Answer:
(2, 0)
Step-by-step explanation:
2x - y = 4
5x + 2y = 10
Solve by elimination by multiplying the top equation by 2, so the y values will cancel out (-2y + 2y = 0)
4x - 2y = 8
5x + 2y = 10
Add them together and solve for x:
9x = 18
x = 2
Plug in 2 as x in one of the equations to find y:
2x - y = 4
2(2) - y = 4
4 - y = 4
-y = 0
y = 0
The solution is (2, 0)
If x3 + ax2 – bx + 10 is divisible by x2 – 3x + 2,
find the values of
1) a-b
2) 2a-b
A
man paid 15600
for a new
car. He
was given a discount of
7%. Find the marked price
of the car
hope it helps.I was reading the same chapter
10. Write a word problem for this equation:
n ($25) = $125
Answer:
The word problem is "How many $25 are there in $125?"
Step-by-step explanation:
Given
[tex]n(\$25) = \$125[/tex]
Required
Write a word problem for the expression
We start by solving the given equation
[tex]n(\$25) = \$125[/tex]
Divide both sides by $25
[tex]\frac{n(\$25)}{\$25} = \frac{\$125}{\$25}[/tex]
[tex]n = \frac{\$125}{\$25}[/tex]
[tex]n = 5[/tex]
This implies that there are 5, $25 in $125
Hence; The word problem is "How many $25 are there in $125?"
find the perimeter of the quadrant whose radius is 21cm
Answer:
75 cm
Step-by-step explanation:
∅=90° , r = 21 cm
Arc length= (2πr∅)/360
=(2π×21×90)/360
=33 cm
Perimeter= arc length + 2(radius)
=33+2(21)
=33 + 42
= 75 cm
simplify the equation. (5xE2 - 3x) - (5xE2 - 3x+1)
Answer:
[tex]\huge \boxed{\mathrm{-1}}[/tex]
Step-by-step explanation:
[tex](5xe^2 - 3x) - (5xe^2 - 3x+1)[/tex]
Distribute negative sign.
[tex]5xe^2 - 3x- 5xe^2 +3x-1[/tex]
Combine like terms.
[tex]0xe^2 +0x-1[/tex]
[tex]0-1=-1[/tex]
Please answer quickly! A radio telescope has a parabolic surface, as shown below. A parabola opening up with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 1 meter and its width from left to right is 20 meters. If the telescope is 1 m deep and 20 m wide, how far is the focus from the vertex?
Answer:
Basing on the description, a parabola checking with vertex at origin, the formula with vertex at origin can be used, x^2 = 4py. p is the focus therefore with the dimensions given, we get yourself a 0.25 and this is the distance of the focus to the vertex.
One type of fabric costs $31.25 for 5 square yards. Another type of fabric costs $71.50 for 11
square yards. Is the relationship between the number of square yards and the cost
proportional between the two types of fabric?
Answer:
as ratio of two type of fabric is different .
hence, the relationship between the number of square yards and the cost
is not proportional between the two types of fabric
Step-by-step explanation:
For a relation to be proportional
a:b = c:d
in other form
a/b = c/d
______________________________________________
Ratio for first type of fabric
cost of fabric/ area of fabric = 31.25/5 = 6.25
Ratio for other type of fabric
cost of fabric/ area of fabric = 71.50/11 = 6.5
as ratio of two type of fabric is different .
hence, the relationship between the number of square yards and the cost
is not proportional between the two types of fabric
Cory remembers that his ATV had 4 gallons of gasoline in the tank on Monday. After driving a total of 40 miles during
the week, he has 2 gallons of gas remaining. Find the slope of the graph representing this situation.
Answer:
-1/20
Step-by-step explanation:
For a graph like this you should make the gallons of gas on y-axis and the miles driven on the x-axis.
To find slope the formula is (y2-y1)/(x2-x1)
So in this case it is 2-4/40-0
-2/40
This reduces to -1/20
-5x-10=10 solve for x
Answer:
x = -4
Step-by-step explanation:
-5x-10=10
Add 10 to each side
-5x-10+10=10+10
-5x = 20
Divide each side by -5
-5x/-5 = 20/-5
x = -4
Answer: x= -4
Step-by-step explanation:
[tex]-5x-10=10[/tex]
add 10 on both sides
[tex]-5x=20[/tex]
divide -5 on both sides
[tex]20/-5=-4[/tex]
[tex]x=-4[/tex]
Which of the following is an irrational number?
5 / 4
√5 / 7
1/ 8
3 / 5
Answer: [tex]\sqrt{5} /7[/tex]
Step-by-step explanation:
5/4 is not an irrational number because it is already in a fraction the same as 1/8 and 3/5.
The square root of 5 is not rational because it cannot be converted to a fraction or in other words is not a perfect square.
Answer:√5 / 7
Step-by-step explanation:
Factorise the following
Answer:
4ny²+4n²-4n-8+y⁴-2y²
To test the belief that sons are taller than their fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data. Are sons taller than their fathers? Use the alphaequals0.10 level of significance. Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.
Height of Father Height of Son
72.4 77.5
70.6 74.1
73.1 75.6
69.9 71.7
69.4 70.5
69.4 69.9
68.1 68.2
68.9 68.2
70.5 69.3
69.4 67.7
69.5 67
67.2 63.7
70.4 65.5
Which conditions must be met by the sample for this test? Select all that apply.
A. The sample size is no more than 5% of the population size.
B. The differences are normally distributed or the sample size is large.
C. The sample size must be large.
D. The sampling method results in a dependent sample.
E. The sampling method results in an independent sample.
Write the hypotheses for the test. Upper
H 0 :
H 1 :
Calculate the test statistic. t 0=?
(Round to two decimal places as needed.)
Calculate the P-value. P-value=?
(Round to three decimal places as needed.) Should the null hypothesis be rejected?
▼ Do not reject or Reject Upper H 0 because the P-value is ▼ less than or greater than the level of significance. There ▼ is or is not sufficient evidence to conclude that sons ▼ are the same height or are shorter than or are taller than or are not the same height as their fathers at the 0.10 level of significance. Click to select your answer(s).
Answer:
1) B. The differences are normally distributed or the sample size is large
C. The sample size mus be large
E. The sampling method results in an independent sample
2) The null hypothesis H₀: [tex]\bar x_1[/tex] = [tex]\bar x_2[/tex]
The alternative hypothesis Hₐ: [tex]\bar x_1[/tex] < [tex]\bar x_2[/tex]
Test statistic, t = -0.00693
p- value = 0.498
Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers at 0.10 level of significance
Step-by-step explanation:
1) B. The differences are normally distributed or the sample size is large
C. The sample size mus be large
E. The sampling method results in an independent sample
2) The null hypothesis H₀: [tex]\bar x_1[/tex] = [tex]\bar x_2[/tex]
The alternative hypothesis Hₐ: [tex]\bar x_1[/tex] < [tex]\bar x_2[/tex]
The test statistic for t test is;
[tex]t=\dfrac{(\bar{x}_1-\bar{x}_2)}{\sqrt{\dfrac{s_{1}^{2} }{n_{1}}-\dfrac{s _{2}^{2}}{n_{2}}}}[/tex]
The mean
Height of Father, h₁, Height of Son h₂
72.4, 77.5
70.6, 74.1
73.1, 75.6
69.9, 71.7
69.4, 70.5
69.4, 69.9
68.1, 68.2
68.9, 68.2
70.5, 69.3
69.4, 67.7
69.5, 67
67.2, 63.7
70.4, 65.5
[tex]\bar x_1[/tex] = 69.6
s₁ = 1.58
[tex]\bar x_2[/tex] = 69.9
s₂ = 3.97
n₁ = 13
n₂ = 13
[tex]t=\dfrac{(69.908-69.915)}{\sqrt{\dfrac{3.97^{2}}{13}-\dfrac{1.58^{2} }{13}}}[/tex]
(We reversed the values in the square root of the denominator therefore, the sign reversal)
t = -0.00693
p- value = 0.498 by graphing calculator function
P-value > α Therefore, we do not reject the null hypothesis
Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers at 0.10 lvel of significance
on a map, the distance between jacksonville FL and tallahasse FL is about 5 inches. According to the scale, 1 inch represents 25 miles. About how far apart are these two cities?
What is the solution to -33 + m = 10?
A. m = -43
B. m = -23
C. m = 23
D. m = 43
Answer:
D. m = 43
Step-by-step explanation:
Answer: D. m=43
Step-by-step explanation:
-33 +m = 10move 33 and make it postive m = 10 + 33m = 43In which direction must the graph of Ax) = x be shifted to produce the graph of g(x) = f(x) - 4?
ОА. up
OB. down
O c. left and down
OD. right and up
Answer: B. down
Step-by-step explanation:
Translation rules:
For a function h(x):
h(x+c) is a left-shift by c units.h(x-c) is a right-shift by c units.h(x)+c is a up-shift by c units.h(x)-c is a down-shift by c units.Here, the graph of f(x) becomes the graph of g(x) =f(x)-4 which is similar to "h(x)-c".
That means , f(x) is shifted 4 units down to become g(x).
So, correct option : B. down
Can someone help me solve parts (a) and (c) please? Thank you!
a) 4x +6
Add up all the sides to calculate perimeter
Answer:
a) 6x + 6
b) 15 x 24
c) see explanation
Step-by-step explanation:
a) 2x + x + 3 + 2x + x + 3 = 6x + 6
b) 6x + 6 = 78
6x = 72
x = 12
2(12) = 24
(12) + 3 = 15
15 x 24
c) 2x(x + 3) = 2x² + 6x
2(12)² + 6(12) = 288 + 72 = 360
15 x 24 is also 360
Which of the following is true? Tangent is positive in Quadrant I. Sine is negative in Quadrant II. Cosine is positive in Quadrant III. Sine is positive in Quadrant IV.
Answer:
A
Step-by-step explanation:
I had this question and got it right the user above explains it in detail
graph a
graph b
graph c
graph d
which of the following isthe√×51? answer is A .0-1
A box contains 20 oranges and 10 grapes what is the probability of picking a grape from the box?
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
First, let's find how many total items there are in the box.
If there are 20 oranges and 10 grapes, then there are [tex]20+10=30[/tex] items in the box.
Now, if there are 10 grapes in this box, we know that the probability of picking a grape is [tex]\frac{10}{30}[/tex] because the total is the denominator and the number of items for that selection is the numerator.
We can simplify this fraction down to [tex]\frac{1}{3}[/tex].
Hope this helped!
Answer:
1/3
Step-by-step explanation:
What is the least common multiple of all positive integers smaller than 8?
Answer:
420
Step-by-step explanation:
We need to find the LCM of 1, 2, 3, 4, 5, 6 and 7. The LCM of 1, 2, and 4 is 4 and the LCM of 3 and 6 is 6 so the list becomes the LCM of 4, 5, 6 and 7. The LCM of 4 and 5 is 20, the LCM of 20 and 6 is 60 and the LCM of 60 and 7 is 420.
Answer:
420
Step-by-step explanation:
Prime factorization:
7 = 7
6 = 2 × 3
5 = 5
4 = 2 × 2
3 = 3
2 = 2
1 = 1
LCM: 7, 6, 5, 4, 3, 2, 1
2 × 2 × 3 × 5 × 7 = 420
1. 3x + 6y = 3 and 7x + 3y = 7
ons for bo
Answer:
(1,0)
Step-by-step explanation:
3x + 6y = 3
7x + 3y = 7
Multiply the second equation by -2
-2( 7x + 3y = 7)
-14x -6y = -14
Add this to the first equation to eliminate y
3x + 6y = 3
-14x -6y = -14
--------------------
-11 x = -11
Divide by -11
x = 1
Now find y
3x + 6y = 3
3 +6y = 3
Subtract 3 from each side
6y = 0
y =0
Answer:
x = 1
y = 0
Step-by-step explanation:
3x + 6y = 3
7x + 3y = 7
=> 3y = 7 - 7x
=> y = -7/3x + 7/3
3x + 6(-7/3x + 7/3) = 3
=> 3x - 14x + 14 = 3
=> -11x = -11
=> -x = -11/11
=> -x = -1
=> x = 1
So, 3(1) + 6y = 3
=> 3 + 6y = 3
=> 6y = 0
=> y = 0/6
=> y = 0
So, x = 1
y = 0
What is the perimeter of this polygon?
A(2, 3)
B(-4, 0)
C(0,-4)
D(4,0)
Answer:2,3 hope it help you
Step-by-step explanation:
Answer:
21.627
Step-by-step explanation:
get the distance between all points then add
If the measure of angle 4 is (11 x) degrees and angle 3 is (4 x) degrees, what is the measure of angle 3 in degrees?
Answer:
is it 2
Step-by-step explanation:
Need help in the b question... Pls send it fast.. urgent and if possible do it in paper and send or just type it.. need answer for question 1. B
Answer:
2.09 or 2 and 9/100
Step-by-step explanation:
2 1/2 - 41/100 =
5/2 - 41/100=
250/100 - 41/100=
209/100=
2 and 9/100 Or 2.09
I hope this helped you.
The projected worth (in millions of dollars) of a large company is modeled by the equation w = 236(1.06) t. The variable t represents the number of years since 2000. What is the projected annual percent of growth, and what should the company be worth in 2011? A. 6%; $448.00 million B. 16%; $474.88 million C. 16%; $250.16 million D. 6%; $422.64 million
Answer:
A. 6%, $448 million
Step-by-step explanation:
a) The base of the exponential term is 1.06, so the projected annual growth is 1.06 -1 = .06 = 6%
__
b) Filling in 11 for t, we find the projected worth to be ...
w = 236(1.06^11) ≈ $448 . . . million
Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
A. 10.5 cm
B. 3.4 cm
C. 8.5 cm
D. 12 cm
Answer:
12 cm is the right answer pls mark me brainliest
The height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles is 12 cm.
What is Area of Triangle?The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.
What is Heron's formula?Heron's formula, formula credited to Heron of Alexandria (c. 62 ce) for finding the area of a triangle in terms of the lengths of its sides. In symbols, if a, b, and c are the lengths of the sides:
Area = √s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c)/2.
Given:
Three sides are: 15cm, 25 cm and 2 cm
Now, Using Heron's formula
semi-perimeter= (25+ 20 + 15)/2
s= 30 cm
Now,
Area of triangle
=√s(s-a)(s-b)(s-c)
=√30* 5 * 10* 15
=√5*2*3*5*2*5*3*5
=5*5*2*3
=150 cm²
Again, area of triangle= 1/2* b* h
150= 1/2* 25* x
12cm= x
Learn more about Area of Triangle here:
https://brainly.com/question/9817285
#SPJ2
need help will give you a good rating us
Answer:
[tex]\boxed{2\pm \frac{\sqrt{2}}{2}}[/tex]
Step-by-step explanation:
[tex]2x^2-8x=-7[/tex]
[tex]\sf Add \ 7 \ on \ both \ sides}.[/tex]
[tex]2x^2-8x+7=-7+7[/tex]
[tex]2x^2-8x+7=0[/tex]
[tex]ax^2 +bx+c=0[/tex]
[tex]\sf Apply \ quadratic \ formula.[/tex]
[tex]a=2 \ \ \ b=-8 \ \ \ c = 7[/tex]
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(-8)\pm\sqrt{(-8)^2-4(2)(7)}}{2(2)}[/tex]
[tex]x=\frac{8\pm\sqrt{64-56}}{4}[/tex]
[tex]x=\frac{8\pm\sqrt{8}}{4}[/tex]
[tex]x=\frac{8\pm2\sqrt{2}}{4}[/tex]
[tex]x=2\pm \frac{\sqrt{2}}{2}[/tex]
Please help me answer this question. -15 - g/3 = -5.
What is g?
Answer:
g = -30
Step-by-step explanation:
-15 - g/3 = -5
Add 15 to each side
-15+15 - g/3 = -5+15
-g/3=10
Multiply by -3 to each side
-g/3 * -3 = 10*-3
g = -30
Answer:
g= -30
Step-by-step explanation:
after writing down the problem, multiply both sides of the equation by 3 to get -45-g= =15. then subtract 15 from both sides to get g=-30, which is your answer. hope this helps!
what is the value of a in the functions equation?
Answer:
y= -2x^2 + 12x -14
Step-by-step explanation:
when I put the points into a graphing calculator this is what I got so I think the answer is -2
Answer:
Step-by-step explanation:
It is -2
complete the square to solve
f(x)=x^2-6x+5
