow his neighbor's lawn every 2 weeks for the 18 weeks of grass growing season. he wants to but a new
Since Adam's expenses exceed his earnings, he will have a negative net earnings. Therefore, Adam will not earn any money this season. In fact, he will have a net loss of $7.50.
To calculate how much Adam will earn this season, subtract his expenses from his total earnings.
Earnings per mowing session: $20
Number of mowing sessions in the grass-growing season: 18 weeks / 2 weeks = 9 sessions
Total earnings: $20 per session * 9 sessions = $180
Expenses:
Cost of the lawn mower: $165
Cost of gasoline per session: $2.50 per session * 9 sessions = $22.50
Total expenses: $165 + $22.50 = $187.50
To find Adam's net earnings, subtract his expenses from his total earnings:
Net earnings = Total earnings - Total expenses
Net earnings = $180 - $187.50
Net earnings = -$7.50
Since Adam's expenses exceed his earnings, he will have a negative net earnings. Therefore, Adam will not earn any money this season. In fact, he will have a net loss of $7.50.
Adam charges $20 to mow his neighbors lawn every 2 weeks for the 18 weeks of grass-growing season. He wants to buy a nice lawn mower for $165 and gasoline costs $2.50 every 2 weeks. How much will Adam earn this season?
Kite ABCD represents a softball field that is being built. If AC = 48 meters, what is the perimeter of the field? 40 meters 70 meters 140 meters 218 meters
Answer:
140 m
Step-by-step explanation:
A kite is a quadrilateral with two distinct pairs of adjacent sides that are equal in length.
The perimeter of the kite is the sum of the length of all its sides. So, the perimeter of kite ABCD can be expressed as:
[tex]\sf Perimeter = AB + BC + CD + DA[/tex]
As BC = AB and CD = DA, then:
[tex]\sf Perimeter = BC + BC + CD + CD\\\\Perimeter = 2(BC + CD)[/tex]
Therefore, to find the perimeter of kite ABCD, we need to determine the lengths of sides BC and CD.
The diagonals of a kite intersect to form two pairs of congruent right triangles, where the sides of the kite are the hypotenuses of these triangles.
in kite ABCD:
Diagonal AC = 48 mDiagonal BD = 18 + 32 = 50 mThe longer diagonal of a kite always bisects the shorter diagonal at a right angle.
Let M be the point of intersection of the diagonals. Therefore:
AM = MC = 24 m
Side BC is the hypotenuse of right triangle BMC, with legs measuring 18 m and 24 m, while side CD is the hypotenuse of right triangle CMD, with legs measuring 32 m and 24 m.
To find the lengths of sides BC and CD, we can use the Pythagorean Theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the two legs.
[tex]\sf BC^2=18^2+24^2 \\\\BC^2=324+576 \\\\BC^2=900\\\\BC=\sqrt{900}\\\\BC=30\; m[/tex]
[tex]\sf CD^2=32^2+24^2 \\\\CD^2=1024+576 \\\\CD^2=1600\\\\CD=\sqrt{1600}\\\\CD=40\; m[/tex]
Now we have determined the length of sides BC and CD, we can substitute them into the perimeter formula:
[tex]\sf Perimeter = 2(30+40) \\\\ Perimeter = 2(70) \\\\ Perimeter = 140 \; m[/tex]
Therefore, the perimeter of kite ABCD is:
[tex]\LARGE\boxed{\boxed{\sf 140\; m}}[/tex]
What is the following product of sqrt 10 times sqrt 10
Whenever we have been given to find the product of two square roots, the two roots cancel out each other. This is because [tex] (\sqrt{number} )^2 = number [/tex]
The power of two and the square root cancel out each other
In the given problem we have to multiply the square root 10 by itself, we have
[tex] \sqrt{10} * \sqrt{10} [/tex]
Now, the next step will be
[tex] (\sqrt{10})^2 [/tex]
Now the square root and the power of 2 cancel each other an d the result will be 10
Answer : 10
how do u simplify this?
4r-3+6s-8r-(4s-6)
A metal rod is 38 meters long. It will be cut into pieces that are each 148
meters long. How many pieces will be made from the rod?
15 points!!! GEOMETRY help please!!
Questions attached!
he walks 200m west and 125m north how far away is he from his starting point
A tennis player lands 25 out of 40 first serves in bounds for a success rate of 62.5%. How many more consecutive first serves must she land in bounds to increase her success rate to 70%.
The tennis player must consecutively land 10 more first serves in bounds to raise their success rate from 62.5% to 70%.
First, let's define the variables:
x = number of additional successful serves needed
40 + x = total number of serves after additional successful serves
25 + x = total number of successful serves after additional successful serves
We set up the equation with the desired success rate of 70%:
(25 + x) / (40 + x) = 0.70
To solve this equation, follow these steps:
Multiply both sides by (40 + x):
25 + x = 0.70 * (40 + x)
Distribute 0.70 on the right side:
25 + x = 28 + 0.70x
Isolate the variable x by subtracting 0.70x from both sides:
25 + x - 0.70x = 28
Combine like terms:
0.30x = 3
Solve for x by dividing both sides by 0.30:
x = 10
Thus, the tennis player must land 10 more consecutive first serves in bounds to increase her success rate to 70%.
I really really need help with this please.
simplify the expression
What is the greatest possible error when measuring to the nearest quarter of an inch? 1/8 in. 1/4 in. 1/2 in.
The greatest possible error when measuring to the nearest quarter of an inch is:
1/8 in.
What is the greatest possible error when measuring to the nearest quarter of an inch?Error in measurement is the difference between the measured value of a quantity and its true value. It is an inevitable part of any measurement, and there are many different sources of error.
The greatest possible error when measuring to the nearest quarter of an inch is 1/8 of an inch.
This is because the smallest measurement interval is 1/4 of an inch, and the greatest possible error is half of the smallest measurement interval.
Therefore, the greatest possible error when measuring to the nearest quarter of an inch is 1/8 in.
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Two corresponding side of similar pentagons are 12 cm and 28 cm.
what is the ratio of the areas of the pentagons?
A. 12/28
B. 27/343
C. 9/49
1.
The balance on Brent Tyson’s Discover card on December 1 is $205.84.
In December, he charges an additional $98.42 of purchases, has returns of $18.63, and makes a payment of $25.
If the finance charges are calculated at 1.5% per month on the unpaid balance, find the new balance on January 1.
To find the new balance on January 1, we need to calculate the total balance after considering purchases, returns, payments, and finance charges.
Calculate the total charges:
Total charges = Previous balance + New purchases − Returns
Total charges = $205.84 + $98.42 − $18.63
Total charges = $285.63
After the payment, ascertain the extra amount due:
Unpaid balance = Total charges − Payment
Unpaid balance = $285.63 − $25
Unpaid balance = $260.63
Calculate the finance charges:
Finance charges=Unpaid balance×Monthly interest rate
Monthly interest rate = 1.5% = 0.015
Finance charges = $260.63 × 0.015
Finance charges ≈ $3.91
Calculate the new balance:
New balance = Unpaid balance + Finance charges
New balance = $260.63 + $3.91
New balance = $264.54
So, the new balance on January 1 is approximately $264.54.
To calculate Brent Tyson's new balance on January 1, we first determine the total charges by adding new purchases and subtracting returns from the previous balance.
Then, we deduct his payment to find the unpaid balance.
Next, we calculate finance charges at a rate of 1.5% per month on the unpaid balance.
Finally, we add the finance charges to the unpaid balance to get the new balance.
After these steps, Brent Tyson's new balance on January 1 is $264.54.
This process ensures we account for all transactions and interest charges to accurately determine the updated balance on his Discover card.
Complete Question:
The balance on Brent Tyson’s Discover card on December 1 is $205.84.
In December, he charges an additional $98.42 of purchases, has returns of $18.63, and makes a payment of $25.
If the finance charges are calculated at 1.5% per month on the unpaid balance, find the new balance on January 1.