The difference of two numbers is 45. Their sum is 55. What are the two numbers?The difference of two numbers is 45. Their sum is 55. What are the two numbers?
Answer:
50, 5
Step-by-step explanation:
X=number 1
x-45=number 2
x+(x-45)=55
2x=100
x=50 number 1
x-45 is number 2
50-45=5 number 2
Graph the equation y = x2 + 8x + 12 on the accompanying set of axes. You must
plot 5 points including the roots and the vertex. Using the graph, determine the
vertex of the parabola.
Answer:
Step-by-step explanation:
Roots: set y = x^2 + 8x + 12 = 0 and solve for x: x + 6 = 0, so x = -6 is one root. The other is x = -2. The corresponding points are (-6, 0) and (-2, 0).
y-intercept: Let x = 0. Then y = 12. The y-intercept is (0, 12).
Axis of symmetry: x = -b / (2a) => x = -8/(2*1) = -4: x = -4
Vertex y-value: evaluate y at x = - 4: (-4)^2 + 8(-4) + 12 = -4: (-4, -4)
Arbitrarily chosen x value: x = 1 => 1^2 + 8(1) + 12 = 21: (1, 21)
The five points are: (-6, 0) and (-2, 0), (0, 12), (-4, -4), (1, 21). The vertex is (-4, -4). The parabolic graph opens UP.
The vertex of the parabolic equation y = x² + 8x + 12 will be at (-4, -4).
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The equation is given below.
y = x² + 8x + 12
Conver the equation into a vertex form. Then we have
y = x² + 8x + 12
y = x² + 8x + 16 - 16 + 12
y = (x + 4)² - 4
The vertex of the parabolic equation y = x² + 8x + 12 will be at (-4, -4).
The graph is given below.
More about the equation of the parabola link is given below.
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Simplify.
7/8 x 1 1/3
A. 7/24
B. 28/24
C. 1 1/6
D. 1 7/24
What is the area?‼️‼️‼️‼️
Which angles are vertical angles and, therefore, congruent? 3 lines intersect to form 8 angles. From top left, clockwise, the angles are A, B, C, D, H, G, F, E. Angle A and Angle D Angle A and Angle G Angle A and Angle E Angle A and Angle F
Answer:
A and F
Step-by-step explanation:
Given
Intersecting lines
Required
The vertical and congruent angles
The two vertical lines are not parallel. So, we cannot conclude any relationship between angles A, B, E, F and angles C, D, H, G
Comparing angles A, B, E and F; we have:
[tex]\angle A = \angle F[/tex] --- Vertical opposite angles
[tex]\angle B = \angle E[/tex] --- Vertical opposite angles
From the given options,
[tex]\angle A = \angle F[/tex] is true
Triangle LMN is similar to triangle OPQ. Find the measure of side QO. Round your answer to the nearest tenth if necessary.
Answer:
90.8
Step-by-step explanation:
20/13 = x/59
13x = 1180
x=90.76
x=90.8
please help me answer this
Answer:
1) glazed = 48 people
Chocolate = 72 people
Jelly = 24 people
Coconut = 16 people
2)9th grade = 219 students
10th grade = 167 students
11th grade = 147 students
12th grade = 151 students
Step-by-step explanation:
We are solving the examples;
1) We are told that there are 20 students in Kayla's first period class.
No. that preferred glazed donuts = 6
No. that preferred chocolate donuts = 9
No. that preferred jelly donut = 3
Number that preferred coconut donut = 2
Now,there are a total of 160 students in the entire grade. So to find the Number of students in this entire grade that will each prefer the types of donuts listed above, we will solve as;
For glazed donuts; 6/20 × 160 = 48 people
For chocolate donuts; 9/20 × 160 = 72 people
For jelly donut; 3/20 × 160 = 24 people
For coconut donut; 2/20 × 160 = 16 people
2) Total number of students is;
9th grade = 300 students
10th grade = 275 students
11th grade = 250 students
12th grade = 280 students
73% of 9th grade prefer valorant. Thus;
73% × 300 ≈ 219 students
61% of 10th grade prefer valorant. Thus;
61% × 275 ≈ 167 students
59% of 11th grade prefer valorant. Thus;
59% × 250 ≈ 147 students
54% of 12th grade prefer valorant. Thus;
54% × 280 ≈ 151 students
I need help quick, please
Answer:
B
Step-by-step explanation:
The shape is maintained exactly, it is rotated, not reflected and we can see it became smaller, so dilate it by a value less than one, but greater than 0. (2/3)
convert this equation to standard form. y=-7x/9+5
Answer:
7x+9y=45
Step-by-step explanation:
Solve for x
|2x+1| + |3x-4| = 5
Answer:
X=0 or x=8/5
Step-by-step explanation:
There are 54 benches and 6 picnic tables in a park. What is the ratio
of the number of picnic tables to the number of benches in its
simplest form??????????????????????????????/
Answer:
1 picnic table : 9 benches
Step-by-step explanation:
You just simplify the equation down to its simplest form, so since they both have the gcf of 6, you divided both sides by 6, which results in the answer above.
reflect C over the y axis
Answer:
C' (- 3, 2 )
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
C (3, 2 ) → C' (- 3, 2 )
Arrange the entries of matrix AB in increasing order of their values.
Answer:
[tex]-186 \to -32 \to 6 \to 27 \to 28\ to 38 \to 56 \to 90 \to 115[/tex]
Step-by-step explanation:
Given
See attachment for A and B
Required
Arrange AB in ascending order
We have:
[tex]A = \left[\begin{array}{ccc}1&7&-1\\5&-2&-9\\-3&8&3\end{array}\right][/tex]
and
[tex]B = \left[\begin{array}{ccc}5&1&7\\3&15&-2\\-1&-9&25\end{array}\right][/tex]
So:
[tex]C = A * B[/tex]
[tex]C = \left[\begin{array}{ccc}1&7&-1\\5&-2&-9\\-3&8&3\end{array}\right] * \left[\begin{array}{ccc}5&1&7\\3&15&-2\\-1&-9&25\end{array}\right][/tex]
[tex]C = \left[\begin{array}{ccc}{27}&{115}&{-32}\\{28}&{56}&{-186}\\{6}&{90}&{38}\end{array}\right][/tex]
Where:
[tex]C_{1,1} =1*5 + 7*3 + (-1) * (-1)[/tex]
[tex]C_{1,2} =1*1 + 7*15 + (-1)*(-9)}[/tex]
[tex]C_{1,3} = 1*7 + 7*(-2) + (-1)*25}[/tex]
[tex]C_{2,1} = 5*5 + (-2)*3 + (-9) * (-1)}[/tex]
[tex]C_{2,2} = 5*1 + (-2)*15 + (-9)*(-9)}[/tex]
[tex]C_{2,3} = 5*7 + (-2)*(-2) + (-9)*25}[/tex]
[tex]C_{3,1} =(-3)*5 + 8*3 + 3 * (-1)[/tex]
[tex]C_{3,2} = (-3)*1 + 8*15 + 3*(-9)[/tex]
[tex]C_{3,3} = (-3)*7 + 8*(-2) + 3*25[/tex]
In increasing order, we have:
[tex]-186 \to -32 \to 6 \to 27 \to 28\ to 38 \to 56 \to 90 \to 115[/tex]
if f(x)=4x+5 what is the value of f(-3)
Answer:
-7
Step-by-step explanation:
f(x)=4x+5
Let x =-3
f(-3)=4*-3+5
Multiply
f(-3)=-12+5
Add
f(-3) = -7
PLEASEEEEE HELPPPP IM BEGGING SOMEONE PLEASEEEEEEEE
Answer:
Step-by-step explanation:
answer is 98 degree because the relation between missing angle and 98 degree is alternate exterior angles and alternate exterior angles are always equal.
answer is 89 degree because the relation between missing angle and 89 degree is corresponding angles and corresponding angles are always equal.
in the 5th question
let's consider the angle there as A so angle A is 98 degree and by the relation of alternate angles the question mark (?) is 98 degree
in 6th question
by the relation of corresponding angles the question mark(?) is 89 degree
Find the measure of the indicated angle to the nearest degree
9514 1404 393
Answer:
25°
Step-by-step explanation:
The relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(?) = 25/60
? = arcsin(25/60) ≈ 24.62°
The indicated angle is about 25°.
Quadratic equation I need help
A 70-year-old male pays 79.79 per month for his term life policy 180-year-old pays 349.30 per month. What is the percent of increase in premium costs from age 70 to 80?
Answer: [tex]337.77\%[/tex]
Step-by-step explanation:
Given
For 70 year old, premium is 79.79 per month
For 80 year old it is 349.30 per month
Percentage increase in premium costs from age 70 to 80 is
[tex]\Rightarrow \%\ \text{increase}=\dfrac{349.30-79.79}{9.79}\times 100\\\\\Rightarrow \%\ \text{increase}=\dfrac{269.51}{79.79}\times 100\\\\\Rightarrow \%\ \text{increase}=337.77\%[/tex]
Nina operate the dog walking service she charges a flat fee for $15 plus $5 per hour. which equation represents this liner relationship.
y= 15x - 5
y= 15x + 5
y= 5x - 15
y= 5x + 15
Answer: I think it’s the first one
Step-by-step explanation:
It says per hour and 15 bucks plus 5 bucks PERhour so you would have to be multiplying I did a question like this long ago hope you get it right
The equation represents this linear relationship for total cost is y= 5x + 15 thus option (D) is correct.
What is a linear function?A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given,
She charges a flat fee of $15 plus $5 per hour.
For x number of hours, the total cost will be as,
y = 15 + 5x
Hence "y= 5x + 15 is the equation that depicts this linear relationship for total cost".
For more about the linear function,
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Find Y
A: 14.3
B: -6.3
C: 7.0
D: 11.6
Answer:
D
Step-by-step explanation:
Using the sine ratio in the right triangle
sin51° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{9}{y}[/tex] ( multiply both sides by y )
y × sin51° = 9 ( divide both sides by sin51° )
y = [tex]\frac{9}{sin51}[/tex] ≈ 11.6 ( to 1 dec. place ) → D
Please help ASAP! Will Mark Brainliest!
Answer:
m = 18
Step-by-step explanation:
10/15 = m/12
Cross multiply using the butterfly method.
15m = 10*12
15m = 120
Divide both sides by 15.
m = 8
I personally like to use ratios but I am not sure if that's what you want. Anyway here's my answer
If there are 3.28 feet in 1 meter, how many yards are in 8 meters? Round answer to the nearest tenth. (Hint: This problem requires two conversions.)
Answer:
8.7
Step-by-step explanation:
The circumference of a circle is 16 ft.
The radius is ?
Answer:
8/pi or approximately 2.55 ft
Step-by-step explanation:
The formula for the circumference is
C = 2 * pi *r
16 = 2 * pi *r
Divide each side by 2 pi
16 / ( 2 pi) = 2 * pi * r/ ( 2 pi)
8 / pi = r
Using 3.14 for pi
8 / 3.14 = r
2.54777 = r
2.55 =r
Answer:
Radius ≈ 2.55 ft.
Step-by-step explanation:
GIVEN :-
Circumference of circle = 16 ft.TO FIND :-
Radius of the circleFORMULAE TO KNOW BEFORE SOLVING :-
For a circle with radius 'r' & circumference 'c' ,
[tex]r = \frac{c}{2\pi }[/tex]
SOLUTION :-
[tex]Radius = \frac{Circumference}{2\pi } = \frac{16}{2\pi } = \frac{8}{\pi } = 2.55 ft. (appx)[/tex]
gave the table write equation in the slope intercept form
pls help thank u!
Answer:
y=2x+6
Hope I helped, have a nice day :)
Answer:
y=2x +6
Step-by-step explanation:
(18-12)
(6-3)
6/3 = 2
m=2
What is the measure of o?
4 cm
e
12 cm
O A. 4 radians
O B. 3s radians
O c. 3 radians
O D. 4radians
plss helppp
==============================================
Work Shown:
L = arc length = 12 cmtheta = angle in radians = unknownr = radius = 4 cmL = theta*r
12 = theta*4
12/4 = theta
3 = theta
theta = 3 radians, choice C is the answer.
--------
Side note: The formula L = theta*r only works if theta is in radians.
If theta is in degrees, then use L = (theta/360)*2pi*r. So you can see that radian mode is much easier in this case.
Perimetrul unui dreptunghi este de 400 m, iar latimea este de 3 ori mai mica decat lungimea acestuia. Cati metri are lungimea dreptunghiului?
Răspuns:
150 m
Explicație pas cu pas:
Reamintim:
Perimetrul unui dreptunghi, P
P = 2 (lungime + lățime)
P = 400
Lățime = x
Lungime = 3x
Astfel, avem:
400 = 2 (3x + x)
400 = 2 (4x)
400 = 8x
Împărțiți ambele părți la 8
50 = x
Lungime = 3x
Lungime = 3 * 50
Lungime = 150 m
(b) factorise
(3m-1)(6-a)-(m+3)(6-a)
Answer:
Step-by-step explanation:
(3m-1)(6-a)-(m+3)(6-a)
=3m(6-a)-1(6-a)-m(6-a)+3(6-a)
=18m-3ma-6+a-6m+ma+18-3a
=12m-2ma+12-2a
=2(6m-ma+6-a)
me pueden ayudar a contestarlo!!
por favor!!
Answer:
english!? sorry
Step-by-step explanation:
What is the area in square centimeters of the triangle below?
Answer:
it's 10 times 7 divided by 2
if x + 1/x = 2. find the value of x³ + 1/x³.
Answer:
2
Step-by-step explanation:
x + 1/x = 2
x + 1 = 2x
x = 1
x³ + 1/x³
1³ + 1/1³.
1 + 1/1 = 1 + 1 = 2