Given:
Steven charges $31.25 for 5 hours and $43.75 for 7 hours.
To find:
The equation that represents the relationship.
Solution:
Let x represent the number of hours Steven babysits and y represent the amount he charges.
Then the two points on the function are (5,31.25) and (7,43.75). So, the equation of the line that passes through these two points is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-31.25=\dfrac{43.75-31.25}{7-5}(x-5)[/tex]
[tex]y-31.25=\dfrac{12.5}{2}(x-5)[/tex]
[tex]y-31.25=6.25(x-5)[/tex]
On further simplification, we get
[tex]y-31.25=6.25(x)-6.25(5)[/tex]
[tex]y-31.25=6.25x-31.25[/tex]
[tex]y=6.25x-31.25+31.25[/tex]
[tex]y=6.25x[/tex]
Therefore, the required equation for the given situation is [tex]y=6.25x[/tex].
Please help me please I will really appreciate
Answer:
Step-by-step explanation:
If we draw this triangle with Q as the vertex angle (the one at the top of the triangle) then the 2 sides are congruent and this is an iosceles triangle. Because this is an isosceles triangle, then the 2 base angles, angle R and angle S are congruent. If Q measures 114 degrees, then angles R and S together have to add up to the difference between 180 and 114:
180 - 114 = 66
Divide that in half so R = S = 33 degrees each
Prove that the following four points will form a rectangle when connected in order
by showing the diagonals are congruent. Show all work.
A(0, -3), B(-4, 0), C(2,8), D(6.5)
Answer:
Step-by-step explanation:
If the diagonals of the rectangle are congruent,
AC = BD
By using formula to calculate the distance between two points,
Distance between two points = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Distance between A(0, -3) and C(2, 8),
AC = [tex]\sqrt{(8+3)^2+(2-0)^2}[/tex]
= [tex]\sqrt{125}[/tex]
= [tex]5\sqrt{5}[/tex]
Similarly, distance between two points B(-4, 0) and D(6, 5),
BD = [tex]\sqrt{(5-0)^2+(6+4)^2}[/tex]
= [tex]\sqrt{125}[/tex]
= [tex]5\sqrt{5}[/tex]
Therefore, both the diagonals are congruent.
Hence, given quadrilateral ABCD is a rectangle.
Please please help me
Answer:
B) 27.2 m^2
Step-by-step explanation:
because to get the area of the parrelelogram, you use the formula (b)(h) or 6.8*4 to get 27.2.
Find a round to the nearest tenth a 150 12 10cm c a=?cm
Answer:
[tex]Using~ the ~ law~ of ~sinse:-[/tex][tex]\frac{a}{SinA} =\frac{b}{SinB}[/tex][tex]\frac{a}{Sin150}[/tex][tex]=\frac{b}{SinB}[/tex][tex]a=\frac{10~sin~150}{Sin~12}[/tex][tex]a=[24] ~cm[/tex]-----------------------hope it helps..have a great day!!Can anybody help me with this one ??
number 14 and 15 pls
Step-by-step explanation:
b= 140 ( alternate angle)
k = 130 ( veetically opposite angles)
may it help ub
cellus
Find the composition of transformations
that map APQR to AP'Q'R'.
R
(Р
Translate [?] unit(s)
to the C) and then
reflect over the 0.
P10
R?
3
4
Answer:
Translate 4 units to the left and reflect over the x-axis
Step-by-step explanation: hope this helps :)
The composition of the transformations given in the figure is translate 4 units to the left and then reflect over the X axis.
What is Geometric Transformation?Transformation of geometrical figures or points is the manipulation of a given figure to some other way.
Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.
After translation, the original figure is shifted from a place to another place without affecting it's size.
After Reflection, figure is flipped. In other words, a figure becomes it's mirror image.
Consider the point P.
Before undergoing reflection, the figure must be above the X axis.
And the point P will be translated 4 units to the left.
After reflection, since the figure moved towards the other side of the X axis, the figure is reflected across the X axis.
Hence the missing parts are filled.
Learn more about Translation and Reflections here :
https://brainly.com/question/30270479
#SPJ7
I need help with my geometry work!
Answer:
43 degrees
Step-by-step explanation:
Write an inequality for the situation.
all real numbers y that are less than 4 or greater than 9
y < 4 or y > 9
4 < y < 9
y < 4 or y < 9
y < 9 or y > 4
Answer:
y < 4 or y > 9
Step-by-step explanation:
The symbol < means less than, while the symbol > means greater than. So, the inequality y < 4 means that y is less than 4, and the inequality y > 9 means that y is greater than 9. When put together you have all real numbers y that are less than 4 or greater than 9.
What’s the answer????????????
Answer:33
Step-by-step explanation:
trust
A cylinder-shaped drainage pipe 66 in. long measures 25.12 in. around.
What is the volume of the drainage pipe?
Answer:
Step-by-step explanation:
25.12 inches around means diameter. So radius = 12.56 inches
volume [tex]= \pi r^2 \times h =\pi \times 12.56^2 \times 66 = 32709.44 \ in^3[/tex]
Answer:
The volume of the drained pipe is 32692.11 in ³.
Step-by-step explanation:
Given :-Diameter of drainage pipe = 25.12 in
So, radius , r = 25.12 in = 12.56 in
Height of drainage pipe, h = 66 in.
To Find :-Volume of the drainage pipe
Solution :-We know that,
Volume of cylinder = π × r ² × h
substitute the values
Volume of pipe = 3.14 × (12.56 in)² × 66 in
simplify
Volume of pipe =3.14 ×157.7536 in² × 66in
multiplying ✖ the values
Volume of the pipe = 32,692.11 in ³
Therefore, the volume of the drained pipe is 32692.11 in ³.
Use the graph at the top to figure out the question. If someone could help they would be great! And brainliest.
Answer: A
Step-by-step explanation:
Each gallon costs 3 dollars.
8(gallons) times $3(for each gallon) = 24(dollars).
what is x
−9.2= 2.5 − 3.9 x
Answer:
3.08 = x
Step-by-step explanation:
-9.2 = 2.5 - 3.9x
-9.2 + (-2.5) = -3.9x
-12 = -3.9x
-12/-3.9 = x
3.08 = x
Hope this helps!
Expand. If necessary, combine like terms. (x+3)(x-3)=
Answer:
[tex] {x}^{2} - 9[/tex]
Step-by-step explanation:
[tex](x−3)(x+3)[/tex]
[tex]x(x+3)−3(x+3)[/tex]
[tex]x \times x+x \times 3−3x−3 \times 3[/tex]
[tex]x \times x−3 \times 3[/tex]
[tex] {x}^{2} - 9[/tex]
Hope it is helpful....Please someone help me if you can't that is okay but please try I am extremely desperate
Answer:
A
Step-by-step explanation:
2x + x = 3x
y - 3y = 2y
Ms. Emily had a total of 428.5 ounces of pretzels to put into 5 bowls for a party. She put an equal number of ounces of pretzels into each bowl. How many ounces of pretzels did Ms. Emily put into each bowl?
Answer:
85.7 ounces.
Step-by-step explanation:
428.5/5 = 85.7
Therefore, Ms. Emily put 85.7 ounces of pretzels into each bowl.
Answer:
85.7 ounces
Step-by-step explanation:
428.5 ounces ÷ 5=85.7 ounces
If XYZ congruent to DEF the what corresponding angle is congruent to angle x (enter your answer using the angle letter only)
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
XYZ is congruent to DEF so:
X = D
Y = E
Z = F
Một xưởng dệt thảm được giao làm một số thảm trong 30 ngày. Thực tế xưởng dệt đã tăng năng xuất lên 25% nên sau 25ngay không những đã làm xong số thảm mà còn làm thêm được 20 chiếc nữa. Tính số lượng thảm mà xưởng đã dệt trong 25 ngày
Gọi số tấm thảm xưởng dệt dệt theo dự định là x ( tấm, x >0 )
⇒ số tấm thảm xưởng dệt dệt trong 1 ngày theo dự định x/30 (tấm)
xưởng dệt dệt đc số tấm thảm trong thực tế là x/20 (tấm)
⇒số tấm thảm xưởng dệt dệt trong 1 ngày thực tế là x+20/25 (tấm)
Vì năng suất tăng 25% nên số tấm thảm dệt được trong 1 ngày thực tế sẽ bằng 125% số tấm thảm dệt đc trong 1 ngày theo dự định nên ta có PT : x+20/25=125% * x/30
me lười làm khúc dưới quá nên tự xử nha.
Work out the volume of this cylinder. Give your answer rounded to the nearest whole number.
Answer:
31793 cm^3
Step-by-step explanation:
Equation
Volume = [tex]\pi[/tex] * r^2 * h
Givens
d = 2*r
d = 30
r = 15
h = 45
[tex]\pi[/tex] = 3.14
Solution
V = 3.14 * 15^2 * 45
V = 31793 rounded.
12.
Find the value of x. If necessary, round to the nearest tenth.
A. 7.0 in.
B. 9.9 in.
C. 14.0 in.
D. 11.9 in.
Answer:
9.9 inches
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the length of the base and h is the length of the height
49 = 1/2 x*x
Multiply each side by 2
2*49 = x^2
98 = x^2
Take the square root of each side
sqrt(98) = sqrt(x^2)
9.899494937 =x
Rounding to the nearest tenth
9.9 =x
PLSS HELP ASAP WILL GIVE BRAINLIEST
Answer:
R (3,-2) S(5,2) T(6,0)
Step-by-step explanation:
The clock has a diameter of 22 inches. What is the circumference of the clock?
Answer:
The circumference is 44
Answer:
34.56
Step-by-step explanation:
C = 2πr = 2 · π · 5.5 ≈ 34.55752
What are the solutions of the equation ( X -25 )^ 2 equals 36
Answer:
x = 31, x = 19
Step-by-step explanation:
[tex](x-25)^2=36\\\sqrt{(x-25)^2}=\sqrt{36}\\x-25=6 or -6\\\\x-25=6\\x=31\\\\x-25=-6\\x=19[/tex]
ctividad 1:
Las edades de un grupo de niños son: 5, 5, 8, 4, 6, 6, 7, 5, 6, 7, 4, 8, 6, 5, 6, 8
Determina las Medidas de Centralización (Media, Mediana y Moda) y las medidas de Dispersión (Desviación media y Desviación estándar).
necesito ayuda
Respuesta:
Media = 6
Mediana = 6
Modo = 6
Desviación media = 1
Desviación estándar = 1.317
Explicación paso a paso:
Dados los datos:
5, 5, 8, 4, 6, 6, 7, 5, 6, 7, 4, 8, 6, 5, 6, 8
Datos reorganizados: 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8
La media: Σx / n = 96/16 = 6
El modo, = 6 (valor más alto que ocurre en los datos, valor de datos con la frecuencia más alta)
La mediana = 1/2 (n + 1) ésimo término
Mediana = 1/2 (17) término = 8.5 th término = (6 + 6) / 2 = 6
La desviación media = Σ (x - media) / n
Usando la calculadora, la desviación media = 1
La desviación estándar = √ (Σ (x - media) ² / n-1)
Desviación estándar = 1.317
What is the product?
(x − 3)(2x2 − 5x + 1)
Answer:
5x2+20x−15
Step-by-step explanation:
Find csc 0, sin 0, and cot 0, where is the angle shown in the figure.
Give exact values, not decimal approximations.
PLZ HELP I BEEN STUCK FOR AN HOUR I WILL MARK BRAINLIEST!!!
Answers:
[tex]\csc(\theta) = \frac{7\sqrt{33}}{33}\\\\\sin(\theta) = \frac{\sqrt{33}}{7}\\\\\cot(\theta) = \frac{4\sqrt{33}}{33}\\\\[/tex]
=============================================
Explanation:
Before we can find the trig ratios, we need to determine the length of the missing side. Apply the pythagorean theorem
[tex]a^2+b^2 = c^2\\\\4^2+b^2 = 7^2\\\\16+b^2 = 49\\\\b^2 = 49-16\\\\b^2 = 33\\\\b = \sqrt{33}[/tex]
The vertical side is [tex]\sqrt{33}[/tex] units long.
------------------------------------
The side we just found is the opposite side to angle [tex]\theta[/tex] (greek letter theta)
The hypotenuse is 7 units long. The hypotenuse is always opposite the right angle.
Divide the hypotenuse over opposite to get the cosecant.
[tex]\csc(\theta) = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc(\theta) = \frac{7}{\sqrt{33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33*33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33^2}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{33}\\\\[/tex]
Note: In the third step, I multiplied top and bottom by sqrt(33) to rationalize the denominator.
------------------------------------
Recall that sine is the reciprocal of cosecant, and vice versa.
So we'll use the same idea as before, but flip the original fraction.
[tex]\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{\sqrt{33}}{7}\\\\[/tex]
The denominator is already a rational number, so there's not much else to do here.
--------------------------------------
Cotangent is the ratio of adjacent over opposite
[tex]\cot(\theta) = \frac{\text{adjacent}}{\text{opposite}}\\\\\cot(\theta) = \frac{4}{\sqrt{33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33*33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33^2}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{33}\\\\[/tex]
The steps are pretty much nearly identical as the section involving csc, except we're using the adjacent in place of the hypotenuse (so that means we use 4 in place of 7).
can someone answer for me pls
x^2 + 10x + 24 ?
Answer: (x+4)(x+6)
Explaination:
x^2 + 10x + 24
x^2 + 6x + 4x + 24
x(x+6) + 4(x+6)
(x+4)(x+6)
Solution: (x+4)(x+6)
What is the measure of arc DEF?
Answer:
c
Step-by-step explanation:
Mr. Theorem writes the expression 6^2 Divided bye 23 on the board. What is the value
Answer:
[tex]1\frac{13}{23}[/tex]
Step-by-step explanation:
6² ÷ 23
36 ÷ 23
[tex]1\frac{13}{23}[/tex]
simplify ,without using a calculator(2 1/2)2 + (0.5)2
Answer:
22
Step-by-step explanation:
Step-by-step explanation:
2 1/2 × 2
=5/2 × 2
=5
(0.5)2
=0.5×2
=1
5+1
=6
