Answer:
[tex]x=-\frac{39}{2}\\ y=51[/tex]
Step-by-step explanation:
[tex]8x+4y=48\\12x+5y=21[/tex]
Let's solve the first equation for x or y. I'll do it for y.
[tex]8x+4y=48[/tex]
Subtract 8x
[tex]4y=-8x+48[/tex]
Divide by 4.
[tex]y=-\frac{8}{4}x+\frac{48}{4}\\[/tex]
Simplify.
[tex]y=-2x+12[/tex]
Now replace the value of y in the second equation for this.
[tex]12x+5y=21\\12x+5(-2x+12)=21[/tex]
Distribute 5
[tex]12x-10x+60=21[/tex]
Subtract 60
[tex]12x-10x=21-60[/tex]
Combine like terms;
[tex]2x=-39[/tex]
Divide by 2.
[tex]x=-\frac{39}{2}[/tex]
Now replace this in any of the equations to find the value of y.
[tex]8x+4y=48\\8(-\frac{39}{2})+4y=48\\[/tex]
8 and 2 can be simplified.
8/2=4
2/2=1
[tex]4(-39)+4y=48[/tex]
Distribute 4.
[tex]-156+4y=48[/tex]
Add 156
[tex]4y=48+156\\4y=204[/tex]
Divide by 4
[tex]y=\frac{204}{4}[/tex]
[tex]y=51[/tex]
Proof:
[tex]8x+4y=48\\8(-\frac{39}{2} )+4(51)=48\\4(-39)+204=48\\-156+204=48\\48=48[/tex]
What is the distance between the points (3, 7) and (15, 16) on a coordinate
plane?
A. 13 units
B. 21 units
C. 17 units
D. 15 units
Answer:15
Step-by-step explanation:
Because you do the distance equation
Tanya has a garden with a trench around it. The garden is a rectangle with length 212m2 \dfrac12 \text{m} 2 2 1 m 2, start fraction, 1, divided by, 2, end fraction, start text, m, end text and width 2 m2 \text{ m} 2 m 2, start text, space, m, end text . The trench and garden together make a rectangle with length 312m3 \dfrac12 \text{m} 3 2 1 m 3, start fraction, 1, divided by, 2, end fraction, start text, m, end text and width 3 m3 \text{ m} 3 m 3, start text, space, m, end text . Find the area of just the trench.
Answer:
[tex]9 \dfrac12 m^2[/tex]
Step-by-step explanation:
Tanya has a garden with a trench around it.
Tanya's garden is a rectangle with length [tex]\dfrac12 \text{m}[/tex] and width 2m.
The trench and garden together make a rectangle with length [tex]3 \dfrac12 \text{m}[/tex] and width 3m.
We are to determine the area of just the trench.
Area of just the trench = Area of the trench and garden together-Area of the garden
[tex]=(3 \dfrac12 X 3)-(\dfrac12 X 2)\\\\=( \dfrac72 X 3)-1\\\\=\dfrac{21}{2}-1\\\\=9 \dfrac12 m^2[/tex]
The area of the trench is [tex]9 \dfrac12 m^2[/tex]
Julie conducts an experiment to find the average word length in a book for a 4th grader and a book for a 8th grader. She finds that for the fourth grade book the mean word length is 5 letters with a range of 6 and for the 8th grade book the mean word length is 6 letters with a range of 9. Which statement is true?
A) On average, the book for the 4th grader has longer words.
B) There is not enough information to know if any of the above are true.
C) The word length varies more in the 8th grade book than the 4th grade book.
D) The longest word in the book for the 4th grader is longer than that in the 8th grade book.
Answer: C
Step-by-step explanation: I chose this answer because in 8th graders, their mean is 6 and their range is 9, that’s a difference of 3. But in 4th graders, their mean is 5 and their range is 6, so there isn’t much of a difference for 4th graders. The answer couldn’t be A, B, or D so I came to the conclusion that it’s C. (Sorry if this explanation doesn’t make sense but I hope I got the right answer.)
The true statement is the word length varies more in the 8th grade book than the 4th grade book.
Mean is a measure of central tendency. It is the average of a set of values. For example, if the numbers in a data set are 3,2,10, the mean is (3 + 2 + 10) /3 = 5
Range is the highest number less the least number in a data set. For example, if the numbers in a data set are 3,2,10, the range is 10 - 2 = 7
The mean word length for the fourth grade book is 5. While, the mean word length for the eighth grade book is 6. This means that on average, the average word length of the eighth grade book is greater than the mean word length for the fourth grade book
The range word length for the fourth grade book is 6. While, the range word length for the eighth grade book is 9. These means that either the longest word in the eighth grade book is more than that of the fourth grade book or that the smallest word in the eighth grade book is less than than that in the fourth grade book. This means that the word length varies more in the 8th grade book than the 4th grade book.
To learn more about mean, please check: https://brainly.com/question/12528427?referrer=searchResults
Which expression is equivalent to 64 − 9x2?
Answer:
it is just 64-18=48
Step-by-step explanation:
you have to just keep 64 the same and do the 9*2. And sum those outcomes.
pls help me thanks :)
Answer:
2+2 is 4 quick math
Step-by-step explanation:
select the appropriate formula for the surface area of the given figure
Answer:
The answer is A
Step-by-step explanation:
This figure is a cylinder and the surface area formula of a cylinder is 2 pi rh + 2pi r^2
A standard deck of playing cards has 13 cards in each of four suits: hearts, clubs, diamonds, and spades. Two cards are chosen from the deck at random. What is the probability of choosing one club and one spade?
Answer:
Probability of choosing one club and one spade = 0.6025
Step-by-step explanation:
Total number of cards= 52 cards
For the first event
Probability of choosing a club
Toatal club = 13 cards
Probability of choosing a club
= 13/52
Probability of choosing a club
= 1/4
Probability of choosing a club
=0.25
For the second event
Probability of choosing a spade
Toatal spade = 13 cards
Probability of choosing a spade
= 13/52
Probability of choosing spadep
= 1/4
Probability of choosing a spade = 0.25
Probability of both = 0.25*0.25
Probability of both = 0.6025
Answer:
D. 0.1275
Step-by-step explanation:
Justo took the Pre-Test on Edg (2020-2021)!!
find the area of the smaller sector. please help last question.
Answer:
The area of smaller sector is:
S = pi x 8^2 x 80/360 = 44.68 m2
Hope this helps!
:)
Can u pls awnser the following :(
Answer:
25% is .25
75% is .75
20% is .2
100% is 1
37.5% is .375
62.5% is .625
87.5% is .875
12.5% is .125
Step-by-step explanation:
Remember DeeP
D. __. ____ P
Decimal. Percent
You move over two decimal places to the left if you want to convert 35%, which is .35.
You move over two decimal places to the right if you want to convert .45 which is 45%.
A rectangular prism has a length 4 1/4 in., a width of 3 in., and height of 1 1/4 in.
which expressions can be used to find the volume of the prism.
Select EACH correct answer.
A.) 1 1/4 (3+4 1/4 )
B.) 4 1/4 times 3 times 1 1/4
C.) 12 3/4 times 1 1/4
D.) 1/2 (12 3/4 times 1 /14)
PLEASE HELP ALL 25 OF MY POINTS
Answer:
B, C.
Step-by-step explanation:
B, because you're multiplying them all, which is what you would do in the normal formula. You would get 255/16, or 15.9375.
C, since you would also get 255/16.
Please tell me if im wrong! im only a student .m.
Mal is putting money into a savings account. She starts with $350 in the savings account, and each week she adds $30.
Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Mal has been adding money. Write an
equation relating S to W. Then use this equation to find the total amount of money in the savings account after 19 weeks.
Answer:
Mal starts with 350 dollar
Each week she adds $30.
W is number of weeks Mal adds money.
S is total amount of money in her account.
=> S =30W + 350
After W = 19 weeks, Mal will have 30 x 19 + 350 = 920 dollar
{(0, 2), (3, 3), (8, 7), (2, 2), (3,9) }
What is the domain and range for each set of ordered pairs
Hey!!!
Here's your answer:
Domain:{(0,2,3,8)}Range:{(2,3,7,9)}Hope it will help u.
have a great day .....Enrique collected 7 more than 2 times as many recyclable bottles as Natasha. Write an expression for the number of bottles they collected altogether
Answer:
12
Step-by-step explanation:
because 7x2 is 12
Answer:
3n+7
Step-by-step explanation:
Let's say the variable n stands for how many recyclable bottles Natasha collected.
Enrique collected 7 more than double of what Natasha has.
SO
2n+7
We also need to include Natasha's share
(2n+7) + n
OR 3n+7
I need help with question number 3
Hey there! I'd be delighted to help you out!
First, let's write down our expression!
[tex](x^2-x)+(8x-2x^2)[/tex]
When we look at this expression, we see that all of the numbers are terms, or numbers that are added. We have four terms in this equation, which are:
[tex]x^2, -x, 8x, -2x^2[/tex]
Now, to simplify, we want to combine like terms. Like terms are numbers that have the same variable (or no variable) and are raised to the same power. 1 and 5 are like terms because they both have no variable and they are both raised to the power of 1 (any number that is itself is raised to this power). 4x and 12x are like terms because they both have an x and a power of 1. 4y and 5x are not like terms because they have different variables. 4x³ and 2x² are not like terms because they are raised to different powers.
Now, we see that with our numbers, x² and -2x² are like terms, and -x and 8x are also like terms. We can combine accordingly.
[tex]x^2-2x^2=-x^2\\\\-x+8x=7x[/tex]
Now we combine to get our simplified expression!
[tex]-x^2+7x[/tex]
I hope that this helps! Have a wonderful day!
kaya has $25 left over after the football game she spent $17 for her ticket. She then bought a hat for $11 how much money did kaya bring to the football game
A triangle has an area of 160 square inches and the base of the
triangle is 40 inches. What is the height of the triangle?
Answer:
8 inches
Step-by-step explanation:
A=h /2
Solving for hb
hb= 2 A /b =2 × 160 /40 = 8 inch
( / means fraction line
About how many times larger is 6.14 x 10-3 than 1.98 x 10-4?
Answer:
About 3.7 times or 4 times.
Step-by-step explanation:
6.14 x 10 - 3 = 61.4-3
61.4 - 3 = 58.4
1.98 x 10 - 4 = 19.8 - 4
19.8 - 4 = 15.8
58.4 ÷ 15.8 = 3.696202531645569620253164556962 ≈ 3.7 times
A pair of shoes usually sells for $60. If the shoes are 40% off, and sales tax is 5%, what is the total price of the shoes, including tax?
Answer:
$39
Step-by-step explanation:
We can solve this by finding 40% of $60 and the tax which is 5% of $60. We'll get 36 and 3. Add these up and you have an answer.
Have a great day!
Gabriel started to calculate the area of the triangle. His work is shown. A = 1 2 bh = 1 2 ( 1 2 ) ( 3 4 ) A triangle has a base of three-fourths inch and a height of one-half inch.
Question:
Gabriel started to calculate the area of the triangle. His work is shown.
A = 1/2 bh=1/2 (1/2) (3/4)
A triangle has a base of three-fourths inch and a height of one-half inch
What is the area of the triangle?
The area of the triangle is ___in.²
Answer:
Area of the triangle = [tex] \frac{3}{16} inch^2 [/tex]
Step-by-step explanation:
We are given the dimensions of the triangle as:
Base, b = ¾ inch
Height, h= ½ inch
To find the area of the triangle, let's use the formula :
Area of a triangle = ½base *height
Solving further, we have:
Area of a triangle = [tex] \frac{1}{2}*\frac{3}{4} * \frac{1}{2} = \frac{3}{16} [/tex]
Area of the triangle = [tex] \frac{3}{16} inch^2 [/tex]
Secant TP and tangent TR intersect at point T Chord SR and chord PO intersect
at point V. Find the values of x and y. If necessary, round to the nearest tenth.
A
x=2
y=4
B. x= 11.6
y = 11.6
C.
X = 11.6
y = 232
D. x = 18.3
y=36.6
Answer:
(C)x=11.6, y=23.2
Step-by-step explanation:
Using Theorem of Intersecting Secant and Tangent
[tex]TQ$ X TP=TR^2[/tex]
[tex]10(10+x+4)=16^2\\10(14+x)=256\\140+10x=256\\10x=256-140\\10x=116\\$Divide both sides by 10\\x=11.6[/tex]
Next, we apply Theorem of Intersecting Chords
PV X VQ=SV X VR
4 X x= 2 X y
Recall: x=11.6
2y=4 X 11.6
2y=46.4
y=46.4/2=23.2
Therefore: x=11.6, y=23.2
The correct option is C
If you have 24 square tiles, how many different rectangles can you make? Each rectangle must use all of the tiles and have no holes or gaps. Sketch each rectangle and label its length and width.
Answer:
4
Step-by-step explanation:
A rectangle has a shorter side and a longer side.
The longer side is called the length and the shorter side is called width.
with the 24 tiles you can make the following rectangles (consider the first number the length and the second number the width, and that each unit represents a tile):
24 x 1
12 x 2
8 x 3
6 x 4
A total of 4 different rectangles.
I am not counting the rectangles than have the same sides shifted, for example 2 x 12 because it is the same as 12 x 2 and we are asked for the rectangles to be different.
I attache an image of the sketch of each rectangle with the labels of length and width (not to scale).
How many leaves on a tree diagram are needed to represent all possible
combinations tossing a coin 5 times?
A. 36
B. 16
C. 32
D. 10
Answer: C 32
Step-by-step explanation:
Answer:
C 32
Step-by-step explanation:
Find the measure of arc YWX.
1350
650
Find the solution set.
x2 + 16x + 64 = 0
Answer:
(x+8)(x+8)
Step-by-step explanation:
Assuming x2 is x^2
(x+8)(x+8) = x^2 + 16x + 64
Continuation
The Zeros Would Be
x = -8
What fraction completes the equation using a like denominator when adding 1/3 + 3/6 ?
1/3 + 3/6 = ?/? + 3/6
Answer:
The answer is 2/6 .
Step-by-step explanation:
In order to make the denorminator the same, you have to multiply both numerator and denorminator by 2 :
[tex] \frac{1 \times 2}{3 \times 2} [/tex]
[tex] = \frac{2}{6} [/tex]
In triangle ABC, c is the hypotenuse, 0=25 degrees, and b=3
Find the length of c
Answer:
c approximately equals 3.31
Step-by-step explanation:
What is 9.9581 rounded to the nearest thousandth?
Answer:
9.958
Step-by-step explanation:
The thousandths spot is where the 8 is so you round 8 with the number behind it 1. Since 1 is below 5, you keep 8 the same and get rid of the 1.
Answer:
9.958
Step-by-step explanation:
find the number in the thousands place, 8 and then look 1 place to the right for the rounding digit 1. Round up if this number is greater than or equal to 5 and round down if it is less then 5.
can someone help me ?
Answer:
10 > v (if you don't trust me, check it yourself. Subsitute v for 10 in the first equation.
Step-by-step explanation:
1) 7 > v - 3
2) add 3 to both sides
3) so 7 plus 3 equals 10
So you basically do this
7 > v - 3 (ad 3 to both sides)
You get 10 > v (which is as simplified as possible)
Hope this helps! :)
I need help ASAP, would really appreciate it, marking first as brainliest.
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Answer:
A and B
Step-by-step explanation:
The lines are both in slope intercept form:
y=Mx+b
Where m is the slope and b is the y intercept.
We have 2 lines:
y=1/3x+3
y=1/3x-2
1/3 is the coefficient of x, which means the slope is 1/3. Both of these lines have the same slope of 1/3. Since they both have the same slope, they are also parallel lines.
Therefore, A: the same slopes and B: parallel lines is correct.
In the photo, the red line is 1/3x+3 and the blue like is 1/3x-2
Someone help me pleaseeeee
Answer:
36°.
Step-by-step explanation:
To find this, we will simply need to know that the sum of the angles of a triangle is 180°. This means that in order to find the measure of the third angle, we will need to subtract the others from 180°.
180 - 99 - 45 = 36°.
The measure of the third angle is 36°.
