Answer: x= -2,y=6
Step-by-step explanation:
4x+y= -2......equation 1
3x+2y=6.....equ2
Y= -2-4x........equation 3
Substitute equation 3 into 2
3x+2(-2-4x)=6
Open the bracket
3x+(-4-8x)=6
3x-4-8x=6
3x-8x=6+4
-5x=10
X= 10/-5
X= -2
Substitute for x in equation 1
4x+y= -2
4(-2)+y= -2
-8+y= -2
Y= -2+8
Y=6
Therefore, x= -2 & y=6
The triangle on the grid will be translated two units down.
Which shows the triangle when it is translated two units down?
Answer:
c
Step-by-step explanation:
The points that show the triangle when it is translated two units down are (2, 3) (0, 1), and (2, 1).
What are transformations?A function, f, that maps to itself are known as a transformation, or f: X- X. The pre-image X becomes the picture X following the transformation. This transformation can use any operation, or a combination of operations, including translation, rotation, reflection, and dilation. Translation, rotation, reflection, and dilation can all be used to move a function in one direction or another.
Given that the initial coordinate of triangles ABC are at points
(2, 1), (0, -1), (2, -1).
The coordinate base of the triangle must be (2, 1) and (2, -1)
When the triangle is translated two units down.
2 will be added to all its y coordinates. While the x coordinate remains the same
The new coordinate will be
(2, 2+1), (0, 2-1), (2, 2-1)
(2, 3) (0, 1) and (2, 1)
Hence the new coordinates are (2, 3) (0, 1), and (2, 1).
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The complete question is,
The triangle on the grid will be translated two units down. On a coordinate plane, triangle A B C has points (2, 1), (0, negative 1), (2, negative 1). Which shows the triangle when it is translated two units down
A traveler is driving across the country and spots Gateway Arch in St. Louis, Missouri. She has read that the arch is 630 feet tall. Her angle of elevation to the top of the arch is 3º. How far away is Gateway Arch, to the nearest tenth of a mile?
Answer:
d = 12,021.1 ft
The Gateway Arch is 12,021.1 ft away
Step-by-step explanation:
Given;
Angle of elevation = 3°
Height of arch = 630 ft
Tanθ = opposite/adjacent
Opposite = 630 ft
Adjacent = d
Substituting the values;
Tan3 = 630/d
d = 630/tan3
d = 12,021.1 ft
The Gateway Arch is 12,021.1 ft away
Answer:
[tex]x = 12021.1\,ft\,(2.3\,mi)[/tex]
Step-by-step explanation:
The distance is given by the following trigonometric equation:
[tex]x = \frac{y}{\tan \alpha}[/tex]
[tex]x = \frac{630\,ft}{\tan 3^{\textdegree}}[/tex]
[tex]x = 12021.1\,ft\,(2.3\,mi)[/tex]
A rectangular restaurant kitchen has a perimeter of 34 meters and an area of 70 square meters. What are the dimensions of the kitchen?
Answer:
The kitchen has a length of 10 meters and a width of 7 meters.
Step-by-step explanation:
10x7=70 meters squared
10+10+7+7=34 meters
Which of the following graphs is described by the function given below?
y=3x + 7x+2
O
O
A. Graph A
B. Graph B
O
C. Graph C
O
D. Graph D
This graph represents function of y = 3x²+7x+2, which is correct option(D).
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
f(x) = ax² + b x + c. The graph of the parabola is downward (or opens down), when the price of a is much less than 0, a < 0. The graph of the parabola is upward (or opens up) when the value of a is more than 0, a > 0.
Given function, y = 3x²+7x+2
Compare the given function to f(x) = ax² + b x + c ,
The graph of given function is upward (or opens up) because the value of 3 is more than 0, 3 > 0.
The x-intercept of given function are (-1/3, 0) and (-2,0)
The y-intercept of given function is (0,2)
Here is a graph represents function of y = 3x²+7x+2
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The correct option is A. Graph A. It shows an upward-opening parabola with a vertex and y-intercept that match the derived values.
1. Direction of the Parabola : Since the coefficient of [tex]\( x^2 \)[/tex] (which is [tex]3[/tex]) is positive, the parabola opens upwards.
2. Vertex : The vertex of a parabola in the form [tex]\( y = ax^2 + bx + c \)[/tex] can be found using the formula for the x-coordinate of the vertex, [tex]\( x = -\frac{b}{2a} \)[/tex]
For the given function:
[tex]\[ a = 3, \quad b = 7 \][/tex]
So,
[tex]\[ x = -\frac{7}{2 \times 3} = -\frac{7}{6} \][/tex]
Next, we find the y-coordinate of the vertex by plugging [tex]\( x = -\frac{7}{6} \)[/tex] back into the equation:
[tex]\[ y = 3\left(-\frac{7}{6}\right)^2 + 7\left(-\frac{7}{6}\right) + 2 \][/tex]
Let's compute that:
[tex]\[ y = 3 \times \frac{49}{36} - \frac{49}{6} + 2 \][/tex]
[tex]\[ y = \frac{147}{36} - \frac{294}{36} + \frac{72}{36} \][/tex]
[tex]\[ y = \frac{147 - 294 + 72}{36} \][/tex]
[tex]\[ y = \frac{-75}{36} \][/tex]
[tex]\[ y = -\frac{25}{12} = -2.083 \][/tex]
Thus, the vertex is approximately at [tex]\(\left( -\frac{7}{6}, -\frac{25}{12} \right)\)[/tex]
3. Y-Intercept : This is the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]
[tex]\[ y = 3(0)^2 + 7(0) + 2 = 2 \][/tex]
The graph should cross the y-axis at [tex]\( y = 2 \)[/tex]
Now, let's compare these features with the provided graphs:
The parabola should open upwards.
The y-intercept should be [tex]2[/tex].
The vertex should be approximately at [tex]\( \left( -\frac{7}{6}, -\frac{25}{12} \right) \)[/tex]
The complete question is
Which of the following graphs is described by the function given below? y=3x^2+7x+2
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Add 5 to me.Then divide by 7.If you add 12 and the subtract 7,you get 10
Answer: 30
Step-by-step explanation:
Let the number be y
Add 5 to me
Y+5............equ1
Divide by 7
Y+5/7
Add 12
Y+5/7+12
Subtract 7
(Y+5)/7+(12-7)=10
12-7=5
Substitute
(Y+5)/7+5=10
Find the lowest common multiple
((Y+5)+7(5))/7=10
(Y+5)+35)/7=10
Cross multiply
Y+5+35=70
Y+40=70
Y=70-40
Y=30
The unknown number is 30
CAN SOMEONE PLEASE SOLVE THIS?????????? NEED HELP!!!!!!!!!!!!!!!!!!!
Answer:
x = 9, GH = 21, CD = 17
Step-by-step explanation:
Quadrilateral CDEF is a trapezoid in which G and H are mid points of the sides CF and DE respectively.
In a trapezoid, segment joining the mid points is equal to the half of the sum of the parallel sides.
[tex] \therefore \: GH = \frac{1}{2} (CD + FE) \\ \\ \therefore \:3x - 6 =\frac{1}{2} (2x - 1 + 25) \\ \\ \therefore \:3x - 6 =\frac{1}{2} (2x + 24) \\ \\ \therefore \:3x - 6 =\frac{1}{2} \times 2 (x + 12) \\ \\ \therefore \:3x - 6 = x + 12 \\ \\ \therefore \:3x - x = 12 + 6 \\ \\ \therefore \:2x = 18 \\ \\ \therefore \:x = \frac{18}{2} \\ \\ \huge\red{ \boxed{\therefore \:x = 9}} \\\\ \because \overline{GH} = 3x - 6 \\ \\\therefore \:\overline{GH} =3 \times 9 - 6 \\ \\ \therefore \:\overline{GH} =27 - 6 \\ \\ \huge\purple{ \boxed{\therefore \:\overline{GH} =21}} \\ \\ \because\overline{CD} = 2x - 1 \\\\ \therefore \:\overline{CD} =2 \times 9 - 1 \\ \\ \therefore \:\overline{CD} =18 - 1 \\ \\ \huge\pink{ \boxed{\therefore \:\overline{CD} =17}} \\ \\ [/tex]
Solve the inequality.
−4>−4/3s
The solution is ___
Answer:
3 < s
Step-by-step explanation:
−4>−4/3s
Multiply each side by -3/4 to isolate s. Remember to flip the inequality since we are multiplying by a negative
-4 * -3/4 < -4/3s * -3/4
3 < s
In a survey of 105 people, there were half as many adults as children. How many children were there?
Answer:
70
Step-by-step explanation:
Set up a system:
C + A = 105
C = 2A
Substitute:
3A = 105
A = 35
C = 70
Answer:
70 children 35 adults
Step-by-step explanation:
X= children
Y=Adults
x+y=105
1/2x=y
x+y=105
1/2x-y+0
x+y+105
x-2y=0
3y=105
y=35
x+35=105
x=70
A fabric store is having a sale.
Any fabric is $10 for 8 yards.
What is the value of the ratio of dollars to yard of fabric?
Answer: $1.25:1yd
Step-by-step explanation:
Take 10 and divide it by 8, which should give you 1.25.
This is the answer, the ratio of dollars to yard of fabric is $1.25 per 1 yard of fabric.
To check this, simply multiply both sides by 8 and you should get the original ratio of $10 for 8 yards of fabric.
What is x rounded to the nearest tenth please help
Answer:
8.9
Step-by-step explanation:
How many different ways can 9 trumpet players in the marching band line up?
Answer:
362880 ways
Step-by-step explanation:
In this case, the order does matter therefore to know how many ways it can be aligned, we must resort to permutations.
The formula for permutations is:
P = n!
we know that there are 9 trumpet players, therefore:
P = 9!
P = 362880
So there are 362,880 ways to line up
A number is selected at random from the set (2, 3, 4, ... 10). Which eventby definition, covers the entire sample space of this experiment?
A.
The number is greater than 2.
OB.
The number is not divisible by 5.
C.
The number is even or less than 12.
OD. The number is neither prime nor composite.
E.
The square root of the number is less than 3.
Answer:
C
Step-by-step explanation:
A doesn't include the term "2"
B doesn't include "5" or "10"
D doesn't include "10"
SO... it's C
A sphere has a radius of 3.5 inches.
What is the volume of the sphere rounded to the nearest tenth?
Use 3.14 for pi.
Answer:
volume = 179.59
please give this the brainliest!!
Step-by-step explanation:
formula = V=4/3πr3
4/3·π·3.5^3
≈179.59438
!!!!!HURRY!!!!!!
Bethany used the steps below in an attempt to solve for angle B in triangle ABC.
Where is bethanys error?
The measure of angle B in triangle ABC is 63.9°. Hence, Bethany has done a mistake in step 2.
Given that, in the triangle ABC, AC=4.1 cm, AB=4.5 cm and BC=2.7 cm.
We need to find the measure of angle B.
What is the trigonometric function to find the angle in the triangle?The trigonometric function to find the angle in the triangle is b²=a²+c²-2ac cosB.
Now, (4.1)²=(4.5)²+(2.7)²-2×4.5×2.7 cosB.
⇒16.81=20.25+7.29-24.3 cosB
⇒16.81-27.54=-24.3 cos B
⇒cos B=0.44
⇒B=63.9°
The measure of angle B in triangle ABC is 63.9°. Hence, Bethany has done a mistake in step 2.
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Answer:
B. Bethany took the square root of each squared term before isolating cosB and solving for B.
Step-by-step explanation:
took the quiz
A pool table is 8 feet long and 4 feet wide. How far is it from one corner pocket to the diagonally opposite corner pocket?
Using the Pythagorean theorem, the diagonal distance from one corner pocket to the diagonally opposite corner pocket on an 8 foot by 4 foot pool table is about 8.94 feet.
To determine the distance from one corner pocket to the diagonally opposite corner pocket on a pool table, we can use the Pythagorean theorem because the pool table forms a rectangle and the diagonal forms a right triangle with the length and width of the table. Given the dimensions of the pool table as 8 feet long and 4 feet wide, we can label these as the two sides of the right triangle.
The Pythagorean theorem states that for a right triangle with sides of lengths a, b, and hypotenuse c, the relationship between these sides is [tex]a^2 + b^2 = c^2[/tex]. Substituting the given values, we have:
Let's denote the length (8 feet) as a and the width (4 feet) as b.Using the theorem, we calculate the hypotenuse c as [tex]\sqrt{(8^2 + 4^2)}.[/tex]Compute the square of each side: [tex]8^2[/tex] = 64 and [tex]4^2[/tex] = 16.Add these together: 64 + 16 = 80.The hypotenuse (diagonal) c is the square root of 80, which simplifies to 4 [tex]\sqrt(5)[/tex] feet or approximately 8.94 feet.Therefore, the diagonal distance from one corner pocket to the diagonally opposite corner pocket is about 8.94 feet.
what is one third of three sevenths equals
Answer:
0.14285714285
Hope this helps :)
Step-by-step explanation:
Answer:
.1428
Step-by-step explanation:
1/3 times 3/7= .1428
May You Please Help Me? :(
In triangle ABC, the length of side AB is 11 inches and the length of side BC is 18 inches. Which of the following could be the length of side AC?
1. 5 inches
2. 31 Inches
3. 34 inches
4. 19 inches
Question 2 and 3, if u just feel like answering one that’s okay
Answer:
[tex]w^{20}[/tex]; [tex]y^7[/tex]
Step-by-step explanation:
[tex](w^4)^5=\\w^{4*5}=\\w^{20}\\\\\frac{y^9}{y^2}=\\ y^{9-2}=\\y^7[/tex]
Answer:
1) =W20
2=Y7
Both 20 and 7 are exponents but i cannot type them in that format since I am on a computer. Hope this helps!
Step-by-step explanation:
Find the mean of 8, 7, 9 graphically.
What is the sum of the numbers?
Answer:
Sum=24
Mean=8
Step-by-step explanation:
To find the sum of all the numbers you simply would do 8+7+9.
That is 24.
When finding mean you add up all your numbers then divide by the total number of number (I know that sounds a bit confusing. In this case there are only 3 numbers, so that is the one you will use for dividing)
Your equation would look like this
24
_
3
Once you divide you should get 8 as your mean or average in other terms.
calculate the area of this figure
Answer:
78.
Step-by-step explanation:
13/2=6.5
6.5X12=78.
78/2=39
39X2=39. You times it by 2 because there are two equivalent sides.
If r is an integer greater than 1, what is the value of (−1)r +1 if: a r is an odd integer
Answer:
The value of the given expresion is zero.
Step-by-step explanation:
I am assuming that, your exprssion is
[tex] {( - 1)}^{r} + 1[/tex]
where r is an integer greater than 1.
Let us see what a negative base 1 to an off exponent give us:
[tex] {( - 1)}^{1} =-1[/tex]
[tex] {( - 1)}^{3} =-1[/tex]
[tex] {( - 1)}^{5} =-1[/tex]
[tex] {( - 1)}^{7} =-1[/tex]
If r is odd, then
[tex] {( - 1)}^{r} = - 1[/tex]
This implies that:
[tex] {( - 1)}^{r} + 1 = - 1 + 1 = 0[/tex]
The value of the given expresion is 0.
- Rick has only 2 hour and 44 minutes until he needs to leave. He wants to watch a movie that goes
for 158 minutes. Does he have enough time to watch the whole movie before he has to leave?
Answer:
No he does not
Step-by-step explanation:
158 / 60 = 2.63
which is about a 3 hour long movie.
Find the area of the semicircle.
Either enter an exact answer in terms of
or use 3.14 for and enter your answer as a decimal.
units
Answer:
8 pie
Step-by-step explanation:
area of a circle is pie(radius squared)
radius is 4
4 squared is 16
divide by two because its a semi circle
Answer:
8pi
Step-by-step explanation:
A=pi*r^2
A=pi(4^2)
A=16pi
16pi would be the area if the circle was complete, but since this is a semicircle you just have to divide by two which would give us:
A=8pi
In a bag of 18
18
oranges, 12
12
have gone bad.
What is the ratio of good oranges to bad oranges?
Answer:
1 :2
Step-by-step explanation:
18 oranges
12 bad
-------
6 good
good: bad
6 :12
Divide each by 6
6/6 : 12/6
1 :2
The ratio of good oranges to bad oranges is 1:2.
To find the ratio of good oranges to bad oranges in a bag containing 18 oranges, where 12 oranges have gone bad, follow these steps:
Determine the number of good oranges:
Total oranges in the bag: 18Bad oranges: 12Good oranges: 18 - 12 = 6Find the ratio of good oranges to bad oranges:
Good oranges: 6Bad oranges: 12Simplify the ratio:
The ratio of good oranges to bad oranges can be written as 6:12.Simplify this by dividing both numbers by their greatest common divisor (GCD), which is 6.Simplified ratio: 6 ÷ 6 : 12 ÷ 6 = 1:2
Consider the original complex figure and the reduction.
Figures not drawn to scale.
What is the scale factor of the reduction?
1/8
1/5
5
9
Answer:
1/8
Step-by-step explanation:
I'm going to try to explain this as easy as possible. What I did was take the original shape and divide it by the new shape. For this question, I solved it by dividing 32(the original base) by 4(the new base) and got 8. So the scale factor of the reduction was 1/8.
Answer:
1/8
Step-by-step explanation:
The only one that makes sense
how do I simplify this? -4k - 13 + 6k +23
-4k + 6k -13 +23
2k +10
you can even write it like this:
2 ( k+ 5)
PLS help meee i have posted this 3 othe times
Answer:
help with what
Step-by-step explanation:
Answer:
What do you want help with?
Step-by-step explanation:
I need tynessa's coloring plzzz
Answer:
4 +2n
Step-by-step explanation:
Tynessa has colored 4 red blocks in each figure. The number of blue blocks in each figure is the same as the figure number in both the top and bottom rows. That is, the total number of blue blocks is 2 times the figure number.
If the figure number is n, Tynessa might write the pattern rule as ...
number of blocks = 4 + 2n
Which expression is an equivalent expression of 12x + 10 + 4y?
A. 2(6x+2y+6)
B. 3(4x + y + 10)
OC. 2(6x + 4y+8)
D.
2(6x + 5+ 2y)
Answer:
D. 2(6x + 5+ 2y)
Step-by-step explanation:
12x + 10 + 4y
Factor out a 2
2(6x+5+2y)
Does anyone knows how to solve this question??
Answer:
24
Step-by-step explanation:
cos(x) is just a trigonometric function. To find it on a right triangle, you take the "adjacent" side, which should be the side next to the angle x, and divide it by the hypotenuse.
In this case, the adjacent side is 12. We don't know the hypotenuse, but we can figure it out using the Pythagorean Theorem: [tex]\sqrt{9^{2}+12^{2}}[/tex] = [tex]\sqrt{225}[/tex] = 15. So, the hypotenuse is 15.
Thus, cos(x) = 12/15 = 4/5. We want 30 * cos(x), so we get: 30 * (4/5) = 24, and that is our answer.
Answer:
24
Step-by-step explanation:
From the mnemonic SOHCAHTOA you would know that cos x = adjacent/hypotenuse.
Adjacent side is given as 12, but we must calculate the hypotenuse.
For that we use Pythagoras.
hypotenuse = √(9²+12²) = 15
Now you can calculate
30×cos(x) = 30×12/15 = 24