Answer:
Step-by-step explanation:
To solve the system of equations 2y + 5x = 13 and 2y-3x = 5 using the substitution method, you can follow these steps:
Begin by solving one of the equations for one of the variables. For example, you could solve the first equation for y:
2y + 5x = 13
2y = 13 - 5x
y = (13 - 5x) / 2
Substitute the expression for y into the second equation and solve for x:
2((13 - 5x) / 2) - 3x = 5
13 - 5x - 3x = 5
-8x = -8
x = 1
Substitute the value of x into the expression for y to find the value of y:
y = (13 - 5(1)) / 2
y = (13 - 5) / 2
y = 8 / 2
y = 4
The solution to the system of equations is (1,4).
Therefore, the correct ordered pair is (1,4).
a triangle undergoes a dilation with a scale factor of 7/10. the resulting triangle is _[blank]_ the original triangle.
The resulting triangle is 7/10 the original triangle.
How triangle dilated with scale factor?The focuses in the direction planes are A(0, 2), B(2, 1), C(- 2, - 2). In the event that the scale factor is 2, each direction point of the first triangle is duplicated by the scale factor 2. Subsequently, the expanded triangle will be A'B'C' and the direction focuses got are A'(0, 4), B'(4, 2), C'(- 4, - 4).
According to question:Let we have a triangle ABC,If this triangle undergoes a dilation with a scale factor of 7/10,
Then changed triangle is A'B'C'
So, relation between them is A'B'C' = 7/10(ABC)
Thus, the resulting triangle is 9/5 multiple of triangle ABC.
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Recall that two angles are complementary if the sum of their measures is 90°. Find the measures of two complementary angles if one angle is 15º more than two times the other angle. What does the smaller angle measure? What does the bigger one measure?
Answer:
smaller = 25, bigger = 65
Step-by-step explanation:
x = smaller
y = bigger
2x + 15 + x = 90
3x + 15 = 90
3x = 75
x = 25
y + x = 90
y + 25 = 90
y = 65
You receive paychecks every two weeks. Your first paycheck is for $217. The second is for $258. The third is for $229. What is the combined value of these three paychecks?
Answer:
The combined value is $704
If you want the average pay as well it is about $235
Step-by-step explanation:
The problem asks for the combined value of the three paychecks. So all you have to do is add them to get 704.
I found the average value by adding them to 704 then dividing it by 3. The 3 came from the amount of values we have which is 3 paychecks. So we divide the total cost by 3 to get 235.
6. Which is equivalent to the following expression?
(3p² +5pq-q²) + (p² +3pq-2q
2
9²)
O3p² +8pq-3q²
O4p² +8pq+q²
O4p4 +8pq-3q
O4p²+8pq-3q²
(1 point)
Answer:
Step-by-step explanation:
5
What is the density of a pumpkin with a mass of 2.0 kg and a volume of 0.0060 m3 ? 330 kg/m3 0.003 kg/m3 0.012 kg/m3 1200 kg/m3
The density of a pumpkin with a mass of 2.0 kg and a volume of 0.0060m³ is 0.003 kg / m³.
What is the density?Density of the matter means space taken by matter.
To find the density, density = mass of matter / volume of mass.
Given that mass of the pumpkin 2.0 kg and a volume of 0.0060 m³.
Now the density from the formula;
Density = mass of pumpkin / volume of pumpkin
Density = 2.0 / 0.0060
Multiply by 10000,
Density = 20000 / 60
Density = 2000 / 6
Density = 1000 / 3
Density = 0.003 kg / m³
Therefore, the density of a pumpkin with a mass of 2.0 kg and a volume of 0.0060m³ is 0.003 kg / m³
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A toy jeep i 12 and 1/2 inche long while an actual jeep meaure 18 3/ 4 feet long what i the value of the ratio length of the toy jeep to the length of the actual Jeep what doe thi ratio mean in the ituation?
Therefore the solution of this question is ratio length = every 1 inch of toy car represents 1.5 feet of actual car
What is ratio?In mathematics, a ratio shows how two numbers are multiplied together. In a bowl of fruit, for instance, the proportion of oranges to lemons is eight to six if there are eight oranges and six lemons. Lemons to oranges are divided 6:8 and oranges to all other fruits are divided 8:14 in a similar fashion.
Here,
A toy Jeep measures 12 1/2 inches.
Before calculating the ratio, let's first convert each size into the same unit of measure and decimal points:
=>12 ½ = 25/2
=> 12.5 inches;
=> 18 ¾ = 75/4
=> 18.75 feet .
The actual length of a jeep is 18.75 feet.
The ratio can now be determined by converting feet to inches.
1 inch of a toy car equals 1.5 feet of an actual car because
=> 1 foot = 12 inches
=> 12.5 inches : 225 inches
=> 225 / 12.5
=> 18 inches
Therefore, every 1 inch of toy car represents 1.5 feet of actual car.
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A group of friends collected toys to donate to children in need. After sorting the toys into
boxes, they found they had 6/7 of a box of stuffed animals, 5/7 of a box of board games, and
1/7 of a box of dolls. In total, how many boxes of toys did the friends collect?
Answer: 12/7
Step-by-step explanation: The answer is 12/7 because here is what we know: A group of friends collected toys to donate to children in need. After sorting the toys into boxes, that's what we know, we also know that they found they had 6/7 of a box of stuffed animals, and we also know that they found 5/7 of a box of board games and
1/7 of a box of doll. What they want to know is In total, how many boxes of toys did the friends collect? so you take 6/7 from the box stuffed animals they found + 5/7 from the box of board games they found which equals 11/7 then you add the 11/7 with the 1/7 the box of dolls they found. In total the friends collect 12/7 boxes. Hope this helps!
extended Response
1. The weights of grapefruits, 0, of a certain variety are approximately Normally
distributed with a mean of 1 pound and a standard deviation of 0.12 pounds.
a. Let 7-36. Find the mean and standard deviation of 7.
b. Let R= G+G+G. Find the mean and standard deviation of R.
c. Let Q=T-R. Find the mean and standard deviation of Q.
The mean weight of 7 grapefruits will be 7 pounds and the standard deviation will be 0.84 pounds.
The mean weight of R will be 3 pounds and the standard deviation will be 0.36 pounds.
The mean weight of Q will be 4 pounds and the standard deviation will be 0.48 pounds.
What is the mean and standard deviation?a. The mean and standard deviation of 7 grapefruits will be 7 times the mean and standard deviation of a single grapefruit, respectively.
b. If G represents the weight of a single grapefruit, then
R = G + G + G
= 3G.
The mean and standard deviation of R will therefore be 3 times the mean and standard deviation of a single grapefruit, respectively.
c. If T represents the total weight of all 7 grapefruits, then
Q = T - R
= 7G - 3G
= 4G.
The mean and standard deviation of Q will be 4 times the mean and standard deviation of a single grapefruit, respectively.
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a certain test is worth 135 points. how many points (rounded to the nearest point) are needed to obtain a score of 85%?
To obtain a score of 85% on a test worth 135 points, one needs to get 115 points. By using proportions, we get the required value.
How to write proportions?A proportion is defined as an equality between two ratios.
Consider two ratios a:b and c:d. Then, the proportion we can write,
a: b = c : d
Then, the simplification we have for this proportion is
a/b = c/d or ad = bc
Calculation:It is given that, a certain test is worth 135 points.
One to get 85% on this test, he/she needs to get X number of points.
So, we can write the proportions as
X : 135 = 85 : 100
⇒ X/135 = 85/100
⇒ X = 85/100 × 135
∴ X = 114.75 ≅ 115 points
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The low temperature on Saturday was 10 degrees below zero degrees Celsius. On Sunday, the low temperature was 30 degrees
warmer.
Which two statements apply to the low temperature on Sunday?
A Temperature on Sunday was 40°C.
B
C
Temperature on Sunday was 20°C.
The temperature on Sunday was 20 degrees below zero degrees Celsius.
The temperature on Sunday was zero degrees Celsius.
L
E
The temperature on Sunday was 20° C
Wes made 8 cups of fresh peanut butter and divided equally among 6 jars.- How much
peanut butter went in each container?
Answer:
Step-by-step explanation:
1 1/3 cups peanut butter
proof:
1 1/3 +1 1/3+1 1/3+1 1/3+1 1/3+1 1/3 = 8 cups
find the coordinate of the midpoint of a segment with the given endpoints T(-5,4) and D(7,2)
Answer: (-1, 3)
Step-by-step explanation:
Midpoint formula: ((x1 + x2) / 2, (y1+y2) / 2)
((-5+7)/2, (4+2) / 2))
((-2/2), (6/2))
(-1, 3)
PLEASE ANSWER FAST y-1/6=15/18
Ira ran out of time while taking a multiple-choice test and plans to guess on the last 666 questions. Each question has 444 possible choices, one of which is correct. Let x=x=x, equals the number of answers ira correctly guesses in the last 666 questions. What is the probability that he answers fewer than 222 questions correctly in the last 666 questions?.
It is possible to calculate the probability that in the last 6 questions, there were fewer than 2 right answers, which is 53.392%.
What is Probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.
The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
In order to better grasp probability, let's look at a straightforward application.
Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.
There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.
According to our question-
The likelihood that responses to fewer than two of the final six questions were right can be calculated using the procedure below:
There are 6 questions with a total of 4 possible answers, hence the value of p is:
The following formula provides the probability:
The following formula is used to calculate the likelihood that Ira would properly answer exactly 1 of the final 6 questions:
P(X = 1) = 0.35595
P(X = 0) = 0.17797 gives the likelihood that Ira will correctly answer 0 out of the final 6 questions.
Accordingly, the likelihood that the last 6 questions' answers contain fewer than 2 valid responses is: P = 0.17797 + 0.35595.
P = 0.53392
P = 53.392%
Hence, the probability that in the last 6 questions, there were fewer than 2 right answers, which is 53.392%.
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write each equation in point slope form.
y+5=-6(x+7)
and y+2 =1/6(x-4)
The equation of line in slope-intercept form is,
a.) y = -6x - 47
b.) y = x/6 - 8/3
What is Equation of line ?
A straight line's general equation is y = mx + b, where m denotes the gradient and y = b denotes the point at which the line crosses the y-axis. On the y-axis, this value b is referred to as the intercept.
We know, slope-intercept form is
y = mx + b
The given equation is in point slope form,
a.) y + 5 = -6 (x + 7)
b.) y + 2 = 1/6 (x-4)
Now, let's write each equation in slope-intercept form,
a.) y + 5 = -6 (x + 7)
y + 5 = -6x - 42
y = -6x - 42 - 5
y = -6x - 47 [which is slope-intercept form]
b.) y + 2 = 1/6 (x-4)
y + 2 = 1/6 * x - 1/6 * 4
y + 2 = x/6 - 2/3
y = x/6 - 2/3 - 2
y = x/6 - [2/3 + 2]
y = x/6 - [(2 + 6) / 3 ]
y = x/6 - 8/3 [which is slope-intercept form]
Hence, the equation of line in slope-intercept form is y = -6x - 47 and y = x/6 - 8/3
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Solve each system by elimination: 3x-8y=13 4x-5y=6
Answer:
Your answer is [tex]x = -1[/tex] and [tex]y = -2[/tex]
Step-by-step explanation:
(attached)
Divide (25)1,658.To find the quotient, start by dividinginto____.
On dividing 1658 by 25 , the quotient is equal to 66.32.
As given in the question,
Dividend is equal to 1,658
Divisor is equal to 25
Unit place value of 1658 is equal to 8.
25 is not a factor of 1658
Smallest number to 1658 divisible by 25 is 1650
Divide 1658 by 25 we get remainder
Dividend = ( Divisor × quotient) + remainder
1658 = 1650 + 8
= ( 25 × 66 ) + 8
Remainder is equal to 8
Quotient is equal to 66
In decimal form
1658 ÷ 25
= 66.32 is quotient.
Therefore, the quotient of dividing 1658 by 25 is equal to 66.32.
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Answer:
check this one
Step-by-step explanation:
this is the answer
how to determine the intercepts of the line with -5x+9y=-18
Answer:
-5x+9y=-18
Dividing both sides by -18
-5x/-18+9y/-18=-18/-18
5x/18-y/2=1
x/(18/5)-y/2=1. eqn(i)
eqn (i) is comparing with x/a+y/b=1, we get
x - intercept (a) =18/5
y-intercept (b) = -2
function rule to find f(9).
1
substitute 9 as x because 9 is in the brackets
then follow bidmas
brackets first so -10 + 9 = -1
now indices so square -1 which is 1.
therefore you answer is 1
Question regarding Modulus attached below.
Answer:
x=4/3, 8/3
Step-by-step explanation:
We will solve this in two steps, one where the right hand side is 2, one where it is -2. This is because the equation is satisfied either way when [tex]|6-3x|[/tex] is equal to either of those values.
Let's start with 2. We have [tex]6-3x=2[/tex]. Subtracting 6 from both sides and then dividing by 3 gives us that x = 4/3. This is the first value.
Now, we solve for when it equals -2. We have [tex]6-3x=-2[/tex]. Subtracting 6 from both sides and then dividing by 3 gives us that x = 8/3. This is the second value.
Feel free to contact me with any questions about my answer. I hope this helps!
Point C is the midpoint of line segment AB and point B is between points A and D. If AD = 20 and BD =12 then what is CD?
Answer:
16
Step-by-step explanation:
AB = 20 - 12 = 8
BC = 8 : 2 = 4
CD = 4 + 12 = 16
Answer:
CD = 16
Step-by-step explanation:
Check the image for the steps
Here are the ingredients needed to make 8 pancakes.
James makes 24 pancakes.
Pancakes
Ingredients to make 8 pancakes
250 ml milk
1 egg
140 g flour
5 g butter
a) Work out how much milk he needs.
Using proportions, James need 750ml for 24 pancakes
ProportionProportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
To find the amount of milk James need, we need to use proportions.
8 pancakes = 250ml milk
24 pancakes = x
cross multiply both side and make x the subject of formula
8 × x = 24 × 250
8x = 6000
Divide both sides by coefficient of x
8x / 8 = 6000 / 8
x = 750
He needs 750 ml of milk
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PLEASE HELP HURRY!!!!
On solving the provided question, we got by the help of Slope formula - [tex]= 5x - y + 5 = 0[/tex]
What is Slope?A line's slope can be calculated as the ratio of how much y rises when x rises by a specific amount. A line's slope, or how much y increases as x increases, is indicated by the word "slope." Along the straight line, the slope is constant (equal) everywhere.
From the figure we got that,
X1 = 0, Y1 = 5
X2 = -1, Y2 = 0
(0,5) and (-1,0)
By the of slope formula
[tex]\frac{y - y1}{x - x1} = (\frac{y2 - y2}{x2 - x1} )(\frac{x - x1}{y - y1} )[/tex]
[tex]{y - 5} = (\frac{0-5}{-1-0} )({x - 0 )\\\\\\[/tex]
[tex]= > 5x - y + 5 = 0[/tex]
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8. Critique Reasoning Franco made this graph to
show the equation y=-x. Is the graph correct?
Explain.
Answer:
No
Step-by-step explanation:
The graph should be a line with negative slope, but the given graph is of a line with positive slope
Two trains, each moving at 20 miles per hour towards each other, are initially 60 miles apart. A bee starts at the front of one train, flies to the other train, then back to the first train, and so on. If the bee always flies at 30 miles per hour, how far does the bee fly before the trains collide? Hint: For how long does the bee fly?
Answer:
45
Step-by-step explanation:
The diameter of a circle is 11 cm. Find its area to the nearest tenth.
The area of the given circle is 95 cm².
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle.
In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
So, we know that the diameter of the circle is 11 cm.
Radius = Diameter/2
11/2
5.5 cm
Area of circle: πr²
3.14(5.5)²
3.14*30.25
94.985
Rounding off: 95 cm²
Therefore, the area of the given circle is 95 cm².
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An animal shelter currently only has 30 dogs and 20 cats. What is the ratio of cats to animals?
Answer:
20:50 or 2:5
Step-by-step explanation:
30 dogs
20 cats
50 total animals
Part to whole relationship:
20:50
rewrite 27 1/3 using roots
The value of the exponent illustrated as 27^1/3 is 3.
How to illustrate the exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
In this situation, it should be noted that 27^1/3 simply means the cube root of 27. This will give a value of 3.
Check: 3 × 3 × 3 = 27.
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can someone please explain this 4x[tex](4x^{2} -5x)- (4x^{2} -4x-8)[/tex]
the answer is -x+8 but I don't get why its +8 and not -8
Your first step of simplifying is to distribute the "–" or "–1" in front of the second set of parentheses through that second set of parentheses. The –1 must be distributed to every term in the second set:
[tex]\begin{aligned}(4x^2-5x)-(4x^2-4x-8)&=(4x^2-5x)\boldsymbol{{}-1}(4x^2-4x-8)\\[0.5em]&=4x^2-5x\boldsymbol{{}-1(4x^2)-1(-4x)-1(-8)}\\[0.5em]&=4x^2-5x\boldsymbol{{}-4x^2+4x+8}\\[0.5em]&=-x+8\\\end{aligned}[/tex]
That's what changes the sign on every term in the second set of parentheses, making that –8 become +8.
Find the x-intercept of the line 5x + 17y = -25
x - intercept =
Find the y-intercept of the line 6x - 7y = -21
y - intercept =
Answer: To find the x-intercept of a line, we set y equal to 0 and solve for x. To find the y-intercept of a line, we set x equal to 0 and solve for y.
For the line 5x + 17y = -25, we set y equal to 0 to find the x-intercept:
0 + 17y = -25
17y = -25
y = -25/17
Since we set y equal to 0, the x-intercept is (0, 0).
For the line 6x - 7y = -21, we set x equal to 0 to find the y-intercept:
6x - 7y = -21
-7y = -21
y = 21/7
Since we set x equal to 0, the y-intercept is (0, 21/7).
Therefore, the x-intercept of the line 5x + 17y = -25 is (0, 0) and the y-intercept of the line 6x - 7y = -21 is (0, 21/7).