Answers
Question 4:
2x + 3y = 17 -- equation 1
5x + 6y = 32 -- equation 2
(equation 1) * 2
4x + 6y = 34 -- equation 3
(equation 2) - (equation 3)
x = -2 -- equation 4
plug (equation 4)'s value of x into (equation 1)
2(-2) + 3y = 17
3y - 4 = 17
3y = 21
y = 7
Thus the answer is x = -2 and y = 7
Question 5:
The vertex form of a quadrilateral looks like this:
[tex]y = a(x-h)^2 + k[/tex]
a : coefficient of [tex]x^2\\[/tex](h,k): coordinate of the vertex.The x-coordinate of the vertex is equal to '-b/2a'. Where b is the
coefficient of x, so:
[tex]h = -\frac{b}{2a} =-\frac{-8}{2*1} =4[/tex]
There is also another formula to find the y-value of the vertex
coordinate, but the easier way to find it is to plug it into the original
equation:
[tex]k=(4)^2-8(4) + 12= 16 -32 + 12 = -16 + 12 = -4[/tex]
Since we know now that h = 4 and k = -4 and that a = 1, lets plug it into
the original equation.
[tex]y = 1*(x-4)^2 - 4 =(x^2-4)-4[/tex]
Thus the answer is [tex]y = (x-4)^2 -4[/tex]
Hope that helps!
Related Questions
You need to mark a fifth teen foot beam into five equal segments .how long is each segment ?
Answers
Answer: 3
Step-by-step:
15/5=3
Each segment of a fifteen-foot beam divided into five equal parts is 3 feet long.
Since acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
To find out the length of each segment of a fifteen-foot beam divided into five equal parts, we have to divide the total length of the beam by the number of segments it is being divided into.
We can do this using the division operation as shown below:
15 ÷ 5 = 3
Therefore, we can conclude that each segment of a fifteen-foot beam divided into five equal parts is 3 feet long.
More about the Algebra link is given below.
brainly.com/question/953809
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It’s a 4 digit number. The tens are double the ones. The thousands are double the tens. The sum of the digit is 19
URGENT
Answers
the thousands are double the tens:
a = 2c = 4d
the sum of the digits is 19:: a+b+c+ d = 19
Substitute for a and c to get:
4d + b + 2d + d = 19
b + 7d = 19
d=2;b=5;0=4;a=8
Ans:8542
please help i am confused
Answers
Answer:
The last answer.
Step-by-step explanation:
Regular means all the side lenghts are the same and all the interior angle measures are the same. Think a stop sign.
Irregular polygons have different side lengths and different interior angle measures.
What’s the greatest mad
Answers
Answer: Jason's team.
Step-by-step explanation: When finding the MAD, you need to find the mean of the data, which they said is 10. The next step is to subtract numbers from the data from the mean, which is 10 for all three dot plots. For example, for Jason's team, we need to subtract all the 7's, 8's, 11's, 12's, and 13's, because those are the only parts of the plot with data. Let's try subtracting 7 - 10. The answer is -3, but we need to make it positive, because that's how data works, so it's actually 3. You keep doing this for all three plots, which is provided below:
Jason's Team: 3, 3, 2, 2, 2, 1, 2, 3, 3, 3.
Hannah's Team: 3, 2, 2, 1, 0, 0, 1, 1, 3, 3.
Dion's Team: 1, 1, 1, 1, 0, 0, 0, 0, 1, 3.
Now, the next step is adding all these values and dividing it by ten, since that's how many numbers there are for the data.
Jason's Team MAD: 2.4.
Hannah's Team MAD: 1.6.
Dion's Team MAD: 0.8
As you can see, Jason's Team has the greatest MAD, which is your answer.
Let me know if this is right! :)
What is the area of triangle rst? 6 square units 9 square units 12 square units 18 square units
Answers
The area of the considered triangle RST is given by: Option A: 9 sq. units.
How to find the area of a triangle?If we have:
Length of its base = b unitsIts height = h units long,Then we get:
Area of a triangle = [tex]\dfrac{b \times h}{2} \: \rm unit^2[/tex]
The missing image is attached below.
If we take the base of the triangle as RS, then as the line UT is perpendicular to RS (as RS is parallel to x axis and UT is parallel to y axis) and touching from the base line RS to T, thus, it can be taken as height.
Thus, we have:
Area of RST = half of length of RS (base) times length of UT (height)
As visible from image, we have:
Length of RS = 6 blocks of unit length = 6 units
Similarly, length of UT = 3 units
Thus, we get:
Area of RST = [tex]\dfrac{6 \times 3}{2} = 9 \: \rm unit^2[/tex]
Thus, the area of the considered triangle RST is given by: Option A: 9 sq. units.
Learn more about area of a triangle here:
https://brainly.com/question/14503701
Writing linear functions
Use the graph or table to write a linear function that relates y to x
Answers
Step-by-step explanation:
3. Slope is postive
x1=6
x2=3
y1=10
y2=6
m=6-10/3-6
m=4/3
y=mx+b find b
10=4/3*3+b
10=4+b
b=6
y=4/3x+b
4.slope is zero
y=b
Y=3
Keiko drove 225 miles using 10 gallons of gas. At this rate, how many gallons of gas would she need to drive 441 miles?
Answers
Answer:
19.6 gallons
Step-by-step explanation:
divide 225 by 10 and you get 22.5 this means you are getting 22.5 miles per gallon so all you have to do is divide 441 by 22.5 and you get 19.6 so you are going to need 19.6 gallons to drive 441 miles
Can someone help me on this question? I’ll give brainliest if you answer soon!!!
Answers
Answer:
68 degrees
Step-by-step explanation:
EHD and CHF are vertical angles, meaning their angle measures are the same.
Answer:
m<CHF = 68°
Step-by-step explanation:
Angles EHD and CHF are vertical angles, so their measures are equal.
m<CHF = m<EHD = 68°
which of the following statements is true?
Answers
Answer:
D. In an axiomatic system, every statement, either its capable of being proven true or false.
Step-by-step explanation:
I'm sure.
Bobby has 58 of a pepperoni pizza in his refrigerator. He eats 14 of this for his lunch. Of the following, which is the best estimate of the fraction of the original pizza left after Bob's lunch?
Answers
Answer:
5/32
Step-by-step explanation:
evaluate 6+4/a + b/3 when a=4 and b=3
Answers
Answer: 31/4 or 7.75
Step-by-step explanation:
At what point does the line given by the following equation cross the y-axis? y = (6/9)X + 9
A. (9,0)
B. (0,6/9)
C. (0,9/6)
D. (0,9)
Answers
Answer:
D
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{6}{9}[/tex] x + 9 ← is in slope- intercept form
with y- intercept c = 9
then the line crosses the y- axis at (0, 9 )
If sin(0)=24/26 what are the other two trigonomic ratios
Answers
Answer:
[tex]\begin{aligned}{&\cos \theta=\frac{10}{26} \\\bf{&\tan \theta=\frac{24}{10}}\end{aligned}[/tex]
Step-by-step explanation:
Since the angle is in the first quadrant, the values of all trigonometric functions are positive. Also. the formulas for the trigonometric functions we need to find from the problem are shown below:
[tex]\begin{aligned}\cos \theta &=\frac{x}{r} \\\tan \theta &=\frac{y}{x}\end{aligned}[/tex]
Based on the formulas listed, the value of y and r are y = 24 and r = 26 respectively. This means that in order to determine the value of the other functions, we need In compute for the value of x using the Pythagorean Theorem:
[tex]\begin{aligned}r^{2} &=x^{2}+y^{2} \\r^{2}-y^{2} &=x^{2}+y^{2}-y^{2} \quad\left[\text { \text{Subtracting \ both \ sides \ of \ the \ equation\ by} } y^{2}\right] \\r^{2}-y^{2} &=x^{2} \\\sqrt{r^{2}-y^{2}} &=\sqrt{x^{2}} \\\sqrt{r^{2}-y^{2}} &=x \\\sqrt{26^{2}-24^{2}} &=x \\10 &=x\end{aligned}[/tex]Then, substituting this to the formula to determine the answers yields:
[tex]\begin{aligned}\cos \theta &=\frac{x}{r} \\&=\frac{10}{26} \\\tan \theta &=\frac{y}{x} \\&=\frac{24}{10}\end{aligned}[/tex]
Therefore, the answers are:
[tex]\begin{aligned}&\cos \theta=\frac{10}{26} \\&\tan \theta=\frac{24}{10}\end{aligned}[/tex]
Answer:
See below
Step-by-step explanation:
We are here given that ,
[tex]\longrightarrow \sin\theta =\dfrac{24}{26}[/tex]
And we would like to find out other trigonometric ratios ( since it is not mentioned about which two I will find out all 6 ) . As we know that ,
[tex]\longrightarrow \sin\theta =\dfrac{perpendicular}{hypotenuse} =\dfrac{p}{h}[/tex]
So that ,
[tex]\longrightarrow \dfrac{p}{h} =\dfrac{24}{26}[/tex]
Let us assume the given ratio to be 24x : 26x .
So we can say that ,
hypotenuse = 26xperpendicular = 24xNow let's find out the value of base , so that we can find out the other ratios .
By Pythagoras Theorem ,
[tex]\longrightarrow (perpendicular) ^2+(base)^2=(hypotenuse) ^2[/tex]
Substitute the respective values ,
[tex]\longrightarrow (26x)^2=(24x)^2+b^2\\[/tex]
[tex]\longrightarrow 676x^2 = 576x^2+b^2\\ [/tex]
[tex]\longrightarrow b^2=100x^2\\[/tex]
[tex]\longrightarrow b =\sqrt{100x^2}\\[/tex]
[tex]\longrightarrow \boldsymbol{ b = 10x } [/tex]
Now we may find the other ratios as ,
[tex]\longrightarrow \cos\theta = \dfrac{base}{hypotenuse}=\dfrac{10x}{26x}=\boxed{\boldsymbol{\dfrac{5}{13}}}\\[/tex]
[tex]\longrightarrow \tan\theta =\dfrac{perpendicular}{base}=\dfrac{24x}{10x}=\boxed{\boldsymbol{\dfrac{12}{5}}}\\[/tex]
[tex]\longrightarrow \cosec\theta =\dfrac{hypotenuse}{perpendicular}=\dfrac{26x}{24x}=\boxed{\boldsymbol{\dfrac{13}{12}}}\\ [/tex]
[tex]\longrightarrow \sec\theta =\dfrac{hypotenuse}{base}=\dfrac{26x}{10x}=\boxed{\boldsymbol{\dfrac{13}{5}}} \\[/tex]
[tex]\longrightarrow \cot\theta =\dfrac{base}{perpendicular}=\dfrac{10x}{24x}=\boxed{\boldsymbol{\dfrac{5}{12}}} [/tex]
And we are done !
Ariana started a savings account with $240. She deposits $30 into her account at the end of each month. She wants to know how many months it will take for her account to have a balance greater than $500.
Answers
Answer:
9 months
Step-by-step explanation:
$500 - $240 = $260
$260/$30 = 8.67(3s.f.) ≈ 9 months
Recheck:
Balance after 9 months = 240 + (30×9) = 240 + 270 = $510
∴ $510 > $500
I need answers asap! | Some blocks are stacked as shown. The face of each block is a square and each block represents one cubic unit, what is the surface area of the figure formed by the blocks?
A. 30 square units
B. 28 square units
C. 24 square units
D. 21 square units
Answers
Answer:
28
Step-by-step explanation:
Find a linear equation with two variables that, together with the
equation 10x + 5y = 1, would comprise a system
with one solution
Answers
Answer:
y = x
Step-by-step explanation:
Any equation that describes a different line will be part of a system with exactly one solution. There are an infinite number of possible equations.
Perhaps one of the simplest is ...
y = x
_____
Together with the given equation, this has the solution ...
x = y = 1/15
The rectangle shown has a perimeter of 56 cm and the given area. Its length is 8 times more than three times its width. Write and solve a system of equations to find the dimensions of the rectangle.
Answers
Answer:
Dimensions of rectangle = 23 cm x 5 cm
Step-by-step explanation:
Equations we can form
Perimeter of 56 cm⇒ 2L + 2W = 56
⇒ L + W = 28
Length is 8 more than 3 times its width⇒ L = 3W + 8
Substitute in previous equation
⇒ 3W + 8 + W = 28
⇒ 4W = 20
⇒ W = 5 cm
⇒ L = 28 - 5 = 23 cm
Janelle says that lines l and m are skew lines.
Planes B and A intersect. Plane B is vertical and contains vertical line n. Plane A is horizontal and contains horizontal line m. Line m and n are perpendicular. Line l is on plane A and it is slightly diagonal.
Is Janelle correct?
Yes, because the lines are not parallel.
Yes, because the lines will intersect.
No, because the lines are in the same plane.
No, because the lines are perpendicular.
Answers
Answer:
C: No, beacause the lines are in the same plane.
Step-by-step explanation:
because skewed lines must lie in different planes.
just trust moi <3
The lines are in the same plane option third "No, because the lines are in the same plane" is correct.
What is a perpendicular line?Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have two lines shown in the picture, line l, and line m.
As we know the skew lines are in different planes and do not intersect.
Thus, the lines are in the same plane option third "No, because the lines are in the same plane" is correct.
Learn more about the perpendicular line here:
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Little helppp please
Answers
Answer:
Answer given above
Step-by-step explanation:
a.) 6 m n^8
b.)2x^8 y^3
c. ) d^3 e
Sam rode a bull for 8 seconds.
Maddie rode a bull for 2 fewer seconds than Sam did.
How long did Maddie ride her bull?
Answers
Answer:
is it 7?
Step-by-step explanation:
if he rode for 8 seconds and it says she rode for 2 seconds FEWER are you not subtracting from 8 to get 7?
consider the equation 21= m +14 1/6 which which step will help to solve this equation
Answers
Answer:
m = 41/6
Step-by-step explanation:
21 = m + 14 1/6Convert everything into improper fractions with a denominator of 6.
21 = m + 14 1/6126/6 = 6m/6 + 85/6126 = 6m + 856m = 126 - 856m = 41m = 41/6Solve the equation for x
Answers
Answer:
5x-18=4x+7 ( vertical opposite angle)
5x-4x=7+18
x=25
Rowan has 3 pieces of yarn, as described below. *a red piece of yarn that is 3/4 foot long *a yellow piece of yarn that is 6/8 foot long * a blue piece of yarn that is 4/12 foot long Wich number sentence correctly compares the lengths of 2 of these pieces of yarn. A 3/4 < 3/6 B 4/12 < 3/4 C 3/4 > 6/8 D 4/12 > 6/8
Answers
Answer:
b
Step-by-step explanation:
because all the orher ones are wrong and not correct.
Given: Line segment A B is parallel to line segment D C and Measure of angle 2 equals measure of angle 4
Prove: Line segment A D is parallel to line segment B C
A parallelogram has points A B C D. Angle D A B is angle 1, Angle A B C is angle 2, Angle B C D is angle 3, and angle C D A is angle 4.
A 2-column table with 7 rows. Column 1 is labeled statements and has entries line segment A B is parallel to line segment D C, measure of angle 2 = measure of angle 4, angle 1 and angle 4 are supplements, question mark, measure of angle 1 + measure of angle 2 = 180 degrees, angle 1 and angle 2 are supplements, line segment A D is parallel to line segment B C. Column 2 is labeled reasons with entries given, given, same side interior angles theorem, definition of supplementary angles, substitution, definition of supplementary angles, converse same side interior angles theorem.
m∠1 = m∠4
m∠2 = m∠3
m∠1 + m∠4 = 180°
m∠2 + m∠3 = 180°
Answers
Answer: m∠1 + m∠4 = 180°
Step-by-step explanation:
If angles 1 and 4 are supplementary, their measures must add to 180 degrees.
put the equation below into vertex form.
y=(x+9)(x+25)
Answers
Answer:
Step-by-step explanation:
What is the volume of this cone? Use 3.14 for pi and round your answer to the
nearest tenth.
In your answer, give the volume of the cone rounded to the nearest tenth, and then
explain how you calculated it.
Answers
Solve the equation 3x = 9 Show and justify each step you take to solve the equation
Answers
Hello!
This is a one-step equation, meaning that we can solve it in just 1 step.
This is the step:
Divide both sides by 33x=9
x=3
That's the answer; we can easily check it:
3*3=9
Hope everything is clear.
Let me know if you have any questions!
Always Remember: Knowledge Is Power!
n 12. Find the volume of the sphere.
Answers
Answer:
2929 1/3 [tex]\pi[/tex] in^3
Step-by-step explanation:
The equation for the volume of a sphere is [tex]\frac{4}{3} \pi r^3[/tex].
Insert 13 for r. Then, simplify.
A farmer has some cows and horses. All the animals are either brown or black. The table shows how many of each
animal is on the farm.
one animal is selected randomly. what is the probability of chowing a horse given that they are brown? round answer to nearest hundredth.
Answers
Answer:
P = 1/5 = 0.20 = (20%)
Step-by-step explanation:
there are 12 horses and 8 cows, in total there are 20 animals
of which 4 horses are brown
Then
[tex]P=\frac{4}{20} =\frac{1}{5}[/tex]
Hope this helps
A circular flower bed is 24m in diameter and has a circular sidewalk around it that is 2m wide. Find the area of the sidewalk in square meters. Use 3.14 for pie (round to nearest 10th)
Answers
Answer:
163.3m²
Step-by-step explanation:
area = Pi(r²)
r = d / 2
r = 12
12² = 144
144 x 3.14 = 452.16
diameter of bigger circle = 24 + 4 (2 on each side)
28 / 2 = 14
14² = 196
196 x 3.14 = 615.44
sidewalk = bigger - smaller
sidewalk = 615.44 - 452.16
sidewalk = 163.3